{ "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 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": "code", "execution_count": 1, "id": "55c8d285-416f-489e-8207-db828c8a7d0f", "metadata": {}, "outputs": [], "source": [ "LAST_REVISED = \"Oct. 11, 2024\"\n", "LIFE123_VERSION = \"1.0.0.beta.39\" # Library version this experiment is based on" ] }, { "cell_type": "code", "execution_count": 2, "id": "f7860d35-db39-4b03-b056-626bdbb8f5e7", "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", "from experiments.get_notebook_info import get_notebook_basename\n", "\n", "from life123 import ChemData, UniformCompartment, MovieTabular, GraphicLog\n", "\n", "import pandas as pd" ] }, { "cell_type": "code", "execution_count": 4, "id": "b0ad0c93-02a5-43f4-8797-4b9f7ba50432", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-> Output will be LOGGED into the file 'enzyme_4.log.htm'\n" ] } ], "source": [ "# Initialize the HTML logging\n", "log_file = get_notebook_basename() + \".log.htm\" # Use the notebook base filename for the log file\n", "\n", "# Set up the use of some specified graphic (Vue) components\n", "GraphicLog.config(filename=log_file,\n", " components=[\"vue_cytoscape_2\"],\n", " extra_js=\"https://cdnjs.cloudflare.com/ajax/libs/cytoscape/3.21.2/cytoscape.umd.js\")" ] }, { "cell_type": "code", "execution_count": 5, "id": "23c15e66-52e4-495b-aa3d-ecddd8d16942", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 3 (at temp. 25 C)\n", "0: S <-> P (kF = 1 / kR = 0.2 / delta_G = -3,989.7 / K = 5) | 1st order in all reactants & products\n", "1: E + S <-> ES* (kF = 100 / kR = 224.07 / delta_G = 2,000 / K = 0.44629) | 1st order in all reactants & products\n", "2: ES* <-> E + P (kF = 200 / kR = 17.851 / delta_G = -5,989.7 / K = 11.204) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {'P', 'ES*', 'E', 'S'}\n", "[GRAPHIC ELEMENT SENT TO LOG FILE `enzyme_4.log.htm`]\n" ] } ], "source": [ "# Initialize the system\n", "chem_data = ChemData()\n", " \n", "# Reaction S <-> P , with 1st-order kinetics, favorable thermodynamics in the forward direction, \n", "# and a forward rate that is much slower than it would be with the enzyme - as seen in the next reaction, below\n", "chem_data.add_reaction(reactants=\"S\", products=\"P\",\n", " forward_rate=1., delta_G=-3989.73)\n", "\n", " \n", "# Reaction E + S <-> ES* , with 1st-order kinetics, and a forward rate that is much faster than it was without the enzyme\n", "# Thermodynamically, the forward direction is at a disadvantage (higher energy state) because of the activation barrier in forming the transient state ES*\n", "chem_data.add_reaction(reactants=[\"E\", \"S\"], products=[\"ES*\"],\n", " forward_rate=100., delta_G=2000) \n", " \n", "# Reaction ES* <-> E + P , with 1st-order kinetics, and a forward rate that is much faster than it was without the enzyme\n", "# Thermodynamically, the total energy change of this reaction and the previous one adds up to the same value as the reaction without the enzyme (-3989.73)\n", "chem_data.add_reaction(reactants=[\"ES*\"], products=[\"E\", \"P\"],\n", " forward_rate=200., delta_G=-5989.73)\n", "\n", "# NOTE: the forward_rate's of the last 2 reactions (the catalyzed ones) were tweaked, \n", "# to lead to a crossover point [S] = [P] at about the same time as in experiment `enzyme3`, in step 2 (when [E] = 0.2)\n", "\n", "chem_data.describe_reactions()\n", "\n", "# Send the plot of the reaction network to the HTML log file\n", "chem_data.plot_reaction_network(\"vue_cytoscape_2\")" ] }, { "cell_type": "markdown", "id": "5f3f488b-4cf1-4123-8dfd-9dfc2b9c64b7", "metadata": {}, "source": [ "Note that `E` is not labeled as an \"enzyme\" because it doesn't appear as a catalyst in any of the registered reactions; it only becomes an enzyme in the context of the _compound_ reaction from (2) and (3)" ] }, { "cell_type": "code", "execution_count": null, "id": "919280b2-fd0f-4557-9008-e154b64a2b66", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "0e771dda-1c0f-4fc0-ab21-049740643897", "metadata": {}, "source": [ "# 1. Set the initial concentrations of all the chemicals - starting with no enzyme" ] }, { "cell_type": "code", "execution_count": 6, "id": "5563e467-a637-44fa-9ba1-d35ddd82c887", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "4 species:\n", " Species 0 (S). Conc: 20.0\n", " Species 1 (P). Conc: 0.0\n", " Species 2 (E). Conc: 0.0\n", " Species 3 (ES*). Conc: 0.0\n", "Set of chemicals involved in reactions: {'P', 'ES*', 'E', 'S'}\n" ] } ], "source": [ "dynamics = UniformCompartment(chem_data=chem_data, preset=\"mid\")\n", "dynamics.set_conc(conc={\"S\": 20.}, snapshot=True) # Initially, no enzyme `E`\n", "dynamics.describe_state()" ] }, { "cell_type": "markdown", "id": "651941bb-7098-4065-a598-e50c0b641ab3", "metadata": { "tags": [] }, "source": [ "### Advance the reactions (for now without enzyme) to equilibrium" ] }, { "cell_type": "code", "execution_count": 7, "id": "76f24d9a-a788-41d8-90a4-db87386f91aa", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "27 total step(s) taken\n", "Norm usage: {'norm_A': 14, 'norm_B': 15, 'norm_C': 14, 'norm_D': 14}\n" ] } ], "source": [ "#dynamics.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n", "\n", "# Perform the reactions\n", "dynamics.single_compartment_react(duration=4.0,\n", " initial_step=0.1, variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 8, "id": "4a19ad2a-fbd2-420a-b958-2daf88bcc841", "metadata": {}, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=S
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Changes in concentrations for 3 reactions (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.004642915437776464, 4.155409316809935 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.1111111111111112, 21.11111111111111 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(colors=['cyan', 'green', 'violet', 'red'], show_intervals=True, title_prefix=\"With ZERO enzyme\")" ] }, { "cell_type": "markdown", "id": "9a793ebf-f544-43ad-a1d3-059f74f3c02b", "metadata": {}, "source": [ "### The reactions, lacking enzyme, are proceeding slowly towards equilibrium, just like the reaction that was discussed in part 1 of the experiment \"enzyme_1\"" ] }, { "cell_type": "code", "execution_count": 9, "id": "d684e2c3-c717-4c95-8852-62729914e48f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: S <-> P\n", "Final concentrations: [S] = 3.37 ; [P] = 16.63\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.93491\n", " Formula used: [P] / [S]\n", "2. Ratio of forward/reverse reaction rates: 5.00001\n", "Discrepancy between the two values: 1.302 %\n", "Reaction IS in equilibrium (within 2% tolerance)\n", "\n", "1: E + S <-> ES*\n", "Final concentrations: [E] = 0 ; [S] = 3.37 ; [ES*] = 0\n", "Reaction IS in equilibrium because it can't proceed in either direction due to zero concentrations in both some reactants and products!\n", "\n", "2: ES* <-> E + P\n", "Final concentrations: [ES*] = 0 ; [E] = 0 ; [P] = 16.63\n", "Reaction IS in equilibrium because it can't proceed in either direction due to zero concentrations in both some reactants and products!\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reactions have reached equilibrium\n", "dynamics.is_in_equilibrium(tolerance=2)" ] }, { "cell_type": "code", "execution_count": 10, "id": "4677fcaa-e90b-4975-a567-cb55b66f91f2", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.7322948238817497, 10.0)" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Locate the intersection of the curves for [S] and [P]:\n", "dynamics.curve_intersect(\"S\", \"P\", t_start=0, t_end=1.0)" ] }, { "cell_type": "code", "execution_count": 11, "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": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(columns=['SYSTEM TIME', 'E', 'ES*', 'P'], tail=1) # Last point in the simulation" ] }, { "cell_type": "code", "execution_count": 12, "id": "d4e378a6-550d-44b1-9d38-110844da1397", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "16.63011072773748" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_equil = dynamics.get_chem_conc(\"P\")\n", "P_equil" ] }, { "cell_type": "code", "execution_count": 13, "id": "ddc9d6bb-ea70-4471-bc1f-b0f1c48fd84c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "11.641077509416236" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_70_threshold = P_equil * 0.70\n", "P_70_threshold" ] }, { "cell_type": "code", "execution_count": 14, "id": "52f5a61b-eaab-46e7-ba0a-01c0b58ce9d1", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.9536647543782931" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.reach_threshold(chem=\"P\", threshold=P_70_threshold)" ] }, { "cell_type": "code", "execution_count": null, "id": "cf52d120-927e-44bb-893d-1673e9fd8bd6", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "978149dc-c503-4ca8-b490-83a2e97b40a8", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "27401e5d-8f3e-4c27-8438-129d3e3408a2", "metadata": {}, "source": [ "# 2. Re-start all the reactions from the same initial concentrations - except for now having a tiny amount of enzyme (two orders of magnitude less than the starting [S])" ] }, { "cell_type": "code", "execution_count": 15, "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": 16, "id": "373ce459-3b57-4ab2-a136-4eb8bedcdd91", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "4 species:\n", " Species 0 (S). Conc: 20.0\n", " Species 1 (P). Conc: 0.0\n", " Species 2 (E). Conc: 0.2\n", " Species 3 (ES*). Conc: 0.0\n", "Set of chemicals involved in reactions: {'P', 'ES*', 'E', 'S'}\n" ] } ], "source": [ "dynamics = UniformCompartment(chem_data=chem_data, preset=\"slower\") # A brand-new simulation, with the same chemicals and reactions as before\n", "\n", "dynamics.set_conc(conc={\"S\": 20., \"E\": E_init},\n", " snapshot=True) \n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 17, "id": "bb87b0c2-6e5d-4e9a-86a1-9eb76cfe2d3a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1476 total step(s) taken\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" ] } ], "source": [ "# Perform the reactions (The duration of the run was manually adjusted for optimal visibility)\n", "dynamics.single_compartment_react(duration=1.3,\n", " initial_step=0.00005, variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 18, "id": "1c999a21-c1ab-4210-a8d8-430cc215d882", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reactions have reached equilibrium\n", "dynamics.is_in_equilibrium(verbose=False)" ] }, { "cell_type": "code", "execution_count": 19, "id": "6991314e-58bf-473a-a0fa-c10f18369246", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.24856557905040474, 9.926581378605173)" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Locate the intersection of the curves for [S] and [P]:\n", "dynamics.curve_intersect(\"S\", \"P\", t_start=0, t_end=1.0)" ] }, { "cell_type": "code", "execution_count": 20, "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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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(colors=['cyan', 'green', 'violet', 'red'], show_intervals=True,\n", " title_prefix=f\"[E] init = {E_init}\", range_x=[0, 0.4])" ] }, { "cell_type": "code", "execution_count": 21, "id": "de531345-b12f-4c43-9954-bf46db6f1141", "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", "dynamics.curve_intersect(\"S\", \"P\", t_start=0, t_end=0.4)" ] }, { "cell_type": "markdown", "id": "41a77229-ad02-4e1e-8c3e-dfe2e6e0a302", "metadata": {}, "source": [ "### Now, let's investigate E and ES* in the very early times" ] }, { "cell_type": "markdown", "id": "738f8578-8cc9-4ed1-98f1-69291581ed24", "metadata": {}, "source": [ "## Notice how even a tiny amount of enzyme (1/100 of the initial [S]) makes a very pronounced difference!" ] }, { "cell_type": "code", "execution_count": 22, "id": "2bdb3ca1", "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", "dynamics.plot_history(chemicals=['E', 'ES*'], colors=['violet', 'red'], show_intervals=True,\n", " title_prefix=f\"Detail when [E] init = {E_init}\", range_x=[0, 0.002])" ] }, { "cell_type": "markdown", "id": "1f1fdafa-f516-4490-99c1-1649a0b4d783", "metadata": {}, "source": [ "### Notice how, with this small initial concentration of [E], the timescale of [E] and [ES*] is vastly faster than that of [P] and [S]" ] }, { "cell_type": "code", "execution_count": 23, "id": "c5297f8f-2e7e-4acb-b029-6235388cbc4a", "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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"aaxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "baxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" }, "bgcolor": "#E5ECF6", "caxis": { "gridcolor": "white", "linecolor": "white", "ticks": "" } }, "title": { "x": 0.05 }, "xaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 }, "yaxis": { "automargin": true, "gridcolor": "white", "linecolor": "white", "ticks": "", "title": { "standoff": 15 }, "zerolinecolor": "white", "zerolinewidth": 2 } } }, "title": { "text": "E and ES when [E] init = 0.2
Changes in concentrations for 3 reactions (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.0014534636732560912, 1.3008499875642017 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.011111111111111112, 0.2111111111111111 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# The full reaction of E and ES*\n", "dynamics.plot_history(chemicals=['E', 'ES*'], colors=['violet', 'red'], show_intervals=True, \n", " title_prefix=f\"E and ES when [E] init = {E_init}\")" ] }, { "cell_type": "markdown", "id": "a63d5742-334a-40c5-823e-27bc37cfb27d", "metadata": {}, "source": [ "Notice how at every onset of instability in [E] or [ES*], the adaptive time steps shrink down" ] }, { "cell_type": "code", "execution_count": 24, "id": "954dccf3-30c0-4d82-a1c0-8b2860ad2d17", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
SYSTEM TIMEEES*P
14761.300850.0805460.11945416.544949
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" ], "text/plain": [ " SYSTEM TIME E ES* P\n", "1476 1.30085 0.080546 0.119454 16.544949" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(columns=['SYSTEM TIME', 'E', 'ES*', 'P'], tail=1) # Last point in the simulation" ] }, { "cell_type": "markdown", "id": "71263cd2-4baf-44a3-b133-d7dcc1e0af94", "metadata": {}, "source": [ "Interestingly, most of the inital [E] of 0.2 is now, at equilibrium, stored as [ES*]=0.119; the energy of the \"activation barrier\" from E + S to ES* might be unrealistically low (2000 Joules). Zooming in on the very earl part of the plot:" ] }, { "cell_type": "code", "execution_count": 25, "id": "ee6e7870-8dad-4ff4-997d-286db0d3a8d6", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "16.54494887428722" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_equil = dynamics.get_chem_conc(\"P\")\n", "P_equil" ] }, { "cell_type": "code", "execution_count": 26, "id": "b6e26868-1b81-49c9-af7c-836b881121c1", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "11.581464212001052" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_70_threshold = P_equil * 0.70\n", "P_70_threshold" ] }, { "cell_type": "code", "execution_count": 27, "id": "ac6a3e1e-3fa1-4bfd-8524-11116731c5cd", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.31446597160581014" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.reach_threshold(chem=\"P\", threshold=P_70_threshold)" ] }, { "cell_type": "code", "execution_count": null, "id": "e80645d6-eb5b-4c78-8b46-ae126d2cb2cf", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "b74e6177-a59f-4e10-ad5b-945e7f8e63d9", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "6d946522-d437-49af-9fe1-0ddc4f2fcbaa", "metadata": { "tags": [] }, "source": [ "# 3. Repeat last step with increasingly-larger initial [E]" ] }, { "cell_type": "code", "execution_count": 28, "id": "7f1bdff5-4816-4b34-af29-81013e431696", "metadata": {}, "outputs": [], "source": [ "E_init = 0.4" ] }, { "cell_type": "code", "execution_count": 29, "id": "9669e103-0a48-42d6-ace4-cc6ca19fd313", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "4 species:\n", " Species 0 (S). Conc: 20.0\n", " Species 1 (P). Conc: 0.0\n", " Species 2 (E). Conc: 0.4\n", " Species 3 (ES*). Conc: 0.0\n", "Set of chemicals involved in reactions: {'P', 'ES*', 'E', 'S'}\n" ] } ], "source": [ "dynamics = UniformCompartment(chem_data=chem_data, preset=\"slower\") # A brand-new simulation, with the same chemicals and reactions as before\n", "\n", "dynamics.set_conc(conc={\"S\": 20., \"E\": E_init},\n", " snapshot=True) \n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 30, "id": "f5140de7-0838-442a-909f-695715fb0918", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1211 total step(s) taken\n", "Number of step re-do's because of elective soft aborts: 1\n", "Norm usage: {'norm_A': 1195, 'norm_B': 1204, 'norm_C': 1195, 'norm_D': 1195}\n" ] } ], "source": [ "# Perform the reactions (The duration of the run was manually adjusted for optimal visibility)\n", "dynamics.single_compartment_react(duration=1.0,\n", " initial_step=0.00005, variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 31, "id": "d6c74db1-b3a2-41d2-8785-04e75ab69870", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reactions have reached equilibrium\n", "dynamics.is_in_equilibrium(verbose=False)" ] }, { "cell_type": "code", "execution_count": 32, "id": "9cb3906d-b25c-4b3e-b695-c24f43b26246", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_pandas() NOTICE: Excessive number of vertical lines (1212) - only showing 1 every 9 lines\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=S
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Changes in concentrations for 3 reactions (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.0011191175259711303, 1.0016101857441617 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.1111111111111112, 21.11111111111111 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(colors=['cyan', 'green', 'violet', 'red'], show_intervals=True, \n", " title_prefix=f\"[E] init = {E_init}\")" ] }, { "cell_type": "code", "execution_count": 33, "id": "0d428e60-9735-4008-b909-59884bac38b0", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.1480911200305407, 9.85341706705381)" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Locate the intersection of the curves for [S] and [P]:\n", "dynamics.curve_intersect(\"S\", \"P\", t_start=0, t_end=0.4)" ] }, { "cell_type": "markdown", "id": "022c06df-44ad-4b15-b329-143cb68c6c02", "metadata": {}, "source": [ "Notice how the timescale of [S] and [P] is becoming faster with a higher initial [E]" ] }, { "cell_type": "code", "execution_count": 34, "id": "54c21fc6-42ee-4dd2-9f50-b84a793adca5", "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 (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "domain": [ 0, 1 ], "range": [ 0, 0.002 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.022222222222222223, 0.4222222222222222 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#The very early part of the reaction\n", "dynamics.plot_history(chemicals=['E', 'ES*'], colors=['violet', 'red'], show_intervals=True,\n", " title_prefix=f\"Detail when [E] init = {E_init}\", range_x=[0, 0.002])" ] }, { "cell_type": "code", "execution_count": 35, "id": "7f6cab84-d18e-48f6-bc27-f7eef1cae9f1", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "plot_pandas() NOTICE: Excessive number of vertical lines (1212) - only showing 1 every 9 lines\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=E
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Changes in concentrations for 3 reactions (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.0011191175259711303, 1.0016101857441617 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.022222222222222223, 0.4222222222222222 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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SYSTEM TIMEEES*P
12111.001610.1619310.23806916.466878
\n", "
" ], "text/plain": [ " SYSTEM TIME E ES* P\n", "1211 1.00161 0.161931 0.238069 16.466878" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(columns=['SYSTEM TIME', 'E', 'ES*', 'P'], tail=1) # Last point in the simulation" ] }, { "cell_type": "code", "execution_count": 37, "id": "e4fd52be-db88-4b57-94a3-217cce0386c0", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "16.466877520220297" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_equil = dynamics.get_chem_conc(\"P\")\n", "P_equil" ] }, { "cell_type": "markdown", "id": "b0d8f75f-55a3-4712-ba46-9eb97833138c", "metadata": {}, "source": [ "#### P_equil continues to decrease with increasing initial [E]" ] }, { "cell_type": "code", "execution_count": 38, "id": "717d906a-659d-4635-9914-3b7eebf2f4df", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "11.526814264154208" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_70_threshold = P_equil * 0.70\n", "P_70_threshold" ] }, { "cell_type": "code", "execution_count": 39, "id": "cc46e532-b71f-4697-97bc-e0cad1328a1e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.18680188203718445" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.reach_threshold(chem=\"P\", threshold=P_70_threshold)" ] }, { "cell_type": "markdown", "id": "887bf402-e6e3-461f-88dc-cf87bbdf40a8", "metadata": {}, "source": [ "#### The time at which the 70% threshold of the equilibrium value of P continues to decrease with increasing initial [E]" ] }, { "cell_type": "code", "execution_count": null, "id": "8a318f52-7710-43df-b9ac-86c8ab690d60", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "6201afdd-cbdf-47f0-9289-ea290386c660", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "802b910e-0fa0-463b-a220-873c5882a33f", "metadata": { "tags": [] }, "source": [ "# 4. Keep increasing the initial [E]" ] }, { "cell_type": "code", "execution_count": 40, "id": "31bbf923-046d-4da3-9c33-c8f57ef3814c", "metadata": {}, "outputs": [], "source": [ "E_init = 1.0" ] }, { "cell_type": "code", "execution_count": 41, "id": "631bd026-58da-4295-9f05-d132577cb0cc", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "4 species:\n", " Species 0 (S). Conc: 20.0\n", " Species 1 (P). Conc: 0.0\n", " Species 2 (E). Conc: 1.0\n", " Species 3 (ES*). Conc: 0.0\n", "Set of chemicals involved in reactions: {'P', 'ES*', 'E', 'S'}\n" ] } ], "source": [ "dynamics = UniformCompartment(chem_data=chem_data, preset=\"slower\") # A brand-new simulation, with the same chemicals and reactions as before\n", "\n", "dynamics.set_conc(conc={\"S\": 20., \"E\": E_init}, snapshot=True) \n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 42, "id": "ba3e8cca-873f-40dc-97b5-38374fcc826c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "866 total step(s) taken\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" ] } ], "source": [ "# Perform the reactions (The duration of the run was manually adjusted for optimal visibility)\n", "dynamics.single_compartment_react(duration=0.4,\n", " initial_step=0.00005, variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 43, "id": "c2b19731-38b2-4d09-bca2-3b666c633eee", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reactions have reached equilibrium\n", "dynamics.is_in_equilibrium(verbose=False)" ] }, { "cell_type": "code", "execution_count": 44, "id": "522e8f39-c7b3-4edf-80f3-3cf25c440e1e", "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": [ -0.00044710418774206927, 0.400158248029152 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.1111111111111112, 21.11111111111111 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(colors=['cyan', 'green', 'violet', 'red'], show_intervals=True, \n", " title_prefix=f\"[E] init = {E_init}\")" ] }, { "cell_type": "code", "execution_count": 45, "id": "93a7b3b5-ffff-4417-b768-bf9886e9ef7e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.06628340509848926, 9.635470546269993)" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Locate the intersection of the curves for [S] and [P]:\n", "dynamics.curve_intersect(\"S\", \"P\", t_start=0, t_end=0.4)" ] }, { "cell_type": "markdown", "id": "46e10d97-2c62-4e6d-9429-cc769a47e596", "metadata": {}, "source": [ "The timescale of [S] and [P] continues to become faster with a higher initial [E]" ] }, { "cell_type": "code", "execution_count": 46, "id": "fb00b2fc-2bc2-433f-b907-019e786f68a1", "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 (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "domain": [ 0, 1 ], "range": [ 0, 0.002 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.05555555555555555, 1.0555555555555556 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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", 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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": [ -0.00044710418774206927, 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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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# The full reaction of E and ES*\n", "dynamics.plot_history(chemicals=['E', 'ES*'], colors=['violet', 'red'], show_intervals=True, \n", " title_prefix=f\"E and ES when [E] init = {E_init}\")" ] }, { "cell_type": "code", "execution_count": 48, "id": "ee454fdd-62fa-48d3-ac1c-b967279bd1e1", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEEES*P
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\n", "
" ], "text/plain": [ " SYSTEM TIME E ES* P\n", "866 0.400158 0.409128 0.590872 16.1715" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(columns=['SYSTEM TIME', 'E', 'ES*', 'P'], tail=1) # Last point in the simulation" ] }, { "cell_type": "code", "execution_count": 49, "id": "264292b6-4ba1-4c36-8ea7-29472756a879", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "16.171500029051185" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_equil = dynamics.get_chem_conc(\"P\")\n", "P_equil" ] }, { "cell_type": "markdown", "id": "97f3ff27-4e2f-4af9-b9f6-ad8e44d6e10a", "metadata": {}, "source": [ "#### P_equil continues to decrease with increasing initial [E]" ] }, { "cell_type": "code", "execution_count": 50, "id": "ceee7058-2661-4259-a2e6-0bd6732cc2ac", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "11.32005002033583" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_70_threshold = P_equil * 0.70\n", "P_70_threshold" ] }, { "cell_type": "code", "execution_count": 51, "id": "6b0b5166-ba0c-4b15-a632-84362fbdcd5c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.08364939325100468" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.reach_threshold(chem=\"P\", threshold=P_70_threshold)" ] }, { "cell_type": "markdown", "id": "c295cb25-41de-4405-83ee-0a5e5db0d304", "metadata": {}, "source": [ "#### The time at which we reach the 70% threshold of the equilibrium value of P continues to decrease with increasing initial [E]" ] }, { "cell_type": "code", "execution_count": null, "id": "cd775a94-b7c3-4c2b-9da2-4bfacd53fa26", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "bd7d5617-cf3c-4c03-bd77-9ccfcb12dc4c", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "2d43197e-eef6-4ea2-a489-ca6ed165b024", "metadata": { "tags": [] }, "source": [ "# 5. Keep increasing the initial [E]" ] }, { "cell_type": "code", "execution_count": 52, "id": "0b2f4582-ea90-41fe-b69a-c565738e4344", "metadata": {}, "outputs": [], "source": [ "E_init = 2.0 # 1/10 of the initial [S]" ] }, { "cell_type": "code", "execution_count": 53, "id": "fb3ca78d-c024-47b9-be04-5c74d7213727", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "4 species:\n", " Species 0 (S). Conc: 20.0\n", " Species 1 (P). Conc: 0.0\n", " Species 2 (E). Conc: 2.0\n", " Species 3 (ES*). Conc: 0.0\n", "Set of chemicals involved in reactions: {'P', 'ES*', 'E', 'S'}\n" ] } ], "source": [ "dynamics = UniformCompartment(chem_data=chem_data, preset=\"slower\") # A brand-new simulation, with the same chemicals and reactions as before\n", "\n", "dynamics.set_conc(conc={\"S\": 20., \"E\": E_init}, snapshot=True) \n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 54, "id": "9336e30c-950b-4bc6-844a-68c3653b0244", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "818 total step(s) taken\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" ] } ], "source": [ "# Perform the reactions (The duration of the run was manually adjusted for optimal visibility)\n", "dynamics.single_compartment_react(duration=0.2,\n", " initial_step=0.00005, variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 55, "id": "76f54bfa-0189-4712-b676-667adb514a8c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reactions have reached equilibrium\n", "dynamics.is_in_equilibrium(verbose=False)" ] }, { "cell_type": "code", "execution_count": 56, "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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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(colors=['cyan', 'green', 'violet', 'red'], show_intervals=True, \n", " title_prefix=f\"[E] init = {E_init}\")" ] }, { "cell_type": "code", "execution_count": 57, "id": "c5bb9972-79ba-43db-a0de-66d9495bcef4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.033892638379102225, 9.277504597225233)" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Locate the intersection of the curves for [S] and [P]:\n", "dynamics.curve_intersect(\"S\", \"P\", t_start=0, t_end=0.4)" ] }, { "cell_type": "markdown", "id": "ddf4a727-1fdc-4b61-953a-d582cda053ce", "metadata": {}, "source": [ "The timescale of [S] and [P] continues to become faster with a higher initial [E]" ] }, { "cell_type": "code", "execution_count": 58, "id": "cab73b69-81c6-48cf-be12-73ddd0e9a4d2", "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", "domain": [ 0, 1 ], "range": [ 0, 0.002 ], "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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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#The very early part of the reaction\n", "dynamics.plot_history(chemicals=['E', 'ES*'], colors=['violet', 'red'], show_intervals=True,\n", " title_prefix=f\"Detail when [E] init = {E_init}\", range_x=[0, 0.002])" ] }, { "cell_type": "code", "execution_count": 59, "id": "1614dba7-9e08-4e15-859c-474ef8e219f6", "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=E
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", 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SYSTEM TIMEEES*P
8180.2017530.8328491.16715115.691155
\n", "
" ], "text/plain": [ " SYSTEM TIME E ES* P\n", "818 0.201753 0.832849 1.167151 15.691155" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(columns=['SYSTEM TIME', 'E', 'ES*', 'P'], tail=1) # Last point in the simulation" ] }, { "cell_type": "code", "execution_count": 61, "id": "5d28e797-ebb8-480a-bdcf-13880757b32b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "15.69115548729148" ] }, "execution_count": 61, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_equil = dynamics.get_chem_conc(\"P\")\n", "P_equil" ] }, { "cell_type": "markdown", "id": "797a8ab4-d051-4e92-bf1b-e1e148de6ca4", "metadata": {}, "source": [ "#### P_equil continues to decrease with increasing initial [E]" ] }, { "cell_type": "code", "execution_count": 62, "id": "94b8d506-9225-4c18-b618-2b87e9d48a3a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "10.983808841104036" ] }, "execution_count": 62, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_70_threshold = P_equil * 0.70\n", "P_70_threshold" ] }, { "cell_type": "code", "execution_count": 63, "id": "968136e5-5497-4e3b-8a2b-25b02d7e9ad7", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.04311547431679562" ] }, "execution_count": 63, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.reach_threshold(chem=\"P\", threshold=P_70_threshold)" ] }, { "cell_type": "markdown", "id": "78dd47e8-668a-44f2-a770-f7cff871915b", "metadata": {}, "source": [ "#### The time at which we reach the 70% threshold of the equilibrium value of P continues to decrease with increasing initial [E]" ] }, { "cell_type": "code", "execution_count": null, "id": "3af50933-541a-4e48-b6de-69fdbf82a5cf", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "ba756ea7-7e7b-4a9b-a847-c9b12975b667", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "1a2e3c92-4ce0-4d3b-bb89-113fe3eabbc1", "metadata": { "tags": [] }, "source": [ "# 6. Keep increasing the initial [E]" ] }, { "cell_type": "code", "execution_count": 64, "id": "30fb7ef6-0dcd-4063-bf6b-5e69e6a9a81e", "metadata": {}, "outputs": [], "source": [ "E_init = 10.0 # 1/2 of the initial [S]" ] }, { "cell_type": "code", "execution_count": 65, "id": "4353621a-ac88-4cd3-a3b2-fec1bbf592f4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "4 species:\n", " Species 0 (S). Conc: 20.0\n", " Species 1 (P). Conc: 0.0\n", " Species 2 (E). Conc: 10.0\n", " Species 3 (ES*). Conc: 0.0\n", "Set of chemicals involved in reactions: {'P', 'ES*', 'E', 'S'}\n" ] } ], "source": [ "dynamics = UniformCompartment(chem_data=chem_data, preset=\"slower\") # A brand-new simulation, with the same chemicals and reactions as before\n", "\n", "dynamics.set_conc(conc={\"S\": 20., \"E\": E_init}, snapshot=True) \n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 66, "id": "6e3b51d3-31c8-4d55-90b6-c54275ebf914", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "836 total step(s) taken\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" ] } ], "source": [ "# Perform the reactions (The duration of the run was manually adjusted for optimal visibility)\n", "dynamics.single_compartment_react(duration=0.05,\n", " initial_step=0.00005, variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 67, "id": "a8169cc9-fa96-4388-bdbd-3672c6e9fa59", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 67, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reactions have reached equilibrium\n", "dynamics.is_in_equilibrium(verbose=False)" ] }, { "cell_type": "code", "execution_count": 68, "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": [ -5.616153913799015e-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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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(colors=['cyan', 'green', 'violet', 'red'], show_intervals=True, \n", " title_prefix=f\"[E] init = {E_init}\")" ] }, { "cell_type": "code", "execution_count": 69, "id": "cea4cabc-470c-4830-ab70-f05d4176b189", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.005877353573479905, 6.680399989705835)" ] }, "execution_count": 69, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Locate the intersection of the curves for [S] and [P]:\n", "dynamics.curve_intersect(\"S\", \"P\", t_start=0, t_end=0.05)" ] }, { "cell_type": "markdown", "id": "7e911332-dbd3-4f05-bda5-1d902d515156", "metadata": {}, "source": [ "#### The timescale of [S] and [P] continues to become faster with a higher initial [E] -- **AND THEY'RE NOW APPROACHING THE TIMESCALES OF E AND ES**" ] }, { "cell_type": "code", "execution_count": 70, "id": "11c4c99b-cc15-488e-ba6a-f8aacd80ed67", "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": [ -5.616153913799015e-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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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# The full reaction of E and ES*\n", "dynamics.plot_history(chemicals=['E', 'ES*'], colors=['violet', 'red'], show_intervals=True, \n", " title_prefix=f\"E and ES when [E] init = {E_init}\")" ] }, { "cell_type": "markdown", "id": "1f97da50-3764-4be6-bdef-ae5eef24a37d", "metadata": {}, "source": [ "#### Notice that at these higher initial concentrations of [E], we're now beginning to see overshoots in [E] and [ES*]" ] }, { "cell_type": "code", "execution_count": 72, "id": "c7d3f38c-331b-47f2-9ae0-31531c62c7e2", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEEES*P
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\n", "
" ], "text/plain": [ " SYSTEM TIME E ES* P\n", "836 0.050265 4.765697 5.234303 12.304598" ] }, "execution_count": 72, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(columns=['SYSTEM TIME', 'E', 'ES*', 'P'], tail=1) # Last point in the simulation" ] }, { "cell_type": "code", "execution_count": 73, "id": "38c003d2-e007-4c47-9c91-3fb6c2a626ea", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "12.304597774138907" ] }, "execution_count": 73, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_equil = dynamics.get_chem_conc(\"P\")\n", "P_equil" ] }, { "cell_type": "markdown", "id": "04f9845c-4a0d-4309-acd6-46fcc1d59136", "metadata": {}, "source": [ "#### P_equil continues to decrease with increasing initial [E]" ] }, { "cell_type": "code", "execution_count": 74, "id": "51356bd2-f34f-4189-8f39-c11804c6062c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "8.613218441897235" ] }, "execution_count": 74, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_70_threshold = P_equil * 0.70\n", "P_70_threshold" ] }, { "cell_type": "code", "execution_count": 75, "id": "f40ab9f2-a1fe-46a0-b755-9e2dd332ce9f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.008274545666098492" ] }, "execution_count": 75, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.reach_threshold(chem=\"P\", threshold=P_70_threshold)" ] }, { "cell_type": "markdown", "id": "319960a1-b1b3-4237-87b2-f634420acec9", "metadata": {}, "source": [ "#### The time at which we reach the 70% threshold of the equilibrium value of P continues to decrease with increasing initial [E]" ] }, { "cell_type": "code", "execution_count": null, "id": "e69e2707-5dfa-465f-9842-64f796c55dac", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "903586d5-e021-4536-bc32-987df21b2e69", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "e813f05f-1cbb-4b9e-8bc3-9902ba313445", "metadata": { "tags": [] }, "source": [ "# 7. Keep increasing the initial [E]" ] }, { "cell_type": "code", "execution_count": 76, "id": "70c6943f-9deb-4ec0-89eb-382c9728e889", "metadata": {}, "outputs": [], "source": [ "E_init = 20.0 # Same as the initial [S]" ] }, { "cell_type": "code", "execution_count": 77, "id": "0e1fec6a-0cca-4ca7-b54e-340fbef124d8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "4 species:\n", " Species 0 (S). Conc: 20.0\n", " Species 1 (P). Conc: 0.0\n", " Species 2 (E). Conc: 20.0\n", " Species 3 (ES*). Conc: 0.0\n", "Set of chemicals involved in reactions: {'P', 'ES*', 'E', 'S'}\n" ] } ], "source": [ "dynamics = UniformCompartment(chem_data=chem_data, preset=\"slower\") # A brand-new simulation, with the same chemicals and reactions as before\n", "\n", "dynamics.set_conc(conc={\"S\": 20., \"E\": E_init}, snapshot=True) \n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 78, "id": "27e46b9b-802e-4de5-b549-062ba7a4866b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n", "757 total step(s) taken\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" ] } ], "source": [ "# Perform the reactions (The duration of the run was manually adjusted for optimal visibility)\n", "dynamics.single_compartment_react(duration=0.02,\n", " initial_step=0.00005, variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 79, "id": "4b74d93a-54a3-4c96-88d8-b9c4fcc34059", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 79, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reactions have reached equilibrium\n", "dynamics.is_in_equilibrium(verbose=False)" ] }, { "cell_type": "code", "execution_count": 80, "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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Changes in concentrations for 3 reactions (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -2.2511058515192968e-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": [ "dynamics.plot_history(colors=['cyan', 'green', 'violet', 'red'], show_intervals=True, \n", " title_prefix=f\"[E] init = {E_init}\")" ] }, { "cell_type": "code", "execution_count": 81, "id": "b44a6da4-b3bb-4297-932b-3df13fe796d0", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.0024715441102170356, 4.283809315596441)" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Locate the intersection of the curves for [S] and [P]:\n", "dynamics.curve_intersect(\"S\", \"P\", t_start=0, t_end=0.02)" ] }, { "cell_type": "markdown", "id": "45539de2-b37b-4749-aa4f-b247c860b3ee", "metadata": {}, "source": [ "#### The timescale of [S] and [P] continues to become faster with a higher initial [E] -- **AND THEY'RE NOW GETTING CLOSE THE TIMESCALES OF E AND ES**" ] }, { "cell_type": "code", "execution_count": 82, "id": "5fcdb4fd-0dba-43b7-880f-4c8b3aceca1e", "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 (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "domain": [ 0, 1 ], "range": [ 0, 0.002 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.1111111111111112, 21.11111111111111 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#The very early part of the reaction\n", "dynamics.plot_history(chemicals=['E', 'ES*'], colors=['violet', 'red'], show_intervals=True,\n", " title_prefix=f\"Detail when [E] init = {E_init}\", range_x=[0, 0.002])" ] }, { "cell_type": "code", "execution_count": 83, "id": "2551a571-f014-41fb-9768-faf3b3a404e5", "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=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": [ -2.2511058515192968e-05, 0.020147397371097706 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.1111111111111112, 21.11111111111111 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# The full reaction of E and ES*\n", "dynamics.plot_history(chemicals=['E', 'ES*'], colors=['violet', 'red'], show_intervals=True, \n", " title_prefix=f\"E and ES when [E] init = {E_init}\")" ] }, { "cell_type": "markdown", "id": "14a5ce9f-8a93-4ad4-a8fa-e26496b0e573", "metadata": {}, "source": [ "#### At these higher initial concentrations of [E], we're now beginning to see overshoots in [E] and [ES*] that overlap less" ] }, { "cell_type": "code", "execution_count": 84, "id": "05426505-fa5c-4b0f-bdae-9eaf3cace1dd", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEEES*P
7570.02014710.9981479.0018539.163739
\n", "
" ], "text/plain": [ " SYSTEM TIME E ES* P\n", "757 0.020147 10.998147 9.001853 9.163739" ] }, "execution_count": 84, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(columns=['SYSTEM TIME', 'E', 'ES*', 'P'], tail=1) # Last point in the simulation" ] }, { "cell_type": "code", "execution_count": 85, "id": "50529736-69a0-404a-ac61-2b5f9b2ba216", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "9.163739207468186" ] }, "execution_count": 85, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_equil = dynamics.get_chem_conc(\"P\")\n", "P_equil" ] }, { "cell_type": "markdown", "id": "60e3e92e-32ba-46f7-8c4c-760ac69054ea", "metadata": {}, "source": [ "#### P_equil continues to decrease with increasing initial [E]" ] }, { "cell_type": "code", "execution_count": 86, "id": "31d1a073-906e-45d0-90d2-d63f8e4d7df2", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "6.41461744522773" ] }, "execution_count": 86, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_70_threshold = P_equil * 0.70\n", "P_70_threshold" ] }, { "cell_type": "code", "execution_count": 87, "id": "c6d79966-d114-4e66-bb94-bcf852fee8be", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.004076150862005783" ] }, "execution_count": 87, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.reach_threshold(chem=\"P\", threshold=P_70_threshold)" ] }, { "cell_type": "markdown", "id": "3c014242-7a93-4368-ac71-0e2aa7dc88f5", "metadata": { "tags": [] }, "source": [ "#### The time at which we reach the 70% threshold of the equilibrium value of P continues to decrease with increasing initial [E]" ] }, { "cell_type": "code", "execution_count": null, "id": "2ca50397-215f-490e-ac27-c2b76cf51dae", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "845d2620-d0a2-4080-a201-a118fede9e48", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "c45bfaac-3a80-473c-a9b5-cc0c55bf1c5f", "metadata": { "tags": [] }, "source": [ "# 8. Keep increasing the initial [E]" ] }, { "cell_type": "code", "execution_count": 88, "id": "06f75fcd-19b7-45dd-bcd5-ea5136280700", "metadata": {}, "outputs": [], "source": [ "E_init = 30.0 # 50% higher than the initial [S]" ] }, { "cell_type": "code", "execution_count": 89, "id": "86ebdf54-6e5e-4450-acc2-9c45fb978d6d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "4 species:\n", " Species 0 (S). Conc: 20.0\n", " Species 1 (P). Conc: 0.0\n", " Species 2 (E). Conc: 30.0\n", " Species 3 (ES*). Conc: 0.0\n", "Set of chemicals involved in reactions: {'P', 'ES*', 'E', 'S'}\n" ] } ], "source": [ "dynamics = UniformCompartment(chem_data=chem_data, preset=\"slower\") # A brand-new simulation, with the same chemicals and reactions as before\n", "\n", "dynamics.set_conc(conc={\"S\": 20., \"E\": E_init}, snapshot=True) \n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 90, "id": "45e38a17-5515-4d69-8b27-168331473dd4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n", "749 total step(s) taken\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" ] } ], "source": [ "# Perform the reactions (The duration of the run was manually adjusted for optimal visibility)\n", "dynamics.single_compartment_react(duration=0.01,\n", " initial_step=0.00005, variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 91, "id": "8d7277d0-1d8f-479a-9110-eace7ef00222", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 91, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reactions have reached equilibrium\n", "dynamics.is_in_equilibrium(verbose=False)" ] }, { "cell_type": "code", "execution_count": 92, "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": [ -1.1233335123518272e-05, 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": [ "dynamics.plot_history(colors=['cyan', 'green', 'violet', 'red'], show_intervals=True, \n", " title_prefix=f\"[E] init = {E_init}\")" ] }, { "cell_type": "code", "execution_count": 93, "id": "64c0b5f9-1a4a-4b65-a927-f4c24839c44c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.0015007776137844029, 2.9518860757696133)" ] }, "execution_count": 93, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Locate the intersection of the curves for [S] and [P]:\n", "dynamics.curve_intersect(\"S\", \"P\", t_start=0, t_end=0.01)" ] }, { "cell_type": "markdown", "id": "cd858e13-44eb-4e0e-a77f-82001e764fbc", "metadata": {}, "source": [ "#### The timescale of [S] and [P] continues to become faster with a higher initial [E] -- **AND THEY'RE NOW COMPARABLE THE TIMESCALES OF E AND ES**" ] }, { "cell_type": "code", "execution_count": 94, "id": "1bf0ed70-9c0a-4c93-b538-0cafeb01921b", "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", "domain": [ 0, 1 ], "range": [ 0, 0.005 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -1.6666666666666665, 31.666666666666668 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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Edtcfu9BYvbpkViOHDaRf/OiOWHPM17jqhBNxofcp3cdBIt9ep31jHvGuTaffx0vHZVvZzxxX+h8y8V5fJyNCVB51XSS6X5l9ULN/bt8G6DNlidxlnIpON367Vs8xbsO3fvgbuuS8sdInm6+dhYtWtHqj4rQt8e4HfojORPeLeKLT7t7vZJy5uY/bXWPqfhSvvW7uxV6KTnVdhE50Or3Y3Mx0qoeF6RNkAnVqeLu/SHXRGe9BpV9I6oYXz0fEiT+P1zOdqYo/8zWVU9GZ6AatmFn525g3JnXj9Vt0qraYrwKt6rW7WTh5SJlcnY5ZxcfqDy8nf+RY9cdudoWvA1W2mxudnehUosJ0j0g0Q2rVx3gPC1WOuVIGf68/0J3+YWW2K93HQVhEp1P7JRpPVvcSq9eWTn1Y9bpUHjeik/Mr4amXZed3zWl14anyOnFRsLqeEs3qma9s9Rm2V95cTh+v3iDfHupCk23Vo2unVn/EhVF0JpoRNZm4uffbjTOn9/F4GkEfK+o5Eo+vm3uxl6JT9TE0otON/yIDdiM6E/2Fwg61yp/NreGtbkTxZnic3DTi/SUez4FeT++16FQ3v0RuCm5m5JyKTjdiN1mxxH2zurkk83o93oxAKqLTDVenY9bqwavfwOz+sAnTTKd6SPJPO19Uu5lOJxH58R5EZtlO/mBKdF2Z+cM4DoJ4ve5mptOJ/Zz8EaPSqLrVvd1uptOcDbeqK9G4sHNhUnmdBpTq9Stb6fdwp0LPzUynPrP7qoifOHXoADm7qdrOzz4OFDMnlJy2JZ79/JjpdCM63dz7zT6Y48zNfdyJ60ii+0xbic7QzXQyJPWXayIxwcbiV15uRKdTvzM3ho8nUNz4dOoDkQcC31j0QAXFRBfG8S5AP0RnvIuK2SufJ6e+h05Fp9Vf3arPbB8+mJHdq3/zIWKKKqubi+njq8qwe/BYzbhZPTjjvfKL5/vipFynY5b7wLMQ5vJDTn2d2sKnk/vGY1/3SVY2sXKQt7o2Et1gnd583fhGJZpdGD3iZBlIlM7jwPQbM5m76ZtTcRnvWnZqv3j3TPUsMc+bNoz3kE/0el8vM5Ho1OuKN96d1MPX8WUXnCHHl36Y92enQs+NT6d+zzZXblH1W63o4rQtQYrORLYyWTp99jkZZ07v4240gZ3vp5NJGy9nOtU4Cc1MpxpY6vVfKovDWzk286DXhYcSuPpfkG4Mb77m5PbH86tRF7DZJ07PywfxqwhVnj576mb21w/Rqfqj/6Vs+itZtduKjRvRaVWmaov5utacbeb2sS+RmgFz83o9kcN3vGViVPn6TLb6jseEPubsAg+sVgCwi853OmaV3cxZcx43fNjNGNpxtFuZIRmBYDX+1I2LxaiTtwd29ar7gFkWjwU+WKQnGs+cxipy38qWdi4fVrZ0en0FNQ7s3kS4GeOpik71ALYSNLr9EolO9unV7Wdla7tZP6tZSM6jVtpQtjHvVWrsqXtEvPHu5A8sq2eMVb1uhB6ntXo9b/XmTdnSPKfaZcXITVusbOjHTKc+pqz0gt4/p/d+Kx/0VNyk4t3L1b1RrZJhZX9do7SF6OT6Qyc6GZyV/4N5c3cz06kPJDV4GTgLvmRer6syzHbygORXC3ogi0qrG1u/gKwe1vp5p0EffohO1Q7Tx8hK6JlrVSZap1OfzbV7WMZjJQXdkTUDzRuS3j47sWSKDdNPzFyn05wp5Lp1kcmf9bXWzBlW3afS63U67VYpsBqDTlw39D5avYa3Ktfkaif+4gkDq7LdvGp0Um88v2sr/03VTn2tw3hRm3qfzDTpOg7UvTTR2xenffNCdHJ7nNgv3viy8gu1ehjr90Cr2AB93WGuy2oyg79jbuqwGsdWzz4nK7FY3YfUvUi/L7gVeiafeG2xEuv6Pdoqn9u2mDb0S3TG0wu87KL59snpvd9unNk9B610gJV/vjk2zfsnn79YvCnkvrSF6GS2oRSd8W4Q6fC9HsmXDu1FG0EABEDADYFEryDdlJMtacErWyyNfjohANHphJJFGvM1LifBzSVJmMgGAiCQVgSsXi2mVQcCbCyeCwHCRlWhJwDRmaSJ4r3adTJlnWSVyAYCIAACoSGgXjnjnpfYJBCdoRmyaEgICEB0hsAIaAIIgAAIgAAIgAAIZDoBiM5MtzD6BwIgAAIgAAIgAAIhIADRGQIjoAkgAAIgAAIgAAIgkOkEIDoz3cLoHwiAAAiAAAiAAAiEgABEZwiMgCaAAAiAAAiAAAiAQKYTgOjMdAujfyAAAiAAAiAAAiAQAgIQnSEwApoAAiAAAiAAAiAAAplOAKIz0y2M/oEACIAACIAACIBACAhAdIbACGgCCIAACIAACIAACGQ6AYjOTLcw+gcCIAACIAACIAACISAA0RkCI6AJIAACIAACIAACIJDpBCA6M93C6B8IgAAIgAAIgAAIhIAARGcIjIAmgAAIgAAIgAAIgECmE4DozHQLo38gAAIgAAIgAAIgEAICEJ0hMAKaAAIgAAIgAAIgAAKZTgCiM9MtjP6BAAiAAAiAAAiAQAgIQHSGwAhoAgiAAAiAAAiAAAhkOgGIzky3MPoHAiAAAiAAAiAAAiEgANEZAiOgCSAAAiAAAiAAAiCQ6QQgOjPdwugfCIAACIAACIAACISAAERnCIyAJoAACIAACIAACIBAphOA6Mx0C6N/IAACIAACIAACIBACAhCdITACmgACIAACIAACIAACmU4AojPTLYz+gQAIgAAIgAAIgEAICEB0hsAIaAIIgAAIgAAIgAAIZDoBiE4PLLxzf60HpaCIZAmUleTLrFW1TckWgXweEIAdPIDoQRGwgwcQPSgCdvAAokdF9OxU4lFJKCZVAhCdqRIU+SE6PYCYQhG4uacAz8OssIOHMFMoCnZIAZ6HWWEHD2GmWBREZ4oAPcwO0ekBTIhODyCmUARu7inA8zAr7OAhzBSKgh1SgOdhVtjBQ5gpFgXRmSJAD7NDdKYI8z//8z9TLMF99pycHJmppaXlmMzqXPQEp4um4bS5uXnRPOLraAniZ07u0Q8yRzRPU1OTSJ9LeXn5Ik2OyBeh5uYIFRQUUCQSESlaKD+/gOpqa6h9aRnVip/t2rWnw1WVVFpWTrU1NVRcXCLrq2+ok2nqa4UbgiirqKiImpuaqbq6itq1LxWfi2X5h6uqqKCwQNRRRIWFhbKexsYGqqurpcaGBpk2Ly9Pps8RbcsVZXH7Wlqa5ffNkdY8+FykuZlyxTnuU0Seb6Ha6mpqam6iqspDVFZeQSWi3dwmTs/l1NfX0aGDX8nzPXodTyUlJZJTRLRx397dklvnrt1lG7kfW7d8QZ06d6PjOnYSjJpo5/at4lwR9erTT5RVKz+XllVQr97H074v99DOHVtpyLCRIm8Tbd60XtZRJpht3rieCkXf+vUfIH7fIOsZePJgWv3pR7Kdvfv2p08+WC7ODxQ8y2n50rfo3AsupV07t8u2qrR8no91a1fRmedcSO8vf0fm4WPnjm10ysgxtOj1l0Xey2i9SMNlc3lbNm2g0WPPpNdeeYEmXnmt+DmXzhh3vkzTvWcfqj5cKcvgtLt3bqOBg4bRhyvepXMnXEavizxTp02np596gqbdcDs9+6eZdM0NM+ipx35Nt951Lz322/+WP/kzfz93ziy6fPI0mY/z/33JW7LudWtXU4+eveU44oPHEvdv2IjR9PYbr9CUaTfFyvrbC7NlHm43t6lzl670wYpl9PUrp8XScPnczgZhUy6Heam2vP3mAlkX91/lmzt7lmzPfmEnlX72nx6VbWX7MANmor7bv2+v5HPhZVeSag/bULWVbcRtG37qmFiew1WHYvUxPz5GjT2LVN2dOneNtXGXGCuqbSs/fj9Wv2r7SYOHx+rlccRlXHr5ROratRs99ugjst3cP8W9UIzzeL+rPnF6vS2qX1y+3h+9PcxB9Zn7oxjz78oGPAb1PA319XKc3HjrtyUDvR5mrbjyOb1tehl8Tu/PujUrY3bjc3o/zDbqfTHrMNOader8zXpUm269/U55r2K3H52H2W++dl+eN1teN3yY502eZp9NdvzZ7JvJxaoOnT+XYeaxaodZj1W5Zhqr9pv2NseNBGPYmj+bdorXbohORbDtf2a96Pz+T/5A819bFrPEgH696MVZD7SyzBU33U8bNu+Q35nnITohOiE6ITohOiE6+Y8V/oMBovPoHxJWAhiis+2FX1u2IOtFJwtKXWTy504dy+mPD90n7fKNex6k/QcqY2nM8xCdEJ0QnRCdEJ0QnRCd1rO0mOlsS4kXvrqzXnSaJuGZz8/WbYmJzLMn303fmTGVJl8yTiadt3Ap/XLmHFoy7+FYVvh0tu3Ahu9U2/JXtcMOsEM4CISjFbgewmEHbgVer4fHFhCdhi1YZA7s31vOdK5cs5Gm3fFjmv37H9Hwwf1lSqvvIDrbdkDj5t62/CE6w8EfdoAdwkUgPK3xU3Sabz/D02v7lljpGftcqaWA6DzCj8XmgYNVrXw2nYjOqieriKYWp2YF5E6JQGGBCIYSR0NjJKVykDk1ArBDavy8yg07eEUytXJgh9T4eZm7rF1B0sWxi917H65plb9jh7LY2862EJ38xvX+nz1OD3zvlthb2GQ6CNGZDDWP8+g+nE5EZ5h9OqNR51r0uojM5s8qcl3GqudG49XVEc1DInq9UUav5+eLhdf5OxH5HYk0H41eF2kKCvKpRkSpc+R1TU01tRfR5ZUiErO8vJyqxfcc9c35OBqco5DrRPQ6B95zRCdHxx8+XEWlIqq9qFhEr4tI9UoRsVwoouM58pujbLm+xoZGGRnfIKLX25eWUr6IMOf0uSKanNvO7YuIiHEZqW5E8/O5ZhG9zhHp3G+OhuejRkSvN4r+VR4Sba0Qkdsygr5IlsXlcLT8V18dkOf79OkrottLZH2cf/eeXbKM7t17yHZyPzZt/EJGC3fs3FlGpG/dupmKRR/79BXR63V18nNFeQfxuS/t3bObtm3dSiNOHSkj6DesXyfrqKjoIH7/XLI5ceBA+mL9elnPoCFD6ZOPPpDt7HfCibTivWU0YODJVC54Ll70Bl186ddp+7atsq0q7YkDT5J5V6/6lC6YcAm9u2SxKDP63XZR9+jTxtKCl1+SeT9b/akou4Ms74sN6+mMs8bR/Bf+SlOvmU7zXniexp93oUzTW0Tes3344LTbRUT+kKGn0PJlS+giUc78eX+h66ZfT08+8TjdfNs36fFHf0e33P5NeuQ3D9E93/0BPfTzn8if/Jm/5yj3q6dOl/k4/9tvvSHr/mzVSurdR9QlxpGsS0RSc/9Gjj6NXlvwN5p+482xsp6f/WeZh9vNberSrRstf3cpXTXtulgaLp/byWOQy+E+q7a8KsrjupityveMaBe358u9e2LpH//DI7KtbB9mMP68CaS+2yvSMZ9Jk/+ZVHvYhqqtbCNu26gxY2N5DlUejNX3d8GPj6+deTapunksqTZu27YllvbD91fE6ldtHzrslFi9PI64jMsnTqJugsXvHnlYtpv7p7hz2+L9rvrE6fW2qH5x+Xp/9PYwB9Vn7o9qP/+ubDBAjEE9D9uEx8md37pHMtDr4etCceVzetv0Mvic3h8e88rOfE7vh9lGvS9mHWZas06dv1mPatMdd94lVvAoln8M6zzMfvO1+9ycZ+iW2+6UHMzzJk+zzyY7/mz2zeRiVYfOn8sw81i1w6zHqlwzjVX7TXub40aCMWzNn007xWt3sqJz6PibSBeYqh2sE7p1Po5++oPbqC1Ep2pHqj8hOlMl6EF+9RfE6sWzZGl2Pp1hFp1YMglLJmHJJCyZhCWTolHlWDIpumQYH1gyyV4ssLBcv3F7q/gNq1xKdPI5NSMaT6jqM6a62x7rjHFjh9PSFSvlG1c+Zlw/ifr06ipnNNWh8liJRXNGlvPfffMUGQxtztQqfQPRaT8OPE/BxtaDgngA8aEi2hG9jnU6sU4n1hHAR1wAACAASURBVOnEOp1nyvVksU7n+fL5gHU6o4/iTF6nk2c5J110ppzNTHSoJRWVyFOTVSo2hD+bOuLhJ+bSzKfnkz65xWJTiUp13nyNr7SJKRZNgcznf/XY8zI2hc/9661XxeJSdI0D0em5pLQvUF+Dk1O7Xafz4M8PUktdC9VNL6KWcv1FtX3dSOENAQQSecMx1VJgh1QJepMfdvCGY6qlwA6pEvQuv9tAIiXGnPhMWr1e11fBiSfseMLr6onnydlINdOpBK5VHi6TZ0J5kkw/z5Q44NlJWzktC9rnXlp0TDkqWNo76tYlIZAoRcI182uo/pN6ajhL+A+OEP6POAIngJt74MgtK4QdYIdwEAhHK3A9hMMO3Iq2FJ3KZc+KhpodjSc6dSEZTyx+sWWnfAWvZk2t6lGB0vo5To+ZzvCMUcctafy8kQ4/d5givcT2iVckHyHnuEIkPIYAbu7hGBSwA+wQDgLhaAWuh3DYIRnRyXncvF7XN5ThvPpMpxknEk8Usk+nOdPphejkfpw+anBswxv91T5EZ3jGqOOWIJAIOxJhRyLsSIQdibAjEXYkyqwdiewCiVhYxotet3q9nuj1dyoznSxW4r1etxK8EJ2O5V04E0J0QnRCdEJ0QnRCdEJ0ZpboVLOdZiS6EnIqyMjOp5PLURHk+itwFqanjxoi19lMRXSyLya34cDBylhQtAok4gAiU5DyzCcfeL0eTk1p2yqITohOiE6ITohOiE6IzswTnbpg1MWAPmvpRHTGK0ePXk/29boKADKDolUbWdzOf21ZrPnsR6oi5/F63VbihTMBb4NZ/Ew95VSKhdCnikXNOyGKPUhLwXcqSNrx64IdYIdwEAhHK3A9hMMO3Aq3gUThaXnmtQTR6x7YlEVn4VtiV5y1TdQ8KJ8azkcUuwdYHReBm7tjVL4mhB18xeu4cNjBMSpfE8IOvuJ1VThEpytcviaG6PQAL4vOvJ0RKpzXINfq5DU7cQRHADf34Fgnqgl2gB3CQSAcrcD1EA47YKYzPHbglkB0pmgP+HTCpxM+nfDphE8nfDrh05mZPp0pSgRkNwhAdKY4JCA6ITohOiE6ITohOiE6ITpTlBNZkR2iM0UzQ3RCdEJ0QnRCdEJ0QnRCdKYoJ7IiO0SnB2Zmn051FC1spNyNzTKYiIOKcPhPAL5T/jN2UgPs4ISS/2lgB/8ZO6kBdnBCKZg0CCQKhrOTWiA6nVCySaOLzrxNIqBoAQKKPMDquAjc3B2j8jUh7OArXseFww6OUfmaEHbwFa+rwiE6XeHyNTFEpwd4ddHJxak1OxsuLaTmE3I9qAFFJCKAm3s4xgfsADuEg0A4WoHrIRx24FZAdIbHFhCdKdoCPp3w6YRPJ3w64dMJn074dMKnM0U5kRXZITpTNDNEJ0QnRCdEJ0QnRCdEJ0RninLCUXZzu0uVibe3vPvmKY7KaMtEEJ0p0ofohOiE6ITohOiE6ITohOhMUU44ys6ic8hJfemnP7jNUfqwJYLo9MAipk8nF8n7sLNvJx+8QxHvVITDHwLwnfKHq9tSYQe3xPxJDzv4w9VtqbCDW2L+pc8kn06ITv/GSdqUbCU6ufFqP/am0/KpUfzH4Q8B3Nz94eq2VNjBLTF/0sMO/nB1Wyrs4JaYf+mTFZ0th1uoaWeTfw2LU3JuWS7l9cizPAvRGbg5wldhPNGp78deP6kQs50+mQ43d5/AuiwWdnAJzKfksINPYF0WCzu4BOZj8mRFZ9OuJqp6vMrHllkXnd8jn8puKYsrOjds3nHMOfh0Bm6mtqkQPp3w6YRPJ3w64dMJn074dGaeTyfPdFa/XB24uMgtzaV2l7fDTGfg5NOgQohOiE6ITohOiE6ITojOzBOdYZQgeL0eRqsE2CaITohOiE6ITohOiE6ITojOIKQHRGcQlENeRzyfTtVs+Hb6a0D4TvnL12npsINTUv6mgx385eu0dNjBKSn/0yXr0+l/y9zXgHU63TPLuBx2opM7XPRiI+XuaCZEsntvftzcvWeaTImwQzLUvM8DO3jPNJkSYYdkqPmTJ5NEpz+EgisV63R6wNqJ6MS6nR6AjlMEbu7+sXVTMuzghpZ/aWEH/9i6KRl2cEPL37QQnf7ydVM6RKcbWhZp4dMJn074dMKnEz6d8OmETyd8OlOUE1mRHaIzRTNDdEJ0QnRCdEJ0QnRCdEJ0pignsiI7RGeKZobohOiE6ITohOiE6ITohOhMUU5kRfbARefZk++mAwetV/hfvXhWWkJ34tOpOsa+nUXzG+Te7A3n51PzIGyPmarR4TuVKkFv8sMO3nBMtRTYIVWC3uSHHbzh6EUp8On0gqI3ZQQqOjnUv1PHcvrjQ/d50/qQlOJGdHKT89Y2yX3ZW8pzCNtjpm5E3NxTZ+hFCbCDFxRTLwN2SJ2hFyXADl5Q9KYMiE5vOHpRSqCic+j4m+iB791Cky8Z50XbQ1OGW9HJDS9aKJZQ2tgsZzp5xhNH8gRwc0+enZc5YQcvaSZfFuyQPDsvc8IOXtJMrSyIztT4eZkbojNFmvDphE8nfDrh0wmfTvh0wqcTPp0pyomsyB6o6OTX6xPOHk133zwlY+BCdEJ0QnRCdEJ0QnRCdEJ0ppOwefiJubK5QeuxQEXnvIVL6Zcz59CSeQ+nk20SthWiE6ITohOiE6ITohOiE6IzCGHjZBtMdmXUjwH9etGLsx6QX6n8M66fJD/PfHo+6ef97kOgotMEYXYuG6LXzT7LaPbn6ymnXlywZ4lo9hHw73Q76OE75ZaYP+lhB3+4ui0VdnBLzJ/0sIM/XJMpNZN8Olk0DjmpL/30B7dZouAVgsaNHd7qPOdRolNlUnosaN0VqOhMZrCkQ55kAon0fsWi2YuI6q8qklHtOJwTwM3dOSs/U8IOftJ1Xjbs4JyVnylhBz/puis7W0TnyjUbadodP6bZv/8RDR/c3xJSVs10uhsm6ZM6VdHJPS18t4nyPjmyjBILTyFAcTgjgJu7M05+p4Id/CbsrHzYwRknv1PBDn4Tdl5+0qJz1y6i9993XpFXKXv2JBo9Oq5otJvp7Nih/JiZTbOwrPDp5E6zX+f9P3u8Vf/TeRkl+HTCpxM+nfDphE8nfDrh05mBPp0ffEA0ZoxXUtJ5OSw444jdZHw62X8z6ICheJ0N9PU6K2t2WtWnftV0cJigOB8ZRBCdEJ0QnRCdEJ0QnRCdGSg6eabz9tvdSAJv0vboQfToo0nNdFrNaLLuCsvkXqCikx1cr5543jGKm8Xocy8tSsuodohOiE6ITohOiE6ITojODBSd3khIT0uxCySyqiye9vK0YQ4LC1R0xtuRSL1yDzqKyiEj22Re+HTqlRT8o4nyxX/262y4ooginRFYlMgI8J2yHaKBJIAdAsFsWwnsYIsokASwQyCYHVWStE+no9KDTZRIdLKWenL2glb+nOoNc1j0VaCiMxNnOnm4eS06ucxWgUWTChHRnuC6xs092JtevNpgB9ghHATC0QpcD+GwA7ci00Tnhs07joGrXBStfD7DIji50YGKzkz06fRLdHK5RQvE/uybmqXgrIfwjHsHw809HDd32AF2CAeBcLQC10M47JBpojM8VJNrSaCik5uI6PXkDKXnysmJvm5vaWk5pjB1LnqC00XTcNrc3LxoHvG1emGfk5N79IPMEc3T1NQk0udSXl4+cZktLRFqbo5QQUEBRSIRkaKF8vMLqK4WPp3w6YRPJ3w64dMJn074dKb+dM/8EgIXnWFD+o17HqT3PlwTa5bVdlD6dLV5HoFEEJ0QnRCdEJ0QnRCdEJ1h0zdhbE/Wi072M9X3gje3kGJRuv9AZat9Szt1LKc/PnSftCdEJ0QnRCdEJ0QnRCdEJ0RnGEVe2NoUiOjkqHV2cuW1ohIdYXB2/f5P/kCfrdsSE5ksQr8zYypNvmScbDq7B/xy5pxWQtWPQCKTE+/NXvhiPeXuEy+24ePZCg98p8JxW4EdYIdwEAhHK3A9hMMO3IpMCiQKD9XkWhKI6EyuaW2TS1+OwGofU6vvghCdTKOV8OTllC4V/pU989oGVIhqxc09HMaAHWCHcBAIRytwPYTDDhCd4bGD1DEisOTYaBSf2hhvnc6wLA7Ps5zzX1tGasbVqeisqmn0iZh1sZGF9RRZHa0zd3wh5Y4uDLT+sFVWWCCCocTR0BgJW9Oyqj2wQzjMDTvADuEgEJ5WlLUrCE9jsrwloRCdYVgcPtFyTlbbdqrv2synU/ypwBHk5qFHr0ejzrXo9bxo9PrRpeZFrHpuNF5dHdE8JKLXxXJNIno9Pz9f/Gkivou0iKj15qPR6yJNQUE+1dTUUFlZufhZTe3bl1Jl5SEqLy+navF9SUmJzFdfX0elIk1dbS0XRUVFxTI6/vDhKiotLaOi4mKRLkKVVZVUKKLjCwuLqLBILIov6mtsaKRaESHf0NBA7UtLKV9E03P6XBF1z23n9kWam2SUfcT4+4nPNTc3i3PRfnPUPR811dXUKPpXeUi0taJCtrtI1MfpuZy6ulr66qsD8nyfPn2ppF2JrI/z794jtkUTR/fuPWQ7uR+bNn5BXbt2o46dO1Oz+Lx162YqFn3s07cf1dfVyc8V5R3E5760d89u2rZ1K404dSQ1iXZvWL9O1lFR0UH8/rlkc+LAgfTF+vWynkFDhtInH30g29nvhBNpxXvLaMDAk6lc8Fy86A26+NKv0/ZtW2VbVdoTB54k865e9SldMOESenfJYlFm9Lvtou7Rp42lBS+/JPN+tvpTUXYHWd4XG9bTGWeNo/kv/JWmXjOd5r3wPI0/70KZpnfv46V9+OC027dvpSFDT6Hly5bQRaKc+fP+QtdNv56efOJxuvm2b9Ljj/6Obrn9m/TIbx6ie777A3ro5z+RP/kzf//0U0/Q1VOny3yc/+233pB1f7ZqJfXuI+oS40jWVV4h+zdy9Gn02oK/0fQbb46V9fzsP8s83G5uU5du3Wj5u0vpqmnXxdJw+dxOHoNcDvdZteVVUR7XxWxVvmdEu7g9X+7dE0v/+B8ekW1l+zCD8edNIPXdXpGO+Uya/M+k2sM2VG1lG3HbRo0ZG8tzqPJgrL6/C358fO3Ms0nVzWNJtXHbti2xtB++vyJWv2r70GGnxOrlccRlXD5xEnUTLH73yMOy3dw/xZ3bFu931SdOr7dF9YvL1/ujt4c5qD5zf1T7+XdlgwFiDOp52CY8Tu781j2SgV4PXxeKK5/T26aXwef0/vCYV3bmc3o/zDbqfTHrMNOader8zXpUm+648y4qFvcq/mNY52H2m6/d5+Y8Q7fcdqfkYJ43eZp9NtnxZ7NvJherOnT+XIaZx6odZj1W5ZpprNpv2tscNxKMYWv+bNopXrshOhXBtv8ZCtHJM4xLV6xss20wzRlO3Sx2Pp1tJjpFI7FkUo4UiS0tUWHZLASufkghKkRnrjjHEj0iz7dQrRCdLPiqhLApE6KmpF17KTo5PZfDN85DB7+S53v0Ol6KZ15aKiKWjdq3d7esonPX7kJ0FgqR2UwIJEIgEQKJEEiEQCIEErW9pAt/C3wXnVbrclphaavN6NmHk48XZz1gaS1Er2OdTojOVdS9Zx+qPhyd6WxfWk67d26jgYOG0Ycr3iV+2L7+ygs0ddp0OYM57Ybb6dk/zaRrbphBTz32a7r1rnvpsd/+t/zJn/n7uXNm0eWTp8l8nP/vS96i0WPPpHVrV1OPnr3p8JFZVZ4h37VzOw0bMZrefuMVmjLtplhZf3thtsyzZdMG2abOXbrSByuW0devnBZLw+VzOxvEHxJczrkXXBo79/abC2Rd/IeHyjd39izZnv1f7omln/2nR2VbN29cLxmcMe58Ut/t37eX1q9dRRCdEJ0QnRCd4Zd8bd9C30Wn3sV4Pp1thUH5bNqJ4ETrdHLeoAKJ4nGSAUZvRXcv4qN5RD41jhEzgCLYKBsOOOyHw8qwA+wQDgLhaAWuh3DYgVuB6PXw2CJQ0RmebnvbkrYWnao3eZ80UcH7TTLKnZdVajhfvF7Oguh23Ny9Hc/JlgY7JEvO23ywg7c8ky0NdkiWnPf5IDq9Z5psiRCdyZLT8oVFdHKTcipbqGBRI+XtiAbNNPfKpcbzCqQIzdQDN/dwWBZ2gB3CQSAcrcD1EA47YKYzPHaQGiXIJZMSvc7mxoRhcXi35gltIJER2M6R7th7HYFEO3dso1NGjqFFr78s/Bsvk/6I7NPIPpHsG8k+kq8JP8iJV14rfs6V/oucBj6d8OnkoLrlS9+SY2X4qWNo5cfvx3xc2bdV+dzyPVT58PLvyq+2X/+BrfI01NdL398bb/22vO0qH12uh/1nla8sn1M+tDxW9Xr5nPIT5hUv1q1ZGfPF5XPKR7dT565ktlHvi1mHmdasU/kDnzR4uGy7Xo9q06233ylXo6iqbWrFw+w3Byy+PG+29IXmwzxv8jT7bLLjz2bfTC5Wdej8uQwzj1U7zHqsyjXTWLXftLc5btRzWbc1f2faKV67MdOpCLb9z0BFp9pi8vRRQ1rt6sM+kxPOHk133zyl7Ym4bEFoRafsh5jdVEsmsegUEdhymSWxbpGa9+SobH3NpOiZFrkUEC+ZxBHd0WWUImL5ocjRJZNEmvz8ArEMErbBRPQ6AokQSATRiUAiBBK5lA9ZmTxQ0akCiU7s25O++f1fxZZIstpaMl2sEXrReWQtT15eKVf8Y9EphSVrS/4B0YklkzDTieh1MUuozybqM3f6DBhmOs+XjybMdEaf0JjpTBelEp52tono5H3MWYCq1+lhWBw+FZOEyaczUT/y1nKgUbP0++SD/Twbx4j1LQeJBeDT+IDvVDiMBzvADuEgEI5W4HoIhx2oMkI9T2gfksagGYGKTn1fc/33tl4cPtVhkC6iU/XzGPEpllZqPiWfmsT/dFxmCTf3VEewN/lhB284ploK7JAqQW/yh94OQoxZHXmHE/Q/Th4SK6bkNljnyxHft9TH3207tyox75yqBNsbi3J5tRa747j/e5xdEpwPiECgotPsE892qkPfajKgvntWTbqJTl185n0eiUW6s+CMnCDE56CctFpqKfQ3d89GWrgLgh3CYR/YIXg7yGXq6luLo9Jc8QZJiKLa+uj6ybHDQrhZCa94Yi2eSLMUZw5FWfDEgquR3+h1/HaH4CpETQkJtKnozATbpJVPZ250D3Ll0sn8pU8n/+T7pfbHaBOJQCJxLk/sR45AImyDieh1RK+HKnr9kNgZauR4ee96avbDdN3E26mopZA+37KKdu7bTueNvoT4tepf3nuGxg+5iDqXdaV9+/fS4s9fo6uHT5f53t2ymEpbymhEp1Hy89Prn6ArO19F5fnltK/hS3rjq1dpWrfpxGLu4/qPqCpSRWeXnCOF5Jt1b1BP8W9IzhCZ99nIszQhdwJ1Ef/4eDTyKN2UexMViX98/CbyG/pW7rfk7/Xi36zILLo9NxqtXin+zY3Mlemtzpv5rcqf2zKXxop/vXN6yzKWtCyhUvFvZM5I+fmzls9op/g3IWfC0TpaZtFtFTPkZz7mHv4rnV58OvU87nj5eU31atpZv4Mu6HhRLM1vt/2KvjnkX2Of393zNpXml9GpPUeTwE/1zfX0zEeP081jovvI87F0u+DcvpxOOT7KmY8nFz9C1467hYryBZ/yXNq0cz2t2/oZXXzGFbE0ry5/kU46fggdf9LA2Hds62um3Ca2II5yPXB4Hy1+J7pTmTqsou4RvR7D0+a/BCo6w7YjkRf0M0J0qlB2qUfFB7FHeVOLEJ3iX574l5MrotdzWqhZRLAXFBSIPcwjMiAJ0evYex3bYGb5NpgHDtEZY86j/QdE9Pq7C+mq826Qt9WZc39BMy7/N6FCIvTqJ/PppJ5D6MTiAfTJ7g/pcH0lndV3PNUfrKNnNjxBN5/8Tflq9oVtz9PYiq9Rr6LetKlyA62p+Ywub/91Wd5Th56kKTlTqFz8+6jlIzos/p2dc7Y8pws8U1zpYvBLEkIy8gZdk3uNzGcKMxaCU3KjdZhpzTrfaDFEJz1LF7S/kLrkRUXnHw7NpG90uZmKSoqpSdxPWazd1Scq1mrbCWF2pN/8uaqxkuZtfZ6uP/UWeV4Jt385Uwi3I7vKzXzjIZox4Z7oI0uItCdfepiuveQ2KiqIJpi/ZA6NGnkm9ejeR35e/v4iat9OCL2Rp0mXKSyZVBJlh6PNCUB0pmiCjBKdgkWrJZNYdOYI0dkiRKf41yz+FeQK0SkEqPiS8oQAxZJJzYQlk7BkUqiWTDr3curSqRs9/r+/p0njrqaydhVRkXKeECmRgugs02m3UEmkiJ54/xGaPlLMONUUypm+yf2uooqWcpq99RmacNzF1LmwC72w63k5A9YrvzctOfwOlTVHZ9B0IWaKNH1m7+WWl2mQ+Hdizomt8pgzfvps3RctX9Ba8e/ynMvlHVoXhFxvlXA8PLtUzDqKgwXejZ2/QYXFxa1m5yJlRM9tfIbO7yn6UdyF9ke+pDe3tp7pbF9+dAbuz+8+TpPOnSp57TsoZkU/XEj/fP4NJLpLKz/7gKprxOyqENg5Rbm0eOkC6tGzN2GdzqPrtrItsE5nioIiC7IHKjrTeT3ORGMhXX06nYxv9lXK3dRE+ZuFw/YOEfmuOW3zX9DNJ+QJ/88cau4pXtOLv8Db4oAPW1tQP7ZO2MHeDrrvX26j+BNPBVjwdaV8ArWgDN2vTwZqaNdfzIevDf32Wu10Vij+OC3Sdj5jH3HxyjV2lLXeFY1FYewQQk7N6vF3XE6k4Ki/Dwu9dAtyxPVgfz0ElQKv14MibV9PoKKTdyTS1+e0b156pMhk0albgB+YOfubKX+TWPNz09Gll1QafgCx+Ix0Eg+f3kKMip9BHLi5B0HZvo6MssORYA8nwpCqjoojPcijzURhRfS6Y/ftljLtD0FNBOYIUcc+eOpIJAB5pk8d6Sj+7EeuPyky6nrwB1FgpUJ0BobatqJARacerW7VsnTcBpP7kS2i8xibiQdz3qYI5e86dhZUPvTY3Ug89CJi//fmTuJzFxHIVMqzIbbj0lUC3Nxd4fItcVvYQZ85bLXUi4oQ1pdyOSIO9RlDOdPYEBWNav1a3wCpa0LNBhozg0r46YJQzhSq68WYDdTFoP6WoS3s4CezdC0bdgiP5SA6w2OLQEVneLrtXUsy2qfT7TaYxe3pcHUllRWUU01TNZWIfxwtz75bpTmlVNdSJ8EX5Qrn+twmqm46TO2LSqUvVgtFRN4qKigsEMFKRSI6sVAGLDU2NlBdXS01NjRQu/alYlvOPLmfcY5oW67YnpO36WxpaZbfNwuHff3gc5HmZsoV5zg0PyLPiyVMqqupqbmJeM9j3su5pF17UWaRLIvLqa+vo0MHv5LnOWK3pATR655Er9/wb7FI478seIomnXM1vbrsRRo/+CJatu5tOq37GfT5vs+oZ1lvqqqqlKYszymjndU7aETpSHpzv4gmLr2WHj74axkJrHwAN9EmGanLkcMrxD8OOFE+hcqfkMegit5V51QwCAeOqHwq8OTL4n20o2kHTehwET114I80uctVtLFxg5jUrKKzup1LT4tAkMlDrqZ9NXtp7Vci6nbEJJr/wfM0ZtiZVCjGL/sDXjnpBhnQUSrG2LAxY2I7/hyuOhTbAYkDsfgYNfasVvt3q73Ld+3YGkur7/+t74ij7xjEOwldevlE6tq1Gz326CN0+eRpcozre1bH+x07Ej0a44W917H3uncqASXpBAIVnfGi1x9+Yi4999Ki2LaY6WQiiE6bvdfFfu31DUJ05pdSfZMQnWJppuIcITpFdDxHoLJYKMopEgHzEaoS/wpzCqlA7OleKJbSiIh1nBpaGqmuUYjOJiE62wnRmQ/R2a//QGpfWi63oDv3gktp187tUiAPPHkwrf70I+LzfKxbu4rOPOdCen/5O7Hvdu7YJiJax9Ci118WeS+j9SINixIub8umDTR67Jn02ssv0MSLp9Frb82jM4ePl0uZ9Ojcmw4fPCTLLRVLyuz6ajsN6jKE/rFtOZ3f4yJasG0+XdX1avrzrqfphh430592PkE3lv+LDPJggaiEnoo0ZnHHkcIvR16WS81wJDEv+cLBI7wUDY8FPsrEPxaLI3JGxCKPVVlSdBaOpY1CdJbllollcbrRikN/pyu7XiWjhXlpl4U7X6KTuw4RY6+edtSJpXSGXEwyEnjKv9GiDxbKaN/SinL64NNl9PV/viYm/PZ/uUdyZb5KjG3euJ6qD4tgknHnx75jccIMQxVIBNEp7caHvp2nKSTNLRx10Q3RCdGZTjokndoaCtGZzttgQnTaiE6e6WyoE6KmjOpra3lhULnMR3ODmOmsFzOdQozyWnYtQpzyLFKh+CfmOqUQbRYzmI3iX5341yD+tRf/OJqeZ0p5ljMnX0TX82xmTnSmM5J7ZKZTLPHEKz/lFopzEbH0k1iflMQ6zWk90ykianv37EefrFpB/XoNpLKiMlr26SK5HiGvSyhFZ/dBtHr7J3RCxYnyHrT2y9V0bu8LaPmOpXRC2QASmGhH9TYaWT6GXt+/gCaUXEhrGtaIN7PlVNZQKqTbJin8eHbwn3L/if4W+ZtclkYJQf4jQYpO8Y+FIEckr2hZIUUji0cWkSwmeb1Bjjbmnywylei8u8O3Y5HGs7/6s5w9fOXAfDq/18X07p7FNOb4r8VmOnntQik6yypo58HtNPzEUbToo4U0ZeIN9NiffkG33nUvqRk+Fsssmjt36RqbFVQzha+/8gINHDRMRNXWxUSkOqdmC1l0f7BCiM4rp0F0HpkZxd7rYgmoN46u/6jPMvO4xN7rUZmDvdfTSe6Fo62hEJ3YBjMcg6GtWyEDlQ4L/1DeG579RYXG4e3TODhDBmV4FKXbKuJWdLpVsIWCYEbeJgnHjDg2i9F9CmPnPOpnkk2mGB+XPoclXQpklbwDi/I3ROBJslZInlefagAAIABJREFUPh98CZNn52VO2MFLmqmVBZ/O1Ph5mdt30almMe0a/cD3bqHJl4yzSxbK81kbSNQG1lCBIzKqmMWpWGamOCIidMVyMg0HotvNKaGnbwsXRJCInzgSLk0jKm4VfawtTZNMIEqy/cBDNlly3uaDHbzlmWxpsEOy5LzPB9HpPdNkS/RddOoNy8Qdibh/EJ3JDj9v8rm+uRt7H7eKelZN0tdNTKWZRsSxWZS5HiGfT9fZQdd2SIUr8sYlADuEY3DADuGwA7cCojM8tghUdIan2961BD6dSfh0ikjx5qZmqhbR6hyRztHoLSKQ6HAVotcLBYt+/QfQ5o0b5CBVwUHsd9i7b3/65IPlMijI10Ai4Qc58cpr6bVX5sqgGQ6U8SR6XfhhqsjpuXNmyUhh9rk8d8Jl9Pclb8kgpnVrV8udXg4fiV4vLRNBSyKgZ9iI0TEfO+WTCZ/O6I44iF7/NV1zwwwqFPcVc7tHBBKNkfcRbIOJbTC9Uz2plQTRmRo/guiE6MQ2mNgGE9HrrQNv1B8GfHtVwVz8x5IekGNumaiLZ14pQK0KwGXokeVmUI++BBRE5/HyiWYG+EB0QnSmKHU8yx646Dx78t104GB0ORTzSMfF4SE6ITohOiE6ITohOnnGvlPnrvKxxkL41tvvlG9xqmqbSBfhptjmlSdenjebpt1wu8xrtX+5nl+Vr2Z3+bMu2CE6V8ZWqlAaA6/XPdOMKRcUqOjkvdc7dSynPz50X8oND1MB8OlsW2vAd6pt+avaYQfYIRwEwtEKXA/hsAO3AqIzPLYIVHQikCg8hs+kluDmHg5rwg6wQzgIhKMVuB7CYQeIzvDYgVsC0emBPTDT6QHEFIrAzT0FeB5mhR08hJlCUbBDCvA8zAo7eAgzxaIw05kiQA+zByo6+fX6hLNH0903T/GwC21bFHw609Cn89BBsfd6M1XVVFNZcQm15/3ced/1HLHDkdjNqF6cOyj2e68U23f2LiikErELktjgSOzaTrRHbMfJR7cCsVWn+LZJ/L5ZpOuSn08dRRm8Uug28blI7A3fJ79Q7PjdQtsizVRWWES9xe46X9ZW0w4RmT1M+H41iYj9jYerqKf4vbykPW3avV3s211I/foNoE27tst6EL2O6HW1WxL2Xo/uI49AoqjPKHw6icztSvmeaQZNYaazbTWSWXugopMXiv/lzDlpucd6PLNBdLaB6GRx2NgodtTMofyGBrGFZhPlif8tdWJvd3Hk1PEim2LnSyH+msU2nPlieSYS2yBGhBBk4VhdWkqNQjQe7NCBOhw8SKWHD1OxyJvf1CT/15aU0P5OneT5fps3U7uaGsoVQjQixOnOnj1l2T137qQikadJlLN+4EDqvns3ddm7V37edMIJsrz+X3xBte3ayc9czwkbN9IukX9zv3405v33qUkI1bWDBsk6Onz1Fa0dPFjmO3ntWvpcfM/H8E8/pX+MHUsV9Q104vZttGzECDp5y1ax/3kBvXnyQLp89Rra2q0rHRT1DKk8TB8dV0EDGgULEcCwOj+HzssrpmW5ETqxsFiWt02I6pHdetDrWzbS+JGn07rtYt9yIXjbiWWKYnuvY8kkwt7rs+RSVhwYowep6FHRuvgzH/6IXkcgkXpmmpH0/L0pms3VCjiNvuqBKsvMB9EZLkHppDWBik726Ux0IHrdicl4+3KedxMzb0JQmYc6F/1ezc9F0/Ie5DJPdGvyaAoh4GIfZI5oniYhvnKFSOO9zblMXkezWeyPXiBEVSQSESmEmBPCp67WQ9FZWUkFeblUKNpYJIRiRAi9JiEua/LzqEEIvrLqasoTIrNECLNc0QYxeKVIZPGWJ9KaR4HIy+c4TYvogxKdh487Tn5/UIjPCiEo2wuRVtzUSPmRFsoTs5J1oo8HStrRoZJi6lNTS+1Ev3NE/zn/HrEWIB/dhbAt5PaJ9m5s3466is+dRduaBM+t7UqoSLSvb3UN1Yl2by0soArR5n77D9DuijLaKuo/dfsOahLlbeh4HPXdtZsqxOzn50KMFosyWHSuE7/zoUQni9YB69fT0rPPpkHifIX4/Ooll9AV8+bRFpGWBbJKy+f5+PjUU+myl1+mty64QObhgwXv15YtoxemTJF5PxFpuGwuj4XuuYsX05xrr6XrX36Fnr9wAp2/YROt6tVdcKijQ+XlsowyMSa2iT4PETb6e/sSurB9Bf2t6iuaNmIkPbXyY5p+xrn0zHvv0LUTJtKTC+bKfdKVCME6ndPEGqSHYnu9f7jiXcl01NizYvu+s9BTvHbt2BpLi5lOzHSqexxmOqP3YYjOYx57of8iUNEZehpJNhA+ne7AFaz6lPK2biH+yf9zDh0SPz+hXPHTydF8fF9q6tNXJuXf8zsdRy0VFVRXUiZ/8nd8RCo6UES8jlPpnJQd1jTMSz/ytx39zPxyhcuAOvK2bY39niuWY+HzsXNHyuH0fM783s/+K7twHcp+bC+2k7RRn+gag/rvfI7T6HkywZ5+coYvoZ90nZcNOzhn5XdK+HT6Tdh5+RCdzlnFTQnRaY2GRSSLyfyVn1LRsiUxoZkIeeOwU6QIaRoufgrByEKExQp/1yyEZuSIANHLwM3dg0GsFaELXCVudWErfz8iWHWBW7Q9KnYjwlVAnc9hcevwj4lkesHjoeWIaOXxokSqErJS1Ko/PHRRa/GHCZdjNb6SaVdb5sH10Jb0j9YNO4TDDtwKiM7w2CJw0cnBRBs275AEHvjeLTT5knHEr91PHzU4bdfvhOiMDmg5c7nyEypctlT+5M9Why4sG4cOl6KycdiIpB/4uLmH44ZiZwc7MasErD47yzOyaqZWn901Z369JmA3K+tGzHLb9PK8bqtZnp0d/K4f5UcJwA7hGQkQneGxRaCiU18cnncm+s6MqVJ0PvzEXHrupUVpGWCUzYFEBcL/s7axgcqEH2KN8F3kgJxDYmapQsxsVbdvTyW1tdRSWEh14n+p8CetFUEswhGUikTEOPZeHykYNNHmTeupR6/jqUzsMc7O9Nh73d3e62OGjqAtGz6n0nbtxQoCBfT+hrU0pWsvenjjGvp2px70twN7aajwt60XPr076mro0l176ecnn0jfe/0tennoYOq7Yycd9+VeemfUSLrh2WfpsWuukb6uu7t3l76y/Puv/8//oRtnzZJBX4eE7+zFCxfGvuN07Bc7dfZseuqmm6RPLAeDvTh5Mt0+c6b0u2V/2TOWL5d5rv/rX+lgj56yvutfWUCLx4+XT4Oz9h2gJ0cMF+3bQ13E9fGL7p3pnppG2lpWSstzW+ifyjvRR2Llg8rS9jSuV196Y9c26tG9F518/Ak0f9kiGnX2+XIc8V7jl14+kbp27UaPPfqI3N+eI751H8B4v+tbTep7liOQiI6JmH/7zQXUQwTfnTR4uLSfzos/Y0eib8dUDgKJwiP4wtCSQEUnz2jO/v2PaPjg/qSLTo5qv/9njxMCiZwNiTYNJBK6sUUE3gjFRByoUy2ipstFABCLzFLxsD0kfpaJB3yN6Epxu1IZuFTfUEftS8uoXohQEZUktoYrgugcBtHJgogjVDlK+u9L3qLRY8+kdWvdiU7Ow1H37UvLqXOXrrGgGxWIoyJgG8TqBbt2bqdzL7g0FqSjhAOLMrUskRIPX639jHYe+JLOO3Us/e/CeTR54BCxpNVOOlxzmM5pV05PHthNVwtRuFfE4a1prKfJO3bT7D496ezP1ogguCZ6ZdDJdOvcufT66adTuVgW68wFC2JClYO+3hZik4Us/+SDxeqjM2ZIkcsrIfznf/wH/bv4z4FfKu3yM86IiV4WtX3FqgenfvxxTOzyKghcxsT33qPuBw7Qw1ddRde9s5TKxDJc/3PeOTTjk1VUIK7D3ww8gW7/Ygvl9+pNj5QU0C11Ioiu9/H05Fd76Z8qOlHpcZ3o2V1baULf/tRZrGwwd9tGGnPSULm017vrP6P2nbrQ8FPHtBJiiF4/Gu0P0TmTbrwVotPZ0zz7UgUqOllo/u6n/3qM6MRMp7uBF6joFDOUOSJKm5cliohmFohZTY7i5iNfRGjXFBfLWcwaEc3ern2piMytpFIxa1crosKLxYwNRGct7RS+jqVijc5e4sG+78s9tFNEJA+B6JSzcGEVnX4tmTTxgsvp8J5d9P661TR52Ch6//NV8lo6XQTBzd66Qa4E0FWsevA/TTVyppNnZ5cVF9K0bTvpfbEc1mGxfuwFn6+nV046kfpu3Uoj1m+gpy+7lMaL2VclOpVwVTO0vDrBg9/7Hn37f/5HzsLG+11PrwtgNYPL5esztyyCDwo/2QuFyN3TsSPNP+ds+pcPPpb9+dmF59N3P/9C/j5PrH4w9FAV9Rdi9sP8XKoUbzzOKS6luvIyIXS/pBkdu8l0f6mvprE9elMv8QfEF0LIr92/ly4+bZw89+e3XqHLp1yLdTqPPCoQvY7odXeqITypAxWd3//JH2jpipXyNbqa6Tyxb0+adsePadJFZ9JPf3BbeMi4aEkm+nQWvfsOlcz+MxW/Mr9VIAj7Y9ZdNlH+59/DcMB3KgxWgA9bOKxAVLE36jN/uE4seyYCvtTKBolWOWi14oHmR2uucuB3YJhThnoAmcqjVkRQn00/Wt0Pl9NwgJlaGUHl0VdLiFcuf+/ERxf3JafW9D8dfDr9Z+y0hkBFJzdKvUrXGzjj+klpvUtRpohODs4o+/lPiAWnHqhRf9Y5VDvtOuKfTm62TgefV+lwc/eKZGrlwA6p8fMqd5B2SLSUl3ku0VJe3Hc9fVjFbjwbWYlgXk655fh+1CTW/1WHvkSYXpa+XFhMAFuI4niCV18ezmxjGO/ZXo11p+VAdDol5X+6wEWn/10KvoZ0F50sMtuLoIPiV16KweMb1eHb7pQzmmG/aQX5kA1+dKVPjbBDOGyVDXbgZbh41lU/9NUNTBHLn/WlvvizuYat/E6b5VVlm+ValR0Oy7trRbz7ulp6zCwtnmDmdOYssp7Xaka5leA+snyZVesTielovc6WOYPodDc2/EwdqOj8xj0P0nsfrjkmYCidl0xK6+h13qVIBD0Ix8vYGMvhXYvEDkBNwl8z8B2JqqqoQOzeU1BQRIUi4p13PmoU0fF1wo+tUfiSss9oHu+TLrZ4zBF+pbliKoF3TGppaZbfN2szCvLBIM7xrka54hzvshSR51uoVuxs1CR8VKvEq0cOIikRkc8c3MTpuZx6EXRy6OBX8jxHBJeIbTF556aI2JVo397dklXnrt1lGzkKf+uWL8R2gd3ouI6dxK5NTdKHs1Dstd6rTz9RFnw6sSNRuQy8UdHh2JGoks4Ydz411NfTs386GnSiR8mb2yLqkfWh3Hv9f5+g84aPoc5H1ozlnbhuO+c8Khb3mtr6ZvrtR8vprpFnSOHbeFCsVKD5slaKXdD+emAP3VIr7sXiqBczpI8XF9Dde/bFlgvjFReUjyzPCMvAsCXLxE5q0TzPnnoKnfOPf1BfEYTGhwpgO0PsPsYCnXcnU6sx8Pk64YvPPrz3/exnsXu/7rvLX5p5+DsV4KYy6T6+8co103A63a+YP/PKEGoVCFX2nGnTaIQIlFO7qVnl49Uj1EoRKp/ZbhbXeVs2x/qJX9qWQKCik/04r5543jGv0hFI5G4QpBpIJDa1FA5NYmvHI1tJckQ5L2XUIoQVi7k22wYTohNLJoUket2vQCIOnoLozEDRKZaqUnvV89087EsmNX35Jf3v3GfoXy6dEnv48NJbvEpBb/EHM8/4rtn/Je2srqQLjj9RpmHBrJYiU5neqakUq5Xk0aiGqP+wEsx31jbGyn2bmsQKDtU05qujO6CpFRR4u2AW0eu6dJHb7U75eGUs39xTh9Mp678QonNN7LtfTL+O7nruebldMB8cwPbSGafL5cniiU75vcWW0e6eukjtFYFARSfPaKoF4fUOYMkkd+ZMWnSyuOQ9yqWzUUt0y3WeBZQzgdGjTfdeh+iE6IToFLPm2Hs97WY600x0mrPMfO/XZ5r587o1K2PLjKnng1qKTH021+C0Kret1+lkUdtt5CB3D1mk9o1AoKIzE2c62TJh9+lkn80Od98ec9Tn1w1V3/0B1VxzvW8DK8iCs8GHLUieydYFOyRLztt8sIO3PJMtDXZIlpz3+eDT6T3TZEsMVHTya/SZT8+PLRDPjV65ZqNcMimdI9jDKjpVNHq7Z5+W4yPTxKYa9Li5J3v5e5sPdvCWZ7KlwQ7JkvM2H+zgLc9USoPoTIWet3kDFZ3cdKslk6xeuXvbTX9LC6PobD/zt2L5owdia2xW3Xs/8f9MPHBzD4dVYQfYIRwEwtEKXA/hsAO3AqIzPLYIXHSGp+vetCSU0evCOZsP9tlsYf9N8Z93BsrlyHR2qOavjnSfo7JjH2QemYuaRFQkotcRvc5RxuvXrqLuPftQ9eFKOWp4y8ndO7fRwEHD6MMV78oACt5ZaOq06fT0U0/QtBtul1HJ19wwIxpQcde9sa0n1U4qc+fMysodiRBI9L4cRxkXvQ6fTnlvCKNPJ0SnN1rHq1IgOo+QTBRBf8VN99OGzdFdPgb060Uvznogxj90opNbJoUli8ej6hKiE0sm8dDYuWMbnTJyDC16/WWxD/llUlDyslEsJHkPc97L/DUhICdeea34OVeKA4jOR6VA5uAWJZjUEj685zjzufCyK2OBGIViSa+333iFpky7ifQgCiyZNLDVfu0ZtWQSRCdEp1eqLMPLCVx0cjDRgYNVllhXL54VOG79dX/HDmVyi0794LVF9x+ojAlNFqCdOpbTHx+6TyYLp+gUDRP7Gx+Z65TthOiE6ITo3C6E9qWxWde331xAPXr2lqL7gxXL6OtXTqO5R8QDlkw6ugSQHtWsi2h9vUwW30po8zjTo5x5Fpxnxfv1h+hkNqbY5vWAX543W74hsDpv8uTP2Hsde68HLpY8qjBQ0WkKNo/64Ekx8WY61R7xky8ZJ+thkfrLmXNaidO29OnkYKHOky+RkemZGihkZ2D4TtkRCuY87BAMZ7taYAc7QsGchx2C4eykFvh0OqEUTJpARWe8dTqD6WriWqxEp4qsn/37H9Hwwf1lAVbftZXo5GChih/eK9vFgnPfvIWh37LSD1vj5u4HVfdlwg7umfmRA3bwg6r7MmEH98z8ygHR6RdZ9+VCdB5hlororKo5uvuCexMkl6PwJ/+Pih74fzJzw13fovoHf5FcQRmQq7CAd1ESHBqjAVQ42oYA7NA23M1aYQfYIRwEwtOKsnYF4WlMlrckUNHJr9cnnD36mG0ww2CDZEVnm/h0HgF2dMf0owTVbkX8Df8uo9XFIX06xc5D/FNFrstYdeH7efSzykMier1RRq/ni+0xZfS72Lc8IvYILigokHuic7EFBflUU1NDZWXl4mc1tRd7o1cK/6Ty8nKqFt/znuWcj/cyLxVp6mprZXwT753O0fGHD1dRaWkZFYl9gFtEmZVVlVQoyud9ywvFXuhcX2NDI9XW1lCD2PasfWkp5Yv90Tl9rtyyM0e2LyL2O5f7rBtbnfG5ZrEDE++nzv3mdvNRI/ZDbhT9qxTbupVXiCAa0W7ee53Tczm81/tXXx2Q5/v06Sv2Zi+R9XH+3Xt2yTK6d+8h28n92LTxC+ratRt17NxZ7MXeRFu3bqZi0cc+fcXe63V18nNFeQfxuS/t3bObtm3dSiNOHSn3f9+wfp2so0Ls2bxh/eeSzYkDB9IX69fLegYNGUqffPSBbGe/E06kFe8towEDT6ZywXPxojfo4ku/Ttu3bZVtVWlPHHiSzLt61ad0wYRL6N0li0WZ0e+2i7pHnzaWFrz8ksz72epPRdkdZHlfbFhPZ5w1jua/8Feaes10mvfC8zT+vAtlmt69j5f24YPTbhf7yw8ZegotX7aELhLlzJ/3F7pu+vX05BOP0823fZMef/R3dMvt36RHfvMQ3SM2Injo5z+RP/kzf89R7ldPnS7zcf6333pD1v3ZqpXUu4+oS4wjWZfwt+T+jRx9Gr224G80/cabY2U9P/vPMg+3m9vUpVs3Wv7uUrpq2nWxNFw+t5PHIJfDfVZteVWUx3UxW5XvGdEubs+Xe/fE0j/+h0dkW9k+zGD8eRNIfbdXpGM+kyb/M6n2sA1VW9lG3LZRY8bG8hyqPBir7++CHx9fO/NsUnXzWFJt3LZtSyzth++viNWv2j502CmxenkccRmXT5xE3QSL3z3ysGw3909x57bF+131idPrbVH94vL1/ujtYQ6qz9wf1X7+XdlggBiDeh62CY+TO791j2Sg18PXheLK5/S26WXwOb0/POaVnfmc3g+zjXpfzDrMtGadOn+zHtWmO+68i4rFvYr/GNZ5mP3ma/e5Oc/QLbfdKTmY502eZp9NdvzZ7JvJxaoOnT+XYeaxaodZj1W5Zhqr9pv2NseNBGPYmj+bdorXbohORbDtfwYqOq38IdseQbQFyfp0hll0IpCIBWmzFNu8DFRECGD+WStEJws+duDnIJKSdu2l6GTByQKVb5yHDn4lz/fodbwUz7y0VKQlQvv27pbjpXPX7kJ0FgqR2Uxbt3whti7sRsd17CREbhPtFIKMBWmvPkJ01tfKz6VlFdRLCLd9X+4REeRCsA0bKQXq5k3rZR0s3Dk6miOf+/UfIH7fIOsZePJgWv3pR7Kdvfv2p08+WC4DMjjanIM6ODBm187tsq0qLZ/nY52Iqj7znAvp/eXvyDx8IHodgUR6EIr+u4qu57GmAqp4S04EEgm3qo+PLvXE15EKQjtp8HB5Xem8+HPY917Ppm0w2R54vR4WpSVUiZgBspow86WF7NOZ6GiL6HXVnniiM5TR60cabTfTCdEJ0QnRGY2cbhB/SLA4R/R6UavIZ4jOchp+6hh5R9VFtxmND9EZfeik497rEJ2+yLmkCw1UdCbdSh8zWu2QNOmiM+mnP7gtVmuidTrl7NH+Wh9bSDIyXY9Qz9aAoXiQ4bDv6/BzXDjs4BiVrwlhB1/xOi4cdnCMyveEmOn0HbHjCrJedDomlSChn6IzV/j7dLriYioQvkrZHKGeyE64uXsxilMvA3ZInaEXJcAOXlBMvQzYIXWGXpUA0ekVydTLCVx0Yu9150aD4HTGCjd3Z5z8TgU7+E3YWfmwgzNOfqeCHfwm7Lx8iE7nrPxOGajoZL/JmU/PJ6t1L2dcPymUUe12BmiTQCK5xWU0It089Oh1+HTCpxM+nfDp5MCgeMFD8OmET6d6hugBY/zdujUrY37QKg18Ou0UAc7bEQhUdPLuPldPPO8YcZlo33O7DrT1eYjOGhFJXSaXNWonosAPiyVleHmkWrFkUnGxWDJJCOP6hjqZpl4smcRrJnGkOEd9V1dXUTu5XJFYMklEhh+uqqKCwgKxFJNYMklEhvMSRY2NDXIJo0axZBKn5ehyTp8jlnPKFWVxxHlLS3RZpGYZnX70kMsoIXod0esIJILoFFH4ZnCQvqUn3zUQSDSbRo89U66mAdHZ1soic+sPVHTG25FIvXJvy+j1ZE0M0QnRiSWTLiPeX3vqtOly/U3eQ/rZP82ka26YEV065q57Y1GvamZt7pxZdPnkaTLfuRMuo78veUs+8NatXS33Q+c/XvjgP2A46nzYiNGxvb3VbIuamdmyaYNcQqpzl66xPdRVGrXvN6LXfy3twevfYsmkm+TYguicSTfe+u3Yow8zncmqAORzQyBQ0ZmJM50M28tAouJXXqKON0yVNjz48KNUc831buyZlWnhOxUOs8MOsEM4CISjFbgewmEHbgV8OsNji0BFZyb6dHopOnlppC7nnUEcQFR17/3yPw57Ari52zMKIgXsEARl+zpgB3tGQaSAHYKg7KwOiE5nnIJIFajo5A4het3arCw0WXCy8OTZTZ7lxOGMAG7uzjj5nQp28Juws/JhB2ec/E4FO/hN2Hn5EJ3OWfmdMnDR6XeHgi4fPp3w6YRPJ3w6L7zsyth2kbyV6dtvvEJTpt3Uym9QBaocrjoU8z39cMW78pY1auxZrbZSVD6pu8SWqR+sWEZfv3Jaq60Y9W0YdV883o7x0ssnEu/f/tijj0i/WUSvXya2qUUgkdqRi8cbtsEMWimgPkUAojPFsQDRCdEJ0QnRCdG5Nya0+ZaqL62jgrn69R/YSjibwkcXz5s3rqf1a1cRc+VDjyw3t6TUA6PMZX70PdERvR7dBhaiM8WHPrKnRCAQ0al8Oa3W4kx0LqWeBZQZohOiE6ITohOiE6KTV2HgGVU+5KoNt98pl3erqm1qJcJNsV1VeYhenjdbrvoQTxCa62PqQpvzmJHnZmS+KcYx0xmQQEA1xxAIRHTy3uWdOpbTHx+6z9IE37jnQdp/oJJenPVAWpoolej1TldcQkXvvkN1l02kA3+ak5b9b+tGw3eqrS0QrR92gB3CQSAcrcD1EA47cCvg0xkeWwQiOuOtz6kwpPM6ndyHZEVn+5m/pYof3iv3VP9y0XKKVFSEZ2SkUUtwcw+HsWAH2CEcBMLRClwP4bADRGd47MAtgej0wB7JiE59eaT9Ly6k+rPO8aAl2VkEbu7hsDvsADuEg0A4WoHrIRx2gOgMjx0CE528KPx3ZkylyZeMs+w9z3T+cuYcWjLv4XDRcdAa+HTCpxM+nfDphE8nfDrh02kdFW/6l/Jj1fRJNQPHOI0egKYexWY+MziM01ntGY/X6w7ETEBJApnp/P5P/kCfrdsS12fTzuczIBZJVQPRCdEJ0QnRCdEJ0QnRCdGZlIjIskyBiE5myrOdfJizmfz9gYNVlI77rnN/IDohOiE6ITohOiE6ITohOrNMPybV3cBEJ7eOZzznv7asVUNPHzU4blR7Uj1qg0xufDrL/vsB4v/sw8m+nDhSJwDfqdQZelEC7OAFxdTLgB1SZ+hFCbCDFxS9KQOv173h6EUpgYpOLxocxjKcik4ED/ljPdzc/eHqtlTYwS13o6t5AAATu0lEQVQxf9LDDv5wdVsq7OCWmH/pITr9Y+u2ZIhOt8Qs0jsVnWpNTuyt7gF0rQjc3L3lmWxpsEOy5LzNBzt4yzPZ0mCHZMl5nw+i03umyZYI0ZksuSP54NMJn074dMKnEz6d8OmETyd8OlOUE1mRHaIzRTNDdEJ0QnRCdEJ0QnRCdEJ0pignsiI7RGeKZobohOiE6ITohOiE6ITohOhMUU5kRXaITg/MbOfTqXw5q+69n/g/Dm8JwHfKW57JlgY7JEvO23ywg7c8ky0NdkiWnPf54NPpPdNkS4ToTJacli+R6Cx69x1i0cn7qu/9cC32V/eAt1kEbu4+QE2iSNghCWg+ZIEdfICaRJGwQxLQfMoC0ekT2CSKhehMApqZJZHoxCynB4BtisDN3X/GTmqAHZxQ8j8N7OA/Yyc1wA5OKAWTBqIzGM5OaoHodEIpQRr4dMKnEz6d8OmETyd8OuHTCZ/OFOVEVmSH6EzRzBCdEJ0QnRCdEJ0QnRCdEJ0pyomsyA7RmaKZITohOiE6ITohOiE6ITohOlOUE1mRHaLTAzNb+XRW/PBeaj/zt1Q94y469F//7UEtKCIeAfhOhWNswA6wQzgIhKMVuB7CYQduBXw6w2MLiE4PbGGKztxDh6jrqEHEP79cvJwah53iQS0oAqIz3GMAD9lw2Ad2gB3CQSA8rYDoDI8tIDo9sIUpOsv++wHi//VnnUP7X1zoQQ0oIhEBPGTDMT5gB9ghHATC0QpcD+GwA2Y6w2MHbglEZ4r2gE8nfDrh0wmfTvh0wqcTPp3w6UxRTmRFdojOFM0M0QnRCdEJ0QnRCdEJ0QnRmaKcyIrsEJ0pmhmiE6ITohOiE6ITohOiE6IzRTmRFdkhOj0ws/Lp5MCh7if2kCXu/mIXtrz0gK2TIuA75YSS/2lgB/8ZO6kBdnBCyf80sIP/jJ3WgEAip6T8TwfR6QFjJToRQOQBzCSKwM09CWg+ZIEdfICaRJGwQxLQfMgCO/gANckiITqTBOdDNohOD6Aq0dll/BlUsOpTGbHOkes4giGAm3swnO1qgR3sCAVzHnYIhrNdLbCDHaHgzkN0BsfariaITjtCNufh0wmfTvh0wqcTPp3w6YRPJ3w6U5QTWZEdojNFM0N0QnRCdEJ0QnRCdEJ0QnSmKCeyIjtEZ4pmhuiE6ITohOiE6ITohOiE6ExRTmRFdohOD8y8f/6r1OmKS7ADkQcskykCvlPJUPM+D+zgPdNkSoQdkqHmfR7YwXumyZYIn85kyXmfD6LTA6Y1195A7Z59mqruvV/+xxEsAdzcg+UdrzbYAXYIB4FwtALXQzjswK2A6AyPLSA6U7XFwYMU6dePeI3OPR+uoebj+6ZaIvK7JICbu0tgPiWHHXwC67JY2MElMJ+Sww4+gU2iWIjOJKD5lAWiM0Ww8OmETyd8OuHTCZ9O+HTCpxM+nSnKiazIDtHpwMxX3HQ/bdi8Q6Yc0K8XvTjrgVguiE6ITohOiE6ITohOiE6ITgdyIuuTQHTaDIFv3PMg7T9QGROaLEA7dSynPz50n8wJ0QnRCdEJ0QnRCdEJ0QnRmfWK0gEAiE4bSGdPvpu+M2MqTb5knEw5b+FS+uXMObRk3sPRnDk5iFp3MND8TALfKT/pOi8bdnDOys+UsIOfdJ2XDTs4Z+V3Svh0+k3YefkQnQlYrVyzkabd8WOa/fsf0fDB/WXKY74TohNR684HnB8pcXP3g6r7MmEH98z8yAE7+EHVfZmwg3tmfuWA6PSLrPtyITo9EJ20aBHR+PHu6SMHCIAACIAACIAACGQJAYjOFEVnmH06c8QsbEtLi+wh/8zLy4t95u/4PP/XD/W5sbGRcnNzqaCgIJa/ublZfo5EIvI7/r26uprKy8vlz9LSUjoklo6qqKiQn0tKSmR9dXV1Mk1tba3Mx99z+VVVVVRWVkbFxcUyHectLCykoqIi+Z/ra2hooJqaGvmT03IfOD+3jduan59PTU1N8nvz4PbxOU7D5XO7+Se3jes/KJa76tChg2w3t4HT8X9u5/79++X5fmI5rHbt2sn6OP/OnTtlNT179pRt5PLXr19P3bt3py5dusjPmzZtkuX1799flsWfuZ4TTjiBdu3aRZs3b6YxY8bItGvXrpV18Hn+nfOdfPLJ9Pnnn8t6hg8fTv/4xz/k+QEDBtDSpUtp0KBBkvGrr75KV1xxBW3ZskW2VaXl83x8/PHHdNlll9Fbb70l8/DBdX/ta1+jF154Qeb95JNPZNlcHtd57rnn0pw5c+imm26i2bNn08UXXyzT9O3bV9qHD07LdY4YMYLefvttWQ7nufHGG+nRRx+lb3/72/TrX/9a/nzwwQfp3//936XvM//kz/w9p+P0nI/zc1+47nh1nX766fTiiy/S7bffHivrqaeeknm43dwmtgG3h8tV9XH53E4eg9xmrkud4/K4X9x/lY/bxWl2794dS8994TLZPsyAmajvOB23eerUqaTawzZUbeV+cdvOOOOMWB62laqPf/LB/VB1cz9UG9leKu3y5ctj9au2n3rqqbF6eRzpZag2cv8Ud25bvN/19Ho5ql9cvt4fvT3MQfWZ+6Paz78rG/AY1POwTbjO++6L+sfr9TBrxZXP6W3Ty+Bzen94zCs78zm9H2Yb9b6YdZhpzTp1/mY9ZptMHma/eTxw3/m64MM8b+a3Kl9nx+fNvplcrOowyzDzWLXDrMeqXDONVftNe5vjRoIxbM2fTTvxd1btVvnxs+0JQHTa2MDOpzPMolPIStG7o6IzN/eI6BRfK6mZk5N79INILWSozMOCiIVWXl6+FHctLREhAiMx0dki0uTnF1BdLQKJEEiEQCIEEiGQCIFECCRqe0kX/hZAdNrYCNHrEJ08s8riPCKE9769u+WI6dy1u5yVbW5qJohOiE6ITohOiE6IzvBLvrZvIUSnAxskWqeTs+/cH31tjKNtCMBhv224m7XCDrBDOAiEoxW4HsJhB24FAonCYwuITg9sAdHpAcQUisDNPQV4HmaFHTyEmUJRsEMK8DzMCjt4CDPFoiA6UwToYXaITg9gQnR6ADGFInBzTwGeh1lhBw9hplAU7JACPA+zwg4ewkyxKIjOFAF6mB2iM0WYCCRCIBF8OuHTCZ9O+HTCpxM+nSnKiazIDtGZopkhOiE6ITohOiE6ITohOiE6U5QTWZEdojNFM0N0QnRCdEJ0QnRCdEJ0QnSmKCeyIjtEZ1aYGZ0EARAAARAAARAAgbYlANHZtvxROwiAAAiAAAiAAAhkBQGIzqwwMzoJAiAAAiAAAiAAAm1LAKKzbfmjdhAAARAAARAAARDICgIQnUma2W6XoiSLzdpsbnnapbc7z6AffmIuPffSIloy7+Gs5W523Ak3PY9d+kTneYvZ9z5cEytuQL9e9OKsB2ALQcCOq1u7JSrv+z/5A81/bRnsYDHygrSDXj3fm2Y+PZ8e+N4tNPmScVl/TQRpB/N6UPBXL56V9XbwAgBEZxIU7fZjT6LIrM7ilqddervz8xYupft/9rhk3rFDGUTnkdFnx80cpHbp7c6fPfnuVuz587ixw+mnP7gN18OBypgA5wdup47l9MeH7rPkYsfZ7jyXr4t9u/qyxTh23Ly+HlR56o/hAwerIDoFlKDtwKLzs3Vb8AewTxc6RGcSYPnh+J0ZU2N/gbKI+eXMORAvSbDkLG552qW3O2/e3DHTGSXilJviZ5fe7rw5XHCzhx2SvIX4ks3t+LVLb3eeO6G/fRk6/iaIzja4L+E+5MvlFCsUotMl35VrNtK0O35Ms3//Ixo+uL/MbfWdy2KzNrlbnnbpGaRT++D1+tFhZ8dVjXWVwy69GzuoMnmGbchJfbN6ptOOaxB2YHE0sH/vuDOr2XCzags7mPcjiE7rZ2ui562d3Zzcl8zX63gb5u0VD9HpkqfdoDYfCi6Lz7rkbnnapXdyU1GQITrDIzrVjT7b/absxrefopPFJr/ShW9t8GJn8bKPj/Evh+gM3g5Wz2/+Y5gP+Jt7I08gOl1ydPtQcFl81iV3y9MuPURnckPIjqufYkcFTehvD5LrRfrnaks7KHqmD136U3Xfg6Dt8KvHnm8VVKe3eMb1k+jum6e470QG5AjaDlaiU8UAZPsfxF4NJ4jOJEg68c1JotiszeKWp116u/OY6bQeak65qdx26e3OczmY4TzWFk646bns0tudN1uAh2yUiFtuduntzpt2wExnOOyA68FbaQLRmQRPt9F0SVSRVVnseJqvN+zS252H6LQeXnbcvLYDXluFww7mKgKwS9QuQV8PEJ3hvB7g4+ytHIHoTJKn23XDkqwma7Il4mn1ELTjn+i8vmSSAjzpojOzOoBFcQjKDuq1mdUAx9qEidfp9Pp60G3O9oBP59FRGdT1YHUdYKazbexgXg+njxqc1UF1XosQiE6viaI8EAABEAABEAABEACBYwhAdGJQgAAIgAAIgAAIgAAI+E4AotN3xKgABEAABEAABEAABEAAohNjAARAAARAAARAAARAwHcCEJ2+I0YFIAACIAACIAACIAACEJ0YAyAAAiAAAiAAAiAAAr4TgOj0HTEqAAEQAAEQAAEQAAEQgOjEGAABEAABEAABEAABEPCdAESn74hRAQiAAAiAAAiAAAiAAEQnxgAIgAAIgAAIgAAIgIDvBCA6fUeMCkAABEAABEAABEAABCA6MQZAAARAAARAAARAAAR8JwDR6TtiVAACIAACIAACIAACIADRiTEAAiAAAiAAAiAAAiDgOwGITt8RowIQAAEQAAEQAAEQAAGITowBEAABEAABEAABEAAB3wlAdPqOGBWAAAiAAAiAAAiAAAhAdGIMgAAIgAAIgAAIgAAI+E4AotN3xKgABEAABEAABEAABEAAohNjAARAwBcCDz8xl2Y+Pf+YsmdcP4nuvnkKnT35bnluybyHj0nD5zp2KKcXZz0gz9mVNXT8TQn70LFDmaznG/c8SO99uMYy7QPfu4UmXzKOrrjpftqweQepzyrxvIVL6f6fPU4D+vWKtcssyEk7xo0dTvNfWxbLOumiM+mnP7jNVb1O+uGLUVEoCIAACKRAAKIzBXjICgIgYE1AiaLZv/8RDR/cP5aIxeMbSz6IiTYWaaePGkx/fOi+WJrv/+QPtHTFypgYdVqWKQ5N0cjnuaz9ByrjikZOo0Sn2S71fSLRqdNQItWqHVbn3NTrpB8YmyAAAiAQNgIQnWGzCNoDAhlAgMWkmsFL1B1TfK1cs5Gm3fHjVrOMTsvyUnR26lguZ0SVaFbtYiFqJ1qdtCOe6HRaL0RnBlwk6AIIZCEBiM4sNDq6DAJ+EzBfjyeqjwXU+o3b5cwmz/ax8NJnPt2UxfUkmmF0Ita4DUNO6kt79n1F3TofJ1998+wrH/ydn6LTab1O+uG3jVE+CIAACLglANHplhjSgwAI2BJQwk9PaPWaWZ3XfSFXL57Vqny3ZdmJTic+nSz+Th81RPpwcnu4fTzr+avHnvdddDqpFz6dtkMQCUAABEJIAKIzhEZBk0AgkwiYAsnqtbsSiirIKF7/3ZSVik8ni04V3MNtUbOvbmYYk/HpdFqvm3Zk0lhCX0AABNKbAERnetsPrQeBtCLAr6k5ctuczbTy5bTrWLyy7GY67V6Pq9frLDpV1LwSsG7EXiqi065eN+2w4/j/27mD3ISBIIii979ItrlADhdNpJGQZeOaFAIZXrbpxs4ziy+C7fcECBB4loDofJa04xD4EIERkF/fP3+fFG5/Zkxt72o/is7/vNYjo3Oc//hO6Xys00rsNdF5dtyV8/iQt50/kwCBCwiIzgtcJKdI4EoCMyDHOW8/0dx7RNKYuxed4272ldd6dHTe2q/EXhud9467ch5Xeu84VwIE3ltAdL739fXXEXiZwN6D0o++s3n27/WV1zqLzvRGor1Paldi7+g85tcC5oW5fTj8/E7n9qJtj+tGope9rR2YAIFCQHQWeFYJECBAgAABAgQyAdGZOZkiQIAAAQIECBAoBERngWeVAAECBAgQIEAgExCdmZMpAgQIECBAgACBQkB0FnhWCRAgQIAAAQIEMgHRmTmZIkCAAAECBAgQKAREZ4FnlQABAgQIECBAIBMQnZmTKQIECBAgQIAAgUJAdBZ4VgkQIECAAAECBDIB0Zk5mSJAgAABAgQIECgERGeBZ5UAAQIECBAgQCATEJ2ZkykCBAgQIECAAIFCQHQWeFYJECBAgAABAgQyAdGZOZkiQIAAAQIECBAoBERngWeVAAECBAgQIEAgExCdmZMpAgQIECBAgACBQkB0FnhWCRAgQIAAAQIEMgHRmTmZIkCAAAECBAgQKAREZ4FnlQABAgQIECBAIBMQnZmTKQIECBAgQIAAgUJAdBZ4VgkQIECAAAECBDIB0Zk5mSJAgAABAgQIECgERGeBZ5UAAQIECBAgQCATEJ2ZkykCBAgQIECAAIFCQHQWeFYJECBAgAABAgQyAdGZOZkiQIAAAQIECBAoBERngWeVAAECBAgQIEAgExCdmZMpAgQIECBAgACBQkB0FnhWCRAgQIAAAQIEMgHRmTmZIkCAAAECBAgQKAREZ4FnlQABAgQIECBAIBMQnZmTKQIECBAgQIAAgUJAdBZ4VgkQIECAAAECBDIB0Zk5mSJAgAABAgQIECgERGeBZ5UAAQIECBAgQCATEJ2ZkykCBAgQIECAAIFCQHQWeFYJECBAgAABAgQyAdGZOZkiQIAAAQIECBAoBH4BTe0JvQpU0O8AAAAASUVORK5CYII=", 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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": [ -1.1233335123518272e-05, 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", "dynamics.plot_history(chemicals=['E', 'ES*'], colors=['violet', 'red'], show_intervals=True, \n", " title_prefix=f\"E and ES when [E] init = {E_init}\")" ] }, { "cell_type": "markdown", "id": "7e1d57c5-4f7a-4e1e-a9e5-0303d60e3020", "metadata": {}, "source": [ "#### At these high initial concentrations of [E], we're now beginning to see [E] and [ES*] no longer overlapping; the overshoot is still present in both" ] }, { "cell_type": "code", "execution_count": 96, "id": "ff72f0a5-b05c-4269-9d98-786e0b53c921", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEEES*P
7490.01005418.41133711.5886636.998847
\n", "
" ], "text/plain": [ " SYSTEM TIME E ES* P\n", "749 0.010054 18.411337 11.588663 6.998847" ] }, "execution_count": 96, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(columns=['SYSTEM TIME', 'E', 'ES*', 'P'], tail=1) # Last point in the simulation" ] }, { "cell_type": "code", "execution_count": 97, "id": "907c937b-bba7-4f7d-8682-86daa9717831", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "6.998846772430818" ] }, "execution_count": 97, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_equil = dynamics.get_chem_conc(\"P\")\n", "P_equil" ] }, { "cell_type": "markdown", "id": "96560369-9a78-40f4-90c3-2ecb441f2bc4", "metadata": {}, "source": [ "#### P_equil continues to decrease with increasing initial [E]" ] }, { "cell_type": "code", "execution_count": 98, "id": "8a14ce96-a237-4610-9e87-38a6231ca263", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "4.899192740701572" ] }, "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": "f6d96e06-599d-4c14-beca-30a37d083617", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.002747856201107546" ] }, "execution_count": 99, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.reach_threshold(chem=\"P\", threshold=P_70_threshold)" ] }, { "cell_type": "markdown", "id": "9dc94f9b-7c97-468d-90b4-c37b7483ca67", "metadata": { "tags": [] }, "source": [ "#### The time at which we reach the 70% threshold of the equilibrium value of P continues to decrease with increasing initial [E]" ] }, { "cell_type": "code", "execution_count": null, "id": "3715cc7b-385f-4119-8b75-2d494ffd892e", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "cef69c73-8295-4f75-8310-ebcc3ec4fc2b", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "f4d60280-db10-4e82-9d6f-02090bdd888d", "metadata": { "tags": [] }, "source": [ "# 9. Keep increasing the initial [E]" ] }, { "cell_type": "code", "execution_count": 100, "id": "a6b8d011-9592-4386-983e-f530b5f90298", "metadata": {}, "outputs": [], "source": [ "E_init = 60.0 # Triple the initial [S]" ] }, { "cell_type": "code", "execution_count": 101, "id": "2b677f97-a5de-486a-89f8-9bc3137b3d7e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "4 species:\n", " Species 0 (S). Conc: 20.0\n", " Species 1 (P). Conc: 0.0\n", " Species 2 (E). Conc: 60.0\n", " Species 3 (ES*). Conc: 0.0\n", "Set of chemicals involved in reactions: {'P', 'ES*', 'E', 'S'}\n" ] } ], "source": [ "dynamics = UniformCompartment(chem_data=chem_data, preset=\"slower\") # A brand-new simulation, with the same chemicals and reactions as before\n", "\n", "dynamics.set_conc(conc={\"S\": 20., \"E\": E_init}, snapshot=True) \n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 102, "id": "07850faa-b7a7-4c58-9017-a95a1e93eb46", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n", "770 total step(s) taken\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" ] } ], "source": [ "# Perform the reactions (The duration of the run was manually adjusted for optimal visibility)\n", "dynamics.single_compartment_react(duration=0.005,\n", " initial_step=0.00005, variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 103, "id": "b850c64e-b44b-4cce-881e-569483921906", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 103, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reactions have reached equilibrium\n", "dynamics.is_in_equilibrium(verbose=False)" ] }, { "cell_type": "code", "execution_count": 104, "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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Changes in concentrations for 3 reactions (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -5.595983095761264e-06, 0.005008404870706331 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -3.333333333333333, 63.333333333333336 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(colors=['cyan', 'green', 'violet', 'red'], show_intervals=True, \n", " title_prefix=f\"[E] init = {E_init}\")" ] }, { "cell_type": "code", "execution_count": 105, "id": "417d9ff2-d739-44af-aff0-72513b3c7d66", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.0007023910558856093, 1.5191639777843677)" ] }, "execution_count": 105, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Locate the intersection of the curves for [S] and [P]:\n", "dynamics.curve_intersect(\"S\", \"P\", t_start=0, t_end=0.005)" ] }, { "cell_type": "markdown", "id": "497f2877-4ce5-41cd-9119-e483df6fcf14", "metadata": {}, "source": [ "#### The timescales of [S] and [P] continues to become faster with a higher initial [E] -- **AND NOW THEY REMAIN COMPARABLE THE TIMESCALES OF E AND ES**" ] }, { "cell_type": "markdown", "id": "89ff44f1-0c42-4a6d-8fe3-b1efab242da1", "metadata": {}, "source": [ "#### At these high initial concentrations of [E], [E] and [ES*] no longer overlapping, and are now getting further apart" ] }, { "cell_type": "code", "execution_count": 106, "id": "449c94a5-dd8e-4681-b654-dce7b685a7c7", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEEES*P
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" ], "text/plain": [ " SYSTEM TIME E ES* P\n", "770 0.005008 44.60637 15.39363 3.832618" ] }, "execution_count": 106, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(columns=['SYSTEM TIME', 'E', 'ES*', 'P'], tail=1) # Last point in the simulation" ] }, { "cell_type": "code", "execution_count": 107, "id": "41db82fe-6607-44f8-9723-9a0d3f7306a6", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3.832618199402545" ] }, "execution_count": 107, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_equil = dynamics.get_chem_conc(\"P\")\n", "P_equil" ] }, { "cell_type": "markdown", "id": "c4951935-f4a1-4790-b198-fd0e2bfc18ca", "metadata": {}, "source": [ "#### P_equil continues to decrease with increasing initial [E]" ] }, { "cell_type": "code", "execution_count": 108, "id": "e7cb5350-03c0-49da-a185-fd7af33f1312", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.682832739581781" ] }, "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": "fbbb456b-0880-4aa2-b300-89d1204ad53d", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.001390053726276219" ] }, "execution_count": 109, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.reach_threshold(chem=\"P\", threshold=P_70_threshold)" ] }, { "cell_type": "markdown", "id": "977bfde9-42e1-4733-bac6-bae954134aac", "metadata": { "tags": [] }, "source": [ "#### The time at which we reach the 70% threshold of the equilibrium value of P continues to decrease with increasing initial [E]" ] }, { "cell_type": "code", "execution_count": null, "id": "6c7df8fa-c510-45db-9e5f-52e62766e52f", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "09d0e661-f920-4070-82e4-e0e0affc188d", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "4a771e38-d7b2-444a-bfe8-b0032cbc79f4", "metadata": { "tags": [] }, "source": [ "# 10. Keep increasing the initial [E]" ] }, { "cell_type": "code", "execution_count": 110, "id": "338fbe68-dde9-4159-a405-973ee8a7c796", "metadata": {}, "outputs": [], "source": [ "E_init = 100.0 # Quintuple the initial [S]" ] }, { "cell_type": "code", "execution_count": 111, "id": "c45f280a-708c-4de0-95dc-03a629dbebfe", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "4 species:\n", " Species 0 (S). Conc: 20.0\n", " Species 1 (P). Conc: 0.0\n", " Species 2 (E). Conc: 100.0\n", " Species 3 (ES*). Conc: 0.0\n", "Set of chemicals involved in reactions: {'P', 'ES*', 'E', 'S'}\n" ] } ], "source": [ "dynamics = UniformCompartment(chem_data=chem_data, preset=\"slower\") # A brand-new simulation, with the same chemicals and reactions as before\n", "\n", "dynamics.set_conc(conc={\"S\": 20., \"E\": E_init}, snapshot=True) \n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 112, "id": "5d5bcb4d-3932-4cee-bb45-7bd19db664a1", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n", "785 total step(s) taken\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" ] } ], "source": [ "# Perform the reactions (The duration of the run was manually adjusted for optimal visibility)\n", "dynamics.single_compartment_react(duration=0.003,\n", " initial_step=0.00005, variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 113, "id": "2ca20feb-38fe-4737-99b7-2b0472453781", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 113, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reactions have reached equilibrium\n", "dynamics.is_in_equilibrium(verbose=False)" ] }, { "cell_type": "code", "execution_count": 114, "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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Changes in concentrations for 3 reactions (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -3.382707968171298e-06, 0.0030275236315133115 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -5.555555555555555, 105.55555555555556 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(colors=['cyan', 'green', 'violet', 'red'], show_intervals=True, \n", " title_prefix=f\"[E] init = {E_init}\")" ] }, { "cell_type": "code", "execution_count": 115, "id": "803d88fa-f551-4f56-96af-37b417c505b4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.0004266715141239805, 0.9491814221946882)" ] }, "execution_count": 115, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Locate the intersection of the curves for [S] and [P]:\n", "dynamics.curve_intersect(\"S\", \"P\", t_start=0, t_end=0.005)" ] }, { "cell_type": "markdown", "id": "ecbaf247-3675-44b8-9bbc-a71f37f341ba", "metadata": {}, "source": [ "#### The timescales of [S] and [P] continues to become faster with a higher initial [E] -- **AND REMAIN COMPARABLE TO THE TIMESCALES OF E AND ES**" ] }, { "cell_type": "markdown", "id": "3491b263-298d-4057-926a-c57ed7eb5444", "metadata": {}, "source": [ "#### At these high initial concentrations of [E], [E] and [ES*] no longer overlapping, and are now getting further apart" ] }, { "cell_type": "code", "execution_count": 116, "id": "92812a67-0f27-4e7f-837b-368a426921d0", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEEES*P
7850.00302882.77909917.2209012.312829
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" ], "text/plain": [ " SYSTEM TIME E ES* P\n", "785 0.003028 82.779099 17.220901 2.312829" ] }, "execution_count": 116, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(columns=['SYSTEM TIME', 'E', 'ES*', 'P'], tail=1) # Last point in the simulation" ] }, { "cell_type": "code", "execution_count": 117, "id": "5c48aa58-e44c-4e18-9c60-c562560aa0e9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.3128291895441793" ] }, "execution_count": 117, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_equil = dynamics.get_chem_conc(\"P\")\n", "P_equil" ] }, { "cell_type": "markdown", "id": "da34f793-1dd1-41a0-a20b-8e15e82654db", "metadata": {}, "source": [ "#### P_equil continues to decrease with increasing initial [E]" ] }, { "cell_type": "code", "execution_count": 118, "id": "98698d70-47a1-4763-be1f-89660bd27ffa", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.6189804326809254" ] }, "execution_count": 118, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P_70_threshold = P_equil * 0.70\n", "P_70_threshold" ] }, { "cell_type": "code", "execution_count": 119, "id": "69acbdb6-7a06-4e96-9ad7-3bdfc3ef92c7", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.0008229365407830671" ] }, "execution_count": 119, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.reach_threshold(chem=\"P\", threshold=P_70_threshold)" ] }, { "cell_type": "code", "execution_count": null, "id": "1806b972-6770-4a1a-be69-1f1504c6da94", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "6974ce46-642c-47a5-96b2-e4f3c9fa6b5d", "metadata": {}, "source": [ "# CONCLUSION: \n", "### as the initial concentration of the Enzyme E increases from zero to lavish values much larger that the concentration of the Substrate S, the reaction keeps reaching an equilibrium faster and faster... \n", "#### BUT the equilibrium concentration of the Product P steadily _reduces_ - and ES*, far from being transient, actually builds up. \n", "#### The **strange world of departing from the customary Michaelis-Menten assumptions** that [E] << [S] and that the rates satisfy k1_reverse >> k2_forward !" ] }, { "cell_type": "code", "execution_count": 120, "id": "073427b4-27a8-407d-bdee-0df89430eb16", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMESPEES*caption
00.020.00.0100.00.0Initialized state
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" ], "text/plain": [ " SYSTEM TIME S P E ES* caption\n", "0 0.0 20.0 0.0 100.0 0.0 Initialized state" ] }, "execution_count": 120, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(head=1) # First point in the simulation" ] }, { "cell_type": "code", "execution_count": 121, "id": "1b5546d6", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMESPEES*caption
7850.0030280.466272.31282982.77909917.220901last reaction step
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" ], "text/plain": [ " SYSTEM TIME S P E ES* caption\n", "785 0.003028 0.46627 2.312829 82.779099 17.220901 last reaction step" ] }, "execution_count": 121, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history(tail=1) # Last point in the simulation" ] }, { "cell_type": "markdown", "id": "9c5c0d06-8dc7-43c9-affa-5ead52f95cb8", "metadata": {}, "source": [ "### When the initial [E] is quite high, relatively little of the reactant S goes into making the product P ; most of S binds with the abundant E, to produce a lasting ES* \n", "The following manual stoichiometry check illustrates it." ] }, { "cell_type": "markdown", "id": "22946daf-a9fc-4b93-a9ff-b97b385299a0", "metadata": {}, "source": [ "#### Manual overall STOICHIOMETRY CHECK:" ] }, { "cell_type": "code", "execution_count": 122, "id": "8e3cdce6-5f0d-404a-aaa1-907b4c5ab241", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-19.53373" ] }, "execution_count": 122, "metadata": {}, "output_type": "execute_result" } ], "source": [ "delta_S = 0.46627 - 20.0\n", "delta_S" ] }, { "cell_type": "code", "execution_count": 123, "id": "4e36063d-e6f9-4dfd-b1f3-79f4aeafdd8f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-17.220900999999998" ] }, "execution_count": 123, "metadata": {}, "output_type": "execute_result" } ], "source": [ "delta_E = 82.779099 - 100.0\n", "delta_E" ] }, { "cell_type": "code", "execution_count": 124, "id": "3dbf7a73", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-17.220900999999998" ] }, "execution_count": 124, "metadata": {}, "output_type": "execute_result" } ], "source": [ "delta_E = 82.779099 - 100.0\n", "delta_E" ] }, { "cell_type": "code", "execution_count": 125, "id": "ffd30805-1f47-4410-a6c8-5c8db4d9bbad", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "17.220901" ] }, "execution_count": 125, "metadata": {}, "output_type": "execute_result" } ], "source": [ "delta_ES = 17.220901 - 0\n", "delta_ES" ] }, { "cell_type": "code", "execution_count": 126, "id": "4d77a7f6-0d90-46e7-9d7a-b155460e546d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 3 (at temp. 25 C)\n", "0: S <-> P (kF = 1 / kR = 0.2 / delta_G = -3,989.7 / K = 5) | 1st order in all reactants & products\n", "1: E + S <-> ES* (kF = 100 / kR = 224.07 / delta_G = 2,000 / K = 0.44629) | 1st order in all reactants & products\n", "2: ES* <-> E + P (kF = 200 / kR = 17.851 / delta_G = -5,989.7 / K = 11.204) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {'P', 'ES*', 'E', 'S'}\n" ] } ], "source": [ "chem_data.describe_reactions()" ] }, { "cell_type": "code", "execution_count": null, "id": "83580347-c7aa-4ac7-aafc-cc81b24de20a", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "95749790-0ab6-4640-b525-4802dcaf9de3", "metadata": {}, "source": [ "19.53373 units of `S` are consumed : a meager 2.312829 of that goes into the production of `P` (rxn 0) ; the remainder of Delta S is:" ] }, { "cell_type": "code", "execution_count": 127, "id": "b7372ba6-8da7-4ee0-a888-d04baea7f4c9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "17.220900999999998" ] }, "execution_count": 127, "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": 128, "id": "271f073f-1e22-456b-825b-2acf555519c9", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "82.7791" ] }, "execution_count": 128, "metadata": {}, "output_type": "execute_result" } ], "source": [ "100 - 17.2209" ] }, { "cell_type": "code", "execution_count": 129, "id": "a1f87fde-d486-40ab-baee-b73b0abf9f6c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: S <-> P\n", "Final concentrations: [S] = 0.4663 ; [P] = 2.313\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.96028\n", " Formula used: [P] / [S]\n", "2. Ratio of forward/reverse reaction rates: 5.00001\n", "Discrepancy between the two values: 0.7945 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n", "1: E + S <-> ES*\n", "Final concentrations: [E] = 82.78 ; [S] = 0.4663 ; [ES*] = 17.22\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 0.446167\n", " Formula used: [ES*] / ([E][S])\n", "2. Ratio of forward/reverse reaction rates: 0.446288\n", "Discrepancy between the two values: 0.027 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n", "2: ES* <-> E + P\n", "Final concentrations: [ES*] = 17.22 ; [E] = 82.78 ; [P] = 2.313\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 11.1175\n", " Formula used: ([E][P]) / [ES*]\n", "2. Ratio of forward/reverse reaction rates: 11.2035\n", "Discrepancy between the two values: 0.7677 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 129, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Also review that the chemical equilibrium holds, with the final simulation values\n", "dynamics.is_in_equilibrium()" ] }, { "cell_type": "code", "execution_count": null, "id": "3c4cee2d-2d29-4666-b067-45a4cd9706b4", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "jupytext": { "formats": "ipynb,py:percent" }, "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.13" } }, "nbformat": 4, "nbformat_minor": 5 }