{ "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 experiment `enzyme_1_a` but with _much-larger amounts of Enzyme_ relative to the initial Substrate concentration.\n", "\n", "#### 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 = \"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
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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 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": 7, "id": "5ff757ef-9c81-48cf-b8d9-7bbf294f8d51", "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 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", "Chemicals involved in reactions: ['E', 'ES', 'S', '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": [ "615 total variable step(s) taken in 1.290 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: 1\n", "Norm usage: {'norm_A': 513, 'norm_B': 516, 'norm_C': 512, 'norm_D': 512}\n", "System Time is now: 0.20067\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": 12, "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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"#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": "Almost as much E as S(0)
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": [ -0.00016778532464916367, 0.20083903360504893 ], "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(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": "b0c97520-4722-4612-8e17-d604db70990f", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEPESESstepcaptionrxn0_rate_2
00.0000000.0000000.00000010.00000020.000000Set concentration0.000000
10.0005000.0000001.8000008.20000018.20000011st reaction step88.200000
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" ], "text/plain": [ " SYSTEM TIME P ES E S step \\\n", "0 0.000000 0.000000 0.000000 10.000000 20.000000 \n", "1 0.000500 0.000000 1.800000 8.200000 18.200000 1 \n", "2 0.000750 0.022050 2.404530 7.595470 17.573420 2 \n", "3 0.000763 0.023523 2.430084 7.569916 17.546393 3 \n", "4 0.000769 0.024267 2.442764 7.557236 17.532969 4 \n", ".. ... ... ... ... ... ... \n", "610 0.195573 19.863565 0.081649 9.918351 0.054786 610 \n", "611 0.196593 19.867645 0.079217 9.920783 0.053138 611 \n", "612 0.197612 19.871602 0.076858 9.923142 0.051540 612 \n", "613 0.198632 19.875442 0.074568 9.925432 0.049990 613 \n", "614 0.199652 19.879167 0.072346 9.927654 0.048487 614 \n", "\n", " caption rxn0_rate_2 \n", "0 Set concentration 0.000000 \n", "1 1st reaction step 88.200000 \n", "2 117.821970 \n", "3 119.074126 \n", "4 119.695434 \n", ".. ... ... \n", "610 4.000798 \n", "611 3.881655 \n", "612 3.766032 \n", "613 3.653827 \n", "614 3.544941 \n", "\n", "[615 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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"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=\"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": [ "490.0" ] }, "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": [ "346.56188605108053" ] }, "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`, 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
00.0000000.0000000.00000010.00000020.000000Set concentration0.000000346.561886
10.0005000.0000001.8000008.20000018.20000011st reaction step88.200000336.810743
20.0007500.0220502.4045307.59547017.5734202117.821970333.097749
30.0007630.0235232.4300847.56991617.5463933119.074126332.933539
40.0007690.0242672.4427647.55723617.5329694119.695434332.851850
..............................
6100.19557319.8635650.0816499.9183510.0547866104.0007983.221698
6110.19659319.8676450.0792179.9207830.0531386113.8816553.125424
6120.19761219.8716020.0768589.9231420.0515406123.7660323.032014
6130.19863219.8754420.0745689.9254320.0499906133.6538272.941384
6140.19965219.8791670.0723469.9276540.0484876143.5449412.853451
\n", "

615 rows × 9 columns

\n", "
" ], "text/plain": [ " SYSTEM TIME P ES E S step \\\n", "0 0.000000 0.000000 0.000000 10.000000 20.000000 \n", "1 0.000500 0.000000 1.800000 8.200000 18.200000 1 \n", "2 0.000750 0.022050 2.404530 7.595470 17.573420 2 \n", "3 0.000763 0.023523 2.430084 7.569916 17.546393 3 \n", "4 0.000769 0.024267 2.442764 7.557236 17.532969 4 \n", ".. ... ... ... ... ... ... \n", "610 0.195573 19.863565 0.081649 9.918351 0.054786 610 \n", "611 0.196593 19.867645 0.079217 9.920783 0.053138 611 \n", "612 0.197612 19.871602 0.076858 9.923142 0.051540 612 \n", "613 0.198632 19.875442 0.074568 9.925432 0.049990 613 \n", "614 0.199652 19.879167 0.072346 9.927654 0.048487 614 \n", "\n", " caption rxn0_rate_2 Michaelis_rate \n", "0 Set concentration 0.000000 346.561886 \n", "1 1st reaction step 88.200000 336.810743 \n", "2 117.821970 333.097749 \n", "3 119.074126 332.933539 \n", "4 119.695434 332.851850 \n", ".. ... ... ... \n", "610 4.000798 3.221698 \n", "611 3.881655 3.125424 \n", "612 3.766032 3.032014 \n", "613 3.653827 2.941384 \n", "614 3.544941 2.853451 \n", "\n", "[615 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=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": [ "# 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
00.0000000.0000000.00000010.00000020.000000Set concentration0.000000346.561886305.920075
10.0005000.0000001.8000008.20000018.20000011st reaction step88.200000336.810743305.920075
20.0007500.0220502.4045307.59547017.5734202117.821970333.097749305.762583
30.0007630.0235232.4300847.56991617.5463933119.074126332.933539305.752055
40.0007690.0242672.4427647.55723617.5329694119.695434332.851850305.746735
.................................
6100.19557319.8635650.0816499.9183510.0547866104.0007983.2216983.645236
6110.19659319.8676450.0792179.9207830.0531386113.8816553.1254243.536609
6120.19761219.8716020.0768589.9231420.0515406123.7660323.0320143.431196
6130.19863219.8754420.0745689.9254320.0499906133.6538272.9413843.328903
6140.19965219.8791670.0723469.9276540.0484876143.5449412.8534513.229639
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615 rows × 10 columns

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" ], "text/plain": [ " SYSTEM TIME P ES E S step \\\n", "0 0.000000 0.000000 0.000000 10.000000 20.000000 \n", "1 0.000500 0.000000 1.800000 8.200000 18.200000 1 \n", "2 0.000750 0.022050 2.404530 7.595470 17.573420 2 \n", "3 0.000763 0.023523 2.430084 7.569916 17.546393 3 \n", "4 0.000769 0.024267 2.442764 7.557236 17.532969 4 \n", ".. ... ... ... ... ... ... \n", "610 0.195573 19.863565 0.081649 9.918351 0.054786 610 \n", "611 0.196593 19.867645 0.079217 9.920783 0.053138 611 \n", "612 0.197612 19.871602 0.076858 9.923142 0.051540 612 \n", "613 0.198632 19.875442 0.074568 9.925432 0.049990 613 \n", "614 0.199652 19.879167 0.072346 9.927654 0.048487 614 \n", "\n", " caption rxn0_rate_2 Michaelis_rate Morrison_rate \n", "0 Set concentration 0.000000 346.561886 305.920075 \n", "1 1st reaction step 88.200000 336.810743 305.920075 \n", "2 117.821970 333.097749 305.762583 \n", "3 119.074126 332.933539 305.752055 \n", "4 119.695434 332.851850 305.746735 \n", ".. ... ... ... ... \n", "610 4.000798 3.221698 3.645236 \n", "611 3.881655 3.125424 3.536609 \n", "612 3.766032 3.032014 3.431196 \n", "613 3.653827 2.941384 3.328903 \n", "614 3.544941 2.853451 3.229639 \n", "\n", "[615 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
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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=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_1_c`, 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": "16b12f2a-42c9-44cd-89ef-91519866a26a", "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 }