{ "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: July 14, 2023" ] }, { "cell_type": "code", "execution_count": 1, "id": "5a07c2cb-c6b8-4614-b1f7-fc582f174c0f", "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": "367ba836", "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 '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(chem_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": "58f4f09c-8af6-46b7-bd85-2f6ca194c42a", "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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" ], "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": "2783a665-fca0-44e5-8d42-af2a96eae392", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: 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": "4faea7f8-0466-4d90-8eba-3d6501cca2d8", "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": "61eead55-fcef-41cd-b29e-f2d5ad5c6078", "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": "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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SYSTEM TIMEABYcaption
00.0000005.000000100.0000000.000000Initial state
10.0002504.00000098.0000001.000000
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..................
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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": "aff608b1-5c78-4070-845a-118afe7c2108", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: 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": "cb4749d0-dc12-44ba-a032-8068c80d9c4c", "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": "007161ef-f4d0-4623-92c5-0fe3d2bda98a", "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
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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": "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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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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920.07291624.3159630.51001849.744991
930.07660524.3169860.51206449.743968
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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": "88f744d6-17fb-4d03-b8cc-bb22b12555e0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: 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": "162ae075-48c4-4d55-ba15-1f19e3b75b9b", "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": { "lines_to_next_cell": 2 }, "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)" ] }, { "cell_type": "code", "execution_count": 25, "id": "665dfff9-e943-44e1-b76d-af363d94c9f8", "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
40.0008002.51759195.0351822.482409
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1120.1245641.8761464.25998547.870007
1130.1319432.1108054.72930447.635348
1140.1422742.2699945.04768247.476159
1150.1567372.3175285.14274947.428625
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117 rows × 5 columns

\n", "
" ], "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": "c3afbcc8-bdae-4938-a3f1-ce00d62816f2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: 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": "48a86d59", "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 }