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"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",
"Background: please see experiment `enzyme_1_a`"
]
},
{
"cell_type": "markdown",
"id": "604b150b-7812-4fd3-9403-69a06dd7e397",
"metadata": {},
"source": [
"#### THE REACTION: \n",
"the enzyme `Adenosinedeaminase`, \n",
"with the substrate `2,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purine`.\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 = \"Sep. 10, 2025\"\n",
"LIFE123_VERSION = \"1.0.0rc7\" # 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",
"import numpy as np\n",
"import plotly.express as px\n",
"\n",
"from life123 import check_version, ReactionEnzyme"
]
},
{
"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) # To check compatibility"
]
},
{
"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": "8b71b0b0-f867-48a5-beaf-7f992b0d7c46",
"metadata": {},
"source": [
"## Assume we're only given values for `kM` and `kcat`\n",
"### What values of `k1_forward`, `k1_reverse` and `k2_forward` are compatible with them?"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "80320572-3ea6-49a2-97cd-487e068e2514",
"metadata": {},
"outputs": [],
"source": [
"# We'll use the following values, taken from experiment `enzyme_1_a`\n",
"kM = 8.27777777777777\n",
"kcat = 49"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "c04db12c-e77f-4b53-8cdb-859194959ca1",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"49"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# k2_forward equals kcat ; not much to say here!\n",
"k2_forward = kcat\n",
"k2_forward"
]
},
{
"cell_type": "markdown",
"id": "57aca1c1-9ea1-4732-ac3b-69c75dc7a1fa",
"metadata": {},
"source": [
"By definition: `kM = (k2_forward + k1_reverse) / k1_forward` \n",
"\n",
"We are given `kM` and `k2_forward` (same as `kcat`), as those are typical quantities measured experimentally, i.e.: \n",
"\n",
"`kM = (kcat + k1_reverse) / k1_forward` \n",
"\n",
"But how to solve for `k1_forward` and `k1_reverse`?? We have just 1 equation and 2 variables! **The system of equations is \"underdetermined\"** : what can we do? \n",
"\n",
"We'll explore fixing a guess for `k1_forward`, and then computing the corresponding `k1_reverse` - or vice versa. \n",
"\n",
"The Life123 class `ReactionEnzyme` conveniently provides the necessary transformations."
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "2ea816ee-4bb1-4f36-9a41-281aa4537586",
"metadata": {},
"outputs": [],
"source": [
"enz = ReactionEnzyme(enzyme=\"E\", substrate=\"S\", product=\"P\")"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "7e34a530-7e5e-404b-8cb2-01e7db85557a",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"99.99999999999986"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Example, using the k1_forward=18. from experiment `enzyme_1_a` (together with the kM and kcat we were given), to determine k1_reverse\n",
"\n",
"k1_reverse = enz.compute_k1_reverse(kM=kM, kcat=kcat, k1_forward = 18.)\n",
"k1_reverse"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "48538108-e169-40e7-a041-f58c39c6273a",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"18.000000000000018"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Conversely, using the k1_reverse=100. from experiment `enzyme_1`, to determine k1_forward\n",
"\n",
"k1_forward = enz.compute_k1_forward(kM=kM, kcat=kcat, k1_reverse = 100.)\n",
"k1_forward"
]
},
{
"cell_type": "markdown",
"id": "c738a101-f8dc-449e-a9fb-57b67e890f4f",
"metadata": {},
"source": [
"#### Naturally, we're getting the same values we had in experiment `enzyme_1_a`, \n",
"namely `k1_forward = 18.` and `k1_reverse = 100.` \n",
"#### But what if neither `k1_forward` nor `k1_reverse` are known?"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "d6bfd6e6-a7b0-4e3e-9bfc-8eee1e4bae62",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "d7fabeec-8221-417a-9004-aab569759ecb",
"metadata": {},
"source": [
"### PART 1. Let's try a variety of values for `k1_reverse`, and determine the corresponding values for `k1_forward`"
]
},
{
"cell_type": "markdown",
"id": "bbf75c6a-08b2-4bf0-9aba-8035a36b1d09",
"metadata": {
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"source": [
"#### `k1_reverse` must be non-negative because it's a reaction rate constant, but in other respects there's no conceptual restriction on its value, as plugged into our equation:\n",
"`kM = (kcat + k1_reverse) / k1_forward`"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "0ec24a33-b30e-48df-9541-a0e7a1f6c575",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 0., 150., 300.])"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"k1_reverse_choices = np.linspace(0., 300., 3) # Even grid of values\n",
"k1_reverse_choices"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "a644dfac-84be-41a7-9661-da3362e19727",
"metadata": {},
"outputs": [
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"data": {
"text/plain": [
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]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"k1_forward_choices = enz.compute_k1_forward(kM=kM, kcat=kcat, k1_reverse = k1_reverse_choices)\n",
"k1_forward_choices"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "dc26d8a8-9e7a-4e78-924a-6690ad6e3dfc",
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},
"geo": {
"bgcolor": "white",
"lakecolor": "white",
"landcolor": "#E5ECF6",
"showlakes": true,
"showland": true,
"subunitcolor": "white"
},
"hoverlabel": {
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},
"hovermode": "closest",
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},
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},
"bgcolor": "#E5ECF6",
"radialaxis": {
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},
"scene": {
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"gridcolor": "white",
"gridwidth": 2,
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},
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},
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},
"title": {
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},
"xaxis": {
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"title": {
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},
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}
}
},
"title": {
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},
"xaxis": {
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"autorange": true,
"domain": [
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"range": [
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"title": {
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"range": [
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"title": {
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},
"type": "linear"
}
}
},
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig = px.line(x=k1_reverse_choices, y=k1_forward_choices, title=\"k1_forward for given k1_reverse values\")\n",
"\n",
"fig.update_layout(xaxis_title='k1_reverse',\n",
" yaxis_title='k1_forward')\n",
"\n",
"fig.add_vline(x=100., line_width=1, line_dash=\"dot\", line_color=\"gray\")\n",
"fig.add_hline(y=18., line_width=1, line_dash=\"dot\", line_color=\"gray\")\n",
"fig.add_scatter(x=[100.], y=[18.], \n",
" mode=\"markers\", marker={\"color\": \"red\"}, name=\"actual values\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "3cf36275-edc9-4b46-9ad3-cf734ee6abdc",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "9ae9e3f9-5bf7-413f-891d-8baa6907c6c1",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "f6d18fd8-3683-4a1e-88fe-e8f9cb9007c7",
"metadata": {},
"source": [
"### PART 2. Conversely, let's try a variety of values for `k1_forward`, and determine the corresponding values for `k1_reverse`"
]
},
{
"cell_type": "markdown",
"id": "72fc35f4-96d9-4184-92bb-c3f5827c4621",
"metadata": {
"tags": []
},
"source": [
"#### There's an extra consideration in pursuing the converse approach, namely we cannot simply give `k1_forward` any non-negative value as we please, because exessively small values would cause `k1_reverse` to become negative, as may be observed from our equation:\n",
"`kM = (kcat + k1_reverse) / k1_forward` \n",
"which can be re-written as: \n",
"`kM * k1_forward = kcat + k1_reverse`, i.e. \n",
"`k1_reverse = kM * k1_forward - kcat` \n",
"\n",
"To insure that `k1_reverse >= 0` we must enforce `kM * k1_forward >= kcat`, i.e. `k1_forward >= kcat / kM` \n",
"\n",
"Hence, the required minimun value for `k1_forward` is `kcat / kM`. This may be conveniently computed with the following function call:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "790b5d25-0700-4cbd-9b95-bcd72468fd5a",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"5.919463087248328"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"enz.min_k1_forward(kM=kM, kcat=kcat)"
]
},
{
"cell_type": "markdown",
"id": "6bf1d0fa-4936-452c-b858-50f30206e598",
"metadata": {},
"source": [
"We'll use the above min value as the start of the range of values that we'll explore for `k1_forward`"
]
},
{
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig = px.line(x=k1_forward_choices, y=k1_reverse_choices, \n",
" title=\"k1_reverse for given k1_forward values
(dashed lines show actual values)\")\n",
"\n",
"fig.update_layout(xaxis_title='k1_forward',\n",
" yaxis_title='k1_reverse')\n",
"\n",
"fig.add_vline(x=18., line_width=1, line_dash=\"dot\", line_color=\"gray\")\n",
"fig.add_hline(y=100., line_width=1, line_dash=\"dot\", line_color=\"gray\")\n",
"fig.add_scatter(x=[18.], y=[100.], \n",
" mode=\"markers\", marker={\"color\": \"red\"}, name=\"actual values\")"
]
},
{
"cell_type": "markdown",
"id": "ba5e7f6e-62db-4dea-b9d2-32d337c73d20",
"metadata": {},
"source": [
"Note that smallest value of `k1_forward` is NOT zero, but rather about 5.92, as discussed earlier"
]
},
{
"cell_type": "markdown",
"id": "45706726-ac4c-4436-b404-5b2e259678f7",
"metadata": {},
"source": [
"### In the continuation experiment, `enzyme_2_b`, we'll explore how variations of `k1_forward` and `k1_reverse` (i.e. using guesses consistent with `kM` and `kcat`) affect the kinetics of our enzymatic reaction..."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "6bb4f7e2-928e-42de-b864-7eb91eafcc1f",
"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
}