{ "cells": [ { "cell_type": "markdown", "id": "5cbc8640", "metadata": {}, "source": [ "# IN-PROGRESS\n", "\n", "## **Enzyme Kinetics** : \n", "\n", "#### Our model: `E + S <-> ES` (with kinetic pars _k1_forward_ and _k1_reverse_), and `ES -> E + P` (_k2_forward_) \n", "\n", "#### In experiment `enzyme_1_a`, we were given _k1_forward_, _k1_reverse_ and _k2_forward_... But what to do if we're **just given kM and kcat** \n", "\n", "In Part 1, we'll \"cheat\" and use the actual value of _k1_forward_ \n", "In Part 2, we'll explore what happens if, lacking an actual value, we **under-estimate** _k1_forward_ \n", "In Part 3, we'll explore what happens if we **over-estimate** _k1_forward_\n", "\n", "Background: please see experiment `enzyme_1_a`" ] }, { "cell_type": "markdown", "id": "604b150b-7812-4fd3-9403-69a06dd7e397", "metadata": {}, "source": [ "#### THE REACTION: \n", "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 = \"Nov. 4, 2024\"\n", "LIFE123_VERSION = \"1.0.0.rc.0\" # Library version this experiment is based on" ] }, { "cell_type": "code", "execution_count": 2, "id": "1e0ae9a9-9d0c-4edf-a5f2-1c589419e6cf", "metadata": {}, "outputs": [], "source": [ "#import set_path # Using MyBinder? Uncomment this before running the next cell!" ] }, { "cell_type": "code", "execution_count": 3, "id": "a29db1c7", "metadata": { "tags": [] }, "outputs": [], "source": [ "#import sys\n", "#sys.path.append(\"C:/some_path/my_env_or_install\") # CHANGE to the folder containing your venv or libraries installation!\n", "# NOTE: If any of the imports below can't find a module, uncomment the lines above, or try: import set_path \n", "\n", "import ipynbname\n", "import pandas as pd\n", "\n", "from life123 import check_version, ChemData, UniformCompartment, ReactionEnz, 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": 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": "8b71b0b0-f867-48a5-beaf-7f992b0d7c46", "metadata": {}, "source": [ "## Assume we're only given values for kM and kcat\n", "What values of k1_forward, k1_reverse and k2_forward are compatible with them?" ] }, { "cell_type": "code", "execution_count": 5, "id": "80320572-3ea6-49a2-97cd-487e068e2514", "metadata": {}, "outputs": [], "source": [ "# The following values are taken from experiment `enzyme_1`\n", "kM = 8.27777777777777\n", "kcat = 49" ] }, { "cell_type": "code", "execution_count": 6, "id": "c04db12c-e77f-4b53-8cdb-859194959ca1", "metadata": {}, "outputs": [], "source": [ "# k2_forward equals kcat ; not much to say here\n", "k2_forward = kcat" ] }, { "cell_type": "markdown", "id": "57aca1c1-9ea1-4732-ac3b-69c75dc7a1fa", "metadata": {}, "source": [ "By contrast kM = (k2_forward + k1_reverse) / k1_forward \n", "\n", "We are given kM and k2_forward, which is the same value as the given kcat. \n", "\n", "But how to solve for k1_forward and k1_reverse?? We have just 1 equation and 2 variables! The system of equations is \"underdetermined\" : what can we do? \n", "\n", "We'll venture some guesses for k1_forward, and compute the corresponding k1_reverse that will satisfy the above equation. \n", "\n", "**k1_reverse = kM * k1_forward - kcat** (kcat has same value as k2_forward)" ] }, { "cell_type": "code", "execution_count": 7, "id": "7e34a530-7e5e-404b-8cb2-01e7db85557a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "99.99999999999986" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Example, using the k1_forward=18. from experiment `enzyme_1`\n", "k1_forward = 18.\n", "k1_reverse = kM * k1_forward - kcat \n", "k1_reverse" ] }, { "cell_type": "markdown", "id": "c738a101-f8dc-449e-a9fb-57b67e890f4f", "metadata": {}, "source": [ "Naturally, we're getting the same value we had for k1_reverse in that experiment. But what if k1_forward is quite different?" ] }, { "cell_type": "code", "execution_count": 8, "id": "51e52128-286b-44ca-bd8a-0680007ef9bb", "metadata": {}, "outputs": [], "source": [ "import numpy as np" ] }, { "cell_type": "code", "execution_count": 9, "id": "eae12ea5-687a-4b62-b4a7-c264df3c3e61", "metadata": {}, "outputs": [], "source": [ "def compute_k1_reverse(kM, kcat, k1_forward, verbose=True):\n", " k1_reverse = kM * k1_forward - kcat \n", " if verbose:\n", " if np.allclose(k1_reverse, 0):\n", " print (f\"k1_reverse: {k1_reverse} , K = INFINITE\")\n", " else:\n", " K = k1_forward / k1_reverse\n", " print(f\"k1_reverse: {k1_reverse} , K = {K}\")\n", " \n", " return k1_reverse" ] }, { "cell_type": "code", "execution_count": 10, "id": "86419426-af7c-4a3a-8f8a-9fb10cfb65d9", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "k1_reverse: 99.99999999999986 , K = 0.18000000000000024\n" ] }, { "data": { "text/plain": [ "99.99999999999986" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "compute_k1_reverse(kM, kcat, k1_forward=18.)" ] }, { "cell_type": "code", "execution_count": 11, "id": "746c07cc-a2d8-4192-b948-167d38a27a7e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "k1_reverse: -48.172222222222224 , K = -0.002075885134355899\n" ] }, { "data": { "text/plain": [ "-48.172222222222224" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "compute_k1_reverse(kM, kcat, k1_forward=0.1)" ] }, { "cell_type": "markdown", "id": "244cfe71-dce0-4b28-b393-734d657602ec", "metadata": {}, "source": [ "#### The negative values aren't good! We must add a constraint that: \n", "kM * k1_forward - kcat > 0 \n", "i.e. k1_forward > kcat/kM\n", "\n", "In other words, `k1_forward_min = kcat/kM`" ] }, { "cell_type": "code", "execution_count": 12, "id": "2ce6dd36-3c9b-4ddc-89a4-c3fb9aa62e15", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "5.919463087248328" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "k1_forward_min = kcat / kM\n", "k1_forward_min" ] }, { "cell_type": "code", "execution_count": 13, "id": "59718c54-fc15-40b9-87c1-1e308998fad2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "k1_reverse: 0.0 , K = INFINITE\n" ] }, { "data": { "text/plain": [ "0.0" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "compute_k1_reverse(kM, kcat, k1_forward=k1_forward_min)" ] }, { "cell_type": "code", "execution_count": 14, "id": "aede8259-9590-4fdb-b2d5-4aea4477e885", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "k1_reverse: 0.6666666666666146 , K = 9.000000000000703\n" ] }, { "data": { "text/plain": [ "0.6666666666666146" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "compute_k1_reverse(kM, kcat, k1_forward=6.)" ] }, { "cell_type": "code", "execution_count": 15, "id": "597b8664-5980-430b-8fb7-532f98dac673", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "k1_reverse: 33.7777777777777 , K = 0.29605263157894807\n" ] }, { "data": { "text/plain": [ "33.7777777777777" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "compute_k1_reverse(kM, kcat, k1_forward=10.)" ] }, { "cell_type": "code", "execution_count": 16, "id": "670e6976-e0a1-495e-aa26-746ca0766baf", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "k1_reverse: 282.1111111111108 , K = 0.14178810555336763\n" ] }, { "data": { "text/plain": [ "282.1111111111108" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "compute_k1_reverse(kM, kcat, k1_forward=40.)" ] }, { "cell_type": "markdown", "id": "3e578024-d229-4bbd-a7da-8df0d3afeb85", "metadata": {}, "source": [ "The fixed point k1_forward = k1_reverse occurs when k1_forward = kM * k1_forward - kcat , i.e. \n", "kM * k1_forward - k1_forward = kcat \n", "k1_forward * (kM - 1) = kcat \n", "k1_forward = kcat / (kM - 1)\n", "Notice that the above makes sense only if kM > 1" ] }, { "cell_type": "code", "execution_count": 17, "id": "32eb3d00-62ce-4743-bf4e-0f02c0179b62", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "6.7328244274809235" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Our kM is indeed > 1, so all good:\n", "\n", "k1_forward_fixed_pnt = kcat / (kM - 1)\n", "k1_forward_fixed_pnt" ] }, { "cell_type": "code", "execution_count": 18, "id": "488b98ef-9a13-4d8f-a17f-9d880e317848", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "k1_reverse: 6.732824427480921 , K = 1.0000000000000004\n" ] }, { "data": { "text/plain": [ "6.732824427480921" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "compute_k1_reverse(kM, kcat, k1_forward=6.7328244274809235)" ] }, { "cell_type": "markdown", "id": "bb739d11-4d13-4bac-b0cb-59bee63155aa", "metadata": {}, "source": [ "Indeed, a fixed point" ] }, { "cell_type": "code", "execution_count": 19, "id": "9551adb3-bf16-4c10-a3ab-0420553a2e37", "metadata": {}, "outputs": [], "source": [ "k1_forward_choices = np.linspace(5.92, 40., 2000) # Grid creation" ] }, { "cell_type": "code", "execution_count": 20, "id": "da0cd43d-8c53-47ae-8652-9a739b5de496", "metadata": {}, "outputs": [], "source": [ "k1_reverse_choices = compute_k1_reverse(kM, kcat, k1_forward=k1_forward_choices, verbose=False)" ] }, { "cell_type": "code", "execution_count": 21, "id": "2671b7bc-81f8-4740-bd26-f0e6213b31f3", "metadata": {}, "outputs": [], "source": [ "import plotly.express as px" ] }, { "cell_type": "code", "execution_count": 22, "id": "21368201-a259-4a5b-8f54-f42ed83f8c60", "metadata": {}, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "x=%{x}
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "px.line(x=k1_forward_choices, y=np.log(K_choices), title=\"log(K) vs. k1_forward\")" ] }, { "cell_type": "code", "execution_count": null, "id": "7b68bc5a-7bb8-47f7-a427-807aafcd47ce", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "9a4febb2-2780-4754-9c70-c2041b1afc07", "metadata": {}, "source": [ "## In the scenario we're exploring, there's LITTLE ENZYME relative to initial substrate concentration" ] }, { "cell_type": "code", "execution_count": 25, "id": "8c9e3f86-b9a5-41da-9e1b-75258017808a", "metadata": {}, "outputs": [], "source": [ "S0 = 20.\n", "E0 = 1." ] }, { "cell_type": "code", "execution_count": null, "id": "67b2734a-0839-4370-a5a9-18883fc15c4c", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "b0ea13d4-9e26-41ec-884a-a56a70445233", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "91a729ee-ad2f-4771-bc84-49ecb9d6a851", "metadata": {}, "source": [ "# 1. Using the known, exact values for `k1_forward` and `k1_reverse` \n", "\n", "Source: *page 16 of \"Analysis of Enzyme Reaction Kinetics, Vol. 1\", by F. Xavier Malcata, Wiley, 2023*" ] }, { "cell_type": "code", "execution_count": 26, "id": "33edfef8-7024-4881-a115-dbd39d3e976a", "metadata": {}, "outputs": [], "source": [ "k1_forward = 18.\n", "k1_reverse = 100." ] }, { "cell_type": "code", "execution_count": 27, "id": "ac9eea69-174c-43e5-9eed-443cbc5e2ba7", "metadata": {}, "outputs": [], "source": [ "chem_data = ChemData(names=[\"P\", \"ES\"])" ] }, { "cell_type": "code", "execution_count": 28, "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": 29, "id": "0f9c3501-0b99-47d9-87fa-3a027ede3799", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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0PP
1ESES
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": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "chem_data.all_chemicals()" ] }, { "cell_type": "markdown", "id": "f8d4ea7f-0591-467c-9df3-d95f53df75f5", "metadata": {}, "source": [ "### Specify the Kinetic Parameters" ] }, { "cell_type": "code", "execution_count": 30, "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', 'S', 'P', 'ES'}\n" ] } ], "source": [ "# Elementary Reaction E + S <-> ES\n", "chem_data.add_reaction(reactants=[\"E\", \"S\"], products=[\"ES\"],\n", " forward_rate=k1_forward, reverse_rate=k1_reverse) \n", "\n", "# Elementary Reaction ES <-> E + P \n", "chem_data.add_reaction(reactants=[\"ES\"], products=[\"E\", \"P\"],\n", " forward_rate=kcat, reverse_rate=0)\n", "\n", "chem_data.describe_reactions()" ] }, { "cell_type": "code", "execution_count": null, "id": "d23a97ea-f252-4e11-a3e9-aea74f58591e", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 31, "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', 'S', 'P', 'ES'}\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": 32, "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": "code", "execution_count": 33, "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", "784 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=1.2, initial_step=0.05)" ] }, { "cell_type": "code", "execution_count": 34, "id": "0198dd94-e55d-4ab4-9de8-087d508edf06", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_pandas() NOTICE: Excessive number of vertical lines (785) - only showing 1 every 6 lines\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=P
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Changes in concentration for `E + S <-> ES` and `ES <-> E + P` (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.0006395845522625827, 1.2017793737013929 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.1111111111111112, 21.11111111111111 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "uc.plot_history(colors=['cyan', 'green', 'violet', 'red'], show_intervals=True, \n", " title_prefix=\"Using exact values for k1_forward and k1_reverse\")" ] }, { "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**, provided that diagnostics were enabled (as we did indeed enable)" ] }, { "cell_type": "code", "execution_count": 35, "id": "3242165e-0193-43a7-b881-96fc04f3b6e0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Reaction: ES <-> E + P\n" ] }, { "data": { "text/html": [ "
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"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": "Reaction rate, dP/dt, over time" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ 0, 1.1947523744399813 ], "title": { "text": "time" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.8935609203310615, 35.97765748629017 ], "title": { "text": "dP/dt" }, "type": "linear" } } }, "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Let's take a look at how the reaction rate varies with time\n", "PlotlyHelper.plot_pandas(df=history_with_rates_exact, \n", " title=\"Reaction rate, dP/dt, over time\",\n", " x_var=\"TIME\", fields=\"rate\", \n", " x_label=\"time\", y_label=\"dP/dt\")" ] }, { "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. Guessing a SMALLER value of `k1_forward` (UNDER-ESTIMATED)" ] }, { "cell_type": "code", "execution_count": 37, "id": "b1ab7d25-1262-4376-ba37-b6888f5ca5d9", "metadata": {}, "outputs": [], "source": [ "chem_data = ChemData(names=[\"P\", \"ES\"])" ] }, { "cell_type": "code", "execution_count": 38, "id": "333dba78-82cd-47b8-9896-0645306f8261", "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": 39, "id": "df47c069-a290-4c48-a80c-fa9721a38b4c", "metadata": {}, "outputs": [], "source": [ "k1_forward = 6.5 # Close to the smallest possible value" ] }, { "cell_type": "code", "execution_count": 40, "id": "6aba5842-4978-4ba8-9a80-ddf14277c710", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "k1_reverse: 4.8055555555555 , K = 1.3526011560693798\n" ] }, { "data": { "text/plain": [ "4.8055555555555" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "k1_reverse = compute_k1_reverse(kM, kcat, k1_forward=k1_forward)\n", "k1_reverse" ] }, { "cell_type": "code", "execution_count": 41, "id": "e364152e-be1a-4ed3-8622-b00d101ac600", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 2 (at temp. 25 C)\n", "0: E + S <-> ES (kF = 6.5 / kR = 4.8056 / delta_G = -748.72 / K = 1.3526) | 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', 'S', 'P', 'ES'}\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=k1_forward, reverse_rate=k1_reverse) \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": 42, "id": "ccfc59f5-a0dc-4b03-a9dd-a6993c4a85cd", "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', 'S', 'P', 'ES'}\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": 43, "id": "255b73b8-493f-485d-8c55-43d63730ff9b", "metadata": {}, "outputs": [], "source": [ "uc.enable_diagnostics() # To save diagnostic information about the simulation - in particular, the REACTION RATES" ] }, { "cell_type": "code", "execution_count": 44, "id": "d9c51bab-7eaa-4735-82d2-aaf8ac787f0e", "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", "788 total step(s) taken\n", "Number of step re-do's because of negative concentrations: 1\n", "Number of step re-do's because of elective soft aborts: 2\n", "Norm usage: {'norm_A': 704, 'norm_B': 709, 'norm_C': 704, 'norm_D': 704}\n" ] } ], "source": [ "# Perform the reactions\n", "uc.single_compartment_react(duration=1.2, initial_step=0.05)" ] }, { "cell_type": "code", "execution_count": 45, "id": "ab344447-39a8-4dd6-aca8-be21e2bba505", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_pandas() NOTICE: Excessive number of vertical lines (789) - only showing 1 every 6 lines\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=P
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"Using smaller value for k1_forward
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": [ -0.0006416548337683672, 1.205669432650762 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.1111111111111112, 21.11111111111111 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "uc.plot_history(colors=['cyan', 'green', 'violet', 'red'], show_intervals=True, \n", " title_prefix=\"Using smaller value for k1_forward\")" ] }, { "cell_type": "markdown", "id": "4432c8c0-c5c5-4311-ac77-bbedfc27b741", "metadata": {}, "source": [ "At first glance, not too different from before, overall, but let's take a closer look" ] }, { "cell_type": "code", "execution_count": 46, "id": "a24e8ab9-697e-417a-ad5a-475ea6200b3b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Reaction: ES <-> E + P\n" ] }, { "data": { "text/html": [ "
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"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": "Reaction rate, dP/dt, over time" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ 0, 1.1987808930356147 ], "title": { "text": "time" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.8779232936082761, 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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=history_with_rates_under, \n", " title=\"Reaction rate, dP/dt, over time\",\n", " x_var=\"TIME\", fields=\"rate\", \n", " x_label=\"time\", y_label=\"dP/dt\")" ] }, { "cell_type": "code", "execution_count": null, "id": "223d5c37-0ad2-465a-9f95-84bebda6ab7a", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "ce1f4c5a-a77c-4fa0-89be-b4f4e05c24db", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "e863f23b-0fb5-490a-9f60-fa1c9caf4c93", "metadata": {}, "source": [ "# 3. Guessing a LARGER value of `k1_forward` (OVER-ESTIMATED)" ] }, { "cell_type": "code", "execution_count": 48, "id": "73124b26-bc38-41f3-b6f6-93d9ae44adc8", "metadata": {}, "outputs": [], "source": [ "chem_data = ChemData(names=[\"P\", \"ES\"])" ] }, { "cell_type": "code", "execution_count": 49, "id": "d7acddc1-ac86-4dc3-b581-3a7f4d4605e1", "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": 50, "id": "fb94e4d4-68d8-4835-aa5c-3667798162ba", "metadata": {}, "outputs": [], "source": [ "k1_forward = 40. # Well above the known value of 18." ] }, { "cell_type": "code", "execution_count": 51, "id": "22912c72-e063-4f8c-bfc0-2e36580f0352", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "k1_reverse: 282.1111111111108 , K = 0.14178810555336763\n" ] }, { "data": { "text/plain": [ "282.1111111111108" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "k1_reverse = compute_k1_reverse(kM, kcat, k1_forward=k1_forward)\n", "k1_reverse" ] }, { "cell_type": "code", "execution_count": 52, "id": "7cc40d06-d756-44b1-a55a-d556cfee46b2", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 2 (at temp. 25 C)\n", "0: E + S <-> ES (kF = 40 / kR = 282.11 / delta_G = 4,842.4 / K = 0.14179) | 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', 'S', 'P', 'ES'}\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=k1_forward, reverse_rate=k1_reverse) \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": 53, "id": "fbc78df2-da88-4ed1-8878-2a6b2373d10a", "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', 'S', 'P', 'ES'}\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": 54, "id": "19c0211a-3a3d-4beb-8099-49b86fa9aec0", "metadata": {}, "outputs": [], "source": [ "uc.enable_diagnostics() # To save diagnostic information about the simulation - in particular, the REACTION RATES" ] }, { "cell_type": "code", "execution_count": 55, "id": "e99b906d-028d-43cf-ba69-13843903545a", "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", "864 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': 829, 'norm_B': 835, 'norm_C': 829, 'norm_D': 829}\n" ] } ], "source": [ "# Perform the reactions\n", "uc.single_compartment_react(duration=1.2, initial_step=0.05)" ] }, { "cell_type": "code", "execution_count": 56, "id": "54e123a5-bcd9-4702-b7d7-8490390960ad", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_pandas() NOTICE: Excessive number of vertical lines (865) - only showing 1 every 6 lines\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=P
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Changes in concentration for `E + S <-> ES` and `ES <-> E + P` (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.0006390195730413113, 1.2007177777446238 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.1111111111111112, 21.11111111111111 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "uc.plot_history(colors=['cyan', 'green', 'violet', 'red'], show_intervals=True, \n", " title_prefix=\"Using smaller value for k1_forward\")" ] }, { "cell_type": "markdown", "id": "1bb0f414-d7d3-4166-ab16-21daee03c4d8", "metadata": {}, "source": [ "At first glance, not too different from before, overall, but let's take a closer look" ] }, { "cell_type": "code", "execution_count": 57, "id": "26038fd3-6dd6-4c59-b805-f1b6e68bbbbe", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Reaction: ES <-> E + P\n" ] }, { "data": { "text/html": [ "
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" ], "text/plain": [ " TIME P ES E S caption rate\n", "0 0.000000 0.000000 0.000000 1.000000 20.000000 0.000000\n", "1 0.000500 0.000000 0.400000 0.600000 19.600000 19.600000\n", "2 0.000750 0.004900 0.484489 0.515511 19.510611 23.739956\n", "3 0.000763 0.005197 0.487513 0.512487 19.507291 23.888118\n", "4 0.000769 0.005346 0.489003 0.510997 19.505651 23.961149\n", ".. ... ... ... ... ... ... ...\n", "859 1.170211 19.713808 0.030426 0.969574 0.255766 1.490884\n", "860 1.176184 19.722714 0.029500 0.970500 0.247787 1.445487\n", "861 1.182158 19.731349 0.028612 0.971388 0.240039 1.401986\n", "862 1.188131 19.739724 0.027735 0.972265 0.232542 1.358993\n", "863 1.194105 19.747842 0.026901 0.973099 0.225257 1.318155\n", "\n", "[864 rows x 7 columns]" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "history_with_rates_over = uc.get_diagnostics().get_system_history_with_rxn_rates(rxn_index=1) # We specify the reaction that involves `P`\n", "history_with_rates_over" ] }, { "cell_type": "code", "execution_count": 58, "id": "651f35be-fe04-41b7-a567-0697ae8e265c", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "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=history_with_rates_over, \n", " title=\"Reaction rate, dP/dt, over time\",\n", " x_var=\"TIME\", fields=\"rate\", \n", " x_label=\"time\", y_label=\"dP/dt\")" ] }, { "cell_type": "code", "execution_count": null, "id": "3d98bdb0-2885-49f2-ad3e-aab03075683c", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "b1633906-9132-4e29-a944-59af34401280", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "75b6c550-9716-4766-86a4-bd4afe2226ac", "metadata": {}, "source": [ "# Comparing the 3 scenarios" ] }, { "cell_type": "markdown", "id": "27443513-5acd-4676-bddd-bedb837488e0", "metadata": {}, "source": [ "#### The concentrations of the intermediate `ES` over time" ] }, { "cell_type": "code", "execution_count": 59, "id": "36fc0e0f-bc37-4bb3-88e3-e755c1d73cdb", "metadata": {}, "outputs": [], "source": [ "es_under = PlotlyHelper.plot_pandas(df=history_with_rates_under, \n", " title=\"underestimated k1_forward\",\n", " x_var=\"TIME\", fields=\"ES\", \n", " x_label=\"time\", y_label=\"ES\", colors = \"yellow\")" ] }, { "cell_type": "code", "execution_count": 60, "id": "13df7a7f-c94e-4cf9-90ee-1c8e99ff5671", "metadata": {}, "outputs": [], "source": [ "es_exact = PlotlyHelper.plot_pandas(df=history_with_rates_exact, \n", " title=\"exact k1_forward\",\n", " x_var=\"TIME\", fields=\"ES\", \n", " x_label=\"time\", y_label=\"ES\", colors = \"green\")" ] }, { "cell_type": "code", "execution_count": 61, "id": "163c2f25-68f5-4361-ae0f-8e6f7e96572a", "metadata": {}, "outputs": [], "source": [ "es_over = PlotlyHelper.plot_pandas(df=history_with_rates_over, \n", " title=\"overestimated k1_forward\",\n", " x_var=\"TIME\", fields=\"ES\", \n", " x_label=\"time\", y_label=\"ES\", colors = \"purple\")" ] }, { "cell_type": "code", "execution_count": 62, "id": "fd48ef57-477e-4974-85ee-4c315e6e7159", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "underestimated k1_forward
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ " PlotlyHelper.combine_plots([p_under, p_exact, p_over], \n", " title=\"P\")" ] }, { "cell_type": "code", "execution_count": null, "id": "bb0c74b1-8c3f-4bfd-8b97-23ca6cbc4ed7", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "2e52dba2-e39f-4af7-9051-b914a941fea7", "metadata": {}, "source": [ "#### The Reaction Rate over time" ] }, { "cell_type": "code", "execution_count": 67, "id": "e64d60e2-1524-496d-b818-89398dc3eb63", "metadata": {}, "outputs": [], "source": [ "r1_under = PlotlyHelper.plot_pandas(df=history_with_rates_under, \n", " title=\"underestimated k1_forward\",\n", " x_var=\"TIME\", fields=\"rate\", \n", " x_label=\"time\", y_label=\"dP/dt\", colors = \"yellow\")" ] }, { "cell_type": "code", "execution_count": 68, "id": "80750429-e2d5-4386-bdf0-1d530ca7fd90", "metadata": {}, "outputs": [], "source": [ "r1_exact = PlotlyHelper.plot_pandas(df=history_with_rates_exact, \n", " title=\"exact k1_forward\",\n", " x_var=\"TIME\", fields=\"rate\", \n", " x_label=\"time\", y_label=\"dP/dt\", colors = \"blue\")" ] }, { "cell_type": "code", "execution_count": 69, "id": "de6dbb69-6f8d-4048-ae30-75acd47c55bc", "metadata": {}, "outputs": [], "source": [ "r1_over = PlotlyHelper.plot_pandas(df=history_with_rates_over, \n", " title=\"overestimated k1_forward\",\n", " x_var=\"TIME\", fields=\"rate\", \n", " x_label=\"time\", y_label=\"dP/dt\", colors = \"purple\")" ] }, { "cell_type": "code", "execution_count": 70, "id": "a68a7586-4c18-4fbc-8a78-eabf7ca74cf9", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "underestimated k1_forward
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