{ "cells": [ { "cell_type": "markdown", "id": "5cbc8640", "metadata": {}, "source": [ "# **Enzyme Kinetics** : \n", "#### An _accurate numerical solution_ of an enzymatic reaction `E + S <-> ES -> E + P` - compared to the **Michaelis-Menten** model approximation and to the alternative **Morrison** model.\n", "\n", "#### Same as experiment `enzyme_1_a` but with _much-larger amounts of Enzyme_ relative to the initial Substrate concentration.\n", "\n", "#### Real-life kinetic parameters. \n", "\n", "Please refer to `enzyme_1_a` for more details." ] }, { "cell_type": "markdown", "id": "604b150b-7812-4fd3-9403-69a06dd7e397", "metadata": {}, "source": [ "#### THE REACTION: \n", "the enzyme `Adenosine deaminase` with the substrate `2,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purine` (same as in experiment `enzyme_1`) \n", "satisfies the customary Michaelis-Menten assumptions that `k1_reverse >> k2_forward`\n", "\n", "However, the initial concentration values choosen below, do NOT satisfy the expected Michaelis-Menten assumptions that `[E] << [S]` \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 pandas as pd\n", "\n", "from life123 import check_version, ChemData, UniformCompartment, ReactionEnzyme, 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) # 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": "91a729ee-ad2f-4771-bc84-49ecb9d6a851", "metadata": {}, "source": [ "# PART 1. Accurate numerical solution" ] }, { "cell_type": "code", "execution_count": 5, "id": "ac9eea69-174c-43e5-9eed-443cbc5e2ba7", "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", "Adenosine deaminase | \n", "E | \n", "violet | \n", "
| 3 | \n", "2,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purine | \n", "S | \n", "darkturquoise | \n", "
| \n", " | SYSTEM TIME | \n", "P | \n", "ES | \n", "E | \n", "S | \n", "step | \n", "caption | \n", "rxn0_rate_2 | \n", "
|---|---|---|---|---|---|---|---|---|
| 0 | \n", "0.000000 | \n", "0.000000 | \n", "0.000000 | \n", "10.000000 | \n", "20.000000 | \n", "\n", " | Set concentration | \n", "0.000000 | \n", "
| 1 | \n", "0.000500 | \n", "0.000000 | \n", "1.800000 | \n", "8.200000 | \n", "18.200000 | \n", "1 | \n", "1st reaction step | \n", "88.200000 | \n", "
| 2 | \n", "0.000750 | \n", "0.022050 | \n", "2.404530 | \n", "7.595470 | \n", "17.573420 | \n", "2 | \n", "\n", " | 117.821970 | \n", "
| 3 | \n", "0.000763 | \n", "0.023523 | \n", "2.430084 | \n", "7.569916 | \n", "17.546393 | \n", "3 | \n", "\n", " | 119.074126 | \n", "
| 4 | \n", "0.000769 | \n", "0.024267 | \n", "2.442764 | \n", "7.557236 | \n", "17.532969 | \n", "4 | \n", "\n", " | 119.695434 | \n", "
| ... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "
| 610 | \n", "0.195573 | \n", "19.863565 | \n", "0.081649 | \n", "9.918351 | \n", "0.054786 | \n", "610 | \n", "\n", " | 4.000798 | \n", "
| 611 | \n", "0.196593 | \n", "19.867645 | \n", "0.079217 | \n", "9.920783 | \n", "0.053138 | \n", "611 | \n", "\n", " | 3.881655 | \n", "
| 612 | \n", "0.197612 | \n", "19.871602 | \n", "0.076858 | \n", "9.923142 | \n", "0.051540 | \n", "612 | \n", "\n", " | 3.766032 | \n", "
| 613 | \n", "0.198632 | \n", "19.875442 | \n", "0.074568 | \n", "9.925432 | \n", "0.049990 | \n", "613 | \n", "\n", " | 3.653827 | \n", "
| 614 | \n", "0.199652 | \n", "19.879167 | \n", "0.072346 | \n", "9.927654 | \n", "0.048487 | \n", "614 | \n", "\n", " | 3.544941 | \n", "
615 rows × 8 columns
\n", "| \n", " | SYSTEM TIME | \n", "P | \n", "ES | \n", "E | \n", "S | \n", "step | \n", "caption | \n", "rxn0_rate_2 | \n", "Michaelis_rate | \n", "
|---|---|---|---|---|---|---|---|---|---|
| 0 | \n", "0.000000 | \n", "0.000000 | \n", "0.000000 | \n", "10.000000 | \n", "20.000000 | \n", "\n", " | Set concentration | \n", "0.000000 | \n", "346.561886 | \n", "
| 1 | \n", "0.000500 | \n", "0.000000 | \n", "1.800000 | \n", "8.200000 | \n", "18.200000 | \n", "1 | \n", "1st reaction step | \n", "88.200000 | \n", "336.810743 | \n", "
| 2 | \n", "0.000750 | \n", "0.022050 | \n", "2.404530 | \n", "7.595470 | \n", "17.573420 | \n", "2 | \n", "\n", " | 117.821970 | \n", "333.097749 | \n", "
| 3 | \n", "0.000763 | \n", "0.023523 | \n", "2.430084 | \n", "7.569916 | \n", "17.546393 | \n", "3 | \n", "\n", " | 119.074126 | \n", "332.933539 | \n", "
| 4 | \n", "0.000769 | \n", "0.024267 | \n", "2.442764 | \n", "7.557236 | \n", "17.532969 | \n", "4 | \n", "\n", " | 119.695434 | \n", "332.851850 | \n", "
| ... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "
| 610 | \n", "0.195573 | \n", "19.863565 | \n", "0.081649 | \n", "9.918351 | \n", "0.054786 | \n", "610 | \n", "\n", " | 4.000798 | \n", "3.221698 | \n", "
| 611 | \n", "0.196593 | \n", "19.867645 | \n", "0.079217 | \n", "9.920783 | \n", "0.053138 | \n", "611 | \n", "\n", " | 3.881655 | \n", "3.125424 | \n", "
| 612 | \n", "0.197612 | \n", "19.871602 | \n", "0.076858 | \n", "9.923142 | \n", "0.051540 | \n", "612 | \n", "\n", " | 3.766032 | \n", "3.032014 | \n", "
| 613 | \n", "0.198632 | \n", "19.875442 | \n", "0.074568 | \n", "9.925432 | \n", "0.049990 | \n", "613 | \n", "\n", " | 3.653827 | \n", "2.941384 | \n", "
| 614 | \n", "0.199652 | \n", "19.879167 | \n", "0.072346 | \n", "9.927654 | \n", "0.048487 | \n", "614 | \n", "\n", " | 3.544941 | \n", "2.853451 | \n", "
615 rows × 9 columns
\n", "| \n", " | SYSTEM TIME | \n", "P | \n", "ES | \n", "E | \n", "S | \n", "step | \n", "caption | \n", "rxn0_rate_2 | \n", "Michaelis_rate | \n", "Morrison_rate | \n", "
|---|---|---|---|---|---|---|---|---|---|---|
| 0 | \n", "0.000000 | \n", "0.000000 | \n", "0.000000 | \n", "10.000000 | \n", "20.000000 | \n", "\n", " | Set concentration | \n", "0.000000 | \n", "346.561886 | \n", "305.920075 | \n", "
| 1 | \n", "0.000500 | \n", "0.000000 | \n", "1.800000 | \n", "8.200000 | \n", "18.200000 | \n", "1 | \n", "1st reaction step | \n", "88.200000 | \n", "336.810743 | \n", "305.920075 | \n", "
| 2 | \n", "0.000750 | \n", "0.022050 | \n", "2.404530 | \n", "7.595470 | \n", "17.573420 | \n", "2 | \n", "\n", " | 117.821970 | \n", "333.097749 | \n", "305.762583 | \n", "
| 3 | \n", "0.000763 | \n", "0.023523 | \n", "2.430084 | \n", "7.569916 | \n", "17.546393 | \n", "3 | \n", "\n", " | 119.074126 | \n", "332.933539 | \n", "305.752055 | \n", "
| 4 | \n", "0.000769 | \n", "0.024267 | \n", "2.442764 | \n", "7.557236 | \n", "17.532969 | \n", "4 | \n", "\n", " | 119.695434 | \n", "332.851850 | \n", "305.746735 | \n", "
| ... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "... | \n", "
| 610 | \n", "0.195573 | \n", "19.863565 | \n", "0.081649 | \n", "9.918351 | \n", "0.054786 | \n", "610 | \n", "\n", " | 4.000798 | \n", "3.221698 | \n", "3.645236 | \n", "
| 611 | \n", "0.196593 | \n", "19.867645 | \n", "0.079217 | \n", "9.920783 | \n", "0.053138 | \n", "611 | \n", "\n", " | 3.881655 | \n", "3.125424 | \n", "3.536609 | \n", "
| 612 | \n", "0.197612 | \n", "19.871602 | \n", "0.076858 | \n", "9.923142 | \n", "0.051540 | \n", "612 | \n", "\n", " | 3.766032 | \n", "3.032014 | \n", "3.431196 | \n", "
| 613 | \n", "0.198632 | \n", "19.875442 | \n", "0.074568 | \n", "9.925432 | \n", "0.049990 | \n", "613 | \n", "\n", " | 3.653827 | \n", "2.941384 | \n", "3.328903 | \n", "
| 614 | \n", "0.199652 | \n", "19.879167 | \n", "0.072346 | \n", "9.927654 | \n", "0.048487 | \n", "614 | \n", "\n", " | 3.544941 | \n", "2.853451 | \n", "3.229639 | \n", "
615 rows × 10 columns
\n", "