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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. 2, 2025\"\n",
"LIFE123_VERSION = \"1.0.0rc6\" # 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()"
]
},
{
"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"
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],
"source": [
"# Example, using the k1_forward=18. from experiment `enzyme_1_a`, 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": [
{
"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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},
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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`"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "b9d2b33a-0e4d-4ae4-a76b-3647b9114256",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 5.92, 27.96, 50. ])"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"k1_forward_choices = np.linspace(5.92, 50., 3) # Even grid of values; notice the start value just above the min required value\n",
"k1_forward_choices"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "7a6ef1bc-8ed9-4e84-a3a1-7b3bffd9d1c2",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([4.44444444e-03, 1.82446667e+02, 3.64888889e+02])"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"k1_reverse_choices = enz.compute_k1_reverse(kM=kM, kcat=kcat, k1_forward = k1_forward_choices)\n",
"k1_reverse_choices"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "de63468d-1ac9-44ae-9193-4c91fe5fdde9",
"metadata": {},
"outputs": [
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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",
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"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` (guesses consistent with `kM` and `kcat`) affect the kinetics of our enzymatic reaction..."
]
},
{
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"id": "6bb4f7e2-928e-42de-b864-7eb91eafcc1f",
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"outputs": [],
"source": []
}
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