{ "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: July 14, 2023" ] }, { "cell_type": "code", "execution_count": 1, "id": "1f552123-2456-42fa-9fea-42582e096c0f", "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": "b0ce3cdd", "metadata": { "tags": [] }, "outputs": [], "source": [ "from experiments.get_notebook_info import get_notebook_basename\n", "\n", "from src.modules.chemicals.chem_data import ChemData 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(chem_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": [ "
\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
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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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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": [ "0: 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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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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concentration change per unit time (brown)" }, "type": "linear" } } }, "image/png": 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", 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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": "66fa79e2", "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 }