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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 = \"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",
"import numpy as np\n",
"import plotly.express as px\n",
"\n",
"from life123 import check_version, ReactionEnz"
]
},
{
"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": "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 `ReactionEnz` conveniently provides the necessary transformations."
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "2ea816ee-4bb1-4f36-9a41-281aa4537586",
"metadata": {},
"outputs": [],
"source": [
"enz = ReactionEnz()"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "7e34a530-7e5e-404b-8cb2-01e7db85557a",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"99.99999999999986"
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},
"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": [
"### 1. Let's try a variety of values for `k1_reverse`, and determine the corresponding values for `k1_forward`"
]
},
{
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"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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"lakecolor": "white",
"landcolor": "#E5ECF6",
"showlakes": true,
"showland": true,
"subunitcolor": "white"
},
"hoverlabel": {
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},
"hovermode": "closest",
"mapbox": {
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},
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"plot_bgcolor": "#E5ECF6",
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},
"bgcolor": "#E5ECF6",
"radialaxis": {
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}
},
"scene": {
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"gridcolor": "white",
"gridwidth": 2,
"linecolor": "white",
"showbackground": true,
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},
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},
"shapedefaults": {
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},
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},
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"bgcolor": "#E5ECF6",
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},
"title": {
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},
"xaxis": {
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},
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"ticks": "",
"title": {
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},
"zerolinecolor": "white",
"zerolinewidth": 2
}
}
},
"title": {
"text": "k1_forward for given k1_reverse values"
},
"xaxis": {
"anchor": "y",
"autorange": true,
"domain": [
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"range": [
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"title": {
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"type": "linear"
},
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"domain": [
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"range": [
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],
"title": {
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},
"type": "linear"
}
}
},
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""
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}
],
"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": "9ae9e3f9-5bf7-413f-891d-8baa6907c6c1",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "f6d18fd8-3683-4a1e-88fe-e8f9cb9007c7",
"metadata": {},
"source": [
"### 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": [
{
"data": {
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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` (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
}