{ "cells": [ { "cell_type": "markdown", "id": "49bcb5b0-f19d-4b96-a5f1-e0ae30f66d8f", "metadata": {}, "source": [ "## `U` (\"Up-regulator\") up-regulates `X` , by sharing a reaction product `D` (\"Drain\") across 2 separate reactions: \n", "### `U <-> 2 D` and `X <-> D` (both mostly forward)\n", "\n", "1st-order kinetics throughout. \n", "\n", "Invoking [Le Chatelier's principle](https://www.chemguide.co.uk/physical/equilibria/lechatelier.html), it can be seen that, starting from equilibrium, when [U] goes up, so does [D]; and when [D] goes up, so does [X]. \n", "Conversely, when [U] goes down, so does [D]; and when [D] goes down, so does [X]. \n", "\n", "LAST REVISED: Nov. 4, 2023" ] }, { "cell_type": "code", "execution_count": 1, "id": "838b9dfc-e3c2-4e9d-bedc-f32a2b6a6dfa", "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": "16962197", "metadata": { "tags": [] }, "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.modules.reactions.reaction_dynamics import ReactionDynamics\n", "\n", "from src.modules.visualization.graphic_log import GraphicLog" ] }, { "cell_type": "code", "execution_count": 3, "id": "cc53849f-351d-49e0-bfa8-22f8d8e22f8e", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-> Output will be LOGGED into the file 'up_regulate_2.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_1\"],\n", " extra_js=\"https://cdnjs.cloudflare.com/ajax/libs/cytoscape/3.21.2/cytoscape.umd.js\")" ] }, { "cell_type": "markdown", "id": "d6d3ca49-589d-49b7-8424-37c7b01bcacf", "metadata": {}, "source": [ "### Initialize the system" ] }, { "cell_type": "code", "execution_count": 4, "id": "23c15e66-52e4-495b-aa3d-ecddd8d16942", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 2 (at temp. 25 C)\n", "0: U <-> 2 D (kF = 8 / kR = 2 / delta_G = -3,436.6 / K = 4) | 1st order in all reactants & products\n", "1: X <-> D (kF = 6 / kR = 3 / delta_G = -1,718.3 / K = 2) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {'D', 'X', 'U'}\n", "[GRAPHIC ELEMENT SENT TO LOG FILE `up_regulate_2.log.htm`]\n" ] } ], "source": [ "# Initialize the system\n", "chem_data = chem(names=[\"U\", \"X\", \"D\"])\n", "\n", "# Reaction U <-> 2D , with 1st-order kinetics for all species\n", "chem_data.add_reaction(reactants=\"U\", products=[(2, \"D\")],\n", " forward_rate=8., reverse_rate=2.)\n", "\n", "# Reaction X <-> D , with 1st-order kinetics for all species\n", "chem_data.add_reaction(reactants=\"X\", products=\"D\",\n", " forward_rate=6., reverse_rate=3.)\n", "\n", "chem_data.describe_reactions()\n", "\n", "# Send the plot of the reaction network to the HTML log file\n", "graph_data = chem_data.prepare_graph_network()\n", "GraphicLog.export_plot(graph_data, \"vue_cytoscape_1\")" ] }, { "cell_type": "markdown", "id": "d1d0eabb-b5b1-4e15-846d-5e483a5a24a7", "metadata": {}, "source": [ "### Set the initial concentrations of all the chemicals" ] }, { "cell_type": "code", "execution_count": 5, "id": "e80645d6-eb5b-4c78-8b46-ae126d2cb2cf", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "3 species:\n", " Species 0 (U). Conc: 50.0\n", " Species 1 (X). Conc: 100.0\n", " Species 2 (D). Conc: 0.0\n", "Set of chemicals involved in reactions: {'D', 'X', 'U'}\n" ] } ], "source": [ "dynamics = ReactionDynamics(chem_data=chem_data)\n", "dynamics.set_conc(conc={\"U\": 50., \"X\": 100., \"D\": 0.})\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": null, "id": "e652b8fa-b7b3-4772-b602-aa15d11d9067", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "0b46b395-3f68-4dbd-b0c5-d67a0e623726", "metadata": { "tags": [] }, "source": [ "# 1. Take the initial system to equilibrium" ] }, { "cell_type": "code", "execution_count": 6, "id": "bcf652b8-e0dc-438e-bdbe-02216c1d52a0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* INFO: the tentative time step (0.03) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.015) [Step started at t=0, and will rewind there]\n", "* INFO: the tentative time step (0.015) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.0075) [Step started at t=0, and will rewind there]\n", "* INFO: the tentative time step (0.0075) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.00375) [Step started at t=0, and will rewind there]\n", "* INFO: the tentative time step (0.00375) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.001875) [Step started at t=0, and will rewind there]\n", "Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n", "60 total step(s) taken\n" ] }, { "data": { "text/html": [ "
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" ], "text/plain": [ " SYSTEM TIME U X D caption\n", "0 0.000000 50.000000 100.000000 0.000000 Initial state\n", "1 0.001875 49.250000 98.875000 2.625000 \n", "2 0.002812 48.885547 98.326211 3.902695 \n", "3 0.003750 48.526223 97.784102 5.163452 \n", "4 0.004687 48.171958 97.248589 6.407496 \n", ".. ... ... ... ... ...\n", "56 0.245706 24.643947 53.475305 97.236801 \n", "57 0.282239 24.546114 52.410700 98.497071 \n", "58 0.337037 24.580376 51.371008 99.468240 \n", "59 0.419235 24.768894 50.563716 99.898495 \n", "60 0.542532 24.971820 50.109144 99.947215 \n", "\n", "[61 rows x 5 columns]" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n", "\n", "# All of these settings are currently close to the default values... but subject to change; set for repeatability\n", "dynamics.set_thresholds(norm=\"norm_A\", low=0.5, high=0.8, abort=1.44)\n", "dynamics.set_thresholds(norm=\"norm_B\", low=0.08, high=0.5, abort=1.5)\n", "dynamics.set_step_factors(upshift=1.5, downshift=0.5, abort=0.5)\n", "dynamics.set_error_step_factor(0.5)\n", "\n", "dynamics.single_compartment_react(initial_step=0.03, target_end_time=0.5,\n", " variable_steps=True, explain_variable_steps=False)\n", "\n", "dynamics.get_history()" ] }, { "cell_type": "code", "execution_count": 7, "id": "b56d1612-a68c-4da3-be37-a7245b6c1a80", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "From time 0 to 0.001875, in 1 step of 0.00187\n", "From time 0.001875 to 0.01219, in 11 steps of 0.000938\n", "From time 0.01219 to 0.01781, in 4 steps of 0.00141\n", "From time 0.01781 to 0.03469, in 8 steps of 0.00211\n", "From time 0.03469 to 0.03785, in 1 step of 0.00316\n", "From time 0.03785 to 0.03943, in 1 step of 0.00158\n", "From time 0.03943 to 0.04418, in 2 steps of 0.00237\n", "From time 0.04418 to 0.04774, in 1 step of 0.00356\n", "From time 0.04774 to 0.04952, in 1 step of 0.00178\n", "From time 0.04952 to 0.05219, in 1 step of 0.00267\n", "From time 0.05219 to 0.05619, in 1 step of 0.004\n", "From time 0.05619 to 0.0582, in 1 step of 0.002\n", "From time 0.0582 to 0.0612, in 1 step of 0.003\n", "From time 0.0612 to 0.0657, in 1 step of 0.00451\n", "From time 0.0657 to 0.06796, in 1 step of 0.00225\n", "From time 0.06796 to 0.07134, in 1 step of 0.00338\n", "From time 0.07134 to 0.0764, in 1 step of 0.00507\n", "From time 0.0764 to 0.07894, in 1 step of 0.00253\n", "From time 0.07894 to 0.08274, in 1 step of 0.0038\n", "From time 0.08274 to 0.08844, in 1 step of 0.0057\n", "From time 0.08844 to 0.09129, in 1 step of 0.00285\n", "From time 0.09129 to 0.09557, in 1 step of 0.00428\n", "From time 0.09557 to 0.1212, in 4 steps of 0.00641\n", "From time 0.1212 to 0.1308, in 1 step of 0.00962\n", "From time 0.1308 to 0.1357, in 1 step of 0.00481\n", "From time 0.1357 to 0.1429, in 1 step of 0.00722\n", "From time 0.1429 to 0.1645, in 2 steps of 0.0108\n", "From time 0.1645 to 0.197, in 2 steps of 0.0162\n", "From time 0.197 to 0.2457, in 2 steps of 0.0244\n", "From time 0.2457 to 0.2822, in 1 step of 0.0365\n", "From time 0.2822 to 0.337, in 1 step of 0.0548\n", "From time 0.337 to 0.4192, in 1 step of 0.0822\n", "From time 0.4192 to 0.5425, in 1 step of 0.123\n", "(60 steps total)\n" ] } ], "source": [ "dynamics.explain_time_advance()" ] }, { "cell_type": "markdown", "id": "cbf6c9c7-8cec-400f-9e70-49ff1a9f485c", "metadata": { "tags": [] }, "source": [ "## Plots of changes of concentration with time" ] }, { "cell_type": "code", "execution_count": 8, "id": "db4e74d0-3f9d-49dc-9553-bf3cdfe785f2", "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=U
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_curves(colors=['red', 'green', 'gray'])" ] }, { "cell_type": "markdown", "id": "962acf15-3b50-40e4-9daa-3dcca7d3291a", "metadata": {}, "source": [ "### Equilibrium" ] }, { "cell_type": "code", "execution_count": 9, "id": "2783a665-fca0-44e5-8d42-af2a96eae392", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: U <-> 2 D\n", "Final concentrations: [D] = 99.95 ; [U] = 24.97\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.0024\n", " Formula used: [D] / [U]\n", "2. Ratio of forward/reverse reaction rates: 4.0\n", "Discrepancy between the two values: 0.06 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n", "1: X <-> D\n", "Final concentrations: [D] = 99.95 ; [X] = 50.11\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 1.99459\n", " Formula used: [D] / [X]\n", "2. Ratio of forward/reverse reaction rates: 2.0\n", "Discrepancy between the two values: 0.2705 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reaction has reached equilibrium\n", "dynamics.is_in_equilibrium()" ] }, { "cell_type": "code", "execution_count": null, "id": "95679484-9ebe-4765-8644-40e94c384f65", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "448ec7fa-6529-438b-84ba-47888c2cd080", "metadata": { "tags": [] }, "source": [ "# 2. Now, let's suddenly increase [U]" ] }, { "cell_type": "code", "execution_count": 10, "id": "7245be7a-c9db-45f5-b033-d6c521237a9c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0.54253165:\n", "3 species:\n", " Species 0 (U). Conc: 70.0\n", " Species 1 (X). Conc: 50.10914435037049\n", " Species 2 (D). Conc: 99.94721484673187\n", "Set of chemicals involved in reactions: {'D', 'X', 'U'}\n" ] } ], "source": [ "dynamics.set_single_conc(species_name=\"U\", conc=70., snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 11, "id": "61eead55-fcef-41cd-b29e-f2d5ad5c6078", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEUXDcaption
590.41923524.76889450.56371699.898495
600.54253224.97182050.10914499.947215
610.54253270.00000050.10914499.947215Set concentration of `U`
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" ], "text/plain": [ " SYSTEM TIME U X D caption\n", "59 0.419235 24.768894 50.563716 99.898495 \n", "60 0.542532 24.971820 50.109144 99.947215 \n", "61 0.542532 70.000000 50.109144 99.947215 Set concentration of `U`" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(tail=3)" ] }, { "cell_type": "markdown", "id": "24455d58-a0ea-43fa-b6ad-95c42a8b34b2", "metadata": {}, "source": [ "### Again, take the system to equilibrium" ] }, { "cell_type": "code", "execution_count": 12, "id": "c06fd8d8-d550-4e35-a239-7b91bee32be9", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* INFO: the tentative time step (0.03) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.015) [Step started at t=0.54253, and will rewind there]\n", "* INFO: the tentative time step (0.015) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.0075) [Step started at t=0.54253, and will rewind there]\n", "* INFO: the tentative time step (0.0075) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.00375) [Step started at t=0.54253, and will rewind there]\n", "Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n", "32 total step(s) taken\n" ] } ], "source": [ "dynamics.single_compartment_react(initial_step=0.03, target_end_time=1,\n", " variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 13, "id": "35850ec7-e78e-4b57-976c-bc0ad6c824d5", "metadata": {}, "outputs": [], "source": [ "#dynamics.get_history()\n", "#dynamics.explain_time_advance()" ] }, { "cell_type": "code", "execution_count": 14, "id": "5af5d869-16ff-4f1d-ab83-4865b42e6376", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=U
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"white", "zerolinewidth": 2 } } }, "title": { "text": "Changes in concentration for `U <-> 2 D` and `X <-> D`" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ 0, 1.0973722423602885 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -8.105633431161618, 154.0070351920707 ], "title": { "text": "concentration" }, "type": "linear" } } }, "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_curves(colors=['red', 'green', 'gray'])" ] }, { "cell_type": "markdown", "id": "158e3787-f2d5-4a01-aaa9-6066e93e584c", "metadata": {}, "source": [ "### The (transiently) high value of [U] led to an increase in [X]" ] }, { "cell_type": "code", "execution_count": 15, "id": "c3afbcc8-bdae-4938-a3f1-ce00d62816f2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: U <-> 2 D\n", "Final concentrations: [D] = 145.1 ; [U] = 36.37\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.98913\n", " Formula used: [D] / [U]\n", "2. Ratio of forward/reverse reaction rates: 4.0\n", "Discrepancy between the two values: 0.2717 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n", "1: X <-> D\n", "Final concentrations: [D] = 145.1 ; [X] = 72.21\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 2.00937\n", " Formula used: [D] / [X]\n", "2. Ratio of forward/reverse reaction rates: 2.0\n", "Discrepancy between the two values: 0.4683 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reaction has reached equilibrium\n", "dynamics.is_in_equilibrium()" ] }, { "cell_type": "code", "execution_count": null, "id": "02d8a758-89b1-4c28-94c9-c73b11f3b8dc", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "f6619731-c5ea-484c-af3e-cea50d685361", "metadata": { "tags": [] }, "source": [ "# 3. Let's again suddenly increase [U]" ] }, { "cell_type": "code", "execution_count": 16, "id": "d3618eba-a673-4ff5-85d0-08f5ea592361", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 1.0973722:\n", "3 species:\n", " Species 0 (U). Conc: 100.0\n", " Species 1 (X). Conc: 72.21103524746438\n", " Species 2 (D). Conc: 145.09842911303875\n", "Set of chemicals involved in reactions: {'D', 'X', 'U'}\n" ] } ], "source": [ "dynamics.set_single_conc(species_name=\"U\", conc=100., snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 17, "id": "e8fe3554-d5ab-4306-b890-4e36289b5b4b", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEUXDcaption
920.98191236.77151671.151097145.362231
931.09737236.37344772.211035145.098429
941.097372100.00000072.211035145.098429Set concentration of `U`
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" ], "text/plain": [ " SYSTEM TIME U X D caption\n", "92 0.981912 36.771516 71.151097 145.362231 \n", "93 1.097372 36.373447 72.211035 145.098429 \n", "94 1.097372 100.000000 72.211035 145.098429 Set concentration of `U`" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(tail=3)" ] }, { "cell_type": "markdown", "id": "0974480d-ca45-46fe-addd-c8d394780fdb", "metadata": {}, "source": [ "### Yet again, take the system to equilibrium" ] }, { "cell_type": "code", "execution_count": 18, "id": "8fe20f9c-05c4-45a4-b485-a51005440200", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* INFO: the tentative time step (0.03) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.015) [Step started at t=1.0974, and will rewind there]\n", "* INFO: the tentative time step (0.015) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.0075) [Step started at t=1.0974, and will rewind there]\n", "* INFO: the tentative time step (0.0075) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.00375) [Step started at t=1.0974, and will rewind there]\n", "* INFO: the tentative time step (0.00375) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.001875) [Step started at t=1.0974, and will rewind there]\n", "Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n", "45 total step(s) taken\n" ] } ], "source": [ "dynamics.single_compartment_react(initial_step=0.03, target_end_time=1.6,\n", " variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 19, "id": "ad01c472-3ebe-4d0d-8913-1bcd85ea7a6c", "metadata": {}, "outputs": [], "source": [ "#dynamics.get_history()\n", "#dynamics.explain_time_advance()" ] }, { "cell_type": "code", "execution_count": 20, "id": "54346a72-bac9-4cc7-ba01-0533ed60371f", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=U
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"range": [ 0, 1.6127957123568928 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -11.657006413255353, 221.4831218518517 ], "title": { "text": "concentration" }, "type": "linear" } } }, "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_curves(colors=['red', 'green', 'gray'])" ] }, { "cell_type": "markdown", "id": "ffbf3294-7a8d-4679-9c4b-5b9a975bf8fc", "metadata": {}, "source": [ "### The (transiently) high value of [U] again led to an increase in [X]" ] }, { "cell_type": "code", "execution_count": 21, "id": "aff608b1-5c78-4070-845a-118afe7c2108", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: U <-> 2 D\n", "Final concentrations: [D] = 208.9 ; [U] = 52.56\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.97443\n", " Formula used: [D] / [U]\n", "2. Ratio of forward/reverse reaction rates: 4.0\n", "Discrepancy between the two values: 0.6392 %\n", "Reaction IS in equilibrium (within 2% tolerance)\n", "\n", "1: X <-> D\n", "Final concentrations: [D] = 208.9 ; [X] = 103.3\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 2.02304\n", " Formula used: [D] / [X]\n", "2. Ratio of forward/reverse reaction rates: 2.0\n", "Discrepancy between the two values: 1.152 %\n", "Reaction IS in equilibrium (within 2% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reaction has reached equilibrium\n", "dynamics.is_in_equilibrium(tolerance=2)" ] }, { "cell_type": "code", "execution_count": null, "id": "7ddbe0ec-53c3-4d25-825a-cbe3bdf8e50a", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "64ebc51b-0dc7-4cff-b231-4c35843a7113", "metadata": { "tags": [] }, "source": [ "# 4. Now, instead, let's DECREASE [U]" ] }, { "cell_type": "code", "execution_count": 22, "id": "52f4843c-0671-4cd9-9c51-74a44feb4fe4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 1.6127957:\n", "3 species:\n", " Species 0 (U). Conc: 5.0\n", " Species 1 (X). Conc: 103.26703387633307\n", " Species 2 (D). Conc: 208.9136350590719\n", "Set of chemicals involved in reactions: {'D', 'X', 'U'}\n" ] } ], "source": [ "dynamics.set_single_conc(species_name=\"U\", conc=5., snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 23, "id": "e5ce5d59", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEUXDcaption
1381.53059853.067054101.964742209.210614
1391.61279652.564398103.267034208.913635
1401.6127965.000000103.267034208.913635Set concentration of `U`
\n", "
" ], "text/plain": [ " SYSTEM TIME U X D caption\n", "138 1.530598 53.067054 101.964742 209.210614 \n", "139 1.612796 52.564398 103.267034 208.913635 \n", "140 1.612796 5.000000 103.267034 208.913635 Set concentration of `U`" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(tail=3)" ] }, { "cell_type": "markdown", "id": "da46e3d8-58d2-4b48-8b32-887613967fce", "metadata": {}, "source": [ "### Take the system to equilibrium" ] }, { "cell_type": "code", "execution_count": 24, "id": "c392f375-c7b4-476b-809e-5cc4f5c14fa4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* INFO: the tentative time step (0.03) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.015) [Step started at t=1.6128, and will rewind there]\n", "* INFO: the tentative time step (0.015) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.0075) [Step started at t=1.6128, and will rewind there]\n", "* INFO: the tentative time step (0.0075) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.00375) [Step started at t=1.6128, and will rewind there]\n", "Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n", "37 total step(s) taken\n" ] } ], "source": [ "dynamics.single_compartment_react(initial_step=0.03, target_end_time=2.3,\n", " variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 25, "id": "6de58fe9-ff1e-40dd-9ac7-83eee458f818", "metadata": {}, "outputs": [], "source": [ "#dynamics.get_history()\n", "#dynamics.explain_time_advance()" ] }, { "cell_type": "code", "execution_count": 26, "id": "c388dae7-c4a6-4644-a390-958e3862d102", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=U
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_curves(colors=['red', 'green', 'gray'])" ] }, { "cell_type": "markdown", "id": "a1629b91-2753-4df7-b6a0-dedf86ac3dc1", "metadata": {}, "source": [ "### The (transiently) LOW value of [U] led to an DECREASE in [X]" ] }, { "cell_type": "code", "execution_count": 27, "id": "31c9c18f-3a7f-4690-8e2f-70fdb02ef5c7", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reaction has reached equilibrium\n", "dynamics.is_in_equilibrium(explain=False)" ] }, { "cell_type": "code", "execution_count": null, "id": "9382dbf7", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "jupytext": { "formats": "ipynb,py:percent" }, "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 }