{ "cells": [ { "cell_type": "markdown", "id": "8d1aaf6c-3d58-4e27-88ac-9482296ac61a", "metadata": {}, "source": [ "### One-bin `2A <-> 3B` reaction, with 1st-order kinetics in both directions, taken to equilibrium\n", "\n", "Diffusion not applicable (just 1 bin)\n", "\n", "LAST REVISED: May 6, 2024" ] }, { "cell_type": "code", "execution_count": 1, "id": "1fe1cc26-5763-4feb-b097-3ff995c10c8b", "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": "592e626f", "metadata": {}, "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.life_1D.bio_sim_1d import BioSim1D\n", "\n", "import plotly.express as px\n", "from src.modules.visualization.graphic_log import GraphicLog" ] }, { "cell_type": "code", "execution_count": 3, "id": "4745cc84-d917-4701-87a8-8c16f9ac428e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-> Output will be LOGGED into the file 'reaction_3.log.htm'\n" ] } ], "source": [ "# Initialize the HTML logging\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_2\"],\n", " extra_js=\"https://cdnjs.cloudflare.com/ajax/libs/cytoscape/3.21.2/cytoscape.umd.js\")" ] }, { "cell_type": "code", "execution_count": 4, "id": "b2660f8d-3447-4874-88d0-da99c0edcfcd", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "1 bins and 2 species:\n", " Species 0 (A). Diff rate: None. Conc: [10.]\n", " Species 1 (B). Diff rate: None. Conc: [50.]\n" ] } ], "source": [ "# Initialize the system\n", "chem_data = chem(names=[\"A\", \"B\"]) # NOTE: Diffusion not applicable (just 1 bin)\n", "\n", "\n", "\n", "# Reaction 2A <-> 3B , with 1st-order kinetics in both directions\n", "chem_data.add_reaction(reactants=[(2,\"A\",1)], products=[(3,\"B\",1)], forward_rate=5., reverse_rate=2.)\n", "\n", "bio = BioSim1D(n_bins=1, chem_data=chem_data)\n", "\n", "bio.set_uniform_concentration(species_index=0, conc=10.)\n", "bio.set_uniform_concentration(species_index=1, conc=50.)\n", "\n", "bio.describe_state()" ] }, { "cell_type": "code", "execution_count": 5, "id": "50961a8b-29af-4001-8d46-2a57ed7ccb0d", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABcaption
0010.050.0Initial state
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" ], "text/plain": [ " SYSTEM TIME A B caption\n", "0 0 10.0 50.0 Initial state" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Save the state of the concentrations of all species at bin 0\n", "bio.add_snapshot(bio.bin_snapshot(bin_address = 0), caption=\"Initial state\")\n", "bio.get_history()" ] }, { "cell_type": "code", "execution_count": 6, "id": "0506f3fa-67d8-4aaf-986b-103f955336bb", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 1 (at temp. 25 C)\n", "0: 2 A <-> 3 B (kF = 5 / kR = 2 / delta_G = -2,271.4 / K = 2.5) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {'A', 'B'}\n" ] } ], "source": [ "chem_data.describe_reactions()" ] }, { "cell_type": "code", "execution_count": 7, "id": "feae8232-392a-44fd-a9cf-0fb426258fee", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[GRAPHIC ELEMENT SENT TO LOG FILE `reaction_3.log.htm`]\n" ] } ], "source": [ "# Send the plot to the HTML log file\n", "chem_data.plot_reaction_network(\"vue_cytoscape_2\")" ] }, { "cell_type": "markdown", "id": "ce4ebe89-8187-4c6f-a526-5609937ac65e", "metadata": { "tags": [] }, "source": [ "### First step" ] }, { "cell_type": "code", "execution_count": 8, "id": "430626a5-2e29-4738-944f-6233edd0e7c7", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0.05:\n", "1 bins and 2 species:\n", " Species 0 (A). Diff rate: None. Conc: [15.]\n", " Species 1 (B). Diff rate: None. Conc: [42.5]\n" ] } ], "source": [ "# First step\n", "bio.react(time_step=0.05, n_steps=1)\n", "bio.describe_state()" ] }, { "cell_type": "markdown", "id": "27067455-0efd-45d3-abd8-9b66b6f48097", "metadata": {}, "source": [ "_Early in the reaction :_\n", "[A] = 15. [B] = 42.5\n", "\n", "We're taking a smaller first step than in experimetn \"reaction_2\", to avoid over-shooting the equilibrium value with too large a step!" ] }, { "cell_type": "code", "execution_count": 9, "id": "63f11bce-17f0-4757-98a3-a40e7621084f", "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
00.0010.050.0Initial state
10.0515.042.5
\n", "
" ], "text/plain": [ " SYSTEM TIME A B caption\n", "0 0.00 10.0 50.0 Initial state\n", "1 0.05 15.0 42.5 " ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Save the state of the concentrations of all species at bin 0\n", "bio.add_snapshot(bio.bin_snapshot(bin_address = 0))\n", "bio.get_history()" ] }, { "cell_type": "markdown", "id": "b12d38ef-c936-47b0-a1de-232fc9d521b7", "metadata": {}, "source": [ "### Numerous more steps" ] }, { "cell_type": "code", "execution_count": 10, "id": "f714a848-01a0-4343-bfbb-89d946a7e343", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 10.05:\n", "1 bins and 2 species:\n", " Species 0 (A). Diff rate: None. Conc: [16.25]\n", " Species 1 (B). Diff rate: None. Conc: [40.625]\n" ] } ], "source": [ "# Numerous more steps\n", "bio.react(time_step=0.1, n_steps=100, snapshots={\"sample_bin\": 0})\n", "\n", "bio.describe_state()" ] }, { "cell_type": "markdown", "id": "ff1860cd-a3c7-47a5-9b9f-3c04560962fa", "metadata": { "tags": [] }, "source": [ "### Equilibrium" ] }, { "cell_type": "markdown", "id": "20ce715e-e24a-4ec3-a93d-d3eb5858aef5", "metadata": {}, "source": [ "Consistent with the 5/2 ratio of forward/reverse rates (and the 1st order reactions),\n", "the systems settles in the following equilibrium: [A] = 16.25 , [B] = 40.625" ] }, { "cell_type": "code", "execution_count": 11, "id": "796bef2e-8a11-4aff-8ce5-0b9bb5f72680", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2 A <-> 3 B\n", "Final concentrations: [A] = 16.25 ; [B] = 40.63\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 2.5\n", " Formula used: [B] / [A]\n", "2. Ratio of forward/reverse reaction rates: 2.5\n", "Discrepancy between the two values: 1.776e-14 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reaction has reached equilibrium\n", "bio.reaction_dynamics.is_in_equilibrium(rxn_index=0, conc=bio.bin_snapshot(bin_address = 0))" ] }, { "cell_type": "code", "execution_count": 12, "id": "7527ea21-fd7d-4514-ab49-cc6c16482c10", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABcaption
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"title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 } } }, "title": { "text": "Changes in concentrations" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ 0, 10.049999999999981 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ 7.777777777777778, 52.22222222222222 ], "title": { "text": "concentration" }, "type": "linear" } } }, "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = px.line(data_frame=bio.get_history(), x=\"SYSTEM TIME\", y=[\"A\", \"B\"], \n", " title=\"Changes in concentrations\",\n", " color_discrete_sequence = ['navy', 'darkorange'],\n", " labels={\"value\":\"concentration\", \"variable\":\"Chemical\"})\n", "fig.show()" ] }, { "cell_type": "markdown", "id": "ca41b04c-8626-45b1-b83d-79a97dd9a3cd", "metadata": {}, "source": [ "### Notice the *early overshoots* (the time step is too large early in the simulation!)\n", "Variable, adaptive time steps are explored at length in the _\"reactions_single_compartment\"_ experiments" ] }, { "cell_type": "code", "execution_count": null, "id": "243badde", "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 }