{ "cells": [ { "cell_type": "markdown", "id": "49bcb5b0-f19d-4b96-a5f1-e0ae30f66d8f", "metadata": {}, "source": [ "## `A` down-regulates `B` , \n", "### by being the *limiting reagent* in reaction `A + 2 B <-> Y` (mostly forward)\n", "1st-order kinetics. \n", "If [A] is low and [B] is high, then [B] remains high. If [A] goes high, [B] goes low. However, at that point, A can no longer bring B up to any substantial extent.\n", "\n", "See also 1D/reactions/down_regulation_1\n", "\n", "LAST REVISED: May 5, 2024" ] }, { "cell_type": "code", "execution_count": 1, "id": "5a07c2cb-c6b8-4614-b1f7-fc582f174c0f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Added 'D:\\Docs\\- MY CODE\\BioSimulations\\life123-Win7' to sys.path\n" ] } ], "source": [ "import set_path # Importing this module will add the project's home directory to sys.path" ] }, { "cell_type": "code", "execution_count": 2, "id": "367ba836", "metadata": { "tags": [] }, "outputs": [], "source": [ "from experiments.get_notebook_info import get_notebook_basename\n", "\n", "from src.modules.chemicals.chem_data import ChemData as chem\n", "from src.modules.reactions.reaction_dynamics import ReactionDynamics\n", "\n", "from src.modules.visualization.graphic_log import GraphicLog" ] }, { "cell_type": "code", "execution_count": 3, "id": "cc53849f-351d-49e0-bfa8-22f8d8e22f8e", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-> Output will be LOGGED into the file 'down_regulate_2.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": "markdown", "id": "d6d3ca49-589d-49b7-8424-37c7b01bcacf", "metadata": {}, "source": [ "### Initialize the system" ] }, { "cell_type": "code", "execution_count": 4, "id": "23c15e66-52e4-495b-aa3d-ecddd8d16942", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 1 (at temp. 25 C)\n", "0: A + 2 B <-> Y (kF = 8 / kR = 2 / delta_G = -3,436.6 / K = 4) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {'Y', 'A', 'B'}\n", "[GRAPHIC ELEMENT SENT TO LOG FILE `down_regulate_2.log.htm`]\n" ] } ], "source": [ "# Initialize the system\n", "chem_data = chem(names=[\"A\", \"B\", \"Y\"])\n", "\n", "# Reaction A + 2 B <-> Y , with 1st-order kinetics for all species\n", "chem_data.add_reaction(reactants=[\"A\" , (2, \"B\", 1)], products=\"Y\",\n", " forward_rate=8., reverse_rate=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": "d1d0eabb-b5b1-4e15-846d-5e483a5a24a7", "metadata": {}, "source": [ "### Set the initial concentrations of all the chemicals" ] }, { "cell_type": "code", "execution_count": 5, "id": "e80645d6-eb5b-4c78-8b46-ae126d2cb2cf", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "3 species:\n", " Species 0 (A). Conc: 5.0\n", " Species 1 (B). Conc: 100.0\n", " Species 2 (Y). Conc: 0.0\n", "Set of chemicals involved in reactions: {'Y', 'A', 'B'}\n" ] } ], "source": [ "dynamics = ReactionDynamics(chem_data=chem_data)\n", "dynamics.set_conc(conc={\"A\": 5., \"B\": 100., \"Y\": 0.},\n", " snapshot=True) # A is scarce, B is plentiful, Y is absent\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": null, "id": "face01c6-9833-4ae3-9762-37a859fdbe63", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "0b46b395-3f68-4dbd-b0c5-d67a0e623726", "metadata": { "tags": [] }, "source": [ "# 1. Take the initial system to equilibrium" ] }, { "cell_type": "code", "execution_count": 6, "id": "bcf652b8-e0dc-438e-bdbe-02216c1d52a0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* INFO: the tentative time step (0.0005) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.00025) [Step started at t=0, and will rewind there]\n", "28 total step(s) taken\n" ] } ], "source": [ "# All of these settings are currently close to the default values... but subject to change; set for repeatability\n", "dynamics.set_thresholds(norm=\"norm_A\", low=0.5, high=1.0, abort=1.44)\n", "dynamics.set_thresholds(norm=\"norm_B\", low=0.2, high=0.5, abort=1.5)\n", "dynamics.set_step_factors(upshift=1.4, downshift=0.5, abort=0.5)\n", "dynamics.set_error_step_factor(0.333)\n", "\n", "dynamics.single_compartment_react(initial_step=0.0005, reaction_duration=0.015,\n", " variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "markdown", "id": "7dc56592-179d-4e4c-b75a-8eb81dcafe71", "metadata": {}, "source": [ "A, as the scarse limiting reagent, stops the reaction. \n", "When A is low, B is also low." ] }, { "cell_type": "code", "execution_count": 7, "id": "58f4f09c-8af6-46b7-bd85-2f6ca194c42a", "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=A
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" ], "text/plain": [ " SYSTEM TIME A B Y caption\n", "0 0.000000 5.000000 100.000000 0.000000 Initial state\n", "1 0.000250 4.000000 98.000000 1.000000 \n", "2 0.000500 3.216500 96.433000 1.783500 \n", "3 0.000625 2.906769 95.813538 2.093231 \n", "4 0.000800 2.517591 95.035182 2.482409 \n", "5 0.001045 2.049858 94.099716 2.950142 \n", "6 0.001388 1.522589 93.045178 3.477411 \n", "7 0.001731 1.136233 92.272466 3.863767 \n", "8 0.002074 0.851194 91.702389 4.148806 \n", "9 0.002417 0.639853 91.279707 4.360147 \n", "10 0.002760 0.482579 90.965159 4.517421 \n", "11 0.003103 0.365222 90.730445 4.634778 \n", "12 0.003446 0.277475 90.554949 4.722525 \n", "13 0.003789 0.211767 90.423533 4.788233 \n", "14 0.004132 0.162507 90.325015 4.837493 \n", "15 0.004475 0.125548 90.251096 4.874452 \n", "16 0.004818 0.097800 90.195600 4.902200 \n", "17 0.005161 0.076958 90.153916 4.923042 \n", "18 0.005504 0.061297 90.122594 4.938703 \n", "19 0.005847 0.049526 90.099053 4.950474 \n", "20 0.006327 0.037139 90.074277 4.962861 \n", "21 0.006807 0.029054 90.058108 4.970946 \n", "22 0.007288 0.023776 90.047553 4.976224 \n", "23 0.007960 0.018952 90.037905 4.981048 \n", "24 0.008632 0.016472 90.032944 4.983528 \n", "25 0.009573 0.014686 90.029373 4.985314 \n", "26 0.010891 0.013887 90.027773 4.986113 \n", "27 0.012736 0.013833 90.027665 4.986167 \n", "28 0.015318 0.013858 90.027716 4.986142 " ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "code", "execution_count": 9, "id": "3180f7aa-390e-4ada-a7ab-3c0db958fcc5", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "From time 0 to 0.0005, in 2 steps of 0.00025\n", "From time 0.0005 to 0.000625, in 1 step of 0.000125\n", "From time 0.000625 to 0.0008, in 1 step of 0.000175\n", "From time 0.0008 to 0.001045, in 1 step of 0.000245\n", "From time 0.001045 to 0.005847, in 14 steps of 0.000343\n", "From time 0.005847 to 0.007288, in 3 steps of 0.00048\n", "From time 0.007288 to 0.008632, in 2 steps of 0.000672\n", "From time 0.008632 to 0.009573, in 1 step of 0.000941\n", "From time 0.009573 to 0.01089, in 1 step of 0.00132\n", "From time 0.01089 to 0.01274, in 1 step of 0.00184\n", "From time 0.01274 to 0.01532, in 1 step of 0.00258\n", "(28 steps total)\n" ] } ], "source": [ "dynamics.explain_time_advance(use_history=True)" ] }, { "cell_type": "markdown", "id": "962acf15-3b50-40e4-9daa-3dcca7d3291a", "metadata": {}, "source": [ "#### Equilibrium" ] }, { "cell_type": "code", "execution_count": 10, "id": "2783a665-fca0-44e5-8d42-af2a96eae392", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: A + 2 B <-> Y\n", "Final concentrations: [A] = 0.01386 ; [B] = 90.03 ; [Y] = 4.986\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3.99663\n", " Formula used: [Y] / ([A][B])\n", "2. Ratio of forward/reverse reaction rates: 4.0\n", "Discrepancy between the two values: 0.08418 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reaction has reached equilibrium\n", "dynamics.is_in_equilibrium()" ] }, { "cell_type": "code", "execution_count": null, "id": "4faea7f8-0466-4d90-8eba-3d6501cca2d8", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "448ec7fa-6529-438b-84ba-47888c2cd080", "metadata": { "tags": [] }, "source": [ "# 2. Now, let's suddenly increase [A]" ] }, { "cell_type": "code", "execution_count": 11, "id": "7245be7a-c9db-45f5-b033-d6c521237a9c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0.015318388:\n", "3 species:\n", " Species 0 (A). Conc: 40.0\n", " Species 1 (B). Conc: 90.02771559198881\n", " Species 2 (Y). Conc: 4.98614220400561\n", "Set of chemicals involved in reactions: {'Y', 'A', 'B'}\n" ] } ], "source": [ "dynamics.set_single_conc(species_name=\"A\", conc=40., snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 12, "id": "61eead55-fcef-41cd-b29e-f2d5ad5c6078", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABYcaption
250.0095730.01468690.0293734.985314
260.0108910.01388790.0277734.986113
270.0127360.01383390.0276654.986167
280.0153180.01385890.0277164.986142
290.01531840.00000090.0277164.986142Set concentration of `A`
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" ], "text/plain": [ " SYSTEM TIME A B Y caption\n", "25 0.009573 0.014686 90.029373 4.985314 \n", "26 0.010891 0.013887 90.027773 4.986113 \n", "27 0.012736 0.013833 90.027665 4.986167 \n", "28 0.015318 0.013858 90.027716 4.986142 \n", "29 0.015318 40.000000 90.027716 4.986142 Set concentration of `A`" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.history.get_dataframe(tail=5)" ] }, { "cell_type": "markdown", "id": "24455d58-a0ea-43fa-b6ad-95c42a8b34b2", "metadata": {}, "source": [ "### Again, take the system to equilibrium" ] }, { "cell_type": "code", "execution_count": 13, "id": "c06fd8d8-d550-4e35-a239-7b91bee32be9", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* INFO: the tentative time step (0.0005) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.00025) [Step started at t=0.015318, and will rewind there]\n", "* INFO: the tentative time step (0.00025) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.000125) [Step started at t=0.015318, and will rewind there]\n", "* INFO: the tentative time step (0.000125) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 6.25e-05) [Step started at t=0.015318, and will rewind there]\n", "* INFO: the tentative time step (6.25e-05) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 3.125e-05) [Step started at t=0.015318, and will rewind there]\n", "47 total step(s) taken\n" ] } ], "source": [ "dynamics.single_compartment_react(initial_step=0.0005, target_end_time=0.055,\n", " variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 14, "id": "cc34ca51-8ec3-4170-abc9-f9bccdd7ce00", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_history(colors=['red', 'darkorange', 'green'],\n", " title=\"Changes in concentrations (reaction A + 2 B <-> Y)\")" ] }, { "cell_type": "markdown", "id": "158e3787-f2d5-4a01-aaa9-6066e93e584c", "metadata": {}, "source": [ "**A**, still the limiting reagent, is again stopping the reaction. \n", "The (transiently) high value of [A] led to a high value of [B]" ] }, { "cell_type": "code", "execution_count": 15, "id": "2415f119-b3cc-477d-b3a4-cd020aab3615", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABYcaption
00.0000005.000000100.0000000.000000Initial state
10.0002504.00000098.0000001.000000
20.0005003.21650096.4330001.783500
30.0006252.90676995.8135382.093231
40.0008002.51759195.0351822.482409
..................
720.0349541.38307312.79386243.603069
730.0384271.19433412.41638343.791809
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77 rows × 5 columns

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" ], "text/plain": [ " SYSTEM TIME A B Y caption\n", "0 0.000000 5.000000 100.000000 0.000000 Initial state\n", "1 0.000250 4.000000 98.000000 1.000000 \n", "2 0.000500 3.216500 96.433000 1.783500 \n", "3 0.000625 2.906769 95.813538 2.093231 \n", "4 0.000800 2.517591 95.035182 2.482409 \n", ".. ... ... ... ... ...\n", "72 0.034954 1.383073 12.793862 43.603069 \n", "73 0.038427 1.194334 12.416383 43.791809 \n", "74 0.043288 1.043380 12.114476 43.942762 \n", "75 0.050094 0.953305 11.934325 44.032838 \n", "76 0.059623 0.925189 11.878093 44.060953 \n", "\n", "[77 rows x 5 columns]" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "code", "execution_count": 16, "id": "aff608b1-5c78-4070-845a-118afe7c2108", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: A + 2 B <-> Y\n", "Final concentrations: [A] = 0.9252 ; [B] = 11.88 ; [Y] = 44.06\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.00938\n", " Formula used: [Y] / ([A][B])\n", "2. Ratio of forward/reverse reaction rates: 4.0\n", "Discrepancy between the two values: 0.2344 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reaction has reached equilibrium\n", "dynamics.is_in_equilibrium()" ] }, { "cell_type": "code", "execution_count": null, "id": "cb4749d0-dc12-44ba-a032-8068c80d9c4c", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "f6619731-c5ea-484c-af3e-cea50d685361", "metadata": { "tags": [] }, "source": [ "# 3. Let's again suddenly increase [A]" ] }, { "cell_type": "code", "execution_count": 17, "id": "d3618eba-a673-4ff5-85d0-08f5ea592361", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0.059622836:\n", "3 species:\n", " Species 0 (A). Conc: 30.0\n", " Species 1 (B). Conc: 11.878093044952234\n", " Species 2 (Y). Conc: 44.06095347752391\n", "Set of chemicals involved in reactions: {'Y', 'A', 'B'}\n" ] } ], "source": [ "dynamics.set_single_conc(species_name=\"A\", conc=30., snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 18, "id": "007161ef-f4d0-4623-92c5-0fe3d2bda98a", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABYcaption
730.0384271.19433412.41638343.791809
740.0432881.04338012.11447643.942762
750.0500940.95330511.93432544.032838
760.0596230.92518911.87809344.060953
770.05962330.00000011.87809344.060953Set concentration of `A`
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" ], "text/plain": [ " SYSTEM TIME A B Y caption\n", "73 0.038427 1.194334 12.416383 43.791809 \n", "74 0.043288 1.043380 12.114476 43.942762 \n", "75 0.050094 0.953305 11.934325 44.032838 \n", "76 0.059623 0.925189 11.878093 44.060953 \n", "77 0.059623 30.000000 11.878093 44.060953 Set concentration of `A`" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.history.get_dataframe(tail=5)" ] }, { "cell_type": "markdown", "id": "0974480d-ca45-46fe-addd-c8d394780fdb", "metadata": {}, "source": [ "### Yet again, take the system to equilibrium" ] }, { "cell_type": "code", "execution_count": 19, "id": "8fe20f9c-05c4-45a4-b485-a51005440200", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* INFO: the tentative time step (0.001) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.5 (set to 0.0005) [Step started at t=0.059623, and will rewind there]\n", "19 total step(s) taken\n" ] } ], "source": [ "dynamics.single_compartment_react(initial_step=0.001, target_end_time=0.09,\n", " variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 20, "id": "4229e039-b484-4849-a446-59409885deb4", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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"white", "zerolinewidth": 2 } } }, "title": { "text": "Changes in concentrations (reaction A + 2 B <-> Y)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ 0, 0.09912593079469205 ], "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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SYSTEM TIMEABYcaption
00.0000005.000000100.0000000.000000Initial state
10.0002504.00000098.0000001.000000
20.0005003.21650096.4330001.783500
30.0006252.90676995.8135382.093231
40.0008002.51759195.0351822.482409
..................
920.07291624.3159630.51001849.744991
930.07660524.3169860.51206449.743968
940.08177124.3163300.51075349.744624
950.08900224.3172860.51266449.743668
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" ], "text/plain": [ " SYSTEM TIME A B Y caption\n", "0 0.000000 5.000000 100.000000 0.000000 Initial state\n", "1 0.000250 4.000000 98.000000 1.000000 \n", "2 0.000500 3.216500 96.433000 1.783500 \n", "3 0.000625 2.906769 95.813538 2.093231 \n", "4 0.000800 2.517591 95.035182 2.482409 \n", ".. ... ... ... ... ...\n", "92 0.072916 24.315963 0.510018 49.744991 \n", "93 0.076605 24.316986 0.512064 49.743968 \n", "94 0.081771 24.316330 0.510753 49.744624 \n", "95 0.089002 24.317286 0.512664 49.743668 \n", "96 0.099126 24.314800 0.507693 49.746154 \n", "\n", "[97 rows x 5 columns]" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "code", "execution_count": 22, "id": "88f744d6-17fb-4d03-b8cc-bb22b12555e0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: A + 2 B <-> Y\n", "Final concentrations: [A] = 24.31 ; [B] = 0.5077 ; [Y] = 49.75\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.02984\n", " Formula used: [Y] / ([A][B])\n", "2. Ratio of forward/reverse reaction rates: 4.0\n", "Discrepancy between the two values: 0.746 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reaction has reached equilibrium\n", "dynamics.is_in_equilibrium()" ] }, { "cell_type": "markdown", "id": "81a8be4a-f374-494e-b647-184e35707295", "metadata": {}, "source": [ "**A**, again the scarse limiting reagent, stops the reaction yet again" ] }, { "cell_type": "code", "execution_count": null, "id": "162ae075-48c4-4d55-ba15-1f19e3b75b9b", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "d40258c5-5520-44a2-8dca-c28864386742", "metadata": {}, "source": [ "# 4. A can down-regulate B, but it cannot bring it up to any significant amount\n", "#### Even if A is completely taken out (i.e., [A] set to 0), [B] can only slightly increase, from the reverse reaction (\"Le Chatelier's principle\".) \n", "Let's try it:" ] }, { "cell_type": "code", "execution_count": 23, "id": "84e83a01-76b1-4a6c-92e3-3f540cb47b1e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0.099125931:\n", "3 species:\n", " Species 0 (A). Conc: 0.0\n", " Species 1 (B). Conc: 0.5076929235350717\n", " Species 2 (Y). Conc: 49.74615353823248\n", "Set of chemicals involved in reactions: {'Y', 'A', 'B'}\n" ] } ], "source": [ "dynamics.set_single_conc(species_name=\"A\", conc=0., snapshot=True) # Completely eliminate A\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 24, "id": "31f1e4d5-8027-41de-90cc-f0492c88a9d9", "metadata": { "lines_to_next_cell": 2 }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "19 total step(s) taken\n" ] } ], "source": [ "dynamics.single_compartment_react(initial_step=0.001, target_end_time=0.16,\n", " variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 25, "id": "665dfff9-e943-44e1-b76d-af363d94c9f8", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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gAAEIQAACEIAABNQSQMgm4Zno3MlYSZuO4Is9t9HZKXjd4rly1ZLbJJMdss4IsX060mjJ4rmyfMWqqJreuN6P7PrH97/BUry5U30DJl1C1hOc/nNt4/UUO1u8NyZLJ69M13Xu8/eXjpB17o19TjyBlIpw/OPja91onefg5u//h/x61V/67dCMPcPV+/Htgdj42WfL1ftxdO8ZjBWdA31pDiRvU/nGQbLn3y9avT4c/icef6TE2/np3+3oXe//cfjYryeP3dYdtRJvV3O8s11jf7w+WyGbyrEsqbCMl1M2QjYeS/8aqTwnyc7GTfeoArX/2tVXLVUhm2mu+jqnMgQgAAEIQAACEIAABCAAgfwigJC1OO9Uzre0eHxGs5hANrs3LcbCaBBISiDZcQ5JC3ABBCAAAQhAAAIQgAAEIAABCGRNACGbNcJwFHB2uzm7946dNrmvoVTfbCocE9AFBNIjkOpuwPSqcjUE7CYw0HEfdk/OdBCAAAQgAAEIQAACEIAABMJDACEbniyy6iT2x7+dYirOSMyqKW6GgGYC3tEDPOuaQVPeeALZvlGa8QAYAAIQgAAEIAABCEAAAhCAQIgIIGRDFAatQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAnYTQMjanS/TQQACEIAABCAAAQhAAAIQgAAEIAABCEAAAiEigJANURi0AgEIQAACEIAABCAAAQhAAAIQgAAEIAABCNhNACFrd75MBwEIQAACEIAABCAAAQhAAAIQgAAEIAABCISIAEI2RGHQCgQgAAEIQAACEIAABCAAAQhAAAIQgAAEIGA3AYSs3fkyHQQgAAEIQAACEIAABCAAAQhAAAIQgAAEIBAiAgjZEIVBKxCAAAQgAAEIQAACEIAABCAAAQhAAAIQgIDdBBCydufLdBCAAAQgAAEIQAACEIAABCAAAQhAAAIQgECICCBkQxQGrUAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAJ2E0DI2p0v00EAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIhIoCQDVEYtAIBCEAAAhCAAAQgAAEIQAACEIAABCAAAQjYTQAha3e+TAcBCEAAAhCAAAQgAAEIQAACEIAABCAAAQiEiABCNkRh0AoEIAABCEAAAhCAAAQgAAEIQAACEIAABCBgNwGErN35Mh0EIAABCEAAAhCAAAQgAAEIQAACEIAABCAQIgII2RCFQSsQgAAEIAABCEAAAhCAAAQgAAEIQAACEICA3QQQsnbny3QQgAAEIAABCEAAAhCAAAQgAAEIQAACEIBAiAggZEMUBq1AAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACdhNAyNqdL9NBAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACISKAkA1RGLQCAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEI2E0AIWt3vkwHAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIhIgAQjZEYdAKBCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgYDcBhKzd+TIdBCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgECICCNkQhUErEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAgN0EELJ258t0EIAABCAAAQhAAAIQgAAEIAABCEAAAhCAQIgIIGRDFAatQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAnYTQMjanS/TQQACEIAABCAAAQhAAAIQgAAEIAABCEAAAiEigJANURi0AgEIQAACEIAABCAAAQhAAAIQgAAEIAABCNhNACFrd75MBwEIQAACEIAABCAAAQhAAAIQgAAEIAABCISIAEI2RGHQCgQgAAEIQAACEIAABCAAAQhAAAIQgAAEIGA3AYSs3fkyHQQgAAEIQAACEIAABCAAAQhAAAIQgAAEIBAiAgjZEIVBKxCAAAQgAAEIQAACEIAABCAAAQhAAAIQgIDdBBCydufLdBCAAAQgAAEIQAACEIAABCAAAQhAAAIQgECICCBkQxQGrUAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAJ2E0DI2p0v00EAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIhIoCQDVEYtAIBCEAAAhCAAAQgAAEIQAACEIAABCAAAQjYTQAha3e+TAcBCEAAAhCAAAQgAAEIQAACEIAABCAAAQiEiABCNkRh0AoEIAABCEAAAhCAAAQgAAEIQAACEIAABCBgNwGErN35Mh0EIAABCEAAAhCAAAQgAAEIQAACEIAABCAQIgII2RCFQSsQgAAEIAABCEAAAhCAAAQgAAEIQAACEICA3QQQsnbny3QQgAAEIAABCEAAAhCAAAQgAAEIQAACEIBAiAggZEMUBq1AAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACdhNAyNqdL9NBAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACISKAkA1RGLQCAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEI2E0AIWt3vkwHAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIhIgAQjZEYdAKBCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgYDcBhKzd+TIdBCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgECICCNkQhUErEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAgN0EELIK8t26q1lBFUrYRKC8tFDKigulrrHNprGYRQGB4sICGVJZIh/UtyqoRgmbCBSIyOhh5bKNf6fYFKuyWUbVlLl/b3R1dSurSSE7CAwbXCqNze3S2t5lx0BMoYxA9aBiae/slqaWDmU1KWQHgUFlRVJUWCD1+9rtGIgplBEoLY5IZXmx7NrLf6sog5rDQmOGledwdZZORgAhm4xQCq8jZFOAlGeXIGTzLPA0xkXIpgErzy5FyOZZ4GmOi5BNE1geXY6QzaOw0xwVIZsmsDy6HCGbR2GnOSpCNk1gIb8cIRvugBCyCvJByCqAaFkJhKxlgSocByGrEKZlpRCylgWqeByErGKgFpVDyFoUpuJRELKKgVpUDiFrUZiKR0HIKgaa43II2RwHkGR5hKyCfBCyCiBaVgIha1mgCsdByCqEaVkphKxlgSoeByGrGKhF5RCyFoWpeBSErGKgFpVDyFoUpuJRELKKgea4HEI2xwEgZPcTWP3wk/LOe9vl8nmzorDU1TfI/EU3yfoNm93P33HzIjl22uS+a5z7vnP97e6fzzptulyz8GIpLyvpex0hG+6HPBfdIWRzQd2MNRGyZuSUiy4Rsrmgbs6aCFlzsgq6U4Rs0MTNWQ8ha05WQXeKkA2auDnrIWTNySqVThGyqVDK3TV5sUN23UsbZc5lS13Kl5w/I0rINre0ydXLbpfpx0yRmTNOkk1btsq3ltwmP1w8VyaOHSPOvctXrJJbly6QmuoquXHFKreOX+oiZHP3AId1ZYRsWJPJfV8I2dxnENYOELJhTSYcfSFkw5FDGLtAyIYxlXD0hJANRw5h7AIhG8ZUwtETQjYcOajqAiGriqSeOnkhZD108XbIOgJ22S0rZclVc13hGitoHQE77qDRrqx1PmIFrfM5hKyeh9PkqghZk9PT2ztCVi9fk6sjZE1OT3/vCFn9jE1dASFranL6+0bI6mds6goIWVOT0983QlY/4yBXQMgGSTv9tfJeyMYTrN4u2PkXfS5q96yDN3YHLUI2/YcuH+5AyOZDypnNiJDNjFs+3IWQzYeUM58RIZs5O9vvRMjannDm8yFkM2dn+50IWdsTznw+hGzm7MJ4Z9iErHdc6BXzZkUdExpGdgP1FLuRM9P+EbIvbZR7H1wTdS5srJA975xT+h6WfkL2nb9Iw6jTMuXPfZYScKRbUWFEmts6LZ2QsTIlUFggUlZSKPtaeTYyZWjrfY6QrSwvkobmDltHZK4sCFSWFcm+1g7p7s6iCLdaSaCitFDa2ruko4uHw8qAsxiqrDgind0i7R1dWVThVhsJlBRFJFIg0tLOs2FjvtnMVBQpkJLiiDTx3yrZYAzNvVXlRYH34vi0X9z9cNS63tGhuRSyzmbMxUtukxXXX+EeT5rNB0I2A3rxjizIeofs8gJpnf4DafvIlRl0xC22EigqiojzL7MWhKytEWc8VyRS4ArZphakW8YQLb6xsqJYGpvaLZ6Q0TIlMKi8SJpaOqUbI5spQmvvKy8tkraOTul0zBsfEPARKC0plK6uboQsT0U/AsWOkI0USCv/rcLTEUOgsLBASooKpbmV/1ax4eGoqigObAxPth48ZmTUhkdPXjobHSeN/5DMX3STsEO2J5a83yGb9RmyywukO1IqO2e+KJ2V4wJ72Fko3AQ4siDc+eSyO44syCX9cK/NkQXhzifX3XFkQa4TCO/6HFkQ3mxy3RlHFuQ6gfCuz5EF4c0m151xZEGuE1C7fpBHFjg7Y7fv3B0lY2On8aTtpRedKw89+k/54+Nr3Uu8HbTe9d516zdsdj911mnT++p6gvfIKRPlldc2RdX46uzPuMLXu+/aKy8e8P2gHB8478rlsm3HLnedqYdPkFuXLnDfXyp2p6//NXbIZvCcxtshGwsy9kiC2B203nEGl8+b1dPBHz4nsul+aR19kuz69J8z6IpbbCSAkLUxVTUzIWTVcLSxCkLWxlTVzYSQVcfStkoIWdsSVTcPQlYdS9sqIWRtS1TdPAhZdSzDUCkoIesJ1FnnnNInQOPN711Xu7u+7+gAT4ouWTzXPSo03rEGftnr1L162e3ywqtv9qvhvOYdSZDM7cWu69z7lzXPyqTxB7pHGvzvnQ/KaSce03e8Qbweph8zZcB5kz0DebFD1pGqcy5bGsXijpsX9Z0LG2vf/a85Nzki9zvX3+7e7zfz7ica/iXdvzhUCjqbpe6kX0nzhPOSMef1PCCAkM2DkDMcESGbIbg8uA0hmwchZzEiQjYLeJbfipC1POAsxkPIZgHP8lsRspYHnMV4CNks4IXw1qCEbDy5OZCQ9R9ZELtJMt5GSr9cHTNquCtk/TI03o7V2M8l3WyZJD//T9eXlZb26yGT+PNCyGYCJp176p+8XqrX/Zd0lQ6VnV/4P+kqqU7ndq61kABC1sJQFY2EkFUE0sIyCFkLQ1U4EkJWIUzLSiFkLQtU4TgIWYUwLSuFkLUsUIXjIGQVwgxBKROFbLw3BXNQHjBqmLv7VYWQ9YSqc66tsys33ocndL1jFZL1kEncCNlMqMXcs7W2UUbcf7wU73lNmg69RPZ8/L8VVKWEyQQQsianp7d3hKxeviZXR8ianJ7+3hGy+hmbugJC1tTk9PeNkNXP2NQVELKmJqe/b4SsfsZBrhCUkE33yIKBdsj2OyY0Blgqu2GdWwbaIZtMyHo7fmecerx4x5Um26WbSa4I2UyoxQrZXc1SvOtFGfHgJ9xX6qf/WPZNnqugMiVMJYCQNTU5/X0jZPUzNnUFhKypyQXTN0I2GM4mroKQNTG1YHpGyAbD2cRVELImphZMzwjZYDgHtUpQQtaZZ6A39XKOC3A+Jo3/kPumW8mOLFj7/GsJ3xxMhZD13rTL6anv/aF8oTj93vvgmqgeELJBPbVprrN1V7N7R9Xz35Oq9de7v6875TfSPO4LaVbiclsIIGRtSVL9HAhZ9UxtqYiQtSVJPXMgZPVwtaEqQtaGFPXMgJDVw9WGqghZG1LUMwNCVg/XXFUNUsh6u2QPHjMySmR678nkvFdTKkI23u5UR8Le+qs/yFdnf0bind+aiqSNPUPWe68p/3tIeW/qtbturyxeclvfG4R59b03Eot3bEImGbNDNhNqMfd4QrZHyn5HqtYvd69onPJN2Xtc9JuJKViOEgYQQMgaEFKOWkTI5gi8AcsiZA0IKYctImRzCD/kSyNkQx5QDttDyOYQfsiXRsiGPKActoeQzSF8DUsHKWS99mPPgPXOfp04dox40nagHbJOHe+69Rs291G55PwZ7m7WVOSrc1OyN/VyrvGkrLfI1MMnyK1LF4izg9YTyc69J4zFAAAgAElEQVRrzgwL539JfrnyT/LDxXPjnmObSXwI2UyoDSBknZfK3/mdDHlyrhR0tUrrAZ+U3aeulO7iKgUrUcIUAghZU5IKvk+EbPDMTVkRIWtKUrnpEyGbG+4mrIqQNSGl3PSIkM0NdxNWRciakFJuekTI5oa7rlVzIWR1zWJjXYSsglT9O2S9csW7X5ahj58nhfv+JR3Vh8ruT90nHZXjFaxGCRMIIGRNSCk3PSJkc8PdhFURsiaklLseEbK5Yx/2lRGyYU8od/0hZHPHPuwrI2TDnlDu+kPI5o69jpURsjqoqquJkFXAMp6QdcpGWuukZs2FUrrtCXeVpkkXSOuBn5aWAz8t3UWDFKxMibASQMiGNZnc94WQzX0GYe0AIRvWZMLRF0I2HDmEsQuEbBhTCUdPCNlw5BDGLhCyYUwlHD0hZMORg6ouELKqSOqpg5BVwDWRkPVKD3r951L13Lcl0r63b7WWg86SlnHnSvPB53KcgYIMwlYCIRu2RMLTD0I2PFmErROEbNgSCVc/CNlw5RGmbhCyYUojXL0gZMOVR5i6QciGKY1w9YKQDVce2XaDkM2WoN77EbIK+CYTss4SkZbdUrl+mZS+/4gU79kQtWrrmNOleeKXpWnibAXdUCIMBBCyYUghnD0gZMOZSxi6QsiGIYXw9oCQDW82ue4MIZvrBMK7PkI2vNnkujOEbK4TCO/6CNnwZpNJZwjZTKgFdw9CVgHrVISsfxnnXNmyf/1FSrY+JmXvPy4FHY1RXbSNOF66IyU9nysokK6SIdJdUiOd5cNFSmqkq9T5Z6h0lQ3t+dV5rWKMgkkooYoAQlYVSfvqIGTty1TVRAhZVSTtrIOQtTNXFVMhZFVQtLMGQtbOXFVMhZBVQdHOGghZu3JFyIY7T4SsgnzSFbKxS5bs/IeU/usxKaldJ8W1z0mkrV5BV/FLdEfKXMkrEun9VaS7wPt9gYjze3Fe7/mn32vuvb3XdTuv++5xX3Ne7qnX7dborRdznVvXW8frx63bu6b7WvYfTZO/Js3jz8u+UJoVELJpAsujyxGyeRR2mqMiZNMElmeXI2TzLPA0xkXIpgErzy5FyOZZ4GmMi5BNA1aeXYqQtStwhGy480TIKsgnWyEb24KzY9Y54iDSVieR1j0Saa113yDM+XNB8y6JtO3u+bN7jff7nQomsa9E44cvk70fvS7wwRCygSM3ZkGErDFRBd4oQjZw5EYtiJA1Kq5Am0XIBorbqMUQskbFFWizCNlAcRu1GELWqLiSNouQTYoopxcgZBXgVy1kFbTUr0RBZ4uIdPf80937j7OH1f191/7PF3T1vO6+tv/3Pff0XlcQ+5pznbNkzzXO3lj3+oLee3rrufd3O/tmY9aU/ev33ZslhJKtT0jVK0ulaeKXZc+JP8+yWvq3I2TTZ5YvdyBk8yXp9OdEyKbPLJ/uQMjmU9rpzYqQTY9XPl2NkM2ntNObFSGbHq98uhoha1faCNlw54mQVZCPCUJWwZhGlSjd+rgMe+QcaR1zmuw648HAe0fIBo7cmAURssZEFXijCNnAkRu1IELWqLgCbRYhGyhuoxZDyBoVV6DNImQDxW3UYghZo+JK2ixCNiminF6AkFWAHyGrAKLiEkW718vIB46XjpqpsvPcZxRXT14OIZucUb5egZDN1+STz42QTc4on69AyOZz+gPPjpDl2UhEACHLs5GIAEKWZyMRAYSsXc8GQrYnz+aWNrl62e3y7tadcuvSBVJTXRWKoBGyCmJAyCqAqLhEpHmnjL5nnHSVjZTts99RXD15OYRsckb5egVCNl+TTz43QjY5o3y+AiGbz+kjZEk/MwII2cy45cNdCNl8SDmzGRGymXEL610I2Z5kNm3ZKit+/YDsbWySS86fIcdOmxyKyBCyCmJAyCqAqLxEt4y5o9KtunVOo4g4qiO4D4RscKxNWwkha1piwfWLkA2OtYkrIWRNTC2YntkhGwxnE1dByJqYWjA9I2SD4WziKghZE1NL3DNCtofN6oef7IP0znvb5fJ5s0IRNEJWQQwIWQUQNZQYfc94iTTvkO2zNktXxWgNKyQuiZANFLdRiyFkjYor0GYRsoHiNm4xhKxxkQXWMEI2MNTGLYSQNS6ywBpGyAaG2riFELLGRTZgwzkRsg89FDzEkhKRM86Iu65zXMGyW1fKBTNPd19fdstKWXLV3FAcW4CQVfCoIGQVQNRQYuT9x0tR3XrZ+dm10jH0SA0rIGQDhWrJYghZS4LUMAZCVgNUi0oiZC0KU/EoCFnFQC0qh5C1KEzFoyBkFQO1qBxC1qIwRSRwIVtbKzJiRPAQnTV37oy7rnNcwV2rH5OF82e7rztnyU4/ZorMnHFS8H3GrIiQVRABQlYBRA0lhj3yWSnd+pjs+tT90vqhT2lYASEbKFRLFkPIWhKkhjEQshqgWlQSIWtRmIpHQcgqBmpROYSsRWEqHgUhqxioReUQshaFmQshu3evyIUXBg9x8GCRO++Mu+6NK1bJuING9wlY5/iCtc+/JtcsvFjKy0qC79W3IkJWAX6ErAKIGkrUPPU1Kd/0W6k74TZpnnSBhhUQsoFCtWQxhKwlQWoYAyGrAapFJRGyFoWpeBSErGKgFpVDyFoUpuJRELKKgVpUDiFrUZi5ELIhw1dX3yDzF90k6zdsjursgFHDZMX1V8jEsWNy2jFCVgF+hKwCiBpKDF53lVT+382y96M/kMYPX65hBYRsoFAtWQwha0mQGsZAyGqAalFJhKxFYSoeBSGrGKhF5RCyFoWpeBSErGKgFpVDyFoUJkJW1r20UZavWCW3Ll0QdWZs7K7ZXKWOkFVAHiGrAKKGEpWv/lgGP7dYGo/4puw9dqmGFRCygUK1ZDGErCVBahgDIasBqkUlEbIWhal4FISsYqAWlUPIWhSm4lEQsoqBWlQOIWtRmAhZccSr83H5vFlRwTqi9t4H1+T82AKErIKvN4SsAogaSpRvultqnrpEmsd/SepO/qWGFRCygUK1ZDGErCVBahgDIasBqkUlEbIWhal4FISsYqAWlUPIWhSm4lEQsoqBWlQOIWtRmAjZ0IeJkFUQEUJWAUQNJUq3Pi7DHjlHWg/4pOw6848aVkDIBgrVksUQspYEqWEMhKwGqBaVRMhaFKbiURCyioFaVA4ha1GYikdByCoGalE5hKxFYSJkQx8mQlZBRAhZBRA1lCiqe1VG3n+cdAyZIjs/95yGFRCygUK1ZDGErCVBahgDIasBqkUlEbIWhal4FISsYqAWlUPIWhSm4lEQsoqBWlQOIWtRmAjZ0IeJkFUQEUJWAUQNJSLNO2X0PeOkq2y4bJ/9roYVELKBQrVkMYSsJUFqGAMhqwGqRSURshaFqXgUhKxioBaVQ8haFKbiURCyioFaVA4ha1GYCNnQh4mQVRARQlYBRC0lumXMHZVu5a1zGkXE0R3BfJSXFkpZcaHUNbYFsyCrGEMAIWtMVIE3ipANHLlRCyJkjYor0GYRsoHiNmoxhKxRcQXaLEI2UNxGLYaQNSqupM2OGVae9BouyB0BhKwC9ghZBRA1lRh9z3iJNO+Q7bM2SVfFAZpW6V8WIRsYauMWQsgaF1lgDSNkA0Nt5EIIWSNjC6RphGwgmI1cBCFrZGyBNI2QDQSzkYsgZI2MLWHTCNlw56lVyNbVN8j8RTfJ+g2b+1GYevgEuXXpAqmprgo3oRS6Q8imAClHl4x4YLoU735FPjj779I+/COBdYGQDQy1cQshZI2LLLCGEbKBoTZyIYSskbEF0jRCNhDMRi6CkDUytkCaRsgGgtnIRRCyRsaGkDU0Nq1C9sYVq1wsl8+bZSie1NpGyKbGKRdXDXvks1K69THZdfp90nrgmYG1gJANDLVxCyFkjYsssIYRsoGhNnIhhKyRsQXSNEI2EMxGLoKQNTK2QJpGyAaC2chFELJGxoaQNTQ2bULW2R27+LrbZOGls2Xi2DGG4kmtbYRsapxycVXNU1+T8k2/lT2f+Jk0HfKVwFpAyAaG2riFELLGRRZYwwjZwFAbuRBC1sjYAmkaIRsIZiMXQcgaGVsgTSNkA8Fs5CIIWSNjQ8gaGhtCVkFwCFkFEDWVGPzct6Ty1Ztk7zHfl8ap/6lplf5lEbKBoTZuIYSscZEF1jBCNjDURi6EkDUytkCaRsgGgtnIRRCyRsYWSNMI2UAwG7kIQtbI2BCyhsamTcg6PJwjC8YdNFpmzjjJUDyptY2QTY1TLq6qfPXHMvi5xbJvyjek/rhlgbWAkA0MtXELIWSNiyywhhGygaE2ciGErJGxBdI0QjYQzEYugpA1MrZAmkbIBoLZyEUQskbGhpBNQKC5pU2uXna7/PHxtX1XHDBqmKy4/opQ/CS/ViG7actWuWv1Y7Jw/mwpLyux68n2TYOQDW+05ZvulpqnLpHm8edJ3cm/CqxRhGxgqI1bCCFrXGSBNYyQDQy1kQshZI2MLZCmEbKBYDZyEYSskbEF0jRCNhDMRi6CkDUyNoRsEiE7/ZgpfRtFVz/8pKx9/jW5ZuHFOfeU2oSsc4bs/EU3yfoNm+OimXr4BLl16QKpqa4y/olHyIY3wtKtf5Vhj5wtbaNPktpP/zmwRhGygaE2biGErHGRBdYwQjYw1EYuhJA1MrZAmkbIBoLZyEUQskbGFkjTCNlAMBu5CELWyNgQsmkI2XUvbZTlK1aFwkdqE7J2PcYDT4OQDW/aRXWvysj7j5OO6smy8/MvBNYoQjYw1MYthJA1LrLAGkbIBobayIUQskbGFkjTCNlAMBu5CELWyNgCaRohGwhmIxdByBoZW7iE7OaHgocYKREZd0a/db0jC2J3yL7z3na5fN6s4PuMWREhqyAChKwCiJpKRJp3yuh7xkl3SY1s+/L7mlbpXxYhGxhq4xZCyBoXWWANI2QDQ23kQghZI2MLpGmEbCCYjVwEIWtkbIE0jZANBLORiyBkjYwtPEK2uVbklhHBQywfIXLpzoRC1n+GrHPRJefPyA8h62wHnnPZ0igwd9y8SI6dNjn4kDStiJDVBFZJ2W4Zc0eliHTLtq/US3ekWEnVZEUQsskI5e/rCNn8zT7Z5AjZZITy+3WEbH7nP9D0CFmejUQEELI8G4kIIGR5NhIRQMja9WyMGVYe7EBte0X+eGGwazqrlQ4WmXFnQiHr3yEbb9ds8A33rKh1h2y8sxmcN/qad+VyufSic/sO1c3V8KrWRciqIqmnzuh7JkikebvsOO8N6Rx0oJ5FYqoiZAPBbOQiCFkjYwukaYRsIJiNXQQha2x02htHyGpHbOwCCFljo9PeOEJWO2JjF0DIGhtd3MYDF7Ihw5dIvjpv7BWGYwu0CVlv8PPOOaXfblhH1N774JpQvKuZiucFIauCor4aIx6YLsW7X5EPzn5a2ocfrW8hX2WEbCCYjVwEIWtkbIE0jZANBLOxiyBkjY1Oe+MIWe2IjV0AIWtsdNobR8hqR2zsAghZY6NDyMYhEE/I5sUO2br6Bll83W2y8NLZMnHsmCg0zi7ZZbeslCVXzZWa6irjn3iEbLgjHPbIZ6V062Oy+7TfSctBMwJpFiEbCGYjF0HIGhlbIE0jZAPBbOwiCFljo9PeOEJWO2JjF0DIGhud9sYRstoRG7sAQtbY6BCyAwjZ2DNkr73y4lD8xD47ZBV8vSFkFUDUWGLI03Ol4q27ZM8JP5OmSV/RuNL+0gjZQDAbuQhC1sjYAmkaIRsIZmMXQcgaG532xhGy2hEbuwBC1tjotDeOkNWO2NgFELLGRoeQNTA6bULWYeGcy7DqwTVy69IFfTthOUPWwKfE8JarXvy+VL28VBqmXSUN074dyDQI2UAwG7kIQtbI2AJpGiEbCGZjF0HIGhud9sYRstoRG7sAQtbY6LQ3jpDVjtjYBRCyxkaHkDUwOq1C1uHhnBc757KlUWjuuHlRv3NlDWTX1zI7ZMOdXsWbv5Ihf58vzRPOl7qTfhFIswjZQDAbuQhC1sjYAmkaIRsIZmMXQcgaG532xhGy2hEbuwBC1tjotDeOkNWO2NgFELLGRoeQNTA67ULWQCZpt4yQTRtZoDeUbH9Shv/509I28mNSO+PxQNZGyAaC2chFELJGxhZI0wjZQDAbuwhC1tjotDeOkNWO2NgFELLGRqe9cYSsdsTGLoCQNTY6hKyB0SFkFYSGkFUAUWOJwn3vy6h7D5G2EcdL7VlPaFxpf2mEbCCYjVwEIWtkbIE0jZANBLOxiyBkjY1Oe+MIWe2IjV0AIWtsdNobR8hqR2zsAghZY6NDyBoYHUJWQWgIWQUQNZc44M6RUtDRKNsu3CndRZWaVxNByGpHbOwCCFljo9PeOEJWO2KjF0DIGh2f1uYRslrxGl0cIWt0fFqbR8hqxWt0cYSs0fH1a37MsHK7BrJsGuVCtq6+QeYvukm++qVPyy/v+bOs37A5LrKph0+IerMvk7kiZMOf3oiHTpTi2ueldsZfpW3kdO0NI2S1IzZ2AYSssdFpbxwhqx2x0QsgZI2OT2vzCFmteI0ujpA1Oj6tzSNkteI1ujhC1uj4ELKGxadcyHrzO2J28XW3ycJLZ8vEsWOisDhv9HXvg2vkmoUXS3lZiWHI+reLkA1/hEOemisVm+6SPR//H2k69KvaG0bIakds7AIIWWOj0944QlY7YqMXQMgaHZ/W5hGyWvEaXRwha3R8WptHyGrFa3RxhKzR8SFkDYsvJ0J205atsuyWlbLkqrlSU11lGDKErImBVa6/QQY//11pPOKbsvfYpdpHQMhqR2zsAghZY6PT3jhCVjtioxdAyBodn9bmEbJa8RpdHCFrdHxam0fIasVrdHGErNHxIWQNiy8nQnb1w0/K2udfY4esYQ+Lye2WvfuQDP3rLGk98EzZdfp92kdByGpHbOwCCFljo9PeOEJWO2KjF0DIGh2f1uYRslrxGl0cIWt0fFqbR8hqxWt0cYSs0fEhZA2LT7mQdXa/zrtyuWzbsSshigNGDZMV11/R7ygDw9j1tcuRBeFPrqj+TRl531HSWXmw7PjiRu0NI2S1IzZ2AYSssdFpbxwhqx2x0QsgZI2OT2vzCFmteI0ujpA1Oj6tzSNkteI1ujhC1uj4ELI+As0tbXL1sttl+jFTZOaMk/pe8d736op5s+TYaZNzGrhyIetNM9AZsjmdWMPiCFkNUFWX7O6UMb8eItLdKdv+bY90F+o9uxghqzpAe+ohZO3JUvUkCFnVRO2qh5C1K0+V0yBkVdK0qxZC1q48VU6DkFVJ065aCFm78hwzrNyugdKcJp6XvHHFKhl30OgoSZtmWWWXaxOyyjo0oBBC1oCQRGTkHz4qRXtekw/Oflrahx+ttWmErFa8RhdHyBodn9bmEbJa8RpfHCFrfITaBkDIakNrfGGErPERahsAIasNrfGFEbLGRxg1QL4LWQeG/8jUVzduluUrVsmtSxeE4v2sELIKvt4QsgogBlBi6JoLpOyd+6TuxF9I88Tzta6IkNWK1+jiCFmj49PaPEJWK17jiyNkjY9Q2wAIWW1ojS+MkDU+Qm0DIGS1oTW+MELW+AhzLmQfeuOhwCGWFJbIGRPPiLuud3TBkVMmyiuvbZLzzjkl50cVeI1qFbIDnSc79fAJobHS2T4tCNlsCQZzf9WL10rVy0ukcepC2XvMNVoXRchqxWt0cYSs0fFpbR4hqxWv8cURssZHqG0AhKw2tMYXRsgaH6G2ARCy2tAaXxgha3yEORWytU21MmLZiMAhjqgYITsX7ky47rqXNsqcy5bKJefPkMvnzQq8v0QLahOy/gN0jzpikty1+jFZOH+2lJeViHNmw4nHHxkaK51tGgjZbAkGc3/55lVS8+QcaTn4HNl96j1aF0XIasVrdHGErNHxaW0eIasVr/HFEbLGR6htAISsNrTGF0bIGh+htgEQstrQGl8YIWt8hDkVsntb98qFqy8MHOLg0sFy58w7E67r+ckw7Y51mtUmZP2H5zoLLbtlpSy5aq57ToNjp+99cI1cs/BiV9Ca/oGQNSPB4l0vy4gHPyYdgw+RnTNf1to0QlYrXqOLI2SNjk9r8whZrXiNL46QNT5CbQMgZLWhNb4wQtb4CLUNgJDVhtb4wghZ4yPMqZANK728FrJDh1TJkp/cJYu/eYErZJ2jDPyCNqyhpdoXQjZVUrm9rqCzTQ74zRCRgkLZ+pU97q+6PhCyusiaXxcha36GuiZAyOoia0ddhKwdOeqYAiGrg6odNRGyduSoYwqErA6qdtREyNqRozcFb+rVQyLvhKz/yIKZM05yjykYd9BocX7vf5czdsja9QUf9mlG/W6KFDa+IzvPXScdNUdoaxchqw2t8YURssZHqG0AhKw2tFYURshaEaOWIRCyWrBaURQha0WMWoZAyGrBakVRhKwVMfYNgZDNUyEb+xg7RxjMX3STrN+wWQ4YNUxWXH+FTBw7xoqnnR2y5sQ47LGZUvqvP8vuU+6UlnEztTWOkNWG1vjCCFnjI9Q2AEJWG1orCiNkrYhRyxAIWS1YrSiKkLUiRi1DIGS1YLWiKELWihgRsobEqO0MWUPmV9ImQlYJxkCKDF63WCr/78fSMO3b0jDtKm1rImS1oTW+MELW+Ai1DYCQ1YbWisIIWSti1DIEQlYLViuKImStiFHLEAhZLVitKIqQtSJGhKwhMWoTsv439bJlJ2yiTBGyhjztIlLxxh0y5B+XSvP4L0rdyb/W1jhCVhta4wsjZI2PUNsACFltaK0ojJC1IkYtQyBktWC1oihC1ooYtQyBkNWC1YqiCFkrYkTIGhIjQlZBUAhZBRADKlGyc60Mf/hU6aiZKjvPfUbbqghZbWiNL4yQNT5CbQMgZLWhtaIwQtaKGLUMgZDVgtWKoghZK2LUMgRCVgtWK4oiZK2IESFrSIzahKwzv/NGXicef6QcO22yITgyaxMhmxm3XNxV0NEoB9w5UrojJbLt33aJFBRqaQMhqwWrFUURslbEqGUIhKwWrNYURchaE6XyQRCyypFaUxAha02UygdByCpHak1BhKw1UbqD8KZe4c5Tq5DdtGWr3LX6MVk4f7aUl5WEm0QW3SFks4CXg1tH3zNeIs07ZMfM9dI5eKKWDhCyWrBaURQha0WMWoZAyGrBak1RhKw1USofBCGrHKk1BRGy1kSpfBCErHKk1hREyFoTJULWgCi1CVnnDNn5i26S9Rs2x8Uw9fAJcuvSBVJTXWUApoFbRMiaFeHwP58pJdufkt2n3SstB52lpXmErBasVhRFyFoRo5YhELJasFpTFCFrTZTKB0HIKkdqTUGErDVRKh8EIascqTUFEbLWRImQNSBKbULWgNmVtYiQVYYykELVaxdIxZu/kb3HL5N9h35Vy5oIWS1YrSiKkLUiRi1DIGS1YLWmKELWmiiVD4KQVY7UmoIIWWuiVD4IQlY5UmsKImStiRIha0CU2oSss0N28XW3ycJLZ8vEsWOiUKx7aaPc++AauWbhxVYcZYCQNeBJ97VY/tZdUvP0XGk56GzZfdoqLc0jZLVgtaIoQtaKGLUMgZDVgtWaoghZa6JUPghCVjlSawoiZK2JUvkgCFnlSK0piJC1JkqErAFR5kTIOmfLLrtlpSy5ai5HFhjwkNjWYtHeN2Xk6qOkbeTHpXbGY1rGQ8hqwWpFUYSsFTFqGQIhqwWrNUURstZEqXwQhKxypNYURMhaE6XyQRCyypFaUxAha02UCFkDosyJkF398JOy9vnXQrND9sYVq+QXdz8cFde1V14sM2ec5H7O6fc719/u/v6s06b365sdsgY86TEtjr77YIm01srOma9Ix+BJygdAyCpHak1BhKw1USofBCGrHKlVBRGyVsWpdBiErFKcVhVDyFoVp9JhELJKcVpVDCFrVZwyZli5XQNZNo1yIevsfp135XLZtmNXQlQHjBomK66/ot9RBrli6whZ5+PyebP6teAcr7B8xaq+NyCLdy1CNlfJZb5uzd/mSPnbq6T++OWy7/D5mRdKcCdCVjlSawoiZK2JUvkgCFnlSK0qiJC1Kk6lwyBkleK0qhhC1qo4lQ6DkFWK06piCFmr4kTIhjxO5ULWm3egM2TDxmQgIeu8Nu6g0X27ZWMFrTMLQjZsiSbvp+KtO2XI0/8uLQd+Rnaf/vvkN6R5BUI2TWB5dDlCNo/CTnNUhGyawPLscoRsngWexrgI2TRg5dmlCNk8CzyNcRGyacDKs0sRsnYFzg7ZcOepTciGe+zo7mKPLPCOK2huaZOrl90u04+Z0idknR3A31pym/xw8dy+Hb4IWZPS7uk10vKBjF45VrojpbLtwg9EIkVKh0DIKsVpVTGErFVxKh0GIasUp3XFELLWRapsIISsMpTWFULIWhepsoEQsspQWlcIIWtXpAjZcOeJkI3JxztyYcniufLhyRNcIXveOafIsdMmu1fGE7INzR3hTpnu4hIYtPIjEtn9qjR99hHpPPCTSik50q2oMCLNbZ1K61LMfAKFBSJlJYWyr5Vnw/w01U7gCNnK8iIJ479T6lv3SH1Lvextq3d/7ZauhMN3dXdJt/N/3e7/T/KrxH1dBrqvp2pK9Qesk6Q/Z8Deldy1UqnV1eVcp+ejpCgi7Z1d4raSxkckUiDu/xVE/+qU8H9OfNe4r3n/F3Ofc0/f60le89f01opd199bKuvGq7m/p+iZ+tWO069zjTftQL2lM7dbMwnvgu79maS67v6avR33ZlFRUiQdnd3S2dV//n61Y9b1apYVlaXxVHGpKQTKiiPS2S3S3pH472xTZqFPtQScf6dECkRa2nk21JI1v1pRpEBKiiPSxH+rmB+miFSVq914ZgWUEA2hVcg6xxbMX3STrN+wud/IUw+f0Hcua4h4uK14xxR85tTpKe2QbWhqD9sI9JMCgdJ/XCklL98sbdP+U1o/dl0Kd6R+SVFRRJx/mbUgZFOHlidXOnLEEbJNLZIk7JYAACAASURBVHwjJ08iT2vMyopiadTw75QPmj4QR6ruba2XxrZGqWvZLXta9kh9a737+fre3zuvN7Q2uK/X98rXhra9ac3AxRCAgJ0EhpTWSEVxuZQVlUt5cYWUO78WlUthpFCKIkXuP8WRYiks6Pm9++fCYil0fu9+rrDn9d7XnNdLCkvc67zPFfde67/GreGvGSnuvaennreWc4/7595r3T8X7u/FqeH0m08fpSWF4nyjCCGbT6mnNmuxI2QjBdLKf6ukBiyPriosLJCSokJpbuW/VWyIvaqi2IYxrJ1Bq5Ad6GzWMBP1nxvLGbJhTiq73krff0yGPfpZaR96pHzw2bXZFYu5myMLlOK0qhhHFlgVp9Jhsj2yYF97o7y44zl5Y/dr8lbdG/Lm7o3yZt3r8kHTjqz7HFRcKYNLq91/hpQOdfdOJvro2QmZYKdid/+dg7E7N3t2Ivp2dCbcqel0MMAuQ/9OwAQ7I6PWHrA3/47ExL1FCiJZs05UYFB5kTS1dPbu1k1tGWe3svMRtaPYt8O4p4p/t3H0te6rvTuJna253QXRO5P71fZdG/VazH1OP17tnvUTrxtvl3KidXt2MvfUitevf113z7N3fcyu7r76MTuxPVZJ1++dt/+u6l7iMbuzvV79vOPtMI+azdeb+wXX7exbj83H+3P8dVs7W1J7kCy+yvm7zRXKBT1S2BO6PULYEc2e/PWksvNn3/U+WezUKS7wCWevZmGRK5Td2oU9wjjd+s69kUikX323XqTQJ6yj64+urpb2zm6+CWzxM5zpaBxZkCk5++/jyAK7MubIgnDnqU3ImvKmXk6fDz++Vi6Y+Sk3qdgjCWLfxCueZOYM2XA/5Im6K+hqldF3jhbn1+2zt0hX2QhlgyBklaG0rhBC1rpIlQ2UrpB9tfZleX7bM/Lyjufl5Z0vyMbd/5ewl+rSIVJdMsQVqtVlQ6SqZHCPYC0ZIkPKaqSqpEoGlw6RwSWDpbq0RqpKB7u/915XNiSFMibAGbIZo7P+xiDOkG3pbJbm9mZp7miSlg7n157ft3e2S1tnm3R2d0h7V7t0dnVIR3eHdHZ17v+z8zn38+3S0dW5/5rODmnrauv5c1dn7+s917r1Op16zueder31u3tf7+qS9q62nmtj6/de09HZ7t7bc02nNHXss/5ZSDZgRdGg/TuanZ3ErtDtEcY9otknoF1BXSKFEeenvvZLZW/HsyugY3Yv99xf6ArnkkiJ204kUth3PIrzTauo41C8PxeI9L3mfQNNIlHHqkS93ndfT7VI1LXOffu/ieZfs+ebZvu/qea+1rue+5rz+95v5nn3ed9o82q6Q/m+yef+0f9/Mce6OK/23LL/2Ji+e3o/1/d679o9OUYfNdPzmf11/DXdgWP6SLZmRZnzDQKRhqbOvt6iagw4R08fsXOUFnL0SbKvQRNeR8iakFLqPSJkU2eViyvzXsh6b9z1x8f375C84+ZFfWfGOqGsfvhJ+c71t7v5nHXadLlm4cVSXtbzPzKcD4RsLh5dNWsOe+QcKd36uOw54X+ladKFaoqKCEJWGUrrCiFkrYtU2UDJhOzru16TB978nTy77R/ywvZ14giS2I/Dh31YjhhxpBw2dIocMnSyTKo5VMZXT1LWI4VyRwAhmzv2YV85CCEbdgaZ9OcIZb8g7uhyhHGPDHYFcZTQ7ZD27nbpckVwu08Y9who93rn/l557Apot95+Ae3U8+5NVN8V0FFCOvX6sULcqcMu6EyeDO4JEwFP8saehe706AnqAaV3ryx3r/cEeIKz0HtqxvnJm96foEn4em9t/+ueUHc/N8CZ4bH3+PuMkt6+nxby7vG+MaA6L+dsYefYgvaONA+tV90I9bIm4HxD7elL1mRdhwL6CGgTsk7LsT/ur2+M3FZGyOaWfzarV756swx+7ippHj9L6k6+I5tSUfciZJWhtK4QQta6SJUNFE/IOme53v3aHXL/G/eKsyPW/+HsbP3o6Oly9Ojj3F+njTpGnB+/5cNOAghZO3NVMRVCVgVFO2tUDyruO7LA+SZerCDeL6C9XczejuJeEdzp27Hs2wHtCmfnNZ+A3r9LumdXs1u7syPqyJQu52CN3jdJdN8A0ndcifeGkD3Hb0S/OWTPtT0HmLivO3/uPRrE/0aSzjEhXc51vdf2veYd5+E7nqTfG1D29uassX+9mGNbeus4T0vfcSq+I1i842GcV91rfMeT9N3jzeG93nfESe8Vsa/7j1fxH1XiHbniOxImlTXdI1J6+3Ouj2Xk7zN6Dt8xL/4+RBD/dv71wVSWEOi+GrEe5ii1Clnnx//vWv2YLJw/O2pHaZiBZNIbQjYTauG4p6juVRl5/3HSVVIt27+8tfd7rdn3hpDNnqGtFRCytiab/Vx+Iev8aO1tL/1U/uf55eKcDet8OMcKnD5uhnxy7BnykVEflQlDDsl+USoYQwAha0xUgTeKkA0cuTEL+oWsMU3TaCAEwnyGrLez23/++X7ZvF8Mx57T3SeTe3W5X1C79j/mTHX/6/4zyD3ZPvA9/QV1lMD2ifaoc9xj+hhQ3iedQ8+jUlxUIOWlRbJ3H29crodwsFW/cOQZwS7IamkR0CZknbNZ5y+6SdZv2By3oamHT5Bbly6QmuqqtBoO48UI2TCmknpPo+8eK5HWD+SDs5+W9uFHp37jAFciZJVgtLIIQtbKWJUM5QnZHz6xXH687kdS2/yBW/dzh8ySr0z9mhw/5gQl61DETAIIWTNzC6JrhGwQlM1cAyFrZm5BdB1mIRvE/KyRmABnyNr1dHCGbLjz1CZkwz222u4Qsmp5Bl1tyFNzpWLTXbL3I1dL41H/pWR5hKwSjFYWQchaGWvWQzm7J/7wxiq5cd21srmu5xuZp449U771iR/I5KFHZF2fAuYTQMian6GuCRCyusiaXxcha36GuiZAyOoia35dhKz5GfonQMiGO0+ErIJ8ELIKIOawRPnmlVLz5MXSNuoTUvuZR5V0gpBVgtHKIrqFrPNjXnHPP/Odm+a+7jsrre88Nt+ZYP4zxfq/3nvmWO85cM6PeSU67837cbKoM8p6z2fzzjHr/ektK/NOZahdLR/I8md+KG/s3uBePn3MifKtj1/rng3LBwQ8AghZnoVEBBCyPBuJCCBkeTYSEUDI8mwkIoCQtevZQMiGO0+tQra5pU2uXna7/PHxtXLAqGGy4vorZMyo4e7nph8zRWbOOCncdFLsDiGbIqiQXhZp+UBGrxwrUlAk2y7YJt1Fg7LuFCGbHcKGtr3S0tkiLR3N0trR6r5ZQGtHi7R29vze+bzzuvtn9/PO53qu8e7peb33872/b3feXKJXTMa+iYHzZ/9ZVP43kPCEY/Tr+980wn3TBt8bTEQL0d7rPCEq3c6borpvrOF/s4eevva/AYSzPu+OnN1zZNrdRww/Um4480dyZM3JprVOvwEQQMgGANnQJRCyhgYXQNsI2QAgG7oEQtbQ4AJoGyEbAOQAl0DIBgg7g6W0CtkbV6yScQeNls+cOl2W3bpSLph5ukwcO0bWvbRR7n1wjVyz8GIr3uwLIZvBkxeyW0Y88DEpqn9Ldp3xB3enbLYf+SBkG9oapLljn/uGQ03tTT2/djRJU1vPn503JdrXvk+aO5qksbWh98+9r/Xe09Tec41zbc/ve968iI/sCZQVlktBQYG4/1dQIBHHAvf+3vlcpCDS85r3Oe/Pvfe4r/vuL5De6/te76kbdX/3/s/1uz+2vlOv7/6IO3DPn71fY+p3Fzgv7F/PN4u/D/+MUfNFXe+uFjNf7599M6SyXsGAfbmruOsk6+uwYVPks5O+IKOHlcu2Xc3ZPwBUsI4AQta6SJUNhJBVhtK6QghZ6yJVNhBCVhlK6wohZO2KFCEb7jy1CVnnTb0WX3ebLLx0trsr1i9kN23ZKstuWSlLrprLm3qF+/nIm+6qXl4qVS9+X5rHfkHqPvmbrOc2Qcj+q+Fd2bFvm2zb97776+6mXeJI1iZPrPaKUleY+qVre5P2nZuVxZVSWlgmpUVlPb8WlkpZcbn7+7Ki0t7POb/3XneuLZXy4gopjTjXRn/eva+wXEoKS9zdqT2SzCcE/YKyV57FCkX3z72yzqmw//UegegJTk/iRaKE4/7Xi4siMqSiRHY3dkQJUef+/dJOfPUL3Hn5sJ+A96ZeCFn7s85kQoRsJtTy4x6EbH7knMmUCNlMqOXHPQjZ/Mg5kykRsplQC+89CNnwZuN0lhMhyw7ZcD8U+dhdYdM2GbVqknRHimTH7Helq6Q6Kwy5FrJv1r0u/2rYItsa35ftjnRtcH7dKtsbt7rydVdLbVbzOTdXFA2SiuIKqSiulIqiCqkoGSSDigf1ft55zflzZc/nnGuKK9w/99zT87pTo+f1nmurSgZn3VfYC+g+Qzbs89NfYgIIWZ6OgQggZHk+EhFAyPJsJCKAkOXZSEQAIcuzkYgAQtauZwMhG+48tQlZZ+zVDz8pa59/TRZ/8wL579vvc48sGDqkSuYvuklmnXMKZ8iG+9nIu+6GPXKOlG59XOpO+bU0j/tiVvMHIWTfqd8k7+x9W97cvUHe2bNZ3q5/SzbveUve27slpd5HVoyWMVUHysiKUTJ60BgZVXlAj1jtlaPlRRWuIHV2ofZ8bpCU9/7qiFQ+MiOAkM2MWz7chZDNh5QznxEhmzk72+9EyNqecObzIWQzZ2f7nQhZ2xPOfD6EbObswngnQjaMqezvSauQdZZxdsPOuWxpFIU7bl4kx06bHG4yaXTHGbJpwArxpeVbHpCaJ2ZLx+BDZOfMl7PqVJWQfa9hi2ypf1s21b3h/uq8C/s79T3ydaCPMZUHyvghE+WAyg+5stX554DKnl9HDTrA/TwfuSGAkM0NdxNWRciakFLuekTI5o592FdGyIY9odz1h5DNHfuwr4yQDXtCuesPIZs79jpWRsjqoKqupnYhq67V8FZCyIY3m7Q66+6SUb8/Qgobt8ju0+6VloPOSut2/8WZCNm36t6QZ7Y+LU+/t0Y27n5V3ti9ccD1R5SPlAlDDnHF6/ghk+SQoZNlbPV4mTz0iIz75kb9BBCy+hmbugJC1tTkgukbIRsMZxNXQciamFowPSNkg+Fs4ioIWRNTC6ZnhGwwnINaBSEbFOnM1tEqZG9csUq279wt1yy8WMrLStwOm1va5Oplt8v0Y6ZwZEFmmXFXCgQq7vmtVC39vrScOUPql96Ywh09l1S8/nMZ8s9vStuoT0jtZx5N+b7YC1MRss5u16ffXyNr//W0/P39NbKnpa7fetWlQ2RSzWGuaJ1Yc6iMr54o46onyKFDDxfnSAE+zCOAkDUvs6A6RsgGRdrMdRCyZuYWRNcI2SAom7kGQtbM3ILoGiEbBGUz10DImplboq4RsuHOU5uQ9cTreeec0u94At7UK9wPhQ3dVd74Ixl83TXSduzxUvunJ1IeqaCzTUbdM04ibXuk9uynpG34MSnf678wnpDd194oT777uDzx7qPyxJZHZGvjv6JqH1JzmBw58mg5atTR7q/OTtd8eJOrjAAbfBNC1uDwNLeOkNUM2PDyCFnDA9TYPkJWI1zDSyNkDQ9QY/sIWY1wDS+NkDU8wJj2EbLhzlObkK2rb5DF190mCy+dLRPHjomisGnLVll2y0pZctVcqamuCjehFLrjyIIUIAV8iSdku8srZNt7tWmtXvXSdVL10g+kedxMqTvlzrTu9S72hOzT7zwna7Y8Ko+/82d5Ztvfo2odO/pjcsaEs+To0ce6ApY3ysoItXE3IWSNiyywhhGygaE2ciGErJGxBdI0QjYQzEYugpA1MrZAmkbIBoLZyEUQskbGlrBphGy489QmZNkhG+7gbe/OE7LOnDueXS+dEyamPHKkdY+MWjVRCjpbZccXX5XOynEp3+tcuKulVn7+8o/lntfukh37tkfde+rYM2XGpM/JmePPlqFlw9Kqy8V2EEDI2pGjjikQsjqo2lMTIWtPlqonQciqJmpPPYSsPVmqngQhq5qoPfUQsvZk6UyCkA13ntqErDO2czTB4iW3yYrrr+jbJevsjp135XK59KJzOUM23M+G0d35hezuX/5WWs75XFrzVK9dIIM2rpB9k78u9dNTO4P2vYYtcvOzS2Tlhl/3rVVZXCmnj5shn5n0WfnkwWfIoOLKtPrgYvsIIGTty1TVRAhZVSTtrIOQtTNXFVMhZFVQtLMGQtbOXFVMhZBVQdHOGghZu3JFyIY7T61C1hndE7DbduzqI3HHzYv6nSsbbkwDd8eRBeFLzy9kG/5zsTQs+k5aTRbu2yKj7j1CugtLZcesTdJVOiTh/fWte2T5Mz+UX7zyP33XnHLwaTLvo1+Xk8aclda6XGw/AYSs/RlnOiFCNlNy+XEfQjY/cs5kSoRsJtTy4x6EbH7knMmUCNlMqOXHPQhZu3JGyIY7T+1CNtzjq+kOIauGo8oqfiHb8umzZPed96ZdvmbNhVL+zmrZ+5GrpfGo/4p7/y0v3CQ/fX6ZOFLW+ZgzdZ58/ejL5NDhE6SsuFDqGtvSXpcb7CaAkLU732ymQ8hmQ8/+exGy9mec6YQI2UzJ2X8fQtb+jDOdECGbKTn770PI2pUxQjbceSJkFeSDkFUAUXEJv5DtPOhg2fHixrRXKN79sox44GPSMfgQqT3rb1G7ZO9/815Z+o+r5d2Gd9y6pxz8Kbn2pBtkwpBD3D97b+qFkE0bu/U3IGStjzjjARGyGaPLixsRsnkRc0ZDImQzwpYXNyFk8yLmjIZEyGaELS9uQsjaFTNCNtx5ahWydfUNMn/RTbJ+w+Z+FKYePkFuXbpAaqqrwk0ohe4QsilACvgSv5B1lt72Xq10l1ek3cXQJ74sZVv+IE2TviJ7TviZvLhjnXzrbwvk5Z0vuLUOqTlMln7yJzJ9zIlRtRGyaaPOmxsQsnkTddqDImTTRpZXNyBk8yrutIZFyKaFK68uRsjmVdxpDYuQTQtXXl2MkLUrboRsuPPUKmRvXLHKnf7yebPCTSHL7hCyWQLUcHuskK194BFp+/gJaa9U1LBJRv5+qnvf3A99SX7++j3u74eXj5BFH/++nH/4RXFrImTTRp03NyBk8ybqtAdFyKaNLK9uQMjmVdxpDYuQTQtXXl2MkM2ruNMaFiGbFq68uhgha1fcCNlw56lNyDq7Yxdfd5ssvHS2TBw7JtwUsuwOIZslQA23xwrZ+iXLZd/c+RmttPfJefJvr/5GnusSGVxS7Z4T+/+OXSgVRYMS1kPIZoQ6L25CyOZFzBkNiZDNCFve3ISQzZuo0x4UIZs2sry5ASGbN1GnPShCNm1keXMDQtauqBGy4c4TIasgH4SsAoiKS8QK2aYL58iem29Je5UtezfL539/uuzYt12OjIismnyuVJ16d9I6CNmkiPL2AoRs3kafdHCEbFJEeX0BQjav4x9weIQsz0YiAghZno1EBBCyPBuJCCBk7Xo2ELLhzlObkHXGdo4sGHfQaJk546RwU8iyO4RslgA13F518zKp+sHV0nb8x6XkmX9I20eOkdpHn0prpc173pQvrD5TdjZtl48O/7Csad0og7o7pO6Td0rz2JkD1kLIpoU6ry5GyOZV3GkNi5BNC1feXYyQzbvIUx4YIZsyqry7ECGbd5GnPDBCNmVUeXchQtauyBGy4c5Tq5DdtGWr3LX6MVk4f7aUl5WEm0QW3SFks4Cn6VZPyO67ZJ4M+sUKd5WttU0pr7bJkbG//5R80LxTTjjwFPnVOb+X4RtulcHPfVu6i6tk5+eel85BByash5BNGXXeXYiQzbvIUx4YIZsyqry8ECGbl7GnNDRCNiVMeXkRQjYvY09paIRsSpjy8iKErF2xI2TDnac2IeucITt/0U2yfsPmuASmHj5Bbl26QGqqq8JNKIXuELIpQAr4kqqbb5CqH3xXGhZcKRW/WymF770rO9e+LB2TDknayRu7N8gXVp8hu1t2yZnjz5b//cxdUhQpFpFuGfanM6V0x9PSNuI4qT3rCRFxFEr/D4RsUsx5ewFCNm+jTzh4QWuLdJeWuX+bjB5WLtt2NQMJAv0IIGR5KBIRQMjybCQigJDl2UhEACHLs5GIAELWrmcDIRvuPLUJ2XCPrbY7hKxaniqq+YVs8WuvSunfnpDdK++T1hMGPj7jzbrX5bO/O0X2ttbLFw47X37yqV9EtVPYvENG/OEYibTulvqP/1T2HXoxQlZFYHlUAyGbR2GnMGrhzh0y/NSPS8Pi70rzBRchZFNglq+XIGTzNfnkcyNkkzPK1ysQsvmafPK5EbLJGeXrFQhZu5JHyIY7T4SsgnwQsgogKi7hF7JSWipVS6+Vxn//huy9blnClRwJ+5lVJ8g79Zvk/Clz5IZT478JWNn7f5Ghj37erbPrUw9K64dO61eTHbKKA7WoHELWojAVjOII2VFTxruVOiYeIkVLfihbTz1bQWVK2EYAIWtbourmQciqY2lbJYSsbYmqmwchq46lbZUQsnYlipANd57ahey6lzbKnMuWRlG44+ZFcuy0yeEmk0Z3CNk0YAV0adWPl0vVtd9xjyxoO+U0GXbumdJ8zuel7pd3Jezg/z16sax+faV8ePhR8pfZ/xyw08pXlsngF66W7sJBUnvOGmkfckTU9QjZgII2cBmErIGhaWzZL2S9ZdqnHS17r/6htJ54ssaVKW0aAYSsaYkF1y9CNjjWpq2EkDUtseD6RcgGx9q0lRCypiU2cL8I2XDnqVXIOjJ2+YpVUWfFOm/0Ne/K5XLpRefKzBkD//h4uNHt7w4hG76kKm/8kQy+7hppXHClNCy8SkYfeqAUNDbKjtfels6Ro/o1/M/3n5Iv3nemDCqulDUXvCBjKhO/YZd38+BnrpTKDT91/7j71Huk5eBz+uoiZMP3TISlI4RsWJIIRx+RHdtl9BET4jbTevInZe81S6T9w0eGo1m6yCkBhGxO8Yd6cYRsqOPJaXMI2ZziD/XiCNlQx5PT5hCyOcWvfHGErHKkSgtqE7LNLW1y9bLb5bxzTum3G9YRtfc+uEauWXixlJeVKB0oF8UQsrmgPvCa/iMLGr71PRnyja9JxT2/lb1LbpDGuZdG3dzR1S6n/vajsmnPm/L9E2+QS46Kfn2glYY8/XWpeOvX7iV7Tvi5NE36svt7hGz4nomwdISQDUsS4ejD2yHbNWKk7NjwjnuGbMPS5VK5/EcSqf3AbXLfVy52z5dtO+bYcDRNFzkhgJDNCXYjFkXIGhFTTppEyOYEuxGLImSNiCknTSJkc4Jd26IIWW1olRTWJmTr6htk8XW3ycJLZ8vEsWOimnV2yS67ZaUsuWqu1FRXKRkkl0UQsrmkH3/tWCFb9qeHZOi/zZLWj50gux58JOqmHz/3I7l+7TUyeegR8sj5a6WwoDCtgaqe/45UrV/u3lN//I2y7/CvI2TTIphfFyNk8yvvZNPGE7LbdjVLQdM+qbzlJ1L53zdJwb5Gt0x3VZV79Erzly6Q9sMmS9fwEcnK87pFBBCyFoWpeBSErGKgFpVDyFoUpuJRELKKgVpUDiFrUZgigpANd57ahCw7ZMMdvO3dxQpZZ94Dxo50xcb2De+IsxvN+Xh379ty8p1HS1tXqzw862k5auTRGaEZtOFnUv3MFY4ykYapV0jHx6+TsuJCqWtsy6geN9lLACFrb7aZTJZIyHq1Irt3y6A775Dyu38tRW++EbVEx6GHSesnTpK2E06S1hNOlq5hwzNpgXsMIYCQNSSoHLSJkM0BdEOWRMgaElQO2kTI5gC6IUsiZA0JKsU2EbIpgsrRZdqErDPP6oeflFUPruEM2RyFm8/L+t/UyzmywPmomXuRlN93r9Tf+FP3R4Cdj/Pu+7T84/0n5fwpc+SGU2/JCln52/dKzZOXiHR3SOuhF0rXGb+Uusb2rGpys30EELL2ZZrNRMmErL928SsvSdlD90vJs/+UkufWSUFLc7SgPWyytE+ZKt0lxdJ52BR3F23HIYdKx4RJ2bTIvSEhgJANSRAhbAMhG8JQQtISQjYkQYSwDYRsCEMJSUsI2ZAEoagNhKwikJrKaBWyTs/OebFzLlsa1f4dNy/qd66spvkCKcuRBYFgTmuReDtkyx9YLTUXXyjOG+Xs+v0f5aG37pN5f75ABpdWyzNf2ej+mu1H6fuPy9C/zpaCzn3SefCZUnvcT6Sz8qBsy3K/RQQQshaFqWCUdIRs7HLF61+WknXPSPGLz0vJ889K0Ruvx+3I2UnbObznpwLcj8KIdFcNlq7qaukaPES6a2rc4xC6qof0fn6I+1r34MHu6101NQompUS2BBCy2RK0936ErL3ZZjsZQjZbgvbej5C1N9tsJ0PIZkswXPcjZMOVR2w32oVsuMdX0x1CVg1HlVXiCVnnTMYDDu45c/HtjZtk+gOfkJ1N22XZqf8jX57yVWXLl9Q+L8MePVcKWndLd1Gl1B+/TJoOuUhZfQqZTQAha3Z+qrvPRsj2+xf6vkYpef45KX79NSl88w0pemOjK2mdNbL96B5U2SNwq6ulY+Ih0nH4EdmW5P40CQwqL5Kmlk7p7u5O804ut4lA99Ch/d6cFCFrU8JqZ0HIquVpUzWErE1pqp0FIauWZ66rIWRzncDA62sVsjeuWCXbd+6WaxZeLOVlJW4n3tmy04+ZIjNnnBRuOil2h5BNEVSAl8UTss7yNRfNlvI/PiDLb7hA/rPxLvnw8KPkL7P/qbyzQa1bpOrxiySy81m3dstBZ8meT9wiXWW8CY9y2IYVRMgaFpjmdlUK2YFajdR+IJG99RKpr5eCxkaJ7Nnd83vnn4a9EtlTJwX1eySyd2/v5/dIxPl8/R4paGjQTIHyEIBAqgQ6xk2Qnc+9GnU5QjZVevl3HUI2/zJPdWKEbKqk8u86hKxdmSNkw52nNiHLm3qFO3jbu0skZMt/v0pq5s2Rw/5rkLxR178PEAAAIABJREFUvk9uOfNXcu4h5ynHUV5a6L6pV8c/rpOqF77r1u8qrZG6k38jrWNOVb4eBc0hgJA1J6sgOg1KyGY7iytv9/YK2731UtDU1PNPc7MUNDu/9vxe2ngjw2xZJ7qfHbK6yJpRN1JXJ4N+fqsgZM3IKyxdImTDkkT4+kDIhi+TsHSEkA1LEmr6QMiq4airijYhW1ffIIuvu00WXjpbJo4dE9X/pi1bZdktK2XJVXOlprpK12yB1WWHbGCoU16o8sYfyeDrrpHGBVfK3t439XJudnaGvXvKh2T6nHY5uPJg+eecjSnXTOdCT8jWNbZJ0Z7XZcjTXxPnKAPno33oNGmYdpW0HHx2OiW51hICCFlLglQ0RmTHdhl9xATpGjlKdrz2toweVi7bdkW/WZeipShjOAHOkDU8wCzbL9y8SUYdN1U6x0+QHevYIZslzry5HSGbN1GnPShCNm1keXMDQtauqBGy4c5Tm5Blh2y4g7e9u6ofL5eqa78jDQuulAafkHXmXnLV4fLTMVtkccHp8h/feEALCr+Q9RYY9PrPpfLFH0phS895johZLehDXxQhG/qIAm3QlB2ygUJhsbgEELL5/WAUvb1JRh47lR2y+f0YpD09QjZtZHlzA0I2b6JOe1CEbNrIQn0DQjbU8Yg2IeuMve6ljbJ4yW2y4vor+nbJOrtj5125XC696FzOkA33s2F0d4mOLOiWbpl26wFS27lX1m/8jAz96e+1zBlPyDoLFXS1S8Wbv5LKV5ZJ4b73esTssKOl4SPflpYDP62lF4qGiwBCNlx55LobhGyuEzBnfYSsOVnp6BQhq4Oq/TURsvZnnOmECNlMydl/H0LWrowRsuHOU6uQdUb3BOy2Hbv6SNxx8yI5dtrkcJNJozuOLEgDVkCXVt28TKp+cHW/HbJPvfdXmX3/2XLkriJ5+b87ZNfqh6X1pFOUd5VIyPYt1NUhg976tVS+cr0UNr7rfrpt+DHS6IjZD52pvB8KhocAQjY8WYShE4RsGFIwoweErBk56eoSIauLrN11EbJ255vNdAjZbOjZfS9C1q58EbLhzlO7kA33+Gq6Q8iq4aiySqIzZK/463xZ+dqv5NsVn5drr7xPOg6bLDufXCdSWKhyeUkqZH2ruUcZrL+hT8y2D/uINE+6wN0x21E1QWlfFMs9AYRs7jMIUwecIRumNMLdC0I23Pno7o4zZHUTtrM+QtbOXFVMhZBVQdHOGghZu3JFyIY7T4SsgnwQsgogKi4RT8h2dLXLlNs+JPvaG2XdnDfkqE+fK8UbN8ieG34iTXO+prSDdISst3DFW7+Wqhd/IIX7/tXXS9vwj0rL+C9K08TzpatshNIeKZYbAgjZ3HAP66oI2bAmE76+ELLhyyTIjhCyQdK2Zy2ErD1Zqp4EIauaqD31ELL2ZOlMgpANd54IWQX5IGQVQFRcIp6Q/dPmB+RrD8+WI0d8RP70pb9L6d+fkmHnnildQ4bIjhdfl+6qKmVdZCJkvcUHvXmHlL95p5Ts/EdUP60HnCItE2ZJ07gvSndxpbJeKRQsAYRssLzDvhpCNuwJhac/hGx4sshFJwjZXFA3f02ErPkZ6poAIauLrPl1EbLmZ+ifACEb7jwRsgryQcgqgKi4RDwhO+/PF8pDb62Wb3/ihzL/IwvcFYfN/ryUPvYXafx/l8veq3+grItshKzXRGHTNinfvErK314lxbtejOqt+eDPStOUb0hXaY2013xYWd8U0k8AIaufsUkrIGRNSiu3vSJkc8s/16sjZHOdgJnrI2TNzC2IrhGyQVA2cw2ErJm5JeoaIRvuPBGyCvJByCqAqLhErJB1jimY+vODpbWzxT2uYEzlge6KRZvfkpHTp0l3YaHsfHa9dB50sJJOVAhZfyNFDZuk/O3fSfmmu6Wo/o2oHrsLy903BGt3/zna/ZWzZ5XEqKUIQlYLVmOLImSNjS7wxhGygSMP1YII2VDFYUwzCFljogq8UYRs4MiNWRAha0xUKTWKkE0JU84uQsgqQI+QVQBRcYlYIXvvxrvkssfmytGjjpUHz/tb1GpDFnxDKn7zS2k+d6bU/eJOJZ2oFrL+porr1kvZuw9KyY5/SvGuFyTSWtevZ3fn7LCjpW3Eca6kdX7lDFol0WZdBCGbNUKrCiBkrYpT6zAIWa14Q18cIRv6iELZIEI2lLGEoimEbChiCGUTCNlQxpJxUwjZjNEFciNCVgFmhKwCiIpLVN18g1T94LvSsOBKafjW92TOQ1+UR995WK458Xr52lH/EbVa4c4dMvLoKVLQ0iw7//GidBx6WNbd6BSysc0VNr4jJbXPS/EHz0lx7QtSsutFKeho7DdDZ8WH3J20HcM/6v7aNuKj0l2s7tzcrKHlSQGEbJ4EneKYzt8/o6aMl64RI2XHhndk9LBy2barOcW7uSyfCCBk8ynt/rMWvb1JRh47VTrGTZCdz70adcGwwaXS2Nwure1d+Q2J6fsRQMjyUCQigJDl2UhEACFr17OBkA13nghZBfkgZBVAVFyi6uZlUvWDq/uE7GErRkpje6O8ePFmGVkxut9qnsDtGDtePvjbM9Jdmd2bZgUpZOOhK97zf1Jc+5IU1z4nxbtekpIPnolLuKNqYs9RByOOkeaxM6Vz0IcUJ0G5WAIIWZ4JPwGELM9DqgQQsqmSsvM6hKydueqeCiGrm7C59RGy5manu3OErG7CwdZHyAbLO93VELLpEotzPUJWAUTFJfw7ZJ/9+hfl9LuPk0k1h8rfLngp4UrDzzxZSp5fJ01f/ors+cnPsuoo10I2rqR1ds/WPidFjqDd9ZIU747PwjmTtqNqnHRWjpeOwZOkc/BY6ayaKB2V46Sj+tCsuHCzCEKWpwAhyzOQCQGEbCbU7LkHIWtPlkFOgpANkrZZayFkzcoryG4RskHS1r8WQlY/42xWQMhmQ6/3XoSsAoiKS/iF7M9nTpDLH/+6fHHyBfLj029LuFLhu+/IiE+dJJFdtbLvq3OlftmPM+4qjEI23jAlO5+Rkl3PSdEHz0vxng1StHdT3OMO/Pc6Rx84bxrWWTlOOqsnSEfleOkcPMGVuF2lwzNmli83ImTzJenU5mSHbGqcuEoEIZvfTwFCNr/zz3R6hGym5Oy/DyFrf8aZToiQzZRcOO9DyIYzF68rhKyCfBCyCiAqLuF/U69vnrhXfvnKz+R7J1wvc6dFnx8bu2zxxg0y/NMnS0FjozRc+S33n0w+TBGy8WaLtO6Sooa3pbBhsxQ1bpHC+k3inFNb1LBZCvf9a0AcbSOmS3ekeP81BQXSXVQpXSVV0l08WLpKh4oUDer98/9v707AJCnrPI//IjPr7G66ups+OHrk0uUYEUFmWkcUxEEO2Zllp/uBxxsEhBlGAUGQYZBBBWHxeEbFHkYG5wHEdpbVVRFFRpeBsQEPFBUYOW2gOfqqru66Mitjn/eNiKyo7Ky8KjIzIvKbPPVkVeQb7/H5B12Zv4qMXOjd9y5Uscc8vkDFXtMm3aEugWwz/0eldx8+1Cu9tY16ZQSyUYsmqz8+1CtZ9YrLbAlk41KJ+M2DQDZ+NYnLjAhk41KJaOZBIBuNY6t6IZCNQJZANgLEiLsIB7LHHHivfrZxvf7tf/xAb9zrqJoj9T60Xkv+8kQ5E+Pa9oUbNPqu99Xcp7xBkgPZaot1inllTUhrAtrtXmibHXnaBrjmq9KHiTWMJ8nN9PsB7UK5vQv8wHY3G9jaYNcEuH1DXpue3eSaINdsM/emTc7cL5ScTDPDt3QfAtmW8iaucwLZxJWsYxMmkO0YfSwGJpCNRRkSNwkC2cSVrG0TJpBtG3XiBiKQTVzJqk6YQDbe9SSQjaA+BLIRIEbcRXDJguHzL9IeS76kscKonvjQJg3kBusaqf/uu7T4tFNs2+HPfE47zzi7rv2CRmkNZGshOFNjykxul5PfLmdyRJnCDmUmtsnJj8gpbPcemxz2HgvaFXYqM7FVmcKInEnTZlutYep+3FwPNxzaTix7oz0jd9ZbJic322+/lOv3guFcn79tUG6213vMtgm2D/ht6ju2CGTrLl9XNOSSBV1R5kgWSSAbCWNiO+GSBYktXUcnTiDbUf5YD04gG+vydHRyBLId5Y98cALZyEkj7ZBANgJOAtkIECPuIghkf3bhGTpywVf1qoX76j/f89uGRhn85u0aOud0u8+O887XyCWXy+3rr6uPbg1k68Kpo5FjQloT4prgNj8sJ7/TBrUm6M34Ya8X7JqfR/ztO+VMbvX3G7btOnkzYa49Q9fJyPXv5WTtz042p6LrKPjZlbddjiNlsnJlvg+2Zaf3V1ZuJue1k9dWMv0HbUPf+326GW8O3tnCQV+hvu1YGa8vc4kJ01d4fLvdH8cfT36f0/P25mvXadq43r1r5mnHLptnMG8zTqn/Tlarc2Nntm3RovedpqKW6KUHNmjFkgFt3DzWuQkxcmwFCGRjW5q2TIxAti3MqRuEQDZ1JY1sQQSykVGmriMC2XSVlEA23vUkkI2gPgSyESBG3EUQyP7zxe/UmYPf1Un7/6X+6YTbGh5l4I51WnTW++1+hQNera1f+RflDzu8Zj8EsjWJ2tLAXELBOyvXBLvb5RRGZc7itV+FCTnFcakwLmdqwm5TwTzmbXfs9nFpyrv3vkw7c++1s/vatn5fbVkVg6RSYEdGL53xpJbtvQ+BbCoLPPdFEcjO3TDJPRDIJrl6nZs7gWzn7OM+MoFs3CvUufkRyHbOvhUjE8i2QjW6PglkI7AkkI0AMeIuFnz+Oi345BU679Ij9cW+h3Txqiv04Td8rKlR+u67V4s++B5lNr1i9x/58IUaufyqqn0RyDZFnZqdbJCrouQW5RS9e2nK3vdkilo4mNXmYdNmSo55rGgecyXX/9nu67V3/PvSz+axUJ92/6Ct7acoOdN9lvYPxgrGU3nfrjcXf562TzNOsWDXMj2P8Dz98Yr+vEP7e/Py52b3D+bkbXNCa7Rr79Kbk59U71MPSENSfsnhyr37fm0c7l6PLj0M6lo2gWxdTKltRCCb2tK2dGEEsi3lTXTnBLKJLl9LJ08g21LetndOINt28oYGJJBtiKtyYwLZCBAj7iL4UK+3/N1K/Udug/71nXfo2H2Ob3qUzPCwdvv4hRr8hneWbf7Ag7Rt7c3KH/Lain0SyDZNnfoduYZs6kvc0ALth3qt2k+6MCPNL8p9zWptfNPXGuqDxt0hQCDbHXWebZV8qFd317/Z1RPINiuX/v0IZNNf42ZXSCDbrFw89yOQjWddglkRyEZQHwLZCBAj7iIIZAev6NGYk9cvPvCkls/bY86j9N/zQy388DnKvrhRyuU0cv7FGrnwEvt9+EYgO2fq1HZAIJva0ja1MBvIHrKf3EOWSB/0Lqmx/Yh/0I7XfrSp/tgpvQIEsumtbT0rI5CtR4k25QIEshwTswkQyHJszCZAIJuuY4NANt71JJCNoD4EshEgRtyFuYbsy1/+ex3wt9LSgWV6+IxnIhshs327drv8Yxq81TuLbeKot2rnOX+r8eNOKI1BIBsZd+o6IpBNXUnntKDsyy9p+cH7qrh0mYbvvkGLfrRakqvNx31bE3u+fU59s3O6BAhk01XPRlfDJQsaFaO9ESCQ5TggkOUYaFSAQLZRsXi3J5CNd30IZCOoD4FsBIgRd2EC2bv+z99rzWrpmFcdp1tO/lbEI0h9P75HQ+ed5Z0tay5j8LrXa/gzn9PkG/5EBLKRc6emQwLZ1JQykoWEA9mXHn1GK575ipyfXCA3N1+vvPNeFYYOjGQcOkm+AIFs8ms4lxUQyM5Fr3v3JZDt3trXWjlnyNYS6t7HCWTTVXsC2XjXk0A2gvoQyEaAGHEX5kO9Pr3+Cl3zZum8Iy7SJW+8MuIRvO6c8THNu/mfNe8fP6fsSy/abVPLV2jy3e+Vc/oZ2rJ8ZUvGpdPkChDIJrd2rZj5LoHskgGNfvcszXv8Rjvc5nd8XxN7vLUVQ9NnwgQIZBNWsIinSyAbMWiXdEcg2yWFbmKZBLJNoHXJLgSy6So0gWy860kgG0F9CGQjQIy4CxPI/tWzV+iH+0tfOf4WnXzAKRGPsGt3g7ffqsFbblbv+vtLD+YPO1xja07T6Jp3qTg01PI5MED8BQhk41+jds6wUiC7cfOYFt+zWv0bvmenMvymL2rna05v57QYK4YCBLIxLEobp0Qg20bsFA1FIJuiYka8FALZiEFT1B2BbIqKKYlANt71JJCNoD4EshEgRtzFgi9cr5X5yzXcL9337ke079D+EY8we3fZDX/QwjtuV9/tt8r5/e9LDSeOOVaF/Q7QxLHH2evOugODbZsTA8VHgEA2PrWIw0xmC2TN3IbuO0eDT3xNbqZfo69+t0Ze/wkV+xfHYdrMoQMCBLIdQI/RkASyMSpGgqZCIJugYrV5qgSybQZP0HAEsgkqVh1TJZCtA6mDTQhkI8AnkI0AMeIuhr/w9zo4+7804PboifOGI+69dnfBNWR3/r/7NbDuNg38728os23bjB0njn6bRt/3QU2tWKH8Hx9KQFubNRUtCGRTUcbIFlEtkDWDLPjFP2jBr6+x4xV7hzRyxFXa+d/OiGx8OkqOAIFscmrVipkSyLZCNf19Esimv8bNrpBAtlm59O9HIJuuGhPIxrueBLIR1IdANgLEiLv46RfO0l9lb9GbCyv1jY88HnHvtbur9KFe/ff8UL333K3+u++SeWFVfssfdIjyh75O+de/QeZSB+bDwbilT4BANn01ncuKagWypu+eLb/Swv88T72bfmaHyi95vba96Yv2nlv3CBDIdk+tK62UQLa769/s6glkm5VLxn7O1Lj5c63kmi/Jsff+l2Pu3ZnbzGP+9sHejHKOq5HRSbuPY/txQ/15/ZS2m339sbxtyTBilo0L9OQcDfTltH1nvvGd2SNeAo605ODj4jUnZjNDgEB2rgfEe9+rzf99tSaOeXvTPW2fGNamsZe1eXyTNu18WZvGXvG+Rl/WptFXtHVis6aK5peg+T1ZlCtXRbco+5/52XXtdrsteFxmu/eYt927N/u6/n7Bvt79zH2Dbd7+0/tO2F/8ybmdNXm4rrjgvrZPuFIgG55E9g/PqP/uH6jn5w+q5zePqOd3v6k4R3Pm7ORhh6tw+Bvsff7Qw9q+FgaMVoBANlrPpPdWTyAbrHHwya9rtwcvUWbiFbvJXFd25IhPqtjH9amTfhzUM38C2XqU0tuGQDa9tW3lypIayDpTY1KxIGcqL8fNS1OT3r3ZZn/OyylOSkXzeFEqTsgxbYp5yc3LmSpI7qTd32tjtnmPmb7sNtM26D/cJnjM3pu2Zkw/5AzCTxXlmPAyHICabUGoabd7j9t9nbK2wXabak6HqN44Zpu/bzFZr7taeSzTNwIINClwIX89aVKuLbsRyM6V2XFsD9s/da12nP03VXv76fP/oZ+/+IAefvnn2jD8jA1dX9z5wlxnwP5VBK4Zf5ve89Hvtt2oViBbaUI9j/xKPb/5tXK/+616fv2wen/1Czk7duzSdNKEs392lCbefrx9rLhwoab2WqniokVtXycDNi5AINu4WZr3aCSQNQ6Zye2a/8urNP/RL1mWwm6v1vief66xAz+g/NAhaabq+rURyHb3IUAg2931b2T19qxJEyIW89qtv6hCPq/x8TFpytumYii4LE55YaYJH/3AsnRv24ZCSRtgmoDS378UjnphqRd+BoFpKEC1/frhqGln5+aHoqExnamdjSyTtr6Auc687OvRjL13HXPvf8nbPmObfcyRY9pnMiq63s/ePo5cs932Nf3llvqffsz2yS2VAhlHymYd5QsEeWkocN+7703DMlK7BgLZuZb2tNOk22+3vYy+633a9oUbZvT4sxfX61v/tc5+bR3fUnG0/uyAls5bpmWDK7Sof7F2H1hqv188uES7DyzT0sHlyjpZu6/9fWn+czLKOBn7vbm335f9nJHZNt02Y3/5eu3t/v7jpf1D/YYf88aa3rcv2z9XtZbvbz7Ua8FVl2vk/Is1ctknWj5e+QDNBLKVJpnd8Kx6/IC25+FfqOfR3yr7h2crrscdnKepvfe24Wxh75WafOsxKi5dXmrrDgzY0LY4tJjwtu1HxPSABLIdxI/h0I0GssESctse08IHL1LfC/eUVpVffJhGDzxTO1/zgRiulCnNVYBAdq6Cyd6fQDY59XMKO+QUxuRMjcrJjylT2Cl7xufUuJwpcyanuTcB5bhkfzaB6LhUMNu9x2xbE5QWzGPePjYINdtNO/8xL0w128xj6Qo03dx8uZmc5PTIzfZImR65md6Z25xe/7GcXKdHyvZ695mc3e46vZK997dlem0/tp25t32G7oOx/HvvsT7z4ssLKm0IOR1glraVwks/AC0FmqGg07Sx4WdZ0Fm23QtPzYs+byy3Ra+7uIZscv5NafdMuYZsu8VbOx7XkG2t71x7J5Cdq6Ckkb+7Ugs+5YV+439+vH56yRm6Y/QBG8I+N/KH0ggL+4b0jv3eqdctO0KHLn29dh9cqiUDSzWvZ34Es6CLsEBaAtlKVXV27lDvrx9W7sknlHn6SfU8/piyzzyl3NNPy5mo/61N5sxaE866JqQNgtqhIRUXBdsWqzjkPeYu9O6nlq/gQJujAIHsHAFTtnuzgex0MPu45j12gwZ/f4t98R/cCkMHamL5UZpc8WZNLn+zpgb3SJlc9y2HQLb7ah5eMYFsNPX3wtJR+5Uxoan53gSn/jYToIZ/lglT/W2ZoI1tb8LS6b6C8NUGqzG4udl5crM5OX6AaYNMG1h6waWb7fWCThs45mzQOSOcLIWYfphpfrZtvYAzCEm9oNMPTG046geodpvps887O9MPUyuFo958gn7if9JHDMobyRQIZCNhTGUnBLLpKiuBbLzrSSBbR33uuPNeXX7tTbblSceu0pUXna6B/t7SnuZDvfp/cKc2fey9+ptjRnX3/jM7fef+p2j1Qe/S2/c5oY7RaBKFQJoD2Wo+2ec2KPf0U8o98V/KPP+cMls2K7NtmzLbtiizdasy27Yqs3VLxUsh1OvuDgx6Ae7CIRUXL1FxaEiuH9xOHPsO+/an8ps5O9ecwVucN09u8NXXnU+6CWTrPdK6o91cA9lAycnv0OCTt2ngydvU+8qDu+BNzf8jTSz/M+VXHKWJpavkuAXlF/1xdyCnZJUEsikpZJPL6IZA1vw7FoShmbwflE75oakJQ822UoA6JhOW2nZ2W9DOnI06Ia+v6W2ZyW1Nyje+m5sdkJszX4PeV9bcm4DUBJb9crN99suGlbl+mbec2/AyN+Bv65NbesyEmv1yc2Yf05cJRvsk2485y9N/zNxXOMEjbteQtScOmM/FMNdJLbpySt9PX3PVPG6vzxp+zH6WRln7ornOqteudD3Xsv5s/8G24Pqspr3dZq77NfPx0riV+gntX3H+psNS3/XPv2Rgr4Ub2Pjfl88vZBesfcb6Aze/3Wx9m3XmzMm7blH5fHANW9+3vCbWNzQvv3betW65pVGASxakq6p993PJgjhXlEC2RnUeevgxXb92nW645nwtWrhAn127zu5xwdlrZgSydz9zp879/ns0at6SJOnYp6R3PSKt/q2UPWm1xlafqvHjCGTb9T9DtwayjfhmNm/yQtqtW7yg1g9uHXO/ebMcE+Ka74eHvWDXtNuyuZEharZ1FyxQcdCEtPPlDg7Knb9Abi4r9ZizJXJSLic3l7NndCiXLX1vt5nHzHbT1uzjtzc/2zNAbJvsdD/+dq9Pr32pn/IxcqbP0BimfTBeaE62TU9Obv9AzbUGDQhk66bqioZRBbLlWL0vP6DeTQ+q56UH1LP5l8rteLqip7kGbWHhazS559HKLzq01MacLVXsW6xi/yIV+3bvilrEfZEEsnGvUGvn1+lA1gSc3lvvvbfhe8GpCTxD20JnkCq/0z8Ddef02/dtcGrC0pEZ29oflvpBqQlNs4MqmiAz26+iDVC9bTZA7ZlnQ9IZ2/yg1Ws7KE1l5bo9kpuzX26xR04hL+ULcvKTUj4vJ5+XCnk5hSlpctJuL23LF7zHTBvzWLCvvfe32X4K/mOh/ib9fkNjaKooZ8pcF9YL2bLmrfbFolwzdqVwz24LBZv+fuXBYCnY9EPHUvAY3reBd2m19v8WekcAAQQQmH5Szx9P4nw0EMjWqI4JYPdZuUKnnPgW27I8oDXbPvaDT+ja9Vfax49aeYzWHn+rVtx1jwZv+Zr6fvyj0gjmTMKdZ56r4u5L7ZOqqd2XaWqvvVRcsYcK++wX5+MkcXMjkG1dyZyRkdAZt9uU2eqfhbt1qzQyrMzOnXLM1+iozOUVnLExZXaMyBkNtu+0QW833FxzFrA5Y9h+OXL97zPZrH39Y7YH20rtnPA2Z7qNfcvf9Fdpv+CDGExfWe9a096HO5h7X9m2CbZVuve2eR/aEN5/lv1m6cvuX/5YMIlac/CHnjGHOuZcPl7FOdQcuwS1q0NVk5Cv71bRMChGhb7M/yvzv/KPKi5dppcefUYrlgxo42bvD3tR3jIT29S76SH1vPyAel55SD3Djyq787m6h3B7FqjYu8QPaBep2LtYxT4T1i6Ra0Jb/+eJPd5qgwxu0Qt0YyBrr5tZ+tRy75PHS2dqhT+5PLzd/3Rye/aW453VZfcpbTff+mfbzfj08+lPNrf7hD8tvfQJ6cH26Otbq8fsxuc19KHTNbViT21b+y8zmu82r0djE4VZP4Alt+13yoy9UtrHO3M0OHs0FKpW2JaZHK41tcge984U7ZfreGeNyjFvd++Tqx5J3n0Qfrpur5yiCUCzNhRVISNNZaRCVm7Bsd+7E66cSUmTkpt35Uy4fvhZkIJQ1ISZpQDVDzgrBKM2MLX7FOzzGW7NC9jnRub3of/cyH6QlPk+2BZ8uFR4W/h7TT+f8vbxnnt4fYT7CT+H8scLP2cK+rRN5J8YAAAZXklEQVSXffWfX5U+FCuY33R/9vd7hTFcM37Z/ErP70r7TO9b6qe0zyzzDz3nK9mY51TBc8fQ2kvb/Menff0P6iqtdXqdfX05ZbIZjZozZMOPB5YzalLBt8I74po/KtgzTgI9OUcDfTlt35mP07SYSzMCjrTk5OOa2ZN92iRAIFsFemx8Uldcd5NWHXFwKZB98tkXdNnVN+pTl56p/V+1p079t1P1jd9+w/Zy7uEX6LI3fXJGj9nnn9Pgv96kwdtvkfm+2q24eLGm9thLU3vupak99lRx75X23mwLzgKc/NM3tenQSPYwBLLJqJ8JZm1Q64e3GfMiZ9J8Uq85Y8T7Cr63Z5aYTwi2Z5oUvO9tmynvPtjHvLiy3095bf3tQRvbz4z9Q2OYM1VK/ZaNEZ6THdc724UXZsk41uI+y1YHspXWb85wy217XD3bHld2x1M2sMlMbFVmYov9csz3k1sUdSCTX/w6FXt2i3tJYje/3lxG+aliQ+8SnRFEBoFkEF6Gg8sgsFTRRB1eYBm8HdX/3vYVBJNl+5b2se8B9vefEZ5Ob4/LNTZjV+C4T2jKDz+LJvAMws+MlHfkmkDUhJ95yZ2UF3xO+gHoeFGaLMoZLUjm+52TNiCVeZ1ffh93gwrzs+GieaeMeReOeXdN6N7t3XWbbZvr8Z7X9/SW9i1tKz2Wk3r7bDuv3wpjhPu37xYybXMz/gA8f6BHBTkaz7szQ08/WJwRhPrBYmlb+R+Cw4GkHxZ64eJ0eGk9uCVCgGvIJqJMHZkk15DtCHvLBuUasi2jjaRjAtk6AtnVJx+tIw870LYsD2SdKx3N752v2/7nbTr5NSdXL8p990lPPy298IL0/PPel/l+wwbve27RC1x2mfTJmSF59IPQIwIVBMb966QFbxGsdh++5lc97WdrY/oJvsyUSoGKv718W/BzuF0r92vXOElc1/z50kc/Gt//lcY2S+Nbpr+Cnye2SuHH8qNSwXx5nx5uvwr+vf1++oPH4rtYZhYrAfMJ4/bs8ulPNren/wdnwgXfh7fZTycPt4lyX9Nv1p+T/Sj06bmEx61nPo3su31Euu0277qX4S/7712Fr/Lt4aIWKgSilULSYFurTpIy/+71mlDSCygrfjXzeJ+5xqp3+aOW9G/mzQ0BBBBAAAEEEJijAIFsFcB6zpD9zP2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SYSTEM TIMEABYcaption
00.0000005.000000100.0000000.000000Initial state
10.0002504.00000098.0000001.000000
20.0005003.21650096.4330001.783500
30.0006252.90676995.8135382.093231
40.0008002.51759195.0351822.482409
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1120.1245641.8761464.25998547.870007
1130.1319432.1108054.72930447.635348
1140.1422742.2699945.04768247.476159
1150.1567372.3175285.14274947.428625
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" ], "text/plain": [ " SYSTEM TIME A B Y caption\n", "0 0.000000 5.000000 100.000000 0.000000 Initial state\n", "1 0.000250 4.000000 98.000000 1.000000 \n", "2 0.000500 3.216500 96.433000 1.783500 \n", "3 0.000625 2.906769 95.813538 2.093231 \n", "4 0.000800 2.517591 95.035182 2.482409 \n", ".. ... ... ... ... ...\n", "112 0.124564 1.876146 4.259985 47.870007 \n", "113 0.131943 2.110805 4.729304 47.635348 \n", "114 0.142274 2.269994 5.047682 47.476159 \n", "115 0.156737 2.317528 5.142749 47.428625 \n", "116 0.176984 2.307597 5.122887 47.438557 \n", "\n", "[117 rows x 5 columns]" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "code", "execution_count": 27, "id": "c3afbcc8-bdae-4938-a3f1-ce00d62816f2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: A + 2 B <-> Y\n", "Final concentrations: [A] = 2.308 ; [B] = 5.123 ; [Y] = 47.44\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.01289\n", " Formula used: [Y] / ([A][B])\n", "2. Ratio of forward/reverse reaction rates: 4.0\n", "Discrepancy between the two values: 0.3221 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that the reaction has reached equilibrium\n", "dynamics.is_in_equilibrium()" ] }, { "cell_type": "markdown", "id": "92c82a23-3c8e-4cff-9efc-7cd708f0f9ad", "metadata": {}, "source": [ "#### As expected, even the complete withdrawal of A (red), brings about only a modest increase of B's concentration, from the reverse reaction (i.e. [B] slightly increases at the expense of [Y].) \n", "#### The change is modest because our reaction A + 2 B <-> Y is mostly in the forward direction (K = 4)\n", "*Le Chatelier's principle* in action: \"A change in one of the variables that describe a system at equilibrium produces a shift in the position of the equilibrium that counteracts the effect of this change.\"" ] }, { "cell_type": "code", "execution_count": null, "id": "48a86d59", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "jupytext": { "formats": "ipynb,py:percent" }, "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }