{
"cells": [
{
"cell_type": "markdown",
"id": "5cbc8640",
"metadata": {},
"source": [
"# **Enzyme Kinetics** : \n",
"\n",
"#### Our model: `E + S <-> ES` (with kinetic parameters _k1_forward_ and _k1_reverse_), and `ES -> E + P` (_k2_forward_) \n",
"\n",
"#### In experiment `enzyme_1_a`, we were given `k1_forward`, `k1_reverse` and `k2_forward`... But what to do if we're **just given `kM` and `kcat`** ? \n",
"\n",
"In Part 1, we'll \"cheat\" and use the actual value of _k1_forward_ \n",
"In Part 2, we'll explore what happens if, lacking an actual value, we **under-estimate** _k1_forward_ \n",
"In Part 3, we'll explore what happens if we **over-estimate** _k1_forward_\n",
"\n",
"Background: please see experiment `enzyme_1_a`"
]
},
{
"cell_type": "markdown",
"id": "604b150b-7812-4fd3-9403-69a06dd7e397",
"metadata": {},
"source": [
"#### THE REACTION: \n",
"the enzyme `Adenosinedeaminase` with the substrate `2,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purine`, \n",
"and the initial concentration values choosen below, all satisfy the customary Michaelis-Menten assumptions that \n",
"`[E] << [S]` and that the reaction rate constants satisfy `k1_reverse >> k2_forward`\n",
"\n",
"Source of kinetic parameters: *page 16 of \"Analysis of Enzyme Reaction Kinetics, Vol. 1\", by F. Xavier Malcata, Wiley, 2023*"
]
},
{
"cell_type": "markdown",
"id": "c123db4f-c802-47f0-a3d3-0b857314d8e5",
"metadata": {},
"source": [
"### TAGS : \"uniform compartment\", \"chemistry\", \"numerical\", \"enzymes\""
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "6e9d0902-6fc9-4692-ac39-0651d08902ca",
"metadata": {},
"outputs": [],
"source": [
"LAST_REVISED = \"Sep. 2, 2025\"\n",
"LIFE123_VERSION = \"1.0.0rc6\" # Library version this experiment is based on"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "1e0ae9a9-9d0c-4edf-a5f2-1c589419e6cf",
"metadata": {},
"outputs": [],
"source": [
"#import set_path # Using MyBinder? Uncomment this before running the next cell!"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "a29db1c7",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"#import sys\n",
"#sys.path.append(\"C:/some_path/my_env_or_install\") # CHANGE to the folder containing your venv or libraries installation!\n",
"# NOTE: If any of the imports below can't find a module, uncomment the lines above, or try: import set_path \n",
"\n",
"from life123 import check_version, ChemData, ReactionRegistry, UniformCompartment, ReactionEnzyme, PlotlyHelper"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "af15ecf0-e083-4fef-b68e-abe794dcc86e",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"OK\n"
]
}
],
"source": [
"check_version(LIFE123_VERSION) # To check compatibility"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "3713fa4d-e9bb-4e33-8734-c1d4d23cf177",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "34d1cefc-f644-410a-9fe4-5204964742ac",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "1b6c8520-6340-4056-a9e4-fd376a64d21c",
"metadata": {},
"source": [
"## Assume we're only given values for `kM` and `kcat`"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "0922af12-fb21-4dd0-8709-13bec73555c3",
"metadata": {},
"outputs": [],
"source": [
"# The following values are taken from experiment `enzyme_1`\n",
"kM = 8.27777777777777\n",
"kcat = 49"
]
},
{
"cell_type": "markdown",
"id": "84744152-f9e6-45a1-9002-a4842c2ef2c0",
"metadata": {},
"source": [
"What values of k1_forward, k1_reverse and k2_forward are compatible with them? \n",
"That question was explored in experiment `enzyme2_a`. Here we'll explore the dynamic consequences of selecting various combinations of values."
]
},
{
"cell_type": "markdown",
"id": "9a4febb2-2780-4754-9c70-c2041b1afc07",
"metadata": {},
"source": [
"## In the scenario we're exploring, there's LITTLE ENZYME relative to initial substrate concentration"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "8c9e3f86-b9a5-41da-9e1b-75258017808a",
"metadata": {},
"outputs": [],
"source": [
"S0 = 20.\n",
"E0 = 1."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "67b2734a-0839-4370-a5a9-18883fc15c4c",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "b0ea13d4-9e26-41ec-884a-a56a70445233",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "91a729ee-ad2f-4771-bc84-49ecb9d6a851",
"metadata": {},
"source": [
"# PART 1. Using the known, exact values for `k1_forward` and `k1_reverse` \n",
"\n",
"Source: *page 16 of \"Analysis of Enzyme Reaction Kinetics, Vol. 1\", by F. Xavier Malcata, Wiley, 2023*"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "33edfef8-7024-4881-a115-dbd39d3e976a",
"metadata": {},
"outputs": [],
"source": [
"k1_forward = 18.\n",
"k1_reverse = 100."
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "ac9eea69-174c-43e5-9eed-443cbc5e2ba7",
"metadata": {},
"outputs": [],
"source": [
"chem_data = ChemData(names=[\"P\", \"ES\"], plot_colors=[\"green\", \"red\"])"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "90f9ec41-6e1b-4558-9400-47e35ece6efc",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"
\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" name | \n",
" label | \n",
" plot_color | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" P | \n",
" P | \n",
" green | \n",
"
\n",
" \n",
" | 1 | \n",
" ES | \n",
" ES | \n",
" red | \n",
"
\n",
" \n",
" | 2 | \n",
" Adenosinedeaminase | \n",
" E | \n",
" violet | \n",
"
\n",
" \n",
" | 3 | \n",
" 2,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purine | \n",
" S | \n",
" darkturquoise | \n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" name label plot_color\n",
"0 P P green\n",
"1 ES ES red\n",
"2 Adenosinedeaminase E violet\n",
"3 2,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purine S darkturquoise"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Our Enzyme\n",
"chem_data.add_chemical(name=\"Adenosinedeaminase\", label=\"E\", plot_color=\"violet\") \n",
"\n",
"# Our Substrate\n",
"chem_data.add_chemical(name=\"2,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purine\", label=\"S\", plot_color=\"darkturquoise\")\n",
"\n",
"chem_data.all_chemicals()"
]
},
{
"cell_type": "markdown",
"id": "f8d4ea7f-0591-467c-9df3-d95f53df75f5",
"metadata": {},
"source": [
"### Specify the Kinetic Parameters"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "3662d205-0779-4cd6-8001-905c44e58ba4",
"metadata": {},
"outputs": [],
"source": [
"rxns = ReactionRegistry(chem_data=chem_data)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "78077d8c",
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Number of reactions: 1\n",
"0: E + S <-> ES -> E + P (Enzymatic reaction) (k1_F = 18 / k1_R = 100 / k2_F = 49)\n",
"Chemicals involved in the above reactions: {\"P\" (green), \"ES\" (red), \"E\" (violet), \"S\" (darkturquoise)}\n"
]
}
],
"source": [
"# Enzymatic reaction `E + S <-> ES -> E + P` \n",
"rxns.add_reaction(reactants=\"S\", products=\"P\", enzyme=\"E\",\n",
" k1_F=k1_forward, k1_R=k1_reverse, k2_F=kcat)\n",
"\n",
"rxns.describe_reactions()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "d23a97ea-f252-4e11-a3e9-aea74f58591e",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": 12,
"id": "aae96512-3d86-4ab0-b167-92943523b7ef",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SYSTEM STATE at Time t = 0:\n",
"4 species:\n",
" Species 0 (P). Conc: 0.0\n",
" Species 1 (ES). Conc: 0.0\n",
" Species 2 (E). Conc: 1.0\n",
" Species 3 (S). Conc: 20.0\n",
"Chemicals involved in reactions: ['ES', 'P', 'S', 'E']\n"
]
}
],
"source": [
"# Here we use the \"slower\" preset for the variable steps, a conservative option prioritizing accuracy over speed\n",
"uc = UniformCompartment(reactions=rxns, preset=\"slower\")\n",
"\n",
"uc.set_conc(conc={\"S\": S0, \"E\": E0}) # Small ampount of enzyme `E`, relative to substrate `S`\n",
"uc.describe_state()"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "e6ad72b8-722a-4606-a611-7dc600529f30",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"784 total variable step(s) taken in 1.548 sec\n",
"Number of step re-do's because of negative concentrations: 2\n",
"Number of step re-do's because of elective soft aborts: 1\n",
"Norm usage: {'norm_A': 706, 'norm_B': 710, 'norm_C': 706, 'norm_D': 706}\n",
"System Time is now: 1.2018\n"
]
}
],
"source": [
"# Perform the reactions\n",
"uc.single_compartment_react(duration=1.2, initial_step=0.05)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "e3378bf9-a48b-486d-8f7e-5f605a940b88",
"metadata": {},
"outputs": [],
"source": [
"history_exact = uc.get_history() # Let's save the historical data for a comparison at the very end"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "0198dd94-e55d-4ab4-9de8-087d508edf06",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"plot_pandas() NOTICE: Excessive number of vertical lines (785) - only showing 1 every 6 lines\n"
]
},
{
"data": {
"text/html": [
" \n",
" "
]
},
"metadata": {},
"output_type": "display_data"
},
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"data": {
"application/vnd.plotly.v1+json": {
"config": {
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"hovertemplate": "Chemical=P
SYSTEM TIME=%{x}
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kpG+RGgXDfrnkZK/i+ZRO8z4DbGWXTjgEJQWpsl4xG594hnTp2I5mz3gw9nU62kyy5+2UIQXmRRG/teMr2dv5qXqTmW86nnT5Wjrvcf9PDVNNNu7XF630JVNMAlbkT6XuxQ3odbEg6qkgS2KsMoeEJRqXRI/Pi/HxA/LCFk1p+kN3e6mmlxWkwDh/iHvZ/ODxLDzECk5vy8TCSZCWZD9cQoTBs2iQAs+QgRQEh8xVAkiBK0Rx87WZFIIUyOHnpVTKkgLxAPe6mPMCjkzZsN+eyPRBRZmokQLxJtTuzRBPBuNHX0ltWl7ga/jGE339LnzFhMQd8CuD63ohBWHjYgQzGePzokzVpIDbVkn2vIxFpqyMnXD/iy8v0ncmQQpkUEUZWQTCftbBXqs1kaydAlk7SHQ5Me9ZrfXS0WaSPaa0JAVmVxizMdm5M9i9qTUuIMUNwWVvuGYQ3fHTR2vcI0KOnXKNiy2ubPU23Fj3lnv+k0pKy2PthLE7EkVSsP9Qqa9dBqdJSwUZMMsPuniWWeyJNoNuH/uZ0BM5Pi/9C4MUROVlgxUOVrsbTnh5mUPs3Kms3Nb4vnz2Tz+nERN/Fmvezp3TPNfxLgy7A1rNteY+WO3YWM3FMoTcakEr7iXZsdhhbfd8MO5gycz5Xvsj064MpiJWps9lnek3jz0bG6ZRRwI/MwZWz7oHfvVUzOWTdbN63Wf09tI1NeAz2pYZH1FY6NZu3lONq9XaQGYHl5+fLQoLXF1bzHZo/lsWBz8260WH4mWbwP23/zolbq0j7k2zDdphJWOHdveX7DpKxmaErV/YohnNmv1WrEmxRjT3025ucVtjOs3LVnOtuBfc9M9yrWzU7NLqZS4xy0tZUiCM0ag0K78zqwWX+Mz4FtpuYWb1IOayvFBnVxuntydWxmz1ptfqM6NxGCfPsBaFUSMFAndVO0FhkAEncuDF79wLKVCNi5dFuNEmwxqfl/5kGinweo96mUPYrvhB+cCdE2IqsJr7xFxlJgFWQdhOLlrmxYOVz7h5vGI8RtuTJUp2pIAJisxY7OzS7fnA9WTn/KDYGp9L3K4MplxOuGNakQDj81XmWcfyzHODrG15fUOuGlerFwJW6wwnwm5cUwj8jc8w8xitMHXDIYjNyujQvN7g9owE3biItPrc/MyWtUO7e4z1zJcxlkCUdcPK/GJR2Lqxj8a1gdXnRnuWXWM6jYXxNNsJlxeu205jsnI3s7JRp7nEqDMrm09JUmC3iLJbMAvQ3N6w8+S1duO2mHJktku93GROZc0PVTvDEGPxsiiTWWiFEWjMY/AbU2B8qBn779Xf2ziBybxRlMHKrYzdYsyuntdAXCtdecXFbQxO34c9Ptm+hUEKZBeZsn1UWY7nCC96DjqHCLs03jd2c6zATTzsVMx15vad5vd+vbs4uhI67RSY46jMY7HTYdDng3nOV4Gt22LJSqd2WbXMb7+9POvc7N6qH14WeF7sSxZXu/a5rx98tIluGjPEdljm57Jx8Whc0MqsMbzgIDqkwmbtXmJa7dhb7YyIZ7Zxx8QJU95plHkmc1s9u3awjB3zipWVrdu5J1l9HnSNaXev8TjECxmnMdnVN9uVWz+d4s5ShhSY70arBb4dYHZZQ9wyuDgpR/THy0TpxYCDPtDdJmXz917fQprryyxsRR2vb/+tttRks0/5IQV226yymS/8LppltqmNuPvFJVXGZxyrlauEnY3LEGarxb9ow6sevN5rfsuHTQrs7MJ4vwZdYPHYZRfDoqx5a98LMXKap2XHYqcvmeeDlzlftj8y7TrtKDP+Rp0mghTI2JYXrLyUlcXVOMfIzvVG2zDiyv1bs34r3XP79brbjViv8HN21NDi2ALQz06B1SI90aTADlPz517s0O4+M9ur1TPQaj1o1badrct+7nWNabXOYldwpzWQnW3LrDWF3drhbiY6VjafMqRAKF0AY14UyixKBSu1y+BhvrFkbjQZRYm+O8kzb4WmGimwuqGD7hS4PYy9kIt0cR9yWlAKm/GCi5cFqpGEyCy8hWwv7lFe+qNip8DcnpdxeemrirL8QJIlw9yelzlE7D5ZuWP6IQVOc535weq2S2kkaVb+uDL2HsZOgczzwcucL7t4lWnXC6ZhkwJZ2/Ky0A8DV75nrF4+yJJQo5sLj3nqpNH67oIgApwYg9+OG+eYdCcFXuww6qTAyxrTab63wsRoE27ztpNssdaUJQVWNp9ypMA4CPPN6sQojUDKTr4yb2S8kAIvk56bYahevATdKUgkKQiyyAyDHBgXyzLboWasgozHKEuVHHP/ojI+c79UkAI3l0IVi3lVMry6NsnOIXZzmJftcy8vVKx2ChgjK59hN+zMaVjtyodBCmSeD17mfJXPJSc/bDNGYZICL7blBSsvZWVxtbIdLzFcxj7x4t/4MnDf/q9pzIj+eiC3cRci3UmBFzu0u3fDdh/idr3sFMi8hHCbt8wvzPhvYRduOwUyaz87m5dxeUxJUsAAWt2sTltVRiXZ+cN58YtlxbEPmJVvpGjLrFwvfpCyD3RZ43MrFzVSwLqwyz8vY9hu41VBDoIuls0Tg4zbSti4GHFLxvjc9GYm9yrPKfDSdjLKCrt3enPJdt36wuaOKUnN/s92cUpBSIFT7JNs/JQZYyvbl50LwiAFbi+E+PngZc6XXbzKtCtDWAS+sqTAy7NOyPZiW06xf2ZswsDVbm61w8dsn8b700hy7T7nMlbj8IKD6IPM7hGX9apDWTch0Q9zeS92aDenOhELr1jJLv7t7g3ZNabVWBj72a+9F5fMgcuZMXIak6wt2vXT3JaVzacsKWAwhcuNeDtrFRkulMOLXk7jxam2rN64GbeljUxetGF8o2gO6rAjGVY3hJU8s+uQlaG4TbJBFylRIwVWmRuMk5oXNwonbPy63Ih6fnYGzP3x8oY/0bgkenxe7DhVdgqEflXYrJ3rI+Nmfmsu+2LByv6MW+V+3IdEf/i3MZBXzHUy2Ye4Ls+1nCpTuGGwP65xfpbdPQmDFBifQU7PB9k5X5YUyLZrlfXFjCn/LUsKhE7NqTednldebMsu4FOM1+xLrxpXYUvGN7Gy2YeMi0j+v3netJu3rezSKw5Cp5z2VSYWwut6xSqGwQtZkLVDu7nfiVh4xSooKZBdY1qNxa6uee3lNCar7ENiXSQyYhrnB6tdKeN8bmXzKU0KjA9C40NGJjuL2TfVmE/Z7tQ8o6Kt0pmK71WfU2A8oCuTsg9Z+Q9bTbheFpJRLCvjq2hedFjl/VaxgA8DH6/jk+1DJpICgY3MHCdLCsRDxXzugMiF7pcUGOdn0W9ecHHgpdUWvN39bpxrRUpBu7nYznbCIgXGBbFTn4y7blzOiiB6IQWy7cpiarVLabV4NN/Lbs86L7bFZc0+/SrPKZDJMiWIhlGXMu4aorzVCz6jrsyy7HY8vOIgu1NgpQ8nHXpZ/IvFqFMgtPn+lCExTotkrzYTlBR4mX+t5iKrgHuZ81isYr3M8q3maeP5VnZrJ7PNR54UyC4QUA4IAAEgAASijYCT+0K0e47eAQEgkCwEvJCeZPUxSu0GcXMCKYiSJtEXIAAEgECaIGB0/TG+SQ3jpPI0gQzDAAJAwAYBrymZMxlIkIJM1j7GDgSAABCIIAJWriuy6R0jOBx0CQgAgSQi4BRPlcRuRbJpkIJIqgWdAgJAAAgAASAABIAAEAACqYEA3IdSQ0/oJRAAAkAACAABIAAEgAAQCA0BkILQoIVgIAAEgAAQAAJAAAgAASCQGgiAFKSGntBLIAAEgAAQAAJAAAgAASAQGgIgBaFBC8FAAAgAASAABIAAEAACQCA1EAApSA09oZdAAAgAASAABIAAEAACQCA0BEAKQoMWgoEAEAACQAAIAAEgAASAQGogAFKQGnpCL4EAEAACQAAIAAEgAASAQGgIgBSEBi0EAwEgAASAABAAAkAACACB1EAApCA19IReAgEgAASAABAAAkAACACB0BAAKQgNWggGAkAACAABIAAEgAAQAAKpgQBIQWroCb0EAkAACAABIAAEgAAQAAKhIQBSEBq0EAwEgAAQAAJAAAgAASAABFIDAZCC1NATegkEgAAQAAJAAAgAASAABEJDAKQgNGghGAgAASAABIAAEAACQAAIpAYCIAWpoSf0EggAASAABIAAEAACQAAIhIYASEFo0EIwEAACQAAIAAEgAASAABBIDQRAClJDT+glEAACQAAIAAEgAASAABAIDQGQgtCghWAgAASAABAAAkAACAABIJAaCIAUpIae0EsgAASAABAAAkAACAABIBAaAiAFoUELwUAACAABIAAEgAAQAAJAIDUQAClIDT2hl0AACAABIAAEgAAQAAJAIDQEQApCgxaCgQAQAAJAAAgAASAABIBAaiAAUpAaekIvgQAQAAJAAAgAASAABIBAaAiAFIQGLQQDASAABIAAEAACQAAIAIHUQACkQIGejp44Q0dPViqQBBFBEKhXJ4dys2tR2fEzQcSgriIEChvXobKjFXTm7DlFEiHGLwK1tfuicYNcOlRe4VcE6ilEIL9+bf2+OHEKzw2FsPoWdWHTurTv65O+66OiegRYJ7gSjwBIgQLMQQoUgKhABEiBAhAVigApUAhmQFEgBQEBVFwdpEAxoAHFgRQEBDCE6iAFIYAqIRKkQAIktyIgBW4IJeZ7kILE4CzbCkiBLFLhlwMpCB9jLy2AFHhBK/yyIAXhY+y1BZACr4ipKQ9SEBDHhx56yFJCrVq19M9rZWVRtvavquoc5eRkU61aWZRXpy6dOV1BJ04cp9y8OpTF3589q5U5S40LmlF+4yaUl1eXDpceopMnTlCHTkVUdriUykpL6LI+/WjF0kXUu3gg7f5yu1a+KVVWVmqyc/TfTbS/+XP+fv68F+imW6fSglfnUPeefahO3Xq0ZPECumHCZFq7+gNip47LNXlLFr1BLdu0pQ4di2jZewupsHkL6lTUnbZ++gkd2L+PBl41XB/L039+hG6ber/e3+3bttCO7Z/TkGGj9e+M8vjvTzeu0/pfQv0GDdW/rzh1kmY/N5MmTbknhteGtR9qn5+iPn0HxT5bvuRtKmjWnC7t0iP2mbkf4osXZj1Jo2+8mRo0aKh/xKQgm6ro8ekP0w/unFZDL3NffIauvHoUFTQtjPvuq7276ePVy2nUdTfVqOP0HRe2kykEzZrxGE287S6qnZtraScr3l+s6buAirr1tLXEha/Ppc6aPtq0u9i2zJ5dO2jj+jU0YvRY2zL8xb49O2ndmlV0zZjxjuX4S6NduBXetmUT7d2ziwZ/d2SsqBMpsNOpUzsyOJjrlxzcr9v0deNvdRtCje/N9uVFwKIFL2v3bRdq276Dl2qxsquWv0v1GzSirj16+arPlTZt+JiOHimj4gFDKAgpcLsHvHbQ7Z7wKm/dmpX63Nf7igFeq9qWD1umKlIQdj9VARr1fgpSYH6OqRg/ZFavM7xeIAVeEVNTHqRAw3HQ9T+hktLyGKIz/jCN+vfpGvv7vgefoLeXrtH/7tKxHc2e8WDsO5ACkAIroiEMxG0BBFJQTThlLpACGZTOlwEp8IaXsXTYi1iQAv+6ETVV6gikoOaLveAaCiYTpECFBrzLyHhSsGvvAZr+Py/R9Ifu1tF78ZV36DePPUubl8yK/f3U316jpfMe1/8ef8dD1KtHR3rgzgn63yAFIAUgBUTYKYiffLFTYP8wciPKXh9jKheHYSw4rWSCFHjVcs3yKvUOUhBsAW+nzSC7JCAFwe8RPxIynhSYQWOSMGLiz+jN539PbVpeUIMEMGkwkgSuj5gCP6anvg5iCtRjGkQiYgqCoKe2bhD3IbU9gTRGQBUpAJpqEEBMgRocVUoBKVCJprwskAITVstXb6Q7fvpobKeAXYumThpNN40Zopc0fw9SIG9sYZcEKQgbYW/yQQq84RVmaZCCMNH1LhukwDtmYdYAKQgTXX+yE0EKigZPppamAOwAACAASURBVF/ee0tsfeevp8mv9fCTf6fXF62MebQE6RFIgQk9JgGjhhbH3IPMRiNIgdhJyFm/kea0aU1D69QPogfUVYBA7RwO6q5Fp06fVSANIoIiwCSNdcFB9riSi0CWdl/UqZ1FJypwbyRXE9Wt5+VqKRG0++JMZVUUupPxfWhYr7a+448rOgiwToJexnhQIevqQb1i7uLJIgXCTV2sI4OOE6QgKII29ZkQ9OzaIWYwXMxtp8AtpoAz9fC/c+fOUXZ2tv7/OnXr0umK03T8+DEtE9H57ENntQxETZsVUpMmBXqZkkMHtQxFJ+jSoq5UWvo1lZYcou/0G0DvLVpI/QYO1rL//JOaNm2mZd44o2Ufqq3/LtD+5s/7a9/PeeFZmjL1bpo75wXq1aeY6tWrR28tmE+3TJ5CKz9Ypo3uHBX3G0hvvvEatW3bTstw05UWLVxALVp8i7p2v4w2fbKe9u3bS1cPv0ZH7LFH/ot+fP/P9DFs3fIpffH5Vrpm9HX6d0Z5/Pf6dR/r/b1qaHUg6amTJ+mvM5+ku+65P4b+Rx+upFNaVqIBg66KffbO229Ss+YXUPce57PxmPshCv/lyT/RhJtvpYYNG+kfMSnQ0jjRIw//nn4y7V9raPlvz/yFRo76HjUrbB733Z7du2jF8qU07qZbatRx+o4L28kUgp547GH64V0/oVyb7EPvLV6oZ5C6rKd9lplX5s6hbpo+2l9sn8nmyx3bae2aD+n6sTUzKBkHtWvnl7R61Qd04/iJrneR0S7cCn+66RPatWsnDR95baxofSYFFZVkdXaZnU6d2pHBwVz/wP6vaLFm0xNvvd1tCDW+N9uXFwGvvfwPLYNWV7q4Q0cv1WJll7y7iBo1yqeevfr4qs+V1n38EZWVHaYrh1xN2tll2kKUSYH3RajbPeC1g273hFd5H678QJ/7+g0Y7LWqbfmwZTJB4/siKCkIu5+qAI16PxvWzdEPIDU/x1SMHzKr1xlOV9mpMiqvKIsr0qWFfbY9Gb3wgr9ZQX6Nt+ccF3rP7dfryWSSRQpk+u+lDEiBF7Qky1oRAq5qDiw2xxS4kQKkJEVKUqQkrblTgJSkzhMTUpJKTtxMfpCSNKXSscpr1rmkSr1nSqDx7iM740Ddc3RX7O+DW/ZQReUpqnVR/Bt6c50jp8u1Bfz5bI0sYI9JLn9WrpX79pG2uvx1eetj7Zjl2Wn53IP+d5h5h2Dtxm2u7jSCFHCcqMhAOXn88JiniOgbrwM3bd0R66rxDT9/d2GLprRv/9exMiJLpTGzpXGHwuxxIgRzf4yXaMecIZPLiGQ4/H+QAlWzyjdyWBFWhsBfm0kAsg/hnAKj+eGcgmo0kH0oflJC9iH7SRrZhwYoCzRWuTAWGstEmckkBWKRzIvtI4bF9p6j5xfwxoU0l8vdq+2Ka2vmQ4WH4xbkvBA/YnjjLrsAZ90P1n74WqL9qLpkZebnNaZGeflxze6670vf3XBa0xmFikW4WHyLxboxLb1Y9NtlqBSEQdQRyWq4HSFXfCbKmEmB+N64DuW1J18cz8qkQGTA5M+4Tb5EenyQAt+mUrOi8O0yf2NkdU7nFFz5xXZacvQYPdb0Ahpbv9qNBVdyEECgcXJwt2sVgcbR0QcCjaOjC+4JAo2jpQ+ZQGN2b+FFu3HxXv1/dn05vxg3vkk3vkHf/c0in2WYXWUShUbrRhfFNdW6YfzfvDBvpC3QjVfrhm3i/ubv800L+FYmOVxBl5Ubv9Dnz819sBu730Bj8wLcCVsr9yGjyzgv3n/xu5k1dhyMZcykgdszx6aKz0TSGjMp4EX9mvVb487Acuq3OXU+SEGi7iCJdv639DBN3rmbWms+/QsvaE35WtwAruQgAFKQHNxBCqKFu1VvQAqipSOQgsTpw2oxL97CizfpX5/eqwfhi0W88Y27l7ftfkYlFsn6YtuwiG5lWMAbF+bmRbl5Qd7KsIiXXYD76XfYdZJJCkSyGV5sz5r9luVQxVt9L6RAyDWTAisZ5kbNrkX8vXAhAikI2xo9ym+7aQvtPHOainLz6KXCliAGHvFTVRykQBWSauRgp0ANjiqkgBSoQFGdDJACb1iKhb3wgedFvXg7L97M8xt7/S38N2/vVb+RFy4uxsW78c26WLgbF+3GBbtYrHMdloXLGQG/pIClygYQ2+0UGEmBW6rPsEmBIBBm1yLjIbsgBRG6mxBojBONcaIxYgrMUxJiCuwnacQUZHZMAb95Fy44wv1GfMYLffG2nt1tnBb2A2kg5Wg/72o/TpfVYl68hRcL+a4XdqCyY6c1X31tp1/LFNi8c2sSi/igb9uDnOprN65MkBmEFPBCff+hUstAY15k82WXfcjo+mMXEGzUiwpSwC7qHKgsYgSM8q0W/HAfihAJMHfFjhScq1WLtCyAevrObO0f56TOycmmWrWytDSkdenM6Qot3ehxys07n5K0Skun2bigGeU3bkJ5eXXpcOkhOqmlJO3QqYjKDpdSWWkJXdanH61Yuoh6Fw+k3V9u19NZVlZWarJz9N9NtL/5c/5+/rwX6KZbp9KCV+dQ9559tDSn9WjJ4gV0w4TJZJxUlix6g1q2aUsdOhbRsvcWUmHzFtSpqDuZM8Q8/edH6LapCDQ22gACjavRQKBx/MwAUgBSYEbAGMCraqcgCkHB/Baf3+ALf3t9ga99tlv/rPrtfdOSxnra2DfPvunraS4W9sIHnhf1zUqaUH7tfDrdqkr3U+c39MKHnRf0Xt7IJzPQ2A8gIAXOqIm4AnNKUuEOJAJ+3XYKuBUmCXwZA31ZTqtvFepBwCpIgeiv8SA1EWjMbRt3BUSfOFsS3If83D0h13EiBXw2Aackra3FGZwDKaDZz82kSVPuiWlkw9oPqeLUKerTd1Dss+VL3qaCZs21HO89Yp/Zpa98YdaTNPrGm6lBg4Z6WXYf0o4EosenP0w/uHNaDc3bLeC/2rubPl69nEZdVzPHv9N33ABIAUiB1RQDUgBSkMqk4PipY9Sk0wWWC31+ky9cdGT97Y1v9XmBz4t69p8X7jf8xl643QiXG7eFvUpCBFJAcS8KVS2bgpCXIDsFov/mVKL8uTGdqAwp4DpWcsSCXAUp4DaMWYtE/0VfzYewsSsRxzqAFKiyVMVy+CREPvhEXOXaIWTTjx6mvxw5rH+Un5VNUxrm0+0NtEAiBCIrRv+8OMQUhAatL8GIKfAFWyiVEFMQCqy+haraKfDTAV7I62/2Nd/76v/v1H/zG3122ZFd6Iu2zYt8/a29tuA3vr3nxT8v8qPqSy+TfcgP1qjjHwEVpMB/65lbs5b2Ntv/CRGZi1vcyM2kQHy552wl3VdygFZUnIiRg/vzCzSCgCCjMEwHpCAMVP3LBCnwj53qmiAFqhENJi8sUrC55BN9cS8W+uzCI97s679Np8bajcLorsMLeuNC3/gmP6i/fTAU1dUGKVCHpSpJIAWqkPQmB6TAG16Wpe1IgSi88tRJ+mN5aYwccPrS6QUXULEWW4BLHQIgBeqwVCEJpEAFimpkgBSowVGVFD+kgBf0n5ZstHzDz2RAdsHPC3n2zReLfV7ki0V/1N/oq8LfLAekICxk/csFKfCPXZCaIAVB0NPqesk+dE4LND6h7cscz61NeVpQcAPNnz5bS2PKMQdVmssRAo2JEFNQ0yAXvj6XOmuB323aXWxrrXt27aCN69fQiNFjHS16356dtG7NKrpmzHhXyzcGoLsVRqBxPEKIKbC3GGQfss4+ZFz0bz60QV/8bz6kLfb13xssATVn4Ckq7K776rPPvvDTL2rWTScAsu47Kn31RaejLhMxBekZU+D23ML3NREAKQhoFV5Igcg+dCo3l45r2Yfqa6TgZO3aWoaibKrPXlzIPgRSYGGPIAXVoMjgYIav5OB+PaPWdeNv9XynmwPZvQgAKQApMCPAC+P9R/ZS444X0PYjm2lH2Ze04/AOPUuPjGuP8N3nxT6/2ec3/PkH61Nt7efKgdco89eP+gI+DKIBUgBS4GV+T+eyIAUBteuHFHBK0gqNFJzSUpKe0kjBWU5beraK8s5VUYGWkrSgSQFSkiL7UMwyZRbD2CmwvpFBCsqoeMAQbTeyFjVukEuHyis8z3huGbi8Ckz3nQLh18+/2bdfvO1veijfMa++1aLf7S1/Ji7gQQqit4C3mwOSnX3I69yE8kQgBQqswC2mwKkJZCpSoIBvRCCmQB2WKiQhpkAFimpkBCEFanqQXlKEq4954W/n5iNGL/z52xe00915LmnSVc/Uc2mzrsre9KcX0okZDWIKEoOzl1YQU+AFLXVlQQoUYBmEFIjmOVPRg9phZW+dPKZ/hDSm3hUDUuAdszBrgBSEia432SAF3vASpasX/bt0n37jDoBTUK9Y+BcVdtNdfKpdfdoQv/UXl59AY38jQC0ZBEAKZFBKbBmQgsTiLVoDKVCAuwpSILphlalompbGdGz9Rgp6mt4iQAqipV+QgujoA6TAWRfmxT/7+Tu99WdXH+Haw785wNe88HdqEaQgOvcG9wSkIFr6EDqJXq/Sv0cgBQF17Dem4IwWU3BCiynIzaujBRpn1cg+dFhLW/rFof1UdfIkrW/dhi4+cYI6a/8GfKc/rVi6iHoXD6TdX26nxgVNtePjKyknJ0f/3UT7mz/n7+fPe4FuunUqLXh1DnXv2Yfq1K1HSxYvoBsmTI47vdCYZYaDMgubt6BOWrYb80nCT//5Ebpt6v16f7dv20I7tn9OQ4aN1hE0+w5+unEdHS4toX6DhurfV2hpWXGicU1jW/H+YspvXEBF3XraWiJiCqqhkcHBDCJiChBTYLQJ2cW/yOpzoPBrPZuPeOvPBMCvq4/R/18VKUBMQSX1vmJAwKf4eVIQxAferhOQSXR5n36edYSdAs+QKakAUhAQxrBIQV5eXW1RfYgOHj9Gq1q2otpHyqn50aN0oKgb9dmwlvr3HQRSMOtJGn3jzdSgQUNdi7xToCV3pcenP0w/uHNaDc3OffEZuvLqUVTQtDDuO6dASrcgSzuZogG3oEqQguHSdyBIgTRUesFNGz6mo0cykxQYff51IqAd3OWUy5/f9HNWH/HWv2LHMSrIbUr9+1e/1FBxgRSoWcALXagkRMg+FL3g5XQkBYOu/wmVlJbHppMuHdvR7BkPqphelMkAKQgIZdik4KS2O9D6kktprbZrUHq4hN7p0JFGbvyEdne7jK78uoTaNmuOnQKQAkL2IesbGTsF6U8KFr7/MpWdOEx7C76ilXuXaSk+d9JujQRYXUZ//+KWA21dflQuOK0WsdgpCPjg1aqr1BFIAUhBcIt0l8CkYNTQYnrgzgl6Yf67Z9cONP2hu90rJ6gESIECoFXGFDh1hzMVPX2sjGYeLady7UwDvsY1aETT8ptSq+wcBSNJbRGIKYiW/hBTEB19pEtMAb/t/1T7x7851afd23/h86/C7ScMLaoiBWH0LRNlIqYgelpP150CIyl48ZV36Km/vUZL5z0eGQWAFChQRaJIgeiqIAePlpfqHyFTUTUyIAUKjFmhCJAChWAGFJWKpIDf+uuL/xgJsD7VV7z9L245wHPAb0BYfVcHKfANXSgVQQpCgTWQUBWk4PXPXw/UBz+Vs2pl0cgOIy2rmncKQAr8IJwCdRJNCgQknMb00fKvac6xIyAHIAWRu1NACqKjkqiTAvMOwIq971uCJ3z/2fUnSNBvsjUDUpBsDcS3D1IQLX1wb1SQgloP1UrKwM49eE6KFBQNnkyTxw+PuRMlpbOmRrFTEFALiYgp6NCpiMoOl1KZls3nMi2K35x9aKeW2Wdl5RnaV3GKSho2pM4HD1KbPsVUuOhNmojsQzENI9CYaN+enZov7iq6Zsx4V8s3ZqVyK7xtyybau2cXDf7u+TckTqTAnNnKTT5/j0BjGZTOl4lqoPFfn/ojfWvIxfThgeWOLkCyBEClb7lAL2yZqkhB2P30ZnH2paPeT8QUpGdMwegXq7MjJvLKycqheePn2ZICY6Bx1AgBdxqkIKC1RIEUiJSkTA7ezcujc3t30budL6XbP1hGrcdPovqL30JKUk3PIAUgBV5u9xdM2a281F204GXq0KkLtW3fwUu1WNlVy9+l+lq8UNcevXzV50pRIAUiC9BK7c2/cAf6UcVd9Ij2c1r7EZcsAbACI+oLTiuiAVLg26xjFVXqHaQgPUlBcCtTK8HsPqRWuhppIAUBcYwSKRDnFKz95zaa36kzdXv3bXps6DD6l1UrqN/lxdQzvzHOKUBKUuwUSN7zIAXVQLml5TXCKdyAVoh4AO0kYPP1c/o5rW+7mTo370LsBuQ377/VYltSta7FVC44QQrUZgoKQ+8gBSAFrpOCggIgBQpATAURyYopcMNm4cnj9ODhQ7Rbcy3iq29ePbpfOx25uE5dt6op+T0CjaOlNsQUREcfYcUUiLf/C7fPt80E1Jf9/wu76QSA4wD45N9Mv1TtFGQ6jqrGj5gCVUiqk6MipkBdb9RIAilQg2PkpUSVFAjgXjp+RCMHJbE0pulKDkAKonWrgBRERx8qSAG7Aq3at1xzA3pfjwWwCgbmTEC88BcEgDMC4aqJAEhBtKwCpCBa+uDepCMpiB7KNXsE9yEFWoo6KeAhWp1xkG7kAKRAgTErFAFSoBDMgKL8kII9R3fpb//f+mYXYLOFKxDHAvTVFv7YBfCmIJACb3iFXRqkIGyEvcsHKfCOmYoaIAUBUYxiTMHuL7dT7+KBNH/eC3STKfvQu4veoN0jR9Omj1ZSxbkqWtKxM92xYT0NbH8JDS7qTsveW0iFzVtQJ+3/5gwxT//5Ebpt6v2UlZVF27dtoR3bP6chw6qj+9eu/oA4CdflWnYkvj7duI4Oa9mS+g0aqv9doQVBz35uJk2ack8M8Q1rP9Q+P0V9+g6KfbZ8ydtUoJ3SfGmXHrHP7DLVmH2+mRRkUxU9Pv1h+sGd02poFoHGCDT2crtnWkwBkwDeBeB4AP4tTgVuS21psPbzct4r3+wCVJMAv7EAs2Y8RhNvu4tq5+Z6UYdt2bD9/5V0UhNi7KcqUpCKYw8Dz6AyEVOAmIKgNpQu9UEKAmoy1UjBksUL6IYJk2nFh8tpbcVJ+nP7b9OQNR/SF4XNqVPnLjRs3Vpq2+JCkIJv7MItyNKOaAizclsArXh/MeU3LqCibj1tLVEmFeeeXTto4/o1NGL0WEeLRkpS+Rs+3UmBIAFiJ0CQAIEQnwrM7j/FDfpRvX259P0JU+XBcyjpdk94bSQVF8YgBV61XLO8Sr2DFIAUBLfI9JAAUhBQj6lKCsSb/Ysvv4KeX/gqLW7ShD5s2YpGb1hH7b7Vku647Arav3UzHdi/jwZeNVxHCTsFNY0FpKAaE5xTEG8bUUxJWn72K3pjy+IaOwGi58Z4AP10YC02gC83Yux1CgUpGEAgBV6tBqTAiIB5Zz44miAFKjBMBxmRIwUcnW083MEI8uYlsyKJeSrEFLgBlw6nIyOmwE3Lif0eMQWJxdvcmggM5p2AVZo70K4jO+OKiJ2A4e2v1VyBusVIQHJ7nRmtqyIFmYFW+KNETEH4GHttATEFXhFTUz5SpGD8HQ/RhS2a0vSH7lYzugRJSQdSIKBKZXIAUpAgg5dsBqRAEiiFxThF6MId8/XdAHNgcOM6jemKC6vjAYw7AQqbhyhJBEAKJIFKUDGQggQB7aEZkAIPYCksGilSUDR4Ms34wzTq36erwiGGLyqdSIFAa6UWGPzH8lJaUXFC/yg/K5umNMyn2xs0pvzs7PBB9dECSIEP0EKsAlIQIrjfiObsQDoR0HYDrFKE8hkBw7SdgO4XdKeRHYfQofKK8DuFFlwRAClwhSihBUAKEgq3VGMgBVIwKS8EUmCAlHcqevXoSA/cOSH26fLVG+mOnz5aA3jhypTqMQWcLWiJlpGoZZu21KFjUY3sQxv37qLZ3S7TycH/ff1V+n+jxtDt+U3o6v0H6MCXXyD70IvP0JUWpyQLg3Hzn0agcXW8iswlE3BtllNycL9u09eNv1WmibgyUQw0tssQJDouUoQOa3ctNSypR0ePlFHxgCHkJyWpkImYAs+mY1kB2YcqqfcV6s6tQKDx+Wx/Kiw0anEKIAUqtOpdRqRIAS/Kx4zoTzeNGeJ9JAFq3PfgE/T20jW6hMnjh1uSArt4hnQnBSLQmHcONv71v+nXI6+lKi0lae+v9tHVBw/RxJHX6TsHSElaaGmBIAUVdOYsJ6uNv+zSzDrdxplKCpxcgjg4mN2BOC7gigv7E8cJiGvTho9BCnw+F1QuOEUXQApACnyaY41qUVvA240rSD9BClRZizc5kSIF/Fb+F7+bSUvnPe5tFIpKWx1BLXYKMp0UMMScfajz5Dtp+tEyOqKdUdBJIwaL+hTrbkVXbPmM8mrVwjkFJlsEKQAp8Do98W7Au+/Np63Ht9DLx+YSBwyLixf9nBVoXOebXYODQQq8In++PEhBdBfwViTLv6arayIlKbIPBbUhmfp2iXTE+vLFV96h3zz2bJyoX957S0JflEeKFHBMgdMVdvYhJ1Jg7Je5H+kYU+Bm4FGMOUBMgZvWEvs9Ygrk8XbaDTC6BHGAsJ8riPuQn/ZQxxkBxBREy0IQUxAtfQiiFr1eBeuR1RpTSBSEwLi+3LX3AD3wq6do9owHgzXsoXakSIGHfodS1ElhokF2ceIrkUoKZbCKhC49dpz+46sDtOTYMV1iY82V6N7mzegnzZpR45xoBiQrGjrEAAHfCOws30lLvlyi/3tlyytUdur8bgBnCRrcdjCN6TRG/31R/kW+2zFWrDp3jrK03TxcQAAIAAEgkHgEnNaY7MbOV7Kzb0aOFFgF9iYqI5EMKbByJ8rEnQLz7WTeOWidU5um5RfQ2PqNEnbnYacgYVBLNYSdgniYnDIFcWwAxwVwgLDf3QAnpWCnQMpkE1YIOwUJg1qqIewUSMGU0EJKYgpefz2hfdYb02IuaeRIy3ZldgoStd61AyZSpEBsn7z5/O+pTcsL9D7z9smIiT+jRPhV+SEFmRJozLqQOdH4dLeeeirTyi2bqNnRo7SxZy+dHIzOrk2zn5tJk6bcE7PFDWs/pIpTp6hP30Gxz5YveZsKmjWnS7v0iH1mF5Rqzg7DpCCbqujx6Q/TD+6cVsPm7U4fdsqu4pZ5BScaV8OME43jzU2caPxV3n6as+U5LW3o+7TbdHgYpwvl2AAOFG7VsE2cgFXL36X6DRpR1x69fD/UEFPgGzpCTAFiCvxbT3zNIMG2dn3IBJlKSEGydka1XVmryy2m4OEn/06zZr8VVzVst3lzPyNFChiwqZNG1wiqYLLw1N9eCz0A2YoU8JbOfT8cGyMpXKZn1w6xLR6QgtG6TZknqTe0Bf+qA1/RX4uK9O8vrjpHtyx6i6b8y49BCgx3IVKSpldKUnGK8Ob3P6JVlavog5PLYtp2yhRknphBCuSXZGEv4OV74lwS2YeiSzQQaJymgcajq9cnCb1ycojmzbMlBaOGFsdluHTqG7ur7z9UGvra19iHSJECu8PL3DIABVW4MSWpkCXYmZm5denYLi6eAKTAmhR8unEdHS4toazv9Nd3DtZrGYvufncRvaidcyDcirBTQARSkPqkQJwdMOez52IHiE2gCbRe+8kuzKO+WnCwV7cgkAL5WR2kILqLbaHFqOsIpCBNSYH8NJKQkjLeKMaOhL32tRp0pEhBsncK/FoFYgrckXvp+BF6VCMHuyvP6IXDiDlATIG7HhJZIp1jCqyIgMBWnCLMMQJmt6BE4m9sCzEFyULeul3EFERLH4gpiJY+uDdK3IciNiwnUsC7Avfcfj3179M11utkJLaJFClIdkyBX/sBKZBHzi4g+eo69fVD0IJcIAVB0FNfN91IgQgU5hiBzYc2xAHGBID/WcUHqEfWu0SQAu+YhVkDpCBMdL3LBinwjlnYNdKVFJSUlteAjj1TrJLsXD2oV8KzEUWKFDBSycw+5NfIQQq8IxfGOQcgBd71EGaNdCAFTARe0kjAW9vnxwUK8yFiw74hAuaThMPE1K9skAK/yIVTD6QgHFz9SgUp8ItcePXSkRSEh5Y6yZEjBeqGlhhJiClwjinoN2ioroiKUyctsw9t1843eKFjJ1pRcUIvd/3GDXRJ8xY0qWdxbOcA2YfmUuei7tSm3cW2Rr1n1w7auH4NjRg91tHw9+3ZqWVWWUXXjBnveoMsWfQGtWzTljp0rA4Wd7rSKfsQHyTGuwEXbW1BM6pm0BHthy8RKDyuE2cMcj5ETGQfatu+gxt0lt8jpkAetqj7q4uRINA4urEPiClATIH8jJPeJUEKAuoXpCAYKRApScXOQcFHK2h/o3za1v5imtIwn25v0Jj2b91MB/bvo4FXxQelIiXpeeMFKbC+kUsO7qdl7y2k68bf6ninCyJgTB16P91PbzR4k7q37kUyRMDYAEiBPdyzZjxGE2+7i2rn5gacfaurgxREd7FtRYiUKF2x3kEKQApU2WWqywEpCKhBkAI1pECoYe47b9LyunVpTquW+kf5Wdl054ED1LnsMH13SPyBICAFIAVut68TKbAiAsYdge5fdqYbx99ODRo0dGumxvcgBSAFZgSwUxBd8gJSAFLgeZJP0wqRIAWcipQPJ/vNY886wpzoQxxkdY6YAlmk5Mv5iTlATIE8vokoGcWYArsYAS+uQYnATnUbiClQjWgweYgpCIaf6tqIKVCNaHB5iCkIjqEfCZEgBX46HqU6IAXhacMLOQApCE8PfiRHhRRw+tCZG56oESyc7kTAqDOQAj8WHF4dkILwsPUjGaTAD2rh1gEpCBdfO+mRIgV2h5cl6kRjvyoAKfCLnHw9GXIAUiCPZyJKJpMUMBHgjEHm9KGZRARAChJh5f7aACnwh1tYtUAKwkLWv1yQAv/YBamZEqQgGae6yYKKmAK1MQXLl7xNBc2a06VdesRUYMw+xqRxIAAAIABJREFUZCQH9y96i2YPvJImNP+WHpD8rfp5lE1V9Pj0h+kHd06rocK5Lz5DV149igqaFsZ999Xe3fTx6uU06rqbatRx+o4L28kUgtyCKnGisboTja0OFLuQLqTrsq6nQx3LPQcLm2NWZOcELoeYAnu03O4JLzhzWQQaR9dXX+gy6jpCTAFiCrzOO+laPiVIwcNP/p1eX7SSls57PHJ6AClILCkQBsDkYM0LT9Of+w2kI1pgMl/fz8+nXzRtSvP+9BhIgc2dkm4pScsryujtHa/TnM+eoxV734+NWpwjcFXToVS59bhr9iEruEAKqlFxI8ZeJ2WQggGkaqcg6ottkILoLbbt7te1qz+gc9qXl/fp5/WWti0fRCZ2CpSpwZOgpJMCq8PKrEYw4w/T4o5/9jTKEAuDFCSHFLBKedHW6tob6eVaVTTnWHUu+ZyqKvr5gvnU7Qc/ouI61WRBXNgpIEoXUiAyBy3UXISYGIhLnCx8dbtRxMRANiUpSIH9JAlSoOYBguxD0d3RwE5B9MgLSIGaecerlKSTAmOH7WIKvA4q0eURU5BoxGu2t+dsJT1+rJQWaIehlZ09qxfom1eP7s8vqEEOkt/bzOiB6pgCzhw0c8N/k/EsAV3PLQfSuM58oNhAatWwTWaA63GUCDT2CFjIxVXtFITczYwRj5iC6Kk6HUnBoOt/QiWl5TXAjlJmzUiRguiZpVyPQArkcAq7FAcanzhXRX88eIhmHi2n8iqQg7Axd5KvghSIgGHOHrT7yM5YcxwwPKX73cQ7AyAC7loGKXDHKJElQAoSibZ7WyAF7hglukS6koJRQ4vpgTsnJBpO6fZACqShsi8IUqAARAUijNmHyrXdgqePlYEcKMDVrwi/pMAuTkBkDprS/UdU1Kyb325lZD2QgmipHaQgWvoAKYiWPrg3IAXJ0UmkSMGuvQdoxMSf2SIRpS0W0UnEFCQ3pmD0jTfHTpxlUmDOPmQkBxPffZv+0bM35RU0pWmaW9HY+o10NSL7kPUtt2TRG9SyTVvq0LHIdXbatmUT7d2ziwZ/9/yp006kwJhRSgi3ixMY1/kWfUeANldQ56Lu1Kbdxa79EQUQU1BGxQOGUBBSgJgCaXNzLIiYAsQUqLGk6Pn/240r2YHGZ7adUQW5vJxaRLUvrm1Znt2HsFMgDyUJwIovL6Jf/G5mLNvQ+DseojEj+tNNY4Z4kJaYoiAF0SYFwgqYHMz5+zM0TyMFn9Svp3+cn5VNUxrm0+gjx2jLmhVISWq6ZRJBCtr3vtTyYDERJyAChrlrC1+fC1LgYVrbtOFjOnoEpMADZLGiYWf1UbVTEHY//WBnVSfq/USgcfSIhoqdgsO/PqzKhD3JafLvTWxJAWIKPEApAo3btGxOt9zznzFSwBmKjCTBg8jQi4IUpAYpYEMQ2YfeqZOnZSs6SisqTuj2UVRaStdt20rfv34i5Wdnx9mM21tSnFNQDZeXnQJ2D3r9gzn0+Zef0swT/xPDm92DxnW6WQsavsUyTgCkwNt0BlLgDS9j6bAXsSAF/nUjaqrUEUhBepKCY38/FtzQvErIImowroEtKcBOgQdAjdmH+P/CXSjKh5fx8BBT4EHJIRb1eqKx3SnJ4xrkU6vsnBB7mhmize5DVu5B4jwBJgPFLQdkBjBJGGUQ96EkdDftm1RFCtIeqAQNEDEFCQLaQzMqdgo8NJeQonAf8ggzuwn16tFRj8w2/j/Kh5eBFHhUcojFvZIC0RUzOeDPxzVoROPqNUI60wD6YlKwcd82WrZrKT26+rdx2YOs3IMCNIWqLgiAFETLREAKoqUPkIJo6YN7A1KQHJ1EKtDYDAHvFojrzed/T21aXpAclFxaxU5BNNTilxQYycGcE0diB6Hx5zjrwJ9uF2qnDL/6xQv06tZXYgJE9qBpfX6BNKL+YPVdC6TAN3ShVAQpCAVW30JBCnxDF1rFdCUFiCkIzWSiIRgxBakXU1DQtDDOeMxxA8aMRU0OHaDBWz6jz68aRlMaNaZhdevH1UVMQTUcHFOwbcdntCh3cY3DxThGwOweZJV9yO2ORkyBG0Lx3yOmwBtextIq/dWFXGQfQvYh/xYZXzNIVh+7PkRNZjqSAlX6D1NOpHYKUvFEY5CC9CMF4oZjcjDrn1vo67Wr6em+/fWPW+fUpnH1G9LtDRrrQckgBUQvbXmOln+8mCoPn6ZXtB8dJy1o+D8G/wf1aNaXWtRrXWMOAylwntZXLX+X6msubF179PI9/4MU+IaOQAqiu4C3Iln+NV1dE4HG6RloHNQuMrE+SEFArYMUpC8pYNPgXYQPP1xGJUNHagehldHuyuq8xyKdaas3XqXvDruWzLsPwqxmzXiMJt52F9XOzbW0tBXvL6b8xgVU1K2nrSXKvCHfs2sHbVy/hkaMHuto0fv27NQWPKvomjHjXS3fKSUpnzTMcQIr976vxwr00H46ZF1CtTrmxXYFvJ5T4NYhGRzMMnBOAVKSutmV1fcgBSAFfuzGqk7U3sDbjStq/cROgSoL9CYnUqQgyucROMGKmAJvRhdW6aAxBTL9sspYxDsHfBBaUW6ejIiULsO7AnM+e45WaGRAXEWF3elftFOGjWcK8Hd+TzROaYAi2nnEFERLMYgpiJY+EFMQLX1wb0AKkqOTSJECPtHYeD5BciDx3ipIgXfMwqiRCFIg+m2VsShdg5LNuwKMgQganqKRgaJm3SzVCVIQhpX7kwlS4A+3sGqBFISFrD+5IAX+cAuzFkhBmOjay44UKTBmG7Lqsji3IDlQ2bcKUhANjSSSFIgR7zlbSTOPHKY5x49SedVZ/WMmB+MaVO8epPJltSsgUomO1c4VcLtACtwQStz3IAWJw1qmJZACGZQSVwakIHFYy7YEUiCLlNpykSMFM/4wjfr36Ro3yhdfeYee+ttrsROO1UIQTBpiCtI/puDj1ctp1HU3WRqKCDTO1uICnj5WpsUdlMfIAccd3KvFHFx/61RqVqeuZf2oxRQYdwV6H7mcvtB+dubtomHtryWnVKJeTjRmIBBo7DzvINBYfl4O2/9fvifOJZF9KLpxCgg0RqCxqvs81eWkBCmI8onGIAUgBVdePSoWaMwZi146cZQWnjhOKypO0M8XzKf/GT6Kbm3SVNs9qHlSclRIgdWuwG11bqfO3+5Ko/qOIz552OkCKYhHZ9GCl6lDpy7Utn0HX88IkAJ52EAKorvYFlqMuo5ACkAK5Gec9C6ZEqQgyicagxSAFBhJgXG64LiD9bOeoj9cPZxO5+ToX5njDpJJCnhX4K3t82nmhifiThvmcwU4VuDQut3Usk1b6tCxyHUWBCkAKXA1km8KuGXkkpWTKgtOq36qch+K+mI7VXQEUgBS4HXeSdfySScFYhfADWArtyK3Oon6HjEFiULauZ1kxBTIjJzJwcKTxyzjDq6uU18/7yCR18q9y2iOnkXo2VizHDjM7kHFLQcqO20YMQWJ1KpzW4gpiI4uuCeqSEG0RpW6vUFMQfR0h5iC5Ogk6aTAOOxkH17GKVF79ehID9w5IU4b9z34BL29dI3+WZeO7Wj2jAfjvgcpSI7xmluNKikQ/TSelCyCksV5B+IwtLCQLK8oo7d3vK6fLcDnCojL6rRhVX0AKVCFZHA5IAXBMVQpAaRAJZrBZYEUBMdQtYR0JQWDrv8JlZSWx+BqVpAfqXjZSJEC1UYlK8+46J88fngcKTAHOVsRB5ACWaTDLRd1UmAkB2+fOk5zjh3V4w74YnIwrF59GlevERXbBCX7Qc8unehwLXB4Sve7le0KWPUNpMCPxsKpA1IQDq5+pYIU+EUunHogBeHgGkRqOpICJgSjhhbHrTF5/XnDNYNqJNgJgl2QuiAFBvSsFGYmAWaSgJgCxBTYxRSwabn5T8977y1arp12PLt165glmuMOZE7yNZ9ovFDbFZi5/om4Q8Y4nej1F4ylRgcbBD7R2DzpIKYgHhEEGts/ltzuCa8PtFT0q1dFClJx7F71a1de5dgRU4CYAlV2aSeHz+EaMfFn9Obzv6c2LS8Iuznf8iNHCsxbK8aRhX1OgRUp4M+mThpNN40ZonfFnAkJpACkIAgpEIHGrYq6W6Y0ndIwnzouW0Jdte/btLvY9kZnUvDRmmVUeWmWpYuQSCe6b89OWrdmFUiBxJT5wqwnafSNN1MD7cwJrxdIAUiBGQGkJI1uliSQgvQkBa+XH/E6dQcun1WrFo1sZP3M4PVki8KCGi7ogRtVKCBSpIDfyl/YoilNf+huhUOUF2VFCjjO4Zf33lKDFAi250YKsrKyiP+dO3eOsrWAUv5/nbp16XTFaTp+/Bjl1alDWbWyqEo7+Oqsls6yadNm1KSgKdXRPi8pOUQnTpygS4u6UOnXX2v/Sug7ffvTe4vfpn4DBtOOHV/o5SvPVFJO7Rz9d4H2N3/eX/t+zovP0ZQ7fkRzX3qRevW+gurVr09vvfEa3TJ5Cq1csYzoHFFxvwH05oLXqO1F7amz1s6ihQuoxbcupK7detCmjRto3949dPXwa3QQH3v0d/Tj+36qj2Hrls/oi21b6Jprr9O/M8rjv9ev+1jv71XfHaZ/f+rkSfrr00/RXXffF1PIR6tXap+fogGDrox99s6it6hZYXPq3qNn7DNzP8QXf3nqCZowcRI1bFh9SFjtnCxtTFX0yMO/p5/c/7Maiv/brL/QyGvGaPIL477bs3sXrfjgfRo3oeaBXE7fsRA7maKBJx5/hH54548pV9sNsLree+dtatykgC7r2Uv/uqzyLL2onXXwfHk5fVJxSv9s0upVVHBpF7q6cxH1r1evhphdWozA4wsfoZNfHqfntB++LspvS//W79+pf+uB1EYLIhbXrp1f0uoPV9CN475v2R/jh0a7cCv86eaNxLKHj7w2VpTduU6dPqvZtmZopstOp07tvDLvJerWvQe1/7Z8ms8DB/bTYs2mJ076gdsQanxvti8vAl57Za5+317coaOXarGyS95bTI00u+7Zq4+v+lxp3ccfUVl5GV151VDtnq1FdWpn0YmK6gP2vFxu94AXWVzW7Z7wKu/DVR/oc1+/AYO8VrUtH7bMvNxs/b44U1kVqM9h9zNQ5wyVo97PhvVqE7sBm59jKsYPmdXrDK8X6yToVWvdJ0FF+Kp/7rJutvXMh/SaXdZ9NaiwUqRIQbIDjf3sFLAuKs5U0emAk7tCnWasKCYF2bU0AqLpIx2u5Roh/C+NGC7TzjwQ1wAt7uDfmhXq5OCFTX+j57V/y3YtPf99m0F0V68f0zUXV+/gJPOqz6SgopLO1uQEyexWRrbN90VeLpOC9Lg3Ul2JTND4vghKClIdh6j0v2HdHDp6sjIq3UE/NARYJ0Gv0du/DCrCc33u9bz2baXqCc8T44tnqYohFgIpMIDrJ6aAqyPQOEQL9SA6VQKNPQxJL7rnbKUWlFwed1oynTlK9E9tV2D783pKU7cTh722qaI8Ao1VoKhGBgKN1eCoSoqqmAJV/cl0OQg0jp4FpGOgsRXKdlkvk6WRSJECBmfMiP4xV51Eg2JFCpB9KNFa8N9eupICnRhoB409uOpX9NYZ7ZVva20XIL9TNVAaOeibV5fub9ZWadYi/1o4XxOkQAWKamSAFKjBUZUUkAJVSKqRA1KgBkeVUtKNFPCuwJ+enhcXTyB2CqJ0DlekSAED9IvfzUx4zlZjSlJh1MagZqdzCtxiCmpp/vfZ2j/2H83JyaZaWvxAnpZy8szpCi1e4Djl5mkxBfy9Fk/AcQWNC5pRfuMmlKct9A6XHqKTmgtJh05FVHa4lMpKS+iyPv1oxdJF1Lt4IO3+crtWvilVVmoxBdqJufyb4xH4c/5+/rwX6KZbp9KCV+dQ9559tFiGerRk8QK6YcJkWrv6Aw4poMs1eUsWvRE7uXbZewupsHkL6qQFtm799BM6sH8fDbxquA7L039+hG6ber/e3+1aPMGO7Z/TkGEINFYRaFzU7XwMhXFi5YPGVi5aTPOPvUqfaz98cRahYb0fooW1W8VSml588CAN37GdCodfS2PrNbQ9EA2BxvKPLQQaV2P11d7d9PHq5TTqupvkwXMoiexDA5QdXqYyA49QWSbKRKBxegYaK5mwFArhF9+btu6Ikxi1bESRIgXmAAyzLsLOPuRH9yAFIAVhkIKXtBOHxUFj36fv0xrtp0fn7+inDrdq2CZmquJAtEX//Jy6bdtKzxX308884KxFw+o2oKLcvDizBimQv8tBCkAKel/hPUDSzsKQfQjZh+RnH+eSxpd66Soz3XYKVOkpbDmRIgVhDzYM+SAFIAWqSAG7CM357FmaoxECcepway1z0O05U+jyHn2p56XFtia89ct/0up1H9FrfQfEdg/0XYW8enR/fkHMtQikQH4WACkAKQApkL9fnEpGffcBOwXYKVBj6akvBaRAgQ4RaKwARAUiUjWmQJw6zIRAXEwGeFdgbKeaaVLdoFp56iQtPHmM5hw/SuWaSxpfYvfg9gaNbV2L3OR6/R4xBV4RC688YgrCw9aPZMQU+EEtvDqIKQgPW7+SsVPgF7lg9UAKguGn1wYpUACiAhGpRgo4XuCPq38bd+rwuM630DiNCBS3DO62wK5FL504qpODzaerzzzgy7x7oAB6SxEgBWEh610uSIF3zMKsAVIQJrreZYMUeMcs7BogBWEjbC0/cqTAGIghIrI51uDqQb2SdqiZm2pACtwQSsz3qUIKjPECAhkmA+Z4AZWo8e7BzKOHaaV2IFqidg9AClRqMJgskIJg+KmuDVKgGtFg8kAKguEXRm2QgjBQdZcZKVJgPNGY04P+9l+nUP8+XcmcFtR9WIkrgZgCxBTIxBQcqNhPK/e+HwseZgtlF6G78u+mb3+rI/Xr811bo134+lzttOnu1KbdxbZl9uzaQRvXr6ERo8c6Gv/nWrl3tMxTf7qib4wccAWr3QNjViq3O2rblk20d88uGvzdkbGiTqTAnNnKTT5/L4ODWU7Jwf3EGbWuG3+rTBNxZRBTUA0Hsg95Nh3LCgg0RqCxGkuKnv+/3biCBESDFKiyFm9yIkUKeEdApGcykgKRyxXZh5CS1Gje5kUb7xRkUxU9Pv1h+sGd02rcCXNffIasFvBOix63BZGdTNH4MzP+SBvbf05vffkalVeU6R8b4wVWvL9YS0FbQHYpSWUXw7KkwBhozLsHfywvjQtMNsYerHv3rViqWrdpBaQgHqFFC17WUgl3obbtO7hBZ/n9quXvUv0Gjahrj16+6nOlTRs+pqNHyqh4wBAKslPgdg947SBSkiIlqVebsSqvMngZgcbRIxogBSruEu8yIkUKmAg8+6efU5uWFxB2CnBOgTBnu7fKUSYFInj44s9a0yPaz2nth88XuF8LHjbGCySTFAh8RVrTmUfL43YP7tiwnnpruxMjulzmOrOAFIAUuBrJNwVACkAKZG3FqRxIQfU5Q6quIG/1sVOgSgvJlxMpUvDwk3+n1xet1A8vE6SgTcvmNGLiz2jy+OH0wJ0Tko+YRQ8QUxANtUQhpsAueDjMeAGV6LvtHuRnZ0s3h5gCaahCLxhkpyD0zmVgA4gpiJbSEVMQLX1wb7BTkBydRIoUMATCVcgIxy/vvYVuGjMkOQhJtApSIAFSAookkxSYg4fZRahY2xlIFTJgVo/YPeDMRbsrz8S+FrEHl9bOdU1tClKQAKOXbAKkQBKoBBUDKUgQ0JLNgBRIApXAYiAFCQTb0FTkSEFyYAjWKkhBMPxU1U4GKbAiA0wEmBAYTx5WNcZkyLHLXDSufkP91OTiOnUtuwVSkAxtWbcJUhAdXXBPQAqipQ+Qgmjpg3sDUpAcnUSKFNz34BP09tI1ZA4ojnJKUmQfyrzsQ8aTh689cg39Q/vJa1TX8rAxN//pKMQU2E095uxD4tyDhSeO1zg1edhXe+miQ4do6NBrYuKQfQiBxla25XZPeH0UqvQtF22HLVMVKQi7n151YVc+6v1EoDECjVXZeqrLiRQp4DiCqZNG13AVQkrSIio7XEplpcg+ZLzhEh1obHXy8P+p/X/oW5e3owm9brOcC9wWQKlECowDNJ+a3GP3LurwdQkdLR5AUxo20XcPQApACkAKziOAlKRISapqwRi1oGC7cQXpJ3YKVFmLNzmRIgW8IyAOLDMOAylJQQoO7N9HA68aHmfdiSIFK1a8Q8sLVtKcz56NtS9OHt73/heWaU5FwXQlBWJ8vHuwSjstecEna6ly/1565bLL9a84temPC5vS92rXp29l5dSYlXBOgfNEjZSk8g+yqL+Fttp9wE6BvH4TsfuAnQLsFAS3yPSQEClSkIo7BWwGiCmIxs2gOqaAMwnN3PAEvbV9fhwZSNXg4bC1ZJfalIOTh9WrT2PrNXQNTg67j5kqHzEF0dK8KlIQrVGlbm8QUxA93WGnIDk6iRQpYDeh3zz2bOwAM4Zk194DekrSKGcgAilIjvGaW1VFCjh4eM5nz9EK7QRicfHOAMiAvJ7Zvej9qlP0v6WHY2cf8O7BsLr1aVz9RrbByfItoKQXBEAKvKAVflmQgvAx9tICSIEXtBJTFqQgMTibW4kUKeDOWaUktXIpSg5c1q2CFERDG0FJgVUmoXGdbiYmBOmSSSiRmuKYgp1lJ+iFo0fIHJwsTk4u1nYR7LIXJbKv6d4WSEG0NAxSEC19gBRESx/cG5CC5OgkcqQgOTD4bxXZh1I/+9CLK/9K29ZvpBlnZ+iGwGcM8K7AWI0QfLV3N328ejmNuu4mSyOZ++IzGR1TIECROdHYePZB4fYvqFXp1/Raj57E7kXFderQ7Q0aO7oXLXx9LnUu6k5ttFOWZa+Sg/tp2XsL6brxt8pWiZUzx6x4EbBowcvUoRMCja0wc4uz8YIzl0VMQXQDeIUuo64jxBQgpsDrvJOu5UEKAmoWpCB1SYHYGcg+UosGaz/vNHqvRlpRkIK21KFjketdIkMKjEIWbPiYPt+3i/6na/eYexF/7xR/AFLgqoa4Aps0jI8eKaPiAUMoyE6B2z3grVdEIAUDlJ1TEPXFNkhB9BbbdvdrkExBYcjEToHXmVVN+ciRAg42Likttxyd+fwCNRAEkwJSkFqk4NJ+l9Ob++fTHC1uYPeRnbrye9f/Dn0v93t028R7axiD24IIOwXVkHklBcbsQxx/8MfyUtp8piIu/qA4r04svSm3AVLgba4CKfCGl7F02IttVe5DYffTP4LxNaPeT+wURI+8gBSouvu8yYkUKRh/x0N0YYumNP2hu72NIsmlEVOQZAV807xTTAGfMSAyCQky0Fc7dXhc55t1NyFc6hHweqKx3eFoHH/gdnqy+t6nl8QgOwXphUQ0RqOKFERjNKnfC8QURE+HIAXJ0UmkSIHdOQXJgUa+VZACeazCLGlFCqwOHGMycL8WM1DcckCY3cl42V5JgREwEX+w8tSpuNOTEaDsz6xACvzhFlYtkIKwkPUnF6TAH25h1gIpCBNde9kgBQpwBylQAKICEUZSYEUGOIvQlO4/oqJm3RS0BhFuCAQhBUbZ7F60suIEzTxaHhd/0Dqntr6DMLZeI2pdu7ZbdzL6e5CCaKkfpCBa+gApiJY+uDcgBcnRSaRIAbsPjRnRn24aMyQ5aPhoFTEF0Yop2HdkB83+y/P0q3O/imlTnDHw4evvWGYKcoobQExBOIHGfk80pks608rCQppz/GiNAGXOYGQmCMg+hEBjH9N66BmNVJGCqPvqC+yj3k/EFCCmwM88kY51IkUK+IyCX/xuJi2d93jKYA1SEA1SwDsDj3/8nzRn0wv0r9rPb7Qf84FjdkHBIAXWt9uSRW9QyzbRIgXGlKS8g7Dw5DFLgiBOUD7z9SGkJEX2Ic/Pk7AXsSAFnlVSo4JKHYEUgBQEt8j0kBApUsAxBU4Xsg+V0GV9+tGKpYuod/FA2v3ldmpc0JQqKyspJydH/91E+5s/5+/nz3uBbrp1Ki14dQ5179mH6tStR0sWL6AbJkwmY/ox4+KPc7oXNm9BnbR88Oa3uU//+RG6ber9lJWVRdu3baEd2z+nIcOSSwr6DL+S/nvzdO0E4md108nRfn5e6+d0zaTv1zhwDKSAaN+endpb0FV0zZjxrjNY1EmBGADHH3x65rRGDrRD0k4ej9tBGH7iFF2x7iMaN+5WxzMQrMDAOQXVqLjtlrkakqkAUpIiJalXm7EqD1JAdLm2HlB1ISWpKiRTW06kSEGqQomYgsRrzipm4PtdJtG/D/i/1Cj7wsR3CC3WQEBVTIEXaJ0IgjgDYVid+hkXg4CYAi9WFH5ZVTsF4fc0M1pATEH09IyYguToJHKkgF2I7vjpo3FozPjDNOrfp2tyEJJoFaRAAiRFRewCiPkE4ksK21Nudi0qO35GUWsQEwSBZJACY3/dCIJVDEKQ8Ua5LkhBtLQDUhAtfYAUREsf3BuQguToJFKk4MVX3qHfPPYsvfn876lNywt0RHbtPUAjJv6MfnnvLZENQAYpCN94nchAq4Zt9A44nVMQfg/RghmBZJMCrwShOK8eFdepm5aKBCmIllpBCqKlD5CCaOkDpCB5+ogUKeDTjKdOGl1j8c9k4am/vRbJAGQEGocbU7By7zKaveQZqjh8gl7Tflo3ukg7X2Ag8c7A+3PfoNE33kwNGjSMkYJsqqLHpz9MP7hzWo27CjEF6RlT4DR9WmUfctpB4DSnw+vWp2F1G9COv8+Ksy8v0/SiBS9Th05dqG37Dl6qxcquWv4u1W/QiLr26OWrPlfCica+oUP2IS0+rfcV6s5xUen/L7SqUiYCjRFo7H+2SK+akSIFdoeXCZciBBpnTqBxeZOj9MfVv6UVe9+nntpPx9qd6MLL2ukZhcTOgDkQlHcKQArGOs5Q6Rho7JUUmMvbZTGatmghHRs+ioY2vYAurZ3rKVAZpMBeKwg0RqCximUUSAECjVXYEWTEIxApUoCdgrNaNqHjl4iKAAAgAElEQVRmlN+4CeXl1aXDpYfo5IkT2hvHIio7XEplpelPCua+8b+0/PBSmlP2d91SeWdgYtNJdHFOBxox7MY46wUpOA/Hnl07aOP6NTRiNEiB0Ui8nlMgCMJbWhajsW/Op5n9B9GRunWJT1Iepu0g9K1Tj67W/uVnZzs+S0AKQArMCBgXsarch1QujMN4A58qMrFTgJ0CkINqBCJFCqIYU2AV+MzAGXctEFMQ/HZiNyGxMyDIwLhON8ftDLi1gpgCN4QS+32UYgr8jFycpLzy1ClaoZ2obLxSLZMRYgr8WEB4dVSRgvB6mFmSEVMQPX0j0Dg5OokUKWAIopZ9SMZ1CaTAv/GaA4h5Z8ArGRCtgxT410MYNVOdFBgx2X3mDC08dZwWnjhegyAU5dbR4hC0IOUIByqDFIRh4f5lghT4xy6MmiAFYaAaTCZIQTD8/NaOHCnwO5Cw6oEUhIOsSjIAUhCOjoJKTSdSYMSCA5XfPnWCVmj/zIeleXUzCoqxbH2QAlmkElMOpCAxOMu2AlIgi1TiyoEUJA5rY0sgBS64W+1cGF2HkH3IW/ahq8Z/jx7VAoj5BOL+2k9hbnNq36NzzE1o+ZK3qaBZc7q0S4+YZswnK4svEFNw3ngRU2B9I3uNKTBKkT3R2BiHsLuy+oyMCR99SOtbtaaCthfTsHpaNiOPB6Yh+5D8AzEV/epVkYJUHLu8Zp1Lqhw7YgoQU6DKLlNdTiRIgYglsDqLwOm7ZIA//o6H9GZnz3hQ/+1GCrKysoj/nTt3jnJycvT/19UCFysqKujYsWNUp04d/bOz2ttH/ldYWEjNmjXTyxw4cICOHz9O3bt3p5KSEjp06BANGjSIFixYQEOGDKFt27bp5c9org21a9fWf/Pf/Dl//8wzz9C9995Lzz77LPXr14/q169PL7/8Mk2dOpWWLl2q92nw4MH6Z9/+9repW7duNH/+fGrZsiX17NmT1q1bR7t376bRo6sX/r/+9a/pF7/4hd7fzZs302effUY33lgd/GuUx39/9NFHen9Hjhypf//5gc/pub88R78+++uY2v6j/X9Q14KudP0118c+e+ONN+iCCy6gXr3Op2I090MUnj59Ot1+++3UqFGjWH3G8L/+67/ol7/8ZQ3zePLJJ+mGG26g5s2bx323c+dOeu+992jy5Mk16jh9x4XtZApB3Jdp06ZRbm6upbm++eab1LRpU+rTp4+tOb/44ot0+eWX0yWXXGJb5p///CetXLmSbr75ZsfbYseOHbRs2TKaNGmSYzn+0mgXboU3bNhALHvMmDFuRfXv7XTqVFkGB3P9r776SrfpH/7wh1L9Mhaysi83IV9WnKZXjxyhL157jRZ/60Laov0TV1vNBsbkN6IxjfOpu3bfN86xD1ZeuHAh5efn0xVXXOHWpO33H374IR0+fJiGDx+ul6nS7vesWrU8y3O7B7wKdLsnvMpje+a576qrrvJa1bY8ZGYmnubnmAqDgszqdQau1EAgEqSAF9oXtmhK0x+62xK1+x58gvbt/zq2EE8mtGZ3IjdSUEtbQGdr/6qqmBRkU61aWZSnHZB05nQFndD8k3PzqklBlbaYrapKv+xDF/XsqO8MvP7ZXLpb+/mD9sNpRfmcga+3fUUVWhBnn76DYirFTkFN6174+lzqXNSd2rS72Nb0sVNgDU0idgqsWubsQy0vuZQ2a6TAzs2oqHaevotQrGUaK8rNixODnQL5WV7lG2PRatgysVMgr1+7kip1hJ0C7BQEt8j0kBAJUmB3PoGAWMavP1HqsOoLAo1roi9zArFqnSHQWDWiweSla0yBX1ScshlxLMK4+g01clBHKuWp1z4gpsArYuGWV0UKwu1l5khHTEH0dI2YguToBKTABXfepbjvh2OpTcsL9JJ8lkLPrh3idjVACs6DmAwyIFoHKUjOJGLXKkiBvT6cgpW5Fqc8LdZcjFRlNAIpiNa9AVIQLX2AFERLH9wbkILk6CQSpIAX2r/91ynUv09XSxT47fwvfjeTls57POEoPfzk32nW7Ldi7Xbp2K6GGxNIAVEyyQBIQcJvC6kGQQqkYNILbdbcCVdWnNRTnm4+U0HlmiuhuHgXQbgaeQ1YFjJACuR1kYiSIAWJQFm+DZACeawSVRKkIFFIx7cTCVLAC+8167faxgy4xRwkB7rqVjM9pqBj3x56zMDBz3breCzRfjhm4MZG44hOVFG/QUP1zytOnaTZz82kSVPuialrw9oPEVPw/mLtBOsCKurW09aMEVNQDY0MDmYQkxlT0KFTF2rbvoPn6Yl3Ed5Z9g79My+X5l7UlkRGIyNJEKcrX6G5G7XWkgxYXZs2fExHj5RR8YAhFIQUfLV3N328ejmNuu4mz2OxqjBrxmM08ba7qLZN8L3XRlT6lou2w5apihSE3U+vurArH/V+IqYAMQWqbD3V5USCFDCIvFvAl3k3gD8vKS2PO0E4SqBnKin4aONy4n+/Lf2Vro7B2k9Rs2406Zq7qFXDNvTpxnV0uLQEpMBlAbQCpED6ds4UUsCAGAON3VyNWufU1g5Pq18jHgGkQNq0ahQMexELUuBfN2EQN5ACkILgFpkeEiJDChhOs6sOf3b1oF62WYmioIJMIwVDJ95I/9j6PK3Z+AEVnmxG/9B+eGfge3nfo4a5+XR5n366WkAKqq3T7a0oSEF1ukyZK1NJgRkbcbrySu3wtJUVp+JcjbisIAkXf/E5tTpxkgYP+i52CmQMzFAGpKCSel8xwCNq9sXDxjNoR0EKQAqC2lC61I8UKUhVUDMlpmDmhv+mmRueoN1HduqqEqlFeWcgChcCjaOghfN9QExBYvTBWY04DsEqHkGQhJH1GlCfRg2o+Fxtys+2Px8hMT1GK6p2CoCkGgQQU6AGR5VSEFOgEk15WSAF8ljZlkx3UvDSluf0uAFBBvq2HEj3a+cMFLdU9yZJgRoIpEAFiupkgBSow9KLJBmSINyNnGISvLSJst4QACnwhlfYpUEKwkbYu3yQAu+YqagBUqAAxXQlBWYy0LrRRfTQgIdpWLtRClBTLwKkQD2mQSSCFARBT11dJglbzlbQIu33+pMnLd2NxAFqVgepqesJJAkEQAqiZQsgBdHSB/cGpCA5OgEpCIh7OsYU7Kz6kp7Y+xgVHmlKrbSfdY026CcQH3l3P9029X79BObt27bQju2f05Bho3UE167+gM5pvxFTEG9QiCmooDNn2TLir62ffkIH9u+jgVchpsBqCgrzRGOxk2AXk2BMgcqpUAsPHaQta1Yg+1DAZ4XRr14VKYi6r76ALOr9REwBYgoC3t5pUx2kIKAq04kUbM/dQYsWvUJbT2+htdrPkLpDaUiToXTr9XfrKD3950dACkz2MvfFZ+jKq0dRQdNCS0sCKQAp8DPFhEkKzP0RgcvirARzCtS2X5fQyM+30pmrr9EzHAV1OXK7J7ziFfUFp9XCGKTAq5Zrllepd5ACkILgFpkeEkAKAuoxHUjBK68/R++WL6K5h1+i0drP8Ton6Nr+46hbVbe4t7kgBTWNBaSgGpNtWzbR3j27aPB3R8ZAcnIfwk6B88STSFJg7olIgbr59ClaoWU3Ov7VHhq85TOa1e98DBHvJhTnaScu16mnH6x2ae1c6QBmkIIBBFIQ8MGrVQcpOL8zHxxNkAIVGKaDDJACBVpM1ZgC8ynEHDPAbkJjO92sAJXEi0BMQeIxd2oRMQXR0UeQw8uYJHx65rSe4cjO5YhHyqlQEZsgp3NVpECuNZRyQwAxBW4IJf57xBQkHnNuEaRAAe6pRgrMZCA/rzFN6f4jPcVoVNKL+lELSIEf1MKrA1IQHrZeJQchBVZtscvRKm0nQewm7Kk8UyOAmXcTWmlEoa+2o6DC7cjrmKNcHqQgWtoBKYiWPrg3IAXJ0QlIgQLcU4UUmMkADz1qZw0EUQdIQRD01NcFKVCPqV+JqkmBuR+8m7DnbKV2mJp2ZsJpbUdB+22OTeA6Ioi5KDc3o4kCSIFfSw6nHkhBOLgGkQpSEAQ9/3VBCvxjp9dMhZiCl+f9jXY13EN/2zqTxmg/T2k/Pyr8MRVfOJCuHDCSlix6g1q2aUsdOhbRsvcWUmHzFtSpqDuZ/b4RU1DTWBBTUI0JYgribWPRgpepQ6cu1LZ9B18zTDJjCswd/mrvbvp49XLP2YfMbkebNRckJgo/XzCfHrl6BJ3OydGbMhMFjk9olZ0jHaOg0rdcjD1smapIQdj99GW8FpWi3k8EGiOmQJWtp7ockIKAGow6Kcj5TgPavGQNvVO5mE5oP5PzbqPrJtxKBz/bHUshClJgv+hxWxCBFIAUWE0hIAXWEysThX/M/H9UNfZmWnX2jBanUE0UrC52OSrSCEJRbp5jMHPUF5xWRAOkIOCDV6uuUu8gBSAFwS0yPSSAFATUY1RJwcHmX9PeD76gR889SpO0n9Km5XRvv3+jT1espRsmTI47VwCkAKTA6jYw2oXbbYKdAuwUuNmI+N6cfci4o+DkesT1OZiZiYL++5v0qCUb1lBlZSX1vkLdCesqF5wgBWoX8GHs5oAUgBTIzl/pXg6kQIGGoxRTYHUKcSpnFPKiHsQUeEEr/LKIKQgfY9kWwo4pkO2HbDljjAIHMXNqVKtgZiHPuKvAhOHSHI041K4t21zCy6naKUh4x9O0QcQURE+xiClIjk5AChTgHgVSsHLvMnpw+U9p86EN+ohSPb2oH7WAFPhBLbw6IAXhYetVcqqRArvxiaxHuyu1FKlaQLOT+5HIfiRckKJEFkAKvFpwuOVBCsLF1490kAI/qAWvA1IQHENKJilIt7MGgqgDpCAIeurrghSox9SvxHQhBVbjF7sK+lkKWppUjlGQJQuttWDn1tquAp/S3CgrSzq42a8eRD2QgqAIqq0PUqAWTxXSQApUoOhdBkiBd8ziaiQrpuDbPYpo6Ya3ae2RjyhH+6mf14C6NO1OAzsOpa/37qfexQNp/rwX6KZbp9KCV+dQ9559qE7derRk8QLEFDQtjNOhUzAxAo2rs1K5XYgpiEcIgcb2FpOoE429kgXusYhZuHTLp9To3Dlq07uvMlckY5yCKlIQduyD230v+33U+4mYAsQUyNpyupcDKQio4USTgjZdLqEPl79Hr51+lS7Wfkq0n65NL6N+bQZRvez61KSgKe3+cjtIwZ3TamjWLlMQSIH1TYBA4ydp9I03U4MGDT3PEiAFyScFdj2QIQsDt22lnMqz9G7nS3UxRlekfG1HgWMYOHVqo1pZ0rELIAXRDQYHKQAp8DzJp2kFkIKAik0kKdi291NadHYh9T7Rm97Vfq5qNJT6fLufTgZytG1wzsABUlBFj09/mH4AUmBp2fv27NRS+a2ia8aMd7V8kAKQAjYSt90yV0MyFUjUToHXfnF5jln4VItX2L12NR3UYhaWdC6iI1VnbdOmCsLArkciKxKf4mwVvwBSAFLgxyat6qxd/UEspXi6yoT7kCrNepMDUuANL8vSYccUmDMKDW9/LT004GFq1bCNgt6njwjEFERLl4gpiI4+0jmmIBEoG3cXOMh5t/YChuMWnDIiiX4xQWiUlf0NaaiOYejYsA5dSNnUrCorEd1HGy4IIKYgeiYCUpAcnYAUKMA9LFJglV6UycCwdqMU9Dr9RIAUREunIAXR0QdIQXi6MBKGcm1XgbMi8e6CU7CzsTdMGvgfn+IsAp9554HTqiYy+Dk8hKIvGaQgejoCKUiOTkAKFOCumhRwRqH7Fv+QVux9X+9dJqYX9aMWkAI/qIVXB6QgPGy9SgYp8IqYuvLCJelIVZW2w1C9y7BFO825TDvdeZe22+B2iXiG1tnZ+o6DIA6tNJfRVlk5IA5uAEp8D1IgAVKCi4AUJBjwb5oDKQiIu8qYgrNnK+l47RO07dTndFL7aZ3dmlrVaU09u/WlssOlVFZaQpf16Ucrli7SA4k5oLixFljMsQSIKSBiUpBNiClwMmnEFMjf8C/MQkwBo5VJMQXCOsLOlmPMPmRFGvZozwJOrcr/nC4REP1xUVedHHBcg5E48Ge8A+E3IFr+bnEuGTaeQfuJQGMEGge1oXSpD1IQUJMqSAHVIjp5+jidqzpHB7Wfr7WfjhcUUQvtp+r0WerQqQikYP8+GnjV8DhtmRdtIAVraMTosY4WDVIgf8ODFFRjBVIgbzNOJf0GGjNpOHKuigRRqI5jqP676eZP6Pj/b+9c4Kuo7jz+v3mHVxLCS1EEFUF5CSKPgoJgra+lUXTBVSnW/Si2dtX60fZT3VpXP2u124+6uhV3baVlLWVbH4UCIgpEUBRBEASkqEDCU0JCAiSEkNw9Zy5zM5nce2fm3kku5H5PPvdzc2fO+Z9zvufMzPmd1xw/Ht4lySml5voG66iDFhGh0YjQyMPu9Z9IuhrFuHTUZU7mXJ9HFIhcojr0/HIsNPaLJHbsBBAFCdaJREWBesWA1NTXSCAYMN43cCKnXs494wLJ71AoFeUHpKa6GlGweYPsRxRIrz7nR62tu0q2y8b1iAI7oLJv9smKZYvlhinf83ylIwoQBS3VMPb7PQU9LhkVFg7WaUrGzkmqge+0g5L14jBHH7YNGhIadbBMWzIFhNcRCEQBosDrDZjpQ16J+eMfUZAgx4onKiTtuhw5eo43Q+wo5I2XG9+sKXBDqfX8sKag9Vg7xcSaAidCrXveL1HgNdXWUQdDPFQcNwRDlRql1iMQJWrNQ2Vmg1RlBj2Z1iMNWihYRYR+n4M+pndb0k6PRHSqU2+NPvkpqPAURXTPtSKBWm/ptRvr2C5T9NrAJu64sqlst7TTaU87rqYLnCIuqPKdKE8/stL5vnw/zGDDIwFEgUdgdu9aFATOz5Dqq1SXvwu3avcKeeC9u6S0aqfhWy8iZkchF+BceEEUuIDUil4QBa0I2yGq004UVDU4wguoNbpuG1OBw872dISBKg+Ny8Pu/aYfbpqd9PSAqBcmS4NqjEd0LtNrhg3oxmuCDWNrOiozGgxxoD8luSfUd1BK26lv43hQSsL/K2HRrt6xrKJ5OLs63TjVqyYjLBby6gKSd0KJierQM9X83evkb+0X1/YJFPxrQdvP5CmYQ0RBgoViiIJuaVI7cp/kLJwvGaU7JVBZGdFqVe0hefvr+eFzedn58h31zgHTBfPypKFTXoIpCgVvyMsXbS9Rd+Jsj0MgtggbVBqCCeSpvpf7+BEFiZa2v+ERBc15BmsbVC9cbM7pR1z0GrrpzbP0oKalBSQnK12qj51oHrmLxq29URspB256GP1uvPpbY1PPWrCTi7oWAUswOyCBrMawkUREaMShQXbmhkSDFhXmwmmnBdRuSsIUFMbIgxIRpmgwRURo9CIkOvSOTdqdlZ5pfJujGGY8kUYKdB4l201KEvNjxGNhmZi1xEM3ZAUlGBrcSao7s0/7pMafqpEjChIs+ahrCnQ3kPqkqSHaNPWt+4My1NxO/Tu3pkZqs7PlSIcOkqP+18fq1bzNenXj6vrNN9Ll4EHDz/5u3eSo8jNk/Xop69JFDqjf45Yvl4XXXisTly6VbeefL13LyqROhctUOxDpb/1bH9fnX50+Xe5/7jmZPW2ajFm5Utqr9QlvFhXJjJkzpXj8eCNN45W9N2+8Uc778ksZvGGDzJ80SXru2iXDPv1U1g0bJqVnnSWT5s0zKD3x85/LI08+aaR308CBsqV/f7npL38xzlnt6d+fjBghB1Sar1240Dhf066dvHDvvfLwM8+EiX8wdqzU5OTIle++Gz624Prrpfu+fTJ8zZrwMXs6zBPP/vjHcucrr0inqqqwX83wqZ/+VB554UUljJqKov++oUiKli2XbocONSn1nT16yPtDL5bbF70dElMWEVNSkC8rzu0jt65dF7GmvDJ6hPzD9p1SmJUT8fzzffvIPV/ukCxdHyzOFIDLVEMtX/UWDj0RvSfzrex0GZiVK30KCqPW1p1qb/R1NUekKC/kJ5qY23W4Utbu3y3fPf+iRmZnR34J3tJPP5azunaXC87u3ej3pEizN263fbVJdu8rkfFjrgn77dxJ1XE1PUEtmWnmvtixUfaV75bxwxoXjzv15i5a/5Zc2HOQ9Mk+NyqH8ImTQ/8Hju2X5XvelZvPvTVimFiN3Vf3vCI3d5siHTI6irjoubX2Mi8ILpD+6u+8wHnOaY3gY0VwhXRQf0MDQ+MKrwOtD65X88yr5PK0y+O2oQPuVn8fNXwkk9MmJ2THDDyzYaZ8P/B91Q6K3vJw01g1G6ZrqlZLXbBORudFX8hZr4rQlesYauiu3fOxnFALeUeeHd2mmzSacQY7psmnWz9SO8XVyYgBl0n73Ayprw/KMbWRRCRX38HdKMS6jdrmCRk+aqwEsv15EVprzv/X05m029VwQk1hUiJCffS7HkJrIEIC1pjepO6fdkFhrn1YemHjvcxVGVs8mdOe0pVobi9pMmzLJkMHVA0OXXdW8WBOg9LH9VQo7fSuTvpj/K+mSuWp57jdpcKi4GjcE8k7awq81mZ//CMKXHB84LEX5Z3iUCN1YL8+Mvflx8KhoooC5UNLgaC6oYUkgUhmIF0y1e4OuermcVztJnFU3QCz1Q1F31K0rwZ14ytUDcQC9clRQcrUiepAQC5SDcZyddPSn5F19bIsM13GqGPb1e9CFUbfOvUtSn93VuH08csrDsmf8jvK3V+XyJ/POlMuLa+Q9kqULOjRTabv3CUfFhYYqRpzsEIWntFNzjlaLQOqjsjiHl3ljJpjMrjysGzM6yR71X7a127+wkj/01deIQ+9t9wQOVu6d5Ot3bpK0cZNxrmVquGs7V329Xbj99qzz5KDSgh855NPJK3ykNQoEfSbyTfKg3+cE2b34eBBciwrSyasWRs+tuhbo6XbwXK5ZOtW41h6yc6wOLn+/aYN8+fvnCp3zJ0nnY5Uh8NrcfX0PbfJz178feOx/FCj93++O1qKijdI10NHw+f0PyU9CuT9i8+V295uTIc+HszJk51nnSEr+xfKP60sbRLG/PHbCb1l0id7pOvh0H7jDQVNG9jPjc2VH3xYI1lR2vzvnp8pBcE8GXowN6J9ffDNPlUyuCxHzjucZaRJf+xuR26VfNrxG7nxm6aLke3+SzMOyOrsv8vko80bO4bf3Ebb7wTfkV7qr3+gf9S0mSe2BLfIruAu+Xbatx39ag+bgptkb3CvXJl2pSv/2tP84HwZqP76BPq4DqN381rasFSmpk11Hcb0+LuG38nNgZulY8Bti7IxiqiiQPUKBp16H1UDcsWhYumY3lEu7jgsYrqN3jzdwxjDbahaJ1UnKmXsOVdIrJECp8btnopd8smOD2XS5bEZuulh1Hn//az/lFvv+IFkqmvfD9eajdhE0hvv7kOx4jwd854IQ2vY5as/kHolKnpcOjq0yPqkiDBFRUhghG68eqcm7UxhYYoPe1rGb9XPuqAs73dhQsnUuzyZbtQXWyRHXapfDRhsbA9rOvtohVV0hNZnNIo8vSuU1R1Yt9p43rblHY0QBQlVwbgDIwoc0M156z2Z+Yd5UvzG84bPKXc/LsMv7icP3RN6QEYTBaZZUxCkB1RvvrqwA0oE5GTkyPH641Jdd1SyM7KNYw3q5tUQrJeC3ELJzylQx3Ok/GiZ1NRVS7+8i6Sitlwqjh+U4V1GyYp9y2RktzFScmS7FGSr9xQ01ElGWqbxrX/r4/r8Wzv+LLf3vVPm73xdLmk3XHLT28mSg4vllh63yeqqj9RARlBG5o2WJeVvy9nZ50j/9hfK0vJ3pXtWdxnQYZBsPvq57K3dKxM7hxp6/1X6vNyT90NJU+ndVvd3+er4V3J1+1DP8OpjHxviZ2TOKOP3htoNUl5/UMa3u8L4fSx4TGZX/l7uSrsrTHxtcK1xfExaYwN1WXCZdFF/gwKDwv6iNSAjNdrqlbzSPZE/TPths5J9reE1uTpwtRQGmva4x+oJdeoljWbTjNypV7Q4WCz56m9IYEjUmuimMbwzqMRTcJ0UpRXFrNGlwVJZE1wjN6Td4HjTiCUKAjWVEjjWOE1uc1aJ7Eovk6tqmjZitR+rPzPSzzsclD1ZR+Sq8sbpYWmHSmKmyRRHfUv3O6Zde0irKJF9+Tny9pDuMr04tIbH7mLF+eLNl8m0BaulU3WtpDukzYjvUKNwnDt1qjHC1/+LkKB244JqlMoc3VoycoR0OnxERm7e3CxovcOUPm1Dj3itLchTc8AzZMKBg+qaVTMUMtNUz3SjOq2PMkJkjVBP39utXrC1qrpKbsrrEjEbOi6naY/WaYS/Xfi6TLtqkmRaGk6mYcOfsufFnY4NY78WGp+OefdStrH8+pF3/TZqLRC6F+TItvJq+XLtR1KrfgcuHm5EbQoM/b85cqH/t4sMfaylhYaVhVW8mKMd1vNWUdJJdSya06hMP3ZBoo93/XyDMbshZ+ilYVPmiIh5wDoyYo2vJUZJEAV+XSne7CAKHHjZRYBdJEhBgdT2vkaqb/mNrwu9vBVjavh26tEMqJuf7jvVIy5NnOp5jce56Y1tZvfk9AMv8Tnly2rL6/xTN723pn3di+vXFISAGh3qogRf1dHjahpG7KkQ6aWxxYBOX1pVpTHi5Mbp0SUn5yZObSPDlS3n+NLUOiPNBOcPAbdrjZwElJmaEx7WLrkRU6bdaOnMVVMC65U+O65Gfk3nRlxZ6cW7XsstO39K6vSw4vcbjc1pUTr3ehRDf7QzRzP0/1bBoX9bRYc5ZcqkZ1+D4ceajNYoGas4scYX2tq2+XPZKmDmXtC7NZJIHDYCiAKHKjHuxvtkxrRJckvRRMPnytUb5e6Hfy2bls8KhVQN0Yp+veX6f+kl5xzoKb0CvYwdhf6x/20JVzY/FzrpOa2JOi8NzEhx+dnojGSfhcaJlrC/4Vlo7I2nFg1aPDg5J0ETSUDpOdPtsjPkcE3jtot+iSct1pzSHXAp6hBPTqWfvPPWkV0zzXAAABLUSURBVKx4U+FWpMWyb46ExZuGiM+O7oVyOKvlF7a2hCCrVOpSiwirK1VrNExXZYyGNHbMaAFcdXINhzWM3pLW7kpsxw517CiVHTs186eP64+fLjh0sJ/msOWSAKLAAdSA8dPl0ftvbyYKFr32tPTq2d0QBbMuFrlDzdrond9bfjH+F/K9Id5flOSyvPAGAQhAAAI7drhjsNN5FMcw5Nae3qTAtlFBzIS4tauNeLXt1b+ZUC9pckcZXxCISGDHGWdGPB5NRFiPT5/3V6gmgQCiwAG600iB0xuN09QQmf7o+fsZan6v/j83N1dqa2vlyJEjkqN239HH6pWa15+uXbtKF7Vrj/azf/9+OXr0qAwZMkTK1K5CBw4ckHHjxslCtaPPxIkTZdu2bYb/OrXYKjMz0/jWv/Vxff7VV1+V+++/X2bPni1jxoyR9u3by5tvvikzZsyQ4uJiI03j1S5E+th5550ngwcPlvnz50vPnj1lmNp5aN26dVJaWiqT1I5E2j3xxBPyyCOPGOndtGmTbNmyRW666SbjnNWe/v2JWmCs03ut2ilJuxq1m9ILL7wgDz/8cJj4Bx98YBy/8srGxaYLFiyQ7t27y/DhoTmd2tnTYR5/9tln5c4775ROnRp7LjTDp556Sh599NFmJfvSSy/J5MmTpZvaxcnqdqqGw7Jly2S62q3J7mKd036j2TTt6LQ8+OCDkhVlUeWiRYuksLBQRqjdmqK5OXPmyCWXXCIXXHBBVD9fffWVrFq1Sm67LfYI1fbt22XFihUyTe1I5eSs9cLJ72effSbadpHa3cqNi1amscK64WAPv3fvXqNO33VX41oWN+nTfiLVL7dh586da1y3/dUOXfG4xYsXS56aXz9qVGiNTjzu448/loqKCrn66sYdnuKx43QNeLXpdE14tafrs773TZgwwWvQqP6xGYFnvCJEUV6hdrarU8+yCWdGbiR6KriT6VihRtXq1Pz/CWoKb8LupM1iZcjYlS9hg40Gmtj0SZAV56td8nQ6vQhUM0lR0lDcu3fIpk9p1NElZFM9k3GtTwBR4MDcaU2BkygIqAZ0uvrol9RkZKQbi4qzc3KlTm0hWV19VLKyQ6KgQTVmG9QQYH7nLpKXrxYaZ+dKRfkBqVHbiPbtP0AOVZTLofIyGTpijHxYvEQuHX25lO74WvlXC43VrgtacOjvAvVbH9fn57/xR7nlezNk4V//T4YMGyE5ue1k+bsLZfLU6WLdKmz5kgXSs1dv6dtvgKxYtli6dush/QcMka2bN8j+fXvk8gmhRsVvf/MfcseMHxvp/XrbF7L967/LxO+EBIN967HNG9ep9JfJmHGhRcq1x2pk7v++ItP++Udh4p+pLS9rjx2TEd8aFz62cvk70rlLN7looBp+Oens6TCP/3HWSzLpptukQ4fQsKWePpQuDfL8s7+S79/zYLOSfX3Oq3LFVddL58KuTc7t3V0qa1evlOtvuKVZmFjntOdoNk1Ds15+LuZOKx++/64q784yYHDkXWa0ncV/e10uVOXRq0/TnYWsid1Vsl02rl8j10y6OWaN3rNLLUhe85FcVzTF8W5jrRdOnrd98bns3qW2JL0yJAK1izV9KFqZxorHDQd7+LJv9hl1+oYp3kfv7PXLiYH1/JKFb6rrdqD0Prevl2Bhvx+tXCrtO3SSQScXPMZj5PPP1srhqkMy+rKJksjLy5yuAa9pc7omvNrzY8GpPc6WtslCY6+l3Ny/n2VkrilIZAvNaDnCZny7JLHQOPFrJB4LiAIHavHuPqQXvWqHKEAUxNp+EVHgvhcbUeDtFo8o8MbL6tvPBqdply1JT8iloy6Lv1BsIf0sI0RB8449PwoqEUGEKPCjBLzbQBS4YBbrPQU6+OHqOrWAL8KbQl3Yxot/BFho7B9LPyyx0NgPiv7YSGSkwJ8UYMVKwK+RAqj6Q8Dv3Yf8SVVqW0EUJKf8EQU+cEcU+ADRBxOIAh8g+mgCUeAjzARNIQoSBOhzcESBz0ATNIcoSBBgCwRHFLQAVBcmEQUuIDl5QRQ4EWqd84iC1uHsNhZEgVtSLe8PUdDyjL3EgCjwQqvl/SIKWp6x1xgQBV6J+eMfUZAgRxYas9A40uJls1o5LapkTQFrCiLdglho7P7G7OfccjPWlrbplyho6XS6L4XYPk/1dLKmgDUFftX1090OoiDBEkQUIAoQBSLsPtT0RsLuQ9FvrE5C2est+VRvcEYSGogCr6Xc3L+f5Y4oQBQkXiPbhgVEQYLliChAFCAKEAX22wiiAFFgJ8DuQ+w+lGBzIxw8kV19oqXhVLPJ9CG/aos3O4gCb7zwDQEIQAACEIAABCAAgTZHAFHQ5oqUDEEAAhCAAAQgAAEIQMAbAUSBN174hgAEIAABCEAAAhCAQJsjgChoc0VKhiAAAQhAAAIQgAAEIOCNAKLAG6+w75Ld++WaW38S/v3yMw/K2BGD4rRGMLcEnN4ubbUz56335MnnZocPDezXR+a+/JjbqPDngsC4G++TsvJKw+f0KVfLQ/dMdRFKxCzHTctnufKPJ2cC9vruhq31erpq3HB59vF7nSPChysCXq+NAeOnc69yRdZ/T1PuflyGX9zP9f3L/xSknsWVqzfK3Q//WpzuUzzHW7duIAri5K1v+DOmTZJbiiaK28odZ1QEO0lA3xxm/mGeFL/xvHHE6UauGzwP3HWz9OrZ3fCvy+z6b4/mxu9TjdJ8tTMbkrpR40Yc63CfbtxmiAmnB4JPSW3zZsxOikWvPW3U91+99CdZs35rTBGsrx/tEMr+Vw+v14b93sS9yv8yiWTRKoq9dGq0TuraZiz2DlWnZwDP8datB4iCOHhHEgFWkRCHSYK4IGAXAXaR4GTC/qB28s/52ATsIsANX91Y3bOvTCZfN85VLxFl4I6AXQTYRYLdir6HPfLLV8IC210s+HJLwOu14dW/23Tgzx0BRJg7Tn76MkcAnESBPU43zxk/05lqthAFcZR4pMaoU691HNEQxEbALry8jtBQRv5VqUiNTqfeaet5r2XnX8rbpqVID8pYIze6LP62ZFV46pem8uj9txsjn7jECMR7bcya+3a4DHTZmaM+iaWG0G4IIArcUPLXT7yigOe4v+Vgt4YoiIOv+UA1p7FoE7qintmjkDm5cfB0G0Q/KK0NF7Nh6ebhGe8NyG3aUs1fJPaRrguTi11IIwr8rTGR7j/268UaoxYRe/YdDE8dMsvDzfQvf1Pe9qx5vTY0ATNMl855hlBj/VPr1gtEQevy1rHF80yOJ0zr5+z0jhFREEf5MVIQBzQfgsQ7UmDeSNyIBx+SmRImvPaGWufu2gFRLolXGa8jBZH8MwUy8XLQFrxeGzqMfWSA9R7+lIVbK4gCt6T88+e1gc9z3D/2sSwhCuLgzJqCOKD5ECSeNQXcSHwAH8VEIvOgGSnwt1y8rimINNULUeBfmXi5NiJdC7FG3fxLJZZMAoiC1q8LXkQBz/HWKx9EQZys2X0oTnAJBHPafUg/SPW8XHPhkv13AlETNAIBpx1WdMMo2o4eiAJ/q5TT7kP26UGmf3O6kJcHtL8pb5vWnK4N+0iA/VrRz5dhg/oyHbWVqgeioJVAW6KJds/hOd76ZWGNEVEQJ3/eUxAnuASDxXpPgf1mYt0n3Bot01USLARL8Fh7sSMK/OPsxlKs9xREWjNgHjNtc124oezeT6xrwy4K7M8T3hnhnnMiPiNNa/S6G04i8adiWHtd1wysnUc8x5NbKxAFyeVP7BCAAAQgAAEIQAACEEg6AURB0ouABEAAAhCAAAQgAAEIQCC5BBAFyeVP7BCAAAQgAAEIQAACEEg6AURB0ouABEAAAhCAAAQgAAEIQCC5BBAFyeVP7BCAAAQgAAEIQAACEEg6AURB0ouABEAAAhCAAAQgAAEIQCC5BBAFyeVP7BCAAAQgAAEIQAACEEg6AURB0ouABEAAAhCAAAQgAAEIQCC5BBAFyeVP7BCAAAQgAAEIQAACEEg6AURB0ouABEAAAhCAAAQgAAEIQCC5BBAFyeVP7BCAAAQgAAEIQAACEEg6AURB0ouABEAAAhCAAAQgAAEIQCC5BBAFyeVP7BCAAAQgAAEIQAACEEg6AURB0ouABEAAAhCAAAQgAAEIQCC5BBAFyeVP7BCAAAQgAAEIQAACEEg6AURB0ouABEAAAhCAAAQgAAEIQCC5BBAFyeVP7BCAAAQgAAEIQAACEEg6AURB0ouABEAAAhCAAAQgAAEIQCC5BBAFyeVP7BCAwGlG4Fcv/UlmzX27Wao3LZ8lc956T558brY8ev/tckvRxCZ+HnjsRXmneI0seu1p6dWzu8Sys3L1Rrn74V/HJKPj0E7HF8mZaTDTNLBfH5n78mNNvJppiHTO9Dhg/PSY6bhq3HDjvM6b6aZPuVoeumeqlOzeL9fc+hPjsOZjddY8mufMtMbKz2lWXUguBCAAgdOGAKLgtCkqEgoBCCSbgNmwtzdw9fERQy80hIDZ0Lb6MRvALz/zoIwdMUjc2LHmVfvfs+9gs0a92Yi2p8ca1trQNgWJeX7cjfdJWXmlxBIFkWxFis/MozUOqyiwCyWTgVUwuMlPsusA8UMAAhBoqwQQBW21ZMkXBCDgOwHda272gscyrhvbwwb1lWcfv9fwZv/t1o4ZR6KiYOYf5hnp0c5Mk26A6+M9unY2jttHESLlL1ajPZYo0Mz+tmSVFL/xvGHWFAt6lEGPMNhHCmKJHN8LFYMQgAAEIGAQQBRQESAAAQi4JGBv3EcLZh0ZWLV2U5MGcSSR4BS9H6Jg9gs/M6bymD35U+5+XIquGStvLVrZ4qJAx3n7j/5dZkybFB5N2bOvTM7s0cWYioUocKoBnIcABCDQ8gQQBS3PmBggAIE2QiDSnPdovdrW6THmtCETgxc7OoyTKIiE17qmQI8I6F56LQTO7FEok68bJ4/88pXwMR2+JUcKtCiYO29ZWBzpkRLzWCRRECs/baQqkQ0IQAACpxwBRMEpVyQkCAIQOB0ImPPxzbTaG/76uG786iky5pSdSPlyY8dJFDitKTBFgTmCodcQ6FECvQZCC4XWEAV6cbXmoePWwkQzsa+/YE3B6VDzSSMEINBWCSAK2mrJki8IQKDVCOiGvZ6bb+9tdzvdyExoNDt+iQIdjxYBn2/dHp6y05qiwBQBpoBCFLRaFSUiCEAAAo4EEAWOiPAAAQhAILQ4Vk+B0Vtt2l20hnUkURCPHT9Fge6N37X3QDgfrSkKdN4f+reZYfGEKODKggAEIHDqEEAUnDplQUogAIFTmIC5Y06XznnhXXR0cs0pL5GmD0UTBXrBrxc7fooCt4ImUlHEu/uQfStU0zai4BSu8CQNAhBIOQKIgpQrcjIMAQgkQiDSy7yiNXpjTR/yYsdJFETKT6SFxpH8+TFSYF1UreOwv7zMqyiIlZ9Eyo6wEIAABCAQnQCigNoBAQhAAAIQgAAEIACBFCeAKEjxCkD2IQABCEAAAhCAAAQggCigDkAAAhCAAAQgAAEIQCDFCSAKUrwCkH0IQAACEIAABCAAAQggCqgDEIAABCAAAQhAAAIQSHECiIIUrwBkHwIQgAAEIAABCEAAAogC6gAEIAABCEAAAhCAAARSnACiIMUrANmHAAQgAAEIQAACEIAAooA6AAEIQAACEIAABCAAgRQngChI8QpA9iEAAQhAAAIQgAAEIIAooA5AAAIQgAAEIAABCEAgxQkgClK8ApB9CEAAAhCAAAQgAAEIIAqoAxCAAAQgAAEIQAACEEhxAoiCFK8AZB8CEIAABCAAAQhAAAKIAuoABCAAAQhAAAIQgAAEUpwAoiDFKwDZhwAEIAABCEAAAhCAAKKAOgABCEAAAhCAAAQgAIEUJ4AoSPEKQPYhAAEIQAACEIAABCCAKKAOQAACEIAABCAAAQhAIMUJIApSvAKQfQhAAAIQgAAEIAABCCAKqAMQgAAEIAABCEAAAhBIcQKIghSvAGQfAhCAAAQgAAEIQAACiALqAAQgAAEIQAACEIAABFKcAKIgxSsA2YcABCAAAQhAAAIQgACigDoAAQhAAAIQgAAEIACBFCeAKEjxCkD2IQABCEAAAhCAAAQggCigDkAAAhCAAAQgAAEIQCDFCSAKUrwCkH0IQAACEIAABCAAAQggCqgDEIAABCAAAQhAAAIQSHECiIIUrwBkHwIQgAAEIAABCEAAAogC6gAEIAABCEAAAhCAAARSnACiIMUrANmHAAQgAAEIQAACEIAAooA6AAEIQAACEIAABCAAgRQngChI8QpA9iEAAQhAAAIQgAAEIIAooA5AAAIQgAAEIAABCEAgxQkgClK8ApB9CEAAAhCAAAQgAAEIIAqoAxCAAAQgAAEIQAACEEhxAoiCFK8AZB8CEIAABCAAAQhAAAKIAuoABCAAAQhAAAIQgAAEUpzA/wMe8jY+ZVvPKQAAAABJRU5ErkJggg==",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"uc.plot_history(show_intervals=True, \n",
" title_prefix=\"Using exact values for k1_forward and k1_reverse\")"
]
},
{
"cell_type": "markdown",
"id": "2d8336ee-4576-4081-9835-9fd7b8bee273",
"metadata": {},
"source": [
"### What is the initial rate of production of the final reaction product `P`? \n",
"One could take the numerical derivative (gradient) of the time values of [P] - but no need to! **Reaction rates are computed in the course of the simulation, and stored in a rate-history dataframe**"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "7f18a18c-061e-481f-ae71-aa7a88399724",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" SYSTEM TIME | \n",
" rxn0_rate_1 | \n",
" rxn0_rate_2 | \n",
" step | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 0.000000 | \n",
" 360.000000 | \n",
" 0.000000 | \n",
" 0 | \n",
"
\n",
" \n",
" | 1 | \n",
" 0.000500 | \n",
" 274.543200 | \n",
" 8.820000 | \n",
" 1 | \n",
"
\n",
" \n",
" | 2 | \n",
" 0.000750 | \n",
" 243.269275 | \n",
" 12.075109 | \n",
" 2 | \n",
"
\n",
" \n",
" | 3 | \n",
" 0.000763 | \n",
" 241.911753 | \n",
" 12.216716 | \n",
" 3 | \n",
"
\n",
" \n",
" | 4 | \n",
" 0.000769 | \n",
" 241.237493 | \n",
" 12.287060 | \n",
" 4 | \n",
"
\n",
" \n",
" | ... | \n",
" ... | \n",
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\n",
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\n",
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784 rows × 4 columns
\n",
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"
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"text/plain": [
" SYSTEM TIME rxn0_rate_1 rxn0_rate_2 step\n",
"0 0.000000 360.000000 0.000000 0\n",
"1 0.000500 274.543200 8.820000 1\n",
"2 0.000750 243.269275 12.075109 2\n",
"3 0.000763 241.911753 12.216716 3\n",
"4 0.000769 241.237493 12.287060 4\n",
".. ... ... ... ...\n",
"779 1.166644 1.308959 1.462999 779\n",
"780 1.173671 1.261193 1.409959 780\n",
"781 1.180698 1.215086 1.358736 781\n",
"782 1.187725 1.170584 1.309274 782\n",
"783 1.194752 1.127638 1.261520 783\n",
"\n",
"[784 rows x 4 columns]"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rates_exact = uc.get_rate_history()\n",
"rates_exact"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "18ac9b9f-c669-43f6-ac36-ed95b76e1ae5",
"metadata": {},
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"text": "Reaction rate, dP/dt, over time"
},
"xaxis": {
"anchor": "y",
"autorange": true,
"domain": [
0,
1
],
"range": [
0,
1.1947523744399813
],
"title": {
"text": "time"
},
"type": "linear"
},
"yaxis": {
"anchor": "x",
"autorange": true,
"domain": [
0,
1
],
"range": [
-1.8935609203310617,
35.97765748629017
],
"title": {
"text": "dP/dt"
},
"type": "linear"
}
}
},
"image/png": 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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Let's take a look at how the reaction rate varies with time\n",
"PlotlyHelper.plot_pandas(df=rates_exact, colors=\"blue\",\n",
" title=\"Reaction rate, dP/dt, over time\",\n",
" x_var=\"SYSTEM TIME\", fields=\"rxn0_rate_2\", \n",
" x_label=\"time\", y_label=\"dP/dt\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "485514fa-5259-4319-9aea-8adac65ae24f",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "e0886793-ace6-49dc-bbef-d2aa0c040001",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "078285f0-00aa-4fbb-9a67-7de0184d6cec",
"metadata": {},
"source": [
"# PART 2. Guessing a SMALLER value of `k1_forward` (UNDER-ESTIMATED)"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "f6bdd115-a3cc-4c94-8636-108078d4a018",
"metadata": {},
"outputs": [],
"source": [
"enz = uc.get_single_reaction(0)"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "d3b58d68-ae80-4016-afa5-398ed450b330",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"5.919463087248328"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"enz.min_k1_forward(kM=kM, kcat=kcat) # The smallest possible value"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "df47c069-a290-4c48-a80c-fa9721a38b4c",
"metadata": {},
"outputs": [],
"source": [
"k1_forward = 6.5 # Close to the smallest possible value"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "2c8330eb-0f1a-4edf-b937-9a1a8d11ae84",
"metadata": {},
"outputs": [
{
"data": {
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"4.8055555555555"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"k1_reverse = enz.compute_k1_reverse(kM, kcat, k1_forward=k1_forward)\n",
"k1_reverse"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "aa8a4fbe-c52f-48f7-b505-01c6cc032f92",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": 22,
"id": "b1ab7d25-1262-4376-ba37-b6888f5ca5d9",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" name | \n",
" label | \n",
" plot_color | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" P | \n",
" P | \n",
" green | \n",
"
\n",
" \n",
" | 1 | \n",
" ES | \n",
" ES | \n",
" red | \n",
"
\n",
" \n",
" | 2 | \n",
" Adenosinedeaminase | \n",
" E | \n",
" violet | \n",
"
\n",
" \n",
" | 3 | \n",
" 2,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purine | \n",
" S | \n",
" darkturquoise | \n",
"
\n",
" \n",
"
\n",
"
"
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"text/plain": [
" name label plot_color\n",
"0 P P green\n",
"1 ES ES red\n",
"2 Adenosinedeaminase E violet\n",
"3 2,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purine S darkturquoise"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"chem_data.all_chemicals() # Nothing changed here; same chemicals as before"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "bebb6d92-7939-4e8c-9a77-dd5abffd949b",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": 23,
"id": "2c8bb1b8-cdd6-4822-aa4c-13db2b425c5f",
"metadata": {},
"outputs": [],
"source": [
"rxns_underest = ReactionRegistry(chem_data=chem_data) # New set of reactions"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "e364152e-be1a-4ed3-8622-b00d101ac600",
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Number of reactions: 1\n",
"0: E + S <-> ES -> E + P (Enzymatic reaction) (k1_F = 6.5 / k1_R = 4.8056 / k2_F = 49)\n",
"Chemicals involved in the above reactions: {\"P\" (green), \"ES\" (red), \"E\" (violet), \"S\" (darkturquoise)}\n"
]
}
],
"source": [
"# Enzymatic reaction `E + S <-> ES -> E + P` \n",
"# In first part of the reaction, a forward rate that is much faster than its revers one\n",
"rxns_underest.add_reaction(reactants=\"S\", products=\"P\", enzyme=\"E\",\n",
" k1_F=k1_forward, k1_R=k1_reverse, k2_F=kcat)\n",
" \n",
"rxns_underest.describe_reactions()"
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "ccfc59f5-a0dc-4b03-a9dd-a6993c4a85cd",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SYSTEM STATE at Time t = 0:\n",
"4 species:\n",
" Species 0 (P). Conc: 0.0\n",
" Species 1 (ES). Conc: 0.0\n",
" Species 2 (E). Conc: 1.0\n",
" Species 3 (S). Conc: 20.0\n",
"Chemicals involved in reactions: ['ES', 'P', 'S', 'E']\n"
]
}
],
"source": [
"# Here we use the \"slower\" preset for the variable steps, a conservative option prioritizing accuracy over speed\n",
"uc = UniformCompartment(reactions=rxns_underest, preset=\"slower\")\n",
"\n",
"uc.set_conc(conc={\"S\": S0, \"E\": E0}) # Small ampount of enzyme `E`, relative to substrate `S`\n",
"uc.describe_state()"
]
},
{
"cell_type": "code",
"execution_count": 26,
"id": "d9c51bab-7eaa-4735-82d2-aaf8ac787f0e",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"788 total variable step(s) taken in 1.839 sec\n",
"Number of step re-do's because of negative concentrations: 1\n",
"Number of step re-do's because of elective soft aborts: 2\n",
"Norm usage: {'norm_A': 704, 'norm_B': 709, 'norm_C': 704, 'norm_D': 704}\n",
"System Time is now: 1.2057\n"
]
}
],
"source": [
"# Perform the reactions\n",
"uc.single_compartment_react(duration=1.2, initial_step=0.05)"
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "7c4ee2db-73ee-4b17-b3fa-943d4a1ea4cc",
"metadata": {},
"outputs": [],
"source": [
"history_underest = uc.get_history() # Let's save the historical data for a comparison at the very end"
]
},
{
"cell_type": "code",
"execution_count": 28,
"id": "ab344447-39a8-4dd6-aca8-be21e2bba505",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"plot_pandas() NOTICE: Excessive number of vertical lines (789) - only showing 1 every 6 lines\n"
]
},
{
"data": {
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"ticks": "",
"zerolinecolor": "white"
}
},
"shapedefaults": {
"line": {
"color": "#2a3f5f"
}
},
"ternary": {
"aaxis": {
"gridcolor": "white",
"linecolor": "white",
"ticks": ""
},
"baxis": {
"gridcolor": "white",
"linecolor": "white",
"ticks": ""
},
"bgcolor": "#E5ECF6",
"caxis": {
"gridcolor": "white",
"linecolor": "white",
"ticks": ""
}
},
"title": {
"x": 0.05
},
"xaxis": {
"automargin": true,
"gridcolor": "white",
"linecolor": "white",
"ticks": "",
"title": {
"standoff": 15
},
"zerolinecolor": "white",
"zerolinewidth": 2
},
"yaxis": {
"automargin": true,
"gridcolor": "white",
"linecolor": "white",
"ticks": "",
"title": {
"standoff": 15
},
"zerolinecolor": "white",
"zerolinewidth": 2
}
}
},
"title": {
"text": "Using SMALLER (under-estimated) value for k1_forward
Reaction `E + S <-> ES -> E + P` . Changes in concentrations with time (time steps shown in dashed lines)"
},
"xaxis": {
"anchor": "y",
"autorange": true,
"domain": [
0,
1
],
"range": [
-0.001007242633793452,
1.205669432650762
],
"title": {
"text": "SYSTEM TIME"
},
"type": "linear"
},
"yaxis": {
"anchor": "x",
"autorange": true,
"domain": [
0,
1
],
"range": [
-1.1111111111111112,
21.11111111111111
],
"title": {
"text": "Concentration"
},
"type": "linear"
}
}
},
"image/png": 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""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"uc.plot_history(show_intervals=True, \n",
" title_prefix=\"Using SMALLER (under-estimated) value for k1_forward\")"
]
},
{
"cell_type": "markdown",
"id": "4432c8c0-c5c5-4311-ac77-bbedfc27b741",
"metadata": {},
"source": [
"At first glance, not too different from before, overall, but let's take a closer look"
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "a24e8ab9-697e-417a-ad5a-475ea6200b3b",
"metadata": {},
"outputs": [
{
"data": {
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"\n",
"\n",
"
\n",
" \n",
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" | \n",
" SYSTEM TIME | \n",
" rxn0_rate_1 | \n",
" rxn0_rate_2 | \n",
" step | \n",
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\n",
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\n",
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" 1 | \n",
"
\n",
" \n",
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" 2 | \n",
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\n",
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\n",
" \n",
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" 4.729203 | \n",
" 4 | \n",
"
\n",
" \n",
" | ... | \n",
" ... | \n",
" ... | \n",
" ... | \n",
" ... | \n",
"
\n",
" \n",
" | 783 | \n",
" 1.171227 | \n",
" 1.169882 | \n",
" 1.318201 | \n",
" 783 | \n",
"
\n",
" \n",
" | 784 | \n",
" 1.178115 | \n",
" 1.125129 | \n",
" 1.268138 | \n",
" 784 | \n",
"
\n",
" \n",
" | 785 | \n",
" 1.185004 | \n",
" 1.082003 | \n",
" 1.219867 | \n",
" 785 | \n",
"
\n",
" \n",
" | 786 | \n",
" 1.191892 | \n",
" 1.040450 | \n",
" 1.173332 | \n",
" 786 | \n",
"
\n",
" \n",
" | 787 | \n",
" 1.198781 | \n",
" 1.000418 | \n",
" 1.128479 | \n",
" 787 | \n",
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\n",
" \n",
"
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],
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" SYSTEM TIME rxn0_rate_1 rxn0_rate_2 step\n",
"0 0.000000 130.000000 0.000000 0\n",
"1 0.000500 120.842601 3.185000 1\n",
"2 0.000750 116.711975 4.626306 2\n",
"3 0.000763 116.515396 4.694958 3\n",
"4 0.000769 116.417346 4.729203 4\n",
".. ... ... ... ...\n",
"783 1.171227 1.169882 1.318201 783\n",
"784 1.178115 1.125129 1.268138 784\n",
"785 1.185004 1.082003 1.219867 785\n",
"786 1.191892 1.040450 1.173332 786\n",
"787 1.198781 1.000418 1.128479 787\n",
"\n",
"[788 rows x 4 columns]"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rates_underest = uc.get_rate_history()\n",
"rates_underest"
]
},
{
"cell_type": "code",
"execution_count": 30,
"id": "dd0d561d-435b-4aa6-8761-6dde0989c445",
"metadata": {},
"outputs": [
{
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Let's take a look at how the reaction rate varies with time\n",
"PlotlyHelper.plot_pandas(df=rates_underest, colors=\"blue\",\n",
" title=\"Reaction rate, dP/dt, over time\",\n",
" x_var=\"SYSTEM TIME\", fields=\"rxn0_rate_2\", \n",
" x_label=\"time\", y_label=\"dP/dt\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "223d5c37-0ad2-465a-9f95-84bebda6ab7a",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "ce1f4c5a-a77c-4fa0-89be-b4f4e05c24db",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "e863f23b-0fb5-490a-9f60-fa1c9caf4c93",
"metadata": {},
"source": [
"# PART 3. Guessing a LARGER value of `k1_forward` (OVER-ESTIMATED)"
]
},
{
"cell_type": "code",
"execution_count": 31,
"id": "fb94e4d4-68d8-4835-aa5c-3667798162ba",
"metadata": {},
"outputs": [],
"source": [
"k1_forward = 40. # Well above the known value of 18."
]
},
{
"cell_type": "code",
"execution_count": 32,
"id": "1db10d9c-96b1-4bf0-87ae-abc0cea690b4",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"282.1111111111108"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"k1_reverse = enz.compute_k1_reverse(kM, kcat, k1_forward=k1_forward)\n",
"k1_reverse"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "4adaea7e-f27a-42dd-a540-4fc88ca247a9",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": 33,
"id": "5fafa258-abcc-4d8f-824c-bde254c1f48b",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" name | \n",
" label | \n",
" plot_color | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" P | \n",
" P | \n",
" green | \n",
"
\n",
" \n",
" | 1 | \n",
" ES | \n",
" ES | \n",
" red | \n",
"
\n",
" \n",
" | 2 | \n",
" Adenosinedeaminase | \n",
" E | \n",
" violet | \n",
"
\n",
" \n",
" | 3 | \n",
" 2,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purine | \n",
" S | \n",
" darkturquoise | \n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" name label plot_color\n",
"0 P P green\n",
"1 ES ES red\n",
"2 Adenosinedeaminase E violet\n",
"3 2,6-Diamino-9-β-D-deoxyribofuranosyl-9-H-purine S darkturquoise"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"chem_data.all_chemicals() # Nothing changed here; same chemicals as before"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "e902907d-f06d-4f2d-8b09-0a4f63817317",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": 34,
"id": "86eceec3-5099-4bd2-838a-cf8207b43ee3",
"metadata": {},
"outputs": [],
"source": [
"rxns_overest = ReactionRegistry(chem_data=chem_data) # New set of reactions"
]
},
{
"cell_type": "code",
"execution_count": 35,
"id": "7cc40d06-d756-44b1-a55a-d556cfee46b2",
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Number of reactions: 1\n",
"0: E + S <-> ES -> E + P (Enzymatic reaction) (k1_F = 40 / k1_R = 282.11 / k2_F = 49)\n",
"Chemicals involved in the above reactions: {\"P\" (green), \"ES\" (red), \"E\" (violet), \"S\" (darkturquoise)}\n"
]
}
],
"source": [
"# Enzymatic reaction `E + S <-> ES -> E + P` \n",
"# In first part of the reaction, a forward rate that is much faster than its reverse one\n",
"rxns_overest.add_reaction(reactants=\"S\", products=\"P\", enzyme=\"E\",\n",
" k1_F=k1_forward, k1_R=k1_reverse, k2_F=kcat)\n",
"\n",
"rxns_overest.describe_reactions()"
]
},
{
"cell_type": "code",
"execution_count": 36,
"id": "fbc78df2-da88-4ed1-8878-2a6b2373d10a",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SYSTEM STATE at Time t = 0:\n",
"4 species:\n",
" Species 0 (P). Conc: 0.0\n",
" Species 1 (ES). Conc: 0.0\n",
" Species 2 (E). Conc: 1.0\n",
" Species 3 (S). Conc: 20.0\n",
"Chemicals involved in reactions: ['ES', 'P', 'S', 'E']\n"
]
}
],
"source": [
"# Here we use the \"slower\" preset for the variable steps, a conservative option prioritizing accuracy over speed\n",
"uc = UniformCompartment(reactions=rxns_overest, preset=\"slower\")\n",
"\n",
"uc.set_conc(conc={\"S\": S0, \"E\": E0}) # Small ampount of enzyme `E`, relative to substrate `S`\n",
"uc.describe_state()"
]
},
{
"cell_type": "code",
"execution_count": 37,
"id": "e99b906d-028d-43cf-ba69-13843903545a",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"864 total variable step(s) taken in 1.882 sec\n",
"Number of step re-do's because of negative concentrations: 2\n",
"Number of step re-do's because of elective soft aborts: 1\n",
"Norm usage: {'norm_A': 829, 'norm_B': 835, 'norm_C': 829, 'norm_D': 829}\n",
"System Time is now: 1.2001\n"
]
}
],
"source": [
"# Perform the reactions\n",
"uc.single_compartment_react(duration=1.2, initial_step=0.05)"
]
},
{
"cell_type": "code",
"execution_count": 38,
"id": "26359ff8-ceb7-4da7-97e2-9a0df0a5053b",
"metadata": {},
"outputs": [],
"source": [
"history_overest = uc.get_history() # Let's save the historical data for a comparison at the very end"
]
},
{
"cell_type": "code",
"execution_count": 39,
"id": "54e123a5-bcd9-4702-b7d7-8490390960ad",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"plot_pandas() NOTICE: Excessive number of vertical lines (865) - only showing 1 every 6 lines\n"
]
},
{
"data": {
"application/vnd.plotly.v1+json": {
"config": {
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"hovertemplate": "Chemical=P
SYSTEM TIME=%{x}
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},
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"showlegend": true,
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"uc.plot_history(show_intervals=True, \n",
" title_prefix=\"Using LARGER (over-estimated) value for k1_forward\")"
]
},
{
"cell_type": "markdown",
"id": "1bb0f414-d7d3-4166-ab16-21daee03c4d8",
"metadata": {},
"source": [
"At first glance, not too different from before, overall, but let's take a closer look"
]
},
{
"cell_type": "code",
"execution_count": 40,
"id": "26855833-c431-44e2-ad6c-d4fe370f3eff",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" SYSTEM TIME | \n",
" rxn0_rate_1 | \n",
" rxn0_rate_2 | \n",
" step | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 0.000000 | \n",
" 800.000000 | \n",
" 0.000000 | \n",
" 0 | \n",
"
\n",
" \n",
" | 1 | \n",
" 0.000500 | \n",
" 357.555556 | \n",
" 19.600000 | \n",
" 1 | \n",
"
\n",
" \n",
" | 2 | \n",
" 0.000750 | \n",
" 265.637774 | \n",
" 23.739956 | \n",
" 2 | \n",
"
\n",
" \n",
" | 3 | \n",
" 0.000763 | \n",
" 262.356893 | \n",
" 23.888118 | \n",
" 3 | \n",
"
\n",
" \n",
" | 4 | \n",
" 0.000769 | \n",
" 260.739940 | \n",
" 23.961149 | \n",
" 4 | \n",
"
\n",
" \n",
" | ... | \n",
" ... | \n",
" ... | \n",
" ... | \n",
" ... | \n",
"
\n",
" \n",
" | 859 | \n",
" 1.170211 | \n",
" 1.335790 | \n",
" 1.490884 | \n",
" 859 | \n",
"
\n",
" \n",
" | 860 | \n",
" 1.176184 | \n",
" 1.296873 | \n",
" 1.445487 | \n",
" 860 | \n",
"
\n",
" \n",
" | 861 | \n",
" 1.182158 | \n",
" 1.255105 | \n",
" 1.401986 | \n",
" 861 | \n",
"
\n",
" \n",
" | 862 | \n",
" 1.188131 | \n",
" 1.219475 | \n",
" 1.358993 | \n",
" 862 | \n",
"
\n",
" \n",
" | 863 | \n",
" 1.194105 | \n",
" 1.178798 | \n",
" 1.318155 | \n",
" 863 | \n",
"
\n",
" \n",
"
\n",
"
864 rows × 4 columns
\n",
"
"
],
"text/plain": [
" SYSTEM TIME rxn0_rate_1 rxn0_rate_2 step\n",
"0 0.000000 800.000000 0.000000 0\n",
"1 0.000500 357.555556 19.600000 1\n",
"2 0.000750 265.637774 23.739956 2\n",
"3 0.000763 262.356893 23.888118 3\n",
"4 0.000769 260.739940 23.961149 4\n",
".. ... ... ... ...\n",
"859 1.170211 1.335790 1.490884 859\n",
"860 1.176184 1.296873 1.445487 860\n",
"861 1.182158 1.255105 1.401986 861\n",
"862 1.188131 1.219475 1.358993 862\n",
"863 1.194105 1.178798 1.318155 863\n",
"\n",
"[864 rows x 4 columns]"
]
},
"execution_count": 40,
"metadata": {},
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}
],
"source": [
"rates_overest = uc.get_rate_history()\n",
"rates_overest"
]
},
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"execution_count": 41,
"id": "651f35be-fe04-41b7-a567-0697ae8e265c",
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Let's take a look at how the reaction rate varies with time\n",
"PlotlyHelper.plot_pandas(df=rates_overest, colors=\"blue\",\n",
" title=\"Reaction rate, dP/dt, over time\",\n",
" x_var=\"SYSTEM TIME\", fields=\"rxn0_rate_2\", \n",
" x_label=\"time\", y_label=\"dP/dt\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "3d98bdb0-2885-49f2-ad3e-aab03075683c",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": 42,
"id": "b1633906-9132-4e29-a944-59af34401280",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" SYSTEM TIME | \n",
" P | \n",
" ES | \n",
" E | \n",
" S | \n",
" step | \n",
" caption | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 0.000000 | \n",
" 0.000000 | \n",
" 0.000000 | \n",
" 1.000000 | \n",
" 20.000000 | \n",
" | \n",
" Set concentration | \n",
"
\n",
" \n",
" | 1 | \n",
" 0.000500 | \n",
" 0.000000 | \n",
" 0.400000 | \n",
" 0.600000 | \n",
" 19.600000 | \n",
" 1 | \n",
" 1st reaction step | \n",
"
\n",
" \n",
" | 2 | \n",
" 0.000750 | \n",
" 0.004900 | \n",
" 0.484489 | \n",
" 0.515511 | \n",
" 19.510611 | \n",
" 2 | \n",
" | \n",
"
\n",
" \n",
" | 3 | \n",
" 0.000763 | \n",
" 0.005197 | \n",
" 0.487513 | \n",
" 0.512487 | \n",
" 19.507291 | \n",
" 3 | \n",
" | \n",
"
\n",
" \n",
" | 4 | \n",
" 0.000769 | \n",
" 0.005346 | \n",
" 0.489003 | \n",
" 0.510997 | \n",
" 19.505651 | \n",
" 4 | \n",
" | \n",
"
\n",
" \n",
" | ... | \n",
" ... | \n",
" ... | \n",
" ... | \n",
" ... | \n",
" ... | \n",
" ... | \n",
" ... | \n",
"
\n",
" \n",
" | 860 | \n",
" 1.176184 | \n",
" 19.722714 | \n",
" 0.029500 | \n",
" 0.970500 | \n",
" 0.247787 | \n",
" 860 | \n",
" | \n",
"
\n",
" \n",
" | 861 | \n",
" 1.182158 | \n",
" 19.731349 | \n",
" 0.028612 | \n",
" 0.971388 | \n",
" 0.240039 | \n",
" 861 | \n",
" | \n",
"
\n",
" \n",
" | 862 | \n",
" 1.188131 | \n",
" 19.739724 | \n",
" 0.027735 | \n",
" 0.972265 | \n",
" 0.232542 | \n",
" 862 | \n",
" | \n",
"
\n",
" \n",
" | 863 | \n",
" 1.194105 | \n",
" 19.747842 | \n",
" 0.026901 | \n",
" 0.973099 | \n",
" 0.225257 | \n",
" 863 | \n",
" | \n",
"
\n",
" \n",
" | 864 | \n",
" 1.200079 | \n",
" 19.755716 | \n",
" 0.026069 | \n",
" 0.973931 | \n",
" 0.218216 | \n",
" 864 | \n",
" last reaction step | \n",
"
\n",
" \n",
"
\n",
"
865 rows × 7 columns
\n",
"
"
],
"text/plain": [
" SYSTEM TIME P ES E S step \\\n",
"0 0.000000 0.000000 0.000000 1.000000 20.000000 \n",
"1 0.000500 0.000000 0.400000 0.600000 19.600000 1 \n",
"2 0.000750 0.004900 0.484489 0.515511 19.510611 2 \n",
"3 0.000763 0.005197 0.487513 0.512487 19.507291 3 \n",
"4 0.000769 0.005346 0.489003 0.510997 19.505651 4 \n",
".. ... ... ... ... ... ... \n",
"860 1.176184 19.722714 0.029500 0.970500 0.247787 860 \n",
"861 1.182158 19.731349 0.028612 0.971388 0.240039 861 \n",
"862 1.188131 19.739724 0.027735 0.972265 0.232542 862 \n",
"863 1.194105 19.747842 0.026901 0.973099 0.225257 863 \n",
"864 1.200079 19.755716 0.026069 0.973931 0.218216 864 \n",
"\n",
" caption \n",
"0 Set concentration \n",
"1 1st reaction step \n",
"2 \n",
"3 \n",
"4 \n",
".. ... \n",
"860 \n",
"861 \n",
"862 \n",
"863 \n",
"864 last reaction step \n",
"\n",
"[865 rows x 7 columns]"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"history_overest = uc.get_history()\n",
"history_overest"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "c03e25cb-a16a-44cc-99cb-8ad287691870",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "38b07326-69fa-4a3d-96c5-c23827aeeb6e",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "75b6c550-9716-4766-86a4-bd4afe2226ac",
"metadata": {},
"source": [
"# Comparing the 3 scenarios"
]
},
{
"cell_type": "markdown",
"id": "27443513-5acd-4676-bddd-bedb837488e0",
"metadata": {},
"source": [
"#### The concentrations of the intermediate `ES` over time"
]
},
{
"cell_type": "code",
"execution_count": 43,
"id": "36fc0e0f-bc37-4bb3-88e3-e755c1d73cdb",
"metadata": {},
"outputs": [],
"source": [
"es_under = PlotlyHelper.plot_pandas(df=history_underest, \n",
" title=\"underestimated k1_forward\",\n",
" x_var=\"SYSTEM TIME\", fields=\"ES\", \n",
" x_label=\"time\", y_label=\"ES\", colors = \"yellow\")"
]
},
{
"cell_type": "code",
"execution_count": 44,
"id": "13df7a7f-c94e-4cf9-90ee-1c8e99ff5671",
"metadata": {},
"outputs": [],
"source": [
"es_exact = PlotlyHelper.plot_pandas(df=history_exact, \n",
" title=\"exact k1_forward\",\n",
" x_var=\"SYSTEM TIME\", fields=\"ES\", \n",
" x_label=\"time\", y_label=\"ES\", colors = \"green\")"
]
},
{
"cell_type": "code",
"execution_count": 45,
"id": "163c2f25-68f5-4361-ae0f-8e6f7e96572a",
"metadata": {},
"outputs": [],
"source": [
"es_over = PlotlyHelper.plot_pandas(df=history_overest, \n",
" title=\"overestimated k1_forward\",\n",
" x_var=\"SYSTEM TIME\", fields=\"ES\", \n",
" x_label=\"time\", y_label=\"ES\", colors = \"purple\")"
]
},
{
"cell_type": "code",
"execution_count": 46,
"id": "fd48ef57-477e-4974-85ee-4c315e6e7159",
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.plotly.v1+json": {
"config": {
"plotlyServerURL": "https://plot.ly"
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"PlotlyHelper.combine_plots([es_under, es_exact, es_over],\n",
" title=\"ES\")"
]
},
{
"cell_type": "markdown",
"id": "98e18ba1-38f7-44c4-bb7f-9cec4a059c66",
"metadata": {},
"source": [
"#### The concentrations of the product `P` over time"
]
},
{
"cell_type": "code",
"execution_count": 47,
"id": "4b961bd7-8c6a-47a2-9439-52675b39dc15",
"metadata": {},
"outputs": [],
"source": [
"p_under = PlotlyHelper.plot_pandas(df=history_underest, \n",
" title=\"underestimated k1_forward\",\n",
" x_var=\"SYSTEM TIME\", fields=\"P\", \n",
" x_label=\"time\", y_label=\"P\", colors = \"yellow\")"
]
},
{
"cell_type": "code",
"execution_count": 48,
"id": "030169b1-dc65-42b6-b830-4b32377f2ae9",
"metadata": {},
"outputs": [],
"source": [
"p_exact = PlotlyHelper.plot_pandas(df=history_exact, \n",
" title=\"exact k1_forward\",\n",
" x_var=\"SYSTEM TIME\", fields=\"P\", \n",
" x_label=\"time\", y_label=\"P\", colors = \"cyan\")"
]
},
{
"cell_type": "code",
"execution_count": 49,
"id": "a53f9f12-a597-4bf1-8ce5-5afb1053583d",
"metadata": {},
"outputs": [],
"source": [
"p_over = PlotlyHelper.plot_pandas(df=history_overest, \n",
" title=\"overestimated k1_forward\",\n",
" x_var=\"SYSTEM TIME\", fields=\"P\", \n",
" x_label=\"time\", y_label=\"P\", colors = \"purple\")"
]
},
{
"cell_type": "code",
"execution_count": 50,
"id": "75b29f07-2ccb-48aa-b755-738ed2183416",
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.plotly.v1+json": {
"config": {
"plotlyServerURL": "https://plot.ly"
},
"data": [
{
"hovertemplate": "underestimated k1_forward
SYSTEM TIME=%{x}
P=%{y}",
"legendgroup": "",
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"PlotlyHelper.combine_plots([p_under, p_exact, p_over],\n",
" title=\"P\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "bb0c74b1-8c3f-4bfd-8b97-23ca6cbc4ed7",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "2e52dba2-e39f-4af7-9051-b914a941fea7",
"metadata": {},
"source": [
"#### The Reaction Rate over time"
]
},
{
"cell_type": "code",
"execution_count": 51,
"id": "e64d60e2-1524-496d-b818-89398dc3eb63",
"metadata": {},
"outputs": [],
"source": [
"r1_under = PlotlyHelper.plot_pandas(df=rates_underest, \n",
" title=\"underestimated k1_forward\",\n",
" x_var=\"SYSTEM TIME\", fields=\"rxn0_rate_2\", \n",
" x_label=\"time\", y_label=\"dP/dt\", colors = \"yellow\")"
]
},
{
"cell_type": "code",
"execution_count": 52,
"id": "80750429-e2d5-4386-bdf0-1d530ca7fd90",
"metadata": {},
"outputs": [],
"source": [
"r1_exact = PlotlyHelper.plot_pandas(df=rates_exact, \n",
" title=\"exact k1_forward\",\n",
" x_var=\"SYSTEM TIME\", fields=\"rxn0_rate_2\", \n",
" x_label=\"time\", y_label=\"dP/dt\", colors = \"blue\")"
]
},
{
"cell_type": "code",
"execution_count": 53,
"id": "de6dbb69-6f8d-4048-ae30-75acd47c55bc",
"metadata": {},
"outputs": [],
"source": [
"r1_over = PlotlyHelper.plot_pandas(df=rates_overest, \n",
" title=\"overestimated k1_forward\",\n",
" x_var=\"SYSTEM TIME\", fields=\"rxn0_rate_2\", \n",
" x_label=\"time\", y_label=\"dP/dt\", colors = \"purple\")"
]
},
{
"cell_type": "code",
"execution_count": 54,
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"PlotlyHelper.combine_plots([r1_under, r1_exact, r1_over],\n",
" title=\"Reaction Rate\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "4d7055e8-d2d9-462a-8121-fd259a05a11c",
"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
}