{ "cells": [ { "cell_type": "markdown", "id": "3bbe8002-bdf3-490c-bde0-80dd3713a3d0", "metadata": {}, "source": [ "## A simple `A <-> B` reaction whose rate constants are to be estimated from a given time evolution of [A] and [B] \n", "### (values given on a *variable-time* grid.)\n", "\n", "Assume the reaction is known to be 1st order (won't verify that.) \n", "\n", "In PART 1, a time evolution of [A] and [B], with known rate constants, is obtained by simulation \n", "\n", "In PART 2, the time evolutions generated in Part 1 are taken as a _starting point,_ to estimate the rate constants of `A <-> B` \n", "\n", "In PART 3, we'll repeat what we did in Part 2, but this time showing the full details of how the answer is arrived at" ] }, { "cell_type": "markdown", "id": "4118b513-1c98-455d-b58f-37898bb03bdd", "metadata": {}, "source": [ "### TAGS : \"numerical\", \"uniform compartment\", \"under-the-hood\"" ] }, { "cell_type": "code", "execution_count": 1, "id": "900caaa3-7883-466c-a2bd-5f61de65b151", "metadata": {}, "outputs": [], "source": [ "LAST_REVISED = \"Nov. 12, 2024\"\n", "LIFE123_VERSION = \"1.0.0.rc.0\" # Library version this experiment is based on" ] }, { "cell_type": "code", "execution_count": 2, "id": "97b7f9e2-99b8-42a1-bede-b9e551b9e024", "metadata": {}, "outputs": [], "source": [ "#import set_path # Using MyBinder? Uncomment this before running the next cell!" ] }, { "cell_type": "code", "execution_count": 3, "id": "3924c013", "metadata": { "lines_to_next_cell": 2, "tags": [] }, "outputs": [], "source": [ "#import sys\n", "#sys.path.append(\"C:/some_path/my_env_or_install\") # CHANGE to the folder containing your venv or libraries installation!\n", "# NOTE: If any of the imports below can't find a module, uncomment the lines above, or try: import set_path \n", "\n", "import ipynbname\n", "import numpy as np\n", "\n", "from life123 import check_version, UniformCompartment, ReactionKinetics, PlotlyHelper, Numerical" ] }, { "cell_type": "code", "execution_count": 4, "id": "1276f744-1b85-46e1-8d9d-f6fa90e73b49", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "OK\n" ] } ], "source": [ "check_version(LIFE123_VERSION)" ] }, { "cell_type": "code", "execution_count": null, "id": "b5208e04-e3b8-4769-8937-d61751e55a47", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "1190f092-c2ff-46f0-bce9-86e38ef13248", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "9329208b-070f-4902-8f37-0f11ddf75ed6", "metadata": {}, "source": [ "# PART 1 - We'll generate the time evolution of [A] and [B] by simulating a reaction of KNOWN rate constants...\n", "## but pretend you don't see this section! (because we later want to estimate those rate constants)" ] }, { "cell_type": "code", "execution_count": 5, "id": "72b4245c-de4e-480d-a501-3495b7ed8bc4", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 1 (at temp. 25 C)\n", "0: A <-> B (kF = 12 / kR = 2 / delta_G = -4,441.7 / K = 6) | 1st order in all reactants & products\n", "Set of chemicals involved in the above reactions: {'B', 'A'}\n" ] } ], "source": [ "# Instantiate the simulator and specify the accuracy preset\n", "uc = UniformCompartment(preset=\"mid\", enable_diagnostics=True)\n", "\n", "# Reaction A <-> B (mostly in the forward direction)\n", "uc.add_reaction(reactants=\"A\", products=\"B\",\n", " forward_rate=12., reverse_rate=2.) \n", " \n", "uc.describe_reactions()" ] }, { "cell_type": "markdown", "id": "98a9fbe5-2090-4d38-9c5f-94fbf7c3eae2", "metadata": {}, "source": [ "### Run the simulation" ] }, { "cell_type": "code", "execution_count": 6, "id": "ae304704-c8d9-4cef-9e0b-2587bb3909ef", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "2 species:\n", " Species 0 (A). Conc: 40.0\n", " Species 1 (B). Conc: 10.0\n", "Set of chemicals involved in reactions: {'B', 'A'}\n" ] } ], "source": [ "uc.set_conc({\"A\": 40., \"B\": 10.}) # Set the initial concentrations\n", "uc.describe_state()" ] }, { "cell_type": "code", "execution_count": 7, "id": "2502cd11-0df9-4303-8895-98401a1df7b8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "39 total step(s) taken in 0.260 sec\n", "Number of step re-do's because of elective soft aborts: 2\n", "Norm usage: {'norm_A': 24, 'norm_B': 22, 'norm_C': 22, 'norm_D': 22}\n", "System Time is now: 0.51497\n" ] } ], "source": [ "uc.single_compartment_react(initial_step=0.01, duration=0.5,\n", " variable_steps=True)" ] }, { "cell_type": "markdown", "id": "199b6238-f6ed-44a8-8130-a003444d7658", "metadata": {}, "source": [ "### Plots of changes of concentration with time" ] }, { "cell_type": "code", "execution_count": 8, "id": "a2c0e793-5457-46a5-9150-388c9f562cf0", "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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Changes in concentrations with time (time steps shown in dashed lines)" }, "xaxis": { "anchor": "y", "autorange": true, "domain": [ 0, 1 ], "range": [ -0.00016873089741361685, 0.5151354298037722 ], "title": { "text": "SYSTEM TIME" }, "type": "linear" }, "yaxis": { "anchor": "x", "autorange": true, "domain": [ 0, 1 ], "range": [ 5.158550723032478, 44.84144927696753 ], "title": { "text": "Concentration" }, "type": "linear" } } }, "image/png": 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cxa/dSV8uT9V96uRxhfGtd9xj+VKzmXJ5Sl9+/smHb+K2UeNQPi7OTHBTYbR1b2oHLwLZVX6rSat1Jo8LM5sT4l049xs0bXElGjVuaiZLAQ8jj7cJEyYEPB+RkgGK18eapnhLC5ziLf4C5MtG8VqjR/Fa42UUmuL1naGVGCheK7QMwlK8FK/aLOzq8VG81g5KitcaL4rXd16+xkDx+kpQ7M8xXhsgBlkUHOMNsgqxMTtOXGq2MbuORcXJVY6hBsVrA2uK1waIQRYFxRtkFWJjdiheY5h2infY6GeQnJSIj9540saacyaqzWl7kDr+BUx97zmktGzsl0QpXhuwUrw2QAyyKCje4gq5cOECCoryUXiuUHktOCd/C5TXfPFbWCTel+/Jz87m49yFczh/4bzyW3S+SHm9IP+WP/K9C0XFf6u/uKCE075XBF2Yi3EVx3NBiUu/jxL/xfSUuNUwSrpiHzU9EUZ0N8TveZwpEinp0r4Uz8V91Hgv5l8bj5pO8T6aMl1M/4LIa6lN5MPTJnmX2qL0UXgRh4zCQzyPdX4Grw34m6fslXx+76Ov4scNaaXCJ1VNwIoZE5X3AiHeGfNX4plX/o0X/3w/hvfvabos+oAUr9fonNuRY7wc41VbW6DHeM+cL0RmQQYy8jOQVZiBTPlbkC7+nYmiDXnIqJ+DnPKnS8RZLMwCIVUh0otSzT976d9SsIXic7NbH/RRgi4TP05ul+EyDBc/k8RPsGypSMUv4me7+AmF7Xk8b3pWc+s+o6GVrFo+KeNa1avh5afHBkS8dnGmeO0i6cd4KF6K13bxfvAmet04ELniR4pTyjTrTCYy1H8LkarvZ56Rci3+zT+X57Klj8M4zBA/R8WP1a1CTEVUiK2ACuXEq/rv6It/l7v0fr3MOoiOikZmzRzlNSY6RnmNEr/Kj3wvKqb4b/VXdMVkOO17MdCFuRhXcTxRSlzafc6fPoeczSdRo2dDTbwXwyjpin00cVSILYdK5WNxOq+oTNpKPpV8F6ej5FP+rf5bzffFskVfUMNoyiTCLJs/B02at0LDy5tcwi3idLdF6T836NyWCaOL0Ns4zM5qlnLdtedgSc/WVXnUHq/8XO0Zu5K1tuesvbzba/jD6Nk5BSvXbkZ6Zo6S1Li7hqJ+3ZpKz1bd1H2MhKnvmcv9H75vBIx67FuXTVGipHitniECEJ7ipXitivdQzgEov6cvvur+fvDMA/iX+BF9T0stOjamPKrFVUPVCkmoElcVVcW/q1Sohmrit/bOZKB5HCokVhICLZZlXIx41Um1ohSsfE9KVoSTYcxudvX4zaanhuOsZqvEyoY3K17Z2x16fXelV+tuk+LdvfeQIkopOrlJkTZtXK9k3FfK71R6NmZOeVH5fOLk6Zj02SyoApThpXBVsaqf6y9py31lHHph6r8kyM//+eFXSvrys0fG3FIyhivz6yoe3+mWjYFjvDZQ5RivDRCDLApvx3hzz54ulmrOwRKxHtaJVY5zutsqxyagWsWkYnEqIr34e/HfVcqrfwu5loSrivjYykFGMTizw8lVxvXiaXKVKjYzY6hGY7xPvfQBtu3cZyhJNUdStrcOuUaRtdrjVSVv1BOVccoesRxb1n4u45MTpMzkVZX+l7OXlomHk6uC8xhWckXxBnHleJk1T+KVk3K2p29F2qkt2H5Svm4Wv1txLPeIxxRrxddG3YT6xb+VL75e/He9hAaKaLn5jwDFG3jxqhOhjHKi9pJdiVcrU9kLNhLmr/sOK5ej1d6zUTpqj1r7mQzPS83+O/ZsjZnitRVnUESmFe/R3MNIuyjX7UKuUrZpJ7eIOatlB+HkpdkSqSoyrQcpU61o5SVhboEjQPF6J165l5VLzfrbibQ9XlW8nsQox3j1PV47xCvL0aV9y5LL3trL3BRv4I5N0ylzjDe8xnjX716Djat+wMEmR7ErYxs2HduEk/knDNtDk2rN0SK5NVrK3+opiD0YJS4PV+WSkT4umWn64LsYkGO8VomVDW92jNfT5CopV1ezmo0uNbu7FOxLj1eW0NWlZiPpU7y+tyFHY6B4Q1u8v2bsxA+HV+LHQyvF6wpcOF1U5taUpIrJaJF0pZBr6+JXKdoaVyqTkLSbXZOLuGSktUOY4rXGyyi0WfGqvV79DGVVZurEK09jvDIedWaxttcr5dylfSvlPlxfxCvHZmUe0jOzS2Zgq5Or5KQqvZRlD1huvNTse1uyHIP6rUf/LUydoScjbNKobsksPPk3xRta4t2XtQc/HFqBNUdWYY14PZC9r1Q7aV3xSvQ90xeJXWugc/22qB3XTLlMbGajeC89JcsML7vCULy+k7QiXq00tSlrz5tmxOsqHu2sZm8vNauTorTnbpmemkcp+FkLVpdkX44rqzOqeanZ9/ZkOgZ1kF5OX9c2IP2Ud6MGxTFe05gdD3j09GGsPLhU6dWuEb3avVm/lspDjUo10bVuL3St01P89hKXjlspn3uaXOV4QZigbQQ4xmuM0tOsZtsqgBFxrWbZBrQz4+QlB6145eWOx8aNLFmCTF5SeX3StFI3kFO8wXUkyZnF8/bMwrxfZynS1W7VxD2u3RTRit+6PdG6ehvDzFO8wVWnduaG4qV47WxP3sQV8ffxaqUrAWrFa3TJweg9itebpmfvPlK28/fMVoS74sCSUpFff/kgdJOirdcLbWq0M5UwxWsKU0gGongp3kA33IgWr1663ohXHeNNrFIF8fGVUa9+A+Tl5SI7KwsdO3bB3Dmz0K1HL+RkZ+HA/n3ocXUfLF44H8NuvAXfzZ2NGwYOUV779L0OP6xegW7deymvt6beiQ/ffxsjU+/ChvVrkZBYBfUbNFTC3jX6fuzetQNbt2wW8dyMH1atUNqRTGf+vNmoX68hWqe0UdJT45Kffzbl30p6NWvWwvp1a5U8yXTltnXzJhw4uA/9BwxR/tbvaxRGvqePR23Qy5YsVPLcoWPnMm1cm19XB8Drf38Rjz1RvJqM0SbjR4Uo7Kq4G7N3zcDSvYtLBRvSbDiGNB2G5meb4fiRYyXl8nTAHT9+TGF89733o0L5csgrOOdpl5LPzZTLTGRvv/k6xox7EHFx5leN8hSvtu49hfX2c7vKbzV9tc7kcWFmk1+qysVEo+CM+4VMzMTlKszMb75G6ytT0KRpc1+icWxfebxNmDDBsfQiPaGIFq/Rep1qg5CD7X26ty3zeCh9j9dQvLm5yJLi7dQZ8+bMRtfuPZGTk10s3l59sGTRfAwdfjO+m/ctbhgwWHnt07efEOhKIc+eyustqXdg8gfv4JaRd+LnDT8hISGxWLwi7J133yfEuxNpWzdhiIhnjRC13LoKaS8Qn9cV8m99ZRscPCDEezEu+fl/PpmspFdDiHeDFK/IU+9r+in7bt2yCYcO7Mf14nO56fc1CiPf08ej8lu+dJGS5/YG4tXm19UB+M9/vIRH/vS04ccztv8Pq75fhk1ZG7FG/Kjb4KZDMbipEG6zYZCrP7nKs7uD/oQUr2A4SpzEK8XF4LQF8Zopl5kTzrtvvYH7fveAreLV1r2ZPHgTxq7yW01brTN5XJjZpHTLl4tCXqH/xDt7xtdo2bqNEG8zM1kKeBh5vFG8zlVDRIvXCLPVMV5VvPEJsscbj9p16iM/P0/pTbZp1xFLF85B+049kHs6G4cP7kenbldj1fKFuG7gjVi+aC569xuovHbr1Rfr165Gh87dldfBN6Zi6qfvY9DwVGzdtB7xlRNRp14DJeyI1NHYu2cXdm3fosSjnU27fPE8kYd6aNYyBUcO7S+JS5Z1+tQpSnrJ1Wti8y+lZyPvTNuMI4cPove1AxQs+n3le/ow8j19PCrTNSuXKHlOaduxDGYzs3/lLMsxDz1Rsq+8lDx12yeYuv1T7M/ai/7iRzwqAFUur44BVwxF/8ZDkVA+sUxaRnl2d3ipM2RvveMeJCXE4Xim+fWSzZTLzKHN24nMULoUhrOarfEyCm11VrPvKUZ2DBSvrv714vU0q7nPrj1Yfvo0JiVfhiHxxb0sbvYRWH1ouRDup/jfji9KIpWLVqS2vBuprUYZytaO1DnGawfF4IyDY7zG9cJZzc61V4rXg3jlx+7u4/3H8RN44tAR3ByfiDeTazlXc2Ge0qebP8TUtE+w8fiGkpIObjJCEe41DYvHpf25Ubz+pBvYuCleijewLRC8ncjXCthWUIDWaTuRFBODzXUb+xpdxO8/ZfP7eHfDG8oTfuR2WeU6imxHtrgLDao0cowPxesYascTongpXscbnS5B9nh9rAF1jDezUiXUFmOazcSMYo7xAlbHeOX47bsb/olfM3cqNfK8+Em+vgFGNEs1rCF38Wt34BhvMQ3t+L6PTd7l7naNcVvNH8d4rRIrG55jvL4ztBIDxWuFlkFYrXgrVYpHpwaNKV7Byax4Z+76Cu+ufwNbTm5U6KbUaIvx7R/B8e9+KzW5So+e4rXWcCneS7yc6PEunPsNmra4Eo0aN7VWUQEKHS7ilQseyU0+nzeYN4rXx9rRivdchYq4tlETiteEeHeLhxN8fvozrDtSfDuQfNLPA0K4I1uOUv7Wz2qmeH1rqBQvxeuuBYWDeOWqgh9Pnac8GEG72qBvR45/9qZ4beAqV65qsnsnjhcVYUFtcQ9tbJwNsYZnFJtP/IKXf3gOy/cvUgpYL7EBxrd9BKPb/C6oCswx3qCqDlsz40SP19YMOxRZqM9qlnegtGvdFD9v3aUQ++iNJx0iZz0Zitc6szJ7SPGOO3QI/xX36j5ZJRm/r5JkQ6zhF8Xff3wBb/70ilKw5ArV8UCHRzGu3R+DsqAUb1BWiy2ZoniNMVoR76rTuUgXHQ2ntx5irYSkcjGGycpbQae+9xx+3Xe4zHr6TufTU3oUrydCJj6X4v3qVCbuO3kEHcQyf7NqmXuMnImowyLIwr1z8fLq/8OO9DSlPPe0GYenur2A+NjKQVs+ijdoq8bnjFG8vou36bYd2F1Y6HNdWI1gV6vmaBJX9oqiepl55pQXlSj16zFYTcff4SleHwmrY7yVxbrEO8QtRb8lV0dquVgU5eRE/MpViIvGl9lTMS3tU4Vy21od8bQQbsXDscrf7Tv3cEmfY7zjUN7gBONtc+UY7yVyTog33CdXjd5/AOnnnO/xTmlQ37DHq15mfvi+EUpFy7/lFqyXmyleb89kF/dTxSsfCHAkNha/VEtCb0ShZn5+RIv34xlvYdHR+Vh2bplCSvZwH+rwuPJvM7edULwUr9lDk7cTmSXlOlyoT66SPVyjbeuyKb7D8UMMFK+PULXizROXmZeLpxQ1E2MfV505G5HiPX/hPP609EFkbjumrKVcrXFNRbpXVLu0WDzF677Rca1mawclxWuNl1HoUBav0TPSZRmD+XIzxet7m4X6PN4T54vQ9uAe0d8FdtVvgopR8l+Rs209uQmPLx6PTSd+Fo9di8VrfcTTlVreGZIAOMYbktVmKtNOXGo2lZEgC2RlclUwZV0u6ZuclFjmsnIwX26meG1oQap4ZVQ3HzuEHwrz8H712hhcKXgnD9lQ7FJRfLX9P3h8yQM4d/4crqrZHv/o+y5aV29jdzKOxUfxOoba8YQoXmPkoSpexxuQDQlSvDZA1Ir3vZwM/C3jJG4RD034V4Q8NOH5lU/iw1+KV4pJbXU3XhPSjVL6/aG7UbyhW3eeck7xUrye2oi/P6d4fSSsHeOtKJaMjLusDmann0CNvDzc27VXWD+PVz4Xd+Lsl8RKMScxX/y80Os13HfVAwpRs0tGusLPyVWcXGX20OQYr1lSrsOF8hiv76V3PgaK10fmevHWrlMfM04dR1RuDnp16IpjyxaifaceyBWLaxw+uB+dul2NVcsXKg+wlw+1lw+ml6/devVVHlrfoXP3kofXT/30fQwanoqtm9YrD5WvU6+BEnZE6mjs3bMLu7ZvUeLRTlZavngeateph2YtU8o8zF57S4n+Afb6hwkcObS/JBkruWUAACAASURBVB8qIm2Y7377VlxaHo9m+U3RIK4hbh14D7rVvbqEJsXrfcPi5Cpr7Chea7yMQlO8vjO0EgPFa4WWQVgj8f6YlY6jWRlISGmL2qtXhJ14NyT8jNfW/k2hcU/y/biuzgD07j2gFB2K1/uGRfFaY0fxWuNF8frOy9cYHBevfHpEemaOYb6D9Z4rT5C1Y7wy7I+F+Rhx7CCuiC2P72s39LR7yHyeVZip9HLn/jpTyfPjnZ/FI52fDpn8W8kox3it0AqtsBzjNa4vTq5yrh07Kl5X076dK65/UtKLV6bS7tCe4ocmXCYemlA+9B+asDtjB8bMux07xbKPSRWTxQSq93DD5YP9AzQIYqV4g6AS/JQFipfi9VPTMh2to+IN5huaTRMzCGgk3j+lHyt+aEJV8dCExNB+aMIvx9fj/rmpOHL6kDKO+0bfSWhQpZEvyIJ+X4o36KvI6wxSvBSv143Hph0pXh9BGo3x5ufnYV9mOj6u3wC3/Lwevbr0DNnJVVU71cL9825DTmE27qg+CgOrD0GffoNKqOknaakfcIzX+4bFMV5r7DjGa42XUWhOrvKdoZUYHBWvvNTcr1cHqAtZW8losIZ1Jd7s7Ey8Va8+hm74SZlcFZN3OuRmNS9cPgtPZzyJCxcuYESzVDxc/xEcOXwQva+9NJGK4r3UMs0shWmmHVO8ZihdCkPxWuNF8frOy9cYHBWvqzU1fS1EIPd3Jd6c7Cwsv6IJGvywAvFtO6LV2bMhJd4vVk/Glg3rMUX8jLpyDF7u8yb0txxJ7hQvxasSsOuLh9XjmeK1Sqxs+FDv8RpN2g3mybqOitfVEyTUZhDMoNw1baMxXhn+69xs/OHUMfSsUAnTatb1/ehwKIY5u2dg7PzbldQeaP8onulefOtQJG0c4w3f2uYYr3HdhvKsZineW4dcU3I1Va7TfCo9G+rzeYOtNTsq3mArvF35cSXePPGknhbioQlF4lLt2jqXo265cnYl6bd4VhxYgtSZxbOV5WP85JOFInGjeMO31ine8BfvxMnT8eXspVgxo3gp22DbKF4basSVeGXUvzt5BN+K8d3nq1bHmMRqNqTmvyh+ObYOI2cMwumzObg7ZSxe6v0v/yUW5DFTvEFeQT5kj+L1Xbyr9q9Cen66D7Xg3a49GvQQtzOWvUtE3+OV84laNWuIl58e611Cft7LcfHKcd5nXvl3qWK9+Of7Mbx/Tz8X1T/RuxvjbdOuIxYsmIN5zZqh+Zkz6JieEbRLRq5YvxAz103DF2f/i5ua34anWk1wu2SkSpNjvJfalV1jnJxcZe1Y5RivNV5Goa2O8Tad2BS703f7nrDFGHY9vAtNkpqU2ctojHfo9d0pXklKdv8nfTYLU997DiktGyvwNqftQer4FzDurqEhOdvZk3iXLhTibdoc8eKhCf2ystCze++gW6v5eN5RPDXtIVTILY/cRmcwZfDXZdZ5lnXFyVXuzxIU7yoFUPvOPSyeTn0LTvH6xk/ubVW8o2eMDkiPd8rwKaZ6vLJMck5RsHrF0R6v/nKA2lyC/Xq8u2ZtRryHWrfBr5kZ6JiRgcE9rwkq8bbp0gWpswaj6EghOlXqgmfv/rvyEHtPD0lgj7dsq6B4KV61VSyc+w2atrgSjRo39d2KDsRgVbwOZMlSEkZuCebLzY6K19XKVerl53Cb1ay2HHXt5lox5bCh7uWWGpS/A98xayiW7V+EK2tchalD56CawfiJv/MQjPFzjDcYa8WePHGM15hjOM1qDvYrqY6KNxx7vLIJu5tcpTbxG47sx5azhfigem0MqlTZnjOIj7H8bv6d+Hb3dDRMvBxTh89Bg8RGPsYYPrtTvOFTl/qSULzhKV79w3eC9TKzpO+oeMNxjNeseD8UK1k9n3kC11eMx8c16gT8rPanpQ/gv1vleEkypg6bg9bV2wQ8T8GUAYo3mGrD3rxQvOEnXntbiP9jc1S8sjiRNqtZTq6SS0aeEitZrdi3G4tbtMb927ZgwKARykPte/cbqLx269VXmUXcoXP3ktnEUz99H4OGp2LrpvWIr5yIOvUaKGFHpI7G3j27sGv7Flw38EZoxxaXL56H2nXqoVnLlDLjtNOnTlHS++++T7Dsh3lIikrCfTf+EV3r9CwzcYpjvPcgKSEOxzMLTB+FHOPlGK/aWDjGa/qwiciAjos33CibmVwlxZsrnlS0dt8eTG/WArdv3YybBt8UEPFGN6+IB1fdg67iZ0TDkbhjyO+UKtHPWKZ4KV6rx6pdXzyspstZzVaJlQ0f6pOrfCfgbAwUr4+8rYh354G9+KhJMwzbvBGjht7iuHi/+HwS3sl5G7+d24OnGz6HDtU6o2vPvhSvpg2oJ/Fb76B4rR4aFO8lYuzxWm09kRXeEfGq91PJe3jdbeE6q1lb5p6H9wrxncV/atTFNRUrOdbaCosKMPSra7Dl5EZlgYy3rpvsWNqhmBDHeEOx1szlmWO8xpxCeVazuZoPnlCOiDd4iuufnJiZ1aym/K+sU/hHVjpurJSAt6tf5p8MGcT6xJIH8fm2j9G2VkfMvnkZoqOiHUs7FBOieEOx1szlmeKleM21FP+FclS8ru7jDeUFNGTVWBHvAdHb7Sp6vXLbXLcxkmJi/Fe7F2OesetLPPjdaOWvRalr0bL6lX5PM9QToHhDvQZd55/ipXgD3bqDQryBXEDjqZc+wKwFq0vqoUmjumUeJSVXQNm995ASRv+5lTHewwf3K2s1z1wyHx937IxxYqx3xPVD/Dqrec2aZZiQ8SxOFZzE85VfwIjBo5BcvWaZ5+hyclVxE+AYr/enJI7xXmLHMV7v21Ek7BkU4pXyW7l2c0Ae4SSlqn1mo/w7OSkRH73xpFL/+uc66j/3RrwLl36Hdzp0QurGn3Fv/2F+Fe/U7ybjtbx/4PrLB2FIziDldiKK1/WhTfF6f9qjeCle71tPZO3pd/Ea3bdrhDhYnlAkvwRs27mvRMZyta3Hxo0seXqSLM/rk6aVfEnwRryrli/ER6LH22v9WvS6dgDSv1/il/t4P101CTt+3oSvY/+HRbetxU9zl1K8Ho5vitf7EyDFS/F633oia0+/i1eL09UYbzAhl6Jt2rie0uNV1/s0epqS9r3cgnPIKyiyVIwX0k/gbTHJalRiFbyWbP8kq18zdqH3fzvizLlCvHndB7it1ShL+Yv0wHLovUp8eaRnn4l0FGFX/vKx0ZDjvNm5Z8OubL4UqEbVOF92574WCDgqXgv5cjyo+jxH7RiuWfEWnb+A8xcuWMrz1sICtNuxGxWjo3GsdUtUiIqytL+nwEO+GIjvfv0Od6TciY+HfeIpOD/XEYhCFGKio3Du/HmyCTMC0eJYE1Ur6tbaMRtmGMoUJzaGdzo4VccUr460dkzXrHitzGrWJnfrsUNYVZiHvyfXwh3xibbV+bsb3sCLq59F7cp1sfi2n1AlrqptcUdKRJzVHL41zVnNxnXL+3ida/OOilcVmaviBcMCGvoZ1v4a45VrLM9c8C3eSWmD28Ukq9uvucGWtZq/+fYz/Hvve/hF/LzdZTJiD0Zh8I2pCnJ1rWZOrnJ9gHGM1/uTD8d4L7HjrGbv21Ek7OmoeKXEenZOQZf2rUpNUJIzhfv16oCH7xvhOHOZpxUzJpakK/MiN3Wmsz9mNcvJVVK88oEH/0pJwXUb1uHaq/shfcNPPj8kYcJHf8C6vJ/Qrk1XPHjFH0seuEDxDjDVtiheU5gMA1G8FK/3rSey9nRUvOrkqisa1sEDT/2zRHj6mcJOVoH2Hl2ZrhP38WrFu7lzN0SvWoZynbojJW2rT+JdeH4R9q/bgYL4M/jg7mk4fuQQxZu2GUcOH0RvMXvczEbxmqFkHIbipXi9bz2RtWdAxDu8f09ICauXlgO5gIYd1e3tGK9Me4OYZDXk2AEkR8dgU73GXmdn5cGlGDljkLL/1GHfolf94ocfcPOOAMd4veMWCntxjNe4ljjG61zrdVS8snfZqllDvPz0WGj/HcgFNOxA7Yt4ZfqDhXh/FgJ+R6zdPFys4Wx1O3/hPPp90Qk70tPw+45P4Mmuz1uNguF1BCje8G0SFC/FG+jW7ah49YWVvV51094XG2goVtP3Vbwf52Ti2YwT6CueVvSZeGqR1e3Z7x/Fx5smocNlXTDr5qVWd2d4AwIUb/g2C4qX4g106w6oeANdeDvS93blKnVylVzCcamYZPVm8+a4ekcabup+DQ6v/1GZiTz10/cxaHgqtm5aj/jKiahTr4EyIWtE6mjs3bMLu7ZvQYWUKpg08zWlKH+69a/I2nwctevUQ7OWKdA/zJ6zmj3XOMd4PTNyFYJjvJfIcFaz9+0oEvZ0VLyhsHKV1Uq3Q7xSphuuaocLG9ejcttOyiQrs+KdmP8WEo5URLe6vfDQjU9h+eJ5FK+mEvUPf/BUvxSvJ0KuP6d4KV7vW09k7Unx+ljfdom3RtdemL9mOVY3b4U/7v0Nw268zWOPd9GPszHh1LO4scJNuLfNOLTv3IPi1dUnxVsMRHu1w8cm73J3ipfi9VfbCrd4HRVvIO/X9WfF+TrGq+btrhOHsCQ/D89WrY7xidXcZvlk/gn0/CwFOWey8d4Nn2Jo05v9WcSIi5tjvOFb5RzjNa5bzmp2rs07Kl65cpX2/l3niunflOwS74L8XNxz4jAalovF6jqN3Gb6yaUP4z9bJ6N/4yGYPHCafwsYgbFTvOFb6RQvxRvo1u2oeLWzmI0KHgxLRnpTIXaJV6Z9/ZH92Hq20O36zWknt6Df1M5KVhfftg4tklt5k23u44YAxRu+zYPipXgD3bodFW+gC+uP9O0a4+3Wq6+yytTpNm2x+afV+L73tXhw4XzDWc3Lk1diy44NGJo4HH8Y9Ry0Y2ucXFW6ljnGW8yDY7yX2oUT4uWsZn+cbcMnTkfF62pW88TJ0/Hl7KWl1kwOFcR2i7dD5+74eOUSvNOtB/6yZBFGjri91O1E8+f/D09kPoYW4uf39R/DsGF3ULxuGgvFS/HqmwfFW/aA+fDtv2PChAmhctoN+XwGhXhDeclIf4h3wZoVeLpTZzy+aAHuv/nOUuL9/JtJeLXwFTzc6BF0iO6oPGyBPV7XxyHFS/FSvJ49RfF6ZmRniKAQb6QvGWlUoXL9ZrmO8/NVa2BMYvHzdNcf+RFD/3cNosSDvH+6e6fyvF1u/iHAMV7/cA2GWJ3o8QZDOa3mgbOarRLzPrzfxav2Zj1l8cU/3w/58IRQ3OycXKWWf07eaYw9eQSXxZTDurqXI0p8MGbebZj760yMb/cInu3xYiiiCpk8U7whU1WWM0rxGiOjeC03Ja938Lt4tTkLx5WrZPn8IV4Z74hjB/FjYT6erVYd7XK24qbp1yM2pjzWjd6F6hVreF3p3NEzAYrXM6NQDUHxUryBbruOijfQhfVH+v4Y45Wzm+WSkR9PeQ+vde2Oa37bg4SMRViQPg9jKo3FuHv/XLJWM8d4O7qtVo7xFuPhrOZLzcQJ8XJWsz/OtuETJ8XrY136U7zyIQnzel2Dcj8vQubhr3E05hj+WPVR3HLbfRSvmPktHxyR0pbiNdOEKV6K11074eQqM0eRfWEcF2+v4Q8jPTPHsAShuICGv8WbNGAYps36KzLz09C19bW44ljdUk8nYo+X4jVzOqB4KV6K18yR4kwYR8Ur12pOTkrER2886UzpHErFX2O8MvtL9i7AXd8OB2IT8PDN6/Dn5PoOlSqyk+EYb/jWvxOXmkORHidXOVdrjoqXk6usV+ytMwZi1cFlQIuHUan5WGWGc5XoaOsRcQ9LBCheS7hCKjDFa1xdFK9zzZjitYG1v3q8C36bg3vm3KLMYL5q8PdYXHgGv09MwpNVk23INaNwR4DiDd/2QfFSvIFu3Y6KNxwfC+jPMd633vsL3i96H7+v8yjqNuiBCXGxuPGXDRh3x304vXcPdm3fwpWrOLnK1DmEY7wc4+UYr6lDxZFAjopXLqbx+qRpIbkms6va8Jd4o9pUwLZ5azGn0jy83Ox1VBYzeP8dXxHV16xE1JCbcGd6BsXLWc2mTxIUL8VL8Zo+XPwe0FHxhuNjAf0l3veLJuHqo91RtWNtpJxrrdw6k1mzJpYtnof3+/TF7IIinNyVxh4ve7ymThIUL8VL8Zo6VBwJ5Kh4HSlRABKxe4x35q6v8MB3d6N+YkOsGZVWqkTjxTKSs8RykvcnVMVfqnH1Kn9VN8d4/UU28PFyjJdjvIFuhRSvDTVgt3j7T+uOzSd+wYtX/xOj2/yuVA43nS3EgCP7lfd+qNMIDcrF2lACRqEnQPGGb5ugeCneQLdux8UrJ1jt3ntIKbf6YAR5CbpL+5Yhe3+vneL9evvn+MOiMWhctSlW3LnRsH384dQxfJ2bjbsrV8FLSTUD3YbCMn2KNyyrVSkUxUvxBrp1Oype7QIacgWrx8aNVJ5INHHydHw5e2lITrqye4z3i9P/QaOsBmjVtxNi1p3BoOGppZ7Hu3zRXLQccTse+vkHtD14AGOG3oq8n39S2lH7zj2wXIwB165TD81apuDIof1Q132Wn2vH+Tb/sg65p7PRtWdfZV/9msb6fY3CyPf08agNeo2bJR21zw92dQDIJezGPPSEy+PDXfzanbhWczENjvFeahVOiJdrNQdabcGdvqPilT3bqe89h5SWjaEVr/rowEhfMnLR97Mx6dQ76F+uP/5v3BuQazUbiXdE6mi8sGkdsnZtR+bVffHgb79RvC6OM4qX4tU3DYq37MHCtZqdFbWj4pWyffflR8qIlz3euejWqy8+n/cBvimYjrur3IOxd/3JrXg37d6Bzzf+hP906oLXDhxE89jy7PEaHDsUL8VL8XqWCsXrmZGdIRwV71MvfYCVazcrl5TVHu8VDesgdfwLGHp9d7z89Fg7y+ZYXHaM8f5ybB0GfXU1KpSriI337kXl8gke8z85JxPPZZxAYyHdFbUbegzPAOYJcIzXPKtQC+lEjzfUmMj8cslI52rNUfHKYqmXlbVFHHfXUDx83wjnSm1zSnaI99HF4zAt7VOMafswnu/5qukcDj12EOsL8/FIlWQ8XiXJ9H4M6J4AxRu+LYTiNa5bite5Nu+4eJ0rmnMp+SrenDPZaP3vuig6X4SVd23C5VWamM78ioI8pB4vniU+57IGaFs+zvS+DOiaAMUbvq2D4qV4A926HRXvvY++ih83pEE/iSqUbyeyY1bzN99+ho9PT8aNFUbgjgFjS2Yiu5tctXfPrpIlI1/7fgF+LixETpu2eGzLFs5q1hxVHOMthsFZzZcahRPi5azmQKstuNN3VLxyXPfWIdeUuawc6ZOrPv76LXxzbjrGJI3DDb2HWxbv+rWr8OnpLHzdpCme2roF1zdqwtuJLh53FC/Fqz8FU7xlpcTJVc6K2lHxunoebyTfTlSzbQMsXfQtVsf9gAer/wEdOne3LF55X+z+c2fxYL26GC6eXjRAiHdwmw68j1ccSxQvxUvxepYKxeuZkZ0hHBVvMPZ41cvfKtQmjepi5pQXSzHWrrZl9LkvY7zPLH8EUza/b3lSlVEjeDXrFN7KSkczMct5kRjvjYmKsrOtRFRcHOMN3+p2oscbivQ4ucq5WnNUvPKS8qTPZpUsoiGLuTltj3I7UaBmNssvA/L2JnWTf/fsnFJya5MU86n07BIZa1ffUvfxVrxFF4rQ+sO6kJOrvkv9AVdWv8rnmh8mZjmvE7Oc7xEPUfgbH6LgNU+K12t0Qb8jxWtcRRSvc03XUfHKYhndTqSu2excsV2nJO813rZzX4lotStsqfnXP1PYW/F+mfYZHln8O3Sp3QPTb1poS/F/OVOAQUcPKHF9WKM2BlasbEu8kRYJxRu+NU7xUryBbt2OizfQBfaUvuzRtmrWUOnxqr1xdZlLbQ9dfc+XWc2f/O9tfH72P3gg4SEM7HezMrbr7RivzJu6VnNatST8tXoSOmRk4L49v2LYjbcpxeZazZ5qHzh18jjketi33nEPkhLicDyzwPNOF0OYWYPaTGSffPgmbhs1DuXj7Ls1jLOaL5F3Qryc1WympUduGIpXU/eytztrweqS252siLdK1aqoHB+PBg0bIjc3F1mZmejctRtmz5yBnr2uRnZ2Fvbt3Yc+1/TB/Pnz0a5fe0z9+r+YFzMPT1Z/Etdd3x8rv1+Onlf3Vl7vuGsU3nl7Iu688y789NNaJCZWQcNGDfHtrNm4b8wY7NyxA5s2bcTNt9yKFd9/r5Si19VX49vZs9CgQUM8I8Lv+G0vRorbjv56/xjl88kffojBQ4egVq3LsPbHH5U89bvueuWzTRs3Yv/+fRg8ZKjy9759+0ryoSLSh5Hv6+NRwy5auEDJc+cuXcocXdr8ujr0XvrbX/H0s//n8sh0F792J6M8uzvcjx07qjC+f8xYxERH4dz586bPDmbKZSayN177Bx546GFUqFDBTHBTYbR1b2oHLwLZVX6rSat1Jo8LM1u0mPsgqlbU7QUzwb0K8/VXX6JNm6vQrHlzr/Z3eid5vE2YMMHpZCM2PcfFKy/dpmfmGAIP5EMS3I0/m+3xVqoUjzr1GiA/Lxc5QmpXte+Mxd99i45deuB0TjYOHdyPLt2vxvdLF+BAvSMo2JaNc2KtjLZZV6HH1ddi3Y8rRdieyuuwm27HZx+/h+HidZN4klDlhETUFXEvWSh6Y7ffg99+3YntaVswYPAI/CTCy62T2HfJwjmoU7cBYps2x11iLeeeO9LQbugtuC2hCr7878foe91AVK9RCxvFE41knmS6ctu+bTMOi6cZ9b1ukPK3zKuaD7Wy9GHk+/p41LCrvl+s5Pmqdp3K1LU2v66OvHfffAUP/OHPLg9Md/FrdzLKs7uj/eSJYwrj2+66B1XiyyM9+4zpk4OZcpmJbPKkf+HOe8YhLs4+8Wrr3kwevAljV/mtpq3WmTwuzGzlY6OVRwNm5541E9yrMPO+nY4WLa/E5Vc082p/p3eSxxvF6xx1R8VrNDHJuaK6Tknf09WG9NcYb/uPr8Cx3COYPmIhutTp4RcM/xGP/Xsy/RgqR0VjUe0GqF8u1i/phGOkHOMNx1otLpMTl5pDkR4nVzlXa46K19V9vM4Vt2xK8suA3PS3EKkh/TGrec7ubzB2/h3KLGY5m9mf2/hTRzErNwfXV4zHxzXq+DOpsIqb4g2r6ixVGIrXuG4pXufafESLVx3DNcKtnWlt932898y5BQt+m6M8DEE+FMGf2/Gic+h3ZB9OibHK56tWx5jEav5MLmzipnjDpirLFITipXgD3bodFa8UWL9eHUL6SUT6CrM6q7lRmxZYvETcyyx+/pz8jBhTHaLMopXP47VrVnPtOvVKLRl57oZBePDkUYxbvgQD+g1Gx9p1sVmMG+eKS9Fde/ZViqRf4emIGO+V+Rl8Y2pJkY1WgdLHowZes3IJ4isnIqVtxzJt3MzsX7mSzpiHnnB5fLiLX7sTV64qpsFZzZdahRPi5azmQKstuNN3VLzyHl79PbDBjcdz7qyK91CymFS1IwfHG2agW24X9O430O/ilfJ84tQxJMydgbROXfGfFldhK8VrWLm8nchzm3cVwswXKu9jd72nWmcjUkebip7iLYuJS0aaajq2BXJUvHKM190WyFnN3hK1Kt4v86aiQ157pFzdFXnb0h0Tb+GF83jr88mYelU79BA94jEHDrLHa1DpFK+3RwJA8V5ixx6v9+0oEvZ0VLzhCtTsylVL9y3EnbOHoXHVplhx50bHcWw/ewZDxZKSueK5v3+qkow/VklyPA+hkiDHeEOlpqzn04ker/VcBX4PTq5yrg4oXhtYmxXvQwvuwTc7p+FPXf4Pf+z0lA0pW49iTt5pjD15RNnx3eqXYVilBOuRRMAeFG/4VjLFa1y3FK9zbd5x8Qb7Ws3eoDcj3vT8U0iZXF+Jfs2oNNRPbOhNUrbsM1E8wegV8SSjcmIFn2k166JrXEVb4g2nSCjecKrN0mWheCneQLduR8UbjE8n8rUCzI7xrvntexw9dBAZl2Wjc14nXDfwRmVSlVOTq2Q5tTNbX1y9FHsyM7D2qrZCvvVQbvcOHDl8EL2vHaAg4axmrtVs9djgGO8lYhzjtdp6Iiu8o+INxufx+lrdZsX72foPkZAfj1Yd2uPsrtyAi1feBjTzxBG817wFGsbE4nWxtvSZo0coXj4kwetDguKleL1uPBG2o6PidbVylXr5OVxnNVdvXgfTN32BJtFNceeg32HV8oVBIV55H+9EsYj7svw8DDp8GLecPo3r+hWv1cweL3u8Vs+FFC/Fa7XNRGp4R8Ubjj1e2XA8jfE+seRBfL7tYzzY/jE83f2vQdXW8sRtRqnHD2F9YQG6ibHeqbXEZeegymFgMsMx3sBwdyJVjvFyjNeJduYuDUfFG45jvJ7Ee67oLFp8WBv55/Kw5Pb1aJ7UMtB1Xib940VFGHn8IHaK2424pnMxHoo36JqpbRmieCle2xqTlxE5Kl6Zx0ib1Txr19cY/90odKrdDTNuWuxlNfl/t91nC0XP9zCOiLWdb4pPxFvJtfyfaBCnQPEGceX4mDWKl+L1sQn5vLvj4vU5x0EWgafJVXPnfoWF5xeif93BSC5MQqduVwfVGK92reatB/fhqZatkCMW2Phdbj7ab9/GtZozC0y3OLvGOD/58E3cNmocysfFmU7bU0Cu1XyJkBPi5axmTy0ysj+neH2sf3fibd4mBfPn/Q/LxM/4Vn9A9vGMoBavvJ0oukdvZcy30cmTuOPX3XjglrtKCPEhCe4bC8W7SgHUvrN/ni/tij7XavbxJCZ251rNvjO0EoMj4lXHdsfdNbTMk4ncfWalIIEK6068OTVycfKXQ9hf9SBuapSKwwf3B7145X28cnWrl7ZvRp+daah0w1A8U626gpfipXjdEbDri4fVY5nitUqsbHiK13eGVmJwRLzycYDJSYn46I0n5U8ElAAAF9pJREFUDfOmf9i8lQIEQ1hXs5rHzLsNc3+diZd6/wt3p4wNhqyazsNX4lajP6YfU8KPqlwFLyfVNL1vOATkGG841KJxGZy41ByK9LhkpHO15oh4Xd2/qxYzlO/jlWUwEq+czdz0g5o4U1SIn+7eiToJ9ZyrVZtSmid6vmPEus4XRHwjxJrOE8XazpGyUbzhW9MUr3HdUrzOtXmK1wbWRuKdv2c27ps7Ujx0vitm3rTEhlQCE8XKgjzcL+Sbc/48rqsQj3/XqCPWeA5MXpxMleJ1krazaVG8FK+zLa5sao6IVy6c8di4kRjev6dheWWP9/VJ07BixsRA87Ccvqsx3o37f8I3udNxW8zt6Natr/Ls21AZ45UQtCtX/XKmEPefOIxav/2KTlmZuPf6YWgQG6uwkktPyrKps6NVgGtWLkF85USktO1YhqmZsUA55jTmoSdc1oe7+LU7GY1Lu6tkPo/X8iFQsoOZevU+dtd7cozXd6oc4/WdoZUYHBHvUy99gG0792HmlBcN8+ZpDNhKgZwO60q8y3Z+h2VFyzCq/N3o2LlXSItXMt0tFtd4ef1qVDh+DN936IjXki7DDRXjKV5Ng7NLPLydyNpRTPFa42UUmuL1naGVGBwRr8yQ7PXKTd+rle+nZ+YgFNdpluUxEu+BU79hw7612BO/F/3P3YD2nXqEvHhlWX/ZtgnzftuFt1PaKHX5eJUk9PvtN/Z4Lx5xFC9vJ1JPvryP14qGIi+sY+KVaGXPd9aC1aUod2nf0uVs51CpDv0Y70ur/w/vbHgdY9v9HhN6vBIqxTCdz3+KZ/m+Jp7pK7eBotf7WvJlqBIdbXr/UAjIMd5QqCXv8sgxXmNunFzlXXvyZi9HxetNBkNhH714r/2iI7af2oZpw+agZ/1rQqEIlvP4XX4uHk8/ivSi82hUrry49FwD3SpUshxPsO5A8QZrzfieL4qX4vW9FfkWA8XrGz9lb614d6an4Zr/dkBSxWRsvu+ADbEHbxT7z57FnzKOQ858ltsL1WrgvoSqwZthCzmjeC3ACrGgFC/FG+gmS/H6WAP6Md6jMUex6dAGNK3UHCP63oGlC+eEzRivq5WrFp08hteaNVNIporFNl4Ti238yFnNXrcsTq6yho6Tq6zxMgrNyVW+M7QSA8VrhZZBWL14fzz9A7JOZ6BzUjdc031ARIhX3k50oF1HPH7qGM4JRleVr4AHd2xHgyrVeDuRF+2L4rUGjeK1xovi9Z2XrzFQvD4S1Io3tkJ5zDr+DSqLnxvqDELb9l0iRrzyPt6t4pajx0+JHr+473fg1s3onVwTd3Yue++2mdm/vI+XTycye2hSvGZJuQ7HHq/vDK3EQPFaoeUirDrGO3XbJ3hsyXj0azQAnwz+nw0xh14U5y9cEOO+JzD1dJaS+QEVK+Opqsm4IrZ8SBWGY7whVV2WMssxXmNcnNVsqRn5FJji9Qlf8c6qeNWHIrzS5y3cdeX9NsQculF8JsT7ohBwjhCx3KR8H0pMCpkCUbwhU1WWM0rxUryWG43NO1C8NgCV4s3ILUDT92sUPxRhtHgoQuXQeyiCDShKRXHifBFezjyFaRd7v23F2O/TQsA9QuC2I4rX7tYQPPFRvBRvoFsjxetjDahjvOUqxmJv/m8oiD+DgQ2GISc7C23EhKNImNXsaa3mheKe35czT2KHGAOW2yN796JnhYroajD+q1YHx3g5xmv20OQYr1lSrsNxjNd3hlZioHit0DIIq4r3bOw5HDt7FLXq1EXrKm0oXoPbif4uVrx6U6x41UfMeK4UFYUOXXpgXEI1wxqgeCles4cmxWuWFMXrOyl7YqB4feSoijcnKgdZF7LQpWUvxItZzezxGj+daLOY8Tx11VLsPXcWy5q3QL1ysRgvFt0YrVt4g+KleM0emhSvWVIUr++k7ImB4rWB43c7lqL/1L5oXLUpVty50YYYwz+K7/JP493sDKwrLFAK20TMen5A9H5HikcJBsPGMd5gqAX/5IFjvMZcOavZP+3NKFaK1wbWj857Av9c+w+Mafswnu/5qg0xRk4UM/Ny8G5WBracLVQKnVI+DuMTq2FYpYSAQqB4A4rfr4lTvBSvXxuYicgpXhOQPAVp/c6V2HZyK6YNFw9FqBeeD0XwxMDXz+V9v+9mZ+LXc8UTsDrFVcAocfl5RIAETPH6WqPBuz/FS/EGunVSvBdrYOLk6fhy9tIyzwuWHw8b/Qx27z2khGzSqC5mTnmxpN7UMd7sqGw0qdUCtevUR35+Hsd4vVyreYoi4HSMmf4Vnh96Iy4rVw4j4xORKn4biPFgdVvjJn7tQWW0vrS7g04dL7z1jnuQlBCH45nFl8LNbGZW5DITD5eMNEPpUhiO8VrjZRSas5p9Z2glhogX74z5K/HMK/9WmCVVTSgj3nsffRWn0rNLZCslnJyUWPIM4Uuzms+ibnJDivdi63MnRjOCkieCb25OxUYxGUvdBscnILVSIq6pWAkUr5XDHJg+dQp69xuI5Oo1re1oIbSZerUQnemgFK9pVC4DUry+M7QSQ8SLV4Xlqsfba/jDeGzcSAzvX7zmsBT165OmlQhaFW9MxXJIrlKT4rVRvGMeegKrC/PE8pM5+F9udkm7biEmYqWmbUO7atXRsV0nt+2dPd5iPBTvpWbixKXmhXO/QdMWV6JR46ZWzscBC0vxOoue4r3I20i8m9P2IHX8C5j63nNIadlYCal/L+ovUYgS96TuHHsclWLjna29CErtWNE5IeBsTBUC3i9uRVK3GyrGY0Clyugv1oROiI62jQjHeG1DGXQROSHeoCu0iQxxVrMJSDYFoXhtEO/ApoPwxfBvbKoSRuOJwIzsbHwmVgZblHu6VNDBCQkYXDkBQ8Rr5SjfJBwtvkxViovB6QL5oENu4USgXEw0ypeLQl5hUTgVy+eyJFa6NIfC58gYgVsCFK+P4s0qzELF6AScOXeeTc1hAkdFz3d2zmnMFj3hpbm5pSUsBDw0MRFDxWu8Fz1huUuF8uWQR/E6XKv+T05ezZDyLThD8WppVxbDZdycIUDxuhGv/MjsGG9CYhVUrBTPMd6LPO2YXCXHeF1t+vjlpej5Yk3oeXmnsaIgr2S3tvv3oXtWFmr06ouu4uEMbcR9wu42zmr2/sTDyVWX2HGM1/t2FAl7UrwexGt2VjPF27fU8eK0eLWJSwnPyxMSFqtjnd6ZhkbppzCjbXslSDXR0+kWVwld48RDGsRva52IKV7vT3sUL8XrfeuJrD0jXrza24nUqh96fXe8/PTYkpZg5j5eijd4xKs9hH/auhFpB/diY8euWCOWp9x7cYEONUyNmBilJ9xVPLKwqxByDbGIx/JFc8H7eK2fCCleitd6q4nMPSJevHZUu3web04+J+HYwdLfcewT48I/iEvRa84UYE1BPg5oZkjLtGsJEcciCndXqYrOiWLo4EwU6moW7vB3/hi//wlwVrMxY85q9n/bU1OgeG1gTfHaADFAUfwqnhH8Q2E+fhS94R/EPcNHzpX9ApUkZNwiNg4txf3D6mvLuDhUEILmFnoEKF6KN9CtluK1oQYoXhsgBkkUO4SIfxES3lF0BrtEb3hTfj5Onjee/SqfqCQX85BCbikuVbcoXx4NY3hLRpBUpctsULwUb6DbKMXrYw2oK1dxjDc4x3jtWLnqqJislSaEnCYuT28/e1a8Foq/C3FB13b67NiOcuL+3z2tUsTl6XLFv9HlUC82tvjfQsp1Y8ohVoRxt3GtZmsHJZeMtMbLKDRXrvKdoZUYKF4rtAzCUrzrkCvuo+3aM3zFa9REii5cwHYxUUtKePtFKVfevBGnz5/HsuYt3LaqWkK+xWIWIhZiLvm3eL+eeG/m5Im4bdQ4lBeXs+3auGTkJZJO9Hh5O5FdLTc846F4faxXijcyxWvUbOSs3jOiH5wk1o8+dK4Ih0RP+VDRWRwW48aHxGXr4r/PQUrb3fbUvG/xZf/BYuWsOFSJjkFVsZpHVbESV1Uh5irRUeLvcuLf4n3Rc1beU15jEO9mtS6Kl+J11+bY4/VRBBZ3p3gtAjMKzjFeGyAGWRT+XKtZkbCUsZCyIuNSYhYz5M+7F7MrVPISdjUh6WJZFwtb/lveu1wF0agkXisIOVcQ4eLEr5wcpvwtZK6+X1H+W4QtDiNW7/Jx6c0gq1YlO070eIOx3J7yxFnNngjZ9znFawNLitcGiEEWhT/F66moOeJydYaY0JV14Twyi4qU3yzRk84Qks4sOl/8vvhc+UwNI/7O99CT9pSuq8+L5SyEpQhZ/koha6RdIvBoyEUH5SrZ8jdGSFy+iseIIFp8l1DfkyPcxWHk+xeUcNr3YuQe4g01HmU/ka7ynghf/LfcR+yvhpPxi/eUfS6+KmGU9+U+URf3EXkvJ76ElBfrcIvbAJV41fwo8WviUeK6+LeSfzV+TRj1fZGwNr/RF4rLUGqTb7ipI/mwlVKbQdgyYeQOyve04i9rhp9rIxVxugpD8Xp7hFjfj+K1zqzMHhSvDRCDLIpAitdbFPIyt5RxhiJnIWUh8Ewh6yzRg84QfxeI1wKcR4E4RxeIzwqEtAvEibhQ/i3/LT7Ll2HEe8rf4t9lp5B5mzvuF8wEHquShNca1wvmLIZV3iheH6uTY7wc41WbkF0rNwXTrGbZj5ISLpGzlLIiZyFpIepC0bMrFvh5ZG/4Sbwjen5tOyivRSKcfL0gfs6Lzpz6nozzvHxPvopengxX/F7x+0VyD/FG8d8X9xPxK++J8Eo84o8L4lf+Oy4jHQ3WrsbWGwYVh7/4vhJGpiv+V5KejER2Y8V/Z4pEWjJeNR0l/kv7F8d18W8l/xfzrL6n5F+8p/xdOr83rf0BG+s3wI7adS6dYdQerJtZ7bJMJZvSAS7dCy71ufbcpQnrMowaXqSvD/P8rG8wYcIEH8+G3N0sAYrXLCkX4SheijecxWvl8LDri4eVNGVY3k5klVjZ8Jxc5TtDKzFQvFZoGYSleCleireYAMV76QTB24l8PLGG+e4Urw0VzDFeGyAGWRShOMYbZAiDNjuc1WxcNZxc5VyTpXhtYE3x2gAxyKKgeIOsQmzMDsVL8drYnLyKiuL1ClvpnSheGyAGWRQUb5BViI3ZoXgpXhubk1dRUbxeYbu0E8d4Ocartga7xjiDaVazlcPDrvJbSVOG5eQqq8TKhufkKt8ZWomB4rVCyyAsxUvxUrzFBCjeSycITq7y8cQa5rtTvD5WMMVL8VK8FK/+NELx+nhiDfPdKd4wr2AWjwRIgARIILgIULzBVR/MDQmQAAmQQJgToHjDvIJZPBIgARIggeAiQPEGV30wNyRAAiRAAmFOgOL1oYKHjX4Gu/ceUmJo0qguZk550YfYuKvTBKzU372PvoofN6SVZJH17XRtWUvPSt1qY544eTomfTYLL/75fgzv39NaogxNAiYJULwmQemDyRPxqfTsEtnKAz05KREfvfGklzFyNycJWK2/XsMfxooZE0uyKP/u2TkFLz891slsMy0TBKzWrRqllO6Xs5ciPTOH4jXBmUG8J0DxeslOnngfGzey5FvxjPkr8fqkaaVOzl5Gzd0cIOBr/T310gfYtnMfr3I4UFdWk/CmblXpyi9XrfuMpnitQmd4SwQoXku4igNvTtuD1PEvYOp7zyGlZWOX73kRNXdxgIAd9SevcLRq1pA9Xgfqy0oS3tStVroyLYrXCnGG9YYAxesFNW8Obi+S4S5+IuBr/cne7qwF4sHry6b4KYeM1lsCVutWL12K11vy3M8KAYrXCq2LYa0e3F4kwV38SMCX+lMn32ivdvgxq4zaIgGrdaufNKdNbtxdQ/HwfSMs5oDBScAzAYrXMyPDEN6MI3mZFHfzAwFv6o89XT9UhB+i9KZutdngpWY/VAqjLEWA4vWyQXg7c9LL5LibzQQ81Z8cw5WbeouY/m+bs8PobCRgtW71SVO8NlYGozIkQPH60DC8vVfQhyS5q40E3NWfVrTq5UujpHm/p40VYmNUZuvWKEmK18aKYFQUL9sACZAACZAACQSaAHu8ga4Bpk8CJEACJBBRBCjeiKpuFpYESIAESCDQBCjeQNcA0ycBEiABEogoAhRvRFU3C0sCJEACJBBoAhRvoGuA6ZMACZAACUQUAYo3oqqbhSUBEiABEgg0AYo30DXA9EmABEiABCKKAMUbUdXNwpIACZAACQSaAMUb6Bpg+iRAAiRAAhFFgOKNqOpmYUmABEiABAJNgOINdA0wfRIgARIggYgiQPFGVHWzsCRAAiRAAoEmQPEGugaYPgmQAAmQQEQRoHgjqrpZWBIgARIggUAToHgDXQNMnwRIgARIIKIIULwRVd0sLAmQAAmQQKAJULyBrgGmTwIkQAIkEFEEKN6Iqm4WlgRIgARIINAEKN5A1wDTd4zAxMnTMemzWWXSG3fXUDx83wj0Gv6w8tmKGRPLhJGfJVVNxMwpLyqfeYqrdZ/RbsuVVDVBSefeR1/FjxvSDMO++Of7Mbx/Twwb/Qx27z0E9W818Iz5K/HMK/9Gk0Z1S/Klj8hMPnp2TsGsBatLdh16fXe8/PRYS+maKYdjFc2ESCDICVC8QV5BzJ49BFQxTH3vOaS0bFwSqRToohXrS8QlRdWlfUt89MaTJWGeeukDrFy7uUTIZuPSC1IvTvm5jOtUerZLccowqnj1+VLfdydeLT1V1Eb5MPrMSrpmymFPTTIWEgh9AhRv6NchS2CCgBSq2pNzF1wvoM1pe5A6/oVSvU2zcdkp3uSkRKVnrH5xUPMlZexJ3Gby4Uq8ZtOleE00QgYhgYsEKF42hYggoL9U7K7QUiK79hxUeriy1yflo+0BW4lLpuOup2lGWDIPrZo1xLGTGahVvZpyGVj2wuUm3/OneM2ma6YcEdHQWEgSMEGA4jUBiUFCn4AqP21JjC65qp9rx0a3LptSCoDVuDyJ18wYrxRgl/atlDFdmR+ZP9n7/eeHX/ldvGbS5Rhv6B8jLIFzBChe51gzpSAhoJeE0SVoVZbqxCtXWbcSly9jvFK86oQnmRe1F26lp+nNGK/ZdK3kI0iaAbNBAgEjQPEGDD0TDgYC8pKtnNGr79Uaje16yq+ruDz1eD1dKlYvNUvxqrOpVYlbEZ4v4vWUrpV8eOLIz0kg3AlQvOFewywfpET/+80ipceo31Sh6Gc7uxKvN3HZKV6ZfznGrN7yZEV4vojXU7pW8sEmSQKRToDijfQWEAHlVyUqi6rv2RrdPiTDuROvnOVsJS67xautMivC81W87tK1ko8IaHIsIgm4JUDxsoFEDAGjxSRcjeF6utRsJS5P4jU7ucqox25FeK7yoV4iVxuCdgENdYxX30j06XJyVcQcRiyoDQQoXhsgMgoSIAESIAESMEuA4jVLiuFIgARIgARIwAYCFK8NEBkFCZAACZAACZglQPGaJcVwJEACJEACJGADAYrXBoiMggRIgARIgATMEqB4zZJiOBIgARIgARKwgQDFawNERkECJEACJEACZglQvGZJMRwJkAAJkAAJ2ECA4rUBIqMgARIgARIgAbMEKF6zpBiOBEiABEiABGwgQPHaAJFRkAAJkAAJkIBZAhSvWVIMRwIkQAIkQAI2EKB4bYDIKEiABEiABEjALAGK1ywphiMBEiABEiABGwhQvDZAZBQkQAIkQAIkYJYAxWuWFMORAAmQAAmQgA0EKF4bIDIKEiABEiABEjBLgOI1S4rhSIAESIAESMAGAhSvDRAZBQmQAAmQAAmYJUDxmiXFcCRAAiRAAiRgAwGK1waIjIIESIAESIAEzBKgeM2SYjgSIAESIAESsIEAxWsDREZBAiRAAiRAAmYJULxmSTEcCZAACZAACdhAgOK1ASKjIAESIAESIAGzBChes6QYjgRIgARIgARsIEDx2gCRUZAACZAACZCAWQIUr1lSDEcCJEACJEACNhCgeG2AyChIgARIgARIwCwBitcsKYYjARIgARIgARsIULw2QGQUJEACJEACJGCWAMVrlhTDkQAJkAAJkIANBCheGyAyChIgARIgARIwS4DiNUuK4UiABEiABEjABgIUrw0QGQUJkAAJkAAJmCVA8ZolxXAkQAIkQAIkYAMBitcGiIyCBEiABEiABMwSoHjNkmI4EiABEiABErCBwP8Dn0Web5KAt3UAAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "uc.plot_history(colors=['darkturquoise', 'green'], show_intervals=True)" ] }, { "cell_type": "markdown", "id": "cdcb5bde-65ff-43dc-ad43-897f5dd726a4", "metadata": {}, "source": [ "Notice the variable time steps (vertical dashed lines), more frequent when there's more change" ] }, { "cell_type": "code", "execution_count": null, "id": "f3007827-f052-4d96-8064-47b10a42ad91", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "042a23ff-84de-4273-ae7b-09b73b740b4c", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "1f447754-5017-4b48-a4f5-fc9049b7de64", "metadata": {}, "source": [ "# PART 2 - This is the starting point of fitting the data from part 1 \n", "### We're given the data of the above curves - i.e. the system history, and we want to estimate the rate constants (forward and reverse) of the reaction `A <-> B`" ] }, { "cell_type": "markdown", "id": "b5f75cfb-45b4-4fd2-ad4c-c2a2084ca62d", "metadata": {}, "source": [ "Let's start by taking stock of the actual data (saved during the simulation of part 1):" ] }, { "cell_type": "code", "execution_count": 9, "id": "f26c98c3-802c-4c38-a726-06ac4a77211a", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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SYSTEM TIMEABcaption
00.00000040.00000010.000000Set concentration
10.00160039.26400010.7360001st reaction step
20.00352038.40058411.599416
30.00544037.56037612.439624
40.00774436.57922913.420771
50.01050935.43982914.560171
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70.01603833.29163216.708368
80.01880332.27948617.720514
90.02156831.30651718.693483
100.02488630.18414819.815852
110.02820429.11391220.886088
120.03152128.09338621.906614
130.03483927.12026222.879738
140.03882026.00675423.993246
150.04280224.95531225.044688
160.04678323.96247426.037526
170.05156122.83747727.162523
180.05633821.78772628.212274
190.06111620.80818929.191811
200.06684919.71136530.288635
210.07258218.70257531.297425
220.07831517.77475532.225245
230.08519516.75073433.249266
240.09207415.82534334.174657
250.10033014.82182935.178171
260.10858613.93430136.065699
270.11849212.99236237.007638
280.13038112.01880637.981194
290.14464611.04497938.955021
300.15891210.26564439.734356
310.1760319.51722240.482778
320.1965748.83436041.165640
330.2212258.25059341.749407
340.2508067.79183542.208165
350.2863047.46931342.530687
360.3289027.27462742.725373
370.3800187.18032842.819672
380.4413597.14814942.851851
390.5149677.14269642.857304last reaction step
\n", "
" ], "text/plain": [ " SYSTEM TIME A B caption\n", "0 0.000000 40.000000 10.000000 Set concentration\n", "1 0.001600 39.264000 10.736000 1st reaction step\n", "2 0.003520 38.400584 11.599416 \n", "3 0.005440 37.560376 12.439624 \n", "4 0.007744 36.579229 13.420771 \n", "5 0.010509 35.439829 14.560171 \n", "6 0.013274 34.344532 15.655468 \n", "7 0.016038 33.291632 16.708368 \n", "8 0.018803 32.279486 17.720514 \n", "9 0.021568 31.306517 18.693483 \n", "10 0.024886 30.184148 19.815852 \n", "11 0.028204 29.113912 20.886088 \n", "12 0.031521 28.093386 21.906614 \n", "13 0.034839 27.120262 22.879738 \n", "14 0.038820 26.006754 23.993246 \n", "15 0.042802 24.955312 25.044688 \n", "16 0.046783 23.962474 26.037526 \n", "17 0.051561 22.837477 27.162523 \n", "18 0.056338 21.787726 28.212274 \n", "19 0.061116 20.808189 29.191811 \n", "20 0.066849 19.711365 30.288635 \n", "21 0.072582 18.702575 31.297425 \n", "22 0.078315 17.774755 32.225245 \n", "23 0.085195 16.750734 33.249266 \n", "24 0.092074 15.825343 34.174657 \n", "25 0.100330 14.821829 35.178171 \n", "26 0.108586 13.934301 36.065699 \n", "27 0.118492 12.992362 37.007638 \n", "28 0.130381 12.018806 37.981194 \n", "29 0.144646 11.044979 38.955021 \n", "30 0.158912 10.265644 39.734356 \n", "31 0.176031 9.517222 40.482778 \n", "32 0.196574 8.834360 41.165640 \n", "33 0.221225 8.250593 41.749407 \n", "34 0.250806 7.791835 42.208165 \n", "35 0.286304 7.469313 42.530687 \n", "36 0.328902 7.274627 42.725373 \n", "37 0.380018 7.180328 42.819672 \n", "38 0.441359 7.148149 42.851851 \n", "39 0.514967 7.142696 42.857304 last reaction step" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = uc.get_history() \n", "df" ] }, { "cell_type": "markdown", "id": "fe1139cb-e3d3-4f4f-aa78-89e400a5c008", "metadata": {}, "source": [ "The reaction is mostly forward; the reactant `A` gets consumed, while the product `B` gets produced" ] }, { "cell_type": "markdown", "id": "543b6f5a-f54c-426e-8dc6-342b62d50078", "metadata": {}, "source": [ "#### Let's extract some columns, as Numpy arrays:" ] }, { "cell_type": "code", "execution_count": 10, "id": "9e3a5eda-d426-4aa3-b1fd-65730a4af8d2", "metadata": {}, "outputs": [], "source": [ "t_arr = df[\"SYSTEM TIME\"].to_numpy() # The independent variable : Time" ] }, { "cell_type": "code", "execution_count": 11, "id": "44a76d0e-5bf0-4d34-b37f-37c11eff9a8f", "metadata": {}, "outputs": [], "source": [ "A_conc = df[\"A\"].to_numpy()" ] }, { "cell_type": "code", "execution_count": 12, "id": "2955b13a-483d-4ad1-962e-f2d968a3d11b", "metadata": {}, "outputs": [], "source": [ "B_conc = df[\"B\"].to_numpy()" ] }, { "cell_type": "markdown", "id": "1d41750e-d6bf-4288-8555-51acfce9e82a", "metadata": {}, "source": [ "### **Here, we take the easy way out,** using a specialized Life123 function!\n", "(in Part 3, we'll do a step-by-step derivation, to see how it works)" ] }, { "cell_type": "code", "execution_count": 14, "id": "344c1ead-1de4-49f7-b3cf-7958513d10b4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Reaction A <-> B\n", "Total REACTANT + PRODUCT has a median of 50, \n", " with standard deviation 5.617e-15 (ideally should be zero)\n", "The sum of the time derivatives of the reactant and the product \n", " has a median of 0 (ideally should be zero)\n", "Least square fit to model as elementary reaction: B'(t) = kF * A(t) - kR * B(t)\n", "\n", "-> ESTIMATED RATE CONSTANTS: kF = 12.19 , kR = 1.925\n" ] }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "d/dt B(t): exact :
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"text/html": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ReactionKinetics.estimate_rate_constants_simple(t=t_arr,\n", " A_conc=A_conc, B_conc=B_conc,\n", " reactant_name=\"A\", product_name=\"B\")" ] }, { "cell_type": "markdown", "id": "94af05ee-037a-4223-a1a7-fa681baf5ae1", "metadata": {}, "source": [ "### The least-square fit is good... and the values estimated from the data for kF and kR are in good agreement with the values we used in the simulation to get that data, respectively 12 and 2 (see PART 1, above) " ] }, { "cell_type": "markdown", "id": "4ac5c182-7d13-459e-b073-b946867a9e49", "metadata": {}, "source": [ "Note that our data set is _quite skimpy_ in the number of points:" ] }, { "cell_type": "code", "execution_count": 15, "id": "0cb00de3-91bb-4b6d-8e66-788ea743100b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "40" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(B_conc)" ] }, { "cell_type": "markdown", "id": "703cab8c-1850-4799-809f-a8fd43d61c26", "metadata": {}, "source": [ "and that it uses a _variable_ grid, with more points where there's more change, such as in the early times:" ] }, { "cell_type": "code", "execution_count": 16, "id": "0d1d5afc-4e04-457a-9548-f608a71cce1a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0. , 0.0016 , 0.00352 , 0.00544 , 0.007744 ,\n", " 0.0105088 , 0.0132736 , 0.0160384 , 0.0188032 , 0.021568 ,\n", " 0.02488576, 0.02820352, 0.03152128, 0.03483904, 0.03882035,\n", " 0.04280166, 0.04678298, 0.05156055, 0.05633812, 0.0611157 ,\n", " 0.06684879, 0.07258188, 0.07831497, 0.08519467, 0.09207438,\n", " 0.10033003, 0.10858568, 0.11849246, 0.13038059, 0.14464635,\n", " 0.15891211, 0.17603102, 0.19657372, 0.22122495, 0.25080644,\n", " 0.28630421, 0.32890155, 0.38001835, 0.44135851, 0.5149667 ])" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t_arr # Time points in our data set" ] }, { "cell_type": "code", "execution_count": 17, "id": "b8aa3145-e2e7-4ac2-a565-9a20a990bbb4", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.0016 , 0.00176 , 0.00192 , 0.002112 , 0.0025344 ,\n", " 0.0027648 , 0.0027648 , 0.0027648 , 0.0027648 , 0.00304128,\n", " 0.00331776, 0.00331776, 0.00331776, 0.00364954, 0.00398131,\n", " 0.00398131, 0.00437944, 0.00477757, 0.00477757, 0.00525533,\n", " 0.00573309, 0.00573309, 0.0063064 , 0.00687971, 0.00756768,\n", " 0.00825565, 0.00908121, 0.01089746, 0.01307695, 0.01426576,\n", " 0.01569234, 0.0188308 , 0.02259696, 0.02711636, 0.03253963,\n", " 0.03904756, 0.04685707, 0.05622848, 0.06747418, 0.07360819])" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.gradient(t_arr) # Notice how it gets larger in later times, as bigger steps get taken" ] }, { "cell_type": "markdown", "id": "742366ab-5fb7-4244-9203-6c89689f743c", "metadata": {}, "source": [ "#### The variable time grid, and the skimpy number of data points, are best seen in the plot that was shown at the end of PART 1" ] }, { "cell_type": "code", "execution_count": null, "id": "a14bf79b-ebf8-4696-a92b-ec98e78ecd90", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "id": "81203644-93d4-4e88-b6f0-219458d0fe8e", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "fb02e6dc-feb7-4b5d-9c7c-ee18ca4727bd", "metadata": {}, "source": [ "# PART 3 - investigate how the `estimate_rate_constants()` function used in part 2 works \n", "#### Again, the starting point are the time evolutions of [A] and [B] , that is the system history that was given to us" ] }, { "cell_type": "markdown", "id": "36f3e683-5794-460f-98a6-c0f404a641d7", "metadata": {}, "source": [ "Let's revisit the Numpy arrays that we had set up at the beginning of Part 2" ] }, { "cell_type": "code", "execution_count": 18, "id": "3df1e539-4874-4953-acd7-089fc38518c6", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0. , 0.0016 , 0.00352 , 0.00544 , 0.007744 ,\n", " 0.0105088 , 0.0132736 , 0.0160384 , 0.0188032 , 0.021568 ,\n", " 0.02488576, 0.02820352, 0.03152128, 0.03483904, 0.03882035,\n", " 0.04280166, 0.04678298, 0.05156055, 0.05633812, 0.0611157 ,\n", " 0.06684879, 0.07258188, 0.07831497, 0.08519467, 0.09207438,\n", " 0.10033003, 0.10858568, 0.11849246, 0.13038059, 0.14464635,\n", " 0.15891211, 0.17603102, 0.19657372, 0.22122495, 0.25080644,\n", " 0.28630421, 0.32890155, 0.38001835, 0.44135851, 0.5149667 ])" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t_arr # The independent variable : Time" ] }, { "cell_type": "code", "execution_count": 19, "id": "d29137a5-5dba-4470-9d74-919f14cd939a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([40. , 39.264 , 38.40058368, 37.56037599, 36.5792285 ,\n", " 35.43982899, 34.34453244, 33.29163175, 32.27948591, 31.30651739,\n", " 30.18414823, 29.1139116 , 28.093386 , 27.12026243, 26.00675446,\n", " 24.95531161, 23.96247447, 22.83747684, 21.78772586, 20.80818856,\n", " 19.71136465, 18.70257539, 17.77475483, 16.75073404, 15.82534273,\n", " 14.82182904, 13.93430053, 12.992362 , 12.01880624, 11.04497851,\n", " 10.2656443 , 9.5172222 , 8.83436019, 8.25059325, 7.7918346 ,\n", " 7.46931299, 7.27462691, 7.18032783, 7.14814942, 7.14269565])" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A_conc" ] }, { "cell_type": "code", "execution_count": 20, "id": "ef430e60-6431-44c9-9b50-469e433270fe", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([10. , 10.736 , 11.59941632, 12.43962401, 13.4207715 ,\n", " 14.56017101, 15.65546756, 16.70836825, 17.72051409, 18.69348261,\n", " 19.81585177, 20.8860884 , 21.906614 , 22.87973757, 23.99324554,\n", " 25.04468839, 26.03752553, 27.16252316, 28.21227414, 29.19181144,\n", " 30.28863535, 31.29742461, 32.22524517, 33.24926596, 34.17465727,\n", " 35.17817096, 36.06569947, 37.007638 , 37.98119376, 38.95502149,\n", " 39.7343557 , 40.4827778 , 41.16563981, 41.74940675, 42.2081654 ,\n", " 42.53068701, 42.72537309, 42.81967217, 42.85185058, 42.85730435])" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "B_conc" ] }, { "cell_type": "markdown", "id": "56744c87-7555-4bfa-a285-a06da3c39ff3", "metadata": {}, "source": [ "#### Let's verify that the stoichiometry is satified. From the reaction `A <-> B` we can infer that any drop in [A] corresponds to an equal increase in [B]. Their sum will remain constants:" ] }, { "cell_type": "code", "execution_count": 21, "id": "5c2b104b-7f9b-4cd6-9315-68a110351717", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([50., 50., 50., 50., 50., 50., 50., 50., 50., 50., 50., 50., 50.,\n", " 50., 50., 50., 50., 50., 50., 50., 50., 50., 50., 50., 50., 50.,\n", " 50., 50., 50., 50., 50., 50., 50., 50., 50., 50., 50., 50., 50.,\n", " 50.])" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A_conc + B_conc" ] }, { "cell_type": "markdown", "id": "b61a3b6c-235b-4452-a7fb-38cf174be0f7", "metadata": {}, "source": [ "#### Just as expected!" ] }, { "cell_type": "code", "execution_count": 22, "id": "db27029c-4c13-40aa-a855-79ec186259f7", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Incidentally, there's a function to verify that the stoichiometry \n", "# of a single reaction holds true across the entire simulation run \n", "# (overkill in this case!)\n", "uc.get_diagnostics().stoichiometry_checker_entire_run() " ] }, { "cell_type": "code", "execution_count": null, "id": "dbd5a0eb-5c1e-4249-b219-20010b648c41", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "a723c800-5c7c-4579-88fb-1fe968f0193e", "metadata": {}, "source": [ "### Now, let's investigate the rates of change of [A] and [B]" ] }, { "cell_type": "code", "execution_count": 23, "id": "83278f03-9f66-44ba-88eb-45a2bd9f742b", "metadata": {}, "outputs": [], "source": [ "# The rate of change of [A] with time\n", "Deriv_A = np.gradient(A_conc, t_arr, edge_order=2)\n", "\n", "# The rate of change of [B] with time\n", "Deriv_B = np.gradient(B_conc, t_arr, edge_order=2)" ] }, { "cell_type": "code", "execution_count": 24, "id": "a85508f3-9149-4906-9320-e74dd21a95cf", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([-6.82121026e-12, 1.36424205e-12, 1.36424205e-12, -4.54747351e-13,\n", " 6.82121026e-13, 4.54747351e-13, 0.00000000e+00, -4.54747351e-13,\n", " 4.54747351e-13, 0.00000000e+00, 4.54747351e-13, 4.54747351e-13,\n", " 4.54747351e-13, -4.54747351e-13, 4.54747351e-13, 0.00000000e+00,\n", " 4.54747351e-13, 4.54747351e-13, 0.00000000e+00, 6.82121026e-13,\n", " -2.27373675e-13, 0.00000000e+00, -4.54747351e-13, 0.00000000e+00,\n", " -3.41060513e-13, -1.13686838e-13, -2.27373675e-13, 0.00000000e+00,\n", " -5.68434189e-14, -1.70530257e-13, 3.97903932e-13, -1.13686838e-13,\n", " 2.27373675e-13, -4.26325641e-14, -4.26325641e-14, -9.94759830e-14,\n", " -5.68434189e-14, -8.52651283e-14, 2.84217094e-14, 1.42108547e-13])" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# As expected from the stoichiometry, the two derivatives are opposites: \n", "# when [A] increases by a certain amount, [B] decreases by that same amount\n", "Deriv_A + Deriv_B # Will be very close to zero throughout" ] }, { "cell_type": "code", "execution_count": 25, "id": "964ab34f-364c-4a46-945f-f39d4e7149d9", "metadata": { "tags": [] }, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "A'(t) :
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "PlotlyHelper.plot_curves(x=t_arr, y=[Deriv_A , Deriv_B], title=\"d/dt A(t) and d/dt B(t) as a function of time\",\n", " x_label=\"t\", y_label=\"Time derivatives\", curve_labels=[\"A'(t)\", \"B'(t)\"],\n", " legend_title=\"Derivative\", colors=['aqua', 'greenyellow'])" ] }, { "cell_type": "markdown", "id": "2e212588-3169-4f82-af8e-c998f1c87c94", "metadata": {}, "source": [ "The rate of changes of both [A] and [B] get smaller as the reaction marches towards equilibrium" ] }, { "cell_type": "code", "execution_count": null, "id": "a5be5194-232a-42d1-9ef0-499687db53fe", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "5eb72a33-d5d9-4675-9602-c8b3fa49d286", "metadata": {}, "source": [ "### Now, let's determine what kF and kR rate constants for `A <-> B` will yield the above data" ] }, { "cell_type": "markdown", "id": "f38690a4-b17d-4ba3-9fa8-26b597002528", "metadata": {}, "source": [ "Assuming that `A <-> B` is an elementary chemical reaction (i.e. occuring in a single step), \n", "OR THAT IT CAN BE APPROXIMATED AS ONE, \n", "then the rate of change of the reaction product concentration `B(t)` is the difference of the forward rate (producing `B`) and the reverse rate (consuming it): \n", "\n", "`B'(t) = kF * A(t) - kR * B(t)`\n", " \n", "We can re-write it as: \n", "`B'(t) = kF * {A(t)} + kR * {- B(t)}`       **(Eqn. 1)** \n", "\n", "`A(t)`, `B(t)` are given to us; `B'(t)` is a gradient we already computed numerically; `kF` and `kR` are the rate constants that we are trying to estimate. \n", "\n", "**If we can do a satisfactory Least Square Fit to express `B'(t)` as a linear function of `{A(t)}` and `{- B(t)}`**, as:\n", "\n", "`B'(t) = a * {A(t)} + b * {- B(t)}` , for some constants a and b, \n", "\n", "then, comparing with Eqn. 1, it immediately follows that \n", "* `kF = a` \n", "\n", "* `kR = b`" ] }, { "cell_type": "markdown", "id": "37d4919c-9218-48c8-953e-e065d9a3fca2", "metadata": {}, "source": [ "Let's carry it out! First, let's verify that `B'(t)` is indeed a linear function of `A(t)`. \n", "We already have, from our data, B'(t) as the Numpy array `Deriv_B` , and we also have A(t) as the Numpy arrays `A_conc`" ] }, { "cell_type": "code", "execution_count": 26, "id": "ed4bb090-6951-46c6-b66a-575ce29bd885", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "A(t)=%{x}
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "PlotlyHelper.plot_curves(x=B_conc, y=Deriv_B, title=\"B'(t) as a function of B(t)\",\n", " x_label=\"B(t)\", y_label=\"B'(t)\", colors=\"gray\")" ] }, { "cell_type": "markdown", "id": "dff549b8-b9d3-4080-8c99-32a4f56c1b3c", "metadata": {}, "source": [ "#### Let's do the least-square fit we had set out to do: `B'(t) = a * {A(t)} + b * {- B(t)}` , for some a, b" ] }, { "cell_type": "code", "execution_count": 28, "id": "f2577edd-5da2-47d5-8b3d-475c8b7d5e38", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(12.185860088176147, 1.924952056726416)" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a, b = Numerical.two_vector_least_square(V = A_conc, W = -B_conc, Y = Deriv_B)\n", "a, b" ] }, { "cell_type": "markdown", "id": "64e075f2-36fb-4334-8a80-4601acc49c7a", "metadata": {}, "source": [ "#### **Voila', those are, respectively, our estimated kF and kR!**" ] }, { "cell_type": "markdown", "id": "c9bb3d0f-f964-4111-ba27-7492b78fa22d", "metadata": {}, "source": [ "#### We just obtained the same values of the estimated `kF` and `kR` as were computed by a call to `estimate_rate_constants()` in Part 2" ] }, { "cell_type": "markdown", "id": "b5630424-9ae2-4506-af8e-5683ee1ad5f1", "metadata": {}, "source": [ "#### Visually verify the least-square fit:" ] }, { "cell_type": "code", "execution_count": 29, "id": "b8e011f9-c337-4926-b473-ed64b10f4eee", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "d/dt B(t) : exact :
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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot B'(t) and its least-square approx\n", "fig_main = \\\n", "PlotlyHelper.plot_curves(x=t_arr, y= [Deriv_B, a * A_conc - b * B_conc],\n", " title=\"d/dt B(t) and its least-square fit\",\n", " x_label=\"t\", y_label=\"d/dt B(t)\",\n", " colors=['green', 'red'],\n", " legend_title=\"Curves\",\n", " curve_labels=[\"d/dt B(t) : exact\", \"d/dt B(t) : least-square fit\"])\n", "fig_main" ] }, { "cell_type": "markdown", "id": "e39163f0-24fd-47bd-9365-3c734a8f83db", "metadata": {}, "source": [ "_Virtually indistinguishable lines! And the same plot as we saw in Part 2!_" ] }, { "cell_type": "code", "execution_count": null, "id": "306660cc-049f-43e2-a4f3-ff5f19b01e00", "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": "3.9.13" } }, "nbformat": 4, "nbformat_minor": 5 }