{ "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, using real-life kinetic parameters. \n", "\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 = \"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": "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": [ "
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namelabelplot_color
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" ], "text/plain": [ " name label plot_color\n", "0 P P green\n", "1 ES ES red\n", "2 Aminopeptidase E violet\n", "3 Leu-Ala-DED S darkturquoise" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Our Enzyme\n", "chem_data.add_chemical(name=\"Aminopeptidase\", label=\"E\", plot_color=\"violet\")\n", "\n", "# Our Substrate\n", "chem_data.add_chemical(name=\"Leu-Ala-DED\", label=\"S\", plot_color=\"darkturquoise\")\n", "\n", "chem_data.all_chemicals()" ] }, { "cell_type": "code", "execution_count": null, "id": "a7550b20-f34c-455f-9319-b9e9ddc5adfc", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "f8d4ea7f-0591-467c-9df3-d95f53df75f5", "metadata": {}, "source": [ "### Specify the Kinetic Parameters" ] }, { "cell_type": "markdown", "id": "6b0b902c-c2bb-4731-9235-3f94ae9ec247", "metadata": {}, "source": [ "Source: *page 16 of \"Analysis of Enzyme Reaction Kinetics, Vol. 1\", by F. Xavier Malcata, Wiley, 2023*" ] }, { "cell_type": "markdown", "id": "5906cdcd-f4ed-489a-b230-8e8933b9597e", "metadata": {}, "source": [ "### Notice that the reaction rate constants below DON'T satisfy the customary `k1_reverse >> k2_forward`" ] }, { "cell_type": "code", "execution_count": 7, "id": "07b23edc-5c8e-4886-a2b8-989b9bbb4e7e", "metadata": {}, "outputs": [], "source": [ "# Here we use the \"slow\" preset for the variable steps, a conservative option prioritizing accuracy over speed\n", "uc = UniformCompartment(chem_data=chem_data, preset=\"slow\")" ] }, { "cell_type": "code", "execution_count": 8, "id": "78077d8c", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 1\n", "0: E + S <-> ES -> E + P (Enzymatic reaction) (k1_F = 160 / k1_R = 0.089 / k2_F = 0.58 / Temp = 25 C)\n", "Chemicals involved in the above reactions: {\"P\" (green), \"ES\" (red), \"E\" (violet), \"S\" (darkturquoise)}\n" ] } ], "source": [ "# Enzymatic reaction `E + S <-> ES -> E + P` \n", "uc.add_reaction(reactants=\"S\", products=\"P\", enzyme=\"E\",\n", " k1_F=160., k1_R=0.089, k2_F=0.58)\n", "\n", "uc.describe_reactions()" ] }, { "cell_type": "code", "execution_count": null, "id": "8913269e-9c1b-493f-8d28-c53f8cb7b5e4", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "d23a97ea-f252-4e11-a3e9-aea74f58591e", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "9a4febb2-2780-4754-9c70-c2041b1afc07", "metadata": {}, "source": [ "## Set the initial concentrations of all the chemicals\n", "### in the scenario we're exploring, there's LITTLE ENZYME relative to initial substrate concentration, \n", "just like we did in experiment `enzyme_1_a`" ] }, { "cell_type": "code", "execution_count": 9, "id": "8c9e3f86-b9a5-41da-9e1b-75258017808a", "metadata": {}, "outputs": [], "source": [ "S0 = 20.\n", "E0 = 1." ] }, { "cell_type": "code", "execution_count": 10, "id": "6abcf6e2-9ce9-4841-b955-1e43808220e8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "4 species:\n", " Species 0 (P). Conc: 0.0\n", " Species 1 (ES). Conc: 0.0\n", " Species 2 (E). Conc: 1.0\n", " Species 3 (S). Conc: 20.0\n", "Chemicals involved in reactions: ['S', 'E', 'ES', 'P']\n" ] } ], "source": [ "uc.set_conc(conc={\"S\": S0, \"E\": E0}) # Small ampount of enzyme `E`, relative to substrate `S`\n", "uc.describe_state()" ] }, { "cell_type": "code", "execution_count": null, "id": "2060605e-39ac-4705-93e5-722e9ba23d0f", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "ef2c10f2-ec7f-497a-bdbf-4fea30ba31a1", "metadata": { "tags": [] }, "source": [ "#### Simulate the very early part of the reaction" ] }, { "cell_type": "code", "execution_count": 11, "id": "e6ad72b8-722a-4606-a611-7dc600529f30", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "173 total variable step(s) taken in 0.352 sec\n", "Norm usage: {'norm_A': 31, 'norm_B': 33, 'norm_C': 31, 'norm_D': 31}\n", "System Time is now: 0.0015061\n" ] } ], "source": [ "# Perform the reactions \n", "# (Note: by default, concentration and rate history is kept for each step; we'll later reduce this frequency)\n", "uc.single_compartment_react(duration=0.0015, initial_step=0.00001)" ] }, { "cell_type": "code", "execution_count": 12, "id": "0198dd94-e55d-4ab4-9de8-087d508edf06", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_pandas() NOTICE: Excessive number of vertical lines (174) - only showing 1 every 2 lines\n" ] }, { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=P
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Reaction `E + S <-> ES -> E + P` . 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Changes in concentrations with time" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ 0, 0.0015061056759486202 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "domain": [ 0, 1 ], "range": [ 0, 1 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Highlight a detail about the initial buildup of ES\n", "uc.plot_history(title_prefix=\"DETAIL at early times\",\n", " range_y=[0, 1])" ] }, { "cell_type": "markdown", "id": "fcf12778-aab2-4c1b-b6d2-d8673d172953", "metadata": {}, "source": [ "### Notice the EXTREMELY fast kinetics involving the production of the intermediate `ES`" ] }, { "cell_type": "markdown", "id": "40a69c0b-d0e9-4c9c-b27f-9a31564c4723", "metadata": {}, "source": [ "If one wishes to exam the history (of concentration or reaction-rate data) in tabular form, it can be done as follows:" ] }, { "cell_type": "code", "execution_count": 14, "id": "ab88b86d-0de1-4cfa-a3a8-61dd5fc08717", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEPESESstepcaption
00.0000000.000000e+000.0000001.00000020.000000Set concentration
10.0000100.000000e+000.0320000.96800019.96800011st reaction step
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" ], "text/plain": [ " SYSTEM TIME P ES E S step \\\n", "0 0.000000 0.000000e+00 0.000000 1.000000 20.000000 \n", "1 0.000010 0.000000e+00 0.032000 0.968000 19.968000 1 \n", "2 0.000021 2.041600e-07 0.066019 0.933981 19.933981 2 \n", "3 0.000024 3.305201e-07 0.075849 0.924151 19.924151 3 \n", "4 0.000025 3.740726e-07 0.078766 0.921234 19.921234 4 \n", ".. ... ... ... ... ... ... \n", "169 0.001437 6.495498e-04 0.988861 0.011139 19.010489 169 \n", "170 0.001454 6.594576e-04 0.989435 0.010565 19.009906 170 \n", "171 0.001472 6.693712e-04 0.989979 0.010021 19.009352 171 \n", "172 0.001489 6.792902e-04 0.990494 0.009506 19.008827 172 \n", "173 0.001506 6.892144e-04 0.990982 0.009018 19.008329 173 \n", "\n", " caption \n", "0 Set concentration \n", "1 1st reaction step \n", "2 \n", "3 \n", "4 \n", ".. ... \n", "169 \n", "170 \n", "171 \n", "172 \n", "173 last reaction step \n", "\n", "[174 rows x 7 columns]" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uc.get_history()" ] }, { "cell_type": "code", "execution_count": 15, "id": "38fe5851-e292-4093-a1ee-dbd77abd566c", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " SYSTEM TIME rxn0_rate_1 rxn0_rate_2 step\n", "0 0.000000 3200.000000 0.000000 0\n", "1 0.000010 3092.640992 0.018560 1\n", "2 0.000021 2978.868127 0.038291 2\n", "3 0.000024 2946.061101 0.043992 3\n", "4 0.000025 2936.333355 0.045684 4\n", ".. ... ... ... ...\n", "168 0.001420 35.636312 0.573188 168\n", "169 0.001437 33.792720 0.573539 169\n", "170 0.001454 32.046189 0.573872 170\n", "171 0.001472 30.391600 0.574188 171\n", "172 0.001489 28.824102 0.574486 172\n", "\n", "[173 rows x 4 columns]" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uc.get_rate_history()" ] }, { "cell_type": "markdown", "id": "25201770-a41f-4e64-bb8d-897dcdf492c0", "metadata": {}, "source": [ "Note that rates are associated with the START times of the intervals. So, at the end time of the simulation, there's no rate." ] }, { "cell_type": "code", "execution_count": null, "id": "ec2e2ac9-02f8-455a-8bd3-1170408a4ece", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "7ffc10cf-d7d8-4a34-a08f-e62e436ec7e3", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "a05b2cfd-7316-4925-8111-85bf11a719f2", "metadata": { "tags": [] }, "source": [ "#### Advance the reactions to equilibrium" ] }, { "cell_type": "code", "execution_count": 16, "id": "aba2c3cd-95ec-4174-9750-603ab130a6f7", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "19936 total variable step(s) taken in 5.810 sec\n", "Number of step re-do's because of negative concentrations: 116\n", "Number of step re-do's because of elective soft aborts: 358\n", "Norm usage: {'norm_A': 16558, 'norm_B': 17520, 'norm_C': 16558, 'norm_D': 16558}\n", "System Time is now: 40.008\n" ] } ], "source": [ "# From now on, the data from 1 of every 10 computation steps will be saved in the history (for later use in plots, etc). \n", "# Until this point, we've used the default of 1\n", "uc.enable_history(frequency=10)\n", "\n", "# Continue the reactions\n", "uc.single_compartment_react(duration=40., initial_step=0.00001)" ] }, { "cell_type": "code", "execution_count": 17, "id": "9b792467-9c37-4b66-8c9c-6c0c9c61db3f", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=P
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Reaction `E + S <-> ES -> E + P` . 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Reaction `E + S <-> ES -> E + P` . 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Highlight a detail about the initial buildup of ES\n", "uc.plot_history(title_prefix=\"DETAIL of ES and E\",\n", " range_y=[0, 1.5])" ] }, { "cell_type": "markdown", "id": "ba28bbea-b725-4e1a-9c64-7dbad40cf2c8", "metadata": {}, "source": [ "#### Notice how the bound enzyme `ES` (red) quickly builds up at the very beginning, from time 0 to roughly 0.01 ... and that, in the longer term, the enzyme returns to its unbound state `E`" ] }, { "cell_type": "code", "execution_count": null, "id": "056f50a9-bb38-4d4c-b518-82302370b254", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "2d8336ee-4576-4081-9835-9fd7b8bee273", "metadata": { "tags": [] }, "source": [ "### What is the initial rate of production of the final reaction product `P`? \n", "One could take the numerical derivative (gradient) of the time values of [P] - but no need to! **Reaction rates are computed in the course of the simulation, and stored in a rate-history dataframe** (as we also saw earlier)" ] }, { "cell_type": "code", "execution_count": 19, "id": "18517784-55eb-420c-87a1-bfaee226cc28", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMErxn0_rate_1rxn0_rate_2step
00.0000003200.0000000.0000000
10.0000103092.6409920.0185601
20.0000212978.8681270.0382912
30.0000242946.0611010.0439923
40.0000252936.3333550.0456844
...............
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216339.1957740.0000080.01373619899
216439.4916780.0000070.01155219909
216539.8364460.0000500.00943019919
216639.9038680.0000050.00906819929
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" ], "text/plain": [ " SYSTEM TIME rxn0_rate_1 rxn0_rate_2 step\n", "0 0.000000 3200.000000 0.000000 0\n", "1 0.000010 3092.640992 0.018560 1\n", "2 0.000021 2978.868127 0.038291 2\n", "3 0.000024 2946.061101 0.043992 3\n", "4 0.000025 2936.333355 0.045684 4\n", "... ... ... ... ...\n", "2162 39.081690 0.000009 0.014678 19889\n", "2163 39.195774 0.000008 0.013736 19899\n", "2164 39.491678 0.000007 0.011552 19909\n", "2165 39.836446 0.000050 0.009430 19919\n", "2166 39.903868 0.000005 0.009068 19929\n", "\n", "[2167 rows x 4 columns]" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rates = uc.get_rate_history()\n", "rates" ] }, { "cell_type": "markdown", "id": "0edb69af-9dbe-4ae7-b434-d6402edecfb5", "metadata": {}, "source": [ "Note that initially we were saving historical data at every simulation step, but later switched to every 10 steps" ] }, { "cell_type": "code", "execution_count": 20, "id": "18ac9b9f-c669-43f6-ac36-ed95b76e1ae5", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "SYSTEM TIME=%{x}
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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Let's take a look at how the reaction rate varies with time\n", "PlotlyHelper.plot_pandas(df=rates, \n", " title=\"Reaction rate, dP/dt, over time\",\n", " x_var=\"SYSTEM TIME\", fields=\"rxn0_rate_2\", \n", " x_label=\"time\", y_label=\"dP/dt\")" ] }, { "cell_type": "markdown", "id": "b223bfcd-1be8-4bdb-9ed2-44ca0637074a", "metadata": {}, "source": [ "### Notice how very different is it from the Reaction rate over time seen in experiment `enzyme_1_a`" ] }, { "cell_type": "code", "execution_count": 21, "id": "9c534460-2958-454a-a2bf-2bf359d460b3", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "SYSTEM TIME=%{x}
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# A closer peek at its very quick buildup\n", "PlotlyHelper.plot_pandas(df=rates, \n", " title=\"Reaction rate, dP/dt, over time (DETAIL at early times)\",\n", " x_var=\"SYSTEM TIME\", fields=\"rxn0_rate_2\", \n", " range_x=[0, 0.0015])" ] }, { "cell_type": "markdown", "id": "bfacc983-b8af-467d-87b2-2fee868d8254", "metadata": {}, "source": [ "As we saw earlier, the time it took for `ES` to build up was about 0.001 \n", "**Ignoring the very brief initial transient phase, the reaction rate starts at about 0.57, and stays at that value until the substrate gets depleted, arount t=33**" ] }, { "cell_type": "code", "execution_count": null, "id": "485514fa-5259-4319-9aea-8adac65ae24f", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "e0886793-ace6-49dc-bbef-d2aa0c040001", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "078285f0-00aa-4fbb-9a67-7de0184d6cec", "metadata": {}, "source": [ "# PART 2. Comparing the results to the Michaelis-Menten model approximation" ] }, { "cell_type": "markdown", "id": "5c15fd87-ee4d-41f5-bcc5-de1dce1a59ec", "metadata": {}, "source": [ "### Let's compute some parameters used by the Michaelis-Menten model \n", "for background reference, see: https://vallance.chem.ox.ac.uk/pdfs/KineticsLectureNotes.pdf (p. 20)" ] }, { "cell_type": "code", "execution_count": 22, "id": "1411f8f6-ab1b-4ef0-97ef-3395058dafc1", "metadata": {}, "outputs": [], "source": [ "rxn = uc.get_single_reaction(0)" ] }, { "cell_type": "code", "execution_count": 23, "id": "e279ef7d-61ca-469f-8418-60ad0b1222e0", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.004181249999999999" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rxn.kM # For the data in this experiment, it comes out to (0.089 + 0.58) / 160." ] }, { "cell_type": "code", "execution_count": 24, "id": "5b073f95-a8ed-4885-8b88-85a04341ecee", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.58" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rxn.kcat" ] }, { "cell_type": "code", "execution_count": 25, "id": "355a083f-d492-4cbb-a5c1-f961236257ad", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.58" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vmax = rxn.compute_vmax(E_tot=E0) # kcat * E0\n", "vmax" ] }, { "cell_type": "code", "execution_count": 26, "id": "09dfe215-e89d-4562-8a54-72973c6d2b2c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.5798787690948362" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "initial_rxn_rate = rxn.compute_rate(S_conc=S0) # (vmax * S0) / (kM + S0)\n", "initial_rxn_rate" ] }, { "cell_type": "markdown", "id": "fbc8da21-6dbf-4957-a4f6-437b50de003f", "metadata": {}, "source": [ "Pretty close the value of about 0.57 we saw earlier, after the initial transient... " ] }, { "cell_type": "code", "execution_count": null, "id": "1d9b8b04-e789-477e-be6a-d180d6f23eaf", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "34fe41ca-b95f-4033-b23f-8240332891a5", "metadata": {}, "source": [ "### Now, let's look at the reaction rate that produces `P` as a function of [S]; we'll compare what we computed earlier vs. what is given by the approximation of the **Michaelis-Menten model**" ] }, { "cell_type": "markdown", "id": "84d5ad99-45b7-4d5f-9e9b-1b658e3e4681", "metadata": {}, "source": [ "First, we'll merge the concentration history and and the rate history into a single dataframe `df`" ] }, { "cell_type": "code", "execution_count": 27, "id": "c3f85515-6bfc-4b7c-a201-8488b0a65149", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEPESESstepcaptionP_rate
00.0000000.000000e+000.0000001.00000020.000000Set concentration0.000000
10.0000100.000000e+000.0320000.96800019.96800011st reaction step0.018560
20.0000212.041600e-070.0660190.93398119.93398120.038291
30.0000243.305201e-070.0758490.92415119.92415130.043992
40.0000253.740726e-070.0787660.92123419.92123440.045684
...........................
216239.0816901.997468e+010.0253070.9746930.000014198890.014678
216339.1957741.997630e+010.0236820.9763180.000014198990.013736
216439.4916781.998007e+010.0199170.9800830.000011199090.011552
216539.8364461.998373e+010.0162580.9837420.000010199190.009430
216639.9038681.998436e+010.0156340.9843660.000009199290.009068
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2167 rows × 8 columns

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" ], "text/plain": [ " SYSTEM TIME P ES E S step \\\n", "0 0.000000 0.000000e+00 0.000000 1.000000 20.000000 \n", "1 0.000010 0.000000e+00 0.032000 0.968000 19.968000 1 \n", "2 0.000021 2.041600e-07 0.066019 0.933981 19.933981 2 \n", "3 0.000024 3.305201e-07 0.075849 0.924151 19.924151 3 \n", "4 0.000025 3.740726e-07 0.078766 0.921234 19.921234 4 \n", "... ... ... ... ... ... ... \n", "2162 39.081690 1.997468e+01 0.025307 0.974693 0.000014 19889 \n", "2163 39.195774 1.997630e+01 0.023682 0.976318 0.000014 19899 \n", "2164 39.491678 1.998007e+01 0.019917 0.980083 0.000011 19909 \n", "2165 39.836446 1.998373e+01 0.016258 0.983742 0.000010 19919 \n", "2166 39.903868 1.998436e+01 0.015634 0.984366 0.000009 19929 \n", "\n", " caption P_rate \n", "0 Set concentration 0.000000 \n", "1 1st reaction step 0.018560 \n", "2 0.038291 \n", "3 0.043992 \n", "4 0.045684 \n", "... ... ... \n", "2162 0.014678 \n", "2163 0.013736 \n", "2164 0.011552 \n", "2165 0.009430 \n", "2166 0.009068 \n", "\n", "[2167 rows x 8 columns]" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = uc.add_rate_to_conc_history(rate_name=\"rxn0_rate_2\", new_rate_name=\"P_rate\")\n", "df" ] }, { "cell_type": "code", "execution_count": 28, "id": "0769aa93-8040-4ae0-b258-9c4e0a379cbd", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEPESESstepcaptionP_rateMichaelis_rate
00.0000000.000000e+000.0000001.00000020.000000Set concentration0.0000000.579879
10.0000100.000000e+000.0320000.96800019.96800011st reaction step0.0185600.579879
20.0000212.041600e-070.0660190.93398119.93398120.0382910.579878
30.0000243.305201e-070.0758490.92415119.92415130.0439920.579878
40.0000253.740726e-070.0787660.92123419.92123440.0456840.579878
..............................
216239.0816901.997468e+010.0253070.9746930.000014198890.0146780.002004
216339.1957741.997630e+010.0236820.9763180.000014198990.0137360.001873
216439.4916781.998007e+010.0199170.9800830.000011199090.0115520.001570
216539.8364461.998373e+010.0162580.9837420.000010199190.0094300.001317
216639.9038681.998436e+010.0156340.9843660.000009199290.0090680.001227
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2167 rows × 9 columns

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" ], "text/plain": [ " SYSTEM TIME P ES E S step \\\n", "0 0.000000 0.000000e+00 0.000000 1.000000 20.000000 \n", "1 0.000010 0.000000e+00 0.032000 0.968000 19.968000 1 \n", "2 0.000021 2.041600e-07 0.066019 0.933981 19.933981 2 \n", "3 0.000024 3.305201e-07 0.075849 0.924151 19.924151 3 \n", "4 0.000025 3.740726e-07 0.078766 0.921234 19.921234 4 \n", "... ... ... ... ... ... ... \n", "2162 39.081690 1.997468e+01 0.025307 0.974693 0.000014 19889 \n", "2163 39.195774 1.997630e+01 0.023682 0.976318 0.000014 19899 \n", "2164 39.491678 1.998007e+01 0.019917 0.980083 0.000011 19909 \n", "2165 39.836446 1.998373e+01 0.016258 0.983742 0.000010 19919 \n", "2166 39.903868 1.998436e+01 0.015634 0.984366 0.000009 19929 \n", "\n", " caption P_rate Michaelis_rate \n", "0 Set concentration 0.000000 0.579879 \n", "1 1st reaction step 0.018560 0.579879 \n", "2 0.038291 0.579878 \n", "3 0.043992 0.579878 \n", "4 0.045684 0.579878 \n", "... ... ... ... \n", "2162 0.014678 0.002004 \n", "2163 0.013736 0.001873 \n", "2164 0.011552 0.001570 \n", "2165 0.009430 0.001317 \n", "2166 0.009068 0.001227 \n", "\n", "[2167 rows x 9 columns]" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's add a column with the rate estimated by the Michaelis-Menten model\n", "df[\"Michaelis_rate\"] = rxn.compute_rate(S_conc=df[\"S\"])\n", "df" ] }, { "cell_type": "code", "execution_count": 29, "id": "6e8cdb8c-0e8e-461f-81a0-f7b75de1d322", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Rates=P_rate
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", "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Let's see how our computed rate compares with the approximations from the Michaelis-Menten model\n", "PlotlyHelper.plot_pandas(df=df, x_var=\"S\", fields=[\"P_rate\", \"Michaelis_rate\"],\n", " title=\"Reaction rate, dP/dt, as a function of Substrate concentration\",\n", " y_label=\"dP/dt\", legend_header=\"Rates\",\n", " vertical_lines_to_add=19, colors=[\"blue\", \"yellow\"])" ] }, { "cell_type": "markdown", "id": "3d6b91c7-dc26-4a04-8a27-4d1b10f4d96e", "metadata": {}, "source": [ "Let's recall that our reactions started with [S]=20 \n", "Virtually overlapped plots, except at the very right! (very early times, when [S] is greater than about 19)" ] }, { "cell_type": "markdown", "id": "60f95830-6892-4ddf-847f-5424c591b0dd", "metadata": {}, "source": [ "The overlap at the very left (small [S], late in the reaction) has a few issues, but not too bad; let's magnify the previous plot:" ] }, { "cell_type": "code", "execution_count": 30, "id": "cf4ee5e6-4c6e-4ba5-a4db-6ca05caaa592", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Rates=P_rate
S=%{x}
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "PlotlyHelper.plot_pandas(df=df, x_var=\"S\", fields=[\"P_rate\", \"Michaelis_rate\"],\n", " title=\"EARLY DETAIL of Reaction rate, dP/dt, as a function of Substrate concentration\",\n", " y_label=\"dP/dt\", legend_header=\"Rates\",\n", " vertical_lines_to_add=19, colors=[\"blue\", \"yellow\"],\n", " range_x=[0, .2])" ] }, { "cell_type": "markdown", "id": "6e3f2c52-49ce-4e48-97ab-24c2274fa2cc", "metadata": {}, "source": [ "## In this scenario, the Michaelis-Menten model is remarkable accurate EXCEPT at the very early times of the reaction (the large values of `S`), which is the brief initial transient phase when `ES` builds up from zero. \n", "### Some discrepancy also at the end of the reaction (when `S` drops to zero)" ] }, { "cell_type": "markdown", "id": "291b603e-45fd-4cb9-a479-82ee4e4ba936", "metadata": {}, "source": [ "#### This is as expected, because the kinetic parameters of this reaction satisfy the key Michaelis-Menten assumptions that `[E] << [S]` , but NOT the other assumption that the rates satisfy `k1_reverse >> k2_forward`" ] }, { "cell_type": "code", "execution_count": null, "id": "413400e9-c049-4661-a1ec-d0e7bf3ef4ea", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "1c05908a-d2ac-43d7-8a74-b7ff62f66f1f", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "6db0551d-719f-43d7-93c5-eeba71814e4c", "metadata": { "tags": [] }, "source": [ "# PART 3. Comparing the results to the Morrison model" ] }, { "cell_type": "markdown", "id": "1271df18-1ef6-4907-a939-4605a9396a22", "metadata": {}, "source": [ "#### Following section 7.1 of _\"Analysis of Enzyme Reaction Kinetics, Vol. 1\", by F. Xavier Malcata, Wiley, 2023_, we'll test out an the alternative **Morrison** approach, which is expected to perform better than the **Michaelis-Menten** model when the Enzyme concentration isn't so small. But, in this scenario, we only have small amounts of enzyme - and we'll see below that no significant improvement is gained by switching model." ] }, { "cell_type": "code", "execution_count": 31, "id": "e6184d05-da5e-4539-b44f-5a15fcaa7a1b", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEPESESstepcaptionP_rateMichaelis_rateMorrison_rate
00.0000000.000000e+000.0000001.00000020.000000Set concentration0.0000000.5798790.579872
10.0000100.000000e+000.0320000.96800019.96800011st reaction step0.0185600.5798790.579872
20.0000212.041600e-070.0660190.93398119.93398120.0382910.5798780.579872
30.0000243.305201e-070.0758490.92415119.92415130.0439920.5798780.579872
40.0000253.740726e-070.0787660.92123419.92123440.0456840.5798780.579872
.................................
216239.0816901.997468e+010.0253070.9746930.000014198890.0146780.0020040.014624
216339.1957741.997630e+010.0236820.9763180.000014198990.0137360.0018730.013685
216439.4916781.998007e+010.0199170.9800830.000011199090.0115520.0015700.011510
216539.8364461.998373e+010.0162580.9837420.000010199190.0094300.0013170.009395
216639.9038681.998436e+010.0156340.9843660.000009199290.0090680.0012270.009034
\n", "

2167 rows × 10 columns

\n", "
" ], "text/plain": [ " SYSTEM TIME P ES E S step \\\n", "0 0.000000 0.000000e+00 0.000000 1.000000 20.000000 \n", "1 0.000010 0.000000e+00 0.032000 0.968000 19.968000 1 \n", "2 0.000021 2.041600e-07 0.066019 0.933981 19.933981 2 \n", "3 0.000024 3.305201e-07 0.075849 0.924151 19.924151 3 \n", "4 0.000025 3.740726e-07 0.078766 0.921234 19.921234 4 \n", "... ... ... ... ... ... ... \n", "2162 39.081690 1.997468e+01 0.025307 0.974693 0.000014 19889 \n", "2163 39.195774 1.997630e+01 0.023682 0.976318 0.000014 19899 \n", "2164 39.491678 1.998007e+01 0.019917 0.980083 0.000011 19909 \n", "2165 39.836446 1.998373e+01 0.016258 0.983742 0.000010 19919 \n", "2166 39.903868 1.998436e+01 0.015634 0.984366 0.000009 19929 \n", "\n", " caption P_rate Michaelis_rate Morrison_rate \n", "0 Set concentration 0.000000 0.579879 0.579872 \n", "1 1st reaction step 0.018560 0.579879 0.579872 \n", "2 0.038291 0.579878 0.579872 \n", "3 0.043992 0.579878 0.579872 \n", "4 0.045684 0.579878 0.579872 \n", "... ... ... ... ... \n", "2162 0.014678 0.002004 0.014624 \n", "2163 0.013736 0.001873 0.013685 \n", "2164 0.011552 0.001570 0.011510 \n", "2165 0.009430 0.001317 0.009395 \n", "2166 0.009068 0.001227 0.009034 \n", "\n", "[2167 rows x 10 columns]" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df[\"Morrison_rate\"] = rxn.compute_rate_morrison(E_tot=E0,\n", " S_tot=df[\"S\"] + df[\"ES\"])\n", "df" ] }, { "cell_type": "code", "execution_count": 32, "id": "2c115147-d5e1-4b9b-81ba-0080de480128", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Rates=P_rate
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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Detail at the very left\n", "PlotlyHelper.plot_pandas(df=df, x_var=\"S\", fields=[\"P_rate\", \"Michaelis_rate\", \"Morrison_rate\"],\n", " title=\"EARLY DETAIL of reaction rate, dP/dt, as a function of Substrate concentration\",\n", " y_label=\"dP/dt\", legend_header=\"Rates\",\n", " vertical_lines_to_add=19,\n", " colors=[\"blue\", \"yellow\", \"orange\"],\n", " range_x=[0, 0.02])" ] }, { "cell_type": "markdown", "id": "d09def65-ccfe-4a46-91a1-dda169d31809", "metadata": {}, "source": [ "# In this scenario, the Morrison model appears better than the Michaelis-Menten one at late reaction times (small `S`, close to zero) - and virtually identical elsewhere " ] }, { "cell_type": "code", "execution_count": null, "id": "ed18cfed-eafe-48a2-b757-ab053a29c20b", "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 }