{ "cells": [ { "cell_type": "markdown", "id": "5cbc8640", "metadata": {}, "source": [ "# **Enzyme Kinetics** : \n", "#### An _accurate numerical solution_ of an enzymatic reaction `E + S <-> ES -> E + P` - compared to the **Michaelis-Menten** model approximation and to the alternative **Morrison** model.\n", "\n", "#### Same as experiments `enzyme_1_a` and `enzyme_1_b` but with _a lavish amount of Enzyme_ relative to the initial Substrate concentration. \n", "Experiment `enzyme_1_b` had a ten-fold increase in enzyme, relative to `enzyme_1_a`. Here, we do _another x10 increase!_\n", "\n", "#### Real-life kinetic parameters. \n", "\n", "Please refer to `enzyme_1_a` and `enzyme_1_b` for more details." ] }, { "cell_type": "markdown", "id": "604b150b-7812-4fd3-9403-69a06dd7e397", "metadata": {}, "source": [ "#### THE REACTION: \n", "the enzyme `Adenosine deaminase` with the substrate `2,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purine` (same as in experiment `enzyme_1`) \n", "satisfies the customary Michaelis-Menten assumptions that `k1_reverse >> k2_forward`\n", "\n", "However, the initial concentration values choosen below, do NOT satisfy the expected Michaelis-Menten assumptions that `[E] << [S]` \n", "\n", "Source of kinetic parameters: *page 16 of \"Analysis of Enzyme Reaction Kinetics, Vol. 1\", by F. Xavier Malcata, Wiley, 2023*" ] }, { "cell_type": "markdown", "id": "c123db4f-c802-47f0-a3d3-0b857314d8e5", "metadata": {}, "source": [ "### TAGS : \"uniform compartment\", \"chemistry\", \"numerical\", \"enzymes\"" ] }, { "cell_type": "code", "execution_count": 1, "id": "6e9d0902-6fc9-4692-ac39-0651d08902ca", "metadata": {}, "outputs": [], "source": [ "LAST_REVISED = \"Sep. 2, 2025\"\n", "LIFE123_VERSION = \"1.0.0rc6\" # Library version this experiment is based on" ] }, { "cell_type": "code", "execution_count": 2, "id": "1e0ae9a9-9d0c-4edf-a5f2-1c589419e6cf", "metadata": {}, "outputs": [], "source": [ "#import set_path # Using MyBinder? Uncomment this before running the next cell!" ] }, { "cell_type": "code", "execution_count": 3, "id": "a29db1c7", "metadata": { "tags": [] }, "outputs": [], "source": [ "#import sys\n", "#sys.path.append(\"C:/some_path/my_env_or_install\") # CHANGE to the folder containing your venv or libraries installation!\n", "# NOTE: If any of the imports below can't find a module, uncomment the lines above, or try: import set_path \n", "\n", "import pandas as pd\n", "\n", "from life123 import check_version, ChemData, UniformCompartment, ReactionEnzyme, PlotlyHelper" ] }, { "cell_type": "code", "execution_count": 4, "id": "af15ecf0-e083-4fef-b68e-abe794dcc86e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "OK\n" ] } ], "source": [ "check_version(LIFE123_VERSION) # To check compatibility" ] }, { "cell_type": "code", "execution_count": null, "id": "3713fa4d-e9bb-4e33-8734-c1d4d23cf177", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "34d1cefc-f644-410a-9fe4-5204964742ac", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "91a729ee-ad2f-4771-bc84-49ecb9d6a851", "metadata": {}, "source": [ "# PART 1. Accurate numerical solution" ] }, { "cell_type": "code", "execution_count": 5, "id": "ac9eea69-174c-43e5-9eed-443cbc5e2ba7", "metadata": {}, "outputs": [], "source": [ "chem_data = ChemData(names=[\"P\", \"ES\"], plot_colors=[\"green\", \"red\"])" ] }, { "cell_type": "code", "execution_count": 6, "id": "90f9ec41-6e1b-4558-9400-47e35ece6efc", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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namelabelplot_color
0PPgreen
1ESESred
2Adenosine deaminaseEviolet
32,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purineSdarkturquoise
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" ], "text/plain": [ " name label plot_color\n", "0 P P green\n", "1 ES ES red\n", "2 Adenosine deaminase E violet\n", "3 2,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purine S darkturquoise" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Our Enzyme\n", "chem_data.add_chemical(name=\"Adenosine deaminase\", label=\"E\", plot_color=\"violet\") \n", "\n", "# Our Substrate\n", "chem_data.add_chemical(name=\"2,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purine\", label=\"S\", plot_color=\"darkturquoise\")\n", "\n", "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 experiments `enzyme_1` and `enzyme_2`" ] }, { "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": 7, "id": "6c65843f-4c9a-4698-a78b-28fcb02312c0", "metadata": {}, "outputs": [], "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\")" ] }, { "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 = 18.0 / k1_R = 100.0 / k2_F = 49.0 / 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=18., k1_R=100., k2_F=49.)\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", "### Unlike in experiments `enzyme_1_a` and `enzyme_1_b`, the reaction is \"awash\" in 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 = 100. # A LAVISH AMOUNT! 10 times more than in experiment `enzyme_2` - and x100 as much as experiment`enzyme_1`" ] }, { "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: 100.0\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": "markdown", "id": "ef2c10f2-ec7f-497a-bdbf-4fea30ba31a1", "metadata": { "tags": [] }, "source": [ "#### Advance the reactions to equilibrium" ] }, { "cell_type": "code", "execution_count": 11, "id": "e6ad72b8-722a-4606-a611-7dc600529f30", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "998 total variable step(s) taken in 2.010 sec\n", "Number of step re-do's because of negative concentrations: 2\n", "Number of step re-do's because of elective soft aborts: 3\n", "Norm usage: {'norm_A': 997, 'norm_B': 1000, 'norm_C': 996, 'norm_D': 996}\n", "System Time is now: 0.050362\n" ] } ], "source": [ "# Perform the reactions\n", "uc.single_compartment_react(duration=0.05, initial_step=0.01) # A much-shorter duration than in previous experiments in the series" ] }, { "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 (999) - only showing 1 every 7 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` . Changes in concentrations with time (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.701989760467668e-05, 0.0503618770122383 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -5.555555555555555, 105.55555555555556 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "uc.plot_history(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": 13, "id": "21d7d644-779b-4ffa-82cd-25d50cdd5300", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEPESESstepcaptionrxn0_rate_2
00.0000000.0000000.000000100.00000020.000000Set concentration0.000000
10.0000100.0000000.36000099.64000019.64000011st reaction step17.640000
20.0000110.0000180.39552399.60447719.604459219.380617
30.0000110.0000190.39729599.60270519.602686319.467446
40.0000110.0000190.39818199.60181919.601800419.510856
...........................
9930.04791817.7754982.10193397.8980670.122569993102.994725
9940.04839717.8248422.05536497.9446360.119793994100.712859
9950.04888117.8735762.00937097.9906300.11705599598.459109
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9970.04986317.9691971.91911498.0808860.11168999794.036596
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998 rows × 8 columns

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" ], "text/plain": [ " SYSTEM TIME P ES E S step \\\n", "0 0.000000 0.000000 0.000000 100.000000 20.000000 \n", "1 0.000010 0.000000 0.360000 99.640000 19.640000 1 \n", "2 0.000011 0.000018 0.395523 99.604477 19.604459 2 \n", "3 0.000011 0.000019 0.397295 99.602705 19.602686 3 \n", "4 0.000011 0.000019 0.398181 99.601819 19.601800 4 \n", ".. ... ... ... ... ... ... \n", "993 0.047918 17.775498 2.101933 97.898067 0.122569 993 \n", "994 0.048397 17.824842 2.055364 97.944636 0.119793 994 \n", "995 0.048881 17.873576 2.009370 97.990630 0.117055 995 \n", "996 0.049370 17.921695 1.963952 98.036048 0.114353 996 \n", "997 0.049863 17.969197 1.919114 98.080886 0.111689 997 \n", "\n", " caption rxn0_rate_2 \n", "0 Set concentration 0.000000 \n", "1 1st reaction step 17.640000 \n", "2 19.380617 \n", "3 19.467446 \n", "4 19.510856 \n", ".. ... ... \n", "993 102.994725 \n", "994 100.712859 \n", "995 98.459109 \n", "996 96.233637 \n", "997 94.036596 \n", "\n", "[998 rows x 8 columns]" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# We specify the reaction that involves `P`\n", "rates = uc.add_rate_to_conc_history(rate_name=\"rxn0_rate_2\")\n", "rates" ] }, { "cell_type": "code", "execution_count": 14, "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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" ] }, "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": "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": [ "# 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": 15, "id": "251dfcc1-0cc2-4bad-af3a-afa2feed4e4c", "metadata": {}, "outputs": [], "source": [ "rxn = uc.get_single_reaction(0)" ] }, { "cell_type": "code", "execution_count": 16, "id": "e279ef7d-61ca-469f-8418-60ad0b1222e0", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "8.277777777777779" ] }, "execution_count": 16, "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": 17, "id": "5b073f95-a8ed-4885-8b88-85a04341ecee", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "49.0" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rxn.kcat" ] }, { "cell_type": "code", "execution_count": 18, "id": "355a083f-d492-4cbb-a5c1-f961236257ad", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "4900.0" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vmax = rxn.compute_vmax(E_tot=E0) # kcat * E0\n", "vmax" ] }, { "cell_type": "code", "execution_count": 19, "id": "09dfe215-e89d-4562-8a54-72973c6d2b2c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3465.6188605108055" ] }, "execution_count": 19, "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_a`, 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": 20, "id": "ff21ba16-795a-40ba-b6e6-6e33dbeda25a", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEPESESstepcaptionrxn0_rate_2Michaelis_rate
00.0000000.0000000.000000100.00000020.000000Set concentration0.0000003465.618861
10.0000100.0000000.36000099.64000019.64000011st reaction step17.6400003447.122503
20.0000110.0000180.39552399.60447719.604459219.3806173445.270565
30.0000110.0000190.39729599.60270519.602686319.4674463445.178054
40.0000110.0000190.39818199.60181919.601800419.5108563445.131800
..............................
9930.04791817.7754982.10193397.8980670.122569993102.99472571.495562
9940.04839717.8248422.05536497.9446360.119793994100.71285969.899661
9950.04888117.8735762.00937097.9906300.11705599598.45910968.323957
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998 rows × 9 columns

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" ], "text/plain": [ " SYSTEM TIME P ES E S step \\\n", "0 0.000000 0.000000 0.000000 100.000000 20.000000 \n", "1 0.000010 0.000000 0.360000 99.640000 19.640000 1 \n", "2 0.000011 0.000018 0.395523 99.604477 19.604459 2 \n", "3 0.000011 0.000019 0.397295 99.602705 19.602686 3 \n", "4 0.000011 0.000019 0.398181 99.601819 19.601800 4 \n", ".. ... ... ... ... ... ... \n", "993 0.047918 17.775498 2.101933 97.898067 0.122569 993 \n", "994 0.048397 17.824842 2.055364 97.944636 0.119793 994 \n", "995 0.048881 17.873576 2.009370 97.990630 0.117055 995 \n", "996 0.049370 17.921695 1.963952 98.036048 0.114353 996 \n", "997 0.049863 17.969197 1.919114 98.080886 0.111689 997 \n", "\n", " caption rxn0_rate_2 Michaelis_rate \n", "0 Set concentration 0.000000 3465.618861 \n", "1 1st reaction step 17.640000 3447.122503 \n", "2 19.380617 3445.270565 \n", "3 19.467446 3445.178054 \n", "4 19.510856 3445.131800 \n", ".. ... ... ... \n", "993 102.994725 71.495562 \n", "994 100.712859 69.899661 \n", "995 98.459109 68.323957 \n", "996 96.233637 66.768545 \n", "997 94.036596 65.233510 \n", "\n", "[998 rows x 9 columns]" ] }, "execution_count": 20, "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": 21, "id": "6e8cdb8c-0e8e-461f-81a0-f7b75de1d322", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Rates=rxn0_rate_2
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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=[\"rxn0_rate_2\", \"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=1.65,\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_a`" ] }, { "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_a`, 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": {}, "source": [ "# PART 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": 22, "id": "d889a598-82b6-49ea-9cba-b0e8e9997c5c", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEPESESstepcaptionrxn0_rate_2Michaelis_rateMorrison_rate
00.0000000.0000000.000000100.00000020.000000Set concentration0.0000003465.618861889.979162
10.0000100.0000000.36000099.64000019.64000011st reaction step17.6400003447.122503889.979162
20.0000110.0000180.39552399.60447719.604459219.3806173445.270565889.978385
30.0000110.0000190.39729599.60270519.602686319.4674463445.178054889.978342
40.0000110.0000190.39818199.60181919.601800419.5108563445.131800889.978321
.................................
9930.04791817.7754982.10193397.8980670.122569993102.99472571.495562100.506658
9940.04839717.8248422.05536497.9446360.119793994100.71285969.89966198.280755
9950.04888117.8735762.00937097.9906300.11705599598.45910968.32395796.082240
9960.04937017.9216951.96395298.0360480.11435399696.23363766.76854593.911274
9970.04986317.9691971.91911498.0808860.11168999794.03659665.23351091.768007
\n", "

998 rows × 10 columns

\n", "
" ], "text/plain": [ " SYSTEM TIME P ES E S step \\\n", "0 0.000000 0.000000 0.000000 100.000000 20.000000 \n", "1 0.000010 0.000000 0.360000 99.640000 19.640000 1 \n", "2 0.000011 0.000018 0.395523 99.604477 19.604459 2 \n", "3 0.000011 0.000019 0.397295 99.602705 19.602686 3 \n", "4 0.000011 0.000019 0.398181 99.601819 19.601800 4 \n", ".. ... ... ... ... ... ... \n", "993 0.047918 17.775498 2.101933 97.898067 0.122569 993 \n", "994 0.048397 17.824842 2.055364 97.944636 0.119793 994 \n", "995 0.048881 17.873576 2.009370 97.990630 0.117055 995 \n", "996 0.049370 17.921695 1.963952 98.036048 0.114353 996 \n", "997 0.049863 17.969197 1.919114 98.080886 0.111689 997 \n", "\n", " caption rxn0_rate_2 Michaelis_rate Morrison_rate \n", "0 Set concentration 0.000000 3465.618861 889.979162 \n", "1 1st reaction step 17.640000 3447.122503 889.979162 \n", "2 19.380617 3445.270565 889.978385 \n", "3 19.467446 3445.178054 889.978342 \n", "4 19.510856 3445.131800 889.978321 \n", ".. ... ... ... ... \n", "993 102.994725 71.495562 100.506658 \n", "994 100.712859 69.899661 98.280755 \n", "995 98.459109 68.323957 96.082240 \n", "996 96.233637 66.768545 93.911274 \n", "997 94.036596 65.233510 91.768007 \n", "\n", "[998 rows x 10 columns]" ] }, "execution_count": 22, "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": 23, "id": "773188b3-f2e5-4fd0-ac47-d79f65fe13b4", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Rates=rxn0_rate_2
S=%{x}
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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "PlotlyHelper.plot_pandas(df=rates, x_var=\"S\", fields=[\"rxn0_rate_2\", \"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=1.65,\n", " colors=[\"blue\", \"yellow\", \"orange\"])" ] }, { "cell_type": "markdown", "id": "7d724ebe-6828-4f55-8fa8-2f5ef04c4090", "metadata": {}, "source": [ "## The **Morrison** model is **VASTLY better** than the Michaelis-Menten one in this *high-enzyme scenario*!" ] }, { "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 }