{ "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: in particular, examine the reaction rates \n", "\n", "(See also the experiment _\"1D/reactions/reaction_1\"_ for a multi-compartment version) \n", "\n", "#### This experiment gets repeated in _\"react_2_b\"_ , with a more sophisticated approach, \n", "#### involving adaptive variable time steps." ] }, { "cell_type": "code", "execution_count": 1, "id": "0fac88df-1c44-4419-8479-a20369b06499", "metadata": {}, "outputs": [], "source": [ "LAST_REVISED = \"July 26, 2024\"\n", "LIFE123_VERSION = \"1.0.0.beta.38\" # Version this experiment is based on" ] }, { "cell_type": "code", "execution_count": 2, "id": "3747d0d5-aeaf-4529-8018-11f42638b34f", "metadata": {}, "outputs": [], "source": [ "#import set_path # Using MyBinder? Uncomment this before running the next cell!\n", " # Importing this module will add the project's home directory to sys.path" ] }, { "cell_type": "code", "execution_count": 3, "id": "b0ce3cdd", "metadata": { "tags": [] }, "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", "import numpy as np\n", "import ipynbname\n", "\n", "from life123 import check_version, UniformCompartment, PlotlyHelper, GraphicLog" ] }, { "cell_type": "code", "execution_count": 4, "id": "4f75ae66-3d5c-474c-8d88-bd8a7ca92aef", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "OK\n" ] } ], "source": [ "check_version(LIFE123_VERSION)" ] }, { "cell_type": "code", "execution_count": 5, "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 = ipynbname.name() + \".log.htm\" # Use the notebook base filename for the log file\n", " # IN CASE OF PROBLEMS, set manually to any desired name\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": "46703103-a97d-426c-bf6e-ad6e397a7ddb", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "ed390e55-5715-4736-aaf5-670981fab8e9", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "9329208b-070f-4902-8f37-0f11ddf75ed6", "metadata": {}, "source": [ "# Initialize the System" ] }, { "cell_type": "code", "execution_count": 6, "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 = UniformCompartment()\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": 7, "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": 8, "id": "cb582868-431c-4022-aa0e-a2f554f80d6c", "metadata": { "lines_to_next_cell": 2 }, "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", "dynamics.plot_reaction_network(\"vue_cytoscape_2\")" ] }, { "cell_type": "code", "execution_count": 9, "id": "ae304704-c8d9-4cef-9e0b-2587bb3909ef", "metadata": {}, "outputs": [], "source": [ "# Initial concentrations of all the chemicals\n", "dynamics.set_conc({\"A\": 10., \"B\": 50.})" ] }, { "cell_type": "code", "execution_count": 10, "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": 11, "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
00.010.050.0Initialized state
\n", "
" ], "text/plain": [ " SYSTEM TIME A B caption\n", "0 0.0 10.0 50.0 Initialized state" ] }, "execution_count": 11, "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": 12, "id": "12cac04d-dd61-4646-9339-8b70e22139e8", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'A': 24.0, 'B': 36.0}" ] }, "execution_count": 12, "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": 13, "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": 14, "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
00.010.050.0Initialized 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 Initialized state\n", "1 0.1 17.0 43.0 first reaction step" ] }, "execution_count": 14, "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": 15, "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": 16, "id": "80fbaee3-bd6f-4197-9270-23374d46a4a7", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABcaption
00.010.00000050.000000Initialized 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 Initialized 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": 16, "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": 17, "id": "b139f5e4-625f-4a5e-8f57-8f00244dced4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([23.99316406, 36.00683594])" ] }, "execution_count": 17, "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": 18, "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": 18, "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": 19, "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": [ -0.0007442489851150202, 1.100744248985115 ], "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
00.010.00000050.000000Initialized state
10.117.00000043.000000first reaction step
20.220.50000039.5000002nd reaction step
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" ], "text/plain": [ " SYSTEM TIME A B caption\n", "0 0.0 10.000000 50.000000 Initialized 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": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = dynamics.get_history() # Revisited from earlier\n", "df" ] }, { "cell_type": "code", "execution_count": null, "id": "e73955b7-21c5-4147-96f1-55bdad8092ba", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "3f3556f4-2474-4233-b6f9-d05ec856dd13", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "f72f4988-4e4b-4268-9f4a-e36300c9dcf1", "metadata": {}, "source": [ "## PART 2 - Now investigate A_dot, i.e. d[A]/dt" ] }, { "cell_type": "markdown", "id": "0ddc7f18-dcc7-4563-b6f7-75049d944669", "metadata": {}, "source": [ "NOTE: there's actually no need to compute this; it can be automatically saved during the reaction, as demonstrated in experiment `react_2_b`" ] }, { "cell_type": "code", "execution_count": 22, "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": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A = list(df.A)\n", "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 Pandas 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
00.010.00000050.000000Initialized state70.000000
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20.220.50000039.5000002nd reaction step26.250000
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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": [ "dynamics.plot_history(chemicals=[\"A\", \"A_dot\"], colors=['darkturquoise', 'brown'], \n", " ylabel=\"concentration (darkturquoise) /
concentration change per unit time (brown)\",\n", " title=\"Concentration of A with time (darkturquoise), 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 approach that employs **_adaptive variable time steps_** , and also automatically saves the reaction rates." ] }, { "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 }