{ "cells": [ { "cell_type": "markdown", "id": "3bbe8002-bdf3-490c-bde0-80dd3713a3d0", "metadata": {}, "source": [ "## An `A <-> B` reaction \n", "with 1st-order kinetics in both directions, taken to equilibrium,\n", "using a simple, coarse fixed-timestep simulation. \n", "\n", "Afterwards, perform some analysis of the results\n", "\n", "See also the experiment _\"1D/reactions/reaction_1\"_ for a multi-compartment version. \n", "\n", "This experiment gets continued in _\"react_2_b\"_ , with a more sophisticated approach, \n", "involving adaptive variable time steps.\n", "\n", "LAST REVISED: Dec. 3, 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": [ "import numpy as np\n", "from experiments.get_notebook_info import get_notebook_basename\n", "\n", "from src.modules.reactions.reaction_dynamics import ReactionDynamics\n", "from src.modules.visualization.plotly_helper import PlotlyHelper\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_2_a.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": "code", "execution_count": null, "id": "eed9fe97-872a-44de-93ba-c499a6f1191b", "metadata": {}, "outputs": [], "source": [] }, { "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": [ "# Instantiate the simulator and specify the chemicals\n", "dynamics = ReactionDynamics(names=[\"A\", \"B\"])\n", "\n", "# Reaction A <-> B , with 1st-order kinetics in both directions\n", "dynamics.add_reaction(reactants=[\"A\"], products=[\"B\"], \n", " forward_rate=3., reverse_rate=2.)\n", "\n", "print(\"Number of reactions: \", dynamics.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 = -1,005.1 / K = 1.5) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {'B', 'A'}\n" ] } ], "source": [ "dynamics.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_2_a.log.htm`]\n" ] } ], "source": [ "# Send a plot of the network of reactions to the HTML log file\n", "graph_data = dynamics.prepare_graph_network()\n", "GraphicLog.export_plot(graph_data, \"vue_cytoscape_1\")" ] }, { "cell_type": "code", "execution_count": 7, "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": 8, "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", "Set of chemicals involved in reactions: {'B', 'A'}\n" ] } ], "source": [ "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 9, "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": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "markdown", "id": "ab7147fe-712c-4c92-b61f-20ff51675ab8", "metadata": {}, "source": [ "### Test your intuition: \n", "#### given that this reaction operates mostly in the forward direction (kF = 3 , kR = 2 , K = 1.5), \n", "#### do you think that A will be consumed and B will be produced??\n", "We can take a sneak preview at the final equilibrium concentrations without actually running the simulation:" ] }, { "cell_type": "code", "execution_count": 10, "id": "12cac04d-dd61-4646-9339-8b70e22139e8", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'A': 24.0, 'B': 36.0}" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.find_equilibrium_conc(rxn_index=0) # This is an EXACT solution" ] }, { "cell_type": "markdown", "id": "ee5b9d1c-3ebe-497a-a0e9-bfb02dcd0693", "metadata": {}, "source": [ "#### The reaction will actually proceed IN REVERSE, because of the large initial concentration of B (which we had set to 50), relative to the small initial concentration of A (10)\n", "Now, let's see the reaction in action!" ] }, { "cell_type": "code", "execution_count": null, "id": "d748df77-1b71-4d16-9e24-212d74a93ff4", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "fc516ca2-e62d-4784-b826-5372ff7f4c75", "metadata": { "tags": [] }, "source": [ "### Run 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, variable_steps=False, \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": "markdown", "id": "98ec8a03-7a9b-403a-8dcd-d9e19c49d656", "metadata": {}, "source": [ "We can already see the reaction proceeding in reverse..." ] }, { "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, variable_steps=False, \n", " snapshots={\"initial_caption\": \"2nd reaction step\",\n", " \"final_caption\": \"last reaction step\"})" ] }, { "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
10.117.00000043.000000first reaction step
20.220.50000039.5000002nd reaction step
30.322.25000037.750000
40.423.12500036.875000
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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": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "markdown", "id": "c7650ed4-365e-43c2-b001-280297c68ece", "metadata": {}, "source": [ "## NOTE: for demonstration purposes, we're using FIXED time steps... \n", "## Typically, one would use the option for adaptive variable time steps (see experiment `react_2_b`)" ] }, { "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() # The current concentrations, in the order the chemicals were added " ] }, { "cell_type": "markdown", "id": "d25eedf3-89f8-4f8c-a49a-d2689103528b", "metadata": {}, "source": [ "NOTE: Consistent with the 3/2 ratio of forward/reverse rates (and the 1st order of the 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: [A] = 23.99 ; [B] = 36.01\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": [ "### As noted earlier, 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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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": [ -0.00046374367622259693, 1.1004637436762226 ], "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": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = dynamics.get_history() # Revisited from earlier\n", "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": 20, "id": "5ee8ec14-442f-4e76-bc86-26b8791f7e70", "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": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A = list(df.A)\n", "A" ] }, { "cell_type": "code", "execution_count": 21, "id": "a390ed46-f014-414f-9b14-69f6da95dc41", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "12" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(A)" ] }, { "cell_type": "code", "execution_count": 22, "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": 23, "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": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A_dot" ] }, { "cell_type": "code", "execution_count": 24, "id": "f5fa1f8e-517f-4fd1-b3bf-51c12ab883f0", "metadata": {}, "outputs": [], "source": [ "df['A_dot'] = A_dot # Add a column to the Pandas dataframe" ] }, { "cell_type": "code", "execution_count": 25, "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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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(chemicals=[\"A\", \"A_dot\"], colors=['navy', 'brown'], \n", " ylabel=\"concentration (blue) /
concentration change per unit time (brown)\",\n", " title=\"Concentration of A with time (blue), and its rate of change (brown)\")" ] }, { "cell_type": "markdown", "id": "85d87078-8fc1-4166-95e1-343b546f9971", "metadata": {}, "source": [ "### At t=0 : \n", "[A]=10 and [A] has a high rate of change (70)\n", "### As the system approaches equilibrium : \n", "[A] approaches a value of 24, and its rate of change decays to zero." ] }, { "cell_type": "markdown", "id": "99cd0942-555b-444e-9c6f-ee1481a2a980", "metadata": {}, "source": [ "#### **NOTE:** 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.) \n", "## In experiment \"react_2_b\", we revisit the same reaction using a better simulator that employs _adaptive variable time steps_" ] }, { "cell_type": "code", "execution_count": null, "id": "531ce53b-7336-440e-bce4-716aafa6c692", "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 }