{ "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: June 4, 2023" ] }, { "cell_type": "code", "execution_count": 1, "id": "d9efa3fd-e95d-4e1c-878a-81ae932b2709", "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": "01bae555-3dcf-42c1-bddc-9477a37f49f8", "metadata": { "tags": [] }, "outputs": [], "source": [ "from src.modules.reactions.reaction_data import ChemData\n", "from src.modules.reactions.reaction_dynamics import ReactionDynamics\n", "\n", "import numpy as np\n", "import plotly.express as px" ] }, { "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(reaction_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": "b0543cac-f3cd-453c-ae9b-c00f01e61fa8", "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": [ -0.0014439847521118263, 3.591190078502112 ], "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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", 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" ] }, "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": "cbb1af2e-3564-460e-a4ae-41e4ec4f719f", "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(reaction_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": "e58db01b-b932-4f60-91c2-a578353a3702", "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": [ -4.258593495398009e-05, 0.10591122023054848 ], "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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SYSTEM TIMEABEcaption
00.00000020.0000000.00000030.0Initial state
10.00025018.5000001.50000030.0
20.00050017.1350002.86500030.0
30.00062516.5139253.48607530.0
40.00075015.9207984.07920230.0
50.00087515.3543624.64563830.0
60.00100014.8134165.18658430.0
70.00112514.2968125.70318830.0
80.00125013.8034566.19654430.0
90.00137513.3323006.66770030.0
100.00152512.7923567.20764430.0
110.00167512.2815697.71843130.0
120.00185511.7017238.29827730.0
130.00207111.0509978.94900330.0
140.00233010.3308469.66915430.0
150.0025899.67789410.32210630.0
160.0029008.96746511.03253530.0
170.0032748.21041111.78958930.0
180.0036477.55508112.44491930.0
190.0040956.87435313.12564730.0
200.0045436.30338713.69661330.0
210.0049915.82448614.17551430.0
220.0055285.34246814.65753230.0
230.0060664.95371615.04628430.0
240.0067114.57747915.42252130.0
250.0074854.23082415.76917630.0
260.0084133.93074416.06925630.0
270.0095283.69104716.30895330.0
280.0108653.51881716.48118330.0
290.0124703.41165016.58835030.0
300.0143963.35734916.64265130.0
310.0167073.33736616.66263430.0
320.0194803.33333716.66666330.0
330.0228083.33332916.66667130.0
340.0268023.33333116.66666930.0
350.0315943.33333016.66667030.0
360.0373453.33333116.66666930.0
370.0442453.33332916.66667130.0
380.0525263.33333116.66666930.0
390.0624633.33332716.66667330.0
400.0743883.33334116.66665930.0
410.0886973.33328416.66671630.0
420.1058693.33356716.66643330.0
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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": "6517c7bd-3243-4326-9c7e-0ca04da6d812", "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 }