{ "cells": [ { "cell_type": "markdown", "id": "49bcb5b0-f19d-4b96-a5f1-e0ae30f66d8f", "metadata": {}, "source": [ "## Macromolecules : Binding Affinity and Fractional Occupancy\n", " \n", "\n", "LAST REVISED: June 23, 2024 (using v. 1.0 beta36)" ] }, { "cell_type": "code", "execution_count": 1, "id": "98adb66e-e336-4a4e-9a47-d48e9f0c8c68", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Added 'D:\\Docs\\- MY CODE\\BioSimulations\\life123-Win7' to sys.path\n" ] } ], "source": [ "import set_path # Importing this module will add the project's home directory to sys.path" ] }, { "cell_type": "code", "execution_count": 2, "id": "c1ac7763", "metadata": { "tags": [] }, "outputs": [], "source": [ "from life123 import ChemData\n", "from life123 import UniformCompartment\n", "from life123 import MovieTabular\n", "\n", "import numpy as np\n", "\n", "import plotly.express as px" ] }, { "cell_type": "code", "execution_count": 3, "id": "23c15e66-52e4-495b-aa3d-ecddd8d16942", "metadata": { "lines_to_next_cell": 2 }, "outputs": [], "source": [ "# Initialize the system\n", "chem = ChemData(names=[\"A\", \"B\", \"C\"])" ] }, { "cell_type": "markdown", "id": "83fd43d2-6a90-4b24-ae2c-5a65718e416d", "metadata": {}, "source": [ "## Explore methods to manage the data structure for macromolecules" ] }, { "cell_type": "code", "execution_count": 4, "id": "e3aa4733-dd9d-485d-a899-a9a03ff40d87", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "['M1']" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "chem.add_macromolecules(\"M1\")\n", "chem.get_macromolecules()" ] }, { "cell_type": "code", "execution_count": 5, "id": "acbd2b50-8bc1-4e23-8816-0da0ee85b461", "metadata": {}, "outputs": [], "source": [ "chem.set_binding_site_affinity(\"M1\", site_number=3, ligand=\"A\", Kd=1.0)\n", "chem.set_binding_site_affinity(\"M1\", site_number=8, ligand=\"B\", Kd=3.2)\n", "chem.set_binding_site_affinity(\"M1\", site_number=15, ligand=\"A\", Kd=10.0)\n", "\n", "chem.set_binding_site_affinity(\"M2\", site_number=1, ligand=\"C\", Kd=5.6) # \"M2\" will get automatically added\n", "chem.set_binding_site_affinity(\"M2\", site_number=2, ligand=\"A\", Kd=0.01)" ] }, { "cell_type": "code", "execution_count": 6, "id": "86e39939-7e26-4cfd-af63-a4a536966927", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "M1 :\n", " Site 3 - Kd (dissociation const) for A : 1.0\n", " Site 8 - Kd (dissociation const) for B : 3.2\n", " Site 15 - Kd (dissociation const) for A : 10.0\n", "M2 :\n", " Site 1 - Kd (dissociation const) for C : 5.6\n", " Site 2 - Kd (dissociation const) for A : 0.01\n" ] } ], "source": [ "chem.show_binding_affinities() # Review the values we have given for the dissociation constants" ] }, { "cell_type": "code", "execution_count": 7, "id": "fecbf8df-1e28-4b0b-99ec-d3d76923dfe4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[3, 8, 15]" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "chem.get_binding_sites(\"M1\")" ] }, { "cell_type": "code", "execution_count": 8, "id": "0c805eec-10a2-44e1-b543-eeb8b39510a7", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{3: 'A', 8: 'B', 15: 'A'}" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "chem.get_binding_sites_and_ligands(\"M1\")" ] }, { "cell_type": "code", "execution_count": 9, "id": "db43fb3f-0f1f-4d46-8371-b23b1deab647", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[1, 2]" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "chem.get_binding_sites(\"M2\")" ] }, { "cell_type": "code", "execution_count": 10, "id": "36a5710b-f3db-4478-a91d-2a3ad4a576da", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{1: 'C', 2: 'A'}" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "chem.get_binding_sites_and_ligands(\"M2\")" ] }, { "cell_type": "code", "execution_count": 11, "id": "afae6257-830f-4636-898f-c5af9529ab78", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "ChemicalAffinity(chemical='C', Kd=5.6)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "aff = chem.get_binding_site_affinity(macromolecule=\"M2\", site_number=1) # A \"NamedTuple\" gets returned\n", "aff" ] }, { "cell_type": "code", "execution_count": 12, "id": "4124f99a-e474-43cd-8854-ce71ad870987", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'C'" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "aff.chemical" ] }, { "cell_type": "code", "execution_count": 13, "id": "647ee66c-f7c7-4677-9c05-2b309d06fd89", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "5.6" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "aff.Kd" ] }, { "cell_type": "code", "execution_count": null, "id": "cf6ed2ea-04b8-48d6-a20b-120f22b4732d", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "7899d8b1-3b0f-4243-895d-6ba51f0174d7", "metadata": {}, "source": [ "## Start setting up the dynamical system" ] }, { "cell_type": "code", "execution_count": 14, "id": "73fb80ce-a07c-464d-81e4-814955b613ee", "metadata": {}, "outputs": [], "source": [ "dynamics = UniformCompartment(chem_data=chem)" ] }, { "cell_type": "code", "execution_count": 15, "id": "85d19965-4a82-4868-9a1f-cbf6fc29b6cd", "metadata": {}, "outputs": [], "source": [ "dynamics.set_macromolecules() # By default, set counts to 1 for all the registered macromolecules" ] }, { "cell_type": "code", "execution_count": 16, "id": "ccd16fb4-f5de-474c-b85d-28a3f64e815b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "3 species:\n", " Species 0 (A). No concentrations set yet\n", " Species 1 (B). No concentrations set yet\n", " Species 2 (C). No concentrations set yet\n", "Macro-molecules, with their counts: {'M1': 1, 'M2': 1}\n", "Fractional Occupancy at the various binding sites for each macro-molecule:\n", " M1 || 3: 0.0 (A) | 8: 0.0 (B) | 15: 0.0 (A)\n", " M2 || 1: 0.0 (C) | 2: 0.0 (A)\n", "Set of chemicals involved in reactions: set()\n" ] } ], "source": [ "dynamics.describe_state()" ] }, { "cell_type": "markdown", "id": "9c712242-7dca-4a90-b743-df1e4e3fbc6e", "metadata": {}, "source": [ "### Inspect some class attributes (not to be directly modified by the end user!)" ] }, { "cell_type": "code", "execution_count": 17, "id": "71326536-e56b-4499-a78a-7149ccc9b727", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'M1': 1, 'M2': 1}" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.macro_system" ] }, { "cell_type": "code", "execution_count": 18, "id": "5ffd0c72-67cd-4150-ad8e-89382622c591", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'M1': {3: ('A', 0.0), 8: ('B', 0.0), 15: ('A', 0.0)},\n", " 'M2': {1: ('C', 0.0), 2: ('A', 0.0)}}" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.macro_system_state" ] }, { "cell_type": "markdown", "id": "0e771dda-1c0f-4fc0-ab21-049740643897", "metadata": {}, "source": [ "### Set the initial concentrations of all the ligands" ] }, { "cell_type": "code", "execution_count": 19, "id": "5563e467-a637-44fa-9ba1-d35ddd82c887", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "3 species:\n", " Species 0 (A). Conc: 10.0\n", " Species 1 (B). Conc: 0.0\n", " Species 2 (C). Conc: 0.56\n", "Macro-molecules, with their counts: {'M1': 1, 'M2': 1}\n", "Fractional Occupancy at the various binding sites for each macro-molecule:\n", " M1 || 3: 0.0 (A) | 8: 0.0 (B) | 15: 0.0 (A)\n", " M2 || 1: 0.0 (C) | 2: 0.0 (A)\n", "Set of chemicals involved in reactions: set()\n" ] } ], "source": [ "dynamics.set_conc(conc={\"A\": 10., \"B\": 0., \"C\": 0.56})\n", "dynamics.describe_state()" ] }, { "cell_type": "markdown", "id": "ad018b3c-e331-4fa9-92d6-b49c63aff226", "metadata": {}, "source": [ "### Determine and adjust the fractional occupancy of the various sites on the macromolecules, based on the current ligand concentrations" ] }, { "cell_type": "code", "execution_count": 20, "id": "6c1dc8cb", "metadata": {}, "outputs": [], "source": [ "dynamics.update_occupancy()" ] }, { "cell_type": "code", "execution_count": 21, "id": "42c2f8f4-bea5-4d21-a1ad-4ab76d34cb3e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "3 species:\n", " Species 0 (A). Conc: 10.0\n", " Species 1 (B). Conc: 0.0\n", " Species 2 (C). Conc: 0.56\n", "Macro-molecules, with their counts: {'M1': 1, 'M2': 1}\n", "Fractional Occupancy at the various binding sites for each macro-molecule:\n", " M1 || 3: 0.8999999930397401 (A) | 8: 1.6007639537264433e-15 (B) | 15: 0.5 (A)\n", " M2 || 1: 0.10000000696026 (C) | 2: 0.9986301366689166 (A)\n", "Set of chemicals involved in reactions: set()\n" ] } ], "source": [ "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 22, "id": "660d99ff-ddd0-419b-b40a-25ac27aa1d1f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "M1 :\n", " Site 3 - Kd (dissociation const) for A : 1.0\n", " Site 8 - Kd (dissociation const) for B : 3.2\n", " Site 15 - Kd (dissociation const) for A : 10.0\n", "M2 :\n", " Site 1 - Kd (dissociation const) for C : 5.6\n", " Site 2 - Kd (dissociation const) for A : 0.01\n" ] } ], "source": [ "dynamics.chem_data.show_binding_affinities() # Review the values we had given for the dissociation constants" ] }, { "cell_type": "markdown", "id": "202f78e9-9c87-43b6-b2e0-9addce298262", "metadata": {}, "source": [ "#### Notes:\n", "**[B] = 0** => Occupancy of binding site 8 of M1 is also zero\n", "\n", "**[A] = 10.0** : \n", " * 10x the dissociation constant of A to site 3 of M1 (resulting in occupancy 0.9) \n", " * same as the dissociation constant of A to site 15 of M1 (occupancy 0.5) \n", " * 1,000x the dissociation constant of A to site 2 of M2 (occupancy almost 1, i.e. nearly saturated)\n", " \n", " \n", "**[C] = 0.56** => 1/10 of the dissociation constant of C to site 1 of M2 (occupancy 0.1)" ] }, { "cell_type": "code", "execution_count": null, "id": "1caef55c-558b-462a-8b5e-a1474fd78092", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "22d48dc6-5876-4982-b37d-c9209a2bd811", "metadata": {}, "source": [ "### Adjust the concentration of one ligand, [A], and update all the fractional occupancies accordingly" ] }, { "cell_type": "code", "execution_count": 23, "id": "222dc35e-0804-455a-8019-2372272a5899", "metadata": {}, "outputs": [], "source": [ "dynamics.set_single_conc(conc=1000., species_name=\"A\", snapshot=False)" ] }, { "cell_type": "code", "execution_count": 24, "id": "f4b30f28-1f55-46e7-a51d-60d0f580828f", "metadata": {}, "outputs": [], "source": [ "dynamics.update_occupancy()" ] }, { "cell_type": "code", "execution_count": 25, "id": "a3c63fb6-fb88-4c08-9617-3405032ffab2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "3 species:\n", " Species 0 (A). Conc: 1000.0\n", " Species 1 (B). Conc: 0.0\n", " Species 2 (C). Conc: 0.56\n", "Macro-molecules, with their counts: {'M1': 1, 'M2': 1}\n", "Fractional Occupancy at the various binding sites for each macro-molecule:\n", " M1 || 3: 0.9986301366689166 (A) | 8: 1.6007639537264433e-15 (B) | 15: 0.9878048761855343 (A)\n", " M2 || 1: 0.10000000696026 (C) | 2: 0.9999830651924357 (A)\n", "Set of chemicals involved in reactions: set()\n" ] } ], "source": [ "dynamics.describe_state()" ] }, { "cell_type": "markdown", "id": "85671b32-485d-46f9-a21d-e6f711e7ed73", "metadata": {}, "source": [ "#### Note how all the various binding sites for ligand A, across all macromolecules, now have a different value for the fractional occupancy (very close to 1 because of the large value of [A] relative to each of the dissociation constants for A.)\n", "The fractional occupancies for the other ligands (B and C) did not change" ] }, { "cell_type": "code", "execution_count": null, "id": "0468fcfe-8511-4c81-9f47-4b2f4a24d76a", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "08d7c9fd-1bfd-459a-bd45-e8c4bfb8130b", "metadata": {}, "source": [ "### Sweep the values of [A] across a wide range, and compute/store how the fractional occupancies of A change" ] }, { "cell_type": "code", "execution_count": 26, "id": "a4ef4ca6-0233-47d3-8209-d3e337a8392c", "metadata": {}, "outputs": [], "source": [ "history = MovieTabular(parameter_name=\"[A]\") # A convenient way to store a sequence of \"state snapshots\" as a Pandas dataframe" ] }, { "cell_type": "code", "execution_count": 27, "id": "60a76c7e-6eb4-423f-8103-683205aaf817", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "`MovieTabular` object with 0 snapshot(s) parametrized by `[A]`\n" ] } ], "source": [ "print(history)" ] }, { "cell_type": "code", "execution_count": 28, "id": "4cfdbf3f-cec9-4f6c-83bc-05fd408411a4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1.00000000e-03 1.13121657e-03 1.27965093e-03 1.44756233e-03\n", " 1.63750649e-03 1.85237447e-03 2.09543670e-03 2.37039271e-03\n", " 2.68142751e-03 3.03327522e-03 3.43129119e-03 3.88153345e-03\n", " 4.39085495e-03 4.96700787e-03 5.61876160e-03 6.35603621e-03\n", " 7.19005348e-03 8.13350762e-03 9.20075859e-03 1.04080506e-02\n", " 1.17737592e-02 1.33186715e-02 1.50663019e-02 1.70432503e-02\n", " 1.92796072e-02 2.18094111e-02 2.46711672e-02 2.79084331e-02\n", " 3.15704819e-02 3.57130522e-02 4.03991964e-02 4.57002403e-02\n", " 5.16968690e-02 5.84803548e-02 6.61539463e-02 7.48344401e-02\n", " 8.46539585e-02 9.57619605e-02 1.08327516e-01 1.22541881e-01\n", " 1.38621407e-01 1.56810832e-01 1.77387011e-01 2.00663126e-01\n", " 2.26993453e-01 2.56778755e-01 2.90472382e-01 3.28587172e-01\n", " 3.71703253e-01 4.20476878e-01 4.75650411e-01 5.38063626e-01\n", " 6.08666489e-01 6.88533617e-01 7.78880636e-01 8.81082680e-01\n", " 9.96695326e-01 1.12747827e+00 1.27542210e+00 1.44277861e+00\n", " 1.63209507e+00 1.84625298e+00 2.08851196e+00 2.36255934e+00\n", " 2.67256626e+00 3.02325124e+00 3.41995189e+00 3.86870625e+00\n", " 4.37634461e+00 4.95059353e+00 5.60019342e+00 6.33503159e+00\n", " 7.16629270e+00 8.10662903e+00 9.17035308e+00 1.03736553e+01\n", " 1.17348508e+01 1.32746577e+01 1.50165127e+01 1.69869280e+01\n", " 1.92158944e+01 2.17373381e+01 2.45896370e+01 2.78162048e+01\n", " 3.14661517e+01 3.55950322e+01 4.02656902e+01 4.55492159e+01\n", " 5.15260277e+01 5.82870963e+01 6.59353291e+01 7.45871367e+01\n", " 8.43742048e+01 9.54454985e+01 1.07969529e+02 1.22136920e+02\n", " 1.38163308e+02 1.56292623e+02 1.76800805e+02 2.00000000e+02]\n" ] } ], "source": [ "# Generate a sweep of [A] values along a log scale, from very low to very high (relative to the dissociation constants)\n", "start = 0.001\n", "stop = 200.\n", "num_points = 100\n", "\n", "log_values = np.logspace(np.log10(start), np.log10(stop), num=num_points)\n", "\n", "print(log_values)" ] }, { "cell_type": "code", "execution_count": 29, "id": "5d4be3d3-6eba-4aa2-a265-a869622a5221", "metadata": {}, "outputs": [], "source": [ "# Set [A] to each of the above values in turn, and determine/store the applicable fractional occupancies (for the sites where A binds)\n", "for A_conc in log_values:\n", " dynamics.set_single_conc(conc=A_conc, species_name=\"A\", snapshot=False)\n", " dynamics.update_occupancy()\n", " history.store(A_conc, {\"M1 site 3\": dynamics.get_occupancy(macromolecule=\"M1\", site_number=3), \n", " \"M1 site 15\": dynamics.get_occupancy(macromolecule=\"M1\", site_number=15), \n", " \"M2 site 2\": dynamics.get_occupancy(macromolecule=\"M2\", site_number=2)})" ] }, { "cell_type": "code", "execution_count": 30, "id": "6976557b-0e17-4dba-8d6b-29b47e48fd0e", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot each of the fractional occupancies as a function of [A]\n", "\n", "fig = px.line(data_frame=df, \n", " x=\"[A]\", y=[\"M2 site 2\", \"M1 site 3\", \"M1 site 15\"],\n", " color_discrete_sequence = [\"seagreen\", \"purple\", \"darkorange\"],\n", " title=\"Fractional Occupancy as a function of Ligand Concentration\",\n", " labels={\"value\":\"Fractional Occupancy\", \"variable\":\"Binding site\"})\n", "\n", "fig.add_hline(y=0.5, line_width=1, line_dash=\"dot\", line_color=\"gray\") # Horizontal line at 50% occupancy\n", "\n", "fig.show()" ] }, { "cell_type": "code", "execution_count": 32, "id": "b40df5f3-43d2-48ff-9c20-db11e85dcc1f", "metadata": {}, "outputs": [], "source": [ "import plotly.graph_objects as go " ] }, { "cell_type": "code", "execution_count": 33, "id": "7527a0da", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Binding site=M2 site 2
[A]=%{x}
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Highlighting 0.1/0.5/0.9 occupancies)" }, "xaxis": { "anchor": "y", "domain": [ 0, 1 ], "range": [ -2.9999999999999996, 2.301029995663981 ], "title": { "text": "[A]" }, "type": "log" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.055390326826049226, 1.0554640619024873 ], "tickvals": [ 0, 1, 0.1, 0.5, 0.9 ], "title": { "text": "Fractional Occupancy" }, "type": "linear" } } }, "image/png": 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", "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Same plot, but use a log scale for [A]\n", "\n", "fig = px.line(data_frame=df, \n", " x=\"[A]\", y=[\"M2 site 2\", \"M1 site 3\", \"M1 site 15\"],\n", " color_discrete_sequence = [\"seagreen\", \"purple\", \"darkorange\"], \n", " log_x=True, range_x=[start,200], \n", " title=\"Fractional Occupancy as a function of Ligand Concentration
(log plot on x-axis. Highlighting 0.1/0.5/0.9 occupancies)\",\n", " labels={\"value\":\"Fractional Occupancy\", \"variable\":\"Binding site\"})\n", "\n", "# Horizontal lines\n", "fig.add_hline(y=0.1, line_width=1, line_dash=\"dot\", line_color=\"gray\")\n", "fig.add_hline(y=0.5, line_width=1, line_dash=\"dot\", line_color=\"gray\")\n", "fig.add_hline(y=0.9, line_width=1, line_dash=\"dot\", line_color=\"gray\")\n", "\n", "# Annotations (x values adjusted for the log scale)\n", "fig.add_annotation(x=-1.715, y=0.65, \n", " text=\"Dissociation constant: 0.01
(HIGHER Binding Affinity)\", font=dict(size=12, color=\"seagreen\"), showarrow=True, ax=-100, ay=-20)\n", "fig.add_annotation(x=0.3, y=0.65, \n", " text=\"Dissociation constant: 1\", font=dict(size=12, color=\"purple\"), showarrow=True, ax=-100, ay=-20)\n", "fig.add_annotation(x=0.6, y=0.3, \n", " text=\"Dissociation constant: 10
(LOWER Binding Affinity)\", font=dict(size=12, color=\"darkorange\"), showarrow=True, ax=100, ay=10)\n", "\n", "fig.add_annotation(x=1.8, y=0.51, \n", " text=\"50% OCCUPANCY\", font=dict(size=14, color=\"gray\"), bgcolor=\"white\", opacity=0.8, showarrow=False)\n", "\n", "# Customize y-axis tick values\n", "additional_y_values = [0.1, 0.5, 0.9] # Additional values to show on y-axis\n", "fig.update_layout(yaxis={\"tickvals\": list(fig.layout.yaxis.domain) + additional_y_values})\n", " \n", "# Add scatter points (dots) to the plot, to highlight the 0.1/0.5/0.9 occupancies\n", "fig.add_scatter(x=[0.01, 1, 10, 0.001, 0.1, 1., 0.1, 10, 100 ], \n", " y=[0.5, 0.5, 0.5, 0.1, 0.1, 0.1, 0.9, 0.9, 0.9], \n", " mode=\"markers\", marker={\"color\": \"red\"}, name=\"key points\")\n", " \n", "fig.show()" ] }, { "cell_type": "markdown", "id": "0de876a0-fc82-4c6e-9057-48d67621c970", "metadata": {}, "source": [ "#### When the binding affinity is lower (i.e. higher Dissociation Constant, Kd, orange curve), it takes higher ligand concentrations to attain the same fractional occupancies" ] }, { "cell_type": "markdown", "id": "9536f94c-2f92-46eb-a38d-067d37540ea5", "metadata": {}, "source": [ "Note that fractional occupancy 0.1 occurs at ligand concentrations of 1/10 the dissociation constant (Kd); \n", "occupancy 0.5 occurs at ligand concentrations equals to the dissociation constant; \n", "occupancy 0.9 occurs at ligand concentrations of 10x the dissociation constant. " ] }, { "cell_type": "markdown", "id": "84f5d4c3-2c13-4cb2-8cb6-8cec172358e2", "metadata": {}, "source": [ "## The above simulation captures what's shown on Fig. 3A of \n", "#### https://doi.org/10.1146/annurev-cellbio-100617-062719 \n", "(\"Low-Affinity Binding Sites and the Transcription Factor Specificity Paradox in Eukaryotes\"), a paper that guided this simulation" ] }, { "cell_type": "markdown", "id": "493d9272-f113-4d72-92be-08e289488775", "metadata": {}, "source": [ "#### In upcoming versions of Life123, the fractional occupancy values will regulate the rates of reactions catalyzed by the macromolecules..." ] }, { "cell_type": "code", "execution_count": null, "id": "25baaff8-1a2c-488f-bd6a-c351ec75bd5a", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "jupytext": { "formats": "ipynb,py:percent" }, "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }