{ "cells": [ { "cell_type": "markdown", "id": "3bbe8002-bdf3-490c-bde0-80dd3713a3d0", "metadata": {}, "source": [ "## `A <-> B` , downregulated by the \"shunt\" (coupled reaction) `A <-> S`\n", "### _Kinetic_ advantage (downregulation in early phase) vs. _Thermodynamic_ advantage (long-term downregulation) \n", "\n", "**[Scenario 1](#down_regulate_1_scenario_1)** : No downregulation on `A <-> B `\n", "\n", "**[Scenario 2](#down_regulate_1_scenario_2)** : The shunt (`A <-> S`) has a *kinetic* advantage but *thermodynamic* DIS-advantage compared to `A <-> B ` \n", "(i.e. `A <-> S` is fast, but energetically unfavored) \n", "\n", "**[Scenario 3](#down_regulate_1_scenario_3)** : The shunt (`A <-> S`) is has a *kinetic* DIS-advantage but a *thermodynamic* advantage compared to `A <-> B` \n", "(i.e. `A <-> S` is slow, but energetically favored) \n", "\n", "All reactions 1st order, mostly forward. Taken to equilibrium.\n", "\n", "LAST REVISED: July 14, 2023" ] }, { "cell_type": "markdown", "id": "61171e99-518e-4019-a731-be7437e95dfd", "metadata": {}, "source": [ "## Bathtub analogy:\n", "A is initially full, while B and S are empty. \n", "If the \"shunt\" S is present, scenario 2 corresponds to a large pipe and a small elevation change... \n", "while scenario 3 corresponds to a narrow pipe and a large elevation change." ] }, { "cell_type": "markdown", "id": "832afe37-f169-41c8-a719-e739336bc5cf", "metadata": {}, "source": [ "![Downregulated by shunt](../../docs/down_regulate_1.png)" ] }, { "cell_type": "code", "execution_count": 1, "id": "c4231a63-e456-48e9-bf4f-d074bbd3490a", "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": "64933384", "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", "import plotly.express as px\n", "from src.modules.visualization.graphic_log import GraphicLog" ] }, { "cell_type": "code", "execution_count": 3, "id": "83c3cc5f-de21-4f66-9988-2806fbf0666d", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-> Output will be LOGGED into the file 'down_regulate_1.log.htm'\n" ] } ], "source": [ "# Initialize the HTML logging (for the graphics)\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_1\"],\n", " extra_js=\"https://cdnjs.cloudflare.com/ajax/libs/cytoscape/3.21.2/cytoscape.umd.js\")" ] }, { "cell_type": "code", "execution_count": null, "id": "001bc666-f2ef-40a3-b46f-30b087ea33da", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "35b5ef15-69da-4fc9-b1e9-fd34a9bafb99", "metadata": {}, "source": [ "# Scenario 1: A <-> B in the absence of the 2nd reaction" ] }, { "cell_type": "markdown", "id": "9329208b-070f-4902-8f37-0f11ddf75ed6", "metadata": {}, "source": [ "### Initialize the System\n", "Specify the chemicals and the reaction" ] }, { "cell_type": "code", "execution_count": 4, "id": "57d8431c-d6d0-462c-af78-e64eeb220e2e", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 1 (at temp. 25 C)\n", "0: A <-> B (kF = 30 / kR = 5 / Delta_G = -4,441.69 / K = 6) | 1st order in all reactants & products\n" ] } ], "source": [ "# Specify the chemicals\n", "chem_data = chem(names=[\"A\", \"B\"])\n", "\n", "# Reaction A <-> B\n", "chem_data.add_reaction(reactants=[\"A\"], products=[\"B\"],\n", " forward_rate=30., reverse_rate=5.)\n", "\n", "chem_data.describe_reactions()" ] }, { "cell_type": "markdown", "id": "f5eabdf2-0e6b-4141-a886-10974dfc6c3a", "metadata": {}, "source": [ "### Set the initial concentrations of all the chemicals, in their index order" ] }, { "cell_type": "code", "execution_count": 5, "id": "67a0375f-a14f-4cbe-965b-81d4c841aeab", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "2 species:\n", " Species 0 (A). Conc: 50.0\n", " Species 1 (B). Conc: 0.0\n" ] } ], "source": [ "dynamics = ReactionDynamics(chem_data=chem_data)\n", "dynamics.set_conc([50., 0.], snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "markdown", "id": "72a2148e-1aae-4ed7-bab3-5781b3a80fb0", "metadata": {}, "source": [ "### Run the reaction" ] }, { "cell_type": "code", "execution_count": 6, "id": "89f23b49-2840-4517-a275-b6a4f97898af", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "49 total step(s) taken\n" ] } ], "source": [ "dynamics.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n", "\n", "# 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=0.08, high=0.5, abort=1.5)\n", "dynamics.set_step_factors(upshift=1.5, downshift=0.5, abort=0.5)\n", "dynamics.set_error_step_factor(0.5)\n", "\n", "# The changes of concentrations vary very rapidly early on; automated variable timesteps will take care of that\n", "dynamics.single_compartment_react(initial_step=0.001, reaction_duration=0.3,\n", " snapshots={\"initial_caption\": \"1st reaction step\",\n", " \"final_caption\": \"last reaction step\"},\n", " variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 7, "id": "80fbaee3-bd6f-4197-9270-23374d46a4a7", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABcaption
00.00000050.0000000.000000Initial state
10.00100048.5000001.5000001st reaction step
20.00150047.7762502.223750
30.00200047.0651662.934834
40.00250046.3665253.633475
50.00300045.6801114.319889
60.00350045.0057094.994291
70.00400044.3431095.656891
80.00450043.6921056.307895
90.00500043.0524936.947507
100.00550042.4240747.575926
110.00600041.8066538.193347
120.00650041.2000378.799963
130.00725040.3060369.693964
140.00800039.43550210.564498
150.00875038.58782011.412180
160.00950037.76239012.237610
170.01062536.55674613.443254
180.01175035.39857414.601426
190.01287534.28600515.713995
200.01400033.21724416.782756
210.01512532.19056517.809435
220.01625031.20431118.795689
230.01793829.78318220.216818
240.01878129.11458520.885415
250.02004728.14130621.858694
260.02194526.74605723.253943
270.02384425.44351624.556484
280.02574224.22752325.772477
290.02764123.09232726.907673
300.02953922.03256027.967440
310.03143821.04320928.956791
320.03428519.65778930.342211
330.03713318.41045131.589549
340.03998017.28743332.712567
350.04282816.27634433.723656
360.04567615.36602834.633972
370.04994714.13664835.863352
380.05421913.09106236.908938
390.05849012.20179437.798206
400.06489711.06731338.932687
410.07130510.18724239.812758
420.0809169.16317440.836826
430.0905268.48358141.516419
440.1049437.80709342.192907
450.1265677.30436442.695636
460.1590047.12100842.878992
470.2076587.15821542.841785
480.2806417.11898542.881015
490.3901147.21045242.789548last reaction step
\n", "
" ], "text/plain": [ " SYSTEM TIME A B caption\n", "0 0.000000 50.000000 0.000000 Initial state\n", "1 0.001000 48.500000 1.500000 1st reaction step\n", "2 0.001500 47.776250 2.223750 \n", "3 0.002000 47.065166 2.934834 \n", "4 0.002500 46.366525 3.633475 \n", "5 0.003000 45.680111 4.319889 \n", "6 0.003500 45.005709 4.994291 \n", "7 0.004000 44.343109 5.656891 \n", "8 0.004500 43.692105 6.307895 \n", "9 0.005000 43.052493 6.947507 \n", "10 0.005500 42.424074 7.575926 \n", "11 0.006000 41.806653 8.193347 \n", "12 0.006500 41.200037 8.799963 \n", "13 0.007250 40.306036 9.693964 \n", "14 0.008000 39.435502 10.564498 \n", "15 0.008750 38.587820 11.412180 \n", "16 0.009500 37.762390 12.237610 \n", "17 0.010625 36.556746 13.443254 \n", "18 0.011750 35.398574 14.601426 \n", "19 0.012875 34.286005 15.713995 \n", "20 0.014000 33.217244 16.782756 \n", "21 0.015125 32.190565 17.809435 \n", "22 0.016250 31.204311 18.795689 \n", "23 0.017938 29.783182 20.216818 \n", "24 0.018781 29.114585 20.885415 \n", "25 0.020047 28.141306 21.858694 \n", "26 0.021945 26.746057 23.253943 \n", "27 0.023844 25.443516 24.556484 \n", "28 0.025742 24.227523 25.772477 \n", "29 0.027641 23.092327 26.907673 \n", "30 0.029539 22.032560 27.967440 \n", "31 0.031438 21.043209 28.956791 \n", "32 0.034285 19.657789 30.342211 \n", "33 0.037133 18.410451 31.589549 \n", "34 0.039980 17.287433 32.712567 \n", "35 0.042828 16.276344 33.723656 \n", "36 0.045676 15.366028 34.633972 \n", "37 0.049947 14.136648 35.863352 \n", "38 0.054219 13.091062 36.908938 \n", "39 0.058490 12.201794 37.798206 \n", "40 0.064897 11.067313 38.932687 \n", "41 0.071305 10.187242 39.812758 \n", "42 0.080916 9.163174 40.836826 \n", "43 0.090526 8.483581 41.516419 \n", "44 0.104943 7.807093 42.192907 \n", "45 0.126567 7.304364 42.695636 \n", "46 0.159004 7.121008 42.878992 \n", "47 0.207658 7.158215 42.841785 \n", "48 0.280641 7.118985 42.881015 \n", "49 0.390114 7.210452 42.789548 last reaction step" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "code", "execution_count": 8, "id": "4fa4035f-00eb-4cc7-a0ff-835bcc8baf52", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "From time 0 to 0.001, in 1 step of 0.001\n", "From time 0.001 to 0.0065, in 11 steps of 0.0005\n", "From time 0.0065 to 0.0095, in 4 steps of 0.00075\n", "From time 0.0095 to 0.01625, in 6 steps of 0.00113\n", "From time 0.01625 to 0.01794, in 1 step of 0.00169\n", "From time 0.01794 to 0.01878, in 1 step of 0.000844\n", "From time 0.01878 to 0.02005, in 1 step of 0.00127\n", "From time 0.02005 to 0.03144, in 6 steps of 0.0019\n", "From time 0.03144 to 0.04568, in 5 steps of 0.00285\n", "From time 0.04568 to 0.05849, in 3 steps of 0.00427\n", "From time 0.05849 to 0.0713, in 2 steps of 0.00641\n", "From time 0.0713 to 0.09053, in 2 steps of 0.00961\n", "From time 0.09053 to 0.1049, in 1 step of 0.0144\n", "From time 0.1049 to 0.1266, in 1 step of 0.0216\n", "From time 0.1266 to 0.159, in 1 step of 0.0324\n", "From time 0.159 to 0.2077, in 1 step of 0.0487\n", "From time 0.2077 to 0.2806, in 1 step of 0.073\n", "From time 0.2806 to 0.3901, in 1 step of 0.109\n", "(49 steps total)\n" ] } ], "source": [ "dynamics.explain_time_advance()" ] }, { "cell_type": "code", "execution_count": 9, "id": "09c03e23-0dd8-4ba0-a5b7-119f5662f23b", "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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"white", "zerolinewidth": 2 } } }, "title": { "text": "Single reaction A <-> B (no downregulation) (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.00023643288814660275, 0.39035069833004116 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ -2.7777777777777777, 52.77777777777778 ], "title": { "text": "concentration" }, "type": "linear" } } }, "image/png": 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ZswV0rMi6nV/hzYZeIBkI99d4O3NVjfPX/M3hN5Mcfyc8Vr5k/QmSv100EGt9W30XCbSzu8uQduPJrapHt4ltsjrugo0hqyesgeIEuhKu8w/044PvSZ2dOdIFY3LtFtMnN4gTdOP8db0/Vk9MZeyfdrY92HEr0GrwgeamiruHjHXt7ON28mGVq5nUWfmhLdh4trNd4cp6sL4EO/aI+mKqQvvUZoWK+u6T/qTH6jEg0I9TvryMc+X1TgX7wU+Us7MtZt+1vtti93ijM6tUvgwG9etUsOCaeN93/nqw751wuAYT6GCybudYEWy/1GVd9MlsnnWod8VY5WO1f4H2EyvnEcGOmVbO9Xz7sCRtPcT3t34Xhj7G/T15xiqTYMcEfk4CJBD7BGJK1v3NndO/zNZs2nHJSq/GW67sHMDNyhpvGwu2IrD+i6vZ49R8V2b2HYbBTvj0LwHf269EvbHvTMWTj9wFs9vR/c2RNpNaX6kPdHLm+wVvFk/fpppVKxf8IBLohDHQ1TAjr2BSKOsLU9/+3p2vt/XcVH27RZ+DzSUPdjgKdNJmNg0kULxA3KzKuvEHAt9VjsUts1auupnlx9/cQNFn4yrCgX6M8Rcj0LxDq1IpY/8UJ3x2t91sJXxx+6bxOOC7n5qNGX/HATv7uL7vWsmHVa7G8RpIsM3GdaDxbGe7wpV14z4R6PhsPOE3bo/Z2DLLYaDjmtXvHjNmZsc5s3JWjs9Wt0XV8UbfFsHXuAK8v/dFOTt98Xd8lX1l3TimjMdUs2NZsPMW/Thttk+Y1bWz71oZd8GOR1amVsiWdX/nj/p4EP8VCxKajY1A+6HVuw2Cfe/zcxIggdgnEFOybvzS8k1doGd465JkR9aNv5rqizKJX1XFQlVPjv0gpOesi5hW5lAHkwGzvuk8jF92vvMFRdv6s7N9bwHWT76Nz8P19wxrvS2Zz1n3FVkrJ4NWBNoKy2g5DJjN/zT23cqJjl4+2EmGlStdeizj3QdWx7ivmImF6/SX2JfFratmC8r5rk/gbzqBv7Hh70cjffz7W7Xc6gJz+jYYf9gLlCPfOZD+tt3qvmx2Imu1rtnxNdg+biUfdk74RR+CTfcw21+D/Sjny9nfdsmQdavHZ3/HHd/9SZQz+34zsvf9XvHdXrP90t88Y9/jiNlxx+odQla2xa4gWz3e+NvXA/3IZ7cvZjlUIetm+6a/Y4XvsUfk6uUnh+GpsR/AeBu82Rjxzb3dfdfKuDM7HolpQ2JtkUitBi946ndR6jn0PZaJ983m8BvPkfydz8XSeUe0nB+xnyQQzQRiTtadTobdKz5O95ftk4AZgVCEiCQjQ8DKGhKR6YkzrQQTb45nOXkJdleSnFYYhQSKHgErFxuKHhVuMQmQgD8ClPUQx4aQmfETv8BdA7oWzJE3m+8dYnhWIwHHCViZd+p4J2O4A4L/1BnzMXLE7dqzs8XL35XdGMZQaNPCuSLF8WxvlFDW7fFiaRKwQoDHISuUWIYESMBIgLIe4njwd8uxnVuNQ2ya1UggYgT0W//8PX4mYh0pgg2Z3SJsZZpMrKLSeRhXCre7rRzP1olR1q2zYkkSsEJAvysolKe9WInPMiRAArFJgLIem3nlVpEACZAACZAACZAACZAACZAACUQxAcp6FCePXScBEiABEiABEiABEiABEiABEohNApT12Mwrt4oESIAESIAESIAESIAESIAESCCKCVDWozh57DoJkAAJkAAJkAAJkAAJkAAJkEBsEqCsx2ZeuVUkQAIkQAIkQAIkQAIkQAIkQAJRTICyHsXJY9dJgARIgARIgARIgARIgARIgARikwBlPTbzyq0iARIgARIgARIgARIgARIgARKIYgKU9ShOHrtOAiRAAiRAAiRAAiRAAiRAAiQQmwQo67GZV24VCZAACZAACZAACZAACZAACZBAFBOgrEdx8th1EiABEiABEiABEiABEiABEiCB2CRAWY/NvHKrSIAESIAESIAESIAESIAESIAEopgAZT2Kk8eukwAJkAAJkAAJkAAJkAAJkAAJxCYBynps5pVbRQIkQAIkQAIkQAIkQAIkQAIkEMUEKOtRnDx2nQRIgARIgARIgARIgARIgARIIDYJUNZjM6/cKhIgARIgARIgARIgARIgARIggSgmQFmP4uSx6yRAAiRAAiRAAiRAAiRAAiRAArFJgLIem3nlVpEACZAACZAACZAACZAACZAACUQxAcp6FCePXScBEiABEiABEiABEiABEiABEohNApT12Mwrt4oESIAESIAESIAESIAESIAESCCKCVDWozh57DoJkAAJkAAJkAAJkAAJkAAJkEBsEqCsx2ZeuVUkQAIkQAIkQAIkQAIkQAIkQAJRTICyHsXJY9dJgARIgARIgARIgARIgARIgARikwBlPTbzyq0iARIgARIgARIgARIgARIgARKIYgKU9ShOHrtOAiRAAiRAAiRAAiRAAiRAAiQQmwQo67GZV24VCZAACZAACZAACZAACZAACZBAFBOgrEdx8th1EiABEiABEiABEiABEiABEiCB2CRAWY/NvHKrSIAESIAESIAESIAESIAESIAEopgAZT2Kk8eukwAJkAAJkAAJkAAJkAAJkAAJxCYBynps5pVbRQIkQAIkQAIkQAIkQAIkQAIkEMUEKOtRnDx2nQRIgARIgARIgARIgARIgARIIDYJUNZjM6/cKhIgARIgARIgARIgARIgARIggSgmQFmP4uSx6yRAAiRAAiRAAiRAAiRAAiRAArFJgLIem3nlVpEACZAACZAACZAACZAACZAACUQxAcp6FCePXScBEiABEiABEiABEiABEiABEohNApT12Mwrt4oESIAESIAESIAESIAESIAESCCKCVDWozh57DoJkAAJkAAJkAAJkAAJkAAJkEBsEqCsx2ZeuVUkQAIkQAIkQAIkQAIkQAIkQAJRTICyHsXJY9dJgARIgARIgARIgARIgARIgARikwBlPTbzyq0iARIgARIgARIgARIgARIgARKIYgKU9ShOHrtOAiRAAiRAAiRAAiRAAiRAAiQQmwQo67GZV24VCZAACZAACZAACZAACZAACZBAFBOgrEdx8th1EiABEiABEiABEiABEiABEiCB2CRAWY/NvHKrSIAESIAESIAESIAESIAESIAEopgAZT2Kk8eukwAJkAAJkAAJkAAJkAAJkAAJxCYBynps5pVbRQIkQAIkQAIkQAIkQAIkQAIkEMUEKOtRnDx2nQRIgARIgARIgARIgARIgARIIDYJUNZjM6/cKhIgARIgARIgARIgARIgARIggSgmQFmXkLyMTC8yzp6XEIkhVBAoluhBqeKJOH4qW0V4xpREoEyJROTm5eF0pldSRIZRQeCyssVw8sx5nPfmqgjPmBIIxMUBVcoXx6H0TAnRGEIVgeSkeJQoFo/0jHOqmmBcCQTKlkyENycPZ7L43SQBp7IQlcslIz0jW8sVX/IIVK1YXF4wRgqJAGU9JGyFKwlRF8LOlzsJUNbdmRffXlHWoyNPlHX354my7v4ciR5S1qMjT5T16MgTZV1NnijrarjaiUpZt0PLT1nKugSICkNQ1hXClRiasi4RpsJQlHWFcCWFpqxLAqk4DGVdMWBJ4SnrkkAqDkNZVwOYsq6Gq52olHU7tEzKjhkzBn8b+RQmTXwX8fEJSExMRHxCAjweDzyeeHg8cYiLi0Nubh7ECVRubi5ycnK0z4sXL4FqNetgVdpSNLomBeLGnc0b12LgnUOwcd0qJCYloU69+vjhuxkYNHgovpk+BaltO+Nk+jEcOXwQ7Tr1wEcTXsPQv4zEonmzUK1mbVx1dWNkZ2Xiv1M+ROfufbU4vfoNxOIFc3BF1eqo37CJthXLFs1FhUqVtXbN/k5bthAlS5VBk5QW2ue+f69cvkTrX0rzVO1z3791VGtW/KRtV/NWbQrRW7tqObxeL1qmtiv0/sa1K3HmzGmktu1U6P1N61cj49RJtG7XpdD7gteJ9GNo06Gb30zu3vErjhzch9QOPf2W2bVjK3bv2o4uPfr5LbN392/YtnkDuvcZYGvUzJzxGVqmtkeVqtUt1zt65BCWL5mP/gPvtlwnWMHPJk9Ev1sHo1Sp0sGKWvrcd0xYqhSgkFVZ18f3PUMfDrfJiNa3MsYi2qEQG5Mp67O++gLXtroBVavVDLE3rGZGQIasT5vyAXr0vRVly5UnZEUEKOvAql+WId7jwbUtb1BEOfywlPXwGUYiAmVdPuUP3huH0aNHyw/MiLYIUNZt4bq0MGWdsh5sCFHWgxHK/5yybo2T06Uo605nIHj7lPXgjNxQgrJOWXfDOIyVPlDW5WeSsi6faSgRKeuhUDPUoaxT1oMNIcp6MEKUdWuE3FGKsu6OPATqBWXd/TkSPaSsU9ajY6RGRy8p6/LzRFmXzzSUiJT1UKj51OGcdQkQFYbgnHWFcCWGtnplXWKTDBUCAZmyHkLzrGKBgAxZt9AMi4RJgLIeJsAIVedt8BECHWYzlPUwAfqpzjnrarjaiUpZt0PLT1nKugSICkNQ1hXClRiasi4RpsJQlHWFcCWFpqxLAqk4DGVdMWBJ4SnrkkAqDkNZVwPYCVmfMXsJ0lZvxpiRQ1A8OUnNhkUg6ok/MjDiiTfx+PBBaJnSIOQWKesho8uvePw4sHa9F42a8TnrYaJUVp2yrgyt1MCUdak4lQWjrCtDKy0wZV0aSqWBKOtK8UoLTlmXhlJpIMq6GrwqZH3n3oMYPup1HDpyvKDTV1xeEZPGPY56tarCKVnPzDqH0eM/RpXKFfC34YPCBkpZDxuhnABizvonnzyHB//yJleDN6wOr9PlavAA56xb29esyjpXg7fGU1UpmbLO1eDVZEmGrHM1eDW5MUalrHPOuvpRVnRaoKzLz7WKOetCxJ8d9zEmv/VEoavNK9dtxZczF2lX0+csTOOVdUM6eWU9zLEtZP3550fjhRfeRMlS8Xx024VHuVHWLw4syrq1nYyybo2T06Uo605nIHj7lPXgjNxQgrJOWXfDOIyVPlDW5WdStqzrV9THPjks4G3h+pX1vt1aa7eRi5fxyru+pb5X6O+/o3fBFXEh/69PmoY/3dYTf3t+QqEY63/9TfvBQLyaNKyLia88hvJlS0O/sp7avBEG9G5fAFT/gUF/Q2/H7A6BF0YNKajLK+vyx2RIEXVZHzXqTVS5grKuP3edsk5Zt7tDUdbtEnOmPGXdGe52WqWs26HlXFnKOmXdudEXey1T1uXnVLasC+mdNnNRgRz767Eux0b5fmPSNBw+ml4wj12I8tNjP8BLTw7Tbp33vYVdyPp9j74C3xgffT77kvdEP8Rt72ay7ttnUeb/Zi3GLX064OCRY1iwdDX+PPhGbVN8f4ygrMsfkyFFPHcOqFYNOHYMmDotGx0754YUh5XUEeCcdXVsZUa2Kusy22Qs+wRkyrr91lnDCgEZsm6lHZYJjwBlPTx+karNOeuRIh1eO5T18Pj5qy1zzrqvcAeSdd8F5vQr5fpVcBGrdo0qha6AG8v8tvuAdmVdLy/a8o3h+15ysWLanHX9ynoosm3sVyj1zZjwNngJY3v0mBz84/l43NAmF19+ky0hIkPIJEBZl0lTXSzKujq2MiNT1mXSVBOLsq6Gq+yolHXZRNXEo6yr4So7KmVdNtH8eG6UdV2qZy1Iu2Sj9dvaZci6uFI+fsIXGPvUMO02ebOXfgXf+Jl+NZ+yrmZMhhT10NHzqF8vAadPx2H2/Gw0S+HV9ZBAKqpEWVcEVnJYyrpkoIrCUdYVgZUYlrIuEabCUJR1hXAlhqasS4SpMBRlXQ1cmbJu5zb4QFfWfa+A+5PocK+sB5N1cRV99sJfClaxF/0Q74mXuK2esq5mTNqOKuas/23kUxj/6nv442QCiiUnok7deHg8Hng84r9xiIuLQ25uHsQJVG5uLnJycrTPixcvgWo162BV2lI0uiYFeQA2b1yLgXcOwcZ1q5CYlIQ69erjh+/D9Yc3AAAgAElEQVRmYNDgofhm+hSktu2Mk+nHcOTwQbTr1AMfTXgNQ/8yEovmzUK1mrVx1dWNoa+W3bl7Xy1Or34DsXjBHFxRtTrqN2yibeOyRXNRoVJlrV2zv9OWLUTJUmXQJKWF9rnv3yuXL9H6p89R9/1bB8nV4LkavNWdyqqsczV4q0TVlJMp61wNXk2OZMg6V4NXkxtjVMo656yrH2VFpwXKuvxcy56zHmiBOeNccLPV4M1ug9elWJWsB5JtfX77wBs7Flosj7IufxyGHVGX9Ynvv4sDBxJxLjsJVzfwoHgJyrqAS1mnrFvdySjrVkk5W46y7ix/K61T1q1Qcr4MZZ2y7vwojJ0eUNbl51K2rIsemj26TZfimlUr+310m6+s67ef+66+/u8v5mDEvTdh09ZdYc9ZF/0V8r1i3dZCK8aLBeZ6d2mNV96dUuiZ7L6L2vHKuvwxGVJEXdYnTXwXJ04kIv14EsqUjUfdenG8sk5Z18YUH91mbdeirFvj5HQpyrrTGQjePmU9OCM3lKCsU9bdMA5jpQ+UdfmZVCHropdmjzwzrtquP7pNPHO9eHKStmFmi8MFenRasMXk9DnoxnL+bq8Xwi5WkddfvnPSN27ZpX0k3tdfvA1e/ngMK2LG2fPIyPRi1844tE9NRnw8sGJdFi6vIm5s58tpApyz7nQGrLVvVdatRWMpVQRkyrqqPhb1uDJkvagzjMT2U9YjQTn8NjhnPXyGkYhAWVdDWeacdTU9jP2oXA1eQo51WReh/vynJMyaGY+hw70Y89J5CdEZIlwClPVwCUamPmU9MpzDbYWyHi5B9fUp6+oZy2iBsi6DovoYlHX1jGW0QFmXQfHSGJR1NVztRKWs26Hlp6xR1tev86B312JITgbWbMpC2XK8ui4BcVghKOth4YtYZcp6xFCH1RBlPSx8EalMWY8I5rAboayHjTAiASjrEcEcdiOU9bARmgagrKvhaicqZd0OLZOyxjnr8fEJSExMxK6dSTh50oNq1T2oXQdcDR5A81ZtCtFbu2o5vF4vWqa2K/T+xrUrcebMaaS27VTo/U3rVyPj1Em0btel0Pti9fwT6cfQpkM3v5ncveNXHDm4D6kdevots2vHVuzetR1devTzW2bv7t+wbfMGdO8zwNao4Zx1a7isyjpXg7fGU1UpmbLO1eDVZEmGrHM1eDW5MUalrHPOuvpRVnRaoKzLz7WqOevyexrbESnrYebXTNbPnk3E1i3xiIuLR2rrPMQn8NFtlPX2qFK1uuXRdvTIISxfMh/9B95tuU6wgp9Nnoh+tw5GqVKlgxW19Lnv4/wsVQpQiLIeLsHI1KesR4ZzOK1Q1sOhF7m6lHXKeuRGW+y3RFmXn2PKunymoUSkrIdCzVDHTNbjExLw68YEZGQkoG5doEatPD5nnVfWKetB9jXKepgHowhVp6xHCHQYzVDWw4AXwaqUdcp6BIdbzDdFWZefYsq6fKahRKSsh0LNp45xzrr+0cxv4vHA/UnaivBiZfiEBAkNMURIBDhnPSRsEa9kVdYj3jE2WIiATFknWjUEZMi6mp4xqpEAZT06xgPnrEdHnijravLEOetquNqJSlm3Q8tPWTNZz80FbmiRjH2/x+GNd87htjtzJLTEEKEQoKyHQi3ydSjrkWceSouU9VCoRbYOZT2yvENtjbIeKrnI1qOsR5Z3qK1R1kMlF7geZV0NVztRKet2aNmQdVF0yifx+PvjSahbLw9L0rIgTqD4ijwBynrkmYfSImU9FGqRr0NZjzxzuy1S1u0Sc6Y8Zd0Z7nZbpazbJeZMecq6Gu6UdTVc7USlrNuhZVLW35x1j8ejLTCX9nMCzp+PQ+NrcnBZZTF3PRc5OTkQnxcvXgLVatbBqrSlaHRNCsRD3sTq5gPvHIKN61YhMSkJderVxw/fzcCgwUPxzfQpSG3bGSfTj+HI4YNo16kHPprwGob+ZSQWzZuFajVr46qrG0NfLbtz975anF79BmLxgjm4omp11G/YRNuKZYvmokKlylq7Zn/7Lh7m+/fK5Uu0/qU0T9Xq+/6to1qz4idtu7jAHBeYC7arWZV1rgYfjKTaz2XKOleDV5MrGbLO1eDV5MYYlbLOOevqR1nRaYGyLj/XnLMun2koESnroVAz1Akk6x5PPPbvi8eunR6ULpOL5i1yKesX2PHRbYEHHleD98+Hsh7mQSvM6pT1MAFGoDplPQKQJTRBWaesSxhGDHGBAGVd/lAoarK+ct1W3PfoK3hh1BAM6N1ePtAQI1LWQwSnVwsm63l5Hvy8zAMxh71pSi7Kls3hlXUAlHXKui8BXlkP82AUoeqU9QiBDqMZynoY8CJYlbJOWY/gcIv5pijr8lNc1GT9jUnTNIiHj6ZjzMghKJ6cJB9qCBEp6yFA861itsCcsczYFxLx3tsJaN8xF59Pz5bQIkPYIcA563ZoOVfWqqw710O2LAjIlHUSVUNAhqyr6RmjGglQ1qNjPHDOenTkibKuJk9FZc76iT8yMPadqXjg3v4Y9/7nGPng7ahXq6oaqDajUtZtAjMrHkzWjx2LQ7MGyShTNg9fTD+HZtfmSmiVIawSoKxbJeVsuViR9aycTGR7s5HlzUR2ThayxL/FezlZ8OZ44c31Igc5yM3NQU5eDnJyc5CXl6u9J/6dK/4t/otc7fNC5S68l5Obi1xRV3wuyot/53jz/5t3IV5BnIsxC+KJ9vMuTMspiONTruB9sdbGhb7mifU2cnE+JwfeHK3HFz4T/RHx8t8T/b/Yjwv91N7LLydYhPsqFp+shYgT/7uweqf4t/ZenP6v/H/nvwqXu6ROfiRD/Qv1DLGNdczbNNTPC1zfrJ/G9i/pc56/7by0z6JviQkenPfm+WFzoY7PNus8xWqoFwmGmynW90fA4wHi4+JwPkes7MKXWwkkxMchLw/IyWWe3Joj0a8kcczLydVyxZccAnc0uhePtLlfTjBDlL17gd27pYcNGrBWLaBOHfNi4hb4pb9swN+GD4K4wl67RhXX3ApPWQ+a2uAFgsm6iPD8M4n44J8JuD41FzO+49X14FTllaCsy2OpMpJsWT99/nS+MHuz8qU5J+viv71CosV7QqKztffz5TobmefPauXFv7POZ2r1fOsaY2pxvJnIOHdKJR7GJgESIAESIAESIIGIERiVOhqv9nheensvvQQ884z0sEEDPv008OKL5sWEoLe7vilapjSAEPfXJ03DxFceQ/mypYPGVV2Ash4m4WBz1j2e/Ksh57Lz8EtaPOLictCgkRflysVxNXivFy1T2xXKwMa1K3HmzGmktu1U6P1N61cj49RJtG7XpdD7YvX8E+nH0KZDN7+Z3L3jVxw5uA+pHXr6LbNrx1bs3rUdXXr081tm7+7fsG3zBnTvM8DWqJk54zO0TOVq8MGg6bK+6/h+nMhMx8nsdKRnHseJ7HSczDqB9MxjOJGVjoyzp9BsXyPMqvRDvmRrYn1Btr3ZOOs9E6wp5Z+XTiqD5PhkFEtIRnJCMsRV4LreuqiaVQWbKm1BfFw8PHHxF/7rQbzn4t/iM3HMEO+J/4mFKvPLXygn3tXeE0+c8Gifaf+PT7hYTo/vyf88Dvl1tTj6fy+8p8cVbWnxjOUQjwRPgvbYSb2/FUsXx5kscfUirqBt8ZnnQp/1cnqftfYu9Fm0Jf5fPKGElgO7q8GLPOdpz5cA8i5cPhF/X/x3fmrz/75YzrSO/nmh+hcuyeRpUQtiBW7zQjmthnl9rU8+/TT237TPcYG207jNxnIX+1KxdDEcO5VVmJNhm/U2zfsMbJ+3FrVaN0CxUsWV7y9FtYGkRA/Ej8kZZ71FFQGObNmnHe8qN6juWgYlk+ORkwtknctxbR/ZMaBcqSRknD2n5YovOQQ2fbUco0ePlhPMEGXKFOCjj6SHDRpw8GDgfpMbBXbuPYjxE77A2KeGaXIubokf8cSbeHz4IE3enX5R1sPMgFVZz83Nw77f47B3Tx5KlMhBs2uBEiX46DbKuvkAjIXV4P/IPokTWcc1wf7j3B9IP3sMJ7KPayKeLt43CPnJ7BOalJ85dzroHlkCJfAQHsI4jAtYVgihLsrJCcVRLKGYJtDJCSVQLD4J2nuaUIv38/+dnCg+L36hXL5k63XFv0XMpAt182X8Yl3xb11CzTpm5QehoBvvggIy56zblXUXbH5UdEHGnHU+uk19qjlnnQvMqR9lRacFzlmXn+uissDcjNlL8Oy4jy8BeP8dvbXb4p1+UdbDzIAdWRcXe1atALzeHNSqHYc6dYvzOeu8sm46At0q67+f2o1Dpw/g4OmDOLrpd2TEZWB/6YP5Qp51EulZ+Ve/hYyH+qqYXAnlksujfHJFlE+ugPLFK6B8sYqoUDz/77LxZXF0yV6k9GuL5MQLwh1frEC+Syc5f8sSZd1a9inr1jjZLUVZt0vMmfKUdcq6MyMvNlulrMvPa1GQ9cyscxg9/mOkNm9UaI6679V2+XStR6SsW2flt6SVOet65dnfxWPYfUkoWy4Pv6zNRunSXAlDQgoChuCcdWuE957ahYMZBzQZF/8/cHpfwb/F38cy/2ct0IVSJRNL5ct2wf8vyLdBwPNFPF/Ia5a/HKWTyuJ0ZtG9JdQWYIcKy7yy7tAmxHyzMmQ95iG5YAMp6y5IgoUucDV4C5BcUISyriYJsb4avJDyp8d+gJeeHFZo9Xdd4gfe2NHxW+Ep64axrSdGvGV8vp7x9og+XVIvefaeHVkXsQfcWAy/LPdg2ANePP/ieTV7F6MWEKCsA/87ewQ7T27H/lP7cPjMQRzIyBfxo2cPY9+pvZavhF9e8gpUK10DVUpWxRUlq6FKqSsKCXm5C+JduUQV2yNQ9gJztjvACpYIUNYtYXK0EGXdUfyWG6esW0blaEHKuqP4LTdOWbeMylbBWJd1WzAcKkxZvwBeF/VZC9JgFHLfFQHFaoHiZZzDYFfWt2/zoHPbYhCPbVmSloXadXh1XeX4L0qyvuePnfjtxHbsOLENO45vwc6TO7AtfbOllcqFgBeIeKlqqFq6GqqWqq79X/9MZZ4o6yrpyotNWZfHUlUkyroqsnLjUtbl8lQVjbKuiqzcuJR1uTz1aJR1NVztRKWsX6ClP1NP/Jm2enPB1XPfZ+35yrudOeviBCo3Nxc5OTnYvSsBe3aXRGKxumja5Ec0uiZFW6dXrG4+8M4h2LhuFRKTklCnXn388N0MDBo8FN9Mn4LUtp1xMv0Yjhw+iHadeuCjCa9h6F9GYtG8WahWszauuroxsrMy8d8pH6Jz975anF79BmLxgjm4omp11G/YRNviZYvmokKlylq7Zn+nLVuIkqXKoElKC+1z379XLl+i9S+lear2ue/f+iBcs+Inbbuat2pTaFyuXbUcXq4G73dfDTZn/ddjG7Qr5ULMtwspP7Edm49v9BuvREJJPJz7ELbX2IPLK1SBuEJetXR1VC1ZHVVKVdWE3O7Ld0zYre9b3qqs6+P7nqEPh9tkROtzgblLcXPOupohKEPWucCcmtwYo1LWOWdd/SgrOi1Q1uXnuijMWZdPTX5EyjoA49Vyccu7LusCt++iA75zG4SsPz7qKUya8C7iExKQkJCIhIQEeDweeOLjESce3Ya4gsfnCFnPzc1BjteDZUtLY9u2ehgwYCFSmufL+q8b1mLQ4CHYuLawrN9291B8PW0KWrfrrD2q7Mihg2jfpQc+eO81/PnhkVg4dxaq16yN+g0aI0vI+qcfonOPvtiwdhX63DQQi+bny/rVjfJlfemPc1FRyHqTfFn3/fvnpQtRqlQZNL02X9Z9/17xc76sX9siX9Z9/9aH6upf8mW9xfU+sr5yOc57vWjVuvCj2zaIR7edPo3W7Qo/um3juvxHt93QvvCj2wQvwaNtR/+Pbtu1/VccPrAPN3Ty/+i2neLRbb9tR9de/h/dtmdX/qPbevQ1ProtLuhe+e30qWh5QweNv9XX0cMHsWTRD6jTsRF2pG/FjvRt2HEi/7+/n9qD3DzzZ5NUKn4ZrqrQAFeWr4/6FRviqvJXa38LGZ/68QT0HzgYpUqXsdqNgOXyx0RpNL22pZR4pYsnIDcvD2eyAj8eJ398f4B7//yIlHbDCRI8+xejizG267dt6NarfzhNOl63QukknDp7Ht6c8O8I+nbG52jRqg2qVq/p+HbFUgeErF9WNhlHT2aFvFmff/ov9O43EGXLlQ85BisGJiDu+hLC/seZojsdbmXaUu1xks1b3eDa4SK+m7y5ecjMdv7RbeEfdV2LOeyOVSpTDCdPZ8Mb049ui+wImPTOOCWPbgs72UUsQJGXdSHne/YdLrit3UzWjYsLmMn6s88+h7fffkuT9MTEJO2/8fEexAtZ156FLJ77mz+yNFHPydFkft++kvj663ro1m0hundvoZVbtWolHnjgQfzySxqSkpLQoEFDTJv2BUaM+AsmT/4YXbt2x7Fj/8P+/fvRp09fvPzyi3j66WfxzTdfo27dumjSpCkyMzMxYcJ7uPnmAUhLS8Odd96FmTO/Rc2aNdGsWb6cz5kzG5UrV0bz5vky7vv3vHlzUaZMGVx/fb6M+/79448Ltf61adNW+9z3b30/WrJksfbP9u07FNq1li1bql1Z79ixsJSnpS3H6dOn0bVrYfleseIXnDx5Et279ygUR/A6duwYevbs5XfX3bBxPfbu2YMbb/QvSZs3/4qtW7diwIBb/MbZvn0b1q1bh0GDbjOUCX7g/PTTT7TtFPz9vby5Xqw/sh6/HEjD8v3L8dvenWiW0RQf4sNLqogff2qVq4UGFRugQaWGaHRZQ+2/DSs1RPlk/yfW77zzNu67709aXmW88sdEWVx//fUywmnP2hUv/fnT/oLmj+/38fjj/09Ku+EECZ79i9E3b96MbVu34OYAYyycvkSqbrwnDrl5wfNkpT9T/vMftGvfDrVq1bZSnGVsEIj3eJCTG/pZ68QJ7+O22+9AhQoVbLTKonYIiGOeJw7IETtUEX0tXrwI8Z54tG1X+Id7N+HwiCTlQfsx2emXnR+Ine5rpNsXedJ2JRfkSd22R3YEvPjiPyjr6pJpOXKRl3VxVf2jz2dfAkzMW3/i4cF45d0phZbzN1s10O6cdb0x73nghpbJOLA/DmNfO4977uMq2JZHro2CbpyzLhZ8W3UoDasOp2HN4ZXYcHQtsnIyC21VYnwS6pStiyvLN7hwhbwhrqpwtXbVXDwXPNZeVm+Dj7Xtjrbt4Zx192dMxm3w7t/K6O8hb4OPjhxyznp05Im3wavJE+esq+FqJ6qjsn7ijwyMeOJNbNyy65I+N2lYFxNfeQzly0b2mcnGK+vFk5O0W+Rr16hS8Ow93znrouOhyrqoy0e52RmuoZV1WtbP5WZj09H1WH3kF6w+tAJrjqzQVmM3vhI8Cbi6QiM0rXwdUi5vrv23UcVrkOBJDG2jo7AWZT06kkZZd3+eKOvuz5HoIWU9OvJEWY+OPFHW1eSJsq6Gq52ojsq62crqdjqvoqyvrKtYDd633/qj3IY/6MVz/yi6c9dU5FPEdELWxTPLF+z5Hgv2/IBFv8+7ZNMaVrwG11zWDM0qN0ezytfhuiqtVG1+1MSlrEdHqijr7s8TZd39OaKsR0eORC8p69GRK8q6mjxR1tVwtRPVMVkXV9WffPkDjHzw9kIPobfTeRVlfWVdtBHoOeuhrgYv5qwXL14C1WrWQdqypZg3tyU8njx07boSt93N1eBT2xaey75pff4Cc63bFV5gTqyeLxaYa9PB/wJzu3f8iiMH9yG1g/8F5qys1L13d/4Cc937GBeYuzgKF+2bj4W7f8CPv8/FrpM7Cj74s2c4zlbLxpW1G2py3rTytUFvYw+2GnwoY/+zyRPR79bB2qJwMl5cDd4eRStjzF5EZ0rLlHWuBq8mhzJknavBq8mNMSqvrHM1ePWjrOi0QFmXn2uuBi+faSgRKeuhUDPUkSHrq9KWYv/+5ti4IQ5t2qzEkAco69Eg6/szfsf8PXOwcM8P+PnAEmR6z2ojQywAJ66ad6vdG13r9Mbvy7aiZWp7VLGzGvyRQ1i+ZD76D7w7zBF6sTplXRrKkAJR1i/FRlkPaSgFrURZD4rIFQUo65R1VwzEGOkEZV1+Iinr8pmGEtExWRed9Z0PHsoGOF1HlqzXrnctPpoUj5SUlWieOhTFElfwOeuG5LrhyvrOnVuwYu1SbLt8Jxbu/R47DVfPxYJv7Wp0Qrc6vdG9bl9cVrxyQe9nzviMsm5hR7V6Gzyfs24BpsIivLKuEK6k0JR1SSAVh6GsU9YVD7EiFZ6yLj/dRUXWxZTn+x59pRDA++/oXfCkMPlk7UV0VNbFyupTZ8zHyBG3QyzmFq2vcBaYM27zhHcT8NKYRNS/OhcLl2Vrj3LjK3wC4cxZP3h6f8HV85/2L8ZZ75mCDlUpWRVda/dC97p9NFFP8hQLv7NFOIJVWS/CiFyx6TJl3RUbFIOdkCHrMYjFdZtEWXddSkw7xDnr0ZEnyrqaPBWFOeu+65PpC6A/PnwQWqY0UAPWRlTHZD3QSvCi/06tBm+DXUFRWbJufJTbq6+fw+B7c0LpDuv4ELAj697c80g7+JN2a7u4er7jxLaCaOL2drFKu5BzIenXVGpG1hIJUNYlwlQYirKuEK6k0JR1SSAVh6GsKwYsKTxlXRJIxWEo62oAF0VZz8w6h9HjPy706G41dK1FdUzWrXUvOkrJknWxtXNmxWPovUmoWDEPP63KRunSedEBwcW9DCbr4vnm3+34CrN2foVl+xYVunpePKGEdtW8S+2e6FWvPyomV3LxlkZ31yjr0ZE/yrr780RZd3+ORA8p69GRJ8p6dOSJsq4mTypkfe8fe7H7xG41HQ4QtVa5WqhTrs4lJcyurLtpEXTKephDRdac9UbXpEBouVjd/LtZI5Cc9AuaXZuI+4fXww/fzcCgwUPxzfQpSG3bGSfTj+HI4YNo16kHPprwGob+ZSQWzZuFajVr46qrG0Of09u5e19sXLcKvfoNxOIFc3BF1eqo37CJtsXLFs1FhUqVIdo1+9t3pW/fv1cuX6LNqU9pnqrV9/1bx7pmxU/adjVv1aYQ6bWrlsPr9aJlartC729cuxJnzpxGJBaYW3N4Bb7Y8im+3j4Ndc7XRgM0wHRMx+Ulr0Cvuv00Qe9cq0dB/4KtBu9vKHHOurWdzKqsc866NZ6qSsmUdS4wpyZLMmSdq8GryY0xKmWdc9bVj7Ki0wJlXX6uVc1Zf2npS3hm4TPyOxwk4tPtnsaLnV80lXXfOetXXF4Rk8Y97oonljku62aT+ie/9YQr5ghYGUUqZD2lxVC8NnYN4uOT8NioK7Fl43TKuqRHt6VnHceXW6fgi82fYHv61oIUD6n6Z1Q/Vx1tu3ZH40pNTVNPWS+MhY9us3KEuFiGq8Ffyouybm8MWS1NWbdKytlylHXKurMjMLZap6zLz6cqWZ+yYQo+WvuR/A4HiTi46WDcf+39prL++qRpmPjKYyhfNv/xxr5X2yPeWUODjsq6GQix6NzwUa/jwXv7Y0Dv9k6ysdS2ClkfeOcQvP/2GqxIKw5PwtW4+aYvKOthyPrO7Zuwdvsv+D5+Pubtng0xL128mlyWgjsa3YcBV9+O/+09iN27tqNLj35+805Zp6xbOij4KURZp6yHM37s1KWs26HlXFnKOmXdudEXey1T1uXnVJWsy+9peBHNfFSsreaWW+Edk3V98v7AGztechVdQPty5iKMGTkkKlaJlzlnXR9uWVlAm5bJOHwoDuPeOIe77uFic3Z3xTPnT+Ozzf/Gh+vew/6MfVr10kmlcXP923F3k6FoVDF/SgBf7iBg9TZ4d/S26PZC5m3wRZei2i2XIetqe8joggBlPTrGAeesR0eeKOtq8qRizrqanoYe1UzWeWUdQKBfLMTV9fETvsDYp4YV3I4QegrU11Qh66LXixbG465BSShfIQ+btmep35AYaeFAxj58sO49fL753zh9/rS2VanVW2Nwo+G4uf6gGNnK2NsMynp05JSy7v48UdbdnyPKenTkSPSSsh4duaKsq8lTUZF13znrbnoqGa+sSxjbqmRddO3hEYmY8WUCuvXIweSp5yT0NnZDrD+6BhPXvInZO79GTl4OxKPWxCJxj10/El3qdcDxU9mxu/ExsGWU9ehIImXd/XmirLs/R5T16MgRZT168kRZV5OroiDrasjJi+qYrItNmDF7CabNXFRoQj/nrK+FmLMuVnEXq61XrnI1pnw8A2+//RD+8cKH6HtzJ64Gbxj/v25Yg/V7VmHauf9i5eHl2icJnkTcVH8gHmnxd9QrdxV27/gVRw7uQ2qHnn73HCvziTlnvTA+LjBn70BsZYzZi+hMaZmyzgXm1ORQhqxzNXg1uTFG5W3wnLOufpQVnRYo6/JzXVTmrMsnJzeio7IuNoWrwdfBqrSl2iPU9Ee3GWW9Tr36+PrLGXjqyYcxbNhHGHBbRxRL4qPbMr1n8fmWT7Dsl/mIz4rDbMxGiYSSuLPxn/DgdY9pj1/TX5T1fBKfTZ6IfrcORqlS+StdhvuirNsjSFm/lBdl3d4Yslqasm6VlLPlKOuUdWdHYGy1TlmXn0/KunymoUR0XNZD6bSb6qhaDV6/si5kXTxnff3GEUiI+wQ7dnTDM2MO4djRovmc9brXNcKH69/DlF8/xqnsP9AKrVA9vjrqtbwG9zd9EKWTylwyPCjrlHU3HDMo65T1SI1DynqkSIfXDmWdsh7eCGJtIwHKuvzxQFmXzzSUiJT1UKj51FE5Z11vKjsb6NQmGXv3xOHR/+fFyCfyHz9WVF5b03/FOyvH4ZsdXxZscvXSNfFwi5EY3PjSZyYauRRL9KBU8UTOWXf5YOGcdZcn6EL3ZN4GHx1bHH29lCHr0bfV0ddjynp05IwLzEVHnijravLEOetquNqJSlm3Q8tP2UjIumh6wykfqMEAACAASURBVHoP+nQrpvXim9nZuK5FroTeuzvE8axjGPvzc/h88+SCjjaseA3+2vLvuPHKWyx1nrJuCZPjhSjrjqfAUgco65YwOVqIsu4ofsuNU9Yto3K0IGXdUfyWG6esW0ZlqyBl3RYuJYUjLuvikW0jnngTf7qtJ/793++xccsu0w1z05L5wchHStZFP94Yl4DXxyWiarU8LF6ehRIlgvUuej+ftO5tvLniZWScy9A2olvt3riv6XB0rNnN1kZR1m3hcqwwZd0x9LYapqzbwuVIYcq6I9htN0pZt43MkQqUdUew226Usm4bmaUKlHVLmJQWiris61sT6DnrYtG5L2cuwpiRQ1A8OUkpgHCDR2rO+qDBQ/HN9Cm4/obOGPPMHwD2o3ip3mh09csY+peRWDRvFqrVrI2rrm6M7KxM/HfKh+jcva+2qnyvfgOxeMEcXFG1Ouo3bKJt8rJFc1GhUmVtYTuzv30XD/P9e+XyJdpq9SnNU7X6vn/rXNes+ElbOK95qzaFUK9dtRxerxctU9sVen/j2pX49eAGvJv+Fvb8sVP7rEedvhhy2Z8Rnx2H1u26FCq/eeNanEg/hjYd/As856znI+MCc+Hu7eHV55z1S/lxgbnwxpS/2jJknavBq8mNMSplnXPW1Y+yotMCZV1+rjlnXT7TUCK6UtbF49vGT/gCY58ahvJl5axcHQocK3UiLeupbTtj547jmPrJYXz77Y147rkXMOyh2JD1fRl78d63Y3H0xGHMxVztsWsvd3wbbat3xKb1q5Fx6iRl3cqg9FOGsh4GPAlVKeuUdQnDyFIIyrolTI4XoqxT1h0fhDHUAcq6/GRS1uUzDSWiK2VdPH89bfVmXllPSoK+Grx+ZV3I+sn0Y1i6+BDGjO6PZ555ATffNgqbN3wX1VfW3171KsaljcENuAEV4ivi+rYdMaTJiIIxTVkPZfcuXIeyHj7DcCJQ1inr4YwfO3Up63ZoOVeWsk5Zd270xV7LlHX5OaWsy2caSsSIy7q4aj581Os4dOS43/5ecXlFTBr3OOrVqhrKNkW8TiTnrBs37tb+xbD8Jw9Sb8jF/32bHfHtltHgqsNpeGTuUOw9tQvFE0pgVOpzGNrsIXjiPDLCazE4Z10aSqWBOGddKV5pwTlnXRpKZYFkyLqyzjFwAQHKenQMBs5Zj448UdbV5Ilz1tVwtRM14rKudy7QnHU7G+CGsk7J+tEjcejYphj+OBmHMS+dx9DhXjfgsNSHE1npeH7ZKEzf+plW/oZq7fFm139BPI5N9ouyLpuomniUdTVcZUelrMsmKj8eZV0+UxURKesqqMqPSVmXz1RFRMq6CqoAZV0NVztRHZN1O510e1mnZF1w+WFOPIbcnYTEJGDBkmzUu9Ldj3PLQx6+2PIpXvzpKZzMOoGyxcrh+XbjMKjBYGVppqwrQys1MGVdKk5lwSjrytBKC0xZl4ZSaSDKulK80oJT1qWhVBqIsq4GL2VdDVc7USnrdmiZlHVigTkxZ/3I4YNo16kHPprwGtZvegrImYncvLp4/4P6rl0NfufJHXhk3v1Yd2QV2qM9GpRrjL/c8gQqFb+sgKxYDf7MmdNIbdupEG3OWQ9zoHI1+PABhhmBc9YvBcjV4MMcVH6qy5B1rgavJjfGqJR1zllXP8qKTguUdfm55px1+UxDieiorAeavx4tz1l3g6zfds8ovPjsHGzYUA/XtWyE58acctWj27y5XszLnYd/rXsX3tzzqFyiCp6p+Txqlqpj+ug2yjpw9MghLF8yH/0H3h3Kfm1ahwvMSUMZUiDKOmU9pIETQiXKegjQHKhCWaesOzDsYrZJyrr81FLW5TMNJaJjsp6ZdQ6jx3+M1OaN0KzxlZg6Yz5Gjrhde676G5Omod31TdEypUEo2xTROm6QdfGc9a/+OxsffngV1q1tig8n/4H/HZ7kiuesz5g3BfN2z8K3577R8nJHw3sxut04/LZhk9/nrFPWKeuBduLsrEztx6h7hj4c0X093MYo65T1cMeQ1fqUdauknC1HWaesOzsCY6t1yrr8fFLW5TMNJaJjsm5cYE503Phc9ZXrtuLLmYui4tFtou9Ozlk3Jv2jfyXguacSUapUHuYvzUaNGnmhjAlpdcSj2MQj2cSrTtkr8UbXf6LVFTdIi281EOesWyXlbDnOWXeWv9XWOWfdKinnysmQded6X3RapqxHR645Zz068kRZV5MnzllXw9VOVFfIeoVypTH2nal48pG7UL5saYjb443ybmeDnCjrFlkX2z70viTM+S4ejRrn4rPp53DZZZEXdrFw3Igf7saSfQu1dAxr9jCeb5cv7U68KOtOULffJmXdPjMnalDWnaBur03Kuj1eTpWmrDtF3l67lHV7vJwqTVlXQ56yroarnaiOybrxNvgBvdtrt77XrlEF4t8zZi9B2urNvLJuJ5MXyp4+HYduHYrh971xaJaSixnfZSM5OYRAIVbZdGw97p15Cw6fOYiSiaUwseen6FKrZ4jR5FSjrMvhqDoKZV01YTnxKetyOKqMQllXSVdebMq6PJYqI1HWVdKVF5uyLo+lMRJlXQ1XO1Edk3XfTorb4kc88SY2btmFKy6viEnjHke9WlXtbIsjZd0yZ33RvFmoVrM2rrq6MX7dmI35c/6FGTNuQZ8+P2PUs7di8YI5uKJqddRv2ETjtGzRXFSoVBmNrkkx/Ttt2UKULFUGTVJaaJ/7/r1y+RIkJiUhpXmq9rn4+9eTGzFm9zM4l5uNRhWb4OO+0/C/Lfshru03b9WmUH7WrlrOOesBRiwXmPMPh3PWHTnUFTQqU9a5GryaXMqQda4GryY3xqiUdc5ZVz/Kik4LlHX5ueacdflMQ4noGlkPpfNuqONGWRcyM3Xyh5gy5Ra0bLEceZ7b0afPt0pl/ZXPn8Ta46uxDMsK3fa+ZsVPlPUZn6FlantUqVrd8pClrFPWLQ+WCBekrEcYeAjNUdZDgOZAFco6Zd2BYRezTVLW5aeWsi6faSgRHZN14wJz0XAF3R9ct8q6WC27bIV++HnJKkyZMhjPPf8VOnWpJv3Kep1rGuBPswah9MFk5MXn4e5eI9Ctdu8CXJR1YCZl3dKxyept8LyybgmnskKUdWVopQWmrEtDqTQQZZ2yrnSAFbHglHX5Caesy2caSkTKeijUfOq4aYE5382Z/FECnv57IsTJ24eTz6FnnxwJW5wfYtfJHbjr25vw+6ndqFa6Bqbc+A3qV3Df4/Y4Z11aypUGsirrSjvB4EEJyJT1oI2xQEgEZMh6SA2zki0ClHVbuBwrzDnrjqG31TBl3RYuy4U5Z90yKmUFHZN1sUXR9Dz1QBlws6yLfr80JhET3k1AYhIw49tsXNciN+wBteLQz7hn5gBknDuFay9viU9vnIEKyRXDjqsiAGVdBVX5MSnr8pmqiEhZV0FVbkzKulyeqqJR1lWRlRuXsi6Xp6polHU1ZCnrarjaieqorItHtE2dMR8jR9yO4slJdvrtqrJul3UBa/iQJHz3bTzKlsvD7HnZqF0n9Ee6Td/6GR5fOALe3PPoVa8/Jnb/BInx7s0fZd1Vu4vfzlDWoyNPlHX354my7v4ciR5S1qMjT5T16MgTZV1NnijrarjaieqYrBtXfzfrcJOGdTHxlce05667+eXmOeudu/fFxnWr0KvfQCyaNwdffVUb06ddh+o18vDyKzNxRbXLbK4GXxrfnPkKE9e+ha7oiuuqXY+/3vy0lh7f1eH1nHHOOuesW91/rco656xbJaqmnExZ52rwanIkQ9a5Grya3BijUtY5Z139KCs6LVDW5eeac9blMw0lomOyHkpn3VgnWmRdPLqtQqXq+H+PtsCmjR7cc893uOPuimh6rbVHty1bMhez9n+DT9P/jQRPIl6uPR6NL29a6NFtxke5UdYvjlYuMGdtz6WsW+PkdCnKutMZCN4+ZT04IzeUoKxT1t0wDmOlD5R1+ZmkrMtnGkpEx2Q90GrwK9dtxZczF2HMyCGuvz0+mmRdPGf9ssubokfnYrg2ZTbKlrsMr7zRBB7Ppc9dNz5X/X+ZRzFu6tPYlbUTW4ptxeS+0xG3x3vJc9Yp6+a7IGXd2qGJsm6Nk9OlKOtOZyB4+5T14IzcUIKyTll3wziMlT5Q1uVnkrIun2koEV0p62Iu+/gJX2DsU8Ncfxu8gB4Nc9aNg2Pvnjj06V4MJ9LjcNc9Xox747zfsbPl+CYM/vYmHD5zEHXLXYWp/b5GzTJ1QhlrjtXhnHXH0Ntq2Kqs2wrKwtIJyJR16Z1jQI2ADFknSvUEKOvqGctogXPWZVBUH4OyroYx56yr4WonqitlfcbsJUhbvTkqrqxHo6yLPotb4W/uUwxnzwJPPnseD/3Ve8m4mb9nDh74/m5kes+i1RU3aCu+l04qY2d8uaIsZd0VaQjaCcp6UESuKEBZd0UaAnaCsu7+HIkeUtajI0+U9ejIE2VdTZ4o62q42okacVkXV82Hj3odh44c99vPKy6viEnjHke9WlXtbItjZaPtyroO6qel8bjj1iTk5AATPzyHfjddfAb7B+vfxfNL/64Vvb3hPXi9yz8d4xtuw5T1cAlGpj5lPTKcw22Fsh4uQfX1KevqGctogbIug6L6GJR19YxltEBZl0Hx0hiUdTVc7USNuKzrnQs0Z93OBjhdNtrmrNdv2ERDtmzRXFSoVBm/bmqBRx9KRN++s9C9V0XcclszvLr8eWxfvQEncRJdbrgRD173GIxz2EV939XfuRq8/5HIOevW9lKrss7V4K3xVFVKpqxzNXg1WZIh61wNXk1ujFEp65yzrn6UFZ0WKOvyc8056/KZhhLRMVkPpbNurBPtst7omhS891YiNq77AYcPX45yA7/E/Mxx6Ime6FS/BwZ3H65hp6wDe3f/hm2bN6B7nwG2hiJl3Rouyro1Tk6Xoqw7nYHg7VPWgzNyQwnKOmXdDeMwVvpAWZefScq6fKahRKSsh0LNUCcWZF1szlvj5+PHw0uwqs5riEMcxtYcj5SardAkpQVl/UK+KeuFdxbfH3DC3JVAWQ+XYGTqU9YjwzmcVijr4dCLXF3KOmU9cqMt9luirMvPMWVdPtNQIjoq6+JW+BFPvImNW3Zd0vcmDeti4iuPcTX4ULIaQh0xP13MUxevuG8m462hd+LW2y5ddC6E0I5X4Zx1x1NgqQNWZd1SMBZSRkCmrCvrZBEPLEPWizjCiGw+ZT0imMNuhHPWw0YYkQCUdTWYOWddDVc7UR2V9TcmTdP6+rfhg+z02XVlo3WBOR3ke6tfw9jlz2l/dj87GXPH3av9+8PJ59Cr78VF51wH3mKHKOsWQTlcjLLucAIsNk9ZtwjKwWKUdQfh22iasm4DloNFKesOwrfRNGXdBiwbRSnrNmApKuqYrMfKAnMiL9Es69O3foa/zh+qDa8p/b5Gp5rdMX5sAt56PVF77+9Pe/HIY/6fw65oXEoNS1mXilNZMMq6MrRSA1PWpeJUEoyyrgSr9KCUdelIlQSkrCvBKj0oZV06Ui0gZV0NVztRKet2aJmUjeY56yfiT+IvG+5HTl4OXq35Bq6rmwqx4Jx4fTBhEb6fXR5paakYeLsXt9/+A0qWKlMwh52rwVsfOFxgzhorq7LO1eCt8VRVSqasczV4NVmSIetcDV5NboxRKeucs65+lBWdFijr8nPNOevymYYS0TFZF50Vt8HXrlEFA3q3D6XvrqgTrbL+7fef49NdH2F57s94svU/kJLRVHuUmy7rYvGwAwfK4e//rw0yM4F77/seA24tiRap+QvOUdatDz/KujVWlHVrnJwuRVl3OgPB26esB2fkhhKUdcq6G8ZhrPSBsi4/k5R1+UxDieiorO/cexBTZ8zHyBG3o3hyUij9d7xONMr63lO78NrU0fg9Zy+ubtwU4zq9V/DcdaOsiyvpCUmtMPi2JKQ0m4v4+DJ45h/XomatPMq6jZFHWbcGi7JujZPTpSjrTmcgePuU9eCM3FCCsk5Zd8M4jJU+UNblZ5KyLp9pKBEdk/VAK8GLDeFq8KGkM3idE1np6PHf1jiQsQ+da/XAJ33/D544T8CK//tfHO64JQlbNntQtlweJk89h1bX5wZvzCUlOGfdJYkI0g2rsh4dWxO7vZQp67FLydktkyHrzm5B0Widsh4deeac9ejIE2VdTZ44Z10NVztRHZN1O510e9loWWDurPcMbp7eFZuOrUeTy1Lw9a0LkBxf3BJecSv8A/cnYf7ceCQkAu9MOIf+N0fHSvGUdUspdrwQZd3xFFjqAGXdEiZHC1HWHcVvuXHKumVUjhakrDuK33LjlHXLqGwVpKzbwqWkMGVdAtZokHVvrhd3fnsjftq/GNVL18Sc235CheSKtrY+Lw948fkE/PP9/JXiH338PEY+6f5nsVPWbaXZscKUdcfQ22qYsm4LlyOFKeuOYLfdKGXdNjJHKlDWHcFuu1HKum1klipQ1i1hUlrIUVnPzDqH0eM/xqwFabji8oqYNO5xVL28kvZeavNGUbHwXDTMWe/Z71a88slTWJaxGLuL7cHsQUuxf+3OQgvKLVs095IF5oyrv4sF5/S/p/83Ad99vQSZmcVQulxrTPzXOaxbvQSJSUlIaZ5aaMCuWfET8gA0b9Wm0PtrVy2H1+tFy9R2hd7fuHYlzpw5jdS2nQq9v2n9amScOonW7boUen/zxrU4kX4MbTp087uj7N7xK44c3IfUDj39ltm1Yyt279qOLj36+S2zd/dv2LZ5A7r3GWBrp+ScdWu4rMo6V4O3xlNVKZmyztXg1WRJhqxzNXg1uTFGpaxzzrr6UVZ0WqCsy88156zLZxpKREdlXV8NvlfnVIyf+AXuGtAV9WpVxcp1W/HlzEUYM3KI6xeeiwZZX11xHQ6t3Y19cfvw/C2v47oqrS5ZUM6OrIuB9tWXSzFjenEsXNAO1zbPxagn5qFMGcq62U5IWbd2aKKsW+PkdCnKutMZCN4+ZT04IzeUoKxT1t0wDmOlD5R1+ZmkrMtnGkpEx2RdLDD35MsfYOSDt2tX042yLlaJHz/hC4x9ahjKly0dynZZrmO8uq9XmvzWE2iZ0qAgxozZS/DsuI+1v/t0SS30I4LbZf37pV9h9IlncBNuQuemvXBL+7u17fCVc7uyLh7dlpFRDE8/2QG/743DTTcvwC0D49G5+/WF2PPKOkBZt7Y7UtatcXK6FGXd6QwEb5+yHpyRG0pQ1inrbhiHsdIHyrr8TFLW5TMNJaIrZT2SV9bFjwb//mIORtx7k3YVX7T95NgPtFvy9av8r0+ahomvPKb9cCDuBhCvvw0fVMDbrXPWv9s5Aw/MuRt5yMOzbV7GA9c+GsoYCVjnRHochtydhBW/eFCteh5eevU8uvVw18JznLMuPe1KAlqVdSWNM6hlAjJl3XKjLGiLgAxZt9UgC4dEgLIeEraIV+Kc9YgjD6lBynpI2IJW4pz1oIiUF3BM1sWWiSvWaas348lH7sK7H3+l3QZfoVxpjHjiTQy6saMjc9b1R8o9PnyQdnVdv1V/QO/2WjKEzBvlXbznRllfcehnDPyqJ8TCcnc1HqI9S13l69GHEvHlFwlaE8Me8OL5F8+rbM5WbMq6LVyOFaasO4beVsOUdVu4HClMWXcEu+1GKeu2kTlSgbLuCHbbjVLWbSOzVIGybgmT0kKOyrouv/c9+kqhjfS9DV0pAZ/g4hb8p8d+gJeeHGa62J3xc3Hl3Y2yvj19C/pN74iMcxnoUacvPu6TfzeA6tdn/0nA039PxLlzQKPGufh4yjnUqCGWl3P2RVl3lr/V1inrVkk5W46y7ix/K61T1q1Qcr4MZd35HFjpAWXdCiXny1DW1eSAsq6Gq52ojsu6nc6qLqvPX9dXotf/Hnhjx4I57L6yLuasj3riGUx4/x0kxItnkCchISEBHo8H8fHxiPPEQfwvNy8PcQByc3ORm5ODOI8HxUuUQM1adZH202I0aXaddrv6xnVrcNd9w7Bu9QokJhVDvauuxqyvv8TgPw3Hl59/inYduyD9+DEcOngAnbv1wvtvvYqHHnsC8+bMRI3adVD9ylro/kk79D91I9aX34iBpQfh5lvvxPwfZqFa9Rpo2LiphnHRgh9QsdJlWrtmfy9dNB+ly5RFynUttc99/16+bJHWvxatWmuf638nJt2Awbcn4ODBOJQsCbw6/kfUrZeL61sXXvV91S8/47z3PFq36VAorWtXr8CZ0xlo26Hwqu/r167CHydPoH2nwqu+b1i3Gunpx9Gxc3e/w2PH1k04sP93dOza23+ZbVuw87dt6NnnJr9ldu3cgS2b1qNP/1ttDcX/++8UtG7bAVWr1bBc78jhg1i8cB4G3Xmv5TrBCv77g/cx8Pa7Uap0mWBFLX3uOyYsVQpQqESxBOTl5SHzXOBpFFlZmfjPx5Mw7EH50zrC3YZA9XdYGGMq25cVW5y4nsnywpsT/g9xX335GVqmtkH1GrVkdY9xAAhZL18qCekZ50Lm8Z+P/4kbbx6EcuUrhByDFQMTSErwQPyYnJHp/kegqspl2s9LEO+J144Dbn2VTE5ATm4esoJ8N7m1/0WlX+VKJiEj87yWK77kEHj3jbEYPXq0nGCMEjIBR2Vd3GJ++Gh6oQXbfIU55C2zWVFvt0rlCgXz0c36YibrTz/zLN55520kxCcgMSnxgqzHa7LuiYtDXNxFWc8xyHrJEiVQu249LF38I669rjnEc8zXrlmF+4c9gJUrfkGxYkmof3UD/N+X0zBs+Aj859PJ6NylK44fO4YDB/ajZ68+GP/qyxj1xNP4buY3qFOnLl7c/gLmbvsef437K26++VZsWfcrBt12J2bPmokaNWqiSdNmGpm5P8zBZZdV1to1+3vh/HkoXbYMWrbMXzDO9+/Fi37U+pfaOv8L1vh3ejpw910eLFwYh44dF6Nd+1w89XT+NAL9tfznZTh/3ov2HToWen/lijRkZJzWttP4WrVqBf44cRJduhWW8jWrV+H48WPo1t3/Y9l+3bQRv+/dg159bvQ7KrZu2Yxt27ai/03+H8u2Y8d2bFy/DgNuvbhegZVhNnXKp+jQoSOq16hppbhW5uDBA1gwby7uvvdPlusEKyh+UBp8930oU0aOrPuOiWDtB/s8IT5Oe8xfThAJzMzMxAeTJuCRRx8PFtJVn1sZY67qsJ/OCME4n5On/bAS7uvzz/6DNm3ao2Ytynq4LH3rF0uMR/b50NcP+dc/J2DgoNtRvgJlXXZu9HgeTxziPXE4781V1YTr4y5dshjx8R7c0KbwD/pu6rj23ZQHSqCbkmLSl6REj7YvSfhqcvmWRq57r459kbIeOdx+W3JM1s2uWuu9jOQCc6JNM1HX+xJszrqbVoP/DTsxetsTuCzxMjzqeQxde/THxnWr0KvfQCxeMAdXVK2O+g2baJsmYzV443PVxerwvs9Zf/WlBGxY+zOAPOzZ2wFvvHMO17fOPynhc9YD7/1HjxzC8iXz0X9g/ur9Ml6fTZ6IfrcORqlScp6wkLZsIUqWKoMmKS1kdA9Wb4Pnc9al4A45iMzb4Pmc9ZDTELCijNvg+Zx1NbkxRuVt8FwNXv0oKzot8DZ4+bnmavDymYYS0TFZNz66TZ/7rW+AE49u029994Xou6CcW1eDX390NfpN7wxv7nltjrqYq+6G15JF8fjbI4k4dFBMAgDuuseL5/7hRalS4V+Vs7p9nLNulZSz5azKurO9ZOsyZZ001RCQIetqesaolPXoGwOcsx4dOaOsq8kT56yr4WonqmOy7pYr6+KHgeGjXsehI8cLcbv/jt4Ft8MHes66qOT0avBiIbkun7fAgYx9uK/JcLzU4U07Y0B52exs4I3xCfjn+4nwngcqX56H1946jy7dQr9F006nKet2aDlXlrLuHHs7LVPW7dBypixl3RnudlvllXW7xJwpT1l3hrvdVinrdolZK09Zt8ZJZSnHZF1slO8zzcV7ujw/eG9/Rx7dFgpsp2X9kXn34/+2fY5GFZtg3h2/hLIJEamz8zcP/vZwIlat9Gjt9e2Xg5fGnUelSmqvslPWI5LesBuhrIeNMCIBKOsRwRxWI5T1sPBFrDJlPWKow2qIsh4WvohVpqyrQU1ZV8PVTlRHZd0o58Yr204+us0OPFHW6TnrH04Yj+fznsctcbfittb3os11XaDP6e3cva+jc9YFnzUrftIWDWve6uJKr59PTcDcWcvh9XqxZm0njH7Bi0G356+Gu3HtSpw5cxqpbTsVSsWm9auRceokWrcrvEr85o1rcSL9GNp0KLxKvLHy7h2/4sjBfUjt4H8Rul07tmL3ru3o0qOf3yGwd/dv2LZ5A7r38b8InVnlmTPEitftUaVqdcvDi3PW/aPinHXLw0hJQZmyzjnrSlKkrQZfpXxxHErPDLkBzlkPGZ3lipR1zlm3PFhYMCgBynpQRLYLcM66bWRKKjgu60q2KoJBnZT1q69vhq///Qn+gX/g+covoGOznrjq6saul3WRnuVL0/Djghy8/17+qu83tM3Bm++ex4ljKyjrACjrlPUIHsZsNUVZt4XLkcKUdUew226Usk5Ztz1oWMEvAcq6/MFBWZfPNJSIlPVQqBnqOCnr7/7xNroe6IC5VX/Ew6UfQbWataNG1vXV4OPiO+CREUnYuycOxYsDf39yGa5pegqteWWdq8H72Td5ZT3Mg1aY1SnrYQKMQHXKegQgS2iCsk5ZlzCMGOICAcq6/KFAWZfPNJSIjsq6WBF+xBNvYuOWXZf0vUnDupj4ymMoX1bOY6ZCgWO1jhNz1j/Z+C88tfhRlC1WDovuWoPKJapY7a4ry739RiLGvZyg9U3MYf/r414MGZZ/a3y4L85ZD5dgZOpzznpkOIfbikxZD7cvrG9OQIask616ApR19YxltMA56zIoqo9BWVfDmHPW1XC1E9VRWTd7DJqdU77q2wAAIABJREFUzrulbKRlfe+pXeg0tQWyc7Iwue90dKvd2y0owurH73vj8PfHEyEe9yZeV9XPxcvjvNot8uG8KOvh0ItcXcp65FiH0xJlPRx6kalLWY8M53BboayHSzAy9SnrkeEcbiuU9XAJmtenrKvhaieqY7Ie6DnrdjbADWUjKeu5ebnoM60dNvxvLQY1vBtvdpnkBgRS+zDvh3iMeTYRu3flP5u9Z+8cjHnpPKrXCG3VeMq61PQoC0ZZV4ZWamDKulScSoJR1pVglR6Usi4dqZKAlHUlWKUHpaxLR6oFpKyr4WonKmXdDi2TspGes767wu9YsHk26ifUxz/ufwef/2sihv5lJBbNmxWVc9ZbprYrRNW4Gvy/JibgjXEJyMiIQ2rqL0i5Nh1tO3ZBpy4Xr7RzNXjrA/izyRPR79bBKFVKztSStGULUbJUGTRJaWG9EwFKWpV1zlmXgjvkIDJlnavBh5yGgBVlyDpXg1eTG2NUyjrnrKsfZUWnBcq6/Fxzzrp8pqFEdEzWRWfFbfC1a1SJmuepmwGOpKx//vkkvH38DVSOq4z7av0ZN/cZjI8mvBazsi54Hz8ep81l/23bapQrdwLff98TDRvlYsRDObhlkBeUdeu7PWXdOisVJa08HlBFu7JjUtZlE5Ufj7Iun6mKiJR1yrqKcVVUY1LW5Weesi6faSgRHZX1nXsPYuqM+Rg54nYUT04Kpf+O14mUrPe/YzBe+9ez+DbnG9xZ5z5cW/w6tOvUI+ZlXU/wwrlrkLb8D7z/7sX5+eK2+D8/8AsaNDjK56xb2BMo6xYgKSxCWb8ULq+sqxlwlHU1XGVHpaxT1mWPqaIcj7IuP/uUdflMQ4nomKwHWglebAhXgy+cTrHyu1gBvsllKfhu4BIkePJXTi9qryOH4/DhpHhM+TQBp/7In9NesWIe7h+egyFDvShd5tJ57ZyzHh2jxOpt8NGxNbHbS5lX1mOXkrNbJkPWnd2CotE6ZT068sw569GRJ8q6mjxxzroarnaiOibrdjrp9rKqF5hbfmApbv2qB0oklMSCO1egZpk6bkeivH+ZmcDnUxLwwT8TIFaRF6+SJYE77/ZixENeXF7lorRT1pWnQ0oDlHUpGJUHoawrRxx2A5T1sBFGJABlPSKYw26Esh42wogEoKyrwUxZV8PVTlTKuh1afsqqlPU/sk+i49TrcPTsYYzv9D7ubPwnCT2OnRC5ucAPs+Pxz/cTsGqlR9uwhETg5lu8ePjRHNS7MheU9ejIN2U9OvJEWXd/nijr7s+R6CFlPTryRFmPjjxR1tXkibKuhqudqI7L+sp1W3Hfo68U6vPkt55Ay5QGdrbDsbKq56xPOTwZFXeXwfY6u3FTZn+ktu2Mk+nHcOTwwSI1Z33T+tXIOHUSrdt1KZRr4wJz69d5MPHdBMz+Lh45OYA4Ye3aPQd/+tN6FEvci9QOPf2OEyvziffu/g3bNm9A9z4DbI23mTM+Q8vU9qhStbrlekePHMLyJfPRf+DdlusEK8g568EIqf3cyhhT2wM50WXKOuesy8mJbxQZss7V4NXkxhiVss456+pHWdFpgbIuP9ecsy6faSgRHZV1IeqvT5qGia88hvJl8x8nJRadGz7qdTx4b/+oWCVepazvO7sXY7Y8jTtxJ+6//3H8NOsHynoAWf//7d0LlFTVne/xf1U3DS1CA754ylNExkcHxNs3o0IgIuKgjAoLRzQGNdyoyUQdWGJGieNSuLp8TLzCRSLK3AQJGiLjiGFEQTRCBAGH4Y2CQUBQGhCEhn7UXftUV1NVVHWds8/ep6q6vr0WC+ja+793ffapqv71qX0q9gDY9WVIZkwrdt4mf/SoSHn5p3LFFdvl/Auvdc64p/pyE6QI64lyfHSbt6dcN8eYt4rZaU1Yz467l1EJ6160steWsE5Yz97R1/RGJqybX1PCunlTnYpZC+vHqk7I5KdmyagRg045i65C/GtvLpVHJ4zL+avE2wrra9askN+se0FWVa+Un532j3LnuAdkweu/Jay7COuxB4L6fPa5vyuSJe+sl7Ztd8gbb4yUVq0icsOoWrntx7XS54K6hseMmyBFWCes6zzJxvq4Ocb81A+qL2E9KGn9cQjr+nZB9iSsE9aDPN6a+liEdfMrTFg3b6pTMWthXV0NftITM2XC3WOkZ9eOCXNXZ9efmjZXpjx0V8MZd507F1QfG3vWH/ngn+SlT6dJv/aXyZs3LQ3qrjTJcYrDYVn+YYnMeLFO3llUJDXV0bt50cV18g+31srf31ib8iryTRIjh+8Ue9ZzeHHipmYyrOfHPc6/WZoI6/l3r/NvxoT1/Fgz9qznxzoR1u2sE3vW7bh6qZq1sN5UzqwrbNNhfVPlehkyZ4Czjn++dZ10K+vpZU1pmyQQf4G5ysqQvDa3yDnjvmVz9IJ06uvG0TXyPyoiUt6vTv7mwpNn3MEMToCwHpy1n5EI6370gulLWA/G2e8ohHW/gsH0J6wH4+x3FMK6X8HU/Qnrdly9VM1aWFeTnL9wmcx7c2le71m3EdZvmD9U/rL7Qxlf/o/yyOVTvKwnbVMIpLsa/OpVYZk7p0je+EOxfPfdyY6dOkfkqqtrZchVdTL4h7WYBiRAWA8I2ucwhHWfgAF0J6wHgGxgCMK6AcQAShDWA0A2MARh3QBiihKEdTuuXqpmNayriXI1+O6yasUH0vfCclGfDL527QqZemKK/KDoB3JH/3ulT++LZNF/zJfRY+9kz3qGq8GnO/C3b10ve3fvTHs1+Koqkdd/v1V2bt8ss2aNci5KF/sqLRW5YmA0uJd/b5Ps3snV4GM2XGDOy1OtCHvWT/XiavDejiG3rU2Eda4G71Zbvx1hnT3r+kcPPZMFCOvmjwn2rJs31amY9bCuM+lc6mPyAnO1kVpZsWqp/Drya5l07mTp12mAdO/Zm7AuIm4+uk03rKt+sSA1cPB1smJ5kby3OOz82brl5Fvl+/TZLFcOXCNl7W5yPhLuwovcvV2ej25z94h1e2b9eNUx+f1vfyO33fkzd4VzpBVhnbAe1KFIWA9K2t84hHXCur8jiN7xAoR188cDYd28qU7FrIb1Z2bMk6/2VSZc9T22l72if9+C++i2j/csl+M7j8jbbf4k/9Lzf0tJSXPCev1RHVRYH3L1dQmPo927QrL4P6Phfe+ebdK37xqZO3eM06ZDx4gMuapWhg6rc86+l5SkfggS1t09NRHW3Tllu5XJt8FzZt3OahLW7biarkpYJ6ybPqYKuR5h3fzqE9bNm+pUzFpY5wJzicu1v+ob+f7svnKk+oj84YZFUtHxCp31pE8KgXR71r1iVZ8QWf5Rkbz7TliWvBuWz7adPOveokX07fJXXV0nQ6+plbPOUpsa+PIi4Dase6lJW/MCJsO6+dlRUQmYCOtI2hcgrNs3NjECe9ZNKNqvQVi3Y8yedTuuXqpmLazz0W2JyzRhyT0yZ/3LclW34fLK373uZQ1pm0HAVFhPHubLndGz7iq8f/Rhkai977EflNVb5NVF6q4aVicXX+Lu7fKFvpCE9fw4Agjrub9OhPXcXyM1Q8J6fqwTYT0/1omwbmedCOt2XL1UzVpY58z6yWXaUrlJBs/pL0XhYnn/ltV8VJuXI9hFW1thPXnopUuK5D3nrHuRfP5ZqOHmM8+MyG0/rpHWZSKXfC8a3tWZeL4SBQjr+XFEENZzf50I67m/RoT1/FgjNUvCen6sFWHdzjoR1u24eqmatbCuJqmuBD9pykyZ8eQD0rNrR2fen32xW8ZPfFru/tH1BbNnffHSBbK8brn0a3+ZnH3oTBn1D+Nk3dpV0qykhD3r9Udztvasxz+Yvti+TTZvcHc1+B3bo2fdlywOS4/u/yaLFw+Rv/713IZyF/StkwsvrpNLyiNySXmd9Ls08ez7vr17ZPmyxXL9qFu9PJ4bbTvnlely3U1j5fTTWxmpydXgvTFygblTvdiz7u0YctvaRFjnavButfXbcWadPev6Rw89kwUI6+aPCfasmzfVqZjVsB4fzvfs3d8w/1eee1AGlPfRuT+B9/F7NfjK0kPy5bptsq74v+WuS+6VbRs2ENa/OyIVl/8gYS3zLazHT/7fX58jbdoNlM1busonK8Oy+pOw7Pry5Jl31ba4WOT8PnVycbn6iLiI9Oj5pezb/Y6MHE1YT35QczX4wJ/mEgY0eWadsG5nLQnrdlxNVyWsE9ZNH1OFXI+wbn71CevmTXUqZj2s60w6l/r4CevNW5TKv335kvQ7/j0p63amXHJ2f9mwbg1hvYmF9VRXg/96X0hWfRyWVStD8snKIln58cmL1anju3PnXXLddW/L6rXjpE3biJx/fp2c11ukV2/1t97b6Dmznt1nDs6sn+pPWLdzTBLW7biarkpYJ6ybPqYKuR5h3fzqE9bNm+pUJKzrqCX1OXy0Wg4fq/FcadrqZ+Txj/5ZerfrI4tvXilFoSLPNeiQWSCoPeuZZ5K+RU2NyPr/Dssnq8KyWgX4VUXy1y8Sz77HeqsfxDt3iUiv81Rwj0jv8yNOiO/dOyJlbfL3KvTsWfdzBAXX1+SZ9eBmXVgjmQjrhSWWnXtLWM+Ou9dR2bPuVSw77QnrdtzZs27H1UtVwroXrTRtdcI6H9VmAN5liXwI66nuyuFvQ7J1S0i2bg3L1s0iW7eEnT87/xqSujQXmFcXs+vVO+KcfVdBvtd50X937JT7IZ6w7vKAznIzwnqWF8DF8IR1F0g50ISwngOL4GIKhHUXSDnQhLBuZxEI63ZcvVQlrHvRMhjWYx/V9sNu18jsv/uDgVlQIp1Avob1xlZ0w/qwbNsakm1bw7JlU0g+2xYS9b10X6edJtJ/QK0MuCya8lu1FunQMSKdOkWkfYdIToR5wnp+PIYJ67m/ToT13F8jNUPCen6sE2E9P9aJsG5nnQjrdly9VCWse9FK0VZnz/qR40fkv75eLUflqNxUMVa2/9dm6Xthuahzn+xZXynfFcCe9UyHne7V4L/Yoc7GR8/AO2fj1Vn5LSFRZ+nvv/9Z+c1v7pBvv22dcngV2jt1jkj79hEnyKuz8eqP+neH+tviO3I1+EyrmHg7e9ZP9WLPurdjyG1rE2Gdq8G71dZvR1hnz7r+0UPPZAHCuvljgj3r5k11KhLWddTi+uiE9fX7PpVDJw7JOW06yNB+18uqFR8Q1utN160hrCsK3bCe7nDetzckCxdMl5atbpO9e8tk1y6RPbtDor6v3lZfWZl6f3xyvXPa1wf6DhG5oM9/Sq/zWstZ5wxwmoWLItKmTKRtu4icfY73t927PbPO1eB9Pmn57G7yzDph3edipOlOWLfjaroqYZ2wbvqYKuR6hHXzq09YN2+qU5GwrqPmI6x//d0+2bp/k4RCYfl+94HSrdt5hPU4T8J6FMN0WFc1M10NXp2V/2pPSHZ9GXaC/O7dIrt3hZx/qz/ffJMY6IcNWyQHD5bJihUVKR9FLVtGg3vbtpH6v8W5sn079b12Im3bJt5+bqdiadU6IkcyXKyRsO7zSctnd8K6T8AAuhPWA0A2MARhnbBu4DCiRL0AYd38oUBYN2+qU5GwrqOW1MftBeZq6qrl+//vQtl1eKc8PvBZuf2i8QZGp0Qmgaa4Zz3TfbZ1u7pCfTTIRwP91/tEDhwQOVAZkkMH1Rn66L/dnqlPNc8zzog4ob4hzDuBX6SdCvj14f+i8jrp0sX72XtbLoVU12RYLyS3IO+ribAe5HwLdSzCen6sPHvW82OdCOt21ok963ZcvVQlrHvRStPWbViPfVRbt7KesmzsWj6qzYC9mxKEdTdK5tuo8N4Q5L8NSeU3sf+LE+ZVqD94UKRyv/q++ndIvjtibh6lpSItSiPSvLlIixYizVtEpIX6d6lI8+aR6Pea13+//t+qfYsWofp2iX1VW1WzpL6vquXUTOhrbv65Womwnqsrc3JehPXcXyM1Q8J6fqwTYT0/1omwbmedCOt2XL1UJax70fIR1g9UVUrF7D5ypPqI/H7kQrm88yADI1PCjQBh3Y1S9tvE9qx/vqP2lCCvgv2BAxHn+yrYHzoUkmPHRI5XiVRVheT4cfW3+n9Ijh7N/n1Rb+eP/8WA8wuDUpFLB9RJy5Z23hEQCoekqEgkHBYpCqtrCIgUFUWc76nwpv52bo/9Xf89da0B57awSEj1jW8XFikuVv0j0X5hkTPKSuS74zUSkbqGfuq2cDhaJ9YuNpeE/xdFnPmpX3rofKl1jtTzxf998t/RrRrO/+PapexTPwF1W/Ltqm/q+tFOqfo4Q8aWNkXNxD6hlPcjYc5x80s1Zqr71NBfRM5o1Vy+OXQ88X40UjPxPru7hoXOGtLnpEBJs7Co16fDR2tgyWGBli2KpLZOpOpEbQ7Pkqm1Ob1EDh894awVX2YEupxbJ5eVtzBTjCraAoR1bbpoR7cXmNtaudl5+3ubkjbS94yLJRwOS2npadLp3O7sWY9bA/asRzGysWfd60Mh168Gf+RIqD7AS32YDznhPhrso7c5Af949Puxf1cdi8T9W6Sqvn1834T29X3VFfcb+7rwwvXSp89Gef31m7xSN9n2t98+W5YuHSg7dnRrsvcxX+/Yz3/+vPz2t7dIZWW7fL0LzDsPBAYPXiI1NUWybNmVeTBbpohAYQn86lePyuTJkwvrTufgvSWs+1wUN2G9uq5GPvryfWek8rMuldOKTyOsr1ouNTU1MqDiioQVIKwT1vP9AnOxM/zR8H/yFwN792yUA99skQ5dRjq/+a+rFamt/xOpE+d76v91taHo35HY/+Pa1X+vtjYU7a/q1PerrYlE69WJOPVideLbOPVP9ouNFZtPQy3VLjafuvqx6vuFJSTVNRGpqamv49yHkNM+Vjv1/TrZTrmoLz9hXb1bQX2pdw2oP7F/n/xe9DR37DZJandKn7i28TVVv1TjpB4zrm3smS1N/1TzTK6ZMOek+WWaU7PisFTX1qWxqZ9nmppq3IFXvCCrPrlZjh4jrPv8MSFtd+ddMKGQVNfaebeNrXmbrHter6VSW1skn29P/FnA5Bh+axUXRd8JU6uelPnKWYGS+ue8hnc45exM82diw4Y+RljPgeUirPtcBDdh/fOD22Tnt19ImxZt5aIzy6W2tpawTlhv9MjjzHp6Hq4G7/NJy2d3k3vW+eg2n4uRpruJPet8zrqdtYmvyp51rgZv/ygrnBHYs25+rbkavHlTnYqEdR21pD6NXWBO7VHvP6uHs1d97vX/IVd0GWxgREp4EWDPuhet7LV1+znr2ZshIysBk2EdUTsCJsK6nZlRlbCef8cAF5jLjzUjrNtZJy4wZ8fVS1XCuhetNG0bC+svrH5anvjoYbnk7H6ycPSHBkajhFcBwrpXsey0J6xnx93rqIR1r2LBtyesB2+uMyJn1nXUgu9DWA/eXGdEwrqOWuY+hPXMRrZbENYNCKcL69W1J6T/y71kf9U38uI1c+TaniMNjEYJrwKEda9i2WlPWM+Ou9dRCetexYJvT1gP3lxnRMK6jlrwfQjrwZvrjEhY11HL3IewntnIdgvCuk/hxvas7zu2V7Yc2CilxafJZR2+71zop66ujj3rIrKGPeuNHnnsWU/Pw551n09aPrubDOvsWfe5GGm6mwjr7Fm3szbxVQnr7Fm3f5QVzgiEdfNrzZ5186Y6FQnrOmpxfdKG9VBYVn/9sRytOSrnn9FX2p/WkbAe50ZYb/zAI6wT1n0+NVnrTli3RmusMGHdGKXVQoR1wrrVA6zAihPWzS84Yd28qU5FwrqOmouwfvB4pWw6sEGaFTWT/9npCudjPzizfhKOsE5YTxZw+zZ4zqz7fNLy2Z2w7hMwgO6E9QCQDQxBWCesGziMKFEvQFg3fygQ1s2b6lQkrOuoJfVJtWd98KuXyub9G2Ty306Vn3zv5wZGoYSuAHvWdeWC7ec2rAc7K0ZLFjAZ1tG1I2AirNuZGVXjBQjr+XE8sGc9P9aJsG5nndizbsfVS1XCuhetNG2Tw/qyne/KzQtGSFnzNrJ63GfSoqjUwCiU0BUgrOvKBduPsB6st+5ohHVdueD6EdaDs/YzEmHdj15wfQnrwVn7GYmw7kcvfV/Cuh1XL1UJ6160XIb10W8Mlz9/uVTuu+wh+afL/tnACJTwI0BY96MXXF/CenDWfkYirPvRC6YvYT0YZ7+jENb9CgbTn7AejLPfUQjrfgVT9yes23H1UpWw7kUrRdvkC8zVhGpk88ENIiGR/h0qpKS4mYRCIamri7BnPc6PPeuNH3hcYC69D3vWfT5p+exuMqxzNXifi5Gmu4mwztXg7axNfFXCOnvW7R9lhTMCYd38WrNn3bypTkXCuo5aXJ/ksP7Vsd2y/8Q3cnbL9tK9bS8Jh0OEdRHpf9nfJkgT1gnryQJuz6wT1n0+afnsTlj3CRhAd8J6AMgGhiCsE9YNHEaUqBcgrJs/FAjr5k11KhLWddTShPW6UES2H94mNVIjl5zTT5o3KyWsf/xniRDWZUDFldK+Y2fXRxtn1jmz7vpgCbghYT1gcI3hCOsaaFnoQlgnrGfhsGuyQxLWzS8tYd28qU5FwrqOWlKf2AXmJiy5R+asf1lG9Rkrz/3wRQOVKWFCgD3rJhTt13B7Zt3+TBihMQGTYR1pOwImwrqdmVE1XoCwnh/HA3vW82OdCOt21ok963ZcvVQlrHvRStNWhfUdB76S/i/3kpraalk2dq30aHOegcqUMCFAWDehaL8GYd2+sYkRCOsmFO3WIKzb9TVVnbBuStJuHcK6XV9T1QnrpiQT6xDW7bh6qUpY96LVSFifuHii/N81z8mwHiPkpeG/N1CVEqYECOumJO3WIazb9TVVnbBuStJeHcK6PVuTlQnrJjXt1SKs27M1WZmwblLzZC3Cuh1XL1UJ6160UrRVF5j7yS9+Jk//6xNSHamWzm26yuktWkk4HJZwuIg96+xZlzfnz2HPuovHmduwzgXmXGBabGIyrHM1eDsLZSKsczV4O2sTX5Wwzp51+0dZ4YxAWDe/1uxZN2+qU5Gw7kJt/sJl8vCTs5yW1w6pkEcnjJPSFiXO/1VYr7siLEc+OCjFxc2kS5uuUlRcTFivd11NWCesu3iMqSaEdZdQWW5GWM/yArgYnrDuAikHmhDWCes5cBg2mSkQ1s0vJWHdvKlORcJ6BrWVazfJ0zPmyfSp90nbslbyzIx5To/7x49uCOv/p/QFue3YrXJGy7OkdWkZYT3OlLAuhHWXz0yEdZdQWW5GWM/yArgYnrDuAikHmhDWCes5cBg2mSkQ1s0vJWHdvKlORcJ6BjUVzrt1aS83DL/SaZkc3qetnCb3LLxHzj+jr7x38yqdNaCPZQH2rFsGNlTebVg3NBxlNAVMhnXNKdAtg4CJsA6yfQHCun1jEyOwZ92Eov0ahHU7xuxZt+PqpSphvRGtY1UnZPJTs6Sif9+GsP7ZF7vll1NmyuOT7pKeXTtKj3/tIdsPbpcXr/mdXNvz773Y0zYgAcJ6QNA+hyGs+wQMqDthPSBoH8MQ1n3gBdiVsB4gto+hCOs+8ALsSli3g01Yt+PqpSph3UVYHzVikAwo7+O0TA7rZVPL5OyWZ8vWn2314k5bBBBAAAEEEEAAAQQQQAABBNIKENZdhPXGzqyrC8wNvWOorHhthRQXF0tJSYnzt7oavPo7FAo5fyKRiDNSbW2t80fd3rJlS+nZs6e89957MmDAAKfNypUr5Z577pHly5dL8+bN5YILLpBXX31V7r33XnnppZfk6quvlq+//lp27twpI0aMkMcee0weeeQR+eMf/+jUuvjii+XYsWPy/PPPy4033ujUGTt2rCxYsEC6du0q5eXlzjzeeustOeecc+TSSy9N+f9FixZJWVmZVFRUOLcn///dd9915nf55Zc7tyf/P8b6/vvvO/dr0KBBCdIffPCBVFdXy+DBgxO+r+Z7+PBhGTp0aML3//KXv8iBAwdk2LBhCd9XXspj+PDhaVfy008/le3bt8vIkSPTtlm/fr1s3LhRbrrpprRtNm/eLGvWrJExY8Z4ekp5+eWXZciQIXLuuee67rdr1y55++235c4773TdJ1PDZ599Vu644w5p3bp1pqaubk8+Jlx1MtAodnxPnDjRQLXgSrg5xoKbTW6MNHv2bBk4cKB069YtNybELBoE1GvILbfcIu3atUMFAWsCS5YskaKiIrnyyuhWQ74QQCB3BFTGmTx5cu5MqEBnQljPsPCZ9qyrA/n+CQ/JjOnPS1FRsTRr1owLzMWZcoE5LjDn9rnV7dvg+eg2t6J22pl8Gzwf3WZnjUy8DZ6PbrOzNvFVeRs8F5izf5QVzgi8Dd78WnOBOfOmOhUJ6xnU3FwNnrAusnL5MmlWUiLl/aNn4mNfhHXCutsnJsK6W6nstiOsZ9ffzeiEdTdK2W9DWCesZ/8obDozIKybX0vCunlTnYqEdRdqjX3Ouup++Gi1HD5W46ISTbIhwAXmsqHufUy3Yd17ZXqYFDAZ1k3Oi1onBUyEdTztCxDW7RubGIELzJlQtF+DsG7HmAvM2XH1UpWw7kUrTVvCugFEiyUI6xZxDZYmrBvEtFiKsG4R11BpwrohSMtlCOuWgQ2VJ6wbgrRchrBuB5iwbsfVS1XCuhctwroBreBLENaDN9cZkbCuoxZ8H8J68OZeRySsexXLTnvCenbcvY5KWPcqlp32hHU77oR1O65eqhLWvWilaMsF5qJ71Nmznv5AenP+HBlQcaW079jZ9dG2b+8eWb5ssVw/6lbXfTI1nPPKdLnuprFy+umtMjV1dfuKD9+Tlqe3lovKo58o4PfLbVjnAnN+pf31NxnWucCcv7VI19tEWOcCc3bWJr4qYZ096/aPssIZgbBufq3Zs27eVKciYV1HLa4PYZ2wnukQIqxnEoreTlh355TtVoT1bK9A5vEJ65mNcqEFYZ2wngvHYVNuIQPYAAAPGklEQVSZA2Hd/EoS1s2b6lQkrOuoJYf1ib+UGdN+zUe3cTX4lEcTYd3dg4yw7s4p260I69legczjE9YzG+VCC8I6YT0XjsOmMgfCuvmVJKybN9WpSFjXUaMPAggggAACCCCAAAIIIIAAAhYFCOsWcSmNAAIIIIAAAggggAACCCCAgI4AYV1HjT4IIIAAAggggAACCCCAAAIIWBQgrFvEpTQCCCCAAAIIIIAAAggggAACOgKEdR01ETlw6LD89MFnZd3Gz50Krzz3oAwo76NZjW5eBVau3SS3/2Kq0+2iC3rI9Kn3Sduy9B9J1lj7z77YLeMnPi179u5vmIabml7nTHuR+QuXycNPznIorh1SIY9OGCelLUoapVHr89S0uTLlobsaXWN89QSOVZ2QyU/NkrfeXeEUeGziOLlh+JUZi6m13LHzK7l//OiEts/MmCcvvbow4Xtua2YclAYNAl5eg5LXmNcseweSl9em5Nee5NcdXpvsrVN8Za/PgfGvY16eM4O5N01nFNPrwmtT0zk2Cu2eENY1Vjz2BFLRv6/zQ616Qf3llJny+KS7pGfXjhoV6eJFINlbvXCu+GRD2uCXqT3r50Vfv636IfbpGfMafrGiXjjVV3LYi40QH0b45Ym+e6ae8esQM39g/Oi0v3yMDyN33Dw8ZVhvbF0zzYfbMwt4fQ1S6/ry3Lflpz8a6fxyTK3hpCkzZcaTD/CalZnbdYtMrzXJhdQ67Ny9r+GXY+qx+NW+yobXMl6bXNP7aujlOVA99qbPfkN+POYa55fHbp4zfU2ugDubXpdMP3MUMDV3PccFCOsaC5R8pi/5ByeNknTxIJB8Ri/TDzSZ2mfq72FqNG1EQL1QduvSvuEH0+Twnq4rZ9btHVbqB81JT8yUCXePaQhtbn+gaezMOmHd3pqpyn5fgwgYdtYn02tNplGTnxN5bcok5v92P8+BanR+/vO/Bqkq2FgXt69tdu4RVRHQFyCsa9ilChk8CWhAanZJts70g2em9pneiqg5TbrFCaT6gcbtD6KEdXuHUqo1yPROldhs3L4NnrfAm18/v69Bbh975mfetCtmeq3JdO+TH3u8NmUS83+7n+fA2C/O1Da6KZPuYiuk/+VoqGBjXZLfBs9rk8EFo5RVAcK6Bq/6Qem1N5cmvO2asK4Bqdkl+Qytm7Aef0bXTfv4tyJqTpNuKcL6qBGDGn6gcRsYCOv2DqVUtn7DevxsY2GDH2TNrqGf1yDOBJpdi/hqXl+bkh8rmbbTJb9N3t49KZzKus+B8du0CH3mjxfb68Jrk/k1o6I9AcK6hq3fsxoaQ9IlTsDr2Quv7QmH5g83zqybNzVR0c/Zi3Rn1pPnlRxgTMy70GvovgbFHoftz26X9loRhW7r5/57fa2JjeU2OPDa5Gd1Uvf18xyoKvLLL/NroioGsS68NtlZO6qaFyCsa5j63S+oMSRd4gS87gv02p4fiOwcbuxZt+Pqp6qffYGEdT/y/vrqvAYR1P2Zu+nt9bUmFkrcvo2a1yY3q+CtjZ/nwNhIbp8Lvc2ssFsHsS6E9cI+xvLp3hPWNVbL65V4NYagSyMCyb9xTbfPL/bW20ztFy39WHp17+z5AlsskjeBTFeDT/cWT35A9ebstXWmK+6mW5dUP6CqH7AWvrtCbrnhKmcabrc6eJ1zobfP9BqUfKaWs3/BHDGZXmuS1yXT44PXpmDWzctzYNXx4wmfrBB7O/zoEYNcfeRlMPeoaYxicl14bWoax0Sh3gvCuubKe/mMW80h6NaIgJvPTY/fJ9tY+/jb1JBuP/+bBfIu0NjnrCeHwuTHmBot1UeFeZ8FPeIFMn2WbfK6JD9eVK1XnnvQuRYBn+cd3LHV2GtQqlCozt7u2bs/YYI8nsyvl5fXpuTP647NJvZ44rXJ/Pqkquj1OZALleXfuvDaFMyaMYodAcK6HVeqIoAAAggggAACCCCAAAIIIKAtQFjXpqMjAggggAACCCCAAAIIIIAAAnYECOt2XKmKAAIIIIAAAggggAACCCCAgLYAYV2bjo4IIIAAAggggAACCCCAAAII2BEgrNtxpSoCCCCAAAIIIIAAAggggAAC2gKEdW06OiKAAAIIIIAAAggggAACCCBgR4CwbseVqggggAACCCCAAAIIIIAAAghoCxDWtenoiAACCCCAAAIIIIAAAggggIAdAcK6HVeqIoAAAggggAACCCCAAAIIIKAtQFjXpqMjAggggAACCCCAAAIIIIAAAnYECOt2XKmKAAIIIIAAAggggAACCCCAgLYAYV2bjo4IIIAAAggggAACCCCAAAII2BEgrNtxpSoCCCCAAAIIIIAAAggggAAC2gKEdW06OiKAAAIIIIAAAggggAACCCBgR4CwbseVqggggAACCCCAAAIIIIAAAghoCxDWtenoiAACCCCAAAIIIIAAAggggIAdAcK6HVeqIoAAAggggAACCCCAAAIIIKAtQFjXpqMjAggggAACCCCAAAIIIIAAAnYECOt2XKmKAAIIIJCjAgcOHZafPvisrNv4ecIMH5s4Tq4ZXCGTn5rlfP/RCeOktEVJQ5vPvtgt4yc+LXf/6Hq5YfiV0lgddfszM+bJS68uTKtw0QU95Jlf3SPPvfiavPXuilPaXTukwpmD+lJzUm1eee5BGVDep6HtsaoTaW+LNZq/cJk8/GT0PqX66nDOGfLkw/9Lnnzh1QYTNbfpU++TtmWtGu6H8lH3K/4rdh9jt8XPJ3ms2P2JN83RQ4RpIYAAAgggkBMChPWcWAYmgQACCCAQhEBy4I6Nqb7/u/mLZcJPx0jV8eNOmB89YlBCOFXBVH3dP360uKkTH0pjwf6B8aNThu32Z7dz6qb6ig/Ad9w8PKHdyrWb5PZfTHW6JQf5xmpV9O97SvCOjZM8l1ggTw7bMYM9e/dLclhv7P4Esc6MgQACCCCAQFMQIKw3hVXkPiCAAAIIuBJQZ5nnvbm04axxuk4qBE+aMlNmPPmA9OzaUdT/n54xr6Gf2zqx+ibCeq/unWT1uq0y4e4xzpxi4frivj3llXl/kimT7kr4RYDJsH7kaJUcOXJURo0Y1DCGCvGntyyV9/68puEXG+kCv6vFoRECCCCAAAIIJAgQ1jkgEEAAAQQKRiA5hDd2x1UY/Wpfpdz3k1Fy369eSDjT7qWOGsNEWFdnw3fs/MqZcuzs/lPT5oo6265+sWAzrKsxu3VpLys+2eC8NV+9+2DSEzOdsdUvMWLvQiCsF8xDiTuKAAIIIBCAAGE9AGSGQAABBBDIDYFUe6pT7cVWs41/m3fyW8C91HET1t3sWVdh/ZK/6SW/nDJTHp90lyz404dOgFbfU3vpbYf1H4+5xtkeoN7Kv3P3PucXB7HvJYf1xu4Pe9Zz47HALBBAAAEEcl+AsJ77a8QMEUAAAQQsCMTv91blk/eDq++pt7tPm72g4e3wqabhpo6pM+uxC9d9vGajtClrJVMeuksqDx4OJKyrs/nO2///fYnDoH5h0K5Nq4T9/ZxZt3CgUhIBBBBAoGAFCOsFu/TccQQQQACBmEC6t7Un71XPJJaujsmwnnxxu9j/bZ9ZV2E9dj8uK+/jvBU/9n/eBp/pyOB2BBBAAAEEvAsQ1r2b0QMBBBBAIE8Flq34VNTHkqmPJIv/UoE39vZydfG2+BAff2G52Pe91jEZ1tUcfjf/HRk+pMK5H0GGdTX2oqUfS6/unZ2L3BHW8/SBwLQRQAABBPJCgLCeF8vEJBFAAAEETAjEPnM8/mPOYm/dVvWTP1s93Zl1r3VMh/XkXzQEsWc91UfLEdZNHJXUQAABBBBAILUAYZ0jAwEEEECgoARiQTv+Tqfar65ub+xt8F7qZArrbi8wp/asJ3+ZOLMem9+6jZ875dW7D6ZPvc85cx//+fLJY6cL61xgrqAeUtxZBBBAAAFLAoR1S7CURQABBBBAAAEEEEAAAQQQQEBXgLCuK0c/BBBAAAEEEEAAAQQQQAABBCwJENYtwVIWAQQQQAABBBBAAAEEEEAAAV0BwrquHP0QQAABBBBAAAEEEEAAAQQQsCRAWLcES1kEEEAAAQQQQAABBBBAAAEEdAUI67py9EMAAQQQQAABBBBAAAEEEEDAkgBh3RIsZRFAAAEEEEAAAQQQQAABBBDQFSCs68rRDwEEEEAAAQQQQAABBBBAAAFLAoR1S7CURQABBBBAAAEEEEAAAQQQQEBXgLCuK0c/BBBAAAEEEEAAAQQQQAABBCwJENYtwVIWAQQQQAABBBBAAAEEEEAAAV0BwrquHP0QQAABBBBAAAEEEEAAAQQQsCRAWLcES1kEEEAAAQQQQAABBBBAAAEEdAUI67py9EMAAQQQQAABBBBAAAEEEEDAkgBh3RIsZRFAAAEEEEAAAQQQQAABBBDQFSCs68rRDwEEEEAAAQQQQAABBBBAAAFLAoR1S7CURQABBBBAAAEEEEAAAQQQQEBXgLCuK0c/BBBAAAEEEEAAAQQQQAABBCwJENYtwVIWAQQQQAABBBBAAAEEEEAAAV0BwrquHP0QQAABBBBAAAEEEEAAAQQQsCRAWLcES1kEEEAAAQQQQAABBBBAAAEEdAUI67py9EMAAQQQQAABBBBAAAEEEEDAkgBh3RIsZRFAAAEEEEAAAQQQQAABBBDQFSCs68rRDwEEEEAAAQQQQAABBBBAAAFLAoR1S7CURQABBBBAAAEEEEAAAQQQQEBXgLCuK0c/BBBAAAEEEEAAAQQQQAABBCwJENYtwVIWAQQQQAABBBBAAAEEEEAAAV0BwrquHP0QQAABBBBAAAEEEEAAAQQQsCRAWLcES1kEEEAAAQQQQAABBBBAAAEEdAUI67py9EMAAQQQQAABBBBAAAEEEEDAkgBh3RIsZRFAAAEEEEAAAQQQQAABBBDQFSCs68rRDwEEEEAAAQQQQAABBBBAAAFLAoR1S7CURQABBBBAAAEEEEAAAQQQQEBXgLCuK0c/BBBAAAEEEEAAAQQQQAABBCwJENYtwVIWAQQQQAABBBBAAAEEEEAAAV0BwrquHP0QQAABBBBAAAEEEEAAAQQQsCRAWLcES1kEEEAAAQQQQAABBBBAAAEEdAUI67py9EMAAQQQQAABBBBAAAEEEEDAkgBh3RIsZRFAAAEEEEAAAQQQQAABBBDQFfj/Wu/dstr2+MMAAAAASUVORK5CYII=", "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_curves(colors=[\"blue\", \"green\"], title=\"Single reaction A <-> B (no downregulation)\", \n", " show_intervals=True)" ] }, { "cell_type": "markdown", "id": "ce63f6dc-f9fc-4875-82aa-bbd05488ecb5", "metadata": {}, "source": [ "#### Notice the intersection at the exact midpoint of the 2 initial concentrations (50 and 0):" ] }, { "cell_type": "code", "execution_count": 10, "id": "477e29f3-17ee-4037-920a-b3e33920f04a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Min abs distance found at data row: 27\n" ] }, { "data": { "text/plain": [ "(0.02453617850732098, 25.000000000000007)" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.curve_intersection('A', 'B', t_start=0, t_end=0.1)" ] }, { "cell_type": "code", "execution_count": 11, "id": "58b4b5e5-ebd0-4bb6-8059-6a460d555106", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: A <-> B\n", "Final concentrations: [B] = 42.79 ; [A] = 7.21\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 5.93438\n", " Formula used: [B] / [A]\n", "2. Ratio of forward/reverse reaction rates: 6.0\n", "Discrepancy between the two values: 1.094 %\n", "Reaction IS in equilibrium (within 2% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that all the reactions have reached equilibrium\n", "dynamics.is_in_equilibrium(tolerance=2)" ] }, { "cell_type": "code", "execution_count": null, "id": "00363317-fe95-4d18-acab-5e6116e01a17", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "3f67c102-0d90-4624-98f3-d6f50719d8c1", "metadata": {}, "source": [ "# Scenario 2: \n", "### downregulated by shunt: \n", "### kinetically fast, \n", "### but with thermodynamical dis-advantage (i.e. energetically un-favored)" ] }, { "cell_type": "code", "execution_count": 12, "id": "589fe009-4bf5-454e-ac37-9abd6ba7ffeb", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 2 (at temp. 25 C)\n", "0: A <-> B (kF = 30 / kR = 5 / Delta_G = -4,441.69 / K = 6) | 1st order in all reactants & products\n", "1: A <-> S (kF = 150 / kR = 100 / Delta_G = -1,005.13 / K = 1.5) | 1st order in all reactants & products\n" ] } ], "source": [ "# Register the new chemical (\"S\")\n", "chem_data.add_chemical(\"S\")\n", "\n", "# Add the reaction A <-> S (fast shunt, poor thermodynical energetic advantage)\n", "chem_data.add_reaction(reactants=[\"A\"], products=[\"S\"],\n", " forward_rate=150., reverse_rate=100.) \n", "\n", "chem_data.describe_reactions()" ] }, { "cell_type": "code", "execution_count": 13, "id": "cb582868-431c-4022-aa0e-a2f554f80d6c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[GRAPHIC ELEMENT SENT TO LOG FILE `down_regulate_1.log.htm`]\n" ] } ], "source": [ "# Send a plot of the network of reactions to the HTML log file\n", "graph_data = chem_data.prepare_graph_network()\n", "GraphicLog.export_plot(graph_data, \"vue_cytoscape_1\")" ] }, { "cell_type": "markdown", "id": "b0345d36-5702-4b40-9221-a765dfcb0bac", "metadata": {}, "source": [ "### Set the initial concentrations of all the chemicals, in their index order" ] }, { "cell_type": "code", "execution_count": 14, "id": "ae304704-c8d9-4cef-9e0b-2587bb3909ef", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "3 species:\n", " Species 0 (A). Conc: 50.0\n", " Species 1 (B). Conc: 0.0\n", " Species 2 (S). Conc: 0.0\n" ] } ], "source": [ "dynamics = ReactionDynamics(chem_data=chem_data) # Notice we're over-writing the earlier \"dynamics\" object\n", "dynamics.set_conc([50., 0, 0.], snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "markdown", "id": "fc516ca2-e62d-4784-b826-5372ff7f4c75", "metadata": { "tags": [] }, "source": [ "### Run the reaction" ] }, { "cell_type": "code", "execution_count": 15, "id": "2502cd11-0df9-4303-8895-98401a1df7b8", "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, and will rewind there]\n", "* 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", "69 total step(s) taken\n" ] } ], "source": [ "dynamics.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n", "\n", "# 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=0.05, 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", "# The changes of concentrations vary very rapidly early on; automated variable timesteps will take care of that\n", "dynamics.single_compartment_react(initial_step=0.001, reaction_duration=0.3,\n", " snapshots={\"initial_caption\": \"1st reaction step\",\n", " \"final_caption\": \"last reaction step\"},\n", " variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 16, "id": "a41e5009-e2b3-4bea-9892-7b9bd8295a07", "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_curves(colors=[\"blue\", \"green\", \"red\"], \n", " title=\"Coupled reactions A <-> B and A <-> S (fast but disadvantaged energetically)\",\n", " show_intervals=True)" ] }, { "cell_type": "markdown", "id": "f4a147c6-cad1-47ca-bc1e-79b43a29e5c0", "metadata": {}, "source": [ "### Notice how the \"alternate (shunt) path\" of the reaction, i.e. S (red) \n", "### has a FAST START (fast kinetics),\n", "### but EVENTUALLY PETERS OUT (energy dis-advantage)" ] }, { "cell_type": "code", "execution_count": 17, "id": "104ccbd8-d2d8-475e-a9e5-40698293a077", "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 0.00225, in 14 steps of 0.000125\n", "From time 0.00225 to 0.00295, in 4 steps of 0.000175\n", "From time 0.00295 to 0.00393, in 4 steps of 0.000245\n", "From time 0.00393 to 0.005302, in 4 steps of 0.000343\n", "From time 0.005302 to 0.006743, in 3 steps of 0.00048\n", "From time 0.006743 to 0.009432, in 4 steps of 0.000672\n", "From time 0.009432 to 0.01226, in 3 steps of 0.000941\n", "From time 0.01226 to 0.01753, in 4 steps of 0.00132\n", "From time 0.01753 to 0.0249, in 4 steps of 0.00184\n", "From time 0.0249 to 0.03524, in 4 steps of 0.00258\n", "From time 0.03524 to 0.04608, in 3 steps of 0.00362\n", "From time 0.04608 to 0.06127, in 3 steps of 0.00506\n", "From time 0.06127 to 0.07544, in 2 steps of 0.00709\n", "From time 0.07544 to 0.1151, in 4 steps of 0.00992\n", "From time 0.1151 to 0.1429, in 2 steps of 0.0139\n", "From time 0.1429 to 0.1818, in 2 steps of 0.0194\n", "From time 0.1818 to 0.209, in 1 step of 0.0272\n", "From time 0.209 to 0.2471, in 1 step of 0.0381\n", "From time 0.2471 to 0.3005, in 1 step of 0.0534\n", "(69 steps total)\n" ] } ], "source": [ "dynamics.explain_time_advance()" ] }, { "cell_type": "code", "execution_count": 18, "id": "bd33b1e8-abd2-4392-9884-8fd56ee0841c", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABScaption
00.00000050.0000000.0000000.000000Initial state
10.00025047.7500000.3750001.8750001st reaction step
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650.1623546.59394033.31505810.091002
660.1818006.37549033.9226089.701902
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690.3004985.90006135.2450138.854926last reaction step
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70 rows × 5 columns

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" ], "text/plain": [ " SYSTEM TIME A B S caption\n", "0 0.000000 50.000000 0.000000 0.000000 Initial state\n", "1 0.000250 47.750000 0.375000 1.875000 1st reaction step\n", "2 0.000500 45.648594 0.732656 3.618750 \n", "3 0.000625 44.667193 0.903381 4.429427 \n", "4 0.000750 43.718113 1.070318 5.211569 \n", ".. ... ... ... ... ...\n", "65 0.162354 6.593940 33.315058 10.091002 \n", "66 0.181800 6.375490 33.922608 9.701902 \n", "67 0.209024 6.163548 34.512062 9.324390 \n", "68 0.247138 5.994349 34.982624 9.023027 \n", "69 0.300498 5.900061 35.245013 8.854926 last reaction step\n", "\n", "[70 rows x 5 columns]" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "code", "execution_count": 19, "id": "b139f5e4-625f-4a5e-8f57-8f00244dced4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: A <-> B\n", "Final concentrations: [B] = 35.25 ; [A] = 5.9\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 5.97367\n", " Formula used: [B] / [A]\n", "2. Ratio of forward/reverse reaction rates: 6.0\n", "Discrepancy between the two values: 0.4388 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n", "1: A <-> S\n", "Final concentrations: [S] = 8.855 ; [A] = 5.9\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 1.50082\n", " Formula used: [S] / [A]\n", "2. Ratio of forward/reverse reaction rates: 1.5\n", "Discrepancy between the two values: 0.05463 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that all the reactions have reached equilibrium\n", "dynamics.is_in_equilibrium()" ] }, { "cell_type": "code", "execution_count": null, "id": "f87fe3c7-2c0d-4e3c-aff0-350bd04ea1a7", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "9e9260a7-5777-4eee-93b8-c46b8364e24f", "metadata": {}, "source": [ "# Scenario 3: \n", "### downregulated by shunt: \n", "### kinetically slow, \n", "### but with thermodynamical advantage (i.e. energetically favored)" ] }, { "cell_type": "code", "execution_count": 20, "id": "04476dab-f845-4533-8f26-fd0eecf8304f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 2 (at temp. 25 C)\n", "0: A <-> B (kF = 30 / kR = 5 / Delta_G = -4,441.69 / K = 6) | 1st order in all reactants & products\n", "1: A <-> S (kF = 3 / kR = 0.1 / Delta_G = -8,431.42 / K = 30) | 1st order in all reactants & products\n" ] } ], "source": [ "# Specify the chemicals (notice that we're starting with new objects)\n", "chem_data = chem(names=[\"A\", \"B\", \"S\"])\n", "\n", "# Reaction A <-> B (as before)\n", "chem_data.add_reaction(reactants=[\"A\"], products=[\"B\"],\n", " forward_rate=30., reverse_rate=5.) \n", "\n", "# Reaction A <-> S (slow shunt, excellent thermodynamical energetic advantage)\n", "chem_data.add_reaction(reactants=[\"A\"], products=[\"S\"],\n", " forward_rate=3., reverse_rate=0.1)\n", "\n", "chem_data.describe_reactions()" ] }, { "cell_type": "markdown", "id": "6154b260-ce64-450a-b069-22cb920818d3", "metadata": {}, "source": [ "### Set the initial concentrations of all the chemicals, in their index order" ] }, { "cell_type": "code", "execution_count": 21, "id": "a45c9ebf-d06e-443f-a1a1-a5b2db6803b7", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "3 species:\n", " Species 0 (A). Conc: 50.0\n", " Species 1 (B). Conc: 0.0\n", " Species 2 (S). Conc: 0.0\n" ] } ], "source": [ "dynamics = ReactionDynamics(chem_data=chem_data)\n", "dynamics.set_conc([50., 0, 0.], snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "markdown", "id": "e6bddc07-e9cf-4236-bd2b-0e1fe0567800", "metadata": { "tags": [] }, "source": [ "### Run the reaction" ] }, { "cell_type": "code", "execution_count": 22, "id": "3800cb7b-475e-4437-a982-af2760355795", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "* INFO: the tentative time step (0.005) leads to a least one norm value > its ABORT threshold:\n", " -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.25 (set to 0.00125) [Step started at t=0, and will rewind there]\n", "454 total step(s) taken\n" ] } ], "source": [ "dynamics.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n", "\n", "# These settings can be tweaked to make the time resolution finer or coarser\n", "dynamics.set_thresholds(norm=\"norm_A\", low=2.0, high=5.0, abort=10.0)\n", "dynamics.set_thresholds(norm=\"norm_B\", low=0.008, high=0.5, abort=2.0) # The \"low\" value here seems especially critical to fend off instabilities\n", "dynamics.set_step_factors(upshift=1.5, downshift=0.25, abort=0.25)\n", "dynamics.set_error_step_factor(0.2)\n", "\n", "# The changes of concentrations vary very rapidly early on; automated variable timesteps will take care of that\n", "dynamics.single_compartment_react(initial_step=0.005, reaction_duration=7.0,\n", " snapshots={\"initial_caption\": \"1st reaction step\",\n", " \"final_caption\": \"last reaction step\"},\n", " variable_steps=True, explain_variable_steps=False)" ] }, { "cell_type": "code", "execution_count": 23, "id": "8a533692-7830-49a2-83f5-8da6aa201935", "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_curves(colors=[\"blue\", \"green\", \"red\"], \n", " title=\"Coupled reactions A <-> B and A <-> S (slow but with energetic advantage)\")" ] }, { "cell_type": "markdown", "id": "05dbe681-2fa9-478c-b4eb-8c322e173c0c", "metadata": {}, "source": [ "### Notice how the \"alternate (shunt) path\" of the reaction, i.e. S (red) \n", "### has a SLOW START (slow kinetics),\n", "### but EVENTUALLY DOMINATES (energy advantage)" ] }, { "cell_type": "code", "execution_count": 24, "id": "f0d7d7ed-158c-4cf4-8d95-ef057ca612d6", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "From time 0 to 0.0025, in 2 steps of 0.00125\n", "From time 0.0025 to 0.03281, in 97 steps of 0.000313\n", "From time 0.03281 to 0.05859, in 55 steps of 0.000469\n", "From time 0.05859 to 0.07617, in 25 steps of 0.000703\n", "From time 0.07617 to 0.09199, in 15 steps of 0.00105\n", "From time 0.09199 to 0.1062, in 9 steps of 0.00158\n", "From time 0.1062 to 0.1205, in 6 steps of 0.00237\n", "From time 0.1205 to 0.2237, in 29 steps of 0.00356\n", "From time 0.2237 to 0.3999, in 33 steps of 0.00534\n", "From time 0.3999 to 0.6402, in 30 steps of 0.00801\n", "From time 0.6402 to 0.9525, in 26 steps of 0.012\n", "From time 0.9525 to 1.349, in 22 steps of 0.018\n", "From time 1.349 to 1.998, in 24 steps of 0.027\n", "From time 1.998 to 3.66, in 41 steps of 0.0405\n", "From time 3.66 to 4.876, in 20 steps of 0.0608\n", "From time 4.876 to 5.971, in 12 steps of 0.0912\n", "From time 5.971 to 6.929, in 7 steps of 0.137\n", "From time 6.929 to 7.134, in 1 step of 0.205\n", "(454 steps total)\n" ] } ], "source": [ "dynamics.explain_time_advance()" ] }, { "cell_type": "code", "execution_count": 25, "id": "8fe4bbce-f10b-4590-9cbd-97998745fc27", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABScaption
00.00000050.0000000.0000000.000000Initial state
10.00125047.9375001.8750000.1875001st reaction step
20.00250045.9718203.6609380.367242
30.00281245.5034684.0862030.410329
40.00312545.0406114.5064130.452976
..................
4506.5185461.5389959.35682439.104182
4516.6553881.5263669.27276439.200870
4526.7922301.5145749.19437639.291050
4536.9290721.5036319.12121439.375155
4547.1343341.4879839.01916839.492848last reaction step
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" ], "text/plain": [ " SYSTEM TIME A B S caption\n", "0 0.000000 50.000000 0.000000 0.000000 Initial state\n", "1 0.001250 47.937500 1.875000 0.187500 1st reaction step\n", "2 0.002500 45.971820 3.660938 0.367242 \n", "3 0.002812 45.503468 4.086203 0.410329 \n", "4 0.003125 45.040611 4.506413 0.452976 \n", ".. ... ... ... ... ...\n", "450 6.518546 1.538995 9.356824 39.104182 \n", "451 6.655388 1.526366 9.272764 39.200870 \n", "452 6.792230 1.514574 9.194376 39.291050 \n", "453 6.929072 1.503631 9.121214 39.375155 \n", "454 7.134334 1.487983 9.019168 39.492848 last reaction step\n", "\n", "[455 rows x 5 columns]" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_history()" ] }, { "cell_type": "markdown", "id": "4f451620-86fd-4e3c-a060-6b506f78c13d", "metadata": {}, "source": [ "### Check the final equilibrium" ] }, { "cell_type": "code", "execution_count": 26, "id": "96424a3f-31da-46bf-81c0-0a85b9bc476d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0: A <-> B\n", "Final concentrations: [B] = 9.019 ; [A] = 1.488\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 6.06134\n", " Formula used: [B] / [A]\n", "2. Ratio of forward/reverse reaction rates: 6.0\n", "Discrepancy between the two values: 1.022 %\n", "Reaction IS in equilibrium (within 12% tolerance)\n", "\n", "1: A <-> S\n", "Final concentrations: [S] = 39.49 ; [A] = 1.488\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 26.5412\n", " Formula used: [S] / [A]\n", "2. Ratio of forward/reverse reaction rates: 30.0\n", "Discrepancy between the two values: 11.53 %\n", "Reaction IS in equilibrium (within 12% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Verify that all the reactions have reached equilibrium\n", "dynamics.is_in_equilibrium(tolerance=12)" ] }, { "cell_type": "markdown", "id": "fbeba7fe-7a4d-4223-aaa1-6b5b9b3cc1b8", "metadata": {}, "source": [ "#### Please note the much-longer timescale from the earlier plots\n", "If we look at early time interval, this is what it looks like:" ] }, { "cell_type": "code", "execution_count": 27, "id": "f8c50006-8c5d-405f-9442-7fd9e5d1274d", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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", "text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = px.line(data_frame=dynamics.get_history().loc[:250], x=\"SYSTEM TIME\", y=[\"A\", \"B\", \"S\"], \n", " title=\"Same plot as above, both only showing initial detail\",\n", " color_discrete_sequence = [\"blue\", \"green\", \"red\"],\n", " labels={\"value\":\"concentration\", \"variable\":\"Chemical\"})\n", "fig.show()" ] }, { "cell_type": "code", "execution_count": 28, "id": "5c44014b-9dee-4d8c-a2de-13478ee7bb63", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Min abs distance found at data row: 71\n" ] }, { "data": { "text/plain": [ "(0.02405919499545674, 23.73396682504195)" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Look at where the curves intersect\n", "dynamics.curve_intersection(\"A\", \"B\", t_start=0, t_end=0.1)" ] }, { "cell_type": "code", "execution_count": 29, "id": "ac0382c7-5940-4db7-b1df-80edd29c3336", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Min abs distance found at data row: 216\n" ] }, { "data": { "text/plain": [ "(0.14412951669101942, 6.026379520544665)" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.curve_intersection(\"A\", \"S\", t_start=0.1, t_end=0.2)" ] }, { "cell_type": "code", "execution_count": null, "id": "d70f2d6b", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }