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"id": "49bcb5b0-f19d-4b96-a5f1-e0ae30f66d8f",
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"## `U` (\"Up-regulator\") up-regulates `X` , by sharing an upstream reagent `S` (\"Source\") across 2 separate reactions: \n",
"### `2 S <-> U` and `S <-> X` (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 [S]; and when [S] goes up, so does [X]. \n",
"Conversely, when [U] goes down, so does [S]; and when [S] goes down, so does [X]. \n",
"\n",
"This experiment is a counterpart of experiment `up_regulate_2`, with \"upstream\" rather than \"downstream\" reactions.\n",
"\n",
"Note: numerical errors in the same reactions (with the same initial conditions) is explored in the experiment \"large_time_steps_2\"\n",
"\n",
"LAST REVISED: May 26, 2023"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "d9efa3fd-e95d-4e1c-878a-81ae932b2709",
"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": "01bae555-3dcf-42c1-bddc-9477a37f49f8",
"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": "cc53849f-351d-49e0-bfa8-22f8d8e22f8e",
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"-> Output will be LOGGED into the file 'up_regulate_3.log.htm'\n"
]
}
],
"source": [
"# Initialize the HTML logging\n",
"log_file = get_notebook_basename() + \".log.htm\" # Use the notebook base filename for the log file\n",
"\n",
"# Set up the use of some specified graphic (Vue) components\n",
"GraphicLog.config(filename=log_file,\n",
" components=[\"vue_cytoscape_1\"],\n",
" extra_js=\"https://cdnjs.cloudflare.com/ajax/libs/cytoscape/3.21.2/cytoscape.umd.js\")"
]
},
{
"cell_type": "markdown",
"id": "d6d3ca49-589d-49b7-8424-37c7b01bcacf",
"metadata": {},
"source": [
"### Initialize the system"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "23c15e66-52e4-495b-aa3d-ecddd8d16942",
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"name": "stdout",
"output_type": "stream",
"text": [
"Number of reactions: 2 (at temp. 25 C)\n",
"0: 2 S <-> U (kF = 8 / kR = 2 / Delta_G = -3,436.56 / K = 4) | 1st order in all reactants & products\n",
"1: S <-> X (kF = 6 / kR = 3 / Delta_G = -1,718.28 / K = 2) | 1st order in all reactants & products\n",
"[GRAPHIC ELEMENT SENT TO LOG FILE `up_regulate_3.log.htm`]\n"
]
}
],
"source": [
"# Initialize the system\n",
"chem_data = chem(names=[\"U\", \"X\", \"S\"])\n",
"\n",
"# Reaction 2 S <-> U , with 1st-order kinetics for all species (mostly forward)\n",
"chem_data.add_reaction(reactants=[(2, \"S\")], products=\"U\",\n",
" forward_rate=8., reverse_rate=2.)\n",
"\n",
"# Reaction S <-> X , with 1st-order kinetics for all species (mostly forward)\n",
"chem_data.add_reaction(reactants=\"S\", products=\"X\",\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",
"graph_data = chem_data.prepare_graph_network()\n",
"GraphicLog.export_plot(graph_data, \"vue_cytoscape_1\")"
]
},
{
"cell_type": "markdown",
"id": "d1d0eabb-b5b1-4e15-846d-5e483a5a24a7",
"metadata": {},
"source": [
"### Set the initial concentrations of all the chemicals"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "e80645d6-eb5b-4c78-8b46-ae126d2cb2cf",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SYSTEM STATE at Time t = 0:\n",
"3 species:\n",
" Species 0 (U). Conc: 50.0\n",
" Species 1 (X). Conc: 100.0\n",
" Species 2 (S). Conc: 0.0\n"
]
}
],
"source": [
"dynamics = ReactionDynamics(reaction_data=chem_data)\n",
"dynamics.set_conc(conc={\"U\": 50., \"X\": 100., \"S\": 0.})\n",
"dynamics.describe_state()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "437be530-28df-4819-a681-0d63a66e9f83",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "0b46b395-3f68-4dbd-b0c5-d67a0e623726",
"metadata": {
"tags": []
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"source": [
"# 1. Take the initial system to equilibrium"
]
},
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"cell_type": "code",
"execution_count": 6,
"id": "853a1827-5628-435b-91dc-cc51316ebcc2",
"metadata": {},
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"source": [
"dynamics = ReactionDynamics(reaction_data=chem_data)\n",
"dynamics.set_conc(conc={\"U\": 50., \"X\": 100., \"S\": 0.})\n",
"#dynamics.describe_state()"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "909a9301-8eda-44af-ba36-9d7167aedd33",
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"name": "stdout",
"output_type": "stream",
"text": [
"INFO: the tentative time step (0.01) 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 0.005) [Step started at t=0, and will rewind there]\n",
"43 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=0.8, 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",
"dynamics.single_compartment_react(initial_step=0.01, target_end_time=1.5,\n",
" variable_steps=True, explain_variable_steps=False)\n",
"\n",
"#df = dynamics.get_history()\n",
"#dynamics.explain_time_advance()"
]
},
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"cell_type": "markdown",
"id": "cbf6c9c7-8cec-400f-9e70-49ff1a9f485c",
"metadata": {
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"source": [
"## Plots of changes of concentration with time"
]
},
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"execution_count": 8,
"id": "c388dae7-c4a6-4644-a390-958e3862d102",
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_curves(colors=['green', 'orange', 'blue'])"
]
},
{
"cell_type": "markdown",
"id": "53406956-8084-43fe-9540-1212e9cc2258",
"metadata": {},
"source": [
"### Note that [S] is initially 0, and that it builds up thru _reverse_ reactions"
]
},
{
"cell_type": "markdown",
"id": "962acf15-3b50-40e4-9daa-3dcca7d3291a",
"metadata": {},
"source": [
"### Equilibrium"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "c3afbcc8-bdae-4938-a3f1-ce00d62816f2",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2 S <-> U\n",
"Final concentrations: [U] = 72.65 ; [S] = 18.19\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.99404\n",
" Formula used: [U] / [S]\n",
"2. Ratio of forward/reverse reaction rates: 4.0\n",
"Discrepancy between the two values: 0.1489 %\n",
"Reaction IS in equilibrium (within 1% tolerance)\n",
"\n",
"S <-> X\n",
"Final concentrations: [X] = 36.52 ; [S] = 18.19\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 2.00759\n",
" Formula used: [X] / [S]\n",
"2. Ratio of forward/reverse reaction rates: 2.0\n",
"Discrepancy between the two values: 0.3793 %\n",
"Reaction IS in equilibrium (within 1% tolerance)\n",
"\n"
]
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"dynamics.is_in_equilibrium()"
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"id": "f5030a8a-2609-4887-91c6-1531d66321fb",
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"cell_type": "markdown",
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"source": [
"# 2. Now, let's suddenly increase [U]"
]
},
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"execution_count": 10,
"id": "e7ced06d-f506-41ee-80d6-d4b2a8ed28bc",
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"text": [
"SYSTEM STATE at Time t = 1.604933:\n",
"3 species:\n",
" Species 0 (U). Conc: 72.64754791961869\n",
" Species 1 (X). Conc: 36.515929976181866\n",
" Species 2 (S). Conc: 18.188974184580783\n"
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"SYSTEM STATE at Time t = 1.604933:\n",
"3 species:\n",
" Species 0 (U). Conc: 100.0\n",
" Species 1 (X). Conc: 36.515929976181866\n",
" Species 2 (S). Conc: 18.188974184580783\n"
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_curves(colors=['green', 'orange', 'blue'])"
]
},
{
"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": "2783a665-fca0-44e5-8d42-af2a96eae392",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2 S <-> U\n",
"Final concentrations: [U] = 92.63 ; [S] = 23.18\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.99634\n",
" Formula used: [U] / [S]\n",
"2. Ratio of forward/reverse reaction rates: 4.0\n",
"Discrepancy between the two values: 0.09147 %\n",
"Reaction IS in equilibrium (within 1% tolerance)\n",
"\n",
"S <-> X\n",
"Final concentrations: [X] = 46.26 ; [S] = 23.18\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 1.99594\n",
" Formula used: [X] / [S]\n",
"2. Ratio of forward/reverse reaction rates: 2.0\n",
"Discrepancy between the two values: 0.2029 %\n",
"Reaction IS in equilibrium (within 1% 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()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "27a1b761-19bb-4ec4-83e7-6b7c85e0f165",
"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": "e82c46d1-482a-41fb-873e-11a42561603d",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SYSTEM STATE at Time t = 3.152333:\n",
"3 species:\n",
" Species 0 (U). Conc: 92.63103996217262\n",
" Species 1 (X). Conc: 46.26386257327225\n",
" Species 2 (S). Conc: 23.178961663145174\n"
]
}
],
"source": [
"dynamics.describe_state()"
]
},
{
"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 = 3.152333:\n",
"3 species:\n",
" Species 0 (U). Conc: 150.0\n",
" Species 1 (X). Conc: 46.26386257327225\n",
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"source": [
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"id": "61eead55-fcef-41cd-b29e-f2d5ad5c6078",
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" SYSTEM TIME | \n",
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\n",
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" 3.152333 | \n",
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"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_curves(colors=['green', 'orange', 'blue'])"
]
},
{
"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": [
{
"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(explain=False)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "019f3e6c-081d-45e1-86e7-1ca485d59998",
"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": "32de9623-5221-420b-a6f2-5414df281d44",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SYSTEM STATE at Time t = 4.709733:\n",
"3 species:\n",
" Species 0 (U). Conc: 134.37031316880427\n",
" Species 1 (X). Conc: 67.07941550667395\n",
" Species 2 (S). Conc: 33.62278239213483\n"
]
}
],
"source": [
"dynamics.describe_state()"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "52f4843c-0671-4cd9-9c51-74a44feb4fe4",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SYSTEM STATE at Time t = 4.709733:\n",
"3 species:\n",
" Species 0 (U). Conc: 80.0\n",
" Species 1 (X). Conc: 67.07941550667395\n",
" Species 2 (S). Conc: 33.62278239213483\n"
]
}
],
"source": [
"dynamics.set_chem_conc(species_name=\"U\", conc=80.)\n",
"dynamics.describe_state()"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "e8fe3554-d5ab-4306-b890-4e36289b5b4b",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" SYSTEM TIME | \n",
" U | \n",
" X | \n",
" S | \n",
" caption | \n",
"
\n",
" \n",
" \n",
" \n",
" | 83 | \n",
" 4.443500 | \n",
" 134.497997 | \n",
" 66.882281 | \n",
" 33.564550 | \n",
" | \n",
"
\n",
" \n",
" | 84 | \n",
" 4.709733 | \n",
" 134.370313 | \n",
" 67.079416 | \n",
" 33.622782 | \n",
" | \n",
"
\n",
" \n",
" | 85 | \n",
" 4.709733 | \n",
" 80.000000 | \n",
" 67.079416 | \n",
" 33.622782 | \n",
" Set concentration of `U` | \n",
"
\n",
" \n",
"
\n",
"
SYSTEM TIME=%{x}
concentration=%{y}",
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_curves(colors=['green', 'orange', 'blue'])"
]
},
{
"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": 28,
"id": "31c9c18f-3a7f-4690-8e2f-70fdb02ef5c7",
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{
"data": {
"text/plain": [
"True"
]
},
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"source": [
"# Verify that the reaction has reached equilibrium\n",
"dynamics.is_in_equilibrium(explain=False)"
]
},
{
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"id": "777ebec9-ed31-4cf3-adfc-b44db383bd39",
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"source": [
"**IDEAS TO EXPLORE**: \n",
"\n",
"* Effect of the stoichiometry and the Delta_G on the \"amplification\" of the signal (from [U] to [X]) \n",
"\n",
"* Effect of a continuously-varying (maybe oscillating [U]), and its being affected by the reactions' kinetics\n",
"\n",
"* Combining this experiment and `up_regulate_2` in a *\"bifan motif\"*"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "6fd8ca29-4a92-4381-8fcb-0acf5e4a1f16",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
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"language": "python",
"name": "python3"
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