{ "cells": [ { "cell_type": "markdown", "id": "5cbc8640", "metadata": {}, "source": [ "# **Enzyme Kinetics** : \n", "#### _Accurate numerical solution_ - compared to the **Michaelis-Menten** model approximation and to the alternative **Morrison** model.\n", "\n", "#### Two Coupled Reactions: `E + S <-> ES`, and `ES -> E + P` , using real-life kinetic parameters. \n", "#### Scenario with _small amount of Enzyme_, relative to the initial Substrate concentration.\n", "\n", "#### Unlike in experiment `enzyme_1_a`, we'll use data from a reaction that **VIOLATES the customary Michaelis-Menten assumption** that the rate constants satisfy `k1_reverse >> k2_forward`" ] }, { "cell_type": "markdown", "id": "604b150b-7812-4fd3-9403-69a06dd7e397", "metadata": {}, "source": [ "### THE REACTION: \n", "the enzyme `Aminopeptidase` with the substrate `Leu-Ala-DED`, \n", "and the initial concentration values choosen below, all satisfy the customary Michaelis-Menten assumptions that `[E] << [S]` BUT the reaction rate constants DON'T satisfy `k1_reverse >> k2_forward`\n", "\n", "For this reaction: k1_forward = 160 , k1_reverse = 0.089 , k2_forward = 0.58 \n", "\n", "Source of kinetic parameters: *page 16 of \"Analysis of Enzyme Reaction Kinetics, Vol. 1\", by F. Xavier Malcata, Wiley, 2023*" ] }, { "cell_type": "markdown", "id": "c123db4f-c802-47f0-a3d3-0b857314d8e5", "metadata": {}, "source": [ "### TAGS : \"uniform compartment\", \"chemistry\", \"numerical\", \"enzymes\"" ] }, { "cell_type": "code", "execution_count": 1, "id": "6e9d0902-6fc9-4692-ac39-0651d08902ca", "metadata": {}, "outputs": [], "source": [ "LAST_REVISED = \"Jan. 12, 2025\"\n", "LIFE123_VERSION = \"1.0.0rc2\" # Library version this experiment is based on" ] }, { "cell_type": "code", "execution_count": 2, "id": "1e0ae9a9-9d0c-4edf-a5f2-1c589419e6cf", "metadata": {}, "outputs": [], "source": [ "#import set_path # Using MyBinder? Uncomment this before running the next cell!" ] }, { "cell_type": "code", "execution_count": 3, "id": "a29db1c7", "metadata": { "tags": [] }, "outputs": [], "source": [ "#import sys\n", "#sys.path.append(\"C:/some_path/my_env_or_install\") # CHANGE to the folder containing your venv or libraries installation!\n", "# NOTE: If any of the imports below can't find a module, uncomment the lines above, or try: import set_path \n", "\n", "import ipynbname\n", "import pandas as pd\n", "\n", "from life123 import check_version, ChemData, UniformCompartment, ReactionEnz, PlotlyHelper" ] }, { "cell_type": "code", "execution_count": 4, "id": "af15ecf0-e083-4fef-b68e-abe794dcc86e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "OK\n" ] } ], "source": [ "check_version(LIFE123_VERSION)" ] }, { "cell_type": "code", "execution_count": null, "id": "3713fa4d-e9bb-4e33-8734-c1d4d23cf177", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "34d1cefc-f644-410a-9fe4-5204964742ac", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "91a729ee-ad2f-4771-bc84-49ecb9d6a851", "metadata": {}, "source": [ "# 1. Accurate numerical solution" ] }, { "cell_type": "code", "execution_count": 5, "id": "959cf00a-47b3-455b-9923-9ec8741cc863", "metadata": {}, "outputs": [], "source": [ "chem_data = ChemData(names=[\"P\", \"ES\"], plot_colors=[\"green\", \"red\"])" ] }, { "cell_type": "code", "execution_count": 6, "id": "90f9ec41-6e1b-4558-9400-47e35ece6efc", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " name label plot_color\n", "0 P P green\n", "1 ES ES red\n", "2 Aminopeptidase E violet\n", "3 Leu-Ala-DED S darkturquoise" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Our Enzyme\n", "chem_data.add_chemical(name=\"Aminopeptidase\", label=\"E\", plot_color=\"violet\")\n", "\n", "# Our Substrate\n", "chem_data.add_chemical(name=\"Leu-Ala-DED\", label=\"S\", plot_color=\"darkturquoise\")\n", "\n", "chem_data.all_chemicals()" ] }, { "cell_type": "code", "execution_count": null, "id": "a7550b20-f34c-455f-9319-b9e9ddc5adfc", "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": "markdown", "id": "5906cdcd-f4ed-489a-b230-8e8933b9597e", "metadata": {}, "source": [ "### Notice that the reaction rate constants below DON'T satisfy the customary `k1_reverse >> k2_forward`" ] }, { "cell_type": "code", "execution_count": 7, "id": "07b23edc-5c8e-4886-a2b8-989b9bbb4e7e", "metadata": {}, "outputs": [], "source": [ "# Here we use the \"slow\" preset for the variable steps, a conservative option prioritizing accuracy over speed\n", "uc = UniformCompartment(chem_data=chem_data, preset=\"slow\")" ] }, { "cell_type": "code", "execution_count": 8, "id": "78077d8c", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 2 (at temp. 25 C)\n", "0: E + S <-> ES (kF = 160 / kR = 0.089 / delta_G = -18,578 / K = 1,797.8) | 1st order in all reactants & products\n", "1: ES <-> E + P (kF = 0.58 / kR = 0) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {\"ES\" (red), \"S\" (darkturquoise), \"P\" (green), \"E\" (violet)}\n" ] } ], "source": [ "# Reaction E + S <-> ES , with 1st-order kinetics, \n", "uc.add_reaction(reactants=[\"E\", \"S\"], products=\"ES\",\n", " forward_rate=160., reverse_rate=0.089) \n", "\n", "# Reaction ES <-> E + P , with 1st-order kinetics, ignoring the reverse reaction\n", "uc.add_reaction(reactants=\"ES\", products=[\"E\", \"P\"],\n", " forward_rate=0.58, reverse_rate=0) \n", "\n", "uc.describe_reactions()" ] }, { "cell_type": "code", "execution_count": null, "id": "8913269e-9c1b-493f-8d28-c53f8cb7b5e4", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "d23a97ea-f252-4e11-a3e9-aea74f58591e", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "9a4febb2-2780-4754-9c70-c2041b1afc07", "metadata": {}, "source": [ "## Set the initial concentrations of all the chemicals\n", "### in the scenario we're exploring, there's LITTLE ENZYME relative to initial substrate concentration, \n", "just like we did in experiment `enzyme_1_a`" ] }, { "cell_type": "code", "execution_count": 9, "id": "8c9e3f86-b9a5-41da-9e1b-75258017808a", "metadata": {}, "outputs": [], "source": [ "S0 = 20.\n", "E0 = 1." ] }, { "cell_type": "code", "execution_count": 10, "id": "6abcf6e2-9ce9-4841-b955-1e43808220e8", "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: {'ES', 'S', 'P', 'E'}\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": "code", "execution_count": null, "id": "2060605e-39ac-4705-93e5-722e9ba23d0f", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "ef2c10f2-ec7f-497a-bdbf-4fea30ba31a1", "metadata": { "tags": [] }, "source": [ "#### Simulate the very early part of the reaction" ] }, { "cell_type": "code", "execution_count": 11, "id": "e6ad72b8-722a-4606-a611-7dc600529f30", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "173 total variable step(s) taken in 0.01 min\n", "Norm usage: {'norm_A': 31, 'norm_B': 33, 'norm_C': 31, 'norm_D': 31}\n", "System Time is now: 0.0015061\n" ] } ], "source": [ "# Perform the reactions \n", "# (Note: by default, concentration and rate history is kept for each step; we'll later reduce this frequency)\n", "uc.single_compartment_react(duration=0.0015, initial_step=0.00001)" ] }, { "cell_type": "code", "execution_count": 12, "id": "0198dd94-e55d-4ab4-9de8-087d508edf06", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_pandas() NOTICE: Excessive number of vertical lines (174) - only showing 1 every 2 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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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": [ -9.710545944220633e-07, 0.0015061056759486202 ], "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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5bs9lm939+YoTK7FiZ7yQvLisY9ND+ZyA7IoTq1kOP8SJGpSd/hoTbGbLp61wei1OpJ5cMxjZ0tidQTIbBHPV64RpocWJk/LtipNCcbXqO1aXdezaW6hAPWVvPucGO6edQokTN/YWQqT4GRCbjbsbLnbPeyqdH+d2O33MThqvxEm+5RRCpDSrgFhxop01/eIAtVTKrjixmuVw04HN8kobnMSc6DuuDBB7da9KC6pUTOysCiiEOLESddKZ31m4QguIdRuX4CTmRF9vLgGj2DoRD2bXqVU52WJcXnlzoXZpzuhPWUGmF6VWNzoz6zOF4OpUnLi1wc6J2U6aQgxq6tjK9z4n+vOQsQ1eiDUvRIpbUZKPOCw0FyProM/tdvpvrjR2RYXVGKHKtxOrZ0c8Shonl3v0ZXohSlR5oQmI1RtktlzLyU3YjB3WzPn6gz+fyzpWJ0x1HVB/7c/qDqBShixvlWtqZmmcnJQLIU5UR9N3VGWTap9ZmmyrPKyWWJutQMlWrx2m0qeciBOrGQQpx0qcmEXw6y876cWJE0FbCK5OxYlbG3KdlO3ud3Ic2C3TrThR1+yNl26UrXZjTnLZa+cHm1kZ+Vwmt7LFCX+/uChb/Tq362cX7MZ15PJttjaY5dWfV4w/hhQHL2xTx73TIGaz84VdBmbpQidOxEi7Ecl2Z06kTL0Ykc/iRHX/j3zEiZRhFiMig5HcB8N4GccqnkR/cjMLILN73boQ4kR1GGPglZlNxjTZ7oVhd/VQrnqdMDWuhLASIsZ+YrzPidkNjoz9VUSVuveOsR/oI9DVAJbtl3YhuBpPBNlEmRJm+jx2fevmxKTPa+VnfZp8Vrq4vaxj7CvKHi8GCK/YeVGOU/5+c/Hj3C7HqtwuQM7tXvvXipfyndmPNKNfvRLDXvQXr8oIzWodrxoUdDlmS0iDtgn1gwAIgAAIgEBzIBDI7eujBk6U3aN3XJt2i2q7sRBRayvsBQEQAAEQAIGgCUCc2PCA2bST3cswNopHEhAAARAAARAAAR0BiBN0BxAAARAAARAAgVARgDgJlTtgDAiAAAiAAAiAAMQJ+gAIgAAIgAAIgECoCECchModMAYEQAAEQAAEQADiBH0ABEAABEAABEAgVAQgTkLlDhgDAiAAAiAAAiAAcYI+AAIgAAIgAAIgECoCECehcgeMAQEQAAEQAAEQgDhBHwABEAABEAABEAgVAYiTULkDxoAACIAACIAACECcoA+AAAiAAAiAAAiEigDESajcAWNAAARAAARAAAQgTtAHQAAEQAAEQAAEQkUA4iRU7oAxIAACIAACIAACECfoAyAAAiAAAiAAAqEiAHESKnfAGBAAARAAARAAAYgT9AEQAAEQAAEQAIFQEYA4CZU7YAwIgAAIgAAIgADECfoACIAACIAACIBAqAhAnITKHTAGBEAABEAABEAA4gR9AARAAARAAARAIFQEIE5C5Q4YAwIgAAIgAAIgAHGCPgACIAACIAACIBAqAhAnoXIHjAEBEAABEAABEIA4QR8AARAAARAAARAIFQGIEw/csW1nPW3b1eBBSSgiCgQq21XQztpGqqlrjIK5sNEDAq1alFLL8lL6dnudB6WhiCgQiMWIunZoRRu27qLuHVtFweRmZSPEiQfuhDjxAGKEioA4iZCzPDIV4sQjkBEqBuIkWGdBnHjAH+LEA4gRKgLiJELO8shUiBOPQEaoGIiTYJ0FceKS/x//+EeadPW1aZd1Xnz2Saqt2UXff/ctNTXFKVbC84OyxYlKSkupvq6W2rRtRzt37KA92rfX0lRUVNCO7duoKR6njp2qqI7TVHbsrJWzR/sO9PknH1Knqq7UtXsvWrvqCy6nhA4+tB+9+fpLdOyJp9EnK1dQZWUnamxqopKSEiovL6OG+sSlJsn38Yfv09HHj6RpD0+l8y+6kpYtnq/Z0m/gUHr0gTto3LkTNHuXLppHx5wwirZ+s5kWL5hLp51xDm1Yv4aW8N+nnj5OK3vaQ1NpzJnjtTYsX7ZIs/XwvoOookULemnWdOrTv5q69+xNMT66X3lxJh18WD/qwZ+lvveWvEsNDQ3Ud0A1lZWVa/bdf/df6aeXTNT2y7Zzx3Z6ZvojdN6Fl6V558F7ptCPJ1yRytfQUE/vL1lAZeXlWp36zViv2rd543qtjcJM7FVbU2MjrVu7mj5asZROGjU2o1dsXL+Wmc2j408ZQ10q26Zd1omzz9at+YpWvLeIThk9zrJHvfbyc3TADw6lnnvtTaWlZabpjCz0iZrYt+vWrLK0UaV9dfYzdNChfVPMjRVJOf+YehtNuPxqUxuExVpuz6fcp6S9VtvLzz9Fh7Hfu/fcS+sXxq2xsYEe/vv/0U8vnWRahOxfs+pL+vzTj+j4k0+3rMfYp4wJpf9Ne3AqXXDJVZZlrOB+Wiv9tB/304rdftdnmP3cdD4ehmh917iJOKGGOrr33rvo/Am/sKzn/aULqL6+Pq1/GxO/8MwTNLB6OHXrsZdpOTt37qCZjz9I4y+6wrIes+PI2FdemjWD+g8eRt0t6pHzzXNPPUbnXnCpZT1yrEh/6c/nCXV8ptfTSC8//zQN4PZ07dbTtJwtmzZo55sRx55MrVq1Nk2zjOuRc1f/QcNM+5Ic69Kv+w/ierqb17NpwzqtHjl/tWjZ0rSeJQvekdMw8z/CdH9dbS29/srzmh1du/fAZR3LnlH4HUUvTv405RF68rnXU6RHVB9O997yyzTyl1xzG81ZsFz7zrgf4gTiBOIE4kSdMCBOMgctiJPCD+TNsYaiFycjx/+aZj92c8q38nnsyKNowrmjtO9EvKzbsCUlWESo9OjWma6feL62H+IE4gTiBOIE4gQzJ81RIATZpqIXJ0b49097kRYuW5kSIyJWbvzNBOp/2AFa0qUrPqXrbro/TdAg5iTILux/3Yg58Z950DUi5iRoD/hfP2JO/GeurxHixMBfZkYG9ztImznZsHkrnXDWJHpt+mTqVlWppTT7DuIk2E7sd+0QJ34TD74+iJPgfeC3BYUWJ8ZZeL/b56Y+s3HQTXlmeSFOdFRk1mTK32fQB288ZClEjE65dfMWunnTZupUUkqdysqoEwd1duJgx8R7KXXkvztzcKr6LPsSYZ/YokpABqr6hjg1NDZFtQmw2yGBsrISKuPAdtzbxiG4KCfndQxtW5bT9l311K51InjfyWaMZ5S8vXt2Sc26ByFOZOZ//BU30mN3Xpe6GuCkTSotxEk+1PLMM/vf79LVN0zNOUtidIrEnPy/089Iq/Unc+dQq7o6quSo+zhHoMuqFVmvI1HijbyqoSWvVtnZshW1qq2h+rZtqYR3lPJqnRJOX8IrP9p06kwxzt+pcxURR4932LMDrfzoA+rStSuvwOhFX33Jq3VYDPXt15/+9dKLdOqo0+nDD97nVT6dqYkHTLVap57rka1Ll660Yvl7dPKpp9F999xFl15xFS14dy6vGCml6iHDaeqdt9MFF11M//32W3p3/lw6ZeRptGXLZpr/zhwad855vHJjNc3nNo0dd45W9n333EHnnHcBtWvXjpYsWsAm1tKAQYOpRYuW9PSMJ2hw9RDqxStSpN3PPTOD+vTtT3v13kerb+GCedoqokHVQ3lFUeKAv/22m+jKq67W9su2fft2mvboP+jiS9NXRfzf7bfSZZdfpa3Oka2BV0UsXDhfK2fQ4KFpPjDWmzqo1q/T2njqqNGavWpr5BUqa1Z/Re8tW0JjzshccbNu7Rot3+gxZ9AebVuliROJOVnNq04WL1pIY88827IHvjCLVy4dcjj13nsfXnFkvlrHyEJfmKyakHqsbFRpZz37FB3ep1+KudEgKedvk2+mib/6ramtwmLVV19wn1pOp52euXJJZXrm6ek0YOAgzddmq3VkVdbdd0ymX0y8xrQe2S99+eOVH9Co0enHkD6DsU8ZC5PVOvfefQf3oV9Zslf9dODgasvVOk9Pf5wGDx1Ge3F7jJuIk3o+XqfefRddduVEy3oWcX+sr6vnY2Boqp8aE8944p809IgR1KtX5qogSbuDV6s9+tAD9PPL/9eyHrPjyNhXZvKxOGTYEewf83q2bdtGT/zzIfrZz6+0rOfd+e9o55TqocNTx6c+sfQV6QfDho/Qzk1m28YN67XzzQknnUqtW7cxTaPqEXtN+xIf6889+zQN5f1W9axft5brmaedv1ry+dVsmzf3be1EPOyII03317KPZ78wi4Zwe7v37Jm3ODn0mAvShIiqTARL9y4dtZn5IMSJpaMd7oA4cQgs3+TGGRN9ObliTkScjOeT76oddbS1qYG+4YN108uzqIGXAMd4qV5cfl3L/CBvTXxUNPDg3oJPyt/zUre2NTX0XZu2vCdOdTxYtdu1SxMnG/ZoT635YNzEy4xF5GxnAXMID47bKjtSbecu1JGXw5bzQF7Oy1LpnTeoxzEnUs1nn1DHjp2oBecvZ+GCpcTpS5iVT7GUmPshlhKbniqwlDgTC5YSO79DrAiQ+Ys/SItLNOtwSpzIPrViVD+zohc0+hWl+jADtYBj5uy3aNXaTVqWW39/KXXrUqnNkKhN5TETFcYZHsk/8vgh2mIQfb1SVrarCvmOv1b5iv6yjnQQ2YzLh/UdoxCrdSpYlNTxTElpuz14fX+cGivKKc6/mIjFxX/b70kl9XW0iUVKCc9KfN2mDfXhXwXr+fs1LED23byJGlnwLOFf4KOXLqFn+ddrX57d2MhllcdFDPE9J1jstOFBqJzT7ehQSft99SV9WT2MBr7wDH019hzq8tGKhMDp059Kn3yU9uT7mbRgMbXjvcW0/7EnUdPWb2jN4nfphB+eQ9s2rKX3Fs7DfU5wn5O08wjuc5J5WsVS4kwmxbaUWGZNJl48LrXi02rwVbeoUGJA0onYGDrw0NRqUONqUTXDr0SCpBdRosSH2m+8fKTGOKM4MQop2X/fP1/Q6pd9PzvvtFS8pX6sxMyJ11LMUJ4CbFaN/ppctvucSN5CB8R+y7Mv38isTFOjNjOzlUXHN3wDK/X5G93nb3l/nXYBydutBQueNnzNvY28s+Bpze9tWdzI3/Jd6+S7fJbvW/MMkdrXlv+W9Npn7ftE+rLkjJK3lha+NATEFp5x2GpAQGzYPFJ4e/IJiFVjip2YDrPLOvrVolYCQATJFReO1WY3jLe+MMsjZcrMitwyQ79fCMqCDzu2SloRPnc+ODOjHLVYxGuPFP3MiRdACy1OnNoo4mRHI//jWZTtLFx28rv8vYNnZeR9J8/UbGehs/tzYt92Fjbynkiv8jfyZ74cxf+83lpqgobFDF+Gap0UPiJkEgKohCr4alg5v8vsTwVH7ZRzmnK5bCXf8ecK+SzvnE6ETuLv5DtPHpVTIq9EqJRzmsQ+/o7zSXllzEn7jstL3sPXVhMhTmxhalaJIE6alTttNSZocaKCV82MVbMtVuJELzisRMXGzd9ol37ULIxZPWpmRr9P0mPmxFYXCj5R2MRJIYjUKMGiiR0WLvyuBE6amOFZnpQYYhGkiSJOm3hPfk5+F6a1LiJuNAGkRIwIINZjmrhhoZPYlxA7rUtjVCpBzLKfxVRiXyKvJoRYACVETyJ/RVJMpfar77R3FklanJDUrxdiUk5CaCkxlcgf3RmnQvRLv8qEOPGLdHjqyUeciPVOLuvob+gpefUzJ0qc5BIP+puGms3c5CtOpB1njzkudYlJf0kJ4iQ8/dTSEtwhNv87xNbz5R+Z2Xnu3ttp6E8vo10SH8MD9fcc+7Jl1lPU4uwfUz0LmnoWMzIb1GLaQ/TtmedRPcfT1HN4sazWafvhCqrn5dkbDjpES1fPnqrntIe8/Sat2nd/Wl9VRbVcbgMP6nVcduXWr6nvyg/ppYGDaRs/20fKbeB/MRZV+329hQZxbM7jvNLCuPX65hs6+tOPacagaqo1rLSRp8rss3kzDf3iM/onR/lbbeN4ZdP7vKLhM16F1ZhcmWRM+/vnn6UbeaDPFyUAACAASURBVPVVk8mzaiRYel9eRVXNNk4z2CiPb5L5Hzmhnjl/Pi3fe29axcHTcX4Gk8wKyf6YPNuJ30tZFV763NN0L69K0n+v5ee0Zcy85+aNtD+vXnqbV3NJ+6TcknhMS59IF6ehczgI78Af0Df87CZZmZWoKa69S7oyZnrks9Npzv/8KL0eLa3Y0UTt+XkoHVd9RauGH8VpEvXLu1anlMU293jjVfr+4MOopms33ielJ+pQNpXyM286Pf0kffsjvmtzso2aDbp05dxPYhzHFefVUiWyMi7ZVq2+ZJ0Nr7yoxWCVde2RrCNhi6RpWc7xWVzP2n8+SlXnXphhq5aO/fPd8mUU537Zqe8AKuV+or7X+Gi2xeizF2ZSD36GT7tuPVJtLdXsZWb8X+OunTRv+mN03PmXaFwT6/yEx+6/v+BnBTVyYP1+/QbyqqCKRDfiZFpy+ZPZzud6DuR6OvXolcyrS8Rpd23/nt7m5/ycfP7FaXn1Za3kuLM4z7IeNICfrZPsk5pNmklxDpFrojlczyH8LJrOumfe6Gcit3Jf+ojLGcyB+y1a87N1knm1NiXL+oCfiSM2HzZoaGJ1o2qI1m5mws/WeWP2c9SHnxVUxdz0eaVASb+Z+9JyrudIfoaYerZO2owop1kmz9ZhPw0YMiIJKsk2WV8dL1J449UXqJ88W6dbd+pW2Zo2bN1F3Tuar/5JFJK+5QqIFQFitVrH7LJOtssubmZOxGqryzpmwgjixMzbIf4O4iR/cRKmB//V8Yl+9bpV9PGK96iaH3ZXzycwEUCa2OHB/JuN62gdP9St5/GnUKt2rWhbHV/uauD9PJDXxRuphh8MWMvLuePHn0oNfEasU0JJ258oq/Kt/9B/99mP/tu1O9WyaKjnk3FiH9eRfB/11OM044wzWTTxflnFJZfUku8SON1zyyYayMtvjeJEf4icvWA+LeWl25937qwtXTduMoiKCPqTYQm8SieiYT8WQf05yPpJFmNW27m8PHQBC8AvZAm7bjBR6ct4UPvN7Bfpz6eZP9RP9u+3aZMW7C2iz2obP+8dmrf/AVo9cZN6KlgM/PLVl+n/GznasoxhLBxbcLp5+x2QIS5VpvO5nrcPOJC+knpMSpKVc794/VW6+ZTEoy3MtuGffUoVHA82d/8Dqc5CgF7Ay1nfOPBgrqeTaRlteIC89M3X6a8nj7Ss5whenVfOl2HncD0NJvWIkP0xt+cNFo+ruD1m2x68OnDCnDdp8omnWNYz4pOPeWavibn8wLQvlXFf+REv333rBwfRKl5NaLb1/O+3dOSnn9DzvLx9u+5hm/q0R7HwL+Gy3jrwINO+VMFtPYv7tdSz2qoeDuI/iut5dsBA2qkEm8Ggoz9eqQnPN39wsKmPpY+cuWSR1t7VlYkbb8oW79/HkpHZDrOlxGrAV8GyuWJOpFy1YkY/eyICZmCfA7X7lLgRJxIrIjasWb85tbJIBcRKIKxRuEibZMNlHUddIbjEECfNQ5xE/anE8jRruUwmvwpf56cf739IH+rCTwvmR8lqJ2HWNTywJ94bWUw9y7NVp/98Ytr3stRd0jZw8PXXq1fRRn5a8MH8hNdEuZyXp14kfyJdjD7hejrzk7Hb8NNb4yyC5Hv5nSvvWj0s+D579D7a94Kfa6JC2Zh65/0169ZQzRefUttjT9T2J2xNtkX+5nw1/3qBSg/rS/yYWO2z1K3ZoGxi0VA2YxrVnnuBZpmyke8wlLK15UfLKc7pdvAMTCPPmKm2avUl6+z6+iu09ZDDaCfP0CTyJmzRWiUL4HjmZf9nZ9Ky/zk7w1YtHdvWg+/ZUsLtWnXQoTyjV5pIJzZLmzT+cRr2xr/pI67n66ouqbY2it3Cnisr27mLfvj6v2jaqDFJjyR+/ycskS1GfT7+iGe4GmkZD+YN7OPk1xoT2UScjHrnLVrIg/AGnqmT+rUpCPkvmagt3+5gLIugh09msZXcp6XTJRvI9ZTyd4t+IOIkUY++rFIWDaNZBC04+BBaqxMNenHX7dutVM0i59V+A2hHSpwk25S0ayjvj3FZ89neJp52U2Yk2s2XVXnfD/keSe9we9fyisWUHZqtCb49WJyIaHteJ06MIvNIbo/MIL59ENej1a2zg4uS2zyMXbyQ5iTFicrvVJyIWWZLcY0LLbJd1kk6O+uSXrfiROrQL/iQz8pGdYsNZYfEuci9wCBOFJEIvBdDzEkE3OCbiQiI9Q11aCpCzEloXOGbIaJbunZwfp8T3wxs5hVhtY4HDoY48QBihIqAOImQszwyFeLEI5ARKgbiJFhnQZx4wB/ixAOIESoC4iRCzvLIVIgTj0BGqBiIk2CdBXHikj9iThBzIte71635ila8t4hOGZ35XB7VxV7jGI0D+JEDPffam59TYv5snfvv/iv99JKJHCqS+XhIue38ujWr6KMVS+mkUdbPvHl19jN00KF9+RkkvS3L+cfU22jC5Veb9n6Jv1nL7fl05Qo6noODrTbcITaTDO4Qm8mk2O4Q63JIQfYkAYgTl10B4gTiBOJkL9OHtTXyqpWH//5/9NNLJ5keZbJ/zaov6XMOvD3+ZPMVPZLxpVnTqU//an4QW++0JaaqUHnw37QHp9IFl1xleTSv4KW3tZzu8H6DLB/8h2frZOLDs3UQc+JyiMw7O8RJ3ugSGSFOIE4gTiBO1GkEMyeYOXE5pCA7Zk686wOIOfGOZRRKQsxJFLzkrY2IOfGWZxRKQ8xJsF7CzIkH/CFOPIAYoSIgTiLkLI9MhTjxCGSEioE4CdZZECce8Ic48QBihIqAOImQszwyFeLEI5ARKgbiJFhnQZy45I+YE8ScIOYEMSeIORnOz6LpaXo2xWodl4NMkWaHOHHpeIgTiBOIE4gTiBOIE5dDScGz57qdfsENcFgBxIlDYMbkECcQJxAnECcQJxAnLoeSgmcXcSLb9RP56d28qQcRZnvqccGNylIBxIkH9BFz4gHECBWBmJMIOcsjUxFz4hHICBXT3GJOjOJEXCEP/Rvc7yCacK71k7aDchnEiQfkIU48gBihIiBOIuQsj0yFOPEIZISKcSNOnv/4+cBaOvoHo03rhjgJzCXBVQxxEhz7IGqGOAmCerB1QpwEyz+I2t2IkynzptCkV8zvjFzItkwcOpEmnzzZljiZ/e936eobptJr0ydTt6rKQpqVV9mYOckL2+5MiDlBzAliThBzos4IuENs5gm1GFfriDj5z1f/cTm6OM++f+X+WcXJk8+9nlZoWIWJGAlx4tz/aTkgTiBOIE4gTiBOEBDrcigpeHazyzoFr9RFBRAnLuBJVogTiBOIE4gTiBOIE5dDScGzQ5wUHHH4KkDMSfh8UkiLEHNSSLrhLBsxJ+H0SyGtchNzUki78i0b4iRfchHOB3ESYeflYTrESR7QIp4F4iTiDszD/OYmTvJAEGgWXNbxAD/EiQcQI1QExEmEnOWRqRAnHoGMUDEQJ8E6C+LEJX/EnCDmBDEniDlBzAliTlwOJchuIABx4rJLQJxAnECcQJxAnECcuBxKkB3ixNs+AHECcQJxAnECcQJx4u3IgtJ8nzkZOf7XtGrtJlPyH7zxUCQ9gpiTSLotb6MRc5I3ushmRMxJZF2Xt+GIOckbnScZfRUn8pChHt06p56K6EkLQlAIxEkInOCjCRAnPsIOSVUQJyFxhI9mQJz4CNukKl/FyaHHXEBhfTyzGzdAnLihF728ECfR85lbiyFO3BKMXn6Ik2B9BnGS5C8PQbrzwZk0+7Gb0zxy/7QXacrfZ2R4SV2CQswJYk4Qc4KYE3WCwLN1Mge0Yny2TrDDevOo3VdxIpd1xpw8gkYePyQ09Jau+JTGX3GjZk/vnl1MxcnCZSvp3lt+aWozxAnECcQJxAnECQJiQzOoNRNDfBUnIgSuu+n+DAEQBpbZZk4gTtbQkgVz6dTTx1FJSQlNe2gqjTlzPLVp246WL4M4gTiBOIE4gTgJwziWzQaZHJizYHlGklt/f2lqwkBCL/TbiOrDLX+YF7q9vooTY8ONjQtytY7dyzpmsyuIOSl0Nw1X+Yg5CZc//LAGMSd+UA5XHc0t5kTEyeB+B9GEc0eZgpaVtGNHHpW2X/JYXTUotLd8FSeFboyb8q3EibFMcZZsQTnMTRuRFwRAAARAoDgJZBMnGzZvpRPOmkSvTZ9M3aoqQwEI4iTpBrviRMWo6Gd5MHMSir7smxGYOfENdWgqwsxJaFzhmyGuZk6ef943OzMqGj3atG47Mye9uleF5oe37+JEH4CqCIZheXG+4gQBsYg5QcwJYk7UuQyrdTLHxaJcrTNlCtGkSf4LlIkTiSZPthQnTmNO9PEofjfGV3EiAuDqG6amTR2p6aQgIQh0K3Ei1+H0y4vl89CBh6ZuJAdxAnECcQJxAnGCgNi0wVvEyX/+4/d4TrT//lnFSbaYE6OxarwOavLAV3EiA/sVF47NWEpsd9aiEJ42m8mZePG4VFCQMcL57DHHpd3hFuIE4gTiBOIE4gTipBDjk5dl5rqsY1aX1ZjtpV1WZfkqTqzuEGsWx+FH472qAzEnXpGMRjmIOYmGn7y0EjEnXtKMRlmuYk5C2MRs4kTG4HsemZUWb6JmToJaReurOAnjzIkXfQjixAuK0SkD4iQ6vvLKUogTr0hGp5zmKE6yxZyY3QclKGEivcRXcRLmmBM3hwzEiRt60csLcRI9n7m1GOLELcHo5W9u4iRqHvBVnAicsK7WyddxiDlBzAliThBzos4fWK2TeSYtytU6+Q4oyJci4Ls4aW7sIU4gTiBOIE4gThAQ29zGtqDbA3Hi0gMQJxAnECcQJxAnECcuhxJkNxDwRZzIKh25j4nc4yTbFmTwjZuegZgTN/SilxcxJ9HzmVuLEXPilmD08iPmJFif+SJOgm1i4WuHOCk84zDVAHESJm/4YwvEiT+cw1QLxEmw3vBVnFjd5yTIm7B5gR/ixAuK0SkD4iQ6vvLKUogTr0hGpxyIk2B9FQpxEuWbsCHmBDEniDlBzAliThBzEuxQ3vxqD4U4uX/aizRz9ltpz7CJCmqIE4gTiBOIE4gTiJOojFlRsbPg4sTsviZmcIJ6uJBbR0GcQJxAnECcQJxAnLgdS5A/nUDBxYm+OquYk6g7BTEnUfegM/sRc+KMV3NIjZiT5uBFZ21objEnZrenFyKyknbk8UOcwfEhta/ixIf2BFIFxEkg2AOrFOIkMPSBVQxxEhj6wCpujuJkcL+DaMK5owJj6qRiiBMntCzSQpx4ADFCRUCcRMhZHpkKceIRyAgVA3ESrLN8FScbNm+lE86aZNniKN6EDTEniDlBzAliTtRJDc/WyTy9F+Ozdeo/qQ9sZC8/sNy0brmsg5kTC7eMHP9rGjvyKBrY50C67qb7U6tzBNqYk0eE8rpXrh4GcQJxAnECcQJxgoBY/VhRM7+Gdr26K9fw4fn+lkNbUqsTW1mKkzkLlmfsQ8wJI1EBsV2rOtJFk25OiRNZ0aMXK557rIAFQpxAnECcQJxAnECcGMVJw6qGAo485kWXVpZmFSeYObFwiX61jvytLuNE+SZs0lTEnPh+DAZaIWJOAsUfSOWIOQkEe6CVIuYkUPzka8yJ/pqX/u8o34QN4iTYDhxE7RAnQVAPtk6Ik2D5B1E7xEkQ1HfX6as4MTZVZk/U9tr0ydStqjJYGnnWjpmTPMFFNBvESUQd58JsiBMX8CKatTmKE8ScRLQz5mM2Yk4Qc4KYE8ScqHMHVutknkWLcbVOPmMJ8qQT8HXmpDneIRbiBOIE4gTiBOIEAbEQF94SgDhxyRPiBOIE4gTiBOIE4sTlUILsBgK+ipMo388kW89BzElxHVeIOSkuf0trEXNSfD5vbjEnUfOgr+JE7hCrv79J1GBZ2Qtx0lw8aa8dECf2ODWnVBAnzcmb9toCcWKPU6FS+SpO9KtzzBoUxdvXSzsgTgrVPcNZLsRJOP1SSKsgTgpJN5xlQ5wE6xdfxUmwTS1M7Yg5QcwJYk4Qc6LOLlitk3mexWqdwow9zb1UX8WJ1Wqd2f9+l+58cGbqdvZRgg5xAnECcQJxAnGCgNgojVtRsDUU4iTKt6+HOIE4gTiBOIE4gTiJwoAfJRtDIU5w+/oodRnYipiT4usDiDkpPp8j5iRYnxdcnKhZkVzNfOzO66j/YQfkSlaw/dkuLckSaHXb3xHVh9O9t/wyzQ4ExBbMLaEsGOIklG4pqFEQJwXFG8rCm6M4MS5KMRvPwuKMgosTfUPDeIdYvXjq3bNLRtzLn6Y8Qus2bEkJEhEqPbp1pusnnp9qGsRJWLqzP3ZAnPjDOUy1QJyEyRv+2NLcxMnI8b+msSOPognnjkoBlPHM+GPbH7q5a/FVnOQ2J7gUVjMn4tAbfzMhNasjYua6m+5PiRjEnCDmBDEniDlBzAliToIbvXLXLPcYO+GsSRSlB+xCnCT9aiZOzBxq/A7iBOIE4gTiBOIE4kQvEZ7/7vvciqFAKUa338O0ZPmh3at7VWhnSoxG+y5OBNCqtZtM4QV5EzY34uQ31/6O6uqbUm166slptKtmF/33228pHm+iWKyE98W1/SWlpVRXW0tt27WjnTt2UPv2e1ITp2lR0YK2bdumpe9c1YVqa2qoU+cqquH3PffsQCs/+oC6dO1KPXr2oq++/IJKSkqpb7/+9K+XXqRTR51OH37wPnXs1JmaGpt4XwmVl5dRfUODVmeXLl1pxfL36ORTT6P77rmLLr3iKlrw7lwqZVuqhwynqXfeThdcdLFm77vz59IpI0+jLVs20/x35tC4c86jtWtW0/y5c2jsuHO0su+75w4657wLqB23YcmiBVTL7RkwaDC1aNGSnp7xBA2uHkK99tqb2x2j556ZQX369qe9eu+j1bdwwTxqqG+gQdVD2cZyzb7bb7uJrrzqam2/bNu3b6dpj/6DLr70F2n95P9uv5Uuu/wqKkvma6ivp4UL52vlDBo8NC2tsV61c8P6dVobTx01WrNXbY2NjbRm9Vf03rIlNOaMcRn9c93aNVq+0WPOoD3atmK2cWpg1rKJOFm96ktavGghjT3zbMtTzguzZtLBhxxOvffeh8rKykzTGVnoEzU1NWn1WNmo0s569ik6vE+/FHNjRVLO3ybfTBN/9VtTG4TFqq++4D61nE47faxle555ejoNGDhI87X0C+PWwP3v7jsm0y8mXmNahuyXvvzxyg9o1OgzLOsx9iljwrq6Wrr37ju4D/3KsgzVTwcOrqYKPtbMtqenP06Dhw6jvbg9xq2srITqa2to6t130WVXTrSsZxH3x/q6ej4Ghqb6qTHxjCf+SUOPGEG9evU2LWfHju306EMP0M8v/1/LesyOI2NfmcnH4pBhR7B/zOuR880T/3yIfvbzKy3reXf+O9o5pXro8NTxqU8sfUX6wbDhI7Rzk9m2ccN67XxzwkmnUuvWbUzTqHrEXtO+xMf6c88+TUN5v1U969et5Xrmaeevli1bmdYzb+7b2ql42BFHmu6vZR/PfmEWDeH2du/Zk9q2LKftu+qpXevEucruNmXzFpq0boPd5J6lm1jVmSb36GZZnjHm5NbfX0ojjx/iWf1eFuSrODGL1/CyMW7KylecSJ219Y1p4sSNHcgbfgISf6AXJ+G3GBa6JSDipKwkRjV1jW6LQv6oEIiRK3Hyn+07fG/p/i1aZBUneoNkzLv6hqkU9GIUK0i+ipMwBsQqMPnGnEh+BMT6fgwGWiECYgPFH0jlCIgNBHuglTa3gFgzmHIl44oLx4Zy9gTiJOkxK3GC1TqBnh9CWTnESSjdUlCjIE4KijeUhTcncSILOe55ZFZavImaOQkynCKb430VJ3JZZ8zJI0Kl0szuwzLx4nEZy62s7nOCgFgExCIgFgGx6iSLZ+tkDjd4tk44tJf+fl3KorAKE7HPV3FiXIYbDpe5swLiBOIE4gTiBOIEq3XcjSTIbSTgqzgxRgobjQmzirPqOhAnECcQJxAnECcQJ5AX3hLwVZx4a3p4SkNAbHh84YcliDnxg3K46kDMSbj84Yc1zSnmxA9eXtcBceIBUYgTDyBGqAiIkwg5yyNTIU48AhmhYiBOgnWW7+JEH5Sj1lfL5Z6zxxyX9ryaYLE4qx3ixBmvqKeGOIm6B53bD3HinFnUc0CcBOtBX8WJ/iZs+mfWZHsicLB4cteOmBPEnCDmBDEniDlBzEnu0QIpnBDwVZzIDIl68JBenKjlvAiI3ca3so/zbeirSG7JXdmxM9/Gfhft0b4Dff7Jh9Spqit17d6L1q7i29eXltDBh/ajN19/iY498TT6ZOUKqqzsRI18a3J1+3q5Tbxsku/jD9+no48fSdMenkrnX3QlLVs8X7uVfr+BQ+nRB+6gcedOoO+/+5aWLppHx5wwirZ+s5kWL5hLp51xDm1Yv4aW8N+nnj5OK3vaQ1NpzJnjqU3bdrR8GcQJxAnECcQJxImTgRdpcxPwVZyIIHlg8q+pW1UlYeYk8WydPdq3p6amOD/vo4J2bIc4kS67k58t8sz0R+i8Cy9L68EP3jOFfjzhCn4uTeI5Fw0N9fT+kgXaM0z69K9OS/vKi/wcm8P68XM4emsiTG2bN67XBJgIugq+1bPamvgZIevWrqaPViylk0ZlPk9m4/q1LOjm0fGnjKEulW1pZ21j6lbmECcQJxAnECe5h1ukcELAV3Fy/7QXaebst2j2YzenxEnXqo7ao5yNNz5z0oig0yLmJGgP+Fs/Yk785R2G2hBzEgYv+GsDYk785W2szVdxIpWb3ZE1zE9GtOMeiBM7lJpPGoiT5uNLuy2BOLFLqvmkgzgJ1pe+i5Ngm1uY2iFOCsM1rKVCnITVM4WzC+KkcGzDWjLESbCe8VWcyEP0nnzudTIGvkZ5KTFW6yAgFjEniDlRp3E8WydzQMOzdYId5KNau6/ixOrxzFhKjIDYn14yMRW4ioDY3Sz0J5YmXom1bs0qy6BdlfbV2c/QQYf2zQgGVvulnH9MvY0mXH616XlLgoPXrvmKPuUVYBIAbLW9/PxTdFjfQdS9J8QJxAkCYqMqAsJqt6/iRGZI1I3X9ECwlBjiBOIkcUTcf/dfSc8C4oTopVnTtdVY3XnlVUzm2g2bLLuf9uBUuuCSqyzPsyt4yXstpzu83yBeGbd7lZY+w+znpvPS+iFaPcZNLutQQx3de+9ddP6EX1jWg5kTzJyEdbCPml2+ipPmOHMiDkfMSdS6vTt7EXPijl8UcyPmJIpec2czYk7c8XOb21dxIpdvrr5haupGbGL8hs1btaXEUV6xA3HithtGKz/ESbT85YW1ECdeUIxWGRAnwfrLV3EiTTVbSmx2qSdYLM5qhzhxxivqqSFOou5B5/ZDnDhnFvUcECfBetB3cRJsc72vHat1sFoHq3UQEKvOLIg5yTzHYrWO9+NOMZQIceLSyxAnECcQJxAnECdYreNyKEF2AwHfxYkExa5au8nUEXjwH56tIx0DS4mxlFh/gsBqnczT5XtL3uVnSzVQ3wHVqWdN6VPJcvGXZs2g/oOHUfcee5meb+VZXs899Ride8GllgOjPIdKyurPDwjVP6NKZWhqaqSXn3+aBlRDnEBdeEvAV3FyyTW3UY9unen6ied724qAS0PMScAO8Ll6xJz4DDwE1SHmJARO8NkExJz4DDzImROr+5wEi8B97RAn7hlGqQSIkyh5yxtbIU684RilUiBOgvWWrzMnECfBOhu1e0MA4sQbjlEqBeIkSt7yxlaIE2845luKr+JELuuMOXkEjTx+SL72hi4fAmIREIuAWATEqhMTVutknqKxWid0w1YkDPJVnMg9Tq676X6a/djNkYBjx0iIE4gTiBOIE4gTBMTaGS+Qxj4BX8WJXNbJtmG1DlbrSP/Aah2s1tGfJ7BaJ/OsidU6mUw2bVhHyxbPp2NOGEUtWrY0HWqWLHiH4rxnYPURpvvramvp9Veep/6DhlHX7j2oa4dWtGHrLuresZX9URUpPSHgqzjxxOIQFoKA2BA6pYAmIeakgHBDWjRiTkLqmAKahZiTAsK1UTTEiQ1IuZJAnOQi1Lz2Q5w0L3/aaQ3EiR1KzSsNxEmw/vRdnODZOsE6HLW7JwBx4p5h1EqAOImax9zbC3HinqGbEnwVJ83xqcQIiEVALAJiERCrTsJYrZM5HGG1jpshunjz+ipO5Nb1V1w4NmMpsYiWOx+cGclVPBAnECcQJxAnECdYrVO8MqIwLfdVnFjdhE1d6sFqHazWkW6O1TpYraM/3WG1TubJH6t1MplgtU5hREJQpfoqTqI4c3L/tBdpyt9nZPhHL6QQEBtU9w2mXsScBMM9yFoRcxIk/WDqRsxJMNxVrb6KkyjGnIg4WbhsJd17yy8tPQVxEmwn9rt2iBO/iQdfH8RJ8D7w2wKIE7+Jp9fnqziRqqO2WgfiJNgOGsbaIU7C6JXC2gRxUli+YSwd4iRYr/guToJtrvPajZd1evfskha4i4BYBMQiIBYBserMgtU6medYrNZxPu4gBxHEicNeIA8vlE1d5hFx8oc//CGtlEceeYR27dpFW7duJRm4YiLBeZO/S0tLqZZvkbzHHnvQ9u3bqUOHDtTU1EQtWrSg77//XkvTpUsXqqmp0d6lnMrKSlq+fDl1796d9tprL/rss8+0cgYOHEizZs2iM844g9577z2qqqqixsZGKikpofLycmpoaNDKk3xLly6lMWPG0O23305XX301zZkzRytjxIgRdOutt9Lll1+u2fv222/TD3/4Q9q0aRO9+eab9JOf/IRWrVql/T1+/Hit7ClTptBFF12ktWH+/PmarUOHDqWWfMvoxx57jIYPH0777LOP1u4nnnhCs3PffffV6nvnnXeovr6ejjjiCM1G2W644Qa69tprtf2ybdu2je677z6aNGlSGte//OUvmu0qn5Qzd+5c7bPUqd+M9ap9a9eu1doozMRetQm3KDM8/QAAHuxJREFUL7/8khYtWkTnnHNORq9YvXq1lm/cuHFUUVGRtl8Yf/HFFxqL8847z7JHzZgxg/r06UP77bcflZWVmaYzstAnkn4i9VjZqNI++eSTNGDAgBRzY0VSzp///Ge6/vrrTW0QFp9//rnWp6S9Vtu0adNoyJAhmq+lXxg36X8333wzXXfddaZFyH7pyytWrKAzzzzTsh5jnzImlONp8uTJ9Nvf/tayDNVPhw0bph1rZtujjz6qHQ/SHrNNjsU77riDrrnmGst6pD/W1dWl9W9j4ocffpiOPvpo2nvvvU3LkfPCPffcQ7/61a8s6zE7jox9RbgdddRRlvXI+eaBBx6giRMnWtYjfV76w5FHHpk6PvWJZZ/0A2mPnJvMtnXr1mnnm9NOO43atGljmkbVI/aa9SU51qVfy36retasWaPVI+evVq3Mbzcv5zE5Xo855hhTO+RcNnPmTK29vXr1suSCHYUn4Is4UbEmt/7+UtNlxFffMJXM9hW++c5rMK4swswJZk4wc4KZE3UmwcxJ5jkVMyfOxxnk8GnmRGYbenTrTNdPPN+U+Z+mPELrNmzJGnQaFmeZLXtGQGxYvOOPHYg58YdzmGpBzEmYvOGPLYg58YezVS2+zJxY3d9EGRXm+5zI8ufZj92c4iefhw48NE1oQZwE24n9rh3ixG/iwdcHcRK8D/y2AOLEb+Lp9UGc5OAvsz5zFixPpTp7zHEZM0AQJ8F2Yr9rhzjxm3jw9UGcBO8Dvy2AOPGbeADiRGYbbvzNBOp/2AGmrZWZk+tuuh+3r9+OO8RKB8EdYnGHWP2JAneIzTxt4g6xmUxwh9hgxYTXtfsyc5LrXiG5YlK8brSX5SEgFgGxCIhFQKw6pyAgNvPsioBYL0ec4inLF3EiOGX2RDZ9/Ib6ftXaTRTF5+qI/RAnECcQJxAnECd48F/xyAZ/WuqbOJHmmD2nxiyGw5+me1cLYk68YxmFkhBzEgUveWsjYk685RmF0hBzEqyXfBUnwTa1cLVDnBSObRhLhjgJo1cKaxPESWH5hrF0iJNgvQJx4gF/iBMPIEaoCIiTCDnLI1MhTjwCGaFiIE6CdRbEiUv+iDlBzAliThBzgpgTxJy4HEqQ3UAA4sRll4A4gTiBOIE4gTiBOHE5lCA7xIm3fQDiBOIE4gTiBOIE4sTbkQWlYebEgz6AmBMPIEaoCMScRMhZHpmKmBOPQEaoGMScBOssiBMP+EOceAAxQkVAnETIWR6ZCnHiEcgIFQNxEqyzIE484A9x4gHECBUBcRIhZ3lkKsSJRyAjVAzESbDOgjhxyR8xJ4g5QcwJYk4Qc4KYE5dDCbIbCECcuOwSECcQJxAnECcQJxAnLocSZIc48bYPQJxAnECcQJxAnECceDuyoDTMnHjQBxBz4gHECBWBmJMIOcsjUxFz4hHICBWDmJNgnQVx4gF/iBMPIEaoCIiTCDnLI1MhTjwCGaFiIE6CdRbEiQf8IU48gBihIiBOIuQsj0yFOPEIZISKgTgJ1lkQJy75I+YEMSeIOUHMCWJOEHPicihBdgMBiBOXXQLiBOIE4gTiBOIE4sTlUILsECfe9gGIE4gTiBOIE4gTiBNvRxaUhpkTD/oAYk48gBihIhBzEiFneWQqYk48AhmhYhBzEqyzIE484A9x4gHECBUBcRIhZ3lkKsSJRyAjVAzESbDOgjjxgD/EiQcQI1QExEmEnOWRqRAnHoGMUDEQJ8E6C+LEJX/EnCDmBDEniDlBzAliTlwOJchuIABx4rJLQJxAnECcQJxAnECcuBxKkB3ixNs+AHECcQJxAnECcQJx4u3IgtIwc+KyD9TMq6Fd79RQvGWM/xHFW/M/+btV4jO1jhFpfye/a8Xf8VfYoksglDEnTU1E/C8m7xTX/lb/Yk3Jz3H1rksr6dT3kj++O9/u7+OJcg37tO/Uv+Q+PqGk1U1ct1ZmxvdJW+V7XbnpZcq+ZN1pdSXqyG3T7nanlZtsSyK/kVWynfz1bn5NVBqLUylzratrTNmbWWayrZqtunJVG/T8NNbpaTKOCNmvbcn35Gctn/a12r87Seo7Y5ocn1NlGuqyLE9fv0XZGXZm2G1oh5WNurrYDeltd9jOnCxzlRfd01bkLIc4cemyb2/41nEJmohhsZIQLSJo5O+SlLghvbiRNCWOq0CGfAnIQFJfRzwKUayuPvF3ffJdvuO/25fFqWbHLqrfVcvp9Pskj0pfnyiD86e+0/Ylysj4TtI2SB61L5EvYQt/p+1Lfpb8DTxINjTwAJ14xwYCIFBAAnohWMBqUPRuAhAnLnuDTOlv+6aOdmxtpFgN/xraxRMj/I9qeJDbxf9q+O+dcSrRPvPf/J3jTZuVkZkXzpl8T8zMJL7Tvk+KG03wlDquIZAMsV07KbZ9O5Xs2E6xHTu0v2M1u7TBm2prE+/JwV37Wz84J4VC6rvkZ32exD7dYJ8qL10AEA/8IkSUcAgEhttKS1jB8r+4vMvUXPJz4rvkZ1l+IN/HdGm1z7vTx5P7Uvm1fSKQd+dLlJH8TtWjytSVlSiD06kyDfu0Mg32pr5Tdhnr0dmbYZO0VV9H8u9EunQmwsDs+1SZMrupY1pRUUbl5WW0o45nRfTl6jhrTFL8dPWpNhjYZthq7ANSj7Yl35OftXza1+pdJdNNyWakMeaxKNNQ1+46sudPtyeRNtNOQxkO64rrZ5wdti/Vjpwsd9uordapbE0btu6i7h3lJIvNTwIQJy5p5x1z0qod7dy1g/Zo3Z5nTpuoItaCttdu0/7uVN6Z6hprqRO/ahpqqD2/Pol/QlX86l7SnVY1raISfh1ecji91vganVR6En0U/4g6xjtSU6yJz6klVFZSTg2lDdqsS1WLKvqw9kM6rupEemT1A3ThwT+nJVsXUmlZKfXfu5oenD+VzjniQvqu/r+05PN36dihp9LX27bQkg/m0mmjf0QbtqyhJQveppFHnUClO3bSY6/Mov85pB+148H/vQ1rqY4FxQCuqOXOHTST7a7etoN6b91KJdt30DO9ulP/r1bRPqtXUxmLj3n770cN3MYR//kPlctMAm83/P73dO2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Changes in concentration for `E + S <-> ES` and `ES <-> E + P`" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ 0, 0.0015061056759486202 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "domain": [ 0, 1 ], "range": [ 0, 1 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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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_y=[0, 1])" ] }, { "cell_type": "markdown", "id": "fcf12778-aab2-4c1b-b6d2-d8673d172953", "metadata": {}, "source": [ "### Notice the EXTREMELY fast kinetics involving the production of the intermediate `ES`" ] }, { "cell_type": "markdown", "id": "40a69c0b-d0e9-4c9c-b27f-9a31564c4723", "metadata": {}, "source": [ "If one wishes to exam the history (of concentration or reaction-rate data) in tabular form, it can be done as follows:" ] }, { "cell_type": "code", "execution_count": 14, "id": "ab88b86d-0de1-4cfa-a3a8-61dd5fc08717", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEPESESstepcaption
00.0000000.000000e+000.0000001.00000020.000000Set concentration
10.0000100.000000e+000.0320000.96800019.96800011st reaction step
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" ], "text/plain": [ " SYSTEM TIME P ES E S step \\\n", "0 0.000000 0.000000e+00 0.000000 1.000000 20.000000 \n", "1 0.000010 0.000000e+00 0.032000 0.968000 19.968000 1 \n", "2 0.000021 2.041600e-07 0.066019 0.933981 19.933981 2 \n", "3 0.000024 3.305201e-07 0.075849 0.924151 19.924151 3 \n", "4 0.000025 3.740726e-07 0.078766 0.921234 19.921234 4 \n", ".. ... ... ... ... ... ... \n", "169 0.001437 6.495498e-04 0.988861 0.011139 19.010489 169 \n", "170 0.001454 6.594576e-04 0.989435 0.010565 19.009906 170 \n", "171 0.001472 6.693712e-04 0.989979 0.010021 19.009352 171 \n", "172 0.001489 6.792902e-04 0.990494 0.009506 19.008827 172 \n", "173 0.001506 6.892144e-04 0.990982 0.009018 19.008329 173 \n", "\n", " caption \n", "0 Set concentration \n", "1 1st reaction step \n", "2 \n", "3 \n", "4 \n", ".. ... \n", "169 \n", "170 \n", "171 \n", "172 \n", "173 last reaction step \n", "\n", "[174 rows x 7 columns]" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uc.get_history()" ] }, { "cell_type": "code", "execution_count": 15, "id": "38fe5851-e292-4093-a1ee-dbd77abd566c", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " SYSTEM TIME rxn0_rate rxn1_rate step\n", "0 0.000000 3200.000000 0.000000 0\n", "1 0.000010 3092.640992 0.018560 1\n", "2 0.000021 2978.868127 0.038291 2\n", "3 0.000024 2946.061101 0.043992 3\n", "4 0.000025 2936.333355 0.045684 4\n", ".. ... ... ... ...\n", "168 0.001420 35.636312 0.573188 168\n", "169 0.001437 33.792720 0.573539 169\n", "170 0.001454 32.046189 0.573872 170\n", "171 0.001472 30.391600 0.574188 171\n", "172 0.001489 28.824102 0.574486 172\n", "\n", "[173 rows x 4 columns]" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uc.get_rate_history()" ] }, { "cell_type": "markdown", "id": "25201770-a41f-4e64-bb8d-897dcdf492c0", "metadata": {}, "source": [ "Note that rates are associated with the START times of the intervals. So, at the end time of the simulation, there's no rate." ] }, { "cell_type": "code", "execution_count": null, "id": "ec2e2ac9-02f8-455a-8bd3-1170408a4ece", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "7ffc10cf-d7d8-4a34-a08f-e62e436ec7e3", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "a05b2cfd-7316-4925-8111-85bf11a719f2", "metadata": { "tags": [] }, "source": [ "#### Advance the reactions to equilibrium" ] }, { "cell_type": "code", "execution_count": 16, "id": "aba2c3cd-95ec-4174-9750-603ab130a6f7", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "... running : currently at System Time 16.81 (doing step size 0.00012) after running for 0.5 min\n", "110938 total variable step(s) taken in 0.67 min\n", "Number of step re-do's because of negative concentrations: 4571\n", "Number of step re-do's because of elective soft aborts: 6\n", "Norm usage: {'norm_A': 110781, 'norm_B': 110800, 'norm_C': 110781, 'norm_D': 110781}\n", "System Time is now: 40.002\n" ] } ], "source": [ "# From now on, the data from 1 of every 10 computation steps will be saved in the history (for later use in plots, etc). \n", "# Until this point, we've used the default of 1\n", "uc.enable_history(frequency=10)\n", "\n", "# Continue the reactions\n", "uc.single_compartment_react(duration=40., initial_step=0.00001)" ] }, { "cell_type": "code", "execution_count": 17, "id": "9b792467-9c37-4b66-8c9c-6c0c9c61db3f", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=P
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", 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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 of ES and E\",\n", " range_y=[0, 1.5])" ] }, { "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": "056f50a9-bb38-4d4c-b518-82302370b254", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "2d8336ee-4576-4081-9835-9fd7b8bee273", "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** (as we also saw earlier)" ] }, { "cell_type": "code", "execution_count": 19, "id": "18517784-55eb-420c-87a1-bfaee226cc28", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMErxn0_raterxn1_ratestep
00.0000003200.0000000.0000000
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" ], "text/plain": [ " SYSTEM TIME rxn0_rate rxn1_rate step\n", "0 0.000000 3200.000000 0.000000 0\n", "1 0.000010 3092.640992 0.018560 1\n", "2 0.000021 2978.868127 0.038291 2\n", "3 0.000024 2946.061101 0.043992 3\n", "4 0.000025 2936.333355 0.045684 4\n", "... ... ... ... ...\n", "11262 39.665419 -0.000790 0.010425 110889\n", "11263 39.670501 -0.000339 0.010393 110899\n", "11264 39.683681 -0.000027 0.010313 110909\n", "11265 39.717866 0.000006 0.010110 110919\n", "11266 39.806534 0.000006 0.009602 110929\n", "\n", "[11267 rows x 4 columns]" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rates = uc.get_rate_history()\n", "rates" ] }, { "cell_type": "markdown", "id": "0edb69af-9dbe-4ae7-b434-d6402edecfb5", "metadata": {}, "source": [ "Note that initially we were saving historical data at every simulation step, but later switched to every 10 steps" ] }, { "cell_type": "code", "execution_count": 20, "id": "18ac9b9f-c669-43f6-ac36-ed95b76e1ae5", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "SYSTEM TIME=%{x}
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Let's take a look at how the reaction rate varies with time\n", "PlotlyHelper.plot_pandas(df=rates, \n", " title=\"Reaction rate, dP/dt, over time\",\n", " x_var=\"SYSTEM TIME\", fields=\"rxn1_rate\", \n", " x_label=\"time\", y_label=\"dP/dt\")" ] }, { "cell_type": "markdown", "id": "b223bfcd-1be8-4bdb-9ed2-44ca0637074a", "metadata": {}, "source": [ "### Notice how very different is it from the Reaction rate over time seen in experiment `enzyme_1_a`" ] }, { "cell_type": "code", "execution_count": 21, "id": "9c534460-2958-454a-a2bf-2bf359d460b3", "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 very quick buildup\n", "PlotlyHelper.plot_pandas(df=rates, \n", " title=\"Reaction rate, dP/dt, over time (DETAIL at early times)\",\n", " x_var=\"SYSTEM TIME\", fields=\"rxn1_rate\", \n", " range_x=[0, 0.0015])" ] }, { "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 0.001 \n", "**Ignoring the very brief initial transient phase, the reaction rate starts at about 0.57, and stays at that value until the substrate gets depleted, arount t=33**" ] }, { "cell_type": "code", "execution_count": null, "id": "485514fa-5259-4319-9aea-8adac65ae24f", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "e0886793-ace6-49dc-bbef-d2aa0c040001", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "078285f0-00aa-4fbb-9a67-7de0184d6cec", "metadata": {}, "source": [ "# 2. Comparing the results to the Michaelis-Menten model approximation" ] }, { "cell_type": "markdown", "id": "5c15fd87-ee4d-41f5-bcc5-de1dce1a59ec", "metadata": {}, "source": [ "### Let's compute some parameters used by the Michaelis-Menten model \n", "for background reference, see: https://vallance.chem.ox.ac.uk/pdfs/KineticsLectureNotes.pdf (p. 20)" ] }, { "cell_type": "code", "execution_count": 22, "id": "37e52d32-9204-4873-a5f1-134368682ab9", "metadata": {}, "outputs": [], "source": [ "reactions = uc.get_reactions()" ] }, { "cell_type": "code", "execution_count": 23, "id": "1411f8f6-ab1b-4ef0-97ef-3395058dafc1", "metadata": {}, "outputs": [], "source": [ "rxn = ReactionEnz(enzyme=\"E\", substrate=\"S\", product=\"P\",\n", " k1_F=reactions.get_forward_rate(0), k1_R=reactions.get_reverse_rate(0), \n", " k2_F=reactions.get_forward_rate(1))" ] }, { "cell_type": "code", "execution_count": 24, "id": "e279ef7d-61ca-469f-8418-60ad0b1222e0", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.004181249999999999" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rxn.kM # For the data in this experiment, it comes out to (0.089 + 0.58) / 160." ] }, { "cell_type": "code", "execution_count": 25, "id": "5b073f95-a8ed-4885-8b88-85a04341ecee", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.58" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rxn.kcat" ] }, { "cell_type": "code", "execution_count": 26, "id": "355a083f-d492-4cbb-a5c1-f961236257ad", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.58" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vmax = rxn.compute_vmax(E_tot=E0) # kcat * E0\n", "vmax" ] }, { "cell_type": "code", "execution_count": 27, "id": "09dfe215-e89d-4562-8a54-72973c6d2b2c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.5798787690948362" ] }, "execution_count": 27, "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": [ "Pretty close the value of about 0.57 we saw earlier, after the initial transient... " ] }, { "cell_type": "code", "execution_count": null, "id": "1d9b8b04-e789-477e-be6a-d180d6f23eaf", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "34fe41ca-b95f-4033-b23f-8240332891a5", "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": "84d5ad99-45b7-4d5f-9e9b-1b658e3e4681", "metadata": {}, "source": [ "First, we'll merge the concentration history and and the rate history into a single dataframe `df`" ] }, { "cell_type": "code", "execution_count": 28, "id": "c3f85515-6bfc-4b7c-a201-8488b0a65149", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEPESESstepcaptionP_rate
00.0000000.000000e+000.0000001.00000020.000000Set concentration0.000000
10.0000100.000000e+000.0320000.96800019.96800011st reaction step0.018560
20.0000212.041600e-070.0660190.93398119.93398120.038291
30.0000243.305201e-070.0758490.92415119.92415130.043992
40.0000253.740726e-070.0787660.92123419.92123440.045684
...........................
1126239.6654191.998202e+010.0179750.9820250.0000051108890.010425
1126339.6705011.998207e+010.0179190.9820810.0000081108990.010393
1126439.6836811.998221e+010.0177810.9822190.0000101109090.010313
1126539.7178661.998256e+010.0174310.9825690.0000101109190.010110
1126639.8065341.998344e+010.0165560.9834440.0000091109290.009602
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11267 rows × 8 columns

\n", "
" ], "text/plain": [ " SYSTEM TIME P ES E S step \\\n", "0 0.000000 0.000000e+00 0.000000 1.000000 20.000000 \n", "1 0.000010 0.000000e+00 0.032000 0.968000 19.968000 1 \n", "2 0.000021 2.041600e-07 0.066019 0.933981 19.933981 2 \n", "3 0.000024 3.305201e-07 0.075849 0.924151 19.924151 3 \n", "4 0.000025 3.740726e-07 0.078766 0.921234 19.921234 4 \n", "... ... ... ... ... ... ... \n", "11262 39.665419 1.998202e+01 0.017975 0.982025 0.000005 110889 \n", "11263 39.670501 1.998207e+01 0.017919 0.982081 0.000008 110899 \n", "11264 39.683681 1.998221e+01 0.017781 0.982219 0.000010 110909 \n", "11265 39.717866 1.998256e+01 0.017431 0.982569 0.000010 110919 \n", "11266 39.806534 1.998344e+01 0.016556 0.983444 0.000009 110929 \n", "\n", " caption P_rate \n", "0 Set concentration 0.000000 \n", "1 1st reaction step 0.018560 \n", "2 0.038291 \n", "3 0.043992 \n", "4 0.045684 \n", "... ... ... \n", "11262 0.010425 \n", "11263 0.010393 \n", "11264 0.010313 \n", "11265 0.010110 \n", "11266 0.009602 \n", "\n", "[11267 rows x 8 columns]" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = uc.add_rate_to_conc_history(rate_name=\"rxn1_rate\", new_rate_name=\"P_rate\")\n", "df" ] }, { "cell_type": "code", "execution_count": 29, "id": "0769aa93-8040-4ae0-b258-9c4e0a379cbd", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEPESESstepcaptionP_rateMichaelis_rate
00.0000000.000000e+000.0000001.00000020.000000Set concentration0.0000000.579879
10.0000100.000000e+000.0320000.96800019.96800011st reaction step0.0185600.579879
20.0000212.041600e-070.0660190.93398119.93398120.0382910.579878
30.0000243.305201e-070.0758490.92415119.92415130.0439920.579878
40.0000253.740726e-070.0787660.92123419.92123440.0456840.579878
..............................
1126239.6654191.998202e+010.0179750.9820250.0000051108890.0104250.000714
1126339.6705011.998207e+010.0179190.9820810.0000081108990.0103930.001106
1126439.6836811.998221e+010.0177810.9822190.0000101109090.0103130.001370
1126539.7178661.998256e+010.0174310.9825690.0000101109190.0101100.001371
1126639.8065341.998344e+010.0165560.9834440.0000091109290.0096020.001301
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11267 rows × 9 columns

\n", "
" ], "text/plain": [ " SYSTEM TIME P ES E S step \\\n", "0 0.000000 0.000000e+00 0.000000 1.000000 20.000000 \n", "1 0.000010 0.000000e+00 0.032000 0.968000 19.968000 1 \n", "2 0.000021 2.041600e-07 0.066019 0.933981 19.933981 2 \n", "3 0.000024 3.305201e-07 0.075849 0.924151 19.924151 3 \n", "4 0.000025 3.740726e-07 0.078766 0.921234 19.921234 4 \n", "... ... ... ... ... ... ... \n", "11262 39.665419 1.998202e+01 0.017975 0.982025 0.000005 110889 \n", "11263 39.670501 1.998207e+01 0.017919 0.982081 0.000008 110899 \n", "11264 39.683681 1.998221e+01 0.017781 0.982219 0.000010 110909 \n", "11265 39.717866 1.998256e+01 0.017431 0.982569 0.000010 110919 \n", "11266 39.806534 1.998344e+01 0.016556 0.983444 0.000009 110929 \n", "\n", " caption P_rate Michaelis_rate \n", "0 Set concentration 0.000000 0.579879 \n", "1 1st reaction step 0.018560 0.579879 \n", "2 0.038291 0.579878 \n", "3 0.043992 0.579878 \n", "4 0.045684 0.579878 \n", "... ... ... ... \n", "11262 0.010425 0.000714 \n", "11263 0.010393 0.001106 \n", "11264 0.010313 0.001370 \n", "11265 0.010110 0.001371 \n", "11266 0.009602 0.001301 \n", "\n", "[11267 rows x 9 columns]" ] }, "execution_count": 29, "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": 30, "id": "6e8cdb8c-0e8e-461f-81a0-f7b75de1d322", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Rates=P_rate
S=%{x}
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"text/html": [ "
" ] }, "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=19, 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": "60f95830-6892-4ddf-847f-5424c591b0dd", "metadata": {}, "source": [ "The overlap at the very left (small [S], late in the reaction) has a few issues, but not too bad; let's magnify the previous plot:" ] }, { "cell_type": "code", "execution_count": 31, "id": "cf4ee5e6-4c6e-4ba5-a4db-6ca05caaa592", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Rates=P_rate
S=%{x}
dP/dt=%{y}", "legendgroup": "P_rate", "line": { "color": "blue", "dash": "solid", "shape": "linear" }, "marker": { "symbol": "circle" }, "mode": "lines", "name": "P_rate", "showlegend": true, "type": "scattergl", "x": [ 20, 19.968, 19.933980949088, 19.92415068426947, 19.921234083779254, 19.91832711375799, 19.91542973971911, 19.912541927316465, 19.909663642343656, 19.906794850733345, 19.9039355185566, 19.90108561202223, 19.8982450974761, 19.8954139414005, 19.892592110413478, 19.88977957126819, 19.886976290852253, 19.884182236187108, 19.88139737442737, 19.87862167286019, 19.875855098904648, 19.873097620111086, 19.870349204160515, 19.86760981886398, 19.864879432161935, 19.862158012123647, 19.859174278428863, 19.85620131744843, 19.853239087194527, 19.849992391731316, 19.846758579323406, 19.843537594823523, 19.840008562203746, 19.83649491862354, 19.832996591745594, 19.829513509616245, 19.825698809767744, 19.821902383011405, 19.818124135097055, 19.81398795604472, 19.809873546892597, 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"title": { "text": "EARLY DETAIL of Reaction rate, dP/dt, as a function of Substrate concentration" }, "xaxis": { "anchor": "y", "domain": [ 0, 1 ], "range": [ 0, 0.2 ], "title": { "text": "S" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.03221548717193534, 0.6120942562667715 ], "title": { "text": "dP/dt" }, "type": "linear" } } }, "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "PlotlyHelper.plot_pandas(df=df, x_var=\"S\", fields=[\"P_rate\", \"Michaelis_rate\"],\n", " title=\"EARLY DETAIL of Reaction rate, dP/dt, as a function of Substrate concentration\",\n", " y_label=\"dP/dt\", legend_header=\"Rates\",\n", " vertical_lines_to_add=19, colors=[\"blue\", \"yellow\"],\n", " range_x=[0, .2])" ] }, { "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. \n", "### Some discrepancy also at the end of the reaction (when `S` drops to 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 key Michaelis-Menten assumptions that `[E] << [S]` , but NOT the other assumption 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": [ "# 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. 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": 32, "id": "e6184d05-da5e-4539-b44f-5a15fcaa7a1b", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEPESESstepcaptionP_rateMichaelis_rateMorrison_rate
00.0000000.000000e+000.0000001.00000020.000000Set concentration0.0000000.5798790.579872
10.0000100.000000e+000.0320000.96800019.96800011st reaction step0.0185600.5798790.579872
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11267 rows × 10 columns

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" ], "text/plain": [ " SYSTEM TIME P ES E S step \\\n", "0 0.000000 0.000000e+00 0.000000 1.000000 20.000000 \n", "1 0.000010 0.000000e+00 0.032000 0.968000 19.968000 1 \n", "2 0.000021 2.041600e-07 0.066019 0.933981 19.933981 2 \n", "3 0.000024 3.305201e-07 0.075849 0.924151 19.924151 3 \n", "4 0.000025 3.740726e-07 0.078766 0.921234 19.921234 4 \n", "... ... ... ... ... ... ... \n", "11262 39.665419 1.998202e+01 0.017975 0.982025 0.000005 110889 \n", "11263 39.670501 1.998207e+01 0.017919 0.982081 0.000008 110899 \n", "11264 39.683681 1.998221e+01 0.017781 0.982219 0.000010 110909 \n", "11265 39.717866 1.998256e+01 0.017431 0.982569 0.000010 110919 \n", "11266 39.806534 1.998344e+01 0.016556 0.983444 0.000009 110929 \n", "\n", " caption P_rate Michaelis_rate Morrison_rate \n", "0 Set concentration 0.000000 0.579879 0.579872 \n", "1 1st reaction step 0.018560 0.579879 0.579872 \n", "2 0.038291 0.579878 0.579872 \n", "3 0.043992 0.579878 0.579872 \n", "4 0.045684 0.579878 0.579872 \n", "... ... ... ... ... \n", "11262 0.010425 0.000714 0.010384 \n", "11263 0.010393 0.001106 0.010354 \n", "11264 0.010313 0.001370 0.010275 \n", "11265 0.010110 0.001371 0.010073 \n", "11266 0.009602 0.001301 0.009567 \n", "\n", "[11267 rows x 10 columns]" ] }, "execution_count": 32, "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": 33, "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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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Detail at the very left\n", "PlotlyHelper.plot_pandas(df=df, x_var=\"S\", fields=[\"P_rate\", \"Michaelis_rate\", \"Morrison_rate\"],\n", " title=\"EARLY DETAIL of reaction rate, dP/dt, as a function of Substrate concentration\",\n", " y_label=\"dP/dt\", legend_header=\"Rates\",\n", " vertical_lines_to_add=19,\n", " colors=[\"blue\", \"yellow\", \"orange\"],\n", " range_x=[0, 0.02])" ] }, { "cell_type": "markdown", "id": "d09def65-ccfe-4a46-91a1-dda169d31809", "metadata": {}, "source": [ "# In this scenario, the Morrison model appears better than the Michaelis-Menten one at late reaction times (small `S`, close to zero) - and virtually identical elsewhere " ] }, { "cell_type": "code", "execution_count": null, "id": "ed18cfed-eafe-48a2-b757-ab053a29c20b", "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 }