{ "cells": [ { "cell_type": "markdown", "id": "5cbc8640", "metadata": {}, "source": [ "## Enzyme Kinetics : accurate numerical solution compared to the Michaelis-Menten model approximation\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", "Two other reactions being assumed negligible, and not included, are : \n", "1) the reverse direction of the 2nd reaction \n", "2) the non-catalyzed E + S <-> P reaction" ] }, { "cell_type": "markdown", "id": "604b150b-7812-4fd3-9403-69a06dd7e397", "metadata": {}, "source": [ "The reaction of the enzyme `Adenosinedeaminase` with the substrate `2,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purine`, \n", "and the initial concentration values choosen below, all satisfy the customary Michaelis-Menten assumptions that \n", "`[E] << [S]` and that the reaction rate constants satisfy `k1_reverse >> k2_forward`\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 = \"Oct. 11, 2024\"\n", "LIFE123_VERSION = \"1.0.0.beta.39\" # 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, GraphicLog, 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": 5, "id": "121fdfdd", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-> Output will be LOGGED into the file 'enzyme_1.log.htm'\n" ] } ], "source": [ "# Initialize the HTML logging (for the graphics)\n", "log_file = ipynbname.name() + \".log.htm\" # Use the notebook base filename for the log file\n", " # IN CASE OF PROBLEMS, set manually to any desired name\n", "\n", "# Set up the use of some specified graphic (Vue) components\n", "GraphicLog.config(filename=log_file,\n", " components=[\"vue_cytoscape_2\"],\n", " extra_js=\"https://cdnjs.cloudflare.com/ajax/libs/cytoscape/3.21.2/cytoscape.umd.js\")" ] }, { "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": 6, "id": "ac9eea69-174c-43e5-9eed-443cbc5e2ba7", "metadata": {}, "outputs": [], "source": [ "chem_data = ChemData(names=[\"P\", \"ES*\"])" ] }, { "cell_type": "code", "execution_count": 7, "id": "90f9ec41-6e1b-4558-9400-47e35ece6efc", "metadata": {}, "outputs": [], "source": [ "# Our Enzyme\n", "chem_data.add_chemical(name=\"Adenosinedeaminase\", 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": 8, "id": "0f9c3501-0b99-47d9-87fa-3a027ede3799", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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namelabel
0PP
1ES*ES*
2AdenosinedeaminaseE
32,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purineS
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" ], "text/plain": [ " name label\n", "0 P P\n", "1 ES* ES*\n", "2 Adenosinedeaminase E\n", "3 2,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purine S" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "chem_data.all_chemicals()" ] }, { "cell_type": "code", "execution_count": null, "id": "dbb1c0b9-33c2-485d-b74b-747ef10eb2cb", "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": "code", "execution_count": 9, "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: {'E', 'P', 'ES*', 'S'}\n" ] } ], "source": [ "# Reaction E + S <-> ES* , with 1st-order kinetics, \n", "# and a forward rate that is much faster than its revers one\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\n", "chem_data.add_reaction(reactants=[\"ES*\"], products=[\"E\", \"P\"],\n", " forward_rate=49.,reverse_rate=0)\n", "\n", "chem_data.describe_reactions()" ] }, { "cell_type": "code", "execution_count": 10, "id": "373afeb1", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[GRAPHIC ELEMENT SENT TO LOG FILE `enzyme_1.log.htm`]\n" ] } ], "source": [ "# Send a plot of the network of reactions to the HTML log file\n", "chem_data.plot_reaction_network(\"vue_cytoscape_2\")" ] }, { "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" ] }, { "cell_type": "code", "execution_count": 11, "id": "8c9e3f86-b9a5-41da-9e1b-75258017808a", "metadata": {}, "outputs": [], "source": [ "S0 = 20.\n", "E0 = 1." ] }, { "cell_type": "code", "execution_count": 12, "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: 1.0\n", " Species 3 (S). Conc: 20.0\n", "Set of chemicals involved in reactions: {'E', 'P', '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": 13, "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": 14, "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 excessively large concentration changes\n", "827 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': 706, 'norm_B': 710, 'norm_C': 706, 'norm_D': 706}\n" ] } ], "source": [ "# Perform the reactions\n", "uc.single_compartment_react(duration=1.5, initial_step=0.05)" ] }, { "cell_type": "code", "execution_count": 15, "id": "0198dd94-e55d-4ab4-9de8-087d508edf06", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_pandas() NOTICE: Excessive number of vertical lines (828) - only showing 1 every 6 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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"landcolor": "#E5ECF6", "showlakes": true, "showland": true, "subunitcolor": "white" }, "hoverlabel": { "align": "left" }, "hovermode": "closest", "mapbox": { "style": "light" }, "paper_bgcolor": "white", "plot_bgcolor": "#E5ECF6", "polar": { "angularaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "bgcolor": "#E5ECF6", "radialaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" } }, "scene": { "xaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" }, "yaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" }, "zaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" } }, "shapedefaults": { "line": { "color": "#2a3f5f" } }, "ternary": { "aaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "baxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "bgcolor": "#E5ECF6", "caxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" } }, "title": { "x": 0.05 }, "xaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 }, "yaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 } } }, "title": { "text": "Small amout of E relative to S(0)
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": [ -0.0025708381913540023, 1.5039403419420914 ], "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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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "uc.plot_history(colors=['cyan', 'green', 'violet', 'red'], title_prefix=\"DETAIL at early times\",\n", " range_x=[0, 0.5], range_y=[0, 2.])" ] }, { "cell_type": "markdown", "id": "ba28bbea-b725-4e1a-9c64-7dbad40cf2c8", "metadata": {}, "source": [ "Notice how the bound enzyme `ES*` 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": {}, "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 alongside other diagnostic data**, if diagnostics were enabled (as we did indeed enable)" ] }, { "cell_type": "code", "execution_count": 17, "id": "01539263-0983-40fe-a823-e4eb21bba34b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Reaction: ES* <-> E + P\n" ] }, { "data": { "text/html": [ "
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" ], "text/plain": [ " START_TIME rate\n", "0 0.000000 0.000000\n", "1 0.000500 8.820000\n", "2 0.000750 12.075109\n", "3 0.000763 12.216716\n", "4 0.000769 12.287060\n", ".. ... ...\n", "822 1.468805 0.285397\n", "823 1.475832 0.274566\n", "824 1.482859 0.264142\n", "825 1.489886 0.254109\n", "826 1.496913 0.244454\n", "\n", "[827 rows x 2 columns]" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rates = uc.get_diagnostics().get_rxn_rates(rxn_index=1) # We specify the reaction that involves `P`\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": "START_TIME=%{x}
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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=\"START_TIME\", fields=\"rate\", \n", " x_label=\"time\", y_label=\"dP/dt\")" ] }, { "cell_type": "code", "execution_count": 19, "id": "9c534460-2958-454a-a2bf-2bf359d460b3", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "START_TIME=%{x}
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# A closer peek at it maximum value\n", "PlotlyHelper.plot_pandas(df=rates, \n", " title=\"Reaction rate, dP/dt, over time (DETAIL at early times)\",\n", " x_var=\"START_TIME\", fields=\"rate\", \n", " x_label=\"time\", y_label=\"dP/dt\",\n", " range_x=[0,0.05], range_y=[33., 34.5])" ] }, { "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 0.01 \n", "**Ignoring the brief initial transient phase, the reaction rate starts at about 34.1**" ] }, { "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": "223ad0ad-664e-4274-b3f1-a08521875df1", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "8.277777777777779" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "kM = (chem_data.get_forward_rate(1) + chem_data.get_reverse_rate(0)) / chem_data.get_forward_rate(0)\n", "kM # (49. + 100.) / 18. in this experiment" ] }, { "cell_type": "code", "execution_count": 21, "id": "9897b2d8-c5bf-4367-b93b-98a1a5d464a1", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "49.0" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "kcat = chem_data.get_forward_rate(1)\n", "kcat" ] }, { "cell_type": "code", "execution_count": 22, "id": "355a083f-d492-4cbb-a5c1-f961236257ad", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "49.0" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vmax = kcat * E0\n", "vmax" ] }, { "cell_type": "code", "execution_count": 23, "id": "1076e140-3da9-45a5-81af-709bac770f76", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "34.656188605108056" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "initial_rxn_rate = (vmax * S0) / (kM + S0)\n", "initial_rxn_rate" ] }, { "cell_type": "markdown", "id": "fbc8da21-6dbf-4957-a4f6-437b50de003f", "metadata": {}, "source": [ "Not too far from the value of about 34.1 we saw earlier... \n", "To keep in mind that the initial part of the reaction is affected by transients" ] }, { "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": null, "id": "3e876bed-51c8-47c3-b18e-ecb4dab5ebbb", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 24, "id": "7ab9965d-d18c-4930-9836-b36e7108cff5", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEPES*EScaption
00.0000000.0000000.0000001.00000020.000000Initialized state
10.0005000.0000000.1800000.82000019.8200001st reaction step
20.0007500.0022050.2464310.75356919.751364
30.0007630.0023560.2493210.75067919.748323
40.0007690.0024320.2507560.74924419.746811
.....................
8221.46880519.9474370.0058240.9941760.046738
8231.47583219.9494430.0056030.9943970.044954
8241.48285919.9513720.0053910.9946090.043237
8251.48988619.9532280.0051860.9948140.041586
8261.49691319.9550140.0049890.9950110.039997
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827 rows × 6 columns

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" ], "text/plain": [ " SYSTEM TIME P ES* E S caption\n", "0 0.000000 0.000000 0.000000 1.000000 20.000000 Initialized state\n", "1 0.000500 0.000000 0.180000 0.820000 19.820000 1st reaction step\n", "2 0.000750 0.002205 0.246431 0.753569 19.751364 \n", "3 0.000763 0.002356 0.249321 0.750679 19.748323 \n", "4 0.000769 0.002432 0.250756 0.749244 19.746811 \n", ".. ... ... ... ... ... ...\n", "822 1.468805 19.947437 0.005824 0.994176 0.046738 \n", "823 1.475832 19.949443 0.005603 0.994397 0.044954 \n", "824 1.482859 19.951372 0.005391 0.994609 0.043237 \n", "825 1.489886 19.953228 0.005186 0.994814 0.041586 \n", "826 1.496913 19.955014 0.004989 0.995011 0.039997 \n", "\n", "[827 rows x 6 columns]" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's retrieve all the values of `S` at the various simulation time\n", "hist = uc.get_history()[:-1] # Dropping the last row, because no rate information is known about the next simulation step not taken!\n", "hist" ] }, { "cell_type": "code", "execution_count": 25, "id": "95cfbd47-8ba2-40ec-8001-569a123df0f4", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEScomputed_rate
00.00000020.0000000.000000
10.00050019.8200008.820000
20.00075019.75136412.075109
30.00076319.74832312.216716
40.00076919.74681112.287060
............
8221.4688050.0467380.285397
8231.4758320.0449540.274566
8241.4828590.0432370.264142
8251.4898860.0415860.254109
8261.4969130.0399970.244454
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827 rows × 3 columns

\n", "
" ], "text/plain": [ " SYSTEM TIME S computed_rate\n", "0 0.000000 20.000000 0.000000\n", "1 0.000500 19.820000 8.820000\n", "2 0.000750 19.751364 12.075109\n", "3 0.000763 19.748323 12.216716\n", "4 0.000769 19.746811 12.287060\n", ".. ... ... ...\n", "822 1.468805 0.046738 0.285397\n", "823 1.475832 0.044954 0.274566\n", "824 1.482859 0.043237 0.264142\n", "825 1.489886 0.041586 0.254109\n", "826 1.496913 0.039997 0.244454\n", "\n", "[827 rows x 3 columns]" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Now, let's put together in the same table (Pandas dataframe) the `S` values from above, and the `rates` we extracted earlier\n", "\n", "assert len(hist) == len(rates) # They'd better match up!\n", "\n", "rate_and_substrate = pd.DataFrame({\n", " \"SYSTEM TIME\": hist[\"SYSTEM TIME\"], # We don't actually need the time, but just for clarity\n", " \"S\": hist[\"S\"],\n", " \"computed_rate\": rates[\"rate\"]\n", "})\n", "\n", "rate_and_substrate" ] }, { "cell_type": "code", "execution_count": 26, "id": "4bcb86d9-6991-48b1-be23-117f8df8bd4c", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEScomputed_rateMichaelis_rate
00.00000020.0000000.00000034.656189
10.00050019.8200008.82000034.564299
20.00075019.75136412.07510934.528950
30.00076319.74832312.21671634.527380
40.00076919.74681112.28706034.526599
...............
8221.4688050.0467380.2853970.275111
8231.4758320.0449540.2745660.264664
8241.4828590.0432370.2641420.254610
8251.4898860.0415860.2541090.244934
8261.4969130.0399970.2444540.235622
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827 rows × 4 columns

\n", "
" ], "text/plain": [ " SYSTEM TIME S computed_rate Michaelis_rate\n", "0 0.000000 20.000000 0.000000 34.656189\n", "1 0.000500 19.820000 8.820000 34.564299\n", "2 0.000750 19.751364 12.075109 34.528950\n", "3 0.000763 19.748323 12.216716 34.527380\n", "4 0.000769 19.746811 12.287060 34.526599\n", ".. ... ... ... ...\n", "822 1.468805 0.046738 0.285397 0.275111\n", "823 1.475832 0.044954 0.274566 0.264664\n", "824 1.482859 0.043237 0.264142 0.254610\n", "825 1.489886 0.041586 0.254109 0.244934\n", "826 1.496913 0.039997 0.244454 0.235622\n", "\n", "[827 rows x 4 columns]" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's a column with the rate estimated by the Michaelis-Menten model\n", "rate_and_substrate[\"Michaelis_rate\"] = vmax * rate_and_substrate[\"S\"] / (kM + rate_and_substrate[\"S\"])\n", "rate_and_substrate" ] }, { "cell_type": "code", "execution_count": 27, "id": "6e8cdb8c-0e8e-461f-81a0-f7b75de1d322", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=computed_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=rate_and_substrate, x_var=\"S\", fields=[\"computed_rate\", \"Michaelis_rate\"],\n", " title=\"Reaction rate, dP/dt, as a function of Substrate concentration\",\n", " y_label=\"dP/dt\")" ] }, { "cell_type": "markdown", "id": "3d6b91c7-dc26-4a04-8a27-4d1b10f4d96e", "metadata": {}, "source": [ "Virtually overlapped plots, except at the very right!" ] }, { "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" ] }, { "cell_type": "markdown", "id": "291b603e-45fd-4cb9-a479-82ee4e4ba936", "metadata": {}, "source": [ "#### This is as expected, because the kinetic parameters of this reaction satisfy the customary Michaelis-Menten assumptions that `[E] << [S]` and that the rates satisfy `k1_reverse >> k2_forward`" ] }, { "cell_type": "code", "execution_count": null, "id": "413400e9-c049-4661-a1ec-d0e7bf3ef4ea", "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 }