{ "cells": [ { "cell_type": "markdown", "id": "c3b90917-d8b3-4644-a485-b22d440272b9", "metadata": {}, "source": [ "## One-bin Association/Dissociation reaction `A + B <-> C`\n", "### with 1st-order kinetics for each species, taken to equilibrium\n", "\n", "Diffusion not applicable (just 1 bin)\n", "\n", "See also the experiment _\"reactions_single_compartment/react_3\"_ " ] }, { "cell_type": "markdown", "id": "1e74fd56-a767-41de-b06a-ee171d7812c7", "metadata": {}, "source": [ "### TAGS : \"reactions 1D\", \"basic\"" ] }, { "cell_type": "code", "execution_count": 1, "id": "1634a05f-032d-483e-a760-76229ce79567", "metadata": {}, "outputs": [], "source": [ "LAST_REVISED = \"June 6, 2025\"\n", "LIFE123_VERSION = \"1.0.0rc6\" # Library version this experiment is based on" ] }, { "cell_type": "code", "execution_count": 2, "id": "a8f89c58-e3b5-4a07-96ec-6f7455db1bf5", "metadata": {}, "outputs": [], "source": [ "#import set_path # Using MyBinder? Uncomment this before running the next cell!" ] }, { "cell_type": "code", "execution_count": 3, "id": "f5117d69", "metadata": {}, "outputs": [], "source": [ "#import sys, os\n", "#os.getcwd()\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, check_version\n", "\n", "from life123 import GraphicLog" ] }, { "cell_type": "code", "execution_count": 4, "id": "5209dfc4-825a-4d41-95f6-aefb7fca75f1", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "OK\n" ] } ], "source": [ "check_version(LIFE123_VERSION)" ] }, { "cell_type": "code", "execution_count": null, "id": "95122f3c-b9c7-4ed4-9190-51350c295f07", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 5, "id": "ada82175-1d15-4213-b834-5a5d8e2dd31e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-> Output will be LOGGED into the file 'reaction_4.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": 6, "id": "d8f2d83d-97bc-4f57-8f71-c0923f0334ed", "metadata": { "lines_to_next_cell": 2 }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "1 bins and 3 chemical species\n" ] }, { "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", " \n", " \n", " \n", "
SpeciesDiff rateBin 0
0ANone10.0
1BNone50.0
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" ], "text/plain": [ " Species Diff rate Bin 0\n", "0 A None 10.0\n", "1 B None 50.0\n", "2 C None 20.0" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Initialize the system. NOTE: Diffusion not applicable (using just 1 bin)\n", "chem_data = ChemData(names=[\"A\", \"B\", \"C\"], plot_colors=['red', 'darkorange', 'green'])\n", "\n", "bio = BioSim1D(n_bins=1, chem_data=chem_data)\n", "\n", "bio.set_uniform_concentration(chem_index=0, conc=10.)\n", "bio.set_uniform_concentration(chem_index=1, conc=50.)\n", "bio.set_uniform_concentration(chem_index=2, conc=20.)\n", "\n", "bio.describe_state()" ] }, { "cell_type": "code", "execution_count": 7, "id": "42760c32-a4f2-4f8b-96c0-8f98b484189d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 1 (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", "Set of chemicals involved in the above reactions: {\"B\" (darkorange), \"C\" (green), \"A\" (red)}\n" ] } ], "source": [ "# Specify the reaction\n", "reactions = bio.get_reactions()\n", "\n", "# Reaction A + B <-> C , with 1st-order kinetics for each species\n", "reactions.add_reaction(reactants=[\"A\" , \"B\"], products=\"C\",\n", " forward_rate=5., reverse_rate=2.)\n", "\n", "reactions.describe_reactions()" ] }, { "cell_type": "code", "execution_count": 8, "id": "25f70c0f-621e-413f-bc93-336d38d462d7", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[GRAPHIC ELEMENT SENT TO LOG FILE `reaction_4.log.htm`]\n" ] } ], "source": [ "# Send the plot of the reaction network to the HTML log file\n", "reactions.plot_reaction_network(\"vue_cytoscape_2\")" ] }, { "cell_type": "code", "execution_count": null, "id": "b351573c-275c-434f-8301-4ed54197e0cc", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 9, "id": "39ec6840-ad21-4afb-9213-f27669817605", "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\n", "bio.enable_history(take_snapshot=True, caption=\"Initial state\")" ] }, { "cell_type": "code", "execution_count": 10, "id": "d89603fb-b14c-40ce-bdea-ebe36c2f726b", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABCcaption
00.010.050.020.0Initial state
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" ], "text/plain": [ " SYSTEM TIME A B C caption\n", "0 0.0 10.0 50.0 20.0 Initial state" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "bio.get_bin_history(bin_address=0)" ] }, { "cell_type": "code", "execution_count": null, "id": "3c71a1a3-f6b8-4f05-bf5a-267e10fe7d7e", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "79e68c64-fe18-4b9b-ba17-cdef6dcf4b35", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "356e4db3-02a6-40bd-a951-841bfc6c5522", "metadata": { "tags": [] }, "source": [ "### First step" ] }, { "cell_type": "code", "execution_count": 11, "id": "b8c0d439-13f7-459c-88e2-0ae357b46c18", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "System Time is now: 0.002\n", "SYSTEM STATE at Time t = 0.002:\n", "1 bins and 3 chemical species\n" ] }, { "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", " \n", " \n", " \n", "
SpeciesDiff rateBin 0
0ANone5.08
1BNone45.08
2CNone24.92
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" ], "text/plain": [ " Species Diff rate Bin 0\n", "0 A None 5.08\n", "1 B None 45.08\n", "2 C None 24.92" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# First step\n", "bio.react(time_step=0.002, n_steps=1)\n", "bio.describe_state()" ] }, { "cell_type": "code", "execution_count": 12, "id": "386d8052-2d92-43b0-b817-ab4a1cce3ba0", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABCcaption
00.00010.0050.0020.00Initial state
10.0025.0845.0824.92
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" ], "text/plain": [ " SYSTEM TIME A B C caption\n", "0 0.000 10.00 50.00 20.00 Initial state\n", "1 0.002 5.08 45.08 24.92 " ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "bio.get_bin_history(bin_address=0)" ] }, { "cell_type": "code", "execution_count": null, "id": "1bf6c537-ae57-46fe-992e-f7d0fc3bb29e", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "88ec4bcc-48dc-45eb-84fc-8e6e0b259612", "metadata": {}, "source": [ "### Numerous more steps" ] }, { "cell_type": "code", "execution_count": 13, "id": "8efdf9ef-bdca-48ff-b139-6e2d9952c1d8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "System Time is now: 0.06\n", "SYSTEM STATE at Time t = 0.06:\n", "1 bins and 3 chemical species\n" ] }, { "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", " \n", " \n", " \n", "
SpeciesDiff rateBin 0
0ANone0.294878
1BNone40.294878
2CNone29.705122
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" ], "text/plain": [ " Species Diff rate Bin 0\n", "0 A None 0.294878\n", "1 B None 40.294878\n", "2 C None 29.705122" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Numerous more steps\n", "bio.react(time_step=0.002, n_steps=29)\n", "\n", "bio.describe_state()" ] }, { "cell_type": "markdown", "id": "6b0be45c-ff0e-43d8-847a-b6e8d0e6e0ec", "metadata": { "tags": [] }, "source": [ "### Equilibrium" ] }, { "cell_type": "markdown", "id": "7f687d0d-75ab-4e29-8070-5b6f1fc80b4b", "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: \n", "[A] = 0.29487831 , [B] = 40.29487831 , [C] = 29.70512169" ] }, { "cell_type": "code", "execution_count": 14, "id": "46a3ea5d-6516-4582-9958-6a80403e8f19", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A + B <-> C\n", "Current concentrations: [A] = 0.2949 ; [B] = 40.29 ; [C] = 29.71\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 2.49999\n", " Formula used: [C] / ([A][B])\n", "2. Ratio of forward/reverse reaction rates: 2.5\n", "Discrepancy between the two values: 0.0003107 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reaction has reached equilibrium\n", "bio.get_reaction_handler().is_in_equilibrium(rxn_index=0, conc=bio.bin_snapshot(bin_address = 0))" ] }, { "cell_type": "code", "execution_count": 15, "id": "6975a1e8-d708-401f-ab7f-78c183f765bf", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABCcaption
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" ], "text/plain": [ " SYSTEM TIME A B C caption\n", "0 0.000 10.000000 50.000000 20.000000 Initial state\n", "1 0.002 5.080000 45.080000 24.920000 \n", "2 0.004 2.889616 42.889616 27.110384 \n", "3 0.006 1.758712 41.758712 28.241288 \n", "4 0.008 1.137262 41.137262 28.862738 \n", "5 0.010 0.784874 40.784874 29.215126 \n", "6 0.012 0.581625 40.581625 29.418375 \n", "7 0.014 0.463266 40.463266 29.536734 \n", "8 0.016 0.393960 40.393960 29.606040 \n", "9 0.018 0.353248 40.353248 29.646752 \n", "10 0.020 0.329288 40.329288 29.670712 \n", "11 0.022 0.315171 40.315171 29.684829 \n", "12 0.024 0.306849 40.306849 29.693151 \n", "13 0.026 0.301940 40.301940 29.698060 \n", "14 0.028 0.299045 40.299045 29.700955 \n", "15 0.030 0.297336 40.297336 29.702664 \n", "16 0.032 0.296328 40.296328 29.703672 \n", "17 0.034 0.295734 40.295734 29.704266 \n", "18 0.036 0.295383 40.295383 29.704617 \n", "19 0.038 0.295176 40.295176 29.704824 \n", "20 0.040 0.295053 40.295053 29.704947 \n", "21 0.042 0.294981 40.294981 29.705019 \n", "22 0.044 0.294939 40.294939 29.705061 \n", "23 0.046 0.294914 40.294914 29.705086 \n", "24 0.048 0.294899 40.294899 29.705101 \n", "25 0.050 0.294890 40.294890 29.705110 \n", "26 0.052 0.294885 40.294885 29.705115 \n", "27 0.054 0.294882 40.294882 29.705118 \n", "28 0.056 0.294880 40.294880 29.705120 \n", "29 0.058 0.294879 40.294879 29.705121 \n", "30 0.060 0.294878 40.294878 29.705122 " ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "bio.get_bin_history(bin_address=0)" ] }, { "cell_type": "markdown", "id": "8a4576cc-d927-4776-a691-2001bba5d1b7", "metadata": {}, "source": [ "## Note: `A` (now largely depleted) is largely the limiting reagent" ] }, { "cell_type": "markdown", "id": "d82cb7fe-0bd2-4b3e-bbec-6f5b70d0e5ae", "metadata": { "tags": [] }, "source": [ "## Plots of changes of concentration with time" ] }, { "cell_type": "code", "execution_count": 17, "id": "9bbcb023-ab41-495d-8d8c-f02a568d48bf", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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