{
"cells": [
{
"cell_type": "markdown",
"id": "5cbc8640",
"metadata": {},
"source": [
"## **Enzyme Kinetics** : \n",
"\n",
"#### Our model: `E + S <-> ES` (with kinetic parameters _k1_forward_ and _k1_reverse_), and `ES -> E + P` (_k2_forward_) \n",
"\n",
"#### In experiment `enzyme_1_a`, we were given `k1_forward`, `k1_reverse` and `k2_forward`... But what to do if we're **just given `kM` and `kcat`** ? \n",
"\n",
"In Part 1, we'll \"cheat\" and use the actual value of _k1_forward_ \n",
"In Part 2, we'll explore what happens if, lacking an actual value, we **under-estimate** _k1_forward_ \n",
"In Part 3, we'll explore what happens if we **over-estimate** _k1_forward_\n",
"\n",
"Background: please see experiment `enzyme_1_a`"
]
},
{
"cell_type": "markdown",
"id": "604b150b-7812-4fd3-9403-69a06dd7e397",
"metadata": {},
"source": [
"#### THE REACTION: \n",
"the enzyme `Adenosinedeaminase` with the substrate `2,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purine`, \n",
"and the initial concentration values choosen below, all satisfy the customary Michaelis-Menten assumptions that \n",
"`[E] << [S]` and that the reaction rate constants satisfy `k1_reverse >> k2_forward`\n",
"\n",
"Source of kinetic parameters: *page 16 of \"Analysis of Enzyme Reaction Kinetics, Vol. 1\", by F. Xavier Malcata, Wiley, 2023*"
]
},
{
"cell_type": "markdown",
"id": "c123db4f-c802-47f0-a3d3-0b857314d8e5",
"metadata": {},
"source": [
"### TAGS : \"uniform compartment\", \"chemistry\", \"numerical\", \"enzymes\""
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "6e9d0902-6fc9-4692-ac39-0651d08902ca",
"metadata": {},
"outputs": [],
"source": [
"LAST_REVISED = \"Dec. 15, 2024\"\n",
"LIFE123_VERSION = \"1.0-rc.1\" # Library version this experiment is based on"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "1e0ae9a9-9d0c-4edf-a5f2-1c589419e6cf",
"metadata": {},
"outputs": [],
"source": [
"#import set_path # Using MyBinder? Uncomment this before running the next cell!"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "a29db1c7",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"#import sys\n",
"#sys.path.append(\"C:/some_path/my_env_or_install\") # CHANGE to the folder containing your venv or libraries installation!\n",
"# NOTE: If any of the imports below can't find a module, uncomment the lines above, or try: import set_path \n",
"\n",
"from life123 import check_version, ChemData, Reactions, UniformCompartment, ReactionEnz, PlotlyHelper"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "af15ecf0-e083-4fef-b68e-abe794dcc86e",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"OK\n"
]
}
],
"source": [
"check_version(LIFE123_VERSION)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "3713fa4d-e9bb-4e33-8734-c1d4d23cf177",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "34d1cefc-f644-410a-9fe4-5204964742ac",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "1b6c8520-6340-4056-a9e4-fd376a64d21c",
"metadata": {},
"source": [
"## Assume we're only given values for `kM` and `kcat`"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "0922af12-fb21-4dd0-8709-13bec73555c3",
"metadata": {},
"outputs": [],
"source": [
"# The following values are taken from experiment `enzyme_1`\n",
"kM = 8.27777777777777\n",
"kcat = 49"
]
},
{
"cell_type": "markdown",
"id": "84744152-f9e6-45a1-9002-a4842c2ef2c0",
"metadata": {},
"source": [
"What values of k1_forward, k1_reverse and k2_forward are compatible with them? \n",
"That question was explored in experiment `enzyme2_a`. Here we'll explore the dynamic consequences of selecting various combinations of values."
]
},
{
"cell_type": "markdown",
"id": "9a4febb2-2780-4754-9c70-c2041b1afc07",
"metadata": {},
"source": [
"## In the scenario we're exploring, there's LITTLE ENZYME relative to initial substrate concentration"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "8c9e3f86-b9a5-41da-9e1b-75258017808a",
"metadata": {},
"outputs": [],
"source": [
"S0 = 20.\n",
"E0 = 1."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "67b2734a-0839-4370-a5a9-18883fc15c4c",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "b0ea13d4-9e26-41ec-884a-a56a70445233",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "91a729ee-ad2f-4771-bc84-49ecb9d6a851",
"metadata": {},
"source": [
"# 1. Using the known, exact values for `k1_forward` and `k1_reverse` \n",
"\n",
"Source: *page 16 of \"Analysis of Enzyme Reaction Kinetics, Vol. 1\", by F. Xavier Malcata, Wiley, 2023*"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "33edfef8-7024-4881-a115-dbd39d3e976a",
"metadata": {},
"outputs": [],
"source": [
"k1_forward = 18.\n",
"k1_reverse = 100."
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "ac9eea69-174c-43e5-9eed-443cbc5e2ba7",
"metadata": {},
"outputs": [],
"source": [
"chem_data = ChemData(names=[\"P\", \"ES\"], plot_colors=[\"green\", \"red\"])"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "90f9ec41-6e1b-4558-9400-47e35ece6efc",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"
\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" name | \n",
" label | \n",
" plot_color | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" P | \n",
" P | \n",
" green | \n",
"
\n",
" \n",
" | 1 | \n",
" ES | \n",
" ES | \n",
" red | \n",
"
\n",
" \n",
" | 2 | \n",
" Adenosinedeaminase | \n",
" E | \n",
" violet | \n",
"
\n",
" \n",
" | 3 | \n",
" 2,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purine | \n",
" S | \n",
" darkturquoise | \n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" name label plot_color\n",
"0 P P green\n",
"1 ES ES red\n",
"2 Adenosinedeaminase E violet\n",
"3 2,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purine S darkturquoise"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Our Enzyme\n",
"chem_data.add_chemical(name=\"Adenosinedeaminase\", label=\"E\", plot_color=\"violet\") \n",
"\n",
"# Our Substrate\n",
"chem_data.add_chemical(name=\"2,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purine\", label=\"S\", plot_color=\"darkturquoise\")\n",
"\n",
"chem_data.all_chemicals()"
]
},
{
"cell_type": "markdown",
"id": "f8d4ea7f-0591-467c-9df3-d95f53df75f5",
"metadata": {},
"source": [
"### Specify the Kinetic Parameters"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "3662d205-0779-4cd6-8001-905c44e58ba4",
"metadata": {},
"outputs": [],
"source": [
"rxns = Reactions(chem_data=chem_data)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "78077d8c",
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Number of reactions: 2 (at temp. 25 C)\n",
"0: E + S <-> ES (kF = 18 / kR = 100 / delta_G = 4,250.9 / K = 0.18) | 1st order in all reactants & products\n",
"1: ES <-> E + P (kF = 49 / kR = 0) | 1st order in all reactants & products\n",
"Set of chemicals involved in the above reactions: {\"ES\" (red), \"E\" (violet), \"S\" (darkturquoise), \"P\" (green)}\n"
]
}
],
"source": [
"# Elementary Reaction E + S <-> ES\n",
"rxns.add_reaction(reactants=[\"E\", \"S\"], products=[\"ES\"],\n",
" forward_rate=k1_forward, reverse_rate=k1_reverse) \n",
"\n",
"# Elementary Reaction ES <-> E + P \n",
"rxns.add_reaction(reactants=[\"ES\"], products=[\"E\", \"P\"],\n",
" forward_rate=kcat, reverse_rate=0)\n",
"\n",
"rxns.describe_reactions()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "d23a97ea-f252-4e11-a3e9-aea74f58591e",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": 12,
"id": "aae96512-3d86-4ab0-b167-92943523b7ef",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SYSTEM STATE at Time t = 0:\n",
"4 species:\n",
" Species 0 (P). Conc: 0.0\n",
" Species 1 (ES). Conc: 0.0\n",
" Species 2 (E). Conc: 1.0\n",
" Species 3 (S). Conc: 20.0\n",
"Set of chemicals involved in reactions: {'ES', 'E', 'S', 'P'}\n"
]
}
],
"source": [
"# Here we use the \"slower\" preset for the variable steps, a conservative option prioritizing accuracy over speed\n",
"uc = UniformCompartment(reactions=rxns, preset=\"slower\")\n",
"\n",
"uc.set_conc(conc={\"S\": S0, \"E\": E0}) # Small ampount of enzyme `E`, relative to substrate `S`\n",
"uc.describe_state()"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "e6ad72b8-722a-4606-a611-7dc600529f30",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"784 total variable step(s) taken in 0.02 min\n",
"Number of step re-do's because of negative concentrations: 2\n",
"Number of step re-do's because of elective soft aborts: 1\n",
"Norm usage: {'norm_A': 706, 'norm_B': 710, 'norm_C': 706, 'norm_D': 706}\n",
"System Time is now: 1.2018\n"
]
}
],
"source": [
"# Perform the reactions\n",
"uc.single_compartment_react(duration=1.2, initial_step=0.05)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "e3378bf9-a48b-486d-8f7e-5f605a940b88",
"metadata": {},
"outputs": [],
"source": [
"history_exact = uc.get_history() # Let's save the historical data for a comparison at the very end"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "0198dd94-e55d-4ab4-9de8-087d508edf06",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"plot_pandas() NOTICE: Excessive number of vertical lines (785) - only showing 1 every 6 lines\n"
]
},
{
"data": {
"text/html": [
" \n",
" "
]
},
"metadata": {},
"output_type": "display_data"
},
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"data": {
"application/vnd.plotly.v1+json": {
"config": {
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"uc.plot_history(show_intervals=True, \n",
" title_prefix=\"Using exact values for k1_forward and k1_reverse\")"
]
},
{
"cell_type": "markdown",
"id": "2d8336ee-4576-4081-9835-9fd7b8bee273",
"metadata": {},
"source": [
"### What is the initial rate of production of the final reaction product `P`? \n",
"One could take the numerical derivative (gradient) of the time values of [P] - but no need to! **Reaction rates are computed in the course of the simulation, and stored in a rate-history dataframe**"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "7f18a18c-061e-481f-ae71-aa7a88399724",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" SYSTEM TIME | \n",
" rxn0_rate | \n",
" rxn1_rate | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 0.000000 | \n",
" 360.000000 | \n",
" 0.000000 | \n",
"
\n",
" \n",
" | 1 | \n",
" 0.000500 | \n",
" 274.543200 | \n",
" 8.820000 | \n",
"
\n",
" \n",
" | 2 | \n",
" 0.000750 | \n",
" 243.269275 | \n",
" 12.075109 | \n",
"
\n",
" \n",
" | 3 | \n",
" 0.000763 | \n",
" 241.911753 | \n",
" 12.216716 | \n",
"
\n",
" \n",
" | 4 | \n",
" 0.000769 | \n",
" 241.237493 | \n",
" 12.287060 | \n",
"
\n",
" \n",
" | ... | \n",
" ... | \n",
" ... | \n",
" ... | \n",
"
\n",
" \n",
" | 779 | \n",
" 1.166644 | \n",
" 1.308959 | \n",
" 1.462999 | \n",
"
\n",
" \n",
" | 780 | \n",
" 1.173671 | \n",
" 1.261193 | \n",
" 1.409959 | \n",
"
\n",
" \n",
" | 781 | \n",
" 1.180698 | \n",
" 1.215086 | \n",
" 1.358736 | \n",
"
\n",
" \n",
" | 782 | \n",
" 1.187725 | \n",
" 1.170584 | \n",
" 1.309274 | \n",
"
\n",
" \n",
" | 783 | \n",
" 1.194752 | \n",
" 1.127638 | \n",
" 1.261520 | \n",
"
\n",
" \n",
"
\n",
"
784 rows × 3 columns
\n",
"
"
],
"text/plain": [
" SYSTEM TIME rxn0_rate rxn1_rate\n",
"0 0.000000 360.000000 0.000000\n",
"1 0.000500 274.543200 8.820000\n",
"2 0.000750 243.269275 12.075109\n",
"3 0.000763 241.911753 12.216716\n",
"4 0.000769 241.237493 12.287060\n",
".. ... ... ...\n",
"779 1.166644 1.308959 1.462999\n",
"780 1.173671 1.261193 1.409959\n",
"781 1.180698 1.215086 1.358736\n",
"782 1.187725 1.170584 1.309274\n",
"783 1.194752 1.127638 1.261520\n",
"\n",
"[784 rows x 3 columns]"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rates_exact = uc.get_rate_history()\n",
"rates_exact"
]
},
{
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"execution_count": 17,
"id": "18ac9b9f-c669-43f6-ac36-ed95b76e1ae5",
"metadata": {},
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Let's take a look at how the reaction rate varies with time\n",
"PlotlyHelper.plot_pandas(df=rates_exact, colors=\"blue\",\n",
" title=\"Reaction rate, dP/dt, over time\",\n",
" x_var=\"SYSTEM TIME\", fields=\"rxn1_rate\", \n",
" x_label=\"time\", y_label=\"dP/dt\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "485514fa-5259-4319-9aea-8adac65ae24f",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "e0886793-ace6-49dc-bbef-d2aa0c040001",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "078285f0-00aa-4fbb-9a67-7de0184d6cec",
"metadata": {},
"source": [
"# 2. Guessing a SMALLER value of `k1_forward` (UNDER-ESTIMATED)"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "f6bdd115-a3cc-4c94-8636-108078d4a018",
"metadata": {},
"outputs": [],
"source": [
"enz = ReactionEnz()"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "d3b58d68-ae80-4016-afa5-398ed450b330",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"5.919463087248328"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"enz.min_k1_forward(kM=kM, kcat=kcat) # The smallest possible value"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "df47c069-a290-4c48-a80c-fa9721a38b4c",
"metadata": {},
"outputs": [],
"source": [
"k1_forward = 6.5 # Close to the smallest possible value"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "2c8330eb-0f1a-4edf-b937-9a1a8d11ae84",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"4.8055555555555"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"k1_reverse = enz.compute_k1_reverse(kM, kcat, k1_forward=k1_forward)\n",
"k1_reverse"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "aa8a4fbe-c52f-48f7-b505-01c6cc032f92",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": 22,
"id": "b1ab7d25-1262-4376-ba37-b6888f5ca5d9",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" name | \n",
" label | \n",
" plot_color | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" P | \n",
" P | \n",
" green | \n",
"
\n",
" \n",
" | 1 | \n",
" ES | \n",
" ES | \n",
" red | \n",
"
\n",
" \n",
" | 2 | \n",
" Adenosinedeaminase | \n",
" E | \n",
" violet | \n",
"
\n",
" \n",
" | 3 | \n",
" 2,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purine | \n",
" S | \n",
" darkturquoise | \n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" name label plot_color\n",
"0 P P green\n",
"1 ES ES red\n",
"2 Adenosinedeaminase E violet\n",
"3 2,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purine S darkturquoise"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"chem_data.all_chemicals() # Nothing changed here; same chemicals as before"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "bebb6d92-7939-4e8c-9a77-dd5abffd949b",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": 23,
"id": "2c8bb1b8-cdd6-4822-aa4c-13db2b425c5f",
"metadata": {},
"outputs": [],
"source": [
"rxns_underest = Reactions(chem_data=chem_data) # New set of reactions"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "e364152e-be1a-4ed3-8622-b00d101ac600",
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Number of reactions: 2 (at temp. 25 C)\n",
"0: E + S <-> ES (kF = 6.5 / kR = 4.8056 / delta_G = -748.72 / K = 1.3526) | 1st order in all reactants & products\n",
"1: ES <-> E + P (kF = 49 / kR = 0) | 1st order in all reactants & products\n",
"Set of chemicals involved in the above reactions: {\"ES\" (red), \"E\" (violet), \"S\" (darkturquoise), \"P\" (green)}\n"
]
}
],
"source": [
"# Reaction E + S <-> ES , with 1st-order kinetics, \n",
"# and a forward rate that is much faster than its revers one\n",
"rxns_underest.add_reaction(reactants=[\"E\", \"S\"], products=[\"ES\"],\n",
" forward_rate=k1_forward, reverse_rate=k1_reverse) \n",
"\n",
"# Reaction ES <-> E + P , with 1st-order kinetics\n",
"rxns_underest.add_reaction(reactants=[\"ES\"], products=[\"E\", \"P\"],\n",
" forward_rate=kcat, reverse_rate=0)\n",
"\n",
"rxns_underest.describe_reactions()"
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "ccfc59f5-a0dc-4b03-a9dd-a6993c4a85cd",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SYSTEM STATE at Time t = 0:\n",
"4 species:\n",
" Species 0 (P). Conc: 0.0\n",
" Species 1 (ES). Conc: 0.0\n",
" Species 2 (E). Conc: 1.0\n",
" Species 3 (S). Conc: 20.0\n",
"Set of chemicals involved in reactions: {'ES', 'E', 'S', 'P'}\n"
]
}
],
"source": [
"# Here we use the \"slower\" preset for the variable steps, a conservative option prioritizing accuracy over speed\n",
"uc = UniformCompartment(reactions=rxns_underest, preset=\"slower\")\n",
"\n",
"uc.set_conc(conc={\"S\": S0, \"E\": E0}) # Small ampount of enzyme `E`, relative to substrate `S`\n",
"uc.describe_state()"
]
},
{
"cell_type": "code",
"execution_count": 26,
"id": "d9c51bab-7eaa-4735-82d2-aaf8ac787f0e",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"788 total variable step(s) taken in 0.03 min\n",
"Number of step re-do's because of negative concentrations: 1\n",
"Number of step re-do's because of elective soft aborts: 2\n",
"Norm usage: {'norm_A': 704, 'norm_B': 709, 'norm_C': 704, 'norm_D': 704}\n",
"System Time is now: 1.2057\n"
]
}
],
"source": [
"# Perform the reactions\n",
"uc.single_compartment_react(duration=1.2, initial_step=0.05)"
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "7c4ee2db-73ee-4b17-b3fa-943d4a1ea4cc",
"metadata": {},
"outputs": [],
"source": [
"history_underest = uc.get_history() # Let's save the historical data for a comparison at the very end"
]
},
{
"cell_type": "code",
"execution_count": 28,
"id": "ab344447-39a8-4dd6-aca8-be21e2bba505",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"plot_pandas() NOTICE: Excessive number of vertical lines (789) - only showing 1 every 6 lines\n"
]
},
{
"data": {
"application/vnd.plotly.v1+json": {
"config": {
"plotlyServerURL": "https://plot.ly"
},
"data": [
{
"hovertemplate": "Chemical=P
SYSTEM TIME=%{x}
Concentration=%{y}",
"legendgroup": "P",
"line": {
"color": "green",
"dash": "solid"
},
"marker": {
"symbol": "circle"
},
"mode": "lines",
"name": "P",
"showlegend": true,
"type": "scattergl",
"x": [
0,
0.0005000000000000001,
0.0007500000000000002,
0.0007625000000000003,
0.0007687500000000002,
0.0007750000000000002,
0.0007812500000000002,
0.0007875000000000001,
0.0007937500000000001,
0.0008,
0.00080625,
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"uc.plot_history(show_intervals=True, \n",
" title_prefix=\"Using SMALLER (under-estimated) value for k1_forward\")"
]
},
{
"cell_type": "markdown",
"id": "4432c8c0-c5c5-4311-ac77-bbedfc27b741",
"metadata": {},
"source": [
"At first glance, not too different from before, overall, but let's take a closer look"
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "a24e8ab9-697e-417a-ad5a-475ea6200b3b",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" SYSTEM TIME | \n",
" rxn0_rate | \n",
" rxn1_rate | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 0.000000 | \n",
" 130.000000 | \n",
" 0.000000 | \n",
"
\n",
" \n",
" | 1 | \n",
" 0.000500 | \n",
" 120.842601 | \n",
" 3.185000 | \n",
"
\n",
" \n",
" | 2 | \n",
" 0.000750 | \n",
" 116.711975 | \n",
" 4.626306 | \n",
"
\n",
" \n",
" | 3 | \n",
" 0.000763 | \n",
" 116.515396 | \n",
" 4.694958 | \n",
"
\n",
" \n",
" | 4 | \n",
" 0.000769 | \n",
" 116.417346 | \n",
" 4.729203 | \n",
"
\n",
" \n",
" | ... | \n",
" ... | \n",
" ... | \n",
" ... | \n",
"
\n",
" \n",
" | 783 | \n",
" 1.171227 | \n",
" 1.169882 | \n",
" 1.318201 | \n",
"
\n",
" \n",
" | 784 | \n",
" 1.178115 | \n",
" 1.125129 | \n",
" 1.268138 | \n",
"
\n",
" \n",
" | 785 | \n",
" 1.185004 | \n",
" 1.082003 | \n",
" 1.219867 | \n",
"
\n",
" \n",
" | 786 | \n",
" 1.191892 | \n",
" 1.040450 | \n",
" 1.173332 | \n",
"
\n",
" \n",
" | 787 | \n",
" 1.198781 | \n",
" 1.000418 | \n",
" 1.128479 | \n",
"
\n",
" \n",
"
\n",
"
788 rows × 3 columns
\n",
"
"
],
"text/plain": [
" SYSTEM TIME rxn0_rate rxn1_rate\n",
"0 0.000000 130.000000 0.000000\n",
"1 0.000500 120.842601 3.185000\n",
"2 0.000750 116.711975 4.626306\n",
"3 0.000763 116.515396 4.694958\n",
"4 0.000769 116.417346 4.729203\n",
".. ... ... ...\n",
"783 1.171227 1.169882 1.318201\n",
"784 1.178115 1.125129 1.268138\n",
"785 1.185004 1.082003 1.219867\n",
"786 1.191892 1.040450 1.173332\n",
"787 1.198781 1.000418 1.128479\n",
"\n",
"[788 rows x 3 columns]"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rates_underest = uc.get_rate_history()\n",
"rates_underest"
]
},
{
"cell_type": "code",
"execution_count": 30,
"id": "dd0d561d-435b-4aa6-8761-6dde0989c445",
"metadata": {},
"outputs": [
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0,
1.1987808930356147
],
"title": {
"text": "time"
},
"type": "linear"
},
"yaxis": {
"anchor": "x",
"autorange": true,
"domain": [
0,
1
],
"range": [
-1.8779232936082764,
35.68054257855725
],
"title": {
"text": "dP/dt"
},
"type": "linear"
}
}
},
"image/png": 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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Let's take a look at how the reaction rate varies with time\n",
"PlotlyHelper.plot_pandas(df=rates_underest, colors=\"blue\",\n",
" title=\"Reaction rate, dP/dt, over time\",\n",
" x_var=\"SYSTEM TIME\", fields=\"rxn1_rate\", \n",
" x_label=\"time\", y_label=\"dP/dt\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "223d5c37-0ad2-465a-9f95-84bebda6ab7a",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "ce1f4c5a-a77c-4fa0-89be-b4f4e05c24db",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "e863f23b-0fb5-490a-9f60-fa1c9caf4c93",
"metadata": {},
"source": [
"# 3. Guessing a LARGER value of `k1_forward` (OVER-ESTIMATED)"
]
},
{
"cell_type": "code",
"execution_count": 31,
"id": "fb94e4d4-68d8-4835-aa5c-3667798162ba",
"metadata": {},
"outputs": [],
"source": [
"k1_forward = 40. # Well above the known value of 18."
]
},
{
"cell_type": "code",
"execution_count": 32,
"id": "1db10d9c-96b1-4bf0-87ae-abc0cea690b4",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"282.1111111111108"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"k1_reverse = enz.compute_k1_reverse(kM, kcat, k1_forward=k1_forward)\n",
"k1_reverse"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "4adaea7e-f27a-42dd-a540-4fc88ca247a9",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": 33,
"id": "5fafa258-abcc-4d8f-824c-bde254c1f48b",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" name | \n",
" label | \n",
" plot_color | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" P | \n",
" P | \n",
" green | \n",
"
\n",
" \n",
" | 1 | \n",
" ES | \n",
" ES | \n",
" red | \n",
"
\n",
" \n",
" | 2 | \n",
" Adenosinedeaminase | \n",
" E | \n",
" violet | \n",
"
\n",
" \n",
" | 3 | \n",
" 2,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purine | \n",
" S | \n",
" darkturquoise | \n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" name label plot_color\n",
"0 P P green\n",
"1 ES ES red\n",
"2 Adenosinedeaminase E violet\n",
"3 2,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purine S darkturquoise"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"chem_data.all_chemicals() # Nothing changed here; same chemicals as before"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "e902907d-f06d-4f2d-8b09-0a4f63817317",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": 34,
"id": "86eceec3-5099-4bd2-838a-cf8207b43ee3",
"metadata": {},
"outputs": [],
"source": [
"rxns_overest = Reactions(chem_data=chem_data) # New set of reactions"
]
},
{
"cell_type": "code",
"execution_count": 35,
"id": "7cc40d06-d756-44b1-a55a-d556cfee46b2",
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Number of reactions: 2 (at temp. 25 C)\n",
"0: E + S <-> ES (kF = 40 / kR = 282.11 / delta_G = 4,842.4 / K = 0.14179) | 1st order in all reactants & products\n",
"1: ES <-> E + P (kF = 49 / kR = 0) | 1st order in all reactants & products\n",
"Set of chemicals involved in the above reactions: {\"ES\" (red), \"E\" (violet), \"S\" (darkturquoise), \"P\" (green)}\n"
]
}
],
"source": [
"# Reaction E + S <-> ES , with 1st-order kinetics, \n",
"# and a forward rate that is much faster than its revers one\n",
"rxns_overest.add_reaction(reactants=[\"E\", \"S\"], products=[\"ES\"],\n",
" forward_rate=k1_forward, reverse_rate=k1_reverse) \n",
"\n",
"# Reaction ES <-> E + P , with 1st-order kinetics\n",
"rxns_overest.add_reaction(reactants=[\"ES\"], products=[\"E\", \"P\"],\n",
" forward_rate=kcat, reverse_rate=0)\n",
"\n",
"rxns_overest.describe_reactions()"
]
},
{
"cell_type": "code",
"execution_count": 36,
"id": "fbc78df2-da88-4ed1-8878-2a6b2373d10a",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SYSTEM STATE at Time t = 0:\n",
"4 species:\n",
" Species 0 (P). Conc: 0.0\n",
" Species 1 (ES). Conc: 0.0\n",
" Species 2 (E). Conc: 1.0\n",
" Species 3 (S). Conc: 20.0\n",
"Set of chemicals involved in reactions: {'ES', 'E', 'S', 'P'}\n"
]
}
],
"source": [
"# Here we use the \"slower\" preset for the variable steps, a conservative option prioritizing accuracy over speed\n",
"uc = UniformCompartment(reactions=rxns_overest, preset=\"slower\")\n",
"\n",
"uc.set_conc(conc={\"S\": S0, \"E\": E0}) # Small ampount of enzyme `E`, relative to substrate `S`\n",
"uc.describe_state()"
]
},
{
"cell_type": "code",
"execution_count": 37,
"id": "e99b906d-028d-43cf-ba69-13843903545a",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"864 total variable step(s) taken in 0.03 min\n",
"Number of step re-do's because of negative concentrations: 2\n",
"Number of step re-do's because of elective soft aborts: 1\n",
"Norm usage: {'norm_A': 829, 'norm_B': 835, 'norm_C': 829, 'norm_D': 829}\n",
"System Time is now: 1.2001\n"
]
}
],
"source": [
"# Perform the reactions\n",
"uc.single_compartment_react(duration=1.2, initial_step=0.05)"
]
},
{
"cell_type": "code",
"execution_count": 38,
"id": "26359ff8-ceb7-4da7-97e2-9a0df0a5053b",
"metadata": {},
"outputs": [],
"source": [
"history_overest = uc.get_history() # Let's save the historical data for a comparison at the very end"
]
},
{
"cell_type": "code",
"execution_count": 39,
"id": "54e123a5-bcd9-4702-b7d7-8490390960ad",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"plot_pandas() NOTICE: Excessive number of vertical lines (865) - only showing 1 every 6 lines\n"
]
},
{
"data": {
"application/vnd.plotly.v1+json": {
"config": {
"plotlyServerURL": "https://plot.ly"
},
"data": [
{
"hovertemplate": "Chemical=P
SYSTEM TIME=%{x}
Concentration=%{y}",
"legendgroup": "P",
"line": {
"color": "green",
"dash": "solid"
},
"marker": {
"symbol": "circle"
},
"mode": "lines",
"name": "P",
"showlegend": true,
"type": "scattergl",
"x": [
0,
0.0005000000000000001,
0.0007500000000000002,
0.0007625000000000003,
0.0007687500000000002,
0.0007750625000000003,
0.0007814381250000002,
0.0007878775062500002,
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"uc.plot_history(show_intervals=True, \n",
" title_prefix=\"Using LARGER (over-estimated) value for k1_forward\")"
]
},
{
"cell_type": "markdown",
"id": "1bb0f414-d7d3-4166-ab16-21daee03c4d8",
"metadata": {},
"source": [
"At first glance, not too different from before, overall, but let's take a closer look"
]
},
{
"cell_type": "code",
"execution_count": 40,
"id": "26855833-c431-44e2-ad6c-d4fe370f3eff",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" SYSTEM TIME | \n",
" rxn0_rate | \n",
" rxn1_rate | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 0.000000 | \n",
" 800.000000 | \n",
" 0.000000 | \n",
"
\n",
" \n",
" | 1 | \n",
" 0.000500 | \n",
" 357.555556 | \n",
" 19.600000 | \n",
"
\n",
" \n",
" | 2 | \n",
" 0.000750 | \n",
" 265.637774 | \n",
" 23.739956 | \n",
"
\n",
" \n",
" | 3 | \n",
" 0.000763 | \n",
" 262.356893 | \n",
" 23.888118 | \n",
"
\n",
" \n",
" | 4 | \n",
" 0.000769 | \n",
" 260.739940 | \n",
" 23.961149 | \n",
"
\n",
" \n",
" | ... | \n",
" ... | \n",
" ... | \n",
" ... | \n",
"
\n",
" \n",
" | 859 | \n",
" 1.170211 | \n",
" 1.335790 | \n",
" 1.490884 | \n",
"
\n",
" \n",
" | 860 | \n",
" 1.176184 | \n",
" 1.296873 | \n",
" 1.445487 | \n",
"
\n",
" \n",
" | 861 | \n",
" 1.182158 | \n",
" 1.255105 | \n",
" 1.401986 | \n",
"
\n",
" \n",
" | 862 | \n",
" 1.188131 | \n",
" 1.219475 | \n",
" 1.358993 | \n",
"
\n",
" \n",
" | 863 | \n",
" 1.194105 | \n",
" 1.178798 | \n",
" 1.318155 | \n",
"
\n",
" \n",
"
\n",
"
864 rows × 3 columns
\n",
"
"
],
"text/plain": [
" SYSTEM TIME rxn0_rate rxn1_rate\n",
"0 0.000000 800.000000 0.000000\n",
"1 0.000500 357.555556 19.600000\n",
"2 0.000750 265.637774 23.739956\n",
"3 0.000763 262.356893 23.888118\n",
"4 0.000769 260.739940 23.961149\n",
".. ... ... ...\n",
"859 1.170211 1.335790 1.490884\n",
"860 1.176184 1.296873 1.445487\n",
"861 1.182158 1.255105 1.401986\n",
"862 1.188131 1.219475 1.358993\n",
"863 1.194105 1.178798 1.318155\n",
"\n",
"[864 rows x 3 columns]"
]
},
"execution_count": 40,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rates_overest = uc.get_rate_history()\n",
"rates_overest"
]
},
{
"cell_type": "code",
"execution_count": 41,
"id": "651f35be-fe04-41b7-a567-0697ae8e265c",
"metadata": {},
"outputs": [
{
"data": {
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},
"data": [
{
"hovertemplate": "SYSTEM TIME=%{x}
rxn1_rate=%{y}",
"legendgroup": "",
"line": {
"color": "blue",
"dash": "solid"
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"symbol": "circle"
},
"mode": "lines",
"name": "",
"orientation": "v",
"showlegend": false,
"type": "scatter",
"x": [
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0.0005000000000000001,
0.0007500000000000002,
0.0007625000000000003,
0.0007687500000000002,
0.0007750625000000003,
0.0007814381250000002,
0.0007878775062500002,
0.0007943812813125002,
0.0008009500941256253,
0.0008075845950668816,
0.0008142854410175504,
0.0008210532954277259,
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"title": {
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Let's take a look at how the reaction rate varies with time\n",
"PlotlyHelper.plot_pandas(df=rates_overest, colors=\"blue\",\n",
" title=\"Reaction rate, dP/dt, over time\",\n",
" x_var=\"SYSTEM TIME\", fields=\"rxn1_rate\", \n",
" x_label=\"time\", y_label=\"dP/dt\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "3d98bdb0-2885-49f2-ad3e-aab03075683c",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": 42,
"id": "b1633906-9132-4e29-a944-59af34401280",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" SYSTEM TIME | \n",
" P | \n",
" ES | \n",
" E | \n",
" S | \n",
" caption | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 0.000000 | \n",
" 0.000000 | \n",
" 0.000000 | \n",
" 1.000000 | \n",
" 20.000000 | \n",
" Set concentration | \n",
"
\n",
" \n",
" | 1 | \n",
" 0.000500 | \n",
" 0.000000 | \n",
" 0.400000 | \n",
" 0.600000 | \n",
" 19.600000 | \n",
" 1st reaction step | \n",
"
\n",
" \n",
" | 2 | \n",
" 0.000750 | \n",
" 0.004900 | \n",
" 0.484489 | \n",
" 0.515511 | \n",
" 19.510611 | \n",
" | \n",
"
\n",
" \n",
" | 3 | \n",
" 0.000763 | \n",
" 0.005197 | \n",
" 0.487513 | \n",
" 0.512487 | \n",
" 19.507291 | \n",
" | \n",
"
\n",
" \n",
" | 4 | \n",
" 0.000769 | \n",
" 0.005346 | \n",
" 0.489003 | \n",
" 0.510997 | \n",
" 19.505651 | \n",
" | \n",
"
\n",
" \n",
" | ... | \n",
" ... | \n",
" ... | \n",
" ... | \n",
" ... | \n",
" ... | \n",
" ... | \n",
"
\n",
" \n",
" | 860 | \n",
" 1.176184 | \n",
" 19.722714 | \n",
" 0.029500 | \n",
" 0.970500 | \n",
" 0.247787 | \n",
" | \n",
"
\n",
" \n",
" | 861 | \n",
" 1.182158 | \n",
" 19.731349 | \n",
" 0.028612 | \n",
" 0.971388 | \n",
" 0.240039 | \n",
" | \n",
"
\n",
" \n",
" | 862 | \n",
" 1.188131 | \n",
" 19.739724 | \n",
" 0.027735 | \n",
" 0.972265 | \n",
" 0.232542 | \n",
" | \n",
"
\n",
" \n",
" | 863 | \n",
" 1.194105 | \n",
" 19.747842 | \n",
" 0.026901 | \n",
" 0.973099 | \n",
" 0.225257 | \n",
" | \n",
"
\n",
" \n",
" | 864 | \n",
" 1.200079 | \n",
" 19.755716 | \n",
" 0.026069 | \n",
" 0.973931 | \n",
" 0.218216 | \n",
" last reaction step | \n",
"
\n",
" \n",
"
\n",
"
865 rows × 6 columns
\n",
"
"
],
"text/plain": [
" SYSTEM TIME P ES E S caption\n",
"0 0.000000 0.000000 0.000000 1.000000 20.000000 Set concentration\n",
"1 0.000500 0.000000 0.400000 0.600000 19.600000 1st reaction step\n",
"2 0.000750 0.004900 0.484489 0.515511 19.510611 \n",
"3 0.000763 0.005197 0.487513 0.512487 19.507291 \n",
"4 0.000769 0.005346 0.489003 0.510997 19.505651 \n",
".. ... ... ... ... ... ...\n",
"860 1.176184 19.722714 0.029500 0.970500 0.247787 \n",
"861 1.182158 19.731349 0.028612 0.971388 0.240039 \n",
"862 1.188131 19.739724 0.027735 0.972265 0.232542 \n",
"863 1.194105 19.747842 0.026901 0.973099 0.225257 \n",
"864 1.200079 19.755716 0.026069 0.973931 0.218216 last reaction step\n",
"\n",
"[865 rows x 6 columns]"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"history_overest = uc.get_history()\n",
"history_overest"
]
},
{
"cell_type": "markdown",
"id": "75b6c550-9716-4766-86a4-bd4afe2226ac",
"metadata": {},
"source": [
"# Comparing the 3 scenarios"
]
},
{
"cell_type": "markdown",
"id": "27443513-5acd-4676-bddd-bedb837488e0",
"metadata": {},
"source": [
"#### The concentrations of the intermediate `ES` over time"
]
},
{
"cell_type": "code",
"execution_count": 43,
"id": "36fc0e0f-bc37-4bb3-88e3-e755c1d73cdb",
"metadata": {},
"outputs": [],
"source": [
"es_under = PlotlyHelper.plot_pandas(df=history_underest, \n",
" title=\"underestimated k1_forward\",\n",
" x_var=\"SYSTEM TIME\", fields=\"ES\", \n",
" x_label=\"time\", y_label=\"ES\", colors = \"yellow\")"
]
},
{
"cell_type": "code",
"execution_count": 44,
"id": "13df7a7f-c94e-4cf9-90ee-1c8e99ff5671",
"metadata": {},
"outputs": [],
"source": [
"es_exact = PlotlyHelper.plot_pandas(df=history_exact, \n",
" title=\"exact k1_forward\",\n",
" x_var=\"SYSTEM TIME\", fields=\"ES\", \n",
" x_label=\"time\", y_label=\"ES\", colors = \"green\")"
]
},
{
"cell_type": "code",
"execution_count": 45,
"id": "163c2f25-68f5-4361-ae0f-8e6f7e96572a",
"metadata": {},
"outputs": [],
"source": [
"es_over = PlotlyHelper.plot_pandas(df=history_overest, \n",
" title=\"overestimated k1_forward\",\n",
" x_var=\"SYSTEM TIME\", fields=\"ES\", \n",
" x_label=\"time\", y_label=\"ES\", colors = \"purple\")"
]
},
{
"cell_type": "code",
"execution_count": 46,
"id": "fd48ef57-477e-4974-85ee-4c315e6e7159",
"metadata": {},
"outputs": [
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"data": {
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
" PlotlyHelper.combine_plots([es_under, es_exact, es_over], \n",
" title=\"ES\")"
]
},
{
"cell_type": "markdown",
"id": "98e18ba1-38f7-44c4-bb7f-9cec4a059c66",
"metadata": {},
"source": [
"#### The concentrations of the product `P` over time"
]
},
{
"cell_type": "code",
"execution_count": 47,
"id": "4b961bd7-8c6a-47a2-9439-52675b39dc15",
"metadata": {},
"outputs": [],
"source": [
"p_under = PlotlyHelper.plot_pandas(df=history_underest, \n",
" title=\"underestimated k1_forward\",\n",
" x_var=\"SYSTEM TIME\", fields=\"P\", \n",
" x_label=\"time\", y_label=\"P\", colors = \"yellow\")"
]
},
{
"cell_type": "code",
"execution_count": 48,
"id": "030169b1-dc65-42b6-b830-4b32377f2ae9",
"metadata": {},
"outputs": [],
"source": [
"p_exact = PlotlyHelper.plot_pandas(df=history_exact, \n",
" title=\"exact k1_forward\",\n",
" x_var=\"SYSTEM TIME\", fields=\"P\", \n",
" x_label=\"time\", y_label=\"P\", colors = \"cyan\")"
]
},
{
"cell_type": "code",
"execution_count": 49,
"id": "a53f9f12-a597-4bf1-8ce5-5afb1053583d",
"metadata": {},
"outputs": [],
"source": [
"p_over = PlotlyHelper.plot_pandas(df=history_overest, \n",
" title=\"overestimated k1_forward\",\n",
" x_var=\"SYSTEM TIME\", fields=\"P\", \n",
" x_label=\"time\", y_label=\"P\", colors = \"purple\")"
]
},
{
"cell_type": "code",
"execution_count": 50,
"id": "75b29f07-2ccb-48aa-b755-738ed2183416",
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.plotly.v1+json": {
"config": {
"plotlyServerURL": "https://plot.ly"
},
"data": [
{
"hovertemplate": "underestimated k1_forward
SYSTEM TIME=%{x}
P=%{y}",
"legendgroup": "",
"line": {
"color": "yellow",
"dash": "solid"
},
"marker": {
"symbol": "circle"
},
"mode": "lines",
"name": "underestimated k1_forward",
"orientation": "v",
"showlegend": true,
"type": "scatter",
"x": [
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0.0005000000000000001,
0.0007500000000000002,
0.0007625000000000003,
0.0007687500000000002,
0.0007750000000000002,
0.0007812500000000002,
0.0007875000000000001,
0.0007937500000000001,
0.0008,
0.00080625,
0.0008125625,
0.000818938125,
0.00082537750625,
0.0008318812813125,
0.0008384500941256251,
0.0008450845950668814,
0.0008517854410175501,
0.0008585532954277256,
0.0008653888283820029,
0.0008722927166658229,
0.0008792656438324812,
0.000886308300270806,
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0.0009006055971062493,
0.0009078616530773118,
0.0009151902696080849,
0.0009225921723041657,
0.0009300680940272074,
0.0009376187749674795,
0.0009452449627171543,
0.0009529474123443259,
0.0009607268864677692,
0.0009685841553324469,
0.0009765199968857713,
0.000984535196854629,
0.0009926305488231755,
0.0010008068543114073,
0.0010090649228545214,
0.0010174055720830666,
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"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
" PlotlyHelper.combine_plots([p_under, p_exact, p_over], \n",
" title=\"P\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "bb0c74b1-8c3f-4bfd-8b97-23ca6cbc4ed7",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "2e52dba2-e39f-4af7-9051-b914a941fea7",
"metadata": {},
"source": [
"#### The Reaction Rate over time"
]
},
{
"cell_type": "code",
"execution_count": 51,
"id": "e64d60e2-1524-496d-b818-89398dc3eb63",
"metadata": {},
"outputs": [],
"source": [
"r1_under = PlotlyHelper.plot_pandas(df=rates_underest, \n",
" title=\"underestimated k1_forward\",\n",
" x_var=\"SYSTEM TIME\", fields=\"rxn1_rate\", \n",
" x_label=\"time\", y_label=\"dP/dt\", colors = \"yellow\")"
]
},
{
"cell_type": "code",
"execution_count": 52,
"id": "80750429-e2d5-4386-bdf0-1d530ca7fd90",
"metadata": {},
"outputs": [],
"source": [
"r1_exact = PlotlyHelper.plot_pandas(df=rates_exact, \n",
" title=\"exact k1_forward\",\n",
" x_var=\"SYSTEM TIME\", fields=\"rxn1_rate\", \n",
" x_label=\"time\", y_label=\"dP/dt\", colors = \"blue\")"
]
},
{
"cell_type": "code",
"execution_count": 53,
"id": "de6dbb69-6f8d-4048-ae30-75acd47c55bc",
"metadata": {},
"outputs": [],
"source": [
"r1_over = PlotlyHelper.plot_pandas(df=rates_overest, \n",
" title=\"overestimated k1_forward\",\n",
" x_var=\"SYSTEM TIME\", fields=\"rxn1_rate\", \n",
" x_label=\"time\", y_label=\"dP/dt\", colors = \"purple\")"
]
},
{
"cell_type": "code",
"execution_count": 54,
"id": "a68a7586-4c18-4fbc-8a78-eabf7ca74cf9",
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.plotly.v1+json": {
"config": {
"plotlyServerURL": "https://plot.ly"
},
"data": [
{
"hovertemplate": "underestimated k1_forward
SYSTEM TIME=%{x}
rxn1_rate=%{y}",
"legendgroup": "",
"line": {
"color": "yellow",
"dash": "solid"
},
"marker": {
"symbol": "circle"
},
"mode": "lines",
"name": "underestimated k1_forward",
"orientation": "v",
"showlegend": true,
"type": "scatter",
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
" PlotlyHelper.combine_plots([r1_under, r1_exact, r1_over], \n",
" title=\"Reaction Rate\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "4d7055e8-d2d9-462a-8121-fd259a05a11c",
"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": "3.9.13"
}
},
"nbformat": 4,
"nbformat_minor": 5
}