{ "cells": [ { "cell_type": "markdown", "id": "3bbe8002-bdf3-490c-bde0-80dd3713a3d0", "metadata": {}, "source": [ "## A simple `A <-> B` reaction between 2 species\n", "with 1st-order kinetics in both directions, taken to equilibrium\n", "\n", "See also the experiment _\"1D/reactions/reaction_1\"_ ; this is the \"single-compartment\" version of it.\n", "\n", "LAST REVISED: May 16, 2023" ] }, { "cell_type": "code", "execution_count": 1, "id": "13e55c1d-609f-4bf0-a004-6c45bcfcbc99", "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": "bdad128a-9214-46f5-aeb9-a7b77c81aa3e", "metadata": { "tags": [] }, "outputs": [], "source": [ "from experiments.get_notebook_info import get_notebook_basename\n", "\n", "from src.modules.reactions.reaction_data import ReactionData as chem\n", "from src.modules.reactions.reaction_dynamics import ReactionDynamics\n", "\n", "import numpy as np\n", "import plotly.express as px\n", "from src.modules.visualization.graphic_log import GraphicLog" ] }, { "cell_type": "code", "execution_count": 3, "id": "83c3cc5f-de21-4f66-9988-2806fbf0666d", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-> Output will be LOGGED into the file 'react_1.log.htm'\n" ] } ], "source": [ "# Initialize the HTML logging (for the graphics)\n", "log_file = get_notebook_basename() + \".log.htm\" # Use the notebook base filename for the log file\n", "\n", "# Set up the use of some specified graphic (Vue) components\n", "GraphicLog.config(filename=log_file,\n", " components=[\"vue_cytoscape_1\"],\n", " extra_js=\"https://cdnjs.cloudflare.com/ajax/libs/cytoscape/3.21.2/cytoscape.umd.js\")" ] }, { "cell_type": "markdown", "id": "9329208b-070f-4902-8f37-0f11ddf75ed6", "metadata": {}, "source": [ "# Initialize the System" ] }, { "cell_type": "code", "execution_count": 4, "id": "72b4245c-de4e-480d-a501-3495b7ed8bc4", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 1\n" ] } ], "source": [ "# Initialize the reaction\n", "chem_data = chem(names=[\"A\", \"B\"])\n", "\n", "# Reaction A <-> B , with 1st-order kinetics in both directions\n", "chem_data.add_reaction(reactants=[\"A\"], products=[\"B\"], \n", " forward_rate=3., reverse_rate=2.)\n", "\n", "print(\"Number of reactions: \", chem_data.number_of_reactions())" ] }, { "cell_type": "code", "execution_count": 5, "id": "00ea560d-9a49-4041-b119-6de11bfcc7af", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 1 (at temp. 25 C)\n", "0: A <-> B (kF = 3 / kR = 2 / Delta_G = -1,005.13 / K = 1.5) | 1st order in all reactants & products\n" ] } ], "source": [ "chem_data.describe_reactions()" ] }, { "cell_type": "code", "execution_count": 6, "id": "cb582868-431c-4022-aa0e-a2f554f80d6c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[GRAPHIC ELEMENT SENT TO LOG FILE `react_1.log.htm`]\n" ] } ], "source": [ "# Send a plot of the network of reactions to the HTML log file\n", "graph_data = chem_data.prepare_graph_network()\n", "GraphicLog.export_plot(graph_data, \"vue_cytoscape_1\")" ] }, { "cell_type": "markdown", "id": "98a9fbe5-2090-4d38-9c5f-94fbf7c3eae2", "metadata": {}, "source": [ "# Start the simulation" ] }, { "cell_type": "code", "execution_count": 7, "id": "c2f4a554-807b-49f9-8ca2-8d929fe6eeef", "metadata": {}, "outputs": [], "source": [ "dynamics = ReactionDynamics(reaction_data=chem_data)" ] }, { "cell_type": "code", "execution_count": 8, "id": "ae304704-c8d9-4cef-9e0b-2587bb3909ef", "metadata": {}, "outputs": [], "source": [ "# Initial concentrations of all the chemicals, in index order\n", "dynamics.set_conc([10., 50.])" ] }, { "cell_type": "code", "execution_count": 9, "id": "a605dacf-2c67-403e-9aa9-5be25fc9f481", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "2 species:\n", " Species 0 (A). Conc: 10.0\n", " Species 1 (B). Conc: 50.0\n" ] } ], "source": [ "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 10, "id": "0ff2c242-a15b-456d-ad56-0ba1041c0b4c", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABcaption
00.010.050.0Initial state
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" ], "text/plain": [ " SYSTEM TIME A B caption\n", "0 0.0 10.0 50.0 Initial state" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "markdown", "id": "fc516ca2-e62d-4784-b826-5372ff7f4c75", "metadata": { "tags": [] }, "source": [ "## Start the reaction" ] }, { "cell_type": "code", "execution_count": 11, "id": "50c7e478-ad0e-4aeb-9cea-dfed47cded21", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1 total step(s) taken\n" ] } ], "source": [ "# First step of reaction\n", "dynamics.single_compartment_react(initial_step=0.1, n_steps=1,\n", " snapshots={\"initial_caption\": \"first reaction step\"})" ] }, { "cell_type": "code", "execution_count": 12, "id": "c9115720-e66e-44f3-bb0a-fabec5b96673", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
SYSTEM TIMEABcaption
00.010.050.0Initial state
10.117.043.0first reaction step
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" ], "text/plain": [ " SYSTEM TIME A B caption\n", "0 0.0 10.0 50.0 Initial state\n", "1 0.1 17.0 43.0 first reaction step" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "code", "execution_count": 13, "id": "2502cd11-0df9-4303-8895-98401a1df7b8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "10 total step(s) taken\n" ] } ], "source": [ "# Numerous more fixed steps\n", "dynamics.single_compartment_react(initial_step=0.1, n_steps=10,\n", " snapshots={\"initial_caption\": \"2nd reaction step\",\n", " \"final_caption\": \"last reaction step\"})" ] }, { "cell_type": "markdown", "id": "c7650ed4-365e-43c2-b001-280297c68ece", "metadata": {}, "source": [ "#### NOTE: for demonstration purposes, we're using FIXED time steps... Typically, one would use the option for automated variable time steps (see experiment `react 2`)" ] }, { "cell_type": "code", "execution_count": 14, "id": "80fbaee3-bd6f-4197-9270-23374d46a4a7", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABcaption
00.010.00000050.000000Initial state
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" ], "text/plain": [ " SYSTEM TIME A B caption\n", "0 0.0 10.000000 50.000000 Initial state\n", "1 0.1 17.000000 43.000000 first reaction step\n", "2 0.2 20.500000 39.500000 2nd reaction step\n", "3 0.3 22.250000 37.750000 \n", "4 0.4 23.125000 36.875000 \n", "5 0.5 23.562500 36.437500 \n", "6 0.6 23.781250 36.218750 \n", "7 0.7 23.890625 36.109375 \n", "8 0.8 23.945312 36.054688 \n", "9 0.9 23.972656 36.027344 \n", "10 1.0 23.986328 36.013672 \n", "11 1.1 23.993164 36.006836 last reaction step" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "markdown", "id": "c034956a-683c-4c3d-8134-ecac9e19a45c", "metadata": {}, "source": [ "### Check the final equilibrium" ] }, { "cell_type": "code", "execution_count": 15, "id": "b139f5e4-625f-4a5e-8f57-8f00244dced4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([23.99316406, 36.00683594])" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_system_conc()" ] }, { "cell_type": "markdown", "id": "d25eedf3-89f8-4f8c-a49a-d2689103528b", "metadata": {}, "source": [ "NOTE: Consistent with the 3/2 ratio of forward/reverse rates (and the 1:1 stoichiometry, and the 1st order reactions), the systems settles in the following equilibrium:\n", "\n", "[A] = 23.99316406\n", " \n", "[B] = 36.00683594\n" ] }, { "cell_type": "code", "execution_count": 16, "id": "765f6f39-4b2e-4a86-b6a9-ace9d1941663", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A <-> B\n", "Final concentrations: [B] = 36.01 ; [A] = 23.99\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 1.50071\n", " Formula used: [B] / [A]\n", "2. Ratio of forward/reverse reaction rates: 1.5\n", "Discrepancy between the two values: 0.04749 %\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": "905adfdd-6d70-4dfc-bb34-c547c4d604b9", "metadata": {}, "source": [ "### Note that, because of the high initial concentration of B relative to A, the overall reaction has proceeded **in reverse**" ] }, { "cell_type": "markdown", "id": "6ac3dd4e-9dd0-4d3a-aa83-76102bd79524", "metadata": { "tags": [] }, "source": [ "## Plots of changes of concentration with time" ] }, { "cell_type": "code", "execution_count": 17, "id": "86976e6f-f453-41c3-9553-b27b1328db6b", "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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"lakecolor": "white", "landcolor": "#E5ECF6", "showlakes": true, "showland": true, "subunitcolor": "white" }, "hoverlabel": { "align": "left" }, "hovermode": "closest", "mapbox": { "style": "light" }, "paper_bgcolor": "white", "plot_bgcolor": "#E5ECF6", "polar": { "angularaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "bgcolor": "#E5ECF6", "radialaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" } }, "scene": { "xaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" }, "yaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" }, "zaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" } }, "shapedefaults": { "line": { "color": "#2a3f5f" } }, "ternary": { "aaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "baxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "bgcolor": "#E5ECF6", "caxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" } }, "title": { "x": 0.05 }, "xaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 }, "yaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 } } }, "title": { "text": "Reaction `A <-> B` . Changes in concentrations with time" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ 0, 1.0999999999999999 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ 7.777777777777778, 52.22222222222222 ], "title": { "text": "concentration" }, "type": "linear" } } }, "image/png": 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Changes in concentrations with time (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.0006278538812785387, 1.1006278538812784 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ 7.777777777777778, 52.22222222222222 ], "title": { "text": "concentration" }, "type": "linear" } } }, "image/png": 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SYSTEM TIMEABcaption
00.010.00000050.000000Initial state
10.117.00000043.000000first reaction step
20.220.50000039.5000002nd reaction step
30.322.25000037.750000
40.423.12500036.875000
50.523.56250036.437500
60.623.78125036.218750
70.723.89062536.109375
80.823.94531236.054688
90.923.97265636.027344
101.023.98632836.013672
111.123.99316436.006836last reaction step
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" ], "text/plain": [ " SYSTEM TIME A B caption\n", "0 0.0 10.000000 50.000000 Initial state\n", "1 0.1 17.000000 43.000000 first reaction step\n", "2 0.2 20.500000 39.500000 2nd reaction step\n", "3 0.3 22.250000 37.750000 \n", "4 0.4 23.125000 36.875000 \n", "5 0.5 23.562500 36.437500 \n", "6 0.6 23.781250 36.218750 \n", "7 0.7 23.890625 36.109375 \n", "8 0.8 23.945312 36.054688 \n", "9 0.9 23.972656 36.027344 \n", "10 1.0 23.986328 36.013672 \n", "11 1.1 23.993164 36.006836 last reaction step" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df" ] }, { "cell_type": "markdown", "id": "f72f4988-4e4b-4268-9f4a-e36300c9dcf1", "metadata": {}, "source": [ "## Now investigate A_dot, i.e. d[A]/dt" ] }, { "cell_type": "code", "execution_count": 21, "id": "5ee8ec14-442f-4e76-bc86-26b8791f7e70", "metadata": {}, "outputs": [], "source": [ "A = list(df.A)" ] }, { "cell_type": "code", "execution_count": 22, "id": "0b932baf-da6b-4fc3-a199-e0fe72ca268e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[10.0,\n", " 17.0,\n", " 20.5,\n", " 22.25,\n", " 23.125,\n", " 23.5625,\n", " 23.78125,\n", " 23.890625,\n", " 23.9453125,\n", " 23.97265625,\n", " 23.986328125,\n", " 23.9931640625]" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A" ] }, { "cell_type": "code", "execution_count": 23, "id": "a390ed46-f014-414f-9b14-69f6da95dc41", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "12" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(A)" ] }, { "cell_type": "code", "execution_count": 24, "id": "b3b1b169-bae2-493b-b652-ce9e82b2ddab", "metadata": {}, "outputs": [], "source": [ "A_dot = np.gradient(A, 0.1) # 0.1 is the constant step size" ] }, { "cell_type": "code", "execution_count": 25, "id": "35c7be1f-95ce-4bac-9fb3-02745a505f92", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([7.00000000e+01, 5.25000000e+01, 2.62500000e+01, 1.31250000e+01,\n", " 6.56250000e+00, 3.28125000e+00, 1.64062500e+00, 8.20312500e-01,\n", " 4.10156250e-01, 2.05078125e-01, 1.02539062e-01, 6.83593750e-02])" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A_dot" ] }, { "cell_type": "code", "execution_count": 26, "id": "f5fa1f8e-517f-4fd1-b3bf-51c12ab883f0", "metadata": {}, "outputs": [], "source": [ "df['A_dot'] = A_dot # Add a column to the dataframe" ] }, { "cell_type": "code", "execution_count": 27, "id": "e3773cfc-88ed-4565-a760-e90fa050d5b9", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABcaptionA_dot
00.010.00000050.000000Initial state70.000000
10.117.00000043.000000first reaction step52.500000
20.220.50000039.5000002nd reaction step26.250000
30.322.25000037.75000013.125000
40.423.12500036.8750006.562500
50.523.56250036.4375003.281250
60.623.78125036.2187501.640625
70.723.89062536.1093750.820312
80.823.94531236.0546880.410156
90.923.97265636.0273440.205078
101.023.98632836.0136720.102539
111.123.99316436.006836last reaction step0.068359
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" ], "text/plain": [ " SYSTEM TIME A B caption A_dot\n", "0 0.0 10.000000 50.000000 Initial state 70.000000\n", "1 0.1 17.000000 43.000000 first reaction step 52.500000\n", "2 0.2 20.500000 39.500000 2nd reaction step 26.250000\n", "3 0.3 22.250000 37.750000 13.125000\n", "4 0.4 23.125000 36.875000 6.562500\n", "5 0.5 23.562500 36.437500 3.281250\n", "6 0.6 23.781250 36.218750 1.640625\n", "7 0.7 23.890625 36.109375 0.820312\n", "8 0.8 23.945312 36.054688 0.410156\n", "9 0.9 23.972656 36.027344 0.205078\n", "10 1.0 23.986328 36.013672 0.102539\n", "11 1.1 23.993164 36.006836 last reaction step 0.068359" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df" ] }, { "cell_type": "code", "execution_count": 28, "id": "e55a1afb-0856-4f5e-997b-6277005eb03b", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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concentration (blue) /
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concentration (blue) /
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concentration change per unit time (brown)" }, "type": "linear" } } }, "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = px.line(data_frame=dynamics.get_history(), x=\"SYSTEM TIME\", y=[\"A\", \"A_dot\"], \n", " title=\"Changes in concentration of A with time (blue) , and changes in its rate of change (brown)\",\n", " color_discrete_sequence = ['navy', 'brown'],\n", " labels={\"value\":\"concentration (blue) /
concentration change per unit time (brown)\", \"variable\":\"Chemical\"})\n", "fig.show()" ] }, { "cell_type": "markdown", "id": "85d87078-8fc1-4166-95e1-343b546f9971", "metadata": {}, "source": [ "### At t=0, [A]=10 and [A] has a high rate of change (70); \n", "### as the system approaches equilibrium, [A] approaches a value of 24, and its rate of change decays to zero.\n", "\n", "The curves are jagged because of limitations of numerically estimating derivatives, as well as the large time steps taken (especially in the early times, when there's a lot of change.)" ] }, { "cell_type": "code", "execution_count": null, "id": "1f552123-2456-42fa-9fea-42582e096c0f", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "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 }