{ "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 = \"Jan. 12, 2025\"\n", "LIFE123_VERSION = \"1.0.0rc2\" # 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\"], 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
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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: 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\" (green), \"S\" (darkturquoise), \"E\" (violet), \"ES\" (red)}\n" ] } ], "source": [ "# Reaction E + S <-> ES , with 1st-order kinetics, \n", "uc.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", "uc.add_reaction(reactants=\"ES\", products=[\"E\", \"P\"],\n", " forward_rate=49., reverse_rate=0) # We are ignoring the reverse reaction\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", "Set of chemicals involved in reactions: {'P', 'S', 'E', 'ES'}\n" ] } ], "source": [ "uc.set_conc(conc={\"S\": S0, \"E\": E0}) # Small ampount of enzyme `E`, relative to substrate `S`\n", "uc.describe_state()" ] }, { "cell_type": "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 0.02 min\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)
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": [ -0.0001368835254300135, 0.20080813180582976 ], "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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" ] }, "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 TIMEPESESstepcaptionrxn1_rate
00.0000000.0000000.00000010.00000020.000000Set concentration0.000000
10.0005000.0000001.8000008.20000018.20000011st reaction step88.200000
20.0007500.0220502.4045307.59547017.5734202117.821970
30.0007630.0235232.4300847.56991617.5463933119.074126
40.0007690.0242672.4427647.55723617.5329694119.695434
...........................
6100.19557319.8635650.0816499.9183510.0547866104.000798
6110.19659319.8676450.0792179.9207830.0531386113.881655
6120.19761219.8716020.0768589.9231420.0515406123.766032
6130.19863219.8754420.0745689.9254320.0499906133.653827
6140.19965219.8791670.0723469.9276540.0484876143.544941
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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 rxn1_rate \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=\"rxn1_rate\")\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=\"rxn1_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": 15, "id": "251dfcc1-0cc2-4bad-af3a-afa2feed4e4c", "metadata": {}, "outputs": [], "source": [ "rxn = ReactionEnz(enzyme=\"E\", substrate=\"S\", product=\"P\",\n", " k1_F=uc.get_reactions().get_forward_rate(0), k1_R=uc.get_reactions().get_reverse_rate(0),\n", " k2_F=uc.get_reactions().get_forward_rate(1))" ] }, { "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 TIMEPESESstepcaptionrxn1_rateMichaelis_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
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615 rows × 9 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 rxn1_rate 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=rxn1_rate
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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=[\"rxn1_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": 22, "id": "d889a598-82b6-49ea-9cba-b0e8e9997c5c", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEPESESstepcaptionrxn1_rateMichaelis_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
\n", "

615 rows × 10 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 rxn1_rate 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=rxn1_rate
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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "PlotlyHelper.plot_pandas(df=rates, x_var=\"S\", fields=[\"rxn1_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 }