{ "cells": [ { "cell_type": "markdown", "id": "4f3151f1-fee2-40d3-9913-d02f15a8fa30", "metadata": {}, "source": [ "## 2 COUPLED reactions: `A + B <-> C` and `C + D <-> E` , \n", "### with 1st-order kinetics for each species, taken to equilibrium\n", "\n", "Both reactions are stronger in their respective forward rates. For the most part, \"C\" is produced by the 1st reaction, and consumed by the 2nd one.\n", "\n", "Diffusion not applicable (just 1 bin)" ] }, { "cell_type": "markdown", "id": "a2773bf7-bc28-4cb9-b990-552f00941840", "metadata": {}, "source": [ "### TAGS : \"reactions 1D\"" ] }, { "cell_type": "code", "execution_count": 1, "id": "f653d100-becb-453a-8810-07a7aa557b2d", "metadata": {}, "outputs": [], "source": [ "LAST_REVISED = \"Jan. 13, 2025\"\n", "LIFE123_VERSION = \"1.0.0rc2\" # Library version this experiment is based on" ] }, { "cell_type": "code", "execution_count": 2, "id": "c27da7de-2903-4744-9317-e5ef1a9cc492", "metadata": {}, "outputs": [], "source": [ "#import set_path # Using MyBinder? Uncomment this before running the next cell!" ] }, { "cell_type": "code", "execution_count": 3, "id": "aa3f2a77", "metadata": {}, "outputs": [], "source": [ "#import sys\n", "#sys.path.append(\"C:/some_path/my_env_or_install\") # CHANGE to the folder containing your venv or libraries installation!\n", "# NOTE: If any of the imports below can't find a module, uncomment the lines above, or try: import set_path \n", "\n", "from experiments.get_notebook_info import get_notebook_basename\n", "\n", "from life123 import ChemData, BioSim1D\n", "\n", "from life123 import GraphicLog, HtmlLog as log" ] }, { "cell_type": "code", "execution_count": 4, "id": "05cc8402-3b3c-468a-bb98-ea4159816a0f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-> Output will be LOGGED into the file 'reaction_8.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": null, "id": "a677d904-7320-4481-9354-7e027bd13ba5", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "2c3ba140-b7be-4c40-8bd1-998ff0640faf", "metadata": {}, "source": [ "# Initialize the System" ] }, { "cell_type": "code", "execution_count": 5, "id": "8b784456-e6d8-43b8-a929-4d83087fc3ea", "metadata": {}, "outputs": [], "source": [ "# Initialize the system\n", "chem_data = ChemData(names=[\"A\", \"B\", \"C\", \"D\", \"E\"]) # NOTE: Diffusion not applicable (just 1 bin)\n", "bio = BioSim1D(n_bins=1, chem_data=chem_data) " ] }, { "cell_type": "code", "execution_count": 6, "id": "9263bf00-efee-46fe-a5da-0d5fdbf2f254", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 2 (at temp. 25 C)\n", "0: A + B <-> C (kF = 5 / kR = 2 / delta_G = -2,271.4 / K = 2.5) | 1st order in all reactants & products\n", "1: C + D <-> E (kF = 8 / kR = 4 / delta_G = -1,718.3 / K = 2) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {'B', 'D', 'E', 'A', 'C'}\n" ] } ], "source": [ "# Specify the reactions\n", "reactions = bio.get_reactions()\n", "\n", "# Reactions A + B <-> C and C + D <-> E , with 1st-order kinetics for each species\n", "reactions.add_reaction(reactants=[\"A\", \"B\"], products=\"C\", forward_rate=5., reverse_rate=2.)\n", "reactions.add_reaction(reactants=[\"C\", \"D\"], products=\"E\", forward_rate=8., reverse_rate=4.)\n", "reactions.describe_reactions()" ] }, { "cell_type": "code", "execution_count": 7, "id": "c05a44f2-085e-418d-be55-8ea403b1b44e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2 COUPLED reactions: A + B C and C + D E\n", "[GRAPHIC ELEMENT SENT TO LOG FILE `reaction_8.log.htm`]\n" ] } ], "source": [ "# Send a header and a plot to the HTML log file\n", "log.write(\"2 COUPLED reactions: A + B <-> C and C + D <-> E\",\n", " style=log.h2)\n", "\n", "# Send the plot to the HTML log file\n", "reactions.plot_reaction_network(\"vue_cytoscape_2\")" ] }, { "cell_type": "code", "execution_count": null, "id": "f449a5f3-6e30-436d-96cc-25e04a487c8f", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "f1298564-11dc-41ab-b9bf-1fcbb3928a90", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "d5aa4f2e-3a5f-421a-ad82-c0bfb95ff39b", "metadata": {}, "source": [ "## Enable History" ] }, { "cell_type": "code", "execution_count": 8, "id": "85f9b073-6a97-471a-a5ff-50c4cf9bed7d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "History enabled for bins None and chemicals None (None means 'all')\n" ] } ], "source": [ "# Let's enable history - by default for all chemicals and all bins (we just have 1 bin)\n", "bio.enable_history()" ] }, { "cell_type": "code", "execution_count": null, "id": "fa7c43f2-78df-4996-86c7-ad7e66a5db1c", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "c2eb41bb-01ae-4734-ab8f-d18b422db6ec", "metadata": {}, "source": [ "### Set the initial state" ] }, { "cell_type": "code", "execution_count": 9, "id": "e63a9bce-3c9d-4b4b-bced-d11ea2a50cdd", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "1 bins and 5 chemical species:\n" ] }, { "data": { "text/html": [ "
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SYSTEM TIMEABCDE
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" ], "text/plain": [ " SYSTEM TIME A B C D E\n", "0 0.0 3.0 5.0 1.0 0.4 0.1" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "bio.get_bin_history(bin_address=0)" ] }, { "cell_type": "code", "execution_count": null, "id": "5f882cd9-ae27-4310-ace6-6d6ad37bce09", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "76a872c4-e89b-4ac7-b31f-c38853ce15f5", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "db7979c8-c39d-418c-bd70-e6e234d71cf7", "metadata": { "tags": [] }, "source": [ "### Start the reaction" ] }, { "cell_type": "code", "execution_count": 11, "id": "a7f29264-8f29-4940-91cd-a832762d9833", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "System Time is now: 0.01\n" ] } ], "source": [ "# First step\n", "bio.react(time_step=0.01, n_steps=1)" ] }, { "cell_type": "code", "execution_count": 12, "id": "ee40770c-ac6c-4842-a8c6-bb1eb11a4108", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0.01:\n", "1 bins and 5 chemical species:\n" ] }, { "data": { "text/html": [ "
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SYSTEM TIMEABCDE
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" ], "text/plain": [ " SYSTEM TIME A B C D E\n", "0 0.00 3.00 5.00 1.000 0.400 0.100\n", "1 0.01 2.27 4.27 1.702 0.372 0.128" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "bio.get_bin_history(bin_address=0)" ] }, { "cell_type": "code", "execution_count": null, "id": "9084bda3-7931-4c69-b7ea-98e067a8bc04", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 14, "id": "b16bd67d-0d25-458d-bf17-d069bc736621", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "System Time is now: 0.02\n" ] } ], "source": [ "# Identical 2nd step\n", "bio.react(time_step=0.01, n_steps=1)" ] }, { "cell_type": "code", "execution_count": 15, "id": "c0798b32-4798-4210-90e3-089ddeb1e877", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0.02:\n", "1 bins and 5 chemical species:\n" ] }, { "data": { "text/html": [ "
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SpeciesDiff rateBin 0
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" ], "text/plain": [ " Species Diff rate Bin 0\n", "0 A None 1.819395\n", "1 B None 3.819395\n", "2 C None 2.107073\n", "3 D None 0.326468\n", "4 E None 0.173532" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "bio.describe_state()" ] }, { "cell_type": "code", "execution_count": 16, "id": "7aa7bea0-d4bd-462e-85ee-645d6d4910db", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABCDE
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" ], "text/plain": [ " SYSTEM TIME A B C D E\n", "0 0.00 3.000000 5.000000 1.000000 0.400000 0.100000\n", "1 0.01 2.270000 4.270000 1.702000 0.372000 0.128000\n", "2 0.02 1.819395 3.819395 2.107073 0.326468 0.173532" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "bio.get_bin_history(bin_address=0)" ] }, { "cell_type": "code", "execution_count": null, "id": "da04cd22-e3ff-48ab-a9c8-d441aa450f48", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "ee6298fe-33a8-456b-9ddb-ffb6e0df29aa", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "100a4ed1-cf8d-40ba-a49c-680ee02a1d49", "metadata": {}, "source": [ "### Numerous more steps" ] }, { "cell_type": "code", "execution_count": 17, "id": "9bf6ad6f-5e63-44c2-a5eb-e27a5d442c45", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "System Time is now: 2.02\n" ] } ], "source": [ "# Numerous more identical steps, to equilibrium\n", "bio.react(time_step=0.01, n_steps=200)" ] }, { "cell_type": "code", "execution_count": 18, "id": "21e62a50-5923-44ed-a9c3-390e48f0ca12", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 2.02:\n", "1 bins and 5 chemical species:\n" ] }, { "data": { "text/html": [ "
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" ], "text/plain": [ " Species Diff rate Bin 0\n", "0 A None 0.505080\n", "1 B None 2.505080\n", "2 C None 3.163167\n", "3 D None 0.068247\n", "4 E None 0.431753" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "bio.describe_state()" ] }, { "cell_type": "code", "execution_count": null, "id": "9a7d980d-bf05-4366-8605-c721e122a84d", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "7c4e149f-3f80-48b1-a910-b828701c2806", "metadata": { "tags": [] }, "source": [ "### Equilibrium" ] }, { "cell_type": "code", "execution_count": 19, "id": "99dd2a45-b7fa-459b-a25f-3475043bdbb7", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A + B <-> C\n", "Final concentrations: [A] = 0.5051 ; [B] = 2.505 ; [C] = 3.163\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 2.5\n", " Formula used: [C] / ([A][B])\n", "2. Ratio of forward/reverse reaction rates: 2.5\n", "Discrepancy between the two values: 8.882e-14 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that each 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": 20, "id": "ab2dbc91-ba95-45a9-9d41-638b78019752", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "C + D <-> E\n", "Final concentrations: [C] = 3.163 ; [D] = 0.06825 ; [E] = 0.4318\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 2\n", " Formula used: [E] / ([C][D])\n", "2. Ratio of forward/reverse reaction rates: 2\n", "Discrepancy between the two values: 3.331e-14 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "bio.reaction_dynamics.is_in_equilibrium(rxn_index=1, conc=bio.bin_snapshot(bin_address = 0))" ] }, { "cell_type": "code", "execution_count": 21, "id": "df7086e8-1ea6-45f0-9fa3-66c84a9475e7", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "At equilibrium: -4.440892098500626e-15 (this should be close to 0 at equilibrium)\n" ] } ], "source": [ "# Do a consistent check with the equilibrium concentrations:\n", "\n", "A_eq = bio.bin_concentration(0, 0)\n", "B_eq = bio.bin_concentration(0, 1)\n", "C_eq = bio.bin_concentration(0, 2)\n", "D_eq = bio.bin_concentration(0, 3)\n", "E_eq = bio.bin_concentration(0, 4)\n", "\n", "Rf0 = reactions.get_forward_rate(0)\n", "Rb0 = reactions.get_reverse_rate(0)\n", "\n", "Rf1 = reactions.get_forward_rate(1)\n", "Rb1 = reactions.get_reverse_rate(1)\n", "\n", "equil = -(Rf0 * A_eq * B_eq - Rf1 * C_eq * D_eq) + (Rb0 * C_eq - Rb1 * E_eq)\n", "\n", "print(\"\\nAt equilibrium: \", equil, \" (this should be close to 0 at equilibrium)\")" ] }, { "cell_type": "code", "execution_count": null, "id": "8b984d7e-8a2e-44e8-aad1-5bb808ff2094", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 22, "id": "8451e0a7-10d1-430f-a968-88a0f83d89ee", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bio.plot_history_single_bin(bin_address=0, \n", " title=\"2 COUPLED reactions: A + B <-> C and C + D <-> E . Concentrations at bin 0\")" ] }, { "cell_type": "markdown", "id": "cde2dbcb-a43c-41f1-a8b3-b801290a8d57", "metadata": {}, "source": [ "A and B get consumed. \n", "C gets produced by the 1st reaction more quickly than consumed by the 2nd one.\n", "D gets consumed, while E gets produced." ] }, { "cell_type": "code", "execution_count": null, "id": "aed58c18-94dd-446f-bb6a-f59eb76db64c", "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": "3.9.13" } }, "nbformat": 4, "nbformat_minor": 5 }