{ "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: Dec. 3, 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: {'X', 'U', 'D'}\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\", 1)],\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: {'X', 'U', 'D'}\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_history(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: [U] = 24.97 ; [D] = 99.95\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: [X] = 50.11 ; [D] = 99.95\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: {'X', 'U', 'D'}\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`
\n", "
" ], "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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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(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: [U] = 36.37 ; [D] = 145.1\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: [X] = 72.21 ; [D] = 145.1\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: {'X', 'U', 'D'}\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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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(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: [U] = 52.56 ; [D] = 208.9\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: [X] = 103.3 ; [D] = 208.9\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: {'X', 'U', 'D'}\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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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(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 }