{ "cells": [ { "cell_type": "markdown", "id": "3bbe8002-bdf3-490c-bde0-80dd3713a3d0", "metadata": {}, "source": [ "## `A <-> B` , downregulated by the \"shunt\" (coupled reaction) `A <-> S`\n", "### _Kinetic_ advantage (downregulation in early phase) vs. _Thermodynamic_ advantage (long-term downregulation) \n", "\n", "**[Scenario 1](#down_regulate_1_scenario_1)** : No downregulation on `A <-> B `\n", "\n", "**[Scenario 2](#down_regulate_1_scenario_2)** : The shunt (`A <-> S`) has a *kinetic* advantage but *thermodynamic* DIS-advantage compared to `A <-> B ` \n", "(i.e. `A <-> S` is fast, but energetically unfavored) \n", "\n", "**[Scenario 3](#down_regulate_1_scenario_3)** : The shunt (`A <-> S`) is has a *kinetic* DIS-advantage but a *thermodynamic* advantage compared to `A <-> B` \n", "(i.e. `A <-> S` is slow, but energetically favored) \n", "\n", "All reactions 1st order, mostly forward. Taken to equilibrium.\n", "\n", "LAST REVISED: May 23, 2023" ] }, { "cell_type": "markdown", "id": "61171e99-518e-4019-a731-be7437e95dfd", "metadata": {}, "source": [ "## Bathtub analogy:\n", "A is initially full, while B and S are empty. \n", "If the \"shunt\" S is present, scenario 2 corresponds to a large pipe and a small elevation change... \n", "while scenario 3 corresponds to a narrow pipe and a large elevation change." ] }, { "cell_type": "markdown", "id": "832afe37-f169-41c8-a719-e739336bc5cf", "metadata": {}, "source": [ "![Downregulated by shunt](../../docs/down_regulate_1.png)" ] }, { "cell_type": "code", "execution_count": 1, "id": "13e55c1d-609f-4bf0-a004-6c45bcfcbc99", "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": "bdad128a-9214-46f5-aeb9-a7b77c81aa3e", "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": "83c3cc5f-de21-4f66-9988-2806fbf0666d", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-> Output will be LOGGED into the file 'down_regulate_1.log.htm'\n" ] } ], "source": [ "# Initialize the HTML logging (for the graphics)\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": "code", "execution_count": null, "id": "c4231a63-e456-48e9-bf4f-d074bbd3490a", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "35b5ef15-69da-4fc9-b1e9-fd34a9bafb99", "metadata": {}, "source": [ "# Scenario 1: A <-> B in the absence of the 2nd reaction" ] }, { "cell_type": "markdown", "id": "9329208b-070f-4902-8f37-0f11ddf75ed6", "metadata": {}, "source": [ "### Initialize the System\n", "Specify the chemicals and the reaction" ] }, { "cell_type": "code", "execution_count": 4, "id": "57d8431c-d6d0-462c-af78-e64eeb220e2e", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 1 (at temp. 25 C)\n", "0: A <-> B (kF = 30 / kR = 5 / Delta_G = -4,441.69 / K = 6) | 1st order in all reactants & products\n" ] } ], "source": [ "# Specify the chemicals\n", "chem_data = chem(names=[\"A\", \"B\"])\n", "\n", "# Reaction A <-> B\n", "chem_data.add_reaction(reactants=[\"A\"], products=[\"B\"],\n", " forward_rate=30., reverse_rate=5.)\n", "\n", "chem_data.describe_reactions()" ] }, { "cell_type": "markdown", "id": "f5eabdf2-0e6b-4141-a886-10974dfc6c3a", "metadata": {}, "source": [ "### Set the initial concentrations of all the chemicals, in their index order" ] }, { "cell_type": "code", "execution_count": 5, "id": "67a0375f-a14f-4cbe-965b-81d4c841aeab", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "2 species:\n", " Species 0 (A). Conc: 50.0\n", " Species 1 (B). Conc: 0.0\n" ] } ], "source": [ "dynamics = ReactionDynamics(reaction_data=chem_data)\n", "dynamics.set_conc([50., 0.], snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "markdown", "id": "72a2148e-1aae-4ed7-bab3-5781b3a80fb0", "metadata": {}, "source": [ "### Run the reaction" ] }, { "cell_type": "code", "execution_count": 6, "id": "89f23b49-2840-4517-a275-b6a4f97898af", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "49 total step(s) taken\n" ] } ], "source": [ "dynamics.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n", "\n", "# All of these settings are currently close to the default values... but subject to change; set for repeatability\n", "dynamics.set_thresholds(norm=\"norm_A\", low=0.5, high=1.0, abort=1.44)\n", "dynamics.set_thresholds(norm=\"norm_B\", low=0.08, high=0.5, abort=1.5)\n", "dynamics.set_step_factors(upshift=1.5, downshift=0.5, abort=0.5)\n", "dynamics.set_error_step_factor(0.5)\n", "\n", "# The changes of concentrations vary very rapidly early on; automated variable timesteps will take care of that\n", "dynamics.single_compartment_react(initial_step=0.001, reaction_duration=0.3,\n", " snapshots={\"initial_caption\": \"1st reaction step\",\n", " \"final_caption\": \"last reaction step\"},\n", " variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 7, "id": "bd33b1e8-abd2-4392-9884-8fd56ee0841c", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABcaption
00.00000050.0000000.000000Initial state
10.00100048.5000001.5000001st reaction step
20.00150047.7762502.223750
30.00200047.0651662.934834
40.00250046.3665253.633475
50.00300045.6801114.319889
60.00350045.0057094.994291
70.00400044.3431095.656891
80.00450043.6921056.307895
90.00500043.0524936.947507
100.00550042.4240747.575926
110.00600041.8066538.193347
120.00650041.2000378.799963
130.00725040.3060369.693964
140.00800039.43550210.564498
150.00875038.58782011.412180
160.00950037.76239012.237610
170.01062536.55674613.443254
180.01175035.39857414.601426
190.01287534.28600515.713995
200.01400033.21724416.782756
210.01512532.19056517.809435
220.01625031.20431118.795689
230.01793829.78318220.216818
240.01878129.11458520.885415
250.02004728.14130621.858694
260.02194526.74605723.253943
270.02384425.44351624.556484
280.02574224.22752325.772477
290.02764123.09232726.907673
300.02953922.03256027.967440
310.03143821.04320928.956791
320.03428519.65778930.342211
330.03713318.41045131.589549
340.03998017.28743332.712567
350.04282816.27634433.723656
360.04567615.36602834.633972
370.04994714.13664835.863352
380.05421913.09106236.908938
390.05849012.20179437.798206
400.06489711.06731338.932687
410.07130510.18724239.812758
420.0809169.16317440.836826
430.0905268.48358141.516419
440.1049437.80709342.192907
450.1265677.30436442.695636
460.1590047.12100842.878992
470.2076587.15821542.841785
480.2806417.11898542.881015
490.3901147.21045242.789548last reaction step
\n", "
" ], "text/plain": [ " SYSTEM TIME A B caption\n", "0 0.000000 50.000000 0.000000 Initial state\n", "1 0.001000 48.500000 1.500000 1st reaction step\n", "2 0.001500 47.776250 2.223750 \n", "3 0.002000 47.065166 2.934834 \n", "4 0.002500 46.366525 3.633475 \n", "5 0.003000 45.680111 4.319889 \n", "6 0.003500 45.005709 4.994291 \n", "7 0.004000 44.343109 5.656891 \n", "8 0.004500 43.692105 6.307895 \n", "9 0.005000 43.052493 6.947507 \n", "10 0.005500 42.424074 7.575926 \n", "11 0.006000 41.806653 8.193347 \n", "12 0.006500 41.200037 8.799963 \n", "13 0.007250 40.306036 9.693964 \n", "14 0.008000 39.435502 10.564498 \n", "15 0.008750 38.587820 11.412180 \n", "16 0.009500 37.762390 12.237610 \n", "17 0.010625 36.556746 13.443254 \n", "18 0.011750 35.398574 14.601426 \n", "19 0.012875 34.286005 15.713995 \n", "20 0.014000 33.217244 16.782756 \n", "21 0.015125 32.190565 17.809435 \n", "22 0.016250 31.204311 18.795689 \n", "23 0.017938 29.783182 20.216818 \n", "24 0.018781 29.114585 20.885415 \n", "25 0.020047 28.141306 21.858694 \n", "26 0.021945 26.746057 23.253943 \n", "27 0.023844 25.443516 24.556484 \n", "28 0.025742 24.227523 25.772477 \n", "29 0.027641 23.092327 26.907673 \n", "30 0.029539 22.032560 27.967440 \n", "31 0.031438 21.043209 28.956791 \n", "32 0.034285 19.657789 30.342211 \n", "33 0.037133 18.410451 31.589549 \n", "34 0.039980 17.287433 32.712567 \n", "35 0.042828 16.276344 33.723656 \n", "36 0.045676 15.366028 34.633972 \n", "37 0.049947 14.136648 35.863352 \n", "38 0.054219 13.091062 36.908938 \n", "39 0.058490 12.201794 37.798206 \n", "40 0.064897 11.067313 38.932687 \n", "41 0.071305 10.187242 39.812758 \n", "42 0.080916 9.163174 40.836826 \n", "43 0.090526 8.483581 41.516419 \n", "44 0.104943 7.807093 42.192907 \n", "45 0.126567 7.304364 42.695636 \n", "46 0.159004 7.121008 42.878992 \n", "47 0.207658 7.158215 42.841785 \n", "48 0.280641 7.118985 42.881015 \n", "49 0.390114 7.210452 42.789548 last reaction step" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "code", "execution_count": 8, "id": "104ccbd8-d2d8-475e-a9e5-40698293a077", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "From time 0 to 0.001, in 1 step of 0.001\n", "From time 0.001 to 0.0065, in 11 steps of 0.0005\n", "From time 0.0065 to 0.0095, in 4 steps of 0.00075\n", "From time 0.0095 to 0.01625, in 6 steps of 0.00113\n", "From time 0.01625 to 0.01794, in 1 step of 0.00169\n", "From time 0.01794 to 0.01878, in 1 step of 0.000844\n", "From time 0.01878 to 0.02005, in 1 step of 0.00127\n", "From time 0.02005 to 0.03144, in 6 steps of 0.0019\n", "From time 0.03144 to 0.04568, in 5 steps of 0.00285\n", "From time 0.04568 to 0.05849, in 3 steps of 0.00427\n", "From time 0.05849 to 0.0713, in 2 steps of 0.00641\n", "From time 0.0713 to 0.09053, in 2 steps of 0.00961\n", "From time 0.09053 to 0.1049, in 1 step of 0.0144\n", "From time 0.1049 to 0.1266, in 1 step of 0.0216\n", "From time 0.1266 to 0.159, in 1 step of 0.0324\n", "From time 0.159 to 0.2077, in 1 step of 0.0487\n", "From time 0.2077 to 0.2806, in 1 step of 0.073\n", "From time 0.2806 to 0.3901, in 1 step of 0.109\n", "(49 steps total)\n" ] } ], "source": [ "dynamics.explain_time_advance()" ] }, { "cell_type": "code", "execution_count": 9, "id": "09c03e23-0dd8-4ba0-a5b7-119f5662f23b", "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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"white", "zerolinewidth": 2 } } }, "title": { "text": "Single reaction A <-> B (no downregulation) (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.00022266795972710875, 0.3903369334016216 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -2.7777777777777777, 52.77777777777778 ], "title": { "text": "concentration" }, "type": "linear" } } }, "image/png": 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", "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_curves(colors=[\"blue\", \"green\"], title=\"Single reaction A <-> B (no downregulation)\", \n", " show_intervals=True)" ] }, { "cell_type": "markdown", "id": "ce63f6dc-f9fc-4875-82aa-bbd05488ecb5", "metadata": {}, "source": [ "#### Notice the intersection at the exact midpoint of the 2 initial concentrations (50 and 0):" ] }, { "cell_type": "code", "execution_count": 10, "id": "477e29f3-17ee-4037-920a-b3e33920f04a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Min abs distance found at data row: 27\n" ] }, { "data": { "text/plain": [ "(0.02453617850732098, 25.000000000000007)" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.curve_intersection('A', 'B', t_start=0, t_end=0.1)" ] }, { "cell_type": "code", "execution_count": 11, "id": "58b4b5e5-ebd0-4bb6-8059-6a460d555106", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A <-> B\n", "Final concentrations: [B] = 42.79 ; [A] = 7.21\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 5.93438\n", " Formula used: [B] / [A]\n", "2. Ratio of forward/reverse reaction rates: 6.0\n", "Discrepancy between the two values: 1.094 %\n", "Reaction IS in equilibrium (within 2% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that all the reactions have reached equilibrium\n", "dynamics.is_in_equilibrium(tolerance=2)" ] }, { "cell_type": "code", "execution_count": null, "id": "001bc666-f2ef-40a3-b46f-30b087ea33da", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "3f67c102-0d90-4624-98f3-d6f50719d8c1", "metadata": {}, "source": [ "# Scenario 2: \n", "### downregulated by shunt: \n", "### kinetically fast, \n", "### but with thermodynamical dis-advantage (i.e. energetically un-favored)" ] }, { "cell_type": "code", "execution_count": 12, "id": "589fe009-4bf5-454e-ac37-9abd6ba7ffeb", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 2 (at temp. 25 C)\n", "0: A <-> B (kF = 30 / kR = 5 / Delta_G = -4,441.69 / K = 6) | 1st order in all reactants & products\n", "1: A <-> S (kF = 150 / kR = 100 / Delta_G = -1,005.13 / K = 1.5) | 1st order in all reactants & products\n" ] } ], "source": [ "# Register the new chemical (\"S\")\n", "chem_data.add_chemical(\"S\")\n", "\n", "# Add the reaction A <-> S (fast shunt, poor thermodynical energetic advantage)\n", "chem_data.add_reaction(reactants=[\"A\"], products=[\"S\"],\n", " forward_rate=150., reverse_rate=100.) \n", "\n", "chem_data.describe_reactions()" ] }, { "cell_type": "code", "execution_count": 13, "id": "cb582868-431c-4022-aa0e-a2f554f80d6c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[GRAPHIC ELEMENT SENT TO LOG FILE `down_regulate_1.log.htm`]\n" ] } ], "source": [ "# Send a plot of the network of reactions 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": "b0345d36-5702-4b40-9221-a765dfcb0bac", "metadata": {}, "source": [ "### Set the initial concentrations of all the chemicals, in their index order" ] }, { "cell_type": "code", "execution_count": 14, "id": "ae304704-c8d9-4cef-9e0b-2587bb3909ef", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "3 species:\n", " Species 0 (A). Conc: 50.0\n", " Species 1 (B). Conc: 0.0\n", " Species 2 (S). Conc: 0.0\n" ] } ], "source": [ "dynamics = ReactionDynamics(reaction_data=chem_data) # Notice we're over-writing the earlier \"dynamics\" object\n", "dynamics.set_conc([50., 0, 0.], snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "markdown", "id": "fc516ca2-e62d-4784-b826-5372ff7f4c75", "metadata": { "tags": [] }, "source": [ "### Run the reaction" ] }, { "cell_type": "code", "execution_count": 15, "id": "2502cd11-0df9-4303-8895-98401a1df7b8", "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, and will rewind there]\n", "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", "69 total step(s) taken\n" ] } ], "source": [ "dynamics.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n", "\n", "# All of these settings are currently close to the default values... but subject to change; set for repeatability\n", "dynamics.set_thresholds(norm=\"norm_A\", low=0.5, high=1.0, abort=1.44)\n", "dynamics.set_thresholds(norm=\"norm_B\", low=0.05, 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", "# The changes of concentrations vary very rapidly early on; automated variable timesteps will take care of that\n", "dynamics.single_compartment_react(initial_step=0.001, reaction_duration=0.3,\n", " snapshots={\"initial_caption\": \"1st reaction step\",\n", " \"final_caption\": \"last reaction step\"},\n", " variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 16, "id": "a41e5009-e2b3-4bea-9892-7b9bd8295a07", "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_curves(colors=[\"blue\", \"green\", \"red\"], \n", " title=\"Coupled reactions A <-> B and A <-> S (fast but disadvantaged energetically)\",\n", " show_intervals=True)" ] }, { "cell_type": "markdown", "id": "f4a147c6-cad1-47ca-bc1e-79b43a29e5c0", "metadata": {}, "source": [ "### Notice how the \"alternate (shunt) path\" of the reaction, i.e. S (red) \n", "### has a FAST START (fast kinetics),\n", "### but EVENTUALLY PETERS OUT (energy dis-advantage)" ] }, { "cell_type": "code", "execution_count": 17, "id": "f0d7d7ed-158c-4cf4-8d95-ef057ca612d6", "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 0.00225, in 14 steps of 0.000125\n", "From time 0.00225 to 0.00295, in 4 steps of 0.000175\n", "From time 0.00295 to 0.00393, in 4 steps of 0.000245\n", "From time 0.00393 to 0.005302, in 4 steps of 0.000343\n", "From time 0.005302 to 0.006743, in 3 steps of 0.00048\n", "From time 0.006743 to 0.009432, in 4 steps of 0.000672\n", "From time 0.009432 to 0.01226, in 3 steps of 0.000941\n", "From time 0.01226 to 0.01753, in 4 steps of 0.00132\n", "From time 0.01753 to 0.0249, in 4 steps of 0.00184\n", "From time 0.0249 to 0.03524, in 4 steps of 0.00258\n", "From time 0.03524 to 0.04608, in 3 steps of 0.00362\n", "From time 0.04608 to 0.06127, in 3 steps of 0.00506\n", "From time 0.06127 to 0.07544, in 2 steps of 0.00709\n", "From time 0.07544 to 0.1151, in 4 steps of 0.00992\n", "From time 0.1151 to 0.1429, in 2 steps of 0.0139\n", "From time 0.1429 to 0.1818, in 2 steps of 0.0194\n", "From time 0.1818 to 0.209, in 1 step of 0.0272\n", "From time 0.209 to 0.2471, in 1 step of 0.0381\n", "From time 0.2471 to 0.3005, in 1 step of 0.0534\n", "(69 steps total)\n" ] } ], "source": [ "dynamics.explain_time_advance()" ] }, { "cell_type": "code", "execution_count": 18, "id": "80fbaee3-bd6f-4197-9270-23374d46a4a7", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABScaption
00.00000050.0000000.0000000.000000Initial state
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650.1623546.59394033.31505810.091002
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" ], "text/plain": [ " SYSTEM TIME A B S caption\n", "0 0.000000 50.000000 0.000000 0.000000 Initial state\n", "1 0.000250 47.750000 0.375000 1.875000 1st reaction step\n", "2 0.000500 45.648594 0.732656 3.618750 \n", "3 0.000625 44.667193 0.903381 4.429427 \n", "4 0.000750 43.718113 1.070318 5.211569 \n", ".. ... ... ... ... ...\n", "65 0.162354 6.593940 33.315058 10.091002 \n", "66 0.181800 6.375490 33.922608 9.701902 \n", "67 0.209024 6.163548 34.512062 9.324390 \n", "68 0.247138 5.994349 34.982624 9.023027 \n", "69 0.300498 5.900061 35.245013 8.854926 last reaction step\n", "\n", "[70 rows x 5 columns]" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "code", "execution_count": 19, "id": "b139f5e4-625f-4a5e-8f57-8f00244dced4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A <-> B\n", "Final concentrations: [B] = 35.25 ; [A] = 5.9\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 5.97367\n", " Formula used: [B] / [A]\n", "2. Ratio of forward/reverse reaction rates: 6.0\n", "Discrepancy between the two values: 0.4388 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n", "A <-> S\n", "Final concentrations: [S] = 8.855 ; [A] = 5.9\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 1.50082\n", " Formula used: [S] / [A]\n", "2. Ratio of forward/reverse reaction rates: 1.5\n", "Discrepancy between the two values: 0.05463 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that all the reactions have reached equilibrium\n", "dynamics.is_in_equilibrium()" ] }, { "cell_type": "code", "execution_count": null, "id": "f87fe3c7-2c0d-4e3c-aff0-350bd04ea1a7", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "9e9260a7-5777-4eee-93b8-c46b8364e24f", "metadata": {}, "source": [ "# Scenario 3: \n", "### downregulated by shunt: \n", "### kinetically slow, \n", "### but with thermodynamical advantage (i.e. energetically favored)" ] }, { "cell_type": "code", "execution_count": 20, "id": "04476dab-f845-4533-8f26-fd0eecf8304f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 2 (at temp. 25 C)\n", "0: A <-> B (kF = 30 / kR = 5 / Delta_G = -4,441.69 / K = 6) | 1st order in all reactants & products\n", "1: A <-> S (kF = 3 / kR = 0.1 / Delta_G = -8,431.42 / K = 30) | 1st order in all reactants & products\n" ] } ], "source": [ "# Specify the chemicals (notice that we're starting with new objects)\n", "chem_data = chem(names=[\"A\", \"B\", \"S\"])\n", "\n", "# Reaction A <-> B (as before)\n", "chem_data.add_reaction(reactants=[\"A\"], products=[\"B\"],\n", " forward_rate=30., reverse_rate=5.) \n", "\n", "# Reaction A <-> S (slow shunt, excellent thermodynamical energetic advantage)\n", "chem_data.add_reaction(reactants=[\"A\"], products=[\"S\"],\n", " forward_rate=3., reverse_rate=0.1)\n", "\n", "chem_data.describe_reactions()" ] }, { "cell_type": "markdown", "id": "6154b260-ce64-450a-b069-22cb920818d3", "metadata": {}, "source": [ "### Set the initial concentrations of all the chemicals, in their index order" ] }, { "cell_type": "code", "execution_count": 21, "id": "a45c9ebf-d06e-443f-a1a1-a5b2db6803b7", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "3 species:\n", " Species 0 (A). Conc: 50.0\n", " Species 1 (B). Conc: 0.0\n", " Species 2 (S). Conc: 0.0\n" ] } ], "source": [ "dynamics = ReactionDynamics(reaction_data=chem_data)\n", "dynamics.set_conc([50., 0, 0.], snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "markdown", "id": "e6bddc07-e9cf-4236-bd2b-0e1fe0567800", "metadata": { "tags": [] }, "source": [ "### Run the reaction" ] }, { "cell_type": "code", "execution_count": 22, "id": "3800cb7b-475e-4437-a982-af2760355795", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "INFO: the tentative time step (0.005) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.25 (set to 0.00125) [Step started at t=0, and will rewind there]\n", "454 total step(s) taken\n" ] } ], "source": [ "dynamics.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n", "\n", "# These settings can be tweaked to make the time resolution finer or coarser\n", "dynamics.set_thresholds(norm=\"norm_A\", low=2.0, high=5.0, abort=10.0)\n", "dynamics.set_thresholds(norm=\"norm_B\", low=0.008, high=0.5, abort=2.0) # The \"low\" value here seems especially critical to fend off instabilities\n", "dynamics.set_step_factors(upshift=1.5, downshift=0.25, abort=0.25)\n", "dynamics.set_error_step_factor(0.2)\n", "\n", "# The changes of concentrations vary very rapidly early on; automated variable timesteps will take care of that\n", "dynamics.single_compartment_react(initial_step=0.005, reaction_duration=7.0,\n", " snapshots={\"initial_caption\": \"1st reaction step\",\n", " \"final_caption\": \"last reaction step\"},\n", " variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 23, "id": "8a533692-7830-49a2-83f5-8da6aa201935", "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_curves(colors=[\"blue\", \"green\", \"red\"], \n", " title=\"Coupled reactions A <-> B and A <-> S (slow but with energetic advantage)\")" ] }, { "cell_type": "markdown", "id": "05dbe681-2fa9-478c-b4eb-8c322e173c0c", "metadata": {}, "source": [ "### Notice how the \"alternate (shunt) path\" of the reaction, i.e. S (red) \n", "### has a SLOW START (slow kinetics),\n", "### but EVENTUALLY DOMINATES (energy advantage)" ] }, { "cell_type": "code", "execution_count": 24, "id": "4fa4035f-00eb-4cc7-a0ff-835bcc8baf52", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "From time 0 to 0.0025, in 2 steps of 0.00125\n", "From time 0.0025 to 0.03281, in 97 steps of 0.000313\n", "From time 0.03281 to 0.05859, in 55 steps of 0.000469\n", "From time 0.05859 to 0.07617, in 25 steps of 0.000703\n", "From time 0.07617 to 0.09199, in 15 steps of 0.00105\n", "From time 0.09199 to 0.1062, in 9 steps of 0.00158\n", "From time 0.1062 to 0.1205, in 6 steps of 0.00237\n", "From time 0.1205 to 0.2237, in 29 steps of 0.00356\n", "From time 0.2237 to 0.3999, in 33 steps of 0.00534\n", "From time 0.3999 to 0.6402, in 30 steps of 0.00801\n", "From time 0.6402 to 0.9525, in 26 steps of 0.012\n", "From time 0.9525 to 1.349, in 22 steps of 0.018\n", "From time 1.349 to 1.998, in 24 steps of 0.027\n", "From time 1.998 to 3.66, in 41 steps of 0.0405\n", "From time 3.66 to 4.876, in 20 steps of 0.0608\n", "From time 4.876 to 5.971, in 12 steps of 0.0912\n", "From time 5.971 to 6.929, in 7 steps of 0.137\n", "From time 6.929 to 7.134, in 1 step of 0.205\n", "(454 steps total)\n" ] } ], "source": [ "dynamics.explain_time_advance()" ] }, { "cell_type": "code", "execution_count": 25, "id": "8fe4bbce-f10b-4590-9cbd-97998745fc27", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABScaption
00.00000050.0000000.0000000.000000Initial state
10.00125047.9375001.8750000.1875001st reaction step
20.00250045.9718203.6609380.367242
30.00281245.5034684.0862030.410329
40.00312545.0406114.5064130.452976
..................
4506.5185461.5389959.35682439.104182
4516.6553881.5263669.27276439.200870
4526.7922301.5145749.19437639.291050
4536.9290721.5036319.12121439.375155
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455 rows × 5 columns

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" ], "text/plain": [ " SYSTEM TIME A B S caption\n", "0 0.000000 50.000000 0.000000 0.000000 Initial state\n", "1 0.001250 47.937500 1.875000 0.187500 1st reaction step\n", "2 0.002500 45.971820 3.660938 0.367242 \n", "3 0.002812 45.503468 4.086203 0.410329 \n", "4 0.003125 45.040611 4.506413 0.452976 \n", ".. ... ... ... ... ...\n", "450 6.518546 1.538995 9.356824 39.104182 \n", "451 6.655388 1.526366 9.272764 39.200870 \n", "452 6.792230 1.514574 9.194376 39.291050 \n", "453 6.929072 1.503631 9.121214 39.375155 \n", "454 7.134334 1.487983 9.019168 39.492848 last reaction step\n", "\n", "[455 rows x 5 columns]" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "markdown", "id": "4f451620-86fd-4e3c-a060-6b506f78c13d", "metadata": {}, "source": [ "### Check the final equilibrium" ] }, { "cell_type": "code", "execution_count": 26, "id": "96424a3f-31da-46bf-81c0-0a85b9bc476d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A <-> B\n", "Final concentrations: [B] = 9.019 ; [A] = 1.488\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 6.06134\n", " Formula used: [B] / [A]\n", "2. Ratio of forward/reverse reaction rates: 6.0\n", "Discrepancy between the two values: 1.022 %\n", "Reaction IS in equilibrium (within 12% tolerance)\n", "\n", "A <-> S\n", "Final concentrations: [S] = 39.49 ; [A] = 1.488\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 26.5412\n", " Formula used: [S] / [A]\n", "2. Ratio of forward/reverse reaction rates: 30.0\n", "Discrepancy between the two values: 11.53 %\n", "Reaction IS in equilibrium (within 12% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that all the reactions have reached equilibrium\n", "dynamics.is_in_equilibrium(tolerance=12)" ] }, { "cell_type": "markdown", "id": "fbeba7fe-7a4d-4223-aaa1-6b5b9b3cc1b8", "metadata": {}, "source": [ "#### Please note the much-longer timescale from the earlier plots\n", "If we look at early time interval, this is what it looks like:" ] }, { "cell_type": "code", "execution_count": 27, "id": "f8c50006-8c5d-405f-9442-7fd9e5d1274d", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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"white", "ticks": "" }, "bgcolor": "#E5ECF6", "caxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" } }, "title": { "x": 0.05 }, "xaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 }, "yaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 } } }, "title": { "text": "Same plot as above, both only showing initial detail" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ 0, 0.28776855468749996 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -2.7777777777777777, 52.77777777777778 ], "title": { "text": "concentration" }, "type": "linear" } } }, "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = px.line(data_frame=dynamics.get_history().loc[:250], x=\"SYSTEM TIME\", y=[\"A\", \"B\", \"S\"], \n", " title=\"Same plot as above, both only showing initial detail\",\n", " color_discrete_sequence = [\"blue\", \"green\", \"red\"],\n", " labels={\"value\":\"concentration\", \"variable\":\"Chemical\"})\n", "fig.show()" ] }, { "cell_type": "code", "execution_count": 28, "id": "5c44014b-9dee-4d8c-a2de-13478ee7bb63", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Min abs distance found at data row: 71\n" ] }, { "data": { "text/plain": [ "(0.02405919499545674, 23.73396682504195)" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Look at where the curves intersect\n", "dynamics.curve_intersection(\"A\", \"B\", t_start=0, t_end=0.1)" ] }, { "cell_type": "code", "execution_count": 29, "id": "ac0382c7-5940-4db7-b1df-80edd29c3336", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Min abs distance found at data row: 216\n" ] }, { "data": { "text/plain": [ "(0.14412951669101942, 6.026379520544665)" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.curve_intersection(\"A\", \"S\", t_start=0.1, t_end=0.2)" ] }, { "cell_type": "code", "execution_count": null, "id": "00363317-fe95-4d18-acab-5e6116e01a17", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "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 }