{ "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` \n", "A direct reaction and the same reaction, catalyzed by an enzyme `E` 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 rate constants satisfy `k1_reverse >> k2_forward` ! \n", "#### We'll **repeat runs with increasingly higher initial concentration of Enzyme**, and 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" ] }, { "cell_type": "markdown", "id": "24d82e5c-e95c-4d56-bffc-23181233cde1", "metadata": {}, "source": [ "### TAGS : \"uniform compartment\", \"chemistry\", \"enzymes\"" ] }, { "cell_type": "code", "execution_count": 1, "id": "55c8d285-416f-489e-8207-db828c8a7d0f", "metadata": {}, "outputs": [], "source": [ "LAST_REVISED = \"Sep. 2, 2025\"\n", "LIFE123_VERSION = \"1.0.0rc6\" # Library version this experiment is based on" ] }, { "cell_type": "code", "execution_count": 2, "id": "f88d9fb7-7ba6-4adc-9af3-379381258243", "metadata": {}, "outputs": [], "source": [ "#import set_path # Using MyBinder? Uncomment this before running the next cell!" ] }, { "cell_type": "code", "execution_count": 3, "id": "47166cb0-c790-4c14-98b5-2db9d9c39e88", "metadata": { "tags": [] }, "outputs": [], "source": [ "#import sys\n", "#sys.path.append(\"C:/some_path/my_env_or_install\") # CHANGE to the folder containing your venv or libraries installation!\n", "# NOTE: If any of the imports below can't find a module, uncomment the lines above, or try: import set_path \n", "\n", "import ipynbname\n", "\n", "from life123 import check_version, ChemData, ReactionRegistry, UniformCompartment, CollectionTabular, GraphicLog\n", "\n", "import pandas as pd" ] }, { "cell_type": "code", "execution_count": 4, "id": "07f02ce7-e296-48e9-8741-3a8ac97cf6c0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "OK\n" ] } ], "source": [ "check_version(LIFE123_VERSION) # To check compatibility" ] }, { "cell_type": "code", "execution_count": null, "id": "0b0c5dc6-0b99-413f-84ba-791ee67c0ddc", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 5, "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 (for the graphics)\n", "log_file = ipynbname.name() + \".log.htm\" # Use the notebook base filename for the log file\n", " # IN CASE OF PROBLEMS, set manually to any desired name\n", "\n", "# Set up the use of some specified graphic (Vue) components\n", "GraphicLog.config(filename=log_file,\n", " components=[\"vue_cytoscape_2\"],\n", " extra_js=\"https://cdnjs.cloudflare.com/ajax/libs/cytoscape/3.21.2/cytoscape.umd.js\")" ] }, { "cell_type": "code", "execution_count": 6, "id": "f864cf71-c8fd-411b-8b9b-e274e7935ef9", "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", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
namelabelplot_color
0SScyan
1EEviolet
2ESESred
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" ], "text/plain": [ " name label plot_color\n", "0 S S cyan\n", "1 E E violet\n", "2 ES ES red\n", "3 P P green" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Initialize the system\n", "chem_data = ChemData(names=[\"S\",\"E\",\"ES\",\"P\"], plot_colors=[\"cyan\",\"violet\",\"red\",\"green\"])\n", "\n", "chem_data.all_chemicals()" ] }, { "cell_type": "code", "execution_count": 7, "id": "33ced2c9-559d-4fcf-8e39-6ec4fd310f84", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 3\n", "0: S <-> P (Elementary Unimolecular reaction) (kF = 1 / kR = 0.2 / delta_G = -3,989.7 / K = 5 / Temp = 25 C)\n", "1: E + S <-> ES (Elementary Synthesis reaction) (kF = 100 / kR = 224.07 / delta_G = 2,000 / K = 0.44629 / Temp = 25 C)\n", "2: ES <-> E + P (Elementary Decomposition reaction) (kF = 200 / kR = 17.851 / delta_G = -5,989.7 / K = 11.204 / Temp = 25 C)\n", "Chemicals involved in the above reactions: {\"S\" (cyan), \"E\" (violet), \"ES\" (red), \"P\" (green)}\n", "[GRAPHIC ELEMENT SENT TO LOG FILE `enzyme_4.log.htm`]\n" ] } ], "source": [ "rxns = ReactionRegistry(chem_data=chem_data)\n", "\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", "rxns.add_reaction(reactants=\"S\", products=\"P\",\n", " kF=1., delta_G=-3989.73, temp=298.15)\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", "rxns.add_reaction(reactants=[\"E\", \"S\"], products=\"ES\",\n", " kF=100., delta_G=2000, temp=298.15) \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", "rxns.add_reaction(reactants=\"ES\", products=[\"E\", \"P\"],\n", " kF=200., delta_G=-5989.73, temp=298.15)\n", "\n", "rxns.describe_reactions()\n", "\n", "# Send the plot of the reaction network to the HTML log file\n", "rxns.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": "f18a1e67-429d-4606-a8d2-0fd07f864711", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "7da44d78-c93e-44d7-875b-92d99d40061a", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "0e771dda-1c0f-4fc0-ab21-049740643897", "metadata": {}, "source": [ "# PART 1. Set the initial concentrations of all the chemicals - starting with no enzyme" ] }, { "cell_type": "code", "execution_count": 8, "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 (E). Conc: 0.0\n", " Species 2 (ES). Conc: 0.0\n", " Species 3 (P). Conc: 0.0\n", "Chemicals involved in reactions: ['ES', 'P', 'E', 'S']\n" ] } ], "source": [ "uc = UniformCompartment(reactions=rxns, preset=\"mid\")\n", "uc.set_conc(conc={\"S\": 20.}) # Initially, no enzyme `E`\n", "uc.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": 9, "id": "76f24d9a-a788-41d8-90a4-db87386f91aa", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "27 total variable step(s) taken in 0.068 sec\n", "Norm usage: {'norm_A': 14, 'norm_B': 15, 'norm_C': 14, 'norm_D': 14}\n", "System Time is now: 4.1508\n" ] } ], "source": [ "#uc.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n", "\n", "# Perform the reactions\n", "uc.single_compartment_react(duration=4.0,\n", " initial_step=0.1)" ] }, { "cell_type": "code", "execution_count": 10, "id": "3cfa0f3a-3d78-436d-b9d8-dbf4573a7f73", "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": [ -0.0034705404693747147, 4.154236941841534 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.1111111111111112, 21.11111111111111 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "uc.plot_history(show_intervals=True, 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": 11, "id": "d684e2c3-c717-4c95-8852-62729914e48f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: S <-> P\n", "Current 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", "Current 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", "Current 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": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reactions have reached equilibrium\n", "uc.is_in_equilibrium(tolerance=2)" ] }, { "cell_type": "code", "execution_count": 12, "id": "4677fcaa-e90b-4975-a567-cb55b66f91f2", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.7322948238817497, 10.0)" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Locate the intersection of the curves for [S] and [P]:\n", "uc.curve_intersect(\"S\", \"P\", t_start=0, t_end=1.0)" ] }, { "cell_type": "code", "execution_count": 13, "id": "0a43f0bf-7718-4e60-8756-989ff3f7f680", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " SYSTEM TIME E ES P\n", "27 4.150766 0.0 0.0 16.630111" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uc.get_history(columns=['SYSTEM TIME', 'E', 'ES', 'P'], tail=1) # Last point in the simulation" ] }, { "cell_type": "code", "execution_count": 14, "id": "d4e378a6-550d-44b1-9d38-110844da1397", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "16.63011072773748" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_equil = uc.get_chem_conc(\"P\")\n", "P_equil" ] }, { "cell_type": "code", "execution_count": 15, "id": "ddc9d6bb-ea70-4471-bc1f-b0f1c48fd84c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "11.641077509416236" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_70_threshold = P_equil * 0.70\n", "P_70_threshold" ] }, { "cell_type": "code", "execution_count": 16, "id": "52f5a61b-eaab-46e7-ba0a-01c0b58ce9d1", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.9536647543782931" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uc.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": [ "# PART 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": 17, "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": 18, "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 (E). Conc: 0.2\n", " Species 2 (ES). Conc: 0.0\n", " Species 3 (P). Conc: 0.0\n", "Chemicals involved in reactions: ['ES', 'P', 'E', 'S']\n" ] } ], "source": [ "uc = UniformCompartment(reactions=rxns, preset=\"slower\") # A brand-new simulation, with the same chemicals and reactions as before\n", "\n", "uc.set_conc(conc={\"S\": 20., \"E\": E_init})\n", "uc.describe_state()" ] }, { "cell_type": "code", "execution_count": 19, "id": "bb87b0c2-6e5d-4e9a-86a1-9eb76cfe2d3a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1476 total variable step(s) taken in 3.162 sec\n", "Number of step re-do's because of elective soft aborts: 1\n", "Norm usage: {'norm_A': 1458, 'norm_B': 1472, 'norm_C': 1458, 'norm_D': 1458}\n", "System Time is now: 1.3008\n" ] } ], "source": [ "# Perform the reactions (The duration of the run was manually adjusted for optimal visibility)\n", "uc.single_compartment_react(duration=1.3,\n", " initial_step=0.00005)" ] }, { "cell_type": "code", "execution_count": 20, "id": "1c999a21-c1ab-4210-a8d8-430cc215d882", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reactions have reached equilibrium\n", "uc.is_in_equilibrium(explain=False)" ] }, { "cell_type": "code", "execution_count": 21, "id": "6991314e-58bf-473a-a0fa-c10f18369246", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.24856557905040474, 9.926581378605173)" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Locate the intersection of the curves for [S] and [P]:\n", "uc.curve_intersect(\"S\", \"P\", t_start=0, t_end=1.0)" ] }, { "cell_type": "code", "execution_count": 22, "id": "ceaf1c9e-9178-4511-af28-0b6918392300", "metadata": {}, "outputs": [ { "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": [ "# Early part of the reaction\n", "uc.plot_history(title_prefix=f\"Early times when E0 = {E_init}\", range_x=[0, 0.4])" ] }, { "cell_type": "code", "execution_count": 23, "id": "de531345-b12f-4c43-9954-bf46db6f1141", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.24856557905040474, 9.926581378605173)" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Locate the intersection of the curves for [S] and [P]:\n", "uc.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": 24, "id": "a5ea2f9c", "metadata": {}, "outputs": [ { "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", "uc.plot_history(chemicals=['E', 'ES', 'P'],\n", " title_prefix=f\"Detail when E0 = {E_init}\", range_x=[0, 0.002], range_y=[0, 0.2])" ] }, { "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": 25, "id": "de42446c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_pandas() NOTICE: 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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" ], "text/plain": [ " SYSTEM TIME E ES P\n", "1476 1.30085 0.080546 0.119454 16.544949" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uc.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": 27, "id": "ee6e7870-8dad-4ff4-997d-286db0d3a8d6", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "16.54494887428722" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_equil = uc.get_chem_conc(\"P\")\n", "P_equil" ] }, { "cell_type": "code", "execution_count": 28, "id": "b6e26868-1b81-49c9-af7c-836b881121c1", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "11.581464212001052" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_70_threshold = P_equil * 0.70\n", "P_70_threshold" ] }, { "cell_type": "code", "execution_count": 29, "id": "ac6a3e1e-3fa1-4bfd-8524-11116731c5cd", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.31446597160581014" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uc.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": "6201afdd-cbdf-47f0-9289-ea290386c660", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "802b910e-0fa0-463b-a220-873c5882a33f", "metadata": { "tags": [] }, "source": [ "# PART 3. Keep increasing the initial [E]" ] }, { "cell_type": "code", "execution_count": 30, "id": "31bbf923-046d-4da3-9c33-c8f57ef3814c", "metadata": {}, "outputs": [], "source": [ "E_init = 1.0" ] }, { "cell_type": "code", "execution_count": 31, "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 (E). Conc: 1.0\n", " Species 2 (ES). Conc: 0.0\n", " Species 3 (P). Conc: 0.0\n", "Chemicals involved in reactions: ['ES', 'P', 'E', 'S']\n" ] } ], "source": [ "uc = UniformCompartment(reactions=rxns, preset=\"slower\") # A brand-new simulation, with the same chemicals and reactions as before\n", "\n", "uc.set_conc(conc={\"S\": 20., \"E\": E_init}) \n", "uc.describe_state()" ] }, { "cell_type": "code", "execution_count": 32, "id": "ba3e8cca-873f-40dc-97b5-38374fcc826c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "866 total variable step(s) taken in 2.016 sec\n", "Number of step re-do's because of elective soft aborts: 1\n", "Norm usage: {'norm_A': 844, 'norm_B': 849, 'norm_C': 844, 'norm_D': 844}\n", "System Time is now: 0.40016\n" ] } ], "source": [ "# Perform the reactions (The duration of the run was manually adjusted for optimal visibility)\n", "uc.single_compartment_react(duration=0.4, \n", " initial_step=0.00005)" ] }, { "cell_type": "code", "execution_count": 33, "id": "c2c326ec-ccd3-46c7-9cab-462029a8f0ce", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reactions have reached equilibrium\n", "uc.is_in_equilibrium(explain=False)" ] }, { "cell_type": "code", "execution_count": 34, "id": "85807dc4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_pandas() NOTICE: 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": [ -0.00033430095908868173, 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": [ "uc.plot_history(show_intervals=True, \n", " title_prefix=f\"E0 = {E_init}\")" ] }, { "cell_type": "code", "execution_count": 35, "id": "93a7b3b5-ffff-4417-b768-bf9886e9ef7e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.06628340509848926, 9.635470546269993)" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Locate the intersection of the curves for [S] and [P]:\n", "uc.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": 36, "id": "fb00b2fc-2bc2-433f-b907-019e786f68a1", "metadata": {}, "outputs": [ { "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", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.00033430095908868173, 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 TIMEEESP
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\n", "
" ], "text/plain": [ " SYSTEM TIME E ES P\n", "866 0.400158 0.409128 0.590872 16.1715" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uc.get_history(columns=['SYSTEM TIME', 'E', 'ES', 'P'], tail=1) # Last point in the simulation" ] }, { "cell_type": "code", "execution_count": 39, "id": "264292b6-4ba1-4c36-8ea7-29472756a879", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "16.171500029051185" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_equil = uc.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": 40, "id": "ceee7058-2661-4259-a2e6-0bd6732cc2ac", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "11.32005002033583" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_70_threshold = P_equil * 0.70\n", "P_70_threshold" ] }, { "cell_type": "code", "execution_count": 41, "id": "6b0b5166-ba0c-4b15-a632-84362fbdcd5c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.08364939325100468" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uc.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": [ "# PART 4. Keep increasing the initial [E]" ] }, { "cell_type": "code", "execution_count": 42, "id": "0b2f4582-ea90-41fe-b69a-c565738e4344", "metadata": {}, "outputs": [], "source": [ "E_init = 2.0 # 1/10 of the initial [S]" ] }, { "cell_type": "code", "execution_count": 43, "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 (E). Conc: 2.0\n", " Species 2 (ES). Conc: 0.0\n", " Species 3 (P). Conc: 0.0\n", "Chemicals involved in reactions: ['ES', 'P', 'E', 'S']\n" ] } ], "source": [ "uc = UniformCompartment(reactions=rxns, preset=\"slower\") # A brand-new simulation, with the same chemicals and reactions as before\n", "\n", "uc.set_conc(conc={\"S\": 20., \"E\": E_init}) \n", "uc.describe_state()" ] }, { "cell_type": "code", "execution_count": 44, "id": "9336e30c-950b-4bc6-844a-68c3653b0244", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "818 total variable step(s) taken in 1.925 sec\n", "Number of step re-do's because of elective soft aborts: 1\n", "Norm usage: {'norm_A': 812, 'norm_B': 816, 'norm_C': 812, 'norm_D': 812}\n", "System Time is now: 0.20175\n" ] } ], "source": [ "# Perform the reactions (The duration of the run was manually adjusted for optimal visibility)\n", "uc.single_compartment_react(duration=0.2,\n", " initial_step=0.00005)" ] }, { "cell_type": "code", "execution_count": 45, "id": "76f54bfa-0189-4712-b676-667adb514a8c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reactions have reached equilibrium\n", "uc.is_in_equilibrium(explain=False)" ] }, { "cell_type": "code", "execution_count": 46, "id": "502e0b54-b059-46d6-830d-b06199c1e666", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_pandas() NOTICE: 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": [ "uc.plot_history(show_intervals=True, \n", " title_prefix=f\"E0 = {E_init}\")" ] }, { "cell_type": "code", "execution_count": 47, "id": "c5bb9972-79ba-43db-a0de-66d9495bcef4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.033892638379102225, 9.277504597225233)" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Locate the intersection of the curves for [S] and [P]:\n", "uc.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": 48, "id": "cab73b69-81c6-48cf-be12-73ddd0e9a4d2", "metadata": {}, "outputs": [ { "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" }, "xaxis": { "anchor": "y", "domain": [ 0, 1 ], "range": [ 0, 0.002 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "domain": [ 0, 1 ], "range": [ 0, 2 ], "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": [ -0.0001685491549924549, 0.20175333852596852 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.1111111111111111, 2.111111111111111 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Show the full reaction of E and ES\n", "uc.plot_history(chemicals=['E', 'ES'], show_intervals=True, \n", " title_prefix=f\"E and ES when E0 = {E_init}\")" ] }, { "cell_type": "code", "execution_count": 50, "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 TIMEEESP
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": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uc.get_history(columns=['SYSTEM TIME', 'E', 'ES', 'P'], tail=1) # Last point in the simulation" ] }, { "cell_type": "code", "execution_count": 51, "id": "5d28e797-ebb8-480a-bdcf-13880757b32b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "15.69115548729148" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_equil = uc.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": 52, "id": "94b8d506-9225-4c18-b618-2b87e9d48a3a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "10.983808841104036" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_70_threshold = P_equil * 0.70\n", "P_70_threshold" ] }, { "cell_type": "code", "execution_count": 53, "id": "968136e5-5497-4e3b-8a2b-25b02d7e9ad7", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.04311547431679562" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uc.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": [ "# PART 5. Keep increasing the initial [E]" ] }, { "cell_type": "code", "execution_count": 54, "id": "30fb7ef6-0dcd-4063-bf6b-5e69e6a9a81e", "metadata": {}, "outputs": [], "source": [ "E_init = 10.0 # 1/2 of the initial [S]" ] }, { "cell_type": "code", "execution_count": 55, "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 (E). Conc: 10.0\n", " Species 2 (ES). Conc: 0.0\n", " Species 3 (P). Conc: 0.0\n", "Chemicals involved in reactions: ['ES', 'P', 'E', 'S']\n" ] } ], "source": [ "uc = UniformCompartment(reactions=rxns, preset=\"slower\") # A brand-new simulation, with the same chemicals and reactions as before\n", "\n", "uc.set_conc(conc={\"S\": 20., \"E\": E_init}) \n", "uc.describe_state()" ] }, { "cell_type": "code", "execution_count": 56, "id": "6e3b51d3-31c8-4d55-90b6-c54275ebf914", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "836 total variable step(s) taken in 1.930 sec\n", "Number of step re-do's because of elective soft aborts: 2\n", "Norm usage: {'norm_A': 834, 'norm_B': 838, 'norm_C': 834, 'norm_D': 834}\n", "System Time is now: 0.050265\n" ] } ], "source": [ "# Perform the reactions (The duration of the run was manually adjusted for optimal visibility)\n", "uc.single_compartment_react(duration=0.05,\n", " initial_step=0.00005)" ] }, { "cell_type": "code", "execution_count": 57, "id": "a8169cc9-fa96-4388-bdbd-3672c6e9fa59", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reactions have reached equilibrium\n", "uc.is_in_equilibrium(explain=False)" ] }, { "cell_type": "code", "execution_count": 58, "id": "a4246902-f175-42db-9658-8eb630bb03c2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_pandas() NOTICE: 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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Changes in concentrations for 3 reactions (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -4.199212826107033e-05, 0.050264577528501185 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.1111111111111112, 21.11111111111111 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "uc.plot_history(show_intervals=True, \n", " title_prefix=f\"E0 = {E_init}\")" ] }, { "cell_type": "code", "execution_count": 59, "id": "cea4cabc-470c-4830-ab70-f05d4176b189", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.005877353573479905, 6.680399989705835)" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Locate the intersection of the curves for [S] and [P]:\n", "uc.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": 60, "id": "11c4c99b-cc15-488e-ba6a-f8aacd80ed67", "metadata": {}, "outputs": [ { "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", "uc.plot_history(chemicals=['E', 'ES', 'P'], \n", " title_prefix=f\"Detail when E0 = {E_init}\", range_x=[0, 0.002], range_y=[0, 10.])" ] }, { "cell_type": "code", "execution_count": 61, "id": "9ceee775-6449-419f-bb39-b42f5fbd5803", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_pandas() NOTICE: 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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Changes in concentrations for 3 reactions (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -4.199212826107033e-05, 0.050264577528501185 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.5555555555555556, 10.555555555555555 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# The full reaction of E and ES\n", "uc.plot_history(chemicals=['E', 'ES'], show_intervals=True, \n", " title_prefix=f\"E and ES when E0 = {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": 62, "id": "c7d3f38c-331b-47f2-9ae0-31531c62c7e2", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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\n", "
" ], "text/plain": [ " SYSTEM TIME E ES P\n", "836 0.050265 4.765697 5.234303 12.304598" ] }, "execution_count": 62, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uc.get_history(columns=['SYSTEM TIME', 'E', 'ES', 'P'], tail=1) # Last point in the simulation" ] }, { "cell_type": "code", "execution_count": 63, "id": "38c003d2-e007-4c47-9c91-3fb6c2a626ea", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "12.304597774138907" ] }, "execution_count": 63, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_equil = uc.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": 64, "id": "51356bd2-f34f-4189-8f39-c11804c6062c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "8.613218441897235" ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_70_threshold = P_equil * 0.70\n", "P_70_threshold" ] }, { "cell_type": "code", "execution_count": 65, "id": "f40ab9f2-a1fe-46a0-b755-9e2dd332ce9f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.008274545666098492" ] }, "execution_count": 65, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uc.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": [ "# PART 6. Keep increasing the initial [E]" ] }, { "cell_type": "code", "execution_count": 66, "id": "70c6943f-9deb-4ec0-89eb-382c9728e889", "metadata": {}, "outputs": [], "source": [ "E_init = 20.0 # Same as the initial [S]" ] }, { "cell_type": "code", "execution_count": 67, "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 (E). Conc: 20.0\n", " Species 2 (ES). Conc: 0.0\n", " Species 3 (P). Conc: 0.0\n", "Chemicals involved in reactions: ['ES', 'P', 'E', 'S']\n" ] } ], "source": [ "uc = UniformCompartment(reactions=rxns, preset=\"slower\") # A brand-new simulation, with the same chemicals and reactions as before\n", "\n", "uc.set_conc(conc={\"S\": 20., \"E\": E_init}) \n", "uc.describe_state()" ] }, { "cell_type": "code", "execution_count": 68, "id": "27e46b9b-802e-4de5-b549-062ba7a4866b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "757 total variable step(s) taken in 1.756 sec\n", "Number of step re-do's because of elective soft aborts: 2\n", "Norm usage: {'norm_A': 743, 'norm_B': 746, 'norm_C': 742, 'norm_D': 742}\n", "System Time is now: 0.020147\n" ] } ], "source": [ "# Perform the reactions (The duration of the run was manually adjusted for optimal visibility)\n", "uc.single_compartment_react(duration=0.02, \n", " initial_step=0.00005)" ] }, { "cell_type": "code", "execution_count": 69, "id": "4b74d93a-54a3-4c96-88d8-b9c4fcc34059", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 69, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reactions have reached equilibrium\n", "uc.is_in_equilibrium(explain=False)" ] }, { "cell_type": "code", "execution_count": 70, "id": "cec660e7-1c5c-4215-9501-1abd52f96df9", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_pandas() NOTICE: 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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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "uc.plot_history(show_intervals=True, \n", " title_prefix=f\"E0 = {E_init}\")" ] }, { "cell_type": "code", "execution_count": 71, "id": "b44a6da4-b3bb-4297-932b-3df13fe796d0", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.0024715441102170356, 4.283809315596441)" ] }, "execution_count": 71, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Locate the intersection of the curves for [S] and [P]:\n", "uc.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": 72, "id": "5fcdb4fd-0dba-43b7-880f-4c8b3aceca1e", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=S
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Concentration=%{y}", "legendgroup": "S", "line": { "color": "cyan", "dash": "solid", "shape": "linear" }, "marker": { "symbol": "circle" }, "mode": "lines", "name": "S", "showlegend": true, "type": "scattergl", "x": [ 0, 5e-05, 5.025e-05, 5.0375000000000005e-05, 5.050000000000001e-05, 5.062500000000001e-05, 5.0750000000000014e-05, 5.087500000000002e-05, 5.100000000000002e-05, 5.112500000000002e-05, 5.1250000000000026e-05, 5.137500000000003e-05, 5.150000000000003e-05, 5.1625000000000035e-05, 5.175000000000004e-05, 5.187500000000004e-05, 5.2000000000000044e-05, 5.212625000000005e-05, 5.2253762500000046e-05, 5.2382550125000046e-05, 5.2512625626250046e-05, 5.2644001882512544e-05, 5.277669190133767e-05, 5.291070882035104e-05, 5.304606590855455e-05, 5.3182776567640095e-05, 5.33208543333165e-05, 5.3460312876649664e-05, 5.3601166005416164e-05, 5.374342766547032e-05, 5.3887111942125024e-05, 5.403223306154627e-05, 5.417880539216174e-05, 5.4326843446083356e-05, 5.447636188054419e-05, 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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": [ -1.68315767511259e-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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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# The full reaction of E and ES\n", "uc.plot_history(chemicals=['E', 'ES'], show_intervals=True, \n", " title_prefix=f\"E and ES when E0 = {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": 74, "id": "05426505-fa5c-4b0f-bdae-9eaf3cace1dd", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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\n", "
" ], "text/plain": [ " SYSTEM TIME E ES P\n", "757 0.020147 10.998147 9.001853 9.163739" ] }, "execution_count": 74, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uc.get_history(columns=['SYSTEM TIME', 'E', 'ES', 'P'], tail=1) # Last point in the simulation" ] }, { "cell_type": "code", "execution_count": 75, "id": "50529736-69a0-404a-ac61-2b5f9b2ba216", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "9.163739207468186" ] }, "execution_count": 75, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_equil = uc.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": 76, "id": "31d1a073-906e-45d0-90d2-d63f8e4d7df2", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "6.41461744522773" ] }, "execution_count": 76, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_70_threshold = P_equil * 0.70\n", "P_70_threshold" ] }, { "cell_type": "code", "execution_count": 77, "id": "c6d79966-d114-4e66-bb94-bcf852fee8be", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.004076150862005783" ] }, "execution_count": 77, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uc.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": [ "# PART 7. Keep increasing the initial [E]" ] }, { "cell_type": "code", "execution_count": 78, "id": "06f75fcd-19b7-45dd-bcd5-ea5136280700", "metadata": {}, "outputs": [], "source": [ "E_init = 30.0 # 50% higher than the initial [S]" ] }, { "cell_type": "code", "execution_count": 79, "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 (E). Conc: 30.0\n", " Species 2 (ES). Conc: 0.0\n", " Species 3 (P). Conc: 0.0\n", "Chemicals involved in reactions: ['ES', 'P', 'E', 'S']\n" ] } ], "source": [ "uc = UniformCompartment(reactions=rxns, preset=\"slower\") # A brand-new simulation, with the same chemicals and reactions as before\n", "\n", "uc.set_conc(conc={\"S\": 20., \"E\": E_init}) \n", "uc.describe_state()" ] }, { "cell_type": "code", "execution_count": 80, "id": "45e38a17-5515-4d69-8b27-168331473dd4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "749 total variable step(s) taken in 1.702 sec\n", "Number of step re-do's because of elective soft aborts: 2\n", "Norm usage: {'norm_A': 743, 'norm_B': 746, 'norm_C': 742, 'norm_D': 742}\n", "System Time is now: 0.010054\n" ] } ], "source": [ "# Perform the reactions (The duration of the run was manually adjusted for optimal visibility)\n", "uc.single_compartment_react(duration=0.01, \n", " initial_step=0.00005)" ] }, { "cell_type": "code", "execution_count": 81, "id": "8d7277d0-1d8f-479a-9110-eace7ef00222", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reactions have reached equilibrium\n", "uc.is_in_equilibrium(explain=False)" ] }, { "cell_type": "code", "execution_count": 82, "id": "dd0211e8-5dfb-4c1c-809c-b7824f04af50", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_pandas() NOTICE: 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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Changes in concentrations for 3 reactions (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -8.39919376403413e-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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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "uc.plot_history(show_intervals=True, \n", " title_prefix=f\"E0 = {E_init}\")" ] }, { "cell_type": "code", "execution_count": 83, "id": "64c0b5f9-1a4a-4b65-a927-f4c24839c44c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.0015007776137844029, 2.9518860757696133)" ] }, "execution_count": 83, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Locate the intersection of the curves for [S] and [P]:\n", "uc.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": 84, "id": "1bf0ed70-9c0a-4c93-b538-0cafeb01921b", "metadata": {}, "outputs": [ { "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" }, "xaxis": { "anchor": "y", "domain": [ 0, 1 ], "range": [ 0, 0.005 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "domain": [ 0, 1 ], "range": [ 0, 30 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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Z/TBm221zO8j7I8P7EIAABCDQDgLRiwLB6OPyMlsEuE4JMZcOVFk+lHd6kbnMwHX6kNRVbMgxmXKsZdattkVnT0LMFOgOp73sytyEqTtWRU/OyTqq1XXKjmnT3tSZxUt3GG/9+h+nG2fLiIKsjm+3jrfrFClzyZg5Al/GflGuZUSB69ZrX6cPVY1/t6/OrBjrvUF5sxtZIt0s03X6kLxvnrDl+qybs3hl226b20E7/tThJQQgAAEI5BFohSjQneU15142rz72DEKZkXB7/bB5Xn4VUZDlp3RUXDe/Zq2Dd3UozIoX3RQaShSIL/YGbZdPeeeol5kp0PW3bbpmkFx7MEz/yogCU5RqH/LOj9cdSPueDH13ht1xtdthnv08rmVEgU5rf7Dyls+YdczqiOf5WXRU3vYt63NTxOciosAVP+2DWVfbDxHKIjzle8rVLvPablvbQd4fGd6HAAQgAIF2EGiNKGgHTreXTd382mZm+A4BCEAAAhCAAAQgUB8BRIFn1jJKrZepaNNF9g94dgNzEIAABCAAAQhAAAIQKEwAUVAYVbGErqUrRU7EKWadVBCAAAQgAAEIQAACEPBPAFHgnykWIQABCEAAAhCAAAQg0CoCiIJWhQtnIQABCEAAAhCAAAQg4J8AosA/UyxCAAIQgAAEIAABCECgVQQQBa0KF85CAAIQgAAEIAABCEDAPwFEgX+mWIQABCAAAQhAAAIQgECrCCAKWhUunIUABCAAAQhAAAIQgIB/AogC/0yxCAEIQAACEIAABCAAgVYRQBS0Klw4CwEIQAACEIAABCAAAf8EEAX+mWIRAhCAAAQgAAEIQAACrSKAKGhVuHAWAhCAAAQgAAEIQAAC/gkgCvwzxSIEIAABCEAAAhCAAARaRQBR0Kpw4SwEIAABCEAAAhCAAAT8E0AU+GeKRQhAAAIQgAAEIAABCLSKAKKgVeHCWQhAAAIQgAAEIAABCPgngCjwzxSLEIAABCAAAQhAAAIQaBUBREGrwoWzEIAABCAAAQhAAAIQ8E8AUeCfKRYhAAEIQAACEIAABCDQKgKIglaFC2chAAEIQAACEIAABCDgnwCiwD9TLEIAAhCAAAQgAAEIQKBVBBAFrQoXzkIAAhCAAAQgAAEIQMA/AURBwnTdhk3qscefmKO7+eqL1apTV879/6KNN6h7tz2c/v/EFcvVls0b/UcCixCAAAQgAAEIQAACEGiIAKLggCjQHf0Hfvio2nDpNeru265Sy449Sn37O/epG2+5U23ben0aIhEQp5y8Ql1y/tkNhYxiIQABCEAAAhCAAAQg4JcAosDB84QPnKf0bIEtAmyR4DccWIMABCAAAQhAAAIQgED9BBAFFnPp9F953a1zMwWrP/5F9fnPnKXOWXt6mlLPJGy//+b6o0WJEIAABCAAAQhAAAIQCEAAUXAAqu7sy3/NPQUya3DFhevniQK9vChATDAJAQhAAAIQgAAEIACBWgkgCizcO555Xq0597I5YZA3U/DSn72kJteOq/3HDNUaOAoLT+CIxWPq9T371J6p6fCFUULtBI4+YpH61UtvqOmZ2oumwMAEhoeH1FuXjKvnXtoTuCTMN0Fg4diIOmh8RO16ZbKJ4imzBgLHHLmohlIowiaAKHC0CVMI5O0pEFGw/52javI/jdK6+owAoqDPAmpVB1HQv/FFFPRvbKVmiIL+jq/UDlHQTIwHXhTIsqGH/mX73GlCehmRXkKUd/qQiIKZQ4fUnk+PNxNBSg1GAFEQDG0UhhEFUYQhiBOIgiBYozGKKIgmFMEcQRQEQ9vV8MCLAqEj+wbMp8w9BRNfn1DTL0+zhKiZ9hu0VERBULyNG0cUNB6CYA4gCoKhjcIwoiCKMAR1AlEQFG+mcURBj9xfv/d1tfef97KEqEeOMWZHFMQYFX8+IQr8sYzNEqIgtoj49QdR4JdnjNYQBc1EBVHQI/eZiRn18v/9MkuIeuQYY3ZEQYxR8ecTosAfy9gsIQpii4hffxAFfnnGaA1R0ExUEAUeuL9444QafmFaTZ2+QO1bMeLBIiZiIIAoiCEK4XxAFIRj27RlREHTEQhbPqIgLN8YrCMKmokCosAD91/946tqwX1Tav/yYTW5ZsyDRUzEQABREEMUwvmAKAjHtmnLiIKmIxC2fERBWL4xWK9DFNj3UMVQ7yo+fO0bt6u7vv+Q2rb1+irZO/IgCnpGqNRzT76hxm+dPQ977/qFanqxB6OYaJwAoqDxEAR1AFEQFG+jxhEFjeIPXjiiIDjixgvwIQou2niDunfbwx11OWP1KeraTRekrzUlCuRUyyuvu1X5ugQXUdB4c+104NkX31Bjf7dPjfz7PpYQRRabXtxBFPRCL/68iIL4Y1TVQ0RBVXLtyIcoaEecevGyV1EgHf6lRyyZN3oud0994bMfV6tOXdmYKOiFiysvosA30R7tiSgYeXZGjX1nLxuOe2QZU3ZEQUzR8O8LosA/01gsIgpiiUQYPxAFYbjGZLUXUSAzBD9+9Ge5y2n0TMGNt9ypdu6aSKt/3roz5+6t0jxESDz2+BNzeMwRfnnvmKOPVM8+9+JcmhNXLFdbNm9UchGutmvOUOj7sOyZAvt4fP2+aUc7sf3+m+f8QRTE1HITX0QUyLPwW3vV0O4Z7iyILD5V3UEUVCXXjnyIgnbEqYqXiIIq1NqTB1HQnlhV9bQXUSCda1fn3vZFd8J159u+vFbS606/XnKkl/7oTrkWDPp+qx3PPK/WnHtZWpS2q1/TaWxRoN83fZZy5Dln7empuDD3C0iZ8ojwkAdRULWVBcqnRcGCH+1To8nP/neOqsn/NBqoNMzWRQBRUBfpZspBFDTDvY5SEQV1UG6uDERBc+zrKrmqKLA74N38de0pkA745z9zVtoZl8775V+9ad6Mg5nGFg1Snrz/0Q+e1jHjYNvdcOk1c6JBOvUP/+vjc538PMa2MEEU5BGr+X0tCoZfUWw4rpl9yOIQBSHpNm8bUdB8DEJ5gCgIRTYOu4iCOOIQ0osmRYHu0Etn++Yt9zirqUf1y4gCbdeeKXDZsAu1lxbJ+3q2AlEQsiVWsK1FgWSd23C8Krmz4CTuLKiAM5osiIJoQhHEEURBEKxRGEUURBGGYE4gCoKhjcZwVVEgFSh6qlDWTIEpCvKO+gwtCrSAsJcWyelFiIJommunI6YoYMNxpEGq4BaioAK0FmVBFLQoWCVdRRSUBNay5IiClgWsgru9iALpqD/3wi7nRmPpZMuTdfqQufQna0OwWR0fokA2RstGZb1HwLTvmgVg+VCFBlVnFlMUSLl6wzE3HNcZBf9lIQr8M43JIqIgpmj49QVR4JdnbNYQBbFFxL8/vYgCva/APpJULwfSG37zZgqkViIS5DE3+oqd437tLem+Ax+iQPt7xYXrU5vy6I3G8m9zVkD7JKcaMVPgv915sWiLgtHH96c3HM8cOqT2fHrcSxkYqZ8AoqB+5nWWiCiok3a9ZSEK6uVdd2mIgrqJ119eL6JAe2sfJSqvm8eAFhEFksdlxzx9SI4k1acT6U67a6Nx1p4CyWOeWqT9177al7DJUiLZ64AoqL9dFirRFgWSieNJC6GLOhGiIOrw9OwcoqBnhNEaQBREGxovjiEKvGCM2ogPURB1BSN1bmgmeSL1rTVuuUTB3PGky4fV5Jqx1tQFR98kgCjo79aAKOjf+CIK+je26aDb2Ig6aHxE7Xplsr8rOsC1QxQ0E3xEgQfuLlHA8aQewDZsAlHQcAACF48oCAy4QfOIggbh11A0oqAGyA0XgShoJgCIAg/cXaJAzOrjSbnMzAPkBkwgChqAXmORiIIaYddcFKKgZuA1F4coqBl4A8UhChqAnhSJKPDAPUsUMFvgAW6DJhAFDcKvoWhEQQ2QGyoCUdAQ+JqKRRTUBLrBYhAFzcBHFHjgniUKmC3wALdBE4iCBuHXUDSioAbIDRWBKGgIfE3FIgpqAt1gMYiCZuAjCjxw7yYKmC3wALghE4iChsDXVCyioCbQDRSDKGgAeo1FIgpqhN1QUYiCZsAjCjxw7yYKmC3wALghE4iChsDXVCyioCbQDRSDKGgAeo1FIgpqhN1QUYiCZsAjCjxwzxMFzBZ4gNyACURBA9BrLBJRUCPsmotCFNQMvObiEAU1A2+gOERBA9CTIhEFHrjniQJmCzxAbsAEoqAB6DUWiSioEXbNRSEKagZec3GIgpqBN1AcoqAB6IgCP9CLiAKZLRj77l41tHtGTa4dV/uPGfJTOFaCEUAUBEMbhWFEQRRhCOIEoiAI1miMIgqiCUUwR/pVFKz++BfVzl0Tc9yWHrFEbdt6fTCOZQ0zU1CWmCN9EVEg2fQtxzOHDqk9nx73UDImQhJAFISk27xtREHzMQjlAaIgFNk47CIK4ohDSC/6URSIIPjoB09Tl5x/9hy6izbeoD7xkdVq1akrQ+IsbBtRUBhVdsKiokAsLPzW7GzB1OkL1L4VIx5Kx0QoAoiCUGTjsIsoiCMOIbxAFISgGo9NREE8sQjlSb+Jgh3PPK/WnHuZuvu2q9SyY48Kha1nu4iCnhEqVUYUjD6+Xy24b0rJbMHkx8bV9GIPDmAiCAFEQRCs0RhFFEQTCu+OIAq8I43KIKIgqnAEccaHKLgriGfdjQ4nb384I4nMFBz9liPUls0bG/CsWJGIgmKcuqYqIwrE0Pgdk2r4hWm1/zdH1eT7Rz14gIkQBBAFIajGYxNREE8sfHuCKPBNNC57iIK44hHCGx+ioKmdmzNdgJzwgfM63j1v3Zkdy4lCsCxjE1FQhlZG2rKigCNKPUCvwQSioAbIDRaBKGgQfuCiEQWBATdsHlHQcABqKN6HKDirBj/tImSYd2vBch/44aNqw6XXqCsuXK/OWXt6wVxhkyEKPPAtKwqkSDYdewAf2ASiIDDghs0jChoOQMDiEQUB4UZgGlEQQRACu+BDFAR20Yv5dRs2qVNOXhHNbAGiwENYq4iCmb3TatEdU+mm432/Naqmkh+euAggCuKKh29vEAW+icZjD1EQTyxCeIIoCEE1Lpv9JgpkVuDr39zasZ9AzxRsvvpiTh+Kq/n15k0VUSAl6k3HanxI7f0Um457i4L/3IgC/0xjsogoiCkafn1BFPjlGZs1REFsEfHvT7+JAiEkswKPPf5EB6zYTiNipsBDW64qCqTosb/bp0b+fZ+aPmZY7V075sEbTPgigCjwRTJOO4iCOOPiwytEgQ+K8dpAFMQbG1+e9aMo8MUmpB1EgQe6vYgC86ZjlhF5CIZHE4gCjzAjNIUoiDAonlxCFHgCGakZREGkgfHoFqLAI8wSphAFJWBlJe1FFIjNuWVEyb/3rl/I3QUeYuLDBKLAB8V4bSAK4o1Nr54hCnolGHd+REHc8fHhHaLAB8XyNhAF5ZnNy9GrKBCDYw8my4h+si+91OyNTy5QQ+NyBQZPkwQQBU3SD182oiA846ZKQBQ0Rb6echEF9XBushREQTP0EQUeuPsQBeZpRFxq5iEoHkwgCjxAjNgEoiDi4PToGqKgR4CRZ0cURB4gD+4hCjxArGAiOlEg10Dv3DXhrMr2+2+uUMXwWXyIAvEyvdTsr/cma4hm1NSqBWrfSSPhnaeETAKIgv5uHIiC/o0voqB/Yys1QxT0d3yldoiCZmIclSiQ45qOOfpIde2mC5qhUbFUX6JAih99ZL9a8MBUog44prRiOLxlQxR4QxmlIURBlGHx4hSiwAvGaI0gCqINjTfHEAXeUJYyFJUoOOED56mYLnEoStKnKJAyzf0Fkx/j/oKicfCdDlHgm2hc9hAFccXDpzeIAp8047OFKIgvJr49QhT4JlrMHqKgGKeuqXyLAils4bf2prcdTy9N7i/4FPcXeAhTaROIgtLIWpUBUdCqcJVyFlFQClfrEiMKWhey0g4jCkoj85IhKlEgy4fWrlmlzll7upfK1WUkhCgw7y9g43FdkewsB1HQDPe6SkUU1EW6/nIQBXVZXjwAACAASURBVPUzr7NEREGdtJspC1HQDPeoRMEDP3xUXf7Vm9S2rdc3Q6NiqSFEgbhibjzmYrOKwekhG6KgB3gtyIooaEGQKrqIKKgIriXZEAUtCVQPbvajKMg6SCemQ3SiEgWyp6DbExM4089QokDKGHliWo3dPZkWx4lEPXzDVMiKKKgArUVZEAUtClZJVxEFJYG1LDmioGUBq+Buv4qCj37wNHXJ+WdXIFJPlqhEQT1V9l9KSFEg3i740T41mvykwuD05KjSFRxV6j+K8y0iCuqg3FwZiILm2IcuGVEQmnCz9hEFzfKvo3REQR2U55cRnSiQJUQbLr2mw9PYTyQKLQpsYbAn2Xg8k2xA5glLAFEQlm/T1hEFTUcgXPmIgnBsY7CMKIghCmF98CEKpn6WHO9e9zOUDOT+hwXOUmX5EDMFJQLy7e/cp6687lZ1921XqWXHHpXm3PHM82rNuZepKy5cH+0G5DpEQYcwSO4w2POxBQiDEm2rSlJEQRVq7cmDKGhPrMp6iigoS6xd6REF7YpXFW99iIKX/uylKkX3nOfwPzk8UxS4LueNaWl8VDMFoqI+/5mz5nX+RSzceMud0W5ArksU2MJg75kL1PSxzBj0/AnOMIAoCEU2DruIgjjiEMILREEIqvHYRBTEE4tQnvgQBa/e/moo97LtJl2yQz51CDMFPshnXV6mlxTFpKbM+tYpCjqEQfIf9hj4aHluG4iCcGxjsIwoiCEKYXxAFIThGotVREEskQjnhw9REM67apZZPlSSGzMFxYF1bD5elWw+PonNx8XpFUuJKCjGqa2pEAVtjVy+34iCfEZtToEoaHP0ivmOKCjGyXeqqJYPNbWnwD471t7YfNHGG9S92x5O2Z+4YrnasnljRxzqninQhZvCgHsMfH80lEIU+Gcak0VEQUzR8OsLosAvz9isIQpii4h/f/pVFLCnoGRbqfv0IdnIfO1f3qGu3XRB6qkWJnqpkr2fQW5dPuXkFR3nzDYlCsTf0Uf2qwUPzO6w5+bjko0tJzmiwC/P2KwhCmKLiD9/EAX+WMZoCVEQY1T8+tSPosAvoTDWopopCFPFclb1aUf6BCRbBLg2PTcpCqR26QVnf5cIg70zajo5qnRqzZiaXlyu3qSeTwBR0N+tAlHQv/FFFPRvbKVmiIL+jq/UDlHQTIwRBRZ3e1Ozvc/Btem5aVEgVRjaOa3G75lSQ7tn1MyhQ0pOJuIug94+VIiC3vjFnhtREHuEqvuHKKjOrg05EQVtiFJvPiIKeuNXNTeiwCJn7w6XE5HMOxK0KNAzCacl+e99vYELMlwRTwTB/nv2qJmn9qfvjvzuuBp6j/sSjaoNZpDyLRofUVP7ptW+/TODVO2Bqeshixao1/ZMqZkBCe/09IySzvIgPENDQ+rghSPq1Tdmb4Ln6S8CoyPDasHokHpj7+zfOp7+I7D4IPouTUQ1ClGgO95ycVm3J/SRpCII3rPyHXP7C8SXvJkC+RP7t8kX06rkD24sz/QP9qrpf5lM3Rn6D6Nq6MxxNbyQ+wzKxmfR2AFREFFsy9aB9NkEDlk0ql5LOo3xfHLDRmuwRIFSB4+Pqlf3IArCtqpmrI+ODKkFiTB4YxJR0EwEwpe6OPl+5qmfQBSioP5qzy/RJQgkVd6eAhEFn0pEwbWvznbCY3nMfQaynGjyd7norGxsWD5Ulli70rN8qF3xKuMty4fK0GpfWpYPtS9mZT1m+VBZYn7SRyUKsi4vC32jsZR73rozO04U0njzTh8SUXB8MpL8Ty/t8RMRj1aGX1FqwX2TavjZ6dSqnE6095RhNTTOrEERzIiCIpTamwZR0N7Y5XmOKMgj1O73EQXtjl8R7xEFRSj5T9MKURDyRmN9BKmN9ozVp8wtI+p2T8HyJOOTyc/fTOxVpyXrz2N80mNLf5RMoyenEzFrUDxCiILirNqYElHQxqgV8xlRUIxTW1MhCtoaueJ+IwqKs/KZshWi4GvfuF3d9f2H1Lat1/usuxdbFyVWrkt+YlxCZFbQnjWYPiY5uvR0ji7t1ggQBV4+ItEaQRREG5qeHUMU9IwwagOIgqjD48U5RIEXjKWNNC4KXJeVuWph3zJcuqaBMvwisfv25CfWJUR2tc1ZAzU+pPadNKImT2JJkat5IAoCfWgiMYsoiCQQAdxAFASAGpFJREFEwQjkCqIgENgcs42LAtO/rD0FzaApXuqJyZGV25PTEK5LNht/sgVHpM3sTe40eHBajfz7gZM5EnEwtWpU7VsxUrzSA5ASUdDfQUYU9G98EQX9G1upGaKgv+MrtetHUSAH2uzcNTEvePpkTddydvNI/DqiHpUoqKPCIcq4PhEDFx4yps5Mjkf75itxnULUrb7Dz0ynew30RmT2G3TSQhSE+LTEYxNREE8sfHuCKPBNNC57iIK44hHCm34VBR/94GmZh9rIsfzm0fs7nnleXfKnN6otmzeGQOy0iSjwgPqHyclD/9vhC1NL/5z8+7iWnWs/+vh+NZqIA7kNWZ50v8FvjarpYwf7lCJEgYcPR8QmEAURB6dH1xAFPQKMPDuiIPIAeXBv0ESBHGgjz7WbLvBAr7qJqESBqKI1516WWZvQl5dVxfjsi2+ozy4eU/ckl121ZQmRq64d+w2SBDJzsO+kUTW1YmggjzFFFFT9RLQjH6KgHXGq4iWioAq19uRBFLQnVlU99SIK7rqravHV8w0ng6kf/rAzvywfypspaHr/bFSiQAM77T+eoC7/6k1zpw3JBWJr16xS56w9vXqgAuYUUfC9RBD8fiIM2rLhOAuH7DdY8PiMGn3kzZmDQd2QjCgI+KGJwDSiIIIgBHIBURAIbCRmEQWRBCKgG15EwZDcJNXAMzO76sJ+8vYUyEmbN2+5pyNb3YPhUYkCvdF42bFvVeu/8JU5USAnFJkioYEQdy1SRIE8702WED01PBT1nQVl2I08Oa1G//XNPQeSd5CWFiEKyrSW9qVFFLQvZkU9RhQUJdXOdIiCN+MmA3lDe91xHEq2OA5Pdu8YD73S/X4lvaw4s6VMJh3gjPJ1npHkItW8ZyaxM5TcpaSfI754WF6W/PfPOis/je8Uo6NKbd3qtNptpsCVQQbEn3thV63H8UcpCladulKJQNAKKeTlZT7agxYFFyWbjf96fCT6OwvK1tnekJzmH4DjTBEFZVtKu9IjCtoVrzLeIgrK0Gpf2qqiIKsDPfJqRsfZ6qiapDI7y106yV07x10657kd8/aFMNfjw//k8Nw0bUtQVhQ00feNShSIKjrl5BXpzmzz3zFfXiaNUouCp5NZgjZvOM77gMkX6tgjyexBckOy3I6sH5k92P+/jPTd3gNEQV6LaPf7iIJ2x6+b94iC+mLr6mg7O9muDnYywmyODs95/cr85Rdmh1riK0u39+1L0jk60+nIufE3qj4aDZSUDNDNjHcpd3H3A0P2L87xeXH3mYaZpHzVrfzE/EyOD+LB9NiMmhl705djlh/cAMywRXYTBdLn/cJnP65kUFw/8po8nD50gIjMFujn7tuuUsuOPSpsxCpa16JAsvfDhuMiGGT2YEROLXoimXrsU4GAKCjSEtqbBlHQ3tjled7XomB353KPeR1wR+d73kizYzTbOYptdbhb39nO6kBndFrTjqp0el1PRme5Wye5W+d4/yHudehp0YcO3kmAXvYU5H1R1Px+tz0Frot8z1h9Su2nEUU1U1BzfLwVZ4qCh0aH1e8tGW/9huOicNKNyU/OqJF/26+GX5S1hZ0zCHKs6f5kJqGNx5siCoq2gnamQxS0M25FvA4lCuxR8bwOeV5n3O6I2+uqW9EJd3W0HZ1sZwdbRpjH5ne65eQ7+zE71GMLhtXC5Gf36/uUqzMtI+dD44PXkS7y2WhLmn4UBW1gH5UoaOuNxqYokKDrDcdtPp60SuPVAmH45/vVyLOdAkH2IOw/ZigRByNq39uTL/wWjHwgCqq0gvbkQRS0J1aZnhqj5mYHXUTBofuG1cRrU2nWeZ1zY3mKLF8xN2PO65gfuL8lFlrzOsxWB9zZ+bZGtV2j2a5RbLvDHUtnu+qeglhiiB/5BBAF+YxCpEAUeKBqi4I7ks3GcsPx+6am1R27c7bleyg/RhMiEEZ2KjXyZCIQkiVG8/4oy0bl5cNqZqnMJCRrIpPfsT2Igtgi4tcfRIFfntqaOZpun35innTS8Z1gLGexO+nmmvHGR86tUXHpXA8ZI93zOuQ5nXG7I26vq46lEx6mpVS3iiiozq4tOREFzUQqKlEQ+30EWSGyRcFEMhD+ocNmjydt4w3HQZpiMqI3miwzGtqZ/Lb2IaTlJX9cp49Mft4yKxD2/VrzswmIgiAtIRqjgygKCnXY7c2fB0bVu3bWGxpN7xg1N0fMk6+PsSNG1BuTyaEI6fdL8mN03s186ai53bE3Njy2YVYzmg9VTY4gCmoC3WAxiIJm4EclCuRGY/N+gmaQlC/VFgVioV+PJy1PJyOHiIRfJiJBNiw/65hJ0EIhWVsqYkGEgvzev7S+taKIAm/RjtJQtKLgwJKYzFF2s9OeMcJuLoGpfXTdGE23R9I7TjoxRtHN5Sx2J91cwlJ05DzUnoIoG/IAOoUo6P+gIwqaiXFUosA8bciFo+6b3YqGxCUK+v140qJsiqbTy41ks/LwM7ObljPPZpZZBUMsyCjgfpllSI5W87m5DFFQNHrtTFdVFJij7R0bTY1TXzrarrF+vWNjqXGyS23nkBfpsGeMqnfrrMc2mo4oaOdnsqjXiIKipNqbDlHQTOyiEwWbr76445xWwfLt79ynbrzlzlpvdSsTDpcoYLagDEF3WlMoyLKjVDDIMoVu508fEAwzhyRnIyfCIV2zm3Ry5LeMOBYdaRSPEAW9x7AJC5lLZMyjGpPR9sXDo+q1PVNqRtrTga0/5hKZpkbb9dKWzFF2o9NeZIS9TJtvIl4hykQUhKAaj01EQTyxCOUJoiAU2e52WyEKmrjVrUw4skQBswVlKJZImyyvGE6uTR9+dXaPgoyypjMLRS+s0aOlIhT0xS3JUgbdwdIjoouPGlVv7N2v9h5UwjeSOgnkHeVYZQNqR6e9zjXt5mZTYx17xyZTc2mMcbyiubG042SXFpzG1aamjShoU7TK+4ooKM+sbTkQBc1ErBWioC03GrtCyN6Cehu2dD5FMIykdyYky4lkiUbye1Y0dFmSVMBN1whukTXS2rS9/MIs0j51pIA7mUmct4naqV23i0qagjeM5l10VFig9VLRrLwFl8gcsmQsnSmYlk2mB27kNGNkxmQQR9tDhKYum4iCukg3Uw6ioBnudZaKKKiT9ptlNS4KXLe4uVC4lhU1g2x+qVkzBZJSzxYcPz2j/mZirzou+c3TLAE9ai2dZz1Cna7pPrBpMxUPrybCIjnifGYmeX2CmPUcMfuCI+ts9SLiquspMRVG2qvuKeiZBQaCE0AUBEfcaAGIgkbx11I4oqAWzPMKaVwUmB71y+VlNmU9W3Dx61PqD9/Y10ykKbU0gXl7ChynwhRZ9qILnneko+GRfWFSaWfNDI7bRG17zguOJFHBG0Zdsx5VTonpqZ49ZkYU9Agw4uyIgoiD48E1RIEHiJGb6EdRsPrjX1Q7d03MkT9xxXK1ZfPGqCIRlSiIikwJZ7rNFIgZPVuwJBlwvvflPcwWlGDbZFI2GjdJP3zZiILwjJsqAVHQFPl6ykUU1MO5yVL6VRR89IOnqUvOPztFKyLhPSvfoa7ddEGTqDvKRhR4CEWeKJAi2FvgAXTNJhAFNQOvuThEQc3AaywOUVAj7AaKQhQ0AL3mIgdBFMR4smZ0osCeXjHbYZvuKbA/P5xEVPM3iofiEAUeIEZsAlEQcXB6dA1R0CPAyLMjCiIPkAf3fIiCu/7HXR48KWdieGhYffgdH3Zmkv6tOVOAKMhhu27DJnXM0UdGNZVSpDkUmSlgtqAIybjSIAriiodvbxAFvonGYw9REE8sQniCKAhBNS6bPkTB0KbkZLkGnpmN7sNJbFEg+2jPW3fm3HKiBlydV2RUMwX9utFYU2e2IIYmX9wHREFxVm1MiShoY9SK+YwoKMaprakQBW2NXHG/fYiCs759VvECPaUcTS7F3Lpua+ZMgbnRODZBIE4jCjw0hKIzBVLUlw5eoP5q4ah639S0umP3gWtUPfiACf8EEAX+mcZkEVEQUzT8+oIo8MszNmuIgtgi4t8fH6LAv1e9WbRnCnqzFiZ3VKJAlg+tXbNKnbP29DC1DWS1jCiQ2YLfWzKunkp+X/fqpPpkcmMuT5wEEAVxxsWXV4gCXyTjs4MoiC8mPj1CFPikGactREEzcYlKFMhFZpd/9Sa1bev1zdCoWGoZUSBF3DE+oi48ZEzJhWb/9NKeiqWSLTQBREFows3aRxQ0yz9k6YiCkHSbt40oaD4GoT1AFIQm7LYflSiQPQXdnjafPmTX672HL0xnC7jQrJmGX6RUWxSM7PhFmm3kqR1z2Uefmn0tff3A+/Lv4d0TamjizUtK5LVR4327/KEk/fDEy0Xcyk0zveQwNXPokq7p9i17m/P9mSVL1LSVN7WXvG4+8pqZbjp53y5zf0YZuRWoKQGioCbQDRSDKGgAeo1FIgpqhN1QUf0oChpCWarYqERBKc8jSlx2pkBc3z4ypM44bGFai39OZguOS2YNeOohMJR0vqVjP5x02qXzLp156ZDrjrzuvC94ZoeamZlRw794s+Nfj4f9V8qMiAhDWJjCRV6X/+vHFCa2INl3/JtiZv/xy+bypKLEsFGEIKKgCKV2pkEUtDNuRb1GFBQl1d50iIJmYoco8MC9iiiQYrnQzAN8y4R0+Bc89uhcZ19G8mc7/Unn/8C/q5aqR773Gx1Tc8Td7KRKGfZIudmhdflg56/q5+ysQ+cshW3LnOEw35PZDXvGwjXrkYooowzXTIc5c1K1LlXymQIkS3yI8DjoqKXqtT1Tav+hnTMhOk7m7EcV0VHFd/L4IYAo8MMxViuIglgj488vRIE/lmUsIQrK0MpIW1UUsOm4Gnzd8V/w2CNKd/pl5F9G+OW9vEc6jdKZl+UuepRaOuR6VFp3Che/89fVG8lG8NePOT7PJO/nEJC4zBcRs8JFRIcpRExhYgsScwmWiDz9iO0isfcRqCzRYQpEc7bDFIdZMx2xL7Xywa1OG4iCOmnXXxaioH7mdZeIKKib+Gx50YkCOYHoscefSJ3bfPXFatWpK5XsNThj9SnRXmpWVRRIHc1Nx38zsZdlRMbnwO78L3j0kWQW4JGunT/d4ZdOvnS0pBMmv2X9u36t6EeNjcZFScWVzhQg5qyJKT5EeBw6+Vo6UyD/1vs/zBkQc/ajTtFhCgQ9K2UusSqyvGrQZzkQBXF9Jn17gyjwTTQ+e4iCZmISlSgwbzSW81y//EefS0VBjFdBm+HqRRSInc8uHlP3jI2oTyWj0tcmx5QO4qMFwPiDf592/OUna/mJdPynTjwpHe2Xjv7Uyt9MOv+JCEh+yq4r78YaUdDfLbHqnoIs0WEuyTJnOzo2ph/YbG4vt6prqZW9t8MlOiTqeilbyD0dIVsXoiAk3eZtIwqaj0FoDxAFoQm77UclCmRG4O7brlLLjj1KmaJAjirdcOk1qp9OHzLDIcuIZNPxRHIj96DcXTCadPrH5OfBf5gVAY/+ZF4L1Z3/qZWJAEhG/EUITJ240mvHH1HQzBdPDKVWFQUhfbeXWWlBYc9y6OVW5vKqGGY5hE1Z4SF5fIsPREHIVtq8bURB8zEI7QGiIDThFogCEQK3fv2P54mCfp8pkNDclNxyvDG57VjuLujHZUTSuZFZgIV/+/9mzgJMvv93klH/k9Te5LeM/O9LRECTDzMFTdIPX3aMoiB0rXsRHeJb1p6OumY6bD7mUitzU/nMYYepsaVHqDcmZy+HtI/atfOZx+vmHRgQOkbYzyeAKMhn1PYUiIJmIhjVTMHXvnG7uuv7D6WXl+mZgmXHvlWtOfcydd66M9Ul55/dDKWcUntdPqTN69OI3jc1re7YvTfKupZxSmYBDrr9W86ZAPmjLCP/IgDk9+T7f7uM6VrSIgpqwdxYIYMoCuqAXWRPh/jR7V6PGDaUu1h1O1pX0tv3f3QTI5Levu/DFiSceuVusYiCOj7JzZaBKGiGf1SiQBDopUImjisuXK/OWXt6M4QKlOpLFJinEbXxUjPpDCy6+650NmA8EQTmaTDyx3Rv0vHf8+H/rCZlP0DDswAFwqoQBUUotTcNoqC9sdOem8LC3FQ+8sqEOmzqNTXx2lSa1D5q19znYR+va55qZYuXponZokT8MY9IdgmT2TRv3umhxYh9IaF9ZLLrQsJYRAqioOmWGL58REF4xq4SohMFzWDorVRfokC8+F6y4fj3k43H8rThUjNTCIgYMB/ZACwzAG+sSYRAhDMBeVFHFOQRavf7iIJ2x6+b96H2FHQ7Wlf8se//6CZGJH2eIKnz1KuqrcF1nK7rVnXXLequG9RTEeO4Dd2cVRlbMKwWJj8vLzjYeXt7LOKlKlPyKYUoaKYVRCUKLtp4g7p328PzNhT385GkrrD/+aJRdc1Bce8v0EuDDvr2rR1VkH0Br5/z6XRZkK/LuJr5aChmCpoCX1O5iIKaQDdQTChR0EBVOoq0RYm8ac56uIRJmubAqVfamOtCQnPJlqRzXUjYBpHSLUaumRZJ7xIxs6933rZu2s76+9btzpGsCyxdszIdZTlEUtNtMXT5iILQhN32oxIFso/g8585a95SoUHYaGyHR04j2j4ypM5MNsp985U4jimVPz4iAmSfgPlHpp+EgBkHZgqa+VKqq1REQV2k6y+nX0VB/STzS3QJFdet6q5b1F03qLuEjrxmzqpIfIeHkxmFXXIp4vwLK9suXvKpv5kiS+joFPbyMtN2N9HzZv7OpWe2b/bJYS7f7b0zrjS2yDrq3e8sg4G0nghEJQpkRkBfWGbWr9+PJHXFMqb9Ba5ZARkNeXXDBekegbbPCGR9lhAFnr5lIjWDKIg0MB7cQhR4gBixiap7ClwCRqrpEjGpELFuWzeRZJ245ZqF0fns2Rj9umtWpkhZEYeod9dmZnq3gYXSBKISBcwUdMbvodFh9XtLxtMXNyUb5j63Z1/pAPeSQWYEFl/95Y5ZgdfPWa9eP/vTrdwjUJYFoqAssXalRxS0K15lvEUUlKHVvrRVRUH7aprvcZbQ0Tnt5WWmxW6iZy6/tfTM9qibfZ3W3jvjqtW8Df6/eDK/8qTwTiAqUSDLhK687ta5C8yktjueeT49kjTmE4h8bjS2I6z3FyxJRPO9L+9RxyX3GIR+bDEgswIyIyAzA/06K+BiiigI3dKatY8oaJZ/yNIRBSHpNm8bUdB8DEJ7wJ6C0ITd9qMSBeKi60hS15KiZnC5Sw0pCqTELyWXmv1VcrlZ6IvNXGLglUsvT2cGBvFBFPR31BEF/RtfREH/xlZqhijo7/hK7RAFzcQ4OlHQDIbeSg0tCsS7Tx46rv4xOYJNhMH3khkDmTnw9SAG3CQRBb5aWJx2EAVxxsWHV4gCHxTjtYEoiDc2vjxDFPgiWc4OoqAcL2fqOkTBxJBSH0pOJHoqOXXhhP0z6o6J3oXB6GOPqCM/s25uz4AsExrkmQE7uIgCDx+OiE0gCiIOTo+uIQp6BBh5dkRB5AHy4B6iwAPECiaiEwWy2XjnrglnVbbff3OFKobPUocokFqYJxJ9au9+de2r1Y4qlY1BsoFY3zGAGGCmIPynJL4SEAXxxcSXR4gCXyTjtIMoiDMuPr1CFPikWdxWVKJg3YZN6pijj1TXbrqgeA0iSFmXKPAhDA7e/BfqkM03zM0OyMyA/PDMJ8BMQX+3CkRB/8YXUdC/sZWaIQr6O75SO0RBMzGOShRk3VNQFxoRJaecvEJdcv7ZHUXqm5blxRNXLFdbNm/seL9OUSAFy6Vmn1yyUMmSoj9Ijin9UnJcad4jswNLP/ahOTEgR4uKGBik04TyGNnvIwrKEmtXekRBu+JVxltEQRla7UuLKGhfzMp6jCgoS8xPekRBwtHs9J+37swOUWDfpuwSDnWLgrLCQJYKyY88LBUq/sFBFBRn1caUiII2Rq2Yz4iCYpzamgpR0NbIFfcbUVCclc+UUYkC6XCvXbNKnbP2dJ91LGxL9jN89IOndYgCWwTYIkGMNyEKbGHg2mMgswNHJBuJFzz6k5TBa5+/YODuGigcfEdCREEv9OLPiyiIP0ZVPUQUVCXXjnyIgnbEqRcvEQW90KueNypRIHcUXP7Vm9S2rddXr1EPOV2iwL5lWd+jYG56bkoUdBMG5jGjzA5UaxSIgmrc2pILUdCWSJX3E1FQnlmbciAK2hStar4iCqpx6zVXVKJA9hR0e0KfPuQSBeKTeZuyFgV333aVWnbsUam7r7yev6a/10B1y/9ockzpR5LLzV5OEv12co/B9//LRjX+5T9Ls0x9+jNq7+V/omaS40Z5yhFYND6ipvZNq33JEbA8/UfgkEUL1Gt7ptTMgIR3OvlukM7yIDxDQ0Pq4IUj6tU39g1CdQeujqMjw2rB6JB6IzmFj6c/CSw+aEF/VizyWkUlCppmVXWm4JUI/vDsSP7W/5+/fFpd/7+vVSf/ZHa50N7L/4uaTAQBTzUCi8YOiIKkM8XTfwQOWTSqXks+u4MS3cESBUodPD6qXk0OYuDpPwKjyWEbCxJh8MYkoqD/ojtbo8XJ9zNP/QSiEwV6JN5Esfnqi9WqU1cGp9O2PQUmEPN0oSff9ja1/u9+oK45/NfUcXRoK7cblg9VRteKjCwfakWYKjnJ8qFK2FqTieVDrQlVZUdZPlQZXU8ZoxIFson3yutuVebSnB3PPK/WnHtZxxKenmrcJbNLFMR6+pBZjYV336UOv+D/UEMTL6uplb+p1v63/6b+9teXqyXJEKhccPYhRlMqNRlEQSVsrcmEKGhNqEo7iigo9BuJ9wAAIABJREFUjaxVGRAFrQpXJWcRBZWw9ZwpKlFgb+rVtXOd+NNzzQ0D5pGk+mVz/0Js9xSYdTePG5XThSauvDq9v+BLB4+pv07WxMtzcbLn4Q8jWOLkM2Z12EIU1EG5uTIQBc2xD10yoiA04WbtIwqa5V9H6YiCOijPLyMqUZB1eZnrxJ9mcLlLber0IVMQuG4m/vNkTd41BzbryJGlX3ptMp094ClGAFFQjFNbUyEK2hq5fL8RBfmM2pwCUdDm6BXzHVFQjJPvVFGJgqZmCnqF2oQoMAXBxJe/pl7b8H85q/G9ZLPsRYeMpbMHxyf7C765e686gdN0CoUcUVAIU2sTIQpaG7pcxxEFuYhanQBR0OrwFXIeUVAIk/dEUYmCpvcUVKVbtygwBcHLN/ylev3sT3d1/enkGMLfP3RcbU9ObJCZgj9MlhN9jlM5csONKMhF1OoEiIJWh6+r84iC/o2t1AxR0N/xldohCpqJcVSiQBA0efpQ1RDUKQq0IJhZcph68ZYtavL9v13IbZkpuDZZSvRXyX0G8pyZbD7+82QTMsuJsvEhCgo1rdYmQhS0NnS5jiMKchG1OgGioNXhK+Q8oqAQJu+JohMF3mtYg8G6RIEpCF747j1q34knla7dHcnm443JJmS9nOjaVybVackFXTzzCSAK+rtVIAr6N76Igv6NrdQMUdDf8ZXaIQqaiTGiwAP3OkSBuWRo53e/V3iGwFU9WU4k+wz+ccFw+vYfJEuJLkqWFDFr0EkLUeDhwxGxCURBxMHp0TVEQY8AI8+OKIg8QB7cQxR4gFjBRBSiQO8luOLC9eqctad3VKPbexXqGyRLaFFw8Oa/UEsuvyT1vcgegqKVvClZSvTnyZIimTXgToP51BAFRVtSO9MhCtoZtyJeIwqKUGpvGkRBe2NX1HNEQVFSftNFIQrWbdikjjn6SHXtpguctZN7Ap597kW1ZfNGv7X3ZC2kKDjo9m+pw5KLyeTpdspQ1arYswbvm5pOLzzjJmSlEAVVW1U78iEK2hGnKl4iCqpQa08eREF7YlXVU0RBVXK95YtCFGTdT6CrNqj3FIw+9oh6y8fOTG8qdt1D0FvoO3Pbswafe2NKfTZZVjTIS4oQBT5bWHy2EAXxxcSXR4gCXyTjtIMoiDMuPr1CFPikWdwWoqA4q8yUIWYKRp7aoZZ+7ENqZMcvlL6p2IOrXU3YNyHLvQabXptSH0pOKhrEB1HQ31FHFPRvfBEF/RtbqRmioL/jK7VDFDQT4yhEgVxa9uU/+pxadepKJwWZKbj8qzepbVuvb4ZSTqm+RYHMDCxdu0YtePQnyYbi31E7k5OG6nweGh1O9xrojciypEjuNhi0U4oQBXW2uvrLQhTUz7yuEhEFdZFuphxEQTPc6ywVUVAn7TfLikIUfO0bt6uH//XxzD0DeXsOmkH3Zqm+RcGSKy5VB994g9q/7G3qVz94SMmdBE085pIiKX/QxAGioIlWV1+ZiIL6WNddEqKgbuL1locoqJd3E6UhCpqgrlQUokCqLrMF8tizAfL6zl0Tavv9NzdDqECpPkWBPmlIhEDVuwgKuFw4iSwp+mZyStFNi2ZPKRokcYAoKNxMWpkQUdDKsBVyGlFQCFNrEyEKWhu6wo4jCgqj8powGlEgtZIZg5u3dC6VOWP1KZmnEnkl0YMxX6JA9hG89QPvTTcWhzhpqIcqpoJg0MQBoqCXFhN/XkRB/DGq6iGioCq5duRDFLQjTr14iSjohV71vFGJgurVaDanD1EgQuCtv3tarRuLq1AbJHGAKKjSQtqTB1HQnliV9RRRUJZYu9IjCtoVryreIgqqUOs9D6Kgd4bKhyiIZR9BURxZ4uBTe/epM5LTivrhKFNEQdHW0M50iIJ2xq2I14iCIpTamwZR0N7YFfUcUVCUlN90iAIPPHsVBWMP/kN6/Ggs+wjKIHGJAxEE/XDPAaKgTEtoX1pEQftiVtRjREFRUu1MhyioN25P7f6Fs8DdkxNq996JLu+97Hwvy54kfuqVHWmeLZ+6pd5KUlpKAFHgoSH0IgrMZUOx7SMog0bEwb1jI+qvx0fnjjKV/G0+sQhRUKYFtC8toqB9MSvqMaKgKKl2pmuzKHB1iJ8+0BE2ozHb4e7sVE8kHXD7NckjaeU9+3k6ozP/1CvuTn63znrdLWVmYzK6yFM7AUSBB+S9iAK9bKiJ+wg8VN1pQu45uGnRqLonEQn6aePsAaIgVAuJwy6iII44hPACURCCajw2i4iCiaRDbY5iu0a17Y63q9Pt6nC7Ott2R1vKFh/64Tn+0Lc5q3Ho+GFqydiSjPeWKHnf9Ry/eFkmFl3WF9//B/2ArnV1QBR4CFlVUWAuG/rV/f+k9h+f/UHx4GbtJlxLi8QJmT2QW5I/mew/iHnvAaKg9iZTa4GIglpx11oYoqBW3M7C7E65PRr+tDFa7eqM62UkYlxGx80OvsRXOuHT02+OJsc0yt2NvquDffzi+Z3uQ8fnd6qXyGuOTnjaOU/es5/jHHYlzXEZnfKszn8TrYk9BU1QZ/mQF+pVREG/LBsqClBmD743Pru8SN93IILghH3TKtbNyYiCotFtZzpEQTvjVsRrRMF8SmYn3R41N0fM7Q56t875hLHEJbaR8SVJR1k61vpxjWrbHW9Xp9vV4XZ1tu2OttgWH3iqEUAUVOPWay5mCnolmOSvIgr6cdlQEZQiCO5IhMH3kqVF/7hgeC5LjAIBUVAkou1Ngyhob+zyPG+bKMjqsGd11s0lLfYourmMpcnRc7tTbo+GH2ctSbGXlJij1tIxN0fIx5K/Hf/rkcvVy69NzTWFmEa589on7+cTQBTkMwqRAlHggWpZUTD62CPpJWXy7Pzu99Tk+3/bgxftM5ElEKQmMSwxQhS0r02V8RhRUIZWu9KGEgW6k22PtOulMOYoux5hz+q01z2ybnbS7VFzc8TcHi3v1jlP8x1YzlLnyHiRPQXtarF4axNAFDTTJhAFHriXFQVLP3amGnvw79Vrn79ATVx5tQcP2m+im0A4Yf+MOjPZf3BashfhtGS5UV0PoqAu0s2UgyhohnsdpWpR8KNfPJ4WZ65n1x14cxRdd+DNDaR6xL2Oznu3DrseUc/qrNuj6OYyln4dPUcU1PEparYMREEz/BEFHriXEQUL775LHbH+U+mdBM/9+Kfpb55OAvp4Uzm96KEFI3N7ECSVLDM6bWp/KhBks/LxxkYz3xwRBb6JxmUPURBXPLQ3urOuO/LmEhr9nmsUXnfiQy6Z0Z13e6Td1XE3O+TmGnTdaa9zZD3OSFf3ClFQnV1bciIKmokUosAD96KiYNA2F3tAmwqCn47MblIWkfBUcuqE+YgoEIHwvkQovDf57VMkIAp8RDBeG4gCv7HR6+LNpTX2qLw9Iq83qoYajdcdc3M9u+7Am2vYdTo6737bRChriIJQZOOxiyhoJhaIAg/ci4qCxVd/WclPP91J4AFfKRMiCmST8nY5zSj5rU8y0ka0SJBTjXqdSUAUlApN6xIjCqwZugPHPtoj9OY6elkzr5fYhOrQ2x15c7277sjrE2HMpTPmCPzhiw5Xb10yrp57aU/r2iUO5xNAFOQzansKREEzEUQUeOBeRBTILMHR7/kNJb8HeXOxB9wdJraPDKVLjB5KTqOwlxpJQnO5kQiF39g/XfhuBESB72jFZa8fRYF04O2Rer35VZ9YY3fqfS23cS2tsUfl7RF5vVHV91KaUBuN42rBg+sNoqD/Y48oaCbGiAIP3IuIAmYJPIAuYEKLBJlJEKFgLzcSE+ZsQjehgCgoALzFSWIVBXoZjmvEXnfs9Yk2erTeR8ded+r1Uhs9Qm+PzuslNqE69D6aFKLAB8V4bSAK4o2NL88QBb5IlrODKCjHy5k6TxQwS+ABckUTIgr+KREHIhK2J3sT5Le95MgWCiIa3pvsUVh+yJh6fc8+tSfZq8DTfwTqEAXmyL3eMKtfs5fiyAi+CIJeHhmJNzfByki9PrXGXnITc6e+FwaSF1HQK8G48yMK4o6PD+8QBT4olreBKCjPbF6OPFGgLyrb8+H/rHbdssVDiZjohYA5mzArFjo3L2vbci7Uiclyo3cloiCdUUh+jksEgyxJ4mk/gbKiwO7gp/+XdfjJra5mB19Owell5D5vxF53/OV8eN2x79ejJ6u2MkRBVXLtyIcoaEecevESUdALvep5EQXV2c3l7CYKRp7aoY569zvTtM//939X+49f5qFETPgmIMLgpyIQcmYUpFyZSRCRIL+PS+5QkN8iGHyefOS7ftjrJCAj8uOL9qqfPP0/1MvJ5lnp3LtG8KWD38vJOObIvb0cR96zl+LQuffTUhEFfjjGagVREGtk/PmFKPDHsowlREEZWhlpu4kCPUvw+jnr1ctf3+yhNEzUReCVxWPqR0ln/+fJzEAqFpKfp5PlSK7lR+KTzCDITIIIhiUzs79FLByavI5gCBs1cx1+1jKdXtff2x389P/paP1h6RId3cGXU3B8b5wNS6//rCMK+i+mZo0QBf0dX6kdoqCZGCMKPHDPEgXmXgJmCTyArtlE1kZj2acgswryu4hY0ILh0ANCwZxhOC5ZnsSSJHdgpaMvm21lpF7Ou9en6MhZ9/oEnapLdWSJzuGLDlPHHJLM3ImYSzr4ekOtOYJPB7/mD52n4hAFnkBGagZREGlgPLqFKPAIs4QpREEJWFlJs0SBPnGIvQQeIDdgouzpQzKDIDMJWjA8dWBjc7fZBV0tmWXQoiGdWUjEghYPIhrkvX7Yy2B39O0lO72M5ktnXp+cozv5rlF8vUSn7J6CBpogRVYkgCioCK4l2RAFLQlUD24iCnqA10NWREEP8HRWlyjgxCEPYBs2UVYUdHNXC4anE6EgMwxPJ3sY9EzD7qHsJUmmzSzhICJCZhyaWqZkdvRl6Y7egKtH9Kt29GU0Pz0958CGWr1cxx7Jr7oOH1HQ8AcsYPGIgoBwIzCNKIggCIFdQBQEBpxhHlHggbtLFHAvgQewDZvwKQryquISDROJWJBZhqcOCIg8G/asw/HJJujZpUnJTEPyW2YeTAGRN/uQNao/2+lPOv8VTtkxO/rmcZm6o1/naTqIgqItqn3pEAXti1kZjxEFZWi1My2ioJm4IQo8cLdFAbMEHqBGYKJOUVCkuqZw2J0sVZKZBlmilP5b/05ey332JGfhv/ykUgd+H7/rCXXongm1JPktr5Xt7JtHaEqn3veIfm59KiZAFFQE14JsiIIWBKkHFxEFPcBrSVZEQTOBQhR44G6LgoM3/4VacvklavL9v6N2fvceDyVgogkCsYmCPAZ6ZP/pqd1qezKK/9CrO9T2fbvVxMQBATDxi1kxUPRZmNzUsORtSsnvw94++6P/Lb+Tn3Qd/4Lk5J1kFkIe2QuR/j7wfzmyVR79ft7sRFHXfKRDFPigGKcNREGccfHlFaLAF8l47SAKmokNosADd1sULP3YmWrswb9XL9/wl+r1sz/toQRMNEEgJlEgS3bSk3gy1uyXuQ3XXsIjp+7Ihlzp4O9OTuSZSDr/uw9PftLjV2eXME0kPzIjUXT/Q1689P4IWc605MBGavm3KSzS95KlT6moOCAuRFTMpTsgPPLKynofUVCVXPz5EAXxx6gXDxEFvdBrR15EQTNxQhR44G6KgrEH/0Et/diH1MySw9Qv/+ezHqxjoikCdYmC7TsfmTt2U5/GU2XdfrfOvpynL8drVt2Ua8dAljKJQNBCQTZOyyNLmtLfyXImeURQzP6/832fMdUCQ2xqkZEKCUM06BkMeV3PYiw5eEypVyfVYj2rYaSPaUbDJ6tBsYUo6O9IIwr6O75SO0RBMzFGFHjgbooCPUvwyqWXK/nhaS+BXkWBa6OueSJPmdF9fdyma82+vCYdfhEFbXm0eNCiQmYl5N+pgDggJPRMhUtcmOlC19kUHbbwMGcu5D29qVv7ZM526Lyy6Vs/pnCZfb8/jp4NHZM8+4iCPELtfh9R0O74FfEeUVCEkv80iAIPTLUokA3Gv/brx6QWZZZAZgt42kugmygI2eGXm3H1Zl2fo/vtjUR3z/WshaTSIiMVEgdmJ2wBoWcxFo2PqJ8lN07L5WVpGiO9r2VSPpjbt2GbsyFZ4kJeN2dHdLqsm7X18izTX1uw5NnwUVdfNhAFvkjGaQdREGdcfHqFKPBJs7gtREFxVpkptSjgGFIPMCMxIUt61Mhr6mc7f65+/tKT6Vr+7S88ouTM/TIj/Ce85TfTc/bNy7ROWHpSsoa/faP7kYTGmxtF9xSYosMWHuYMh7wnezD0jMes0JhdRqUfU7TMvt95WlRMYqQs6CzB4RIx2naW8JD3XaJG57NnYGxflyVC77CDF6hdr0w6q9GtXMnAjE3Z6NebHlFQL+8mSkMUNEFdKUSBB+5aFMgsgcwW7Pzu95KTh37bg2VMhCBgbtrd/sJPjM27Scc/EQMyC1DkocNfhFK8aYqKgqZroJdTZQkLed2cFdHp7HyzIqRTpOi0eu+HWVdbsHSz2zSjJsq3l5Vl+dBNFJl57KVo3epkL1PrljZPQLnySh5zmVsRvmX8t+1lCcqschEFRSLS7jSIgmbihyjwwF1Egd5gvH/Z29TzP/43D1YxUYWAdOh/uvPRuY7+0wcu2Cp72ZYs31menMBzSHLc5ruOWJmezsMIf5WIxJunLaIgXoKdnrlEiKSwZ0fMXC4xU0R8mPtNXHzE7tjosJqcmj0i136yBI9O1+YZm7a0F19+FhVnucKpx9PMtP28Wagq9e42a1bFnpmnrCCrWl5ZofmJJeNViyJfDwQQBT3A01lFFLDB2APIHBN56/hl1L/IY2/aNdfw/8bSlXMbdnvdaFzEF9I0RwBR0Bz70CXXsafAXlaWVaduosjM000g2bbtZWrdeOYJKFfeoj6befWxxVVimyUoq9giT38QePM4hv6oT1tqgSjwEKlf/vyXbDD2wNG1rKfsOn7zWM4T3pKs3U/W88synypHciIKPAQ1YhOIgoiD06NrdYiCHl0kew8EzOVDRcVZV+F04IjlHlyay1pG3BUtL6RoylpSWNS3ounKCs0HF7iXOhYtj3TVCCAKqnHryDXxlf/KDcY5HH0t67HX8cuov4z0h9i4iyjw8OGI2ASiIOLg9OgaoqBHgJFnZ09B5AHy4B57CjxArGACUVABmp1lctXq9AbjQd1gbHf4dyfr+vWFXE8dWNNfBHPRZT1FbPlIgyjwQTFeG4iCeGPTq2eIgl4Jxp0fURB3fHx4hyjwQbG8DURBeWadOX6SrGM/+eT0ToLnfvzTvrubwFzSM3vLbrUOvyzr0Rt19Rn8VZf19BqyovkRBUVJtTMdoqCdcSviNaKgCKX2pkEUtDd2RT1HFBQl5TcdoqAAz4s23qDu3fZwmvLEFcvVls0b38y1aZNSX/qSeu3zF6iJK68uYC2OJK5Nu3IW/2zHP/ldYoTftY7fXNYjYqCND6KgjVEr7jOioDirtqVEFLQtYuX8RRSU49XG1IiCZqKGKMjh/u3v3KduvOVOtW3r9WnKdRs2qVNOXqEuOf/s2ZzLlyv15JPRLB1KO/VJ51469nPHcVbs7Ev1XCP8/dDhL/JxQxQUodTeNIiC9sYuz3NEQR6hdr+PKGh3/Ip4jygoQsl/GkRBDlNbBNgiQSU3mMrSoV/+z2f9RyexaHbyZzv7L8+9pkf1y96yqzv7csuu3LYrm3Rnl/YcpvTSnuMWL0v/PcgPoqC/o48o6N/4Igr6N7ZSM0RBf8dXaocoaCbGiIIc7qs//kX1+c+cpc5Ze3qa8oEfPqo2XHqN2n7/zbM5E1FgLx2Szrr5PP3Kjrn/yui9PBPJSL508OV5Knlf/i2j+7P/n13CU/RmXbMscymPdPqPTzr3Zmc/xCk9zTTd8KUiCsIzbrIEREGT9MOWjSgIy7dp64iCpiMQvnxEQXjGrhIQBTncT/jAeeqKC9fPEwV333aVWnbsUWpoU3LAccDnsIWHqbcf9nYlv/WP+X/97yXJaL/8mwcCEIAABCAAAQhAAAJlCSAKcojlzhSUJU56CEAAAhCAAAQgAAEIREYAUZATkNw9BZEFFHcgAAEIQAACEIAABCBQlgCiIIdY7ulDZYmTHgIQgAAEIAABCEAAApERQBQUCEjXewoK5CcJBCAAAQhAAAIQgAAEYiaAKKgYHYRCRXA1Zysbp7z0ssdk567ZU6LOW3fmm/dVGPWSzembr75YrTp1Zc21Hbzi8uJlE+mWfsczz6s15142l8WMof2eJJo7gWzwsNdW4yKfN9OZbull1vfK626dS27GT58qp9+cd0llbTUenIK6fd5cFPLSd4uvaU9/B/D5DdvWisZDe5GXvtt3tyzzfuzxJzoqlPX3OWyt228dUVAhhiwpqgCtgSxl45SXXr6U5Ll20wXpb7vzb3ZIEAXhA54XL9uDvPTmoQL20cOSVx59NLG0hWefe7HzdvPwVR6oEvI+bzaMbul1h1KfGve1b9yuHv7Xx+fiJ/8/7T+eMCfkpZNxzNFHzn3WBwp8TZXt9nlzudAtfV58tT1pIz9+9GfpwA6iIFygi8ZDe5CXPu+7e96lsuGq1veWEQUVQszm4wrQGshSNk556W0RYHdCpIr6yw1RED7gefGyPeiWft79I0lm++Qx0968SwzDV3fgSijyeTOhdEtviwC7E2LDtdMPHPzAFS77ectLXyS+kubZ53aqT3xkdeddQ4HrOojmi8TD5JKXPu+7HlHgr5UhCiqw5JjSCtAayFI2Tt3SuzoRro4DoqC+QPuMr6uT3+0PDZ3GsHEu+nnLGmmU180YuQR8t2V+0rbes/IdzBQECnPZz1te+rz4mm3BJTACVXNgzebFwwaTlz7vu95ePsTSoepND1FQgV3ehWYVTJIlAIGyceqWfsczv0pHl/TyA93puOv7D6ltW6+f8x5RECCQGSZ9xnfLnT9QdiyzlpAQ4/Ax1h23vM+b9iQvvSuWdvsRW7pzwZ6CsDGWTnrRz1vWd60Z027xlfw33nLn3Pc0oiBsbPXnyF5+5/q8aU/yPp9lvut1fJmtrxZnREEFbnmqtYJJsgQgUDZOzBQECEJAkz7jmzcSqauhBYF5y3nAKg6s6aZnCtgzErbpFf28aS/y0ncbaf5//r9t6t5tDzsrZIrOsDUeLOt5I/82jbz0Zb/rWU5Uvb0hCiqwy1vfVsEkWQIQKBunvPRF1jgzihwgkBkm8+JlZ+t1TwGCoL7YSklFPm+mRz73FLBnJGys8/YI2KXnpc9bk27aY6YgbGzFepl4FEnf63d9+Br3TwmIggqxzNsJX8EkWQIQyIuTfHHdvOWeuVMo8tIXOQ0FURAgkBkm8+Ilf0jk2bJ5Y/o7L323002Ykq4vrrqkvM+biABz7XAvpw9JW9HtRMq32079te//EvNOH7Lj6+P0IaGKKAjftvJOE7K/T/PSd/vulrzX/uUdc/t/9NGmzAJVizOioBo3VfZ89IrFkK1HAt3iZIsCKSovrt3OQTffE1usS+4xeAWy551dbYqCvPh2OwfdLMd0i2VEBYLUQ5Junze70yjFVL2nQH8XaFf57PYQtIJZ8+4dsOOblz7vnHvtFqKgYIB6TFbkXhBz3X9e/Lp910tbMR/2E1QPHqKgOjtyQgACEIAABCAAAQhAoC8IIAr6IoxUAgIQgAAEIAABCEAAAtUJIAqqsyMnBCAAAQhAAAIQgAAE+oIAoqAvwkglIAABCEAAAhCAAAQgUJ0AoqA6O3JCAAIQgAAEIAABCECgLwggCvoijFQCAhCAAAQgAAEIQAAC1QkgCqqzIycEIAABCEAAAhCAAAT6ggCioC/CSCUgAAEIQAACEIAABCBQnQCioDo7ckIAAhCAAAQgAAEIQKAvCCAK+iKMVAICEIAABCAAAQhAAALVCSAKqrMjJwQgAAEIQAACEIAABPqCAKKgL8JIJSAAAQhAAAIQgAAEIFCdAKKgOjtyQgACEIAABCAAAQhAoC8IIAr6IoxUAgIQgAAEIAABCEAAAtUJIAqqsyMnBCAAAQhAAAIQgAAE+oIAoqAvwkglIAABCEAAAhCAAAQgUJ0AoqA6O3JCAAIQgAAEIAABCECgLwggCvoijFQCAhCAAAQgAAEIQAAC1QkgCqqzIycEIDCABL72jdvVzVvumVfz7fffrL79nfvUldfdqq64cL06Z+3pHWku2niDunfbw+ru265Sy449SnWz88APH1UbLr2mK10pQx4pz/VoH7RPJ65YrrZs3tiRVPvgek8nPOED53X144zVp6TvS930c966M9Ul55+tdjzzvFpz7mXpy8LHfMw66ve0r93qM4BNjipDAAIQqIUAoqAWzBQCAQj0AwHdsbc7uPL6qe9+VyoEdEfbTKM7wJuvvlitOnWlKmLH5CXpn33uxXmdet2Jtv0x85odbS1I9PurP/5FtXPXhOomCly2XOXpOpplmKLAFkqagSkYitSnH9oRdYAABCAQIwFEQYxRwScIQCBKAjJqrkfBuzkone33rHyHunbTBWky+/9F7egyehUFN95yZ+qPPNon6YDL60e/5Yj0dXsWwVW/bp32bqJAmN31/YfUtq3Xp2a1WJBZBplhsGcKuomcKBsGTkEAAhDoAwKIgj4IIlWAAATqIWB37rNKNWcGHvqX7R0dYpdIyPPehyi49et/nC7l0SP56zZsUmvXrFLfufuB4KJAylz/ha+oz3/mrLnZlGef26mOOXppuhQLUZDXAngfAhCAQHgCiILwjCkBAhDoEwKuNe9Zo9rm8hi9bEhjKGNH8uSJAhdec0+BzAjIKL0IgWOOPlJ94iOr1eVfvWnuNckfcqZARMGWO38wJ45kpkS/5hIF3erTJ02JakAAAhCIjgCiILqQ4BAEINAGAno9vvbV7vjL69L5lSUyesmOq15F7OSJgrw9BVoU6BkM2UMgswSyB0KEQh3woP94AAAD9UlEQVSiQDZXCw8pW4SJMLH3X7CnoA0tHx8hAIF+JYAo6NfIUi8IQKA2AtKxl7X59mh70eVG2tEsO75EgZQjIuCxx5+YW7JTpyjQIkALKERBbU2UgiAAAQjkEkAU5CIiAQQgAIHZzbGyBEaO2rSfrI61SxRUseNTFMho/NO/fGGuHnWKAqn7JX9645x4QhTwyYIABCAQDwFEQTyxwBMIQCBiAvrEnKVHLJk7RUfc1UteXMuHskSBbPgtY8enKCgqaFyhqHr6kH0UqraNKIi4weMaBCAwcAQQBQMXcioMAQj0QsB1mVdWp7fb8qEydvJEgas+ro3GrnQ+ZgrMTdVShn15WVlR0K0+vcSOvBCAAAQgkE0AUUDrgAAEIAABCEAAAhCAwIATQBQMeAOg+hCAAAQgAAEIQAACEEAU0AYgAAEIQAACEIAABCAw4AQQBQPeAKg+BCAAAQhAAAIQgAAEEAW0AQhAAAIQgAAEIAABCAw4AUTBgDcAqg8BCEAAAhCAAAQgAAFEAW0AAhCAAAQgAAEIQAACA04AUTDgDYDqQwACEIAABCAAAQhAAFFAG4AABCAAAQhAAAIQgMCAE0AUDHgDoPoQgAAEIAABCEAAAhBAFNAGIAABCEAAAhCAAAQgMOAEEAUD3gCoPgQgAAEIQAACEIAABBAFtAEIQAACEIAABCAAAQgMOAFEwYA3AKoPAQhAAAIQgAAEIAABRAFtAAIQgAAEIAABCEAAAgNOAFEw4A2A6kMAAhCAAAQgAAEIQABRQBuAAAQgAAEIQAACEIDAgBNAFAx4A6D6EIAABCAAAQhAAAIQQBTQBiAAAQhAAAIQgAAEIDDgBBAFA94AqD4EIAABCEAAAhCAAAQQBbQBCEAAAhCAAAQgAAEIDDgBRMGANwCqDwEIQAACEIAABCAAAUQBbQACEIAABCAAAQhAAAIDTgBRMOANgOpDAAIQgAAEIAABCEAAUUAbgAAEIAABCEAAAhCAwIATQBQMeAOg+hCAAAQgAAEIQAACEEAU0AYgAAEIQAACEIAABCAw4AQQBQPeAKg+BCAAAQhAAAIQgAAEEAW0AQhAAAIQgAAEIAABCAw4AUTBgDcAqg8BCEAAAhCAAAQgAAFEAW0AAhCAAAQgAAEIQAACA04AUTDgDYDqQwACEIAABCAAAQhAAFFAG4AABCAAAQhAAAIQgMCAE0AUDHgDoPoQgAAEIAABCEAAAhBAFNAGIAABCEAAAhCAAAQgMOAEEAUD3gCoPgQgAAEIQAACEIAABBAFtAEIQAACEIAABCAAAQgMOAFEwYA3AKoPAQhAAAIQgAAEIAABRAFtAAIQgAAEIAABCEAAAgNO4P8HUOU4xQ3m5jgAAAAASUVORK5CYII=", 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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": [ -8.39919376403413e-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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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# The full reaction of E and ES\n", "uc.plot_history(chemicals=['E', 'ES'], show_intervals=True, \n", " title_prefix=f\"E and ES when E0 = {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": 86, "id": "ff72f0a5-b05c-4269-9d98-786e0b53c921", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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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": 86, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uc.get_history(columns=['SYSTEM TIME', 'E', 'ES', 'P'], tail=1) # Last point in the simulation" ] }, { "cell_type": "code", "execution_count": 87, "id": "907c937b-bba7-4f7d-8682-86daa9717831", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "6.998846772430818" ] }, "execution_count": 87, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_equil = uc.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": 88, "id": "8a14ce96-a237-4610-9e87-38a6231ca263", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "4.899192740701572" ] }, "execution_count": 88, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_70_threshold = P_equil * 0.70\n", "P_70_threshold" ] }, { "cell_type": "code", "execution_count": 89, "id": "f6d96e06-599d-4c14-beca-30a37d083617", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.002747856201107546" ] }, "execution_count": 89, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uc.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": [ "# PART 8. Keep increasing the initial [E]" ] }, { "cell_type": "code", "execution_count": 90, "id": "a6b8d011-9592-4386-983e-f530b5f90298", "metadata": {}, "outputs": [], "source": [ "E_init = 60.0 # Triple the initial [S]" ] }, { "cell_type": "code", "execution_count": 91, "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 (E). Conc: 60.0\n", " Species 2 (ES). Conc: 0.0\n", " Species 3 (P). Conc: 0.0\n", "Chemicals involved in reactions: ['ES', 'P', 'E', 'S']\n" ] } ], "source": [ "uc = UniformCompartment(reactions=rxns, preset=\"slower\") # A brand-new simulation, with the same chemicals and reactions as before\n", "\n", "uc.set_conc(conc={\"S\": 20., \"E\": E_init}) \n", "uc.describe_state()" ] }, { "cell_type": "code", "execution_count": 92, "id": "07850faa-b7a7-4c58-9017-a95a1e93eb46", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "770 total variable step(s) taken in 1.758 sec\n", "Number of step re-do's because of elective soft aborts: 3\n", "Norm usage: {'norm_A': 765, 'norm_B': 767, 'norm_C': 764, 'norm_D': 764}\n", "System Time is now: 0.0050084\n" ] } ], "source": [ "# Perform the reactions (The duration of the run was manually adjusted for optimal visibility)\n", "uc.single_compartment_react(duration=0.005,\n", " initial_step=0.00005)" ] }, { "cell_type": "code", "execution_count": 93, "id": "b850c64e-b44b-4cce-881e-569483921906", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 93, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reactions have reached equilibrium\n", "uc.is_in_equilibrium(explain=False)" ] }, { "cell_type": "code", "execution_count": 94, "id": "28c1e572-a798-4605-82ba-9b7430bda4bf", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_pandas() NOTICE: 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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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "uc.plot_history(show_intervals=True, \n", " title_prefix=f\"E0 = {E_init}\")" ] }, { "cell_type": "code", "execution_count": 95, "id": "417d9ff2-d739-44af-aff0-72513b3c7d66", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.0007023910558856093, 1.5191639777843677)" ] }, "execution_count": 95, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Locate the intersection of the curves for [S] and [P]:\n", "uc.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": 96, "id": "449c94a5-dd8e-4681-b654-dce7b685a7c7", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " SYSTEM TIME E ES P\n", "770 0.005008 44.60637 15.39363 3.832618" ] }, "execution_count": 96, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uc.get_history(columns=['SYSTEM TIME', 'E', 'ES', 'P'], tail=1) # Last point in the simulation" ] }, { "cell_type": "code", "execution_count": 97, "id": "41db82fe-6607-44f8-9723-9a0d3f7306a6", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3.832618199402545" ] }, "execution_count": 97, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_equil = uc.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": 98, "id": "e7cb5350-03c0-49da-a185-fd7af33f1312", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.682832739581781" ] }, "execution_count": 98, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_70_threshold = P_equil * 0.70\n", "P_70_threshold" ] }, { "cell_type": "code", "execution_count": 99, "id": "fbbb456b-0880-4aa2-b300-89d1204ad53d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.001390053726276219" ] }, "execution_count": 99, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uc.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": [ "# PART 9. Keep increasing the initial [E]" ] }, { "cell_type": "code", "execution_count": 100, "id": "338fbe68-dde9-4159-a405-973ee8a7c796", "metadata": {}, "outputs": [], "source": [ "E_init = 100.0 # Quintuple the initial [S]" ] }, { "cell_type": "code", "execution_count": 101, "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 (E). Conc: 100.0\n", " Species 2 (ES). Conc: 0.0\n", " Species 3 (P). Conc: 0.0\n", "Chemicals involved in reactions: ['ES', 'P', 'E', 'S']\n" ] } ], "source": [ "uc = UniformCompartment(reactions=rxns, preset=\"slower\") # A brand-new simulation, with the same chemicals and reactions as before\n", "\n", "uc.set_conc(conc={\"S\": 20., \"E\": E_init}) \n", "uc.describe_state()" ] }, { "cell_type": "code", "execution_count": 102, "id": "5d5bcb4d-3932-4cee-bb45-7bd19db664a1", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "785 total variable step(s) taken in 1.815 sec\n", "Number of step re-do's because of elective soft aborts: 3\n", "Norm usage: {'norm_A': 784, 'norm_B': 787, 'norm_C': 783, 'norm_D': 783}\n", "System Time is now: 0.0030275\n" ] } ], "source": [ "# Perform the reactions (The duration of the run was manually adjusted for optimal visibility)\n", "uc.single_compartment_react(duration=0.003,\n", " initial_step=0.00005)" ] }, { "cell_type": "code", "execution_count": 103, "id": "2ca20feb-38fe-4737-99b7-2b0472453781", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 103, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reactions have reached equilibrium\n", "uc.is_in_equilibrium(explain=False)" ] }, { "cell_type": "code", "execution_count": 104, "id": "38b01a6e-4c2a-47a2-b4bf-793f90470590", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_pandas() NOTICE: 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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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "uc.plot_history(show_intervals=True, \n", " title_prefix=f\"E0 = {E_init}\")" ] }, { "cell_type": "code", "execution_count": 105, "id": "803d88fa-f551-4f56-96af-37b417c505b4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.0004266715141239805, 0.9491814221946882)" ] }, "execution_count": 105, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Locate the intersection of the curves for [S] and [P]:\n", "uc.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], the time curves of [E] and [ES] no longer overlapping, and are now getting further apart" ] }, { "cell_type": "code", "execution_count": 106, "id": "92812a67-0f27-4e7f-837b-368a426921d0", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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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": 106, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uc.get_history(columns=['SYSTEM TIME', 'E', 'ES', 'P'], tail=1) # Last point in the simulation" ] }, { "cell_type": "code", "execution_count": 107, "id": "5c48aa58-e44c-4e18-9c60-c562560aa0e9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.3128291895441793" ] }, "execution_count": 107, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_equil = uc.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": 108, "id": "98698d70-47a1-4763-be1f-89660bd27ffa", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.6189804326809254" ] }, "execution_count": 108, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_70_threshold = P_equil * 0.70\n", "P_70_threshold" ] }, { "cell_type": "code", "execution_count": 109, "id": "69acbdb6-7a06-4e96-9ad7-3bdfc3ef92c7", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.0008229365407830671" ] }, "execution_count": 109, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uc.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": 110, "id": "073427b4-27a8-407d-bdee-0df89430eb16", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMESEESPstepcaption
00.020.0100.00.00.0Set concentration
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" ], "text/plain": [ " SYSTEM TIME S E ES P step caption\n", "0 0.0 20.0 100.0 0.0 0.0 Set concentration" ] }, "execution_count": 110, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uc.get_history(head=1) # First point in the simulation" ] }, { "cell_type": "code", "execution_count": 111, "id": "1b5546d6", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMESEESPstepcaption
7850.0030280.4662782.77909917.2209012.312829785last reaction step
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" ], "text/plain": [ " SYSTEM TIME S E ES P step \\\n", "785 0.003028 0.46627 82.779099 17.220901 2.312829 785 \n", "\n", " caption \n", "785 last reaction step " ] }, "execution_count": 111, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uc.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": 112, "id": "8e3cdce6-5f0d-404a-aaa1-907b4c5ab241", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-19.53373" ] }, "execution_count": 112, "metadata": {}, "output_type": "execute_result" } ], "source": [ "delta_S = 0.46627 - 20.0\n", "delta_S" ] }, { "cell_type": "code", "execution_count": 113, "id": "4e36063d-e6f9-4dfd-b1f3-79f4aeafdd8f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-17.220900999999998" ] }, "execution_count": 113, "metadata": {}, "output_type": "execute_result" } ], "source": [ "delta_E = 82.779099 - 100.0\n", "delta_E" ] }, { "cell_type": "code", "execution_count": 114, "id": "3dbf7a73", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-17.220900999999998" ] }, "execution_count": 114, "metadata": {}, "output_type": "execute_result" } ], "source": [ "delta_E = 82.779099 - 100.0\n", "delta_E" ] }, { "cell_type": "code", "execution_count": 115, "id": "ffd30805-1f47-4410-a6c8-5c8db4d9bbad", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "17.220901" ] }, "execution_count": 115, "metadata": {}, "output_type": "execute_result" } ], "source": [ "delta_ES = 17.220901 - 0\n", "delta_ES" ] }, { "cell_type": "code", "execution_count": 116, "id": "4d77a7f6-0d90-46e7-9d7a-b155460e546d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 3\n", "0: S <-> P (Elementary Unimolecular reaction) (kF = 1 / kR = 0.2 / delta_G = -3,989.7 / K = 5 / Temp = 25 C)\n", "1: E + S <-> ES (Elementary Synthesis reaction) (kF = 100 / kR = 224.07 / delta_G = 2,000 / K = 0.44629 / Temp = 25 C)\n", "2: ES <-> E + P (Elementary Decomposition reaction) (kF = 200 / kR = 17.851 / delta_G = -5,989.7 / K = 11.204 / Temp = 25 C)\n", "Chemicals involved in the above reactions: {\"S\" (cyan), \"E\" (violet), \"ES\" (red), \"P\" (green)}\n" ] } ], "source": [ "rxns.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": 117, "id": "b7372ba6-8da7-4ee0-a888-d04baea7f4c9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "17.220900999999998" ] }, "execution_count": 117, "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": 118, "id": "271f073f-1e22-456b-825b-2acf555519c9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "82.7791" ] }, "execution_count": 118, "metadata": {}, "output_type": "execute_result" } ], "source": [ "100 - 17.2209" ] }, { "cell_type": "code", "execution_count": 119, "id": "a1f87fde-d486-40ab-baee-b73b0abf9f6c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: S <-> P\n", "Current 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", "Current 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", "Current 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": 119, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Also review that the chemical equilibrium holds, with the final simulation values\n", "uc.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": "3.9.13" } }, "nbformat": 4, "nbformat_minor": 5 }