{ "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", "#### Same as experiment `enzyme_1_a` but with _much-larger amounts of Enzyme_ relative to the initial Substrate concentration.\n", "\n", "#### Two Coupled Reactions: `E + S <-> ES`, and `ES -> E + P` , using 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 = \"Nov. 4, 2024\"\n", "LIFE123_VERSION = \"1.0.0.rc.0\" # 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": "ac9eea69-174c-43e5-9eed-443cbc5e2ba7", "metadata": {}, "outputs": [], "source": [ "chem_data = ChemData(names=[\"P\", \"ES\"])" ] }, { "cell_type": "code", "execution_count": 6, "id": "90f9ec41-6e1b-4558-9400-47e35ece6efc", "metadata": {}, "outputs": [], "source": [ "# Our Enzyme\n", "chem_data.add_chemical(name=\"Adenosine deaminase\", label=\"E\") \n", "\n", "# Our Substrate\n", "chem_data.add_chemical(name=\"2,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purine\", label=\"S\");" ] }, { "cell_type": "code", "execution_count": 7, "id": "0f9c3501-0b99-47d9-87fa-3a027ede3799", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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namelabel
0PP
1ESES
2Adenosine deaminaseE
32,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purineS
\n", "
" ], "text/plain": [ " name label\n", "0 P P\n", "1 ES ES\n", "2 Adenosine deaminase E\n", "3 2,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purine S" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "chem_data.all_chemicals()" ] }, { "cell_type": "markdown", "id": "f8d4ea7f-0591-467c-9df3-d95f53df75f5", "metadata": {}, "source": [ "### Specify the Kinetic Parameters \n", "This part is identical to experiment `enzyme_1`" ] }, { "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": "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 = 18 / kR = 100 / delta_G = 4,250.9 / K = 0.18) | 1st order in all reactants & products\n", "1: ES <-> E + P (kF = 49 / kR = 0) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {'P', 'E', 'ES', 'S'}\n" ] } ], "source": [ "# Reaction E + S <-> ES , with 1st-order kinetics, \n", "chem_data.add_reaction(reactants=[\"E\", \"S\"], products=[\"ES\"],\n", " forward_rate=18., reverse_rate=100.) \n", "\n", "# Reaction ES <-> E + P , with 1st-order kinetics, ignoring the reverse reaction\n", "chem_data.add_reaction(reactants=[\"ES\"], products=[\"E\", \"P\"],\n", " forward_rate=49., reverse_rate=0) # We are ignoring the reverse reaction\n", "\n", "chem_data.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", "### Unlike in experiment `enzyme_1`, there's *substantially more enzyme* relative to initial substrate concentration" ] }, { "cell_type": "code", "execution_count": 9, "id": "8c9e3f86-b9a5-41da-9e1b-75258017808a", "metadata": {}, "outputs": [], "source": [ "S0 = 20.\n", "E0 = 10. # 10 times more than in experiment `enzyme_1` ; almost as much enzyme as substrate!" ] }, { "cell_type": "code", "execution_count": 10, "id": "aae96512-3d86-4ab0-b167-92943523b7ef", "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: 10.0\n", " Species 3 (S). Conc: 20.0\n", "Set of chemicals involved in reactions: {'P', 'E', 'ES', 'S'}\n" ] } ], "source": [ "# Here we use the \"slower\" preset for the variable steps, a conservative option prioritizing accuracy over speed\n", "uc = UniformCompartment(chem_data=chem_data, preset=\"slower\")\n", "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": 11, "id": "8adf7167-0a21-4a32-9e6c-220aa6b82da6", "metadata": {}, "outputs": [], "source": [ "uc.enable_diagnostics() # To save diagnostic information about the simulation - in particular, the REACTION RATES" ] }, { "cell_type": "markdown", "id": "ef2c10f2-ec7f-497a-bdbf-4fea30ba31a1", "metadata": { "tags": [] }, "source": [ "#### Advance the reactions to equilibrium" ] }, { "cell_type": "code", "execution_count": 12, "id": "e6ad72b8-722a-4606-a611-7dc600529f30", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Some steps were backtracked and re-done, to prevent negative concentrations or overly large concentration changes\n", "615 total step(s) taken\n", "Number of step re-do's because of negative concentrations: 2\n", "Number of step re-do's because of elective soft aborts: 1\n", "Norm usage: {'norm_A': 513, 'norm_B': 516, 'norm_C': 512, 'norm_D': 512}\n" ] } ], "source": [ "# Perform the reactions\n", "uc.single_compartment_react(duration=0.2, initial_step=0.05) # A much-shorter duration than the 1.5 of experiment `enzyme_1`" ] }, { "cell_type": "code", "execution_count": 13, "id": "0198dd94-e55d-4ab4-9de8-087d508edf06", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_pandas() NOTICE: Excessive number of vertical lines (616) - only showing 1 every 5 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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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": [ -0.00016028054974472823, 0.2008315288301445 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.1111111111111112, 21.11111111111111 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "uc.plot_history(colors=['green', 'red', 'violet', 'darkturquoise'], show_intervals=True, \n", " title_prefix=\"Almost as much E as S(0)\")" ] }, { "cell_type": "markdown", "id": "ba28bbea-b725-4e1a-9c64-7dbad40cf2c8", "metadata": {}, "source": [ "The general shapes of the various curves is reminiscent of their counterparts in experiment `enzyme_1`, but notice: \n", "\n", "1. The product `P` is being produced on a much-faster timescale than before\n", "2. The maximum amount of the bound enzyme `ES` is no longer puny; in fact, it's a good fraction of the initial [S]\n", "3. The buildup of `ES`, at the very beginning, no longer looks instantaneous relatively to the main reaction: by the time `ES` reaches its maximum value, a non-trivial amount of product `P` has been produced\n", "\n", "In short, the \"transient\" is not so \"transient\"!" ] }, { "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": {}, "source": [ "### What is the rate of production of the final reaction product `P`? " ] }, { "cell_type": "code", "execution_count": 14, "id": "21d7d644-779b-4ffa-82cd-25d50cdd5300", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Reaction: ES <-> E + P\n" ] }, { "data": { "text/html": [ "
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" ], "text/plain": [ " TIME P ES E S caption rate\n", "0 0.000000 0.000000 0.000000 10.000000 20.000000 0.000000\n", "1 0.000500 0.000000 1.800000 8.200000 18.200000 88.200000\n", "2 0.000750 0.022050 2.404530 7.595470 17.573420 117.821970\n", "3 0.000763 0.023523 2.430084 7.569916 17.546393 119.074126\n", "4 0.000769 0.024267 2.442764 7.557236 17.532969 119.695434\n", ".. ... ... ... ... ... ... ...\n", "610 0.195573 19.863565 0.081649 9.918351 0.054786 4.000798\n", "611 0.196593 19.867645 0.079217 9.920783 0.053138 3.881655\n", "612 0.197612 19.871602 0.076858 9.923142 0.051540 3.766032\n", "613 0.198632 19.875442 0.074568 9.925432 0.049990 3.653827\n", "614 0.199652 19.879167 0.072346 9.927654 0.048487 3.544941\n", "\n", "[615 rows x 7 columns]" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rates = uc.get_diagnostics().get_system_history_with_rxn_rates(rxn_index=1) # We specify the reaction that involves `P`\n", "rates" ] }, { "cell_type": "code", "execution_count": 15, "id": "18ac9b9f-c669-43f6-ac36-ed95b76e1ae5", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "TIME=%{x}
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0, 0.19965166338253335 ], "title": { "text": "time" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -16.152449080846004, 306.8965325360741 ], "title": { "text": "dP/dt" }, "type": "linear" } } }, "text/html": [ "
" ] }, "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=\"TIME\", fields=\"rate\", \n", " x_label=\"time\", y_label=\"dP/dt\")" ] }, { "cell_type": "markdown", "id": "bfacc983-b8af-467d-87b2-2fee868d8254", "metadata": {}, "source": [ "**The initial transient phase is no longer miniscule in duration**" ] }, { "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": 16, "id": "251dfcc1-0cc2-4bad-af3a-afa2feed4e4c", "metadata": {}, "outputs": [], "source": [ "rxn = ReactionEnz(enzyme=\"E\", substrate=\"S\", product=\"P\",\n", " k1_F=chem_data.get_forward_rate(0), k1_R=chem_data.get_reverse_rate(0), \n", " k2_F=chem_data.get_forward_rate(1))" ] }, { "cell_type": "code", "execution_count": 17, "id": "e279ef7d-61ca-469f-8418-60ad0b1222e0", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "8.277777777777779" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rxn.kM # For the data in this experiment, it comes out to (49. + 100.) / 18." ] }, { "cell_type": "code", "execution_count": 18, "id": "5b073f95-a8ed-4885-8b88-85a04341ecee", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "49.0" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rxn.kcat" ] }, { "cell_type": "code", "execution_count": 19, "id": "355a083f-d492-4cbb-a5c1-f961236257ad", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "490.0" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vmax = rxn.compute_vmax(E_tot=E0) # kcat * E0\n", "vmax" ] }, { "cell_type": "code", "execution_count": 20, "id": "09dfe215-e89d-4562-8a54-72973c6d2b2c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "346.56188605108053" ] }, "execution_count": 20, "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": [ "#### Both `vmax` and the initial reaction rate are 10x what they were in experiment `enzyme_1`, because we started with an `E0` 10 times as large" ] }, { "cell_type": "code", "execution_count": null, "id": "1d9b8b04-e789-477e-be6a-d180d6f23eaf", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "2f8ba6c4-1d82-450d-86b6-0e96d695632a", "metadata": {}, "source": [ "### Now, let's look at rate as a function of [S]; we'll compare what we computed earlier vs. as given by the approximation of the Michaelis-Menten model" ] }, { "cell_type": "code", "execution_count": 21, "id": "ff21ba16-795a-40ba-b6e6-6e33dbeda25a", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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TIMEPESEScaptionrateMichaelis_rate
00.0000000.0000000.00000010.00000020.0000000.000000346.561886
10.0005000.0000001.8000008.20000018.20000088.200000336.810743
20.0007500.0220502.4045307.59547017.573420117.821970333.097749
30.0007630.0235232.4300847.56991617.546393119.074126332.933539
40.0007690.0242672.4427647.55723617.532969119.695434332.851850
...........................
6100.19557319.8635650.0816499.9183510.0547864.0007983.221698
6110.19659319.8676450.0792179.9207830.0531383.8816553.125424
6120.19761219.8716020.0768589.9231420.0515403.7660323.032014
6130.19863219.8754420.0745689.9254320.0499903.6538272.941384
6140.19965219.8791670.0723469.9276540.0484873.5449412.853451
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615 rows × 8 columns

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" ], "text/plain": [ " TIME P ES E S caption rate \\\n", "0 0.000000 0.000000 0.000000 10.000000 20.000000 0.000000 \n", "1 0.000500 0.000000 1.800000 8.200000 18.200000 88.200000 \n", "2 0.000750 0.022050 2.404530 7.595470 17.573420 117.821970 \n", "3 0.000763 0.023523 2.430084 7.569916 17.546393 119.074126 \n", "4 0.000769 0.024267 2.442764 7.557236 17.532969 119.695434 \n", ".. ... ... ... ... ... ... ... \n", "610 0.195573 19.863565 0.081649 9.918351 0.054786 4.000798 \n", "611 0.196593 19.867645 0.079217 9.920783 0.053138 3.881655 \n", "612 0.197612 19.871602 0.076858 9.923142 0.051540 3.766032 \n", "613 0.198632 19.875442 0.074568 9.925432 0.049990 3.653827 \n", "614 0.199652 19.879167 0.072346 9.927654 0.048487 3.544941 \n", "\n", " Michaelis_rate \n", "0 346.561886 \n", "1 336.810743 \n", "2 333.097749 \n", "3 332.933539 \n", "4 332.851850 \n", ".. ... \n", "610 3.221698 \n", "611 3.125424 \n", "612 3.032014 \n", "613 2.941384 \n", "614 2.853451 \n", "\n", "[615 rows x 8 columns]" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's add a column with the rate estimated by the Michaelis-Menten model\n", "rates[\"Michaelis_rate\"] = rxn.compute_rate(S_conc=rates[\"S\"])\n", "rates" ] }, { "cell_type": "code", "execution_count": 22, "id": "6e8cdb8c-0e8e-461f-81a0-f7b75de1d322", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Rates=rate
S=%{x}
dP/dt=%{y}", "legendgroup": "rate", "line": { "color": "blue", "dash": "solid" }, "marker": { "symbol": "circle" }, "mode": "lines", "name": "rate", "showlegend": true, "type": "scattergl", "x": [ 20, 18.2, 17.57342, 17.546393026008335, 17.532969047879124, 17.519589436987665, 17.506253992122957, 17.492962513211893, 17.479582324192286, 17.466113222470067, 17.452555012189844, 17.43890750436671, 17.4251705170185, 17.411343875298492, 17.39742741162847, 17.383420965832144, 17.369324385268854, 17.35513752496752, 17.340860247760794, 17.326492424419357, 17.312033933786307, 17.297484662911593, 17.282844507186454, 17.268113370477753, 17.253291165262237, 17.238377812760564, 17.223373243071133, 17.208277395303572, 17.19309021771188, 17.17781166782714, 17.162441712589715, 17.146980328480893, 17.131427501653892, 17.115783228064167, 17.100047513598923, 17.08422037420579, 17.068301836020563, 17.05229193549396, 17.036190719517258, 17.019998245546798, 17.00371458172725, 16.987339807013527, 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" ] }, "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=rates, x_var=\"S\", fields=[\"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=12.1,\n", " colors=[\"blue\", \"yellow\"])" ] }, { "cell_type": "markdown", "id": "3d6b91c7-dc26-4a04-8a27-4d1b10f4d96e", "metadata": {}, "source": [ "Let's recall that our reactions started out with [S]=20 \n", "The curve overlap is still passable at later times (left part of graph, when [S] drops below about 12), but is rather bad at earlier times (when [S] > 12) \n", "**We no longer have the striking overlap we had in experiment `enzyme_1`**" ] }, { "cell_type": "markdown", "id": "6e3f2c52-49ce-4e48-97ab-24c2274fa2cc", "metadata": {}, "source": [ "## In this scenario, with a lot more initial enzyme `E` than in experiment `enzyme_1`, the Michaelis-Menten model suffers from poor accuracy for an non-trivial early time, because the transient early phase (when `ES` builds up from zero) is no longer very brief" ] }, { "cell_type": "markdown", "id": "291b603e-45fd-4cb9-a479-82ee4e4ba936", "metadata": {}, "source": [ "#### This is as expected, because we substantially deviated from the Michaelis-Menten assumptions that `[E] << [S]`" ] }, { "cell_type": "code", "execution_count": null, "id": "2245bc83-14ec-4dac-ab1e-9be2333f8681", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "bab5822d-adb1-465e-8f2b-7792e712bb18", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "d15a9824-b994-4165-8e41-6b28ac39c1fd", "metadata": { "tags": [] }, "source": [ "# 3. Comparing the results to the Morrison model" ] }, { "cell_type": "markdown", "id": "632dbff5-e5fb-421b-8891-6e1c5e6baded", "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" ] }, { "cell_type": "code", "execution_count": 23, "id": "d889a598-82b6-49ea-9cba-b0e8e9997c5c", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " TIME P ES E S caption rate \\\n", "0 0.000000 0.000000 0.000000 10.000000 20.000000 0.000000 \n", "1 0.000500 0.000000 1.800000 8.200000 18.200000 88.200000 \n", "2 0.000750 0.022050 2.404530 7.595470 17.573420 117.821970 \n", "3 0.000763 0.023523 2.430084 7.569916 17.546393 119.074126 \n", "4 0.000769 0.024267 2.442764 7.557236 17.532969 119.695434 \n", ".. ... ... ... ... ... ... ... \n", "610 0.195573 19.863565 0.081649 9.918351 0.054786 4.000798 \n", "611 0.196593 19.867645 0.079217 9.920783 0.053138 3.881655 \n", "612 0.197612 19.871602 0.076858 9.923142 0.051540 3.766032 \n", "613 0.198632 19.875442 0.074568 9.925432 0.049990 3.653827 \n", "614 0.199652 19.879167 0.072346 9.927654 0.048487 3.544941 \n", "\n", " Michaelis_rate Morrison_rate \n", "0 346.561886 305.920075 \n", "1 336.810743 305.920075 \n", "2 333.097749 305.762583 \n", "3 332.933539 305.752055 \n", "4 332.851850 305.746735 \n", ".. ... ... \n", "610 3.221698 3.645236 \n", "611 3.125424 3.536609 \n", "612 3.032014 3.431196 \n", "613 2.941384 3.328903 \n", "614 2.853451 3.229639 \n", "\n", "[615 rows x 9 columns]" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rates[\"Morrison_rate\"] = rxn.compute_rate_morrison(E_tot=E0,\n", " S_tot=rates[\"S\"] + rates[\"ES\"])\n", "rates" ] }, { "cell_type": "code", "execution_count": 24, "id": "773188b3-f2e5-4fd0-ac47-d79f65fe13b4", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Rates=rate
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "PlotlyHelper.plot_pandas(df=rates, x_var=\"S\", fields=[\"rate\", \"Michaelis_rate\", \"Morrison_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=12.1,\n", " colors=[\"blue\", \"yellow\", \"orange\"])" ] }, { "cell_type": "markdown", "id": "7d724ebe-6828-4f55-8fa8-2f5ef04c4090", "metadata": {}, "source": [ "## The Morrison model appears to be only mildly better than the Michaelis-Menten one in this scenario... \n", "In the next experiment, `enzyme_3`, we'll see how the Morrison model is the absolute winner when the amount of enzyme is even larger" ] }, { "cell_type": "code", "execution_count": null, "id": "3f002b91-ddce-4486-869a-353dc81a5698", "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 }