{ "cells": [ { "cell_type": "markdown", "id": "49bcb5b0-f19d-4b96-a5f1-e0ae30f66d8f", "metadata": {}, "source": [ "## `U` (\"Up-regulator\") up-regulates `X` , by sharing a reaction product `D` (\"Drain\") across 2 separate reactions: \n", "### `U <-> 2 D` and `X <-> D` (both mostly forward)\n", "\n", "1st-order kinetics throughout. \n", "\n", "Invoking [Le Chatelier's principle](https://www.chemguide.co.uk/physical/equilibria/lechatelier.html), it can be seen that, starting from equilibrium, when [U] goes up, so does [D]; and when [D] goes up, so does [X]. \n", "Conversely, when [U] goes down, so does [D]; and when [D] goes down, so does [X]. \n", "\n", "LAST REVISED: June 23, 2024 (using v. 1.0 beta36)" ] }, { "cell_type": "code", "execution_count": 1, "id": "838b9dfc-e3c2-4e9d-bedc-f32a2b6a6dfa", "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": "16962197", "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 'up_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: 2 (at temp. 25 C)\n", "0: U <-> 2 D (kF = 8 / kR = 2 / delta_G = -3,436.6 / K = 4) | 1st order in all reactants & products\n", "1: X <-> D (kF = 6 / kR = 3 / delta_G = -1,718.3 / K = 2) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {'X', 'U', 'D'}\n", "[GRAPHIC ELEMENT SENT TO LOG FILE `up_regulate_2.log.htm`]\n" ] } ], "source": [ "# Initialize the system\n", "chem_data = chem(names=[\"U\", \"X\", \"D\"])\n", "\n", "# Reaction U <-> 2D , with 1st-order kinetics for all species\n", "chem_data.add_reaction(reactants=\"U\", products=[(2, \"D\", 1)],\n", " forward_rate=8., reverse_rate=2.)\n", "\n", "# Reaction X <-> D , with 1st-order kinetics for all species\n", "chem_data.add_reaction(reactants=\"X\", products=\"D\",\n", " forward_rate=6., reverse_rate=3.)\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 (U). Conc: 50.0\n", " Species 1 (X). Conc: 100.0\n", " Species 2 (D). Conc: 0.0\n", "Set of chemicals involved in reactions: {'X', 'U', 'D'}\n" ] } ], "source": [ "dynamics = UniformCompartment(chem_data=chem_data, preset = \"fast\")\n", "dynamics.set_conc(conc={\"U\": 50., \"X\": 100.})\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": null, "id": "e652b8fa-b7b3-4772-b602-aa15d11d9067", "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", "42 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': 17, 'norm_C': 17, 'norm_D': 17}\n" ] }, { "data": { "text/html": [ "
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SYSTEM TIMEUXDcaption
00.00000050.000000100.0000000.000000Initialized state
10.00233349.06688098.6003203.265920
20.00419948.34650597.5145345.792455
30.00606547.64631696.4550518.252317
40.00793246.96576295.42120410.647272
50.00979846.30430894.41234212.979043
60.01166445.66143293.42783115.249305
70.01353045.03662892.46705517.459688
80.01633044.12579091.06059220.687828
90.01856943.42789789.97600723.168198
100.02080942.75361788.92266125.570105
110.02304842.10217587.89960527.896044
120.02640741.15814686.40908231.274626
130.02909540.44137785.26793633.849309
140.03178239.75385784.16594836.326338
150.03446939.09443183.10169838.709439
160.03715738.46199182.07382241.002196
170.04118837.55221180.58459544.310983
180.04441336.86919979.45404046.807562
190.04763836.21991078.36951449.190667
200.05086335.60274277.32902751.465488
210.05570034.72288275.83150954.722726
220.05957034.07144374.70608057.151033
230.06343933.45896773.63497459.447093
240.06924432.59535072.10560462.703696
250.07388831.96678670.97009065.096338
260.07853231.38379669.89954767.332862
270.08549830.57295568.38521270.468877
280.09107029.99538267.27680472.732432
290.09942929.20548665.72654375.862484
300.10611628.65768864.61132778.073296
310.11614727.92430163.07214981.079249
320.12417127.43291461.98727783.146895
330.13620826.79292760.51298285.901165
340.14824526.28087159.24461888.193640
350.16630025.66953157.60364891.057291
360.18074425.33382656.55717492.775174
370.20241024.96289655.23516094.839047
380.23490924.63709053.71114997.014671
390.28365824.48755952.18907298.835810
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" ], "text/plain": [ " SYSTEM TIME U X D caption\n", "0 0.000000 50.000000 100.000000 0.000000 Initialized state\n", "1 0.002333 49.066880 98.600320 3.265920 \n", "2 0.004199 48.346505 97.514534 5.792455 \n", "3 0.006065 47.646316 96.455051 8.252317 \n", "4 0.007932 46.965762 95.421204 10.647272 \n", "5 0.009798 46.304308 94.412342 12.979043 \n", "6 0.011664 45.661432 93.427831 15.249305 \n", "7 0.013530 45.036628 92.467055 17.459688 \n", "8 0.016330 44.125790 91.060592 20.687828 \n", "9 0.018569 43.427897 89.976007 23.168198 \n", "10 0.020809 42.753617 88.922661 25.570105 \n", "11 0.023048 42.102175 87.899605 27.896044 \n", "12 0.026407 41.158146 86.409082 31.274626 \n", "13 0.029095 40.441377 85.267936 33.849309 \n", "14 0.031782 39.753857 84.165948 36.326338 \n", "15 0.034469 39.094431 83.101698 38.709439 \n", "16 0.037157 38.461991 82.073822 41.002196 \n", "17 0.041188 37.552211 80.584595 44.310983 \n", "18 0.044413 36.869199 79.454040 46.807562 \n", "19 0.047638 36.219910 78.369514 49.190667 \n", "20 0.050863 35.602742 77.329027 51.465488 \n", "21 0.055700 34.722882 75.831509 54.722726 \n", "22 0.059570 34.071443 74.706080 57.151033 \n", "23 0.063439 33.458967 73.634974 59.447093 \n", "24 0.069244 32.595350 72.105604 62.703696 \n", "25 0.073888 31.966786 70.970090 65.096338 \n", "26 0.078532 31.383796 69.899547 67.332862 \n", "27 0.085498 30.572955 68.385212 70.468877 \n", "28 0.091070 29.995382 67.276804 72.732432 \n", "29 0.099429 29.205486 65.726543 75.862484 \n", "30 0.106116 28.657688 64.611327 78.073296 \n", "31 0.116147 27.924301 63.072149 81.079249 \n", "32 0.124171 27.432914 61.987277 83.146895 \n", "33 0.136208 26.792927 60.512982 85.901165 \n", "34 0.148245 26.280871 59.244618 88.193640 \n", "35 0.166300 25.669531 57.603648 91.057291 \n", "36 0.180744 25.333826 56.557174 92.775174 \n", "37 0.202410 24.962896 55.235160 94.839047 \n", "38 0.234909 24.637090 53.711149 97.014671 \n", "39 0.283658 24.487559 52.189072 98.835810 \n", "40 0.356781 24.617071 50.973253 99.792605 \n", "41 0.466466 24.907587 50.264503 99.920324 \n", "42 0.630993 25.003005 49.964069 100.029921 " ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n", "\n", "dynamics.single_compartment_react(initial_step=0.03, target_end_time=0.5,\n", " variable_steps=True, explain_variable_steps=False)\n", "\n", "dynamics.get_history()" ] }, { "cell_type": "code", "execution_count": 7, "id": "b56d1612-a68c-4da3-be37-a7245b6c1a80", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "From time 0 to 0.002333, in 1 step of 0.00233\n", "From time 0.002333 to 0.01353, in 6 steps of 0.00187\n", "From time 0.01353 to 0.01633, in 1 step of 0.0028\n", "From time 0.01633 to 0.02305, in 3 steps of 0.00224\n", "From time 0.02305 to 0.02641, in 1 step of 0.00336\n", "From time 0.02641 to 0.03716, in 4 steps of 0.00269\n", "From time 0.03716 to 0.04119, in 1 step of 0.00403\n", "From time 0.04119 to 0.05086, in 3 steps of 0.00322\n", "From time 0.05086 to 0.0557, in 1 step of 0.00484\n", "From time 0.0557 to 0.06344, in 2 steps of 0.00387\n", "From time 0.06344 to 0.06924, in 1 step of 0.0058\n", "From time 0.06924 to 0.07853, in 2 steps of 0.00464\n", "From time 0.07853 to 0.0855, in 1 step of 0.00697\n", "From time 0.0855 to 0.09107, in 1 step of 0.00557\n", "From time 0.09107 to 0.09943, in 1 step of 0.00836\n", "From time 0.09943 to 0.1061, in 1 step of 0.00669\n", "From time 0.1061 to 0.1161, in 1 step of 0.01\n", "From time 0.1161 to 0.1242, in 1 step of 0.00802\n", "From time 0.1242 to 0.1482, in 2 steps of 0.012\n", "From time 0.1482 to 0.1663, in 1 step of 0.0181\n", "From time 0.1663 to 0.1807, in 1 step of 0.0144\n", "From time 0.1807 to 0.2024, in 1 step of 0.0217\n", "From time 0.2024 to 0.2349, in 1 step of 0.0325\n", "From time 0.2349 to 0.2837, in 1 step of 0.0487\n", "From time 0.2837 to 0.3568, in 1 step of 0.0731\n", "From time 0.3568 to 0.4665, in 1 step of 0.11\n", "From time 0.4665 to 0.631, in 1 step of 0.165\n", "(42 steps total)\n" ] } ], "source": [ "dynamics.explain_time_advance()" ] }, { "cell_type": "markdown", "id": "cbf6c9c7-8cec-400f-9e70-49ff1a9f485c", "metadata": { "tags": [] }, "source": [ "## Plots of changes of concentration with time" ] }, { "cell_type": "code", "execution_count": 8, "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=U
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(colors=['red', 'green', 'gray'])" ] }, { "cell_type": "markdown", "id": "962acf15-3b50-40e4-9daa-3dcca7d3291a", "metadata": {}, "source": [ "### Equilibrium" ] }, { "cell_type": "code", "execution_count": 9, "id": "2783a665-fca0-44e5-8d42-af2a96eae392", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: U <-> 2 D\n", "Final concentrations: [U] = 25 ; [D] = 100\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.00072\n", " Formula used: [D] / [U]\n", "2. Ratio of forward/reverse reaction rates: 4\n", "Discrepancy between the two values: 0.0179 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n", "1: X <-> D\n", "Final concentrations: [X] = 49.96 ; [D] = 100\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 2.00204\n", " Formula used: [D] / [X]\n", "2. Ratio of forward/reverse reaction rates: 2\n", "Discrepancy between the two values: 0.1019 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 9, "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": "95679484-9ebe-4765-8644-40e94c384f65", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "99031e2d-6cb2-4ec0-9bed-1f7ca4413d93", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "448ec7fa-6529-438b-84ba-47888c2cd080", "metadata": { "tags": [] }, "source": [ "# 2. Now, let's suddenly increase [U]" ] }, { "cell_type": "code", "execution_count": 10, "id": "7245be7a-c9db-45f5-b033-d6c521237a9c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0.63099291:\n", "3 species:\n", " Species 0 (U). Conc: 70.0\n", " Species 1 (X). Conc: 49.96406885180444\n", " Species 2 (D). Conc: 100.02992131107243\n", "Set of chemicals involved in reactions: {'X', 'U', 'D'}\n" ] } ], "source": [ "dynamics.set_single_conc(species_name=\"U\", conc=70., snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 11, "id": "61eead55-fcef-41cd-b29e-f2d5ad5c6078", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEUXDcaption
410.46646624.90758750.26450399.920324
420.63099325.00300549.964069100.029921
430.63099370.00000049.964069100.029921Set concentration of `U`
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" ], "text/plain": [ " SYSTEM TIME U X D caption\n", "41 0.466466 24.907587 50.264503 99.920324 \n", "42 0.630993 25.003005 49.964069 100.029921 \n", "43 0.630993 70.000000 49.964069 100.029921 Set concentration of `U`" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(tail=3)" ] }, { "cell_type": "markdown", "id": "24455d58-a0ea-43fa-b6ad-95c42a8b34b2", "metadata": {}, "source": [ "### Again, take the system to equilibrium" ] }, { "cell_type": "code", "execution_count": 12, "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", "24 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: 9\n", "Norm usage: {'norm_A': 51, 'norm_B': 28, 'norm_C': 28, 'norm_D': 28}\n" ] } ], "source": [ "dynamics.single_compartment_react(initial_step=0.03, target_end_time=1,\n", " variable_steps=True)" ] }, { "cell_type": "code", "execution_count": 13, "id": "35850ec7-e78e-4b57-976c-bc0ad6c824d5", "metadata": {}, "outputs": [], "source": [ "#dynamics.get_history()\n", "#dynamics.explain_time_advance()" ] }, { "cell_type": "code", "execution_count": 14, "id": "5af5d869-16ff-4f1d-ab83-4865b42e6376", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=U
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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(colors=['red', 'green', 'gray'])" ] }, { "cell_type": "markdown", "id": "158e3787-f2d5-4a01-aaa9-6066e93e584c", "metadata": {}, "source": [ "### The (transiently) high value of [U] led to an increase in [X]" ] }, { "cell_type": "code", "execution_count": 15, "id": "c3afbcc8-bdae-4938-a3f1-ce00d62816f2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: U <-> 2 D\n", "Final concentrations: [U] = 36.7 ; [D] = 145.3\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.9596\n", " Formula used: [D] / [U]\n", "2. Ratio of forward/reverse reaction rates: 4\n", "Discrepancy between the two values: 1.01 %\n", "Reaction IS in equilibrium (within 2% tolerance)\n", "\n", "1: X <-> D\n", "Final concentrations: [X] = 71.31 ; [D] = 145.3\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 2.03768\n", " Formula used: [D] / [X]\n", "2. Ratio of forward/reverse reaction rates: 2\n", "Discrepancy between the two values: 1.884 %\n", "Reaction IS in equilibrium (within 2% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reaction has reached equilibrium\n", "dynamics.is_in_equilibrium(tolerance=2)" ] }, { "cell_type": "code", "execution_count": null, "id": "02d8a758-89b1-4c28-94c9-c73b11f3b8dc", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "ff612c5c-14f8-40ae-856d-e57611e6280c", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "f6619731-c5ea-484c-af3e-cea50d685361", "metadata": { "tags": [] }, "source": [ "# 3. Let's again suddenly increase [U]" ] }, { "cell_type": "code", "execution_count": 16, "id": "d3618eba-a673-4ff5-85d0-08f5ea592361", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 1.0692249:\n", "3 species:\n", " Species 0 (U). Conc: 100.0\n", " Species 1 (X). Conc: 71.30574896594584\n", " Species 2 (D). Conc: 145.29798215919604\n", "Set of chemicals involved in reactions: {'X', 'U', 'D'}\n" ] } ], "source": [ "dynamics.set_single_conc(species_name=\"U\", conc=100., snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 17, "id": "e8fe3554-d5ab-4306-b890-4e36289b5b4b", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEUXDcaption
660.97739237.44109369.408954145.702851
671.06922536.69513071.305749145.297982
681.069225100.00000071.305749145.297982Set concentration of `U`
\n", "
" ], "text/plain": [ " SYSTEM TIME U X D caption\n", "66 0.977392 37.441093 69.408954 145.702851 \n", "67 1.069225 36.695130 71.305749 145.297982 \n", "68 1.069225 100.000000 71.305749 145.297982 Set concentration of `U`" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(tail=3)" ] }, { "cell_type": "markdown", "id": "0974480d-ca45-46fe-addd-c8d394780fdb", "metadata": {}, "source": [ "### Yet again, take the system to equilibrium" ] }, { "cell_type": "code", "execution_count": 18, "id": "8fe20f9c-05c4-45a4-b485-a51005440200", "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", "34 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: 14\n", "Norm usage: {'norm_A': 81, 'norm_B': 44, 'norm_C': 44, 'norm_D': 44}\n" ] } ], "source": [ "dynamics.single_compartment_react(initial_step=0.03, target_end_time=1.6,\n", " variable_steps=True)" ] }, { "cell_type": "code", "execution_count": 19, "id": "ad01c472-3ebe-4d0d-8913-1bcd85ea7a6c", "metadata": {}, "outputs": [], "source": [ "#dynamics.get_history()\n", "#dynamics.explain_time_advance()" ] }, { "cell_type": "code", "execution_count": 20, "id": "54346a72-bac9-4cc7-ba01-0533ed60371f", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=U
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(colors=['red', 'green', 'gray'])" ] }, { "cell_type": "markdown", "id": "ffbf3294-7a8d-4679-9c4b-5b9a975bf8fc", "metadata": {}, "source": [ "### The (transiently) high value of [U] again led to an increase in [X]" ] }, { "cell_type": "code", "execution_count": 21, "id": "aff608b1-5c78-4070-845a-118afe7c2108", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: U <-> 2 D\n", "Final concentrations: [U] = 52.11 ; [D] = 208.3\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.99727\n", " Formula used: [D] / [U]\n", "2. Ratio of forward/reverse reaction rates: 4\n", "Discrepancy between the two values: 0.06828 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n", "1: X <-> D\n", "Final concentrations: [X] = 104.1 ; [D] = 208.3\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 2.00191\n", " Formula used: [D] / [X]\n", "2. Ratio of forward/reverse reaction rates: 2\n", "Discrepancy between the two values: 0.09565 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 21, "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": "7ddbe0ec-53c3-4d25-825a-cbe3bdf8e50a", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "8c6d9c07-d5ef-4343-b361-f73fb4775699", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "64ebc51b-0dc7-4cff-b231-4c35843a7113", "metadata": { "tags": [] }, "source": [ "# 4. Now, instead, let's DECREASE [U]" ] }, { "cell_type": "code", "execution_count": 22, "id": "52f4843c-0671-4cd9-9c51-74a44feb4fe4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 1.6922388:\n", "3 species:\n", " Species 0 (U). Conc: 5.0\n", " Species 1 (X). Conc: 104.05849412376946\n", " Species 2 (D). Conc: 208.31604776017218\n", "Set of chemicals involved in reactions: {'X', 'U', 'D'}\n" ] } ], "source": [ "dynamics.set_single_conc(species_name=\"U\", conc=5., snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 23, "id": "e5ce5d59", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEUXDcaption
1011.55513352.537879102.920098208.607876
1021.69223952.114595104.058494208.316048
1031.6922395.000000104.058494208.316048Set concentration of `U`
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" ], "text/plain": [ " SYSTEM TIME U X D caption\n", "101 1.555133 52.537879 102.920098 208.607876 \n", "102 1.692239 52.114595 104.058494 208.316048 \n", "103 1.692239 5.000000 104.058494 208.316048 Set concentration of `U`" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(tail=3)" ] }, { "cell_type": "markdown", "id": "da46e3d8-58d2-4b48-8b32-887613967fce", "metadata": {}, "source": [ "### Take the system to equilibrium" ] }, { "cell_type": "code", "execution_count": 24, "id": "c392f375-c7b4-476b-809e-5cc4f5c14fa4", "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", "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: 18\n", "Norm usage: {'norm_A': 102, 'norm_B': 57, 'norm_C': 57, 'norm_D': 57}\n" ] } ], "source": [ "dynamics.single_compartment_react(initial_step=0.03, target_end_time=2.3,\n", " variable_steps=True)" ] }, { "cell_type": "code", "execution_count": 25, "id": "6de58fe9-ff1e-40dd-9ac7-83eee458f818", "metadata": {}, "outputs": [], "source": [ "#dynamics.get_history()\n", "#dynamics.explain_time_advance()" ] }, { "cell_type": "code", "execution_count": 26, "id": "c388dae7-c4a6-4644-a390-958e3862d102", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=U
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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(colors=['red', 'green', 'gray'])" ] }, { "cell_type": "markdown", "id": "a1629b91-2753-4df7-b6a0-dedf86ac3dc1", "metadata": {}, "source": [ "### The (transiently) LOW value of [U] led to an DECREASE in [X]" ] }, { "cell_type": "code", "execution_count": 27, "id": "31c9c18f-3a7f-4690-8e2f-70fdb02ef5c7", "metadata": {}, "outputs": [ { "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(explain=False)" ] }, { "cell_type": "code", "execution_count": null, "id": "9382dbf7", "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 }