{ "cells": [ { "cell_type": "markdown", "id": "5cbc8640", "metadata": {}, "source": [ "# **Enzyme Kinetics**\n", "### An _accurate numerical solution_ of an enzymatic reaction `E + S <-> ES -> E + P` is computed - and then it gets compared to the **Michaelis-Menten model** approximation and to the alternative **Morrison model**.\n", "\n", "#### Real-life kinetic parameters are being used. \n", "#### Scenario with **_small amount of Enzyme_**, relative to the initial Substrate concentration.\n", "\n", "* In the follow-up experiments `enzyme_1_b` and `enzyme_1_c`, the enzyme concentration gets progressively increased. \n", "* A side-tour in experiment `enzyme_1_a_technical` takes an under-the-hood look at how the enzymatic reaction is internally modeled with 2 coupled elementary reactions" ] }, { "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`, \n", "and the initial concentration values choosen below, all satisfy the customary Michaelis-Menten assumptions that `[E] << [S]` and that the reaction rate constants satisfy `k1_reverse >> k2_forward` \n", "\n", "For this reaction: k1_forward = 18, k1_reverse = 100, k2_forward = 49 \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\", \"numerical\", \"enzymes\"" ] }, { "cell_type": "code", "execution_count": 1, "id": "6e9d0902-6fc9-4692-ac39-0651d08902ca", "metadata": { "tags": [] }, "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": { "tags": [] }, "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, ReactionEnzyme, GraphicLog, PlotlyHelper" ] }, { "cell_type": "code", "execution_count": 4, "id": "af15ecf0-e083-4fef-b68e-abe794dcc86e", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "OK\n" ] } ], "source": [ "check_version(LIFE123_VERSION) # To check compatibility" ] }, { "cell_type": "code", "execution_count": 5, "id": "121fdfdd", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-> Output will be LOGGED into the file 'enzyme_1_a.log.htm'\n" ] } ], "source": [ "# Initialize the HTML logging (for the graphics)\n", "log_file = ipynbname.name() + \".log.htm\" # Use the notebook base filename for the log file\n", " # IN CASE OF PROBLEMS, set manually to any desired name\n", "\n", "# Set up the use of some specified graphic (Vue) components\n", "GraphicLog.config(filename=log_file,\n", " components=[\"vue_cytoscape_2\"],\n", " extra_js=\"https://cdnjs.cloudflare.com/ajax/libs/cytoscape/3.21.2/cytoscape.umd.js\")" ] }, { "cell_type": "code", "execution_count": null, "id": "3713fa4d-e9bb-4e33-8734-c1d4d23cf177", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "34d1cefc-f644-410a-9fe4-5204964742ac", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "91a729ee-ad2f-4771-bc84-49ecb9d6a851", "metadata": {}, "source": [ "# PART 1. Accurate numerical solution" ] }, { "cell_type": "code", "execution_count": 6, "id": "ac9eea69-174c-43e5-9eed-443cbc5e2ba7", "metadata": { "tags": [] }, "outputs": [], "source": [ "chem_data = ChemData(names=[\"P\", \"ES\"], plot_colors=[\"green\", \"red\"])" ] }, { "cell_type": "code", "execution_count": 7, "id": "90f9ec41-6e1b-4558-9400-47e35ece6efc", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
namelabelplot_color
0PPgreen
1ESESred
2Adenosine deaminaseEviolet
32,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purineSdarkturquoise
\n", "
" ], "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": 7, "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": "code", "execution_count": null, "id": "0f9c3501-0b99-47d9-87fa-3a027ede3799", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "f8d4ea7f-0591-467c-9df3-d95f53df75f5", "metadata": {}, "source": [ "### Specify the Kinetic Parameters" ] }, { "cell_type": "markdown", "id": "6b0b902c-c2bb-4731-9235-3f94ae9ec247", "metadata": {}, "source": [ "Source: *page 16 of \"Analysis of Enzyme Reaction Kinetics, Vol. 1\", by F. Xavier Malcata, Wiley, 2023*" ] }, { "cell_type": "code", "execution_count": 8, "id": "3be7173f-fc38-4a4f-a3f3-9c74e5f2ee58", "metadata": { "tags": [] }, "outputs": [], "source": [ "# Here we use the \"slower\" preset for the variable steps, a very conservative option prioritizing accuracy over speed\n", "uc = UniformCompartment(chem_data=chem_data, preset=\"slower\")" ] }, { "cell_type": "code", "execution_count": 9, "id": "142f6d4d-ce4e-4ea1-b52b-f5c8c245d6b8", "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)\n", "Chemicals involved in the above reactions: {\"P\" (green), \"ES\" (red), \"E\" (violet), \"S\" (darkturquoise)}\n" ] } ], "source": [ "# Here we use native support for enzymatic reactions\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": 10, "id": "373afeb1", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[GRAPHIC ELEMENT SENT TO LOG FILE `enzyme_1_a.log.htm`]\n" ] } ], "source": [ "# Send a plot of the network of reactions to the HTML log file\n", "uc.plot_reaction_network(\"vue_cytoscape_2\")" ] }, { "cell_type": "code", "execution_count": null, "id": "8913269e-9c1b-493f-8d28-c53f8cb7b5e4", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "d23a97ea-f252-4e11-a3e9-aea74f58591e", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "9a4febb2-2780-4754-9c70-c2041b1afc07", "metadata": {}, "source": [ "## Set the initial concentrations of all the chemicals\n", "### in the scenario we're exploring, there's LITTLE ENZYME relative to initial substrate concentration \n", "In the follow-up experiments `enzyme_1_b` and `enzyme_1_c`, the enzyme concentration gets progressively increased." ] }, { "cell_type": "code", "execution_count": 11, "id": "8c9e3f86-b9a5-41da-9e1b-75258017808a", "metadata": { "tags": [] }, "outputs": [], "source": [ "S0 = 20.\n", "E0 = 1." ] }, { "cell_type": "code", "execution_count": 12, "id": "aae96512-3d86-4ab0-b167-92943523b7ef", "metadata": { "tags": [] }, "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", "Chemicals involved in reactions: ['E', 'ES', 'P', 'S']\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": 13, "id": "e6ad72b8-722a-4606-a611-7dc600529f30", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "827 total variable step(s) taken in 1.774 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': 706, 'norm_B': 710, 'norm_C': 706, 'norm_D': 706}\n", "System Time is now: 1.5039\n" ] } ], "source": [ "# Perform the reactions\n", "uc.single_compartment_react(duration=1.5, initial_step=0.05)" ] }, { "cell_type": "code", "execution_count": 14, "id": "0198dd94-e55d-4ab4-9de8-087d508edf06", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_pandas() NOTICE: Excessive number of vertical lines (828) - only showing 1 every 6 lines\n" ] }, { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=P
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"color": "#2a3f5f" }, "geo": { "bgcolor": "white", "lakecolor": "white", "landcolor": "#E5ECF6", "showlakes": true, "showland": true, "subunitcolor": "white" }, "hoverlabel": { "align": "left" }, "hovermode": "closest", "mapbox": { "style": "light" }, "paper_bgcolor": "white", "plot_bgcolor": "#E5ECF6", "polar": { "angularaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "bgcolor": "#E5ECF6", "radialaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" } }, "scene": { "xaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" }, "yaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" }, "zaxis": { "backgroundcolor": "#E5ECF6", "gridcolor": "white", "gridwidth": 2, "linecolor": "white", "showbackground": true, "ticks": "", "zerolinecolor": "white" } }, "shapedefaults": { "line": { "color": "#2a3f5f" } }, "ternary": { "aaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "baxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "bgcolor": "#E5ECF6", "caxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" } }, "title": { "x": 0.05 }, "xaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 }, "yaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 } } }, "title": { "text": "Small amout of E relative to S(0)
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": [ -0.0012564246799850387, 1.5039403419420914 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.1111111111111112, 21.11111111111111 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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Reaction `E + S <-> ES -> E + P` . 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cJJ1dAtFIgXpTqTdRclCYZ1Cq7nhlneCRfGPleaMVkYJu+SWnQmOTgrRuaTpT0OvLuIhc1GX5ULe3v+ozRbgU+Tip4/KhZPvzCEURZjavlYOOvDIsyy3yGaJmn9KWY5aRgm6fdclBaK9ZSl3S0vY+5OnvLmYK8nw/FPnMzzt4zVNuEaaupSBv3yoy0HfBVb5n0m4+5JVQGT/5krMCss1fvODM9uyCEgF5MIbch6N/xtRdCor0Q5ufleRVnkB0UqC/cZNv1uQdkCwseT9889yRKSIFRT70inyhlw//eylNZwqqlIIia/CT9XIhB/pgucwSJZP26O2zlU+SWSjtS9bLxfIhG+8lV3kUXdqU9zMk6zNM9SfXUqAPpoqySx7DmpXehRTk+X4o8plv83upCFOXUlCkbxVhVeTavFzT+k6RPVx6neTgX93IlHm8+tpvxPx5c9obufVZiLpLQZF+WPS9z/VuCEQpBRJF2ps17ybcrPVwRdbFyg8A+ZCjtLWRKlTJD64i6yDzfqHb6hahSYGMRdb583nW8vbiYkMOTAfLqo5FBvOuuejcfLSvV9z03zdNClS/73bnUvbrD0/9YNcjSZPrn7P2KZlIQbe9T3n3TyX7Qlrfz/tZ4EIKet0Qkt8PRT7z8w5e85SbR1gU37xSUOS7TuVdpG912/uXZOOCa9Zna94nmevvT9l+tY8g6+fymrR2FOGgOOeZPZLXFo1h3mVCqh7J64v0wyKf/VzrjkC0UiCRqCU36u5s2ulDCp0c9MpjvORRW2l33PRpad3kVRn6HobkZqEsyUh7Q6Tll1w6JOvcdClIO7lB/1Arsoyi29un7JIbla7MzECyPkWkoGouVbevyEddLFKg4mujz9p4eFnWpkh9mY6+HLPMTIGMY9qNBvVZl+f0IZmH/KyVR2WqZRjyqev653Pe2RMXUqB/B3X7fsj7mZ9XCvKWm3bqS5Kp/H9eKVAxTR692e37qtvpfzKd3rfSJDRrsJnFIO27NC9X1Zf05T15Tx9S9VQnOSU/N7M+t9P6ZVEOKqby2Nc8eyGKjlfS9jAUkYW8/bDIZz/XuiMQtRSoDyn5RaF/yeQ5nSW5NlU/Tzn5xtLvmKpQpB1nqn5n+zkF6sxgmX+TTh9KWz8sGdgYqLp7SxXPOc9+mOSgI+3c71C5FG1fXoJNlALFJs9nXJEbC8kYSYFRZ6GXlQL981nVWw645MbLtH0AWe93/bNWDbr0PpJnIORKCvQBcbc6Jb9D0gQx7+BVldPre0kfLCbfU0mmaZvr0waPyX7S67tOlpu3b+nfb6q+Np9TkOeUKSUVOq8i+4zSpETvI8m8smY8knsbenHIO1OQFo9uMSwy+Fei1m0jdLd+mPdzn+vcEgheCtw2n9whAAEIQKAqAt2WL1RVB8qBAAQgAIF0AkgBPQMCEIAABKwT0Jf+qMzz7vuyXhkyhAAEIACBngSQgp6IuAACEIAABIoSSFsOlPd4x6JlcT0EIAABCJgTQArMGZIDBCAAAQhAAAIQgAAEoiaAFEQdPioPAQhAAAIQgAAEIAABcwJIgTlDcoAABCAAAQhAAAIQgEDUBJCCqMNH5SEAAQhAAAIQgAAEIGBOACkwZ0gOEIAABCAAAQhAAAIQiJoAUhB1+Kg8BCAAAQhAAAIQgAAEzAkgBeYMyQECEIAABCAAAQhAAAJRE0AKog4flYcABCAAAQhAAAIQgIA5AaTAnCE5QAACEIAABCAAAQhAIGoCSEHU4aPyEIAABCAAAQhAAAIQMCeAFJgzJAcIQAACEIAABCAAAQhETQApiDp8VB4CEIAABCAAAQhAAALmBJACc4bkAAEIQAACEIAABCAAgagJIAVRh4/KQwACEIAABCAAAQhAwJwAUmDOkBwgAAEIQAACEIAABCAQNQGkIOrwUXkIQAACEIAABCAAAQiYE0AKzBmSAwQgAAEIQAACEIAABKImgBREHT4qDwEIQAACEIAABCAAAXMCSIE5Q3KAAAQgAAEIQAACEIBA1ASQgqjDR+UhAAEIQAACEIAABCBgTgAp6MHw7vsfFdeuWte56qgZh4v1a5abkycHCEAAAhCAAAQgAAEIBEIAKegRiMuWrxaX/dHZYvq0w9pXzj3rUnHGZ2eLZZcsCiSEVAMCEIAABCAAAQhAAAJmBJCCgvykJMjXTSuWFkzJ5RCAAAQgAAEIQAACEAiTAFJQMC4Ll6wQxx87g5mCgty4HAIQgAAEIAABCEAgXAJIQYHYqP0Fzz92Z4FUXAoBCEAAAhCAAAQgAIGwCSAFOeOjhOChu67v7C9QSV/9zc6cuTTrsm3vbhWz1x4h5N/fXfCwmD3thKgAHHzAeLFj116xa89AVPWmsvkITDl4ovj1mzvFwGC+67kqHgL9/X3ig5MmiNfe3BVPpalpbgL7jR8j3jdhjNiyfXfuNFwYF4Gph0yMq8I1qS1SkCOQ3YRAJkcK0iHe8cy3xfLHl4lPTTtR3LtgQw7SYV2CFIQVD9u1QQpsEw0nP6QgnFi4qAlS4IJqWHkiBX7igRT04L7y1nvEnes3iG5LhpCCdIhnf+9U8bev/FisOGGluOiYL/np4QalIgUG8CJIihREEKSSVUQKSoKLJBlSEEmgDKqJFBjAM0iKFPSAJ48g3bxl26ir9GVESMFoiJteeVx8/nu/LyZNOEhsuuCF9t+xvZCC2CJWrL5IQTFeMV2NFMQUreJ1RQqKM4stBVLgJ2JIgQXuSMFoiNc8cYW4/enV4uJjl4pr5txggXL1WSAF1TOvskSkoEra1ZaFFFTLu+rSkIKqiVdfHlJQPXNZIlJggTtSMBJi7BuMVWuQAgtvjoCzQAoCDo5h1ZACQ4CBJ0cKAg+QheohBRYglsgCKSgBLZkEKRhJJPYNxkiBhTdFBFkgBREEqWQVkYKS4CJJhhREEiiDaiIFBvAMkiIFBvBUUqRgJMTYNxgjBRbeFBFkgRREEKSSVUQKSoKLJBlSEEmgDKpZhRQcedJicfVXzhfnzD/ZoKb+k8oDcR780Sax8b6bjSuDFBgj5EhSHWEdNhgjBRbeFBFkgRREEKSSVUQKSoKLJBlSEEmgDKppQwouW75aPLLxqRG1OGXu8eKmFUvbP/MlBb2OuS+KDSkoSszx9cwUvAe4DhuMkQLHb5hAskcKAgmEg2ogBQ6gBpQlUhBQMBxVxVQK5IB/8sGTRt09X7hkhfjyhWeJObNmepMC28iQAttEDfNDCoYA1mWDMVJg+IaIJDlSEEmgSlQTKSgBLaIkSEFEwSpZVRMpkDMEP332Fz2X06iZgtvWPtA5en7xwlPFsksWjai1FInnXnyp8zP9SHr5u6lTDhGvvvabzjVHzThcrF+zXOhH2uszFE88+axYcsWNQs9HZi7ro7/U79OOxtefnYUUlOxkrpIhBUNk67LBGClw9U4JK1+kIKx42KwNUmCTZnh5IQXhxcR2jUykQA6u0wb3yTqqQbgafKvB+pobLm/PJMiXGvSrJUdq6Y8alCthUGlefuV1Me/cK9tpVb7qZ+qapBSo3+t1luXIl9zvIKVA3y8gy5QvKR7yhRTY7n2G+SEFQwDrssEYKTB8Q0SSHCmIJFAlqokUlIAWURKkIKJglaxqWSlIDsC7FZ+2p0AOwL94wZntwbgcvF/1zTtGzTjo1ySlQZYnf3/GZ2ePmHFI5qvPFMhB/VNPv9gZ5PdClhQTpKAXsYp/jxQIUacNxkhBxW8gT8UhBZ7AV1AsUlABZI9FIAUe4VdUtE8pUAN6Odi+c/2G1Baru/pFpEDlm5wpSMsjWWhyaZH8vZqtQAoq6pR5i0EKhKjTBmOkIG/Pj/s6pCDu+HWrPVJQ39jKliEF9Y6vbF1ZKZBp854qlDVToEtBr6M+XUuBEojk0qJrV61DCkJ9GzRdCuq2wRgpCPWdZrdeSIFdniHlhhSEFA37dUEK7DMNLUcTKZAD9dfe2JK60VgOsuUr6/QhfelP1oZgnZUNKZAbo+VGZbVHQM8/bRaA5UOh9dZEfZouBXXbYIwUBP6Gs1Q9pMASyACzQQoCDIrFKiEFFmEGmpWJFKh9BckjSdVyILXht9dMgUQjJUG+9I2+Mp8P/atD2/sObEiBqq/+IDW10ViWrc8KqDpt3rKNmYJA+65ouhTUbYMxUhDqO81uvZACuzxDyg0pCCka9uuCFNhnGlqOJlKg2pI8SlT+XD8GNI8UyDRp+einD8kjSdXpRGrQnrbROGtPgUyjn1qk6q/qmnwIm1xKJPc6sKcgtF47XJ8mS0EdNxgjBYG+0SxXCymwDDSg7JCCgILhoCpIgQOogWVpQwoCa1IU1ekbbL2iqGnAlWyyFNRxgzFSEPCbzWLVkAKLMAPLCikILCCWq4MUWAYaYHZIgZ+gIAUWuDdVCuq6wRgpsPCmiCALpCCCIJWsIlJQElwkyZCCSAJlUE2kwACeQVKkwACeStpUKajrBmOkwMKbIoIskIIIglSyikhBSXCRJEMKIgmUQTWRAgN4BkmRAgN4TZeCum4wRgosvCkiyAIpiCBIJauIFJQEF0kypCCSQBlUEykwgGeQFCkwgNdkKajzBmOkwMKbIoIskIIIglSyikhBSXCRJEMKIgmUQTWRAgN4BkmRAgN4TZaCOm8wRgosvCkiyAIpiCBIJauIFJQEF0kypCCSQBlUEykwgGeQFCkwgNdUKaj7BmOkwMKbIoIskIIIglSyikhBSXCRJEMKIgmUQTWRAgN4BkmRAgN4TZWCum8wRgosvCkiyAIpiCBIJauIFJQEF0kypCCSQBlUEykwgGeQFCkwgNdUKaj7BmOkwMKbIoIskIIIglSyikhBSXCRJEMKIgmUQTWRAgN4BkmRAgN4TZSCJmwwRgosvCkiyAIpiCBIJauIFJQEF0kypCCSQBlUs45SMPesS8XmLds6VI6acbhYv2a5ASX7SZECC0yb9JyCJmwwRgosvCkiyAIpiCBIJauIFJQEF0kypCCSQBlUs65ScMZnZ4tllyxqk5GScNzMj4mbViw1IGU3KVJggWdTpKApG4yRAgtvigiyQAoiCFLJKiIFJcFFkgwpiCRQBtVsghTcff+j4ra1D4iN991sQMpuUqTAAs+mSEFTNhgjBRbeFBFkgRREEKSSVUQKSoKLJBlSEEmgDKppQwoe/KcHDWpQLml/X7847WOnpSaWMwP6TAFSUI5x8KmaIgVN2WCMFAT/lrNSQaTACsYgM0EKggyLtUohBdZQBpuRDSnoW9HnpX2DywdzScGRJy0Wixee2llO5KWyiUKZKbAQhSZIQZM2GCMFFt4UEWSBFEQQpJJVRApKgoskGVIQSaAMqmlDCs68+0yDGpRLOrZ/rLhv4X2ZUqBvNA5NCGSlkYJycR+RqglS8K0nrxM3tv5cfOxScc2cGyxQCz+Lgw8YL3bs2it27RkIv7LUsDABpKAwsmgSIAXRhKpURZGCUtiiSmRDCkJrcHL5UGj1QwosRaTuUtC0DcbMFFh6YwSeDVIQeIAMqocUGMCLIClSEEGQDKuIFBgCLJmcmYKS4PRkdZeCh196UPz7H3xBfGraieLeBRssEIsjC2YK4ohT2VoiBWXJhZ8OKQg/RiY1RApM6MWRFinwEyekwAL3uktB0zYYM1Ng4U0RQRZIQQRBKllFpKAkuEiSIQWRBMqgmnWUAgMclSVFCiygrrMUPL/5Z+KUe35XTJpwkNh0wQvtv5vyYqag3pFGCuobX6SgvrGVLUMK6h1f2TqkwE+MkQIL3OssBU3cYMxMgYU3RQRZIAURBKlkFZGCkuAiSYYURBIog2oiBQbwDJI2VgqeePJZseSKG8Xzj93ZFZ+6LnmRnq6uUtDUDcZIgcEnSkRJkYKIglWwqkhBQWCRXY4URBawEtVFCkpAs5CkcVLw8iuvi3nnXtlBl1cKul1XVylo6gZjpMDCJ0sEWSAFEQSpZBWRgpLgIkmGFEQSKINqIgUG8AySepcCeW6r/jAHvS29BkyPqtcAACAASURBVOwG7Rby8dLXrlqXe6agiVLQ1A3GSIHJOyuetEhBPLEqWlOkoCixuK5HCuKKV5naIgVlqJmn8SoFC5esEFOnHCJuWrHUvCUFcygqBd1kpY4zBU3eYIwUFHwzRXo5UhBp4HJUGynIASniS5CCiIOXs+pIQU5Qli/zKgVHnrRYrLnhcjFn1kzLzeqdXV4pSOYkRUa+1q9Z3vnV9h17ehcY2RX/+W+/If7zT74h/vj4/1d88zP/X2S1t1PdiRPGiD17B8TefYN2MiSXoAjsP3GceGfXHjHYkPAODAwKOVhuwquvr0+8f78x4u2de5vQ3Ma1ceyYfjFubJ/Y+e6+xrW9KQ0+4H3jmtLUoNqJFPTYaJyMVtoG5e01/OKZ/l8OFVt3bRU/POdRMefDJwbVaauqzMTxw1LQGkzxqh+B/SeOFe+03rtNiW6zpECI908YK97ehRTU750rxNgxfWJcSwx27kYK6hhf2aYDWp/PvKon4FUK5F33+fPmiHPmn1x5y8vOFKRJQd2WD2165XHx+e/9fuOeYJzshDynoPK3ZaUFsnyoUtyVFsbyoUpxV14Yy4cqR155gSwfqhx5u0CvUiAH2Fd98w6x8b6bK299lhSsvPUecef6DZ0NyJctXy0u+6OzxfRph7XrKDdGHzfzYyP2QdRNCpq+wVh1RqSg8rdlpQUiBZXirrQwpKBS3JUXhhRUjrzyAusoBVkH66iDbNS4VId99VfOr/TGuVcpkHsKur1cnD6UPJJUlr944ali2SWL2lVJSoH6v6rnUTMOH7GfQP68TlIgn01wxO1TG/kE42RfRAoq/x6otECkoFLclRaGFFSKu/LCkILKkVdeYF2l4IzPzu6MN3WoaTeq5Xh12Z/cNmrM6TIYXqXAZcOqzLtOUtDkJxgjBVW+a/yXhRT4j4GrGiAFrsiGkS9SEEYcXNaiaVIgV6XIl4/TOPU4epeCtCcG+zqRqGwHr5MUyFkCOVvw3QUPi9nTTiiLpBbpmCmoRRgzG4EU1De+SEF9YytbhhTUO76ydVak4MEHqwfV3y/EaaelliuXD/WaKfA9/vUqBWq65KG7ru+s2VfLe6peR2XSc+oiBWwwHtkLkAKTd0X4aZGC8GNUtoZIQVlycaRDCuKIk0ktrUhB62hiL6+Mc6577SlILleXdXexjL4bE69SIAF98YIzR22ikLJw29oHvGxALtOB6iIFbDBGCsr0/1jTIAWxRq53vZGC3oxivgIpiDl6+epuRQrOPDNfYTavGts6SvW++wrPFKQlkCd0vvbGlkrHwl6lIOvhZWnHftqMme286iAFbDAe3SuYKbD9TgkrP6QgrHjYrA1SYJNmeHkhBeHFxHaNrEiB7UoZ5tdt+VBa1j7Gwl6lgJkCwx5mMbnaYHzqRz8n/uy09RZzjjcrpCDe2OWpOVKQh1Kc1yAFccYtb62Rgryk4r2uaVIgZwW+fOFZYs6smZ2gyZ/J1/o1yysLpFcpYE9BZXHuWRAbjJkp6NlJanYBUlCzgGrNQQrqG1vZMqSg3vGVraurFGzesm1U8OS+gbRDd06Ze3zlpxF5lQJJhtOH/L+51QbjIw89RjyycJP/CgVSA2YKAgmEo2ogBY7ABpAtUhBAEBxWASlwCDeQrOsoBYGg7VoN71IQA6RedYx9T4HaYHz5rKvEV1t/eA0RQArq3ROQgvrGFymob2yZKah3bFXrkAI/cUYKLHCPWQrYYJzdAZACC2+OgLNACgIOjmHVkAJDgIEnZ6Yg8ABZqB5SYAFiiSyQghLQkklilgI2GCMFFt4CUWaBFEQZtlyVRgpyYYr2IqQg2tDlrjhSkBuV1Qu9SIE8ilQ+nOzaVeu6NqbqhzaUJRuzFLDBGCko2+9jT4cUxB7B7PojBfWNrWwZUlDv+MrWIQV+YuxFCvw01V2psUqB2mA8acJB4oWLX3UHKNKcWT4UaeByVhspyAkqwsuQggiDVqDKSEEBWJFeihT4CZxXKch6eBlPNK6mM7DBuDtnpKCafuirFKTAF3n35SIF7hn7LAEp8Em/mrKRgmo4J0sJUgp8PMXNBH+MMwVqg7Fst5wlkLMFvEYSQArq3SOQgvrGFymob2xly5CCesdXtg4p8BPjIKVg5a33iAd/tElsvO9mP1QKlhqjFKgNxp+adqK4d8GGgi1uxuVIQb3jjBTUN75IQX1jixTUO7aqdUiBnzhXLgVpDytLa/qaGy4f8bhnP3jylRqjFLDBuHdskYLejGK+AimIOXrd644U1De2SEG9Y4sU+I1v5VKgNzdrT4FfJMVLj00K2GCcL8ZIQT5OsV6FFMQaud71Rgp6M4r5CpYPxRy9fHWv40zB3LMuFZu3bBsFIKSTNr1KQb6uEf5VsUnBhT9cKDb88/cFTzDu3reQgvDfeyY1RApM6IWdFikIOz6mtUMKTAmGn76uUnDGZ2eLZZcsCjYASIGF0MQkBXKD8ey1Rwj5NxuMkQIL3T/aLJCCaEPXs+JIQU9EUV+AFEQdvlyVRwpyYbJ+kVcpePmV18W8c6/MbFRIUyrdyMckBWwwzv8eYqYgP6sYr0QKYoxavjojBfk4xXoVUhBr5PLX24YU7PnFnvwF2rqyT4hx/9e41Nzk8iFmCrqAVoBm/86R4qpv3tE5bWjhkhVi/rw54pz5J9sKk9N8YpKCU9bPFs+/8Yz47oKHxexpJzjlEnvmSEHsEexef6SgvvFFCuobW9kypKDe8ZWtsyEFb37jTS+gPvAfP5ApBewp6BIStdF4+rQPivO//KcdKZAnFOmS4CWqBQqNRQrYYFwgqK1LkYJivGK7GimILWL564sU5GcV45VIQYxRK1ZnG1Lw9j1vFyvUxtX9Quz/hf2ZKSjDUj99SP5bLRfi4WVlaPZOc80TV4jbn17NBuPeqNpXIAU5QUV6GVIQaeByVBspyAEp4kuQgoiDl7PqNqQgZ1GVXcbyoR6o5TKh44+d0d6Jrf+bh5fZ76NsMC7OFCkoziymFEhBTNEqVlekoBiv2K5GCmKLWPH6IgXFmdlI4XWjcbIBcrZAvR6663oxfdphNtroPI8Ylg/d8cy3xfLHlwmeYJy/OyAF+VnFeCVSEGPU8tUZKcjHKdarkIJYI5e/3nWVAvYU5O8D0V4ZgxSc/b1Txd++8mM2GBfoZUhBAVgRXooURBi0nFVGCnKCivQypCDSwBWodh2loEDzvV3qdaaAJxpXE3c2GJfjjBSU4xZLKqQglkgVrydSUJxZTCmQgpiiVa6uSEE5bqapkAJTgq30oc8UsMG4XJCRgnLcYkmFFMQSqeL1RAqKM4spBVIQU7TK1RUpKMfNNJVXKYjteQRZsEOWAn2D8SOL/k4cOflo0z7TmPRIQb1DjRTUN75IQX1jK1uGFNQ7vrJ1SIGfGHuVAvlEY/35BH4QmJcashSwwbh8fJGC8uxiSIkUxBClcnVECspxiyUVUhBLpMrXEykoz84kpVcp0E8bSmuEem6BSQOrSBuyFKgNxn9++l+J3z/8jCpw1KYMpKA2oUxtCFJQ3/giBfWNLTMF9Y6tah1S4CfO3qVgzQ2XizmzZo5o/d33PypuW/tA5wnHftDkLzVUKdA3GG+64AUxacJB+RvFlTy8rOZ9ACmob4CRgvrGFimod2yRAr/xDVIKeKKxnU6hNhhffOxScc2cG+xk2qBcmCmod7CRgvrGFymob2yRgnrHFinwG98gpYAnGpt3Cn2D8XcXPCxmTzvBPNOG5YAU1DvgSEF944sU1De2SEG9Y4sU+I1v5VKgZgF6NTttWVGvNL5+H+LyITYYm/cGpMCcYcg5IAUhR8esbkiBGb/QU7PROPQImdePPQXmDMvkULkU6JWM6eFl3ZY0hSgFaoPxihNWiouO+VKZvtH4NEhBvbsAUlDf+CIF9Y0tMwX1jm3dZwrmnnWp2LxlWyeIkw+eFNT+Wa9SEEPXlsemzjv3yk5V005ECk0Knt/8M3HKPb/b3ljMBuPyvQwpKM8uhpRIQQxRKldHpKAct1hSMVMQS6TK17OOMwVSCM747Gyx7JJFHTCXLV8t/vD0uaMO3ClPziwlUpCTnzwR6dpV60QMUvCtJ68TN7b+sME4Z3AzLkMKzPiFnhopCD1C5euHFJRnF0NKpCCGKJnVsW5SoG4wP3TX9WL6tMPM4DhM7V0KklMpeltDek5BLFLABmN77xakwB7LEHNCCkKMip06IQV2OIaaC1IQamTs1cuGFDy47S17FcqZU39fnzjtwANSr5bj3SmHHizWr1meM7fqL/MqBQuXrBBTpxwiblqxtPqWFywxSwre+s5bou+8iQVzc3f5D/7/B8Q53/u8OGH6XPGDhT9yV1ADcp44YYzYs3dA7N032IDWNq+J+08cJ97ZtUcMNiS8AwODQg6Wm/Dqa30xv3+/MeLtnXub0NzGtXHsmH4xbmyf2Pnuvsa1vSkNPuB944yb2vePPzPOo0wGg584OjNZ8qG9ixeeOmI5UZnybKbxKgUxbTTOkoI3v/GmGPsf0q3QZqDy5nX6Pf9GPP7yRnH9yd8Sl/zOl/Mm47oUAhPHD0tBazDFq34E9p84VrzTGjQ2JbrNkgIh3j9hrHh7F1JQv3euEGPH9IlxLTHYuRspqGN8ZZsOaH0+m77O/OdfmmZROL2s9X0f/UiudOoAm6u/cr44Z/7JudK4vggpyEm4mxTsuHC86JvQnzMnd5fJpUNH3D6VDcaWELN8yBLIQLNh+VCggbFQLZYPWYAYcBYsHwo4OJaqZmP5kKWqOM1Grpg5/tgZwcwWeJUCCWP+vDnBGFK3yHeTgp3njRfiQP9SwAZju+9dpMAuz9ByQwpCi4i9+iAF9liGmBNSEGJU7NapblIgZwVu+bP7RuwnUDMFIT2Xy6sUSCBXffOOoM5oTXbr5JGk8vf6GjC5fCgUKZCzBHK2gCcY2/lwQgrscAw1F6Qg1MiY1wspMGcYcg5IQcjRsVO3ukmBpCJvhD/34ksjAIV2GpFXKUhuuEh2pZBOH8rq5qFIwaZXHhef/97viyMPPUY8snCTnXdlw3NBCurdAZCC+sYXKahvbGXLkIJ6x1e2ro5SEEPUvEpBDIB61VFKwe75E8S+qX5P9VBPML581lXiq60/vMwJIAXmDEPOASkIOTpmdUMKzPiFnhopCD1C5vVDCswZlskBKShDTUsTghSwwdgwiBnJkQI3XEPJFSkIJRL264EU2GcaUo5IQUjRcFMXpMAN1165IgW9CPX4fQhSoDYYn/rRz4k/O229YYtIrgggBfXuC0hBfeOLFNQ3trJlSEG94ytbhxT4ibF3KdA3Xqgd2HKvwSlzj4/ioWZtKThtvNj3EX+nD7HB2M2bBylwwzWUXJGCUCJhvx5IgX2mIeWIFIQUDTd1QQrccO2Vq1cp0J9oLB//fN3XLhJzZs0U8vjP29Y+EPSpRAqslII9J48Te2eM6cXaye/VBuNJEw4SL1z8qpMympopUlDvyCMF9Y0vUlDf2DJTUO/YqtYhBX7i7FUK5IyAOo5JlwJ1dmsspw/5lAI2GLt74yAF7tiGkDNSEEIU3NQBKXDDNZRcmSkIJRLu6oEUuGPbLWevUiBFYN0tXxfTpx0mmCko3gHUBmOZUs4SyNkCXvYIIAX2WIaYE1IQYlTs1AkpsMMx1FyQglAjY69eSIE9lkVy8ioFK2+9Rzz4o03tZUJKCqZP+6CYd+6VIx4QVqRBVV8rlw/t/eRYsaf1p+qX2mD8qWkninsXbKi6+NqXhxTUO8RIQX3jixTUN7ayZUhBveMrW4cU+ImxVymQTVZLhfTmX/2V88U580/2Q6RgqT6l4JT1s8XzbzzDE4wLxizv5UhBXlJxXocUxBm3PLVGCvJQivcapCDe2OWtOVKQl5Td67xLgd3mVJ+bLylgg7H7WCMF7hn7LAEp8EnfbdlIgVu+vnNHCnxHwH35SIF7xmkleJWCy5avFo9sfEokNxTHdiTp3mPGiD2fHldpBC97dIn4q5+vEzzB2B12pMAd2xByRgpCiIKbOiAFbriGkitSEEok3NUDKXDHtlvOXqVA7iP44gVnjloqFNuRpHt/uyUFv1edFMgNxrPXHiHk32wwdvfGQQrcsQ0hZ6QghCi4qQNS4IZrKLkiBaFEwl09kAJ3bIOVAjkjoB5YplcytiNJq5aCO575tlj++DLBBmO3bxqkwC1f37kjBb4j4K58pMAd2xByRgpCiILbOiAFbvlm5c5MgSF3uadgcNoYsesPqpspUM8m+O6Ch8XsaScYtoDkWQSQgnr3DaSgvvFFCuobW9kypKDe8ZWtQwr8xNirFMhlQteuWtd5gJlE8PIrr7ePJI3lBKKqpUDfYLzpghd4NoHD9w1S4BBuAFkjBQEEwVEVkAJHYAPJFikIJBAOq4EUOITbJWuvUiDrlXYkadqSIj94epcqpWDg0H7x7tnje19s4YprnrhC3P70ajYYW2DZKwukoBehuH+PFMQdv261RwrqG1tmCuodW9U6pMBPnL1LgZ9m2yu1PVNwYJ/Ydd4Ee5lm5KRvMH5k0d+JIycf7bzMJheAFNQ7+khBfeOLFNQ3tkhBvWOLFPiNL1JgyL9KKWCDsWGwCiZHCgoCi+xypCCygBWoLlJQAFaEl7J8KMKgFawyMwUFgVm63LsUyGNJN2/Zltqc5PMLLLXZajZSCuRr5x/vZzXftMzUBuMVJ6wUFx3zJeflNb0ApKDePQApqG98kYL6xpaZgnrHlpkCv/H1KgULl6wQU6ccIm5asdQvBYPSq5ICNhgbBKlkUqSgJLhIkiEFkQSqRDWRghLQIkrCTEFEwSpZVWYKSoIzTOZVCrKeU2DYpkqTb7tlmxjYOiB2ntfaaHxgv7Oy1Qbji49dKq6Zc4Ozcsj4PQJIQb17A1JQ3/giBfWNLTMF9Y4tMwV+44sUGPJXUrDrC+PF4ORsKRj73M/E2F+9LMY9+0y7xDGtfydfg5MmiYEDJ4348b7pv9X+//LHr2g/wVhKwYxPfG7kNR+ePuL/A618BicdZNgykiMF9e4DSEF944sU1De2SEG9Y4sU+I2vVymQy4fmz5sjzpl/sl8KBqW/ve5tseeXe8Tu+RPEvql9o3J63z1/KQ644Tox5uV/MSjFLKkUBCkK+mvfh4dkQ732DsuH+v++hGgoOVG/H5B5agLTFpHk/yMXE6TArN+FnhopCD1C5euHFJRnF0NKlg/FECWzOrJ8yIxf2dRepUA+o+Cqb94hNt53c9n6e0+XJQV927aKQy5YJMb/5MftOspB9Z6jjm7/Uf9PVr5v2zbR30qnv+SMwsP//P32LMGnpp0oPnTgb4mxmmD0vZWSxqOAZAWkl5hIqZCioV7JWRP5O/mzLClJSoyN2RKkwPvby2kFkAKneL1mjhR4xe+8cKTAOWLvBSAFfkLgVQrknoJurxhOH3rngXfE7md2iz0njxN7Z4zpNGfyH5zaFgIpA9uvuErsWHReqQhLGTji9qntJxeXfYKxFJT+lnAkZUP9vz+HWCSXO0l50fNMyon8nSw3lFdypkOfKckSkokTxog9ewfEu9NGLs/aq82y1HGGJJSYua4HUuCasL/8kQJ/7KsoGSmogrLfMpACP/y9SoGfJtstdccjO8S7//1dsWdOSwqOHpKC96/5tph01bK2EGz+64dF8i52kRp868nrxI2tP7FvMC4qJslZEyku8mcdkUlIyZhfjVyeFYqUdJORbku2us2MICJF3kHZ1yIFdjiGmAtSEGJU7NUJKbDHMtSckAI/kfEuBXIJ0ZIrbhzR+jU3XC7mzJrph0jBUnf9eJfYuXGn2PvJsWJP648c/E457oj231IIdn/6hII5jrxczhLI2YLvLnhYzJ5mlpdRRSJPnNzToc98JGdKlJComYLBX44Ujm7Lt3zLSHKZVlsuhvd6JGdEdFlNSog+G9Jrf0msXQMpiDVyveuNFPRmFPMVSEHM0ctXd6QgHyfbV3mVgrvvf1Rcu2qdeOiu68X0aYe12/byK6+LeedeKa7+yvlRbEB+98l3xY6Hd4i9v91aavJ74zqzBLs/fWJLCjYYxUs9m+DIQ48RjyzcZJQXiYsTsLGnoJuMjE3MbujXdpsZSS7V8rmJXZ8JMRWQ5AxIcpaleAS7p0AKbBMNJz+kIJxYuKgJUuCCalh5IgV+4uFVCuTTjL94wZmjBv9SFm5b+0AUG5D3/NMe8fb6t8W+w/vF7nnjhdpLYGOWQD3B+PJZV4mvtv7wqpaADSmotsaiPUM1eq/H0LKr5IxINwnRZ0OSS7N8SIg+A5JXPpLCok7LUjMfhx60n3hDtE4NO5Dje6vup67LQwpcE/abP1Lgl38VpSMFVVAeXYZXKch6eJlaUhTDRuN9L+8Tb/3FW2JwWmum4BOvisOO+3j7GQGv/fQFo2cF2Nhg7KdL1afUGKWgavq6IAzNYJQXEN8zIMmlV2ozetayq6wlV1XPeFQd8xjKQwpiiFL5OiIF5dnFkhIp8BMpr1JQh5mCfa+3pOA7b4mBQ/vF2C23tzcY7zjnfLH1ljVGEVUbjOUxpPcuMFuGZFSRBidGCsIJfhn5GLFvRJtBUTMfY/r7xOCbWys7JSuPdOhH8erSoT8XRJcOG0fvhhNlezVBCuyxDDEnpCDEqJSs01sDom93ayZ799Bznvq2D7T//uCn9i+ZIclMCHiVgjrsKRjYNSC2rWzdHZ3QJyZuvEDs98Pvi62rv1P6CFIVTDYYm3RrO2mRAjscQ80luacgufRKSUXWsqvkvg+15MrXjEfW/g79lCu1dCpLOPRN5a73dLjsF0iBS7r+80YK/MdA1mDw3daA/l0hxrw9/ODW3YOt/w8K0fpZ++/W/9W/1aBftAb9Mo2Qv+/y+sB//EAYjWxYLbxKgWQd++lDsg1vfuPNdrc56MaPtu86vv7Tn7ePIy37UhuM5bMJXrj41bLZkM6QAFJgCDDw5FVvNM4jHfpRvLp06M8F0fd4VHXalf55ppZVpcmGDLl+rTrFqmrZQAoCf/MZVg8pMASokmfcpe97a3jAvn3o7zHbhxIMDg/6O7+3UI3BA1sztq2bqn3jh8Ri3wFDmR569oEWcieLogS8S0HRCod4/ZabW0sQWm+iSd86RvQNbhf/+3+aDeQv/OFCsaH1FGM2GPuNNlLgl7/r0quWAtft0ZdYFZnlyBIO1xvKszaP553Z6LaMCilw3dv85o8UtPi3BvTtAXviLn1nwG5wlz53dFuD+cEJLVkYHtQPjB9s/7t1foMQrUG++nf7bzXo319e05pJmNDftRj2FOSOgtULkQILOLf8+Vui75V9Yv8//5zYd8TBYsva9aVzlRuMZ689ov1sAjlLIGcLePkhgBT44V5VqXWTAlfcsmY49CN1U4UkZR9HexDz8sjnftiut5qpkHtGdg8/jbyXaKgZDV00TGZ7bbeJ/EYSiF4KMgb0vZbdSApV3KUXBwzdtZd38dt/HzA0gG8P+sdLCeg9qDfts0iBKcFy6b1IgdpLkPYsgm6/K9fE0akuW75aPLLxqfYvjppxuFi/Znlm1mnLm+TF+slISgre/1/PE3tO+qjYdu0Npat6xzPfFssfXybYYFwaobWESIE1lEFmhBT4DYsuG/rJVWmyoS+lStu74XIZVdqMhn4ildocnrZPg03hbvqYLylQa+jTNsZWeodeG7ALfcBu6S69m6gVyxUpKMbL1tVepGDhkhVi6pRDxE0rlqa2Qw7aX33tN10H62UBJJ+BIOty/LEzxLJLFqVmmed41DfufUuM/R/7xMQffl3sOu84o03G6tkEPMG4bITtpUMK7LEMMSekIMSomNdJzkTI5UOHDOwUW37163aGaaKhn06VJhquZjR6SUbaZnBfezPMo+Emh1JS0OvuvKxq1hr6HBtji7RU3YEvOqBvl3Fg92U3ReoR8rVIgZ/oeJGCrOcTKAR5BuJlcSUloNeD0vLU5Y0N28XYv98r9vub68X25QvE3qOOLlU9NhiXwuYsEVLgDG0QGSMFQYTBSSVs7ilIm9HQT6RS8pC2MVw/icqVZHTbBK4fcauuU8fbxrJUKu3u/PidrSXqY/vFjl/vGeo/icH80M+G1tzbXG4j80tujO2so1dLbobv1ifX0TdpQG/jTY0U2KBYPI/GSUHy2Qi9Bv1py4eSD1X79d++LcY9ukeM+/kPxPZrTy790LJrnrhC3P70ajYYF+/HTlIgBU6wBpMpUhBMKKxXxKYU2K5cGclQMxn6yVMuJCOPYOjLpJIzGCOem1HizrzrwXw7/+HlNvKf7ZNuhjfFqgF/+28Pa+ht97PY80MK/ETQixTIgfl1X7tIzJk1M7XVciB+1TfvEBvvu9k6FTlLoe9lUIP+h+66XkyfdljP8uRMg3zp+xC2/9O7Yu/6HWLM4Cui7z/M6JlH2gVbd20VR9/+fwv5908WPyVmHlputqFU4SRKJTBxQusp1XsHxN593c9TBl+cBPafOE68s2uPGGxIeAcGBtvLaprw6uvrE+/fb4x4e+fe2je3719+2Wlj/8svt//dP7yZu2/rViFaG77lUbftf7de7X/Ln7X+L//d/tlwHoP7HSgG95skBlp/5N/yNXDQ9KG/PzD0t7pG/528tvNn4lA6W6++/eRpNkMn2vTtN7R0pq+1Aba/9c99+w8/8Er+vn3dextgBw4YemP3TxpjqyrkUyGBA943rsLSKEoR8CIFK2+9Rzz19IuZewZ67TkwCV/RmYJkWWkzC+88+Qux++HJrQ+sPjFmabmn8N36D7eIKx/9qjhh+lzxg0X/zaSJpLVEYOL4YSloDaZ41Y/A/hPHindag8amRLdZUiDE+yeMFW/vqr8UDGzbNzRQlg+MGn4q7ODwz+RpNoO7hnr44PCde7WcZlA+PEr9btvQUhubr/43hwVl69Df8tU//O/+rb8a+n/KNWMS1wz+1keG6n/QQa1Z+JZ8TDpIJYJc9QAAGwtJREFU9H3gINHfEr/dHxoWld8aei7Q0DXquiE5Ueltto283BM4oPX5zKt6Al6kQDZTDs7lKzkbIH++ecu2Eaf72MRSdE9Bsuw0Kdj67dvF4JbPty/dceH4nufvprVHbTBeccJKcdExX7LZZPIqSYDlQyXBRZKM5UORBKpENUNePqTWyMtmjXoSbOtn3U6x6Tw8yvLG1w7ixLnz8ufqYVJFl9mo5U3qZKm0fRid52kMH1/rcg+Gvqdi8MDWbEhLMORSqHYbPzwkF8l9F+9t+h6SEV7VEWD5UHWs9ZK8SYGshJwxuHP9hhEtP2Xu8ZmnEtlA1Ov0IVUntW9AnoR02R+d3VlaJKXluJkfG1HH7VdeLQa3nyL2/auZYtcXxovBycVOB9A3GG+64AWeTWAj0BbyQAosQAw4C6Qg4OAYVs2mFKQO4uXgPbmRdfhhUe3B/vATYNvNcLTh1XQg3x4Etx4k1X4FfKJNmlxMeOet9kbjXf/0P9vVr0ou9JOjkk/2Th5NG9uGbsO3nPXkSIF1pLky9CoFuWro4KJuzylISkFSXNKea7Dj314gBsQpYs/HTxe7Txsv9n2kmBSoDcYXH7tUXDOn/DMOHKBqdJZIQb3DjxTUNL6tZTLtI0nHjxdbNu8eamRrwN4nl8vIJTby7+Gfqf/3q2U36rrW722fWpMcxLf/n9z02v7Z8AOj1JnzrR+x8XVkXy1zJGmZmQu1sdv2czCSsxbq4Xppz7yQm7ljOSnK5icKUmCTZv68GikF+fHku3LX6WeKwZ1HiF2fuVLs/eRYsaf1J+9Lf4IxzybIS62a65CCajj7KgUp8EVeKzd5Qo0cjA/fWU8bwMuUqXfhXS2nkQUOL6npNYiXv08+AVb+LIa78QH0hEJVKCMFhQrIuFg/OUrNTqhnYMhN2/1yGdRbciP38L/lpu7W/+XP233X4tO884pFrDMWSIGNHls8D6SgOLNRKfYcfawY3DNNvPNv/1IMThsjdv1B/l3zD7/0oPj3P/gCTzC2EAfbWSAFtomGlR9SUCAeapNq68a7uqveufsuB/Jvadu1h8+Ml3fkK70DP9wcNTAf+75+sXf44JnOWfL68ZMp58m3rxs/nFHAS2oKRK6Wl/qSAlswk7MWWWIhy5PH0boWi+RSqBD2WCAFtnpbsXyQgmK8Uq/e1zodYXD3AWL7H/+4fVdp54Xymyffiw3G+Tj5uAop8EG9ujJrJwXDA/f2Hcm33zt6tMidd7WRVebhbPmMFuLkk13lr7oN4OXv1VIa+W91F35QO4pS/tzmnoLqeiQl5SUQuxTkbWe36/KKRXv2QpuxsLkUSu2xaD+7Qtu8bWMZFFJgo5cUzwMpKM5sdIrW0Wjy9eb1b7bWrA6Kd8/fTwzIh6L0eMmlQ0fcPrW9sZgNxr1oVf97pKB65lWW6EUK0u64ywF4jyUzvu66q3h0lsW0bnr0jR/6vOsM3uV/htfBy3/q1wr92grvwCMFVb6Tqi8LKTBnnlwKled0KNt7LJIbt/UTod73X9eaN5IcChNACgojSyT45S+FOPzw9lFmb173jBjz0oDYc/I4sXdG7wemfOvJ68SNrT9sMDYNgpv0SIEbrqHkmpQC/ZSZPn2ZTNagXTYkZalMu33qxBmXa92TIHutfU9ZOtMexGubXeuyfAYpCOVd5qYeSIEbrkVzVWKRPHY2ub9C5qsvg8o1W9GUp0oWhe74eqTAFLAmBb+5+zkx7tE9Yt9vjxW7f6/3ZmM5SyBnC9hgbBoEN+mRAjdcy+Saa8AuB+8pa9tlefrmVLVEZkzrhJqBnfJEmuoeX5Z2x13WL/UseP30GfnvlLvuyWUzZdjWMQ1SUMeovtcmpKAe8e02W3HQly6uRyMjawVSYBqwjRuFOOkksfvTJ4otf7lBTFi3K9e+AvVsgiMPPUY8snCTaS1I74AAUpADasY6dpmysyQmOVjXznPXl8W0S1PLaJJpclTF+BLtTvugtkwma9Auf562VKZ9vTr/Xf6HDavGoSmaAVJQlFhc1yMFccWrTG3ZU1CGmnkapMCU4V/8hRCLF4sd55wvtt6yRky4d7fof6P3EiK1wfjyWVeJr7b+8AqPQIxSoN9Rl0T1DadlB+ojNp9WuRxG7xJ5Buzy+pS17e3Be8oSmUMP2k9s3rWrddpMseeKhNdTqVGSAFJQ7z6BFNQ7vrJ1SIGfGCMFptwTUjD2xX3tJUTdjiZVG4xl0S9c/CpPMDaNgaP0VqRAu5OeXKeuH+nYHrDrS1+0u+ntwb3+hFT5A5931DXendNj2gPykYPrzpKY5GA9Y1mMvKzKO+xeNho76qtkO5IAUlDvHoEU1Du+SIG/+CIFpuxXrBDimmvE9iuuav/pbw3exv/1u+0BXtaGY7XB+FPTThT3LthgWgPS5yHQbXAuB+TaIFs9NGnihDFiz94BsXfnQPtJqOrVdYDu6066xYG6zCpr82md1rAjBXneOHFegxTEGbe8tUYK8pKK9zpmCvzEDikw5X7ZZUKsWiW2XbdSvLPkS+3cxv6sNVvwRGu24MA+sfsPJow6nvR3135c/Oqtf2nUBuPkspZRd80zBuad8CTunCfXoutLXGSaKs5Yz9N19DvpyXXqI450lJnpS1+0u+nJQbr8f5V31PO0M8ZrkIIYo5avzkhBPk6xXoUUxBq5/PVGCvKzsnklUmBK89/9OyHuvFNsXf0dsWPReZ3cJtzf2lvw6sCQGHxmnBiYNrS0Qm0wls8mkEuHqngVHpCnDap7LGcZNSgP4I65znbEMpf2ALzLUpfhoxvVTMEeeZCU9jw6/S56coBepzvpVfRNn2UgBT7puy0bKXDL13fuSIHvCLgvHylwzzitBKTAlPuCBULcf7/Ysu6vxK55Z3RykwPx/R7a2xaD9qt153ff1D7x0OYHxfNvPSs+NO0j4gsff08i5CWpd7eHz0FXGY86rUX+Ql/6kpWPaTtN0+tnqLfySt41bw+u9Qe+aWeqy9/J60cMzLUjGuXvR5yvLn9g4cQXK3sKTLmR3hkBpMAZWu8ZIwXeQ+C0AkiBU7xBZI4U+AkDUmDK/TOfEeKxx8Tmv364dSzpCaNyk0uJxrQ2H8sTiby9ig7IZUW1pSxlBuV1uGOOFHjrsZUUjBRUgtlLIUiBF+yVFYoUVIbaW0FIgR/0SIEp99bTjEXrAWav//Tn7acaZ75aG13/2xMPiBdeekbIZxOcOvn00ZcmBuLtwXhr+ZH+at8xH36Ikfr5iPXl8ocW7pKbYqlDeqSgDlHMbgNSUN/4IgX1ja1sGVJQ7/jK1iEFfmKMFJhyzysFrXLUswl4grEp9GrSIwXVcPZVClLgi7z7cpEC94x9loAU+KRfTdlIQTWck6UgBabc+4bu5L+6eUfXnPQNxpsueIFnE5hyryA9UlABZI9FIAUe4TsuGilwDNhz9kiB5wBUUDxSUAHklCKQAlPuOaXgmieuELc/vVrwBGNT4NWlRwqqY+2jJKTAB/VqykQKquHsqxSkwBf56spFCqpjrZeEFJhyb0mB3Esg9xRkveQTjGevPULIvx9Z9HfiyMlHm5ZK+goIIAUVQPZYBFLgEb7jopECx4A9Z48UeA5ABcUjBRVAZqbAAeQcUnDHM98Wyx9fJniCsQP+DrNEChzCDSBrpCCAIDiqAlLgCGwg2SIFgQTCYTWQAodwu2TNTIEp95YU7Jl5jHjjbzZl5qQ2GK84YaW46Jihpx7zCp8AUhB+jExqiBSY0As7LVIQdnxMa4cUmBIMPz1S4CdGSIEp95YU7P70ia3nFGxIzYkNxqaA/aVHCvyxr6JkpKAKyn7KQAr8cK+qVKSgKtL+ykEK/LBHCky595ACtcH44mOXimvm3GBaGukrJIAUVAjbQ1FIgQfoFRWJFFQE2lMxSIEn8BUWixRUCFsrCikw5d6Sgh3nnC+23rJmVE76BmOeTWAKuvr0SEH1zKssESmokna1ZSEF1fKuujSkoGri1ZeHFFTPXJaIFJhy7yIFbDA2hes3PVLgl7/r0pEC14T95Y8U+GNfRclIQRWU/ZaBFPjhjxSYcu8iBWwwNoXrNz1S4Je/69KRAteE/eWPFPhjX0XJSEEVlP2WgRT44Y8UmHJvScH2K65q/9FfbDA2Bes/PVLgPwYua4AUuKTrN2+kwC9/16UjBa4J+88fKfATA6TAlHuGFLDB2BSs//RIgf8YuKwBUuCSrt+8kQK//F2XjhS4Juw/f6TATwyQAlPuKVLABmNTqGGkRwrCiIOrWiAFrsj6zxcp8B8DlzVAClzSDSNvpMBPHJACU+4tKdi6+jtix6LzOjmxwdgUahjpkYIw4uCqFkiBK7L+80UK/MfAZQ2QApd0w8gbKfATB6TAlHuKFKgNxqv+zXfE2b/9niyYFkX6agkgBdXyrro0pKBq4tWVhxRUx9pHSUiBD+rVlokUVMtblYYUmHJPSAEbjE2BhpMeKQgnFi5qghS4oBpGnkhBGHFwVQukwBXZcPJFCvzEAikw5Z6Qggt/uFBs+Ofvi8tnXSW+2vrDK14CSEG8sctTc6QgD6U4r0EK4oxb3lojBXlJxXsdUuAndkiBKfeWFGz+64fF7k+fIOQG4yNun9rO8YWLXxWTJhxkmjvpPRJACjzCr6BopKACyJ6KQAo8ga+oWKSgItAei0EK/MBHCky5a1LwrSevEze2/pz60c+JPzttvWnOpPdMACnwHADHxSMFjgF7zB4p8Ai/gqKRggogey4CKfATAKTAlPuwFLxx/Ewxe+0R7dmC7y54WMyedoJpzqT3TAAp8BwAx8UjBY4Be8weKfAIv4KikYIKIHsuAinwEwCkIAf3y5avFo9sfKp95VEzDhfr1yx/L1VLCl7/6c/Fytf+sj1L8KlpJ4p7F2zIkSuXhE4AKQg9Qmb1QwrM+IWcGikIOTrmdUMKzBmGngNS4CdCSEEP7nff/6i4be0DYuN9N7evXLhkhTj+2Bli2SWLhlK2pOAXmzaJTz42j1kCP33YWalIgTO0QWSMFAQRBieVQAqcYA0mU6QgmFA4qwhS4Axt14yRgh7ckxKQlAQpBZf8l8+J27Z8n1kCP33YWalIgTO0QWSMFAQRBieVQAqcYA0mU6QgmFA4qwhS4AwtUmCCdu5Zl4ovXnCmOGf+ye1snnjyWbHkihvF84/dOZRtSwo+8DUhtu4nxH//f/6H+NAB002KI21ABJCCgILhoCpIgQOogWSJFAQSCEfVQAocgQ0oW6TATzCYKejB/ciTFourv3L+KCl46K7rxfRph7WloO8aIVadukpc+q8v9RNFSoUABCAAAQhAAAIQgIABAaSgB7yeMwUG8EkKAQhAAAIQgAAEIACBEAggBT2i0HNPQQhRpA4QgAAEIAABCEAAAhAwIIAU9IDX8/QhA/gkhQAEIAABCEAAAhCAQAgEkIIcUej6nIIc6bkEAhCAAAQgAAEIQAACIRNACkpGB1EoCS6wZHLPyOYt29q1Wrzw1PeeP9GlnitvvUc89fSLIx9iF1i7qI4QL7/yuph37pUdFGtuuFzMmTUzE43eF+RFva6HsV8Cchb32lXrOpXonAiXUS15aIT+6nW939ZRetH4KmLqfZ/38xzSfggUGUOpUx+TNeU9bD92SEEJpiwpKgEtwCTyQ0m+blqxtP23HDR0GwjqX1KjnmwdYPuaXiX9kIBRRwkn4MiBxE3fubfTF1Ss+dIJsxepgZ86Ba6XqMv4b/qH5zvSL69/8EebOg+lDLOVza1V0fgmhWDywZPEGZ+dnesmT3Mp+2t50TFUr89vfy2pX8lIQYmYsvm4BLQAkyQlICkJWVWW17362m+YKQgwpqpKaV8iyZPEulU/OSgJuKmNrFpSAorGi0FG2N2mbHzlZ7oUxWV/cps4/tgZSEGgYS46huL9Wl0gkYISrDmmtAS0wJKkDSJ63W1UTUAKAgtmSnVGPXm8dU3yi6hbK/gSCjvGaQLfa6ZPb5FM/9Nnf8FMQaBhLhNfPf5F3uuBIqh1tYqOodKWDzGL66aLIAUluPZ8oFmJPElSLQH1IdN5CF2r+LxLCpCCamNVprS0WMqBwtQph3SWCHXLV35psfygDPlq0qTFMvm5nFYT2S/uXL+h/SsGFdXEqkwpReObHGQiBWWoV5fGdAwl4ytf69csr67SDSkJKSgR6KKWW6IIkjgmwEyBY8CeszeZKZDv7+NmfiyXPHhuZmOLL3MnWYfFnpGwu06R+CYPFNBbdsrc43kfBxhq0zEUM7nugooUlGBbdD1ciSJIUgEB9hRUANlTEWX3FCAEngJWsNiya85VMUX3IBSsHpcbEjCNLzMFhgFwnNx0DIUUuAsQUlCCbdGd8yWKIEkFBHqdPiSlIe1YO5YPVRAcC0X0On0oGd+seFuoCllYJtDrdBo1aFCniclB5uzfObJzJK1aRsQSIsuBsZRdr/j2ih9SYCkQjrLpNYZKLg+S37mX/dHZYvq0w9o14uaNo8C0skUKSrItcsZuySJIVgGBbs8pSA4Sk+dmy+pxln0FQSpZRK/nFOjxTYutLJblByXhV5Cs2zn2SSlgo2IFAbFcRLf4IgWWYXvIrtsYKikF+l4gWVWOBHcXMKTAHVtyhgAEIAABCEAAAhCAQBQEkIIowkQlIQABCEAAAhCAAAQg4I4AUuCOLTlDAAIQgAAEIAABCEAgCgJIQRRhopIQgAAEIAABCEAAAhBwRwApcMeWnCEAAQhAAAIQgAAEIBAFAaQgijBRSQhAAAIQgAAEIAABCLgjgBS4Y0vOEIAABCAAAQhAAAIQiIIAUhBFmKgkBCAAAQhAAAIQgAAE3BFACtyxJWcIQAACEIAABCAAAQhEQQApiCJMVBICEIAABCAAAQhAAALuCCAF7tiSMwQgAAEIQAACEIAABKIggBREESYqCQEIQAACEIAABCAAAXcEkAJ3bMkZAhCAAAQgAAEIQAACURBACqIIE5WEAAQgAAEIQAACEICAOwJIgTu25AwBCEAAAhCAAAQgAIEoCCAFUYSJSkIAAhCAAAQgAAEIQMAdAaTAHVtyhgAEIAABCEAAAhCAQBQEkIIowkQlIQABCEAAAhCAAAQg4I4AUuCOLTlDAAI1JLDy1nvEnes3jGrZ84/dKe6+/1Fx7ap14uqvnC/OmX/yiGsuW75aPLLxKfHQXdeL6dMOE93yeeLJZ8WSK27sSk+WIV+yvLSXqoOq01EzDhfr1ywfcamqQ9rv1IVHnrS4az1OmXt8+/eybeq1eOGpYtkli8TLr7wu5p17ZfvHko/+0tuofqfq2q09NexSNAkCEIBAEASQgiDCQCUgAIEYCKiBfXKAK38+6xMfb4uAGmjr16gB8JobLhdzZs0UefLRecjrX33tN6MG9WoQnayPnlYfaCshUb+fe9alYvOWbaKbFKTllVaeaqNehi4FSVFSDHRhyNOeGPoJdYQABCAQIwGkIMaoUWcIQMALAXnXXN0F71YBOdg+bubHxE0rlrYvS/4/bz6qDFMpuG3tA+36yJeqkxyAy59POfTg9s+Tswhp7es2aO8mBZLZgz/aJDbed3M7WyULcpZBzjAkZwq6SY6XwFMoBCAAgQYQQAoaEGSaCAEI2CGQHNxn5arPDGz6h+dHDIjTJKFX7WxIwbpbvt5eyqPu5C9cskLMnzdH3P/QE86lQJZ5/pf/VHzxgjM7symvvrZZTJ0yub0UCyno1QP4PQQgAAH3BJAC94wpAQIQqAmBtDXvWXe19eUxatmQwlAkH5mmlxSk4dX3FMgZAXmXXorA1CmHiD88fa646pt3dH4m07ucKZBSsP6Bv+nIkZwpUT9Lk4Ju7alJV6IZEIAABIIjgBQEFxIqBAEIxEBArcdXdU0O/OXP5eBXLpFRS3bS2pUnn15S0GtPgZICNYMh9xDIWQK5B0KKQhVSIDdXSx6ybCkmkkly/wV7CmLo+dQRAhCoKwGkoK6RpV0QgEBlBOTAXq7NT95tz7vcSFU0Kx9bUiDLkRLw3IsvdZbsVCkFSgKUQCEFlXVRCoIABCDQkwBS0BMRF0AAAhAY2hwrl8DIozaTr6yBdZoUlMnHphTIu/H/63+/0WlHlVIg277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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Highlight a detail about the initial buildup of ES\n", "uc.plot_history(title_prefix=\"DETAIL at early times\",\n", " range_x=[0, 0.5], range_y=[0, 2.])" ] }, { "cell_type": "markdown", "id": "ba28bbea-b725-4e1a-9c64-7dbad40cf2c8", "metadata": {}, "source": [ "#### Notice how the bound enzyme `ES` (red) quickly builds up at the very beginning, from time 0 to roughly 0.01 ... and that, in the longer term, the enzyme returns to its unbound state `E`" ] }, { "cell_type": "code", "execution_count": null, "id": "0b89741b-e652-4030-abca-8567b3200ded", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "327163fb-5f35-474c-836e-32c17d487030", "metadata": { "tags": [] }, "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 in a rate-history dataframe**. \n", "#### Note the enzymatic reactions have 2 rates" ] }, { "cell_type": "code", "execution_count": 16, "id": "39db903a-7619-4c60-8a6c-1b36b37ba84b", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMErxn0_rate_1rxn0_rate_2step
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" ], "text/plain": [ " SYSTEM TIME rxn0_rate_1 rxn0_rate_2 step\n", "0 0.000000 360.000000 0.000000 0\n", "1 0.000500 274.543200 8.820000 1\n", "2 0.000750 243.269275 12.075109 2\n", "3 0.000763 241.911753 12.216716 3\n", "4 0.000769 241.237493 12.287060 4\n", ".. ... ... ... ...\n", "822 1.468805 0.253941 0.285397 822\n", "823 1.475832 0.244291 0.274566 823\n", "824 1.482859 0.235005 0.264142 824\n", "825 1.489886 0.226068 0.254109 825\n", "826 1.496913 0.217468 0.244454 826\n", "\n", "[827 rows x 4 columns]" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rates = uc.get_rate_history() # We'll be interested in rxn1_rate (the reaction that leads to `P`)\n", "rates" ] }, { "cell_type": "code", "execution_count": 17, "id": "f63a5168-1dc7-4b6b-a164-78a5b607e4fa", "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": "code", "execution_count": 18, "id": "d19d0316-7bd0-411d-9ca1-065c7c5795b9", "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": [ "# A closer peek at its maximum value\n", "PlotlyHelper.plot_pandas(df=rates, \n", " title=\"Reaction rate, dP/dt, over time (DETAIL at early times)\",\n", " x_var=\"SYSTEM TIME\", fields=\"rxn0_rate_2\", \n", " range_x=[0,0.05], range_y=[33., 34.5])" ] }, { "cell_type": "markdown", "id": "bfacc983-b8af-467d-87b2-2fee868d8254", "metadata": {}, "source": [ "As we saw earlier, the time it took for `ES` to build up was about 0.01 \n", "**Ignoring the brief initial transient phase, the reaction rate starts at about 34.1**" ] }, { "cell_type": "code", "execution_count": null, "id": "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": 19, "id": "7d82da8a-57bd-4e34-ba67-e3962c1234f1", "metadata": { "tags": [] }, "outputs": [], "source": [ "rxn = uc.get_single_reaction(0)" ] }, { "cell_type": "code", "execution_count": 20, "id": "e279ef7d-61ca-469f-8418-60ad0b1222e0", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "8.277777777777779" ] }, "execution_count": 20, "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": 21, "id": "5b073f95-a8ed-4885-8b88-85a04341ecee", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "49.0" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rxn.kcat" ] }, { "cell_type": "code", "execution_count": 22, "id": "355a083f-d492-4cbb-a5c1-f961236257ad", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "49.0" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vmax = rxn.compute_vmax(E_tot=E0) # kcat * E0\n", "vmax" ] }, { "cell_type": "code", "execution_count": 23, "id": "09dfe215-e89d-4562-8a54-72973c6d2b2c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "34.656188605108056" ] }, "execution_count": 23, "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": [ "Not too far from the value of about 34.1 we saw earlier... \n", "To keep in mind that the initial part of the reaction is affected by transients" ] }, { "cell_type": "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 the reaction rate that produces `P` as a function of [S]; we'll compare what we computed earlier vs. what is given by the approximation of the **Michaelis-Menten model**" ] }, { "cell_type": "markdown", "id": "a5f993a2-84fd-4ca6-838b-c7af9aeaef86", "metadata": {}, "source": [ "First, we'll merge the concentration history and and the rate history into a single dataframe `df`" ] }, { "cell_type": "code", "execution_count": 24, "id": "94f14cc7-e188-4a6d-b833-1f588ce34d40", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEPESESstepcaptionP_rate
00.0000000.0000000.0000001.00000020.000000Set concentration0.000000
10.0005000.0000000.1800000.82000019.82000011st reaction step8.820000
20.0007500.0022050.2464310.75356919.751364212.075109
30.0007630.0023560.2493210.75067919.748323312.216716
40.0007690.0024320.2507560.74924419.746811412.287060
...........................
8221.46880519.9474370.0058240.9941760.0467388220.285397
8231.47583219.9494430.0056030.9943970.0449548230.274566
8241.48285919.9513720.0053910.9946090.0432378240.264142
8251.48988619.9532280.0051860.9948140.0415868250.254109
8261.49691319.9550140.0049890.9950110.0399978260.244454
\n", "

827 rows × 8 columns

\n", "
" ], "text/plain": [ " SYSTEM TIME P ES E S step \\\n", "0 0.000000 0.000000 0.000000 1.000000 20.000000 \n", "1 0.000500 0.000000 0.180000 0.820000 19.820000 1 \n", "2 0.000750 0.002205 0.246431 0.753569 19.751364 2 \n", "3 0.000763 0.002356 0.249321 0.750679 19.748323 3 \n", "4 0.000769 0.002432 0.250756 0.749244 19.746811 4 \n", ".. ... ... ... ... ... ... \n", "822 1.468805 19.947437 0.005824 0.994176 0.046738 822 \n", "823 1.475832 19.949443 0.005603 0.994397 0.044954 823 \n", "824 1.482859 19.951372 0.005391 0.994609 0.043237 824 \n", "825 1.489886 19.953228 0.005186 0.994814 0.041586 825 \n", "826 1.496913 19.955014 0.004989 0.995011 0.039997 826 \n", "\n", " caption P_rate \n", "0 Set concentration 0.000000 \n", "1 1st reaction step 8.820000 \n", "2 12.075109 \n", "3 12.216716 \n", "4 12.287060 \n", ".. ... ... \n", "822 0.285397 \n", "823 0.274566 \n", "824 0.264142 \n", "825 0.254109 \n", "826 0.244454 \n", "\n", "[827 rows x 8 columns]" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = uc.add_rate_to_conc_history(rate_name=\"rxn0_rate_2\", new_rate_name=\"P_rate\")\n", "df" ] }, { "cell_type": "code", "execution_count": 25, "id": "4bcb86d9-6991-48b1-be23-117f8df8bd4c", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEPESESstepcaptionP_rateMichaelis_rate
00.0000000.0000000.0000001.00000020.000000Set concentration0.00000034.656189
10.0005000.0000000.1800000.82000019.82000011st reaction step8.82000034.564299
20.0007500.0022050.2464310.75356919.751364212.07510934.528950
30.0007630.0023560.2493210.75067919.748323312.21671634.527380
40.0007690.0024320.2507560.74924419.746811412.28706034.526599
..............................
8221.46880519.9474370.0058240.9941760.0467388220.2853970.275111
8231.47583219.9494430.0056030.9943970.0449548230.2745660.264664
8241.48285919.9513720.0053910.9946090.0432378240.2641420.254610
8251.48988619.9532280.0051860.9948140.0415868250.2541090.244934
8261.49691319.9550140.0049890.9950110.0399978260.2444540.235622
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827 rows × 9 columns

\n", "
" ], "text/plain": [ " SYSTEM TIME P ES E S step \\\n", "0 0.000000 0.000000 0.000000 1.000000 20.000000 \n", "1 0.000500 0.000000 0.180000 0.820000 19.820000 1 \n", "2 0.000750 0.002205 0.246431 0.753569 19.751364 2 \n", "3 0.000763 0.002356 0.249321 0.750679 19.748323 3 \n", "4 0.000769 0.002432 0.250756 0.749244 19.746811 4 \n", ".. ... ... ... ... ... ... \n", "822 1.468805 19.947437 0.005824 0.994176 0.046738 822 \n", "823 1.475832 19.949443 0.005603 0.994397 0.044954 823 \n", "824 1.482859 19.951372 0.005391 0.994609 0.043237 824 \n", "825 1.489886 19.953228 0.005186 0.994814 0.041586 825 \n", "826 1.496913 19.955014 0.004989 0.995011 0.039997 826 \n", "\n", " caption P_rate Michaelis_rate \n", "0 Set concentration 0.000000 34.656189 \n", "1 1st reaction step 8.820000 34.564299 \n", "2 12.075109 34.528950 \n", "3 12.216716 34.527380 \n", "4 12.287060 34.526599 \n", ".. ... ... ... \n", "822 0.285397 0.275111 \n", "823 0.274566 0.264664 \n", "824 0.264142 0.254610 \n", "825 0.254109 0.244934 \n", "826 0.244454 0.235622 \n", "\n", "[827 rows x 9 columns]" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's add a column with the rate estimated by the Michaelis-Menten model\n", "df[\"Michaelis_rate\"] = rxn.compute_rate(S_conc=df[\"S\"])\n", "df" ] }, { "cell_type": "code", "execution_count": 26, "id": "6e8cdb8c-0e8e-461f-81a0-f7b75de1d322", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Rates=P_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=df, x_var=\"S\", fields=[\"P_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=18.9, colors=[\"blue\", \"yellow\"])" ] }, { "cell_type": "markdown", "id": "3d6b91c7-dc26-4a04-8a27-4d1b10f4d96e", "metadata": {}, "source": [ "Let's recall that our reactions started with [S]=20 \n", "Virtually overlapped plots, except at the very right! (very early times, when [S] is greater than about 19)" ] }, { "cell_type": "markdown", "id": "6e3f2c52-49ce-4e48-97ab-24c2274fa2cc", "metadata": {}, "source": [ "## In this scenario, the Michaelis-Menten model is remarkable accurate EXCEPT at the very early times of the reaction (the large values of `S`), which is the brief initial transient phase when `ES` builds up from zero" ] }, { "cell_type": "markdown", "id": "291b603e-45fd-4cb9-a479-82ee4e4ba936", "metadata": {}, "source": [ "#### This is as expected, because the kinetic parameters of this reaction satisfy the Michaelis-Menten assumptions that `[E] << [S]` and that the rates satisfy `k1_reverse >> k2_forward`" ] }, { "cell_type": "code", "execution_count": null, "id": "413400e9-c049-4661-a1ec-d0e7bf3ef4ea", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "1c05908a-d2ac-43d7-8a74-b7ff62f66f1f", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "6db0551d-719f-43d7-93c5-eeba71814e4c", "metadata": { "tags": [] }, "source": [ "# PART 3. Comparing the results to the Morrison model" ] }, { "cell_type": "markdown", "id": "1271df18-1ef6-4907-a939-4605a9396a22", "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. \n", "But, in this scenario, we only have small amounts of enzyme - and we'll see below that no significant improvement is gained by switching model." ] }, { "cell_type": "code", "execution_count": 27, "id": "e6184d05-da5e-4539-b44f-5a15fcaa7a1b", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEPESESstepcaptionP_rateMichaelis_rateMorrison_rate
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10.0005000.0000000.1800000.82000019.82000011st reaction step8.82000034.56429934.292188
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827 rows × 10 columns

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" ], "text/plain": [ " SYSTEM TIME P ES E S step \\\n", "0 0.000000 0.000000 0.000000 1.000000 20.000000 \n", "1 0.000500 0.000000 0.180000 0.820000 19.820000 1 \n", "2 0.000750 0.002205 0.246431 0.753569 19.751364 2 \n", "3 0.000763 0.002356 0.249321 0.750679 19.748323 3 \n", "4 0.000769 0.002432 0.250756 0.749244 19.746811 4 \n", ".. ... ... ... ... ... ... \n", "822 1.468805 19.947437 0.005824 0.994176 0.046738 822 \n", "823 1.475832 19.949443 0.005603 0.994397 0.044954 823 \n", "824 1.482859 19.951372 0.005391 0.994609 0.043237 824 \n", "825 1.489886 19.953228 0.005186 0.994814 0.041586 825 \n", "826 1.496913 19.955014 0.004989 0.995011 0.039997 826 \n", "\n", " caption P_rate Michaelis_rate Morrison_rate \n", "0 Set concentration 0.000000 34.656189 34.292188 \n", "1 1st reaction step 8.820000 34.564299 34.292188 \n", "2 12.075109 34.528950 34.291025 \n", "3 12.216716 34.527380 34.290945 \n", "4 12.287060 34.526599 34.290905 \n", ".. ... ... ... ... \n", "822 0.285397 0.275111 0.276209 \n", "823 0.274566 0.264664 0.265721 \n", "824 0.264142 0.254610 0.255628 \n", "825 0.254109 0.244934 0.245914 \n", "826 0.244454 0.235622 0.236566 \n", "\n", "[827 rows x 10 columns]" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df[\"Morrison_rate\"] = rxn.compute_rate_morrison(E_tot=E0,\n", " S_tot=df[\"S\"] + df[\"ES\"])\n", "df" ] }, { "cell_type": "code", "execution_count": 28, "id": "2c115147-d5e1-4b9b-81ba-0080de480128", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Rates=P_rate
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"ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 } } }, "title": { "text": "Reaction rate, dP/dt, as a function of Substrate concentration" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ 0.03999702266555944, 20 ], "title": { "text": "S" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.925343811394892, 36.581532416502945 ], "title": { "text": "dP/dt" }, "type": "linear" } } }, "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Let's take a closer look at the rightmost portion\n", "PlotlyHelper.plot_pandas(df=df, x_var=\"S\", fields=[\"P_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=18.9,\n", " colors=[\"blue\", \"yellow\", \"orange\"],\n", " range_x=[17, 20], range_y=[32,35])" ] }, { "cell_type": "markdown", "id": "d09def65-ccfe-4a46-91a1-dda169d31809", "metadata": {}, "source": [ "# In this scenario, the Morrison model appears to be only very mildly better than the Michaelis-Menten one at the early reaction times (large [S], close to the initial value of 20.) - and virtually identical everywhere else. \n", "Then why even bother with it? In the next two experiments, `enzyme_2` and `enzyme_3`, we'll see how the Morrison model becomes progressively better than Michaelis-Menten at increasingly higher amounts of enzyme." ] }, { "cell_type": "code", "execution_count": null, "id": "2b6f6e1a-f620-457a-b4f6-cb0fde4fc035", "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 }