{ "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": [ "
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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: 2 (at temp. 25 C)\n", "0: E + S <-> ES (kF = 160 / kR = 0.089 / delta_G = -18,578 / K = 1,797.8) | 1st order in all reactants & products\n", "1: ES <-> E + P (kF = 0.58 / kR = 0) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {\"E\" (violet), \"S\" (darkturquoise), \"P\" (green), \"ES\" (red)}\n" ] } ], "source": [ "# Reaction E + S <-> ES , with 1st-order kinetics, \n", "uc.add_reaction(reactants=[\"E\", \"S\"], products=\"ES\",\n", " forward_rate=160., reverse_rate=0.089) \n", "\n", "# Reaction ES <-> E + P , with 1st-order kinetics, ignoring the reverse reaction\n", "uc.add_reaction(reactants=\"ES\", products=[\"E\", \"P\"],\n", " forward_rate=0.58, reverse_rate=0) \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", "Set of chemicals involved in reactions: {'E', 'S', 'P', 'ES'}\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 0.00 min\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", "uc.single_compartment_react(duration=0.0015, initial_step=0.00001,\n", " snapshots={\"frequency\": 10})" ] }, { "cell_type": "code", "execution_count": 12, "id": "0198dd94-e55d-4ab4-9de8-087d508edf06", "metadata": {}, "outputs": [ { "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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Changes in concentration for `E + S <-> ES` and `ES <-> E + P` (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -9.818159556379533e-07, 0.001507087491904258 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.1111111111111112, 21.11111111111111 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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Changes in concentration for `E + S <-> ES` and `ES <-> E + P`" }, "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": "code", "execution_count": null, "id": "38fe5851-e292-4093-a1ee-dbd77abd566c", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "ec2e2ac9-02f8-455a-8bd3-1170408a4ece", "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": 14, "id": "aba2c3cd-95ec-4174-9750-603ab130a6f7", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "... running : currently at System Time 21.73 (doing step size 0.00024) after running for 0.5 min\n", "110938 total variable step(s) taken in 0.57 min\n", "Number of step re-do's because of negative concentrations: 4571\n", "Number of step re-do's because of elective soft aborts: 6\n", "Norm usage: {'norm_A': 110781, 'norm_B': 110800, 'norm_C': 110781, 'norm_D': 110781}\n", "System Time is now: 40.002\n" ] } ], "source": [ "# Continue the reactions\n", "uc.single_compartment_react(duration=40., initial_step=0.00001, \n", " snapshots={\"frequency\": 10})" ] }, { "cell_type": "code", "execution_count": 15, "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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Changes in concentration for `E + S <-> ES` and `ES <-> E + P`" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ 0, 40.00249087452776 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "domain": [ 0, 1 ], "range": [ 0, 1.5 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "text/html": [ "
" ] }, "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**" ] }, { "cell_type": "code", "execution_count": 17, "id": "18517784-55eb-420c-87a1-bfaee226cc28", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMErxn0_raterxn1_rate
00.0000003200.0000000.000000
10.0000312878.6934690.055717
20.0000412785.3321150.072003
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............
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1110939.685826-0.0000160.010300
1111039.7234300.0000060.010077
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11112 rows × 3 columns

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" ], "text/plain": [ " SYSTEM TIME rxn0_rate rxn1_rate\n", "0 0.000000 3200.000000 0.000000\n", "1 0.000031 2878.693469 0.055717\n", "2 0.000041 2785.332115 0.072003\n", "3 0.000052 2688.859254 0.088879\n", "4 0.000066 2566.953047 0.110271\n", "... ... ... ...\n", "11107 39.665738 -0.000750 0.010423\n", "11108 39.671328 -0.000294 0.010388\n", "11109 39.685826 -0.000016 0.010300\n", "11110 39.723430 0.000006 0.010077\n", "11111 39.820965 0.000005 0.009522\n", "\n", "[11112 rows x 3 columns]" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rates = uc.get_rate_history()\n", "rates" ] }, { "cell_type": "code", "execution_count": 18, "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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"automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 } } }, "title": { "text": "Reaction rate, dP/dt, over time (DETAIL at early times)" }, "xaxis": { "anchor": "y", "domain": [ 0, 1 ], "range": [ 0, 0.0015 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.03221513145797702, 0.6120874977015633 ], "title": { "text": "Y" }, "type": "linear" } } }, "text/html": [ "
" ] }, "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=\"rxn1_rate\", \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": [ "# 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": 20, "id": "37e52d32-9204-4873-a5f1-134368682ab9", "metadata": {}, "outputs": [], "source": [ "reactions = uc.get_reactions()" ] }, { "cell_type": "code", "execution_count": 21, "id": "1411f8f6-ab1b-4ef0-97ef-3395058dafc1", "metadata": {}, "outputs": [], "source": [ "rxn = ReactionEnz(enzyme=\"E\", substrate=\"S\", product=\"P\",\n", " k1_F=reactions.get_forward_rate(0), k1_R=reactions.get_reverse_rate(0), \n", " k2_F=reactions.get_forward_rate(1))" ] }, { "cell_type": "code", "execution_count": 22, "id": "e279ef7d-61ca-469f-8418-60ad0b1222e0", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.004181249999999999" ] }, "execution_count": 22, "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": 23, "id": "5b073f95-a8ed-4885-8b88-85a04341ecee", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.58" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rxn.kcat" ] }, { "cell_type": "code", "execution_count": 24, "id": "355a083f-d492-4cbb-a5c1-f961236257ad", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.58" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vmax = rxn.compute_vmax(E_tot=E0) # kcat * E0\n", "vmax" ] }, { "cell_type": "code", "execution_count": 25, "id": "09dfe215-e89d-4562-8a54-72973c6d2b2c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.5798787690948362" ] }, "execution_count": 25, "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": 26, "id": "c3f85515-6bfc-4b7c-a201-8488b0a65149", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEPESEScaptionP_rate
00.0000000.000000e+000.0000001.00000020.000000Set concentration0.000000
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........................
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" ], "text/plain": [ " SYSTEM TIME P ES E S \\\n", "0 0.000000 0.000000e+00 0.000000 1.000000 20.000000 \n", "1 0.000031 6.703630e-07 0.096064 0.903936 19.903936 \n", "2 0.000041 1.294956e-06 0.124144 0.875856 19.875855 \n", "3 0.000052 2.140174e-06 0.153239 0.846761 19.846759 \n", "4 0.000066 3.520858e-06 0.190123 0.809877 19.809874 \n", "... ... ... ... ... ... \n", "11107 39.665738 1.998202e+01 0.017971 0.982029 0.000005 \n", "11108 39.671328 1.998208e+01 0.017910 0.982090 0.000008 \n", "11109 39.685826 1.998223e+01 0.017758 0.982242 0.000010 \n", "11110 39.723430 1.998262e+01 0.017375 0.982625 0.000010 \n", "11111 39.820965 1.998357e+01 0.016417 0.983583 0.000009 \n", "\n", " caption P_rate \n", "0 Set concentration 0.000000 \n", "1 0.055717 \n", "2 0.072003 \n", "3 0.088879 \n", "4 0.110271 \n", "... ... ... \n", "11107 0.010423 \n", "11108 0.010388 \n", "11109 0.010300 \n", "11110 0.010077 \n", "11111 0.009522 \n", "\n", "[11112 rows x 7 columns]" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = uc.add_rate_to_conc_history(rate_name=\"rxn1_rate\", new_rate_name=\"P_rate\")\n", "df" ] }, { "cell_type": "code", "execution_count": 27, "id": "0769aa93-8040-4ae0-b258-9c4e0a379cbd", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEPESEScaptionP_rateMichaelis_rate
00.0000000.000000e+000.0000001.00000020.000000Set concentration0.0000000.579879
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" ], "text/plain": [ " SYSTEM TIME P ES E S \\\n", "0 0.000000 0.000000e+00 0.000000 1.000000 20.000000 \n", "1 0.000031 6.703630e-07 0.096064 0.903936 19.903936 \n", "2 0.000041 1.294956e-06 0.124144 0.875856 19.875855 \n", "3 0.000052 2.140174e-06 0.153239 0.846761 19.846759 \n", "4 0.000066 3.520858e-06 0.190123 0.809877 19.809874 \n", "... ... ... ... ... ... \n", "11107 39.665738 1.998202e+01 0.017971 0.982029 0.000005 \n", "11108 39.671328 1.998208e+01 0.017910 0.982090 0.000008 \n", "11109 39.685826 1.998223e+01 0.017758 0.982242 0.000010 \n", "11110 39.723430 1.998262e+01 0.017375 0.982625 0.000010 \n", "11111 39.820965 1.998357e+01 0.016417 0.983583 0.000009 \n", "\n", " caption P_rate Michaelis_rate \n", "0 Set concentration 0.000000 0.579879 \n", "1 0.055717 0.579878 \n", "2 0.072003 0.579878 \n", "3 0.088879 0.579878 \n", "4 0.110271 0.579878 \n", "... ... ... ... \n", "11107 0.010423 0.000749 \n", "11108 0.010388 0.001145 \n", "11109 0.010300 0.001378 \n", "11110 0.010077 0.001366 \n", "11111 0.009522 0.001290 \n", "\n", "[11112 rows x 8 columns]" ] }, "execution_count": 27, "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": 28, "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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1 ], "range": [ 5.406403134120343e-06, 20 ], "title": { "text": "S" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.03221548717193534, 0.6120942562667715 ], "title": { "text": "dP/dt" }, "type": "linear" } } }, "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": 29, "id": "cf4ee5e6-4c6e-4ba5-a4db-6ca05caaa592", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Rates=P_rate
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], "range": [ 0, 0.2 ], "title": { "text": "S" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.03221548717193534, 0.6120942562667715 ], "title": { "text": "dP/dt" }, "type": "linear" } } }, "text/html": [ "
" ] }, "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": [ "# 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": 30, "id": "e6184d05-da5e-4539-b44f-5a15fcaa7a1b", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEPESEScaptionP_rateMichaelis_rateMorrison_rate
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" ], "text/plain": [ " SYSTEM TIME P ES E S \\\n", "0 0.000000 0.000000e+00 0.000000 1.000000 20.000000 \n", "1 0.000031 6.703630e-07 0.096064 0.903936 19.903936 \n", "2 0.000041 1.294956e-06 0.124144 0.875856 19.875855 \n", "3 0.000052 2.140174e-06 0.153239 0.846761 19.846759 \n", "4 0.000066 3.520858e-06 0.190123 0.809877 19.809874 \n", "... ... ... ... ... ... \n", "11107 39.665738 1.998202e+01 0.017971 0.982029 0.000005 \n", "11108 39.671328 1.998208e+01 0.017910 0.982090 0.000008 \n", "11109 39.685826 1.998223e+01 0.017758 0.982242 0.000010 \n", "11110 39.723430 1.998262e+01 0.017375 0.982625 0.000010 \n", "11111 39.820965 1.998357e+01 0.016417 0.983583 0.000009 \n", "\n", " caption P_rate Michaelis_rate Morrison_rate \n", "0 Set concentration 0.000000 0.579879 0.579872 \n", "1 0.055717 0.579878 0.579872 \n", "2 0.072003 0.579878 0.579872 \n", "3 0.088879 0.579878 0.579872 \n", "4 0.110271 0.579878 0.579872 \n", "... ... ... ... ... \n", "11107 0.010423 0.000749 0.010382 \n", "11108 0.010388 0.001145 0.010349 \n", "11109 0.010300 0.001378 0.010262 \n", "11110 0.010077 0.001366 0.010040 \n", "11111 0.009522 0.001290 0.009487 \n", "\n", "[11112 rows x 9 columns]" ] }, "execution_count": 30, "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": 31, "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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" ] }, "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": "9f8c79ce-5a1f-41f1-8a6c-09a1a0eeca64", "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 }