{ "cells": [ { "cell_type": "markdown", "id": "49bcb5b0-f19d-4b96-a5f1-e0ae30f66d8f", "metadata": {}, "source": [ "## `A` up-regulates `B` , \n", "### by being *the limiting reagent* in the reaction `A + X <-> 2B` (mostly forward), where `X` is plentiful\n", "1st-order kinetics. \n", "If [A] is low, [B] remains low, too. Then, if [A] goes high, then so does [B]. However, at that point, A can no longer bring B down to any substantial extent.\n", "\n", "See also the experiment \"1D/reactions/up_regulation_1\"\n", "\n", "LAST REVISED: June 14, 2024 (using v. 1.0 beta33)" ] }, { "cell_type": "code", "execution_count": 1, "id": "53fed9be-020d-4500-a68b-1638f9159fca", "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": "ad48644a", "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.uniform_compartment import UniformCompartment\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_1.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 + X <-> 2 B (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: {'A', 'X', 'B'}\n", "[GRAPHIC ELEMENT SENT TO LOG FILE `up_regulate_1.log.htm`]\n" ] } ], "source": [ "# Initialize the system\n", "chem_data = chem(names=[\"A\", \"X\", \"B\"])\n", "\n", "# Reaction A + X <-> 2B , with 1st-order kinetics for all species\n", "chem_data.add_reaction(reactants=[\"A\" , \"X\"], products=[(2, \"B\", 1)],\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 (X). Conc: 100.0\n", " Species 2 (B). Conc: 0.0\n", "Set of chemicals involved in reactions: {'A', 'X', 'B'}\n" ] } ], "source": [ "dynamics = UniformCompartment(chem_data=chem_data, preset=\"fast\")\n", "dynamics.set_conc(conc={\"A\": 5., \"X\": 100.},\n", " snapshot=True) # A is scarce, X is plentiful, B is absent\n", "dynamics.describe_state()" ] }, { "cell_type": "markdown", "id": "0b46b395-3f68-4dbd-b0c5-d67a0e623726", "metadata": { "tags": [] }, "source": [ "### Take the initial system to equilibrium" ] }, { "cell_type": "code", "execution_count": 6, "id": "dde62826-d170-4b39-b027-c0d56fb21387", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "27 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": [ "dynamics.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n", "\n", "dynamics.single_compartment_react(initial_step=0.0005, duration=0.015,\n", " variable_steps=True)" ] }, { "cell_type": "code", "execution_count": 7, "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=A
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Changes in concentrations with time (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.0480658672798945e-05, 0.015962043158672796 ], "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 X B caption\n", "0 0.000000 5.000000 100.000000 0.000000 Initialized state\n", "1 0.000300 3.800000 98.800000 2.400000 \n", "2 0.000600 2.900384 97.900384 4.199232 \n", "3 0.000900 2.221427 97.221427 5.557147 \n", "4 0.001200 1.706432 96.706432 6.587135 \n", "5 0.001500 1.314329 96.314329 7.371341 \n", "6 0.001800 1.014939 96.014939 7.970122 \n", "7 0.002100 0.785843 95.785843 8.428314 \n", "8 0.002400 0.610246 95.610246 8.779509 \n", "9 0.002700 0.475484 95.475484 9.049033 \n", "10 0.003000 0.371960 95.371960 9.256080 \n", "11 0.003300 0.292375 95.292375 9.415250 \n", "12 0.003600 0.231157 95.231157 9.537685 \n", "13 0.003900 0.184048 95.184048 9.631904 \n", "14 0.004200 0.147783 95.147783 9.704434 \n", "15 0.004500 0.119859 95.119859 9.760283 \n", "16 0.004800 0.098352 95.098352 9.803295 \n", "17 0.005100 0.081787 95.081787 9.836426 \n", "18 0.005400 0.069025 95.069025 9.861949 \n", "19 0.005700 0.059193 95.059193 9.881614 \n", "20 0.006150 0.047830 95.047830 9.904340 \n", "21 0.006600 0.040378 95.040378 9.919244 \n", "22 0.007050 0.035490 95.035490 9.929020 \n", "23 0.007725 0.030681 95.030681 9.938638 \n", "24 0.008737 0.027190 95.027190 9.945620 \n", "25 0.010256 0.026007 95.026007 9.947986 \n", "26 0.012534 0.026292 95.026292 9.947415 \n", "27 0.015952 0.025975 95.025975 9.948051 " ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "code", "execution_count": 9, "id": "b56d1612-a68c-4da3-be37-a7245b6c1a80", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "From time 0 to 0.0057, in 19 steps of 0.0003\n", "From time 0.0057 to 0.00705, in 3 steps of 0.00045\n", "From time 0.00705 to 0.007725, in 1 step of 0.000675\n", "From time 0.007725 to 0.008737, in 1 step of 0.00101\n", "From time 0.008737 to 0.01026, in 1 step of 0.00152\n", "From time 0.01026 to 0.01253, in 1 step of 0.00228\n", "From time 0.01253 to 0.01595, in 1 step of 0.00342\n", "(27 steps total)\n" ] } ], "source": [ "dynamics.explain_time_advance()" ] }, { "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 + X <-> 2 B\n", "Final concentrations: [A] = 0.02597 ; [X] = 95.03 ; [B] = 9.948\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.03037\n", " Formula used: [B] / ([A][X])\n", "2. Ratio of forward/reverse reaction rates: 4\n", "Discrepancy between the two values: 0.7592 %\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": "15355aeb-f702-4d10-9d13-8365f6a76772", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "0405ad75-a0a8-489c-bae8-b2516690fc33", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "448ec7fa-6529-438b-84ba-47888c2cd080", "metadata": { "tags": [] }, "source": [ "# STEP 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 = 0.015951562:\n", "3 species:\n", " Species 0 (A). Conc: 50.0\n", " Species 1 (X). Conc: 95.02597471866889\n", " Species 2 (B). Conc: 9.948050562662225\n", "Set of chemicals involved in reactions: {'A', 'X', 'B'}\n" ] } ], "source": [ "dynamics.set_single_conc(species_name=\"A\", conc=50., 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 TIMEAXBcaption
240.0087370.02719095.0271909.945620
250.0102560.02600795.0260079.947986
260.0125340.02629295.0262929.947415
270.0159520.02597595.0259759.948051
280.01595250.00000095.0259759.948051Set concentration of `A`
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" ], "text/plain": [ " SYSTEM TIME A X B caption\n", "24 0.008737 0.027190 95.027190 9.945620 \n", "25 0.010256 0.026007 95.026007 9.947986 \n", "26 0.012534 0.026292 95.026292 9.947415 \n", "27 0.015952 0.025975 95.025975 9.948051 \n", "28 0.015952 50.000000 95.025975 9.948051 Set concentration of `A`" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(tail=5)" ] }, { "cell_type": "markdown", "id": "b183d3e6-7957-4557-bce6-176909a05a1e", "metadata": {}, "source": [ "Notice the discontity in [A] in the last 2 rows" ] }, { "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": [ "Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n", "51 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': 35, 'norm_B': 19, 'norm_C': 19, 'norm_D': 19}\n" ] } ], "source": [ "dynamics.single_compartment_react(initial_step=0.0005, target_end_time=0.035,\n", " variable_steps=True)" ] }, { "cell_type": "code", "execution_count": 14, "id": "ea3bc6ce-e7c3-4ba4-873a-0104286a2fe3", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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Changes in concentrations with time (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -2.566035240062046e-05, 0.039080716706144956 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -6.042437745730693, 114.80631716888317 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(colors=['red', 'darkorange', 'green'], show_intervals=True)" ] }, { "cell_type": "markdown", "id": "44beb909-5071-47e5-9499-482cf37f9ce3", "metadata": {}, "source": [ "`A`, still the **limiting reagent**, is again eventually stopping the reaction... \n", "The (transiently) high value of [A] led to a high value of [B] \n", "Notice how the variable time steps automatically adapt." ] }, { "cell_type": "code", "execution_count": 15, "id": "35850ec7-e78e-4b57-976c-bc0ad6c824d5", "metadata": {}, "outputs": [], "source": [ "#dynamics.get_history()\n", "\n", "#dynamics.explain_time_advance()" ] }, { "cell_type": "code", "execution_count": 16, "id": "aff608b1-5c78-4070-845a-118afe7c2108", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: A + X <-> 2 B\n", "Final concentrations: [A] = 0.5992 ; [X] = 45.63 ; [B] = 108.7\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.97761\n", " Formula used: [B] / ([A][X])\n", "2. Ratio of forward/reverse reaction rates: 4\n", "Discrepancy between the two values: 0.5598 %\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": "5ef6d068-952e-404d-9c10-5a0d6aa31528", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "7ddbe0ec-53c3-4d25-825a-cbe3bdf8e50a", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "f6619731-c5ea-484c-af3e-cea50d685361", "metadata": { "tags": [] }, "source": [ "# STEP 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 = 0.039055056:\n", "3 species:\n", " Species 0 (A). Conc: 30.0\n", " Species 1 (X). Conc: 45.62521424281943\n", " Species 2 (B). Conc: 108.74957151436116\n", "Set of chemicals involved in reactions: {'A', 'X', 'B'}\n" ] } ], "source": [ "dynamics.set_single_conc(species_name=\"A\", conc=30., snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 18, "id": "e5ce5d59", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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800.03905530.00000045.625214108.749572Set concentration of `A`
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" ], "text/plain": [ " SYSTEM TIME A X B caption\n", "76 0.028635 0.690343 45.716318 108.567364 \n", "77 0.030829 0.612807 45.638782 108.722436 \n", "78 0.034119 0.592086 45.618060 108.763879 \n", "79 0.039055 0.599240 45.625214 108.749572 \n", "80 0.039055 30.000000 45.625214 108.749572 Set concentration of `A`" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(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": [ "28 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: 3\n", "Norm usage: {'norm_A': 22, 'norm_B': 14, 'norm_C': 14, 'norm_D': 14}\n" ] } ], "source": [ "dynamics.single_compartment_react(initial_step=0.0005, target_end_time=0.070,\n", " variable_steps=True)" ] }, { "cell_type": "code", "execution_count": 20, "id": "c388dae7-c4a6-4644-a390-958e3862d102", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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Changes in concentrations with time" }, "xaxis": { "anchor": "y", "domain": [ 0, 1 ], "range": [ 0, 0.02 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -9.121208467938018, 173.3029608908223 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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", "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Zoom in on the early part of the last plot\n", "dynamics.plot_history(colors=['red', 'darkorange', 'green'], xrange=[0, 0.02])" ] }, { "cell_type": "code", "execution_count": 22, "id": "f7938dc5-95cc-47ad-bdbe-ceaa31ba1dfc", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.00045562195425603814, 3.333333333333333)" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Look up the first intersection of the [A] and [B] curves\n", "dynamics.curve_intersect(\"A\", \"B\", t_start=0, t_end=0.01)" ] }, { "cell_type": "code", "execution_count": 23, "id": "f044d268-7262-4154-bb29-f02b0f702242", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "WARNING: curve_intersect(): Discontinuity detected at `SYSTEM TIME` = 0.015951562499999995\n" ] }, { "data": { "text/plain": [ "(0.015951562499999995, 9.948050562662225)" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# The next intersection isn't particulary meaning; just an artifact of the sudden jump in [A]\n", "dynamics.curve_intersect(\"A\", \"B\", t_start=0.01, t_end=0.02)" ] }, { "cell_type": "code", "execution_count": 24, "id": "dbee4d33-07c0-4872-bf15-c88bd66fb7d7", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.01638486713665179, 36.649350187554084)" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# The final intersection\n", "dynamics.curve_intersect(\"A\", \"B\", t_start=0.016, t_end=0.02)" ] }, { "cell_type": "code", "execution_count": 25, "id": "c3afbcc8-bdae-4938-a3f1-ce00d62816f2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: A + X <-> 2 B\n", "Final concentrations: [A] = 2.284 ; [X] = 17.91 ; [B] = 164.2\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.01395\n", " Formula used: [B] / ([A][X])\n", "2. Ratio of forward/reverse reaction rates: 4\n", "Discrepancy between the two values: 0.3487 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 25, "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": "3e5baa56", "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 }