{ "cells": [ { "cell_type": "markdown", "id": "49bcb5b0-f19d-4b96-a5f1-e0ae30f66d8f", "metadata": {}, "source": [ "## Comparing the reaction `A <-> B` with and without an enzyme\n", "\n", "LAST REVISED: July 14, 2023" ] }, { "cell_type": "code", "execution_count": 1, "id": "cbb1af2e-3564-460e-a4ae-41e4ec4f719f", "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": "087c0d08", "metadata": { "tags": [] }, "outputs": [], "source": [ "from src.modules.chemicals.chem_data import ChemData\n", "from src.modules.reactions.reaction_dynamics import ReactionDynamics" ] }, { "cell_type": "markdown", "id": "d6d3ca49-589d-49b7-8424-37c7b01bcacf", "metadata": {}, "source": [ "# 1. WITHOUT ENZYME\n", "### `A` <-> `B`" ] }, { "cell_type": "code", "execution_count": 3, "id": "23c15e66-52e4-495b-aa3d-ecddd8d16942", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 1 (at temp. 25 C)\n", "0: A <-> B (kF = 1 / kR = 0.2 / Delta_G = -3,989.73 / K = 5.00001) | 1st order in all reactants & products\n" ] } ], "source": [ "# Initialize the system\n", "chem_data = ChemData(names=[\"A\", \"B\"])\n", "\n", "# Reaction A <-> B , with 1st-order kinetics, and a forward rate that is slower than it would be with the enzyme of part 2\n", "chem_data.add_reaction(reactants=\"A\", products=\"B\",\n", " forward_rate=1., delta_G=-3989.73)\n", "\n", "chem_data.describe_reactions()" ] }, { "cell_type": "markdown", "id": "0e771dda-1c0f-4fc0-ab21-049740643897", "metadata": {}, "source": [ "### Set the initial concentrations of all the chemicals" ] }, { "cell_type": "code", "execution_count": 4, "id": "5563e467-a637-44fa-9ba1-d35ddd82c887", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "2 species:\n", " Species 0 (A). Conc: 20.0\n", " Species 1 (B). Conc: 0.0\n" ] } ], "source": [ "dynamics = ReactionDynamics(chem_data=chem_data)\n", "dynamics.set_conc(conc={\"A\": 20., \"B\": 0.},\n", " snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "markdown", "id": "651941bb-7098-4065-a598-e50c0b641ab3", "metadata": { "tags": [] }, "source": [ "### Take the initial system to equilibrium" ] }, { "cell_type": "code", "execution_count": 5, "id": "76f24d9a-a788-41d8-90a4-db87386f91aa", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* INFO: the tentative time step (0.1) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.05) [Step started at t=0, and will rewind there]\n", "30 total step(s) taken\n" ] } ], "source": [ "dynamics.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n", "\n", "# All of these settings are currently close to the default values... but subject to change; set for repeatability\n", "dynamics.set_thresholds(norm=\"norm_A\", low=0.5, high=0.8, abort=1.44)\n", "dynamics.set_thresholds(norm=\"norm_B\", low=0.08, high=0.5, abort=1.5)\n", "dynamics.set_step_factors(upshift=1.5, downshift=0.5, abort=0.5)\n", "dynamics.set_error_step_factor(0.5)\n", "\n", "dynamics.single_compartment_react(initial_step=0.1, reaction_duration=3.0,\n", " variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 6, "id": "e58db01b-b932-4f60-91c2-a578353a3702", "metadata": {}, "outputs": [], "source": [ "#dynamics.explain_time_advance()" ] }, { "cell_type": "code", "execution_count": 7, "id": "4a19ad2a-fbd2-420a-b958-2daf88bcc841", "metadata": {}, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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Changes in concentrations with time (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.0021756036931818183, 3.591921697443182 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.1111111111111112, 21.11111111111111 ], "title": { "text": "concentration" }, "type": "linear" } } }, "image/png": 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", "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_curves(colors=['darkorange', 'green'], show_intervals=True, title_prefix=\"WITHOUT enzyme\")" ] }, { "cell_type": "markdown", "id": "ef7ed670-39dd-4e44-afec-82dbd6e6a431", "metadata": {}, "source": [ "#### Note how the time steps get automatically adjusted, as needed by the amount of change - include a complete step abort/redo at time=0" ] }, { "cell_type": "code", "execution_count": 8, "id": "550dc065-6f3a-4961-b1ea-d52e0aa0baff", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Min abs distance found at data row: 18\n" ] }, { "data": { "text/plain": [ "(0.7406363068115296, 10.0)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.curve_intersection(\"A\", \"B\", t_start=0, t_end=1.0)" ] }, { "cell_type": "code", "execution_count": 9, "id": "19e66cfc-8e1c-4332-b85d-2b8ced01d4b3", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: A <-> B\n", "Final concentrations: [B] = 16.6 ; [A] = 3.398\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.88533\n", " Formula used: [B] / [A]\n", "2. Ratio of forward/reverse reaction rates: 5.000005788498923\n", "Discrepancy between the two values: 2.293 %\n", "Reaction IS in equilibrium (within 3% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reaction has reached equilibrium\n", "dynamics.is_in_equilibrium(tolerance=3)" ] }, { "cell_type": "code", "execution_count": null, "id": "6517c7bd-3243-4326-9c7e-0ca04da6d812", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "27401e5d-8f3e-4c27-8438-129d3e3408a2", "metadata": {}, "source": [ "# 2. WITH ENZYME `E`\n", "### `A` + `E` <-> `B` + `E`" ] }, { "cell_type": "markdown", "id": "878edb65-e2f9-46d0-b3ba-3a82c064243b", "metadata": {}, "source": [ "### Note: for the sake of the demo, we'll completely ignore the concomitant reaction A <-> B\n", "This in an approximation that we'll drop in later experiments" ] }, { "cell_type": "code", "execution_count": 10, "id": "ffaef48b-e95b-4cb9-ab9f-c526a159222e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 1 (at temp. 25 C)\n", "0: A + E <-> B + E (kF = 10 / kR = 2 / Delta_G = -3,989.73 / K = 5.00001) | Enzyme: E | 1st order in all reactants & products\n" ] } ], "source": [ "# Initialize the system\n", "chem_data = ChemData(names=[\"A\", \"B\", \"E\"])\n", "\n", "# Reaction A + E <-> B + E , with 1st-order kinetics, and a forward rate that is faster than it was without the enzyme\n", "# Thermodynamically, there's no change from the reaction without the enzyme\n", "chem_data.add_reaction(reactants=[\"A\", \"E\"], products=[\"B\", \"E\"],\n", " forward_rate=10., delta_G=-3989.73)\n", "\n", "chem_data.describe_reactions() # Notice how the enzyme `E` is noted in the printout below" ] }, { "cell_type": "markdown", "id": "12a8ca3f-a25c-4902-baef-586805338279", "metadata": {}, "source": [ "### Notice how, while the ratio kF/kR is the same as it was without the enzyme (since it's dictated by the energy difference), the individual values of kF and kR are now each 10 times bigger" ] }, { "cell_type": "markdown", "id": "d1d0eabb-b5b1-4e15-846d-5e483a5a24a7", "metadata": {}, "source": [ "### Set the initial concentrations of all the chemicals" ] }, { "cell_type": "code", "execution_count": 11, "id": "e80645d6-eb5b-4c78-8b46-ae126d2cb2cf", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "3 species:\n", " Species 0 (A). Conc: 20.0\n", " Species 1 (B). Conc: 0.0\n", " Species 2 (E). Conc: 30.0\n" ] } ], "source": [ "dynamics = ReactionDynamics(chem_data=chem_data)\n", "dynamics.set_conc(conc={\"A\": 20., \"B\": 0., \"E\": 30.},\n", " snapshot=True) # Plenty of enzyme `E`\n", "dynamics.describe_state()" ] }, { "cell_type": "markdown", "id": "0b46b395-3f68-4dbd-b0c5-d67a0e623726", "metadata": { "tags": [] }, "source": [ "### Take the initial system to equilibrium" ] }, { "cell_type": "code", "execution_count": 12, "id": "dde62826-d170-4b39-b027-c0d56fb21387", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "*** CAUTION: negative concentration in chemical `A` in step starting at t=0. It will be AUTOMATICALLY CORRECTED with a reduction in time step size, as follows:\n", " INFO: the tentative time step (0.1) leads to a NEGATIVE concentration of `A` from reaction A + E <-> B + E (rxn # 0): \n", " Baseline value: 20 ; delta conc: -600\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.25 (set to 0.025) [Step started at t=0, and will rewind there]\n", "\n", "*** CAUTION: negative concentration in chemical `A` in step starting at t=0. It will be AUTOMATICALLY CORRECTED with a reduction in time step size, as follows:\n", " INFO: the tentative time step (0.025) leads to a NEGATIVE concentration of `A` from reaction A + E <-> B + E (rxn # 0): \n", " Baseline value: 20 ; delta conc: -150\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.25 (set to 0.00625) [Step started at t=0, and will rewind there]\n", "\n", "*** CAUTION: negative concentration in chemical `A` in step starting at t=0. It will be AUTOMATICALLY CORRECTED with a reduction in time step size, as follows:\n", " INFO: the tentative time step (0.00625) leads to a NEGATIVE concentration of `A` from reaction A + E <-> B + E (rxn # 0): \n", " Baseline value: 20 ; delta conc: -37.5\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.25 (set to 0.0015625) [Step started at t=0, and will rewind there]\n", "* INFO: the tentative time step (0.0015625) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.4 (set to 0.000625) [Step started at t=0, and will rewind there]\n", "* INFO: the tentative time step (0.000625) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.4 (set to 0.00025) [Step started at t=0, and will rewind there]\n", "Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n", "42 total step(s) taken\n" ] } ], "source": [ "dynamics.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n", "\n", "# All of these settings are currently close to the default values... but subject to change; set for repeatability\n", "dynamics.set_thresholds(norm=\"norm_A\", low=0.5, high=0.8, abort=1.44)\n", "dynamics.set_thresholds(norm=\"norm_B\", low=0.08, high=0.5, abort=1.5)\n", "dynamics.set_step_factors(upshift=1.2, downshift=0.5, abort=0.4)\n", "dynamics.set_error_step_factor(0.25)\n", "\n", "dynamics.single_compartment_react(initial_step=0.1, reaction_duration=0.1,\n", " variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "markdown", "id": "33d9466e-c41e-4e92-a8fd-3b594aa201b0", "metadata": {}, "source": [ "#### Note how the (proposed) initial step - kept the same as the previous run - is now _extravagantly large_, given the much-faster reaction dynamics. However, the variable-step engine intercepts and automatically corrects the problem!" ] }, { "cell_type": "code", "execution_count": 13, "id": "b0543cac-f3cd-453c-ae9b-c00f01e61fa8", "metadata": {}, "outputs": [], "source": [ "#dynamics.explain_time_advance()" ] }, { "cell_type": "code", "execution_count": 14, "id": "8cc14786-cc9f-4399-9203-290526d3a326", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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Changes in concentrations with time (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -6.416280866399666e-05, 0.1059327971042585 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.6666666666666665, 31.666666666666668 ], "title": { "text": "concentration" }, "type": "linear" } } }, "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_curves(colors=['darkorange', 'green', 'violet'], show_intervals=True, title_prefix=\"WITH enzyme\")" ] }, { "cell_type": "code", "execution_count": 15, "id": "2cf77dd1-040e-4e3a-9867-678479a3dda6", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Min abs distance found at data row: 15\n" ] }, { "data": { "text/plain": [ "(0.0024615346985334676, 10.0)" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.curve_intersection(\"A\", \"B\", t_start=0, t_end=0.02)" ] }, { "cell_type": "code", "execution_count": 16, "id": "c3afbcc8-bdae-4938-a3f1-ce00d62816f2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: A + E <-> B + E\n", "Final concentrations: [B] = 16.67 ; [E] = 30 ; [A] = 3.334 ; [E] = 30\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.99958\n", " Formula used: ([B][E]) / ([A][E])\n", "2. Ratio of forward/reverse reaction rates: 5.000005788498923\n", "Discrepancy between the two values: 0.008527 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reaction has reached equilibrium\n", "dynamics.is_in_equilibrium()" ] }, { "cell_type": "markdown", "id": "97efd24d-c771-4354-a924-eb21bc3d070c", "metadata": {}, "source": [ "## Thanks to the (abundant) enzyme, the reaction reaches equilibrium roughtly around t=0.02, far sooner than the roughly t=3.5 without enzyme\n", "The concentrations of `A` and `B` now become equal (cross-over) at t=0.00246 , rather than t=0.740" ] }, { "cell_type": "code", "execution_count": 17, "id": "47c6d97b-a778-47c1-9cad-e75433a32f66", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " SYSTEM TIME A B E caption\n", "0 0.000000 20.000000 0.000000 30.0 Initial state\n", "1 0.000250 18.500000 1.500000 30.0 \n", "2 0.000500 17.135000 2.865000 30.0 \n", "3 0.000625 16.513925 3.486075 30.0 \n", "4 0.000750 15.920798 4.079202 30.0 \n", "5 0.000875 15.354362 4.645638 30.0 \n", "6 0.001000 14.813416 5.186584 30.0 \n", "7 0.001125 14.296812 5.703188 30.0 \n", "8 0.001250 13.803456 6.196544 30.0 \n", "9 0.001375 13.332300 6.667700 30.0 \n", "10 0.001525 12.792356 7.207644 30.0 \n", "11 0.001675 12.281569 7.718431 30.0 \n", "12 0.001855 11.701723 8.298277 30.0 \n", "13 0.002071 11.050997 8.949003 30.0 \n", "14 0.002330 10.330846 9.669154 30.0 \n", "15 0.002589 9.677894 10.322106 30.0 \n", "16 0.002900 8.967465 11.032535 30.0 \n", "17 0.003274 8.210411 11.789589 30.0 \n", "18 0.003647 7.555081 12.444919 30.0 \n", "19 0.004095 6.874353 13.125647 30.0 \n", "20 0.004543 6.303387 13.696613 30.0 \n", "21 0.004991 5.824486 14.175514 30.0 \n", "22 0.005528 5.342468 14.657532 30.0 \n", "23 0.006066 4.953716 15.046284 30.0 \n", "24 0.006711 4.577479 15.422521 30.0 \n", "25 0.007485 4.230824 15.769176 30.0 \n", "26 0.008413 3.930744 16.069256 30.0 \n", "27 0.009528 3.691047 16.308953 30.0 \n", "28 0.010865 3.518817 16.481183 30.0 \n", "29 0.012470 3.411650 16.588350 30.0 \n", "30 0.014396 3.357349 16.642651 30.0 \n", "31 0.016707 3.337366 16.662634 30.0 \n", "32 0.019480 3.333337 16.666663 30.0 \n", "33 0.022808 3.333329 16.666671 30.0 \n", "34 0.026802 3.333331 16.666669 30.0 \n", "35 0.031594 3.333330 16.666670 30.0 \n", "36 0.037345 3.333331 16.666669 30.0 \n", "37 0.044245 3.333329 16.666671 30.0 \n", "38 0.052526 3.333331 16.666669 30.0 \n", "39 0.062463 3.333327 16.666673 30.0 \n", "40 0.074388 3.333341 16.666659 30.0 \n", "41 0.088697 3.333284 16.666716 30.0 \n", "42 0.105869 3.333567 16.666433 30.0 " ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "code", "execution_count": null, "id": "5e6c18d4", "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 }