{ "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: June 23, 2024 (using v. 1.0 beta36)" ] }, { "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 life123 import ChemData as chem\n", "from life123 import UniformCompartment\n", "\n", "from life123 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_2\"],\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 = -3,436.6 / K = 4) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {'B', 'Y', 'A'}\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\", 1)], 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", "chem_data.plot_reaction_network(\"vue_cytoscape_2\")" ] }, { "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", "Set of chemicals involved in reactions: {'B', 'Y', 'A'}\n" ] } ], "source": [ "dynamics = UniformCompartment(chem_data=chem_data, preset=\"fast\")\n", "dynamics.set_conc(conc={\"A\": 5., \"B\": 100.},\n", " snapshot=True) # A is scarce, B is plentiful, Y is absent\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": null, "id": "0f240808-c4b5-4cec-aded-abcd3063aed7", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "face01c6-9833-4ae3-9762-37a859fdbe63", "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": [ "Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n", "31 total step(s) taken\n", "Number of step re-do's because of negative concentrations: 0\n", "Number of step re-do's because of elective soft aborts: 1\n", "Norm usage: {'norm_A': 8, 'norm_B': 7, 'norm_C': 7, 'norm_D': 7}\n" ] } ], "source": [ "# All of these settings are currently close to the default values... but subject to change; set for repeatability\n", "\n", "dynamics.single_compartment_react(initial_step=0.0005, duration=0.015,\n", " variable_steps=True)" ] }, { "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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300.0141090.01387490.0277474.986126
310.0175270.01380690.0276124.986194
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" ], "text/plain": [ " SYSTEM TIME A B Y caption\n", "0 0.000000 5.000000 100.000000 0.000000 Initialized state\n", "1 0.000300 3.800000 97.600000 1.200000 \n", "2 0.000600 2.910608 95.821216 2.089392 \n", "3 0.000900 2.242506 94.485013 2.757494 \n", "4 0.001200 1.735641 93.471282 3.264359 \n", "5 0.001500 1.348242 92.696483 3.651758 \n", "6 0.001800 1.050487 92.100974 3.949513 \n", "7 0.002100 0.820655 91.641309 4.179345 \n", "8 0.002400 0.642668 91.285336 4.357332 \n", "9 0.002700 0.504484 91.008968 4.495516 \n", "10 0.003000 0.396991 90.793982 4.603009 \n", "11 0.003300 0.313246 90.626493 4.686754 \n", "12 0.003600 0.247926 90.495852 4.752074 \n", "13 0.003900 0.196930 90.393861 4.803070 \n", "14 0.004200 0.157089 90.314178 4.842911 \n", "15 0.004500 0.125945 90.251890 4.874055 \n", "16 0.004800 0.101589 90.203179 4.898411 \n", "17 0.005100 0.082535 90.165071 4.917465 \n", "18 0.005400 0.067626 90.135251 4.932374 \n", "19 0.005700 0.055956 90.111912 4.944044 \n", "20 0.006000 0.046821 90.093642 4.953179 \n", "21 0.006300 0.039669 90.079338 4.960331 \n", "22 0.006600 0.034069 90.068138 4.965931 \n", "23 0.007050 0.027492 90.054983 4.972508 \n", "24 0.007500 0.023054 90.046108 4.976946 \n", "25 0.007950 0.020060 90.040120 4.979940 \n", "26 0.008625 0.017029 90.034059 4.982971 \n", "27 0.009300 0.015477 90.030954 4.984523 \n", "28 0.010312 0.014284 90.028568 4.985716 \n", "29 0.011831 0.013804 90.027607 4.986196 \n", "30 0.014109 0.013874 90.027747 4.986126 \n", "31 0.017527 0.013806 90.027612 4.986194 " ] }, "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 0.0066, in 22 steps of 0.0003\n", "From time 0.0066 to 0.00795, in 3 steps of 0.00045\n", "From time 0.00795 to 0.0093, in 2 steps of 0.000675\n", "From time 0.0093 to 0.01031, in 1 step of 0.00101\n", "From time 0.01031 to 0.01183, in 1 step of 0.00152\n", "From time 0.01183 to 0.01411, in 1 step of 0.00228\n", "From time 0.01411 to 0.01753, in 1 step of 0.00342\n", "(31 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: [A] = 0.01381 ; [B] = 90.03 ; [Y] = 4.986\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.01174\n", " Formula used: [Y] / ([A][B])\n", "2. Ratio of forward/reverse reaction rates: 4\n", "Discrepancy between the two values: 0.2934 %\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": "ab2df7cf-1462-4159-993d-d84a5151042b", "metadata": {}, "outputs": [], "source": [] }, { "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 = 0.017526562:\n", "3 species:\n", " Species 0 (A). Conc: 40.0\n", " Species 1 (B). Conc: 90.0276115740671\n", " Species 2 (Y). Conc: 4.986194212966452\n", "Set of chemicals involved in reactions: {'B', 'Y', 'A'}\n" ] } ], "source": [ "dynamics.set_single_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
280.0103120.01428490.0285684.985716
290.0118310.01380490.0276074.986196
300.0141090.01387490.0277474.986126
310.0175270.01380690.0276124.986194
320.01752740.00000090.0276124.986194Set concentration of `A`
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" ], "text/plain": [ " SYSTEM TIME A B Y caption\n", "28 0.010312 0.014284 90.028568 4.985716 \n", "29 0.011831 0.013804 90.027607 4.986196 \n", "30 0.014109 0.013874 90.027747 4.986126 \n", "31 0.017527 0.013806 90.027612 4.986194 \n", "32 0.017527 40.000000 90.027612 4.986194 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": [ "40 total step(s) taken\n", "Number of step re-do's because of negative concentrations: 0\n", "Number of step re-do's because of elective soft aborts: 5\n", "Norm usage: {'norm_A': 32, 'norm_B': 19, 'norm_C': 19, 'norm_D': 19}\n" ] } ], "source": [ "dynamics.single_compartment_react(initial_step=0.0005, target_end_time=0.055,\n", " variable_steps=True)" ] }, { "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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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(colors=['red', 'darkorange', 'green'],\n", " title=\"Changes in concentrations (reaction A + 2 B <-> Y)\")" ] }, { "cell_type": "markdown", "id": "158e3787-f2d5-4a01-aaa9-6066e93e584c", "metadata": {}, "source": [ "**A**, still the limiting reagent, is again stopping the reaction. \n", "The (transiently) high value of [A] led to a high value of [B]" ] }, { "cell_type": "code", "execution_count": 15, "id": "2415f119-b3cc-477d-b3a4-cd020aab3615", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABYcaption
00.0000005.000000100.0000000.000000Initialized state
10.0003003.80000097.6000001.200000
20.0006002.91060895.8212162.089392
30.0009002.24250694.4850132.757494
40.0012001.73564193.4712823.264359
..................
680.0361351.48998713.00758643.496207
690.0389911.29559212.61879643.690602
700.0432751.10960212.24681643.876592
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73 rows × 5 columns

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" ], "text/plain": [ " SYSTEM TIME A B Y caption\n", "0 0.000000 5.000000 100.000000 0.000000 Initialized state\n", "1 0.000300 3.800000 97.600000 1.200000 \n", "2 0.000600 2.910608 95.821216 2.089392 \n", "3 0.000900 2.242506 94.485013 2.757494 \n", "4 0.001200 1.735641 93.471282 3.264359 \n", ".. ... ... ... ... ...\n", "68 0.036135 1.489987 13.007586 43.496207 \n", "69 0.038991 1.295592 12.618796 43.690602 \n", "70 0.043275 1.109602 12.246816 43.876592 \n", "71 0.049702 0.974898 11.977408 44.011296 \n", "72 0.059343 0.922923 11.873458 44.063271 \n", "\n", "[73 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: [A] = 0.9229 ; [B] = 11.87 ; [Y] = 44.06\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.021\n", " Formula used: [Y] / ([A][B])\n", "2. Ratio of forward/reverse reaction rates: 4\n", "Discrepancy between the two values: 0.525 %\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": "code", "execution_count": null, "id": "d19d42e2-631e-4dd9-94f0-7853bdb23c4e", "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 = 0.059342556:\n", "3 species:\n", " Species 0 (A). Conc: 30.0\n", " Species 1 (B). Conc: 11.873458232380969\n", " Species 2 (Y). Conc: 44.06327088380949\n", "Set of chemicals involved in reactions: {'B', 'Y', 'A'}\n" ] } ], "source": [ "dynamics.set_single_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
690.0389911.29559212.61879643.690602
700.0432751.10960212.24681643.876592
710.0497020.97489811.97740844.011296
720.0593430.92292311.87345844.063271
730.05934330.00000011.87345844.063271Set concentration of `A`
\n", "
" ], "text/plain": [ " SYSTEM TIME A B Y caption\n", "69 0.038991 1.295592 12.618796 43.690602 \n", "70 0.043275 1.109602 12.246816 43.876592 \n", "71 0.049702 0.974898 11.977408 44.011296 \n", "72 0.059343 0.922923 11.873458 44.063271 \n", "73 0.059343 30.000000 11.873458 44.063271 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": [ "21 total step(s) taken\n", "Number of step re-do's because of negative concentrations: 0\n", "Number of step re-do's because of elective soft aborts: 2\n", "Norm usage: {'norm_A': 11, 'norm_B': 9, 'norm_C': 9, 'norm_D': 9}\n" ] } ], "source": [ "dynamics.single_compartment_react(initial_step=0.001, target_end_time=0.09,\n", " variable_steps=True)" ] }, { "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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"white", "zerolinewidth": 2 } } }, "title": { "text": "Changes in concentrations (reaction A + 2 B <-> Y)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ 0, 0.0927817749260832 ], "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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" ], "text/plain": [ " SYSTEM TIME A B Y caption\n", "0 0.000000 5.000000 100.000000 0.000000 Initialized state\n", "1 0.000300 3.800000 97.600000 1.200000 \n", "2 0.000600 2.910608 95.821216 2.089392 \n", "3 0.000900 2.242506 94.485013 2.757494 \n", "4 0.001200 1.735641 93.471282 3.264359 \n", ".. ... ... ... ... ...\n", "90 0.070570 24.334850 0.543158 49.728421 \n", "91 0.073304 24.317670 0.508797 49.745601 \n", "92 0.077404 24.319757 0.512972 49.743514 \n", "93 0.083555 24.317814 0.509086 49.745457 \n", "94 0.092782 24.321984 0.517426 49.741287 \n", "\n", "[95 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: [A] = 24.32 ; [B] = 0.5174 ; [Y] = 49.74\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.95248\n", " Formula used: [Y] / ([A][B])\n", "2. Ratio of forward/reverse reaction rates: 4\n", "Discrepancy between the two values: 1.188 %\n", "Reaction IS in equilibrium (within 2% 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(tolerance=2)" ] }, { "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": "code", "execution_count": null, "id": "44f33779-d742-442f-9923-733e6056627f", "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 = 0.092781775:\n", "3 species:\n", " Species 0 (A). Conc: 0.0\n", " Species 1 (B). Conc: 0.5174262547179348\n", " Species 2 (Y). Conc: 49.741286872641005\n", "Set of chemicals involved in reactions: {'B', 'Y', 'A'}\n" ] } ], "source": [ "dynamics.set_single_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", "Number of step re-do's because of negative concentrations: 0\n", "Number of step re-do's because of elective soft aborts: 0\n", "Norm usage: {'norm_A': 9, 'norm_B': 10, 'norm_C': 9, 'norm_D': 9}\n" ] } ], "source": [ "dynamics.single_compartment_react(initial_step=0.001, target_end_time=0.16,\n", " variable_steps=True)" ] }, { "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
00.0000005.000000100.0000000.000000Initialized state
10.0003003.80000097.6000001.200000
20.0006002.91060895.8212162.089392
30.0009002.24250694.4850132.757494
40.0012001.73564193.4712823.264359
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1100.1154321.7442224.00587047.997065
1110.1215071.9878124.49305047.753475
1120.1306192.2070244.93147547.534262
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115 rows × 5 columns

\n", "
" ], "text/plain": [ " SYSTEM TIME A B Y caption\n", "0 0.000000 5.000000 100.000000 0.000000 Initialized state\n", "1 0.000300 3.800000 97.600000 1.200000 \n", "2 0.000600 2.910608 95.821216 2.089392 \n", "3 0.000900 2.242506 94.485013 2.757494 \n", "4 0.001200 1.735641 93.471282 3.264359 \n", ".. ... ... ... ... ...\n", "110 0.115432 1.744222 4.005870 47.997065 \n", "111 0.121507 1.987812 4.493050 47.753475 \n", "112 0.130619 2.207024 4.931475 47.534262 \n", "113 0.144288 2.316339 5.150105 47.424947 \n", "114 0.164791 2.304340 5.126107 47.436947 \n", "\n", "[115 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: [A] = 2.304 ; [B] = 5.126 ; [Y] = 47.44\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.0159\n", " Formula used: [Y] / ([A][B])\n", "2. Ratio of forward/reverse reaction rates: 4\n", "Discrepancy between the two values: 0.3974 %\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 }