{ "cells": [ { "cell_type": "markdown", "id": "49bcb5b0-f19d-4b96-a5f1-e0ae30f66d8f", "metadata": {}, "source": [ "## Enzyme Kinetics in a NON Michaelis-Menten modality\n", "#### 3 Coupled Reactions: `S <-> P` , `E + S <-> ES*`, and `ES* <-> E + P` . Variation of experiment enzyme_3 \n", "A direct reaction and the same reaction, catalyzed and showing the intermediate state. \n", "Re-run from same initial concentrations of S (\"Substrate\") and P (\"Product\"), for various concentations of the enzyme `E`: from zero to hugely abundant \n", "### We'll REJECT the customary Michaelis-Menten assumptions that [E] << [S] and that the rates satisfy k1_reverse >> k2_forward ! \n", "#### We'll explore exotic scenarios with lavish amount of enzyme, leading to diminishing (though fast-produced!) products, and a buildup of the (not-so-transient!) ES* intermediate\n", "\n", "LAST REVISED: May 31, 2024 (using v. 1.0 beta32)" ] }, { "cell_type": "code", "execution_count": 1, "id": "cbb1af2e-3564-460e-a4ae-41e4ec4f719f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Added 'D:\\Docs\\- MY CODE\\BioSimulations\\life123-Win7' to sys.path\n" ] } ], "source": [ "import set_path # Importing this module will add the project's home directory to sys.path" ] }, { "cell_type": "code", "execution_count": 2, "id": "087c0d08", "metadata": { "tags": [] }, "outputs": [], "source": [ "from experiments.get_notebook_info import get_notebook_basename\n", "\n", "from src.modules.chemicals.chem_data import ChemData\n", "from src.modules.reactions.reaction_dynamics import ReactionDynamics\n", "from src.modules.movies.movies import MovieTabular\n", "from src.modules.visualization.graphic_log import GraphicLog\n", "\n", "import pandas as pd" ] }, { "cell_type": "code", "execution_count": 3, "id": "b0ad0c93-02a5-43f4-8797-4b9f7ba50432", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-> Output will be LOGGED into the file 'enzyme_4.log.htm'\n" ] } ], "source": [ "# Initialize the HTML logging\n", "log_file = get_notebook_basename() + \".log.htm\" # Use the notebook base filename for the log file\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": 4, "id": "23c15e66-52e4-495b-aa3d-ecddd8d16942", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 3 (at temp. 25 C)\n", "0: S <-> P (kF = 1 / kR = 0.2 / delta_G = -3,989.7 / K = 5) | 1st order in all reactants & products\n", "1: E + S <-> ES* (kF = 100 / kR = 224.07 / delta_G = 2,000 / K = 0.44629) | 1st order in all reactants & products\n", "2: ES* <-> E + P (kF = 200 / kR = 17.851 / delta_G = -5,989.7 / K = 11.204) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {'ES*', 'P', 'S', 'E'}\n", "[GRAPHIC ELEMENT SENT TO LOG FILE `enzyme_4.log.htm`]\n" ] } ], "source": [ "# Initialize the system\n", "chem_data = ChemData(names=[\"S\", \"P\", \"E\", \"ES*\"])\n", " \n", "# Reaction S <-> P , with 1st-order kinetics, favorable thermodynamics in the forward direction, \n", "# and a forward rate that is much slower than it would be with the enzyme - as seen in the next reaction, below\n", "chem_data.add_reaction(reactants=\"S\", products=\"P\",\n", " forward_rate=1., delta_G=-3989.73)\n", "\n", " \n", "# Reaction E + S <-> ES* , with 1st-order kinetics, and a forward rate that is much faster than it was without the enzyme\n", "# Thermodynamically, the forward direction is at a disadvantage (higher energy state) because of the activation barrier in forming the transient state ES*\n", "chem_data.add_reaction(reactants=[\"E\", \"S\"], products=[\"ES*\"],\n", " forward_rate=100., delta_G=2000) \n", " \n", "# Reaction ES* <-> E + P , with 1st-order kinetics, and a forward rate that is much faster than it was without the enzyme\n", "# Thermodynamically, the total energy change of this reaction and the previous one adds up to the same value as the reaction without the enzyme (-3989.73)\n", "chem_data.add_reaction(reactants=[\"ES*\"], products=[\"E\", \"P\"],\n", " forward_rate=200., delta_G=-5989.73)\n", "\n", "# NOTE: the forward_rate's of the last 2 reactions (the catalyzed ones) were tweaked, \n", "# to lead to a crossover point [S] = [P] at about the same time as in experiment `enzyme3`, in step 2 (when [E] = 0.2)\n", "\n", "chem_data.describe_reactions()\n", "\n", "# Send the plot of the reaction network to the HTML log file\n", "chem_data.plot_reaction_network(\"vue_cytoscape_2\")" ] }, { "cell_type": "markdown", "id": "5f3f488b-4cf1-4123-8dfd-9dfc2b9c64b7", "metadata": {}, "source": [ "Note that `E` is not labeled as an \"enzyme\" because it doesn't appear as a catalyst in any of the registered reactions; it only becomes an enzyme in the context of the _compound_ reaction from (2) and (3)" ] }, { "cell_type": "code", "execution_count": null, "id": "919280b2-fd0f-4557-9008-e154b64a2b66", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "0e771dda-1c0f-4fc0-ab21-049740643897", "metadata": {}, "source": [ "# 1. Set the initial concentrations of all the chemicals - starting with no enzyme" ] }, { "cell_type": "code", "execution_count": 5, "id": "5563e467-a637-44fa-9ba1-d35ddd82c887", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "4 species:\n", " Species 0 (S). Conc: 20.0\n", " Species 1 (P). Conc: 0.0\n", " Species 2 (E). Conc: 0.0\n", " Species 3 (ES*). Conc: 0.0\n", "Set of chemicals involved in reactions: {'ES*', 'P', 'S', 'E'}\n" ] } ], "source": [ "dynamics = ReactionDynamics(chem_data=chem_data, preset=\"mid\")\n", "dynamics.set_conc(conc={\"S\": 20.}, snapshot=True) # Initially, no enzyme `E`\n", "dynamics.describe_state()" ] }, { "cell_type": "markdown", "id": "651941bb-7098-4065-a598-e50c0b641ab3", "metadata": { "tags": [] }, "source": [ "### Advance the reactions (for now without enzyme) to equilibrium" ] }, { "cell_type": "code", "execution_count": 6, "id": "76f24d9a-a788-41d8-90a4-db87386f91aa", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "27 total step(s) taken\n" ] } ], "source": [ "#dynamics.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n", "\n", "# Perform the reactions\n", "dynamics.single_compartment_react(duration=4.0,\n", " initial_step=0.1, variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 7, "id": "4a19ad2a-fbd2-420a-b958-2daf88bcc841", "metadata": {}, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=S
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Changes in concentrations for 3 reactions (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.003641023159098385, 4.154407424531257 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.1111111111111112, 21.11111111111111 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(colors=['cyan', 'green', 'violet', 'red'], show_intervals=True, title_prefix=\"With ZERO enzyme\")" ] }, { "cell_type": "markdown", "id": "9a793ebf-f544-43ad-a1d3-059f74f3c02b", "metadata": {}, "source": [ "### The reactions, lacking enzyme, are proceeding slowly towards equilibrium, just like the reaction that was discussed in part 1 of the experiment \"enzyme_1\"" ] }, { "cell_type": "code", "execution_count": 8, "id": "d684e2c3-c717-4c95-8852-62729914e48f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: S <-> P\n", "Final concentrations: [S] = 3.37 ; [P] = 16.63\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.93491\n", " Formula used: [P] / [S]\n", "2. Ratio of forward/reverse reaction rates: 5.00001\n", "Discrepancy between the two values: 1.302 %\n", "Reaction IS in equilibrium (within 2% tolerance)\n", "\n", "1: E + S <-> ES*\n", "Final concentrations: [E] = 0 ; [S] = 3.37 ; [ES*] = 0\n", "Reaction IS in equilibrium because it can't proceed in either direction due to zero concentrations in both some reactants and products!\n", "\n", "2: ES* <-> E + P\n", "Final concentrations: [ES*] = 0 ; [E] = 0 ; [P] = 16.63\n", "Reaction IS in equilibrium because it can't proceed in either direction due to zero concentrations in both some reactants and products!\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reactions have reached equilibrium\n", "dynamics.is_in_equilibrium(tolerance=2)" ] }, { "cell_type": "code", "execution_count": 9, "id": "4677fcaa-e90b-4975-a567-cb55b66f91f2", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.7322948238817497, 10.0)" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Locate the intersection of the curves for [S] and [P]:\n", "dynamics.curve_intersect(\"S\", \"P\", t_start=0, t_end=1.0)" ] }, { "cell_type": "code", "execution_count": 10, "id": "0a43f0bf-7718-4e60-8756-989ff3f7f680", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEEES*P
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" ], "text/plain": [ " SYSTEM TIME E ES* P\n", "27 4.150766 0.0 0.0 16.630111" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(columns=['SYSTEM TIME', 'E', 'ES*', 'P'], tail=1) # Last point in the simulation" ] }, { "cell_type": "code", "execution_count": 11, "id": "d4e378a6-550d-44b1-9d38-110844da1397", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "16.63011072773748" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_equil = dynamics.get_chem_conc(\"P\")\n", "P_equil" ] }, { "cell_type": "code", "execution_count": 12, "id": "ddc9d6bb-ea70-4471-bc1f-b0f1c48fd84c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "11.641077509416236" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_70_threshold = P_equil * 0.70\n", "P_70_threshold" ] }, { "cell_type": "code", "execution_count": 13, "id": "52f5a61b-eaab-46e7-ba0a-01c0b58ce9d1", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.9536647543782931" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.reach_threshold(chem=\"P\", threshold=P_70_threshold)" ] }, { "cell_type": "code", "execution_count": null, "id": "cf52d120-927e-44bb-893d-1673e9fd8bd6", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "978149dc-c503-4ca8-b490-83a2e97b40a8", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "27401e5d-8f3e-4c27-8438-129d3e3408a2", "metadata": {}, "source": [ "# 2. Re-start all the reactions from the same initial concentrations - except for now having a tiny amount of enzyme (two orders of magnitude less than the starting [S])" ] }, { "cell_type": "code", "execution_count": 14, "id": "dd68db69-c705-4eed-9075-589a1359876f", "metadata": {}, "outputs": [], "source": [ "E_init = 0.2 # A tiny bit of enzyme `E`: 1/100 of the initial [S]" ] }, { "cell_type": "code", "execution_count": 15, "id": "373ce459-3b57-4ab2-a136-4eb8bedcdd91", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "4 species:\n", " Species 0 (S). Conc: 20.0\n", " Species 1 (P). Conc: 0.0\n", " Species 2 (E). Conc: 0.2\n", " Species 3 (ES*). Conc: 0.0\n", "Set of chemicals involved in reactions: {'ES*', 'P', 'S', 'E'}\n" ] } ], "source": [ "dynamics = ReactionDynamics(chem_data=chem_data, preset=\"slower\") # A brand-new simulation, with the same chemicals and reactions as before \n", "\n", "dynamics.set_conc(conc={\"S\": 20., \"E\": E_init},\n", " snapshot=True) \n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 16, "id": "bb87b0c2-6e5d-4e9a-86a1-9eb76cfe2d3a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* INFO: the tentative time step (2.5e-05) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.1 (set to 2.5e-06) [Step started at t=5e-05, and will rewind there]\n", "1476 total step(s) taken\n" ] } ], "source": [ "# Perform the reactions (The duration of the run was manually adjusted for optimal visibility)\n", "dynamics.single_compartment_react(duration=1.3,\n", " initial_step=0.00005, variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 17, "id": "1c999a21-c1ab-4210-a8d8-430cc215d882", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reactions have reached equilibrium\n", "dynamics.is_in_equilibrium(verbose=False)" ] }, { "cell_type": "code", "execution_count": 18, "id": "6991314e-58bf-473a-a0fa-c10f18369246", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.24856557905040474, 9.926581378605173)" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Locate the intersection of the curves for [S] and [P]:\n", "dynamics.curve_intersect(\"S\", \"P\", t_start=0, t_end=1.0)" ] }, { "cell_type": "code", "execution_count": 19, "id": "ceaf1c9e-9178-4511-af28-0b6918392300", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_curves() WARNING: Excessive number of vertical lines (1477) - only showing 1 every 10 lines\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=S
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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(colors=['cyan', 'green', 'violet', 'red'], show_intervals=True, \n", " title_prefix=f\"[E] init = {E_init}\", xrange=[0, 0.4])" ] }, { "cell_type": "code", "execution_count": 20, "id": "de531345-b12f-4c43-9954-bf46db6f1141", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.24856557905040474, 9.926581378605173)" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Locate the intersection of the curves for [S] and [P]:\n", "dynamics.curve_intersect(\"S\", \"P\", t_start=0, t_end=0.4)" ] }, { "cell_type": "markdown", "id": "41a77229-ad02-4e1e-8c3e-dfe2e6e0a302", "metadata": {}, "source": [ "### Now, let's investigate E and ES* in the very early times" ] }, { "cell_type": "markdown", "id": "738f8578-8cc9-4ed1-98f1-69291581ed24", "metadata": {}, "source": [ "## Notice how even a tiny amount of enzyme (1/100 of the initial [S]) makes a very pronounced difference!" ] }, { "cell_type": "code", "execution_count": 21, "id": "2bdb3ca1", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_curves() WARNING: Excessive number of vertical lines (1477) - only showing 1 every 10 lines\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=E
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#The very early part of the reaction\n", "dynamics.plot_history(chemicals=['E', 'ES*'], colors=['violet', 'red'], show_intervals=True, \n", " title_prefix=f\"Detail when [E] init = {E_init}\", xrange=[0, 0.002])" ] }, { "cell_type": "markdown", "id": "1f1fdafa-f516-4490-99c1-1649a0b4d783", "metadata": {}, "source": [ "### Notice how, with this small initial concentration of [E], the timescale of [E] and [ES*] is vastly faster than that of [P] and [S]" ] }, { "cell_type": "code", "execution_count": 22, "id": "c5297f8f-2e7e-4acb-b029-6235388cbc4a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_curves() WARNING: Excessive number of vertical lines (1477) - only showing 1 every 10 lines\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=E
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YqG3U8RFlyZsBVSZijHQLGCbzvyz+ghYqdPdlL4HhN96m7ZLv61yPl50zSz54ASoX2kNl7FVvFJeYoBV2Wbvp6jG5b2dzr2orl81AoRoxQUEL9qCvtcNcNF6Gp050fheHbGTy10TZrEDaEOxefRQ2GHSDYdeRoJuWyQ1AtXmTesXqSr4Eu+7rO263vMpjKmb8JizVnkwFu7hB8r9hHjwE+zBffetukFEFu2wDYTad+tXr90CqE3yq64xoU5CNBz1ce11PcbQDVYyY9i3IfUEux+uaVT/3SsdlqYsxuvumvPLt5RbmNwZBD15iHve7B8g2GOUeIK/Q+vnymgr2oGtDFtq6hSfhgijmGh6rDZ/XZHzLbdoWL80TxqZM5x+/sfIS7Dp3SvnbIVG3n3trLrSHKEPYnVd720qwh7lvC61meq+CYI/4ZBA2u5h8TcVqGAMXZatP86pBm5YZ9AQoC1XVv1LHRdwsvHwmg3yMhRgz+ZrTdBXQJF3Qqg5zCLppqcz9LmrBTr7RetmZuGnZFuyiLepkrKvXVLD7MVC/Xg0j2GXRLnMz2ayj60+Y8Te9YZrOG0EPk6Icv3q99i2IvGpEKvUBTC3btI9BQk/cpOJoB3ES7F4PyWL8TMLc6uYSnauBlyucn72KcTQV7K59aXzqVbvzqlPnJ23iViQecGQXwaCNxTIj+Zsmnif44MAQskjn8k48enTGBvI4Cvag+UJmJNLqolip37zodEA292sv+5BtQtid6f3Gz4bDuMSo9xGvxSW/+lT3MDWt170Kgt30zpmjdDrfL7+iTcW1TsyKcvMh2HVfBZoiE3lNbjyFuMJu8nBnW7B7rURFEey2VlZVuxPXkMnG5jitsItr2uS6CFph57KCXoRiakOmK1emgj2udmDbJSbMCnuuIxeJuoVAD1phD3K7YfvKZtVWXKth7gHq9S1sXxaGpiI5zAq7vLLLPt28z4jdieR7H2/sVedr07Z43S9trLCHEexeDzUmrqTiYTPo4VxnfybuXn66x3Se4jJyKdjVbwBMdRCnC7pXQbCHoZmjtGLFy2/FjwfGL6yjauBhfNLCPAR4XazqBW+yUi0mdRZO7M8mHyYXv+7iDNMXr+Hzqpv7JHw8TX2Yw6wE+/mSc1uZkekKq6nYEpOTTsD5rXSa+hhzuV5f0+vYmJZrypX7wKs+6ptJ/dwKZLtoCx927pvumvDaYKWz42x82NVycrFfRfYj9rKDMPs51PHIlx2ofvsqqzA2birMRR2mfTa9HYl7iZpenVu8BJLp3Ow1Nuq9wcveTerhcTn52LGk7v9S5xFTkWzqwy7YcbkiQprqBqj73E9QmvqK2xDsYeZ603ufzs7UsQ9zvzaxB53YVh8CTRa8cinY/cZcvgazuVeZ2ozp3BCXdLH1YZcvfP5dNSZ1tSCMget2HIuHg6Cd7NwWnehWXRM4nZcfoWi7LowkhzjkFT5RnrxiE0aY2FhhF/2RV2jUDXm6vonP5DE0FRTMUcdCfTrXpRFjxaGlxM79MII97E2K6xPlyw+Zsq+zfPPyaouOja5/Opsz5aobSzGBmqxUB3HURVWSx9/UXUSeKL3GWPg3mriKBdUr5gG1LO6vSSQkbq9u7HV9D9pXoZvT4mYHQS5rYWw8qmAXokQXRpfHnQ+/N8bq3DB115jfwgWvHOuuH7ar3//iO66A1pXJbVPvS1HuAbp5WPettalgF3ODzqVG11+xYuwV9lGXJ0xbdALKhmCXbUqeE0T/5H6Iz3TpZG66PTfqPTKMnhH34CC7042/rFHaQrCb3LfD3qtMF0XjIsLDtCP2gp074+X3Ld8Ywxi4mBzV+KAs7HRxVVVh7WUQwvjEAPAFNOLAA9w43aoA0PkXcj6d0JEH1OQrVzG5ZuMTZ2I86mZdtU26vgX5s4l6g8ZRbp/XuKh9kNsXJDTVdqp+sTyOpiJFtIPbKd4NoNqB7Ded6zjs8rczfuJP5mX6hji/lXiT8Q8Szl52qF5jnM7kAUOUZ1Kv/IAlt0MeO3VOYhvjQ96vIvLq2qzamc4OwlwL6s3W9MGN26hrn6kdiLlUDYkqczO18VwIdtP7hZd96fzgdUJGngOD4rCrNip4MzP5HqSzY929z/QeoLNjdc4MK5JVPl52olukYQ460SjGImxb1DG0Jdi5HrXfbBPs7qPavS4dL8KpPuy6/TJR9Iy4DmV70s2N6tzMNneC8w0196UtBDu30csPXxde1eReZTLHe13/cf+8XQj2uEP0a19Sfana85ig7SAAArkjEMYHNne1tt+SwKv9jh1aHm8CYbwQ4t0Tfesg2HM0amwosuuFvJpgGoooR01BMSAAAiCQVwI6d4C8NqAdVQbB3o4GC01tVwSSPg9BsOfIHL2+1jH5milHTUAxIAACINAmBOT5zyQsaJs0MiaVQrDHZCDQjEQREG5qSdZcEOyJMll0BgRAAARAAARAAARAIGkEINiTNqLoDwiAAAiAAAiAAAiAQKIIQLAnajjRGRAAARAAARAAARAAgaQRgGBP2oiiPyAAAiAAAiAAAiAAAokiAMGeqOFEZ0AABEAABEAABEAABJJGAII9aSOK/oAACIAACIAACIAACCSKAAR7ooYTnQEBEAABEAABEAABEEgaAQj2pI0o+gMCIAACIAACIAACIJAoAhDsiRpOdAYEQAAEQAAEQAAEQCBpBCDYkzai6A8IgAAIgAAIgAAIgECiCECwJ2o40RkQAAEQAAEQAAEQAIGkEYBgT9qIoj8gAAIgAAIgAAIgAAKJIgDBnqjhRGdAAARAAARAAARAAASSRgCCPWkjiv6AAAiAAAiAAAiAAAgkigAEe6KGE50BARAAARAAARAAARBIGgEI9qSNKPoDAiAAAiAAAiAAAiCQKAIQ7IkaTnQGBEAABEAABEAABEAgaQQg2JM2ougPCIAACIAACIAACIBAoghAsCdqONEZEAABEAABEAABEACBpBGAYE/aiKI/IAACIAACIAACIAACiSIAwZ6o4URnQAAEQAAEQAAEQAAEkkYAgj1pI4r+gAAIgAAIgAAIgAAIJIoABHuihhOdAQEQAAEQAAEQAAEQSBoBCPakjSj6AwIgAAIgAAIgAAIgkCgCEOyJGk50BgRAAARAAARAAARAIGkEINhzMKLbv2yg7Tsbc1ASipAJlJcVU6fKMqqprQcYCwS6VpVRY1ML7aiD7VrAS3t3LaetOxqoobHZRvEFXWZJcRH1dPh+tqWuoDnY6nxVRSmVlhTRNsd+ceSeQPfOHejL+iaq29WU+8ItldinR6WlklGsKQEIdlNSPukg2HMAUVMEBLsdrqJUCHa7fCHY7fGFYLfHlkuGYLfLF4LdLt+klg7BnoORhWDPAUQIdjsQfUqFYLeLHILdHl8IdntsIdjtsuXSIdjtM05iDRDsEUf1Zz/7WbqEoqIi9/eSkhIqKS2lxoZG6lhVRR07VjmflVKx83lFZSVtqdlEu3bV07CDDqUtW2poe+02GjV6HL3wzGN01vnT6KEHZ7j/8t/8eX19Pa1cvpS+cfIkmvvSs7RPn340eOhw+rtzftCQg2jAwEG0YtkS2rB+LU049iS3DU89NsvNu0/f/bR/q+k50dsLX3fTjhx9RLpPu5y6uT0XXHJ1Bilu89NzZlH1+Ze1Irhg3stU1akLDR9xWKtzG9Z9TIsWzqdTJ1VrycvnxQr7osVL0/1/4J5bXTZrVq9I91du95rVK9NpuYJHZ82kCcedTD169nLrE/k7lJe7f8sMRYPUNDqefmn5nB8Dv3O6NqugghiK9KoNqOUIwb7qg9XaMZHZyG1Wx161pZpNn9PcF5+hydVT01Xq+qyzN84w68G76JSJ1dS5S9eMJsu2r/bFr6+69qj5VTvRGadXe9W0wgbPPqvayCXmntt/TZdc9UPt9RClHaptq/Wodq6bE5Ysfot2fFFLY8cfk9EU3TXiZ7t+84XXdShXqLLXCXbT8TFNx/V79d9rsEyvzTD2G2QY4nrhdGJOFuOz9J233Ow8p8s2Lv+uXpuc96JLr6SqjpWuS4w61jp+umvTi4UfI918LPofNBY6+1XZmY69XzvUMr3mK69xY55XXDGdmorKjF1iguZyr7q8rju1f+p9k8tT7QIuMUFXov3zBSnYz5h6Pa1as86le8CAvvT4zBs9SV94zc305tvLMs6/9+rM9N8Q7BDs/AAhHgCEYUCwQ7BDsO+ZNiHY/W/m2QoyLhWCPcUWgr21jUGw2xfR+ayh4AQ7C/CazbVpkc7ivUf3LnT/LddquR85cTq9Nue29Lkf3XQ3zVu4JP0ZBDsEOwR75rc7WGFPfcsDwQ7Bbnozh2BPkcIKu95isrUPCHbTK7B9pCs4wc4C/PvTptDEE8e7IzTnuXn02xmzM0S539AtWbaaqi//Oc268wYaPnSgmxQ+7HaMHZtO7XAVpcKH3S5f+LDb4wsfdntsuWRsOrXLFz7sdvkmtfSCEuw6sa37zG+wb7vvUXr4yVcyBD4Eu53LA4LdDlcIdrtcRekQ7PY4Q7DbYwvBbpctlw7B3ppxkLeD/VHJvoawOjLbmiDYNSvmXjDFoNx43cXpFfqtN26lDhMrqemrxdmOAfJ5EChx4gB3KC2hnfWIE27DSMo7lFBzcwvihNuA65TZ0YllzXGWmTGO3BLgDf4dK0poB95/kVuwu0srKy2mYifWfX07ihNuBYSlQivLS5x5t8V5D0b7eUdD545lkWjo9gN279Y5vfjZFoKdPSyu/9W9JGu6bDoJwZ4NtYA8UVbYRd5p551O0y+anK7Jy4e9tLTMuSAbqFNVJzdSTKkTNYajx1RUdqTNmzZSXX0djXCiqNTUbKTabdto7BHj6YnH/kYXX3YF3XvXH9x/+W/+vL6unt5/7106feJ/0vPPPkX99t2PDjzoYHpizl9p2IEH0wGDBtN7S9+ltZ98TCecdKrbtkdm/Z+bd999+2v/VtNzojfmv+am/fq4I9P9q3faye258jvXZNDlNj88+890sRNNQD1efeVF6tK5C408bHSrc5988hEteH0efav6HO1oyeeFYF+y9P10/+/4/S0um1UrV6T7K7ebPxesuII/P3AfHe8w6dXrK259In95eYX7t8xQNEhNo+Ppl5bP+THwO6drswoqiKFIr9qAWo4Q7Ks//FA7JjIbuc3q2Ku29Pnnn9ELjp2ee8FF6Sp1fdbZG2e49+476Mwp51KXrplRYmTbV/vi11dde9T8qp3ojNOrvWpaYYPV1dVGgv2W39xE1/zgx9rrIUo7VNtW61HtXDcnvP3WQqrdXktHHX1cRlN014if7frNF17XoVyhyl4n2E3HxzQd1+/Vf6/BMr02w9hvkGGI64XTiTlZjM/bi/7pZuc5XbZx+Xf12uS8l19xFVU6UWJYsKtjreOnuza9WPgx0s3Hov9BY6GzX5Wd6dj7tUMt02u+8ho35nnV9OlOJLlyY8EeNJd71eV13an9U++bXJ5qF1EE+4FHTSVZnIv2soj/Ss+96Jc/vpTaQrAHXVum5yHYTUmFTKfzYecnLDnyi1qkeAqT/dZFGmw6xaZTbDrFplN5zkBYxz1hVAUXRInxv1Flu6mQS0WUmBRbRIlpbWNx2HTKonzl6rWB+wSFYOdeiMh8XiJfjtwn6zLWd+NHD3cDg2zeut0Fwous+/bt5a6ki0Pk0Qlt9ZsAsUjrFzEQgj2kEDdNHhQlho2GDxHqMWhTKgQ7BDsEOwQ7BHuKgFc8ewh2CHZBAHHYCysOO6+un378OHcV3e8Q4bZlLwYW4IMG9ktH8VP1G+8pnPGnJ9ILrpyehboQ5OK86nojNJ4qtNWHCz7/u3secevnc9+75FvpYCOyVoRgN1XgWaTzi8OuGwRdFcLnacv/20LF4zrQjhHwYc9iKHyzYNNprolmlocoMXb5YtOpPb7YdGqPLZeMKDF2+RbKplPdvj8vsjqXGA6j/f6Kj9wFVC9RzCL9zNOOdl2VxQq7eGtjKIMAACAASURBVDjQ5ZFDc8vnuV0cAdDUn10OQALBbvd6yVnpEOw5Q9mqIAh2e2y5ZAh2u3wh2O3xhWC3xxaC3S5bLh2CvTXjIMEuXJN1oyNW5b0EuyzCvYT2Bx+td91m/NyjxQq+3AZOD8Fu/5rJSQ0Q7DnBqC0Egt0eWwh2u2y5dAh2e4wh2O2xhWC3y7aQBDv3NYxLjPoSS3mFXQj2IEHNPuzqCnsuBDv3Y8zIoWn3HNkdB4Ld/jWTkxrgww4fdviww4ddnkyw6RSbTk+dVB3q/oJNpylceNOp3myytY/2sOmURblXlBidS4yfy0qUFXYm7+USo3tYgGAPNcXFIzEEOwQ7BDsEOwR7igA2nX5MixbOJwh2Iq/Npdh0WlibTsUquxrxRYhgsSE1yCWGyxGRWuRVdhb1Y0YOc9+NE0Ww85vruQ2bt9amI9qITae82VQV87zizgdcYuKhxY1aAcEOwQ7BDsEOwQ7BzgT8xKjfDSXbFVQuE2EdU2QR1rG1hcVhhV20ShcWUV4tNxHssmiXeysEfFTBzmXKQUn4b9FGfjB44oX56WrZb15EqIFLjJFcbvtE8GG3NwbwYbfHlkvGplO7fOHDbo8vfNjtseWSESXGLt9C2XRql2LhlV7U4hyF1+3c9RiCPXcs1ZIg2O2xhWC3y5ZLh2C3xxiC3R5bCHa7bLl0CHb7jJNYAwR7xFGFYI8I0Cc7BLs9thDsdtlCsNvlC8Fuly9W2O3yhWC3yzeppUOwRxxZ+LDDhx0+7PBhl6cRRIlBlBhsOsWmUy9p8cA9hbfpNKLMQvbdBCDYI5oCBDsEOwQ7BDsEe4oAosQgSoy4FhAlRi8uINgjiq4Czg7BHnHwIdgh2CHYIdgh2CHYmQCixAxPXwoQ7BDsEeUVsisEINgjmgR82CMC9MkOH3Z7bLlkRImxyxebTu3xhQ+7PbZcMnzY7fKFD7tdvkktHYI94shCsEcECMFuD2BAyRDsdtFDsNvjC8Fujy0Eu122XDoEu33GSawBgj3iqEKwRwQIwW4PIAR7m7HliiHY7eGHYLfHFoLdLlsIdvt8k1oDBHvEkYUPO3zY4cMOH3Z5GkGUGESJQZQYRInxkhbYdBpRdBVwdgj2iIMPwQ7BDsEOwQ7BniKAKDGIEiOuBWw61YsLCPaIoisH2ZcsW03Vl/9cW9K0806n6RdNzkEtuS8Cgj0iUwh2CHYIdgh2CHYIdiaAKDGIEhMkKSDYgwjZPy8E+6w7b6DhQwfarzBHNUCwRwQJH/aIAH2yI0qMPbZcMjad2uULH3Z7fOHDbo8tl4woMXb5YtOpXb5BpUOwBxFK6HkIdnsDC8Fujy0Eu122XDoEuz3GEOz22EKw22XLpReiYG/a1ETNXzTbh6vUUNKzhIo7FWd8CsGe92GIR4UQ7PbGAYLdHlsIdrtsIdjt8oVgt8sXK+x2+RaiYN/5wk6qe7POLlhN6ZXHV1LFmAqtYNc1Bj7seR+i/FUIH3b4sMOHHT7s8oyDKDGIEoMoMYgS46VCCtWHve71Omr4oCF/4mx3TRVHVFDZ/mVYYc87+RhWCMEOwQ7BDsEOwZ4igCgxiBIjrgVEidELlkIV7HGSb3CJidNo5LEtEOwQ7BDsEOwQ7BDsTABRYhAlJkh+QLAHEbJ/HoLdPuNY1sA+7GU9llN9v1pq3Lc/tXTtRs1du8ayre2tUfBhtztiiBJjly82ndrjCx92e2y5ZPiw2+VbiD7sdomGKx1x2MPxSkzq7Rc+SZ3/eHpGf1iwNznivWH4IY6A70qN/fajpv36p/5zPoegNxt+CHYzTtmmgmDPlpxZPgh2M07ZpIJgz4aaeR4IdnNW2aSEYM+GGvIgDntEG6g/9GwqX/wQNRx0MBXXbqOSjz8KLJEFO6/Ec55m/vfA4a6wZ4Hf3MUR+46wx0EEwW7XCiDY7fKFYLfHF4LdHlussNtly6VDsNtnnMQaINgjjqrWh724mEqd/xoaG6mqhahTQwOV1tVR6Y4dVLV1C23s1o3qKiro8IULaWOvXrTV+XvCq6/S7Opquvp//5du/d736KpH/koPn3E6jdu6nXYM+Cq9X1JEJ4w7il765EPqPWAgDR46nP7+zGM0aMhBNGDgIFqxLNOP+KnHZtGo0eNon777uT1U/1bTc5q3F77uph05+og0lV319fTQgzPogkuuziC13Xk4eXrOLKo+Hz7s8GGHD7t8cSBKDKLEIEoMosR4SQv4sEcUXQWcHYI94uBntel042e068sv6eCqzrRly2baXreTjvhsI83pvTdNv+ceuu3CC13hzgKehTyL+3dGjKAps2bR4xMn0n6ffUYHr1tPsydNomFUTF/duzct3asrrS0ppgnfONV1uYFgn+SOrBq1gidLWWDLDz3CFNQ0ugcev7R8bsG8l6mqUxcaPuKwVhbmd07XZrUA041tqg2o5YgV9lUfrKZFC+eTKjJkNnKb1Yc19eGvZtPnNPfFZ2hy9dR0lbo+6x4QOcOsB++iUyZWU2fn2yb5mPvSs7RPn37uw6p6+PVV1x41v1d0EzmdV3vVsiDYIdgh2CHYIdgjiitkb0UAgj2iUWQl2Gs20a5d9TTsoEMdwV5DLIB4NfwFZ8WcxeRDD9xJ5xx7Kr3w6nP09V1N1LBpI71fVkLfeu55enrYEBqwYgWNWLzYFfSHOP8OWb6cFjuC/qMBA+iMOXNcwf7guefR1+t2Ub+yDq7LzV+/dOo4dAx9ZeThbo+xwl7ucoBgbyEIdu9whBDsb9GOL2pp7PhjMmZK3UOt38Om3zdyXtehH3udS4zpA5VpOq5/yWJ9/71uG6YP02EeOINuUeIBl9OJbz3F+Cx95y03O39rKj+Uyr+rD9Oc96JLr6SqjpW0bUcDqWOt46d7mEZYR/3IYYU9yKJx3otATgT7kROn02bHdUN3vPfqzETTb95rPyre+gl99vayvPmeF29zfOU/+cj1l+f/Std+7P5btvRdKtq2lfi838E+8jr/+bhtiIUPu91LBz7sdvnCh90eX/iw22PLJWPTqV2+8GG3yzeppUcW7GdMvZ56dO9C999ybVIZ+farpbIbFdVto08/2BCb6C8s3nkDbNmSdxxh74h55z/+3WRTrBzhpmlfJ7qN819bbYaFYLd7SUGw2+ULwW6PLwS7PbYQ7HbZcukQ7PYZJ7GGyIL9wKOm0o3XXUwTTxyfRD7BfSoqctOs3/RlcNoYpODVd16F59X4sKvzcnQbXqUX4Sp5td5GZBsIdrsGA8Fuly8Euz2+EOz22EKw22ULwW6fb1JrSKRg51X/VWvWuWN2wIC+9PjMGwPHz+vNV3Oem0fX/+reVvmFq48VH3YnKgv7srNPO/u21zuRWlYuX0rfOHkSyb6CNqLEFDmCfvQ+/dKr843r1tLdA/rRD26/PcPVhiPbPDB1qrs5VhzC1ebFg4ZRJ2fD5cEDDnBdb+SXSQX5eMrnhWBftHhpuv/Cn3LN6hW0Yf1amnDsSRnRbcSGP2bFBzad7okUpBoxNp3uIYJNp/p9LV4+3PBh199SguY3rxtR0AZxvxsYfNhTdHT7slRupvsXdHubvMbAa5O8V3r4sAfKMSTwIBBZsLM4Pu7IUTT9osmxgHzhNTdTzebatEg3cdmRffBn3XkDDR86MN0XFuy/nTGbXptzm7Z/SRPs3EmvsI7Cd57da7Zv3Up/q9tO0/71Tnq1XgB6/sQTqatzfuyCBRlint8Eu2bIEJq33770ze69XFcb1W9evuF1XLPKeSnV3bTsk7W06D+/5T6wQLCbv/48SARAsEOwyxGTdIIHgh2bTrHp1F/aQLDHQvq1WSNuu+9Rt+58aODIgj1I0OabIovv70+bknbRMW2f3wo7BLtZHHax8XWeI7S7OYJ9tBO9RrjeCDtY40SymXvUUXTBzJkZYp5fGMUCfk3//vRGZTmd+cVO6vybm9w0yx2Rv/B736fjvnkOBLvDw3QVD4I9ZWII6zjI5XDP7b+mS676Yfq6U4UYBHvruxWixCBKTJCGgWAPIhS/80Lv6Vo27bzT0+KbXb7lQ/bYEJ4cnJ6PGX96wtijI1sikQW72iG1IfmMEqMT3V5CXG1nGJeYjD61Mx/2bA0laj4h5ovZf/69JaGi2nDddSef5rrXiE2wcYtoE5VPW+SHD7td6vBht8cXPuz22HLJiBJjly82ndrlG1S6iS7kxd/xo4fTL398abo4Fumqi7XQwPnQupEFexCYfJ63IdjV9qsuN8SC3Vk1pg8/zGdXk1XXmjVETjx5clbl6Z13Ur87L4wKPBw/epe9E4Pe/ddZnU//zudwgAAIgAAIgAAIgIBEIEiwB53notrlCnucrCAfgl3UkX6acgR7syMUP120LE4o2n1bOiyYT11/+VMqe32eu7ped9Kp7so8b4pNhat0Qlf6xJuPU3jKuA4GVtjtjgxW2O3xxQq7PbZcMlbY7fItyBV2x0WWPv3ULlhd6Y5LLfXunXHGRJDzCnv3bl0Cg5a0Kx92pqCLpNJWoR51Puwc5SXo6wqTAZT7mtQoMdxHr02nssX7vblQ9xp6kTfI/1o+3+23N1HHX/6CFl99Db0zalSrTaefrlxOxw78mhslhoX8+NUf0oc1G2nJV/am6j/9ya3yrmnT3Le/9t49Udx83XU0/f77qaxXb9dnfs6AfelrPb9C+40aQ+xHz5FudBEwvPzBvaJl+DHwO8dtDopYEsRQsIYPe4oEfNjhwy7PXaaRQjgPfNjhwx6kMOHDHkRo9/nvfY9IiipnmCt6st/9jui739UKdl3hfj7s8rnoDQtfQmSXGH66YGd7ObqKEL9t0bmgKDH8NQYfqh+Sl2DnBwA5QowadaaQosTkW7B3/Hg1dRs1nN7+2Y20ZED/UFFiTjjiGHcV/pF5L9EJzgbWfT5y3gTrrMzfctopdLVzAVfU1bndmV1dTYc4LjhD+OnfOXhl/jdXXknTlrxPpX37UcOBw53PutHfamto5JHH0D5998u4yiDYW4dT0wlk3UOKl3DyugHqXn9u8nACwQ7BDsF+RMZCgLwooF6bPKdddOmVVNWxkrbtgGAPklUQ7EGEdp//1a+Inn/eMHEOk13rvNTTiVwnH6YLtHIeoXXbajGa2xJZsLOgPfO0o1uFtOHOPfzkK57hEHM4HK2K8ovDrhPsclhHLqx7t87pdstl8bkxI4dmvNUVgv2yVvxztcLuxmEvJVr03r9zGof9nIlnU+VnG1wB//Tn6+mgTz+jYW/MT7vZ8Co8x5cXop47yDHnJzh+9fs2t6Q2v+5+cdSdzfV09glnUIeee2e86RYr7M/Q5OqpaduAYPee8dToLUFzo+kKsRpLGlFiUmRN+XFarLBDsAddjxDsQYTidz4bwc698NK7+ephZMHu9aZT4SYT5IqSr45aqwc+7NbQtsWbTuVY866//O6INqXOaj1HuvE7XBHvxJp3XyDlrMy3OKv1uljz1oCFLBg+7CGBhUwOH/aQwEIkhw97CFhZJIUPexbQQmQpSB/2EHxsJw0S7Kxf/zjr2QxPjDho2siCPY4r7LYHO6N8CHZruNtCsPt1hsV8EYelXPquK95L136cDk8ZJOblTbCukN/taiNW661B9CkYgt0udQh2e3wh2O2x5ZIh2O3yhWC3yzeodJM47Kp3BZfZ1gvQkQV73HzYgwYq5+ch2HOOVBQYN8Ee1FE11rxpRBsu112Vd1xt2F8+X6vzEOxBIxrtPAR7NH5+uSHY7bGFYLfLlkuHYLfPOIk1RBbsDCVOUWLyPUjwYbfsw15ZRosWL82pD7v8OnbVz5ftx0aUGNnV5rXP1lHXzZvp6//4BxXXbmvlaqNGtuHV+RYW8rt959f07UtvdCihM8b8h/Miqf4ZvvOy/SNKTIoGNp1i06l8XcCHvVfGBlRsOm2tGnT3BS9tAR/2fKuuwq0vJ4K9cPERQbBDsMsPAOJaCLvpVKzO879/qaulk9ZuoL5v/VMbb36N85KouUcdRRfMnOlWp7rbNPbbz12xf3TzZ26Izt6Dh2ovUbHCvuqD1bRo4Xw6dVI1lS5fRj2mnEGbH5xNz6xbQ4OGHEQDBg4iuT9qSE/1lfaIErPSfcA8+6xq2upE2WhobPadIrHplChIIKkiW7fCbirETdPxoGHTKTadBukbCPYgQjifKwIQ7BFJQrBDsOdCsMtmqMZhVzfCbvh8A73hRNA5/5G/uj71Xi+QEpFt9tuyxV2JZxEvotuwH3356FHU2KkrrdxWS2+99w6ddtzJ1PXHP6COD/2Jtv3i1zRnv74Q7NLAmAq9Nash2Hv07JUxs/q9t4ETQrDPolGjx7UKG2tyexKCkdM+PWcWVZ9/WfpbwqXvvOUWwQ/u8ryCsI5H+KINskc5MwS7iZUiTS4IZC3YOToMx1nnGOx+R1s76ecCkm8Z8GG3hri9+bBbAxFQsCro5c2wfoJeFMsr9HxwOS2dOlPRF9vdt8t+WX2u64bD7jgiTVv1sT3WCx92e6MGH3Z7bLlkbDq1yxc+7Hb5JrX0rAV7UoGE7pcj2JuOnECfPfZs6KzI4E8Agj03FiIEPbvbiOg2vCG24r13iXiF3nmpVNAh+9HzxtimfR23G+c/93deuffxpQ8qO6nnIdjtjSwEuz22EOx22XLpEOz2GSexhsiC3SsOe1u+OCmvAwXBbg03BLs1tG7Bwod952c1TqjKd6jqrjuo4pkniUqdt1U1NlL9Ef9BHH/eZJVetFSORc9uN+xPz/+KzwtptR6C3Z79QrDbYwvBbpctBLt9vkmtwZpgj0OQ+XwMGnzY4cNu24ddteMN6z5ObxL1s/GwUWJOO2USVT72V6q6dwaVOi+MevDOu2nQ8ENTm05fepY6l5TSqC/r6IstNfQ3Z0PrZStWO240W+n9+i/p4x49aOLDD7vN+bR3b3p84kS6bMaMdPOed14N3XXrVhq7YIHrXsPC/VVn4yz/+/WGpgxh/8C/l9Bpzttjq/r2y+jeXKcN+/TpR4OHDm/Vbb++IkoMosTIBmO6F4HzYNMpNp0G6Qj4sAcRwvlcEbAm2H900900b+ESem3ObblqayzLgWCHYE+KYOcoMe7hrK47EwO98PenQm06Pfqwce5q/NYV79NLq5bTOVTmvlyK3W9erexA3Tasp7Hz56c3yXKkGz4mvPpqxrV963e/60bA6eYIfF6Zb+6SWqF/eshg6lvRkYZ27Nxq1f6Jl5/13LQHwQ7BDsGOTadsA6YPa9h0ShmRwZhdnx6VsdRghdSorAS7Lu66DtqN111ME08cn2ieEOwQ7IkT7LuvWPmmlcuwjuKNsW//83VXvI/d1ZQW9uxjP+Pro+m82bOp+yefZMwdvGrff80aGrF4cas5hSPiHPn+Mtr3y51pv3p2xWGx/+k++9Dfd2yjKcOdqDiOrz0f/AAgH2pkHt2kZXqzR5SYkwlRYnY//Bre/YK+DfMrBlFiUnTU8LJRrmEIdgh2w0s3r8myEuxyC7182PPai7asDD7s1ujDh90aWrfguL/pVAh78XIpdr8p+eRj9z8+3A20IX3sZaJCtLOId8W9454jRD5vqBXC3kvkB41OW/mwd1jgPAg5oTzrTjo1qInt9jx82O0OHaLE2OWLTad2+Sa19MiCPalgjPsFwW6MKmxCCPawxMKlj7tgD9eblIBnce8Ke+d3dsVxxb4j8Pkz/juKwBft8RP6vKIvxH+XPntTba++7ouT8rXZlh9yeo0c4tb32dvLwiJsN+kh2O0OFQS7Xb4Q7Hb5JrV0CPaoIwvBHpWgZ34Idmto3YKTJtjD0mJRz0dKxO8W+mL1XhH5nE6kD1uPnF5suGVhn17Rd8Q1H+lV/d2r+/J5Tu+mUVx55LKL6uuo8tFHqNv0y9x0EOxRRqqw80Kw2x1/CHa7fJNaemTBvmTZaqq+/OeefJL+4iT4sMOHHT7sS2jD+rU04diT3HlAt8lT9oEXk4WXT7hX1IW4RIk5vHcqeo0s9OXV/JWdqui9jhV01uJ/UfOHa9y0fqExf/bTn9JPnP9MD96s21JR4frs88EuO9wWfqBoGHYglb3/nivYZ10wlYY1NtFX++zrpru1ZgNddehY93d+GLjv9Zfo7ONOo/KyMje9zgfYK0rKA/fcSjq799oLgDed+o9uFB/22X/4H5p62+206ZmX6MnXXsSbTnfPQzripvtQ4MMOH3bT+Tif6SIL9iMnTqfxo4fTmJHD6LczZqejwpwx9Xo67shRNP2iyfnsT97rgmCHYIdgLyzBzq959zv8Np2KVXrhusNC/7bVy+jqHvvs8c3fvcov3Hj4X07PB+f3iq6jtml2dTUd4mzQHbJ8uXtKfTC4+brr6Or//V+qqKtzzy8eMYI+GjCATn37X+miFowaRdv22ouO/ffKtKsPn/z9oK/SxfVNVN6SSipcgf6ybRN9o6or9eixt5teHFt69KQn5r9C5xyX8qtXXYSCBJIqtHQuMaZizDQdt7M9hHV8+Le/oKl3/oG2f/9H9EhVBwh2CPb0dec+KD/6F5p+//1Uf9SxVPvzX7nn1OtNzFnfOHnSnmt/3stU1akLDR9xmPsZosSoM2z+/44s2MWm0/3796ErfvS7tGDnSDKygM9/1/JTIwQ7BDsEOwS7PNvkI0pMUX09HdZ/f7fa8tf/4a6QVzz7FFXNuD3dlFnnnUdf69efvrYm5frzm6/tT9f9/WX3d34IuOX0U+mqhx+hil273AcBIdjPmDNnz0177Fja1q0bnfDccxkTqir2xcm7pk0jzt/7008z0m91yuBIPvyAoDu4rQc7EYC+9lFqQzEfwm2If5+3/1edjlbQ17/40j3neCJSRVkJ7XQiDAlXojecv/nguP7iM7Uu5rTw07Xux6N3f1PCv4uNxWr6d1evoO2lJTR2/DHadqsfmr4jQc2XzQr7Xpd929lcXEN3HjaSpt59N+247Cqa/ZUeEOwQ7GnzYsH+zJ/vpe/d8N/ui/BqHk9dxxDsRpdz7BLlTLBz+EYW78IFplBenMR3jqYjJ9Bnjz0bu8Ft7w2CD7vdESx0H3a7dInaIkpMp1v/h1ocf/euP7iaGg46mDa+uiB0N2VfffFNABei+vCLaD18jtPxtwXiEN8OiL/ZZUc+wrw9N3QH8pjBb08BN0N+6NA1S2xQDmqyiF5UtvRdd1yZt/xwxvn587qTT3OL8npg8atH7JngNBUdSoi/xdhR1xjUtPR5r4ce4wKUhPnaqJ1t+6Lky4cPe9EX24k6lFP3b53uPtTLgj2btmOFPRtquc0TWbCz68uwwf3plz++lOTfC+XFSRDsuTVIuTQIdntsuWQIdrt820Kwuz1yXnzV7QffoZ2nT6b6o4+z28kclS5CeMrFyQ8L/LnYGMy/FzsLJZ06llLtjoa0K5GcV36YyPh890ZjtdnqA4VJnhx1HcXEgIDYDJ6vprD9tjgvp9vtURaqWr8HI7Zj8ZAovnkTD9r8QMcPZdke5fPmZpsV+XJEILJgV9vBq+zimHXnDTR86MAcNTWmxWCF3drAQLBbQ+sWDMFul2+bCXa73YpF6XEJ6xgUOcjvQUB9CPEDKzY188p5h/nzqOPDf6Gdk8+kykcecrPtmHaVK9TE4fXA4leH/K0I82W3o8Ymc0kZ1NewhpOUb2HC9ju26Z0HDBxtSyDngr1tu5P/2uHDDh92+LDDh12eefLhw871BW1+Vf1U77n913TJVT9MN1WN9IIoMa3vH3HedMrfSvTefx+69bvfpUlfHUw7T5tET8+ZBR/2LHzY1W94nv/nPBrc76v01X36BoqK/3vxKTp93NHUuWNVYFpO8MdnH6XLz5jkrK6XUr2zB8Pk4A3bhw0+kPr07OVGhPI6ePWd3ab44BX10nP/k/58/DfoyiefptIPVrp7Xbbedhc98+EKGrJXTxrYrbubdvXWzbR8yyY62bEjccxb9xF1KutAI3rt437U4/QTTJqKNBYJRBbshf6mUwh2CHYIdgh2CPYUAYR1/JgWLZxPp06qDnXbzmbTqSuizjiRZhw+EoLdYaF74FQHwTRCUFDUIrlcrzC0XgbAD8pXXDGdmorKqM5QsGdrH198/ik9/be/0IVFHajrf/3Q3eOw+cHZ2HQa6uqMT2II9ohjAcEOwQ7BDsEOwQ7BzgTyGSWG66t64D6a+ckHEOwQ7FolI95/cPYp36ReYw+h2v93M31ZfS4Ee0Td11bZIwv2Qom37jlA8GG3ZrvwYbeG1i0YPux2+cKH3R7fuPiw2+uhYcnNzVR19x9o51nnORsK9/iwG+b2TIY3nUYl6J8/H1Fict0DRInJNdHw5UUW7PymUzn+evgmtPMcEOzWBhCC3RpaCHa7aN3SIdjtQYZgt8eWS4Zgt8sXgt0u36SWHlmwy1FhdJBEXPakAkRYR3sjC8Fujy2XjBV2u3wh2O3xhWC3xxaC3S5bLh2C3T7jJNYQWbAnEUqYPsGHHT7s8GGHD7s8ZyBKzMnUw4lmIR/Cl7b6/NbzBacL2uSnbhbUCXbTDYWm6bhdcY4SI/iKTY/8N6LErKUJWUSJUe/5QfYop4/zplOv6w5vOg2j8uKTNrJg94oSc9t9j9LDT75Cr825LT69tdASCHYIdgh2CHYI9hQBRInJb5QYZg7BnrI9RIlpLXAg2C2IvjYs0ppgn/PcPLr+V/dS0l1iINgh2CHYIdgh2CHYmUC+o8RAsO+58iDYIdjbUEvnpWprgv1HN91N8xYuSfwKO/uwN552On3+x1l5GbBCqgQ+7HZHGz7sdvnCh90eX/iw22PLJWPTqV2+8GG3yzeppWcl2MXqeRCUG6+7mCaeOD4oWd7PcyjKVWvWufUeMKAvPT7zxsA2cDSc6st/TrPuvIGGDx24J70j2BvOPZ82/u+MwDKQIBwBCPZwvMKmhmAPSyxcegj2cLzCpIZgD0MrfFoI9vDMwuSAYA9DC2kFgawEu4yvvb3p9MJrpd7kIwAAIABJREFUbqaazbVpkc7ivUf3LnT/Ldd6WsWRE6fT5q3b3fMQ7Pm7eCDY7bKGYLfLF4LdHl8IdntsuWQIdrt8Idjt8k1q6ZEFe3sDw+L7+9OmpFf++duC386YHei647XCDh92+LDDhx0+7PI8iCgxiBJz6qTqULfGbF897y4iPXgXnTIxVR+ixCBKjGx42HQa6jKMfeKCEuw60e3p6qIMHQT71RlE/MK0LZj3MlV16kLDRxzW6gII2pQlnxcr7IsWL6WVy5fSN06eRA/ccyuxQF6zegVtWJ+anOUwbUIscVo+1KgVIn+H8nL3vC58l5qG03ndUHVpOb0fA79zujarEIMYivRBIkCssK/6YDUtWjifVJEhs5HbrI69utmrZtPnNPfFZ2hy9dR003V99gqv5xUmbe5Lz9I+ffrR4KHDW9mVX1917VEL8IpuIqczDQcIwQ7BDsHuvQHXb/7yC6cYFGITm05b600I9thr8FANzIlgl11G1NrjFCUmn4K9tLSMGhobqFNVJ+pYVUWlpaVUUlJCFZUdafOmjVRXX0cjHEFbU7ORardto7FHjKcnHvsbXXzZFXTvXX9w/+W/+fP6unp6/7136fSJ/0nPP/sU9dt3PzrwoIPpiTl/pWEHHkwHDBpM7y19l9Z+8jGdcNKp7hA8Muv/3Lz77ttf+7eanhO9Mf81N+3Xxx2ZHsZ6p53cniu/c03G0HKbH579Z7r40itbGdyrr7xIXTp3oZGHjW517pNPPqIFr8+jb1WfozVU+XxJSRF1KC2hJUvfT/f/jt/f4rJZtXJFur9yu/lzwYor+PMD99HxDpNevb7i1ifyl5dXuH/LDEWD1DQ6nn5p+ZwfA79zujaroIIYivSqDajllHcooebmFlr94YfaMZHZyG1Wx161pc8//4xecOz03AsuSlep67PO3jjDvXffQWdOOZe6KK9al21f7YtfX3XtUfOrdqIzTq/2qmmFDVZXV1PdriaXsd9xy29uomt+8GPfNPJJ03aotq3Wo9q5bk54+62FVLu9lo46+riM9umuET/b9ZsvvK5Dvz4XOXuHOlaU0I6djelkplxM03HBXv33GizTazOM/QYZhrheOJ2Yk8X4vL3on252ntNlG5d/V69Nznv5FVdRZcdKqnfsVx1rHT/dtenFwo+Rbj4W/Q8aC539quxMx96vHWqZXvOV17gxz6umT6eS0nJqbGoOGl73fNBc7lWI13Wn9k+9b3J5ql107lhm1FYkskcgsmA38QG31/xwJdsQ7O6bTs+/gL68855wjUHqQAJCsO+s33NTDsyEBMYEhGBvaDS7aRgXjIQugY4VpUaCHbjCE9AJ9vClIIcXgbLSYiouLnIFO47cE6gsL3EW9FqMBXvuWxC+RAj28MxynSOyYG9vm051Puwm8eIRJSbXphdcHjadBjOKkgKbTqPQC86LTafBjLJNgU2n2ZIzy4dNp2acsk2FTafZkivsfAUn2IOixPA3BnyooR4h2PN/oUCw22UOwW6XLwS7Pb4Q7PbYcskQ7Hb5QrDb5ZvU0iMLdha4xx05iqZfNLndMPKLw64T7KqPfvdundNRZRAlBlFiECUGUWLkyQ+bTrHpFJtOsenUSxBxoIIrrphOTUVlrsucyREUQMCrDGw6NaHbftJEFuymYRHbD5JwLYVgh2CHYIdgh2BPEfCKtuMXVYrz+UUH4fNqhB7dCrtpFB/TdFxvUGQS9W5hGsFJzZetIONyENYxRRNRYlprFwj2cHou7qkjC3b2Yfc74hQlxsZgQLBDsEOwQ7BDsEOwMwEI9j0hV71YIKwjVthtaLFCKDOyYC8ESL59dKLENJx2Lm38490FjyLXAODDnmuimeXBh90uX/iw2+MLH3Z7bLlk+LDb5Qsfdrt8k1o6BHvUkYVgj0rQMz8EuzW0bsEQ7Hb5QrDb4wvBbo8tBLtdtlw6BLt9xkmsISeCXd7EeeN1F9PEE8cTu8qMGTmU7r/l2iRy29MnCHZr4wvBbg0tBLtdtG7pEOz2IEOw22MLwW6XLQS7fb5JrSGyYJdfnCTHOL/tvkfp4SdfSUdTSSpA+LDDhx0+7PBhl+c3RIlBlBhEiUGUGC/NgygxSVWD9vsVWbDzSvqsO2+g4UMHkizYOXqMyQuJ7HfRbg0Q7BDsEOwQ7BDsKQKIEvMxLVo4nyDYIdgh2O1qr0IsPbJgZ5H+h19+r5Vgxwp7KTU2NFLHqirq2LGKSkpKqbikhCoqK2lLzSbatauehh10KG3ZUkMcemnU6HH0wjOPEYu/hx6c4f7Lf/Pn9fX1tHL5UvrGyZNo7kvP0j59+tHgocMzQqGpIa3UMGHq37oQWLpwZ7ucurk9F1xydcb14RembcG8l6mqUxcaPuKwVtdUUBQF+bxwiVm0eGm6/7w6wWzWrF5BG9avpQnHnpQR8k2sbjIrnYAQ+TuUl7vndeHk1DSczivsmi4tp/dj4HfOT/QImEEMRbqgUHHCh33VB6u1IkNmI7dZHXvVlmo2fU5zX3yGJldPTY+/rs9e4fVEmLrOXbpm2I9s+6ph+fVV1x41v5fQlNOZhgPECjtW2PMq2O+dQadOPItaOhA9PWcWVZ9/GYl5aek7b7kmPHL0ERkPU7K9q9cm573o0iupqmMlbdvRkC5LzJm660B3bSJKjF5SYoW9EKV2bvocWbD/6Ka7ad7CJa7ri1hh379/H6q+/Od0+vHj6Jc/vjQ3LY1rKfBhtzYy8GG3htYtGJtO7fKFD7s9vvBhT7Etfb+Jyl5toF3HlFLTkNKcAUeUmJyh1BaU902ntc1U8ddd1DiujBqHlGTVuT49KrPKh0y5IxBZsHNThPuL3Kxp553ert5+mjVSCPas0QVlhGAPIhTtPAR7NH5BuSHYgwhlfx6CPcWuw+O7qGRdMwR79qbUJjnzJtgbW6jkw2aiL1uow+uN1Ny3hOrPKMuqzxDsWWHLaaacCPactqi9FQbBbm3EINitoXULhmC3yxeC3R5fCHaionqiivvqXMhYYc+BrTmr0Pk6unUqo527mql+V1OoKosbipxxb/HM09SJqOQL57TTl5a9S6jDs7uoqLaFWnoUU1GN81kX570xx2Qn2L8yvCpUW5E49wQiC/YLr7mZ3nx7GalvNC2UsI7YdIpNp9h0ik2n8tQMH/YC8mFXRN6GTz+hRe86m06Pn+KahCuegg6njCcWPUKHDRxLffbaV5/aEefFu4iaOztlrndcYVY0UeOwEipZ2kgzm2fSxEFnUoujp+Yse5jOG3Ex3ffWHXTuARfRu5v/5ZZ3+N5j6eHVf6Zj+pxAPSv2zvj99c/mUqfSznRo55FETj33rPsDfbvvxVRRUk6NTS3u3+fvcxGVF6f2/SysXeD+O7rL2HRbX9r8AvUt6UtDi4emP1vXuJberHuTJnf6ZkafvD7nRE/veIqGdhhKA8v2d9rS4j6UiONfLf+iL5yfI4uO1DJ6v+V9Wu/8HFd0nCfxN1vedM+NKRrjOypPtzxNQ5yf/YucdgQczH9y8WTq4vyYHHc130VTi6dSufNjejza8iiNdn76FfUzzeKmq3V+Hm1+1K1PPtT+fdDyAS13fk4pOiWd7LWW16iT83No0aHuZ3v9916h6kbi3BOILNjZb/3M045u5f6CTafYdIpNp/qNt9h0mprIsOk0xeGe239Nl1z1Q+PZPXDzq7MA1+EfDfTMpqfogEMPogEDB2nrUTdM6zaiL1n8Fu34opbGjj8mo31em62zjhLz1GM0aMAwGrBfqq18yGL3rWXz3c8O65sSicXON5udOpZSrbMpsnh7Kv0/173h/nt4369TkSNuWzQrkZxWJzjdVctdrVcuF9c7IrFuu6dIVAdtbctaWuj8TC6abDyenDBbQcZ5hWB0y9ktzoQoXNyy2G0HC9SHmh+i44qPo72dH/l3VZipglL9Wyd6X2x5kfo4P8OKhqX77cXCj5GfULYt2Hn1WRwZDw4BI/lA7R9pkvNQ0qXYTLDfvW0GfbvrhdTB+fFeK8+s9NEv/kZjKsZQ3477Ukv5nnaqTSva7qyidy52ynVcYRxXqW2dttNjtX9zBXuL83zQ0jPlv/7MpidpSJXzYFR5gPv36p2raPmOZXRyz9PSRc7b6jzIlXSmEfwg5xw9LjTrXyjDR+JQBCILdl5JFy9LkmtGWEcIdgh2CHYxJyBKjPe8nEvBXvp2o1tR2YJGeqr8Gdr/6OHhBfvhJ6Qb+97iRfTFl7U07uCj3dVXqk+5DfzxVWcF11nJLXdWYfkQAlms4vZq2Dujw9u/3EaPbfkrXdDl26n0ztf08hG0ommyMmqShus0Tcdpg0SiLPI4vbp6zOIp6OBV88c/clbYe36d+lbpV1CLHJHGUWBou7Pq7PzwUbI8NdZCsDfvVUSPOcLOXWFfdAedPf5iWvLx226awwZ+nf765p/pqGHHU8/OvTJ+n7/iVepU0YUOHuRE9XKG849P3kYXnnY5dayooB11je7fZ594KZWXpcY6/fA0dFy6a68seo726b0vDfragenP1G8bxAmvz/n83199nAYNTD24FZU7wlNahPZ6eBTl6h44VfaBD7u7M+iih3mNo1dUK6/0+YoSU+R4S9XWbaVnZs+iqU1TM/zX1f6p0dW47eqcDR/2oCvZ/vnIgr3QV9gJPuzWrBQ+7NbQugXDh90uX5s+7Owq0OKIZ9enlX1Uy1uo9ENnVe2dlIgTR+PhTuQQR+TxwS4VrujeffBqnHsorgd2qehLd4WZsnKoE7ssbvlwpl2qKCtx/IAdH+DOrVccm1nc6jwOuugFNK9aNpd5rHd65GkLTnKdHZ52/JObnfHf6Yj4Tc3UdEgp7ToiN5FiECXG7ujmbdOp0w1+sOvwcrQNp0wDgt2uTZiUHlmws+vLjD89kX55Ele6ZNlqN6xjQUSKgWA3sbOs0kCwZ4XNOBMEuzGqrBLqBLsQ2ml3D7FqvdtH2a1ICOzdrh6uQN0trtWV6awaFpBJXjXOEM2OAHaFsDgkodxKICsit5UgjiiCsel0zzCUP+64Ba1rcsU6i/ZcHBDsuaDoXUY+BTu3onx2PTXvW0IN47K3Dwh2uzZhUnpkwc6V6MI66txkTBrU7tJAsFsbMgh2a2jdgiHYs+TrbBJMR2tQBLdwDWFf6Q6lRdTohFPjlfBcC215RZpFddGmJneDXnOPIiqucep0/HGbvpbyVxWr0s6uwYxVZ44o4T4MKK4HWVLJazYI9j24S99rotLXnFjsZ5dTs+SHHWVAINij0AvOm2/BHtyi4BQQ7MGMbKfIiWC33cg4l48oMYgSgygx7TNKDAvcoi84EkUL/fXFB+moocdTL+fHPZxVbuFCIjYkLtyWio4RFGFCF3FBzGFpod3B8Une7QJy+ye/oysPvSbloywLbGkVWohrZ2eb52bdIsfDpXhF6utvFuxPdn+GBg1pJ5tOnbc6y21V53zV91gn2E39k03TcRuC/KbVdpq+hVjNF/RWYr97oPCh5jR402nq7ddeh+nYJ8GH3Z3GnLeoC5uQmcCHPc6q0rttEOwRxw2CHYIdgj0mgv1AZ9Nej/1ScYo53N5uN5NNGz+nl9c9T9W9zk25lmh8tuWoGV5TgtisOLqrE6lECO7dbiJiUyC7hnxYu4pWbFxGZx77LfqipZF2FTt1+riA5HLTKbfdjc3tPAxAsOtH0lS0QbBX0jYnCo8aEUjHb+5Lz9I+ffrR4KHD09C9Hl78Hmr8hHLQwxM2nba2dwj2iAIvZtlzIth54+nmrZLDpdRJNT57zPofuTkQ7BDsEOwWBbsjvF1/b0d8v/KvZ6lvRT8a2vVAR3g7opxXyFmcOyL8sTrvOMUbaSO92PwinVV8Vsb17q52cwg0R9zO+tyJUd3XiVG9d2qF3XUj2e1CIvyv316eChs4cvQRvvNGW8dh53Bu5GwwfW6ZE3EDK+ytxgqCvRfJ4TfVaCAs0C+69Eqq6gjBLkKi+l3wcY0SgxX2yPIudgVEFuxnTL2eenTvQvffcm3sOpeXBsGH3Rpm+LBbQ+sW3FY+7LIrCq+Es783+36rIlx+aYoJCXez5O6Vbxbc6VVvRXy3dGJ3FJMSo6WxGSUmWsvaf274sNsdQ/iw2+ULH3a7fJNaemTB7hWHPanAWvULgt3aUEOwW0PrL9g5ul2z878S7xd0eLWMNzy6q97sjuKEmssQ4s5KeNjNlyzCRaQSd9XbiUziRiRhFxN+EQjHp86TAA87GhDsYYmZp4dgN2eVTUoI9myomeeBYDdnhZR7CECwR7UGCPaoBD3zQ7BbQ6sV7LxpsWSVE3HiXSfiiCO866aWp1eidavi7sZMXh3f7ZZiuiIuu6KIlXB3U2U7EOFhRgSCPQytcGkh2MPxCpsagj0ssXDpIdjD8ULqFIHIgp1dYo47chRNvyjcq5iTMgDwYYcPe7v3YX93Nb29+HWaVP5N93XW5IQjpMYWeqrsaRpaMYwG7voqzat7jTo5P4cWHUq1zo94BTpfx++3vE/rnZ/jio5zo5NsLK+hF7c+T1OGnUdCiM//9yvUsZvz5texh6cvfS9fYi+fUN3GNlGYX5SNmk2f09wXn6HJ1VM9px3Zp9crkanvc1v7sIv2qxv41M2t6mZC3aY9r41+al5RpxdHr81vXm1VxwBRYrzvmIgSk2KDTaetbQSbTpOiNHMk2DkG+29nzKbX5tyWLDKGvYFgh2CPu2Dv03M/JzZ3KmoK+4zzJk72Fy91/m12YoSv3foJLXR+JhdlPnTLr4v/R/Fr1Nl5ffkhe42kbRW1NOfjR+icIy92V8WXr3uPNmxZS/9xfCqcmk4gqxvbOB0Ee2qSyXWUGAh2/03Bpg9ezDEoMol6m0BYR0SJCZIO/LB7xRXTqamojOr4Tb0GR7ZhPyHYDeC2oySRV9jZh93vQJSYKurYsYpKSkqpuKSEKioraUvNJtq1q56GHXQobdlS48ZKHTV6HL3gxCJm8ffQgzPcf/lv/ry+vp5WLl9K3zh5EsmrjPIKmrq6oF7g6t+61QjdjWyXUze354JLrs4YZr8VM504E5mDbmjyeeESs2jx0nT/xcremtUraMP6VMxdud1idZNZ8aGu+Kkrg7owYrrVQ68J02ul0Y+B3zldm4NEAbuitBLkm1rosc8ecWKGj6Z+Df18r9G1LWvpzaKF9E1yBHuZs7re0ELNXy2hp3c+RYP3P5D6DxlMb/zzZarq5KyQjzisVWxf1ZYg2Fe69nr2WdW01QmL19DoPCz5HBDsREFxr7HC7m1AWGFPscEKe2sbgWBvR2rcoKmRBbtBHclO4viw7zrqHNr013uS3c826B182FPQvQS5qe+47DPe0tN5A+Zuf/GqrqXUWEW0k5qdjZzOZtEGJ8jKvCYqWe7EDj/Gec35kOxfY90G5hK7KuHDbm9I4MNujy2XDB92u3zhw26Xb1JLh2CPOrIQ7FEJeuYvJMGejq6ycY/LihtRhSOrsCuLz8GCvKWn8xp6/teJoiIEuRthxSeCii6sY9HmFip/ahfVn1RGLXs7kVhwZE0Agj1rdIEZIdgDEUVKAMEeCV9gZgj2QERIoCGQE8HOfuzX/+rejOJvvO5imnji+ORDh2C3NsZJEuzyKjmHO0xHWDEIdZheIXdDHJoL8qCBaas47EHtSsp5CHZ7IwnBbo8tlwzBbpcvBLtdvkktPbJgv+2+R2nGn56gWXfeQMOHDnQ5LVm2mqov/zlNO+/0xEePwaZTbDoVm07lVfI3/v0qdXZiFh5afGirVfLXWvZEXBETS0vP1Bs32WVl9r//TEeNOtF962ZzD/48c/oJ2gcgUgdtVBKCfdUHq2nRwvl06qTqjIpkv2LZ7171i4QPe+b4IErMydSjZ+qNseJAlBh/CRF0rfrlhg97ig582FtbCXzYkyXdIwv2IydOpzNPO7qVMGch//CTryQ+egwEe2EJ9r4V+6Ze/rM72sq979xBF/S4kCpqyjJmBlWUy24rr30x13ntdxc62NnA6b72vkfmC4qCQgxCsO+JRGHycIKwjoNcTAjrmLIWRInplbEZX90EzxvpL7r0SmeOqqRtzqZpdWO9jp8u5KrXPOU3f/ltPg6K2APBDsGeLHneujeRBbvXm06FmwyixCBKjGx2QWKzraPEsOvKzAdupXOOupQqtzkifPfLgR7b4ERcaXIirhRlRly5q/kumlo81XEfd14ytPutnPwyoNc3O6K8e1c6eMioVqvkuY4S4zVJBa3aYYV9D7mgh6QwQg8r7FhhV7+tChISQdcqVtiDQ2xCsEOwB11n7f18ZMEexxV2fpnTqjXr3LE5YEBfenzmjb7j5Jde55/PhaUfRODDbu0acH3Yy8uo5ouAXZchW6D6k7MrC8coL9rkvOEzaIOn5Lribu50NmbqVslDNqlNksOH3S52+LDb4wsfdntsuWT4sNvlCx92u3yTWnpkwR43H/YLr7mZajbXpkU6i/Ee3bvQ/bdcqx3DoPSBL4aCYLd2bVRsduKLz66nhnGl1HCIEwUlxBFZlMsbPNuxKPdDBsEewqCySArBngU0wywQ7IagskwGwZ4lOMNsEOyGoJAsg0Bkwc6lxSlKDK/4f3/alHSEmiDBHZQ+KD9BsFu7pMqXNlHxPxqo6ZBS2nVE65jgaVHu+JMXb+eXB5mtlMtRV9h/nF1Y+I2dIhyitQ7FrGAIdrsDAsFujy8Euz22WGG3y5ZLh2C3zziJNeREsMcFjIhOo4tYI38m2muSXvcwIvvlY9OpnU2np489kzr8s5GK1jbTyu4f0vKiZXTSwNPpvn+mNnmu3rqS1jeup+OKjqM3W950h3RM0Rj6oOUDWu78nFxxihubfNbnf6ZjBp9A3ffr7cYpv/+p2+isC6ZRh/JU6JUkvOnU6/oL8ouFD/secvBh10fZ8Nro5/WGXy+OiBLjf5cMulb9ciNKTIoOfNhbWwmixMRFneamHRDsTvhJU4HPyFUXGi/BXlZWRg0NDdS5c2eqqqqi0tJS97/KykrauHEj1dXV0eGHH+7+vnXrVpowYQLNnj2brr76arr11lvdf/lv/pzTvvPOOzRlyhR6/PHHqX///jRixAj3/CGHHEJDhgyhxYsX00cffURnnHGGaxkPPPCAm3fAgAHav9X0nGju3LluWs4nDq6b23PttZkuRdxmroPbqR7PP/88de3alcaOHdvq3Jo1a9x6LrjggvS5pq1N1LKthfjfNSvX0OurX6dJ9ZPS54UIP6XoFBKbPPmz9SXr6aT9TqI3tr9BxZ2K6T/G/Aet+HwFLf1kKU05e4qb/6677nKZ9O7tCHbnuPnmm902V1RUuH/LDEWFahodT7+0fM6Pgd85XZtViDqGrUBrbECXhj/zKk9mI7dZHXvVlj799FPXTi+7bM/DnK7POnvj9rC9sX1069Yto8my7at9Ue1dPq9rj5pftRMdK6/2qmmXL1+evl69mMuf8xzyk5/8xCSpm8a0Haptq/Wodq6bExYsWEDbtm2jE044IaN9umvEz3b95guv61Cu0KTPJmnC8OO0Xv0Pey0FDa6f/QblFdcLpxNzshifN99MLWbwnC7buPy7em2qY6v+reOsuza95hW/+Us3H4v+B42Fzn5VdqY24tcOtUyv+cpr3LyuHb9xztY+vK47tX+6OSvoPhVklzifewJZC3bhu66Lte53Lvdd2FOiyYq5XH/Y9JxX5BGr7FhhN1thFzHK16/6iBatXkCTev+nGx6xiF8iJB1rW9bSQudnctHk9KcszpdVLKcTDz6D7nv7Djr7xEtpde0q2vD5Wppw7EkZYdpEhI5vnJwS/OqKn7oyiBX2FkIc9tZ2opunTMMBIkoMosQgSgwRwjrq1Q7fg664Yjo1FZVR3a4mI0mU7TcwWGE3wttuEmUt2MNu5swXEZ1POr+F1Su8ZNj0rcJVOj7sO4++lrY8Yr5Cli8W+a5HfnFQyRccdcUR5PWtRbnaLjlGedqn3InW0uH1xnTSned2cP3MceSOAHzYc8dSVxJ82O3xhQ+7PbZcMjad2uULH3a7fJNaetaC3Sv+ugDVVnHYg6K+8IMGHyLUY1B6FvSvzbktPf6tHlQKSLDzJs+iLxwBLr04yBXl25tTn/kccoxy6uxs9OTwiByJpZPzn/ImT1FMxZdFVLa4iXZ90kD1UzwSJfXKzEO/INjtQoZgt8cXgt0eWwh2u2y5dAh2+4yTWEPiBDsPkl9cdVWwm6QXMd057ZiRQzNDRCZMsEcOh+i8ubOlZ1E64gqLcvVNnqYXkhuHvdKJw16b2zjspvUnPR0Eu90RhmC3xxeC3R5bCHa7bCHY7fNNag1ZC3bVlUQFFBgOMSFE26MPO7uurFixhNav/YSO63OCs0KeWjVfuOUNIscLhaOtiKPeeaPQzOaZdFlxyle9ZffKeG35dnrsg4fpnJMvbfXiIL83ecb9TafcR10EDC8fQq9oGX4M8KbTlHV5+YSLqBedu3TNmCV0rz8XCfx8PGs2fU5zX3yGJldP9Zx1ECUGUWJ0xuEVJcfLkILmN6982fooc3mIEpOiiigxra0LPuwJEZq7u5G1YP/RTXfT+ys+8nyLaJCPe1IwxlGw8yr5U3MeosP2H0f9WvoSOYL88Q8eoTFlY6jfl87fzvF+y/u03vnhsIjicMMjOuHOD+89zg2ByCvjOyvr6S+v30vnnzU9w4fcL0wbBLsTXWLey1TVqQsNH3FYK1OHYIdgl43intt/TZdc9UPjKdF086u6oVqtR33Y1AkehHV8i3Z8UUtjxx9jND4Q7MPTnLDpVG8y2HRqdCkhkYZA1oKdy+JVdj5kH2/x+eat2z03eiZpJNpEsPfqR0P6HEQvvDKHBncfSgeUH0DLP1pK679cS9/YlRLgj7Y8SqOdn35F/Vr9zavk7ze+T+uK1tFRw5xwbc5mTnZdeWvFfCLnhaIjRx+RHqJd9fX00IMz6IJLMsM3QrBSLwMpAAAWwklEQVSnEGGFvfXKlm5FW/eQghX2lA1BsOvfhyDfJ1Rb0bnEmD7ImKbj+rHC3tBqjtPx0337BcEOwZ4krReHvkQS7NwBXml/4gVH6ElHKz/vOPTUVhuED/t9/52zKCbpzZ1OhBXa2ExuxJXdbivEGzwDXLq1UVfa4Zs84cNuy2hT5cKH3S5f+LDb4wsfdntsuWREibHLF5tO7fJNaumRBXtSwRj3a7dg3zbjBuPNldpoK44gd9zFnVCITUaCnDo7q+KaDZ5+UVeM+xSThBDsdgcCgt0uXwh2e3wh2O2xhWC3y5ZLh2C3zziJNUCwRx3V3YK99tb/pqY+qTjhcqQVqt29Qr47JrnJCjmX4W7u3C3IW5wQ5BwGMeVXzp9HbXT7yA/BbnecINjt8oVgt8cXgt0eWwh2u2wh2O3zTWoNEOwRRzbDh52K3NJKnJ9S56fB+anin6Iq97OSlhKqLKqkmqIaqndU/UGdRtDm0hra3lBLo4aNo+cXzaGzzp5Gf5k1g846fxq98MxjNGr0OKp3/MhXLl9K/PZO2VdQ3lSmbhhTow6of+s2mOl8E+HDnjIQRInZs4lW3b+g2hJ82Fe61+vZZ1XT1h3OLNCY+TZfdcqBDzt82BElJnVV6N48La6XoP0EiBLTWswgSkxEgRez7BDsEQdEK9iLHMFe5Aj2Fkewd+hEleUdqaSslEpKS6i8c0fasnUT7dpVT8MOOpS2bHEEe+02V5izQGehzps8IdirSaywL1q8NP3AIjZ5rlm9gjasX0sTjj0pIzygeC08P9zwoYbrUzeJ6m4QCOvY+uYpbxqFYN+zKVs3fQgbhGDfQ8dvk3qQUOPz2HTqfaNCWMcUGwh2CPaIci722SHYIw5RK8HuLLKXlDir6aWl1NjQSB2rqqhjR2eFvaSUip3PKyoraUsNBPupk6q15OXIAhDsvQIZ+Zlv0KqdcIlZ9cFqWrRwPqljIj/MQLB7x41XxwCC/WTq0TPTdiHY/W80QdeqX24Idgh2L/vACntEgRez7BDsUQfE8WGvv/6/qeZ7P4paEvIrBODDbtck4MNuly982O3xhQ+7PbZcMqLE2OWLTad2+Sa1dAj2qCMLwR6VoGd+CHZraN2CIdjt8oVgt8cXgt0eWwh2u2y5dAh2+4yTWAMEe9RRhWCPShCC3RpB/4Ih2O2Ch2C3xxeC3R5bCHa7bCHY7fNNag0Q7BFHtk3edNqnHw0eOjxjRz2ixKTe0IpNp3sMOsgvFj7se1ipm5N104LpGzLhww4fdq89Ol63m6Br1e82BR/2FB1sOm1tJfBhjyjwYpYdgj3igECwX9aKoO419CKR1+uqdeex6RSbTmXj0r3+XJz3Ezy6MJOq0UKw6wWPVyg9XSQlZurFEZtO/W80EOwpPgjrqLeTbO0Dgj2iwItZdgj2iAMCwQ7BziE4O5Rnvs3K76HF75yf6DF96DERsZwGK+x7Ln4Idgh23a0gKPa3midoQcLrdpOtIOPysMKeoooV9tbWBcEeUeDFLDsEe9QBgQ97VIKe+bHp1Bpat2D4sNvlCx92e3zhw26PLZeMKDF2+WLTqV2+SS0dgj3qyEKwRyUIwW6NoH/BEOx2wUOw2+MLwW6PLQS7XbZcOgS7fcZJrAGCPeqoQrBHJQjBbo0gBHsboXWrhWC3Rx+C3R5bCHa7bCHY7fNNag0Q7BFHFj7s8GGHD/sS2rB+LU049iT3atJt8tT57XtFXRE+uZ27dM24OrHpNIXDNFqNuoHvntt/TZdc9cM0U3XjqM4HGJtO36IdX9TS2PHHGN0p4MM+PM3Ji4UfI2w61ZtZtnsc4MNudNm2m0QQ7BGHCoIdgh2CHYJdnkYQ1hFhHRHWkQiCXS8u+EH5iiumU1NRGdXtajJSIBDsRpgSnwiCPeIQQ7BDsEOwQ7BDsKcIIKzjx7Ro4XyCYIdg95IWEOwRRVcBZ4dgjzr48GGPStAzP6LEWEPrFoxNp3b5wofdHl/4sNtjyyUjSoxdvth0apdvUkuHYI86shDsUQlCsFsj6F8wBLtd8BDs9vhCsNtjC8Fuly2XDsFun3ESa4BgjzqqEOxRCUKwWyMIwd5GaN1qIdjt0Ydgt8cWgt0uWwh2+3yTWgMEe8SRhQ87fNjhww4fdnkawaZTbDqFDzt82L2kBXzYI4quAs4OwR5x8CHYIdgh2CHYIdhTBLDpFJtOxbWAKDF6cQHBHlF0FXB2CPaIgw/BDsEOwQ7BDsEOwc4EEIcdcdiDJAUEexAhnPciAMEe1Tbgwx6VoGd+RImxhtYtGJtO7fKFD7s9vvBht8eWS0aUGLt8senULt+klg7BHnVkIdijEoRgt0bQv2AIdrvgIdjt8YVgt8cWgt0uWy4dgt0+4yTWAMEedVQh2KMShGC3RhCCvY3QutVCsNujD8Fujy0Eu122EOz2+Sa1Bgj2iCMLH3b4sMOHHT7s8jSCKDGIEoMoMYgS4yUt4MMeUXQVcHYIdoPBP2Pq9bRqzTo35QED+tLjM29M54Jgh2CHYIdgh2BPEUCUGESJEdcCosToxQUEu4HoQhItAQj2AMO48JqbqWZzbVqks3jv0b0L3X/LtW5OCHYIdgh2CHYIdgh2JoAoMYgSE6Q1IdiDCOG8FwEI9gDbOHLidPr+tCk08cTxbso5z82j386YTa/NuS2VEz7s1q4uRImxhtYtGJtO7fKFD7s9vvBht8eWS0aUGLt8senULt+klg7B7jOyS5atpurLf06z7ryBhg8d6KZs9RkEu7VrA4LdGloIdrto3dIh2O1BhmC3xxaC3S5bLh2C3T7jJNYAwZ4DwU4//SnRT36SRPtAn0AABEAABEAABEAABNqYAAR7RMHu5cNeVlZGDQ0N1LlzZ6qqqqLS0lL3v8rKStq4cSPV1dXR4Ycf7v6+detWmjBhAs2ePZuuvvpquvXWW91/+W/+nNO+8847NGXKFHr88cepf//+NGLECPf8IYccQkOGDKHFixfTRx99RGeccYbbowceeMDNO2DAAO3fanpONHfuXDct5xMH183tufbalM++OLjNXAe3Uz2ef/556tq1K40dO7bVuTVr1rj1XHDBBVryuvPLly9P9//mm2926+TPRH/ldstpuYK77rrLZdK7d2+3PpG/oqLC/VtmKBqkptHx9EvL5/wY+J3TtVkFFcRQpFdtQAvc+dCrPJmN3GZ17FVb+vTTT107veyyPfsbdH3W2Ru3ke2N7aNbt24ZTZZtX+2LX1917VHzq3aiY+XVXjWtaoNe3MXnPIf8JMQDv2k7VNtW61HtXDcnLFiwgLZt20YnnHBCRjd014if7frNF17XoVyhSZ9N0nCZpuk4rVf/w15LQTZgeq3qyhHXi5ineH4U4/Pmm2+6WXhOl21c/l29NtWxVf/W8dNdm17zit/8pZuPRZ+DxkJnvyov07H3a4daptd85TXmXteOn41kax9e153aP92cFXSfCrJpnM89AQj2AKY6H/brf3UvvffqTDcnNp1i0yk2nWLTqTyNIKwjwjoirCPCOnpJC2w6zb2QLZQSIdgDRhpRYurpoQdn0AWXZK6kb6/dRk/PmUXV50OwQ7BDsEOwpwggrCPCOoprAWEd9eICgr1Q5HXu+wnBbsDULw47Z9/+ZQNt39loUBKShCGATadhaIVPiygx4ZmFyYFNp2FohUuLTafheIVNjSgxYYmFS49Np+F4IXWKAAR7DiwBgj0HEDVFQLDb4SpKhWC3yxeC3R5fCHZ7bLlkCHa7fCHY7fJNaukQ7DkYWQj2HECEYLcD0adUCHa7yCHY7fGFYLfHFoLdLlsuHYLdPuMk1gDBHnFUsekUPuzwYYcPuzyNYNMpNp1i0yk2nXpJC/iwRxRdBZwdgj3i4EOwQ7BDsEOwQ7CnCGDTKTadimsBm0714gKCPaLoKuDsEOwRBx+CHYIdgh2CHYIdgp0JeInUoNvMU4/NolGjx9E+ffcLStrq/KwH76JTJla7n4vIXSwKeV5a+s5b7ucjRx+R8TAlP1gtmPcyVXXqQsNHHOam5bwXXXolVXWspG07Gty/5Tnu7YWvp8sUjZn70rO0T59+NHjo8HT7INgh2EMbMzL4EoBgh4GAAAiAAAiAAAiAAAiAQIwJQLDHeHDQNBAAARAAARAAARAAARCAYIcNgAAIgAAIgAAIgAAIgECMCUCwx3hw0DQQAAEQAAEQAAEQAAEQgGCPYANBb0CNUHTBZA3D8MJrbqY3316Wwea9V2cWDKtsOhqGr1z+j266m554YT7NuvMGGj50YDZVF0SebPgeeNTUNJtp551O0y+aXBCswnYyLNsjJ06nzVu3p6vB3BCW+J70S5atpurLf47rP3uEbk5Tjri3RQRdINkh2LMcaL7AajbX0uMzb3RL4JtLj+5d6P5brs2yxMLLFpYh35Bfm3NbGhSLynkLl2R8VngUvXsclq8oac5z8+iPs56lVWvW4YbtY1Bh+Yqb943XXUwTTxwPU80hW55/hw3uT7/88aVuqerYALY5AfnBBw/s5tzUlGE44t6WPedCygnBnuVo8wX2/WlT0jdeFjm/nTEb4jEEz6gMTVcvQjQpUUmz5csrwHyjxgqbvzmE5cui8rgjR2FF3eAqC8s2bHqDJhR0EsytuRn+bDlmmy83rUYpcSUAwZ7FyOguJlxg4UDmguFt9z1KDz/5Ch6SNOiz5cui8tvVJ9H+/ftAsPuYdDZ8+UGoe7fOGW4bWMFsDTkbtsKFS7jB4OEo3Hyspsb9LBo/kTtbjri35YZ/0kqBYM9iRLO5oWRRTaKzRGUI9wJ/88iGL4uezzZtcd26sr3RJNpopc6F5auzV1VkFgq7oH6GZcvliTxy2fBhDyLtfR7Xf/bs5JzZcMS9LTfsk1gKBHsWo5rNDSWLahKdJQpDkRcb9sLdcP1uHqpLVzY3mkQbrNK5sPbrxZNX3eHTngk3LFvOLdy4xAZpXqGc8acnCKI9u6sS13923NRcYTni3pYb7kktBYI9y5HV+Uxe/6t7cYMIwTMbhiwsmTNcCYJBh+EruOpKxYORnnUYvkJUquIcgj06WyFyZHEeVigFX02FlQL8cjPeYTji3pYb5kkuBYI9y9ENGyEiy2oSnS2IIfuh8iEi8WBjbzhzCMtXLj3MjSZcq5KTOixfTr9y9dr0ngtEOfK2hbBs+cFnzMih6ShdYBvtOsP1H42fyO3FEfe23PAttFIg2COMeNg4wRGqSmxWP4bypKbzURVQ4FLgbR6mfNUScMM2u+TC8pXT8wZUOUypWY2FkyosWzm+PdhmbydqPHuwzI6lH0fc27JjWui5INgL3QLQfxAAARAAARAAARAAgVgTgGCP9fCgcSAAAiAAAiAAAiAAAoVOAIK90C0A/QcBEAABEAABEAABEIg1AQj2WA8PGgcCIAACIAACIAACIFDoBCDYC90C0H8QAAEQAAEQAAEQAIFYE4Bgj/XwoHEgAAIgAAIgAAIgAAKFTgCCvdAtAP0HARAAARAAARAAARCINQEI9lgPDxoHAiAAAiAAAiAAAiBQ6AQg2AvdAtB/EAABEAABEAABEACBWBOAYI/18KBxIAACIAACIAACIAAChU4Agr3QLQD9BwEQAAEQAAEQAAEQiDUBCPZYDw8aBwIgAAIgAAIgAAIgUOgEINgL3QLQfxAAARAAARAAARAAgVgTgGCP9fCgcSAAAiAAAiAAAiAAAoVOAIK90C0A/QcBEAABEAABEAABEIg1AQj2WA8PGgcCIAACIAACIAACIFDoBCDYC90C0H8QAAEQAAEQAAEQAIFYE4Bgj/XwoHEgAAIgAAIgAAIgAAKFTgCCvdAtAP0HARAAARAAARAAARCINQEI9lgPDxoHAiBgi8Bt9z1KM/70RKvip513Ok2/aDIdOXG6e+61Obe1SsPnunfrQo/PvNE9F1TWgUdN9e1G926d3XouvOZmevPtZdq0N153MU08cTydMfV6WrVmHYm/ReI5z82j6391Lx0woG+6XWpBJu0YP3o4PfHC/HTW048fR7/88aWh6jXph61xRbkgAAIgkEQCEOxJHFX0CQRAwJeAEJSz7ryBhg8dmE7LwvvF1xalBS8L3DEjh9L9t1ybTvOjm+6meQuXpIW8aVmqsFYFN5/nsmo213oKbk4jBLvaLvG5n2CXoQiBr2uH7lyYek36ARMFARAAARAwJwDBbs4KKUEABBJCgIW4WDn265IqXJcsW03Vl/88Y3XbtKxcCvYe3bu4K/HigUO0i0V8kOA3aYeXYDetF4I9IRcKugECIBAbAhDssRkKNAQEQCBfBNilZdDAfhkr5151s/hcuXqtu6LOq8wsWuUV9zBlcR1+K9smQpfbMGxwf/ps0xb6Ss+9XHcVXvXngz+zKdhN6zXpR77GGvWAAAiAQBIIQLAnYRTRBxAAgVAEhGgWmYQPuVchsu/3e6/OzEgWtqwgwW7iw87CeczIYa7POreH28er7b+75xHrgt2kXviwhzJHJAYBEACBQAIQ7IGIkAAEQCDJBIQ7ieijzlVGiGyxIdWLR5iyoviws2AXG0G5LWLVP8zKdjY+7Kb1hmlHkm0LfQMBEACBXBGAYM8VSZQDAiDQ7gmwawlHSFFX0XW+60Gd9Srr/2/vDlIThgIoinb/C+m0G+jiyi98CEGNX0X0ejotNXnnZfCwMR69w350S8u8JWYM9vl0mjn+V4byPYP96Lgr53Hk6PcECBAg8PVlsLsKCBD4KIExvr9/fv/fod7/zCG6f3rMucF+y2s9crCP8x/30M9HT64M5XsG+9FxV87joy4+YQkQIHCjgMF+I5w/I0DgPQW2t61s30nfPmll+6HSkfLSYB9PjRk/177Wowf7toWVoXzvYL903JXzeM+ryFkTIEDguQIG+3O9HY0AgRcROPUlQufuUT+6JWbltY4G+7UfOj31H4KVoXzuPOatPLOm7RcnzXvY9xXuj+tDpy9ykTsNAgQyAgZ7pkpBCBAgQIAAAQIEigIGe7FVmQgQIECAAAECBDICBnumSkEIECBAgAABAgSKAgZ7sVWZCBAgQIAAAQIEMgIGe6ZKQQgQIECAAAECBIoCBnuxVZkIECBAgAABAgQyAgZ7pkpBCBAgQIAAAQIEigIGe7FVmQgQIECAAAECBDICBnumSkEIECBAgAABAgSKAgZ7sVWZCBAgQIAAAQIEMgIGe6ZKQQgQIECAAAECBIoCBnuxVZkIECBAgAABAgQyAgZ7pkpBCBAgQIAAAQIEigIGe7FVmQgQIECAAAECBDICBnumSkEIECBAgAABAgSKAgZ7sVWZCBAgQIAAAQIEMgIGe6ZKQQgQIECAAAECBIoCBnuxVZkIECBAgAABAgQyAgZ7pkpBCBAgQIAAAQIEigIGe7FVmQgQIECAAAECBDICBnumSkEIECBAgAABAgSKAgZ7sVWZCBAgQIAAAQIEMgIGe6ZKQQgQIECAAAECBIoCBnuxVZkIECBAgAABAgQyAgZ7pkpBCBAgQIAAAQIEigIGe7FVmQgQIECAAAECBDICBnumSkEIECBAgAABAgSKAgZ7sVWZCBAgQIAAAQIEMgIGe6ZKQQgQIECAAAECBIoCBnuxVZkIECBAgAABAgQyAgZ7pkpBCBAgQIAAAQIEigIGe7FVmQgQIECAAAECBDICBnumSkEIECBAgAABAgSKAgZ7sVWZCBAgQIAAAQIEMgIGe6ZKQQgQIECAAAECBIoCBnuxVZkIECBAgAABAgQyAgZ7pkpBCBAgQIAAAQIEigIGe7FVmQgQIECAAAECBDICf7FX7HLWHQ+mAAAAAElFTkSuQmCC", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# The full reaction of E and ES*\n", "dynamics.plot_history(chemicals=['E', 'ES*'], colors=['violet', 'red'], show_intervals=True, \n", " title_prefix=f\"E and ES when [E] init = {E_init}\")" ] }, { "cell_type": "markdown", "id": "a63d5742-334a-40c5-823e-27bc37cfb27d", "metadata": {}, "source": [ "Notice how at every onset of instability in [E] or [ES*], the adaptive time steps shrink down" ] }, { "cell_type": "code", "execution_count": 23, "id": "954dccf3-30c0-4d82-a1c0-8b2860ad2d17", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEEES*P
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\n", "
" ], "text/plain": [ " SYSTEM TIME E ES* P\n", "1476 1.30085 0.080546 0.119454 16.544949" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(columns=['SYSTEM TIME', 'E', 'ES*', 'P'], tail=1) # Last point in the simulation" ] }, { "cell_type": "markdown", "id": "71263cd2-4baf-44a3-b133-d7dcc1e0af94", "metadata": {}, "source": [ "Interestingly, most of the inital [E] of 0.2 is now, at equilibrium, stored as [ES*]=0.119; the energy of the \"activation barrier\" from E + S to ES* might be unrealistically low (2000 Joules). Zooming in on the very earl part of the plot:" ] }, { "cell_type": "code", "execution_count": 24, "id": "ee6e7870-8dad-4ff4-997d-286db0d3a8d6", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "16.54494887428722" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_equil = dynamics.get_chem_conc(\"P\")\n", "P_equil" ] }, { "cell_type": "code", "execution_count": 25, "id": "b6e26868-1b81-49c9-af7c-836b881121c1", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "11.581464212001052" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_70_threshold = P_equil * 0.70\n", "P_70_threshold" ] }, { "cell_type": "code", "execution_count": 26, "id": "ac6a3e1e-3fa1-4bfd-8524-11116731c5cd", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.31446597160581014" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.reach_threshold(chem=\"P\", threshold=P_70_threshold)" ] }, { "cell_type": "code", "execution_count": null, "id": "e80645d6-eb5b-4c78-8b46-ae126d2cb2cf", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "b74e6177-a59f-4e10-ad5b-945e7f8e63d9", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "6d946522-d437-49af-9fe1-0ddc4f2fcbaa", "metadata": { "tags": [] }, "source": [ "# 3. Repeat last step with increasingly-larger initial [E]" ] }, { "cell_type": "code", "execution_count": 27, "id": "7f1bdff5-4816-4b34-af29-81013e431696", "metadata": {}, "outputs": [], "source": [ "E_init = 0.4" ] }, { "cell_type": "code", "execution_count": 28, "id": "9669e103-0a48-42d6-ace4-cc6ca19fd313", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "4 species:\n", " Species 0 (S). Conc: 20.0\n", " Species 1 (P). Conc: 0.0\n", " Species 2 (E). Conc: 0.4\n", " Species 3 (ES*). Conc: 0.0\n", "Set of chemicals involved in reactions: {'ES*', 'P', 'S', 'E'}\n" ] } ], "source": [ "dynamics = ReactionDynamics(chem_data=chem_data, preset=\"slower\") # A brand-new simulation, with the same chemicals and reactions as before \n", "\n", "dynamics.set_conc(conc={\"S\": 20., \"E\": E_init},\n", " snapshot=True) \n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 29, "id": "f5140de7-0838-442a-909f-695715fb0918", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* INFO: the tentative time step (2.5e-05) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.1 (set to 2.5e-06) [Step started at t=5e-05, and will rewind there]\n", "1211 total step(s) taken\n" ] } ], "source": [ "# Perform the reactions (The duration of the run was manually adjusted for optimal visibility)\n", "dynamics.single_compartment_react(duration=1.0,\n", " initial_step=0.00005, variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 30, "id": "d6c74db1-b3a2-41d2-8785-04e75ab69870", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reactions have reached equilibrium\n", "dynamics.is_in_equilibrium(verbose=False)" ] }, { "cell_type": "code", "execution_count": 31, "id": "9cb3906d-b25c-4b3e-b695-c24f43b26246", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_curves() WARNING: Excessive number of vertical lines (1212) - only showing 1 every 9 lines\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=S
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Changes in concentrations for 3 reactions (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.0008778353950430866, 1.0016101857441617 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.1111111111111112, 21.11111111111111 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(colors=['cyan', 'green', 'violet', 'red'], show_intervals=True, \n", " title_prefix=f\"[E] init = {E_init}\")" ] }, { "cell_type": "code", "execution_count": 32, "id": "0d428e60-9735-4008-b909-59884bac38b0", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.1480911200305407, 9.85341706705381)" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Locate the intersection of the curves for [S] and [P]:\n", "dynamics.curve_intersect(\"S\", \"P\", t_start=0, t_end=0.4)" ] }, { "cell_type": "markdown", "id": "022c06df-44ad-4b15-b329-143cb68c6c02", "metadata": {}, "source": [ "Notice how the timescale of [S] and [P] is becoming faster with a higher initial [E]" ] }, { "cell_type": "code", "execution_count": 33, "id": "54c21fc6-42ee-4dd2-9f50-b84a793adca5", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_curves() WARNING: Excessive number of vertical lines (1212) - only showing 1 every 9 lines\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=E
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Changes in concentrations for 3 reactions (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.0008778353950430866, 1.0016101857441617 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.022222222222222223, 0.4222222222222222 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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SYSTEM TIMEEES*P
12111.001610.1619310.23806916.466878
\n", "
" ], "text/plain": [ " SYSTEM TIME E ES* P\n", "1211 1.00161 0.161931 0.238069 16.466878" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(columns=['SYSTEM TIME', 'E', 'ES*', 'P'], tail=1) # Last point in the simulation" ] }, { "cell_type": "code", "execution_count": 36, "id": "e4fd52be-db88-4b57-94a3-217cce0386c0", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "16.466877520220297" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_equil = dynamics.get_chem_conc(\"P\")\n", "P_equil" ] }, { "cell_type": "markdown", "id": "b0d8f75f-55a3-4712-ba46-9eb97833138c", "metadata": {}, "source": [ "#### P_equil continues to decrease with increasing initial [E]" ] }, { "cell_type": "code", "execution_count": 37, "id": "717d906a-659d-4635-9914-3b7eebf2f4df", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "11.526814264154208" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_70_threshold = P_equil * 0.70\n", "P_70_threshold" ] }, { "cell_type": "code", "execution_count": 38, "id": "cc46e532-b71f-4697-97bc-e0cad1328a1e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.18680188203718445" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.reach_threshold(chem=\"P\", threshold=P_70_threshold)" ] }, { "cell_type": "markdown", "id": "887bf402-e6e3-461f-88dc-cf87bbdf40a8", "metadata": {}, "source": [ "#### The time at which the 70% threshold of the equilibrium value of P continues to decrease with increasing initial [E]" ] }, { "cell_type": "code", "execution_count": null, "id": "8a318f52-7710-43df-b9ac-86c8ab690d60", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "6201afdd-cbdf-47f0-9289-ea290386c660", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "802b910e-0fa0-463b-a220-873c5882a33f", "metadata": { "tags": [] }, "source": [ "# 4. Keep increasing the initial [E]" ] }, { "cell_type": "code", "execution_count": 39, "id": "31bbf923-046d-4da3-9c33-c8f57ef3814c", "metadata": {}, "outputs": [], "source": [ "E_init = 1.0" ] }, { "cell_type": "code", "execution_count": 40, "id": "631bd026-58da-4295-9f05-d132577cb0cc", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "4 species:\n", " Species 0 (S). Conc: 20.0\n", " Species 1 (P). Conc: 0.0\n", " Species 2 (E). Conc: 1.0\n", " Species 3 (ES*). Conc: 0.0\n", "Set of chemicals involved in reactions: {'ES*', 'P', 'S', 'E'}\n" ] } ], "source": [ "dynamics = ReactionDynamics(chem_data=chem_data, preset=\"slower\") # A brand-new simulation, with the same chemicals and reactions as before \n", "\n", "dynamics.set_conc(conc={\"S\": 20., \"E\": E_init}, snapshot=True) \n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 41, "id": "ba3e8cca-873f-40dc-97b5-38374fcc826c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* INFO: the tentative time step (2.5e-05) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.1 (set to 2.5e-06) [Step started at t=5e-05, and will rewind there]\n", "866 total step(s) taken\n" ] } ], "source": [ "# Perform the reactions (The duration of the run was manually adjusted for optimal visibility)\n", "dynamics.single_compartment_react(duration=0.4,\n", " initial_step=0.00005, variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 42, "id": "c2b19731-38b2-4d09-bca2-3b666c633eee", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reactions have reached equilibrium\n", "dynamics.is_in_equilibrium(verbose=False)" ] }, { "cell_type": "code", "execution_count": 43, "id": "522e8f39-c7b3-4edf-80f3-3cf25c440e1e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_curves() WARNING: Excessive number of vertical lines (867) - only showing 1 every 6 lines\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=S
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Changes in concentrations for 3 reactions (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.000350708368123709, 0.400158248029152 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.1111111111111112, 21.11111111111111 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(colors=['cyan', 'green', 'violet', 'red'], show_intervals=True, \n", " title_prefix=f\"[E] init = {E_init}\")" ] }, { "cell_type": "code", "execution_count": 44, "id": "93a7b3b5-ffff-4417-b768-bf9886e9ef7e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.06628340509848926, 9.635470546269993)" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Locate the intersection of the curves for [S] and [P]:\n", "dynamics.curve_intersect(\"S\", \"P\", t_start=0, t_end=0.4)" ] }, { "cell_type": "markdown", "id": "46e10d97-2c62-4e6d-9429-cc769a47e596", "metadata": {}, "source": [ "The timescale of [S] and [P] continues to become faster with a higher initial [E]" ] }, { "cell_type": "code", "execution_count": 45, "id": "fb00b2fc-2bc2-433f-b907-019e786f68a1", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_curves() WARNING: Excessive number of vertical lines (867) - only showing 1 every 6 lines\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=E
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Changes in concentrations for 3 reactions (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "domain": [ 0, 1 ], "range": [ 0, 0.002 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.05555555555555555, 1.0555555555555556 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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Changes in concentrations for 3 reactions (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.000350708368123709, 0.400158248029152 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.05555555555555555, 1.0555555555555556 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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", 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SYSTEM TIMEEES*P
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\n", "
" ], "text/plain": [ " SYSTEM TIME E ES* P\n", "866 0.400158 0.409128 0.590872 16.1715" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(columns=['SYSTEM TIME', 'E', 'ES*', 'P'], tail=1) # Last point in the simulation" ] }, { "cell_type": "code", "execution_count": 48, "id": "264292b6-4ba1-4c36-8ea7-29472756a879", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "16.171500029051185" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_equil = dynamics.get_chem_conc(\"P\")\n", "P_equil" ] }, { "cell_type": "markdown", "id": "97f3ff27-4e2f-4af9-b9f6-ad8e44d6e10a", "metadata": {}, "source": [ "#### P_equil continues to decrease with increasing initial [E]" ] }, { "cell_type": "code", "execution_count": 49, "id": "ceee7058-2661-4259-a2e6-0bd6732cc2ac", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "11.32005002033583" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_70_threshold = P_equil * 0.70\n", "P_70_threshold" ] }, { "cell_type": "code", "execution_count": 50, "id": "6b0b5166-ba0c-4b15-a632-84362fbdcd5c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.08364939325100468" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.reach_threshold(chem=\"P\", threshold=P_70_threshold)" ] }, { "cell_type": "markdown", "id": "c295cb25-41de-4405-83ee-0a5e5db0d304", "metadata": {}, "source": [ "#### The time at which we reach the 70% threshold of the equilibrium value of P continues to decrease with increasing initial [E]" ] }, { "cell_type": "code", "execution_count": null, "id": "cd775a94-b7c3-4c2b-9da2-4bfacd53fa26", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "bd7d5617-cf3c-4c03-bd77-9ccfcb12dc4c", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "2d43197e-eef6-4ea2-a489-ca6ed165b024", "metadata": { "tags": [] }, "source": [ "# 5. Keep increasing the initial [E]" ] }, { "cell_type": "code", "execution_count": 51, "id": "0b2f4582-ea90-41fe-b69a-c565738e4344", "metadata": {}, "outputs": [], "source": [ "E_init = 2.0 # 1/10 of the initial [S]" ] }, { "cell_type": "code", "execution_count": 52, "id": "fb3ca78d-c024-47b9-be04-5c74d7213727", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "4 species:\n", " Species 0 (S). Conc: 20.0\n", " Species 1 (P). Conc: 0.0\n", " Species 2 (E). Conc: 2.0\n", " Species 3 (ES*). Conc: 0.0\n", "Set of chemicals involved in reactions: {'ES*', 'P', 'S', 'E'}\n" ] } ], "source": [ "dynamics = ReactionDynamics(chem_data=chem_data, preset=\"slower\") # A brand-new simulation, with the same chemicals and reactions as before \n", "\n", "dynamics.set_conc(conc={\"S\": 20., \"E\": E_init}, snapshot=True) \n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 53, "id": "9336e30c-950b-4bc6-844a-68c3653b0244", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* INFO: the tentative time step (2.5e-05) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.1 (set to 2.5e-06) [Step started at t=5e-05, and will rewind there]\n", "818 total step(s) taken\n" ] } ], "source": [ "# Perform the reactions (The duration of the run was manually adjusted for optimal visibility)\n", "dynamics.single_compartment_react(duration=0.2,\n", " initial_step=0.00005, variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 54, "id": "76f54bfa-0189-4712-b676-667adb514a8c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reactions have reached equilibrium\n", "dynamics.is_in_equilibrium(verbose=False)" ] }, { "cell_type": "code", "execution_count": 55, "id": "502e0b54-b059-46d6-830d-b06199c1e666", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_curves() WARNING: Excessive number of vertical lines (819) - only showing 1 every 6 lines\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=S
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(colors=['cyan', 'green', 'violet', 'red'], show_intervals=True, \n", " title_prefix=f\"[E] init = {E_init}\")" ] }, { "cell_type": "code", "execution_count": 56, "id": "c5bb9972-79ba-43db-a0de-66d9495bcef4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.033892638379102225, 9.277504597225233)" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Locate the intersection of the curves for [S] and [P]:\n", "dynamics.curve_intersect(\"S\", \"P\", t_start=0, t_end=0.4)" ] }, { "cell_type": "markdown", "id": "ddf4a727-1fdc-4b61-953a-d582cda053ce", "metadata": {}, "source": [ "The timescale of [S] and [P] continues to become faster with a higher initial [E]" ] }, { "cell_type": "code", "execution_count": 57, "id": "cab73b69-81c6-48cf-be12-73ddd0e9a4d2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_curves() WARNING: Excessive number of vertical lines (819) - only showing 1 every 6 lines\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=E
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#The very early part of the reaction\n", "dynamics.plot_history(chemicals=['E', 'ES*'], colors=['violet', 'red'], show_intervals=True, \n", " title_prefix=f\"Detail when [E] init = {E_init}\", xrange=[0, 0.002])" ] }, { "cell_type": "code", "execution_count": 58, "id": "1614dba7-9e08-4e15-859c-474ef8e219f6", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_curves() WARNING: Excessive number of vertical lines (819) - only showing 1 every 6 lines\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=E
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367jM67rqJ8rPFUv1UgtQeWiPIOOofrOExNhW2E3tFtaPy3U7zbWqUSGbVqGasUBLC3bb19pJDpooxwue6OIODtPJzK+J0qxAFiHYo+aofdB2gVGhI7aLlssFIOjzLv3q1ZV6Cfawr+/UuM1VHlcxE3fCCvqTq2DXF0j1M8mNh2af5KvvsAtkVsFu+kCSTadx/cbdkIYJvmDojB6TzcdtN9dRx1MZ/SAoRlznZgtfMNuJOmaD70eVU20FF2PCrpvmyndUWFicDWw3Xvo8HncNMH0wyzXAXKGNi+V1Fey2Y8MU2mELTzoEUZ9rlK2WLl/R61tu17FEaZ4kPuV6/omzVZRgDwunNL8d0n3HhbfmoT10G9rvosbbKMGe5LqttZrrtQrBnvHOIGl1ffJ1FatJHFy3HbybDzq0a5u2O0BTqAbjK8O46ItFVMykLcZYizGXrzldVwFdytlWdRQH20UryDzuoNbszAttlJ/pi1bRgl2PJXgyDuvXVbDHMQh+vZpEsJui3eTmslknbD5J7O96wXQ9b9huJnU7cf1G7VvQdYMZqYI3YMG2XedoE3r6IlVGPyiTYI+6Sdb2c0lzG3YuCQs1iAqFi/NXbUdXwe77V0hMfdDvovoMi5N2CSvSNzhmiKBtY7HJyPymSZ0n1EslhjBFumpvypETe20gL6Ngt50vTEa6bFgWq+A3L2E6IM31Oso/TJ/Qfud6vYnz4SQhMcHrSNTiUlx/wfCwYNmoaxWC3fXKmVO5sNivuKZdxXWYmNXt1kOwh30V6IpM13W58LTiCrvLzV3Rgj1qJSqLYC9qZTXod/oYctnYXKYVdn1MuxwXthV21ZbtQSiuPuS6cuUq2MvqB0WHxCRZYc87c5HuWwt02wq7LexG+VeaVVt9rCa5BgSPb+37pjB0FclJVtjNlV0V0632GalwIvPapzb2Bs/XrmOJul4WscKeRLBH3dS4hJLqm03bzXmY/7mEe8XpHtfzlGojT8Ee/AbAVQepcrZrFYI9Cc2cyuoVr7gVP2WYuLSOQQdPEpOW5CYg6mANHvAuK9X6pK6Ek4pnM18uB3/YwZlkLlHmi+pbzUnHeLrGMCdZCY6LJVdjVYxcV1hdxZY+OYUJuLiVTtcYY9Vu1Nf0YWxc23XlquagVn2CTyaNCysw/aIRMexqbmHHRNQGqzA/ThPDHmwnj/0qZhxxlB8k2c8RtEe9/CAYtx9klcTHXYW57sN1zq6XI30tCZYPnluiBJLruTnKNsFrQ5S/u/Sj7HL8xyZJcP9X8DziKpJdY9g1O9WuzpAWDAMMez9OULrGihch2JOc612vfWF+FrR9kuu1iz+Eie3gTaDLgleegj3O5uYxmOZa5eozrueGspQrbQy7eeCr34POFFwtSOLgYTuO9c2BbSe7GkuY6A6GJqhyUXGEeuxhaSRVikO1wqfbM1dskgiTIlbY9XzMFZrghrywuen3TBu6CgrFMYxF8O48rIy2lUotpXfuJxHsSS9Sqj/dvnmTacY6mxevqLGEsQmbX5jPuXINs6U+gbqsVNs4hmVVMu3vGi5iniijbKzjG11CxWz96vNAsC01X5dMSGq8YbYPm7ttX0XYOa1sfmALWUvi41kFuxYlYWl0ld3VK+6JsWFhmGHHWNzChVo5Djt+lF/95Dtf9AV0WJtqbMHrUpZrQNh5OOxba1fBrs8NYSE1YfPVK8ZRaR/D6iQZS5iAKkKwmz5lnhP0/Mx56PfCypncwvbcBK+RSfSMvgbb/C7M/qZGaYRgd7luJ71WuS6KlkWEJxlH6QW7mkxU3Ld5YUzi4PrkGMwPqoRdWF7VoLCOcgjtfNoA6gCasPdufp7uoAAIiy9U9cKEjmlQl69c9ck1TUyci/MEN+sGxxQ2N1s8m+7XZkdzfFF2Cc7BHJ9NaAbHGYyLVXZ0FSl6HGqc+tkAQT8w46bzzsNufjsTJ/5MXq5PiItbiXexv004R/lh8BhT5VxuMHR7Lv2aN1jmOEzbBc9JysfUy9yvouuGjTnoZ2F+kORYCF5sXW/c1BjDxufqB/pcGkyJanJz9fE8BLvr9SLKv8Li4MOEjHkOtOVhD/qo5q2YmdegMD8Ou/a5XgPC/Dh4zkwqkoN8ovwkbJFGcQgTjdoWSccStGFRgl31E5y38gkV7hP0+7ByahEuGMMetl8mi57Rx6HpT2HnxuC5Wfncsd431GoujRDsaoxRcfhh6VVdrlUu5/io47/s7zeFYC87xLjxVTWWqpltwtghAIH8CCSJgc2v1+ZtCV7NaztGXm4CSaIQyj2T8NEh2HOymnIUM/TCXE1wTUWU01BoBgIQgEBdCYSFA9R1AE3UGYK9iYzFUJuKQNXPQwj2nNwx6msdl6+ZchoCzUAAAhBoCAHz/OeSFrQhgyxJpwj2khiCYVSKgA5Tq7LmQrBXymWZDAQgAAEIQAACEIBA1Qgg2KtmUeYDAQhAAAIQgAAEIFApAgj2SpmTyUAAAhCAAAQgAAEIVI0Agr1qFmU+EIAABCAAAQhAAAKVIoBgr5Q5mQwEIAABCEAAAhCAQNUIINirZlHmAwEIQAACEIAABCBQKQII9kqZk8lAAAIQgAAEIAABCFSNAIK9ahZlPhCAAAQgAAEIQAAClSKAYK+UOZkMBCAAAQhAAAIQgEDVCCDYq2ZR5gMBCEAAAhCAAAQgUCkCCPZKmZPJQAACEIAABCAAAQhUjQCCvWoWZT4QgAAEIAABCEAAApUigGCvlDmZDAQgAAEIQAACEIBA1Qgg2KtmUeYDAQhAAAIQgAAEIFApAgj2SpmTyUAAAhCAAAQgAAEIVI0Agr1qFmU+EIAABCAAAQhAAAKVIoBgr5Q5mQwEIAABCEAAAhCAQNUIINirZlHmAwEIQAACEIAABCBQKQII9kqZk8lAAAIQgAAEIAABCFSNAIK9ahZlPhCAAAQgAAEIQAAClSKAYK+UOZkMBCAAAQhAAAIQgEDVCCDYq2ZR5gMBCEAAAhCAAAQgUCkCCPZKmZPJQAACEIAABCAAAQhUjQCCvWoWZT4QgAAEIAABCEAAApUigGCvlDmZDAQgAAEIQAACEIBA1Qgg2HOw6Jp3NsqadZtyaIkmWoHAsK07ZFNXj6xdj8+0gr3zmGNH/3YZ7vnN66s25NEcbbQIgfcPGygr126UjZu6W2TGTDMrga0H9Zf+/dpklec35mv0dltlbZr6GQkg2DMCVNUR7DlAbKEmEOwtZOycpopgzwlkizWDYG8xg+cwXQR7DhALagLBngNYBHsOEFuoCQR7Cxk7p6ki2HMC2WLNINhbzOA5TBfBngPEgppAsGcE+61vfSuyhfb2dunp6ZH2fv2kn/e/p7tHBgwcKGvfXiNDhg6Tjo4B3v8O6Rgw0GujR6StXbo2bZKlr7woo3bcRUbsMErWrXtHlix+Wj4y6aPy+vJlsmb1Kjlg4iHy+9/OlM4zzpVb58yUjx9/isy96zb/p/pbvT/zhqvlhKmd8uSCh2XrwUPlQ+PGy403TJczz7lQFj72Z28Mq2XSYUfJ3D/eLqNG7yR7eJ+bvz/y0P3+vPafeKjfp25XvTd/3t1+m+MnHOiXmT1zhkw++njZbvsR/t9qbGqMag7qZbalYf38p/8k53zhyzV2K95Y7s/h1M5ptfeC/eoP/uu238rue+4jY8bu3ot9sE39oWahmJsvk0PQiME5mp8r+zz80APyiVM6Q20fNl+z4PJXF8sTCxfIUcdOjfQd0xZRhZ5etFCWvvqyTP7YcbFebBuPrhzFO6zxdzdsqPlTbOebP1yy+Bl55qknfB91fQX9yqVenN3i6rsyCmvDxVZxfQePl7CyNsEe5fsuzNLY39Zu2PFsqxP3eVJ/c+3Lhb1rW2a5JMdSmvZdeWQV7FmOi6TzijsfJ23LtXzUtcS1ftpyRfuHy7ii5o5gd6HXmDIIdgv3z170fXnwkUW9Sj1574za3wh2BHvQhWwXOQS728kOwb6FE4I92Q2im4f1XVxwrWcrV7QgQ7DbLOD2OYK978IXgt3NdxpRCsFuoX741AvkvjlX1kp99bvXyLyHFtbeQ7Aj2BHs9lMXK+zRjFxWeRHsCHbTgxDs9nOOSwkEO4LdxU/KUgbBntASCxctls7zvy0zr7pUxo8b69cmhj0hxBYvTgx7iztAiunbBHuKJqnSAgSyhsS0ACKmGCDACnt5XQLBntA2V143W2763T29Vt0R7AkhtnhxBHuLO0CK6SPYU0CjiiDYcYKkBBol2E+edolst+1Q+cUVFycdcsPLhy3kFjEoBHsCqtool33lbJk65TC/5srLVsqAqVtJ1wfaE7RE0VYmMHBAP+n2NiCTG7mVvSDZ3Nvb22SQ5zfvkLs/GbgWL/0+L6f2+ne7/PMNLwi4EFCLA+p8s8HzG/M15H0dLtUjy4TtB9x2+JDa4mcjBPucO+bJJZdfK6amSzNJBHsaagXW0QY57zMnyQVnnVrrySWGXWWI6devv5cxplsGDhwka9aslmHDhnvZYbwMMV6mmIFe5hiVTaatrc3LEtMlL730guy8864ycvRoeWftWnn2maflsMMny7JlS2X1qlUy6dDD5Dczfy1nf+7zctOsX8lJU/9a/nD77/2f6m/1/rXX/Kucdvqn5ZFH/iRDhwyVvcfvK9de/TP5/Bcvkkf+/JCs9sZwxJFHy51evZ123kX23mffXr//zwP3+XM8+JDD/T51u+q9e++5y29z/wMn+mV+df11csxxn5ARI3bw/1ZjU2NUc1Avsy0N7op//q5c9A9fq3Fcvvw1fw6fPvOs2nvBfvUHt8z5D9lr731lt9336GXxYJv6Q81i6LDeWWJMDkHXCc7R/FzZZ/798+STnZ8K9biw+ZoFX3j+WVmw4HE58eS/ivRY0y5RhZ58YoG8/NKLcqzHPu5lG4+uG8U7rO0NG9bX/MnlsFM+/JcnF/g+6voK+pVLvTi75cEorA0XW8X1HTxewsraBHuU77swS2N/W7thx7OtTtznSf3NtS8X9q5tmeWSHEtp2nflkVWwu5470swhWCfufJxH+2FtRF1LiuqviGMt7Vij5l6EYN/7iGliinM9ZiXid9h+G/ne1z4njRDsadkF6yHY8yKZQzv6LsyMW9fNugh20jpuSRGpuZHWkbSOtkOTLDFbCNlCYkjraPOm8M9dNvymaZksMcmpkdYxObMsNeqV1lGJ8mcWv9wrjDhs3Fqwq890Zr4okW9m7jN1mUoSctjE8X5ikDdXrvG7UYusO+84wl9J1y9dJ0xoB78J0Iu0cRkDEexZPDHHukqs/2D6rEhnQ7CTJabPSpGRwz7MFUnr6HaAItgR7JqAa1YUN8/aUgrBHk/MlqI2Ke+48gj2PGna26qXYFer6ycdc4i/ih73UoL92SWv+AJbRzEoAb772J1qce1KNK94c7XcPOMyvym1p3D6L28RnWpblVdCXQty/Xkw9EbVVW0EhXbw5kJ9/sOf/8bvX332pXM+WUs2osYb1Y6dfroSxLDHcNPGDCuiY57e+n9vSfshA2TtBGLY07lg69Vi02nr2TzrjG0r7Fnbp341CbDptJp2LXJWeW46Ddv3FzX2sJAYlUb7L0+/ECqudTtKpJ924pG+yNcr7PrmIGzl20zNbX6u2lMZAF3j2c0EJKywF+mRObaNYM8RZos0hWBvEUPnOE0Ee44wW6gpBHsLGTunqZZVsOvQ5LBp6lX5KMFuivAoof3cC6/6YTPmgzGDfekVfPN9VR7BnpPzFd0Mgr1owtVrH8FePZsWPSMEe9GEq9k+gr2adi1yVnkKdjXOJCExwbSO5gq7Fuw2Qa1i2IMr7HkIdjWPg/YfVwvPMcNxEOxFemSObRPDTgx70J1scZ/EsLsdgMSwb+FkE+xsOnXzqWApYtjjudnOZemoh9cihj1Pmva26hXDbtt0qkR5VJaYsJCYuJCVLCvsilhUSEzYzQKC3e5jpSuBYEewI9jth+WSxc/IM089IR8//hR74XnOmeMAACAASURBVM0lEOwIdk2ATae9DxtXHllX2BHszqerRAWLziLkMph6CXa9yh7M+KJFsN6QaothV+3oTC3mKrsS9Qftv5f/bJwsgl09uV6N4c2Vq2tJRvSmU7XZNCjm1Yq7ehES4+JtJSmDYEewI9jtByOCPZqRyyovK+wb5MYbpsuZ51xod7YEJVzYJ2iuVrRoQYZgT2OVvnWiRGs+rUe3UrR/uIy/noLdFNvm2MzVchfBHtWOmSUmbUiMEuzqpbPV6HHqMaobg1v+8EBt+CpuXmeoISTGxeNKUEbFsLft3V/emdy/BKNhCM1AgBj2ZrBSucZoE+zlGi2jKQuBrCvsZZkH46gfgbxj2Os38ur3RFrHjDZGsGcE2ILVEewtaPSMU0awZwTYotUR7C1q+AzTRrBngFdwVQR7RsAI9owAW7A6gr0FjZ5xygj2jABbtDqCvUUNn2HaCPYM8AquimDPCJgYdmLYgy5k26hFlhi3g45Np1s42QQ7WWLcfCpYihj2eG62c1k66uG1yBKTJ017W/WOYbePiBI2Agh2GyHL5wh2BDuC3X4Qsek0mpGLaESws+nU9CA2ndrPOS4l2HS6j4wZu3svVKywu3hOY8og2DNyR7Aj2BHs9oMIwY5gt3tJdAlXgZq0D5ebpaRtqvJFZwFx5ZE1JIYV9jTWt9cp2j/sIxBhhd2FUrnKINgz2oMY9owAW7A6MewtaPSMU7atsGdsnuoVJZBVsFcUC9OKIcAKe3ndA8Ge0TYI9owAW7A6gr0FjZ5xygj2jABbtDqCvUUNn2HaCPYM8AquimDPCBjBnhFgC1ZHsLeg0TNOGcGeEWCLVkewt6jhM0wbwZ4BXsFVEewZARPDTgx70IVscZ9kiXE76MgSs4WTTbCTJcbNp4KliGGP52Y7l6WjHl6LLDF50rS3RQy7nVHZSiDYM1oEwY5gR7DbDyI2nUYzchGNCHayxJgexKZT+znHpQRZYlozS8zCRYul8/xvh7rIeZ85SS4461QX96l7GQR7RuQIdgQ7gt1+ECHYEex2L4ku4SpQk/bhcrOUtE1VvugsIK48sobEsMKexvr2OkX7h30ErZ0lRgv2mVddKuPHjXXBVYoyCPaMZlAx7O0795e1J/bP2BLVW4UAMeytYun85mlbYc+vJ1qqEoGsgr1KLJiLG4FWiGFHsLv5QuVKIdgrZ9LCJ4RgLxxx5TpAsFfOpHWZEIK9Lpgr1UlRgr3rjS7pfru77qz6bd9P2ge39+oXwV53M5SjQwR7OezQTKNAsDeTtcoxVgR7OezQbKNAsDebxRo/3qIE+7o/rJP1D66v+wS3OmYrGXTQoFDBHjYYYtjrbqL6dUgMOzHsQW+zxX2SJcbt+CRLzBZONsFOlhg3nwqWIoY9npvtXJaOengtssTkSdPeVr2zxKy/f71sfG6jfWA5lxh06CDp+GAHK+w5c23K5hDsCHYEu/3QZdNpNCMX0YhgJ0uM6UFsOrWfc1xKkCWmtbPEsOnU5SipUBkEO4IdwW4/oBHsCHa7l0SXcBWoSftwuVlK2qYqX3QWEFceWUNiWGFPY317naL9wz4CssSotI4IdhdPqVAZYtgrZMw6TYUY9jqBrlA3thX2Ck2VqeRIIKtgz3EoNNUkBIqKYS/T9MnDXiZr1HEsCPY6wq5IVwj2ihiyjtNAsNcRdoW6QrBXyJh1mkorCPY6ocy9G/KwZ0SKYM8IsAWrI9hb0OgZp4xgzwiwRasj2FvU8BmmjWDPAK/gqgj2jIBjY9h7RHq8f/16vP9tbdLj/R/Q3k/e7u6SIYOHSMdAb/dyR4d0DBjojcIr3NYuXZs2ydJXXpRRO+4iI3YYJevWvSNLFj8tH5n0UXl9+TI/NvKAiYeIir3sPONcuXXOTPn48afI3Ltu83+qv9X7M2+4Wk6Y2ilPLnhYth48VD40brzceMN0OfOcC8XcjT/3j7fLqNE7yR7e5+bvZuxiMN5u/ry7/TbHTzjQpxfM5hGMCw2LgwxmtVjxxnJ/Dqd2TqtZJCrOL2qjUFSmDM1iyNBhvawdl5UgOEezorLPww89IJ84pTPUe2xxn2SJcTvoyBKzhZNNsJMlxs2ngqWIYY/nZjuXpaMeXossMXnStLdV7ywx9hFRwkYAwW4jZPk8VrB3dUlPe7v0937284S4EuwDN2yQ1UOHyvC33pIB3vsd3ucDPOHePWgrkUGDZNPWW8srK99EsHvcEezv3UhFvZ5etFCWvvqyTP7YcbFe6nrRTbIRynXTmx4Ym06jTeQiGhHsZIkxPcj1+Mu6wu567sh4GfWrI9jzoOjeBoLdnVVZSiLYM1oiVrB7bXvr5v7qej+12t7TLQM3bpI1Azpk+KpVMmD9ehmwcaMM8n4qMe8ZQzb17y9LxoyRXV9+WUavXStrRo2WZ4YMkUO8Fe2l3s/VXpn9D/koK+x79k1HxQp7uDO7XnQR7CL7Tzw08RnB/GYqcWWvAoLdTs1VoNpb6l3ChX3SNlX5JMdSmvZdeSDY4+mS1rE10zqmOebKUKcugv3wqRfImyvXhM73yXtnlIFD6jGoGHYZ1ibrPjVQ2j0RPmL/Pf2fK26+QzYc+tHYdvu9+IK0eyEuHQsfl34vvej/f+93732vjahX97Bh0rXzrrJx/H6yce/x0rWL9/s++0rPsOGiPuNVbgLEsJfbPmUcnW2FvYxjZkyNJ5BVsDd+Boyg3gSIYa83cff+ChfsJ0+7RLbbdqj84oqL3UfVRCVNwT7w/v+W7U6e4gt1JdizvJRgV8JdCfiOJxdKm/e3i5jX4l393LTTLjUxr/7mVQ4CCPZy2KGZRoFgbyZrlWesCPby2KJZRoJgL6+lChfsex8xTS77ytkydcph5aWQYWSmYB/29S/L1tN/Kmu+fIn/v6iXWpnveGKBtwq/0hfz+m/1M+oVXJXv8Vbi1Y0FQr4oK0W3i2CvP/Nm7xHB3uwWbMz4EeyN4d7MvSLYy2u9lhXsOnG+7UlXc+6YJ5dcfm0fC+pQntI96fQ/fiXTRu4i1z//lHQ+t0Qe69oow195WT48f778+O/+Ti6+/HKZP2mSrBo+XI694w65eepU2XnNGtlr4Pvk1vH7yKj3j5DdDzxYHnrrDekZONCP6SVLTG/zkyVGxDWGVpNj02n0RcAljtom2MkSk+4i68I+TcvEsCenxqbT5Myy1GDTaRZ6jalbuGBXITFHH36AXHDWqY2ZYUivZky9i2D/wfRZct+cK0PHXzrBHpHWcdyOu8q//+ev5Lxh28uC55+VNevWypRbb5Xf7/9h2XXJEpnw2GO+eNe/zz3iCC8efrgcvLFL3vzAB2TWiO3kjAkHebHy+8kDC99LFUlaR9I6qjShLi8EO4LdxU+iyiS9QXTtC8EeT8p1w7or77hyCPY8KLq3gWB3ZxVX8srrZvsf10PjFi7Y1Qp1nODNB1nyVpKssFdBsMflYd9x4Fay70svyV2vvSK7vP6GfPj+eXL/TqOlzcteM/nee2Wltxp//bRpcuGPfuSDvuPkk2Xw+wbLh4dt48fJ/7q9WyYfPFm28TbBqhd52O/3OURlHCEPu9vxSh72LZxYYSeto3nUuN7AZA2JQbC7nauSlir6GxiX8bSyYNf6L4zTeZ85qSa+VUi3+dptzI5y84zL/LfUYvSzS14RVV69pv/yFjE/d7FB0jKFC/bghIMDbFSWmCSCPRgSY45Zx7D3bPMH2faM02X98SfKmzfMSmqHUpY3Y+NVrLxt02tU9hri5Hublxj2Urp7qQdlE+ylHjyDaxiBrIK9YQOn44YRaIUYdhf9pyIxDps4Xr73tc/VbKFEuhbs+k2tceuhZQsX7A3zOkvHLgYLa+KzF31fVry5umY0Jdjbh7fLsK5/E/nSl0S8OHH54Q/LOu18xuWF0IgXQiPq5+OPb/l95crw9r0VevFyy8uECSL7eavw6qf6r97nBQEIQAACEIAABOpEwKb/bJ+rYVZyhb1O/BN342KQsEZ1PX03pVfYByz6Rz9DzKrv/JOsPe8LicdThQppVuRVTPym8fv6oTXqp/q76rnkWWGvgrfXdw6ssNeXd1V6Y4W9Kpas3zwKW2F/6imRZcvqNxHd0557iowc2atfF/2nVti3HT60z4p6cAKVimFXkwvLtNLoVI8uBgvzLD2X0maJidh0GhfDPmr0TrLHuPFiPrHRjF3MmiXm0f+6Tfotf00OXrPWT0OpQmu++9enyje++c0a4mXeAaU2vZ47fXotd7y/2XWH98unP/px/0FRWshHxd7xpNPwc6FrHGqSuErXGFo9IjadRl+nXDY+2gQ7WWLS6QAX9mlaTnIspWnf9fjLKthdzx1p5hCsw6bTPCi6t1H3GHYVgbB5H5z7KHMoqSIeVOSD8Uobw27Gt+cwssRNFB4So+4+VDC+mY1Fw2rk5KMEu/qaQ710nJK6yzIzxAQfBNUsWWIaKdjDTvpKYJx30ul+Pnm1Mv/Ws/8rd3h3s5/7t1/UnvIa3OyqHwo1e7/x8qHtd5BdDjiol5BHsCPY58+7u1cGI9czYhZhYt7ouvZnlnMRjQh2Np2aPoNgT3Ok9a0TJVrzaT26laJv6FzGX3fB7qWUljvvdBlavmUu9h7aOWVKqGC3ZQk0K2kt28jF5sIFuxK8p514ZJ+UN2ryN/3unsh0iflarHdrZlpH9cm2w4fUxhEU7DpOSbdw0P7jej21FcEuEszmkTVLjA6tWfvCEvnP9Wvk8zff4j/1VT39Vb1mdXbKfl4M/Z7qKzbvpYX89yceIBduN0o2etlqNu6zb83oM2+4Wk6Y2ilDhg7rfdA+9mdZ+/ZqmXTYUX3cLU74kYedPOymwyDY+56tV7yxXObedZuc2jktl1O5q0BN2pnLzVLSNlX5ogWZKw9W2OOth2DfR8aM3b0XpMJCYtIcSAXVSRthEaVnCxpmn2YLF+xRTzoNhpbUa8J59+PHsHuvYT/4gC8oX3tkEU8PzRvy5vaCMfID7/9vf3U+6qWEvP8015138f+X5cmuxLAX5CAVbta2wl7hqTO1DASyCvYMXVO1SQkg2N8L4/63mbf3il8vg2YtXLCXcYU9z+NIC/ZtLt3Wb/bVN97Js3naciCgRLsv3l960Q+x0WE2NiG/ce/xtdX5eqaeRLA7GJUivQgg2HGINAQQ7GmotXadVhLsYZbWodrB6ApVth6pG+O8r3DBXtYY9rwOST+t41svyrAfTvA3RS57bmleTdNOBgLq2w4VRqM2uKqNrubqfFiz9cwhj2DPYNgWrYpgb1HDZ5w2gj0jwBas3gqCvVnNWrhgV2DKmCUmL4MRw55/DLu2TVQcaJYsMaaQX/D8s7Jm3VqZcuutfUJr7vQ2qQzz8spPXOSFOHkZavy4+M0r8i94GW3+9MJz8olTOkPdyLaBkSeduh19POl0CyebYCdLjJtPBUsRwx7PzXYuS0c9vBZZYvKkaW+r7ptO7UOihIVAXQR7la2AYG8uwW76onmBCK7I39vWLdsseV4Ouf32Pu67xHsI1NwjjpBP331Prxh5JeqVuP/z/z7h19l/4qGhro9gdzsjINgR7JqA6yZLN8/aUgrBjmDffc++Gy+T+lHS8kVvSnYZD4LdhVK5yiDYM9oDwV4NwR50A50lZr8P7N4ntOZVLwPGfXuNkzNnzAj1nntOnirdI3aQSf06/FV5LeR1HnkEu9tBh2BHsCPYw48V1xuYrCExrLC7nauSlkKwJyVGeUWgMMGussOo4H2Vgz3u1egg/qxusOrKVdL/nl/J1r/9grzzN5+RlVdenbVJ6jcBgaQx8mpKOk6+7cMTZJOXdvKdUTv76SfrueG1CdAyxBACtpAYoEEgjEBWwQ7V1iNADHt5bV6YYC/vlPMdGYI9X55VaC2YflJtfDXzyIfNUeeS939ujpXf5IXXIOar4BHZ54Bgz86wFVtAsLei1bPNGcGejV+RtQsX7FF52Bv54KQ8gSrB3nH7z+R9t39N1p73BVn1nX/Ks3naqhABLeQHv/ay9Cx5QXqef96agtLMXtPjZSHSITbd3kOgEPMVcg7LVBDsrWPrPGeKYM+TZmu0hWAvr50bJtjLkIQ+D7MQw17tGPbxEw7s4yZ5P+lUhde0rVrp55Jv835XaSjvHNRfxnhPcv3w//xPpJs+evDBsmTPPeXY9ZtEi/nuYcP7hNm4xqEmiat0jaHVg1+y+Bl55qkn5OPHn+J82BHDvgWVTbCTJcbZrXoVZNNpPDfXc0c6+r1rkSUmD4rubbDp1J1VWUo2TLB/9bvXyLyHFsp9c64sC4tU40CwI9iDjmO7yCXZdLrn6F1qm17Vg6H8h0NtDrFZ8IEPyAtexpqT58wJ9V0dZjPvg2Ol6/0j5KBttu+zAdasiGCPzuwTd3KY+8fbZdTonWSPceNTnUNcRCOCfYPceMN0OfOcC1Mxjqrkwj5Nh0mOpTTtu94wZ11ht53L0ow9qg6CPU+a9rYQ7HZGZStRiGAPy7seNvHLvnK2TJ1yWNmYJBoPgh3BXqRgjxOBzzzykCzzVq6P3dhdW5lXYr59tffQKO/pr/qlUlCq1+R77629p0JteozV+E077SKrhgyW/1i3Rj51zEnWcBtXwaA7ZIU9+rTiIhoR7Ah204Ncjz8Ee/zlPEq0JhIBKQoXfUPnMiQEuwulcpUpRLCbU4yKYS8XhvSjUTHsg35xvgx87EY/Q4zKFMMLAnEE6vGkUx1m0/HEAl+893/5xfdEvcMGWD12tUKvN7527byLl2N+Fy/TzXshN0rs6zSVWLt4AjbBXvwI6KEZCWQV7M04Z8acjQAx7Nn4FVm7cMFe5ODL0DaCvQxWaK4x1EOw24jotJRKzGtBr3+3ZbTRbZur9ErIm6JeiX02xtqs4P45gt2dFSW3EECw4w1JCSDYkxKrX3kEe0bWb//ybRl46RTpWHK/rLj5Dv/Jl7wg0OgV9qwWMFfo270NsTp+Xv2uVu3VJllVxuVlinct7JWYVxtl9So+K/bxJBHsLp5GmSABBDs+kZQAgj0psfqVL1ywL1y0WDrP/3bkjJr9wUnEsBPDHnRu20atJJtO42LYn160UJa++rJM/thxsWcM23h05SRxlX4M7fVXyWennOIL+KCoV6v1Ziz9U142m8cnTJDTZ86MHKtesdcr8/+233g5pqddth88tCbuleCPW7nXT6gNy+4TB8mVUVgbbDrtS2WF9zTguXfdJqd2TsvlauYas520M5f9A0nbVOWTHEtp2nflkVWwZzkuks6LTadJiWUrTwx7Nn6NqF24YD986gVy2MTxctD+e8kPps+qZYU5edolcvThB8gFZ53aiHnn1ieCHcHesoLdMWuHEu8vLH5a/vf5Z+XEQYN7rdZrYR+2Yn/1eef5GXBGLlsWeryaAt9fuffCcO4Zsb0M3nqwTHjfEF/kq/fVTxWLr15RueuzCBMEO4I9SADBnvwSi2BPzixLDQR7FnqNqVu4YNebTj+462j5P1/9YU2wq0wypoBvzPSz94pgR7Aj2O3HkUuWGB2Go1fmZ774rBz79joZuXKlv2HWF/cqFCeQBcfs/c4pU2SYV37S/PmRg9JCXxVQQl4JepX6smfgQJnU3uGv4Kv3TIGvBX9Y6A6CHcGOYLefA2wlEOw2Qvl+jmDPl2c9WqubYFfpG5V41yEwVXlwkophf98X95L2lS/Ja48ssqbDq4dR6aPcBMqw6bTchNxGZwp8PyTHE/RK2CtBr/77v29+X/2tXma6S7dewkuZol8JfL2Sr36ql7+6773vi34vu45+6RV+HdoTfD9qTMSwZ7FW69bNGhLTuuRad+bEsJfX9oULdhX6stceu8r3vvY5MX+vyoOTEOzlde6yjgzB3ljLaKGvRtH/pc0i3xP2QbFvCnxVTr2SbLZNO0szbEffDLS3eTcb220j6983tNaseVOg3jS/GYi6EdDfFJhjiwoTSjt+6pWHAIK9PLZolpEg2MtrqcIFe3DqapVdv2ZedamMHze2vHQcRqYE++Azhvgllz23lNzUDsxavQiCvfk9wBT9/oq+Fvzez/eE/Xur/L7o955Oq196hV+H9rxX1j3jTr3IRYn4MMGv9wqEjS14UxEsE3aT0afM5n0ItrmHjc1Wp+o3Kwh2mwfweZAAgr28PlF3wV5eFOlGRgw7MexBz7FtYKxMlhjHTaeKj0sMe5Dj7JkzZPLRx8t2249wPjirkCXGDNvRNwP9+rXLkPVvy5qlr9dYmDcFV7yvQ/7vsjf8GwX90jcRJjz9TYH5nu5v5fDhcv20aXLhj37kzDuq4LKRI+XmqVPl3OnTM7elGlg/aJD8+O/+Ti6+/PJc2tONqPmqJwCPWbIkcbtxYn/l4MHyq+OPky/c9JtE7epvVGyV1vfvL9MPP0T+7p7/ji06oH+bbOrqke4eW4tbPjfn9cD22/ofHPLGm+4NpCz5522GyZqODjly+RspW0hebc6OI2XvVWtk97fXJq9sqRF3s7q6rU1uGtRPzl63Kfd+XRu8ZWB/2WtTl+zm+Yf5UuF37d5Xehve7er1/pDvf8e1acoVRKBwwV71J50i2BHswWMTwd73bIVgjz6Du6QWtMWw//yn/yTnfOHLmS4TZmaTqFj/MMGv9wqYnb++aaP819pV8inpqH3TEDY4vdcgbuDqxmPD2rVWgRo2NhuQXx11ZGrBHtd2njc/Yf0UdQMT7GvuEUf4b6mbmqJf8ydNklXeTeOxd9xRdFe19md1dsp+jz0mez71VN36VB0V7R8uk0k8954Ed30uA6BMYgII9sTIeldAsCPYEez2gwjB3lyC3W7R+BKtkIc9bgPzmnfWyi0P3COfOvoTiVDqb1RslTZ0bZIbnnxMztn3wNiiw7YeIG+v3yRdXd22Jmufm/N6cN3b/vsHbTXYuX7ago+uWytrerrko8Y+jbRtudb7/Zq3ZNzAreSDAwa5VnEuZ34DFqzECrszRgoaBAoX7FXJtx7lNetuWCRbnbmXnx1GZYnhBQEbAWLYbYT4PEjAtsIOMQiEESCGHb9ISoAY9qTE6le+cMGunnRq5l+v39Tq0xOCvT6cq9QLgr1K1qzPXBDs9eFctV4Q7FWzaPHzQbAXzzhtD4ULdjMrTNggdV72tBNodD0Ee6Mt0Hz9I9ibz2aNHjGCvdEWaM7+EezNabdGjhrB3kj68X0XLtjLO/V8RkYMOzHsQU9i02nfY4sY9ujzTRk3nWY9O7ZCDHscI3MDb1aWYfXf3bBBbnTI0pRVsNvOZXnOjSed5knT3hZPOrUzKluJwgV7VJaYK6+bLTf97h65b86VZWOSaDwIdgQ7gt1+yCDYEex2L4ku4SpQk/bhcrOUtE1VHsGenBqCPTmzLDUQ7FnoNaZuwwT7nDvmySWXXyvNHhKDYEewI9jtJy8EO4Ld7iUIdldGrjcwrLDHE40Sra52SFuu6Bs6l3Eh2F0olatMwwT7V797jcx7aGHTr7Bvuv4u6T/t47Lh0I/Kipvrlz+2XG7EaJIQIIY9CS3KKgLEsOMHaQhkFexp+qROcxMghr289itEsOvVc9u0L/vK2TJ1ymG2YqX4XGW76Tz/2zLzqktl/LixtTEh2EthnqYaBIK9qcxVisEi2EthhqYbBIK96UzW8AEj2BtugsgBFCLYzd6q8KTTw6deIG+uXONPKyjYu67+T+l33l/L+uNPlDdvmFVeSzOy0hBAsJfGFE0zEAR705iqVANFsJfKHE0xGAR7ec1UuGAv79STjSxqhZ0YdmLYg55ky6yw/NXF8sTCBXLUsVMjnXDuH2+XUaN3kj3GjY8s8/SihbL01Zdl8seOi3Vm23h05SRxla4xtLptYtijTeSy8dEm2H/+03+Sc77w5WQntUDpJPa3dUSWmFVy65yZ0nnGuTZUqT53Pf6yCnbXc0eqSQQqsek0D4rubRDD7s6qLCUR7I6WQLBvufjMn3e3bD14qIyf8N5jsWfPnCGTjz5ettt+hP93UICEnfSDAiPsAh8lIKJONFGiZeYNV8sJUztlyNBhvawdd4EIztGsuPSVF+Xhhx6QT5zSGeo9toscgt3toAv6lUutOLvF1bfZLK6uy81VXH0Eu92yrgLV3lLvEi7sk7apyud58xPWvysPBHu89dh0uo+MGbt7L0issKc54utTpy6C3QwpCU6rWbLEZBHs/fr1k379+ktPT7cMHDhI1qxZLcOGDZeOAR3S0THAe2+g91mPtLW1SdemLnnppRdk5513lZGjR8s7a9fKs888LYcdPlmWLVsqq1etkkmHHia/mflrOftzn5ebZv1KTpr61/KH23/v/1R/q/evveZf5bTTPy2PPPInGTpkqOw9fl+59uqfyee/eJE88ueHZLU3hiOOPFru9OrttPMusvc++/b6/X8euM831cGHHO73qdtV7917z11+m/sfONEv86vrr5NjjvuEjBixg/+3Gpsao5qDepltaftf8c/flYv+4Ws1d1i+/DV/Dp8+86zae8F+9Qe3zPkP2WvvfWW33ffo5U7BNvWHmsXQYb0Fu8kh6JfBOZqfK/vMv3+efLLzU6FHadh8zYIvPP+sLFjwuJx48l9FHuWmXaIKPfnEAnn5pRflWI993Ms2Hl03indY2xs2rK/5k8upSvnwX55c4Puo6yvoVy714uyWB6OwNlxsFdd38HgJK9ve3iaDBvSTd9ZvCm0qyvddmKWxv63dsOPZVifu86T+5tqXC3vXtsxySY6lNO278njfoP6y/t0u6e7uSdNN6Lk7VUMOleLOxw7VUxWJupakaixBpaL9w2UoUXNX3+ap880Gz2/M15D3dbg0S5kCCRQu2E+edolst+1Q+cUVFxc4jeKbjhLsMmOGyN/+rWz89Bmy/uprix8IPTQ9gYGe8FIX0I2bupt+LkygPgRsgr0+o6CXZiOQVbA323wZb3YCCPbsDItqoXDBXoVNpwq+TbC/8zefkZVXXl2Urbdm7wAAIABJREFUnWi3QgTYdFohY9ZpKrYY9joNg26ajEDWkJgmmy7DzYEAITE5QCyoCQS7I9hIwf6tb4l885vy9vlfk9X/7+uOrVGslQkg2FvZ+unmjmBPx63VayHYW90Dks8fwZ6cWb1qFC7YVUjM0YcfIBecdWq95pR7P8EY/G2HD6k98IksMWw6DTqcbQMjm07dDlE2nW7hZBPsZIlx86lgKTadxnOzncvSUQ+vRZaYPGna2yJLjJ1R2UoULtjVQ5R+MH1W0z/RNMpwCHYEO4LdflojrWM0IxfRiGDfIDfeMF3OPOdCu7MlKOHCPkFztaJkiUlODcGenFmWGgj2LPQaU7dwwa5i2ONezZIlBsFOWkftA6R1FHFNK6eZIdgR7FkucUn9zbUvBDsr7Lvv2Te1oav/pC1X9A2dy7gQ7C6UylWmcMFerukWMJrNMexrP/01WfUjYtgLIFy5Jolhr5xJC5+QbYW98AHQQVMSIIa9Kc3W0EETw95Q/LGdI9iz2gbBnpVgy9VHsLecyTNPGMGeGWFLNoBgb0mzZ5o0gj0TvkIr10Wwq42nzy55xZ/IZV85W6ZOOUxUqMxB+49r+vzsKge7ysW+9syfyaofTCvUWDReDQII9mrYsZ6zQLDXk3Z1+kKwV8eW9ZoJgr1epJP3U7hgNx+cpLKt/P15p/uC/crrZstNv7un6TejsumUTafBw86WWYEsMW4nKrLEbOFkE+xkiXHzqWApYtjjudnOZemoh9di02meNO1tEcNuZ1S2EoULdrWSPvOqS2X8uLFiCnaVPeaSy68VNp12SMeAgZ5feI+ObmuXrk2bRG1qHLXjLjJih1Gybt07smTx0/KRSR+V15cvE7VZ5YCJh4i60HSeca7cOmemfPz4U2TuXbf5P9Xf6v2ZN1wtJ0ztlCcXPCxbDx4qHxo3vpZlwTwxzv3j7TJq9E6yh/e5+bt5og5ukJk/726/zfETDvT9OSisghfBsJN+UGCseGO5P4dTO7d8SxG1MSfqRBMlWjSLIUOH9Tr+4i4QwTmaFdl0yqZT0x/M4ybNCd5FNCLYyRJj+pbrJtysK+wI9jRHtL0Om07tjCjRl0Dhgl2J9J9970t9BDsr7MOko2OA9x/BrtwSwd774HQRgU8vWihLX31ZJn/suNhzm+tFN8lFxFUw6IGRJSbaRAh2+6U5qb/ZW3yvhAt717bMckmOpTTtu/JAsMfTjVr8SWOTJHWK9g+XsbDC7kKpXGUKF+xf/e41Mu+hhX7oi15h/+Cuo6Xz/G/LScccIt/72ufKRSTpaHQM+yk/lVU//2zS2pRvQQLEsLeg0TNO2bbCnrF5qqchsLo7Ta3YOv3ezrfJYVsPkLfXb5KurgRj3eCNYUOC8vkOuTqteRzb322+6ahzTXt7m2x4t6vX4N8/ZUjzTaZiIy5csCteOvzFZHfeZ05q6qef1uaCYK/YIVH8dBDsxTOuWg91F+whYrR9Y5u0bfBC98JeUeLVIlraPEHTE9Xm5n7a17hZ0x/buxHjC2vCK9+mxCkvCEDASmCbf9zGWoYCxRKoi2AvdgoNbv2UU7w7kjny9t/8UlZf+VcNHgzdNwMBBHszWKmBYzTEr15x7devXQYP6i+rlq7fMrCAGA6KX391LyBI29YEVk4RrakN3TO0LXXdqIo9Q9pzbXNA/zbZ1NUj3QnuY8TbUtU9INdhtGRjbQPbpKcJObLCXl53LVywf/ai78uDjyzqs7m0KmkdyRLDptPg4W2LGSdLjNsJscxZYtTKbM/msIH/nnuHjN5+J/nQrvuIbBbbvVaF17ynloICWovn2av/Uw7qmSg7te3kBiak1E+6fyJfbP9i6vqq4mrv3+zu2TKtfZqEitEBngDxREjYqzvwbfkb61+Xu1+9U04f95lY0eILQ7XnPu41tF02bNwg/37HNfK3J14QWVKNrbvDXZm2DWyX390209/Erzb55/kqOkaZGPZ8rEUMe9+nvJLWMR/fKqKVwgW7ils/7cQj+4S/sOmUTafnfOHLNZ9m02nvw5tNp31vBF1OgHHZfXR9LbbNEI8/P3a/iBeyOXHkwaJXqk2BrcV12+q+gvCunrtktPdvr7a9XIbYp8zsntky0funBbsplvWKqxdSKv37tcn6rbb0b67g/ezBK+S8wy/qLX49QRoUw12DQ4boCWL1ylNkhh3PqeBsruQqUJP2wabTeGK2xYekvOPKk9YxT5r2tth0amdUthKFC3a1kq4flmROnrSOCHYE+9TI8wGC3S7YtfCubdTzVrcfWHSvDOk/VCZsu78fG61Xun3BHRP+8WDPg74tDmo7yPkcrYX1XRs9wT5wRxm39d5SW2kesmUluvZeQEBr8Xzrf90k+0+KX+W1xbCTh93ZbL0KItgR7Lvv2XeVOZ03udfK8+bYvdfeJRHsack1rl7hgr3qK+xy5JEi994ra/72Flnzj0eJbF6tapxJ6bnsBIhhD7dQLwG+OVOFEty1FW/1++aNhWEr3Uns7ottI8RDiWpzxdoX2YbA1uEWKoyixxbCkWQgjmVtgt2xGYq1GIGsaR1bDBfT9QgQElNeNyhcsKvQl+m/vKX28CSFYuGixX5ax0pkijEE+ztfOkq6Rue7aai8rsPI0hJoOcHurXybq+BahLep2G5PmKvV77QCXAlvHTZiiu5abPTmG+haKEiT3lAj2NMeba1dD8He2vZPM3sEexpq9alTuGBX0whL6xgWJlOfKefcC4I9Z6DVb64qgl2tiLe9rVLjecLbE+V++Iknws0wlKRCPCjAxQstCRXfTSq803o3gj0tudauh2BvbfunmT2CPQ21+tSpi2Cvz1Qa0wtZYsgSE/Q820atZskS074iXIwrgb5h9Tq5fv0MObf9XOuBp0T44p7FsujdRTLlAydKTYQr0e2Fl6jV77BQkzJniTEn7bLfIA6SSxy1TbATw251w9ACLuzTtFx0jLLrJtysgt12LkvDJqoOm07zpGlvixh2O6OylUCwZ7QIgh3B3oyCvbY6rrKebA5ZWfPmKpnzym/kzI5p1gfKbPBiWWb0zJDPvf98P9WfH/OtV8MNIa73dCxZ/Iw889QT8vHjvecWOL4Q7FtAIdg3yI03TJczz7nQ0XvciiHY4zkh2N38KGmpom/oXMaDYHehVK4ydRHsauPpmyvDH1f35L0zykUk4WgQ7Aj2sgp2vUL+54fv93OAT9x60nux4ipmPOQJj2YebjWnnu3VBktDjCtR7olx9d6GAe/Kv890F1AI9ugTi4toRLAj2E0PYoU94YU6ojh52MnDno8n1aeVwgX7ydMuke22HSq/uOLi+syo3r184AMiS5bIqi89Juv/aqx07dm/3iOgvyYjkFcMuxLd7StUukLv5xvez83x4y6bOP1MJ95TFZX47tm+zQ9L8VfD1VMOt2tMJpQmM2Ndh2sT7HUdDJ01DYGsITFNM1EGmhsBYthzQ5l7Q4UL9qg87LnPpFENGoL93WPGysaPINgbZYpm6TeJYA+KcrVq7mdWeaPLGraiV8iVIFePyO72VswR5M3iJb3HiWBvTrs1etQI9kZboPn6R7CX12YI9qy2QbBnJdhy9cMEux++4oWr9Fopt4jy2iq5n9pw8yr5+zeHsWwX/gj5loNdkQkj2CtiyDpPA8FeZ+AV6A7BXl4jFi7YVUjM0YcfIBecdWp5KWQYGTHsxLAH3Sdqo5ZeLX/luWflLy88KccN+YSfErFNhbMEXvpx9+MGeY+7V6Ernijv9kS4v7nTC11RYSv/u3ihLH31ZZn8seNiPdh141iSjVCuMbR6YMSwR5uIGHb7CTipv9lbfK+EC3vXtsxySY6lNO278sgq2F3PHWnmEKxDlpg8KLq3waZTd1ZlKVm4YFc52H8wfZbcN+fKssw513Eg2BHsQYd6dO79XthKj0zcZpIXY943hOW5nufkKe/fCW0n1Kqa4SsqnvyeF/8gI8fsLHuMHx/pr08vQrAH4cyfd7dsPXiojJ9wYKLjPIswIa1jX9Qr3lguc++6TU7tnJbIDlGFXQVq0s4Q7PHEshwXSW2BYE9KLFt5BHs2fo2oXbhgVzHscS+yxHRIxwC1A9ATdm3t0rVpkyx95UUZteMuMmKHUbJu3TuyZPHT8pFJH5XXly8TtXJzwMRD/JWhzjPOlVvnzPRT5amLo/qp/lbvz7zhajlhaqc8ueBhX8B8aNz4Wlo088Roig3zd/NEHVwtCoqiYPq94EUw7KQfzBsddoGPWqWKOtFE5aLWLIYMHdbLFeMuEHHCT9nn4YcekJM+enotjEWHtKjV8gd7HvT7OajtoF79qRCWnu37yQvtz8lf3lkkH594cm3lPHiMuIhABHvfMwuCPf1lJM9VYQT7qtq5OL1Fomu63sCwwh5PnywxZIkp4vgsqs3CBXtRAy9Nu23vxQq/9e03pXvHfrLh5I7SDI2BZCdgbvrs96qXDvGN9x4mFBbGonsLrpaLF1duZl5Jsuk0+wxooQoEiGGvghXrP4esgr3+I6bHRhMghr3RFojuH8Ge1TYI9qwES1E/tTDXseUqZ/nm320TQrDbCPF5kACCHZ9IQwDBnoZaa9dBsJfX/nUR7CqO/ZLLr+1F4bKvnC1TpxxWXjKuIzMEuxJs6z+twlt4lZVAPYV5FAMEe1m9o7zjQrCX1zZlHhmCvczWKefYEOzltIsaVeGC/crrZsv0X94iM6+6VMaPG+uTWLhosXSe/2057zMnNX32GDadlnfTqY4r//Vd18gpIz8pw9YN6RXK8mjPo/K29+/wtsN9v/RDWTavks9bPlcGbzNU9j7kI32OXh3D/olTOkOPbNtGreWvLpYnFi6Qo46dGnlmIIa9r1+5nEaJYXehFF6GGPb07II182QZNipi2POxFTHsxLDn40n1aaVwwX741AvktBOP7CPMlZC/6Xf3NH32GAR74wW7FubTb/0X+cJuX/I3gpox5jO6Z8ip7afKUO+fKcwf3fiorGlfIwdPOspPmWi+XDadItiny5nnXOh0piKtYzQml0wlthX2qA3XTsbZXChPkcmmUzadJvE9fyHvsT/L2rdXy6TDjkpaNXV5BDuCPbXzNKBi4YI96kmnOkyGLDFkiVF+75IlRgvzOx+YI+MGjZMPdn2wlzD/SfdP5IvtX6wdRnrF/PqXrpOTDj1dBu8wvJcwz5olBsGOYFfO5vJtSNy5HcFuv/K5rijbW+pdwoV90jZV+TxvflhhT2MBtzoIdgS7m6eUo1Thgr2MK+zqYU7PLnnFt8BuY3aUm2dcFmmNsPh7Vbh2o7E5hv3Nn630xeOG0wf2Wa0th6mbZxS+MPcyscjr3dJ/6XtPALVmZUmx+bNRRIhhbxT55u3XtsLevDNj5EUSIIa9SLrVbJsY9vLatXDBXrYY9s9e9H1Z8ebqmkhX4n27bYfKL664ONRK1gc/bRbsK65bJe2vdMm7UwdI1+j28lq8RCOrbQD1hHm/Fd6GijVKmHd5Yj18kL3SJSrG3v5eM11iiaYWOxQEe7NYqjzjRLCXxxbNNBIEezNZqxxjRbCXww5hoyhcsKtOy5QlRq34//15p9cy1NgEue1z0YL9V55gX+wJ9uM8wf4BBLvpbL2E+dueMFe5zOOE+eYHDPVs3ybqqZ/BPOblPZzcRoZgd+NEqS0EEOx4QxoCCPY01Fq7DoK9vPavi2Avy/R1dpqwjDXme+Z4w242zLh7Np1u2XS6/ZAR0r6iW2754yyZOGKS7LR+J1+YP7S+75M/Vbz5BVt90X/ypxLmr8lyuff5P8ipn5wm6omg6lX2J50Sw04Mu/JTYtj7nuHZdMqm06TXfTadJiWWrXxU/D6CPRvXImsj2DenmIwS7EH4wZAaF8Hev39/6dfPE6Y9PTJw4EBZvXq1DB8+XAYMGOD/HzRokP9Zm7dav2nTJlmyZImMGTNGdtxxR1m7dq089dRTctRRR8mrr74qK1eulMmTJ8v1118vF154of/z9NNPl5tvvtn/qd//8Y9/LGeeeaY8+OCDMmzYMJkwYYKo9y6++GKZP3++rFq1So499li/3q677up/bv4+d+5cf+qqL9Wnble9d+etd8qQ9iGy/7b7S8+qHpnx8Aw5uv1o2f7d7f06s3tmy0Tv305tO/l/P9TvIWkf3C6H7XmYtA1rk/4j+8tl3r6Bb3zjGzW8y5Yt8/s/99xza+8F+9UfzJo1S/bbbz/Zc889e5lH2cJsU3+oWSjm5svkELTznXfe6XObNGlSn+NP2UfxUXzDXia7sM+VPR9//HHfXlEv0xZRZR577DF54YUX5OSTT449R9jGoytH8Q5rfP369TV/cjlBucw52M7VV1/tz23kyJEuXfhl4uwW14gro7A2XGwV17c6ttRxpo75tK8o30/SXhL729oNO55tdeI+T+pvrn3lwT6srzxZ5nH8ufIIlstyXCTtM+58nLQt1/JR1xLX+mnLFe0fLuNq1NxdxkaZcAKFCXYdux6Waz3usyINlWaFPTge3YZeZXcR7O2eWPcFe3ePDPAE+9q318iQocOko2OA97+8WWLa1okcuPvBsuallfK7x26SM0ae5a+Yz1t/nwz2/n247cM+nhu7b3xPsA98v79i/tu3/kMOGDtJRu+2qx9j/vDj9/vl9p94aA1nMA2dS5YYXTlqZSAqtd3MG66WE6Z2+szNF1lient3kswWSbN2kNYx+szmkqnEFhJDWsd0Vw4X9mlaTnIspWnf9fjLGhJje6ZEmrFH1WGFPU+a9rZYYbczKluJwgS7bTNncKW6XmDCYtjVU1hd00v2SUfprYp3eyvUy//wFxk4a4P/8J31pw2o13Ry6UenS2z3stzo32OzslQ8xjwXqDGNEMNeNOHqtW8T7NWbMTPKg0BWwZ7HGGijuQgQElNeexUm2KPyr2sUjcrDbssSo2401EunelQC/745V9Ys2OdGZLNgX/bwItnqZ+v9cuvP8kJcNsdhl8X0tY2fqzdnZFEbP73UiQjz+lsIwV5/5s3eI4K92S3YmPEj2BvDvZl7RbCX13otJ9iVKeLysAcFu1lW1T1o/3G9U0Aagn3QTe/6AriRqR31Crl4wlz97j3IMzYji5qTfsBQzxAvK0sTp0ss72HWe2QI9maxVHnGiWAvjy2aaSQI9mayVjnGimAvhx3CRlGYYA+GngQ7t6ZLLC+zXiNrSAz7hw+R3/9+pnzqI2fLLY/fJCdsc5L8ccWdckL3CTK7e7ZMa58mM7pnyKntp8rjPY/78ebjBu4l1787Q84Z+3/k0Y2PyhpPyR886Si557E7ZNTonWSPceN7ZbswYxeD8Zjz590tWw8eKuMnHOizmD1zhkw++njZbvsR/t/BuNCwOEhi2BfIUcdOjfRyl8wjTy9aKEtffVkmf+y42KPFNQ41SdytawytHhgx7NEmcomjtgl2YtjTXTBc2KdpOcmxlKZ91+Mvq2B3PXekmUOwDjHseVB0b4MYdndWZSlZmGD/6nevkb88/ULkU0RtMe5lAWQbR1GCffSoXWTEkJGy7p13ZMnSZ2TStofK8jXLZPW7q+Wgnol+JhYlzJVAP6H9BLmr+y7/5+y22XLG6LPk+teuk5P2O00WvvWobL39MNlj/Hi58Yb30vCZJ0ZTGJq/I9h735SYfrD0lRfl4YceENI6ktZR+YXLzVXcecRFNCLYN9TOX7ZzcpLPXdgnaU+XRbAnp4ZgT84sSw0EexZ6jalbmGBX01Gr7OplxoDr999cucZ5o2dj0Lj1mkmw9/eyxHj/BrR5m1Q3eeErG720jl2b5JUNL/spEXfo2UHWealanut5Tg5uO9jLVL5cVnv/Jg7wBPuG2fKZ3c+SOS/+Ro6dOFXueeIO+fiJp8itc2ZK5xnnis6M8uSCh/3V8A95K+gIdrLExHl1EpHhusKn+2OFPZq8i2hEsCPYTQ9yPf5YYY+/jkeJVrerf/pSSc616XtJN3dCYooinr3dQgW7Gp5aab/lDw/0GmmfOPDs82hcC0YMuxpEx582SX/vv9p0uvHA/iJDvaeebuj2/ov0U0/5XONt9Fzd4z0VqNvb9Bk9bFVfpUgU72f3dl4mGi/7zHu/t5duQ2vj4Ddnz8SwN6fdGjlqm2Bv5Njou7wEsgr28s6MkRVFAMFeFNns7RYu2LMPseQteIK96/DJ8tpvb68NdMDdm6TfU5usA0eUWxFVsgCCvZJmLXRSCPZC8Va2cQR7ZU1b2MQQ7IWhzdwwgj0rwhDBrprs97yXpeX5Lml/11sV9yJe2gZ6wn6w94FacWelPCv1pq6PYG9q8zVk8Aj2hmBv+k4R7E1vwrpPAMFed+TOHSLYnVGFF8wUw17yJ52qGaunk5Ilprft2XQq4hpDq8kRwx59oiGG3X4STupv9hbfK+HC3rUts1zRMcquPLIKdrLEpLG+vU7R/mEfgQibTl0olasMgj2jPRDspHUMupDtIrf81cXyxELSOtoOvWC6UFt59Xkw5ahLHVXGZrO4dsgS05fOijeWy9y7bpNTO6e5miC2nKtATdoZgj2eWJbjIqktyBKTlFi28gj2bPwaURvBnpE6gh3BjmC3H0SssEczchGNtpAY8rDbfTCshAv7NC0XvYLqegPDCnu89cgSs4+MGbt7L0iExKQ54utTB8GelXNEDHvWZqlfXQLEsFfXtkXNzCbYi+qXdpubQFbB3tyzZ/RpCCDY01CrTx0Ee1bOCPasBFuuPoK95UyeecII9swIW7IBBHtLmj3TpBHsmfAVWhnBnhUvgj0rwZarj2BvOZNnnjCCPTPClmwAwd6SZs80aQR7JnyFVkawZ8RLDDsx7EEXsm3UYtOp20HHptMtnGyCnRh2N58KliKGPZ6b7VyWjnp4LTad5knT3habTu2MylYCwZ7RIgh2BDuC3X4Qsek0mpGLaESwb5Abb5guZ55zod3ZEpRwYZ+guVpRNp0mp4ZgT84sSw0EexZ6jamLYM/IHcGOYEew2w8iBDuC3e4l0SVcs6Ik7QPBzgr77nv2zZSS1I+Sli/6hs5lPAh2F0rlKoNgz2oPL4Z946fPkNd/ND1rS9RvEQLEsLeIoXOcpm2FPceuaKpCBIhhr5Ax6zQVYtjrBDpFNwj2FNB6VUGwZyXYcvUR7C1n8swTRrBnRtiSDSDYW9LsmSaNYM+Er9DKCPaseBHsWQm2XH0Ee8uZPPOEEeyZEbZkAwj2ljR7pkkj2DPhK7Qygj0jXmLYiWEPupAtswJZYtwOOrLEbOFkE+xkiXHzqWApYtjjudnOZemoh9di02meNO1tEcNuZ1S2Egj2jBZBsCPYEez2g4hNp9GMXEQjgp0sMaYHuW7CzbrCjmC3n9vSlGDTaRpq1EGwZ/QBBDuCHcFuP4gQ7Ah2u5dEl3AVqEn7cLlZStqmKl+0IHPlgWCPt17UKnMamyepU7R/uIyFFXYXSuUqg2DPag9i2LMSbLn6xLC3nMkzT9i2wp65AxqoJIGsgr2SUJhULAFi2MvrIAj2rLZBsGcl2HL1EewtZ/LME0awZ0bYkg0g2FvS7JkmjWDPhK/Qygj2rHgR7FkJtlx9BHvLmTzzhBHsmRG2ZAMI9pY0e6ZJI9gz4Su0MoI9I15i2IlhD7qQbaMWWWLcDjqyxGzhZBPsZIlx86lgKWLY47nZzmXpqIfXIktMnjTtbRHDbmdUthII9owWQbAj2BHs9oOITafRjFxEI4KdLDGmB7Hp1H7OcSnBptN9ZMzY3XuhYoXdxXMaUwbBnpE7gh3BjmC3H0QIdgS73UuiS7gK1KR9uNwsJW1TlS86C4grj6whMaywp7G+vU7R/mEfgQgr7C6UylUGwZ7VHsSwZyXYcvWJYW85k2eesG2FPXMHNFBJAlkFeyWhMKlYAqywl9dBEOxZbYNgz0qw5eoj2FvO5JknjGDPjLAlG0Cwt6TZM00awZ4JX6GVEexZ8XqCfcMl/ygrvvTVrC1Rv0UIINhbxNA5ThPBniPMFmoKwd5Cxs5pqgj2nEAW0AyCPSNUYtiJYQ+6kC3ukywxbgcdWWK2cLIJdrLEuPlUsBQx7PHcbOeydNTDa5ElJk+a9raIYbczKlsJBLuDRU6edok8u+QVv+RuY3aUm2dcVquFYEewI9jtBxGbTqMZuYhGBDtZYkwPYtOp/ZzjUoIsMWSJcfGTspRBsFss8dmLvi8r3lxdE+lKvG+37VD5xRUX+zUR7Ah2BLv9dIZgR7DbvSS6hKtATdqHy81S0jZV+aKzgLjyyBoSwwp7Guvb6xTtH/YRkCXGhVHZyiDYLRY5fOoF8vfnnS5Tpxzml5xzxzz5wfRZct+cK9+rSQx72Xy69OMhhr30JirdAG0r7KUbMAMqBYGsgr0Uk2AQdSVADHtdcSfqDMEeg2vhosXSef63ZeZVl8r4cWP9kn3eQ7AncjgKiyDY8YKkBBDsSYlRXhFAsOMHSQkg2JMSq195BHsOgl2++U2Rb3yjflajJwhAAAIQgAAEIACBliGAYM8o2F1i2Pv37y/9+vWTnp4eGThwoKxevVqGDx8uAwYM8P8PGjTI/6zNW63ftGmTLFmyRMaMGSM77rijrF27Vp566ik56qij5NVXX5WVK1fK5MmT5frrr5cLL7zQ/3n66afLzTff7P/U7//4xz+WM888Ux588EEZNmyYTJgwQdR7F198scyfP19WrVolxx57rF9v11139T83f587d65PRvWl+tTtqvfuvPNOv81Jkyb5Za6++mo5+eSTZeTIkf7fqqyqp+agXmZbGrfi9g3jJmfZsmV+/+eee27NIsF+9QezZs2S/fbbT/bcc89e1gu2qT/ULBRz82VyCLpBcI7m58o+ak6Kb9grbL5mOWXPxx9/3LdX1Mu0RVSZxx57TF544QWffdzLNh5dN4p3WNvr16+v+VNs55s/dJlzsJ2gX7n0E2e3PBiFteFiq7i+g8eLyzyDZaJ8P0lbSexvazfseLZ81nhYAAANV0lEQVTVifs8qb+59pUH+7C+8mSZx/HnyiNYzvXckbZ91/NxHu2HtRF1LSmqvzTn2qLG0qi5FzWfVmgXwW6xclgM+yWXXytP3jvDr+ki2Ns9se4L9u4eGeAJ9rVvr5EhQ4dJR8cA73+HdAwY6LXU48XDt0uXJ9iXvvKijNpxFxmxwyhZt+4dWbL4afnIpI/K68uX+ZuZDph4iKjNUp1nnCu3zpkpHz/+FJl7123+T/W3en/mDVfLCVM75ckFD8vWg4fKh8aNlxtvmC5nnnOhmOmz5v7xdhk1eifZw/vc/N3cbBTcIDN/3t1+m+MnHOgzCKbfC27kCtu4FExDt+KN5f4cTu2cVrNI1MacqJ39UantNAvF3HzFpRELztGsp+zz8EMPyCdO6Qz1HttGLdI6up1aSeu4hZMtJIa0jm4+FSzFptN4brZzWTrq4bVI65gnTXtbpHW0MypbCQS7xSJkiTm0T8YDBDuC3TVLhT68yBITfaJxEY0IdtI6mh7kevxljWFHsBcj2cgSUwzXqreKYHewcFwedlV9zTsbZc26TQ4tUQQCbDrFB5ITsAn25C1SoxUIZBXsrcCIOfYmwKbT8noEgj0H2yDYc4DYQk2QJaaFjJ3TVBHsOYFssWYQ7C1m8Bymi2DPAWJBTSDYcwCLYM8BYgs1gWBvIWPnNFUEe04gW6wZBHuLGTyH6SLYc4BYUBMI9oxg2XTKptOgC9niPtl06nbQsel0CyebYGfTqZtPBUu57B9I03LRMcrEsKexSt86URsv82k9upWi/cNl/Gw6daFUrjII9oz2QLAj2BHs9oOITafRjFxEI4KdTaemByHY7ecclxII9n1kzNjde6Fihd3FcxpTBsGekTuCHcGOYLcfRAh2BLvdS6JLuArUpH243CwlbVOVL3oF1ZVH1pAY27eFadhE1SGtY5407W2xwm5nVLYSCPayWYTxQAACEIAABCAAAQhAwCCAYMcdIAABCEAAAhCAAAQgUGICCPYSG4ehQQACEIAABCAAAQhAAMGOD0AAAhCAAAQgAAEIQKDEBBDsGYxjewJqhqap2mQEkvpCXPk5d8yTSy6/tg+BJ++d0WRUGG4SAkl9SLW9cNFi6Tz/2zLzqktl/LixSbqjbJMSyNNPONc0qRNkHHYSH/rsRd+XBx9Z1KtHrkUZDZCyOoI9JTjlxCveXC03z7jMb0EdANttO1R+ccXFKVukWrMSSOoLtvLqIvqD6bPkvjlXNisSxp2QgM0nwpo7fOoF8ubKNf5HCPaEwJu0eN5+wrmmSR0hw7CT+pA6z5jXoq9+9xqZ99BCrk8ZbJC2KoI9JTnlxH9/3ukydcphfguc+FKCrEC1pL5gK48vVcApEk7B5hNRzbHCnhB0kxfP20841zS5Q6QYflof0l1xzkkBPacqCPYUIMMcFidOAbICVZL6gkv5sK+p+QqyAs4SMQUXn0CwV9f+rjMrwk8417jSr0a5LD6kCVx53Wy56Xf3sMLeAJdAsKeAnofTp+iWKiUkkNQXkpZXUw5+hVlCDAwpA4E0PsFqVwbgTVq1Hn7CuaZJncNx2Fl8SHWh61/2lbNr0QWOXVMsBwII9hQQszp9ii6pUlICSX0haXnzJMkqe0mdIOOw0vgEgj0j9CasXg8/0X1wrmlCB3EYch4+dN5nTpILzjrVoTeK5E0AwZ6SaFgcmMrswYkuJdAmrpbUF5KW119b41tN7CSWoSf1CQR7dX0hbmZF+wnnmur7VRof0n7B5vbG+geCPSX/pDutU3ZDtSYgYPMFlUFIvXRGIVv54K58MhA1gRNkHKLNJ4I+hGDPCLxJq+ftJ5xrmtQRMgw7qQ+xMTkD7JyrItgzAE2SyzRDN1RtAgJxvhAmtmzln13ySm3WB+0/jnShTeADWYdo8wnzpk/9bqZ1VH9vO3wIG8GyGqEJ6ufpJ2Zbauqca5rAAXIYoqsP6RCasC6JY8/BEAmbQLAnBEZxCEAAAhCAAAQgAAEI1JMAgr2etOkLAhCAAAQgAAEIQAACCQkg2BMCozgEIAABCEAAAhCAAATqSQDBXk/a9AUBCEAAAhCAAAQgAIGEBBDsCYFRHAIQgAAEIAABCEAAAvUkgGCvJ236ggAEIAABCEAAAhCAQEICCPa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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# The full reaction of E and ES*\n", "dynamics.plot_history(chemicals=['E', 'ES*'], colors=['violet', 'red'], show_intervals=True, \n", " title_prefix=f\"E and ES when [E] init = {E_init}\")" ] }, { "cell_type": "code", "execution_count": 59, "id": "03807baf-28a8-45ad-a31a-53003a13d02e", "metadata": {}, "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", "
SYSTEM TIMEEES*P
8180.2017530.8328491.16715115.691155
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" ], "text/plain": [ " SYSTEM TIME E ES* P\n", "818 0.201753 0.832849 1.167151 15.691155" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(columns=['SYSTEM TIME', 'E', 'ES*', 'P'], tail=1) # Last point in the simulation" ] }, { "cell_type": "code", "execution_count": 60, "id": "5d28e797-ebb8-480a-bdcf-13880757b32b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "15.69115548729148" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_equil = dynamics.get_chem_conc(\"P\")\n", "P_equil" ] }, { "cell_type": "markdown", "id": "797a8ab4-d051-4e92-bf1b-e1e148de6ca4", "metadata": {}, "source": [ "#### P_equil continues to decrease with increasing initial [E]" ] }, { "cell_type": "code", "execution_count": 61, "id": "94b8d506-9225-4c18-b618-2b87e9d48a3a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "10.983808841104036" ] }, "execution_count": 61, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_70_threshold = P_equil * 0.70\n", "P_70_threshold" ] }, { "cell_type": "code", "execution_count": 62, "id": "968136e5-5497-4e3b-8a2b-25b02d7e9ad7", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.04311547431679562" ] }, "execution_count": 62, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.reach_threshold(chem=\"P\", threshold=P_70_threshold)" ] }, { "cell_type": "markdown", "id": "78dd47e8-668a-44f2-a770-f7cff871915b", "metadata": {}, "source": [ "#### The time at which we reach the 70% threshold of the equilibrium value of P continues to decrease with increasing initial [E]" ] }, { "cell_type": "code", "execution_count": null, "id": "3af50933-541a-4e48-b6de-69fdbf82a5cf", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "ba756ea7-7e7b-4a9b-a847-c9b12975b667", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "1a2e3c92-4ce0-4d3b-bb89-113fe3eabbc1", "metadata": { "tags": [] }, "source": [ "# 6. Keep increasing the initial [E]" ] }, { "cell_type": "code", "execution_count": 63, "id": "30fb7ef6-0dcd-4063-bf6b-5e69e6a9a81e", "metadata": {}, "outputs": [], "source": [ "E_init = 10.0 # 1/2 of the initial [S]" ] }, { "cell_type": "code", "execution_count": 64, "id": "4353621a-ac88-4cd3-a3b2-fec1bbf592f4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "4 species:\n", " Species 0 (S). Conc: 20.0\n", " Species 1 (P). Conc: 0.0\n", " Species 2 (E). Conc: 10.0\n", " Species 3 (ES*). Conc: 0.0\n", "Set of chemicals involved in reactions: {'ES*', 'P', 'S', 'E'}\n" ] } ], "source": [ "dynamics = ReactionDynamics(chem_data=chem_data, preset=\"slower\") # A brand-new simulation, with the same chemicals and reactions as before \n", "\n", "dynamics.set_conc(conc={\"S\": 20., \"E\": E_init}, snapshot=True) \n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 65, "id": "6e3b51d3-31c8-4d55-90b6-c54275ebf914", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* INFO: the tentative time step (2.5e-05) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.1 (set to 2.5e-06) [Step started at t=5e-05, and will rewind there]\n", "* INFO: the tentative time step (2.5e-06) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.1 (set to 2.5e-07) [Step started at t=5e-05, and will rewind there]\n", "836 total step(s) taken\n" ] } ], "source": [ "# Perform the reactions (The duration of the run was manually adjusted for optimal visibility)\n", "dynamics.single_compartment_react(duration=0.05,\n", " initial_step=0.00005, variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 66, "id": "a8169cc9-fa96-4388-bdbd-3672c6e9fa59", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 66, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reactions have reached equilibrium\n", "dynamics.is_in_equilibrium(verbose=False)" ] }, { "cell_type": "code", "execution_count": 67, "id": "a4246902-f175-42db-9658-8eb630bb03c2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_curves() WARNING: Excessive number of vertical lines (837) - only showing 1 every 6 lines\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=S
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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(colors=['cyan', 'green', 'violet', 'red'], show_intervals=True, \n", " title_prefix=f\"[E] init = {E_init}\")" ] }, { "cell_type": "code", "execution_count": 68, "id": "cea4cabc-470c-4830-ab70-f05d4176b189", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.005877353573479905, 6.680399989705835)" ] }, "execution_count": 68, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Locate the intersection of the curves for [S] and [P]:\n", "dynamics.curve_intersect(\"S\", \"P\", t_start=0, t_end=0.05)" ] }, { "cell_type": "markdown", "id": "7e911332-dbd3-4f05-bda5-1d902d515156", "metadata": {}, "source": [ "#### The timescale of [S] and [P] continues to become faster with a higher initial [E] -- **AND THEY'RE NOW APPROACHING THE TIMESCALES OF E AND ES**" ] }, { "cell_type": "code", "execution_count": 69, "id": "11c4c99b-cc15-488e-ba6a-f8aacd80ed67", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_curves() WARNING: Excessive number of vertical lines (837) - only showing 1 every 6 lines\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=E
SYSTEM TIME=%{x}
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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#The very early part of the reaction\n", "dynamics.plot_history(chemicals=['E', 'ES*'], colors=['violet', 'red'], show_intervals=True, \n", " title_prefix=f\"Detail when [E] init = {E_init}\", xrange=[0, 0.002])" ] }, { "cell_type": "code", "execution_count": 70, "id": "9ceee775-6449-419f-bb39-b42f5fbd5803", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_curves() WARNING: Excessive number of vertical lines (837) - only showing 1 every 6 lines\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=E
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# The full reaction of E and ES*\n", "dynamics.plot_history(chemicals=['E', 'ES*'], colors=['violet', 'red'], show_intervals=True, \n", " title_prefix=f\"E and ES when [E] init = {E_init}\")" ] }, { "cell_type": "markdown", "id": "1f97da50-3764-4be6-bdef-ae5eef24a37d", "metadata": {}, "source": [ "#### Notice that at these higher initial concentrations of [E], we're now beginning to see overshoots in [E] and [ES*]" ] }, { "cell_type": "code", "execution_count": 71, "id": "c7d3f38c-331b-47f2-9ae0-31531c62c7e2", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEEES*P
8360.0502654.7656975.23430312.304598
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" ], "text/plain": [ " SYSTEM TIME E ES* P\n", "836 0.050265 4.765697 5.234303 12.304598" ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(columns=['SYSTEM TIME', 'E', 'ES*', 'P'], tail=1) # Last point in the simulation" ] }, { "cell_type": "code", "execution_count": 72, "id": "38c003d2-e007-4c47-9c91-3fb6c2a626ea", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "12.304597774138907" ] }, "execution_count": 72, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_equil = dynamics.get_chem_conc(\"P\")\n", "P_equil" ] }, { "cell_type": "markdown", "id": "04f9845c-4a0d-4309-acd6-46fcc1d59136", "metadata": {}, "source": [ "#### P_equil continues to decrease with increasing initial [E]" ] }, { "cell_type": "code", "execution_count": 73, "id": "51356bd2-f34f-4189-8f39-c11804c6062c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "8.613218441897235" ] }, "execution_count": 73, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_70_threshold = P_equil * 0.70\n", "P_70_threshold" ] }, { "cell_type": "code", "execution_count": 74, "id": "f40ab9f2-a1fe-46a0-b755-9e2dd332ce9f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.008274545666098492" ] }, "execution_count": 74, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.reach_threshold(chem=\"P\", threshold=P_70_threshold)" ] }, { "cell_type": "markdown", "id": "319960a1-b1b3-4237-87b2-f634420acec9", "metadata": {}, "source": [ "#### The time at which we reach the 70% threshold of the equilibrium value of P continues to decrease with increasing initial [E]" ] }, { "cell_type": "code", "execution_count": null, "id": "e69e2707-5dfa-465f-9842-64f796c55dac", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "903586d5-e021-4536-bc32-987df21b2e69", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "e813f05f-1cbb-4b9e-8bc3-9902ba313445", "metadata": { "tags": [] }, "source": [ "# 7. Keep increasing the initial [E]" ] }, { "cell_type": "code", "execution_count": 75, "id": "70c6943f-9deb-4ec0-89eb-382c9728e889", "metadata": {}, "outputs": [], "source": [ "E_init = 20.0 # Same as the initial [S]" ] }, { "cell_type": "code", "execution_count": 76, "id": "0e1fec6a-0cca-4ca7-b54e-340fbef124d8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "4 species:\n", " Species 0 (S). Conc: 20.0\n", " Species 1 (P). Conc: 0.0\n", " Species 2 (E). Conc: 20.0\n", " Species 3 (ES*). Conc: 0.0\n", "Set of chemicals involved in reactions: {'ES*', 'P', 'S', 'E'}\n" ] } ], "source": [ "dynamics = ReactionDynamics(chem_data=chem_data, preset=\"slower\") # A brand-new simulation, with the same chemicals and reactions as before \n", "\n", "dynamics.set_conc(conc={\"S\": 20., \"E\": E_init}, snapshot=True) \n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 77, "id": "27e46b9b-802e-4de5-b549-062ba7a4866b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* INFO: the tentative time step (2.5e-05) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.1 (set to 2.5e-06) [Step started at t=5e-05, and will rewind there]\n", "* INFO: the tentative time step (2.5e-06) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.1 (set to 2.5e-07) [Step started at t=5e-05, and will rewind there]\n", "Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n", "757 total step(s) taken\n" ] } ], "source": [ "# Perform the reactions (The duration of the run was manually adjusted for optimal visibility)\n", "dynamics.single_compartment_react(duration=0.02,\n", " initial_step=0.00005, variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 78, "id": "4b74d93a-54a3-4c96-88d8-b9c4fcc34059", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reactions have reached equilibrium\n", "dynamics.is_in_equilibrium(verbose=False)" ] }, { "cell_type": "code", "execution_count": 79, "id": "cec660e7-1c5c-4215-9501-1abd52f96df9", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_curves() WARNING: Excessive number of vertical lines (758) - only showing 1 every 6 lines\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=S
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Changes in concentrations for 3 reactions (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.765766640762288e-05, 0.020147397371097706 ], "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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067VTWaxjNh439le9YKqeUpxuJmU7dvu1Wrcg6xozUhlvwOK9KXECPXmRCuI8CBKwW90kS/uppLnVQ7tZPatzvdW5Wj9/pR1VgV2bXyYx9cZ5Z3WMmMVJq4QVyRscfYig08Jivbb6b5r4PMEbf2uth3Rub+K44S0WkAcR2J3OF3qNZFmzLFbGb17MOEAlLMk4/9zMO9Xrjd05101IjPE6YuVcUrluu71WAdhVr5w+lTOL/bJr2g2Qqp4YVNt0A+xmXwWqSibrqlx4MtHDrnJzl2hgt/JEeQH2RHlWjfNOzneVhc1B8rDLk7nKceHkYee2jAtMjTqpziFVz5UqsAd1HiQ6JMaNh93vzEVy39JR4eRhdwq74bkUj9dWzkE31wDjvJVzXw+GqtdCNx52vWeXY7p5nRGHE+mvfbyo2Hi+Vu2L1fUyER52N8BudVOjEkoqbzadbs7N5p9KuJc8R6qumbLS2E9gN34DoMpBXM7pWgVgd6OmT2Wlx8vO48eGsUvraHVHanZijdfDbuaRkBK4iWHXy8YnHwYn45PHVA5+s4NT9ebDzd21LMsayxhP1RhmN55gu1hy7gNrpOphVYUtbtfKe2jn6VSNMZZzRr9mwnhR1l/QVNtV1ZXHwF4f41OB7cIK9HMjFTHsVseE1QIrs7kcTwy7sR0/1qvo44itwjXcrOcw2iNZ88AYt2/UympsbuBKFdhVb5CsznHyWmL83HhusQIk1XOzVT+N1yov1wC2y6QzR8Q8cdZ4HlGFZNUYdqkdtyszpOm/EbZ63w4oVWPF3cwp1W/43JzrVa99ZvPMaHs312vVeecU667i8PIT2O1srj8G47lWqc4Zn1A1ac0ENoZdf+Dz38bJZPQWuJngZiuO5c2B00p27ovZXa4xNIHLWcURyr6bpZHkFIfs4ZPt6W8s3IBJIjzscjz6u3Tjgjyzscn39DZUBQrW0UwL4925WRlpK04tJVfuuwF2txcp3p9sX3+TqY911l+8rPpipo3Z+MzmnKquZraUJ1AVT7WTjmZZlfT2V71g6s+EVjaW8Y0qoWJO+5XnAWNbPF6VTEjcXzPbm43daV2F2TktaPPAKWTNzRxXBXM5J8zKW61nYLvzZvfEWLMwTLNjzAp85LnQ7PjhefXQ727UANqsTe6b8brk5Rpgdh42+9ZaFdjlucEspMZsvNIOVmkfzeq46YsZISUC2Hk/ciz6c4J8Tz8Ou3J63czmqPEa6YZnVOedmf31jJIKYFe5bru9Vtl9C5Y0sk7QjgIP7Dxuq7hv/YXRzQSXJ0djflAGO7O8qipZYvRgKW3FB/OQAcdoebqNAGAWX8j1zEBHb3uVr1zlyTWemDiVeSYBSZY19slsbE7xbLItJzvq+2dlF+MY9P1zAk1jP41xsWxHVUiR/eB+ymcDGOeBPm7a7zzs+m9n7OBPr5fqE+LsPPEq9ncCZ6t5KE/w+s9VbjBkeZX96m+w9PvR2854TuI5xpt+vYqsa9Zn4zwzmwdujgXjxVb1xs3svMXvqc4DeS41pkTV66Y6x/0AdtXrhdX8MouDNwMZ/TnQKQ8770tfRtqGNdNfg8zmsdm1T/UaYDaPjedMt5Bs1Mdqnpg5aVgHM2iUtnDbF6MNEwXsvB/juHlOcLiPcd6blWMnnDGG3Wy9jBeekcehfj4Z551ef6kdz7kJ4htqHksqgJ37YRWHb5ZeVeVapXKOtzr+g/5+WgB70EW0619YY6nS2SboOxSAAv4p4DUUxb+epEdL0Cs97IRepp8CbqIQ0m90RAB2n6zGE0UfeqG/m1VNReRTV9AMFIACUCCpCpiFAyS1A2m0MwB7GhkLXU0rBcJ+HgKw+zQdrb7WUfmayacuoBkoAAWgQEoU0J//VNKCpqSTAdkpgD0ghkA3QqWADFMLM3MB2EM1ZTEYKAAFoAAUgAJQAApAgbApAGAPm0UxHigABaAAFIACUAAKQIFQKQBgD5U5MRgoAAWgABSAAlAACkCBsCkAYA+bRTEeKAAFoAAUgAJQAApAgVApAGAPlTkxGCgABaAAFIACUAAKQIGwKQBgD5tFMR4oAAWgABSAAlAACkCBUCkAYA+VOTEYKAAFoAAUgAJQAApAgbApAGAPm0UxHigABaAAFIACUAAKQIFQKQBgD5U5MRgoAAWgABSAAlAACkCBsCkAYA+bRTEeKAAFoAAUgAJQAApAgVApAGAPlTkxGCgABaAAFIACUAAKQIGwKQBgD5tFMR4oAAWgABSAAlAACkCBUCkAYA+VOTEYKAAFoAAUgAJQAApAgbApAGAPm0UxHigABaAAFIACUAAKQIFQKQBgD5U5MRgoAAWgABSAAlAACkCBsCkAYA+bRTEeKAAFoAAUgAJQAApAgVApAGAPlTkxGCgABaAAFIACUAAKQIGwKQBgD5tFMR4oAAWgABSAAlAACkCBUCkAYA+VOTEYKAAFoAAUgAJQAApAgbApAGAPm0UxHigABaAAFIACUAAKQIFQKQBgD5U5MRgoAAWgABSAAlAACkCBsCkAYA+bRTEeKAAFoAAUgAJQAApAgVApAGAPlTkxGCgABaAAFIACUAAKQIGwKQBgD5tFMR4oAAWgABSAAlAACkCBUCkAYA+VOTEYKAAFoAAUgAJQAApAgbApAGD3waIVh2qporLOh5bQRCYo0Do/m/Jys2nfgZpMGC7G6JMCHdvm076DtVRb1+BTi2gm7Ark50aosFUu7SmvDvtQMT4fFWhXmEc1tfV0qLo+2mrX9q183AOaikcBAHs8qhnqANh9EDGDmgCwZ5CxfRwqgN1HMTOkKQB7hhja52EC2H0W1KfmAOw+CAlg90HEDGoCwJ5BxvZxqAB2H8XMkKYA7BliaJ+HCWD3WVCfmgOwexTyN7/5jWkLWVlZ0fezsiKUnZ0t/m8UL6L8/AKKRCJUVVmplWndplD7HRF16urrqLq6ikpKOlJJh47a+xvWraHj+g+kNoXFtPjDd2nMmWfTju1btc+6dO1O68pW07DhI+mzpYu036tWfEZ9+51AFeX76eCBchp68ih6bs4suvzqm7T63M7AISfRM088SBdfNkPb3+vzSmnaZddqdeTf3L4sk5ef36Ku8TNjPeP/XP7F0tk0Zvwkat+hk9b3Hdu+1vp87gXTolqtXP6p1ucRo8+IvmdWzqw9fq+mujo6VqNh9GPRf7Zu7UpNT9bVuC1b+pH21tDho2I+MxujvtCmjetpfdkq+t6kC1rUlcC+a0+FZV9lBauxq45NX85OGzfjNpa10y9GNPGGfg6afW723hN/upeuvuFW1eJauff/9aZ2fBwrjh03m9kcVK3vpS7vw26+qQK7XRuq4+By8djJqn2vuhjb3bN7F73/zht04bTpbobkWPafb7yknTt79+nrWNZtAeP5z219p/Jm8z0RwF465zE6Z8o0Kipu69Qlz5/7OQdVO5OKfcq+vfZSqXYN79Ktp2p3fS0nr2kzfjITITG+KutPYxkP7Ffccg8tWba2hZqrF8xu8f/k6bfThk3btPeO6d2NXp59Z/RzAPsMYpgHsMcekAB285NUPBdEADsRgP3wfAKwxx5bAHZ/oCie85M/eyYCsPulZDjbyXhgP23KTFo47+GodX9x1+P04dKV0fcY6PfsLY9COsN7+5Jievq+27Q6AHYAO38zYbYB2AHsbi8b8LCrKQZgB7CrzRT3pQDspQQPu/t5k4waGQ/sRpFXrt1I0677LZU++isa2L8PMdD/bMZUmjJxtFZ03lsf0h9nPd8C8hHDnoypGp59IIY9PLZM5khUPezJ7BP2FWwFEhESE+wRo3d+KIAYdj9U9L8NALtB04efepHmvvqeBuRGeOeiZu8B2P2fmGFuEcAeZusmbmwA9sRpG9aWAexhtWxix5UKYDdGLyR2hP62bsaF/u6hqTUAu05VKfqdP79K86irAPvu331HtVNaU2GfSCLsgzZDqEBujliEHMmiqprDOW5DOEwMyWcFWhfkaHOmoYGXrmODAs4KZGdnUV5ONlVW4zkhzmqhhFSgIC+b6sV5Rv/Mh6LWuZ4EMlsvWNKuKBqtkApg54iJ2+9+kiTzxTtAAHu8ysVZTwo+49LzaeaVF2qtqAC7Ugy7yAiTI7LENDZfZwsKCihLAFulyBLDuWQKC4ua7p5ElpjaulqqrqqmDh07ip+mbCpla1bTgIGDqLiomBa89w5NOPtc2rrla+2z7j160ppVK2nEqNG0+KMPtd+ff/YJHT9gEJXv30flFeV06sjR9ORjf6brb7xFq8/tDD1pOD3y0H101bU/0fY39/m/0lXXXC/q7I/+ze3LMpzZRl/X+JmxnvF/Lv/XZ56is0TfO3U6Uuv7li2btT7/cNqPolZb9ulSrc9jx42PvmdWzqw9fo8z3sixGqeCfiz6z1av+kLTk3U1bh8vWqi9derI02I+MxujvtCG9etozeov6PwpP2hRVwL7/oqDln2VFazGrjo2fTk7bdyM21jWTr8Y0cQbxnlkVsb43n1/uItu+a9fqhSNlpn/5mva8THghEGu6pnNQdUGvNTlfdjNN1Vgt2tDdRxcLh47WbXvVRdju7t2fUNvC/tecvmVbobkWPaVeX/Xzp3H9D3WsazbAsbzn9v6TuXN5nsigP3Jxx+hi6ZeQsVtE58lxs856KSf/DwV+5T7fqH0b9o1vEePXqrd9bWcvKbdcMONvgL7gLHTSQ/nstMM8Ud2OIJ+/8trKBXA7pd4AHa/lFRoR95lybh1fRWzGHa+I5OZZJSAHWkdNUmR1rFpZiGt4+HUogqHp1YEWWKQJUY/V7DoNPbIQZYY1bOJfTksOvV30SlD+fqNW1us+zOzgAR2/kxm7rOCfH1mPz23Ma+NHj5QSxyyd1+Ftht2wvbo1knzpMtN1jEDbeM3AdKJa5dREMDuz7Hn2IrZIlJ9JWSJacrVjjzsyMNudTAhD/thZbzmG0eWGMdTtlYAwA5gV5sp7ksB2P0Fdvaun3/WSM2LbrfJ9Nn6KAcG8L59ukez8hl5jNccznr2lagDlcszqEsgl58bQ2+4H5ye2wjaxpsL/vz+J17Q9s+f3Xz1D7VkJLxxf63acT/r1GpkdAy7NJaZVPqYJrs87N/9z3cU6ZRNB3/gLb5LzVwoFQYFsOg0DFZM/hiw6DT5mqf7HrHoNN0tmJr++7Xo1Lgu0AnY9SmzuSyn2V6zbrMpXMu2GNIvOm+cFsosPezy5sDM861P3a3/nNvjDIGq8exOCUoSYbmMBnY/BGVgp7YiHv1H+X40hzYyQAEAewYYOQFDBLAnQNSQNwlgD7mBEzS8IAK7DF02G7L0ylsBux7CrUD7y83btbAZ44Mz9fuTHnz9e1weITEJmoh+N6sBu9gqf1Lgd9NoL6QKANhDatgEDwvAnmCBQ9g8gD2ERk3CkPwCdu6qm5AYOw+7BHYnoOYYdqOH3Q9g53GcMrR/NDxHH44DYE/CpPRjF1h0iied4kmnK2nH9q005syzlQ6peGJEsegUi071kwsx7LGHGhadKp1+HAvFc35ybFSxwGsvldKw4SOpS7eeijX8LVZRvp9en+dvDLvTolMOUbHKEmMWEmMXsuLFw85KWoXEmN0sANj9nXtJaQ3ADmAHsAPY5ckGi07NT7tedTG2CmAHsCfqAg9g9xfYpZfdmPFFQrBckGqW1lEP7NyOzNSi97JzmVOGHq89O8cLsPNiUu7D3n3l0Yw2ctEpLzY1wjx73HlDSEyijsQEtAtgB7AD2AHsAHb7kyuAPTatrd+XI3jY/VEUwO4/sOthW28lY3IPu5AYWc8uvaJXYOd96JOM8P+yj3xj8Mrbi6Ld57h5maEGITH+HHsJb+XgCweppqyGas7Oo/qj8LTThAsegh0ghj0ERkzBEBDDngLR03yXiGFPcwOmqPt+xrCnaAih3C2yxHg0a+XblVS1pIpqRuVQ/eAcj62heiYoAGDPBCv7P0YAu/+ahr1FAHvYLZyY8QHYE6Or1w2H7c4AACAASURBVFYB7B4VrPqgiirfr6S6k3OoVvxggwJOCgDYnRTC52YKANgxL9wqAGB3qxjKswIA9mDOAwC7R7sghh0x7IhhRwy7PI14jdXGk07VTshYdBqrE2LY1eaOUynEsCcmht1Jd3zurACA3Vkj2xIAdgA7gB3ADmC3P5F6vZExtg5gB7B7vHRbVgewA9gTNbe8tgtg96gggB3ADmAHsAPYAexOl5IXS2fTmPGTqH2HTk5F4/ocHva4ZIupBGAHsPszk/xvBcDuUdP6b+qp/PFyaizOoqpL8j22huqZoABi2DPByv6PETHs/msa9hYRwx52CydmfIhhT4yuXlsFsHtUsLGqkfb9YR81ClavurLAY2uongkKANgzwcr+jxHA7r+mYW8RwB52CydmfAD2xOjqtVUAu1cFRf3v7t1HVN2oATuDOzYoYKcAgB3zIx4FAOzxqJbZdQDsmW3/eEcPYI9XucTWA7B71Bcx7IhhRww7YtjlacTr4kpkiVE7IWPRaaxOiGFXmztOpRDDjhh2pzmSqs8B7B6VB7AD2AHsAHYAu/2J1OuNjLF1ADuA3eOl27I6gD1zgH3A2Okt5sExvbvRy7PvTNTU8twugN2jhAB2ADuAHcAOYAewO11KkCXGSaHYz1MBz6nYpxz5ay+V0rDhI6lLt57uxfKhRkX5fnp9XmYA+2lTZtLo4QPp97+8Jqrc5Om3A9h9mEeBbmL/vw5Sw6IaPO000FYKTucQwx4cW6RTTxDDnk7WCkZfEcMeDDukWy/CHsO+cu1Gmnbdb6n00V/RwP590sY88LD7YKotKyupcF4VNfTJpuqJuT60iCbCrACAPczWTdzYAOyJ0zasLQPYw2rZxI4rEcBeJrq8M7HdNm29n3i3s8kn7GEvaVccaI+6sdsAdh8mUPm6Kqp/vpIauglgnwxg90HSUDcBYA+1eRM2OAB7wqQNbcMA9tCaNqEDSwSw3yx6/EBCe23e+P3i7Z9a7NcYwz7j0vNp5pUXpqCXarsEsKvpZFkKMeyIYUcMO2LY5QnC6+JKZIlROyFj0WmsTsgSozZ3nEohhj0xMex3C+HnO4mfgM9vE21OVGj34adepFnPvkJ3/vwqmjJxtEKN5BcBsHvUHMAOYAewA9gB7PYnUq83MsbWAewAdo+XbsvqAPbEAHui7OVnuxwmc9F54wLrZQewe7Q2gB3ADmAHsAPYAexOlxJkiXFSKPbzVMBzKvYpR44sMe7nSDw15r31If2l9M0W8ev83u13P0mrF8yOp8mk1AGw+yBzxaFaqimtpMi2eqqZkkf1XSM+tIomwqoAYtjDatnEjgsx7InVN4ytI4Y9jFZN/JgSEcOe+F672wOncNywaVuLSkGGde4ogN2djU1LM7Dv+lc1lSwX4D4qh+oH5/jQKpoIqwIA9rBaNrHjArAnVt8wtg5gD6NVEz+mTAD2xKvo/x4A7D5oysD+zdJqar+wVoN1hnZsUMBKAQA75kY8CgDY41Ets+sA2DPb/vGOHsAer3KJrQdg96gvYtgRw44YdsSwy9OI18WVyBKjdkLGotNYnZAlRm3uOJVCDHvmLjp1mhup/hzA7tECAHYAO4AdwA5gtz+Rer2RMbYOYAewe7x0W1YHsAPYEzW3vLYLYPeoIIAdwA5gB7AD2AHsTpcSZIlxUij281TAcyr2KUeOLDHu50gm1UgJsHOuy737Kkx1DvoqXbNOcwx7RWUd7fp7DfXa1UDVU/OpoX1WJs0jjNWFAohhdyEWikYVQAw7JoNbBRDD7lYxlGcFEMMezHmQdGDnVDrtS4rp6fv4+VPh2CSw579ci9SO4TBpQkcBYE+ovKFtHMAeWtMmbGAA9oRJG+qGAezBNG/SgX3A2OmBfvRrPGaSwP7Nx/XU+3OkdoxHw0yqA2DPJGv7N1YAu39aZkpLAPZMsbS/4wSw+6unX60B2JuVXLl2I0277rdU+uivaGD/PlF95dOvjILL0B3EsCOGHTHsiGGX5weviyuRJUbt0oZFp7E6IUuM2txxKoUYdiw6dZojqfo86cDOITHjTxtGM6+8MFVjjtmvPqbeDNj/OOt5WjjvYdP+AtgB7AB2ADuA3f507vVGxtg6gB3AniiAALAD2BM1t7y2m3RgZ4+1HQB7HVC89e087AD2Jig3nsieeeJBuvgyADuAHcAOYAewO117kCXGSaHYz1MBz6nYpxw5ssS4nyPx1JC8p69b0q7I0jEbzz4SUSfpwM4x7HZbqrLEuAmJMfZRxrDzuGqerqa2VY1UdWUBNeYnwmRoM90VQAx7ulswNf1HDHtqdE/nvSKGPZ2tl7q+hz2G3Yz3rrjlHlq/cWugoT3pwJ66KejgAbKIYTfWYqPu2VtOL8++07TBrc8eoDabaqnosiLK6ZUT1OGiX1AACkABKAAFoAAUyDgFzIDdymkbJHEA7M3WUDWWLKf3sus97OsWN9DgZTVUMyqH6gcD2IM02YPSF3jYg2KJ9OoHPOzpZa8g9BYe9iBYIf36kAgPe9nuMtp5YGfSxejXoR91LuzcYr8AdhdmMMu8cufPr6IpE0e7aMXfoqrALvvumCWGxIOTmp+dlJUVoezsbNHhRvEiys8voEgkQlWVldogWrcp1H5HsrKorr6OqqurqKSkI5V06Ki9v2HdGjqu/0BqU1isxZGPOfNs2rF9q/ZZl67daV3Zaho2fCR9tnSR9nvVis+ob78TqKJ8Px08UE5DTx5Fz82ZRZdffVOLOHQZg877e31eKXEsNteRf3P7+jh1xLC3nHNGrYwzctPG9bS+bBV9b9IFLT6SwL5rT0XULlazece2rzW7nnvBNNsJr7eTVcGa6mrH/cm6dtlKjO2vW4sYdqmJ18WVyBKjdl7HotNYnZAlRm3uOJVCDHtiFp3ePP9memDxA07y+/75/RPup5+O+GmLds14jxOi8GYVPeF7x+JoMOke9oefepFmPftKi/SJUrwZl56fsuwxVsDOGWT0GWKMD36yzBIDYG8B/jw3jYuuzGDUDHisoNVsEZcdlFpBrR1w2gEUgL3pjANgP3zmBbCbX4W86mJsFcAOYI+Dd5SqANgTA+x3f3g3zf9yvpIN/Cx026jbaOIxE02BXf/mKUP7B/6BnkkHdgbgi84bFwPmDPJzX30vJQH/+rSObED9amEG9A2btkXtajQqgB1ZYpAlBh52eNjtL7EA9liHhZ9Qwm3Bw+6PogD2xAC7P9bxpxXViAp/9uZfK0kHdqsnnRpDTfwbYuJb0sew8942/KOWBn5TT9VT86mhfXNcTOK7gT2kiQKIYU8TQwWsm4hhD5hB0qA7iGFPAyMFsIuJiGEP0jAB7IrWCKKHXbHrlsWMwL5rfh31+rKOas4QC0/7YeGpV33DVh/AHjaLJmc8APbk6BymvQDYw2TN5I0FwJ48rd3sKeke9qDGsLsRzVjWCOyfrGmk0xdUa1liOFsMNiigVwDAjvkQjwIA9nhUy+w6APbMtn+8ow87sMerS6rrJR3YecBBzBITryFsY9i5UU4WgywxmrxYdNo0y5Al5l0t49HAIScpH3ZP/OleuvqGW5XLc0GzmF6VBrzEW3upy31DlhgVCxFh0WmsTohhV5s7TqUQwx7+GHanORDUz1MC7EEVI55+Adix6BSLTrHoVJ47AOzmZ1GvuhhbBbAD2OO5XqvUAbAD2FXmSSrKANg9qm4F7Oxa15abwsMeVRgednjYWYF4LojwsBOphsS4yaFvd/qLx05W7QHYkSUmnkutn3NQdf+p2Kfs22svlWrPUunSradqd30tJ1MVz/jJTKqpradD1fXR9ru2b+XrvtCYewWSBuycHYbzrHMOdrtN/wRR98NJTQ1jDDv34rOF9TR6ZS2eeJoakwR6r4hhD7R5Ats5VWAP7ADQsaQrgBj2pEseih0ihj2YZkwasAdz+P70ygzY39lIdN5bVdTQJ5uqJ+b6syO0EgoFAOyhMGPSBwFgT7rkab9DAHvamzAlAwCwp0R2x50mHdit8rCn8sFJjio5FDAD9rfLs2jyXyupsTiLqi7J97oL1A+RAgD2EBkziUMBsCdR7JDsCsAeEkMmeRgA9iQLrri7wAB7uj44yTKGPUsErzdqIeyUFYlQdna2+KuR36L8/AKKiPeqKis1M7VuU6j9jog6dfV1VF1dRSUlHamkQ0ft/Q3r1tBx/QdqmTU4vm7MmWfTju1btc+6dO1O68pWa3Fvny1dpP1eteIz6tvvBOJ4tIMHymnoyaPouTmz6PKrb2oRP/zMEw/SxZfN0Pb3+rxS4sWTMoZNLqSUZfLy82Nij/WfGesZ/+e+Ioa96ahElhhkibE6PyNLjNqVC4tOY3VClhi1ueNUCjHsWHTqNEdS9XlggP0Xdz1OHy5dSQvnPZwqLeLarxKwCxDPzuF87AD2MeMnUfsOnTStd2z7WrvJOPeCaVHtzRanmZUzuwHg92qqq6M3J0aD6m8w9J+tW2ud5cQOoMxuSvTtbtq4ntaXraLvTbqgRVcA7AB2AHtcp9toJQA7gN3bDLKuDWAHsCdqbnltNynAbpZ33azjd/78KpoycbTXMSW1vmVaRwHpjdLDDmDXbAIPe9PUBLAD2AHs3k7TAHYAu7cZBGA3UwBZYhI1q/xpNynAru+qVQy7P8NJTStmMezck6cOZtMNzxxEHHtqzBLYvSKGPbCmCXTHEMMeaPMEsnOIYQ+kWQLfqbDHsK9cu5GmXfdbUztwNsOZV14YSBslHdgDqYLHTlkB+9z8bBr3dCX13N9A1VPzqaG9lpkdW4YrAGDP8AkQ5/AB7HEKl8HVAOwZbHwPQ88UYC999Fc0sH8fD0oltyqA3Qe9rYB9dU6EvplfS+f8W+RjPyOH6vtxHDu2TFcAwJ7pMyC+8QPY49Mtk2sB2DPZ+vGPHcAev3aJrJl0YLf7KoIHmm4PTrKLYefxcFaYSKNYdBoRsJ6NRadYdIoY9ngWdeFJp3jSqf5CiBj2WCxAlhh/UCme85M/eyYK85NO63fXU8OBBr+kUm4nu0M2RQojLcpLDoWH3UHG06bMpNHDB9IpQ4+nP856PpoVZvL022n8acMCGztkNSxVYM+hHGrMBbAD2AHs8VwQAewAdgC7/cUVwK7McLYF4zk/+bPncAN75duVVLWkyi+plNtpdVYrKjilwBTYzRpBDLtOFbno9OheXeknv7g/CuycSUYP8MrWSHFBFWDPEtnYcxsFsLOHXdzoIQ870jrm5WbTrj0Vliko5bS2SmlpnPZWKSv15exSXhrbs0tnaSxrlxbT7PCM54IIYAewA9gB7Mm43MdzfvKrX2H2sFd9VEW1X9b6JZVyOwWjCij36JZPm4eHXVE+fZYY/luGwKTrg5N42FYx7PwZx7G/WNZId4m7S45h51h2bJmtAGLYM9v+8Y4eMezxKpe59RDDnrm29zJyxLB7US9xdZMew86hL8cf24t+/8trSP93uj44yQnY+fOrqnPpb09VIL1j4uZxWrUMYE8rcwWmswD2wJgibToCYE8bUwWqowD2QJkj2pmkA7tRBvayyy3dFgDIftt52LnMlUV5dPesA1p6x5opeVTfteUCiGBODfQqUQoA2BOlbLjbBbCH276JGB2APRGqhr/NTAF2M0sihj3E89sphl0beiQissVkU269yBkjWD2vdYF4K0JVlZXax63bFDYVE09Erauvo+rqKiop6UglHTpq729Yt4aO6z+Q2hQWE8fXjTnzbNqxfav2WZeu3Wld2WoaNnwkfbZ0kfZ71YrP6LiefejA1s108NtddOrBSnq6tpJuXPclvdeuiNru208nf72FHhh3Os1YuIiqc3Po/04+ia7ZtIX2i7+f79WDrqyup/oePWnW3m/osoFDKbv30fTR+jXUpn1HGjjkJG3f+rhp+YS0aZddq31m/J/fw5NOmw4EPOkUTzq1OiXarR1QBXY36w/sTs1+xvKuXP4pHTxQTiNGn+HL1QBZYmJlxKJTX6aWdo3la628zvnTqlorYY5hV1MApewUSLqHPWxPOlUC9qwI1ebkUKsakdJIPDspr43/wH5yr6Np2Scf0eiNm2hZNtGJH3xA+9q1o/3iZ8yCBfTgT39Kt919N82fOFEA+z4asXgx3fPzn9NNDzxAVQUF9Mz06drfXEf+zRNHlimoqtLqFovfwzd+RbUnDKIHTh5KV+S2ppyevWlfp040b9Uymjb9OgB78xG3aeN6Wl+2ir436YIWxyCA3f0FEYtOsehUfxAB2AHsiUI7AHspzfjJTKqpradDwnEnt67tWyVKcrSrqACAXVEoq2IqwJ4lgL1GAHt+bYPIyS6yxAhAzsrz7mHPOijCbPbupXVffUljX3+N3h87VoPzJSNG0ODly2lP/+NpX+fOdKrw7j/eqT3N6NCF3q+rpsLCIhrSqQs98cWndNmAIVRdX0/z/r2Kfty2A5U31NM/9n1LVx2soewtX9NDfY+i697/kArFPv554hBq9803GuwbYV6C/g0vvkQNxW1p99BhVHp0b7r8qH4a3Nf37AUPe/MkArAD2OFh93biBbAD2L3NIOvaAHYAe6Lmltd2kw7s6Zpv3U5opxh2rntHm1w68O96euSVQ9TQLZuqJ7dMM+TGkNlfb6aiP9xFrZ97NlqtoW1bqhl1OlWPPI1qRp+uQXIitsj+/QLkNxP3gX9ytn6t/c5d9QVl7d9H/LnVxtAu4b12wECqHThYhN30Iu57Jm2IYc8ka/s3VtWQGP/2iJbSXQHEsKe7BVPT/7DHsKdGVe97TTqwc/5Lff5170NIfQsqwP5xboRuacil5Q83AW3VJfla1hg3mxmoH7r4Uqo6+1yqmnSem6YSVlbCuxHm+X+AfJMCAPaETb9QNwxgD7V5EzI4AHtCZA19owD2YJo46cCuzwpjJonMyx5Mucx7pQLsXHPEEQX089cO0cUralznZC+6907iH7kxqFf81y+1UJN02KRnPnflCi3Uhn/yP/rA1isfVo88gD0dZmzw+ghgD55Ngt4jAHuCLVQu1qWFcCsWEQG1dQ1UqY9hP6pNCEeaXkNKOrCnlzzOvVWNYc/OFmEworlGEcPetj5PZISJUGV202N67bLEZFVU0JciS8yQZcu0xaK88HPckOG0rbopw4xVlpi+/U7QMrVwZoahJ4+KPlFTH58ns7xwVprX55USZ3gxZnfRZ4Ixxvb5lSVm8rBTtZAa9sKv2P41HRShNRNeezUaXrOpd28tPv/y2bO1MUuQ/8vQwTS+fWcq6XOMCLUZrIXW2D3N0+ppoHZP6rTLuGGWCUc/Y7Do1Pz4iSdGFItOXS46FWvFhg441fIEFqkVz1+uFicjm23RF+9RYetiGtTpROcTYXOJSIV50RU7l9GB6nIa1WuseYEK+74YK+2u+pbe3T6fLupzSfQjq30rd14UfGP3q9SvTX/q0+qYmGpZFd7grLTi/+jM1t+jjtlN2b88b8J+WXxRad7eaXyHuorX8VnHe27aroHZDbPpwsiFVCxeid4WNi6kQvE6MUt9DnrtUyr2Kfv8YuOLNFy8umd19zqMuOqXUzm92PAiTY9Mj6l/xP87Iq42Uck/BZIO7FZZYh5+6kWa++p7tHDew/6NLgktuQH2epHcsUqkbixsyKeCuiwB7AK6I1mWwN5BpH4s+Nc/aVXvXjT4y42Ue9bZ9OG2zUppHdMJ2M+9YFrUUvr0bzK8ZsfmjbSkYh9d+sabWvy8jJN/bMYMmjxvHnXeuVOrz8B+UMD7I+edQ9flFUbBXn4LAWCvjt64OR0ablID2t3wmO0n7YDd4EXLPmAyquYyX3wtwLSqnEYeO5ZMAdIETCM1or1m8Fpa3rSge3jxCO23HhI57WsD3/E3b1nl5pC7pHGJVuKUrFOczGz7uZ/g8nnj53RAvE7LOs1Tn2Tlb+lbeqfhHbo4crEv7clGXm98nfqJ19FZR/vaLjf2XMNzND4ynjqKVyI2ALs/qrqZ927DWp16+OKBf9ApBadQt5wUAXtDOb0k+vDjtlcI52KjIJbDW8lN7Zy6j88TrEBggH3eWx/S7Xc/SekWEuMG2IV/nQ6Ji25Wdj6VVApgzxLAnmMO7B0aGqnbRx9Soyi/cuhQOq5vf2otcq6r5mEPA7DLub9j29dajnkJ9hLkS7/6N036ajN1+/STKMhzikqZwlLWZ5Dnxa1/vHCKeOpsPeV079liwSs87LFnmcADezMgx3iKdXC9YMV86lrUnfp1HCAeDHD40qMHZA2K2dNcc/jz5fsFdMcJl17B1A/Y1trIEdDfpgn6rbbGIvsHuH24730qzC6iQV2Hql+GiszX5Th52BuK1HfBJXdX7KIFa96mH5xy2MNOxd4fSDd/8ct0bM/j6aiufWM6VN/0uIy4txdfm0NjRk6k9iWd4m5DXzErXzzfI//wO8jD7ousyMMuvm1HWkd/5pLfrQQG2H9x1+P04dKVaedhZ4OoxrBz2ZsL82hufjYtf2h/05NPz8jR4tn1G2d/aTez+QFEt95OFeIHm7MC8S54rRMwr4XZiMw1MtymsW27hGWvycgY9maQjnqn2aNcLUIMxG8NoLUDqQma9UCth2krj7LzzPBWIsaLlpclQKklmJoCpwm8mpYT4EU68NL3lvfTkNukS/viPCo/VKfFlmqbD4DqTRnUDroCiGEPuoWC2T8sOlW3C0eH8DbzygvVK8VZMinALr3nTn288+dX0ZSJo52KJeRzzl4z7brfUumjv6KB/fu02AenotywaZv23jG9u9HLsw8v/uT33AA7Z4v5QXG+WHharaV4ZBjgjDFyK3jjVSq5bKr2L4M6YN27ufULXnNXrxQLXfc7LnjlvUp4bxDwLmGe3/OaijItgV0AdwtvNgN4M2xnCeBuFF5qCdpRyDbE2Hq35OEWohBtgOcWQKwD5hbvGwBZD8XaHgIKwlh06ucMyoy2AOyZYWe/Rxl2YJe8Z6bbjEvPj8K3MUmKnv8kF3J53mY9+4opH/ppm6QAu77DQXzS6WlTZtLefU2rpYzAfsUt99CeveVRSGcjtS8ppqfvuy06LDfAzpU4W8wWEbsuvex1J+dQrfjhhZftJ0/QYrQB635Oc+u24vHKS5jnB0Q15ZLvqf1oYN/8kCi73qcc2AVsRz3dOvBmD7cRuv3yakvAjoZhiHvUhjwRjiI8yI3iN29RqNYBdQuYDihIJ2emqi86TVZ/sJ/gKwBgD76NgtjDTAF2MwettAdz4ejhA+n3v7wmaiLmP6PDVkJ9MsK5kw7sQZyc3CcrDzsb7WczpkY9//xtwR9nPR8N3XEbw85fblcXtKKK7AgVHzhE+XWNVBgppMbWDeIhRJupTnxeKWKuj+jag0o6NC1O2iCyxBzXfyC1KSxGDLtuAr1YOpvGjJ9E7Tscjgn1M0sMw/znC9/VUk+O3r4j5gFR8umuNz3wQMy0Zk/8mqEn0cpj+tB5kbwWQF/QqYRyO7SnXXsqHBeBGuP3zY4fzhQx+5kH6UcTrqF8saBZPK62CbwZwJuzdvDixZryKuIMD9dGmsKt7DZjLLUG3DpvNsO1hO21362m7Qe20rgTz46GdnC8rzHGVu4v7RadOoml+1y/aNpFtWhRu7UDqh52N+sP7PoYj52s2vOqi7FdPOk0VmnEsMdzxMXW8XPeu+3Ray+V0rDhI6lLt55uq/pSXmY+C3sMu11EhR0P6kXOCA+7L7MqAY2YGVDlvXiAPSe/gHbmZFPrQ4eotSD0ooY2Aqx2UKSqgmratKHKI46gkpKOAPZmO1tBa6KBnXdvBT8M8wd37aSXl35IVx2o0vLKc475iEilKR8SVdavH60YMoSmlpbGzNjGdu3owFFH0yPnTqKZ335HdWIhbCMvjhWgzzH1HEPfWNCWdmwUC26/+IjOH/xDDb45/CSLY70FpDOESw/4Yw2Paam48q2CoUUPqsWLgf2adjNIerr14M0eby0cRDD/p2sXaZ7voac5h6iFPkuMi/ONVzAFsKuJDWAHsKvNFPelAOwJWnRaVkbUnNHNvVU81BDXYercuUUDTsDOhdlZW9KuOMajbuxJ6GLYjQPUh6AYP0vG1wpmpleBc7M7LyVgF+kZc0QedpmRrUBkMvlWeNgjAtjzBXsdcbBWgNe3FBHlanr0oKq6eurQsaP4afIcl61ZTQMGDqLiomJa8N47NEE82XSrAETeuotQjDWrVtKIUaNpscgqw78//+wTOn7AICoXnuHyinI6deRoevKxP9P1N96i1ed2hp40nB556D666tqfUHVVNc19/q901TXXizr7o39z+7JMvrjJ0Nc1fmasZ/yfy//1mafoLNH3Tp2O1Pq+RaRo5D7/cNqPoiZZ9ulSrc9jx42PvmdWzqw9fo9zysuxGu2sH4v+s9UiFIn1ZF2N28eLFmpvnToyNh2d2Rhl/cjmzfTlRwtp1Z5v6fsVB4j/55+srzdpv3kzy2ij3z8D+6ZjjqMFp59G/7FoOzUcIaBevNdYUEz1nQc2/d1K/Ai4f6x6Fl3R7SrKby1ouxm6SXjF2ctNBaJVEc9dI1zxT85+VJsHTpvduI117fQz249xHjn1hT+/7w930S3iQWFutvlvvqYdHwNEmJKbzWwOqtb3Upf3Yad764IcqqqppwaRQcpuc2M7u3bisZNVe151Mba7a9c39Law7yWXX6lqGqVyr8z7u3buPKbvsUrl3RQynv/c1FUpazbfs7OzKE84hyqr+btbf7YnH3+ELpp6CRULB0OiNz/noGpfU7FP2bcXSv+mXcN7CKdNKjZ5TbvhhhupXpxnogvcRWeKWud669LNNxOZfBvtrVGF2vffT/TTn7YoGG8Muz6+XWHPvhdJekiMWQy476OKo8F4gZ13VV1bTzW17h6q8beciMgVnk2nf/UVLThxqBZ2cWj6n6n+LnEBamueGi2OYaFKihRo/JYXZYo8tiITEIl82fw7q5wnSyM17KqnyHdfhLZRZwAAIABJREFUU1aV8MbvFItgRd7uyD7xf+V+7Xe2+Ins26Lcc80b306Ae8/e1NBLeOeF95699Y3CW69luxHvkSwjfmNLTwVUgT09R4deJ0KBRAB7IvqJNoOlQIFgE9+B/e67iebPT/5AbxPrDcUDJ/Wbiofd2FH2pPPC0lQmR0k6sAdx0Skbxk0MuzFfvNtFp3Ii8OLTh75/IU0RD/+p6z2KKq54NSZrTPJnN/aopIBcuMnx4iJUJbInNkzFtp0CsdiyUPwIL3ij8H5z+ElDh6ZwFG2hZfssbfExPyiKQ2wi4oaOw274R/ub39OF3yj1ubkQh93wglleJMt/M9zz/7xwljftcwZ98V4i01u66TPKYtEp5oB7BbDo1L1mqEGERafms4CjQy46b1xSUjia9QDA3qyKFbAnIkuMNATHq5476Xtavu89r3xM2Z930WKS6wfnUM2olrnZcRJJvgIM4VqKQuEt56wqWbub/s/a7fxtShOIR5oynwgg136LUBWG8YKuOZSXm037DsgE5N7GxmDP39DkNMM9p63UYN4A91xGPiXW7R7l02Kb4uubYF+CfhPYN309rod9+b/bfaG8uQKqi06hHxSQCgDYMRfiUSDTgZ2Ti/yl9M0W8etBeLhn0oGdQ2LGnzYsZXcoZpPXGFNf0q6oxQOc7PKwK8WwZ0UoW8Sw85NOOfqU48E5Xr36u72CcEQ4TV4etTmihPIas6h+f62ImqimkqIOdETvphh2ZIlp+aRTaUM/Fp0ylK9bt5K2b91C47tOiIFyqydP8hMG97c7SPN2v0CXDL0qCuTa0xCb0w9u2rie1petou9NuqDFtJNpHf3KEsONP/PEg3TxZTMoL9/iCTyijMygc8WEKVHvPHvr9YDPbbH3/qNu4uaxuprGLHjPEfKXi4W1m3v3psnimyKrTQI/w/0/h59MhSJT0knf7W+CfOnZb/6tB32+QeBt1ivP09U33Orq2mOWNUOlAS8LR73U5b5h0amKhYiw6DRWJ2SJUZs7TqWw6DRBi06dhE/i5yox7Hruk11L1RpLuf+kA7sxLWISbZSQXcUL7Nk1NVR1oCnn3jdHHkmtBcB3Fo7buqpaqqmspvZZ7amkU0dq6BQBsG/zBuyc9jCyp4H+8urDdMngq6jVvjztmwzpKV/TuIa2i9f4rMMLXdku7CVf0riUqLXIlnLMqU0ecvaccyiL4GKZAmvaZeZpEoMK7JdffZPjsWAER5n5hr34GuDrQH9NbRVtFcsuzilbF/2MPfxWHv35Ip6w7b59NGLxYsd+yAK/ueMO+rX44Y2/keJQHblJqJeef/n+G0cfRd3FwqkB4smg8qZAfiZvIPh/WV9+tnzvt3TwQDmNGH2Gcv9kQQC7uWRedTG2CmAHsLs+OBUrANjDD+yKUyFwxZIO7MYnRxkVSfUdjFsLxQvsObu/pUoB6Q2c4rHkCG23vYX7PauujmoOVVH7+vbUobGDAPYsWre/DHnYly6icy+Y1sI8Rg87g3ntzkr6vzcfp6sGXt/kLd9dLzzFTdXMUh8yeK9pVUbbsrbR2OMnRKGcY8h5s/N4ZhKw2x0XTmkdZcgOt8HA/+G2zeIZBAfpxFZtot59/oxDeOSmv0Hg9353xY+jwK56jL48ZQr12rSJhixfrlpFK7d4xAjx7Uk7mvDWW9r/erjn/2X8v75RWebTI9pSRW4ujdu1O+YmQWtL9y2CWf2lO7dqbw/v3F37rb+ZaF+cR+WH6qKZG4z9ku0hD7src7co/M83XqK+/U6g3n36xt+IRU2zbwT93IlfHvby6v20v3qfZdfef/E1Gn7WOGpV2MbP7pu2Vfbp51TQug31Pt7/rD1WnbfbZ3nNfiq30carIF8tXEOd+nenNh2KvTYVV/2aQ9W0SfRh6JTh2nmGE2rI7fuDxPURW0oVSDqwp3S0Cdq520Wn+R99IJ5oOlHzFO78cgfdXJhHc/Oz6aLqerq/Oa45u6yO8t5tSsXVcFQ21ZyRq3l1sTUt8JSx5Tk7mhd76sDcTKNGsaCTveMM4nJxZ0N7jilPvqIpf9Jp8ofs6x71NwDcMN8E8CY9/3JnLW4AdDcD/Lm8IdDXj9YTIUHpvhm/hTAbj/GbBdPjpnm9gqoeVjckTvWN9bZWHL55c6q7pbnsPpG+lH+cNgau/QJK3WzGtrkNhje/NwZlBmbVbROSPqlKhXIeFWj8tX06WY/No7qCAgB2BZGcirgFdoZ1hvaKW2/XfrZEsogzxvC2+Lsq6tGcZzmyvZ7y3hQ52oWHmGGz5owcaujKsfCZsWlgLkJXImKRZzQLiw2YM3w3dhD57juItQAcS96xaZGn9JYHRTUAe1AsodYPPdxzDQ734ZAg/WYsw5/pbxhkWbP3tLK6m4StFYdvGMzalW31tnaCqg0MpaAAFPCkQCbdMPX+DsDuabL4UDklwK4P5pc5LTlU5pSh/enp+0TOzDTb3AC73ru+a1mZ5mXnzczLzu8zsOa9VSOgtelg4QwytSflpMQznCizGMFcH19utk8zME+VtzweTQDs8agWjDpbyptgWg/V7K2VX5PrPcPS88vlZT3+2+id1X/m1yjbVYnUbOLHblMBfrN2ehRbP9RlVL39A1/a5rel4vxYt7BKX5y0kesqnMrF8zm3zTdqQdvsbuiC1lf0J80VkE9+TPNhpHP3kw7s+gcncXaWn82YSlMmjiZOSj/31fdaZGdJB2HdxrCLR3FSqwMiR6B42milyA7DW+s2hVQnQqY3iSfS5dbWUsfKSmpf0pFKOnTUPucsMf2PGEDFe9rQwtqFND53PG1tt4MajxALVXt0p3Vlq2nY8JH0mYjz5t+rVnymxWFyjDUvnht68ih6bs4s4sWG+gU1MrMIPx309XmlxIsnjXHZ+uwjxsU4+s+M9cziu1/822wad8JE6lTTQfOYb9+9hZbuX0wXZl0YNfXnjZ/TAfE6Les07aaEPeZbC7bS0l2L6fwzpwpv+eEwFj+yxPCO7WKwEcM+yvEwdIphNzYQz6KuJ/50b9xZYjr36anF5Mr4UwnY/LuiOaxBwjXDc68DPahVfQG9E3lH67oboB5BI6ideL0lXvFsY2kstRVAuyz/c616cd5hwM3LyaK6+kbqVtQSinsUNeXPl1v+tmwBxW0p/yj+munwZgbaDM+8D+PGfVjzyWfUprCYBg45KZ6htKiDRadE6RLD7mTs0jmP0TlTpolLWOKfdBrPucKp/06fu9mn3zdMryx6j046dgB17dCUIS7ZW8Whg8R9uG7yBVoMe6UI05XbkSf2S3Z3sD+DAkkHdvaklz76KxrYvw/pgT0IOS7jmR2ugF3coWZVHqICAeSNXbtRlYB33hjYefsuO0Ll9XXUpkqExRzRoQWwH9d/IBXmFNHHn76nZTPhrCa8dTmiO63NXktDTxlFn30eAGCfcrWWs7xiyz56ZcVcuvzIK6O5y59reI7GR8ZTR/HibWujAHHxuqDjD7TQFQ5l+bxaAHuNyNAx7szotwg7PGaJkXa1Sn0IYI+d+W4WLiYL2CdeNjUGuqVHm4FbxiZLD/aIg6fQ+vp1tFy83Gx20C2ht7sOmvVe4z4He1N2TRZV9ayn7jqQNsKyvr7+M6R1VLMUssTE6uTXolMnCwDYnRSK//PXXirVnG5durW8CY+/RXc1paNtxk9miqe319MhHbB3bd/KXWMo7bsCSQd2hvQ///7mGGDPCA+78J5n1VRTPn+11LETVQlw1wN7vYhl39lQTzkC2Avbd6BjhZedN2Me9rHDJtLOMvHEy0NEXcWrTLyG5w2nJZGlNKzvqfTF3uXUd1BiPOyFBcU06KhhWqjOX+Y/TJcefxUVfJdHFYf200t7/k7TI9O1PpeL14sNL0b/5/eeizxHZ3aZQCVdO2kLP7eXb6FPN3xM53z/cPYXM08cgD02Q47xTOAmD3s8aR3tzjzxAnu7Ph2joSXsxWb4Zi84e771oSfsHb+l+ma6Q7zcbFNoCm0Sr435X2lea723miFZA+1m77KEa35/94YdVFdZQyeNPF3bnV0IiLE/Xj3JAHY1CwPYAexqM8V9KTcedvet29cAsPutaLjaSzqw/+Kux+nDpSu10BfpYT+6V1eadt1v6fyzRtLvf3lN2imsGsMuF5vuefktqh7VBAPGjbPFcDw7Lzx9YX91dAGqWVlejJrzRR1lbRdP4twW+/RNLWc4Z0cRT9psFNE32tM2eWt+sE9Mm+XNbXDecn4IZ4VY8Mm/xf9ZFQ0apDttMoyF96Ut9mzOXR60hZ9O40jk52GOYecMF1vEoknp7Wbw3nbgaw3AZShK0+fu44EZnCV0S6+2DAdh4ObwDvk+l9MgXUB5WDY86TQslkzeOPCk0+RpHaY9hf1Jp+lqq6QDOwslw1/0os249PxAPf3UjUFVgN1qsanZfs5qm0+rcyIt0jw69kfAdvZXTdlUsgXAq8C1Y5smBbQ0iEVN2Vei2VgMDxSKp91MqpPOwL569xcajEuPOIei8N/aey5BnAFchobw33r41oeehA28453rAPZ4lcvcegD2zLW9l5ED2L2ol7i6KQH2xA0nNS2rAHvRvXcS/xyccQPt/929th3Vp3n8e3k1nVob6z13Gil737MOiJj5b8WiEfE3x5U3Vjd5yCNND1iN2aQHPothnD3yvCaWvfG8+JPfa37Cp9O+8bm9AkEGdgnkq779ooVnfPXuFcpecQni7O2WXnH2gGt/C693DxH/HSbPd7LmO4A9WUqHZz8A9vDYMpkjAbAnU231fSUd2K+45R5asmwtGZ9omq5pHVUXneaI2HUSseuN4smmea1bU0Q85dQYwx7J4iwQdSKRTBVVihj3z7p0pmJRZ+DKldRPLDrljA0cXzfmzLNpx/amJyJ26ZpGWWJKZ9OY8ZOoffMKeLPYdMSwtzx4reL3jYe4agz7/z3zKB13zlAtPGWN8JYzoPPfRiDnbCW8LRAv/Tagw6Am6G72iDOIF37XmmrF8wPGjT9XCcTjiRH1kiXmWHHsuNm8xKF7qct9RAy7mqUQwx6rExadqs0dp1LxnJ+c2lT9HDHsqkplZrmkAzvHrV903riY8JdQLzoVcytXZIRpFEDeIGA9X0C7E7CXiAWn73brTAdF3aGrVtEQkaYRwH54cSofrkjrePikZQR2BnEOVWEol2ErG3aX0ZXVV9Dd4mW1SSAfWT+C8rML6OjBA7S48AEdBlvCeLyLTt2kCwSwi3XqIlRu38FaLd2a3eYmw49dO36Ci9cbGWM/AewA9kQhm5/z3m0fAexuFcus8kkHdvaky4cl6aUOdVpH4SXPramhhtxcEWqSpwzsecLL/mpehI4TwF4wYBCNaFUID7tu0gDYSfOQM5h/PX8tfdpjOW06sFF7z2wroAK6Wbxe6fC65iFnOJehKhxLrppe0Ng2gP2wIl7BFB52tQswgB3ArjZT3JcCsJcS0jq6nzfJqJF0YA+bh52N5BTDrpIdxsrYMmsMf75YhB1w9hhs6a1APDHsTYs8N9PH2xZGId0KzFkd6Sk/oeMg6lbYk/i3nZc8vRXNjN6retgzQw2MUkUBxLCrqIQyRgUQwx7MOZF0YOfQl1nPvhJ9eBLLsnLtRi2tY7pmirED9sj+/dT56C7U0LYt7VpWpv12u93XKof+2DpXKdWj27ZRPvkKOAG79Jov3r6QePGn3YJPBnPpLT9e93fyR4U9JloBAHuiFQ5f+wD28Nk0GSMCsCdDZff7SDqwcxfN0jqahcm4H05qatgBe+vnnqV2M6/V8q5z/vV4N5nqcYCIX/17eY22GBVbeiqgB3ZVOOesKuwhZ0/5iK6naXHlp3Yzz+Wfnqqg104KANidFMLnRgUA7JgT8SgAYI9HtcTXSQmwJ35YyduDY5YYAdaR+nrKzs6hxlzxI7qmuui0pMPhJ512PX4glXYsoRFvv03bzzmPxm7cpA0SWWIOZ51hPWrE4t7n5swis6d5WmVSsYvBtosplo9xnnbZtaYTbtPG9bS+bBV9b9IF2uf8sCD2ln/6zUf00dYPqOybtaaLQKXHnL3ng/IH0/71u+n7P5huO6lVs8RYaWNs3M3CRcSwH1YPMezm09SrLsZWEcMeqzOyxPhz3UcMO2LY/ZlJ/rcCYPeoqSOwN4iHGfFPvkhmLrLExAvsx4nUdLVFbals4b9o3uTJdNbGr2hIXSOAXZcmMmjAvnD5P+nLf6+lFR1W0+pvV8QsBuVFoLdk3ULLjlqpxZyf2u20mDhzv9M6AtidD3gvcOmlLvcMi06d7cMlAOwAdrWZ4r4UgB3A7n7WJKdGSoCdF57u3Wf+9B5jfvbkyBD/XmyBncNW2MPOPyKVo/jHE7DLtI7zzz+fjvz6a+LwmPFHdqN1Zatp2PCR9NnSRdrvVSs+o74iDSR7gA8eKKehJ4+Kep31JyPpleW876/PKyX2FBu9xnrPrfFEpv/MWM/M+2zM6hK2POwc3rJIeM459nzRtg+oa3UXGiJepeIlNw5jGdJ5MI3pNZa65fWlhS+9bvptgCwPYG9SAmkdkdZRf5YGsAPY479q29cEsAPYEzW3vLabdGCfPP12al9STE/fd5vXvgemvlUMe5tZf6K2/30rHbr4Utr38GO+9Xd1ToQ4pp23nx2qpVsq63xrGw2pK2AEdA550W8ytIVjzjn2XMacOy06Ve8BSmaSAohhzyRr+zNWxLD7o2OmtYIY9mBaPOnAbpWHPZjyqPXKCthLLptKBW+8qsE6Q7ufmz7d49VVdXSHeKAKtsQqwKkVPxae8/lfvaZ50M0AnaH81K6jNTjX5zXX9wzAnlg7hbV1AHtYLZu4cQHYE6dtmFsGsAfTugB2H+xiBeyczpHTOn6zbC3V9+zlw55aNvFxboSuKMqjchEbf1F1Pf1GQDuyx/gnMwM5gzkDOoM6A7vRg64C6MYeAdj9s1EmtQRgzyRr+zNWALs/OmZaKwD2YFo86cDOITHjTxtGM6+8MJiKuOyVZQw7t9OcejFLZIjJzs7mN3yJYR9z5tm0Y/tWracNPXrSgnWr6Z0xY+icBQvonGEjadfyTxHDfvVNMZZUyRIjw1wkpI+lsVo7C8SLUyuOFJ7zCUedq3nQ24mXjP03mzbGLDGyjAT2XXsqLDPayLKIYW9SAjHsiGHXH2OIYY894yBLjMuLt0VxxLAjht2fmeR/K0kHds7B/sdZz9PCeQ/7P5oUtOgI7ML7nRXJThiwc1rHlf9eTX89Yywd/8EHtOb00+mSjxbTsOMGYNGpYT5YAfsbi/5Bqzcup380/D3Gi35p8eV0dLtj6YRhw2LynrtN6whgb1IgngsigB3ADmC3v8AB2P0BgHjOT/7smei1l0q1xBFduvX0q0lX7chr2oyfzKSa2no6JL65l1vX9q1ctYXC/iuQdGDnGHa7LTRZYniQ7GFPArBzlpgep4yi1z9bRK+PHUujlyyhY447gUbs2YssMbrJJoG9iqrorY2vRGPR+1QfRb3Fa554cdw5e8/Zi87e9A0rVmktDB0+KmbaAtibJEEe9sNTA2kdzc/uXnUxtgoPe6zOAHZ/AAnADg+7PzPJ/1aSDuz+DyH1LZrFsB85tD9lf72Zvl2wmGpPGJS0Tt7RJpeeKMjR9seLUW85VIe4dqGFXDA6t+xvWjy6fuMc6CO7Hw51SbSxEMOeaIXD2T5i2MNp10SOCjHsiVQ3vG0jhj2YtgWw+2AXI7DzQlNecNrQti3tWlam/U7mxsB+X+scbTFqj4ZGuv9ADZ1a25DMLgRiX3aQzl70i/r9yDabS6IGAWBPlLLhbhfAHm77JmJ0APZEqBr+NgHswbRxSoCd49hvv/vJForc+fOraMrE0cFUyaFXRmDP/+gDaj95ouZZZw97KrYtkSy6UmSQ4ZztmeRtt4P0iX3Oiy4YtUq5mAxbAdiToXL49gFgD59NEz0iAHuiFQ5n+wD2YNo16cD+8FMv0qxnX6HSR39FA/v30VRZuXYjTbvutzTj0vPTLnuM7aJTHhzHsGdFErro1OpJp7srymlhZQX96cxx9NMHH6S//detdNvrb9IxrYto4JCTKExPOp279lktJn3Bxn/ST8XrbvHiTUL6xD7n00tzZtPFl82gvPymh07JzS4G2+5R8Yhhb1IQMeyH55LXWG27+aYK7HZtuLkM+RnL61UXY78Rwx5rScSwu5nd1mX9nPdue4RFp24Vy6zySQf206bMpIvOGxcD5gzyc199L+2yxwQZ2BkoDx4op7qRo2nF07Porttuo4nz51PvNkV00/FD6aXHH9AAtrq6Kpqe0Aih+swqxhOZ/jNjPTOYfbF0No0ZP4nad+ikHWVmKQvNLuxWqQ2fffYRWlNSRvO2/z36EKMCKqD/jPwntR/XIybcRSWto/HwB7DHLrY1agRgB7A7XTYB7ETG85+TZm4/B7C7Vcy8PIAdi079mUn+t5J0YLd60qkMkwlVlhi2Vwo97BLYh548Ssv3vefGn9H6he/SLhFTv+aUU+jme+6l718uPM5VlWkD7Bzy8kLZX2mu+Dmn/Gwts8tO8eKFo1cNvp5O6ngqLXzpdbo8zjzsAPYmBdx4aQHsAHanSxOAHcDuNEfMPk8FPKdin3Ls8LDHM0syp07SgT3dPOxm8fY8PfQ3FvoYdrnglMts330ocDOJY9tvLswjfkoqb7wo9ZZDtdqTUoO8cciLMcMLx6FzyMuVg67X0jGmy4YY9nSxVLD6qRoSE6xeozepVAAx7KlUP333jRj2YNou6cCebjHsKg960gN77qovqOPYESldcKoy1RjY/9gqN9Dgzt70+z65S0vDyH/L7aL+l0YzvKiMNWhlAOxBs0h69AfAnh52ClIvAexBskb69AXAHkxbJR3YWYZ0yhLjFthbP/cstZt5LR26+FLa9/BjwbS6rldz87NFCshcYs97UDzuZt50GfLCi0eL85ObJtNvIwLY/VY0M9oDsGeGnf0cJYDdTzUzpy0AezBtnRJgD6YU5r0yu7nQh8PYLjoV8eu8pSpLjDGGneO69fF5+iwxc+eV0hM33URcZ/ozz9DTN95IV1fWUclDf6T/aM6skshFp9KbXv7VbqKqRnpLvORTR6f3uIq2rP6Szr1gWgsjmS3iqqmu1uL1EcMeO5/ttDGWRgx7OY0YfYbrU5XXWG1kiVGTHFliYnXColO1ueNUCjHsWHTqNEdS9TmA3aXyV9xyD+3ZW04vz75Tq6kC7JFIhHJycqixsVGrU1BQQPzeoUNNMe5FRUXab36vtraWqqqqqFOnTnTkkUdqdVatWkVDhgyhtmKx6HyR5WXy5Mm0eXNTiEivXr1oxYoVNGbMGHr//fe130uWLKHBgwfTvn37aL94iBO/96BI63ibyBLD9bmdESNG0D333EM3CUjn/T0jIJ3/flLU+VL8fbf4m7dfiDL54u/Jos/f6OryZ7I+j4f3Jdvgz4z/83uPPfaY1vfOnTtrbW/atIlenv8yLWi3gOaVzdPeGyFefdv0pTPGn0HTh0yPluOxXX755dr/cjO2x+/zWORYWxQ29Ff/2fLlyzU9uW/GjffLG2to3MzGqC9TVlam2Wbq1KkxdZ36KiuwRmZjVx2bvpydNm7GbSxrp5/ZwPVz0FQYkzf5OPv1r3+tWlwr9/LLL2vHBx87brbFixdrx82ECRPcVNPKeqnL9e3mm2pn/GiD9xWPnaz66FUXY7s7d+7U7HvttdeqyqJU7vnnn9fOnf369VMq76aQ2fnKTX2nsvHOd6d2jZ/z+ZXPxe3atXNb1XV5P+eg6s5TsU/ZN76G8rWmd+/eqt31tZzTNc3XnaEx1wokDdhl7LpZrnW7z1yPKMEVZM546WVXAfZ08LC/Ljzs0y67VvOw89+9rrxOi3Efc98f6AGGegHlP37zLTqlVSGdN3CYpnK8aR1zi/LprY2v0HMfP03HH+pPs8WLN45Nn1RwDhU1FrbwblqldYSH/fBkt0pZqT8c4GFXOzl48ZJ7qcu9g4ddzUbwsMfqBA+72txxKgUPOzzsTnMkVZ8nDdgnT7+d2pcU09P33WY6VqPnOlWCOO3XLP2kXHQqM8Q0CA/2zi93ODWVFp/z4tT5edn0vIh1L28O8SkWXn8Olzm1roFOrW1QHofZIlIOe7nl5F/G5ExXbjQNCyKGPQ2NFoAuI4Y9AEZIsy4ghj3NDBaQ7iKGPSCGMHQjacBulX9d9ieoedg5DeXCeQ9HZTO78ZDAnv/RB9R+8sTAZ4iJZyoyrDO0M7zLlJDcDgP7hJp6mirSQjLIm20S1HkxqdxO7Xa6lumFveqZtgHYM83i/owXwO6PjpnUCoA9k6zt31gB7P5p6WdLAHYHNRnQN2zaFi11ytD+Md8SSGBvM+tP1Pa/b02bDDHxTiQzr7sZvHM6xj8ubUrLKDcGdH7AEWd9ydQNwJ6plvc2bgC7N/0ysTaAPROt7n3MAHbvGiaihaQBO3uqfzZjKk2ZONp0HCrpExMhgNc2LWPYm8NHuP10jGHneHbe9LHRxti+2U88SMeIWPcH2hXRlgP76Qdz5mjx7rR8NnV/93/pBxXfowfES2Z7GfHNMBp/1hRq36GT1rZZbLpZDDBi2BfFZMgxzlvEsMceyWYxvSrHu5c4dC91uW+IYVexEBFi2NXmeyKAvXTOY3TOlGlUVJz49LqpiCdPxT6lNfGkU7XjP1NLJQ3Yf3HX47Rm3eZodhWj4E4x7kE1UCYDux4Sd1SU0wtzn6R78p8UKWI2UTvxmh65ih44bwAN6H46TWzdgzrOfoomnXk2gF2EFuXlZtOuPRWWKSjlfLe6WQGwO58RAOyjnEWyKeEnuHi9kTF2E8AOYPc0uZM07932EcDuVrHMKp80YGdZ2cvOmz4mXL6/d18F6fObp4sZAOwzaN7GufT4kodowoHDHvUrB/6cqldV0yM33RhdrDpDpHX85/nn07CSTiL2vZ6GfrWJypZm6K0SAAAfmElEQVR81MJ7DA97y5kPYG/S44k/3UtX33Crq9MCgB3A7mrCiML/fOMl6tvvBOrdp6/bqo7lzbJaOVZyUQBZYlyIBWA3VUBmiZvxk5lUI67Rh8TaNLl1bd/KH4HRStwKJBXYuZfsaX/l7UUtOmwWFx73iFJQkWPYD+7cQ52P7qLtffvupvzqYd94Eel9n9xFvKiUN5nxRb+QlBerrs7J0harviV+5BNVpTYDRKaZkeKHF64OqGu0XLgaJi0Rwx4mayZvLIhhT57WYdlTIkJiwqINxmGtAGLYgzk7kg7swZTBW68Y2A/9+0s6UixIre/Zi75ZttZbgwGvrQLqVkNgYGdwZ4BnkJepImV5zjpzQn0DjRC/R4ofq8wzAZfItnsA9nS2Xur6DmBPnfbpumcAe7paLrX9BrCnVn+rvQPYfbALA3vtP16iksumUtWk82jvnOd9aDV4TXgBdbPRSO/7xzkRWiRiuvXpIo0e+OObc773aDBPHRk8tax7BGBPJ2sFp68A9uDYIl16AmBPF0sFq58A9mDZQ/YGwO7RLpkQw14woh3d//ndNKC8P+0Tr23FO7SHHVV+uJcuvmwG5eXnR5+QKrPLyFg4+T/LbIzhNMZnM8C//8WntOFgBX101oSoB773pk009v33abZ4HDZ73Nnzzh74vDlP0bgzJlHPDh2jVrR7mqdVJpV1a1fSju1baYxYEGvc7LJ2mI1RX3/TxvW0vmwVfW/SBS2alcCORacnKR99iGEnUgV2uzmrLLgoiEWnbtRyLosYdmeNjCX8nIOqe0/FPmXfsOhU1UqZWQ7A7tHuYQZ29qh/++5muq/xPqoSrx/mXUTDeo2gSyfM0FTTA7ARXuMBdm5Tv+hUeuBXbd9C5R9/SE9Ov7xFCA0vYp03eTLldjpSxL83QXy3ykra9eSfafrVIr2kYQOwVztmpZGSuYE+uxses8MrngsigB3Arp9LyBITe2Rh0anHi3lz9XjOT/7smQjA7peS4WwHwO7RrmEE9rkiPeMTeU9qi0l/Ll4vFP2Dbhj+n9RzTzdqU1hMA4c0eUYTDezSNHpPPMfAc+jMGhFGUyzSRM6bfD592aVpsS9vBVVV9NMHH6Q/33qr5onnEBoOpxlQ30ifPHo//UfzNwJ6s8PDHnsQANjLacToM1yfHbymL0QedjXJAewAdrWZ4r4UgL2UkCXG/bxJRg0Auw8qcwx76/59KfvrzdqCU154mo4bP5H01wtvpdW7v9C6b5b1JYjj0kP8quyI6WJW2W8GePbG60G+h4D5ZC5uRQx7EGdR8PukGhIT/JGgh8lSADHsyVI6XPtBDHsw7Qlg98EuDOxFbfK0lnZ+uYMa2ib+CXA+dDvaBHvSOT0jh8CkE6jbacAQv1p44fk3e+PZK29MKamvrwf5bgLg9f/7qTW3BWD3W9HMaA/Anhl29nOUAHY/1cyctgDswbQ1gN0Huxxcu4HaHN837VI6moH6Rf0uoasG30DF+el106FqRumN3ypAfovwxjPI78+imPSSZjBfLBLUcHhNW7HwlUNs4vXMA9hVrYVyegUA7JgPbhUAsLtVDOVZAQB7MOcBgN2jXdIxhr02p54+iSyl3KX19IB4FYjX9bk30HkX/4jaidfr80pJZnfRx6kbY/tSEcOuN5dZ1oV4s8Rs2LGVIhPP1bzw27IFzDd76I9e+IG2ywVjxsTMlHb79tEVzzxDL8y8UQuz0QM9e+hz162j70QGGmSJaSldPDGiWHSKRaf6WYQY9tgLFxaderyYN1eP5/zkz56x6NQvHcPaDoDdo2XTDdjnvPIIvb/rXXqr6k1tQenmY3fQNSfMpGXvLNQg3ZjdJVOA3S6t436RbrJ61GktYJ6Bfn/FfvrBnDn0wE2xGWl4WvUrK6MhK1bQRz+8iIoFwDPEM9T3ER79o0T9yL4D9M2Tj9L4a2/SPjPbjKkvraarVQYcfXm7mxlju1h0ikWnfoKL18W4xvkJYAewe7x0W1b3c9677SOyxLhVLLPKA9g92jtdgH3OXx6mJ1s/Fc2lXtHhEP1H+VT6j8t/QtXVVVGvOoC95YRwysP+qvg2YvAV12kwL73zDPirhZf+iPX/pu5ffEGlU6eazjKZ0ebu227TPteAXgf2HHrTTeSgz1m0kLr88EfRz9sKtjcukgWwqwGMyuHuBS691OW+IUuMioWIAOxq8z0RITGlcx6jc6ZMo6LixIdNpgKeU7FPaU0Au9rxn6mlAOw+WL720ssp969zaP/v7qWDM27woUX/mgjjglL/1ElOSwzy5c1AXy6869/kZdNWET+/u75Bg3z5mdveSMBnr7300PcQbRaJ/xn2+X3+3V3E2/NmBvpu94nyqVMAMeyp0z5d95wIYE9XLdBvdQUQw66uVTJLAth9ULvu/MmU8+ortHfO81Q16TwfWvTehBmoXznoerp6SLBuKLyPNP1asFp0agR79tRzPD3/ZtCXnzstknVSRMI9e/P1sK9BvnhPAj+3I8tK6Ne/57QffO6vAgB2f/XMhNYA7JlgZf/HCGD3X1M/WgSw+6BiQ+/eFNm8mb5dsJhqTxjkQ4vemnhi+Z/oqS8e0R58xNtF/S+lW07+pZZXHVvqFfArS4wEeAnzPDLOfsMeewn5/HurgH7e7NJaxqMKh+Ww1543Cf9GoGePv9y66+L0pfdfq8shPrrP8E2AuTUA7PHM0syuA2DPbPvHO3oAe7zKJbYegN2jvloMuwAXEmCk37J0/2dlRSg7O1t83CheRPn5BRSJRKiqslKr0rpNofY7IurU1ddpMeUlJR2ppENH7f0N69bQcf0Hak8Z5fi6MWeeTbxIkrcuXbvTurLVNGz4SHprwYv0SvXL1OfQUbRcvMYeOZ5GtB9JY0adHX0kvT4+T8Y9I4Z9paYn62rcnGLY9Rl1jHU3bVxP68tWBS5LzBnX/lTrKoO9HvYZ7is4xaV4P++jhVqZZac3ZceR0M9/G8F/yPLl1FvcsM6bPFnpaJo4fz7tE88qWDxihFJ59vJf+T+/paf+36+08npvP/9vtmCXbxQK3nyN6nv0jN5E628Y5I71Nw7yvd3LPqGC8v3U77QzY/rndDOBGHZzk3rVxdgqYthjdUaWGKXTiWMhxLDjSaeOkyRFBQDsHoUPArCvXP0ZLctfTrS5hhaI17jcM6h//8E0qPhEOnignIaePArALuxstTBznUi9mEnAfvnV5llt9IeCSpaYcgH4HJ6zbc1K+mb7Fuo04RytCT3Qs8dfbpz3nrfO//onlbctpn8PbwJ2vmngmwS5mYX83CFujO/49a9dHa1TXn6ZNvXqRcuHDHFVb8TixdRu/356a8IEV/X4G4eRom7R/nJafNZZMXX130JYNTxg4fuUL+7qvx19ekyRAvHMgBqRPlR+GaH/9kJfOF8sUuateuRpLdrQhzqpDKxqwTuUVdSW8oedrBU3u7lRaYfL8E1QXUU5dR5z+CbI+M2KalvanPl2F61653UaefGP3VTTytrddP3zjZeob78TqHefvq7bdapglobWqY6bzwHsbtSyLgtgB7D7M5P8bwXA7lHTVAL7wdoD9MnBJVSz45AG6hNyJtIxgwZQx30l2kWHM74A2A8bGMBeHb1xc5r2KsAu27C74THbj9sLIt8AvPXQPTTxxqZsOnpvP/9vFurDNwpGD7u8YdD3iW8W+JsF/dZr6RKqF3BpBt1O6wfihX25/7Hvv6/9aZb338lmfrbBbbn9JsSuf151MbbdeedO4huyWddeqyqLUrlpzz9PywcPprJ+/ZTKuyk047HHtG+hdnbu7Kaacln9DaoMV+OZzd/2NvC3wD5tUx9+iF6/9DI60K6dTy1aNzPi7bepQtzcrz5F7ds4PzqUin3Kfk8SaYI/H3M67ejV24+huG6jUDxb5Jxn59ALN94kAgeaIgLk9rXOqeK6YVTwRQEAu1cZFywgGjdO5Ok+nfa8/JbX1pTrz137LN33yV2IU1dWLDgF/YphD86I0BNWQH7jYKeG8WbDWFauPTBro6h1Lh2qrqf65nUB+m8vVCwg1zaolDUrY3ZzE29bTXq1/GbFS1tu6jrddLlpC2WhQKYo4N8tX6Yo5v84AexeNZ09m+jHP9ayw3CWmERvb218le748NYoqE/scx7dMfpeLChNtPA+tg9g91HMDGoKi04zyNgehypvHvNEGFWbghz6rqLGY4uonkkKFLfJpVoRflcpHARyO+WIgkySIJBjBbB7NUszsB+6+FLa9/BjXluzrI986gmTNukNA9iTLnkodghgD4UZkzoIZIlJqtyh2RmyxATTlAB2j3ZJdAz7gZoK2rRhPS2tX0L7xGuieFUdVU+DCpoW0umzxHy2dJGWLWbVis8Qw26ysBIx7OkZw87z/Ik/3UtX33Crq6PVbBGeSgNeMpp4qct9w5NOVSyEJ52aqYRFp2pzx6mU2zU2Tu25+RxPOnWjVuaVBbB7tHkigX1v9l76Ytfn1LtGZLoQr95HHkOdv+lgmdYRwE5UU20NpQB2ALvK4e4Fur3UBbCrWKepDNI6xmoFYFefP3YlAezIEuPPTPK/FQC7R00TAewHDlXQzsYdtLl+M2WJ14mRE+mYfsdT55LutnnYAewA9rz8fMsZbXczY6wUpCwx8LA3WUc1JMaN7ZIFLl5vZIz9BLAD2D1eui2rA9gB7ImaW17bBbB7VVBkiCGRKYYzxHCmGC8bx6nf/K9r6eNtH2jN8JNJ+Qml/KRSbOFRADHs4bFlMkeiCuzJ7BP2FWwFEMMebPsEtXeIYQ+mZQDsXu1y1FFEmzbRN8vWUn3PXnG1hgWlccmWtpUA7GlrupR2HMCeUvnTcucA9rQ0W8o7DWBPuQlMOwBg92qXI44gEg8b2PnlDmoQj1t3sxlBnev+bPjt9MN+lyBNoxsh06wsgD3NDBaQ7gLYA2KINOoGgD2NjBWgrgLYA2QMXVcA7B7tEk8Me05eLlXUlFNjbYO293LxKsprS+1bt6eshiyqrq6ikpKOVNKho/b5hnVr6Lj+A6lNYTFi2HX2MnvUNxadIoZdThFkiRnl6ezmZywvYtiJzM5XngxkqIxFp/6o6ee8d9sjZIlxq1hmlQewK9h78vTbacOmbVrJY3p3o5dn3xmt5QbYGxobqLahhg40HKAG8WotXjmRHCoqaks5WbkUEY+QrquvA7AfKKcRo8+Iarxj29fEC2rPvWBaC2sB2A/LYZUBRy8YFp0qHOyiiBe49FKXe4e0jmo2wqLTWJ0A7Gpzx6kUgB2LTp3mSKo+B7A7KH/FLffQnr3lUUhneG9fUkxP33ebVlMF2EWiF6oTr4aGBmoUryrxapXbmgoaCwSkR6h1m0KtLQC7OSwB2GNvVozTFsCuBjAqJ1ov0O2lLoBdxTpNZQDsavM9ESExpXMeo3OmTKOiYnchoOrWPVwyFfCcin3KEcPDHs8syZw6AHYHW582ZSb9bMZUmjJxtFZy3v9v7/5D7yrrOIA/OXP+M1szVDBwjIytEsU/1EKbEKUFbct/3B/pxB85IZEMmiYoCJoLtGSF82ezoLYC3bRES0hziRMSdY4J2pqgZaLmj9DRAvs+Z52v93t2v/f8uvfu3ue+7j9u3/s8z3me1+f53u9753vO8cGt4cb1m8Jjm9ft6xnPin99WXjtZxtnjBSvT39w1/3hzmd/GuKf81d84kt88kt8AozXZAq4hn0y69521a5hbys4ef0HEdgnT3HyVuwa9tGsucDeoy7bd+4KKy+5Nmy85epw3JJFWcv9vjYV2Pd+89zw17Vrw47XnwkP/e234fGX/zT152enR84fz/j5o78oqI/m98FQZyWwD5U7mYMJ7MmUcmgLEdiHRp3UgQT20SynwN6HwP7jU0L4zpkzB5p/6PywYvGKsOr4VeH0haePZvXNigABAgQIECBAYOQFBPaWgT1ew/7BBx9MXRkzdaF6x6vz7wcddFA4+OCDs3bxdeihU9euT33tvffey/4+b9687L/xa3v37g179uwJRxxxRDjyyCOzPs8991w44YQTwsemHhv50EMPheXLl4eXXtp3mc0xxxwTnnnmmbB06dLw6KOPZv/dtm1bOP7446eeNvlWePvtt7Ov3XzzzWHNmjVZ/zjOKaecEtZO/Vbgsssuy4539913Z3+OffI/x/HzNnHOnX2L7xX7Ff8e2996663Z3I866qhs7runnl8f57xq1appuSeeeCKb8xlnnDH9tW7tuo0XvxbXkq+1WNrOtXS+9/TTT2eecW7FV5xffEXD4qvbGjvbPP/881ltzj777P36ls017zDb2quurbNdL5s66y627eXXbeHFfdQVp/DF+H12zTXXVGk63WbLli3Z90f83qnz6rYHq/Zv0zceo9d+qzqHfowRj9WkTrPNsa1LcdxXX301xPpefPHFVVkqtdu0aVP22bl48eJK7es0Kn7+1elbpW3T/V5l7M428fM1fmbPnz+/btfa7fu5B6se/EAcM59b/Nkbf9YsXLiw6nT72q7sZ1pfD2aw2gICewlZt2vYr7rhjrDjkQ1Zz+ym0y6vzsD+kakbS+fMmTPVKt5yGsLcufsC+5733896uun0w6e/dLtpz02nbjq9/Sc/DBd9+3u1PuA81tFjHWttmKnGf3jg3nDs4s+FhYuOrdu1tL3HOpYS7dfgQNwAeiCOmS/cTaf198gk9RDYS6pd6SkxAnt49523w+82bwwrz913xqv49/i14g+sbkFcYJ+5mWb7x0pxy3lKzP7fhAK7wF73h7nAXi7mKTHlRk1bCOxN5Sajn8Beoc69nsOehdP39oZ33/9vhZE0ITD1G5W5c8IhH50T3vr3f3AQqCzgptPKVBr+X8BNp7ZCEwE3nTZRG3wfgb0PxgJ7HxAnaAiBfYKK3celCux9xJyQoQT2CSl0n5cpsPcZtE/DCex9gBTY+4A4QUMI7BNU7D4uVWDvI+aEDCWwT0ih+7xMgb3PoH0aTmBvCemm09XhkLlzXcPeZR/t3vVCeOH558KXv/aNGe/mgf21N94Nv/r5+rDqostm3YWuYd9H46bTEKoG9qee/HNmduJJrmGv+/HuGvZyMdewlxs1beEa9qZyk9FPYG9ZZ4FdYM9vtC1uJYG9+zdXk6cwCOwCe+dueuP118KjDz8Qzlp5XstP8JndBfZyToG93KhpC4G9qdxk9BPYW9ZZYBfYBfbt4R9/fzks/dJXK303CeyzM/U6O+4M+4duAvv+e6jbU5EGcUmMwF7pY65RI4G9EdvEdBLYJ6bUFkqAAAECBAgQIDCOAgL7OFbNnAkQIECAAAECBCZGQGCfmFJbKAECBAgQIECAwDgKCOzjWDVzJkCAAAECBAgQmBgBgb1Fqcv+D6gthtZ1xAXq1r6sfa/3Nz+4NVx1wx37iex4ZMOIK5lemUDZvij2r9J++85dYeUl14aNt1wdjluyqGwK3h9xgSo171xClfaz7RGfNSO+GVpMr8q+qLqPzr98bdj21M4Zs/HzqEVxKnYV2CtCFZvFDfvGm++ELRuuy96K3wyHLzgs3HXTmoYj6jYuAnVrX9a+7P34Q/TG9ZvCY5vXjQuReVYQKKt7k8+c01ZcGt58692sq8BeoQgj3mTYe8RnzYhviIbT6/c+ip8znT+Prrz+trD1ye1+RjWsT9VuAntVqUK7uGG/u/rssOLMU7N3fNA1hBzDbnVrX9a+7H17aww3SYUpl9W9OETV9s6wV8AfkyZVa54vp2r7XmfYnRwYk81RY5pV90XdfZS395lToxgtmgrsDfC6bU4btgHkGHapW/uy9pGgePlCsU+3X1P79eMYbp6OKZfti+KlLHXa+ywa773RKwT1qm0/9ojPmjT2Tucq6uyL2K9u+9hn3Z33hF/f/0dn2Ae8fQT2BsBNNnSDw+gyggJ1a1/WvkpgLzIUf705gkymVCJQti8EdltoFPaIz5rx34eD3EedAf+6Ky6cvuJg/NVGcwUCe4O61P0GaHAIXUZUoG7ty9o3Cez5mM6yj+gmqTCtsn0hsFdATLzJKOwRnzXjv8mGsY9Wn7MsXHrBWeOPNeIrENgbFqjbNWHxSR5CVEPQMepWt/Zl7cveL9Lkv7a218Zo03SZat26V23vkpjx3heds69a87xP1fZV94jPmjT2UtV9UWcf5XvDze3D2yMCe0PrunddNzyMbiMoUFb7+MSg+MqfIFTWvuz94h35nkg0gpuiwZTK6l53H+VTqBrGGkxZlyELDHuP+KwZcoGHdLh+7yMPQhhS4QqHEdhbuNd9rmmLQ+k6YgK9al8MWnHqZXulbLwXd78yLXDyiUs8PnTE9kPT6ZTVvfMfflX2UedjHWP7BfPnuRGsaXFGpN8w90jnseLyfdaMyCbowzT6tY/yEwLdpuQ69j4UqscQAvtgfY1OgAABAgQIECBAoJWAwN6KT2cCBAgQIECAAAECgxUQ2Afra3QCBAgQIECAAAECrQQE9lZ8OhMgQIAAAQIECBAYrIDAPlhfoxMgQIAAAQIECBBoJSCwt+LTmQABAgQIECBAgMBgBQT2wfoanQABAgQIECBAgEArAYG9FZ/OBAgQIECAAAECBAYrILAP1tfoBAgQIECAAAECBFoJCOyt+HQmQIAAAQIECBAgMFgBgX2wvkYnQIAAAQIECBAg0EpAYG/FpzMBAgQIECBAgACBwQoI7IP1NToBAgQIECBAgACBVgICeys+nQkQIECAAAECBAgMVkBgH6yv0QkQIECAAAECBAi0EhDYW/HpTIAAAQIECBAgQGCwAgL7YH2NToAAAQIECBAgQKCVgMDeik9nAgQIECBAgAABAoMVENgH62t0AgQIECBAgAABAq0EBPZWfDoTIDCuAuvuvCes/8V9+01/9TnLwqUXnBVOW3Fp9t5jm9ft1ya+t2D+YWHLhuuy98rG+uzp5/VkWjB/Xnac8y9fG7Y9tbNr2+uuuDCsOPPUsPy8q8KLu18J+d/zxpsf3BquuuGO8KmFR0/PqzhQlXmcetJx4b7fPz7dddlXvhB+8P1v1TpulXWM674xbwIECBwIAYH9QKg7JgECB1QgD5Qbb7k6HLdk0fRcYvB++LG/TAfeGHBPPnFJuOumNdNtrrz+trD1ye3TQb7qWMVgXQzc8f041htvvjNr4I5t8sBenFf+9V6BvRM9D/jd5tHtvTrHrbKOA7oBHJwAAQJjJiCwj1nBTJcAgfYCMYjnZ457jVYMrtt37gorL7l2xtntqmP1M7AfvuCw7Ex8/g+OfF4xxJcF/irzmC2wVz2uwN5+jxqBAAECnQICu/1AgMDECcRLWo5d9MkZZ85nQ4jh84VdL2dn1ONZ5hhaO8+41xkrHqPXme0qQTfO4TOfPib88/V/hSM/8fHscpV41j++4tcGGdirHrfKOiZu01kwAQIEWggI7C3wdCVAYDwF8tCczz6/hny21XRe+73jkQ0zmtUdqyywV7mGPQbnk0/8THbNepxPnF882/6j238z8MBe5biuYR/P7wuzJkBgdAUE9tGtjZkRIDAEgfxykvxQ3S6VyUN2fkPqbNOqM1aba9hjYM9vBI1zyc/61zmz3eQa9qrHrTOPIZTYIQgQIDD2AgL72JfQAggQ6JdAvLQkPiGleBa927XrZcecbayyM+xll7Tkl8TEwJ4/nSYP/3WCcpvAXnbcOvMoc/Q+AQIECIQgsNsFBAhMlEAM37+89+HsDHXxlQfR4tNjZgvsTcbqZ2CP84/X0OePnqwTlNsE9rLj1pnHRG0+iyVAgEBDAYG9IZxuBAiMp0DnZSudZ9I7n7TSeVNpXGWvwB6fGhNfVcfqd2DvrEKdoNw2sPc6bp15jOcuMmsCBAgMV0BgH663oxEgMCIC3f4nQrNdo152SUydscoCe9WbTrv9hqBOUJ5tHvmlPHmZOv/HSfk17MUSFo/rptMR2eSmQYBAMgICezKltBACBAgQIECAAIEUBQT2FKtqTQQIECBAgAABAskICOzJlNJCCBAgQIAAAQIEUhQQ2FOsqjURIECAAAECBAgkIyCwJ1NKCyFAgAABAgQIEEhRQGBPsarWRIAAAQIECBAgkIyAwJ5MKS2EAAECBAgQIEAgRQGBPcWqWhMBAgQIECBAgEAyAgJ7MqW0EAIECBAgQIAAgRQFBPYUq2pNBAgQIECAAAECyQgI7MmU0kIIECBAgAABAgRSFBDYU6yqNREgQIAAAQIECCQjILAnU0oLIUCAAAECBAgQSFFAYE+xqtZEgAABAgQIECCQjIDAnkwpLYQAAQIECBAgQCBFAYE9xapaEwECBAgQIECAQDICAnsypbQQAgQIECBAgACBFAUE9hSrak0ECBAgQIAAAQLJCAjsyZTSQggQIECAAAECBFIUENhTrKo1ESBAgAABAgQIJCMgsCdTSgshQIAAAQIECBBIUUBgT7Gq1kSAAAECBAgQIJCMgMCeTCkthAABAgQIECBAIEUBgT3FqloTAQIECBAgQIBAMgICezKltBACBAgQIECAAIEUBQT2FKtqTQQIECBAgAABAskICOzJlNJCCBAgQIAAAQIEUhQQ2FOsqjURIECAAAECBAgkIyCwJ1NKCyFAgAABAgQIEEhRQGBPsarWRIAAAQIECBAgkIyAwJ5MKS2EAAECBAgQIEAgRQGBPcWqWhMBAgQIECBAgEAyAgJ7MqW0EAIECBAgQIAAgRQFBPYUq2pNBAgQIECAAAECyQgI7MmU0kIIECBAgAABAgRSFBDYU6yqNREgQIAAAQIECCQjILAnU0oLIUCAAAECBAgQSFFAYE+xqtZEgAABAgQIECCQjMD/AHgIPYQvKU05AAAAAElFTkSuQmCC", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(colors=['cyan', 'green', 'violet', 'red'], show_intervals=True, \n", " title_prefix=f\"[E] init = {E_init}\")" ] }, { "cell_type": "code", "execution_count": 80, "id": "b44a6da4-b3bb-4297-932b-3df13fe796d0", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.0024715441102170356, 4.283809315596441)" ] }, "execution_count": 80, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Locate the intersection of the curves for [S] and [P]:\n", "dynamics.curve_intersect(\"S\", \"P\", t_start=0, t_end=0.02)" ] }, { "cell_type": "markdown", "id": "45539de2-b37b-4749-aa4f-b247c860b3ee", "metadata": {}, "source": [ "#### The timescale of [S] and [P] continues to become faster with a higher initial [E] -- **AND THEY'RE NOW GETTING CLOSE THE TIMESCALES OF E AND ES**" ] }, { "cell_type": "code", "execution_count": 81, "id": "5fcdb4fd-0dba-43b7-880f-4c8b3aceca1e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_curves() WARNING: Excessive number of vertical lines (758) - only showing 1 every 6 lines\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=E
SYSTEM TIME=%{x}
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Changes in concentrations for 3 reactions (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "domain": [ 0, 1 ], "range": [ 0, 0.002 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.1111111111111112, 21.11111111111111 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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", 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Changes in concentrations for 3 reactions (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.765766640762288e-05, 0.020147397371097706 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.1111111111111112, 21.11111111111111 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# The full reaction of E and ES*\n", "dynamics.plot_history(chemicals=['E', 'ES*'], colors=['violet', 'red'], show_intervals=True, \n", " title_prefix=f\"E and ES when [E] init = {E_init}\")" ] }, { "cell_type": "markdown", "id": "14a5ce9f-8a93-4ad4-a8fa-e26496b0e573", "metadata": {}, "source": [ "#### At these higher initial concentrations of [E], we're now beginning to see overshoots in [E] and [ES*] that overlap less" ] }, { "cell_type": "code", "execution_count": 83, "id": "05426505-fa5c-4b0f-bdae-9eaf3cace1dd", "metadata": {}, "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", "
SYSTEM TIMEEES*P
7570.02014710.9981479.0018539.163739
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" ], "text/plain": [ " SYSTEM TIME E ES* P\n", "757 0.020147 10.998147 9.001853 9.163739" ] }, "execution_count": 83, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(columns=['SYSTEM TIME', 'E', 'ES*', 'P'], tail=1) # Last point in the simulation" ] }, { "cell_type": "code", "execution_count": 84, "id": "50529736-69a0-404a-ac61-2b5f9b2ba216", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "9.163739207468186" ] }, "execution_count": 84, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_equil = dynamics.get_chem_conc(\"P\")\n", "P_equil" ] }, { "cell_type": "markdown", "id": "60e3e92e-32ba-46f7-8c4c-760ac69054ea", "metadata": {}, "source": [ "#### P_equil continues to decrease with increasing initial [E]" ] }, { "cell_type": "code", "execution_count": 85, "id": "31d1a073-906e-45d0-90d2-d63f8e4d7df2", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "6.41461744522773" ] }, "execution_count": 85, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_70_threshold = P_equil * 0.70\n", "P_70_threshold" ] }, { "cell_type": "code", "execution_count": 86, "id": "c6d79966-d114-4e66-bb94-bcf852fee8be", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.004076150862005783" ] }, "execution_count": 86, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.reach_threshold(chem=\"P\", threshold=P_70_threshold)" ] }, { "cell_type": "markdown", "id": "3c014242-7a93-4368-ac71-0e2aa7dc88f5", "metadata": { "tags": [] }, "source": [ "#### The time at which we reach the 70% threshold of the equilibrium value of P continues to decrease with increasing initial [E]" ] }, { "cell_type": "code", "execution_count": null, "id": "2ca50397-215f-490e-ac27-c2b76cf51dae", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "845d2620-d0a2-4080-a201-a118fede9e48", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "c45bfaac-3a80-473c-a9b5-cc0c55bf1c5f", "metadata": { "tags": [] }, "source": [ "# 8. Keep increasing the initial [E]" ] }, { "cell_type": "code", "execution_count": 87, "id": "06f75fcd-19b7-45dd-bcd5-ea5136280700", "metadata": {}, "outputs": [], "source": [ "E_init = 30.0 # 50% higher than the initial [S]" ] }, { "cell_type": "code", "execution_count": 88, "id": "86ebdf54-6e5e-4450-acc2-9c45fb978d6d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "4 species:\n", " Species 0 (S). Conc: 20.0\n", " Species 1 (P). Conc: 0.0\n", " Species 2 (E). Conc: 30.0\n", " Species 3 (ES*). Conc: 0.0\n", "Set of chemicals involved in reactions: {'ES*', 'P', 'S', 'E'}\n" ] } ], "source": [ "dynamics = ReactionDynamics(chem_data=chem_data, preset=\"slower\") # A brand-new simulation, with the same chemicals and reactions as before \n", "\n", "dynamics.set_conc(conc={\"S\": 20., \"E\": E_init}, snapshot=True) \n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 89, "id": "45e38a17-5515-4d69-8b27-168331473dd4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* INFO: the tentative time step (5e-05) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.1 (set to 5e-06) [Step started at t=0, and will rewind there]\n", "* INFO: the tentative time step (5.05e-06) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.1 (set to 5.05e-07) [Step started at t=5e-06, and will rewind there]\n", "Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n", "749 total step(s) taken\n" ] } ], "source": [ "# Perform the reactions (The duration of the run was manually adjusted for optimal visibility)\n", "dynamics.single_compartment_react(duration=0.01,\n", " initial_step=0.00005, variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 90, "id": "8d7277d0-1d8f-479a-9110-eace7ef00222", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 90, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reactions have reached equilibrium\n", "dynamics.is_in_equilibrium(verbose=False)" ] }, { "cell_type": "code", "execution_count": 91, "id": "dd0211e8-5dfb-4c1c-809c-b7824f04af50", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_curves() WARNING: Excessive number of vertical lines (750) - only showing 1 every 6 lines\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=S
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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(colors=['cyan', 'green', 'violet', 'red'], show_intervals=True, \n", " title_prefix=f\"[E] init = {E_init}\")" ] }, { "cell_type": "code", "execution_count": 92, "id": "64c0b5f9-1a4a-4b65-a927-f4c24839c44c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.0015007776137844029, 2.9518860757696133)" ] }, "execution_count": 92, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Locate the intersection of the curves for [S] and [P]:\n", "dynamics.curve_intersect(\"S\", \"P\", t_start=0, t_end=0.01)" ] }, { "cell_type": "markdown", "id": "cd858e13-44eb-4e0e-a77f-82001e764fbc", "metadata": {}, "source": [ "#### The timescale of [S] and [P] continues to become faster with a higher initial [E] -- **AND THEY'RE NOW COMPARABLE THE TIMESCALES OF E AND ES**" ] }, { "cell_type": "code", "execution_count": 93, "id": "1bf0ed70-9c0a-4c93-b538-0cafeb01921b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_curves() WARNING: Excessive number of vertical lines (750) - only showing 1 every 6 lines\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=E
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Changes in concentrations for 3 reactions (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "domain": [ 0, 1 ], "range": [ 0, 0.005 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.6666666666666665, 31.666666666666668 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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", 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Changes in concentrations for 3 reactions (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -8.81142413282108e-06, 0.010053834935548853 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.6666666666666665, 31.666666666666668 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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", "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# The full reaction of E and ES*\n", "dynamics.plot_history(chemicals=['E', 'ES*'], colors=['violet', 'red'], show_intervals=True, \n", " title_prefix=f\"E and ES when [E] init = {E_init}\")" ] }, { "cell_type": "markdown", "id": "7e1d57c5-4f7a-4e1e-a9e5-0303d60e3020", "metadata": {}, "source": [ "#### At these high initial concentrations of [E], we're now beginning to see [E] and [ES*] no longer overlapping; the overshoot is still present in both" ] }, { "cell_type": "code", "execution_count": 95, "id": "ff72f0a5-b05c-4269-9d98-786e0b53c921", "metadata": {}, "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", "
SYSTEM TIMEEES*P
7490.01005418.41133711.5886636.998847
\n", "
" ], "text/plain": [ " SYSTEM TIME E ES* P\n", "749 0.010054 18.411337 11.588663 6.998847" ] }, "execution_count": 95, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(columns=['SYSTEM TIME', 'E', 'ES*', 'P'], tail=1) # Last point in the simulation" ] }, { "cell_type": "code", "execution_count": 96, "id": "907c937b-bba7-4f7d-8682-86daa9717831", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "6.998846772430818" ] }, "execution_count": 96, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_equil = dynamics.get_chem_conc(\"P\")\n", "P_equil" ] }, { "cell_type": "markdown", "id": "96560369-9a78-40f4-90c3-2ecb441f2bc4", "metadata": {}, "source": [ "#### P_equil continues to decrease with increasing initial [E]" ] }, { "cell_type": "code", "execution_count": 97, "id": "8a14ce96-a237-4610-9e87-38a6231ca263", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "4.899192740701572" ] }, "execution_count": 97, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_70_threshold = P_equil * 0.70\n", "P_70_threshold" ] }, { "cell_type": "code", "execution_count": 98, "id": "f6d96e06-599d-4c14-beca-30a37d083617", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.002747856201107546" ] }, "execution_count": 98, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.reach_threshold(chem=\"P\", threshold=P_70_threshold)" ] }, { "cell_type": "markdown", "id": "9dc94f9b-7c97-468d-90b4-c37b7483ca67", "metadata": { "tags": [] }, "source": [ "#### The time at which we reach the 70% threshold of the equilibrium value of P continues to decrease with increasing initial [E]" ] }, { "cell_type": "code", "execution_count": null, "id": "3715cc7b-385f-4119-8b75-2d494ffd892e", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "cef69c73-8295-4f75-8310-ebcc3ec4fc2b", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "f4d60280-db10-4e82-9d6f-02090bdd888d", "metadata": { "tags": [] }, "source": [ "# 9. Keep increasing the initial [E]" ] }, { "cell_type": "code", "execution_count": 99, "id": "a6b8d011-9592-4386-983e-f530b5f90298", "metadata": {}, "outputs": [], "source": [ "E_init = 60.0 # Triple the initial [S]" ] }, { "cell_type": "code", "execution_count": 100, "id": "2b677f97-a5de-486a-89f8-9bc3137b3d7e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "4 species:\n", " Species 0 (S). Conc: 20.0\n", " Species 1 (P). Conc: 0.0\n", " Species 2 (E). Conc: 60.0\n", " Species 3 (ES*). Conc: 0.0\n", "Set of chemicals involved in reactions: {'ES*', 'P', 'S', 'E'}\n" ] } ], "source": [ "dynamics = ReactionDynamics(chem_data=chem_data, preset=\"slower\") # A brand-new simulation, with the same chemicals and reactions as before \n", "\n", "dynamics.set_conc(conc={\"S\": 20., \"E\": E_init}, snapshot=True) \n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 101, "id": "07850faa-b7a7-4c58-9017-a95a1e93eb46", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* INFO: the tentative time step (5e-05) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.1 (set to 5e-06) [Step started at t=0, and will rewind there]\n", "* INFO: the tentative time step (5e-06) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.1 (set to 5e-07) [Step started at t=5e-06, and will rewind there]\n", "* INFO: the tentative time step (5e-07) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.1 (set to 5e-08) [Step started at t=5e-06, and will rewind there]\n", "Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n", "770 total step(s) taken\n" ] } ], "source": [ "# Perform the reactions (The duration of the run was manually adjusted for optimal visibility)\n", "dynamics.single_compartment_react(duration=0.005,\n", " initial_step=0.00005, variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 102, "id": "b850c64e-b44b-4cce-881e-569483921906", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 102, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reactions have reached equilibrium\n", "dynamics.is_in_equilibrium(verbose=False)" ] }, { "cell_type": "code", "execution_count": 103, "id": "28c1e572-a798-4605-82ba-9b7430bda4bf", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_curves() WARNING: Excessive number of vertical lines (771) - only showing 1 every 6 lines\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=S
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Changes in concentrations for 3 reactions (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -4.389487178533156e-06, 0.005008404870706331 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -3.333333333333333, 63.333333333333336 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(colors=['cyan', 'green', 'violet', 'red'], show_intervals=True, \n", " title_prefix=f\"[E] init = {E_init}\")" ] }, { "cell_type": "code", "execution_count": 104, "id": "417d9ff2-d739-44af-aff0-72513b3c7d66", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.0007023910558856093, 1.5191639777843677)" ] }, "execution_count": 104, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Locate the intersection of the curves for [S] and [P]:\n", "dynamics.curve_intersect(\"S\", \"P\", t_start=0, t_end=0.005)" ] }, { "cell_type": "markdown", "id": "497f2877-4ce5-41cd-9119-e483df6fcf14", "metadata": {}, "source": [ "#### The timescales of [S] and [P] continues to become faster with a higher initial [E] -- **AND NOW THEY REMAIN COMPARABLE THE TIMESCALES OF E AND ES**" ] }, { "cell_type": "markdown", "id": "89ff44f1-0c42-4a6d-8fe3-b1efab242da1", "metadata": {}, "source": [ "#### At these high initial concentrations of [E], [E] and [ES*] no longer overlapping, and are now getting further apart" ] }, { "cell_type": "code", "execution_count": 105, "id": "449c94a5-dd8e-4681-b654-dce7b685a7c7", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEEES*P
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" ], "text/plain": [ " SYSTEM TIME E ES* P\n", "770 0.005008 44.60637 15.39363 3.832618" ] }, "execution_count": 105, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(columns=['SYSTEM TIME', 'E', 'ES*', 'P'], tail=1) # Last point in the simulation" ] }, { "cell_type": "code", "execution_count": 106, "id": "41db82fe-6607-44f8-9723-9a0d3f7306a6", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3.832618199402545" ] }, "execution_count": 106, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_equil = dynamics.get_chem_conc(\"P\")\n", "P_equil" ] }, { "cell_type": "markdown", "id": "c4951935-f4a1-4790-b198-fd0e2bfc18ca", "metadata": {}, "source": [ "#### P_equil continues to decrease with increasing initial [E]" ] }, { "cell_type": "code", "execution_count": 107, "id": "e7cb5350-03c0-49da-a185-fd7af33f1312", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.682832739581781" ] }, "execution_count": 107, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_70_threshold = P_equil * 0.70\n", "P_70_threshold" ] }, { "cell_type": "code", "execution_count": 108, "id": "fbbb456b-0880-4aa2-b300-89d1204ad53d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.001390053726276219" ] }, "execution_count": 108, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.reach_threshold(chem=\"P\", threshold=P_70_threshold)" ] }, { "cell_type": "markdown", "id": "977bfde9-42e1-4733-bac6-bae954134aac", "metadata": { "tags": [] }, "source": [ "#### The time at which we reach the 70% threshold of the equilibrium value of P continues to decrease with increasing initial [E]" ] }, { "cell_type": "code", "execution_count": null, "id": "6c7df8fa-c510-45db-9e5f-52e62766e52f", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "09d0e661-f920-4070-82e4-e0e0affc188d", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "4a771e38-d7b2-444a-bfe8-b0032cbc79f4", "metadata": { "tags": [] }, "source": [ "# 10. Keep increasing the initial [E]" ] }, { "cell_type": "code", "execution_count": 109, "id": "338fbe68-dde9-4159-a405-973ee8a7c796", "metadata": {}, "outputs": [], "source": [ "E_init = 100.0 # Quintuple the initial [S]" ] }, { "cell_type": "code", "execution_count": 110, "id": "c45f280a-708c-4de0-95dc-03a629dbebfe", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "4 species:\n", " Species 0 (S). Conc: 20.0\n", " Species 1 (P). Conc: 0.0\n", " Species 2 (E). Conc: 100.0\n", " Species 3 (ES*). Conc: 0.0\n", "Set of chemicals involved in reactions: {'ES*', 'P', 'S', 'E'}\n" ] } ], "source": [ "dynamics = ReactionDynamics(chem_data=chem_data, preset=\"slower\") # A brand-new simulation, with the same chemicals and reactions as before \n", "\n", "dynamics.set_conc(conc={\"S\": 20., \"E\": E_init}, snapshot=True) \n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 111, "id": "5d5bcb4d-3932-4cee-bb45-7bd19db664a1", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* INFO: the tentative time step (5e-05) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.1 (set to 5e-06) [Step started at t=0, and will rewind there]\n", "* INFO: the tentative time step (2.5e-06) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.1 (set to 2.5e-07) [Step started at t=5e-06, and will rewind there]\n", "* INFO: the tentative time step (2.5e-07) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.1 (set to 2.5e-08) [Step started at t=5e-06, and will rewind there]\n", "Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n", "785 total step(s) taken\n" ] } ], "source": [ "# Perform the reactions (The duration of the run was manually adjusted for optimal visibility)\n", "dynamics.single_compartment_react(duration=0.003,\n", " initial_step=0.00005, variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 112, "id": "2ca20feb-38fe-4737-99b7-2b0472453781", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 112, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reactions have reached equilibrium\n", "dynamics.is_in_equilibrium(verbose=False)" ] }, { "cell_type": "code", "execution_count": 113, "id": "38b01a6e-4c2a-47a2-b4bf-793f90470590", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_curves() WARNING: Excessive number of vertical lines (786) - only showing 1 every 6 lines\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=S
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Changes in concentrations for 3 reactions (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -2.6533949443587305e-06, 0.0030275236315133115 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -5.555555555555555, 105.55555555555556 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(colors=['cyan', 'green', 'violet', 'red'], show_intervals=True, \n", " title_prefix=f\"[E] init = {E_init}\")" ] }, { "cell_type": "code", "execution_count": 114, "id": "803d88fa-f551-4f56-96af-37b417c505b4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.0004266715141239805, 0.9491814221946882)" ] }, "execution_count": 114, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Locate the intersection of the curves for [S] and [P]:\n", "dynamics.curve_intersect(\"S\", \"P\", t_start=0, t_end=0.005)" ] }, { "cell_type": "markdown", "id": "ecbaf247-3675-44b8-9bbc-a71f37f341ba", "metadata": {}, "source": [ "#### The timescales of [S] and [P] continues to become faster with a higher initial [E] -- **AND REMAIN COMPARABLE TO THE TIMESCALES OF E AND ES**" ] }, { "cell_type": "markdown", "id": "3491b263-298d-4057-926a-c57ed7eb5444", "metadata": {}, "source": [ "#### At these high initial concentrations of [E], [E] and [ES*] no longer overlapping, and are now getting further apart" ] }, { "cell_type": "code", "execution_count": 115, "id": "92812a67-0f27-4e7f-837b-368a426921d0", "metadata": {}, "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", "
SYSTEM TIMEEES*P
7850.00302882.77909917.2209012.312829
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" ], "text/plain": [ " SYSTEM TIME E ES* P\n", "785 0.003028 82.779099 17.220901 2.312829" ] }, "execution_count": 115, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(columns=['SYSTEM TIME', 'E', 'ES*', 'P'], tail=1) # Last point in the simulation" ] }, { "cell_type": "code", "execution_count": 116, "id": "5c48aa58-e44c-4e18-9c60-c562560aa0e9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.3128291895441793" ] }, "execution_count": 116, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_equil = dynamics.get_chem_conc(\"P\")\n", "P_equil" ] }, { "cell_type": "markdown", "id": "da34f793-1dd1-41a0-a20b-8e15e82654db", "metadata": {}, "source": [ "#### P_equil continues to decrease with increasing initial [E]" ] }, { "cell_type": "code", "execution_count": 117, "id": "98698d70-47a1-4763-be1f-89660bd27ffa", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.6189804326809254" ] }, "execution_count": 117, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_70_threshold = P_equil * 0.70\n", "P_70_threshold" ] }, { "cell_type": "code", "execution_count": 118, "id": "69acbdb6-7a06-4e96-9ad7-3bdfc3ef92c7", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.0008229365407830671" ] }, "execution_count": 118, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.reach_threshold(chem=\"P\", threshold=P_70_threshold)" ] }, { "cell_type": "code", "execution_count": null, "id": "1806b972-6770-4a1a-be69-1f1504c6da94", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "6974ce46-642c-47a5-96b2-e4f3c9fa6b5d", "metadata": {}, "source": [ "# CONCLUSION: \n", "### as the initial concentration of the Enzyme E increases from zero to lavish values much larger that the concentration of the Substrate S, the reaction keeps reaching an equilibrium faster and faster... \n", "#### BUT the equilibrium concentration of the Product P steadily _reduces_ - and ES*, far from being transient, actually builds up. \n", "#### The **strange world of departing from the customary Michaelis-Menten assumptions** that [E] << [S] and that the rates satisfy k1_reverse >> k2_forward !" ] }, { "cell_type": "code", "execution_count": 119, "id": "073427b4-27a8-407d-bdee-0df89430eb16", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMESPEES*caption
00.020.00.0100.00.0Initialized state
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" ], "text/plain": [ " SYSTEM TIME S P E ES* caption\n", "0 0.0 20.0 0.0 100.0 0.0 Initialized state" ] }, "execution_count": 119, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(head=1) # First point in the simulation" ] }, { "cell_type": "code", "execution_count": 120, "id": "1b5546d6", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMESPEES*caption
7850.0030280.466272.31282982.77909917.220901
\n", "
" ], "text/plain": [ " SYSTEM TIME S P E ES* caption\n", "785 0.003028 0.46627 2.312829 82.779099 17.220901 " ] }, "execution_count": 120, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(tail=1) # Last point in the simulation" ] }, { "cell_type": "markdown", "id": "9c5c0d06-8dc7-43c9-affa-5ead52f95cb8", "metadata": {}, "source": [ "### When the initial [E] is quite high, relatively little of the reactant S goes into making the product P ; most of S binds with the abundant E, to produce a lasting ES* \n", "The following manual stoichiometry check illustrates it." ] }, { "cell_type": "markdown", "id": "22946daf-a9fc-4b93-a9ff-b97b385299a0", "metadata": {}, "source": [ "#### Manual overall STOICHIOMETRY CHECK:" ] }, { "cell_type": "code", "execution_count": 121, "id": "8e3cdce6-5f0d-404a-aaa1-907b4c5ab241", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-19.53373" ] }, "execution_count": 121, "metadata": {}, "output_type": "execute_result" } ], "source": [ "delta_S = 0.46627 - 20.0\n", "delta_S" ] }, { "cell_type": "code", "execution_count": 122, "id": "4e36063d-e6f9-4dfd-b1f3-79f4aeafdd8f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-17.220900999999998" ] }, "execution_count": 122, "metadata": {}, "output_type": "execute_result" } ], "source": [ "delta_E = 82.779099 - 100.0\n", "delta_E" ] }, { "cell_type": "code", "execution_count": 123, "id": "3dbf7a73", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-17.220900999999998" ] }, "execution_count": 123, "metadata": {}, "output_type": "execute_result" } ], "source": [ "delta_E = 82.779099 - 100.0\n", "delta_E" ] }, { "cell_type": "code", "execution_count": 124, "id": "ffd30805-1f47-4410-a6c8-5c8db4d9bbad", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "17.220901" ] }, "execution_count": 124, "metadata": {}, "output_type": "execute_result" } ], "source": [ "delta_ES = 17.220901 - 0\n", "delta_ES" ] }, { "cell_type": "code", "execution_count": 125, "id": "4d77a7f6-0d90-46e7-9d7a-b155460e546d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 3 (at temp. 25 C)\n", "0: S <-> P (kF = 1 / kR = 0.2 / delta_G = -3,989.7 / K = 5) | 1st order in all reactants & products\n", "1: E + S <-> ES* (kF = 100 / kR = 224.07 / delta_G = 2,000 / K = 0.44629) | 1st order in all reactants & products\n", "2: ES* <-> E + P (kF = 200 / kR = 17.851 / delta_G = -5,989.7 / K = 11.204) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {'ES*', 'P', 'S', 'E'}\n" ] } ], "source": [ "chem_data.describe_reactions()" ] }, { "cell_type": "code", "execution_count": null, "id": "83580347-c7aa-4ac7-aafc-cc81b24de20a", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "95749790-0ab6-4640-b525-4802dcaf9de3", "metadata": {}, "source": [ "19.53373 units of `S` are consumed : a meager 2.312829 of that goes into the production of `P` (rxn 0) ; the remainder of Delta S is:" ] }, { "cell_type": "code", "execution_count": 126, "id": "b7372ba6-8da7-4ee0-a888-d04baea7f4c9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "17.220900999999998" ] }, "execution_count": 126, "metadata": {}, "output_type": "execute_result" } ], "source": [ "19.53373 - 2.312829" ] }, { "cell_type": "markdown", "id": "78d8e067-1704-44d8-8f10-a7888d44c277", "metadata": {}, "source": [ "That extra Delta S of 17.2209 combines with an equal amount of `E` to produce the same amount, 17.2209, of ES* (rxn 1) \n", "\n", "`E`, now depleted by that amount of 17.2209, reaches the value:" ] }, { "cell_type": "code", "execution_count": 127, "id": "271f073f-1e22-456b-825b-2acf555519c9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "82.7791" ] }, "execution_count": 127, "metadata": {}, "output_type": "execute_result" } ], "source": [ "100 - 17.2209" ] }, { "cell_type": "code", "execution_count": 128, "id": "a1f87fde-d486-40ab-baee-b73b0abf9f6c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: S <-> P\n", "Final concentrations: [S] = 0.4663 ; [P] = 2.313\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.96028\n", " Formula used: [P] / [S]\n", "2. Ratio of forward/reverse reaction rates: 5.00001\n", "Discrepancy between the two values: 0.7945 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n", "1: E + S <-> ES*\n", "Final concentrations: [E] = 82.78 ; [S] = 0.4663 ; [ES*] = 17.22\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 0.446167\n", " Formula used: [ES*] / ([E][S])\n", "2. Ratio of forward/reverse reaction rates: 0.446288\n", "Discrepancy between the two values: 0.027 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n", "2: ES* <-> E + P\n", "Final concentrations: [ES*] = 17.22 ; [E] = 82.78 ; [P] = 2.313\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 11.1175\n", " Formula used: ([E][P]) / [ES*]\n", "2. Ratio of forward/reverse reaction rates: 11.2035\n", "Discrepancy between the two values: 0.7677 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 128, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Also review that the chemical equilibrium holds, with the final simulation values\n", "dynamics.is_in_equilibrium()" ] }, { "cell_type": "code", "execution_count": null, "id": "3c4cee2d-2d29-4666-b067-45a4cd9706b4", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "jupytext": { "formats": "ipynb,py:percent" }, "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": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }