{ "cells": [ { "cell_type": "markdown", "id": "5cbc8640", "metadata": {}, "source": [ "## **Enzyme Kinetics** : \n", "#### _Accurate numerical solution_ - compared to the **Michaelis-Menten** model approximation and to the alternative **Morrison** model.\n", "\n", "#### Two Coupled Reactions: `E + S <-> ES`, and `ES -> E + P` , using real-life kinetic parameters. \n", "#### Scenario with _small amount of Enzyme_, relative to the initial Substrate concentration.\n", "\n", "#### Unlike in experiment `enzyme_1_a`, we'll use data from a reaction that **VIOLATES the customary Michaelis-Menten assumption** that the rate constants satisfy `k1_reverse >> k2_forward`" ] }, { "cell_type": "markdown", "id": "604b150b-7812-4fd3-9403-69a06dd7e397", "metadata": {}, "source": [ "### THE REACTION: \n", "the enzyme `Aminopeptidase` with the substrate `Leu-Ala-DED`, \n", "and the initial concentration values choosen below, all satisfy the customary Michaelis-Menten assumptions that `[E] << [S]` BUT the reaction rate constants DON'T satisfy `k1_reverse >> k2_forward`\n", "\n", "For this reaction: k1_forward = 160 , k1_reverse = 0.089 , k2_forward = 0.58 \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 ipynbname\n", "import pandas as pd\n", "\n", "from life123 import check_version, ChemData, 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": "91a729ee-ad2f-4771-bc84-49ecb9d6a851", "metadata": {}, "source": [ "# 1. Accurate numerical solution" ] }, { "cell_type": "code", "execution_count": 5, "id": "959cf00a-47b3-455b-9923-9ec8741cc863", "metadata": {}, "outputs": [], "source": [ "chem_data = ChemData(names=[\"P\", \"ES\"], plot_colors=[\"green\", \"red\"])" ] }, { "cell_type": "code", "execution_count": 6, "id": "90f9ec41-6e1b-4558-9400-47e35ece6efc", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
| \n", " | name | \n", "label | \n", "plot_color | \n", "
|---|---|---|---|
| 0 | \n", "P | \n", "P | \n", "green | \n", "
| 1 | \n", "ES | \n", "ES | \n", "red | \n", "
| 2 | \n", "Aminopeptidase | \n", "E | \n", "violet | \n", "
| 3 | \n", "Leu-Ala-DED | \n", "S | \n", "darkturquoise | \n", "
| \n", " | SYSTEM TIME | \n", "rxn0_rate | \n", "rxn1_rate | \n", "
|---|---|---|---|
| 0 | \n", "0.000000 | \n", "3200.000000 | \n", "0.000000 | \n", "
| 1 | \n", "0.000031 | \n", "2878.693469 | \n", "0.055717 | \n", "
| 2 | \n", "0.000041 | \n", "2785.332115 | \n", "0.072003 | \n", "
| 3 | \n", "0.000052 | \n", "2688.859254 | \n", "0.088879 | \n", "
| 4 | \n", "0.000066 | \n", "2566.953047 | \n", "0.110271 | \n", "
| ... | \n", "... | \n", "... | \n", "... | \n", "
| 11107 | \n", "39.665738 | \n", "-0.000750 | \n", "0.010423 | \n", "
| 11108 | \n", "39.671328 | \n", "-0.000294 | \n", "0.010388 | \n", "
| 11109 | \n", "39.685826 | \n", "-0.000016 | \n", "0.010300 | \n", "
| 11110 | \n", "39.723430 | \n", "0.000006 | \n", "0.010077 | \n", "
| 11111 | \n", "39.820965 | \n", "0.000005 | \n", "0.009522 | \n", "
11112 rows × 3 columns
\n", "| \n", " | SYSTEM TIME | \n", "P | \n", "ES | \n", "E | \n", "S | \n", "caption | \n", "P_rate | \n", "
|---|---|---|---|---|---|---|---|
| 0 | \n", "0.000000 | \n", "0.000000e+00 | \n", "0.000000 | \n", "1.000000 | \n", "20.000000 | \n", "Set concentration | \n", "0.000000 | \n", "
| 1 | \n", "0.000031 | \n", "6.703630e-07 | \n", "0.096064 | \n", "0.903936 | \n", "19.903936 | \n", "\n", " | 0.055717 | \n", "
| 2 | \n", "0.000041 | \n", "1.294956e-06 | \n", "0.124144 | \n", "0.875856 | \n", "19.875855 | \n", "\n", " | 0.072003 | \n", "
| 3 | \n", "0.000052 | \n", "2.140174e-06 | \n", "0.153239 | \n", "0.846761 | \n", "19.846759 | \n", "\n", " | 0.088879 | \n", "
| 4 | \n", "0.000066 | \n", "3.520858e-06 | \n", "0.190123 | \n", "0.809877 | \n", "19.809874 | \n", "\n", " | 0.110271 | \n", "
| ... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "
| 11107 | \n", "39.665738 | \n", "1.998202e+01 | \n", "0.017971 | \n", "0.982029 | \n", "0.000005 | \n", "\n", " | 0.010423 | \n", "
| 11108 | \n", "39.671328 | \n", "1.998208e+01 | \n", "0.017910 | \n", "0.982090 | \n", "0.000008 | \n", "\n", " | 0.010388 | \n", "
| 11109 | \n", "39.685826 | \n", "1.998223e+01 | \n", "0.017758 | \n", "0.982242 | \n", "0.000010 | \n", "\n", " | 0.010300 | \n", "
| 11110 | \n", "39.723430 | \n", "1.998262e+01 | \n", "0.017375 | \n", "0.982625 | \n", "0.000010 | \n", "\n", " | 0.010077 | \n", "
| 11111 | \n", "39.820965 | \n", "1.998357e+01 | \n", "0.016417 | \n", "0.983583 | \n", "0.000009 | \n", "\n", " | 0.009522 | \n", "
11112 rows × 7 columns
\n", "| \n", " | SYSTEM TIME | \n", "P | \n", "ES | \n", "E | \n", "S | \n", "caption | \n", "P_rate | \n", "Michaelis_rate | \n", "
|---|---|---|---|---|---|---|---|---|
| 0 | \n", "0.000000 | \n", "0.000000e+00 | \n", "0.000000 | \n", "1.000000 | \n", "20.000000 | \n", "Set concentration | \n", "0.000000 | \n", "0.579879 | \n", "
| 1 | \n", "0.000031 | \n", "6.703630e-07 | \n", "0.096064 | \n", "0.903936 | \n", "19.903936 | \n", "\n", " | 0.055717 | \n", "0.579878 | \n", "
| 2 | \n", "0.000041 | \n", "1.294956e-06 | \n", "0.124144 | \n", "0.875856 | \n", "19.875855 | \n", "\n", " | 0.072003 | \n", "0.579878 | \n", "
| 3 | \n", "0.000052 | \n", "2.140174e-06 | \n", "0.153239 | \n", "0.846761 | \n", "19.846759 | \n", "\n", " | 0.088879 | \n", "0.579878 | \n", "
| 4 | \n", "0.000066 | \n", "3.520858e-06 | \n", "0.190123 | \n", "0.809877 | \n", "19.809874 | \n", "\n", " | 0.110271 | \n", "0.579878 | \n", "
| ... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "
| 11107 | \n", "39.665738 | \n", "1.998202e+01 | \n", "0.017971 | \n", "0.982029 | \n", "0.000005 | \n", "\n", " | 0.010423 | \n", "0.000749 | \n", "
| 11108 | \n", "39.671328 | \n", "1.998208e+01 | \n", "0.017910 | \n", "0.982090 | \n", "0.000008 | \n", "\n", " | 0.010388 | \n", "0.001145 | \n", "
| 11109 | \n", "39.685826 | \n", "1.998223e+01 | \n", "0.017758 | \n", "0.982242 | \n", "0.000010 | \n", "\n", " | 0.010300 | \n", "0.001378 | \n", "
| 11110 | \n", "39.723430 | \n", "1.998262e+01 | \n", "0.017375 | \n", "0.982625 | \n", "0.000010 | \n", "\n", " | 0.010077 | \n", "0.001366 | \n", "
| 11111 | \n", "39.820965 | \n", "1.998357e+01 | \n", "0.016417 | \n", "0.983583 | \n", "0.000009 | \n", "\n", " | 0.009522 | \n", "0.001290 | \n", "
11112 rows × 8 columns
\n", "| \n", " | SYSTEM TIME | \n", "P | \n", "ES | \n", "E | \n", "S | \n", "caption | \n", "P_rate | \n", "Michaelis_rate | \n", "Morrison_rate | \n", "
|---|---|---|---|---|---|---|---|---|---|
| 0 | \n", "0.000000 | \n", "0.000000e+00 | \n", "0.000000 | \n", "1.000000 | \n", "20.000000 | \n", "Set concentration | \n", "0.000000 | \n", "0.579879 | \n", "0.579872 | \n", "
| 1 | \n", "0.000031 | \n", "6.703630e-07 | \n", "0.096064 | \n", "0.903936 | \n", "19.903936 | \n", "\n", " | 0.055717 | \n", "0.579878 | \n", "0.579872 | \n", "
| 2 | \n", "0.000041 | \n", "1.294956e-06 | \n", "0.124144 | \n", "0.875856 | \n", "19.875855 | \n", "\n", " | 0.072003 | \n", "0.579878 | \n", "0.579872 | \n", "
| 3 | \n", "0.000052 | \n", "2.140174e-06 | \n", "0.153239 | \n", "0.846761 | \n", "19.846759 | \n", "\n", " | 0.088879 | \n", "0.579878 | \n", "0.579872 | \n", "
| 4 | \n", "0.000066 | \n", "3.520858e-06 | \n", "0.190123 | \n", "0.809877 | \n", "19.809874 | \n", "\n", " | 0.110271 | \n", "0.579878 | \n", "0.579872 | \n", "
| ... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "
| 11107 | \n", "39.665738 | \n", "1.998202e+01 | \n", "0.017971 | \n", "0.982029 | \n", "0.000005 | \n", "\n", " | 0.010423 | \n", "0.000749 | \n", "0.010382 | \n", "
| 11108 | \n", "39.671328 | \n", "1.998208e+01 | \n", "0.017910 | \n", "0.982090 | \n", "0.000008 | \n", "\n", " | 0.010388 | \n", "0.001145 | \n", "0.010349 | \n", "
| 11109 | \n", "39.685826 | \n", "1.998223e+01 | \n", "0.017758 | \n", "0.982242 | \n", "0.000010 | \n", "\n", " | 0.010300 | \n", "0.001378 | \n", "0.010262 | \n", "
| 11110 | \n", "39.723430 | \n", "1.998262e+01 | \n", "0.017375 | \n", "0.982625 | \n", "0.000010 | \n", "\n", " | 0.010077 | \n", "0.001366 | \n", "0.010040 | \n", "
| 11111 | \n", "39.820965 | \n", "1.998357e+01 | \n", "0.016417 | \n", "0.983583 | \n", "0.000009 | \n", "\n", " | 0.009522 | \n", "0.001290 | \n", "0.009487 | \n", "
11112 rows × 9 columns
\n", "