{ "cells": [ { "cell_type": "markdown", "id": "49bcb5b0-f19d-4b96-a5f1-e0ae30f66d8f", "metadata": {}, "source": [ "## `A` down-regulates `B` , \n", "### by being the *limiting reagent* in reaction `A + 2 B <-> Y` (mostly forward)\n", "1st-order kinetics. \n", "If [A] is low and [B] is high, then [B] remains high. If [A] goes high, [B] goes low. However, at that point, A can no longer bring B up to any substantial extent.\n", "\n", "See also 1D/reactions/down_regulation_1\n", "\n", "LAST REVISED: May 23, 2023" ] }, { "cell_type": "code", "execution_count": 1, "id": "d9efa3fd-e95d-4e1c-878a-81ae932b2709", "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": "01bae555-3dcf-42c1-bddc-9477a37f49f8", "metadata": { "tags": [] }, "outputs": [], "source": [ "from experiments.get_notebook_info import get_notebook_basename\n", "\n", "from src.modules.reactions.reaction_data import ReactionData as chem\n", "from src.modules.reactions.reaction_dynamics import ReactionDynamics\n", "\n", "import numpy as np\n", "import plotly.express as px\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 'down_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: 1 (at temp. 25 C)\n", "0: A + 2 B <-> Y (kF = 8 / kR = 2 / Delta_G = -3,436.56 / K = 4) | 1st order in all reactants & products\n", "[GRAPHIC ELEMENT SENT TO LOG FILE `down_regulate_2.log.htm`]\n" ] } ], "source": [ "# Initialize the system\n", "chem_data = chem(names=[\"A\", \"B\", \"Y\"])\n", "\n", "# Reaction A + 2 B <-> Y , with 1st-order kinetics for all species\n", "chem_data.add_reaction(reactants=[(\"A\") , (2, \"B\")], products=[(\"Y\")],\n", " forward_rate=8., reverse_rate=2.)\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 (A). Conc: 5.0\n", " Species 1 (B). Conc: 100.0\n", " Species 2 (Y). Conc: 0.0\n" ] } ], "source": [ "dynamics = ReactionDynamics(reaction_data=chem_data)\n", "dynamics.set_conc(conc={\"A\": 5., \"B\": 100., \"Y\": 0.},\n", " snapshot=True) # A is scarce, B is plentiful, Y is absent\n", "dynamics.describe_state()" ] }, { "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 (0.0005) 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 0.00025) [Step started at t=0, and will rewind there]\n", "28 total step(s) taken\n" ] } ], "source": [ "# 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=1.0, abort=1.44)\n", "dynamics.set_thresholds(norm=\"norm_B\", low=0.2, high=0.5, abort=1.5)\n", "dynamics.set_step_factors(upshift=1.4, downshift=0.5, abort=0.5)\n", "dynamics.set_error_step_factor(0.333)\n", "\n", "dynamics.single_compartment_react(initial_step=0.0005, reaction_duration=0.015,\n", " variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "markdown", "id": "7dc56592-179d-4e4c-b75a-8eb81dcafe71", "metadata": {}, "source": [ "A, as the scarse limiting reagent, stops the reaction. \n", "When A is low, B is also low." ] }, { "cell_type": "code", "execution_count": 7, "id": "665dfff9-e943-44e1-b76d-af363d94c9f8", "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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", 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SYSTEM TIMEABYcaption
00.0000005.000000100.0000000.000000Initial state
10.0002504.00000098.0000001.000000
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" ], "text/plain": [ " SYSTEM TIME A B Y caption\n", "0 0.000000 5.000000 100.000000 0.000000 Initial state\n", "1 0.000250 4.000000 98.000000 1.000000 \n", "2 0.000500 3.216500 96.433000 1.783500 \n", "3 0.000625 2.906769 95.813538 2.093231 \n", "4 0.000800 2.517591 95.035182 2.482409 \n", "5 0.001045 2.049858 94.099716 2.950142 \n", "6 0.001388 1.522589 93.045178 3.477411 \n", "7 0.001731 1.136233 92.272466 3.863767 \n", "8 0.002074 0.851194 91.702389 4.148806 \n", "9 0.002417 0.639853 91.279707 4.360147 \n", "10 0.002760 0.482579 90.965159 4.517421 \n", "11 0.003103 0.365222 90.730445 4.634778 \n", "12 0.003446 0.277475 90.554949 4.722525 \n", "13 0.003789 0.211767 90.423533 4.788233 \n", "14 0.004132 0.162507 90.325015 4.837493 \n", "15 0.004475 0.125548 90.251096 4.874452 \n", "16 0.004818 0.097800 90.195600 4.902200 \n", "17 0.005161 0.076958 90.153916 4.923042 \n", "18 0.005504 0.061297 90.122594 4.938703 \n", "19 0.005847 0.049526 90.099053 4.950474 \n", "20 0.006327 0.037139 90.074277 4.962861 \n", "21 0.006807 0.029054 90.058108 4.970946 \n", "22 0.007288 0.023776 90.047553 4.976224 \n", "23 0.007960 0.018952 90.037905 4.981048 \n", "24 0.008632 0.016472 90.032944 4.983528 \n", "25 0.009573 0.014686 90.029373 4.985314 \n", "26 0.010891 0.013887 90.027773 4.986113 \n", "27 0.012736 0.013833 90.027665 4.986167 \n", "28 0.015318 0.013858 90.027716 4.986142 " ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "code", "execution_count": 9, "id": "3180f7aa-390e-4ada-a7ab-3c0db958fcc5", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "From time 0 to 0.0005, in 2 steps of 0.00025\n", "From time 0.0005 to 0.000625, in 1 step of 0.000125\n", "From time 0.000625 to 0.0008, in 1 step of 0.000175\n", "From time 0.0008 to 0.001045, in 1 step of 0.000245\n", "From time 0.001045 to 0.005847, in 14 steps of 0.000343\n", "From time 0.005847 to 0.007288, in 3 steps of 0.00048\n", "From time 0.007288 to 0.008632, in 2 steps of 0.000672\n", "From time 0.008632 to 0.009573, in 1 step of 0.000941\n", "From time 0.009573 to 0.01089, in 1 step of 0.00132\n", "From time 0.01089 to 0.01274, in 1 step of 0.00184\n", "From time 0.01274 to 0.01532, in 1 step of 0.00258\n", "(28 steps total)\n" ] } ], "source": [ "dynamics.explain_time_advance(use_history=True)" ] }, { "cell_type": "markdown", "id": "962acf15-3b50-40e4-9daa-3dcca7d3291a", "metadata": {}, "source": [ "#### Equilibrium" ] }, { "cell_type": "code", "execution_count": 10, "id": "c3afbcc8-bdae-4938-a3f1-ce00d62816f2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A + 2 B <-> Y\n", "Final concentrations: [Y] = 4.986 ; [A] = 0.01386 ; [B] = 90.03\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.99663\n", " Formula used: [Y] / ([A][B])\n", "2. Ratio of forward/reverse reaction rates: 4.0\n", "Discrepancy between the two values: 0.08418 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 10, "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": "5a07c2cb-c6b8-4614-b1f7-fc582f174c0f", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "448ec7fa-6529-438b-84ba-47888c2cd080", "metadata": { "tags": [] }, "source": [ "# 2. Now, let's suddenly increase [A]" ] }, { "cell_type": "code", "execution_count": 11, "id": "7245be7a-c9db-45f5-b033-d6c521237a9c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0.015318388:\n", "3 species:\n", " Species 0 (A). Conc: 40.0\n", " Species 1 (B). Conc: 90.02771559198881\n", " Species 2 (Y). Conc: 4.98614220400561\n" ] } ], "source": [ "dynamics.set_chem_conc(species_name=\"A\", conc=40., snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 12, "id": "007161ef-f4d0-4623-92c5-0fe3d2bda98a", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABYcaption
250.0095730.01468690.0293734.985314
260.0108910.01388790.0277734.986113
270.0127360.01383390.0276654.986167
280.0153180.01385890.0277164.986142
290.01531840.00000090.0277164.986142Set concentration of `A`
\n", "
" ], "text/plain": [ " SYSTEM TIME A B Y caption\n", "25 0.009573 0.014686 90.029373 4.985314 \n", "26 0.010891 0.013887 90.027773 4.986113 \n", "27 0.012736 0.013833 90.027665 4.986167 \n", "28 0.015318 0.013858 90.027716 4.986142 \n", "29 0.015318 40.000000 90.027716 4.986142 Set concentration of `A`" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.history.get_dataframe(tail=5)" ] }, { "cell_type": "markdown", "id": "24455d58-a0ea-43fa-b6ad-95c42a8b34b2", "metadata": {}, "source": [ "### Again, take the system to equilibrium" ] }, { "cell_type": "code", "execution_count": 13, "id": "c06fd8d8-d550-4e35-a239-7b91bee32be9", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "INFO: the tentative time step (0.0005) 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 0.00025) [Step started at t=0.015318, and will rewind there]\n", "INFO: the tentative time step (0.00025) 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 0.000125) [Step started at t=0.015318, and will rewind there]\n", "INFO: the tentative time step (0.000125) 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 6.25e-05) [Step started at t=0.015318, and will rewind there]\n", "INFO: the tentative time step (6.25e-05) 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 3.125e-05) [Step started at t=0.015318, and will rewind there]\n", "47 total step(s) taken\n" ] } ], "source": [ "dynamics.single_compartment_react(initial_step=0.0005, target_end_time=0.055,\n", " variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 14, "id": "58f4f09c-8af6-46b7-bd85-2f6ca194c42a", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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SYSTEM TIMEABYcaption
00.0000005.000000100.0000000.000000Initial state
10.0002504.00000098.0000001.000000
20.0005003.21650096.4330001.783500
30.0006252.90676995.8135382.093231
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..................
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730.0384271.19433412.41638343.791809
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" ], "text/plain": [ " SYSTEM TIME A B Y caption\n", "0 0.000000 5.000000 100.000000 0.000000 Initial state\n", "1 0.000250 4.000000 98.000000 1.000000 \n", "2 0.000500 3.216500 96.433000 1.783500 \n", "3 0.000625 2.906769 95.813538 2.093231 \n", "4 0.000800 2.517591 95.035182 2.482409 \n", ".. ... ... ... ... ...\n", "72 0.034954 1.383073 12.793862 43.603069 \n", "73 0.038427 1.194334 12.416383 43.791809 \n", "74 0.043288 1.043380 12.114476 43.942762 \n", "75 0.050094 0.953305 11.934325 44.032838 \n", "76 0.059623 0.925189 11.878093 44.060953 \n", "\n", "[77 rows x 5 columns]" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "code", "execution_count": 16, "id": "2783a665-fca0-44e5-8d42-af2a96eae392", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A + 2 B <-> Y\n", "Final concentrations: [Y] = 44.06 ; [A] = 0.9252 ; [B] = 11.88\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.00938\n", " Formula used: [Y] / ([A][B])\n", "2. Ratio of forward/reverse reaction rates: 4.0\n", "Discrepancy between the two values: 0.2344 %\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": "code", "execution_count": null, "id": "4faea7f8-0466-4d90-8eba-3d6501cca2d8", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "f6619731-c5ea-484c-af3e-cea50d685361", "metadata": { "tags": [] }, "source": [ "# 3. Let's again suddenly increase [A]" ] }, { "cell_type": "code", "execution_count": 17, "id": "d3618eba-a673-4ff5-85d0-08f5ea592361", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0.059622836:\n", "3 species:\n", " Species 0 (A). Conc: 30.0\n", " Species 1 (B). Conc: 11.878093044952234\n", " Species 2 (Y). Conc: 44.06095347752391\n" ] } ], "source": [ "dynamics.set_chem_conc(species_name=\"A\", conc=30., snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 18, "id": "61eead55-fcef-41cd-b29e-f2d5ad5c6078", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABYcaption
730.0384271.19433412.41638343.791809
740.0432881.04338012.11447643.942762
750.0500940.95330511.93432544.032838
760.0596230.92518911.87809344.060953
770.05962330.00000011.87809344.060953Set concentration of `A`
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" ], "text/plain": [ " SYSTEM TIME A B Y caption\n", "73 0.038427 1.194334 12.416383 43.791809 \n", "74 0.043288 1.043380 12.114476 43.942762 \n", "75 0.050094 0.953305 11.934325 44.032838 \n", "76 0.059623 0.925189 11.878093 44.060953 \n", "77 0.059623 30.000000 11.878093 44.060953 Set concentration of `A`" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.history.get_dataframe(tail=5)" ] }, { "cell_type": "markdown", "id": "0974480d-ca45-46fe-addd-c8d394780fdb", "metadata": {}, "source": [ "### Yet again, take the system to equilibrium" ] }, { "cell_type": "code", "execution_count": 19, "id": "8fe20f9c-05c4-45a4-b485-a51005440200", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "INFO: the tentative time step (0.001) 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 0.0005) [Step started at t=0.059623, and will rewind there]\n", "19 total step(s) taken\n" ] } ], "source": [ "dynamics.single_compartment_react(initial_step=0.001, target_end_time=0.09,\n", " variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 20, "id": "cc34ca51-8ec3-4170-abc9-f9bccdd7ce00", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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"white", "zerolinewidth": 2 } } }, "title": { "text": "Changes in concentrations (reaction A + 2 B <-> Y)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ 0, 0.09912593079469205 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -5.555555555555555, 105.55555555555556 ], "title": { "text": "concentration" }, "type": "linear" } } }, "image/png": 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SYSTEM TIMEABYcaption
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" ], "text/plain": [ " SYSTEM TIME A B Y caption\n", "0 0.000000 5.000000 100.000000 0.000000 Initial state\n", "1 0.000250 4.000000 98.000000 1.000000 \n", "2 0.000500 3.216500 96.433000 1.783500 \n", "3 0.000625 2.906769 95.813538 2.093231 \n", "4 0.000800 2.517591 95.035182 2.482409 \n", ".. ... ... ... ... ...\n", "92 0.072916 24.315963 0.510018 49.744991 \n", "93 0.076605 24.316986 0.512064 49.743968 \n", "94 0.081771 24.316330 0.510753 49.744624 \n", "95 0.089002 24.317286 0.512664 49.743668 \n", "96 0.099126 24.314800 0.507693 49.746154 \n", "\n", "[97 rows x 5 columns]" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "code", "execution_count": 22, "id": "aff608b1-5c78-4070-845a-118afe7c2108", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A + 2 B <-> Y\n", "Final concentrations: [Y] = 49.75 ; [A] = 24.31 ; [B] = 0.5077\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.02984\n", " Formula used: [Y] / ([A][B])\n", "2. Ratio of forward/reverse reaction rates: 4.0\n", "Discrepancy between the two values: 0.746 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reaction has reached equilibrium\n", "dynamics.is_in_equilibrium()" ] }, { "cell_type": "markdown", "id": "81a8be4a-f374-494e-b647-184e35707295", "metadata": {}, "source": [ "**A**, again the scarse limiting reagent, stops the reaction yet again" ] }, { "cell_type": "code", "execution_count": null, "id": "cb4749d0-dc12-44ba-a032-8068c80d9c4c", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "d40258c5-5520-44a2-8dca-c28864386742", "metadata": {}, "source": [ "# 4. A can down-regulate B, but it cannot bring it up to any significant amount\n", "#### Even if A is completely taken out (i.e., [A] set to 0), [B] can only slightly increase, from the reverse reaction (\"Le Chatelier's principle\".) \n", "Let's try it:" ] }, { "cell_type": "code", "execution_count": 23, "id": "84e83a01-76b1-4a6c-92e3-3f540cb47b1e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0.099125931:\n", "3 species:\n", " Species 0 (A). Conc: 0.0\n", " Species 1 (B). Conc: 0.5076929235350717\n", " Species 2 (Y). Conc: 49.74615353823248\n" ] } ], "source": [ "dynamics.set_chem_conc(species_name=\"A\", conc=0., snapshot=True) # Completely eliminate A\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 24, "id": "31f1e4d5-8027-41de-90cc-f0492c88a9d9", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "19 total step(s) taken\n" ] } ], "source": [ "dynamics.single_compartment_react(initial_step=0.001, target_end_time=0.16,\n", " variable_steps=True, explain_variable_steps=False)\n" ] }, { "cell_type": "code", "execution_count": 25, "id": "4229e039-b484-4849-a446-59409885deb4", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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" ], "text/plain": [ " SYSTEM TIME A B Y caption\n", "0 0.000000 5.000000 100.000000 0.000000 Initial state\n", "1 0.000250 4.000000 98.000000 1.000000 \n", "2 0.000500 3.216500 96.433000 1.783500 \n", "3 0.000625 2.906769 95.813538 2.093231 \n", "4 0.000800 2.517591 95.035182 2.482409 \n", ".. ... ... ... ... ...\n", "112 0.124564 1.876146 4.259985 47.870007 \n", "113 0.131943 2.110805 4.729304 47.635348 \n", "114 0.142274 2.269994 5.047682 47.476159 \n", "115 0.156737 2.317528 5.142749 47.428625 \n", "116 0.176984 2.307597 5.122887 47.438557 \n", "\n", "[117 rows x 5 columns]" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "code", "execution_count": 27, "id": "88f744d6-17fb-4d03-b8cc-bb22b12555e0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A + 2 B <-> Y\n", "Final concentrations: [Y] = 47.44 ; [A] = 2.308 ; [B] = 5.123\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.01289\n", " Formula used: [Y] / ([A][B])\n", "2. Ratio of forward/reverse reaction rates: 4.0\n", "Discrepancy between the two values: 0.3221 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "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()" ] }, { "cell_type": "markdown", "id": "92c82a23-3c8e-4cff-9efc-7cd708f0f9ad", "metadata": {}, "source": [ "#### As expected, even the complete withdrawal of A (red), brings about only a modest increase of B's concentration, from the reverse reaction (i.e. [B] slightly increases at the expense of [Y].) \n", "#### The change is modest because our reaction A + 2 B <-> Y is mostly in the forward direction (K = 4)\n", "*Le Chatelier's principle* in action: \"A change in one of the variables that describe a system at equilibrium produces a shift in the position of the equilibrium that counteracts the effect of this change.\"" ] }, { "cell_type": "code", "execution_count": null, "id": "162ae075-48c4-4d55-ba15-1f19e3b75b9b", "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 }