this is just Monte Carlo integration with cosine-weighted sampling. that’s why it works and the others don’t.
\ncosine weighting enforces the correct solid-angle measure, so the flux gradient obeys Gauss’s law. uniform hemisphere or tangent-plane sampling breaks that, which is why the field comes out wrong. the 2/π factor is the usual cosine-hemisphere normalization.
\nin physics terms, you’re doing a Monte Carlo solution of Poisson’s equation via flux sampling, and the Schwarzschild behavior drops out naturally when the sampling measure matches the geometry. not a single “owner” it’s standard Monte Carlo done with the right weighting.
\n", "answer_id": 45329, "answer_text": "this is just Monte Carlo integration with cosine-weighted sampling. that’s why it works and the others don’t.\n\n\n\n\ncosine weighting enforces the correct solid-angle measure, so the flux gradient obeys Gauss’s law. uniform hemisphere or tangent-plane sampling breaks that, which is why the field comes out wrong. the 2/π factor is the usual cosine-hemisphere normalization.\n\n\n\n\nin physics terms, you’re doing a Monte Carlo solution of Poisson’s equation via flux sampling, and the Schwarzschild behavior drops out naturally when the sampling measure matches the geometry. not a single “owner” it’s standard Monte Carlo done with the right weighting.", "answer_url": "https://scicomp.stackexchange.com/a/45329", "author": "Linda Anderson", "author_url": "https://scicomp.stackexchange.com/users/56218/linda-anderson", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-01-05T09:26:54+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45322, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Linda Anderson", "profile_url": "https://scicomp.stackexchange.com/users/56218/linda-anderson", "user_type": "registered"}, "created_at": "2026-01-05T09:26:54+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "8F296337-1611-4B90-B028-6FDD3F098E8A", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/8F296337-1611-4B90-B028-6FDD3F098E8A/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Linda Anderson", "profile_url": "https://scicomp.stackexchange.com/users/56218/linda-anderson", "user_type": "registered"}, "created_at": "2026-01-05T09:27:15+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "317C93D3-B055-47E3-8255-35BB56F95C1B", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/317C93D3-B055-47E3-8255-35BB56F95C1B/view-source"}], "score": 5, "updated_at": "2026-01-05T09:27:15+00:00"}, {"answer_html": "The first answer fails to mention that there is a purely quantum method (labeled C)) -- the cosine weighting is only a classical approximation (labeled B)). The following is the important part of the C++ code (which uses standard multi-threading):
\nvoid worker_thread(\n long long unsigned int start_idx,\n long long unsigned int end_idx,\n unsigned int thread_seed,\n const real_type emitter_radius,\n const real_type receiver_distance,\n const real_type receiver_distance_plus,\n const real_type receiver_radius,\n real_type& result_count,\n real_type& result_count_plus)\n{\n // Thread-local random number generator\n std::mt19937 local_gen(thread_seed);\n std::uniform_real_distribution<real_type> local_dis(0.0, 1.0);\n\n real_type local_count = 0;\n real_type local_count_plus = 0;\n\n // Update progress every N iterations to reduce atomic overhead\n const long long unsigned int progress_update_interval = 10000;\n long long unsigned int local_progress = 0;\n\n for (long long unsigned int i = start_idx; i < end_idx; i++)\n {\n vector_3 location = random_unit_vector(local_gen, local_dis);\n location.x *= emitter_radius;\n location.y *= emitter_radius;\n location.z *= emitter_radius;\n\n vector_3 surface_normal = location;\n surface_normal.normalize();\n\n\n // A) Newtonian gravitation\n //vector_3 normal =\n // surface_normal;\n\n // B) Schwarzschild gravitation\n //vector_3 normal = \n // random_cosine_weighted_hemisphere(\n // surface_normal, local_gen, local_dis);\n\n // C) Quantum gravitation\n vector_3 r = random_unit_vector(local_gen, local_dis);\n r.x *= emitter_radius;\n r.y *= emitter_radius;\n r.z *= emitter_radius;\n vector_3 normal = (location - r).normalize();\n\n\n local_count += intersect(\n location, normal,\n receiver_distance, receiver_radius);\n\n local_count_plus += intersect(\n location, normal,\n receiver_distance_plus, receiver_radius);\n\n // Update global progress periodically\n local_progress++;\n if (local_progress >= progress_update_interval)\n {\n global_progress.fetch_add(\n local_progress, std::memory_order_relaxed);\n \n local_progress = 0;\n }\n }\n\n // Add any remaining progress\n if (local_progress > 0)\n {\n global_progress.fetch_add(\n local_progress, std::memory_order_relaxed);\n }\n\n result_count = local_count;\n result_count_plus = local_count_plus;\n}\nQuestion
\nWhat is the name of the numerical technique used to generate the appropriate gravitational acceleration by using a set of gravitational field lines that are not necessarily normal to the surface of the emitter?
\nI have found that using cosine weighted pseudorandom field lines produces the result predicted by Schwarzschild's general relativity. It's a very simple calculation. Please help me identify its owner.
\nIntroduction
\nIn the past, I have written a short tutorial for C++ programmers on isotropic Newtonian gravitation.\nIn that old tutorial, I build an isotropic gravitational field through the use of pseudorandomly generated field lines.\nIn that old tutorial I use a sphere as the receiver.\nThe paper for that old tutorial is at Newtonian gravitation from scratch, for C++ programmers.
\nIn this question, I point out a match between the numerical gravitation and the gravitational time dilation from Schwarzschild's general relativity (see the book Gravitation, by Misner et al).\nHere, I use an axis-aligned bounding box (AABB) as the receiver.
\nIn this question I use Planck units, where $c = G = \\hbar = k = 1$.
\nMethod
\nWhere $r_{e}$ is the emitter's Schwarzschild radius, $r_{r}$ is the receiver AABB radius (e.g. half of the AABB side length), and $1\\mathrm{e}11$ and $0.01$ are arbitrary constants:\n\\begin{equation}\nr_{e} = \\sqrt{\\frac{1\\mathrm{e}11 \\log(2)}{\\pi}},\n\\end{equation}\n\\begin{equation}\nr_{r} = r_{e} \\times 0.01.\n\\end{equation}\nThe event horizon area is:\n\\begin{equation}\nA_{e} = 4 \\pi r_{e}^2.\n\\end{equation}\nThe binary entropy (e.g. field line count, see the papers about the holographic principle) is:\n\\begin{equation}\nn_{e} = \\frac{A_{e}}{4 \\log(2)} = 1\\mathrm{e}11.\n\\end{equation}\nWhere $R$ is the distance from the emitter's centre, the derivative is:\n\\begin{equation}\n\\alpha = \\frac{\\beta(R + \\epsilon) - \\beta(R)}{\\epsilon}.\n\\end{equation}\nHere $\\beta$ is the get intersecting line density function.\nThe gradient strength is:\n\\begin{equation}\ng = \\frac{-\\alpha}{r_{r}^2}.% \\approx \\frac{n_e}{2 R^3}.\n\\end{equation}\nFrom this I get the Newtonian acceleration $a_N$, where $r_e \\ll R$:\n\\begin{equation}\na_N =\\frac{g R \\log 2}{8 M_{e}} = \\sqrt{\\frac{n_e \\log 2}{4 \\pi R^4}} = \\frac{M_{e}}{R^2}.\n\\end{equation}\nI can also get a general relativistic acceleration $a_S$, where $r_e < R$:\n\\begin{equation}\na_S = \\frac{g R \\log 2}{8 M_{e}},\n\\end{equation}\nAt close proximity, where $r_e \\approx R$, the metric produced is related to the Schwarzschild metric -- curved space, curved time:\n\\begin{equation}\nt = \\sqrt{1 - \\frac{r_e}{R}},\n\\end{equation}\n\\begin{equation}\n\\frac{dt}{dR} = \\frac{r_e}{2 t R^2}.\n\\end{equation}\n\\begin{equation}\na_S \\approx \\frac{dt}{dR} \\frac{2}{\\pi} = \\frac{r_e}{\\pi t R^2}.\n\\end{equation}\nAt far proximity, where $r_e \\ll R$, $t \\approx 1$, and $dt/dR \\approx 0$, the metric produced is Newtonian -- curved space, practically flat time.
\nUsing numerical relativity, I tried pseudorandom hemisphere and pseudorandom tangent plane field lines, but they did not work.\nThe only technique that works is cosine weighted pseudorandom field lines.\nThat is to say, as per the code for this tutorial (https://github.com/sjhalayka/schwarzschild_falloff_field_lines), the cosine weighted pseudorandom field lines produce the correct result, off by a factor of $2 / \\pi$.
\nFigure
\n![\"axis-aligned](\"https://i.sstatic.net/XWbsh2qc.png\")
This figure shows an axis-aligned bounding box and an isotropic emitter, looking from slightly above.\nAn example field line (red) and intersecting line segment (green) are given.\nThe bounding box is filled with these green intersecting line segments.\nIt is the gradient of the density of these line segments that forms the gravitational acceleration.\nNote that the field line is normal to the surface of the emitter (producing Newtonian gravitation).
\nC++ code
\ndouble get_intersecting_line_density(\n const long long unsigned int n,\n const double emitter_radius,\n const double receiver_distance,\n const double receiver_distance_plus,\n const double receiver_radius)\n{\n double count = 0;\n double count_plus = 0;\n\n generator.seed(static_cast<unsigned>(0));\n\n for (long long unsigned int i = 0; i < n; i++)\n {\n vector_3 location = random_unit_vector();\n\n location.x *= emitter_radius;\n location.y *= emitter_radius;\n location.z *= emitter_radius;\n\n vector_3 surface_normal = location;\n surface_normal.normalize();\n\n vector_3 normal = \n random_cosine_weighted_hemisphere(\n surface_normal);\n\n std::optional<double> i_hit = intersect(\n location, normal, \n receiver_distance, receiver_radius);\n\n if (i_hit)\n count += *i_hit / (2.0 * receiver_radius);\n \n i_hit = intersect(\n location, normal,\n receiver_distance_plus, receiver_radius);\n\n if (i_hit)\n count_plus += *i_hit / (2.0 * receiver_radius);\n }\n\n return count_plus - count;\n}\nThank you for your time!
\n", "question_id": 45322, "question_license": "CC BY-SA 4.0", "question_score": 5, "question_text": "Question\n\n\n\n\nWhat is the name of the numerical technique used to generate the appropriate gravitational acceleration by using a set of gravitational field lines that are not necessarily normal to the surface of the emitter?\n\n\n\n\nI have found that using cosine weighted pseudorandom field lines produces the result predicted by Schwarzschild's general relativity. It's a very simple calculation. Please help me identify its owner.\n\n\n\n\nIntroduction\n\n\n\n\nIn the past, I have written a short tutorial for C++ programmers on isotropic Newtonian gravitation.\nIn that old tutorial, I build an isotropic gravitational field through the use of pseudorandomly generated field lines.\nIn that old tutorial I use a sphere as the receiver.\nThe paper for that old tutorial is at Newtonian gravitation from scratch, for C++ programmers (https://www.techrxiv.org/users/685306/articles/1250456-newtonian-gravitation-from-scratch-for-c-programmers).\n\n\n\n\nIn this question, I point out a match between the numerical gravitation and the gravitational time dilation from Schwarzschild's general relativity (see the book Gravitation, by Misner et al (https://search.worldcat.org/title/585119)).\nHere, I use an axis-aligned bounding box (AABB) as the receiver.\n\n\n\n\nIn this question I use Planck units, where $c = G = \\hbar = k = 1$.\n\n\n\n\nMethod\n\n\n\n\nWhere $r_{e}$ is the emitter's Schwarzschild radius, $r_{r}$ is the receiver AABB radius (e.g. half of the AABB side length), and $1\\mathrm{e}11$ and $0.01$ are arbitrary constants:\n\\begin{equation}\nr_{e} = \\sqrt{\\frac{1\\mathrm{e}11 \\log(2)}{\\pi}},\n\\end{equation}\n\\begin{equation}\nr_{r} = r_{e} \\times 0.01.\n\\end{equation}\nThe event horizon area is:\n\\begin{equation}\nA_{e} = 4 \\pi r_{e}^2.\n\\end{equation}\nThe binary entropy (e.g. field line count, see the papers about the holographic principle) is:\n\\begin{equation}\nn_{e} = \\frac{A_{e}}{4 \\log(2)} = 1\\mathrm{e}11.\n\\end{equation}\nWhere $R$ is the distance from the emitter's centre, the derivative is:\n\\begin{equation}\n\\alpha = \\frac{\\beta(R + \\epsilon) - \\beta(R)}{\\epsilon}.\n\\end{equation}\nHere $\\beta$ is the get intersecting line density function.\nThe gradient strength is:\n\\begin{equation}\ng = \\frac{-\\alpha}{r_{r}^2}.% \\approx \\frac{n_e}{2 R^3}.\n\\end{equation}\nFrom this I get the Newtonian acceleration $a_N$, where $r_e \\ll R$:\n\\begin{equation}\na_N =\\frac{g R \\log 2}{8 M_{e}} = \\sqrt{\\frac{n_e \\log 2}{4 \\pi R^4}} = \\frac{M_{e}}{R^2}.\n\\end{equation}\nI can also get a general relativistic acceleration $a_S$, where $r_e < R$:\n\\begin{equation}\na_S = \\frac{g R \\log 2}{8 M_{e}},\n\\end{equation}\nAt close proximity, where $r_e \\approx R$, the metric produced is related to the Schwarzschild metric -- curved space, curved time:\n\\begin{equation}\nt = \\sqrt{1 - \\frac{r_e}{R}},\n\\end{equation}\n\\begin{equation}\n\\frac{dt}{dR} = \\frac{r_e}{2 t R^2}.\n\\end{equation}\n\\begin{equation}\na_S \\approx \\frac{dt}{dR} \\frac{2}{\\pi} = \\frac{r_e}{\\pi t R^2}.\n\\end{equation}\nAt far proximity, where $r_e \\ll R$, $t \\approx 1$, and $dt/dR \\approx 0$, the metric produced is Newtonian -- curved space, practically flat time.\n\n\n\n\nUsing numerical relativity, I tried pseudorandom hemisphere and pseudorandom tangent plane field lines, but they did not work.\nThe only technique that works is cosine weighted pseudorandom field lines.\nThat is to say, as per the code for this tutorial (https://github.com/sjhalayka/schwarzschild_falloff_field_lines (https://github.com/sjhalayka/schwarzschild_falloff_field_lines)), the cosine weighted pseudorandom field lines produce the correct result, off by a factor of $2 / \\pi$.\n\n\n\n\nFigure\n\n\n\n\n[image: axis-aligned bounding box; source: https://i.sstatic.net/XWbsh2qc.png] (https://i.sstatic.net/XWbsh2qc.png)\n\n\n\n\nThis figure shows an axis-aligned bounding box and an isotropic emitter, looking from slightly above.\nAn example field line (red) and intersecting line segment (green) are given.\nThe bounding box is filled with these green intersecting line segments.\nIt is the gradient of the density of these line segments that forms the gravitational acceleration.\nNote that the field line is normal to the surface of the emitter (producing Newtonian gravitation).\n\n\n\n\nC++ code\n\n\n\n\ndouble get_intersecting_line_density(\n const long long unsigned int n,\n const double emitter_radius,\n const double receiver_distance,\n const double receiver_distance_plus,\n const double receiver_radius)\n{\n double count = 0;\n double count_plus = 0;\n\n generator.seed(static_castYour loop structure to accumulate the acceleration is wrong:
\n# Acceleration components\nax = [0] * 3\nay = [0] * 3\n\n[...]\n\nfor i in range(10**5):\n for j in range(len(x)):\n for k in range(len(x)):\n if j != k: # so that a body doesn't interact with its self\n # Gravitational acceleration exerted by body k on body j\n ax[j] = -G * (mass[j] + mass[k]) * (x[j] - x[k]) / (((x[j]-x[k])**2 + (y[j]-y[k])**2)**0.5)**3\n ay[j] = -G * (mass[j] + mass[k]) * (y[j] - y[k]) / (((x[j]-x[k])**2 + (y[j]-y[k])**2)**0.5)**3\n [...]\nax and ay always increase, since they are never reset to zero. In this way, you accumulate the contributions for all bodies over all time steps. Instead, you should compute the acceleration starting back from zero in each time step i.
I really don't think you should be adding your masses (if you do, you tend to eject planets from the solar system).
\nAlso, I feel the need to remind you that
\n- \n
- you need to vectorise - Python is inherently brutally slow, so it doesn't surprise me that you're worrying about printing simulation time; \n
- you should be treating this as an IVP and leveraging a good library, which will (for our purposes) always do better than a naive implementation. \n
Stopping short of rewriting this as an IVP for you, the vectorised version can look like:
\nimport numpy as np\nimport matplotlib.pyplot as plt\n\n\nn = 201 # Step count\nyears = 0.95 # Duration (years)\ndt = years/(n-1) # Time step (years/step)\n\n# Masses expressed in solar masses, derived from kg\n# https://ssd.jpl.nasa.gov/planets/phys_par.html\nmass = np.array(( # (5,)\n 1.988475e30, # Sol\n 0.330103e24, # Mercury\n 4.867310e24, # Venus\n 5.972170e24, # Earth\n 0.641691e24, # Mars\n))/1.988475e30\n\n# Distances in astronomical units (AU)\n# 1 AU = 1.495978707e11 m\n# Positions, having an initial value set to body's semi-major axis\n# https://en.wikipedia.org/wiki/Category:Planets_of_the_Solar_System\nall_p = np.empty((n, mass.size, 2))\nall_p[0] = (\n (0., 0.), # Sol\n (0.387098, 0.), # Mercury\n (0.723332, 0.), # Venus\n (1., 0.), # Earth\n (1.52368055, 0.), # Mars\n)\n\n# Velocity (AU/year), derived from km/s\n# https://en.wikipedia.org/wiki/Category:Planets_of_the_Solar_System\nv = np.array(( # (5,2)\n (0., 0. ), # Sol\n (0., 47.36 ), # Mercury\n (0., 35.02 ), # Venus\n (0., 29.7827), # Earth\n (0., 24.07 ), # Mars\n)) * (1e3/1.495978707e11 *60*60*24*365.2425)\n\n# Universal gravitational constant in AU^3/(solar mass * year^2)\nG = 4 * np.pi**2\n\n"""\nExclusive body interaction indices; effectively:\nfor j in; for k in; if j != k\n [[0, 0, 0, 1, 1, 2],\n [1, 2, 3, 2, 3, 3]]\n"""\nindices = np.stack(np.triu_indices(n=mass.size, m=mass.size, k=1)) # (2,10)\nj, k = indices # each (10,)\n\n"""\nInteraction matrix such that A (5,10) . ||r||^-3 (10) . r(10,2) = dv(5,2)\nExample for a smaller system with four bodies:\n jk jk jk jk jk jk\n 01 02 03 12 13 23\nj0 1 1 1 \nj1 -1 1 1\nj2 -1 -1 1\nj3 -1 -1 -1 signs are to effectively swap xy[j] - xy[k]\n\n[[-9.7e-10, -1.2e-09, -1.3e-10, -0.0e+00, -0.0e+00, -0.0e+00],\n [ 3.9e-04, -0.0e+00, -0.0e+00, -1.2e-09, -1.3e-10, -0.0e+00],\n [-0.0e+00, 3.9e-04, -0.0e+00, 9.7e-10, -0.0e+00, -1.3e-10],\n [-0.0e+00, -0.0e+00, 3.9e-04, -0.0e+00, 9.7e-10, 1.2e-09]]\n"""\nA = np.zeros((mass.size, j.size)) # (5,10)\ni = np.arange(j.size) # (10,)\ndt_G_mass = dt*G*mass # (5,)\nA[j, i] = (-dt_G_mass)[k]\nA[k, i] = (dt_G_mass)[j]\n\n# Symplectic Euler integration for the N-body gravitational problem\nfor i in range(n-1):\n pj, pk = all_p[i, indices] # Interaction previous positions, each (10,2)\n r = pj - pk # (10,2) # Interaction displacement, effectively xy[j] - xy[k]\n\n # Interaction norms, effectively: 1/(((x[j]-x[k])**2 + (y[j]-y[k])**2)**0.5)**3\n norms = np.linalg.norm(r, axis=1, keepdims=1)**-3 # (10,1)\n\n # Gravitational acceleration exerted by body k on body j\n v += A @ (norms * r) # Effectively: vxy[l] += axy[l] * dt\n all_p[i+1] = all_p[i] + v*dt # Effectively: xy[l] += vxy[l] * dt\n\nfig, ax = plt.subplots()\nfor name, data in zip(\n ('Sol', 'Mercury', 'Venus', 'Earth', 'Mars'),\n all_p.transpose((1, 2, 0)),\n):\n ax.plot(*data, label=name)\nax.legend()\nplt.show()\n![\"orbit\"](\"https://i.sstatic.net/LhxHLqTd.png\")
![\"detail\"](\"https://i.sstatic.net/4hfjqDYL.png\")
Your loop structure to accumulate the acceleration is wrong:
\n# Acceleration components\nax = [0] * 3\nay = [0] * 3\n\n[...]\n\nfor i in range(10**5):\n for j in range(len(x)):\n for k in range(len(x)):\n if j != k: # so that a body doesn't interact with its self\n # Gravitational acceleration exerted by body k on body j\n ax[j] = -G * (mass[j] + mass[k]) * (x[j] - x[k]) / (((x[j]-x[k])**2 + (y[j]-y[k])**2)**0.5)**3\n ay[j] = -G * (mass[j] + mass[k]) * (y[j] - y[k]) / (((x[j]-x[k])**2 + (y[j]-y[k])**2)**0.5)**3\n [...]\nax and ay always increase, since they are never reset to zero. In this way, you accumulate the contributions for all bodies over all time steps. Instead, you should compute the acceleration starting back from zero in each time step i.
I really don't think you should be adding your masses (if you do, you tend to eject planets from the solar system).
\nAlso, I feel the need to remind you that
\n- \n
- you need to vectorise - Python is inherently brutally slow, so it doesn't surprise me that you're worrying about printing simulation time; \n
- you should be treating this as an IVP and leveraging a good library, which will (for our purposes) always do better than a naive implementation. \n
Stopping short of rewriting this as an IVP for you, the vectorised version can look like:
\nimport numpy as np\nimport matplotlib.pyplot as plt\n\n\nn = 201 # Step count\nyears = 0.95 # Duration (years)\ndt = years/(n-1) # Time step (years/step)\n\n# Masses expressed in solar masses, derived from kg\n# https://ssd.jpl.nasa.gov/planets/phys_par.html\nmass = np.array(( # (5,)\n 1.988475e30, # Sol\n 0.330103e24, # Mercury\n 4.867310e24, # Venus\n 5.972170e24, # Earth\n 0.641691e24, # Mars\n))/1.988475e30\n\n# Distances in astronomical units (AU)\n# 1 AU = 1.495978707e11 m\n# Positions, having an initial value set to body's semi-major axis\n# https://en.wikipedia.org/wiki/Category:Planets_of_the_Solar_System\nall_p = np.empty((n, mass.size, 2))\nall_p[0] = (\n (0., 0.), # Sol\n (0.387098, 0.), # Mercury\n (0.723332, 0.), # Venus\n (1., 0.), # Earth\n (1.52368055, 0.), # Mars\n)\n\n# Velocity (AU/year), derived from km/s\n# https://en.wikipedia.org/wiki/Category:Planets_of_the_Solar_System\nv = np.array(( # (5,2)\n (0., 0. ), # Sol\n (0., 47.36 ), # Mercury\n (0., 35.02 ), # Venus\n (0., 29.7827), # Earth\n (0., 24.07 ), # Mars\n)) * (1e3/1.495978707e11 *60*60*24*365.2425)\n\n# Universal gravitational constant in AU^3/(solar mass * year^2)\nG = 4 * np.pi**2\n\n"""\nExclusive body interaction indices; effectively:\nfor j in; for k in; if j != k\n [[0, 0, 0, 1, 1, 2],\n [1, 2, 3, 2, 3, 3]]\n"""\nindices = np.stack(np.triu_indices(n=mass.size, m=mass.size, k=1)) # (2,10)\nj, k = indices # each (10,)\n\n"""\nInteraction matrix such that A (5,10) . ||r||^-3 (10) . r(10,2) = dv(5,2)\nExample for a smaller system with four bodies:\n jk jk jk jk jk jk\n 01 02 03 12 13 23\nj0 1 1 1 \nj1 -1 1 1\nj2 -1 -1 1\nj3 -1 -1 -1 signs are to effectively swap xy[j] - xy[k]\n\n[[-9.7e-10, -1.2e-09, -1.3e-10, -0.0e+00, -0.0e+00, -0.0e+00],\n [ 3.9e-04, -0.0e+00, -0.0e+00, -1.2e-09, -1.3e-10, -0.0e+00],\n [-0.0e+00, 3.9e-04, -0.0e+00, 9.7e-10, -0.0e+00, -1.3e-10],\n [-0.0e+00, -0.0e+00, 3.9e-04, -0.0e+00, 9.7e-10, 1.2e-09]]\n"""\nA = np.zeros((mass.size, j.size)) # (5,10)\ni = np.arange(j.size) # (10,)\ndt_G_mass = dt*G*mass # (5,)\nA[j, i] = (-dt_G_mass)[k]\nA[k, i] = (dt_G_mass)[j]\n\n# Symplectic Euler integration for the N-body gravitational problem\nfor i in range(n-1):\n pj, pk = all_p[i, indices] # Interaction previous positions, each (10,2)\n r = pj - pk # (10,2) # Interaction displacement, effectively xy[j] - xy[k]\n\n # Interaction norms, effectively: 1/(((x[j]-x[k])**2 + (y[j]-y[k])**2)**0.5)**3\n norms = np.linalg.norm(r, axis=1, keepdims=1)**-3 # (10,1)\n\n # Gravitational acceleration exerted by body k on body j\n v += A @ (norms * r) # Effectively: vxy[l] += axy[l] * dt\n all_p[i+1] = all_p[i] + v*dt # Effectively: xy[l] += vxy[l] * dt\n\nfig, ax = plt.subplots()\nfor name, data in zip(\n ('Sol', 'Mercury', 'Venus', 'Earth', 'Mars'),\n all_p.transpose((1, 2, 0)),\n):\n ax.plot(*data, label=name)\nax.legend()\nplt.show()\n
I implemented the following code to simulate an $N$-body gravitational system (here: the Sun, Earth, and Mars).
\nThe code is:
\nimport numpy as np\nimport matplotlib.pyplot as plt\nimport time\nimport winsound as ws\nfrom matplotlib.animation import FuncAnimation\n\n# Universal gravitational constant in AU^3/(solar mass * year^2)\nG = 4 * (np.pi)**2\n\n# Distance from the Sun in astronomical units (AU)\n# 1 AU ≈ 149.6 million km\n\n# Initial x coordinates\nx = [\n 1, # Earth\n 1.5237, # Mars\n 0 # Sun\n]\n\n# Initial y coordinates\ny = [\n 0, # Earth\n 0, # Mars\n 0 # Sun\n]\n\n# Lists storing the x coordinates during the simulation\nxpos = [[], [], []]\n\n# Lists storing the y coordinates during the simulation\nypos = [[], [], []]\n\n# Initial velocity components (AU/year)\nvx = [0, 0, 0]\n\n# Initial tangential velocities (AU/year)\nvy = [\n 6.281991687112502, # Earth\n 5.0867271316753815, # Mars \n 0 # Sun\n]\n\n# Acceleration components\nax = [0] * 3\nay = [0] * 3\n\n# Masses expressed in solar masses\nmass = [\n 3.002513826043238e-06, # Earth\n 3.2267471091000503e-07, # Mars \n 1 # Sun\n]\n\n# Time step (years)\ndt = 0.00001\n\nstart_time = time.time()\n\n# Symplectic Euler integration for the N-body gravitational problem\nfor i in range(10**5):\n for j in range(len(x)):\n for k in range(len(x)):\n if j != k: # so that a body doesn't interact with its self\n # Gravitational acceleration exerted by body k on body j\n ax[j] = -G * (mass[j] + mass[k]) * (x[j] - x[k]) / (((x[j]-x[k])**2 + (y[j]-y[k])**2)**0.5)**3\n ay[j] = -G * (mass[j] + mass[k]) * (y[j] - y[k]) / (((x[j]-x[k])**2 + (y[j]-y[k])**2)**0.5)**3\n\n for l in range(len(x)):\n\n # Velocity update\n vx[l] += ax[l] * dt\n vy[l] += ay[l] * dt\n\n # Store trajectory\n xpos[l].append(x[l])\n ypos[l].append(y[l])\n\n # Position update\n x[l] += vx[l] * dt\n y[l] += vy[l] * dt\n\nend_time = time.time()\n\nprint(f"Simulation time: {end_time-start_time:.2f} s")\n\n# Audible notification when the simulation is finished\nws.Beep(400, 1000)\n\nplt.plot(xpos[0], ypos[0], label="Earth", color="green")\nplt.plot(xpos[1], ypos[1], label="mars", color="violet")\nplt.plot(xpos[2], ypos[2], label="sun", color="red")\n\nplt.legend()\nplt.show()\nThis produces the following result:
\n![\"The](\"https://i.sstatic.net/f5j0wZO6.png\")
At first glance, one might think the problem comes from the fact that I overwrite the acceleration instead of accumulating the contributions from all the other bodies.
\nSo I changed
\nax[j] = -G * (mass[j] + mass[k]) * (x[j] - x[k]) / (((x[j]-x[k])**2 + (y[j]- y[k])**2)**0.5)**3\nay[j] = -G * (mass[j] + mass[k]) * (y[j] - y[k]) / (((x[j]-x[k])**2 + (y[j]-y[k])\nto
\nax[j] += -G * (mass[j] + mass[k]) * (x[j] - x[k]) / (((x[j]-x[k])**2 + (y[j]- y[k])**2)**0.5)**3\nay[j] += -G * (mass[j] + mass[k]) * (y[j] - y[k]) / (((x[j]-x[k])**2 + (y[j]-y[k])**2)**0.5)**3\nsince the total acceleration acting on body j should be the sum of the accelerations produced by every other body.
\nHowever, this actually makes the simulation even worse. The result becomes:
\n![\"the](\"https://i.sstatic.net/cWWHipMg.png\")
So I feel that I am missing something more fundamental.
\nAnother thing I do not understand is the behavior of the Sun in the first version. Since the acceleration is overwritten, the Sun ends up accelerating only because of the last body processed in the loop (Mars). However, the Sun is much more massive than either Earth or Mars (1 >> 3.0025e-6 and 1 >> 3.2267e-7), so I would not expect such a large acceleration. Why does this happen?
\nLikewise, why does the += version diverge so quickly instead of improving the simulation?
\nMy ultimate goal is to simulate the Solar System (the Sun and the eight planets) using this double loop, but if the simulation is already unstable with only three bodies, I am clearly doing something wrong.
\nFinally, I intentionally initialized the Sun with zero position, zero velocity, and zero acceleration because I wanted it to remain fixed at the origin, assuming that the Solar System barycenter is approximately at the center of the Sun.
\n", "question_id": 45499, "question_license": "CC BY-SA 4.0", "question_score": 2, "question_text": "I implemented the following code to simulate an $N$-body gravitational system (here: the Sun, Earth, and Mars).\n\n\n\n\nThe code is:\n\n\n\n\nimport numpy as np\nimport matplotlib.pyplot as plt\nimport time\nimport winsound as ws\nfrom matplotlib.animation import FuncAnimation\n\n# Universal gravitational constant in AU^3/(solar mass * year^2)\nG = 4 * (np.pi)**2\n\n# Distance from the Sun in astronomical units (AU)\n# 1 AU ≈ 149.6 million km\n\n# Initial x coordinates\nx = [\n 1, # Earth\n 1.5237, # Mars\n 0 # Sun\n]\n\n# Initial y coordinates\ny = [\n 0, # Earth\n 0, # Mars\n 0 # Sun\n]\n\n# Lists storing the x coordinates during the simulation\nxpos = [[], [], []]\n\n# Lists storing the y coordinates during the simulation\nypos = [[], [], []]\n\n# Initial velocity components (AU/year)\nvx = [0, 0, 0]\n\n# Initial tangential velocities (AU/year)\nvy = [\n 6.281991687112502, # Earth\n 5.0867271316753815, # Mars \n 0 # Sun\n]\n\n# Acceleration components\nax = [0] * 3\nay = [0] * 3\n\n# Masses expressed in solar masses\nmass = [\n 3.002513826043238e-06, # Earth\n 3.2267471091000503e-07, # Mars \n 1 # Sun\n]\n\n# Time step (years)\ndt = 0.00001\n\nstart_time = time.time()\n\n# Symplectic Euler integration for the N-body gravitational problem\nfor i in range(10**5):\n for j in range(len(x)):\n for k in range(len(x)):\n if j != k: # so that a body doesn't interact with its self\n # Gravitational acceleration exerted by body k on body j\n ax[j] = -G * (mass[j] + mass[k]) * (x[j] - x[k]) / (((x[j]-x[k])**2 + (y[j]-y[k])**2)**0.5)**3\n ay[j] = -G * (mass[j] + mass[k]) * (y[j] - y[k]) / (((x[j]-x[k])**2 + (y[j]-y[k])**2)**0.5)**3\n\n for l in range(len(x)):\n\n # Velocity update\n vx[l] += ax[l] * dt\n vy[l] += ay[l] * dt\n\n # Store trajectory\n xpos[l].append(x[l])\n ypos[l].append(y[l])\n\n # Position update\n x[l] += vx[l] * dt\n y[l] += vy[l] * dt\n\nend_time = time.time()\n\nprint(f\"Simulation time: {end_time-start_time:.2f} s\")\n\n# Audible notification when the simulation is finished\nws.Beep(400, 1000)\n\nplt.plot(xpos[0], ypos[0], label=\"Earth\", color=\"green\")\nplt.plot(xpos[1], ypos[1], label=\"mars\", color=\"violet\")\nplt.plot(xpos[2], ypos[2], label=\"sun\", color=\"red\")\n\nplt.legend()\nplt.show()\n\n\n\n\n\nThis produces the following result:\n\n\n\n\n[image: The resulte of the code above; source: https://i.sstatic.net/f5j0wZO6.png] (https://i.sstatic.net/f5j0wZO6.png)\n\n\n\n\nAt first glance, one might think the problem comes from the fact that I overwrite the acceleration instead of accumulating the contributions from all the other bodies.\n\n\n\n\nSo I changed\n\n\n\n\nax[j] = -G * (mass[j] + mass[k]) * (x[j] - x[k]) / (((x[j]-x[k])**2 + (y[j]- y[k])**2)**0.5)**3\nay[j] = -G * (mass[j] + mass[k]) * (y[j] - y[k]) / (((x[j]-x[k])**2 + (y[j]-y[k])\n\n\n\n\n\nto\n\n\n\n\nax[j] += -G * (mass[j] + mass[k]) * (x[j] - x[k]) / (((x[j]-x[k])**2 + (y[j]- y[k])**2)**0.5)**3\nay[j] += -G * (mass[j] + mass[k]) * (y[j] - y[k]) / (((x[j]-x[k])**2 + (y[j]-y[k])**2)**0.5)**3\n\n\n\n\n\nsince the total acceleration acting on body j should be the sum of the accelerations produced by every other body.\n\n\n\n\nHowever, this actually makes the simulation even worse. The result becomes:\n\n\n\n\n[image: the result of the modified code; source: https://i.sstatic.net/cWWHipMg.png] (https://i.sstatic.net/cWWHipMg.png)\n\n\n\n\nSo I feel that I am missing something more fundamental.\n\n\n\n\nAnother thing I do not understand is the behavior of the Sun in the first version. Since the acceleration is overwritten, the Sun ends up accelerating only because of the last body processed in the loop (Mars). However, the Sun is much more massive than either Earth or Mars (1 >> 3.0025e-6 and 1 >> 3.2267e-7), so I would not expect such a large acceleration. Why does this happen?\n\n\n\n\nLikewise, why does the += version diverge so quickly instead of improving the simulation?\n\n\n\n\nMy ultimate goal is to simulate the Solar System (the Sun and the eight planets) using this double loop, but if the simulation is already unstable with only three bodies, I am clearly doing something wrong.\n\n\n\n\nFinally, I intentionally initialized the Sun with zero position, zero velocity, and zero acceleration because I wanted it to remain fixed at the origin, assuming that the Solar System barycenter is approximately at the center of the Sun.", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Omar Osman Mahamoud", "profile_url": "https://scicomp.stackexchange.com/users/57039/omar-osman-mahamoud", "user_type": "registered"}, "created_at": "2026-07-26T12:32:03+00:00", "raw_file": "raw/codex_api_v1/388d30597d4ce2c68c96b784f7bf92098fad8c44850c54687d3a3028cce83504_1790825358707940600_0.json", "raw_sha256": "798328140b22ca830f996dc29957e2ed66bad007670d3eb6cfce6a5d1c2b82b7", "revision_guid": "61294F33-1CB8-459E-AB4B-4941AD8D2670", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/61294F33-1CB8-459E-AB4B-4941AD8D2670/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2026-07-27T11:52:44+00:00", "raw_file": "raw/codex_api_v1/388d30597d4ce2c68c96b784f7bf92098fad8c44850c54687d3a3028cce83504_1790825358707940600_0.json", "raw_sha256": "798328140b22ca830f996dc29957e2ed66bad007670d3eb6cfce6a5d1c2b82b7", "revision_guid": "3F7393D0-FAE5-408C-BCD8-32B84FC1BD39", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://scicomp.stackexchange.com/revisions/3F7393D0-FAE5-408C-BCD8-32B84FC1BD39/view-source"}], "source_site": "scicomp", "source_url": "https://scicomp.stackexchange.com/questions/45499/n-body-gravitation", "split": "holdout", "split_group": "45d6b72512daab67fd2b92518c117829c50d23b2add0374b0be035746ba7ae04", "tags": ["python", "computational-physics", "simulation", "numerical-integration", "physics"], "thread_id": "scicomp:45499", "title": "N-body gravitation"}} {"accepted_status": [false, false], "candidate_answers": [{"answer_html": "Check your assumptions.
\nIt looks like you're using a formula that assumes linear, additive variance. Your data suggest a system that does not follow these assumptions, so the equations are not valid for the situation you describe.
\nSee also https://en.m.wikipedia.org/wiki/All_models_are_wrong - much of the difficulty in applying simple mathematical formulae to real world data is in deciding/recognizing when your model is sufficiently wrong that it's no longer useful.
\n", "answer_id": 114208, "answer_text": "Check your assumptions.\n\n\n\n\nIt looks like you're using a formula that assumes linear, additive variance. Your data suggest a system that does not follow these assumptions, so the equations are not valid for the situation you describe.\n\n\n\n\nSee also https://en.m.wikipedia.org/wiki/All_models_are_wrong (https://en.m.wikipedia.org/wiki/All_models_are_wrong) - much of the difficulty in applying simple mathematical formulae to real world data is in deciding/recognizing when your model is sufficiently wrong that it's no longer useful.", "answer_url": "https://biology.stackexchange.com/a/114208", "author": "Bryan Krause", "author_url": "https://biology.stackexchange.com/users/27148/bryan-krause", "author_user_type": "moderator", "content_license": "CC BY-SA 4.0", "created_at": "2024-02-29T04:29:34+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:30.839943+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/2139ae0ecb1bf62b149af3f8e91d7ce461ad269d38020aaf05922333eabb51a1_0.json", "raw_sha256": "2610bc07f1691b2794681a23d0459bba24822de1f31c7b48d79495b29b0b1285", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/114428;114427;114412;114410;114399;114395;114391;114386;114385;114381;114378;114377;114376;114374;114372;114371;114370;114361;114354;114353;114348;114342;114331;114329;114324;114321;114319;114307;114305;114304;114299;114298;114295;114290;114281;114277;114273;114266;114256;114239;114238;114222;114216;114213;114211;114207;114197;114192;114185;114180;114178;114175;114174;114173;114172;114169;114161;114156;114155;114148;114145;114144;114139;114136;114135;114127;114119;114117;114114;114111;114110;114103;114098;114096;114094;114089;114085;114078;114076;114069;114067;114065;114058;114055;114048;114045;114038;114031;114028;114027;114025;114021;114020;114012;114006;113998;113997;113988;113986;113983/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 114207, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Bryan Krause", "profile_url": "https://biology.stackexchange.com/users/27148/bryan-krause", "user_type": "moderator"}, "created_at": "2024-02-29T04:29:34+00:00", "raw_file": "raw/codex_api_v1/20c6382e006dfc70ceae89b5b384391a51cd420854d2e23edb6c44d00de6688e_1790824066738015300_0.json", "raw_sha256": "4baa513e3d4757eb58cf2dd23c824e0e27e58aa0c4e8ec570c22801fd30dcaa7", "revision_guid": "F56112DE-B89E-4603-A0F8-388A12ED9A46", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/F56112DE-B89E-4603-A0F8-388A12ED9A46/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "user438383", "profile_url": "https://biology.stackexchange.com/users/27357/user438383", "user_type": "registered"}, "created_at": "2024-04-01T09:41:44+00:00", "raw_file": "raw/codex_api_v1/c09c25974111e465f43435e13249e671865a3c492931b0256ef7f890bfa5e2e0_1790824064569681800_0.json", "raw_sha256": "0b302246b77e7a9d8782e0c9b89ad24379ff8e65cc316aa696d777ef4a6f718d", "revision_guid": "87407451-524F-4F50-91E7-9C2FDC0C1E39", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/87407451-524F-4F50-91E7-9C2FDC0C1E39/view-source"}], "score": 1, "updated_at": "2024-04-01T09:41:44+00:00"}, {"answer_html": "From this paper discussing the pitfalls of using the breeder's equation:
\n\n\nThe breeder's equation provides a useful framework for conceptualizing the process of adaptive evolution by natural selection: selection causes phenotypic changes in a population, and genetic variation transmits these changes to future generations. This is not wrong, but given the assumptions we have discussed, it may generally be very inappropriate to apply this framework as a predictive tool in nature. There is consequently a problem with the enthusiastic way in which evolutionary biologists, ourselves included, have transferred this model from being a tool to conceptualise trait evolution and analyse artificial selection experiments (a context in which the inherent assumptions can be more readily approximated) to a predictive model in the field. Estimates of selection based on selection gradients are undoubtedly a conceptual step forward, but they do not escape reliance on the assumption that all traits and environmental factors that jointly influence studied traits and fitness have been identified, meaningfully measured and adequately modelled.
\n
So if this is indeed an artificial selection experiment and you have actually designed the experiment to control for all possible sources of e.g. environmental variation, then it may be appropriate to use the breeder's equation model. However, we don't know anything about the source of your data, so it's difficult to evaluate whether your data are from an adequately controlled e.g. common garden style experiment.
\nMoreover:
\n\n\nNo model can be expected to provide accurate predictions if its assumptions are seriously violated. The simple approaches we discuss here for predicting evolutionary change actually make many simplifying assumptions (e.g. constant population demography, discrete generations, constant environmental conditions; Merilä et al., 2001a), and we are certainly not the first to highlight the potential for predictions to fail when when these models are applied to natural systems (Hadfield, 2008; Price et al., 1988; van Tienderen & de Jong, 1994) or to call for caution in this regard.
\n
They are clearly focusing on natural populations, which I don't think you are. But on the off chance that your "selected" parental population is not selected explicitly on your height measurement, then that is probably the reason why your estimates are wonky.
\nIf you are in fact doing an artificial selection experiment, your estimates are probably wonky because some of those bolded factors were not controlled for.
\nFor example, if these are bean plants, the parental and offspring generations may have been grown in different years with different climatic conditions. Even in a laboratory environment with well controlled conditions, unless the parents and offspring are grown at literally the exact same time side by side (which presents obvious logistical challenges) with positional rotation and constant care, it can be hard to fully reject the hypothesis of some unknown environmental factor impacting your data.
\n", "answer_id": 114420, "answer_text": "From this paper (https://onlinelibrary.wiley.com/doi/10.1111/j.1420-9101.2010.02084.x) discussing the pitfalls of using the breeder's equation:\n\n\n\n\n\n\n\nThe breeder's equation provides a useful framework for conceptualizing the process of adaptive evolution by natural selection: selection causes phenotypic changes in a population, and genetic variation transmits these changes to future generations. This is not wrong, but given the assumptions we have discussed, it may generally be very inappropriate to apply this framework as a predictive tool in nature. There is consequently a problem with the enthusiastic way in which evolutionary biologists, ourselves included, have transferred this model from being a tool to conceptualise trait evolution and analyse artificial selection experiments (a context in which the inherent assumptions can be more readily approximated) to a predictive model in the field. Estimates of selection based on selection gradients are undoubtedly a conceptual step forward, but they do not escape reliance on the assumption that all traits and environmental factors that jointly influence studied traits and fitness have been identified, meaningfully measured and adequately modelled.\n\n\n\n\n\n\n\nSo if this is indeed an artificial selection experiment and you have actually designed the experiment to control for all possible sources of e.g. environmental variation, then it may be appropriate to use the breeder's equation model. However, we don't know anything about the source of your data, so it's difficult to evaluate whether your data are from an adequately controlled e.g. common garden style experiment.\n\n\n\n\nMoreover:\n\n\n\n\n\n\n\nNo model can be expected to provide accurate predictions if its assumptions are seriously violated. The simple approaches we discuss here for predicting evolutionary change actually make many simplifying assumptions (e.g. constant population demography, discrete generations, constant environmental conditions; Merilä et al., 2001a), and we are certainly not the first to highlight the potential for predictions to fail when when these models are applied to natural systems (Hadfield, 2008; Price et al., 1988; van Tienderen & de Jong, 1994) or to call for caution in this regard.\n\n\n\n\n\n\n\nThey are clearly focusing on natural populations, which I don't think you are. But on the off chance that your \"selected\" parental population is not selected explicitly on your height measurement, then that is probably the reason why your estimates are wonky.\n\n\n\n\nIf you are in fact doing an artificial selection experiment, your estimates are probably wonky because some of those bolded factors were not controlled for.\n\n\n\n\nFor example, if these are bean plants, the parental and offspring generations may have been grown in different years with different climatic conditions. Even in a laboratory environment with well controlled conditions, unless the parents and offspring are grown at literally the exact same time side by side (which presents obvious logistical challenges) with positional rotation and constant care, it can be hard to fully reject the hypothesis of some unknown environmental factor impacting your data.", "answer_url": "https://biology.stackexchange.com/a/114420", "author": "Maximilian Press", "author_url": "https://biology.stackexchange.com/users/22392/maximilian-press", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-04-01T18:40:03+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:32.233008+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/29e10377e709be0879cc174e9be11ba5513feaafd20aa842a20668af70c6d683_0.json", "raw_sha256": "535e870bb8fe62b3db0c0b66043a398cf2f6d26fcd7ad4a13a2a7e2a09999ee9", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/114428;114427;114412;114410;114399;114395;114391;114386;114385;114381;114378;114377;114376;114374;114372;114371;114370;114361;114354;114353;114348;114342;114331;114329;114324;114321;114319;114307;114305;114304;114299;114298;114295;114290;114281;114277;114273;114266;114256;114239;114238;114222;114216;114213;114211;114207;114197;114192;114185;114180;114178;114175;114174;114173;114172;114169;114161;114156;114155;114148;114145;114144;114139;114136;114135;114127;114119;114117;114114;114111;114110;114103;114098;114096;114094;114089;114085;114078;114076;114069;114067;114065;114058;114055;114048;114045;114038;114031;114028;114027;114025;114021;114020;114012;114006;113998;113997;113988;113986;113983/answers?filter=withbody&order=asc&page=2&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 114207, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Maximilian Press", "profile_url": "https://biology.stackexchange.com/users/22392/maximilian-press", "user_type": "registered"}, "created_at": "2024-04-01T18:40:03+00:00", "raw_file": "raw/codex_api_v1/22e8417b315063b6d3b906d11f4422eb4ac33f788b9058bddc9dd7bfc046cafc_1790824071906161300_0.json", "raw_sha256": "84dcb0018b97f3e9f1f4320ffea98714a55b6054974fc678a4c6cac9e312e078", "revision_guid": "6FCA9402-4994-4682-A01B-EF960A0D14BF", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/6FCA9402-4994-4682-A01B-EF960A0D14BF/view-source"}], "score": 1, "updated_at": "2024-04-01T18:40:03+00:00"}], "ground_truth": "community signals only; no scientific truth label", "product": "ranking", "question": "Here is my data:\n\n\n\n\nMean height score of the total parental population: 5.2\n\n\n\n\nMean height score of selected parents (those chosen for breeding due to their higher height): 6.4\n\n\n\n\nMean height score of the offspring (resulting from the selected parents): 7.8\n\n\n\n\nSelection differential (S) for height:\nS = Mean height score of selected parents - Mean height score of the total parental population\nS = 6.4 - 5.2 = 1.2\n\n\n\n\nResponse to selection (R):\nR = 7.8 - 5.2 = 2.6\n\n\n\n\nh^2 = R / S\n\n\n\n\nh^2 = 2.6 / 1.2 = 2.167\n\n\n\n\nI confirmed that the data are not wrong. What is the interpretation of this h^2 value?\n\n\n\n\nI am looking for explanations for why h^2 would be above one.", "record_id": "Scientific-Answer-Ranking:biology:114207", "scores": [1, 1], "split": "holdout", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "Check your assumptions.
\nIt looks like you're using a formula that assumes linear, additive variance. Your data suggest a system that does not follow these assumptions, so the equations are not valid for the situation you describe.
\nSee also https://en.m.wikipedia.org/wiki/All_models_are_wrong - much of the difficulty in applying simple mathematical formulae to real world data is in deciding/recognizing when your model is sufficiently wrong that it's no longer useful.
\n", "answer_id": 114208, "answer_text": "Check your assumptions.\n\n\n\n\nIt looks like you're using a formula that assumes linear, additive variance. Your data suggest a system that does not follow these assumptions, so the equations are not valid for the situation you describe.\n\n\n\n\nSee also https://en.m.wikipedia.org/wiki/All_models_are_wrong (https://en.m.wikipedia.org/wiki/All_models_are_wrong) - much of the difficulty in applying simple mathematical formulae to real world data is in deciding/recognizing when your model is sufficiently wrong that it's no longer useful.", "answer_url": "https://biology.stackexchange.com/a/114208", "author": "Bryan Krause", "author_url": "https://biology.stackexchange.com/users/27148/bryan-krause", "author_user_type": "moderator", "content_license": "CC BY-SA 4.0", "created_at": "2024-02-29T04:29:34+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:30.839943+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/2139ae0ecb1bf62b149af3f8e91d7ce461ad269d38020aaf05922333eabb51a1_0.json", "raw_sha256": "2610bc07f1691b2794681a23d0459bba24822de1f31c7b48d79495b29b0b1285", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/114428;114427;114412;114410;114399;114395;114391;114386;114385;114381;114378;114377;114376;114374;114372;114371;114370;114361;114354;114353;114348;114342;114331;114329;114324;114321;114319;114307;114305;114304;114299;114298;114295;114290;114281;114277;114273;114266;114256;114239;114238;114222;114216;114213;114211;114207;114197;114192;114185;114180;114178;114175;114174;114173;114172;114169;114161;114156;114155;114148;114145;114144;114139;114136;114135;114127;114119;114117;114114;114111;114110;114103;114098;114096;114094;114089;114085;114078;114076;114069;114067;114065;114058;114055;114048;114045;114038;114031;114028;114027;114025;114021;114020;114012;114006;113998;113997;113988;113986;113983/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 114207, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Bryan Krause", "profile_url": "https://biology.stackexchange.com/users/27148/bryan-krause", "user_type": "moderator"}, "created_at": "2024-02-29T04:29:34+00:00", "raw_file": "raw/codex_api_v1/20c6382e006dfc70ceae89b5b384391a51cd420854d2e23edb6c44d00de6688e_1790824066738015300_0.json", "raw_sha256": "4baa513e3d4757eb58cf2dd23c824e0e27e58aa0c4e8ec570c22801fd30dcaa7", "revision_guid": "F56112DE-B89E-4603-A0F8-388A12ED9A46", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/F56112DE-B89E-4603-A0F8-388A12ED9A46/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "user438383", "profile_url": "https://biology.stackexchange.com/users/27357/user438383", "user_type": "registered"}, "created_at": "2024-04-01T09:41:44+00:00", "raw_file": "raw/codex_api_v1/c09c25974111e465f43435e13249e671865a3c492931b0256ef7f890bfa5e2e0_1790824064569681800_0.json", "raw_sha256": "0b302246b77e7a9d8782e0c9b89ad24379ff8e65cc316aa696d777ef4a6f718d", "revision_guid": "87407451-524F-4F50-91E7-9C2FDC0C1E39", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/87407451-524F-4F50-91E7-9C2FDC0C1E39/view-source"}], "score": 1, "updated_at": "2024-04-01T09:41:44+00:00"}, {"answer_html": "From this paper discussing the pitfalls of using the breeder's equation:
\n\n\nThe breeder's equation provides a useful framework for conceptualizing the process of adaptive evolution by natural selection: selection causes phenotypic changes in a population, and genetic variation transmits these changes to future generations. This is not wrong, but given the assumptions we have discussed, it may generally be very inappropriate to apply this framework as a predictive tool in nature. There is consequently a problem with the enthusiastic way in which evolutionary biologists, ourselves included, have transferred this model from being a tool to conceptualise trait evolution and analyse artificial selection experiments (a context in which the inherent assumptions can be more readily approximated) to a predictive model in the field. Estimates of selection based on selection gradients are undoubtedly a conceptual step forward, but they do not escape reliance on the assumption that all traits and environmental factors that jointly influence studied traits and fitness have been identified, meaningfully measured and adequately modelled.
\n
So if this is indeed an artificial selection experiment and you have actually designed the experiment to control for all possible sources of e.g. environmental variation, then it may be appropriate to use the breeder's equation model. However, we don't know anything about the source of your data, so it's difficult to evaluate whether your data are from an adequately controlled e.g. common garden style experiment.
\nMoreover:
\n\n\nNo model can be expected to provide accurate predictions if its assumptions are seriously violated. The simple approaches we discuss here for predicting evolutionary change actually make many simplifying assumptions (e.g. constant population demography, discrete generations, constant environmental conditions; Merilä et al., 2001a), and we are certainly not the first to highlight the potential for predictions to fail when when these models are applied to natural systems (Hadfield, 2008; Price et al., 1988; van Tienderen & de Jong, 1994) or to call for caution in this regard.
\n
They are clearly focusing on natural populations, which I don't think you are. But on the off chance that your "selected" parental population is not selected explicitly on your height measurement, then that is probably the reason why your estimates are wonky.
\nIf you are in fact doing an artificial selection experiment, your estimates are probably wonky because some of those bolded factors were not controlled for.
\nFor example, if these are bean plants, the parental and offspring generations may have been grown in different years with different climatic conditions. Even in a laboratory environment with well controlled conditions, unless the parents and offspring are grown at literally the exact same time side by side (which presents obvious logistical challenges) with positional rotation and constant care, it can be hard to fully reject the hypothesis of some unknown environmental factor impacting your data.
\n", "answer_id": 114420, "answer_text": "From this paper (https://onlinelibrary.wiley.com/doi/10.1111/j.1420-9101.2010.02084.x) discussing the pitfalls of using the breeder's equation:\n\n\n\n\n\n\n\nThe breeder's equation provides a useful framework for conceptualizing the process of adaptive evolution by natural selection: selection causes phenotypic changes in a population, and genetic variation transmits these changes to future generations. This is not wrong, but given the assumptions we have discussed, it may generally be very inappropriate to apply this framework as a predictive tool in nature. There is consequently a problem with the enthusiastic way in which evolutionary biologists, ourselves included, have transferred this model from being a tool to conceptualise trait evolution and analyse artificial selection experiments (a context in which the inherent assumptions can be more readily approximated) to a predictive model in the field. Estimates of selection based on selection gradients are undoubtedly a conceptual step forward, but they do not escape reliance on the assumption that all traits and environmental factors that jointly influence studied traits and fitness have been identified, meaningfully measured and adequately modelled.\n\n\n\n\n\n\n\nSo if this is indeed an artificial selection experiment and you have actually designed the experiment to control for all possible sources of e.g. environmental variation, then it may be appropriate to use the breeder's equation model. However, we don't know anything about the source of your data, so it's difficult to evaluate whether your data are from an adequately controlled e.g. common garden style experiment.\n\n\n\n\nMoreover:\n\n\n\n\n\n\n\nNo model can be expected to provide accurate predictions if its assumptions are seriously violated. The simple approaches we discuss here for predicting evolutionary change actually make many simplifying assumptions (e.g. constant population demography, discrete generations, constant environmental conditions; Merilä et al., 2001a), and we are certainly not the first to highlight the potential for predictions to fail when when these models are applied to natural systems (Hadfield, 2008; Price et al., 1988; van Tienderen & de Jong, 1994) or to call for caution in this regard.\n\n\n\n\n\n\n\nThey are clearly focusing on natural populations, which I don't think you are. But on the off chance that your \"selected\" parental population is not selected explicitly on your height measurement, then that is probably the reason why your estimates are wonky.\n\n\n\n\nIf you are in fact doing an artificial selection experiment, your estimates are probably wonky because some of those bolded factors were not controlled for.\n\n\n\n\nFor example, if these are bean plants, the parental and offspring generations may have been grown in different years with different climatic conditions. Even in a laboratory environment with well controlled conditions, unless the parents and offspring are grown at literally the exact same time side by side (which presents obvious logistical challenges) with positional rotation and constant care, it can be hard to fully reject the hypothesis of some unknown environmental factor impacting your data.", "answer_url": "https://biology.stackexchange.com/a/114420", "author": "Maximilian Press", "author_url": "https://biology.stackexchange.com/users/22392/maximilian-press", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-04-01T18:40:03+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:32.233008+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/29e10377e709be0879cc174e9be11ba5513feaafd20aa842a20668af70c6d683_0.json", "raw_sha256": "535e870bb8fe62b3db0c0b66043a398cf2f6d26fcd7ad4a13a2a7e2a09999ee9", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/114428;114427;114412;114410;114399;114395;114391;114386;114385;114381;114378;114377;114376;114374;114372;114371;114370;114361;114354;114353;114348;114342;114331;114329;114324;114321;114319;114307;114305;114304;114299;114298;114295;114290;114281;114277;114273;114266;114256;114239;114238;114222;114216;114213;114211;114207;114197;114192;114185;114180;114178;114175;114174;114173;114172;114169;114161;114156;114155;114148;114145;114144;114139;114136;114135;114127;114119;114117;114114;114111;114110;114103;114098;114096;114094;114089;114085;114078;114076;114069;114067;114065;114058;114055;114048;114045;114038;114031;114028;114027;114025;114021;114020;114012;114006;113998;113997;113988;113986;113983/answers?filter=withbody&order=asc&page=2&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 114207, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Maximilian Press", "profile_url": "https://biology.stackexchange.com/users/22392/maximilian-press", "user_type": "registered"}, "created_at": "2024-04-01T18:40:03+00:00", "raw_file": "raw/codex_api_v1/22e8417b315063b6d3b906d11f4422eb4ac33f788b9058bddc9dd7bfc046cafc_1790824071906161300_0.json", "raw_sha256": "84dcb0018b97f3e9f1f4320ffea98714a55b6054974fc678a4c6cac9e312e078", "revision_guid": "6FCA9402-4994-4682-A01B-EF960A0D14BF", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/6FCA9402-4994-4682-A01B-EF960A0D14BF/view-source"}], "score": 1, "updated_at": "2024-04-01T18:40:03+00:00"}], "domain": "biology", "external_links": ["https://en.m.wikipedia.org/wiki/All_models_are_wrong", "https://onlinelibrary.wiley.com/doi/10.1111/j.1420-9101.2010.02084.x"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:08.576606+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/1051d4f3e38449f1419d1973ac812b2286659e454a76f89a23fdaa941dfadddb_0.json", "raw_sha256": "583dcd577e20d33b29e9f8818a7ab6a1fab039c19ab79927e16096cff23fa61d", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=7&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "BigMistake", "question_author_url": "https://biology.stackexchange.com/users/75355/bigmistake", "question_author_user_type": "registered", "question_created_at": "2024-02-29T03:22:02+00:00", "question_html": "Here is my data:
\nMean height score of the total parental population: 5.2
\nMean height score of selected parents (those chosen for breeding due to their higher height): 6.4
\nMean height score of the offspring (resulting from the selected parents): 7.8
\nSelection differential (S) for height:\nS = Mean height score of selected parents - Mean height score of the total parental population\nS = 6.4 - 5.2 = 1.2
\nResponse to selection (R):\nR = 7.8 - 5.2 = 2.6
\nh^2 = R / S
\nh^2 = 2.6 / 1.2 = 2.167
\nI confirmed that the data are not wrong. What is the interpretation of this h^2 value?
\nI am looking for explanations for why h^2 would be above one.
\n", "question_id": 114207, "question_license": "CC BY-SA 4.0", "question_score": 1, "question_text": "Here is my data:\n\n\n\n\nMean height score of the total parental population: 5.2\n\n\n\n\nMean height score of selected parents (those chosen for breeding due to their higher height): 6.4\n\n\n\n\nMean height score of the offspring (resulting from the selected parents): 7.8\n\n\n\n\nSelection differential (S) for height:\nS = Mean height score of selected parents - Mean height score of the total parental population\nS = 6.4 - 5.2 = 1.2\n\n\n\n\nResponse to selection (R):\nR = 7.8 - 5.2 = 2.6\n\n\n\n\nh^2 = R / S\n\n\n\n\nh^2 = 2.6 / 1.2 = 2.167\n\n\n\n\nI confirmed that the data are not wrong. What is the interpretation of this h^2 value?\n\n\n\n\nI am looking for explanations for why h^2 would be above one.", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "BigMistake", "profile_url": "https://biology.stackexchange.com/users/75355/bigmistake", "user_type": "registered"}, "created_at": "2024-02-29T03:22:02+00:00", "raw_file": "raw/codex_api_v1/20c6382e006dfc70ceae89b5b384391a51cd420854d2e23edb6c44d00de6688e_1790824066738015300_0.json", "raw_sha256": "4baa513e3d4757eb58cf2dd23c824e0e27e58aa0c4e8ec570c22801fd30dcaa7", "revision_guid": "74F74F3B-968B-409B-B758-97AB1EA345FD", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/74F74F3B-968B-409B-B758-97AB1EA345FD/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "BigMistake", "profile_url": "https://biology.stackexchange.com/users/75355/bigmistake", "user_type": "registered"}, "created_at": "2024-02-29T03:36:09+00:00", "raw_file": "raw/codex_api_v1/20c6382e006dfc70ceae89b5b384391a51cd420854d2e23edb6c44d00de6688e_1790824066738015300_0.json", "raw_sha256": "4baa513e3d4757eb58cf2dd23c824e0e27e58aa0c4e8ec570c22801fd30dcaa7", "revision_guid": "A4B13087-186F-45EC-A427-DB662578DFE4", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/A4B13087-186F-45EC-A427-DB662578DFE4/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "BigMistake", "profile_url": "https://biology.stackexchange.com/users/75355/bigmistake", "user_type": "registered"}, "created_at": "2024-02-29T05:58:53+00:00", "raw_file": "raw/codex_api_v1/20c6382e006dfc70ceae89b5b384391a51cd420854d2e23edb6c44d00de6688e_1790824066738015300_0.json", "raw_sha256": "4baa513e3d4757eb58cf2dd23c824e0e27e58aa0c4e8ec570c22801fd30dcaa7", "revision_guid": "D447808C-D7D4-4241-B7C2-A11211A08284", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/D447808C-D7D4-4241-B7C2-A11211A08284/view-source"}, {"content_license": null, "contributor": {"display_name": "Community", "profile_url": "https://biology.stackexchange.com/users/-1/community", "user_type": "moderator"}, "created_at": "2024-03-30T06:01:20+00:00", "raw_file": "raw/codex_api_v1/c09c25974111e465f43435e13249e671865a3c492931b0256ef7f890bfa5e2e0_1790824064569681800_0.json", "raw_sha256": "0b302246b77e7a9d8782e0c9b89ad24379ff8e65cc316aa696d777ef4a6f718d", "revision_guid": "4D22225F-33D8-4050-B18C-2EF52C62B49C", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/4D22225F-33D8-4050-B18C-2EF52C62B49C/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Maximilian Press", "profile_url": "https://biology.stackexchange.com/users/22392/maximilian-press", "user_type": "registered"}, "created_at": "2024-04-01T18:13:32+00:00", "raw_file": "raw/codex_api_v1/c09c25974111e465f43435e13249e671865a3c492931b0256ef7f890bfa5e2e0_1790824064569681800_0.json", "raw_sha256": "0b302246b77e7a9d8782e0c9b89ad24379ff8e65cc316aa696d777ef4a6f718d", "revision_guid": "9642B35B-D8E9-4203-AA2F-11D0813C78C9", "revision_number": 4, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/9642B35B-D8E9-4203-AA2F-11D0813C78C9/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/114207/interpretation-of-narrow-sense-heritability-over-one-using-r-s-h2", "split": "holdout", "split_group": "f302586999c52ffc28888d6813b076db250af71d0add79b0e4e6d96b37f26c08", "tags": ["genetics", "evolution", "population-genetics", "selection"], "thread_id": "biology:114207", "title": "Interpretation of narrow-sense heritability over one (using R/S = h^2)"}} {"accepted_status": [false, true], "candidate_answers": [{"answer_html": "Think about it this way: if you're compiling a budget or asset report then you want to know about cash flows - income vs. expenditures - regardless of what form that "cash" might take. Sometimes, you want to know how much "cash at hand" you have, and you'll count only the most liquid assets, but often you'll also need to know the total value of any assets that can be converted into cash at all - not just stocks and bonds, but real estate, let's say, and a lot of other possible in-betweens.
\nIn that they are used here (in the context of nutrition), calories are basically like energy currency with varying degrees of liquidity. You might have some assets, like carbs, which are like publicly traded stock shares that can be fairly easily converted to ATP with little commission. Proteins, then, might be more like specialized assets. But the crucial point is, proteins are still energy assets. When you are evaluating your wealth for the purposes of taxes or to take out a mortgage, the bank/IRS will still want to know your net worth considering any property contributing to that net worth. Because proteins can be converted to energy, they still add up to the overall energy budget.
\nImagine you have a financial portfolio where you're investing more into stocks (proteins) than what is optimal for your growth targets. The same way that if you have excess cash in your financial portfolio (after meeting your investment and savings goals), you might invest it into more stocks or bonds, the excess energy provided by proteins will need to be stored somewhere.
\nIn the body, consuming more protein than needed for muscle repair and other functions leads to excess calories. Since the body sees this as an "excess cash flow," it converts proteins into glucose (sort of- the details are complicated) and stores it as fat (which is, in our parable, like the savings account).
\n", "answer_id": 114091, "answer_text": "Think about it this way: if you're compiling a budget or asset report then you want to know about cash flows - income vs. expenditures - regardless of what form that \"cash\" might take. Sometimes, you want to know how much \"cash at hand\" you have, and you'll count only the most liquid assets, but often you'll also need to know the total value of any assets that can be converted into cash at all - not just stocks and bonds, but real estate, let's say, and a lot of other possible in-betweens.\n\n\n\n\nIn that they are used here (in the context of nutrition), calories are basically like energy currency with varying degrees of liquidity. You might have some assets, like carbs, which are like publicly traded stock shares that can be fairly easily converted to ATP with little commission. Proteins, then, might be more like specialized assets. But the crucial point is, proteins are still energy assets. When you are evaluating your wealth for the purposes of taxes or to take out a mortgage, the bank/IRS will still want to know your net worth considering any property contributing to that net worth. Because proteins can be converted to energy, they still add up to the overall energy budget.\n\n\n\n\nImagine you have a financial portfolio where you're investing more into stocks (proteins) than what is optimal for your growth targets. The same way that if you have excess cash in your financial portfolio (after meeting your investment and savings goals), you might invest it into more stocks or bonds, the excess energy provided by proteins will need to be stored somewhere.\n\n\n\n\nIn the body, consuming more protein than needed for muscle repair and other functions leads to excess calories. Since the body sees this as an \"excess cash flow,\" it converts proteins into glucose (sort of- the details are complicated) and stores it as fat (which is, in our parable, like the savings account).", "answer_url": "https://biology.stackexchange.com/a/114091", "author": "That Guy", "author_url": "https://biology.stackexchange.com/users/6027/that-guy", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-02-14T01:23:19+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:30.839943+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/2139ae0ecb1bf62b149af3f8e91d7ce461ad269d38020aaf05922333eabb51a1_0.json", "raw_sha256": "2610bc07f1691b2794681a23d0459bba24822de1f31c7b48d79495b29b0b1285", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/114428;114427;114412;114410;114399;114395;114391;114386;114385;114381;114378;114377;114376;114374;114372;114371;114370;114361;114354;114353;114348;114342;114331;114329;114324;114321;114319;114307;114305;114304;114299;114298;114295;114290;114281;114277;114273;114266;114256;114239;114238;114222;114216;114213;114211;114207;114197;114192;114185;114180;114178;114175;114174;114173;114172;114169;114161;114156;114155;114148;114145;114144;114139;114136;114135;114127;114119;114117;114114;114111;114110;114103;114098;114096;114094;114089;114085;114078;114076;114069;114067;114065;114058;114055;114048;114045;114038;114031;114028;114027;114025;114021;114020;114012;114006;113998;113997;113988;113986;113983/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 114085, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "That Guy", "profile_url": "https://biology.stackexchange.com/users/6027/that-guy", "user_type": "registered"}, "created_at": "2024-02-14T01:23:19+00:00", "raw_file": "raw/codex_api_v1/4aa156cabb1f3edbc4e0a74ff84deb30f9cd06be13c7d021adab58e209db850d_1790824057164545000_0.json", "raw_sha256": "42ee08c1af6f231bf4bd10a51fd8384910e076e5d887f51c6dd79384012b46ec", "revision_guid": "DB58FD36-B3B1-48DE-9176-BDFD87B3E878", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/DB58FD36-B3B1-48DE-9176-BDFD87B3E878/view-source"}], "score": 0, "updated_at": "2024-02-14T01:23:19+00:00"}, {"answer_html": "Preamble
\nI had not intended to answer this question as I felt it lacked the clarity required for this site. However I now think that it is necessary to correct the assertion that “protein has to be converted into glucose to generate energy”, especially as this is echoed by the answer from @ThatGuy. I shall clarify the question by interpreting the word “relevant” primarily to mean general “purpose” or “utility”, and shall consider this in relation to the Food and Agriculture Organization of the United Nations (FAO), one scientific body that has published values for energy values of nutrients.
Summary
- \n
The dietary nutrients carbohydrate, fat and protein can have\ndifferent metabolic fates in the body depending on individual\ncircumstances. The assumption that “protein is mostly used by the\nbody for purposes other than extraction of energy” does not apply\nin many circumstances.
\n \nEnergy values for food are concerned only with the situation in which the nutrient is used to produce its maximum biological energy yield as ATP, using the appropriate metabolic pathways.
\n \nThese values are not simple bomb calorimeter values. They are calculated separately for protein, carbohydrate, and fat, taking into account their different metabolism. For proteins this takes into account the different metabolism of the 20 amino acids, although it should be emphasized none of these need to be converted to glucose to generate energy.
\n \nThere are several different purposes to which these values can and are used, but the FAO is primarily concerned with their use to assess basic nutritional needs and their fulfilment in the countries of the world in which malnutrition may occur.
\n \n
The FAO and standard energy values for nutrients
\nAs mentioned above, I will consider this question in relation to the FAO, the Food and Agriculture Organization of the United Nations, a body that has produced energy values of different nutrients — values that appear to be used by government organizations and commercial food groups in many countries. The source of my information is this report on the subject, produced in 2003, to which the reader is referred for fuller details.
What did the FAO envisage that the results of their work would be used for?
\nTo quote from Section 1.1 of the report:
- \n
- assessment of the energy needs of countries… living under\ndifferent circumstances; \n
- assessment of food availability within regions and countries; \n
- assessment of the potential ability of available food supplies to meet a country’s … needs, \n
- assessment of individuals’ diets (although the recommendations are not meant for this purpose)); \n
- as a basis for food labelling, with implications for consumer information/education about specific foods, regulatory compliance regarding nutrient content and claims, and trade. \n
This should answer the original poster’s concern with the “relevance” of energy values. The purpose envisaged was clearly with energy requirements in countries in which energy malnutrition was a problem, not affluent Western countries suffering from easily preventable diseases caused by overconsumption of food (although they are not irrelevant in the latter).
\nDid the FAO take into account the different metabolic fates of different energy supplying nutrients?
\nYes. It was constituted of personnel who, unlike the poster, were biological scientists with a sound understanding of the physiology and biochemistry of metabolism. To quote from section 1.3 of the report:
\n\n“Energy requirement recommendations remain “theoretical” and of little practical value until they can be related to foods… Two pieces of information are needed in order to translate individual foods, and ultimately diets, into energy intakes that can be compared with the requirement recommendations…\n…amounts of components must be converted into energy content using an agreed set of physiology-related factors that correspond to the energy-producing potential of the components in the human body. Thus, in order to make accurate estimates of energy intake, it is essential to have energy conversion factors for each component that denote the energy per gram for that component. However, it has long been recognized that the energy contents of protein, fat and carbohydrate differ, both inherently in the compounds themselves and owing to their different digestion, absorption and metabolism.”
\n
So the scientists on this body were well aware of the problems in producing energy values for different nutrients, and the paper considers proteins, fats and carbohydrates separately and in detail in sections 2 and 3 of this report. For each of these (and for different sources of the same constituent) they produced separate values of various measures, with final values in Section 4.
\nHowever the value of 17 kJoules per gram protein (=4kcal/g)) quoted by the original poster is the FAO value of Net Metabolizable Energy (NME) — i.e. the energy produced in circumstances when all the protein amino acids are oxidized to produce ATP. This is relevant to individuals in protein equilibrium but in net energy deficit.
\n(The overall energy values they suggest for fat is 37 kJoules/g, and for carbohydrate 17 kJoules/g).
\nSummary of metabolite interconversions in obtaining metabolic energy from proteins, fats and carbohydrates
\n![\"Pathways](\"https://i.sstatic.net/f0Z0s.png\")
The diagram above is my own attempt at a biochemical summary for the situation when carbohydrate, fat or protein are being solely used to generate energy. Although some ATP is generated directly in one pathway, most of the carbon skeletons are oxidized in the TCA cycle, shown. Not shown is the NADH produced in the TCA cycle and its oxidation in the electron transport chain to produce a proton-motive force which drives the conversion of ADP to ATP — a molecule that can be considered as a source of metabolic energy.
\nIn the energy-deficit scenario carbohydrates are converted to glucose, then to pyruvate in glycolysis (with some direct generation of ATP) and then to Acetyl CoA which for oxidation in the TCA cycle.
\nIn this scenario fat (triglyceride) is converted to fatty acids and glycerol, the latter feeding into glycolysis, and the former being oxidized to Acetyl CoA, and hence to the TCA cycle.
\nIn this scenario, in which they are not required for protein biosynthesis, each of the 20 amino acids from protein undergoes different metabolic conversions, as shown. All these can lead to the TCA cycle, and, as is evident, none involve conversion to glucose†. (The removal of nitrogen from the amino acids, actually consumes energy, but this is allowed for in the FAO calculations.)
\nAnalogy (for those that find them useful)
\nIf I buy a gold trinket in an antique shop it will (in Britain at least) bear a hallmark indicating the purity of the gold. If I am interested in keeping the piece until the price of gold increases and then selling it for its gold content (perhaps after melting it down) then the hallmark information is of primary relevance to me. If, however, I am interested in the trinket because of its beauty or because it may be a rare piece from a famous designer, the hallmark, although reassuring, would have little “relevance” to my purpose.
Even shorter analogy (to demonstrate my sense of humour)
\nOne man’s meat is another man’s poison.
\n†The misconception about protein and glucose may have arisen in the following way. In extreme starvation the primary metabolic consideration is to supply the brain with glucose, on which it is absolutely dependent. To do this muscle protein is broken down to amino acids, some of which (e.g. those in the diagram that go to pyruvate) can be converted to glucose in the liver by the reversal of glycolysis (gluconeogenesis). However in a normal diet this is unlikely to happen because there will be a plentiful supply of glucose from carbohydrate, and it is certainly not the scenario in which energy values of protein are calculated.\n", "answer_id": 114128, "answer_text": "Preamble\n\nI had not intended to answer this question as I felt it lacked the clarity required for this site. However I now think that it is necessary to correct the assertion that “protein has to be converted into glucose to generate energy”, especially as this is echoed by the answer from @ThatGuy. I shall clarify the question by interpreting the word “relevant” primarily to mean general “purpose” or “utility”, and shall consider this in relation to the Food and Agriculture Organization of the United Nations (FAO), one scientific body that has published values for energy values of nutrients.\n\n\n\n\nSummary\n\n\n\n\n\n\n\n\nThe dietary nutrients carbohydrate, fat and protein can have\ndifferent metabolic fates in the body depending on individual\ncircumstances. The assumption that “protein is mostly used by the\nbody for purposes other than extraction of energy” does not apply\nin many circumstances.\n\n\n\n\n\n\n\n\n\nEnergy values for food are concerned only with the situation in which the nutrient is used to produce its maximum biological energy yield as ATP, using the appropriate metabolic pathways.\n\n\n\n\n\n\n\n\n\nThese values are not simple bomb calorimeter values. They are calculated separately for protein, carbohydrate, and fat, taking into account their different metabolism. For proteins this takes into account the different metabolism of the 20 amino acids, although it should be emphasized none of these need to be converted to glucose to generate energy.\n\n\n\n\n\n\n\n\n\nThere are several different purposes to which these values can and are used, but the FAO is primarily concerned with their use to assess basic nutritional needs and their fulfilment in the countries of the world in which malnutrition may occur.\n\n\n\n\n\n\n\n\nThe FAO and standard energy values for nutrients\n\nAs mentioned above, I will consider this question in relation to the FAO, the Food and Agriculture Organization of the United Nations, a body that has produced energy values of different nutrients — values that appear to be used by government organizations and commercial food groups in many countries. The source of my information is this report on the subject, produced in 2003 (https://www.fao.org/3/Y5022E/y5022e00.htm#Contents), to which the reader is referred for fuller details.\n\n\n\n\nWhat did the FAO envisage that the results of their work would be used for?\n\nTo quote from Section 1.1 of the report:\n\n\n\n\n\nassessment of the energy needs of countries… living under\ndifferent circumstances;\n\n\n\n\nassessment of food availability within regions and countries;\n\n\n\n\nassessment of the potential ability of available food supplies to meet a country’s … needs,\n\n\n\n\nassessment of individuals’ diets (although the recommendations are not meant for this purpose));\n\n\n\n\nas a basis for food labelling, with implications for consumer information/education about specific foods, regulatory compliance regarding nutrient content and claims, and trade.\n\n\n\n\n\nThis should answer the original poster’s concern with the “relevance” of energy values. The purpose envisaged was clearly with energy requirements in countries in which energy malnutrition was a problem, not affluent Western countries suffering from easily preventable diseases caused by overconsumption of food (although they are not irrelevant in the latter).\n\n\n\n\nDid the FAO take into account the different metabolic fates of different energy supplying nutrients?\n\nYes. It was constituted of personnel who, unlike the poster, were biological scientists with a sound understanding of the physiology and biochemistry of metabolism. To quote from section 1.3 of the report:\n\n\n\n\n\n\n\n“Energy requirement recommendations remain “theoretical” and of little practical value until they can be related to foods… Two pieces of information are needed in order to translate individual foods, and ultimately diets, into energy intakes that can be compared with the requirement recommendations…\n…amounts of components must be converted into energy content using an agreed set of physiology-related factors that correspond to the energy-producing potential of the components in the human body. Thus, in order to make accurate estimates of energy intake, it is essential to have energy conversion factors for each component that denote the energy per gram for that component. However, it has long been recognized that the energy contents of protein, fat and carbohydrate differ, both inherently in the compounds themselves and owing to their different digestion, absorption and metabolism.”\n\n\n\n\n\n\n\nSo the scientists on this body were well aware of the problems in producing energy values for different nutrients, and the paper considers proteins, fats and carbohydrates separately and in detail in sections 2 and 3 of this report. For each of these (and for different sources of the same constituent) they produced separate values of various measures, with final values in Section 4.\n\n\n\n\nHowever the value of 17 kJoules per gram protein (=4kcal/g)) quoted by the original poster is the FAO value of Net Metabolizable Energy (NME) — i.e. the energy produced in circumstances when all the protein amino acids are oxidized to produce ATP. This is relevant to individuals in protein equilibrium but in net energy deficit.\n\n\n\n\n(The overall energy values they suggest for fat is 37 kJoules/g, and for carbohydrate 17 kJoules/g).\n\n\n\n\nSummary of metabolite interconversions in obtaining metabolic energy from proteins, fats and carbohydrates\n\n[image: Pathways for energy generation from nutrients; source: https://i.sstatic.net/f0Z0s.png] (https://i.sstatic.net/f0Z0s.png)\n\n\n\n\nThe diagram above is my own attempt at a biochemical summary for the situation when carbohydrate, fat or protein are being solely used to generate energy. Although some ATP is generated directly in one pathway, most of the carbon skeletons are oxidized in the TCA cycle, shown. Not shown is the NADH produced in the TCA cycle and its oxidation in the electron transport chain to produce a proton-motive force which drives the conversion of ADP to ATP — a molecule that can be considered as a source of metabolic energy.\n\n\n\n\nIn the energy-deficit scenario carbohydrates are converted to glucose, then to pyruvate in glycolysis (with some direct generation of ATP) and then to Acetyl CoA which for oxidation in the TCA cycle.\n\n\n\n\nIn this scenario fat (triglyceride) is converted to fatty acids and glycerol, the latter feeding into glycolysis, and the former being oxidized to Acetyl CoA, and hence to the TCA cycle.\n\n\n\n\nIn this scenario, in which they are not required for protein biosynthesis, each of the 20 amino acids from protein undergoes different metabolic conversions, as shown. All these can lead to the TCA cycle, and, as is evident, none involve conversion to glucose†. (The removal of nitrogen from the amino acids, actually consumes energy, but this is allowed for in the FAO calculations.)\n\n\n\n\nAnalogy (for those that find them useful) \n\nIf I buy a gold trinket in an antique shop it will (in Britain at least) bear a hallmark indicating the purity of the gold. If I am interested in keeping the piece until the price of gold increases and then selling it for its gold content (perhaps after melting it down) then the hallmark information is of primary relevance to me. If, however, I am interested in the trinket because of its beauty or because it may be a rare piece from a famous designer, the hallmark, although reassuring, would have little “relevance” to my purpose.\n\n\n\n\nEven shorter analogy (to demonstrate my sense of humour)\n\nOne man’s meat is another man’s poison.\n\n\n \n\n\n†The misconception about protein and glucose may have arisen in the following way. In extreme starvation the primary metabolic consideration is to supply the brain with glucose, on which it is absolutely dependent. To do this muscle protein is broken down to amino acids, some of which (e.g. those in the diagram that go to pyruvate) can be converted to glucose in the liver by the reversal of glycolysis (gluconeogenesis). However in a normal diet this is unlikely to happen because there will be a plentiful supply of glucose from carbohydrate, and it is certainly not the scenario in which energy values of protein are calculated.", "answer_url": "https://biology.stackexchange.com/a/114128", "author": "David", "author_url": "https://biology.stackexchange.com/users/22057/david", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-02-19T18:06:07+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:30.839943+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/2139ae0ecb1bf62b149af3f8e91d7ce461ad269d38020aaf05922333eabb51a1_0.json", "raw_sha256": "2610bc07f1691b2794681a23d0459bba24822de1f31c7b48d79495b29b0b1285", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/114428;114427;114412;114410;114399;114395;114391;114386;114385;114381;114378;114377;114376;114374;114372;114371;114370;114361;114354;114353;114348;114342;114331;114329;114324;114321;114319;114307;114305;114304;114299;114298;114295;114290;114281;114277;114273;114266;114256;114239;114238;114222;114216;114213;114211;114207;114197;114192;114185;114180;114178;114175;114174;114173;114172;114169;114161;114156;114155;114148;114145;114144;114139;114136;114135;114127;114119;114117;114114;114111;114110;114103;114098;114096;114094;114089;114085;114078;114076;114069;114067;114065;114058;114055;114048;114045;114038;114031;114028;114027;114025;114021;114020;114012;114006;113998;113997;113988;113986;113983/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 114085, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "David", "profile_url": "https://biology.stackexchange.com/users/22057/david", "user_type": "registered"}, "created_at": "2024-02-19T18:06:07+00:00", "raw_file": "raw/codex_api_v1/20c6382e006dfc70ceae89b5b384391a51cd420854d2e23edb6c44d00de6688e_1790824066738015300_0.json", "raw_sha256": "4baa513e3d4757eb58cf2dd23c824e0e27e58aa0c4e8ec570c22801fd30dcaa7", "revision_guid": "C0F09253-175C-4D5D-BC1C-FD4DB80E83C0", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/C0F09253-175C-4D5D-BC1C-FD4DB80E83C0/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "David", "profile_url": "https://biology.stackexchange.com/users/22057/david", "user_type": "registered"}, "created_at": "2024-02-19T19:26:50+00:00", "raw_file": "raw/codex_api_v1/20c6382e006dfc70ceae89b5b384391a51cd420854d2e23edb6c44d00de6688e_1790824066738015300_0.json", "raw_sha256": "4baa513e3d4757eb58cf2dd23c824e0e27e58aa0c4e8ec570c22801fd30dcaa7", "revision_guid": "6C1DF573-FC6D-44E1-A97C-CE0BACEE6CF1", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/6C1DF573-FC6D-44E1-A97C-CE0BACEE6CF1/view-source"}], "score": 4, "updated_at": "2024-02-19T19:26:50+00:00"}], "ground_truth": "community signals only; no scientific truth label", "product": "ranking", "question": "Non-biologist speaking here. As you can probably see from the title, I'm having trouble wrapping my head around concepts related to the body's energy balance amd the role of macronutrients. Let me explain in more detail.\n\n\n\n\nIf a person consumes excessive amounts of calories for a certain period of time (i.e. more than they need) they will start to gain weight in the form of fat. Conversely, an extended caloric deficit will lead to weight loss. So far, so good.\n\n\n\n\nNow, each macronutrient has a certain amount of calories per gram of nutrient - if I'm not mistaken 1 g of protein has 4 kcal.\n\n\n\n\nOn the other hand, according to different sources that I've been reading lately, the body does not really use protein for energy gain unless in extreme circumstances. In other words, carbohydrates and fat can readily be \"converted\" to ATP for energy gain while the conversion of protein into glucose and then ATP is very inefficient. At least that's my understanding, if there's already a misconception here feel free to correct it.\n\n\n\n\nProteins are mostly used to build and repair different structures in the body. I will use the reparation and buildup of muscle tissue as an example. And here comes my main question: if proteins aren't being \"burned\" by the body to extract energy in the form of ATP, why are the calories consumed in the form of protein really relevant? In other words, if the protein that I eat is being used by the body to build stuff such as muscle, haemoglobin etc. and not being burned, why do I care about the calories that protein has? Why will excess protein calories make me fat?\n\n\n\n\nI obviously \"know\" that calories from protein matter, but I don't understand why this is the case. I feel like I'm really not grasping something essential here. I hope that the question is clear and that an interesting discussion could follow. If anyone could give a more detailed explanation of what's going on in the body in this scenario, that would be much appreciated.", "record_id": "Scientific-Answer-Ranking:biology:114085", "scores": [0, 4], "split": "holdout", "thread": {"accepted_answer_id": 114128, "answers": [{"answer_html": "
Think about it this way: if you're compiling a budget or asset report then you want to know about cash flows - income vs. expenditures - regardless of what form that "cash" might take. Sometimes, you want to know how much "cash at hand" you have, and you'll count only the most liquid assets, but often you'll also need to know the total value of any assets that can be converted into cash at all - not just stocks and bonds, but real estate, let's say, and a lot of other possible in-betweens.
\nIn that they are used here (in the context of nutrition), calories are basically like energy currency with varying degrees of liquidity. You might have some assets, like carbs, which are like publicly traded stock shares that can be fairly easily converted to ATP with little commission. Proteins, then, might be more like specialized assets. But the crucial point is, proteins are still energy assets. When you are evaluating your wealth for the purposes of taxes or to take out a mortgage, the bank/IRS will still want to know your net worth considering any property contributing to that net worth. Because proteins can be converted to energy, they still add up to the overall energy budget.
\nImagine you have a financial portfolio where you're investing more into stocks (proteins) than what is optimal for your growth targets. The same way that if you have excess cash in your financial portfolio (after meeting your investment and savings goals), you might invest it into more stocks or bonds, the excess energy provided by proteins will need to be stored somewhere.
\nIn the body, consuming more protein than needed for muscle repair and other functions leads to excess calories. Since the body sees this as an "excess cash flow," it converts proteins into glucose (sort of- the details are complicated) and stores it as fat (which is, in our parable, like the savings account).
\n", "answer_id": 114091, "answer_text": "Think about it this way: if you're compiling a budget or asset report then you want to know about cash flows - income vs. expenditures - regardless of what form that \"cash\" might take. Sometimes, you want to know how much \"cash at hand\" you have, and you'll count only the most liquid assets, but often you'll also need to know the total value of any assets that can be converted into cash at all - not just stocks and bonds, but real estate, let's say, and a lot of other possible in-betweens.\n\n\n\n\nIn that they are used here (in the context of nutrition), calories are basically like energy currency with varying degrees of liquidity. You might have some assets, like carbs, which are like publicly traded stock shares that can be fairly easily converted to ATP with little commission. Proteins, then, might be more like specialized assets. But the crucial point is, proteins are still energy assets. When you are evaluating your wealth for the purposes of taxes or to take out a mortgage, the bank/IRS will still want to know your net worth considering any property contributing to that net worth. Because proteins can be converted to energy, they still add up to the overall energy budget.\n\n\n\n\nImagine you have a financial portfolio where you're investing more into stocks (proteins) than what is optimal for your growth targets. The same way that if you have excess cash in your financial portfolio (after meeting your investment and savings goals), you might invest it into more stocks or bonds, the excess energy provided by proteins will need to be stored somewhere.\n\n\n\n\nIn the body, consuming more protein than needed for muscle repair and other functions leads to excess calories. Since the body sees this as an \"excess cash flow,\" it converts proteins into glucose (sort of- the details are complicated) and stores it as fat (which is, in our parable, like the savings account).", "answer_url": "https://biology.stackexchange.com/a/114091", "author": "That Guy", "author_url": "https://biology.stackexchange.com/users/6027/that-guy", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-02-14T01:23:19+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:30.839943+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/2139ae0ecb1bf62b149af3f8e91d7ce461ad269d38020aaf05922333eabb51a1_0.json", "raw_sha256": "2610bc07f1691b2794681a23d0459bba24822de1f31c7b48d79495b29b0b1285", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/114428;114427;114412;114410;114399;114395;114391;114386;114385;114381;114378;114377;114376;114374;114372;114371;114370;114361;114354;114353;114348;114342;114331;114329;114324;114321;114319;114307;114305;114304;114299;114298;114295;114290;114281;114277;114273;114266;114256;114239;114238;114222;114216;114213;114211;114207;114197;114192;114185;114180;114178;114175;114174;114173;114172;114169;114161;114156;114155;114148;114145;114144;114139;114136;114135;114127;114119;114117;114114;114111;114110;114103;114098;114096;114094;114089;114085;114078;114076;114069;114067;114065;114058;114055;114048;114045;114038;114031;114028;114027;114025;114021;114020;114012;114006;113998;113997;113988;113986;113983/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 114085, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "That Guy", "profile_url": "https://biology.stackexchange.com/users/6027/that-guy", "user_type": "registered"}, "created_at": "2024-02-14T01:23:19+00:00", "raw_file": "raw/codex_api_v1/4aa156cabb1f3edbc4e0a74ff84deb30f9cd06be13c7d021adab58e209db850d_1790824057164545000_0.json", "raw_sha256": "42ee08c1af6f231bf4bd10a51fd8384910e076e5d887f51c6dd79384012b46ec", "revision_guid": "DB58FD36-B3B1-48DE-9176-BDFD87B3E878", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/DB58FD36-B3B1-48DE-9176-BDFD87B3E878/view-source"}], "score": 0, "updated_at": "2024-02-14T01:23:19+00:00"}, {"answer_html": "Preamble
\nI had not intended to answer this question as I felt it lacked the clarity required for this site. However I now think that it is necessary to correct the assertion that “protein has to be converted into glucose to generate energy”, especially as this is echoed by the answer from @ThatGuy. I shall clarify the question by interpreting the word “relevant” primarily to mean general “purpose” or “utility”, and shall consider this in relation to the Food and Agriculture Organization of the United Nations (FAO), one scientific body that has published values for energy values of nutrients.
Summary
- \n
The dietary nutrients carbohydrate, fat and protein can have\ndifferent metabolic fates in the body depending on individual\ncircumstances. The assumption that “protein is mostly used by the\nbody for purposes other than extraction of energy” does not apply\nin many circumstances.
\n \nEnergy values for food are concerned only with the situation in which the nutrient is used to produce its maximum biological energy yield as ATP, using the appropriate metabolic pathways.
\n \nThese values are not simple bomb calorimeter values. They are calculated separately for protein, carbohydrate, and fat, taking into account their different metabolism. For proteins this takes into account the different metabolism of the 20 amino acids, although it should be emphasized none of these need to be converted to glucose to generate energy.
\n \nThere are several different purposes to which these values can and are used, but the FAO is primarily concerned with their use to assess basic nutritional needs and their fulfilment in the countries of the world in which malnutrition may occur.
\n \n
The FAO and standard energy values for nutrients
\nAs mentioned above, I will consider this question in relation to the FAO, the Food and Agriculture Organization of the United Nations, a body that has produced energy values of different nutrients — values that appear to be used by government organizations and commercial food groups in many countries. The source of my information is this report on the subject, produced in 2003, to which the reader is referred for fuller details.
What did the FAO envisage that the results of their work would be used for?
\nTo quote from Section 1.1 of the report:
- \n
- assessment of the energy needs of countries… living under\ndifferent circumstances; \n
- assessment of food availability within regions and countries; \n
- assessment of the potential ability of available food supplies to meet a country’s … needs, \n
- assessment of individuals’ diets (although the recommendations are not meant for this purpose)); \n
- as a basis for food labelling, with implications for consumer information/education about specific foods, regulatory compliance regarding nutrient content and claims, and trade. \n
This should answer the original poster’s concern with the “relevance” of energy values. The purpose envisaged was clearly with energy requirements in countries in which energy malnutrition was a problem, not affluent Western countries suffering from easily preventable diseases caused by overconsumption of food (although they are not irrelevant in the latter).
\nDid the FAO take into account the different metabolic fates of different energy supplying nutrients?
\nYes. It was constituted of personnel who, unlike the poster, were biological scientists with a sound understanding of the physiology and biochemistry of metabolism. To quote from section 1.3 of the report:
\n\n“Energy requirement recommendations remain “theoretical” and of little practical value until they can be related to foods… Two pieces of information are needed in order to translate individual foods, and ultimately diets, into energy intakes that can be compared with the requirement recommendations…\n…amounts of components must be converted into energy content using an agreed set of physiology-related factors that correspond to the energy-producing potential of the components in the human body. Thus, in order to make accurate estimates of energy intake, it is essential to have energy conversion factors for each component that denote the energy per gram for that component. However, it has long been recognized that the energy contents of protein, fat and carbohydrate differ, both inherently in the compounds themselves and owing to their different digestion, absorption and metabolism.”
\n
So the scientists on this body were well aware of the problems in producing energy values for different nutrients, and the paper considers proteins, fats and carbohydrates separately and in detail in sections 2 and 3 of this report. For each of these (and for different sources of the same constituent) they produced separate values of various measures, with final values in Section 4.
\nHowever the value of 17 kJoules per gram protein (=4kcal/g)) quoted by the original poster is the FAO value of Net Metabolizable Energy (NME) — i.e. the energy produced in circumstances when all the protein amino acids are oxidized to produce ATP. This is relevant to individuals in protein equilibrium but in net energy deficit.
\n(The overall energy values they suggest for fat is 37 kJoules/g, and for carbohydrate 17 kJoules/g).
\nSummary of metabolite interconversions in obtaining metabolic energy from proteins, fats and carbohydrates
\n
The diagram above is my own attempt at a biochemical summary for the situation when carbohydrate, fat or protein are being solely used to generate energy. Although some ATP is generated directly in one pathway, most of the carbon skeletons are oxidized in the TCA cycle, shown. Not shown is the NADH produced in the TCA cycle and its oxidation in the electron transport chain to produce a proton-motive force which drives the conversion of ADP to ATP — a molecule that can be considered as a source of metabolic energy.
\nIn the energy-deficit scenario carbohydrates are converted to glucose, then to pyruvate in glycolysis (with some direct generation of ATP) and then to Acetyl CoA which for oxidation in the TCA cycle.
\nIn this scenario fat (triglyceride) is converted to fatty acids and glycerol, the latter feeding into glycolysis, and the former being oxidized to Acetyl CoA, and hence to the TCA cycle.
\nIn this scenario, in which they are not required for protein biosynthesis, each of the 20 amino acids from protein undergoes different metabolic conversions, as shown. All these can lead to the TCA cycle, and, as is evident, none involve conversion to glucose†. (The removal of nitrogen from the amino acids, actually consumes energy, but this is allowed for in the FAO calculations.)
\nAnalogy (for those that find them useful)
\nIf I buy a gold trinket in an antique shop it will (in Britain at least) bear a hallmark indicating the purity of the gold. If I am interested in keeping the piece until the price of gold increases and then selling it for its gold content (perhaps after melting it down) then the hallmark information is of primary relevance to me. If, however, I am interested in the trinket because of its beauty or because it may be a rare piece from a famous designer, the hallmark, although reassuring, would have little “relevance” to my purpose.
Even shorter analogy (to demonstrate my sense of humour)
\nOne man’s meat is another man’s poison.
\n†The misconception about protein and glucose may have arisen in the following way. In extreme starvation the primary metabolic consideration is to supply the brain with glucose, on which it is absolutely dependent. To do this muscle protein is broken down to amino acids, some of which (e.g. those in the diagram that go to pyruvate) can be converted to glucose in the liver by the reversal of glycolysis (gluconeogenesis). However in a normal diet this is unlikely to happen because there will be a plentiful supply of glucose from carbohydrate, and it is certainly not the scenario in which energy values of protein are calculated.\n", "answer_id": 114128, "answer_text": "Preamble\n\nI had not intended to answer this question as I felt it lacked the clarity required for this site. However I now think that it is necessary to correct the assertion that “protein has to be converted into glucose to generate energy”, especially as this is echoed by the answer from @ThatGuy. I shall clarify the question by interpreting the word “relevant” primarily to mean general “purpose” or “utility”, and shall consider this in relation to the Food and Agriculture Organization of the United Nations (FAO), one scientific body that has published values for energy values of nutrients.\n\n\n\n\nSummary\n\n\n\n\n\n\n\n\nThe dietary nutrients carbohydrate, fat and protein can have\ndifferent metabolic fates in the body depending on individual\ncircumstances. The assumption that “protein is mostly used by the\nbody for purposes other than extraction of energy” does not apply\nin many circumstances.\n\n\n\n\n\n\n\n\n\nEnergy values for food are concerned only with the situation in which the nutrient is used to produce its maximum biological energy yield as ATP, using the appropriate metabolic pathways.\n\n\n\n\n\n\n\n\n\nThese values are not simple bomb calorimeter values. They are calculated separately for protein, carbohydrate, and fat, taking into account their different metabolism. For proteins this takes into account the different metabolism of the 20 amino acids, although it should be emphasized none of these need to be converted to glucose to generate energy.\n\n\n\n\n\n\n\n\n\nThere are several different purposes to which these values can and are used, but the FAO is primarily concerned with their use to assess basic nutritional needs and their fulfilment in the countries of the world in which malnutrition may occur.\n\n\n\n\n\n\n\n\nThe FAO and standard energy values for nutrients\n\nAs mentioned above, I will consider this question in relation to the FAO, the Food and Agriculture Organization of the United Nations, a body that has produced energy values of different nutrients — values that appear to be used by government organizations and commercial food groups in many countries. The source of my information is this report on the subject, produced in 2003 (https://www.fao.org/3/Y5022E/y5022e00.htm#Contents), to which the reader is referred for fuller details.\n\n\n\n\nWhat did the FAO envisage that the results of their work would be used for?\n\nTo quote from Section 1.1 of the report:\n\n\n\n\n\nassessment of the energy needs of countries… living under\ndifferent circumstances;\n\n\n\n\nassessment of food availability within regions and countries;\n\n\n\n\nassessment of the potential ability of available food supplies to meet a country’s … needs,\n\n\n\n\nassessment of individuals’ diets (although the recommendations are not meant for this purpose));\n\n\n\n\nas a basis for food labelling, with implications for consumer information/education about specific foods, regulatory compliance regarding nutrient content and claims, and trade.\n\n\n\n\n\nThis should answer the original poster’s concern with the “relevance” of energy values. The purpose envisaged was clearly with energy requirements in countries in which energy malnutrition was a problem, not affluent Western countries suffering from easily preventable diseases caused by overconsumption of food (although they are not irrelevant in the latter).\n\n\n\n\nDid the FAO take into account the different metabolic fates of different energy supplying nutrients?\n\nYes. It was constituted of personnel who, unlike the poster, were biological scientists with a sound understanding of the physiology and biochemistry of metabolism. To quote from section 1.3 of the report:\n\n\n\n\n\n\n\n“Energy requirement recommendations remain “theoretical” and of little practical value until they can be related to foods… Two pieces of information are needed in order to translate individual foods, and ultimately diets, into energy intakes that can be compared with the requirement recommendations…\n…amounts of components must be converted into energy content using an agreed set of physiology-related factors that correspond to the energy-producing potential of the components in the human body. Thus, in order to make accurate estimates of energy intake, it is essential to have energy conversion factors for each component that denote the energy per gram for that component. However, it has long been recognized that the energy contents of protein, fat and carbohydrate differ, both inherently in the compounds themselves and owing to their different digestion, absorption and metabolism.”\n\n\n\n\n\n\n\nSo the scientists on this body were well aware of the problems in producing energy values for different nutrients, and the paper considers proteins, fats and carbohydrates separately and in detail in sections 2 and 3 of this report. For each of these (and for different sources of the same constituent) they produced separate values of various measures, with final values in Section 4.\n\n\n\n\nHowever the value of 17 kJoules per gram protein (=4kcal/g)) quoted by the original poster is the FAO value of Net Metabolizable Energy (NME) — i.e. the energy produced in circumstances when all the protein amino acids are oxidized to produce ATP. This is relevant to individuals in protein equilibrium but in net energy deficit.\n\n\n\n\n(The overall energy values they suggest for fat is 37 kJoules/g, and for carbohydrate 17 kJoules/g).\n\n\n\n\nSummary of metabolite interconversions in obtaining metabolic energy from proteins, fats and carbohydrates\n\n[image: Pathways for energy generation from nutrients; source: https://i.sstatic.net/f0Z0s.png] (https://i.sstatic.net/f0Z0s.png)\n\n\n\n\nThe diagram above is my own attempt at a biochemical summary for the situation when carbohydrate, fat or protein are being solely used to generate energy. Although some ATP is generated directly in one pathway, most of the carbon skeletons are oxidized in the TCA cycle, shown. Not shown is the NADH produced in the TCA cycle and its oxidation in the electron transport chain to produce a proton-motive force which drives the conversion of ADP to ATP — a molecule that can be considered as a source of metabolic energy.\n\n\n\n\nIn the energy-deficit scenario carbohydrates are converted to glucose, then to pyruvate in glycolysis (with some direct generation of ATP) and then to Acetyl CoA which for oxidation in the TCA cycle.\n\n\n\n\nIn this scenario fat (triglyceride) is converted to fatty acids and glycerol, the latter feeding into glycolysis, and the former being oxidized to Acetyl CoA, and hence to the TCA cycle.\n\n\n\n\nIn this scenario, in which they are not required for protein biosynthesis, each of the 20 amino acids from protein undergoes different metabolic conversions, as shown. All these can lead to the TCA cycle, and, as is evident, none involve conversion to glucose†. (The removal of nitrogen from the amino acids, actually consumes energy, but this is allowed for in the FAO calculations.)\n\n\n\n\nAnalogy (for those that find them useful) \n\nIf I buy a gold trinket in an antique shop it will (in Britain at least) bear a hallmark indicating the purity of the gold. If I am interested in keeping the piece until the price of gold increases and then selling it for its gold content (perhaps after melting it down) then the hallmark information is of primary relevance to me. If, however, I am interested in the trinket because of its beauty or because it may be a rare piece from a famous designer, the hallmark, although reassuring, would have little “relevance” to my purpose.\n\n\n\n\nEven shorter analogy (to demonstrate my sense of humour)\n\nOne man’s meat is another man’s poison.\n\n\n \n\n\n†The misconception about protein and glucose may have arisen in the following way. In extreme starvation the primary metabolic consideration is to supply the brain with glucose, on which it is absolutely dependent. To do this muscle protein is broken down to amino acids, some of which (e.g. those in the diagram that go to pyruvate) can be converted to glucose in the liver by the reversal of glycolysis (gluconeogenesis). However in a normal diet this is unlikely to happen because there will be a plentiful supply of glucose from carbohydrate, and it is certainly not the scenario in which energy values of protein are calculated.", "answer_url": "https://biology.stackexchange.com/a/114128", "author": "David", "author_url": "https://biology.stackexchange.com/users/22057/david", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-02-19T18:06:07+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:30.839943+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/2139ae0ecb1bf62b149af3f8e91d7ce461ad269d38020aaf05922333eabb51a1_0.json", "raw_sha256": "2610bc07f1691b2794681a23d0459bba24822de1f31c7b48d79495b29b0b1285", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/114428;114427;114412;114410;114399;114395;114391;114386;114385;114381;114378;114377;114376;114374;114372;114371;114370;114361;114354;114353;114348;114342;114331;114329;114324;114321;114319;114307;114305;114304;114299;114298;114295;114290;114281;114277;114273;114266;114256;114239;114238;114222;114216;114213;114211;114207;114197;114192;114185;114180;114178;114175;114174;114173;114172;114169;114161;114156;114155;114148;114145;114144;114139;114136;114135;114127;114119;114117;114114;114111;114110;114103;114098;114096;114094;114089;114085;114078;114076;114069;114067;114065;114058;114055;114048;114045;114038;114031;114028;114027;114025;114021;114020;114012;114006;113998;113997;113988;113986;113983/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 114085, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "David", "profile_url": "https://biology.stackexchange.com/users/22057/david", "user_type": "registered"}, "created_at": "2024-02-19T18:06:07+00:00", "raw_file": "raw/codex_api_v1/20c6382e006dfc70ceae89b5b384391a51cd420854d2e23edb6c44d00de6688e_1790824066738015300_0.json", "raw_sha256": "4baa513e3d4757eb58cf2dd23c824e0e27e58aa0c4e8ec570c22801fd30dcaa7", "revision_guid": "C0F09253-175C-4D5D-BC1C-FD4DB80E83C0", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/C0F09253-175C-4D5D-BC1C-FD4DB80E83C0/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "David", "profile_url": "https://biology.stackexchange.com/users/22057/david", "user_type": "registered"}, "created_at": "2024-02-19T19:26:50+00:00", "raw_file": "raw/codex_api_v1/20c6382e006dfc70ceae89b5b384391a51cd420854d2e23edb6c44d00de6688e_1790824066738015300_0.json", "raw_sha256": "4baa513e3d4757eb58cf2dd23c824e0e27e58aa0c4e8ec570c22801fd30dcaa7", "revision_guid": "6C1DF573-FC6D-44E1-A97C-CE0BACEE6CF1", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/6C1DF573-FC6D-44E1-A97C-CE0BACEE6CF1/view-source"}], "score": 4, "updated_at": "2024-02-19T19:26:50+00:00"}], "domain": "biology", "external_links": ["https://i.sstatic.net/f0Z0s.png", "https://www.fao.org/3/Y5022E/y5022e00.htm#Contents"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:08.576606+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/1051d4f3e38449f1419d1973ac812b2286659e454a76f89a23fdaa941dfadddb_0.json", "raw_sha256": "583dcd577e20d33b29e9f8818a7ab6a1fab039c19ab79927e16096cff23fa61d", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=7&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "ilovemaths", "question_author_url": "https://biology.stackexchange.com/users/78872/ilovemaths", "question_author_user_type": "registered", "question_created_at": "2024-02-13T09:48:53+00:00", "question_html": "
Non-biologist speaking here. As you can probably see from the title, I'm having trouble wrapping my head around concepts related to the body's energy balance amd the role of macronutrients. Let me explain in more detail.
\nIf a person consumes excessive amounts of calories for a certain period of time (i.e. more than they need) they will start to gain weight in the form of fat. Conversely, an extended caloric deficit will lead to weight loss. So far, so good.
\nNow, each macronutrient has a certain amount of calories per gram of nutrient - if I'm not mistaken 1 g of protein has 4 kcal.
\nOn the other hand, according to different sources that I've been reading lately, the body does not really use protein for energy gain unless in extreme circumstances. In other words, carbohydrates and fat can readily be "converted" to ATP for energy gain while the conversion of protein into glucose and then ATP is very inefficient. At least that's my understanding, if there's already a misconception here feel free to correct it.
\nProteins are mostly used to build and repair different structures in the body. I will use the reparation and buildup of muscle tissue as an example. And here comes my main question: if proteins aren't being "burned" by the body to extract energy in the form of ATP, why are the calories consumed in the form of protein really relevant? In other words, if the protein that I eat is being used by the body to build stuff such as muscle, haemoglobin etc. and not being burned, why do I care about the calories that protein has? Why will excess protein calories make me fat?
\nI obviously "know" that calories from protein matter, but I don't understand why this is the case. I feel like I'm really not grasping something essential here. I hope that the question is clear and that an interesting discussion could follow. If anyone could give a more detailed explanation of what's going on in the body in this scenario, that would be much appreciated.
\n", "question_id": 114085, "question_license": "CC BY-SA 4.0", "question_score": 3, "question_text": "Non-biologist speaking here. As you can probably see from the title, I'm having trouble wrapping my head around concepts related to the body's energy balance amd the role of macronutrients. Let me explain in more detail.\n\n\n\n\nIf a person consumes excessive amounts of calories for a certain period of time (i.e. more than they need) they will start to gain weight in the form of fat. Conversely, an extended caloric deficit will lead to weight loss. So far, so good.\n\n\n\n\nNow, each macronutrient has a certain amount of calories per gram of nutrient - if I'm not mistaken 1 g of protein has 4 kcal.\n\n\n\n\nOn the other hand, according to different sources that I've been reading lately, the body does not really use protein for energy gain unless in extreme circumstances. In other words, carbohydrates and fat can readily be \"converted\" to ATP for energy gain while the conversion of protein into glucose and then ATP is very inefficient. At least that's my understanding, if there's already a misconception here feel free to correct it.\n\n\n\n\nProteins are mostly used to build and repair different structures in the body. I will use the reparation and buildup of muscle tissue as an example. And here comes my main question: if proteins aren't being \"burned\" by the body to extract energy in the form of ATP, why are the calories consumed in the form of protein really relevant? In other words, if the protein that I eat is being used by the body to build stuff such as muscle, haemoglobin etc. and not being burned, why do I care about the calories that protein has? Why will excess protein calories make me fat?\n\n\n\n\nI obviously \"know\" that calories from protein matter, but I don't understand why this is the case. I feel like I'm really not grasping something essential here. I hope that the question is clear and that an interesting discussion could follow. If anyone could give a more detailed explanation of what's going on in the body in this scenario, that would be much appreciated.", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "ilovemaths", "profile_url": "https://biology.stackexchange.com/users/78872/ilovemaths", "user_type": "registered"}, "created_at": "2024-02-13T09:48:53+00:00", "raw_file": "raw/codex_api_v1/4aa156cabb1f3edbc4e0a74ff84deb30f9cd06be13c7d021adab58e209db850d_1790824057164545000_0.json", "raw_sha256": "42ee08c1af6f231bf4bd10a51fd8384910e076e5d887f51c6dd79384012b46ec", "revision_guid": "6199EFE5-5C64-44B4-838B-67BBF66882CD", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/6199EFE5-5C64-44B4-838B-67BBF66882CD/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/114085/if-protein-is-mostly-used-by-the-body-for-purposes-other-than-extraction-of-ener", "split": "holdout", "split_group": "d206ed925a36ab39b40471389f70303ba0611ec45ea595b364b730826b3f19ed", "tags": ["proteins", "nutrition", "energy-metabolism", "energy", "carbohydrates"], "thread_id": "biology:114085", "title": "If protein is mostly used by the body for purposes other than extraction of energy, why are calories from protein relevant?"}} {"accepted_status": [false, false], "candidate_answers": [{"answer_html": "Yes, these are known as nested genes, and there are actually several, even in the human genome. A paper I found while answering this question (Kumar, 2009) claims the human genome has 158 nested protein coding genes.
\nThe most common type of nested gene, at least in the human genome, is where one gene is found on the plus strand and another on the minus strand, with the smaller gene being in an intron of the larger one. For example, the human gene LPAR6 is contained entirely within the human gene RB1, but RB1 is on the forward strand and LPAR6 on the reverse. See the UCSC genome browser:
\n![\"UCSC](\"https://i.sstatic.net/7Y0zIHeK.png\")
The same article I linked to earlier also describes another kind of nested gene where the smaller gene falls in an exon of the larger one. This is rarer in metazoans, but does exist.
\nFinally, microbial genomes seem to have many overlapping genes that share coding sequence. See Johnson and Chisholm, 2004
\nReferences
\n- \n
- Kumar A. An overview of nested genes in eukaryotic genomes. Eukaryot Cell. 2009 Sep;8(9):1321-9. doi: 10.1128/EC.00143-09. \n
- Johnson ZI, Chisholm SW. Properties of overlapping genes are conserved across microbial genomes. Genome Res. 2004 Nov;14(11):2268-72. \n
- Sanna, C.R., Li, WH. & Zhang, L. Overlapping genes in the human and mouse genomes. BMC Genomics 9, 169 (2008). \n
Short Answer
\nAlthough the definition of the term gene is open to debate, in answer to what I feel is the most likely meaning of the original poster’s question:
“Yes. Cases do exist in which a region of DNA can be transcribed and translated to produce two different proteins in which a part of the amino acid sequence of each is encoded by the same stretch of the DNA.”
\nOne description of this situation is Overlapping Genes, and a review of such genes is provided in a 2022 Nature review by Wright et al., entitled “Overlapping genes in natural and engineered genomes”.
\nComplexity of the question
\nThere are a number of complicating factors in considering overlapping genes in general, only some of which apply to this situation:
- \n
- Prokaryotes or Eukaryotes? — these differ in their RNA transcripts and their translation \n
- Same or different mRNAs producing the two proteins? \n
- Same or different direction for the gene (i.e. DNA strand transcribed) \n
- If same mRNA, is same reading frame used? \n
- Overlap of protein-encoding regions of mRNA or overlap with untranslated region of mRNA? \n
The review by Wright et al. includes a figure illustrating some of these possibilities, a modified section of which I reproduce below. (It also makes a distinction between overlapping and nested genes.) The poster’s question is clearly framed in terms of (a) in the figure, so I shall focus on that initially.
\n![\"Types](\"https://i.sstatic.net/IIFGGJWk.png\")
Why are examples of gene overlap uncommon?
\nThe information that such overlaps can occur is of much less value than knowing what problems lead them to being uncommon and how these problems are overcome. The key point is that there are specific signals for initiating and translating part of the mRNA into protein — in effect, ‘rules’ for where the protein starts and stops. Overlapping protein products translated from the same mRNA would require the rules to be broken.
The problem with overlapping proteins translated in different directions ((c) and (d)) is the unlikelihood that both translations could encode functional proteins, and, even if they did, evolutionary changes in one could have deleterious effects on the other. The same problem is encountered if different reading frames are used to translate a single mRNA in the same direction.
\nOvercoming the problems
\nFor situation (a) let us simplify by assuming there is a common mRNA for two protein products (always true for prokaryotes, as far as I am aware).
In most prokaryotes there is a site just 5′ to the initiating AUG codon (RBS or Shine–Dalgarno sequence) to which the small ribosomal subunit binds. In order to have alternative AUG starting codons, as in (a) (or (b)), there would have to be alternative ribosome binding sites, the second within the coding sequence specifying the first protein product. Such dual function is not impossible, but I am unaware of any examples of it.
\nIn eukaryotes an initiation complex of the small ribosomal subunit and the initiator tRNA normally binds to the 5’ methylated cap of the mRNA and then scans along the mRNA, initiating translation at the first AUG or the first AUG in a ‘suitable context’. The difference between a ‘suitable’ and ‘unsuitable’ context for an initiating AUG is not always clear-cut, and this leads to situations where, for the same mRNA, some ribosomes initiate at the first AUG and others at the second (or subsequent) AUG, leading to different proteins.
\n![\"Alternative](\"https://i.sstatic.net/kEXMhKOb.jpg\")
Examples in the genome of Drosophila melanogaster have been well documented.\nThe two forms of the Drosophila Apoptotic signal-regulating kinase 1 are illustrated below:
\n![\"Example](\"https://i.sstatic.net/9kQCvBKN.png\")
It can seen that form B of the protein starts at amino acid 169 of form C, although both terminate at the same position. The nomenclature indicates that the proteins are, in fact, considered as variant products of the same gene, Ask1.
\nIn this and all the other examples of which I am aware in Drosophila the alternative AUG is in the same reading frame as the first one. Although I have already mentioned the problem if the same stretch of DNA encoded entirely different proteins, there is at least one reported exampl. This involves the human ribosomal protein gene RPL36, and an alternative protein, alt-RPL36, translated from the same transcript.
\n![\"RPL36](\"https://i.sstatic.net/UD6dhazE.png\")
In this case the abnormal initiation codon, GUG, used to start the alternative protein. The viability of such a situation obviously depends on the biological function of the proteins involved, for which the reader is directed to the original publication.
\nThe situation regarding termination of translation is the same for prokaryotes and eukaryotes, and examples of an elongated forms of a protein was first shown in the 70s for small RNA bacteriophages. Examples are also common in eukaryotic single-stranded RNA viruses, although less so in cellular mRNAs. There are two main mechanisms for a ribosome to continue past a termination codon. The first is termed ‘read-through’ in which the termination codon (a ‘leaky’ stop codon) is erroneously recognized by an aminoacyl-tRNA. The second involves ‘frameshift’ — an erroneous (but specific) change of reading frame just before the termination codon. Readthrough and frameshift have been extensively reviewed, e.g. by Palemer and LeJeune. An example of readthrough in Drosophila is shown below for a component of a ubiquitin ligase:
\n![\"Readthrough](\"https://i.sstatic.net/V0lLbcrt.png\")
[‘X’ indicates an unknown amino acid inserted at the stop codon.]
\nA Final Example
\nI managed to find a gene or genes to illustrate three of the four cases in the initial figure. This is Syn, the Drosophila gene for synapsin:
![\"Drosophila](\"https://i.sstatic.net/iVAI5JAj.png\")
Protein Syn-PE is the product using the first AUG and stop codon, whereas Syn-PF (from the same transcript) is produced by skipping both of these, and is thus an example of (a). Syn-PD is the longest protein, produced by reading through the first stop codon, so it nests within it Syn-PA, produced by skipping the first AUG. This is an example of (b). Syn-PA is actually produced from a different (terminally truncated) transcript, but this would not appear to contribute to the type of protein produced.
\nThe gene, Syn, contains another gene, Timp, in the opposite direction. The coding region of the latter (composed of several exons) is contained entirely within an intron of Syn — an example of (d)
\n![\"Syn](\"https://i.sstatic.net/E4BaU9uZ.png\")
The protein-coding regions of the RNA transcripts in the diagram are indicated in orange.
\n", "answer_id": 118041, "answer_text": "Short Answer\n\nAlthough the definition of the term gene is open to debate, in answer to what I feel is the most likely meaning of the original poster’s question:\n\n\n\n\n“Yes. Cases do exist in which a region of DNA can be transcribed and translated to produce two different proteins in which a part of the amino acid sequence of each is encoded by the same stretch of the DNA.”\n\n\n\n\nOne description of this situation is Overlapping Genes, and a review of such genes is provided in a 2022 Nature review by Wright et al., entitled “Overlapping genes in natural and engineered genomes” (https://doi.org/10.1038/s41576-021-00417-w).\n\n\n\n\nComplexity of the question\n\nThere are a number of complicating factors in considering overlapping genes in general, only some of which apply to this situation:\n\n\n\n\n\nProkaryotes or Eukaryotes? — these differ in their RNA transcripts and their translation\n\n\n\n\nSame or different mRNAs producing the two proteins?\n\n\n\n\nSame or different direction for the gene (i.e. DNA strand transcribed)\n\n\n\n\nIf same mRNA, is same reading frame used?\n\n\n\n\nOverlap of protein-encoding regions of mRNA or overlap with untranslated region of mRNA?\n\n\n\n\n\nThe review by Wright et al. includes a figure illustrating some of these possibilities, a modified section of which I reproduce below. (It also makes a distinction between overlapping and nested genes.) The poster’s question is clearly framed in terms of (a) in the figure, so I shall focus on that initially.\n\n\n\n\n[image: Types of gene overlap and nesting; source: https://i.sstatic.net/IIFGGJWk.png] (https://i.sstatic.net/IIFGGJWk.png)\n\n\n\n\nWhy are examples of gene overlap uncommon?\n\nThe information that such overlaps can occur is of much less value than knowing what problems lead them to being uncommon and how these problems are overcome. The key point is that there are specific signals for initiating and translating part of the mRNA into protein — in effect, ‘rules’ for where the protein starts and stops. Overlapping protein products translated from the same mRNA would require the rules to be broken.\n\n\n\n\nThe problem with overlapping proteins translated in different directions ((c) and (d)) is the unlikelihood that both translations could encode functional proteins, and, even if they did, evolutionary changes in one could have deleterious effects on the other. The same problem is encountered if different reading frames are used to translate a single mRNA in the same direction.\n\n\n\n\nOvercoming the problems\n\nFor situation (a) let us simplify by assuming there is a common mRNA for two protein products (always true for prokaryotes, as far as I am aware).\n\n\n\n\nIn most prokaryotes there is a site just 5′ to the initiating AUG codon (RBS or Shine–Dalgarno sequence) to which the small ribosomal subunit binds. In order to have alternative AUG starting codons, as in (a) (or (b)), there would have to be alternative ribosome binding sites, the second within the coding sequence specifying the first protein product. Such dual function is not impossible, but I am unaware of any examples of it.\n\n\n\n\nIn eukaryotes an initiation complex of the small ribosomal subunit and the initiator tRNA normally binds to the 5’ methylated cap of the mRNA and then scans along the mRNA, initiating translation at the first AUG or the first AUG in a ‘suitable context’. The difference between a ‘suitable’ and ‘unsuitable’ context for an initiating AUG is not always clear-cut, and this leads to situations where, for the same mRNA, some ribosomes initiate at the first AUG and others at the second (or subsequent) AUG, leading to different proteins.\n\n\n\n\n[image: Alternative AUGs in eukaryotic initiation; source: https://i.sstatic.net/kEXMhKOb.jpg] (https://i.sstatic.net/kEXMhKOb.jpg)\n\n\n\n\nExamples in the genome of Drosophila melanogaster (https://doi.org/10.1534/g3.115.018937) have been well documented.\nThe two forms of the Drosophila Apoptotic signal-regulating kinase 1 are illustrated below:\n\n\n\n\n[image: Example of alternative inititiation Ask1; source: https://i.sstatic.net/9kQCvBKN.png] (https://i.sstatic.net/9kQCvBKN.png)\n\n\n\n\nIt can seen that form B of the protein starts at amino acid 169 of form C, although both terminate at the same position. The nomenclature indicates that the proteins are, in fact, considered as variant products of the same gene, Ask1.\n\n\n\n\nIn this and all the other examples of which I am aware in Drosophila the alternative AUG is in the same reading frame as the first one. Although I have already mentioned the problem if the same stretch of DNA encoded entirely different proteins, there is at least one reported exampl. This involves the human ribosomal protein gene RPL36, and an alternative protein, alt-RPL36, translated from the same transcript.\n\n\n\n\n[image: RPL36 and alt-RPL36; source: https://i.sstatic.net/UD6dhazE.png] (https://i.sstatic.net/UD6dhazE.png)\n\n\n\n\nIn this case the abnormal initiation codon, GUG, used to start the alternative protein. The viability of such a situation obviously depends on the biological function of the proteins involved, for which the reader is directed to the original publication (https://doi.org/10.1038/s41467-020-20841-6).\n\n\n\n\nThe situation regarding termination of translation is the same for prokaryotes and eukaryotes, and examples of an elongated forms of a protein was first shown in the 70s for small RNA bacteriophages. Examples are also common in eukaryotic single-stranded RNA viruses, although less so in cellular mRNAs. There are two main mechanisms for a ribosome to continue past a termination codon. The first is termed ‘read-through’ in which the termination codon (a ‘leaky’ stop codon) is erroneously recognized by an aminoacyl-tRNA. The second involves ‘frameshift’ — an erroneous (but specific) change of reading frame just before the termination codon. Readthrough and frameshift have been extensively reviewed, e.g. by Palemer and LeJeune (https://doi.org/10.1111/brv.12657). An example of readthrough in Drosophila is shown below for a component of a ubiquitin ligase:\n\n\n\n\n[image: Readthrough example in Drosophila; source: https://i.sstatic.net/V0lLbcrt.png] (https://i.sstatic.net/V0lLbcrt.png)\n\n\n\n\n[‘X’ indicates an unknown amino acid inserted at the stop codon.]\n\n\n\n\nA Final Example\n\nI managed to find a gene or genes to illustrate three of the four cases in the initial figure. This is Syn, the Drosophila gene for synapsin:\n\n\n\n\n[image: Drosophila Synapsins; source: https://i.sstatic.net/iVAI5JAj.png] (https://i.sstatic.net/iVAI5JAj.png)\n\n\n\n\nProtein Syn-PE is the product using the first AUG and stop codon, whereas Syn-PF (from the same transcript) is produced by skipping both of these, and is thus an example of (a). Syn-PD is the longest protein, produced by reading through the first stop codon, so it nests within it Syn-PA, produced by skipping the first AUG. This is an example of (b). Syn-PA is actually produced from a different (terminally truncated) transcript, but this would not appear to contribute to the type of protein produced.\n\n\n\n\nThe gene, Syn, contains another gene, Timp, in the opposite direction. The coding region of the latter (composed of several exons) is contained entirely within an intron of Syn — an example of (d)\n\n\n\n\n[image: Syn / Timp gene overlap; source: https://i.sstatic.net/E4BaU9uZ.png] (https://i.sstatic.net/E4BaU9uZ.png)\n\n\n\n\nThe protein-coding regions of the RNA transcripts in the diagram are indicated in orange.", "answer_url": "https://biology.stackexchange.com/a/118041", "author": "David", "author_url": "https://biology.stackexchange.com/users/22057/david", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2025-10-22T14:58:28+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:16.948131+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/46a41fae37d5c2c243f9abcbf6829a0045f46a51c624fbba2b897c320cdcba71_0.json", "raw_sha256": "e039e310d0106dc61f992ee05bbb0b0b57ded1c5092f97df2c52989edd5eaf68", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/118153;118142;118137;118126;118122;118117;118113;118102;118099;118097;118094;118081;118076;118072;118069;118065;118059;118056;118043;118039;118036;118030;118029;118025;118022;118018;117994;117992;117990;117987;117983;117981;117975;117971;117956;117953;117951;117945;117943;117941;117934;117926;117924;117920;117916;117914;117907;117892;117889;117887;117883;117876;117872;117867;117861;117860;117856;117855;117850;117849;117844;117840;117833;117821;117819;117817;117815;117814;117805;117794;117782;117774;117771;117767;117766;117761;117759;117756;117747;117732;117726;117724;117709;117701;117694;117693;117681;117680;117677;117671;117668;117664;117662;117659;117651;117641;117632;117624;117623;117607/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 118030, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "David", "profile_url": "https://biology.stackexchange.com/users/22057/david", "user_type": "registered"}, "created_at": "2025-10-22T14:58:28+00:00", "raw_file": "raw/codex_api_v1/c1f1c77b4be84acc978369dace8896d84167a5ca52eb6711a00d4b338d7f0104_1790824159864978900_0.json", "raw_sha256": "5798821fb87997611f2dd8389abcef2303f9edc567f4cd87a06a697319e695cd", "revision_guid": "F5F9C4F0-1A35-413E-A982-604A4077F37D", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/F5F9C4F0-1A35-413E-A982-604A4077F37D/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "David", "profile_url": "https://biology.stackexchange.com/users/22057/david", "user_type": "registered"}, "created_at": "2025-10-23T09:43:23+00:00", "raw_file": "raw/codex_api_v1/c1f1c77b4be84acc978369dace8896d84167a5ca52eb6711a00d4b338d7f0104_1790824159864978900_0.json", "raw_sha256": "5798821fb87997611f2dd8389abcef2303f9edc567f4cd87a06a697319e695cd", "revision_guid": "FA837F22-1CFB-4ECB-9EE4-CDB286C3E793", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/FA837F22-1CFB-4ECB-9EE4-CDB286C3E793/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "David", "profile_url": "https://biology.stackexchange.com/users/22057/david", "user_type": "registered"}, "created_at": "2025-10-23T15:07:39+00:00", "raw_file": "raw/codex_api_v1/c1f1c77b4be84acc978369dace8896d84167a5ca52eb6711a00d4b338d7f0104_1790824159864978900_0.json", "raw_sha256": "5798821fb87997611f2dd8389abcef2303f9edc567f4cd87a06a697319e695cd", "revision_guid": "3E779E18-2165-438C-807B-4E06CB91EB06", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/3E779E18-2165-438C-807B-4E06CB91EB06/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "David", "profile_url": "https://biology.stackexchange.com/users/22057/david", "user_type": "registered"}, "created_at": "2025-10-23T15:29:26+00:00", "raw_file": "raw/codex_api_v1/c1f1c77b4be84acc978369dace8896d84167a5ca52eb6711a00d4b338d7f0104_1790824159864978900_0.json", "raw_sha256": "5798821fb87997611f2dd8389abcef2303f9edc567f4cd87a06a697319e695cd", "revision_guid": "B9365A76-737D-473D-83B1-6D78786F917C", "revision_number": 4, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/B9365A76-737D-473D-83B1-6D78786F917C/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "David", "profile_url": "https://biology.stackexchange.com/users/22057/david", "user_type": "registered"}, "created_at": "2025-10-23T15:42:36+00:00", "raw_file": "raw/codex_api_v1/c1f1c77b4be84acc978369dace8896d84167a5ca52eb6711a00d4b338d7f0104_1790824159864978900_0.json", "raw_sha256": "5798821fb87997611f2dd8389abcef2303f9edc567f4cd87a06a697319e695cd", "revision_guid": "C6A13355-DAEA-4BED-9EF6-178996F3A82A", "revision_number": 5, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/C6A13355-DAEA-4BED-9EF6-178996F3A82A/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "David", "profile_url": "https://biology.stackexchange.com/users/22057/david", "user_type": "registered"}, "created_at": "2025-10-27T15:40:29+00:00", "raw_file": "raw/codex_api_v1/c1f1c77b4be84acc978369dace8896d84167a5ca52eb6711a00d4b338d7f0104_1790824159864978900_0.json", "raw_sha256": "5798821fb87997611f2dd8389abcef2303f9edc567f4cd87a06a697319e695cd", "revision_guid": "9DAF8614-ADFA-496A-AD92-9F5AB2064C8C", "revision_number": 6, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/9DAF8614-ADFA-496A-AD92-9F5AB2064C8C/view-source"}], "score": 4, "updated_at": "2025-10-27T15:40:29+00:00"}], "ground_truth": "community signals only; no scientific truth label", "product": "ranking", "question": "Suppose you have a sequence of 130 nucleotides (nt) in a genome. Can there be two different genes in which, for example, the first starts at nt 10 and ends at nt 40 and the second starts at nt 30 and ends at nt 60? (Thus they will include the same section of the genome from nt 30 to nt 40) Or do all genes occupy exclusive sections of a genome?", "record_id": "Scientific-Answer-Ranking:biology:118030", "scores": [13, 4], "split": "holdout", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "Yes, these are known as nested genes, and there are actually several, even in the human genome. A paper I found while answering this question (Kumar, 2009) claims the human genome has 158 nested protein coding genes.
\nThe most common type of nested gene, at least in the human genome, is where one gene is found on the plus strand and another on the minus strand, with the smaller gene being in an intron of the larger one. For example, the human gene LPAR6 is contained entirely within the human gene RB1, but RB1 is on the forward strand and LPAR6 on the reverse. See the UCSC genome browser:
\n
The same article I linked to earlier also describes another kind of nested gene where the smaller gene falls in an exon of the larger one. This is rarer in metazoans, but does exist.
\nFinally, microbial genomes seem to have many overlapping genes that share coding sequence. See Johnson and Chisholm, 2004
\nReferences
\n- \n
- Kumar A. An overview of nested genes in eukaryotic genomes. Eukaryot Cell. 2009 Sep;8(9):1321-9. doi: 10.1128/EC.00143-09. \n
- Johnson ZI, Chisholm SW. Properties of overlapping genes are conserved across microbial genomes. Genome Res. 2004 Nov;14(11):2268-72. \n
- Sanna, C.R., Li, WH. & Zhang, L. Overlapping genes in the human and mouse genomes. BMC Genomics 9, 169 (2008). \n
Short Answer
\nAlthough the definition of the term gene is open to debate, in answer to what I feel is the most likely meaning of the original poster’s question:
“Yes. Cases do exist in which a region of DNA can be transcribed and translated to produce two different proteins in which a part of the amino acid sequence of each is encoded by the same stretch of the DNA.”
\nOne description of this situation is Overlapping Genes, and a review of such genes is provided in a 2022 Nature review by Wright et al., entitled “Overlapping genes in natural and engineered genomes”.
\nComplexity of the question
\nThere are a number of complicating factors in considering overlapping genes in general, only some of which apply to this situation:
- \n
- Prokaryotes or Eukaryotes? — these differ in their RNA transcripts and their translation \n
- Same or different mRNAs producing the two proteins? \n
- Same or different direction for the gene (i.e. DNA strand transcribed) \n
- If same mRNA, is same reading frame used? \n
- Overlap of protein-encoding regions of mRNA or overlap with untranslated region of mRNA? \n
The review by Wright et al. includes a figure illustrating some of these possibilities, a modified section of which I reproduce below. (It also makes a distinction between overlapping and nested genes.) The poster’s question is clearly framed in terms of (a) in the figure, so I shall focus on that initially.
\n
Why are examples of gene overlap uncommon?
\nThe information that such overlaps can occur is of much less value than knowing what problems lead them to being uncommon and how these problems are overcome. The key point is that there are specific signals for initiating and translating part of the mRNA into protein — in effect, ‘rules’ for where the protein starts and stops. Overlapping protein products translated from the same mRNA would require the rules to be broken.
The problem with overlapping proteins translated in different directions ((c) and (d)) is the unlikelihood that both translations could encode functional proteins, and, even if they did, evolutionary changes in one could have deleterious effects on the other. The same problem is encountered if different reading frames are used to translate a single mRNA in the same direction.
\nOvercoming the problems
\nFor situation (a) let us simplify by assuming there is a common mRNA for two protein products (always true for prokaryotes, as far as I am aware).
In most prokaryotes there is a site just 5′ to the initiating AUG codon (RBS or Shine–Dalgarno sequence) to which the small ribosomal subunit binds. In order to have alternative AUG starting codons, as in (a) (or (b)), there would have to be alternative ribosome binding sites, the second within the coding sequence specifying the first protein product. Such dual function is not impossible, but I am unaware of any examples of it.
\nIn eukaryotes an initiation complex of the small ribosomal subunit and the initiator tRNA normally binds to the 5’ methylated cap of the mRNA and then scans along the mRNA, initiating translation at the first AUG or the first AUG in a ‘suitable context’. The difference between a ‘suitable’ and ‘unsuitable’ context for an initiating AUG is not always clear-cut, and this leads to situations where, for the same mRNA, some ribosomes initiate at the first AUG and others at the second (or subsequent) AUG, leading to different proteins.
\n
Examples in the genome of Drosophila melanogaster have been well documented.\nThe two forms of the Drosophila Apoptotic signal-regulating kinase 1 are illustrated below:
\n
It can seen that form B of the protein starts at amino acid 169 of form C, although both terminate at the same position. The nomenclature indicates that the proteins are, in fact, considered as variant products of the same gene, Ask1.
\nIn this and all the other examples of which I am aware in Drosophila the alternative AUG is in the same reading frame as the first one. Although I have already mentioned the problem if the same stretch of DNA encoded entirely different proteins, there is at least one reported exampl. This involves the human ribosomal protein gene RPL36, and an alternative protein, alt-RPL36, translated from the same transcript.
\n
In this case the abnormal initiation codon, GUG, used to start the alternative protein. The viability of such a situation obviously depends on the biological function of the proteins involved, for which the reader is directed to the original publication.
\nThe situation regarding termination of translation is the same for prokaryotes and eukaryotes, and examples of an elongated forms of a protein was first shown in the 70s for small RNA bacteriophages. Examples are also common in eukaryotic single-stranded RNA viruses, although less so in cellular mRNAs. There are two main mechanisms for a ribosome to continue past a termination codon. The first is termed ‘read-through’ in which the termination codon (a ‘leaky’ stop codon) is erroneously recognized by an aminoacyl-tRNA. The second involves ‘frameshift’ — an erroneous (but specific) change of reading frame just before the termination codon. Readthrough and frameshift have been extensively reviewed, e.g. by Palemer and LeJeune. An example of readthrough in Drosophila is shown below for a component of a ubiquitin ligase:
\n
[‘X’ indicates an unknown amino acid inserted at the stop codon.]
\nA Final Example
\nI managed to find a gene or genes to illustrate three of the four cases in the initial figure. This is Syn, the Drosophila gene for synapsin:
Protein Syn-PE is the product using the first AUG and stop codon, whereas Syn-PF (from the same transcript) is produced by skipping both of these, and is thus an example of (a). Syn-PD is the longest protein, produced by reading through the first stop codon, so it nests within it Syn-PA, produced by skipping the first AUG. This is an example of (b). Syn-PA is actually produced from a different (terminally truncated) transcript, but this would not appear to contribute to the type of protein produced.
\nThe gene, Syn, contains another gene, Timp, in the opposite direction. The coding region of the latter (composed of several exons) is contained entirely within an intron of Syn — an example of (d)
\n
The protein-coding regions of the RNA transcripts in the diagram are indicated in orange.
\n", "answer_id": 118041, "answer_text": "Short Answer\n\nAlthough the definition of the term gene is open to debate, in answer to what I feel is the most likely meaning of the original poster’s question:\n\n\n\n\n“Yes. Cases do exist in which a region of DNA can be transcribed and translated to produce two different proteins in which a part of the amino acid sequence of each is encoded by the same stretch of the DNA.”\n\n\n\n\nOne description of this situation is Overlapping Genes, and a review of such genes is provided in a 2022 Nature review by Wright et al., entitled “Overlapping genes in natural and engineered genomes” (https://doi.org/10.1038/s41576-021-00417-w).\n\n\n\n\nComplexity of the question\n\nThere are a number of complicating factors in considering overlapping genes in general, only some of which apply to this situation:\n\n\n\n\n\nProkaryotes or Eukaryotes? — these differ in their RNA transcripts and their translation\n\n\n\n\nSame or different mRNAs producing the two proteins?\n\n\n\n\nSame or different direction for the gene (i.e. DNA strand transcribed)\n\n\n\n\nIf same mRNA, is same reading frame used?\n\n\n\n\nOverlap of protein-encoding regions of mRNA or overlap with untranslated region of mRNA?\n\n\n\n\n\nThe review by Wright et al. includes a figure illustrating some of these possibilities, a modified section of which I reproduce below. (It also makes a distinction between overlapping and nested genes.) The poster’s question is clearly framed in terms of (a) in the figure, so I shall focus on that initially.\n\n\n\n\n[image: Types of gene overlap and nesting; source: https://i.sstatic.net/IIFGGJWk.png] (https://i.sstatic.net/IIFGGJWk.png)\n\n\n\n\nWhy are examples of gene overlap uncommon?\n\nThe information that such overlaps can occur is of much less value than knowing what problems lead them to being uncommon and how these problems are overcome. The key point is that there are specific signals for initiating and translating part of the mRNA into protein — in effect, ‘rules’ for where the protein starts and stops. Overlapping protein products translated from the same mRNA would require the rules to be broken.\n\n\n\n\nThe problem with overlapping proteins translated in different directions ((c) and (d)) is the unlikelihood that both translations could encode functional proteins, and, even if they did, evolutionary changes in one could have deleterious effects on the other. The same problem is encountered if different reading frames are used to translate a single mRNA in the same direction.\n\n\n\n\nOvercoming the problems\n\nFor situation (a) let us simplify by assuming there is a common mRNA for two protein products (always true for prokaryotes, as far as I am aware).\n\n\n\n\nIn most prokaryotes there is a site just 5′ to the initiating AUG codon (RBS or Shine–Dalgarno sequence) to which the small ribosomal subunit binds. In order to have alternative AUG starting codons, as in (a) (or (b)), there would have to be alternative ribosome binding sites, the second within the coding sequence specifying the first protein product. Such dual function is not impossible, but I am unaware of any examples of it.\n\n\n\n\nIn eukaryotes an initiation complex of the small ribosomal subunit and the initiator tRNA normally binds to the 5’ methylated cap of the mRNA and then scans along the mRNA, initiating translation at the first AUG or the first AUG in a ‘suitable context’. The difference between a ‘suitable’ and ‘unsuitable’ context for an initiating AUG is not always clear-cut, and this leads to situations where, for the same mRNA, some ribosomes initiate at the first AUG and others at the second (or subsequent) AUG, leading to different proteins.\n\n\n\n\n[image: Alternative AUGs in eukaryotic initiation; source: https://i.sstatic.net/kEXMhKOb.jpg] (https://i.sstatic.net/kEXMhKOb.jpg)\n\n\n\n\nExamples in the genome of Drosophila melanogaster (https://doi.org/10.1534/g3.115.018937) have been well documented.\nThe two forms of the Drosophila Apoptotic signal-regulating kinase 1 are illustrated below:\n\n\n\n\n[image: Example of alternative inititiation Ask1; source: https://i.sstatic.net/9kQCvBKN.png] (https://i.sstatic.net/9kQCvBKN.png)\n\n\n\n\nIt can seen that form B of the protein starts at amino acid 169 of form C, although both terminate at the same position. The nomenclature indicates that the proteins are, in fact, considered as variant products of the same gene, Ask1.\n\n\n\n\nIn this and all the other examples of which I am aware in Drosophila the alternative AUG is in the same reading frame as the first one. Although I have already mentioned the problem if the same stretch of DNA encoded entirely different proteins, there is at least one reported exampl. This involves the human ribosomal protein gene RPL36, and an alternative protein, alt-RPL36, translated from the same transcript.\n\n\n\n\n[image: RPL36 and alt-RPL36; source: https://i.sstatic.net/UD6dhazE.png] (https://i.sstatic.net/UD6dhazE.png)\n\n\n\n\nIn this case the abnormal initiation codon, GUG, used to start the alternative protein. The viability of such a situation obviously depends on the biological function of the proteins involved, for which the reader is directed to the original publication (https://doi.org/10.1038/s41467-020-20841-6).\n\n\n\n\nThe situation regarding termination of translation is the same for prokaryotes and eukaryotes, and examples of an elongated forms of a protein was first shown in the 70s for small RNA bacteriophages. Examples are also common in eukaryotic single-stranded RNA viruses, although less so in cellular mRNAs. There are two main mechanisms for a ribosome to continue past a termination codon. The first is termed ‘read-through’ in which the termination codon (a ‘leaky’ stop codon) is erroneously recognized by an aminoacyl-tRNA. The second involves ‘frameshift’ — an erroneous (but specific) change of reading frame just before the termination codon. Readthrough and frameshift have been extensively reviewed, e.g. by Palemer and LeJeune (https://doi.org/10.1111/brv.12657). An example of readthrough in Drosophila is shown below for a component of a ubiquitin ligase:\n\n\n\n\n[image: Readthrough example in Drosophila; source: https://i.sstatic.net/V0lLbcrt.png] (https://i.sstatic.net/V0lLbcrt.png)\n\n\n\n\n[‘X’ indicates an unknown amino acid inserted at the stop codon.]\n\n\n\n\nA Final Example\n\nI managed to find a gene or genes to illustrate three of the four cases in the initial figure. This is Syn, the Drosophila gene for synapsin:\n\n\n\n\n[image: Drosophila Synapsins; source: https://i.sstatic.net/iVAI5JAj.png] (https://i.sstatic.net/iVAI5JAj.png)\n\n\n\n\nProtein Syn-PE is the product using the first AUG and stop codon, whereas Syn-PF (from the same transcript) is produced by skipping both of these, and is thus an example of (a). Syn-PD is the longest protein, produced by reading through the first stop codon, so it nests within it Syn-PA, produced by skipping the first AUG. This is an example of (b). Syn-PA is actually produced from a different (terminally truncated) transcript, but this would not appear to contribute to the type of protein produced.\n\n\n\n\nThe gene, Syn, contains another gene, Timp, in the opposite direction. The coding region of the latter (composed of several exons) is contained entirely within an intron of Syn — an example of (d)\n\n\n\n\n[image: Syn / Timp gene overlap; source: https://i.sstatic.net/E4BaU9uZ.png] (https://i.sstatic.net/E4BaU9uZ.png)\n\n\n\n\nThe protein-coding regions of the RNA transcripts in the diagram are indicated in orange.", "answer_url": "https://biology.stackexchange.com/a/118041", "author": "David", "author_url": "https://biology.stackexchange.com/users/22057/david", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2025-10-22T14:58:28+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:16.948131+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/46a41fae37d5c2c243f9abcbf6829a0045f46a51c624fbba2b897c320cdcba71_0.json", "raw_sha256": 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"https://i.sstatic.net/iVAI5JAj.png", "https://i.sstatic.net/kEXMhKOb.jpg"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:01.208074+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/f1b387b48f36041f506f18fa9796531023c7eae1e796ec622ad56833c02bea98_0.json", "raw_sha256": "3f8214c87c0fe16dd016324597332ca392e0ba98600877cc746483ef492ce03d", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=2&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Root Groves", "question_author_url": "https://biology.stackexchange.com/users/78184/root-groves", "question_author_user_type": "registered", "question_created_at": "2025-10-17T13:36:28+00:00", "question_html": "Suppose you have a sequence of 130 nucleotides (nt) in a genome. Can there be two different genes in which, for example, the first starts at nt 10 and ends at nt 40 and the second starts at nt 30 and ends at nt 60? (Thus they will include the same section of the genome from nt 30 to nt 40) Or do all genes occupy exclusive sections of a genome?
\n", "question_id": 118030, "question_license": "CC BY-SA 4.0", "question_score": 12, "question_text": "Suppose you have a sequence of 130 nucleotides (nt) in a genome. Can there be two different genes in which, for example, the first starts at nt 10 and ends at nt 40 and the second starts at nt 30 and ends at nt 60? (Thus they will include the same section of the genome from nt 30 to nt 40) Or do all genes occupy exclusive sections of a genome?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Root Groves", "profile_url": "https://biology.stackexchange.com/users/78184/root-groves", "user_type": "registered"}, "created_at": "2025-10-17T13:36:28+00:00", "raw_file": "raw/codex_api_v1/c1f1c77b4be84acc978369dace8896d84167a5ca52eb6711a00d4b338d7f0104_1790824159864978900_0.json", "raw_sha256": "5798821fb87997611f2dd8389abcef2303f9edc567f4cd87a06a697319e695cd", "revision_guid": "2423E323-9CBE-4587-B6E3-DACB2CCAB2D1", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/2423E323-9CBE-4587-B6E3-DACB2CCAB2D1/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Shayan", "profile_url": "https://biology.stackexchange.com/users/114723/shayan", "user_type": "registered"}, "created_at": "2025-10-17T13:46:29+00:00", "raw_file": "raw/codex_api_v1/c1f1c77b4be84acc978369dace8896d84167a5ca52eb6711a00d4b338d7f0104_1790824159864978900_0.json", "raw_sha256": "5798821fb87997611f2dd8389abcef2303f9edc567f4cd87a06a697319e695cd", "revision_guid": "CE9187C3-9651-49B6-8BD3-ABEF518DE2AD", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/CE9187C3-9651-49B6-8BD3-ABEF518DE2AD/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Root Groves", "profile_url": "https://biology.stackexchange.com/users/78184/root-groves", "user_type": "registered"}, "created_at": "2025-10-17T13:47:02+00:00", "raw_file": "raw/codex_api_v1/c1f1c77b4be84acc978369dace8896d84167a5ca52eb6711a00d4b338d7f0104_1790824159864978900_0.json", "raw_sha256": "5798821fb87997611f2dd8389abcef2303f9edc567f4cd87a06a697319e695cd", "revision_guid": "3800C50E-6A9A-46B0-9F31-ACF3AAFFC50D", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/3800C50E-6A9A-46B0-9F31-ACF3AAFFC50D/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Shayan", "profile_url": "https://biology.stackexchange.com/users/114723/shayan", "user_type": "registered"}, "created_at": "2025-10-17T13:54:23+00:00", "raw_file": "raw/codex_api_v1/c1f1c77b4be84acc978369dace8896d84167a5ca52eb6711a00d4b338d7f0104_1790824159864978900_0.json", "raw_sha256": "5798821fb87997611f2dd8389abcef2303f9edc567f4cd87a06a697319e695cd", "revision_guid": "7ABBD05C-D2B2-4E97-B5A8-52627FCD0027", "revision_number": 4, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/7ABBD05C-D2B2-4E97-B5A8-52627FCD0027/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2025-10-17T21:45:44+00:00", "raw_file": "raw/codex_api_v1/c1f1c77b4be84acc978369dace8896d84167a5ca52eb6711a00d4b338d7f0104_1790824159864978900_0.json", "raw_sha256": "5798821fb87997611f2dd8389abcef2303f9edc567f4cd87a06a697319e695cd", "revision_guid": "E4A90C5D-E6B8-4587-9603-8846C699C392", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/E4A90C5D-E6B8-4587-9603-8846C699C392/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "David", "profile_url": "https://biology.stackexchange.com/users/22057/david", "user_type": "registered"}, "created_at": "2025-10-18T18:36:42+00:00", "raw_file": "raw/codex_api_v1/c1f1c77b4be84acc978369dace8896d84167a5ca52eb6711a00d4b338d7f0104_1790824159864978900_0.json", "raw_sha256": "5798821fb87997611f2dd8389abcef2303f9edc567f4cd87a06a697319e695cd", "revision_guid": "1534053C-3D62-4C59-A6FB-D404C1E4A596", "revision_number": 5, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/1534053C-3D62-4C59-A6FB-D404C1E4A596/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/118030/can-genes-overlap", "split": "holdout", "split_group": "0b793049e1e57b5fc8e6cdbce5973537243bec75d85808c1d6a0d3c0893d2336", "tags": ["genomics", "gene"], "thread_id": "biology:118030", "title": "Can genes overlap?"}} {"accepted_status": [false, true], "candidate_answers": [{"answer_html": "Each lobe typically contains two theca, meaning a typical anther has four theca in total, each theca then contains two microsporangia. The lobe is composed of two theca, two pairs of microsporangia, separated by the stomium, which is an area of dehiscence.
\n", "answer_id": 116274, "answer_text": "Each lobe typically contains two theca, meaning a typical anther has four theca in total, each theca then contains two microsporangia. The lobe is composed of two theca, two pairs of microsporangia, separated by the stomium, which is an area of dehiscence.", "answer_url": "https://biology.stackexchange.com/a/116274", "author": "Moracen", "author_url": "https://biology.stackexchange.com/users/103307/moracen", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2025-03-24T07:52:39+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:19.947691+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/df693642d727b738d2a533740632235c18a06cefec7a1e337c9589214a4ec91e_0.json", "raw_sha256": "9df534f437f3b2f12d33db8536999ec4e6ffa10f2f59394799d9fe01c3c1ad16", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/117606;117602;117598;117594;117585;117579;117570;117568;117565;117559;117558;117555;117552;117548;117538;117524;117523;117522;117520;117515;117510;116509;116508;116504;116499;116491;116485;116483;116461;116454;116453;116445;116441;116435;116430;116426;116425;116414;116412;116406;116401;116399;116396;116395;116394;116392;116389;116384;116370;116367;116363;116361;116352;116351;116347;116345;116343;116338;116337;116332;116331;116324;116320;116316;116314;116312;116306;116292;116290;116284;116280;116277;116271;116270;116268;116267;116257;116256;116253;116250;116249;116240;116237;116233;116219;116214;116212;116205;116204;116200;116198;116187;116184;116173;116172;116167;116162;116149;116142;116129/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 116268, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Moracen", "profile_url": "https://biology.stackexchange.com/users/103307/moracen", "user_type": "registered"}, "created_at": "2025-03-24T07:52:39+00:00", "raw_file": "raw/codex_api_v1/6a8d1217a71337b035f168c28f3cef00c95606938297595ce7816a6ee2aabc47_1790824139846857200_0.json", "raw_sha256": "915362f28bff22e7e44f536acc7b10e33f23a77bbb5e547906a8fdc7cf7e3e89", "revision_guid": "2C7B74B8-E717-475B-A40F-D1E072A4D55F", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/2C7B74B8-E717-475B-A40F-D1E072A4D55F/view-source"}], "score": 0, "updated_at": "2025-03-24T07:52:39+00:00"}, {"answer_html": "Wow, I'm not surprised there's confusion. For fairly basic botanical anatomy, there is a lot of variability out there about the answer.
\nTypical anthers have four microsporangia. This is probably the most consistent fact to keep in mind. These are labeled as #4 in the picture below. (Note that in this image the wall separating the two microsporangia of each lobe [the septum] has begun to split.)
\n![\"Schematic](\"https://i.sstatic.net/8pvuHCTK.png\" "\\"Schematic")
Most definitions I've seen say that the paired microsporangia make up the theca (#2 in the figure). So, the figure above has two thecae separated by the connective (#3).
\nWikipedia says that a theca consists of the surrounding tissue layers, such as the epidermis and tapetum (an inner layer of cells). New York Botanical Garden, NYBG, says that a theca is a chamber where the pollen is produced, "same as a pollen sac." (But note that the Wikipedia definition and the caption to the figure state that the pollen sac is the same as the microsporangium.)
\nThe Missouri Botanical Garden, MoBot, provides the Latin definition of theca: "that in which anything is enclosed, an envelope, hull, cover, case, sheath, etc." They agree with the NYBG in that thecae are "the pollen-producing sectors (microsporangia) of an anther, the pollen-sac."
\nThe NYBG discussion is a little more comprehensive. They point out that the number of thecae changes during development, stating:
\n\n\nIn neotropical [plant family] Lecythidaceae, up until near the time of anther dehiscence there are two anther thecae on each side of the anther connective but the walls between these thecae break down so there are only two thecae by the time the anthers dehisce (one on each side of the anther).
\n
As far as I can tell, there's nothing particularly unusual about the anthers of Lecythidaceae, so we can say that generally, while the microsporangia are still completely separated, an anther has four thecae. Then, when the septum has broken and the two microsporangia are fused, the anther has two thecae. (Think of the two microsporangia now forming "one chamber".)
\nAs for "lobes", I think it's still safe to say that each pair of microsporangia form a lobe (e.g., the left and right halves of the anther in the figure). This term is used a bit more casually. The more technical term is "bilocular". This implies two locules, but has the same difficulty as theca: the locules are the spaces within the chambers, and can go from four locules to two locules as the anther develops.
\nIt may also help to review pictures of developing anthers. Early in development the microsporangia are in the process of producing the pollen and there's not really any empty space within them. Only later do these areas actually become hollow as the pollen grains mature, and this hollow space is the locule.
\n\n
Image by Ben Stefanowitsch - Created for Wikimedia Commons by Ben Stefanowitsch, CC BY-SA 2.5, https://commons.wikimedia.org/w/index.php?curid=703358
\n", "answer_id": 116276, "answer_text": "Wow, I'm not surprised there's confusion. For fairly basic botanical anatomy, there is a lot of variability out there about the answer.\n\n\n\n\nTypical anthers have four microsporangia. This is probably the most consistent fact to keep in mind. These are labeled as #4 in the picture below. (Note that in this image the wall separating the two microsporangia of each lobe [the septum] has begun to split.)\n\n\n\n\n[image: Schematic cross section of an anther. 1: Filament 2: Theca 3: Connective 4: Pollen sac (also known as sporangium); source: https://i.sstatic.net/8pvuHCTK.png]\n\n\n\n\nMost definitions I've seen say that the paired microsporangia make up the theca (#2 in the figure). So, the figure above has two thecae separated by the connective (#3).\n\n\n\n\nWikipedia (https://en.wikipedia.org/wiki/Theca) says that a theca consists of the surrounding tissue layers, such as the epidermis and tapetum (an inner layer of cells). New York Botanical Garden (https://sweetgum.nybg.org/science/glossary/glossary-details/?irn=3365), NYBG, says that a theca is a chamber where the pollen is produced, \"same as a pollen sac.\" (But note that the Wikipedia definition and the caption to the figure state that the pollen sac is the same as the microsporangium.)\n\n\n\n\nThe Missouri Botanical Garden (https://www.mobot.org/mobot/latindict/keyDetail.aspx?keyWord=tTeca), MoBot, provides the Latin definition of theca: \"that in which anything is enclosed, an envelope, hull, cover, case, sheath, etc.\" They agree with the NYBG in that thecae are \"the pollen-producing sectors (microsporangia) of an anther, the pollen-sac.\"\n\n\n\n\nThe NYBG discussion is a little more comprehensive. They point out that the number of thecae changes during development, stating:\n\n\n\n\n\n\n\nIn neotropical [plant family] Lecythidaceae, up until near the time of anther dehiscence there are two anther thecae on each side of the anther connective but the walls between these thecae break down so there are only two thecae by the time the anthers dehisce (one on each side of the anther).\n\n\n\n\n\n\n\nAs far as I can tell, there's nothing particularly unusual about the anthers of Lecythidaceae, so we can say that generally, while the microsporangia are still completely separated, an anther has four thecae. Then, when the septum has broken and the two microsporangia are fused, the anther has two thecae. (Think of the two microsporangia now forming \"one chamber\".)\n\n\n\n\nAs for \"lobes\", I think it's still safe to say that each pair of microsporangia form a lobe (e.g., the left and right halves of the anther in the figure). This term is used a bit more casually. The more technical term is \"bilocular\". This implies two locules, but has the same difficulty as theca: the locules are the spaces within the chambers, and can go from four locules to two locules as the anther develops.\n\n\n\n\nIt may also help to review pictures of developing anthers. Early in development the microsporangia are in the process of producing the pollen and there's not really any empty space within them. Only later do these areas actually become hollow as the pollen grains mature, and this hollow space is the locule.\n\n\n\n\n\n\n\nImage by Ben Stefanowitsch - Created for Wikimedia Commons by Ben Stefanowitsch, CC BY-SA 2.5 (https://creativecommons.org/licenses/by-sa/2.5), https://commons.wikimedia.org/w/index.php?curid=703358 (https://commons.wikimedia.org/w/index.php?curid=703358)", "answer_url": "https://biology.stackexchange.com/a/116276", "author": "Darlingtonia", "author_url": "https://biology.stackexchange.com/users/1197/darlingtonia", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2025-03-24T21:55:39+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:19.947691+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/df693642d727b738d2a533740632235c18a06cefec7a1e337c9589214a4ec91e_0.json", "raw_sha256": "9df534f437f3b2f12d33db8536999ec4e6ffa10f2f59394799d9fe01c3c1ad16", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/117606;117602;117598;117594;117585;117579;117570;117568;117565;117559;117558;117555;117552;117548;117538;117524;117523;117522;117520;117515;117510;116509;116508;116504;116499;116491;116485;116483;116461;116454;116453;116445;116441;116435;116430;116426;116425;116414;116412;116406;116401;116399;116396;116395;116394;116392;116389;116384;116370;116367;116363;116361;116352;116351;116347;116345;116343;116338;116337;116332;116331;116324;116320;116316;116314;116312;116306;116292;116290;116284;116280;116277;116271;116270;116268;116267;116257;116256;116253;116250;116249;116240;116237;116233;116219;116214;116212;116205;116204;116200;116198;116187;116184;116173;116172;116167;116162;116149;116142;116129/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 116268, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Darlingtonia", "profile_url": "https://biology.stackexchange.com/users/1197/darlingtonia", "user_type": "registered"}, "created_at": "2025-03-24T21:55:39+00:00", "raw_file": "raw/codex_api_v1/6a8d1217a71337b035f168c28f3cef00c95606938297595ce7816a6ee2aabc47_1790824139846857200_0.json", "raw_sha256": "915362f28bff22e7e44f536acc7b10e33f23a77bbb5e547906a8fdc7cf7e3e89", "revision_guid": "3928595F-2D7C-4424-9440-D3A124B297D5", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/3928595F-2D7C-4424-9440-D3A124B297D5/view-source"}], "score": 2, "updated_at": "2025-03-24T21:55:39+00:00"}], "ground_truth": "community signals only; no scientific truth label", "product": "ranking", "question": "My textbook states that\na typical anther is bilobed with each lobe having two theca.\n\n\n\n\nIf I go by the definition of theca as given on Wikipedia it states that the theca consists of the 2 microsporangia which are sharing a common stomium\n\n\n\n\nI am confused between the definition of lobe and theca.\ndoes my textbook imply that the lobe is the composite structure of 2 microsporangia on each side which share the same line of dehiscence?", "record_id": "Scientific-Answer-Ranking:biology:116268", "scores": [0, 2], "split": "holdout", "thread": {"accepted_answer_id": 116276, "answers": [{"answer_html": "Each lobe typically contains two theca, meaning a typical anther has four theca in total, each theca then contains two microsporangia. The lobe is composed of two theca, two pairs of microsporangia, separated by the stomium, which is an area of dehiscence.
\n", "answer_id": 116274, "answer_text": "Each lobe typically contains two theca, meaning a typical anther has four theca in total, each theca then contains two microsporangia. The lobe is composed of two theca, two pairs of microsporangia, separated by the stomium, which is an area of dehiscence.", "answer_url": "https://biology.stackexchange.com/a/116274", "author": "Moracen", "author_url": "https://biology.stackexchange.com/users/103307/moracen", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2025-03-24T07:52:39+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:19.947691+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/df693642d727b738d2a533740632235c18a06cefec7a1e337c9589214a4ec91e_0.json", "raw_sha256": "9df534f437f3b2f12d33db8536999ec4e6ffa10f2f59394799d9fe01c3c1ad16", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/117606;117602;117598;117594;117585;117579;117570;117568;117565;117559;117558;117555;117552;117548;117538;117524;117523;117522;117520;117515;117510;116509;116508;116504;116499;116491;116485;116483;116461;116454;116453;116445;116441;116435;116430;116426;116425;116414;116412;116406;116401;116399;116396;116395;116394;116392;116389;116384;116370;116367;116363;116361;116352;116351;116347;116345;116343;116338;116337;116332;116331;116324;116320;116316;116314;116312;116306;116292;116290;116284;116280;116277;116271;116270;116268;116267;116257;116256;116253;116250;116249;116240;116237;116233;116219;116214;116212;116205;116204;116200;116198;116187;116184;116173;116172;116167;116162;116149;116142;116129/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 116268, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Moracen", "profile_url": "https://biology.stackexchange.com/users/103307/moracen", "user_type": "registered"}, "created_at": "2025-03-24T07:52:39+00:00", "raw_file": "raw/codex_api_v1/6a8d1217a71337b035f168c28f3cef00c95606938297595ce7816a6ee2aabc47_1790824139846857200_0.json", "raw_sha256": "915362f28bff22e7e44f536acc7b10e33f23a77bbb5e547906a8fdc7cf7e3e89", "revision_guid": "2C7B74B8-E717-475B-A40F-D1E072A4D55F", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/2C7B74B8-E717-475B-A40F-D1E072A4D55F/view-source"}], "score": 0, "updated_at": "2025-03-24T07:52:39+00:00"}, {"answer_html": "Wow, I'm not surprised there's confusion. For fairly basic botanical anatomy, there is a lot of variability out there about the answer.
\nTypical anthers have four microsporangia. This is probably the most consistent fact to keep in mind. These are labeled as #4 in the picture below. (Note that in this image the wall separating the two microsporangia of each lobe [the septum] has begun to split.)
\n
Most definitions I've seen say that the paired microsporangia make up the theca (#2 in the figure). So, the figure above has two thecae separated by the connective (#3).
\nWikipedia says that a theca consists of the surrounding tissue layers, such as the epidermis and tapetum (an inner layer of cells). New York Botanical Garden, NYBG, says that a theca is a chamber where the pollen is produced, "same as a pollen sac." (But note that the Wikipedia definition and the caption to the figure state that the pollen sac is the same as the microsporangium.)
\nThe Missouri Botanical Garden, MoBot, provides the Latin definition of theca: "that in which anything is enclosed, an envelope, hull, cover, case, sheath, etc." They agree with the NYBG in that thecae are "the pollen-producing sectors (microsporangia) of an anther, the pollen-sac."
\nThe NYBG discussion is a little more comprehensive. They point out that the number of thecae changes during development, stating:
\n\n\nIn neotropical [plant family] Lecythidaceae, up until near the time of anther dehiscence there are two anther thecae on each side of the anther connective but the walls between these thecae break down so there are only two thecae by the time the anthers dehisce (one on each side of the anther).
\n
As far as I can tell, there's nothing particularly unusual about the anthers of Lecythidaceae, so we can say that generally, while the microsporangia are still completely separated, an anther has four thecae. Then, when the septum has broken and the two microsporangia are fused, the anther has two thecae. (Think of the two microsporangia now forming "one chamber".)
\nAs for "lobes", I think it's still safe to say that each pair of microsporangia form a lobe (e.g., the left and right halves of the anther in the figure). This term is used a bit more casually. The more technical term is "bilocular". This implies two locules, but has the same difficulty as theca: the locules are the spaces within the chambers, and can go from four locules to two locules as the anther develops.
\nIt may also help to review pictures of developing anthers. Early in development the microsporangia are in the process of producing the pollen and there's not really any empty space within them. Only later do these areas actually become hollow as the pollen grains mature, and this hollow space is the locule.
\n\n
Image by Ben Stefanowitsch - Created for Wikimedia Commons by Ben Stefanowitsch, CC BY-SA 2.5, https://commons.wikimedia.org/w/index.php?curid=703358
\n", "answer_id": 116276, "answer_text": "Wow, I'm not surprised there's confusion. For fairly basic botanical anatomy, there is a lot of variability out there about the answer.\n\n\n\n\nTypical anthers have four microsporangia. This is probably the most consistent fact to keep in mind. These are labeled as #4 in the picture below. (Note that in this image the wall separating the two microsporangia of each lobe [the septum] has begun to split.)\n\n\n\n\n[image: Schematic cross section of an anther. 1: Filament 2: Theca 3: Connective 4: Pollen sac (also known as sporangium); source: https://i.sstatic.net/8pvuHCTK.png]\n\n\n\n\nMost definitions I've seen say that the paired microsporangia make up the theca (#2 in the figure). So, the figure above has two thecae separated by the connective (#3).\n\n\n\n\nWikipedia (https://en.wikipedia.org/wiki/Theca) says that a theca consists of the surrounding tissue layers, such as the epidermis and tapetum (an inner layer of cells). New York Botanical Garden (https://sweetgum.nybg.org/science/glossary/glossary-details/?irn=3365), NYBG, says that a theca is a chamber where the pollen is produced, \"same as a pollen sac.\" (But note that the Wikipedia definition and the caption to the figure state that the pollen sac is the same as the microsporangium.)\n\n\n\n\nThe Missouri Botanical Garden (https://www.mobot.org/mobot/latindict/keyDetail.aspx?keyWord=tTeca), MoBot, provides the Latin definition of theca: \"that in which anything is enclosed, an envelope, hull, cover, case, sheath, etc.\" They agree with the NYBG in that thecae are \"the pollen-producing sectors (microsporangia) of an anther, the pollen-sac.\"\n\n\n\n\nThe NYBG discussion is a little more comprehensive. They point out that the number of thecae changes during development, stating:\n\n\n\n\n\n\n\nIn neotropical [plant family] Lecythidaceae, up until near the time of anther dehiscence there are two anther thecae on each side of the anther connective but the walls between these thecae break down so there are only two thecae by the time the anthers dehisce (one on each side of the anther).\n\n\n\n\n\n\n\nAs far as I can tell, there's nothing particularly unusual about the anthers of Lecythidaceae, so we can say that generally, while the microsporangia are still completely separated, an anther has four thecae. Then, when the septum has broken and the two microsporangia are fused, the anther has two thecae. (Think of the two microsporangia now forming \"one chamber\".)\n\n\n\n\nAs for \"lobes\", I think it's still safe to say that each pair of microsporangia form a lobe (e.g., the left and right halves of the anther in the figure). This term is used a bit more casually. The more technical term is \"bilocular\". This implies two locules, but has the same difficulty as theca: the locules are the spaces within the chambers, and can go from four locules to two locules as the anther develops.\n\n\n\n\nIt may also help to review pictures of developing anthers. Early in development the microsporangia are in the process of producing the pollen and there's not really any empty space within them. Only later do these areas actually become hollow as the pollen grains mature, and this hollow space is the locule.\n\n\n\n\n\n\n\nImage by Ben Stefanowitsch - Created for Wikimedia Commons by Ben Stefanowitsch, CC BY-SA 2.5 (https://creativecommons.org/licenses/by-sa/2.5), https://commons.wikimedia.org/w/index.php?curid=703358 (https://commons.wikimedia.org/w/index.php?curid=703358)", "answer_url": "https://biology.stackexchange.com/a/116276", "author": "Darlingtonia", "author_url": "https://biology.stackexchange.com/users/1197/darlingtonia", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2025-03-24T21:55:39+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:19.947691+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/df693642d727b738d2a533740632235c18a06cefec7a1e337c9589214a4ec91e_0.json", "raw_sha256": "9df534f437f3b2f12d33db8536999ec4e6ffa10f2f59394799d9fe01c3c1ad16", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/117606;117602;117598;117594;117585;117579;117570;117568;117565;117559;117558;117555;117552;117548;117538;117524;117523;117522;117520;117515;117510;116509;116508;116504;116499;116491;116485;116483;116461;116454;116453;116445;116441;116435;116430;116426;116425;116414;116412;116406;116401;116399;116396;116395;116394;116392;116389;116384;116370;116367;116363;116361;116352;116351;116347;116345;116343;116338;116337;116332;116331;116324;116320;116316;116314;116312;116306;116292;116290;116284;116280;116277;116271;116270;116268;116267;116257;116256;116253;116250;116249;116240;116237;116233;116219;116214;116212;116205;116204;116200;116198;116187;116184;116173;116172;116167;116162;116149;116142;116129/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 116268, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Darlingtonia", "profile_url": "https://biology.stackexchange.com/users/1197/darlingtonia", "user_type": "registered"}, "created_at": "2025-03-24T21:55:39+00:00", "raw_file": "raw/codex_api_v1/6a8d1217a71337b035f168c28f3cef00c95606938297595ce7816a6ee2aabc47_1790824139846857200_0.json", "raw_sha256": "915362f28bff22e7e44f536acc7b10e33f23a77bbb5e547906a8fdc7cf7e3e89", "revision_guid": "3928595F-2D7C-4424-9440-D3A124B297D5", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/3928595F-2D7C-4424-9440-D3A124B297D5/view-source"}], "score": 2, "updated_at": "2025-03-24T21:55:39+00:00"}], "domain": "biology", "external_links": ["https://commons.wikimedia.org/w/index.php?curid=703358", "https://creativecommons.org/licenses/by-sa/2.5", "https://en.wikipedia.org/wiki/Theca", "https://i.sstatic.net/8pvuHCTK.png", "https://sweetgum.nybg.org/science/glossary/glossary-details/?irn=3365", "https://www.mobot.org/mobot/latindict/keyDetail.aspx?keyWord=tTeca"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:02.598621+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/5d480e4bd1bd45ab525a4baf3227fba404f89b6af9dad33215fd9fa7c302a211_0.json", "raw_sha256": "d723c7a62c8386d143891d26ae30b2234242ed3dac9599b11f141712ea994a96", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=3&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Maanav Mehta", "question_author_url": "https://biology.stackexchange.com/users/102911/maanav-mehta", "question_author_user_type": "registered", "question_created_at": "2025-03-21T19:24:36+00:00", "question_html": "My textbook states that\na typical anther is bilobed with each lobe having two theca.
\nIf I go by the definition of theca as given on Wikipedia it states that the theca consists of the 2 microsporangia which are sharing a common stomium
\nI am confused between the definition of lobe and theca.\ndoes my textbook imply that the lobe is the composite structure of 2 microsporangia on each side which share the same line of dehiscence?
\n", "question_id": 116268, "question_license": "CC BY-SA 4.0", "question_score": 2, "question_text": "My textbook states that\na typical anther is bilobed with each lobe having two theca.\n\n\n\n\nIf I go by the definition of theca as given on Wikipedia it states that the theca consists of the 2 microsporangia which are sharing a common stomium\n\n\n\n\nI am confused between the definition of lobe and theca.\ndoes my textbook imply that the lobe is the composite structure of 2 microsporangia on each side which share the same line of dehiscence?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Maanav Mehta", "profile_url": "https://biology.stackexchange.com/users/102911/maanav-mehta", "user_type": "registered"}, "created_at": "2025-03-21T19:24:36+00:00", "raw_file": "raw/codex_api_v1/d15f4865285273ae6317f3f3c349227e1b259d6015b55aa14ef5accac806b399_1790824130296338000_0.json", "raw_sha256": "611d5d0f66539d270d10e88493add03469f6e7c1f54b654a8efbaea5fbbc2960", "revision_guid": "66255F40-F7CC-4811-BC78-514A67AB153E", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/66255F40-F7CC-4811-BC78-514A67AB153E/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Maanav Mehta", "profile_url": "https://biology.stackexchange.com/users/102911/maanav-mehta", "user_type": "registered"}, "created_at": "2025-03-23T18:39:11+00:00", "raw_file": "raw/codex_api_v1/d15f4865285273ae6317f3f3c349227e1b259d6015b55aa14ef5accac806b399_1790824130296338000_0.json", "raw_sha256": "611d5d0f66539d270d10e88493add03469f6e7c1f54b654a8efbaea5fbbc2960", "revision_guid": "47FD8A29-82CF-4509-870C-5B27A9892296", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/47FD8A29-82CF-4509-870C-5B27A9892296/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/116268/what-is-a-lobe-in-an-anther", "split": "holdout", "split_group": "4dbce1befd920a548c1ed6d7fd0b529543b05a599624e7d5c0fe383eeed993a7", "tags": ["botany", "plant-anatomy"], "thread_id": "biology:116268", "title": "What is a lobe in an anther?"}} {"accepted_status": [false, false, false], "candidate_answers": [{"answer_html": "There isn't really a good answer, since we don't have a singular quantifiable measure of intelligence for humans, let alone other species.
\nAny human measures of intelligence might not apply properly to an animal, because it's based on either human behaviours, or specific human cultures/context. An animal that does not confirm to either might not complete the test as expected, or not recognise it as one at all.
\n", "answer_id": 112750, "answer_text": "There isn't really a good answer, since we don't have a singular quantifiable measure of intelligence for humans, let alone other species.\n\n\n\n\nAny human measures of intelligence might not apply properly to an animal, because it's based on either human behaviours, or specific human cultures/context. An animal that does not confirm to either might not complete the test as expected, or not recognise it as one at all.", "answer_url": "https://biology.stackexchange.com/a/112750", "author": "techno156", "author_url": "https://biology.stackexchange.com/users/27285/techno156", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2023-08-07T18:48:54+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:38.885561+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/a145de97eabc007745b45919875489a41261075cbdf33d916d9640ba4ad0bd35_0.json", "raw_sha256": "e7d8d4315eef8e039a452d2811869cbe305575c6ff8a6bef8f80d6dfb58c5bfd", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/112982;112980;112979;112977;112972;112967;112962;112956;112952;112948;112941;112938;112937;112936;112927;112925;112923;112919;112909;112905;112904;112898;112895;112893;112884;112881;112880;112879;112873;112872;112870;112869;112867;112850;112849;112848;112841;112835;112831;112824;112818;112811;112808;112807;112790;112789;112785;112777;112773;112770;112762;112759;112757;112756;112746;112739;112738;112737;112731;112705;112703;112700;112699;112698;112693;112691;112687;112685;112677;112671;112667;112663;112659;112653;112647;112646;112645;112636;112625;112621;112615;112614;112613;112610;112598;112593;112592;112586;112580;112575;112574;112564;112558;112552;112550;112549;112544;112539;112535;112531/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 112739, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "techno156", "profile_url": "https://biology.stackexchange.com/users/27285/techno156", "user_type": "registered"}, "created_at": "2023-08-07T18:48:54+00:00", "raw_file": "raw/codex_api_v1/a04a0f8b9b816f605414240c86ef0796529040fa885a4b1183bd818d12b64e65_0.json", "raw_sha256": "630e8bf25473aeb8900409dec408d29d2bdc2011bc3b72f26995c17452a2c689", "revision_guid": "00EE888A-33A5-4F00-84AB-76170FACECAA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/00EE888A-33A5-4F00-84AB-76170FACECAA/view-source"}], "score": 1, "updated_at": "2023-08-07T18:48:54+00:00"}, {"answer_html": "EQ or EZ can be helpful with several qualifiers.
\n- \n
you should account for differences among groups, birds for instance have smaller brains than mammals for what most would consider similar intelligence, bird brains have higher synaptic density than mammals likely due to weight constraints during evolution. the brain has evolved along sperate paths with different mass efficiencies. EQ gets less and less useful the further you get from mammals and primates. invertebrates in particular become very problematic since the brain is not extremally centralized like it is in vertebrates, so even estimating what is and is not the brain runs into issues.
\n \nImprovements have been done to EQ by using the only the parts of the brain responsible things we associate with intelligence, this helps account for drastic difference in sensory parts of the brain which affect overall brain size, but again this breaks down when you get away from mammals because the brains works differently in those groups. You also run into the issue that folding of the brain increases neuron density faster than mass so it can deflate EQ scores while making the animal more intelligent.
\n \n
If you really want to estimate intelligence, then just like in humans, behavior is your best metric, but this is not going to be a easy to research number. I have a similar issue to your conundrum and I won't eat anything that appears to understand the concept of death : elephants, great apes and some other primates, dolphins including orca and, grey parrots. I generally iffy on eating anything that has complex problem solving and tool use. I won't eat any primate at all for other reasons (disease). But this requires knowledge of animal behavior. You will never get a nice easy number to look at, intelligence is just too complex a thing.
\n", "answer_id": 112766, "answer_text": "EQ or EZ can be helpful with several qualifiers.\n\n\n\n\n\n\n\nyou should account for differences among groups, birds for instance have smaller brains than mammals for what most would consider similar intelligence, bird brains have higher synaptic density than mammals likely due to weight constraints during evolution. the brain has evolved along sperate paths with different mass efficiencies. EQ gets less and less useful the further you get from mammals and primates. invertebrates in particular become very problematic since the brain is not extremally centralized like it is in vertebrates, so even estimating what is and is not the brain runs into issues.\n\n\n\n\n\n\n\n\n\nImprovements have been done to EQ by using the only the parts of the brain responsible things we associate with intelligence, this helps account for drastic difference in sensory parts of the brain which affect overall brain size, but again this breaks down when you get away from mammals because the brains works differently in those groups. You also run into the issue that folding of the brain increases neuron density faster than mass so it can deflate EQ scores while making the animal more intelligent.\n\n\n\n\n\n\n\n\nIf you really want to estimate intelligence, then just like in humans, behavior is your best metric, but this is not going to be a easy to research number. I have a similar issue to your conundrum and I won't eat anything that appears to understand the concept of death : elephants, great apes and some other primates, dolphins including orca and, grey parrots. I generally iffy on eating anything that has complex problem solving and tool use. I won't eat any primate at all for other reasons (disease). But this requires knowledge of animal behavior. You will never get a nice easy number to look at, intelligence is just too complex a thing.", "answer_url": "https://biology.stackexchange.com/a/112766", "author": "John", "author_url": "https://biology.stackexchange.com/users/28022/john", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2023-08-09T15:21:38+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:38.885561+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/a145de97eabc007745b45919875489a41261075cbdf33d916d9640ba4ad0bd35_0.json", "raw_sha256": "e7d8d4315eef8e039a452d2811869cbe305575c6ff8a6bef8f80d6dfb58c5bfd", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/112982;112980;112979;112977;112972;112967;112962;112956;112952;112948;112941;112938;112937;112936;112927;112925;112923;112919;112909;112905;112904;112898;112895;112893;112884;112881;112880;112879;112873;112872;112870;112869;112867;112850;112849;112848;112841;112835;112831;112824;112818;112811;112808;112807;112790;112789;112785;112777;112773;112770;112762;112759;112757;112756;112746;112739;112738;112737;112731;112705;112703;112700;112699;112698;112693;112691;112687;112685;112677;112671;112667;112663;112659;112653;112647;112646;112645;112636;112625;112621;112615;112614;112613;112610;112598;112593;112592;112586;112580;112575;112574;112564;112558;112552;112550;112549;112544;112539;112535;112531/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 112739, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "John", "profile_url": "https://biology.stackexchange.com/users/28022/john", "user_type": "registered"}, "created_at": "2023-08-09T15:21:38+00:00", "raw_file": "raw/codex_api_v1/fe6e1ab1e4f14040deb1423c04616e4dd0e7de39b583b42e88a31f79f9375e98_1790824028764975800_0.json", "raw_sha256": "08e023ccc811ec000989abb19f483814e44277588eeabf130aa5dbaf177079bf", "revision_guid": "EC59CE9D-E136-48CD-B5EB-8EF24A4218AC", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/EC59CE9D-E136-48CD-B5EB-8EF24A4218AC/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "John", "profile_url": "https://biology.stackexchange.com/users/28022/john", "user_type": "registered"}, "created_at": "2023-08-10T01:01:59+00:00", "raw_file": "raw/codex_api_v1/fe6e1ab1e4f14040deb1423c04616e4dd0e7de39b583b42e88a31f79f9375e98_1790824028764975800_0.json", "raw_sha256": "08e023ccc811ec000989abb19f483814e44277588eeabf130aa5dbaf177079bf", "revision_guid": "7A188AFD-F482-45DF-8528-951E2EBEDA54", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/7A188AFD-F482-45DF-8528-951E2EBEDA54/view-source"}], "score": 1, "updated_at": "2023-08-10T01:01:59+00:00"}, {"answer_html": "There is no easy way to quantify intelligence because it's poorly defined. I would suggest narrowing your focus on measurable behaviour as a proxy for intelligence, and looking at the many behavioral research studies on commonly consumed animals.
\n- \n
- Would you eat an animal that has social bonds? \n
- Would you eat an animal that is able to be taught new skills? \n
- Would you eat an animal that demonstrates problem solving? \n
There is good evidence that chickens, pigs, cows, sheep, fish, all form social bonds, can learn new skills, and solve novel problems. All of those things are a key part in survival and reproduction in many animal species.
\nYou might find the mirror self-recognition test worth looking into, particularly as something that highlights the absurdity of trying to design a test across species.
\nHere's a list of animals by number of neurons which may help you on your quest - if you can find evidence that number of neurons is an adequate proxy to intelligence for your purposes. There is another on that page about number in the cerebrum. Not a lot of fish on there though.
\n", "answer_id": 112772, "answer_text": "There is no easy way to quantify intelligence because it's poorly defined. I would suggest narrowing your focus on measurable behaviour as a proxy for intelligence, and looking at the many behavioral research studies on commonly consumed animals.\n\n\n\n\n\nWould you eat an animal that has social bonds?\n\n\n\n\nWould you eat an animal that is able to be taught new skills?\n\n\n\n\nWould you eat an animal that demonstrates problem solving?\n\n\n\n\n\nThere is good evidence that chickens, pigs, cows, sheep, fish, all form social bonds, can learn new skills, and solve novel problems. All of those things are a key part in survival and reproduction in many animal species.\n\n\n\n\nYou might find the mirror self-recognition test (https://en.wikipedia.org/wiki/Mirror_test) worth looking into, particularly as something that highlights the absurdity of trying to design a test across species.\n\n\n\n\nHere's a list of animals by number of neurons (https://en.wikipedia.org/wiki/List_of_animals_by_number_of_neurons) which may help you on your quest - if you can find evidence that number of neurons is an adequate proxy to intelligence for your purposes. There is another on that page about number in the cerebrum. Not a lot of fish on there though.", "answer_url": "https://biology.stackexchange.com/a/112772", "author": "Spare", "author_url": "https://biology.stackexchange.com/users/76533/spare", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2023-08-10T03:06:01+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:38.885561+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/a145de97eabc007745b45919875489a41261075cbdf33d916d9640ba4ad0bd35_0.json", "raw_sha256": "e7d8d4315eef8e039a452d2811869cbe305575c6ff8a6bef8f80d6dfb58c5bfd", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/112982;112980;112979;112977;112972;112967;112962;112956;112952;112948;112941;112938;112937;112936;112927;112925;112923;112919;112909;112905;112904;112898;112895;112893;112884;112881;112880;112879;112873;112872;112870;112869;112867;112850;112849;112848;112841;112835;112831;112824;112818;112811;112808;112807;112790;112789;112785;112777;112773;112770;112762;112759;112757;112756;112746;112739;112738;112737;112731;112705;112703;112700;112699;112698;112693;112691;112687;112685;112677;112671;112667;112663;112659;112653;112647;112646;112645;112636;112625;112621;112615;112614;112613;112610;112598;112593;112592;112586;112580;112575;112574;112564;112558;112552;112550;112549;112544;112539;112535;112531/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 112739, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Spare", "profile_url": "https://biology.stackexchange.com/users/76533/spare", "user_type": "registered"}, "created_at": "2023-08-10T03:06:01+00:00", "raw_file": "raw/codex_api_v1/fe6e1ab1e4f14040deb1423c04616e4dd0e7de39b583b42e88a31f79f9375e98_1790824028764975800_0.json", "raw_sha256": "08e023ccc811ec000989abb19f483814e44277588eeabf130aa5dbaf177079bf", "revision_guid": "F7CAC700-9475-4670-B8DD-A58BC023F3CE", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/F7CAC700-9475-4670-B8DD-A58BC023F3CE/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Spare", "profile_url": "https://biology.stackexchange.com/users/76533/spare", "user_type": "registered"}, "created_at": "2023-08-10T03:10:16+00:00", "raw_file": "raw/codex_api_v1/fe6e1ab1e4f14040deb1423c04616e4dd0e7de39b583b42e88a31f79f9375e98_1790824028764975800_0.json", "raw_sha256": "08e023ccc811ec000989abb19f483814e44277588eeabf130aa5dbaf177079bf", "revision_guid": "CCFC03A7-9A9C-4509-B329-C10AC00620B6", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/CCFC03A7-9A9C-4509-B329-C10AC00620B6/view-source"}], "score": 1, "updated_at": "2023-08-10T03:10:16+00:00"}], "ground_truth": "community signals only; no scientific truth label", "product": "ranking", "question": "What is a good cross-species measure of intelligence?\n\n\n\n\nI want to use this information to decide which animals to eat, so preferably it would have been measured for most commonly eaten animals.\n\n\n\n\nI read about the Encephalization Quotient. Would EQ be a good choice? Is there somewhere I can find a list of animals and their EQ?", "record_id": "Scientific-Answer-Ranking:biology:112739", "scores": [1, 1, 1], "split": "holdout", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "There isn't really a good answer, since we don't have a singular quantifiable measure of intelligence for humans, let alone other species.
\nAny human measures of intelligence might not apply properly to an animal, because it's based on either human behaviours, or specific human cultures/context. An animal that does not confirm to either might not complete the test as expected, or not recognise it as one at all.
\n", "answer_id": 112750, "answer_text": "There isn't really a good answer, since we don't have a singular quantifiable measure of intelligence for humans, let alone other species.\n\n\n\n\nAny human measures of intelligence might not apply properly to an animal, because it's based on either human behaviours, or specific human cultures/context. An animal that does not confirm to either might not complete the test as expected, or not recognise it as one at all.", "answer_url": "https://biology.stackexchange.com/a/112750", "author": "techno156", "author_url": "https://biology.stackexchange.com/users/27285/techno156", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2023-08-07T18:48:54+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:38.885561+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/a145de97eabc007745b45919875489a41261075cbdf33d916d9640ba4ad0bd35_0.json", "raw_sha256": "e7d8d4315eef8e039a452d2811869cbe305575c6ff8a6bef8f80d6dfb58c5bfd", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/112982;112980;112979;112977;112972;112967;112962;112956;112952;112948;112941;112938;112937;112936;112927;112925;112923;112919;112909;112905;112904;112898;112895;112893;112884;112881;112880;112879;112873;112872;112870;112869;112867;112850;112849;112848;112841;112835;112831;112824;112818;112811;112808;112807;112790;112789;112785;112777;112773;112770;112762;112759;112757;112756;112746;112739;112738;112737;112731;112705;112703;112700;112699;112698;112693;112691;112687;112685;112677;112671;112667;112663;112659;112653;112647;112646;112645;112636;112625;112621;112615;112614;112613;112610;112598;112593;112592;112586;112580;112575;112574;112564;112558;112552;112550;112549;112544;112539;112535;112531/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 112739, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "techno156", "profile_url": "https://biology.stackexchange.com/users/27285/techno156", "user_type": "registered"}, "created_at": "2023-08-07T18:48:54+00:00", "raw_file": "raw/codex_api_v1/a04a0f8b9b816f605414240c86ef0796529040fa885a4b1183bd818d12b64e65_0.json", "raw_sha256": "630e8bf25473aeb8900409dec408d29d2bdc2011bc3b72f26995c17452a2c689", "revision_guid": "00EE888A-33A5-4F00-84AB-76170FACECAA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/00EE888A-33A5-4F00-84AB-76170FACECAA/view-source"}], "score": 1, "updated_at": "2023-08-07T18:48:54+00:00"}, {"answer_html": "EQ or EZ can be helpful with several qualifiers.
\n- \n
you should account for differences among groups, birds for instance have smaller brains than mammals for what most would consider similar intelligence, bird brains have higher synaptic density than mammals likely due to weight constraints during evolution. the brain has evolved along sperate paths with different mass efficiencies. EQ gets less and less useful the further you get from mammals and primates. invertebrates in particular become very problematic since the brain is not extremally centralized like it is in vertebrates, so even estimating what is and is not the brain runs into issues.
\n \nImprovements have been done to EQ by using the only the parts of the brain responsible things we associate with intelligence, this helps account for drastic difference in sensory parts of the brain which affect overall brain size, but again this breaks down when you get away from mammals because the brains works differently in those groups. You also run into the issue that folding of the brain increases neuron density faster than mass so it can deflate EQ scores while making the animal more intelligent.
\n \n
If you really want to estimate intelligence, then just like in humans, behavior is your best metric, but this is not going to be a easy to research number. I have a similar issue to your conundrum and I won't eat anything that appears to understand the concept of death : elephants, great apes and some other primates, dolphins including orca and, grey parrots. I generally iffy on eating anything that has complex problem solving and tool use. I won't eat any primate at all for other reasons (disease). But this requires knowledge of animal behavior. You will never get a nice easy number to look at, intelligence is just too complex a thing.
\n", "answer_id": 112766, "answer_text": "EQ or EZ can be helpful with several qualifiers.\n\n\n\n\n\n\n\nyou should account for differences among groups, birds for instance have smaller brains than mammals for what most would consider similar intelligence, bird brains have higher synaptic density than mammals likely due to weight constraints during evolution. the brain has evolved along sperate paths with different mass efficiencies. EQ gets less and less useful the further you get from mammals and primates. invertebrates in particular become very problematic since the brain is not extremally centralized like it is in vertebrates, so even estimating what is and is not the brain runs into issues.\n\n\n\n\n\n\n\n\n\nImprovements have been done to EQ by using the only the parts of the brain responsible things we associate with intelligence, this helps account for drastic difference in sensory parts of the brain which affect overall brain size, but again this breaks down when you get away from mammals because the brains works differently in those groups. You also run into the issue that folding of the brain increases neuron density faster than mass so it can deflate EQ scores while making the animal more intelligent.\n\n\n\n\n\n\n\n\nIf you really want to estimate intelligence, then just like in humans, behavior is your best metric, but this is not going to be a easy to research number. I have a similar issue to your conundrum and I won't eat anything that appears to understand the concept of death : elephants, great apes and some other primates, dolphins including orca and, grey parrots. I generally iffy on eating anything that has complex problem solving and tool use. I won't eat any primate at all for other reasons (disease). But this requires knowledge of animal behavior. You will never get a nice easy number to look at, intelligence is just too complex a thing.", "answer_url": "https://biology.stackexchange.com/a/112766", "author": "John", "author_url": "https://biology.stackexchange.com/users/28022/john", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2023-08-09T15:21:38+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:38.885561+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/a145de97eabc007745b45919875489a41261075cbdf33d916d9640ba4ad0bd35_0.json", "raw_sha256": "e7d8d4315eef8e039a452d2811869cbe305575c6ff8a6bef8f80d6dfb58c5bfd", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/112982;112980;112979;112977;112972;112967;112962;112956;112952;112948;112941;112938;112937;112936;112927;112925;112923;112919;112909;112905;112904;112898;112895;112893;112884;112881;112880;112879;112873;112872;112870;112869;112867;112850;112849;112848;112841;112835;112831;112824;112818;112811;112808;112807;112790;112789;112785;112777;112773;112770;112762;112759;112757;112756;112746;112739;112738;112737;112731;112705;112703;112700;112699;112698;112693;112691;112687;112685;112677;112671;112667;112663;112659;112653;112647;112646;112645;112636;112625;112621;112615;112614;112613;112610;112598;112593;112592;112586;112580;112575;112574;112564;112558;112552;112550;112549;112544;112539;112535;112531/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 112739, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "John", "profile_url": "https://biology.stackexchange.com/users/28022/john", "user_type": "registered"}, "created_at": "2023-08-09T15:21:38+00:00", "raw_file": "raw/codex_api_v1/fe6e1ab1e4f14040deb1423c04616e4dd0e7de39b583b42e88a31f79f9375e98_1790824028764975800_0.json", "raw_sha256": "08e023ccc811ec000989abb19f483814e44277588eeabf130aa5dbaf177079bf", "revision_guid": "EC59CE9D-E136-48CD-B5EB-8EF24A4218AC", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/EC59CE9D-E136-48CD-B5EB-8EF24A4218AC/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "John", "profile_url": "https://biology.stackexchange.com/users/28022/john", "user_type": "registered"}, "created_at": "2023-08-10T01:01:59+00:00", "raw_file": "raw/codex_api_v1/fe6e1ab1e4f14040deb1423c04616e4dd0e7de39b583b42e88a31f79f9375e98_1790824028764975800_0.json", "raw_sha256": "08e023ccc811ec000989abb19f483814e44277588eeabf130aa5dbaf177079bf", "revision_guid": "7A188AFD-F482-45DF-8528-951E2EBEDA54", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/7A188AFD-F482-45DF-8528-951E2EBEDA54/view-source"}], "score": 1, "updated_at": "2023-08-10T01:01:59+00:00"}, {"answer_html": "There is no easy way to quantify intelligence because it's poorly defined. I would suggest narrowing your focus on measurable behaviour as a proxy for intelligence, and looking at the many behavioral research studies on commonly consumed animals.
\n- \n
- Would you eat an animal that has social bonds? \n
- Would you eat an animal that is able to be taught new skills? \n
- Would you eat an animal that demonstrates problem solving? \n
There is good evidence that chickens, pigs, cows, sheep, fish, all form social bonds, can learn new skills, and solve novel problems. All of those things are a key part in survival and reproduction in many animal species.
\nYou might find the mirror self-recognition test worth looking into, particularly as something that highlights the absurdity of trying to design a test across species.
\nHere's a list of animals by number of neurons which may help you on your quest - if you can find evidence that number of neurons is an adequate proxy to intelligence for your purposes. There is another on that page about number in the cerebrum. Not a lot of fish on there though.
\n", "answer_id": 112772, "answer_text": "There is no easy way to quantify intelligence because it's poorly defined. I would suggest narrowing your focus on measurable behaviour as a proxy for intelligence, and looking at the many behavioral research studies on commonly consumed animals.\n\n\n\n\n\nWould you eat an animal that has social bonds?\n\n\n\n\nWould you eat an animal that is able to be taught new skills?\n\n\n\n\nWould you eat an animal that demonstrates problem solving?\n\n\n\n\n\nThere is good evidence that chickens, pigs, cows, sheep, fish, all form social bonds, can learn new skills, and solve novel problems. All of those things are a key part in survival and reproduction in many animal species.\n\n\n\n\nYou might find the mirror self-recognition test (https://en.wikipedia.org/wiki/Mirror_test) worth looking into, particularly as something that highlights the absurdity of trying to design a test across species.\n\n\n\n\nHere's a list of animals by number of neurons (https://en.wikipedia.org/wiki/List_of_animals_by_number_of_neurons) which may help you on your quest - if you can find evidence that number of neurons is an adequate proxy to intelligence for your purposes. There is another on that page about number in the cerebrum. Not a lot of fish on there though.", "answer_url": "https://biology.stackexchange.com/a/112772", "author": "Spare", "author_url": "https://biology.stackexchange.com/users/76533/spare", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2023-08-10T03:06:01+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:38.885561+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/a145de97eabc007745b45919875489a41261075cbdf33d916d9640ba4ad0bd35_0.json", "raw_sha256": "e7d8d4315eef8e039a452d2811869cbe305575c6ff8a6bef8f80d6dfb58c5bfd", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/112982;112980;112979;112977;112972;112967;112962;112956;112952;112948;112941;112938;112937;112936;112927;112925;112923;112919;112909;112905;112904;112898;112895;112893;112884;112881;112880;112879;112873;112872;112870;112869;112867;112850;112849;112848;112841;112835;112831;112824;112818;112811;112808;112807;112790;112789;112785;112777;112773;112770;112762;112759;112757;112756;112746;112739;112738;112737;112731;112705;112703;112700;112699;112698;112693;112691;112687;112685;112677;112671;112667;112663;112659;112653;112647;112646;112645;112636;112625;112621;112615;112614;112613;112610;112598;112593;112592;112586;112580;112575;112574;112564;112558;112552;112550;112549;112544;112539;112535;112531/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 112739, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Spare", "profile_url": "https://biology.stackexchange.com/users/76533/spare", "user_type": "registered"}, "created_at": "2023-08-10T03:06:01+00:00", "raw_file": "raw/codex_api_v1/fe6e1ab1e4f14040deb1423c04616e4dd0e7de39b583b42e88a31f79f9375e98_1790824028764975800_0.json", "raw_sha256": "08e023ccc811ec000989abb19f483814e44277588eeabf130aa5dbaf177079bf", "revision_guid": "F7CAC700-9475-4670-B8DD-A58BC023F3CE", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/F7CAC700-9475-4670-B8DD-A58BC023F3CE/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Spare", "profile_url": "https://biology.stackexchange.com/users/76533/spare", "user_type": "registered"}, "created_at": "2023-08-10T03:10:16+00:00", "raw_file": "raw/codex_api_v1/fe6e1ab1e4f14040deb1423c04616e4dd0e7de39b583b42e88a31f79f9375e98_1790824028764975800_0.json", "raw_sha256": "08e023ccc811ec000989abb19f483814e44277588eeabf130aa5dbaf177079bf", "revision_guid": "CCFC03A7-9A9C-4509-B329-C10AC00620B6", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/CCFC03A7-9A9C-4509-B329-C10AC00620B6/view-source"}], "score": 1, "updated_at": "2023-08-10T03:10:16+00:00"}], "domain": "biology", "external_links": ["https://en.wikipedia.org/wiki/List_of_animals_by_number_of_neurons", "https://en.wikipedia.org/wiki/Mirror_test"], "medical_sensitive": true, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:12.794960+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/01e5186067e30dc1b8d7a145670ab7edd6b017797b271a481af8b7b7f55f13c2_0.json", "raw_sha256": "6c3960de7e1d3d7920bb88d02e2184614c219b391f39d9bddc2a582fdc9a71e7", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=10&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "the universe is awesome", "question_author_url": "https://biology.stackexchange.com/users/76487/the-universe-is-awesome", "question_author_user_type": "registered", "question_created_at": "2023-08-06T01:55:59+00:00", "question_html": "What is a good cross-species measure of intelligence?
\nI want to use this information to decide which animals to eat, so preferably it would have been measured for most commonly eaten animals.
\nI read about the Encephalization Quotient. Would EQ be a good choice? Is there somewhere I can find a list of animals and their EQ?
\n", "question_id": 112739, "question_license": "CC BY-SA 4.0", "question_score": 0, "question_text": "What is a good cross-species measure of intelligence?\n\n\n\n\nI want to use this information to decide which animals to eat, so preferably it would have been measured for most commonly eaten animals.\n\n\n\n\nI read about the Encephalization Quotient. Would EQ be a good choice? Is there somewhere I can find a list of animals and their EQ?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "the universe is awesome", "profile_url": "https://biology.stackexchange.com/users/76487/the-universe-is-awesome", "user_type": "registered"}, "created_at": "2023-08-06T01:55:59+00:00", "raw_file": "raw/codex_api_v1/a04a0f8b9b816f605414240c86ef0796529040fa885a4b1183bd818d12b64e65_0.json", "raw_sha256": "630e8bf25473aeb8900409dec408d29d2bdc2011bc3b72f26995c17452a2c689", "revision_guid": "B2E984E6-BE8A-4DEB-A5E7-7E7EAB1341C7", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/B2E984E6-BE8A-4DEB-A5E7-7E7EAB1341C7/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/112739/measures-of-animal-intelligence", "split": "holdout", "split_group": "567866b9122ef0c0b7d891c0884a1119a3c469b359d82ef1a8fcd2bf93db273d", "tags": ["intelligence", "measurement", "animal-psychology"], "thread_id": "biology:112739", "title": "Measures of animal intelligence"}} {"accepted_status": [false, false], "candidate_answers": [{"answer_html": "Update: As noted by commenter, the example stated in the question is not actually Michaelis-Menten but is rather an example of binding kinetics. See also the other answer, which is likely more relevant.
\nI would suggest, if you would like to find the steady-state concentration of $[AB]$, that you can solve this yourself mathematically. Try differentiating and setting the $\\Delta [AB]$ side of the equation to zero, and solving. You will find:
\n$ \\Delta [AB] = (k_{on}[A][B] - k_{off}[AB])\\Delta t$
\n$ 0 = (k_{on}[A][B] - k_{off}[AB])\\Delta t$
\nRearranging:
\n$k_{on}[A][B] = k_{off}[AB] $
\nAnd finally:
\n$\\frac{[AB]}{[A][B]} = \\frac{k_{on}}{k_{off}}$
\nNote that if the $k$ are constant, this amounts to the law of mass action.
\nYou can also do a forward simulation (see R code):
\n# association/dissociation kinetics\nkinetic_sim = function(k_on, k_off, a, b) {\n ab = 0\n ab_ts = c()\n a_ts = c()\n b_ts = c()\n for (i in 1:1000) {\n ab_old = ab\n ab = ab * (1 - k_off) + k_on * (a * b)\n a = a - a*b*k_on + ab_old * k_off\n b = b - a*b*k_on + ab_old * k_off\n #cat(i, a, b, ab, k_on*a*b, k_off*ab, "\\n", sep=" ")\n ab_ts = append(ab_ts, ab)\n a_ts = append(a_ts, a)\n b_ts = append(b_ts, b)\n \n }\n return(list(ab_ts, a_ts, b_ts))\n}\nout = kinetic_sim(.1, .2, 1, 1)\nplot(out[[1]] / (out[[2]] * out[[3]]), ylab="[AB] / ([A] * [B])", xlab="time step")\nplot(out[[1]], ylab="[AB]", xlab="time step")\n![\"concentration](\"https://i.sstatic.net/Lw4hnYdr.png\")
\n![\"concentration](\"https://i.sstatic.net/pzN8ZZif.png\")
You can see that both the ratio and the final concentration equilibrate.
\n", "answer_id": 114769, "answer_text": "Update: As noted by commenter, the example stated in the question is not actually Michaelis-Menten but is rather an example of binding kinetics. See also the other answer, which is likely more relevant.\n\n\n\n\nI would suggest, if you would like to find the steady-state concentration of $[AB]$, that you can solve this yourself mathematically. Try differentiating and setting the $\\Delta [AB]$ side of the equation to zero, and solving. You will find:\n\n\n\n\n$ \\Delta [AB] = (k_{on}[A][B] - k_{off}[AB])\\Delta t$\n\n\n\n\n$ 0 = (k_{on}[A][B] - k_{off}[AB])\\Delta t$\n\n\n\n\nRearranging:\n\n\n\n\n$k_{on}[A][B] = k_{off}[AB] $\n\n\n\n\nAnd finally:\n\n\n\n\n$\\frac{[AB]}{[A][B]} = \\frac{k_{on}}{k_{off}}$\n\n\n\n\nNote that if the $k$ are constant, this amounts to the law of mass action.\n\n\n\n\nYou can also do a forward simulation (see R code):\n\n\n\n\n# association/dissociation kinetics\nkinetic_sim = function(k_on, k_off, a, b) {\n ab = 0\n ab_ts = c()\n a_ts = c()\n b_ts = c()\n for (i in 1:1000) {\n ab_old = ab\n ab = ab * (1 - k_off) + k_on * (a * b)\n a = a - a*b*k_on + ab_old * k_off\n b = b - a*b*k_on + ab_old * k_off\n #cat(i, a, b, ab, k_on*a*b, k_off*ab, \"\\n\", sep=\" \")\n ab_ts = append(ab_ts, ab)\n a_ts = append(a_ts, a)\n b_ts = append(b_ts, b)\n \n }\n return(list(ab_ts, a_ts, b_ts))\n}\nout = kinetic_sim(.1, .2, 1, 1)\nplot(out[[1]] / (out[[2]] * out[[3]]), ylab=\"[AB] / ([A] * [B])\", xlab=\"time step\")\nplot(out[[1]], ylab=\"[AB]\", xlab=\"time step\")\n\n\n\n\n\n[image: concentration of ratio [AB]:[A]*[B] over time; source: https://i.sstatic.net/Lw4hnYdr.png] (https://i.sstatic.net/Lw4hnYdr.png)\n[image: concentration of ratio [AB] over time; source: https://i.sstatic.net/pzN8ZZif.png] (https://i.sstatic.net/pzN8ZZif.png)\n\n\n\n\nYou can see that both the ratio and the final concentration equilibrate.", "answer_url": "https://biology.stackexchange.com/a/114769", "author": "Maximilian Press", "author_url": "https://biology.stackexchange.com/users/22392/maximilian-press", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-05-27T18:34:26+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:27.977583+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/1cbf95322a17dce0fd00a109179063ffe60bcd4bddc6e720f0ca398ee7aa9da8_0.json", "raw_sha256": "a096c86028a279b01346143890b4827bd8ed05afc0a76bd7c8bcb840211dc20e", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/114983;114969;114966;114963;114939;114936;114918;114909;114904;114899;114888;114885;114881;114875;114874;114873;114872;114864;114857;114850;114846;114841;114834;114827;114821;114819;114813;114804;114791;114784;114768;114765;114762;114760;114758;114755;114745;114741;114739;114738;114732;114730;114726;114714;114706;114695;114691;114690;114686;114683;114677;114675;114666;114660;114656;114653;114642;114641;114632;114628;114620;114618;114613;114601;114599;114597;114581;114577;114573;114567;114558;114555;114553;114552;114547;114545;114543;114542;114541;114539;114529;114524;114516;114502;114501;114498;114495;114492;114481;114476;114474;114470;114453;114451;114449;114448;114446;114440;114438;114435/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 114768, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Maximilian Press", "profile_url": "https://biology.stackexchange.com/users/22392/maximilian-press", "user_type": "registered"}, "created_at": "2024-05-27T18:34:26+00:00", "raw_file": "raw/codex_api_v1/41500cf35bca9ae31b7ea454bad8679af7e3276d71713db5d1815d84a971bb0e_1790824088925435600_0.json", "raw_sha256": "a764902131a161e2a7978a1f607c4912689efa157d70c2752a5b31e3a042aacb", "revision_guid": "2F432EEF-5BF3-4FFE-B7E3-7AB1C8116BB1", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/2F432EEF-5BF3-4FFE-B7E3-7AB1C8116BB1/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Maximilian Press", "profile_url": "https://biology.stackexchange.com/users/22392/maximilian-press", "user_type": "registered"}, "created_at": "2024-05-27T19:01:38+00:00", "raw_file": "raw/codex_api_v1/41500cf35bca9ae31b7ea454bad8679af7e3276d71713db5d1815d84a971bb0e_1790824088925435600_0.json", "raw_sha256": "a764902131a161e2a7978a1f607c4912689efa157d70c2752a5b31e3a042aacb", "revision_guid": "F76C5C34-436D-4C68-9446-B7AA8D46C53D", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/F76C5C34-436D-4C68-9446-B7AA8D46C53D/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Maximilian Press", "profile_url": "https://biology.stackexchange.com/users/22392/maximilian-press", "user_type": "registered"}, "created_at": "2024-05-27T23:07:19+00:00", "raw_file": "raw/codex_api_v1/41500cf35bca9ae31b7ea454bad8679af7e3276d71713db5d1815d84a971bb0e_1790824088925435600_0.json", "raw_sha256": "a764902131a161e2a7978a1f607c4912689efa157d70c2752a5b31e3a042aacb", "revision_guid": "66A6E2A9-6D6D-44A5-9689-4CA42FD819D5", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/66A6E2A9-6D6D-44A5-9689-4CA42FD819D5/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "TAR86", "profile_url": "https://biology.stackexchange.com/users/32467/tar86", "user_type": "registered"}, "created_at": "2024-05-28T18:28:08+00:00", "raw_file": "raw/codex_api_v1/41500cf35bca9ae31b7ea454bad8679af7e3276d71713db5d1815d84a971bb0e_1790824088925435600_0.json", "raw_sha256": "a764902131a161e2a7978a1f607c4912689efa157d70c2752a5b31e3a042aacb", "revision_guid": "F6B6E1D3-9103-4319-8C45-5BA53EDE0E07", "revision_number": 4, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/F6B6E1D3-9103-4319-8C45-5BA53EDE0E07/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Maximilian Press", "profile_url": "https://biology.stackexchange.com/users/22392/maximilian-press", "user_type": "registered"}, "created_at": "2024-05-29T15:54:51+00:00", "raw_file": "raw/codex_api_v1/41500cf35bca9ae31b7ea454bad8679af7e3276d71713db5d1815d84a971bb0e_1790824088925435600_0.json", "raw_sha256": "a764902131a161e2a7978a1f607c4912689efa157d70c2752a5b31e3a042aacb", "revision_guid": "F7F491C7-A6AE-4CC7-A285-9BCB342B71FB", "revision_number": 5, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/F7F491C7-A6AE-4CC7-A285-9BCB342B71FB/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Maximilian Press", "profile_url": "https://biology.stackexchange.com/users/22392/maximilian-press", "user_type": "registered"}, "created_at": "2024-05-29T16:02:07+00:00", "raw_file": "raw/codex_api_v1/41500cf35bca9ae31b7ea454bad8679af7e3276d71713db5d1815d84a971bb0e_1790824088925435600_0.json", "raw_sha256": "a764902131a161e2a7978a1f607c4912689efa157d70c2752a5b31e3a042aacb", "revision_guid": "7B9A63C5-69E0-473A-8EB0-676C7D3E95EC", "revision_number": 6, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/7B9A63C5-69E0-473A-8EB0-676C7D3E95EC/view-source"}], "score": 4, "updated_at": "2024-05-29T16:02:07+00:00"}, {"answer_html": "There is a misunderstanding here that is very common when first learning about chemical kinetics. First you say:
\n\n\nif $k_{\\rm on}$ and $k_{\\rm off}$ are both constant
\n
but then:
\n\n\nif the velocity is constant
\n
This is not one and the same!
\n$k$ is the rate constant of reaction.* The actual reaction rate (i.e., the change in concentration over time) is given in your example by:
\n$v_{\\rm on} = k_{\\rm on}[A][B]$ for the forward (binding) reaction, and
\n$v_{\\rm off} = k_{\\rm off}[AB]$ for the reverse (unbinding) reaction.
\nSuppose that $k_{\\rm on} > k_{\\rm off}$. Then at first $v_{\\rm on} > v_{\\rm off}$ and the product AB is produced faster than it degrades. Therefore the concentration of AB increases. On the other hand, A and B are consumed in the reaction, so their concentrations decrease.
\nNow look at the equations for reaction rates above! The rate of the forward reaction, $v_{\\rm on}$, depends on concentrations of starting materials, $[A][B]$; and the rate of the reverse reaction, $v_{\\rm off}$, depends on the concentration of product, $[AB]$. Therefore, as the reaction proceeds, $v_{\\rm on}$ must decrease and $v_{\\rm off}$ must increase until they reach equilibrium where both rates are equal.
\n\n
* Note: As a convention, reaction rate constants are usually denoted by lowercase $k$. Uppercase $K$ is reserved for equilibrium constants, or the Michaelis constant $K_M$, or a number of other constants.
\n", "answer_id": 114774, "answer_text": "There is a misunderstanding here that is very common when first learning about chemical kinetics. First you say:\n\n\n\n\n\n\n\nif $k_{\\rm on}$ and $k_{\\rm off}$ are both constant\n\n\n\n\n\n\n\nbut then:\n\n\n\n\n\n\n\nif the velocity is constant\n\n\n\n\n\n\n\nThis is not one and the same!\n\n\n\n\n$k$ is the rate constant of reaction.* The actual reaction rate (i.e., the change in concentration over time) is given in your example by:\n\n\n\n\n$v_{\\rm on} = k_{\\rm on}[A][B]$ for the forward (binding) reaction, and\n\n\n\n\n$v_{\\rm off} = k_{\\rm off}[AB]$ for the reverse (unbinding) reaction.\n\n\n\n\nSuppose that $k_{\\rm on} > k_{\\rm off}$. Then at first $v_{\\rm on} > v_{\\rm off}$ and the product AB is produced faster than it degrades. Therefore the concentration of AB increases. On the other hand, A and B are consumed in the reaction, so their concentrations decrease.\n\n\n\n\nNow look at the equations for reaction rates above! The rate of the forward reaction, $v_{\\rm on}$, depends on concentrations of starting materials, $[A][B]$; and the rate of the reverse reaction, $v_{\\rm off}$, depends on the concentration of product, $[AB]$. Therefore, as the reaction proceeds, $v_{\\rm on}$ must decrease and $v_{\\rm off}$ must increase until they reach equilibrium where both rates are equal.\n\n\n\n\n\n\n\n* Note: As a convention, reaction rate constants are usually denoted by lowercase $k$. Uppercase $K$ is reserved for equilibrium constants, or the Michaelis constant $K_M$, or a number of other constants.", "answer_url": "https://biology.stackexchange.com/a/114774", "author": "knomologs", "author_url": "https://biology.stackexchange.com/users/81058/knomologs", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-05-28T07:12:10+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:27.977583+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/1cbf95322a17dce0fd00a109179063ffe60bcd4bddc6e720f0ca398ee7aa9da8_0.json", "raw_sha256": "a096c86028a279b01346143890b4827bd8ed05afc0a76bd7c8bcb840211dc20e", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/114983;114969;114966;114963;114939;114936;114918;114909;114904;114899;114888;114885;114881;114875;114874;114873;114872;114864;114857;114850;114846;114841;114834;114827;114821;114819;114813;114804;114791;114784;114768;114765;114762;114760;114758;114755;114745;114741;114739;114738;114732;114730;114726;114714;114706;114695;114691;114690;114686;114683;114677;114675;114666;114660;114656;114653;114642;114641;114632;114628;114620;114618;114613;114601;114599;114597;114581;114577;114573;114567;114558;114555;114553;114552;114547;114545;114543;114542;114541;114539;114529;114524;114516;114502;114501;114498;114495;114492;114481;114476;114474;114470;114453;114451;114449;114448;114446;114440;114438;114435/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 114768, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "knomologs", "profile_url": "https://biology.stackexchange.com/users/81058/knomologs", "user_type": "registered"}, "created_at": "2024-05-28T07:12:10+00:00", "raw_file": "raw/codex_api_v1/41500cf35bca9ae31b7ea454bad8679af7e3276d71713db5d1815d84a971bb0e_1790824088925435600_0.json", "raw_sha256": "a764902131a161e2a7978a1f607c4912689efa157d70c2752a5b31e3a042aacb", "revision_guid": "313FA75B-43C6-4396-8899-8F5A827A0F14", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/313FA75B-43C6-4396-8899-8F5A827A0F14/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Ilmari Karonen", "profile_url": "https://biology.stackexchange.com/users/239/ilmari-karonen", "user_type": "registered"}, "created_at": "2024-05-28T08:54:26+00:00", "raw_file": "raw/codex_api_v1/41500cf35bca9ae31b7ea454bad8679af7e3276d71713db5d1815d84a971bb0e_1790824088925435600_0.json", "raw_sha256": "a764902131a161e2a7978a1f607c4912689efa157d70c2752a5b31e3a042aacb", "revision_guid": "9D91925C-3E92-4DDA-BB75-8BF48F945F36", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/9D91925C-3E92-4DDA-BB75-8BF48F945F36/view-source"}], "score": 11, "updated_at": "2024-05-28T08:54:26+00:00"}], "ground_truth": "community signals only; no scientific truth label", "product": "ranking", "question": "I would like to understand the classic kinetic model of association / dissociation that tries to describe the concentration of a compound $[\\ce{AB}]$.\nLet's say we have a model:\n\n\n\n\n$\\ce{A + B} \\xrightleftharpoons[k_{\\text{off}}]{k_{\\text{on}}} \\ce{AB}$\n\n\n\n\nSo $k_{\\text{on}}$ is the rate of binding and $k_{\\text{off}}$ is the rate of unbinding and the rate equation is:\n\n\n\n\n$\\frac{d[\\ce{AB}]}{dt}=k_{\\text{on}}[\\ce{A}][\\ce{B}]-k_{\\text{off}}[\\ce{AB}]$\n\n\n\n\nI don't understand why texts say that if $k_{\\text{on}}$ and $k_{\\text{off}}$ are both constant then we reach a steady state, i.e., $k_{\\text{on}}\\ce{AB}=k_{\\text{off}}[\\ce{AB}]$ I mean: if, for example, the rate of binding, is greater then the rate of unbinding, shouldn't the concentration of the final compound increase up to infinity? What I have in mind is: we produce 4 proteins per second and degrade 2 proteins per second, then the net production is 2 proteins per second so, as time goes by, the concentration should increase and doesn't reach a plateau.\n\n\n\n\nWhy do we instead reach a plateau in the final concentration? I can understand the plateau in the plot of the reaction velocity but still, if the velocity is constant, still the concentration of the final compound should increase.", "record_id": "Scientific-Answer-Ranking:biology:114768", "scores": [4, 11], "split": "holdout", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "Update: As noted by commenter, the example stated in the question is not actually Michaelis-Menten but is rather an example of binding kinetics. See also the other answer, which is likely more relevant.
\nI would suggest, if you would like to find the steady-state concentration of $[AB]$, that you can solve this yourself mathematically. Try differentiating and setting the $\\Delta [AB]$ side of the equation to zero, and solving. You will find:
\n$ \\Delta [AB] = (k_{on}[A][B] - k_{off}[AB])\\Delta t$
\n$ 0 = (k_{on}[A][B] - k_{off}[AB])\\Delta t$
\nRearranging:
\n$k_{on}[A][B] = k_{off}[AB] $
\nAnd finally:
\n$\\frac{[AB]}{[A][B]} = \\frac{k_{on}}{k_{off}}$
\nNote that if the $k$ are constant, this amounts to the law of mass action.
\nYou can also do a forward simulation (see R code):
\n# association/dissociation kinetics\nkinetic_sim = function(k_on, k_off, a, b) {\n ab = 0\n ab_ts = c()\n a_ts = c()\n b_ts = c()\n for (i in 1:1000) {\n ab_old = ab\n ab = ab * (1 - k_off) + k_on * (a * b)\n a = a - a*b*k_on + ab_old * k_off\n b = b - a*b*k_on + ab_old * k_off\n #cat(i, a, b, ab, k_on*a*b, k_off*ab, "\\n", sep=" ")\n ab_ts = append(ab_ts, ab)\n a_ts = append(a_ts, a)\n b_ts = append(b_ts, b)\n \n }\n return(list(ab_ts, a_ts, b_ts))\n}\nout = kinetic_sim(.1, .2, 1, 1)\nplot(out[[1]] / (out[[2]] * out[[3]]), ylab="[AB] / ([A] * [B])", xlab="time step")\nplot(out[[1]], ylab="[AB]", xlab="time step")\n\n
You can see that both the ratio and the final concentration equilibrate.
\n", "answer_id": 114769, "answer_text": "Update: As noted by commenter, the example stated in the question is not actually Michaelis-Menten but is rather an example of binding kinetics. See also the other answer, which is likely more relevant.\n\n\n\n\nI would suggest, if you would like to find the steady-state concentration of $[AB]$, that you can solve this yourself mathematically. Try differentiating and setting the $\\Delta [AB]$ side of the equation to zero, and solving. You will find:\n\n\n\n\n$ \\Delta [AB] = (k_{on}[A][B] - k_{off}[AB])\\Delta t$\n\n\n\n\n$ 0 = (k_{on}[A][B] - k_{off}[AB])\\Delta t$\n\n\n\n\nRearranging:\n\n\n\n\n$k_{on}[A][B] = k_{off}[AB] $\n\n\n\n\nAnd finally:\n\n\n\n\n$\\frac{[AB]}{[A][B]} = \\frac{k_{on}}{k_{off}}$\n\n\n\n\nNote that if the $k$ are constant, this amounts to the law of mass action.\n\n\n\n\nYou can also do a forward simulation (see R code):\n\n\n\n\n# association/dissociation kinetics\nkinetic_sim = function(k_on, k_off, a, b) {\n ab = 0\n ab_ts = c()\n a_ts = c()\n b_ts = c()\n for (i in 1:1000) {\n ab_old = ab\n ab = ab * (1 - k_off) + k_on * (a * b)\n a = a - a*b*k_on + ab_old * k_off\n b = b - a*b*k_on + ab_old * k_off\n #cat(i, a, b, ab, k_on*a*b, k_off*ab, \"\\n\", sep=\" \")\n ab_ts = append(ab_ts, ab)\n a_ts = append(a_ts, a)\n b_ts = append(b_ts, b)\n \n }\n return(list(ab_ts, a_ts, b_ts))\n}\nout = kinetic_sim(.1, .2, 1, 1)\nplot(out[[1]] / (out[[2]] * out[[3]]), ylab=\"[AB] / ([A] * [B])\", xlab=\"time step\")\nplot(out[[1]], ylab=\"[AB]\", xlab=\"time step\")\n\n\n\n\n\n[image: concentration of ratio [AB]:[A]*[B] over time; source: https://i.sstatic.net/Lw4hnYdr.png] (https://i.sstatic.net/Lw4hnYdr.png)\n[image: concentration of ratio [AB] over time; source: https://i.sstatic.net/pzN8ZZif.png] (https://i.sstatic.net/pzN8ZZif.png)\n\n\n\n\nYou can see that both the ratio and the final concentration equilibrate.", "answer_url": "https://biology.stackexchange.com/a/114769", "author": "Maximilian Press", "author_url": "https://biology.stackexchange.com/users/22392/maximilian-press", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-05-27T18:34:26+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:27.977583+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/1cbf95322a17dce0fd00a109179063ffe60bcd4bddc6e720f0ca398ee7aa9da8_0.json", "raw_sha256": "a096c86028a279b01346143890b4827bd8ed05afc0a76bd7c8bcb840211dc20e", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/114983;114969;114966;114963;114939;114936;114918;114909;114904;114899;114888;114885;114881;114875;114874;114873;114872;114864;114857;114850;114846;114841;114834;114827;114821;114819;114813;114804;114791;114784;114768;114765;114762;114760;114758;114755;114745;114741;114739;114738;114732;114730;114726;114714;114706;114695;114691;114690;114686;114683;114677;114675;114666;114660;114656;114653;114642;114641;114632;114628;114620;114618;114613;114601;114599;114597;114581;114577;114573;114567;114558;114555;114553;114552;114547;114545;114543;114542;114541;114539;114529;114524;114516;114502;114501;114498;114495;114492;114481;114476;114474;114470;114453;114451;114449;114448;114446;114440;114438;114435/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 114768, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Maximilian Press", "profile_url": "https://biology.stackexchange.com/users/22392/maximilian-press", "user_type": "registered"}, "created_at": "2024-05-27T18:34:26+00:00", "raw_file": "raw/codex_api_v1/41500cf35bca9ae31b7ea454bad8679af7e3276d71713db5d1815d84a971bb0e_1790824088925435600_0.json", "raw_sha256": "a764902131a161e2a7978a1f607c4912689efa157d70c2752a5b31e3a042aacb", "revision_guid": "2F432EEF-5BF3-4FFE-B7E3-7AB1C8116BB1", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/2F432EEF-5BF3-4FFE-B7E3-7AB1C8116BB1/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Maximilian Press", "profile_url": "https://biology.stackexchange.com/users/22392/maximilian-press", "user_type": "registered"}, "created_at": "2024-05-27T19:01:38+00:00", "raw_file": "raw/codex_api_v1/41500cf35bca9ae31b7ea454bad8679af7e3276d71713db5d1815d84a971bb0e_1790824088925435600_0.json", "raw_sha256": "a764902131a161e2a7978a1f607c4912689efa157d70c2752a5b31e3a042aacb", "revision_guid": "F76C5C34-436D-4C68-9446-B7AA8D46C53D", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/F76C5C34-436D-4C68-9446-B7AA8D46C53D/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Maximilian Press", "profile_url": "https://biology.stackexchange.com/users/22392/maximilian-press", "user_type": "registered"}, "created_at": "2024-05-27T23:07:19+00:00", "raw_file": "raw/codex_api_v1/41500cf35bca9ae31b7ea454bad8679af7e3276d71713db5d1815d84a971bb0e_1790824088925435600_0.json", "raw_sha256": "a764902131a161e2a7978a1f607c4912689efa157d70c2752a5b31e3a042aacb", "revision_guid": "66A6E2A9-6D6D-44A5-9689-4CA42FD819D5", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/66A6E2A9-6D6D-44A5-9689-4CA42FD819D5/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "TAR86", "profile_url": "https://biology.stackexchange.com/users/32467/tar86", "user_type": "registered"}, "created_at": "2024-05-28T18:28:08+00:00", "raw_file": "raw/codex_api_v1/41500cf35bca9ae31b7ea454bad8679af7e3276d71713db5d1815d84a971bb0e_1790824088925435600_0.json", "raw_sha256": "a764902131a161e2a7978a1f607c4912689efa157d70c2752a5b31e3a042aacb", "revision_guid": "F6B6E1D3-9103-4319-8C45-5BA53EDE0E07", "revision_number": 4, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/F6B6E1D3-9103-4319-8C45-5BA53EDE0E07/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Maximilian Press", "profile_url": "https://biology.stackexchange.com/users/22392/maximilian-press", "user_type": "registered"}, "created_at": "2024-05-29T15:54:51+00:00", "raw_file": "raw/codex_api_v1/41500cf35bca9ae31b7ea454bad8679af7e3276d71713db5d1815d84a971bb0e_1790824088925435600_0.json", "raw_sha256": "a764902131a161e2a7978a1f607c4912689efa157d70c2752a5b31e3a042aacb", "revision_guid": "F7F491C7-A6AE-4CC7-A285-9BCB342B71FB", "revision_number": 5, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/F7F491C7-A6AE-4CC7-A285-9BCB342B71FB/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Maximilian Press", "profile_url": "https://biology.stackexchange.com/users/22392/maximilian-press", "user_type": "registered"}, "created_at": "2024-05-29T16:02:07+00:00", "raw_file": "raw/codex_api_v1/41500cf35bca9ae31b7ea454bad8679af7e3276d71713db5d1815d84a971bb0e_1790824088925435600_0.json", "raw_sha256": "a764902131a161e2a7978a1f607c4912689efa157d70c2752a5b31e3a042aacb", "revision_guid": "7B9A63C5-69E0-473A-8EB0-676C7D3E95EC", "revision_number": 6, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/7B9A63C5-69E0-473A-8EB0-676C7D3E95EC/view-source"}], "score": 4, "updated_at": "2024-05-29T16:02:07+00:00"}, {"answer_html": "There is a misunderstanding here that is very common when first learning about chemical kinetics. First you say:
\n\n\nif $k_{\\rm on}$ and $k_{\\rm off}$ are both constant
\n
but then:
\n\n\nif the velocity is constant
\n
This is not one and the same!
\n$k$ is the rate constant of reaction.* The actual reaction rate (i.e., the change in concentration over time) is given in your example by:
\n$v_{\\rm on} = k_{\\rm on}[A][B]$ for the forward (binding) reaction, and
\n$v_{\\rm off} = k_{\\rm off}[AB]$ for the reverse (unbinding) reaction.
\nSuppose that $k_{\\rm on} > k_{\\rm off}$. Then at first $v_{\\rm on} > v_{\\rm off}$ and the product AB is produced faster than it degrades. Therefore the concentration of AB increases. On the other hand, A and B are consumed in the reaction, so their concentrations decrease.
\nNow look at the equations for reaction rates above! The rate of the forward reaction, $v_{\\rm on}$, depends on concentrations of starting materials, $[A][B]$; and the rate of the reverse reaction, $v_{\\rm off}$, depends on the concentration of product, $[AB]$. Therefore, as the reaction proceeds, $v_{\\rm on}$ must decrease and $v_{\\rm off}$ must increase until they reach equilibrium where both rates are equal.
\n\n
* Note: As a convention, reaction rate constants are usually denoted by lowercase $k$. Uppercase $K$ is reserved for equilibrium constants, or the Michaelis constant $K_M$, or a number of other constants.
\n", "answer_id": 114774, "answer_text": "There is a misunderstanding here that is very common when first learning about chemical kinetics. First you say:\n\n\n\n\n\n\n\nif $k_{\\rm on}$ and $k_{\\rm off}$ are both constant\n\n\n\n\n\n\n\nbut then:\n\n\n\n\n\n\n\nif the velocity is constant\n\n\n\n\n\n\n\nThis is not one and the same!\n\n\n\n\n$k$ is the rate constant of reaction.* The actual reaction rate (i.e., the change in concentration over time) is given in your example by:\n\n\n\n\n$v_{\\rm on} = k_{\\rm on}[A][B]$ for the forward (binding) reaction, and\n\n\n\n\n$v_{\\rm off} = k_{\\rm off}[AB]$ for the reverse (unbinding) reaction.\n\n\n\n\nSuppose that $k_{\\rm on} > k_{\\rm off}$. Then at first $v_{\\rm on} > v_{\\rm off}$ and the product AB is produced faster than it degrades. Therefore the concentration of AB increases. On the other hand, A and B are consumed in the reaction, so their concentrations decrease.\n\n\n\n\nNow look at the equations for reaction rates above! The rate of the forward reaction, $v_{\\rm on}$, depends on concentrations of starting materials, $[A][B]$; and the rate of the reverse reaction, $v_{\\rm off}$, depends on the concentration of product, $[AB]$. Therefore, as the reaction proceeds, $v_{\\rm on}$ must decrease and $v_{\\rm off}$ must increase until they reach equilibrium where both rates are equal.\n\n\n\n\n\n\n\n* Note: As a convention, reaction rate constants are usually denoted by lowercase $k$. Uppercase $K$ is reserved for equilibrium constants, or the Michaelis constant $K_M$, or a number of other constants.", "answer_url": "https://biology.stackexchange.com/a/114774", "author": "knomologs", "author_url": "https://biology.stackexchange.com/users/81058/knomologs", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-05-28T07:12:10+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:27.977583+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/1cbf95322a17dce0fd00a109179063ffe60bcd4bddc6e720f0ca398ee7aa9da8_0.json", "raw_sha256": "a096c86028a279b01346143890b4827bd8ed05afc0a76bd7c8bcb840211dc20e", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/114983;114969;114966;114963;114939;114936;114918;114909;114904;114899;114888;114885;114881;114875;114874;114873;114872;114864;114857;114850;114846;114841;114834;114827;114821;114819;114813;114804;114791;114784;114768;114765;114762;114760;114758;114755;114745;114741;114739;114738;114732;114730;114726;114714;114706;114695;114691;114690;114686;114683;114677;114675;114666;114660;114656;114653;114642;114641;114632;114628;114620;114618;114613;114601;114599;114597;114581;114577;114573;114567;114558;114555;114553;114552;114547;114545;114543;114542;114541;114539;114529;114524;114516;114502;114501;114498;114495;114492;114481;114476;114474;114470;114453;114451;114449;114448;114446;114440;114438;114435/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 114768, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "knomologs", "profile_url": "https://biology.stackexchange.com/users/81058/knomologs", "user_type": "registered"}, "created_at": "2024-05-28T07:12:10+00:00", "raw_file": "raw/codex_api_v1/41500cf35bca9ae31b7ea454bad8679af7e3276d71713db5d1815d84a971bb0e_1790824088925435600_0.json", "raw_sha256": "a764902131a161e2a7978a1f607c4912689efa157d70c2752a5b31e3a042aacb", "revision_guid": "313FA75B-43C6-4396-8899-8F5A827A0F14", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/313FA75B-43C6-4396-8899-8F5A827A0F14/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Ilmari Karonen", "profile_url": "https://biology.stackexchange.com/users/239/ilmari-karonen", "user_type": "registered"}, "created_at": "2024-05-28T08:54:26+00:00", "raw_file": "raw/codex_api_v1/41500cf35bca9ae31b7ea454bad8679af7e3276d71713db5d1815d84a971bb0e_1790824088925435600_0.json", "raw_sha256": "a764902131a161e2a7978a1f607c4912689efa157d70c2752a5b31e3a042aacb", "revision_guid": "9D91925C-3E92-4DDA-BB75-8BF48F945F36", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/9D91925C-3E92-4DDA-BB75-8BF48F945F36/view-source"}], "score": 11, "updated_at": "2024-05-28T08:54:26+00:00"}], "domain": "biology", "external_links": ["https://i.sstatic.net/Lw4hnYdr.png", "https://i.sstatic.net/pzN8ZZif.png"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:07.165481+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/b97a755f39b54a1e8a057fa5e484426784aa17a1971c6ef0ca759105de983078_0.json", "raw_sha256": "4c9dcc077d306d60a8b8a237ad3f9b3144c0d5885fa62ef1bfdd55d2fbbdaf6a", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=6&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Salmon", "question_author_url": "https://biology.stackexchange.com/users/81048/salmon", "question_author_user_type": "registered", "question_created_at": "2024-05-27T17:53:29+00:00", "question_html": "I would like to understand the classic kinetic model of association / dissociation that tries to describe the concentration of a compound $[\\ce{AB}]$.\nLet's say we have a model:
\n$\\ce{A + B} \\xrightleftharpoons[k_{\\text{off}}]{k_{\\text{on}}} \\ce{AB}$
\nSo $k_{\\text{on}}$ is the rate of binding and $k_{\\text{off}}$ is the rate of unbinding and the rate equation is:
\n$\\frac{d[\\ce{AB}]}{dt}=k_{\\text{on}}[\\ce{A}][\\ce{B}]-k_{\\text{off}}[\\ce{AB}]$
\nI don't understand why texts say that if $k_{\\text{on}}$ and $k_{\\text{off}}$ are both constant then we reach a steady state, i.e., $k_{\\text{on}}\\ce{AB}=k_{\\text{off}}[\\ce{AB}]$ I mean: if, for example, the rate of binding, is greater then the rate of unbinding, shouldn't the concentration of the final compound increase up to infinity? What I have in mind is: we produce 4 proteins per second and degrade 2 proteins per second, then the net production is 2 proteins per second so, as time goes by, the concentration should increase and doesn't reach a plateau.
\nWhy do we instead reach a plateau in the final concentration? I can understand the plateau in the plot of the reaction velocity but still, if the velocity is constant, still the concentration of the final compound should increase.
\n", "question_id": 114768, "question_license": "CC BY-SA 4.0", "question_score": 9, "question_text": "I would like to understand the classic kinetic model of association / dissociation that tries to describe the concentration of a compound $[\\ce{AB}]$.\nLet's say we have a model:\n\n\n\n\n$\\ce{A + B} \\xrightleftharpoons[k_{\\text{off}}]{k_{\\text{on}}} \\ce{AB}$\n\n\n\n\nSo $k_{\\text{on}}$ is the rate of binding and $k_{\\text{off}}$ is the rate of unbinding and the rate equation is:\n\n\n\n\n$\\frac{d[\\ce{AB}]}{dt}=k_{\\text{on}}[\\ce{A}][\\ce{B}]-k_{\\text{off}}[\\ce{AB}]$\n\n\n\n\nI don't understand why texts say that if $k_{\\text{on}}$ and $k_{\\text{off}}$ are both constant then we reach a steady state, i.e., $k_{\\text{on}}\\ce{AB}=k_{\\text{off}}[\\ce{AB}]$ I mean: if, for example, the rate of binding, is greater then the rate of unbinding, shouldn't the concentration of the final compound increase up to infinity? What I have in mind is: we produce 4 proteins per second and degrade 2 proteins per second, then the net production is 2 proteins per second so, as time goes by, the concentration should increase and doesn't reach a plateau.\n\n\n\n\nWhy do we instead reach a plateau in the final concentration? I can understand the plateau in the plot of the reaction velocity but still, if the velocity is constant, still the concentration of the final compound should increase.", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Salmon", "profile_url": "https://biology.stackexchange.com/users/81048/salmon", "user_type": "registered"}, "created_at": "2024-05-27T17:53:29+00:00", "raw_file": "raw/codex_api_v1/41500cf35bca9ae31b7ea454bad8679af7e3276d71713db5d1815d84a971bb0e_1790824088925435600_0.json", "raw_sha256": "a764902131a161e2a7978a1f607c4912689efa157d70c2752a5b31e3a042aacb", "revision_guid": "8F6A9C82-AB24-4AAA-AEA4-4CCEC307A30D", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/8F6A9C82-AB24-4AAA-AEA4-4CCEC307A30D/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2024-05-28T01:55:54+00:00", "raw_file": "raw/codex_api_v1/41500cf35bca9ae31b7ea454bad8679af7e3276d71713db5d1815d84a971bb0e_1790824088925435600_0.json", "raw_sha256": "a764902131a161e2a7978a1f607c4912689efa157d70c2752a5b31e3a042aacb", "revision_guid": "67E06F37-A278-489B-9151-42F43CC33901", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/67E06F37-A278-489B-9151-42F43CC33901/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Eonema", "profile_url": "https://biology.stackexchange.com/users/61325/eonema", "user_type": "registered"}, "created_at": "2024-05-28T18:27:34+00:00", "raw_file": "raw/codex_api_v1/41500cf35bca9ae31b7ea454bad8679af7e3276d71713db5d1815d84a971bb0e_1790824088925435600_0.json", "raw_sha256": "a764902131a161e2a7978a1f607c4912689efa157d70c2752a5b31e3a042aacb", "revision_guid": "1BE03709-7FDD-4B62-AC28-EA9679360587", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/1BE03709-7FDD-4B62-AC28-EA9679360587/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "terdon", "profile_url": "https://biology.stackexchange.com/users/1306/terdon", "user_type": "moderator"}, "created_at": "2024-05-29T09:20:12+00:00", "raw_file": "raw/codex_api_v1/41500cf35bca9ae31b7ea454bad8679af7e3276d71713db5d1815d84a971bb0e_1790824088925435600_0.json", "raw_sha256": "a764902131a161e2a7978a1f607c4912689efa157d70c2752a5b31e3a042aacb", "revision_guid": "EA80ADAF-D374-4B5D-AD65-EB7FFB2E5272", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/EA80ADAF-D374-4B5D-AD65-EB7FFB2E5272/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Maximilian Press", "profile_url": "https://biology.stackexchange.com/users/22392/maximilian-press", "user_type": "registered"}, "created_at": "2024-05-29T15:57:09+00:00", "raw_file": "raw/codex_api_v1/41500cf35bca9ae31b7ea454bad8679af7e3276d71713db5d1815d84a971bb0e_1790824088925435600_0.json", "raw_sha256": "a764902131a161e2a7978a1f607c4912689efa157d70c2752a5b31e3a042aacb", "revision_guid": "65B6CB44-E4EC-42B0-A71E-63D9F3F3ADB1", "revision_number": 4, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/65B6CB44-E4EC-42B0-A71E-63D9F3F3ADB1/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "David", "profile_url": "https://biology.stackexchange.com/users/22057/david", "user_type": "registered"}, "created_at": "2024-06-01T17:40:24+00:00", "raw_file": "raw/codex_api_v1/41500cf35bca9ae31b7ea454bad8679af7e3276d71713db5d1815d84a971bb0e_1790824088925435600_0.json", "raw_sha256": "a764902131a161e2a7978a1f607c4912689efa157d70c2752a5b31e3a042aacb", "revision_guid": "DF937FB9-3603-49F8-9865-D03B3F660F75", "revision_number": 5, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/DF937FB9-3603-49F8-9865-D03B3F660F75/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/114768/understanding-association-kinetics", "split": "holdout", "split_group": "8b0f36cc135364768cd90ac330640c6f0b50ae8f7a33283b023303c13e7f6e98", "tags": ["biochemistry", "enzymes", "kinetics"], "thread_id": "biology:114768", "title": "Understanding association kinetics"}}