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"## Coupled pair of reactions: `A <-> B` , and `A + E <-> B + E`\n",
"A direct reaction and the same reaction, catalyzed\n",
"### Enzyme `E` initially zero, and then suddenly added mid-reaction\n",
"\n",
"LAST REVISED: June 14, 2024 (using v. 1.0 beta33)"
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"Added 'D:\\Docs\\- MY CODE\\BioSimulations\\life123-Win7' to sys.path\n"
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"source": [
"import set_path # Importing this module will add the project's home directory to sys.path"
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"id": "087c0d08",
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"from src.modules.chemicals.chem_data import ChemData\n",
"from src.modules.reactions.uniform_compartment import UniformCompartment"
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"Number of reactions: 2 (at temp. 25 C)\n",
"0: A <-> B (kF = 1 / kR = 0.2 / delta_G = -3,989.7 / K = 5) | 1st order in all reactants & products\n",
"1: A + E <-> B + E (kF = 10 / kR = 2 / delta_G = -3,989.7 / K = 5) | Enzyme: E | 1st order in all reactants & products\n",
"Set of chemicals involved in the above reactions (not counting enzymes): {'A', 'B'}\n",
"Set of enzymes involved in the above reactions: {'E'}\n"
]
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"# Initialize the system\n",
"chem_data = ChemData(names=[\"A\", \"B\", \"E\"])\n",
"\n",
"# Reaction A <-> B , with 1st-order kinetics, favorable thermodynamics in the forward direction, \n",
"# and a forward rate that is much slower than it would be with the enzyme - as seen in the next reaction, below\n",
"chem_data.add_reaction(reactants=\"A\", products=\"B\",\n",
" forward_rate=1., delta_G=-3989.73)\n",
"\n",
"# Reaction A + E <-> B + E , with 1st-order kinetics, and a forward rate that is faster than it was without the enzyme\n",
"# Thermodynamically, there's no change from the reaction without the enzyme\n",
"chem_data.add_reaction(reactants=[\"A\", \"E\"], products=[\"B\", \"E\"],\n",
" forward_rate=10., delta_G=-3989.73)\n",
"\n",
"chem_data.describe_reactions() # Notice how the enzyme `E` is noted in the printout below"
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"### Set the initial concentrations of all the chemicals - starting with no enzyme"
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"SYSTEM STATE at Time t = 0:\n",
"3 species:\n",
" Species 0 (A). Conc: 20.0\n",
" Species 1 (B). Conc: 0.0\n",
" Species 2 (E). Conc: 0.0\n",
"Set of chemicals involved in reactions (not counting enzymes): {'A', 'B'}\n",
"Set of enzymes involved in reactions: {'E'}\n"
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"dynamics = UniformCompartment(chem_data=chem_data, preset=\"mid\")\n",
"dynamics.set_conc(conc={\"A\": 20.},\n",
" snapshot=True) # Initially, no enzyme `E`\n",
"dynamics.describe_state()"
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"### Advance the reactions (for now without enzyme), but stopping well before equilibrium"
]
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"execution_count": 5,
"id": "76f24d9a-a788-41d8-90a4-db87386f91aa",
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"Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n",
"7 total step(s) taken\n",
"Number of step re-do's because of negative concentrations: 0\n",
"Number of step re-do's because of elective soft aborts: 0\n",
"Norm usage: {'norm_A': 1, 'norm_B': 2, 'norm_C': 1, 'norm_D': 1}\n"
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"dynamics.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n",
"\n",
"# Perform the reactions\n",
"dynamics.single_compartment_react(duration=0.25,\n",
" initial_step=0.05, variable_steps=True)"
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"#dynamics.explain_time_advance()"
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"backgroundcolor": "#E5ECF6",
"gridcolor": "white",
"gridwidth": 2,
"linecolor": "white",
"showbackground": true,
"ticks": "",
"zerolinecolor": "white"
},
"yaxis": {
"backgroundcolor": "#E5ECF6",
"gridcolor": "white",
"gridwidth": 2,
"linecolor": "white",
"showbackground": true,
"ticks": "",
"zerolinecolor": "white"
},
"zaxis": {
"backgroundcolor": "#E5ECF6",
"gridcolor": "white",
"gridwidth": 2,
"linecolor": "white",
"showbackground": true,
"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": "WITH zero enzyme
Changes in concentration for `A <-> B` and `A + E <-> B + E` (time steps shown in dashed lines)"
},
"xaxis": {
"anchor": "y",
"autorange": true,
"domain": [
0,
1
],
"range": [
-0.00017082785808147176,
0.2601708278580815
],
"title": {
"text": "SYSTEM TIME"
},
"type": "linear"
},
"yaxis": {
"anchor": "x",
"autorange": true,
"domain": [
0,
1
],
"range": [
-1.1111111111111112,
21.11111111111111
],
"title": {
"text": "Concentration"
},
"type": "linear"
}
}
},
"image/png": 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""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_history(colors=['darkorange', 'green', 'violet'], show_intervals=True, title_prefix=\"WITH zero enzyme\")"
]
},
{
"cell_type": "markdown",
"id": "9a793ebf-f544-43ad-a1d3-059f74f3c02b",
"metadata": {},
"source": [
"### The reactions, lacking enzyme, are proceeding slowly towards equilibrium, just like the reaction that was discussed in part 1 of the experiment \"enzyme_1\""
]
},
{
"cell_type": "markdown",
"id": "27401e5d-8f3e-4c27-8438-129d3e3408a2",
"metadata": {},
"source": [
"# Now suddently add a lot of enzyme"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "713dae1e-1c51-4d95-8439-c79d9dcce2e3",
"metadata": {},
"outputs": [],
"source": [
"dynamics.set_single_conc(30., species_name=\"E\", snapshot=True) # Plenty of enzyme `E`"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "e80645d6-eb5b-4c78-8b46-ae126d2cb2cf",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SYSTEM STATE at Time t = 0.26:\n",
"3 species:\n",
" Species 0 (A). Conc: 15.43679907511829\n",
" Species 1 (B). Conc: 4.56320092488171\n",
" Species 2 (E). Conc: 30.0\n",
"Set of chemicals involved in reactions (not counting enzymes): {'A', 'B'}\n",
"Set of enzymes involved in reactions: {'E'}\n"
]
}
],
"source": [
"dynamics.describe_state()"
]
},
{
"cell_type": "markdown",
"id": "0b46b395-3f68-4dbd-b0c5-d67a0e623726",
"metadata": {
"tags": []
},
"source": [
"### Take the system to equilibrium"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "dde62826-d170-4b39-b027-c0d56fb21387",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n",
"30 total step(s) taken\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': 22, 'norm_B': 20, 'norm_C': 20, 'norm_D': 20}\n"
]
}
],
"source": [
"dynamics.single_compartment_react(duration=0.04,\n",
" initial_step=0.005, variable_steps=True)"
]
},
{
"cell_type": "markdown",
"id": "b4f7e3b5-e4b5-4dd8-a8c3-4e0c231ecdb9",
"metadata": {},
"source": [
"#### Note how the (proposed) initial step - in spite of having been reduced from the earlier run - is now appearing _large_, given the much-faster reaction dynamics. However, the variable-step engine intercepts and automatically corrects the problem!"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "b0543cac-f3cd-453c-ae9b-c00f01e61fa8",
"metadata": {},
"outputs": [],
"source": [
"#dynamics.explain_time_advance()"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "8cc14786-cc9f-4399-9203-290526d3a326",
"metadata": {},
"outputs": [
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Changes in concentration for `A <-> B` and `A + E <-> B + E` (time steps shown in dashed lines)"
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Xeo5iHUnfR1GymjTeLslq3EV7Ug7l3lfVeD3t70uT51SL8THFD7Jq7xoR7JqEzdgL/ohoqm9EHcd5WeUXGrIXeqKssottcQtecIZNK2blw8qx4F5/6XdLC7+wcuWmDPFjs2F3Nn057Ms/2IawMmFTl2R+GQ774uAdVfZcojpWWJuCbQ/mO4ZNP+AX2qd4uWp80RR2zKipCmHTIYMXZuWOK36QsmOxnD6+iXVFTRnjZcS+Jk55YxfFTzz9gr+4TXAT+3HU1E4e26gPlXLnx46ZJM7BkUp+DmKfU2kD+1AU34uy72XZD09R1vj7qVK55Ox4ukGSesT2J5XWOFlNa2pP8PMz6n3J83T2mLAjXXnjf5ZOO0p2gp957HOUfb7KfKbJ9gmxnJhHFCVQKvXaJqs6JDV4/jqkNYp10l/3XZLVqJkzUdPB+Xsm7Ed3/jl3mPejfNj7LPh9EvWDhcw1h8r3Pn/flvu+9K+thMXz+DGCs0VUruHC6pP9kSUsBiIzUVZfWbxk0Pd51GdV8DMzWC7sh8WwPhIU5UraEoxhXJ+Svf6K6hfB6wH+mS7yjLreCZsJFVZWLCcy++6Pr/e/P/gWdn0h0++i+ic/F5lrgWDOqo5r8LD3VVhbgn0v6hra1h+UnJdV1YsL8U0jBjTsQ4J9aLMPfnFRj7CL3ah8uLBk6jC5jppexfYPCm/wwjPsIlVW4KPeKOxCPOy4sh/yYcdnHwbsQ4P/WhMWt6jn2AeN+MaK+lUuLDaM7Z33/740qhSW5xk8rvjBFSan4odi3Btb7GvBD0j22lZbjhy0+EsYt7hpwGGyKstVpc9GfQFFLRag2gb/SyClVVuDX+pJLoR1jKSWk55KjxElq3ESW64t5V5n8Q/26zAx5l+S4udH1KhEWN9JErNy5xB8/+rgZYuspiGpcdKqOlob9d2t+p0edtHtyjTguHzxuJG7KLFg35Vh7zPGSOb9J3PNEfWekrkWifu+DEtZCHvvx13Dsbbxa4ywKfWynyVh5YLnJ76/ROmMk8sw2RWfi4trmNjxz1+VtpQTyuB1sez1V1S9UddlwVksjNvHn3w6KK1Ipk+x4waPIcqs+B0Vds0k2++iUjRUfgCXlVXZa3BxVhBfMyV4HRk2+zQu3STtUe9y38lRrzsvq6qjBlHTgOOkQITHgywKS7kRLv7mj/vyCXbicnks/PhRx2ZvwL0//3ext/WI+1UnOAVAdvq0zNSYqC+ssDdJ1BTG4HnL/BoUFWN+XP6FE/dmlfmw4f1FlhkvH2wHe15FVlW4yvbZuA+WMFnV0YZKP8zC9guLgepnhvjFl5ZUB9se9WNCuQvFqNdNtZuzEo8X96OGOD253ChTGiOrwfeBTFpJuf6pQ1bjjiETS/4DgapAlju3qNejLpbj6otbYEn2h9Go93xSWY1qt+4F2uLy/iuR1bDp/lHvv0qvOeKkJGz6oHgtEvc9HdVO9hn+8t/eLElouWsj/jkR933/4l9fj11ZPO4Y7PyZGETFJ+z6Ier7NtjGIB9x8S12XJ7KEWSi0hZVWQ3rU7JTRVWuB6LaFUw3iromZCz5yu9RsQ9rj2y/izquynWezPWj7LVZ3OeD+LkS954TmYn8bVyPBLJajFC5zh18I4kXTrKdK048gp046o0RFBr+RqlkBa80ZFVG+uPe3MHzlpVVmQ+MuA9Y8QPRlKxGTfWK+wVV7IfB81HhKttnVWVVRxsqvWAO2092dkPcMSuR1bBpSirv0UplNWzKVNivr7oYB6d38XrFX7NlZTWqT8r8AFbJ+ajM0Ij8ESBk2mJUWRlxjPvFW+UcK5HVMHmU/YGgUlll5xSWGxU2whd2/lGfoWFlZc5FduRNJRblPkOj+oUuWY36DpX9rg37ETXqRwKW2hL3ORd14Rx3rsEfwOK+Y8TPGnF6pMwPPOI58WPG/TihIohRn4FhdYjXIqwdCxa9RXwaLv9cZbE7/KB9SnKm0haTshoVq6jP3qgUI/HHK/7dWG6dmrBbsgX7n2y/i7smlLn25Mx1ymq5gQz+44b4GSmbYgVZ1fUJL9Qj+6XGd1EZWeVf+OIFYFjnlr3wl/2QZW3lx5a58Am7YJS5MEpDVmXeuHHSGJwCJiurMr/0xf2SzzjzDz8TssrbIl5AhR233AeS+Eu2ClfZPlvuQiv4haGjDbo+JsJyOcS6Zd4jYvlKp+iqnE+lxyg3fVV1NLlcm8UvQPFCMKy/yspq1Hs9LVkN+0FBPG8ZuQnjpGNkVbVvlhM5HfXpPkbcdN8k0si+g5KOrFYa+3Lvm+DrwVEj8XXTsqpyzVFOeKI+Z6NktdxnNauPX2irXEeF1Sv7o2HY54PMVOrg97jMIlri+1OcGs7eI0xUWSoaF9SvHrKfvzZKuetSxkxlSmfUFOQkI6tR1wNRo89s+mvwsyrs+0P8nuR9rdxUbFYu2P9k+92yjz7x10wJ+1yQueZNQ1ajfijmxxJ/aAn7US/uhxjIquonuUT54PzscrvIyqrKL4CyF/4qH7JJOgsXoXK36EhDVm0fWWX9o9yqqGnLqsqvoCqyqmNUM8kHL2Orow3l3sOyr6uIs2ydrFylQhl3DLFO2V8/xfrKyWrSPMBg22U/R9l+tspqlBzzNste1AbZ2CKrvF3ihYouaRXrrHTKblyfTDLC7JKsmpgGrDKyqvtWZMFrkXLXVeWuWeK+Y2TEjH9uVfI+4J/RXFhUvsdVRlbF73wmpaKksx9h+AJa4o+EKm0p90NDubVc+HegzIqxsrKqcs0V1n7+QwtnVW6mJO9nYWl9YfWr/nAUxTiNkVXVWQOsbZxP1Gd3Ev9QuZZSKev8NGDeicpNPWG/IsTduibYuVXyp2RlVSVfQ1YaWLlfXjJ4GWzZkYg0ZLXctAqWU6CSxyA7siozL19GpNmbR+WDM+7DLiqGKufPy4YJjGzerkoOjWy/i5IQlXOTGQ1X+TATy5bLPSwndzLH1SGtSSWVt7Pc+egeWZXNwVKR1ai+J/t5JhOzoMBFXbSq/gga/OHAxvus6pBWHZLKWWFktfDDF9vCfkCNm36rMgomK6sqn/1h7zWZa5G478sooZP9oSz43RPWnrjPI/E4YfsGv0dVBFHl81K8phX7RtTzrIxKW0zKalzeMBNx/vkb9xkfllsdvOYNxl5WVmX7Q1w5lfeNTlmV/V5kLNho/G67jB8U+nKphpX8oKPyHaxa1nlZZSfMO2rYsHbwlz3ZEYGwX3bFL+pKclZZW8O+oKPm4EdNcWbl2dQQJt/8/MRfV2QvtNKQVXaO/HxEwWJtEhdJCGt3GBtZWeVs2a99IovgxUDYcdm+rH3s1hpsuo2KrFbyIRYmUmKuhvghEdeWsC9AWa6yP7DEfaDEjZgF4xDV72V+nVX9UGPly8lbOZlVOSZnrjoiGvY+UTmuWDbufCttX1xbwo4nTpurJGe13PtC59TMcp+RSUb2bBtZDcaRf+6rjohyJqr7RfWjKFmV+QE6rm+6NLJa7gfUqO+/NGSVf5eFXUeJ1xxx8Qx+7oe9z6K+N3i/DF4ks88F8U4CYXWGfXbwcmGr95f7LAn7bA5+5qkIYth7J+4zho8Uht3ahjEOMlJpi0lZ5X0qOJgUllMf9oMqLyd+5oRdF/N48Ws/FVmV7XflvvNkRjh1yiq/bmV54sEZCeyc2O2UmNTzdot9Ka7vxQ38VHp9omO/mpBVDoJflIlggm8SWVlldYhyyv7N6uKJ7pXKqihVvJ1xN6MPm5sfdluZYGeQeeOkJauiLIjtCraJx4KXibvPavCX53KyxesM++INHpeX5e1TldVgPwm7z+pm8QkszMLaye9tG/wiCuZV6LzPaqWrPvMvoagLV5nYpjmyKjPtNfgFp+MDtVp1xOVf6l7BlJ9j8Jis37ItuLCF7DRgtm9wgQ3Wdtbfo/KFKuUtM9Is04fCjq9DVuPOS+azvVIuJvcL+77mx0/yq74OWY3ioPu9VG7qavD9IHOf1eB3pezIKj9nmWuOKD5hea/B/hr1fRn2/g/rD/y7hd/fMq7PhJ2LzFTjsOs09pz4I1wlghjkEyXNUd9NUT9KVtKWYAxVfgBR/e4OnjfjKI6s8rYEy7G+E/z+CFuEKfi+VJFV2X7HyoV957Hb7TBhlPlc1i2rrE1RebdiPw+75o3re2kNIiT5fqkpWU0Copr7yq62V8024tggAAIgAAIgAAJ6CahMI9R7ZDdrAy8344ZW208gycJ2aZ8dZDVtwoH6xemm/CXVX6kMNxmHAwEQAAEQAAEQSImAzEh/Sod2rlrIqnMhQ4MdIWDz5xBk1XAnChuOr3TVScNNx+FAAARAAARAAAQ0E4hbd0PzoZyvDrLqfAhxApYREKfmy0xnrkbzIavVoI5jggAIgAAIgAAIgAAIgAAIgAAIxBKArKKDgAAIgAAIgAAIgAAIgAAIgAAIWEcAsmpdSNAgEAABEAABEAABEAABEAABEAAByCr6AAiAAAiAAAiAAAiAAAiAAAiAgHUEIKvWhQQNAgEQAAEQAAEQAAEQAAEQAAEQgKyiD4AACIAACIAACIAACIAACIAACFhHALJqXUjQIBAAARAAARAAARAAARAAARAAAcgq+gAIgAAIgAAIgAAIgAAIgAAIgIB1BCCr1oUEDQIBEAABEAABEAABEAABEAABEICsog+AAAiAAAiAAAiAAAiAAAiAAAhYRwCyal1I0CAQAAEQAAEQAAEQAAEQAAEQAAHIKvoACIAACIAACIAACIAACIAACICAdQQgq9aFBA0CARAAARAAARAAARAAARAAARCArKIPgAAIgAAIgAAIgAAIgAAIgAAIWEcAsmpdSNAgEAABEAABEAABEAABEAABEAAByCr6AAiAAAiAAAiAAAiAAAiAAAiAgHUEIKvWhQQNAgEQAAEQAAEQAAEQAAEQAAEQgKyiD4AACIAACIAACIAACIAACIAACFhHALJqXUjQIBAAARAAARAAARAAARAAARAAAcgq+gAIgAAIgAAIgAAIgAAIgAAIgIB1BCCr1oUEDQIBEAABEAABEAABEAABEAABEICsog+AAAiAAAiAAAiAAAiAAAiAAAhYRwCyal1I0CAQAAEQAAEQAAEQAAEQAAEQAAHIKvoACIAACIAACIAACIAACIAACICAdQQgq9aFBA0CARAAARAAARAAARAAARAAARCArGroA10beqlrY5+GmlCFKwTaWxqouamB1qzb5EqT0U5NBLYc3kJr1vdSb19OU42oxgUCLU1ZGtrWRKs6e1xoLtqokcCojmba0NNP3Zv6NdaKqmwnkM1kaMzIFlq+utv2pqJ9mgl0tDX6NbJr+7Gj2zTXjupUCUBWVYmFlIesaoDoWBWQVccCprG5kFWNMB2qCrLqULA0NxWyqhmoI9VBVh0JVArNhKymADVBlZDVBPD4rpBVDRAdqwKy6ljANDYXsqoRpkNVQVYdCpbmpkJWNQN1pDrIqiOBSqGZkNUUoCaoErKaAB7b9ac//Smd94MfYRpwQo6u7b70rUX00bIPaP8DD3Ot6WhvQgImZPWl+X/2W7nXPl9K2Nr62P25eX+kIUOH0cRJX0jthGtJVp/+w2O0zdhxtMuEianxqqWK5z7xIO3yud1p7PY71dJppXYuv/vtbNp7nwNom223T+0YJio2Jav/fsuvKJ/rp4w37ZgoQ9lsljqGj/Ae56mpsZkam9iU1Ay1tw+hrq5O79rjPdpv8sG0fl0nvb54IR197DfpiUcfoOknn0l33nYdnXjyWbR0yRv00Ycf0IGHHEGrVq6gp598lI6bPsPHtnDBC/6+rA6+8f2aW1pKz8V9D93261/Q6ef8MDQMrH0vzn+Wjjp2emyYZt91Cx05bTp1DBteNpyVfGZ1da6lR+bM9rmoblxWr7nqcpo5c6bq7iivmUDdy+pFl99KDz3x7CCsi+bOGvTvY2ZcTG8tXeY/t/P4benBWZeVXoesau6RjlQHWXUkUCk0E7KaAtSEVSANaIsAACAASURBVEJW1QBWcuGndoTaKg1ZVYsnZFWNF2QVsqrWY+qvdN3LKhPRSy84lSZO2NGP/g2/eYDue/gpembODf6/v33elbRqdWdJUFn50aOG0R3XXOC/DlmtvzcNO2PIan3GnZ01ZNW+2ENW1WICWVXjBVlV4wVZVeMFWYWsqvWY+itd97IaDPnCxUto+tk/o9k3XeIL7JRp59L5Z51A0w6f7Bed8/g8uvrme0syy55Dzmr9vXGQs1p/MednbEJW65euvWdeS9OA7aVsZ8uQs2pnXNJulalpwGmfB+pXJ4CcVXVmae4BWQ3QZSOpby75wJfRoLiyomHPQVbT7KJ21g1ZtTMuJloFWTVB2b5jQFbti4mpFkFWTZG26ziQVbviYbI11ZTV4AxOk+ed9FhhjpS0TrY/ZLVIkY2grl7T5f+L56zKympPbz9t6sU9F3V0SFfqaGrMUkM2g/vuuRIwje1sb230457L5TXWiqpsJ9DQkKHmxgba2IN7atseK93ta/Puq93bl6e+fnzP62Zrc31swaMhrQ20zrvXZlpb7v0+yt2H+7imxTdpvdkDmmn4IUOSVjNofzYo9vxLiwc9N2pER2nGZjVklc0avfiK2+myC08rzSSt5KQhq5VQq2AflrN6890P+cIqI6ssZ/XCH/0YsloBa5d3ee3VhfTB++/RoYcd6fJpoO0VEDAhq3959hm/ZfsfMKWCFtbfLnOfepKGdQyjvb6wT2onX0uy+vvHfkfjttuedtt9j9R41VLFjzz037TrbnvQZ3b6bC2dVmrncv/se2i/L02m7bbbIbVjmKjYlKzeOPtaynl/Ge+PbVnvb3imkMfZ5P01en/stXbvr8v7+yD/AU3JTKF13t+r+Vfp69mv0+9yv6MZ2Rl0S+4W/79v59+mD72/QzOH0ife35O5J+nE7Il+nS/nX/b3ZXXwje/XQgOrAT+ff95/ed/Mvpvhvj53PX03+93QMLD2zff+jsscFxumWblZdFz2OBrm/ZXbnsw/SWO9v10zu5YrWnq9kzrpgdwDPo9KN3aeOlcD3m3qDBLFlLeLCexWW4ykn//oDKqGrFbKJ7gfZFUXSYl6WGeKy1llvz7w0VcssCQBtAaLYIGlGgyq5CmZmAaMW9dIBqNYDAssqfHCAktqvLDAkhovLLAkzyu7rJ/u+O31lMt4surN3sCta8LZVfKZZduta8Q0w7gewmWVleEjsFGCK47Qcm9h+7HZopP3mUjz5i8szRo966Sv0XbbjvFHUPnG9wmTzOAIMNv/3FOP8xeeDY4Mx81IlX83RJes+2nALKB85V+Gid3KhgUXqwHr6F61WwdktXZjW+7MIKvlCJl/HbKqxrySCz+1I9RWaciqWjwhq/K8IKv1c59VNhD2ta8c4I+elpNVdrtMLodcPj+747jSnUiCdyoRZ4Xy8iy1kcsofz043ZiVZbfjDMpqUKzZ69fedr9/fPba90//RukuKkyuo+qRfyfEl6x7WRXvocpRqdxnle2DBZZ0dUd36sECS+7ESndLTciq7jajvuQEsMBScoau1oAFllyNXLJ2m1hgiclqy4O91D82S5umNSdrMPbWRkD3AktcBmVyQsOmAbOBtFffeDdULPlJs8G3448+yB/95COrXIzDRk7FwTnxdVYfuyuKTFtZWfGWn5gGrK0L6q8Isqqfqe01QlZtj1B67YOspsfW5pohqzZHJ922QVbT5Wtr7ZBVWyOTfrtsllW+GFIYBT4aGyWrooBGSebb737oTxUODtyJxxMXpeXPR631oyNadT+yqgMiZFUHRbfqgKy6FS+drYWs6qTpTl2QVXdipbulkFXdRN2oD7LqRpzSaKVuWWVtVJkGPHrUsNKUX7avOLLKZbWcTLKc1eDIqg5ZZeex714TSu0rtzCtjvhAVhNSxAJLCQE6ujtyVh0NnIZmm5BVLLCkFijkrKrxQs6qGi/krKrxQs6qPC/krNZPzmq5BZaYkEatBhw2DThumm6SkVXWe6OmAYeJMmRV/v1etZKQ1aqhr+qBIatVxV/Vg0NWq4o/9OCQVbWYQFbVeEFW1XhBVuV5QVbrR1b56GpwZV8ugHzxpXI5q6weviKvOLrKhHbfvXb175OaRFYnTtjRv33O6jWdpcVm+QJLbGGloMiykVa2YRqw/PveeEnIqnHkVhwQsmpFGKrSCMhqVbDHHhSyqhYTyKoaL8iqGi/IqjwvyGp9yaoommIvEUdJZWQ1qh4ur0llldUfXICWt5FJ8UNPPFtqPsuTvfnuhyCr8m/76pREzmp1uFfzqMhZrSb96h7bhKxW9wxx9DACyFmt336BnNX6jD1yVusz7uys08hZrV+ayc8cOavJGeLWNRoYulYFZNW1iOlrL2RVH0uXaoKsuhQtvW2FrOrl6UptkFVXIqW/nZBV/UyT1AhZTUKvuC9GVjVAdKwKyKpjAdPYXMiqRpgOVQVZdShYmpsKWdUM1JHqIKuOBCqFZkJWU4CaoErIagJ4bFfkrCYE6OjuyFl1NHAamm1CVrEasFqgkLOqxgs5q2q8kLOqxgs5q/K8kLNafzmr8r0DJTkByGrCvgBZTQjQ0d0hq44GTkOzIasaIGquArKqBhSyqsYLsqrGC7IqzwuyClmV7y31WxKymjD2kNWEAB3dHbLqaOA0NBuyqgGi5iogq2pAIatqvCCrarwgq/K8IKuQVfneUr8lIasaYo+cVQ0QHasCOauOBUxjc03IqsbmoipNBJCzqgmkg9UgZ9XBoGloMnJWNUB0tArkrNoVOMiqhnhAVjVAdKwKyKpjAdPYXMiqRpgOVQVZdShYmpsKWdUM1JHqIKuOBCqFZkJWU4CaoErIagJ4fFfIqgaIjlUBWXUsYBqbC1nVCNOhqiCrDgVLc1Mhq5qBOlIdZNWRQKXQTMhqClATVAlZTQCP7Yqc1YQAHd0dOauOBk5Ds03IKlYDVgsUclbVeCFnVY0XclbVeCFnVZ4XclaRsyrfW+q3JGQ1YewhqwkBOro7ZNXRwGloNmRVA0TNVUBW1YBCVtV4QVbVeEFW5XlBViGr8r0l3ZK7TZ1BO4/flh6cdVm6B6qgdshqBdDEXSCrCQE6ujtk1dHAaWg2ZFUDRM1VQFbVgEJW1XhBVtV4QVbleUFWIavyvSW9kjf85gF68pkXafWaTvq3n3+fJk7YMb2DVVAzZLUCaMFdkLOqAaJjVSBn1bGAaWyuCVnV2FxUpYkAclY1gXSwGuSsOhg0DU1GzqoGiI5WUW85q8fMuJgOnbI3vbzoTdpqi5H08x+dYVXkIKsawgFZ1QDRsSogq44FTGNzIasaYTpUFWTVoWBpbipkVTNQR6qDrDoSqBSamaqsrlhA1LMmhVaXqXLMJKKWEZsVWrh4CU0/+2c0+6ZL6O13P6Srb76Xnplzg/n2xRwRsqohHJBVDRAdqwKy6ljANDYXsqoRpkNVQVYdCpbmpkJWNQN1pDrIqiOBSqGZqcrqfQcRvT83hVaXqfL4p4i2m7pZIT4FmOeqstxVJq42TQWGrCbsLshZTQjQ0d2Rs+po4DQ024SsYjVgtUAhZ1WNF3JW1XghZ1WNF3JW5XkhZ7UOc1bnfp+Ija6a3qZeS8RGVwMbnwJ87qnH+a98+7wrrZsKDFlN2FkgqwkBOro7ZNXRwGloNmRVA0TNVUBW1YBCVtV4QVbVeEFW5XlBVutQVuW7R+ol+RTg4IFGjeiwaiowZDVhV4CsJgTo6O6QVUcDp6HZkFUNEDVXAVlVAwpZVeMFWVXjBVmV5wVZhazK9xb9JYNTgPkR2FTgyy48jaYdPln/QSuoEbJaAbTgLshZ1QDRsSqQs+pYwDQ214SsamwuqtJEADmrmkA6WA1yVh0MmoYmI2dVA0RHq0g1Z9UiJlOmnUvHH30Q8SnAvGlsKjDb7rjmAitaC1nVEAbIqgaIjlUBWXUsYBqbC1nVCNOhqiCrDgVLc1Mhq5qBOlIdZNWRQKXQzHqR1RTQpVIlZFUDVsiqBoiOVQFZdSxgGpsLWdUI06GqIKsOBUtzUyGrmoE6Uh1k1ZFApdBMyGoKUBNUCVlNAI/tipzVhAAd3R05q44GTkOzTcgqVgNWCxRyVtV4IWdVjRdyVtV4IWdVnhdyVpGzKt9b6rckZDVh7CGrCQE6ujtk1dHAaWg2ZFUDRM1VQFbVgEJW1XhBVtV4QVbleUFWIavyvaV+S0JWE8YespoQoKO7Q1YdDZyGZkNWNUDUXAVkVQ0oZFWNF2RVjRdkVZ4XZBWyKt9b6rdkVWSVrT61ek1XKPVFc2c5Fw3krDoXssQNRs5qYoTOVmBCVp2FU8MNR85qDQe3zKkhZ7U+Y4+c1fqMOztr5KzaFXvjsnrMjItp9Khh1iyHrCMckFUdFN2qA7LqVrx0thayqpOmO3VBVt2Jle6WQlZ1E3WjPsiqG3FKo5WQ1TSoVl6ncVm17UazlaMb2BOyqoOiW3VAVt2Kl87WQlZ10nSnLsiqO7HS3VLIqm6ibtQHWXUjTmm0ErKaBtXK64SsVs7O3xM5qwkBOro7clYdDZyGZpuQVawGrBYo5Kyq8ULOqhov5Kyq8ULOqjwv5KwiZ1W+t9RvSeOyyqYBHzplbzr31ONqgjpktSbCqHwSkFVlZDWzA2TVvlBCVtViAllV4wVZVeMFWZXnBVmFrMr3lvotaVxW5zw+j66++V56Zs4NNUEdsloTYVQ+CciqMrKa2QGyal8oIatqMYGsqvGCrKrxgqzK84KsQlble4v+kgsXL6HpZ/9ss4ovu/A0mnb4ZP0HrLBG47LKclbjNqwGXGEksZtRAshZNYrbqoOZkFWrThiN8QkgZ7V+OwJyVusz9shZrc+4s7Oul5xVLquzb7qEJk7Y0Q/4RZffSvPmL7RqUNG4rNZi18cCS7UY1fhzgqzWX8z5GUNW6zP2kNX6jDs7a8hqfcYeslqfca93WWUzYC++4nayafAQsqrhvQhZ1QDRsSogq44FTGNzIasaYTpUFWTVoWBpbipkVTNQR6qDrDoSqBSamebI6oLlC2hN95oUWh1f5aStJ9GI1hGDCoWNrH77vCv9Mndcc4HxNkYdsCqyyq1dbJRt86NlI4ScVVlStVUOOau1FU+VszEhq1gNWCUiRMhZVeOFnFU1XshZVeOFnFV5XshZrb+c1YPuPIjmLp0r30k0lXzqlKdo6vipobIaPMRZJ33NqoVwjcvqDb95gG6++yES50dzs7cNjkz/gKzKUKq9MpDV2oup7BlBVmVJmSsHWVVjDVlV4wVZVeMFWZXnBVmtP1n9/u+/T2x01fR27WHXEhtdFbewkVVMA/YITZl2Lh1/9EGbGTuT2PsefsqqhF6ZjgRZlaFUe2Ugq7UXU9kzgqzKkjJXDrKqxhqyqsYLsqrGC7IqzwuyWn+yKt870i8ZJqvsqGwxXHFQMf2WxB/B+MgqAxA25ddGk5cNDnJWZUnVTjnkrNZOLFXPxISsqrYJ5dMngJzV9BnbegTkrNoamXTbhZzVdPnaXHuaOas2nXeYrPIZsHW9wFKtjayyTgdZtemtZ6YtkFUznG08CmTVxqik3ybIavqMbT0CZNXWyKTbLshqunxtrr3eZDUYC5tElbXN+MhqreWsQlZt/rhJr22Q1fTY2l4zZNX2CKXTPshqOlxdqBWy6kKU9LcRsqqfqSs11ousuhIP47LKwGA1YFe6B9oZRQA5q/XbN0zIKlYDVutfyFlV44WcVTVeyFlV44WcVXleyFlFzqp8b6nfklWRVZtws/sJPf/S4kFNCg5/HzPjYnpr6TK/zM7jt6UHZ11WKo8FlmyKprm2QFbNsbbtSJBV2yKCW9eoRgSyqkYMsqrGC7IqzwuyClmV7y31W7LuZZXl0D4z54ZSD7jo8ltp3vyFpeeYzK5a3VkSVCauo0cNK90sF7Jan28eyGp9xp2dNWTVvthjZFUtJpBVNV6QVTVekFV5XpBVyKp8b6nfksZkla0CzO6jyu6xGrdVO6k3uDIWk9nzzzqBph0+2W82m8J89c33DhJcLLBUf28g5KzWX8z5GZuQ1fqla++ZI2fV3tik3TLkrKZN2M76kbNqZ1xMtAo5qyYoyx/DmKzKN6m6JcX7vYYt6Rz2HGS1ujGrxtEhq9WgbscxIat2xMF0KyCrponbczzIqj2xMNkSyKpJ2nYdC7JqVzyMy2rUfVZFSawWIi6i/D6wUrL64q8o/+J1lPf+qGko5Vu38Juf9x+PLpxKYyvl2rcqPG5ooXzb1oUyDa2UH1J8PtPoPR5XeD7rPR66bbUw4LgSBJoas9SQzVD3pn6J0ihSSwTaWxv9uOdy3nseW90QaGjIUHNjA23s6aubc8aJFgi0tTRQb1+e+vpzQFJHBDKZDA1pbaB1G9N7z+fe76Pcfd2UGddADSe01RFdu0+1uSnrN3BTb4462pvsbmwdtM4aWeUrBFdrGjAXUzZV+dxTj/NDLyOrLGd15tCfpNNVGpo9oW33JLiN8o3ef73H+Sbvv41DvP96H2rec/7z4n/Z88VyhX1ZmZCyzd7z7HVPnrGpE3jt1YX0wfvv0aGHHam+M/ZwmoAJWf3Ls8/4jPY/YIrTrEw1fu5TT9KwjmG01xf2Se2QtSSrv3/sdzRuu+1pt933SI1XLVX8yEP/Tbvutgd9ZqfP1tJppXYu98++h/b70mTabrsdUjuGiYpNyeqNs6+lXCZHGe8HMfIEuSGbpeHDR/in2NTcTI2NTexpGjJkKHWuXUvvv/8uTT3oUOrs6qRFC1+hE078Fs357f102hnfoRuvv4ZOO/Of6K033/CvUQ474ihaseJjesJ7z3/rlFP9Ol96Yb6/L6uDb3y/lpbW0nNx30PXXHU5nfeDH4WGgbXvuT/Po29M/4fYMN1+6410/AnfomHDh5cNZyWfWYzVfff+h89FdeOyesXll9LMmTNVd0d5zQSskdXgwkaazzO2Oi7Ks2+6hCZO2HFQ2bCc1YuvuJ24VDNZPf9736H167oo07eBMr3e//q9/7HH/RuFf3uP2fPsdfYafz3scZ9Xtm99sZz3ONeTDo5sgy+s+QZPhpnUsv8y8fVl13vM/uv9O1d6vSC+/vPNnjCHli++zutjQsw+ZWtswwJLNRZQhdMxMQ0Yt65RCIhXFAssqfHCAktqvLDAkhovLLAkzwsLLGGBJfneUr8ljchq2H1Vw5Dz6bcmwxG2YJJ4/KqvBpzvD4gvE9kNlPVltvC4IMfFx4Mk2CvTW5RkJs5cjFlZX5yLdXivpbUVhFaQYPa4yRNdX4qLzwdfL44UD7wuSLIg0jlfiD0Z9qZNm94gq6aJ23M8yKo9seAtgayqxQSyqsYLsqrGC7IqzwuyClmV7y31W9KIrIp4o3JWqxECPs23nDjH3WeV7ev0Akv5fEFcw0aBNwVGiUNGgbPiSHJJnoVRZL/e9R6ldPL78v5U6fAR4YERY0F2xRFkLsWDxFko67/ORooHpsXwvoIFlqrxjrXjmCZk1Y4zRStEAlhgqX77AxZYqs/YY4Gl+ow7O+t6WWApzoPEtMhq9wTjslrtE07j+E7LahpAAnUWRLgosMHpz+Job+QoMRshLgo1G1X2R4V5fYX/Ui6lBRAy2eJ0aD4KXBgRzrQMpYwnvr0Zb5Esb3Q3x0eHg+IbN1VamErtzZU2EAkcQgcByKoOiu7VAVl1L2a6WgxZ1UXSrXogq27FS2dr601Ww9IgdfJMWhdkNSlB10dWNZx/tatgOb2byXBpxJdPf+ZTnqOmTIu5xKIMFyW5f1Nqp1kYAR7IEY4dEfbziIvizKZTl6ZSh4wI8/xjVj6L1ex0BRCyqoukW/VAVt2Kl87WQlZ10nSnLsiqO7HS3VLIqm6iyeozLqtxQ87sVKq1GnClGNkCS2xFtK4UlzavtG3YTxMBb9Q2Wxr1Lcju2++8Qx9+vIqmTtxKyAUuTpsWRoE3m17Nco3563whLj+HuFtTYzevholqaWEsPrXZ/29Rdou5v6Uygxbb4otvRU2lLqxMnc9uPlU6tROqcsUmZBULLKkFGTmraryQs6rGCzmraryQsyrPCzmr9Zez2r/cu/Vdt/nbYDVu3UiZ1sGz+MLueiLfe82VNC6rbHXdyftMpH332pWuvvleembODf7ZsrzQQ6fsXbptjDkEyY4EWU3Gz9W9tS6wlPeWrOeLZJUWveLiOzB9OsumU2/yZJeXHSS7fGS4kCPsS3JgWnVqrNlUaT79mYuvxOJZOb7QFl9hWhTpkBFj8o5jwwZZtSEKg9sAWVWLCWRVjRdkVY0XZFWeF2S1/mS1664u6ns3pdS1mK439KSh1DR+8Cw75KxGAOMLLO20w1j6p4uuLclquVV55d/6ZktCVs3ytuVoWmXVwEkVVn8WVoEurQ4tSC1fZIuvNF281ZIvyWH5xIHVpcmT7rQ2NnK72VRpP+c3YsQ37HZLwdszlfKM2erU8lOlIatpRbnyeiGrauwgq2q8IKtqvCCr8rwgq/Unqxuf2Eh9y83LavtX2qlh64ZBnRMjq2Vkddrhk4mJK5/2y29v49o0YHaaWGBJ/oO5VkpiNeDBkWTTmP3bJ5VGe8V7DgdWhy7dg7h4L+Gw2yqxhbTEvOM0F9HyTiVyqrSYI1wcPW4b0kHd+VbqYwLt30qpcD/i0ugyf26zxbXaaqX71+V5IGe1LsPunzRyVusz9shZrc+4s7NGzqpdsTc+DZhN9911lx3o5z86w5/6yx9fdPmtNG/+wtJIq12Y4lsDWXUpWnraClnVw1GpFi93uGH9stIujevfLT1u6BIer39v4Pl14mOxzDLK5Au/bDZs8OpMazXpwAnmWkd7UjvUfzbXPNz73wj/cV583OI93zS88HxDC+VatyrV0t+xw8Djli38vGO/XNNQr9xoJZworEYAsqrGq5ZKQ1ZrKZry5wJZlWdVayUhq3ZF1LisBk+fja7yzfalk6NCB1m1q1ObaA1k1QRl88fwZbgorkxiudBmveczxec7aBV1b9xAuVyeshs/9kaTe/yGNnQvJ+orPvafLyyale1e5Y06rzN3MtlG6m/fdkBq27Yq3StYlGLKNgwux/bJFKYI5doEEfbuM9wfIczmTqr6R4KsVj8G1WoBZLVa5Kt7XMhqdflX8+j1JqthrHGf1Wr2QM3HRs6qZqCOVOdazqojWJ1oZpKcVV9cewvimu1Z5a0yXXwceP65JQXRPWBspy+7bGPizKSZbw2CEGc2raHsprXG+YkjxXlvwax+b7S3cHKDhTnnC3OL/xIbNWbSzLa8Vy43RBBr73GeGguvtYzwR59lNuSsylAaKIOcVTVeyFlV44WcVXleyFmtv5xV+d6BkpyA8ZFVvsASy1mthQ2yWgtRVD8HyKo6s1rZI4msyjJIcusaNqKb3fBx6VCDRogFKWb3J2Yjw3xrEKZMZ7tXeqPB6wve6Qk1F2byhFmcii17PknL5b3RXSa8fOsbOjAdmgnzHz8eTx3NvfSFrdYNGi0WxZjt29+2NVFjQZrzmcFCXW4qdS2NrEJW1XokZFWNF2RVnhdkFbIq31vqtyRkNWHsIasJATq6O2TV0cBpaLbtsqrhFKWr8KdB9xWnO/eu9UZ31xT2DeQX+3nB+f6C/HrlMj2FUWBfrEVhZtOti7nEKtOnf99zOA3PrqH9mp6Tbnu5goXR4ML9g5nY5oduSw0NGerty/u5wrnW4igyO11h5JiV7x+yfan6oASz0Weea+yXFfKQy7VJ1+uQVTWSkFU1XpBVeV6QVciqfG+p35LGZdXV+6nGdRHkrNbfGwg5q/UXc37GJmS1fumGnznL+c1uLEyHZpu4uJYozMHRYlGM2X7iYlpMisVR4mpNpRbPODiCzEaNc8UFuVg5NmWaiTPb/MW3hNHmXAtbvKuw4Bbb+tn0am+adaHs4LxjlSnW6ItYDbhe+wByVus18vWzGrArETYuq+yePuL9VV0BFddOyGotRFHtHCCrarxqqTRktZaiufm5ZHK9numx2y31FG/H5N2WyZsy3Uw91N7QR51dXYXnc/x2TV654q2byCtXuo0Te8zubeyVI2/02X/e30d47L1O/nNeWa+86S3f0OwJLbsFU0vxXsPe40b278L/iD32X2fPe/ciZuXYLZnYa3wf9lq2uL+/n3eLJm+qdeneyOy14n2S/WP5dXrHdWjDAksOBUtjUyGrGmE6VlW9LLDkSliMy6q4+m8YJNxn1ZWuU9/thKzWb/whq/UZ+1RzVvO5gswyQfZFWRBc//miPItS7N/XuCi+TICZFPuvB6SY3wPZl+Zi/VyQvXrJO7bRLZMtyuuACJek2BfiwfI8SIqLEs3l2X/NF2Au0sXH3nN+nb5Ie/9rKvyXvGNXskFWK6Hm/j61KKurvRkqf1n2J3p99avU433erPDWN1jvLfrHnpfZPvHK9xRXupcpH1dG5bhJj1Xp/ufvczH98ohLK90d+2kiYFxWNbXbmmqQs2pNKIw2BDmrRnFbdTATsppkgSWrYBlqDFYDVgPNc1b/bpe/K4hxacRXkGImslxuuRQL/y2NFgdEuiDNwqh0QJ79Y/VvUmuwhtJsNJeN6vqju02e3LL/slHf4mN/NJiNGpdeZ/8uyO8jb7TRhLFNNH7L9sGj0Hz0WZRoYRS6MGrt1iiyBtSEnFV5imnnrG41aQd6/s1nqPNvn9B/tf03vfXp67Sf9zfC+3vc++PbhXQh/cr76/b++DaVpvoP53p/we0nVPgL28bTeG/PqTTL+4vb/pn+2S+zxvsrt02jabTU+1vg/clu7BxneH/svCrd2DnOnDmz0t2xnyYCxmU1ajXgG37zAN338FP0zJwbNJ2amWogq2Y423YUyKptETHXHsiqOdayR4KsypIqlKvqAkv+KLIwzVoc8RWl2J8uXSjnjxgHpdiX7BAp5qPP/ii1sJ83Eu0NI6uBKpa+t3s6fb5xAX2u8TW1/b17GRem+xQXywAAIABJREFUUQvTrL1RXl9iRSn2R4GZKHsrVXORDpmaTVyEmWSXpLg4Jbs4PZtP4/aGkdXaqrE0ZFUeZhqyOunIyfSfz/yGuldvoPv776OtvT8mezd7f0OahtIxQ46l7Vq2p+adh9AoLy9+G2/xuDcfXUC7HDaJGpoKee5sW/HaB/5/t5kw3i8jbo/fdS8dfvIJoSe6evkKeuuVRbTPVw6iUW2j/WOGbbPvuoWOnIYFluR7S/2WtEZW5zw+jy6+4nZybRowZLU+3zyQ1fqMOztryKp9sYesqsWkqrKq1lRtpVlOMMsNLuQjF6dP82nT7DmWM8wF2R8NLk6Z9h4/sphot9EbaMeOzmJOMp9q7Qkwn7rN9+HTs/36WL1eDrThrZBDzCRWyDcW84oHSTHPI+Yjzp4wh4o0m1pdHH0Wp1gXH/vHyjb5ZwpZlQ+4Tlk98Lij6MG77qKrclfR57w/NsL54rCX6e9HHUS7rNyJ9j/qy7TbFnvQwgUv0Pp1nbTf5INLDb3ztuvoxJPPouaWwq292BY3w+e2X/+CTj/nh6En+tGy9+jF+c/SUcdOjwUBWZXvJ/Ve0hpZvejyW2ne/IXOjayyDoQFlurvbYSc1fqLOT9jE7Jav3TtPfNUc1btPW20zCNQcc6qd7smfzEuJrTCglylkWK+2JY4vToo0mw/f6GuomhvJsXsdT6Ve+BYlK9sFLnigGe8UWQ2usuFVsg9LkyHFhbvYjnGTJjFkWI+ulwsV1qMi+cdc0H2Jbw4Xbt4rIrbXGZHl3JW53/4LJ35+D/4OagtHrOTJ55GZ0763mYjommxqrV6scCSXRE1Iqt81LTcqV924Wk07fDJ5YpZ9zpk1bqQpN4gyGrqiK09AGTV2tCk2jDIaqp4ra68Ylmt0lnxxboKC27xlauF0WQ2hVpcnKs0XbqwyJc/+hyUYv857zU/57jw2Bfwokiz59j9lU1vpQW5/FWoi9Op/VWrBx6XpFhYzZrL82YiLeyXaWqnkSM6aOX6TGkVbL4iNr8tVNLzZSOrLQ/2Uv/YLG2aVll+8/9bNIsuevq71Ofxn7LdwXT9l39DY9q3Stq0ut4fsmpX+I3IqnjKUTmrdmFRaw1kVY1XLZSGrNZCFCs7B8hqZdxc3wuy6noEK2+/a7Ja+Zkm3zPbvcoT2HWlisR7IrMFuxo2Li+9lu3xyvatL/27cB/kfv/fTLjZPZT5lt20hrKb1gbKmpdjkRC7D3JeuA9y39AdBl72Rn37W7cu/btQVrgPcruXA8pGo1dvSfTiVMpv0UXdx3uPFTa2Ku/MZ35Id//tdn+vs/b8Z7po/59RY/H+ygpVoWiAAGTVri5hXFbtOv3krUHOanKGLtaAnFUXo6anzSZkFasBq8UKOatqvOoxZ1WN0ODSc594kHb53O40dvudklRTN/saz1n1RhQb1nuiW9yyvWs9sR1YYTbrvZbho77e1GxfioWymR5Bgrs9mWYjyN6WyfdR88YPqT9XmFKd6VtHTMZ1br39X6KrNn6Vcpk+z10b2FEom81Sx/AR3uM8NTU2U6O/6FGG2tuHUFdXJ7GcUJZv+vjiOdS6qpnuabiHTm86g0497XziuadLl7xBH334AR14yBG0auUKevrJR+m46TP8piNntXwEuaxec9XlWA24PK7US0BWEyKGrCYE6OjukFVHA6eh2ZBVDRA1VwFZVQMKWVXjBVlV42VcVtWaJ126XM4qG/ll06X5Jo4isxHj7MaVpdc2G0Ve957/Wm7ttnT9Ox2UI09WG+VlNfeZBpr/zp9pT+9v4iH70Uf/u4Smn3wmZFWIblfnWnpkzmyfi+oGWVUllm75qsjqlGnn0uo1XaFnhtWA0w04atdDALKqh6OLtUBW7YsaZFUtJpBVNV6QVTVe9SKralTCSze+vYJuf+weZVl9MvMkDc0Ppf0bD6Dj/s8p9MSjD0BWA4ghqzp6qB11GJfVY2ZcTKNHDaM7rrnADgIaWoGcVQ0QHasCOauOBUxjc03IqsbmoipNBJCzqgmkg9UgZ9XBoGlocrmRVQ2HoOwHvdTyUL+XZzqPNpy8G/W3b1O22u//4Uy6b/HddOTOx9Kth99TtjwKqBNAzqo6szT3MC6rWGApzXCiblMEIKumSNt3HMiqfTEx0SLIqgnKdh4DsmpnXNJulRFZLa4GzGS1+/gtqHfUpNjT+tN7f6Dv/M8MavAWZ7rxK7PoS+Ompo2hLuuHrNoVdsiqhnhgZFUDRMeqgKw6FjCNzYWsaoTpUFWQVYeCpbmpkFXNQB2pzrSsbjoqTz3jvhxL5/w/nk2zX72TTp90Dv1k8i8cIeleMyGrdsXMuKyyacCHTtmbzj31OLtIVNgaLLBUITjHd0POquMBTNB8E7KK1YDVAoScVTVeyFlV44WcVTVeyFmV58Xus3rHb68v5Kxmvf28285ErQb8ae5TWrzsFdo+vz1t//nP0vDMcHp98UI6+thvImc1BDlyVuX7oe0ljcvqnMfn0dU330vPzLnBdjZS7YOsSmGquUKQ1ZoLqfQJQValURkrCFlVQw1ZVeMFWVXjBVmV5zVYVnOerDZHyupf17xETMDGe3/s1jXr13VCVmNQQ1bl+6HtJY3LKstZjduwGrDtXQbtYwQgq/XbDyCr9sUesqoWE8iqGi/IqhovyKo8r0GymuknamgJldUVGz6m+Sv/Qts2jaMte7eArEoghqxKQHKkiHFZdYSLUjORs6qEqyYKI2e1JsJY0UmYkNWKGoadUiWAnNVU8VpdOXJWrQ5Pao0znbPaOu4n9MlR80LP55D//AK9tupVP0+V5atiS5cAclbT5ataO2RVlVhIeciqBoiOVQFZdSxgGpsLWdUI06GqIKsOBUtzUyGrmoE6Up1ZWf0zDRnxj/Tx/1lM+cYhgwi9tHw+Hf1fU2lM+1b03CmLqaWh1RGC7jYTsmpX7Koiq2yRpbeWLvNJXHbhaTTt8MnEpgfvu9cEJ++/Clm1q1ObaA1k1QRlO48BWbUzLmm3CrKaNmF764es2hubNFtmUlYbml6gYU1foRXTXqS+ERMGnda//ul8uuOVm+jcvX9AF+7/0zRPGXUXCUBW7eoKxmWVieroUcN8KZ0y7Vw6/6wTfFm94TcP0H0PP+XcwktYYMmuDm2qNchZNUXavuOYkFWsBqwWd+SsqvFCzqoaL+SsqvFCzqo8r8E5q5u8BZa8nNWGJuoYPsKrJE+NjU00/+NnqTfXS1N2PJioh+ijZe8hZ1UCMXJWJSA5UsS4rLIR1Nk3XUITJ+w4SFbZKsEXX3E7YYElR3pOnTcTslq/HQCyal/sIatqMYGsqvGCrKrxgqzK8yrJqre4UoaZKFsNuKG5JKs9+R7668qXqK2pnabu9GXq6uqErErihaxKgnKgmHFZZaOp//bz728mqxhZdaC3oIklApDV+u0MkFX7Yg9ZVYsJZFWNF2RVjRdkVZ5XUFYz2SbKeCsC85HVT7o/oXe63qKxHePo89vuDVmdMFEaLmRVGpX1BY3L6kWX30rz5i/0p/vyacA77TCWpp/9M/raVw6gn//oDOuhBRuInFXnQpa4wchZTYzQ2QpMyKqzcGq44chZreHgljk15KzWZ+xN5qzSyBU0sudztPEzx9OnB84qAT/jsW/SI2/PoWsPuYWOn3BSfQaiCmeNnNUqQI85pHFZZW3hU37Fdp110tfo3FOPs4uOZGsgq5KgaqgYZLWGgql4KpBVRWA1UhyyWiOBrOA0IKsVQKuBXUzKan6LtTRqw2do05j9aOVX/+jTW71xFX31/sn08brl9NgJf6bPjd61Bqi6cQqQVbviVBVZtQtB8tZAVpMzdK0GyKprEdPXXsiqPpYu1QRZdSlaetsKWdXL05XaTMpqbqseGt21DfW3j/VuX/Oal7vaSE+9+z/0rYePoS9usz/N+fofXMFWE+2ErNoVRuOy+u3zrqTnX1q82UJKrt66BqsB29WhTbUGOaumSNt3HBOyitWA1eKOnFU1XshZVeOFnFU1XshZlec1kLOa8xdYyngrAGca26ljxCj6ZMPH9MH692hMxza088hdqL19CHJWkbMq37lqqKRxWWV5qscffdBmU36xwFIN9ao6OBXIah0EOeIUIav2xR6yqhYTyKoaL8iqGi/IqjyvwbLa68mqtypwY6snq1vQ+53v0MqelbTT6F1oqyHbQFbHjqNdIKvynauGShqXVTaCetmFp/n3VhU33LqmhnpVHZwKZLUOggxZdSbIkFW1UEFW1XhBVtV4QVbleYXKqnfrmrbhI2nJp2/Sxnw37bH1ntTeNASyClmV71g1VtK4rNbayCrrD8hZrbF3hcTpIGdVAlKNFjExslqj6Jw+LeSsOh2+RI1HzmoifM7ubDJntX9sllq3+780dOHV1DXpYvrtiL3olN99nfYfO4X+67jfO8vQ1YYjZ9WuyBmXVTbd9+a7H6LZN13i32uVbQsXL/FvXePqisCQVbs6tYnWQFZNULbzGJBVO+OSdqsgq2kTtrd+yKq9sUmzZaZltWnCnTT8L9+jDTufRP/avD1dM/8yOnPS9+iSyT9P8zRRdwgByKpd3cK4rLLTD7t1TdjUYLtQRbcGsupKpPS1E7Kqj6VrNUFWXYuYnvZCVvVwdLEWyKqLUUveZtOymv3iUzTqf46lnq0PpCN72+gP7z5O/3bYnXTMZ7+R/GRQgxIByKoSrtQLV0VWUz8rgwfAasAGYVt0KOSsWhQMw00xIatYDVgtqMhZVeOFnFU1XshZVeOFnFV5XoNyVrNEmVy3t3OePsp0ev+fp89uMYGGtg71nssgZxU5q/Idq8ZKQlaLAeVTkcXpyTzWx8y4mN5ausz/587jt6UHZ11W6gaQ1Rp7R0ieDmRVElQNFoOs2hdUyKpaTCCrarwgq2q8IKvyvAbJakOGMv3d1J/vow9pDQ1t7qCdR/8dNTY1Qlb/8BhtA1mV71g1VrIqssoWWVq9pisU5aK5s4wjFtsTlFV2X9hVqztLgsrEdfSoYXTHNRf47YSsGg+XFQeErFoRhqo0ArJaFeyxB4WsqsUEsqrGC7KqxguyKs9rM1n1RlZ7c3203JPVLdrH0Ljh20NWPZyVfGZ1da6lR+bMpuknnykfkGJJPg34mqsup5kzZyrvjx30EjAuq0HZ03s6ldcWNbLKRPb8s04o3WqH5dteffO99MycG0oHQ85q5dxd3RM5q65GLnm7Tchq8laiBt0EkLOqm6g79SFn1Z1Y6Wyp6ZzVTdOaadSTX6eD3nyMnusn+o+jH6SDdviyzlNCXZIEkLMqCcpQMeOyGnWfVUPnG3mYMFmVfQ6yWu3omT8+ZNU8c1uOCFm1JRJm2wFZNcvbpqNBVm2Khrm2VENWh8z/F9p6/r8Ry1x948wVNKSJ5atiM00AsmqaePzxIKtFPrJiGlaup7efNvXm7IosWpMqgabGLDVkM9S9yfv5E1tdEWhvbfTjnsvl6+q86/1kG7x8subGBtrY01fvKOru/NtaGqi3L099/fier6fgZzIZGtLaQOs2pveez73fR7n7uikzroEaTmijl5/9Vzrwz1fSnu0j6envfFxPuK061+Ymb7Urb2PX9h3tTVa1rR4bY1xW2TTgQ6fsTeeeepxVvCuVVZazeuGPfgxZtSqa6TfmtVcX0gfvv0eHHnZk+gfDEawiYEJW//LsM/4573/AFKvO3dbGzH3qSRrWMYz2+sI+qTWxlmT194/9jsZttz3ttvseqfGqpYofeei/adfd9qDP7PTZWjqt1M7l/tn30H5fmkzbbbdDascwUbEpWb1x9rWUy+Qo4/0gxhZX2ugtspRpWEfbjd6NmpqbqbGxiTxvpiFDhlLn2rX0/vvv0tSDDqXOrk5atPAVOuHEb9Gc395Pp53xHbrx+mvotDP/id568w3/GuWwI46iFSs+pie89/y3TjnVx/bSC/P9fVkdfOP7tbS0lp6L+x5iuZzn/eBHoWFg7Xvuz/PoG9P/ITZMt996Ix1/wrdo2PDhZcNZyWcWY3Xfvf/hc1HduKxecfmlyFlVhZdCeeOyGpbzmcJ5KVepkrN68RW3E18ICgssKaOuiR2wwFJNhLGikzAxDRi3rlELDRZYUuNVyWIlakeordJYYEktnlhgSZ5XcIGl3lwv9eR6qDWzhkaPnkhNTS1YYMnDWclnFhZYku+Htpc0LqssZzVuq8ZqwKw9UbKK1YBt78LVaR9ktTrcbTgqZNWGKAxuA2RVLSaVXPipHaG2SkNW1eIJWZXnFZTVntwmbzXgTTQiu4Y6OnakhvZRkFXIqnyHqtGSxmXVRo7BW+mMGtExaLXfuPussvPBAks2RjXdNmGBpXT52ly7CVm1+fzrtW1YYKleI0+EBZbqM/bVWGDpiHu/RK988jL9qY1o0l4XUNeeuG1KNXofFliqBvXoY0JWNcQDsqoBomNVQFYdC5jG5kJWNcJ0qCrIqkPB0txUyKpmoI5UZ1pW1x7VR/vc+Xe0pns1vdOep63GHUqrvvyQI7Rqq5mQVbviWRVZZXmrLO9T3C678LTSvUztQlS+NZDV8oxqrQRktdYiKn8+kFV5VrVUErJaS9FUOxfIqhqvWiltWlYXHbiEpt6zF23fMY7eadnoYczTJ0fOo/6O8bWC1JnzgKzaFSrjsnrDbx6gm+9+iGbfdAlNnLCjT4Pni5510tesWyW4XLiwwFI5QrX5OnJWazOuMmdlQlaxwJJMJAbKIGdVjRdyVtV4IWdVjRdyVuV5iTmruWyONvVvIvJuizeuuYcym7ooO2I8ZYdu7VWYofb2IdTlreL70bL3aL/JB9P6dZ30+uKFdPSx36QnHn2App98Jt1523V04sln0dIlb9BHH35ABx5yBK1auYKefvJROm76jMI194IX/H1ZHXzj+zW3tJSei/seuu3Xv6DTz/lh6Imy9r04/1k66tjpsSBm33ULHTltOnUMK78acCWfWVhgSb4f2l7SuKyy/NDjjz5oMyllEnvfw08NyhW1HR5rH2TVhSjpbyNkVT9TV2qErNoXKciqWkwqufBTO0JtlYasqsUTsirPa5Cserev2eQtrpTNNtA2bRnKbvyYGoZsSZmRO0FW//AYbTN2HO0yYaI0XMiqNCrrCxqXVbYacNiUXz41uFqrAVcaKchqpeTc3g+y6nb8krQespqEXjr7QlbVuEJW1XhBVtV4QVbleYmy2pfppz7v1jWNDY00ZmgbNXQtpcaWdqIt2f2QMbIKWZXvV7VW0ris1trIKusQyFmttbdF+fNBzmp5RrVawoSs1io7l88LOasuRy9Z25Gzmoyfq3ubzlk9o/1M+u0b99IvD/o3+tb4L9OWv5tM1L+RVh41j/qG7ewqRifbjZxVu8JmXFZrLWcVsmpXhzbVGsiqKdL2HQeyal9MTLQIsmqCsp3HgKzaGZe0W2VaVr+aO4L+98O/0OxjfkdTtjuYRj35dWr94DH69MBZtPEzx6d9uqhfIABZtas7GJdVdvpYDdiuToDWqBOArKozq5U9IKu1Ekm184CsqvGqpdKQ1VqKpvy5mJXVDO2xZnf6aN0y+vNJC2n88J2oY8Fl/v/W7fZd6vziFfINR8nEBCCriRFqraAqsqr1DKpcGXJWqxyAKh0eOatVAm/BYU3IKlYDVgs0clbVeCFnVY0XclbVeCFnVZ6XmLPane+mTCZDbU1DaNjwEZTd1Elt616nhpah1LvF3lgNGAssyXesGisJWU0YUMhqQoCO7g5ZdTRwGpoNWdUAUXMVkFU1oJBVNV6QVTVekFV5XlxW+72VgHs8Wc1msp6stlOHJ6sZb7Glts5XqYm6qW/Lfah12BjcugarAct3rhoqaUxWea5q2L1U416znTVk1fYIpdM+yGo6XF2oFbJqX5Qgq2oxgayq8YKsqvGCrMrzGpDVfk9We6jBu21Na2ObL6tEeWpbv4Raej6mvlG7UcvonSGrkFX5zlVDJY3J6jEzLqbRo4bRHddcEIrv2+ddSatWd9KDsy5zDi9WA3YuZIkbjJzVxAidrcCErDoLp4YbjpzVGg5umVNDzmp9xt5kzuq7He/Tnms/T9/Z63z60QH/twS8469XUsfLP6X1u/4Trd3nl/UZiCqcNXJWqwA95pDGZDXq/qq8ba7eZ5W1H7JqV6c20RrIqgnKdh4DsmpnXNJuFWQ1bcL21g9ZtTc2abbMpKy+0fYW7bd+H/r51Ovo5N1PL51W8yfzaYtHplLfyF1pxTEvpHm6qFsgAFm1qztAVjXEA7KqAaJjVUBWHQuYxuZCVjXCdKgqyKpDwdLcVMiqZqCOVGdSVhc2/40O7P57uvvo39LBOxw2QCjXR9v8v7GU6VtHK76+kPo6dnKEntvNhKzaFT9jsjpl2rl0/lkn0LTDvZsch2xsZPXqm++lZ+bcYBehMq1BzqpT4dLWWOSsakPpXEUmZBWrAat1C+SsqvFCzqoaL+SsqvFCzqo8L56z2kd9tMn7a21opYaGxlLOalNjM7Wuf5saN7xPLaN2pNVN4+mjZe/RfpMPpvXrOun1xQvp6GO/SU88+gBNP/lMuvO26+jEk8+ipUveoI8+/IAOPOQIWrVyBT395KN03PQZfsMWLnjB35fVwTe+X3NLS+m5uO+h2379Czr9nB+Gnihr34vzn6Wjjp0eC2L2XbfQkdOmU8ew4WWBVfKZ1dW5lh6ZM9vnorpxWb3mqstp5syZqrujvGYCxmT1ostvpVffeDcyJ7VcTqvm89ZWHWRVG0qnKoKsOhUurY2FrGrFqaUyyKoaxkou/NSOUFulIatq8YSsyvMSZbU300stTFa9RZb4AktMVptz66h51QvU3pSjT0Yd4snq+5BVCcSQVQlIjhQxJquMBxtdZVtw9JQ9v3pNFy2aO8sRbAPNhKw6FzItDYasasHoZCWQVfvCBllViwlkVY0XZFWNF2RVnpcoq32ZPl9Ws9nsIFltbGqklhXPUUffclrZ8UX64NNeyKoEYsiqBCRHihiVVcaEjbA+9MSzg/Dsu9eEyFWCXeCInFUXoqS3jchZ1cvTpdpMyKpLPOqlrchZrZdIb36eyFmtz9ibzFmdl59HN33mdrr9q7NDYbe/dTeNmHcm9W6xN3164CzkrqbcJZGzmjJgxeqNy6pi+5woDll1IkxaGwlZ1YrTqcogq06FS1tjIavaUDpXEWTVuZBpabBpWX3480/QTyb/IrTtmVwPjZx7CrW+9xB17fmv1PX5i7ScIyoJJwBZtatnQFY1xAOyqgGiY1VAVh0LmMbmQlY1wnSoKsiqQ8HS3FTIqmagjlRnWlZf+tJrdPqkcyLptC19gEb+aQb1DduZPv37f6feUZ93hKR7zYSs2hUzyGrCeCBnNSFAR3dHzqqjgdPQbBOyitWA1QKFnFU1XshZVeOFnFU1XshZlecl5qxSA1FDpjE0Z5UoQ+3tQ6j7g/n03rp2mrrDRlo1cgpWA45BjZxV+X5oe0nIasIIQVYTAnR0d8iqo4HT0GzIqgaImquArKoBhayq8YKsqvGCrMrzEmU105ChbKYhVlbXr1xKy1auoy93/IVWbPN1WvzuKty6JgI3ZFW+H9peErKaMEKQ1YQAHd0dsupo4DQ0G7KqAaLmKiCrakAhq2q8IKtqvCCrCrw+6KNZc27w7rLaR9nGrDd+mo2V1a6uTv8+q4e1PE6rhu1Pr3SOgaxCVhU6nJtFIasa4oacVQ0QHasCOauOBUxjc03IqsbmoipNBJCzqgmkg9UgZ9XBoGlosomc1TVvf0Lb/L6Dns88T7udOdm/x2q5rbHrbRrz2z39YqsO/m/qGfflcrvgdUUCyFlVBJZycciqBsCQVQ0QHasCsupYwDQ2F7KqEaZDVUFWHQqW5qZCVjUDdaQ6WVn9aN0y6sv1+WfV099Nn2z4uHSGa3vWUmfPmtK/Wdn+fL//7z7vv40fEl380Q/phYYXPVn9kjSZjgWXEftfvnEofXLkXOobuav0vihYngBktTwjkyUgqxpoQ1Y1QHSsCsiqYwHT2FzIqkaYDlUFWXUoWJqbClnVDDSl6tb3rqPVG1eVal/dvYo2eM/x7f3Od0uPe/p7BkklK7u+d/1gqfQEtKkpS13dGwaX9Y7BjqVj+xJ9iR7OPkwLmxfRzqftrVTlyKdPobZ37veF9dOpd1L3uCOU9kfhaAKQVbt6B2Q1YTyQs5oQoKO7I2fV0cBpaLYJWcVqwGqBQs6qGi/krKrxQs6qGi+Ws7rjHhOoY8sR/o79+T5iI4p8Y1K4euPK0r9XeCORmzx5ZBsbbRxcdrCAslFLNnoZJqBqrdRXepuh21JjttGvkK3my/7Nt+Etw2lYS4ED28a0b0UtDS3Fsg00qXcSvfPSYurP5CjrLbDEVv3NZrPUMZztk6emxmZqbGJ1F1YD5jmr+00+mNZ3rqI3Fr1M/9hyC83uPpG+fcAQ+vX/DqUTTz6Lli55gz768AM68JAjaNXKFfT0k4/ScdNn+MdduOAFWr+uk1gdfLvztuv8/ZpbCm1jW9z30G2//gWdfs4PQyGynNoX5z9LRx07PRby7LtuoSOnTaeOYcPLBqOSzywssFQWqzMFIKsJQwVZTQjQ0d0hq44GTkOzIasaIGquArKqBrSSCz+1I9RWaRdlNZ/PU0+um3r6eqi7byN1e4LX3ev923/Oe+w9x0YX2eON/YXH3b3sv8XX2X/ZPn5Z/nhgH16nv59fV7F+778n5U+iud7fUu/PxJbxRK6loZVam1oL/2X/ayw+bmrzn2OC2NrY5r/mPy4+z55j/2Zl2vznvMdZVlcbtXl1bD1yGK3fkKVW/7lCnaVjec/J5JjGMeCrAec8WWWrASvJqiecry9eSCdM7KWHX/qUvtd+LV2x8V/pmyedRkveXw5Z7VxLj8yZTdNPPlO5G/KR1WuuupxmzpypvD920EsAspqQJ2Q1IUBHd4esOho4Dc2GrGr4JEJTAAAc/0lEQVSAqLkKyKoaUMiqGq+kssryGX2hy4lCWJRIQSgLwlco50ukIJTdvlAOCKEvn0WJLMhnQUTZ/uw1JqniCKTaGVdeurGhiU7JnUwvNL9IK5tXFcSOi6MolL4kDohjSSKLz/v7FPdrE4TSl8xsQTzZ676YehLZ7D2ne5PNWU1yXB2yevSx36T/eege+l7rlXTVp2fTuSPuoFe2OJOWZnelv//yMRhZhawm6aJW7AtZ1RAG5KxqgOhYFchZdSxgGptrQlY1NhdVaSKAnFVNIKtcTUn4mNgJI4wFSWQjiAWh5MLHJLGhsZc6N26g9ZuKI5SiRBZHFdl+BbkcEEo+Msn+yxfgMXn6g0YNi3LHRxhLEsmFj4njoNFITwgbvJFI/7kBOSyMOvLRSyaMxZFIv/7CCCWfEmvyXNM4lilZbXmwl/rHZmnTtOZEp9G49nUa/pfvUcvyPxXq8aYm947YlTZtdQBtGrM/bdpiH+rv2CHRMeplZ+Ss2hVpyKqGeEBWNUB0rArIqmMB09hcyKpGmA5VBVnVGywmb4Upp8VppP6oYHG6acSUVV8iBaH09+dTVfmoJJvaWhxhLE1z9Uc1B+rXeybla2PyNmiEURC7QaOGfLRQHIkURhiZPDIh9KezsueFEcbSNFdfPgfEsXzrUCKKgGuyys+DyerQV35BzR8/Sxkhv5e9nmvbino8ee0bOZH627f1/r0F5ZqG+48r3fqHePsWc3YrrcO2/SCrdkUEsqohHpBVDRAdqwKy6ljANDYXsqoRpkNV1bKslqSxNA11YIRRlMHNRw0LOYz+iKI/JXUgf5GX9UcohSmrhbxIr5wnj339vcZ7gD/1lAsfzz8cJISFaauFaaaFkcIRbUO9hXOaqYGavTzGgemnpZHIYlk/r5E/5iOZRaGsldFG4wGr4gFdlVWOjIlq08qXqPmT+dS84i/e/56lrLfqMTZ5Al2TLqaOQy6V3wElUyEAWU2IFTmrCQE6ujtyVh0NnIZmm5BVrAasFqhayVntz/UPGgEsCZ8/ZTVMCD1RLC6KU8pfFEYYmRCW5JDv7z33xc696b3sB/RK5q+lRXfYgjwmt4ZMwyAh5FNWS4vg+MIoLGjD/+0LYWHKKs9bZKOKbf5oojBlledK8mmuQt5jJsMWspHfkuasyh+pNkqy1YD33ucA2mbb7Z0+IVOyesdvr6ckCyyxnNUnHn3AX0iIr+obtRpwY9fbtOj5/6F1nZ/SIWOW+iOv2Y0f06+WTKFztrjPW0hqUylmf1q3p//474e+vFkcL13+j/Tjrf89NL7v9mxJz3TuTqe0zYqN/3Ub/plOaZ1FI7ID96GN2uHBnmm0Q3YpTWpaIN2n1uRG0J3dM7yFp34lvU+w4E/X/QQLLFVMT9+OkNWELCGrCQE6ujtk1dHAaWg2ZFUDRM1VpCGr7FYa4qhhPrPJW62zl1Z0dg1aJZWvhFoaVWR5kGzkkC2Iwxe+4aupes91Fxe+4RIpTlllI5R9ufRHG6fRNH+l1gXeH9vY4jRsFLE0asjEzn+uKIR+ziKfXipIZCDfsSSRTBx9WRRzHYXHTC69YzRmmzT3hHSqg6yqcYWsyvPStcCSrKyyluHWNeXjg9WAyzMyWQKympA2ZDUhQEd3h6w6GjgNzYasaoBYYRWrN66i9b3r/L3ZvRo/7S7cq/HDV96hDdmN1LL9EOG1gelu7D6OTCb59n7nu6XHG7z6VgtT48RjVNjMxLsN8+7NOFy4N+OW/r0ZW/162XRS8T6OQ5qG0KjW0aVjFsoOrIy63bCBBVXam4b6ZRc+O59GjdmSJk78Ag3xnsMWTwCyqtZDIKvyvCCruM+qfG+p35KQVQ2xR86qBoiOVYGcVccCprG5JmRVY3NTr4otlPPRumWl43zii2G3/++1PWups6cwxYvJInuNbx+tX+aNIvb7/1y9caUvn4Vy3YPKiWKZ+smEHICJIRNENnGU3YdxVOuYUqnhnlQOE6TSL+tNb2Ubm+YqSiUrx8rzjb3WkGn0/xkU0GqcJ44ZTWBURzNt6Omn7k2F/oqtPgiYmgasazXg+oiKmbPEAktmOMseBbIqSyqmHGRVA0THqoCsOhYwjc11RVY7PVFcWxLFwQL4oSeX/Z5kso2NKm4oiiITRnGUURRFUULZ6CYbgTS9jWobXRoJZCONbBSRb+IIYnC0caQ3msieCysbrEc8hnh+tbzAkuk4unY8yKprEdPTXsiqHo4u1gJZtStqkFUN8YCsaoDoWBWQVccCprG5SWVVHInszw+MSorPsxHH5d7II9/EaaxspJKNWLJN3J/9m41wVuN+jqIoilNWfWn0bo3AtsasN9LIbnFQ3MTpquKoY1Ae+cimxhBWVBVktSJsNbETZLUmwqh8EpBVZWQ1swNk1a5QQlYTxgM5qwkBOro7clYdDZxEs8VRQzEvki2M88mG5dTR3kSfrl9Py9ct92tj01uZTPqPvYV0So+F6azBqbLlmjGVpvpF5np/lW4sF5GNErKNTTcVp6SOZVNQi/fF86eyNhempzZ7uY5jhNFKURRHtm5RGp0U6660fTr3S2OBpWD7aklWn/7DY7TN2HG0y4SJOsNQs3UhZ1UttMhZleeFnFXkrMr3lvotCVlNGHvIakKAju4OWa1e4MQFcDo3DeREivmR7HGX9xrbWBk+EimKqLiwjslprcH8xHEdAwvg8BHKLVeOouGeQPZsW8iRE6exBkVR3H/MkIGFeKoXIfNHhqyqMYesqvGCrKrxgqzK84KsQlble0v9loSsJow9ZDUhQEd3h6xuHjh2j8iN/RuI3X5jY2/xv33ef708yIHnxNeLj719WM4ku1/kRlae7e/vN/CYv85uB5Lm1tbY7i+i4//X/5/3uEl47D03sn2oN1Lp3c8xy8oFXm9g+7dTe3Gf1kH1Feplslpuw31WyxEa/DpkVY0XZFWNF2RVjRdkVZ4XZBWyKt9b6rckZFVD7JGzqgGiY1W4mLPK7t9YEkFPBjdsYjLI/8cFc7AsbijzOqvPF0lfLjfSptzA7UF0h7TBy3lsYzJYEkRBKrlgejmSYYJZEM6Q8t79IAuCOvB6JsPWfY3ekuas6uaC+swQqKVpwGaI1c5RkLNaO7FUORPkrKrQqq2yyFm1K56QVQ3xgKxqgOhYFWnIKhM9PrpYEMBwgeTCucEfeRRkMzAayV4LCikT1rS2pobm0ohiaVQyZoRysEAOjFDyUckwwWzODtw/Mq3zKFcvZLUcodp8HbJam3GVOSvIqgyl2isDWa29mMqeEWRVlpSZcpBVDZwhqxogOlAFm4LKZNK/zUe2h3rz3sI6nWsDU1eLI418OmxQIPnUVj4aKU6Z9fZhU2nT2mSmuJZEkU+BDYw6igJZ6RTXtM7PVL2QVVOk7ToOZNWueJhsDWTVJG17jgVZtScWplsCWTVNPP54kNWE8UDOakKAmnbPU744HTVsNJLnQvI8SNnRSCF3komqJ575fN5v8STvb7z3N8f707E1ZBq8UcniFNZinqMvg2F5k4EcSnEUM25UkpXDlpyACVlFzqpanJCzqsYLOatqvJCzqsYLOavyvJCzipxV+d5SvyUhqxKxP2bGxfTW0sI9D3cevy09OOuy0l6QVQmAXhF2647Bi+dspO5APqQ/9bUohYMW6CnmQ/rTWvnUV3EBHzaK6Y14dnujlGlt7JYeYs7jrrkJNLZ/a1o86q1BOZIDI5ObL8wzaForE06eL1mUU3YMbPYTgKzaFyPIqlpMIKtqvCCrarwgq/K8IKuQVfneUr8lIatlYv/t866kVas7S4LKxHX0qGF0xzUX+HvWiqz29m8atPjOwMqshQV3NmwqLqITKpOF0cxSnqU49dWfDltcfMe7H2VaGxs19EVRHHX0V2aNX9l1M4Es7b/5Qj5s9JNvWA04rUjaXy9k1b4YQVbVYgJZVeMFWVXjBVmV5wVZhazK95b6LQlZLRP7KdPOpfPPOoGmHT7ZLznn8Xl09c330jNzbijtaSJntae/W7i1x+Dbf/ijjf7oorCSa2BxnsKtP8TXA4+919joZxobu1XHoAV3PIEMm+Lqy2bx1h+hK7fy1VwjVnZNo+1RdaaxwJLJ9uNYlRMwIauVtw57pkUAOatpkbW/XuSs2h+jNFqInNU0qLpRJ3JW7YoTZDUmHgsXL6HpZ/+MZt90CU2csKNfMuw5Jqsrujo3k8nSvSP56GLI6q5sxJJNXy2t6srvNSncr5JPfc3lc6n0HrbCKhuBLORMht9bMmrl1tJUVuHekmEL+bCVYmtpg6zWUjTVzgWyqsarVkpDVmslkurnAVlVZ1YLe0BWayGKlZ0DZLUybmntBVlNKKtP3P0EfXHpF9OKD+oFARAAARAAARAAARCoYQKNOzRSx8kdNXyGODUQqJwAZDWhrLKc1e9mv1t5BLCnkwRezb9KH3p/h2YOdbL9aLTdBJ7PP+83cN/MvnY31JLWPZN/hoZ6f3tm9rSkRXY348n8kzTW+9s1s6vdDbWkdY/kH6HPeX87ZXaypEV2N+OB/AO0j/c3LjPO7oZa0rqbcjdRLpOjTEOGMpkMZbNZGjlypN+65uZmampq8p8fOnQorVmzhpYuXUqHHXYYrV27lhYsWEAzZsyg2bNn0/e+9z268sor/f++9tpr9O6779IxxxxDy5cvpwcffJDOPPNMv87nnnvO35fVwTe+X2tra+m5p59+2n984IEHbkaKXfvOnDkzlCBrH9v3lFNOiSV83XXX+WVGjBhRNhKs/TvssANNmjSpbFlegLG68847fR6VbnHnWWmd2E+dAGS1DLOwnNWLr7idFs2d5e9ZKwssqXed+t4DCyzVb/xNTAPGrWvU+hcWWFLjhQWW1HhhgSU1XlhgSY3Xv9/yK8p791hnQkpUkNWO4Uzg8tTU2EyNTY3+8+3tQ6jLSzn7aNl7tN/kg2n9uk56ffFCOvrYb9ITjz5A008+k+687To68eSzaOmSN+ijDz+gAw85glatXEFPP/koHTd9ht+whQte8PdldfCN79fcMnBXgrjvodt+/Qs6/Zwfhp4oa9+L85+lo46dHgti9l230JHTsMCSWm+pz9KQ1TJxr5fVgOuz+1d+1pDVytm5vidk1b4IQlbVYgJZVeMFWVXjBVlV4wVZHV4WWCWfWV2da+mRObN9iVfdeM7qNVddHjmCrFonyldOALIqwS7uPqtsdxOrAUs0E0UMEsACSwZhW3YoE7Jq2SmjOR4BLLBUv90ACyzVZ+xNLLBUn2TtP2sssGRXjCCrGuIBWdUA0bEqIKuOBUxjcyGrGmE6VBVk1aFgaW4qZFUzUEeqg6w6EqgUmglZTQFqgiohqwng8V0hqxogOlYFZNWxgGlsLmRVI0yHqoKsOhQszU2FrGoG6kh1kFVHApVCMyGrKUBNUCVkNQE8tisWWEoI0NHdkbPqaOA0NNuErGKBJbVAIWdVjVcl+V9qR6it0shZVYsnclbVeCFnFTmraj2m/kpDVhPGHLKaEKCju0NWHQ2chmZDVjVA1FwFZFUNKGRVjRdkVY0XZFWNF2QVsqrWY+qvNGQ1YcwhqwkBOro7ZNXRwGloNmRVA0TNVUBW1YBCVtV4QVbVeEFW1XhBViGraj2m/kpDVusv5jhjEAABEAABEAABEAABEAABELCeAGTV+hChgSAAAiAAAiAAAiAAAiAAAiBQfwQgq/UXc5wxCIAACIAACIAACIAACIAACFhPALJqfYjQQBAAARAAARAAARAAARAAARCoPwKQ1QQxP2bGxfTW0mV+DTuP35YenHVZgtqwa7UJqMYzrvycx+fRxVfcvtkpLZo7q9qnieNLEFDtC6zKhYuX0PSzf0azb7qEJk7YUeIoKFJtAjrjjPd8taOZ7PgqfeHb511Jz7+0eNAB8dmejL+pvXXGGe95U1FL5zgqfeGiy2+lh554Fu/5dEJRtlbIallE4QXYl9Wq1Z0lQWWdfvSoYXTHNRdUWCN2qyYB1XiWK8++xK6++V56Zs4N1TwtHLsCAuViG1bllGnn0uo1Xf5LkNUKoFdhF91xxnu+CkHUdEjVvsDe7+JnO7uQnTd/IT7vNcUjrWp0xxnv+bQilX69qn2BXeNfesGppR+ib/jNA3Tfw0/hPZ9+qPwjQFYrBM2+rM4/6wSadvhkvwZ8aFUI0pLdVONZrjz6gyWBraAZ5WIbVSVGViuAXcVddMcZ7/kqBjPhoSvtC/yweO8nDICh3XXHGe95Q4FL4TC6+0IKTUSVAgHIagXdIeyLCV9WFYC0ZBfVeMqUD5sehGlilgQ8phkysYWs2h/Hci1MI854z5ejbufrSfoCPyOMstgZW7FVacQZ73n74x7WQh19gY3MvrnkA4ysGuoCkNUKQOvo6BUcFrukREA1nqrlWbODU05SOhVUm5BAJbHlh8QPVgnhG9zdRJzxnjcY0ASHStIX2GH5/pddeFppplWC5mDXlAiYiDPe8ykFT3O1SfqCmPKDAQjNgYmpDrJaAeskHb2Cw2GXlAmoxlO1vHhBgw+3lIOZsPpKYgtZTQi9CrubiDM/Bt7zVQiwwiF19IWzTvoanXvqcQpHRVHTBEzEGe9501Gt7HhJ+gI/IptNcfPdDxE+3yuLgepekFVVYsXyYfPd2eqv6LgVAq3ybqrxVC3Ppwuhf1Q50BKHV40tZFUCqoVF0o4z3vMWBj2iSZX0BR5fLKiGOHMCeM/Xdl8Int1uU2dgQUVDIYesVghadSWxCg+D3QwRKBdPthIc2/jticqVD64WidWiDQVSw2HKxTbYFyCrGqBXoQrdccZ7vgpB1HRI1b6AhXU0gTdcje444z1vOIAaD6faF7ACuEb4FVQFWa0AGt9F5R5NCQ6DXQ0RiItnmKCUK8/vwcuav+9eE3BbI0Nx1HGYcrEVf7hgj8U8FvbvUSM6sPCCjkCkXIfOOIt14T2fcuBSqF62L/AphGFNQN5qCoHRXKXOOOM9rzk4hquT7QusWcFYs+cwU85cwCCr5ljjSCAAAiAAAiAAAiAAAiAAAiAAApIEIKuSoFAMBEAABEAABEAABEAABEAABEDAHAHIqjnWOBIIgAAIgAAIgAAIgAAIgAAIgIAkAciqJCgUAwEQAAEQAAEQAAEQAAEQAAEQMEcAsmqONY4EAiAAAiAAAiAAAiAAAiAAAiAgSQCyKgkKxUAABEAABEAABEAABEAABEAABMwRgKyaY40jgQAIgAAIgAAIgAAIgAAIgAAISBKArEqCQjEQAAEQAAEQAAEQAAEQAAEQAAFzBCCr5ljjSCAAAiAAAiAAAiAAAiAAAiAAApIEIKuSoFAMBEAABEAABEAABEAABEAABEDAHAHIqjnWOBIIgAAIgAAIgAAIgAAIgAAIgIAkAciqJCgUAwEQAAEQAAEQAAEQAAEQAAEQMEcAsmqONY4EAiAAAiAAAiAAAiAAAiAAAiAgSQCyKgkKxUAABEAABEAABEAABEAABEAABMwRgKyaY40jgQAIgAAIgAAIgAAIgAAIgAAI/P/27t5VjiqMA/D8A4Z4FSwUlKBCImlSGJAIVmIVg5WNEFREizQ2fgQshPjRaJFCMSoBQQRBYyqRFEKCoKBNkBRKsNBC8AP8C+QsnGXvZnfnzHv33dy9+9wud+a8551nJsWPc2Zuo4Cw2gjlNAIECBAgQIAAAQIECBBYnYCwujprMxEgQIAAAQIECBAgQIBAo4Cw2gjlNAIECBAgQIAAAQIECBBYnYCwujprMxEgQIAAAQIECBAgQIBAo4Cw2gjlNAIECBBYnsDZj77o3v/k4g0Fn3/qeHfqmSe6h0+cGh27fOHsDeeUY1v793VfnT8zOtZX64FHTi5sfGv/LaN5nn7x7e77n67NPPfMy892Jx471j1+8nT3629/dPXf9eQLX1/pTr/1YXfvPXeO+5ou1NLHsQcPdxe/+W489PijD3VvvvrcoHlbrmN5d1IlAgQIECCQJyCs5tmqTIAAAQIzBGqY+uy917rDBw+Mzyih89LlH8dhr4S7o0cOdh+/89L4nFfe+KC78sPVcYhtrTUdKqfDZjleav39z39zw2Y5p4bV6b7q7xeF1UmKGm5n9THr2JB5W67Dg0mAAAECBNZBQFhdh7ukRwIECOwhgRJC64rhosuaDm1Xr13vnnzh9W2rmq21lhlWb9vaN1qBrWG79lUCbF/YbeljXlhtnVdY3UP/WVwKAQIENlxAWN3wB8DlEyBAYNUCZRvvfQfu2rZiOq+HErx+uf77aCW1rC6WwDa50jqkVplj0YpmS8grPRy6/+7uz7/+7e64/dbRFt2y2lt+yu8yw2rrvC3Xsep7bj4CBAgQIBAREFYjasYQIECAQFigBsZaoL4zOq/g5LueP397fttpQ2v1hdWWd1ZLaDx65NDoHdXST+mvrLK+e+7z9LDaMq93VsOPpoEECBAgsMsEhNVddkO0Q4AAgU0SqFto6zXP2h5cA2b9+NI8nyG1dvLOagmr9aNHpZe62jtkRTPyzmrrvEP62KRnzbUSIECAwPoJCKvrd890TIAAgT0pULbTli/hTq+eznpXtQ9gXq2+ldW+bbx1G3AJq/UrxDX4DgmJOwmrffMO6aPP0XECBAgQIHAzBYTVm6lvbgIECGyYQAmen355abQyOf1TQ9j0V4LnhdVIrWWG1dJ/eWe2/nmdISFxJ2G1b94hfWzY4+dyCRAgQGDNBITVNbth2iVAgMA6C0xu1Z1cQZ38ou7kB5TKtS4Kq+XrwOWntdayw+rkvRgSEncaVhfNO6SPdX6W9E6AAAECe19AWN3799gVEiBAYNcJTH40qTY3753Uvm3AQ2r1hdXWDyzNWhkeEhLn9VG3L1eT+g7v5Pbj6Zs5Pa8PLO26x11DBAgQIBAUEFaDcIYRIECAAAECBAgQIECAQJ6AsJpnqzIBAgQIECBAgAABAgQIBAWE1SCcYQQIECBAgAABAgQIECCQJyCs5tmqTIAAAQIECBAgQIAAAQJBAWE1CGcYAQIECBAgQIAAAQIECOQJCKt5tioTIECAAAECBAgQIECAQFBAWA3CGUaAAAECBAgQIECAAAECeQLCap6tygQIECBAgAABAgQIECAQFBBWg3CGESBAgAABAgQIECBAgECegLCaZ6syAQIECBAgQIAAAQIECAQFhNUgnGEECBAgQIAAAQIECBAgkCcgrObZqkyAAAECBAgQIECAAAECQQFhNQhnGAECBAgQIECAAAECBAjkCQirebYqEyBAgAABAgQIECBAgEBQQFgNwhlGgAABAgQIECBAgAABAnkCwmqercoECBAgQIAAAQIECBAgEBQQVoNwhhEgQIAAAQIECBAgQIBAnoCwmmerMgECBAgQIECAAAECBAgEBYTVIJxhBAgQIECAAAECBAgQIJAnIKzm2apMgAABAgQIECBAgAABAkEBYTUIZxgBAgQIECBAgAABAgQI5AkIq3m2KhMgQIAAAQIECBAgQIBAUEBYDcIZRoAAAQIECBAgQIAAAQJ5AsJqnq3KBAgQIECAAAECBAgQIBAUEFaDcIYRIECAAAECBAgQIECAQJ6AsJpnqzIBAgQIECBAgAABAgQIBAWE1SCcYQQIECBAgAABAgQIECCQJyCs5tmqTIAAAQIECBAgQIAAAQJBAWE1CGcYAQIECBAgQIAAAQIECOQJCKt5tioTIECAAAECBAgQIECAQFBAWA3CGUaAAAECBAgQIECAAAECeQLCap6tygQIECBAgAABAgQIECAQFBBWg3CGESBAgAABAgQIECBAgECegLCaZ6syAQIECBAgQIAAAQIECAQFhNUgnGEECBAgQIAAAQIECBAgkCcgrObZqkyAAAECBAgQIECAAAECQQFhNQhnGAECBAgQIECAAAECBAjkCQirebYqEyBAgAABAgQIECBAgEBQ4H+rn9Sk00GKQwAAAABJRU5ErkJggg==",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_history(colors=['darkorange', 'green', 'violet'], show_intervals=True, title_prefix=\"WITH enzyme added mid-reaction\")"
]
},
{
"cell_type": "markdown",
"id": "3171fd78-a103-4523-8c43-6e29695f49d2",
"metadata": {},
"source": [
"## Notice the dramatic acceleration of the reaction as soon as the enzyme `E` is added at t = 0.275!\n",
"The reactions simulator automatically switches to small time steps is in order to handle the rapid amount of change"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "c3afbcc8-bdae-4938-a3f1-ce00d62816f2",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0: A <-> B\n",
"Final concentrations: [A] = 3.333 ; [B] = 16.67\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 5.00003\n",
" Formula used: [B] / [A]\n",
"2. Ratio of forward/reverse reaction rates: 5.00001\n",
"Discrepancy between the two values: 0.0005878 %\n",
"Reaction IS in equilibrium (within 1% tolerance)\n",
"\n",
"1: A + E <-> B + E\n",
"Final concentrations: [A] = 3.333 ; [E] = 30 ; [B] = 16.67\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 5.00003\n",
" Formula used: ([B][E]) / ([A][E])\n",
"2. Ratio of forward/reverse reaction rates: 5.00001\n",
"Discrepancy between the two values: 0.0005878 %\n",
"Reaction IS in equilibrium (within 1% tolerance)\n",
"\n"
]
},
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Verify that the reaction has reached equilibrium\n",
"dynamics.is_in_equilibrium()"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "47c6d97b-a778-47c1-9cad-e75433a32f66",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" SYSTEM TIME | \n",
" A | \n",
" B | \n",
" E | \n",
" caption | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 0.000000 | \n",
" 20.000000 | \n",
" 0.000000 | \n",
" 0.0 | \n",
" Initialized state | \n",
"
\n",
" \n",
" | 1 | \n",
" 0.050000 | \n",
" 19.000000 | \n",
" 1.000000 | \n",
" 0.0 | \n",
" | \n",
"
\n",
" \n",
" | 2 | \n",
" 0.110000 | \n",
" 17.872000 | \n",
" 2.128000 | \n",
" 0.0 | \n",
" | \n",
"
\n",
" \n",
" | 3 | \n",
" 0.140000 | \n",
" 17.348608 | \n",
" 2.651392 | \n",
" 0.0 | \n",
" | \n",
"
\n",
" \n",
" | 4 | \n",
" 0.170000 | \n",
" 16.844058 | \n",
" 3.155942 | \n",
" 0.0 | \n",
" | \n",
"
\n",
" \n",
" | 5 | \n",
" 0.200000 | \n",
" 16.357672 | \n",
" 3.642328 | \n",
" 0.0 | \n",
" | \n",
"
\n",
" \n",
" | 6 | \n",
" 0.230000 | \n",
" 15.888796 | \n",
" 4.111204 | \n",
" 0.0 | \n",
" | \n",
"
\n",
" \n",
" | 7 | \n",
" 0.260000 | \n",
" 15.436799 | \n",
" 4.563201 | \n",
" 0.0 | \n",
" | \n",
"
\n",
" \n",
" | 8 | \n",
" 0.260000 | \n",
" 15.436799 | \n",
" 4.563201 | \n",
" 30.0 | \n",
" Set concentration of `E` | \n",
"
\n",
" \n",
" | 9 | \n",
" 0.260200 | \n",
" 14.562445 | \n",
" 5.437555 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 10 | \n",
" 0.260400 | \n",
" 13.751254 | \n",
" 6.248746 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 11 | \n",
" 0.260600 | \n",
" 12.998663 | \n",
" 7.001337 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 12 | \n",
" 0.260800 | \n",
" 12.300439 | \n",
" 7.699561 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 13 | \n",
" 0.261000 | \n",
" 11.652656 | \n",
" 8.347344 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 14 | \n",
" 0.261200 | \n",
" 11.051668 | \n",
" 8.948332 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 15 | \n",
" 0.261440 | \n",
" 10.382581 | \n",
" 9.617419 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 16 | \n",
" 0.261728 | \n",
" 9.649278 | \n",
" 10.350722 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 17 | \n",
" 0.262074 | \n",
" 8.860854 | \n",
" 11.139146 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 18 | \n",
" 0.262419 | \n",
" 8.170849 | \n",
" 11.829151 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 19 | \n",
" 0.262834 | \n",
" 7.446204 | \n",
" 12.553796 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 20 | \n",
" 0.263249 | \n",
" 6.830109 | \n",
" 13.169891 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 21 | \n",
" 0.263663 | \n",
" 6.306303 | \n",
" 13.693697 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 22 | \n",
" 0.264161 | \n",
" 5.771892 | \n",
" 14.228108 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 23 | \n",
" 0.264659 | \n",
" 5.333546 | \n",
" 14.666454 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 24 | \n",
" 0.265256 | \n",
" 4.902084 | \n",
" 15.097916 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 25 | \n",
" 0.265853 | \n",
" 4.563692 | \n",
" 15.436308 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 26 | \n",
" 0.266570 | \n",
" 4.245215 | \n",
" 15.754785 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 27 | \n",
" 0.267430 | \n",
" 3.961966 | \n",
" 16.038034 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 28 | \n",
" 0.268462 | \n",
" 3.727647 | \n",
" 16.272353 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 29 | \n",
" 0.269700 | \n",
" 3.551273 | \n",
" 16.448727 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 30 | \n",
" 0.271186 | \n",
" 3.434292 | \n",
" 16.565708 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 31 | \n",
" 0.272969 | \n",
" 3.369263 | \n",
" 16.630737 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 32 | \n",
" 0.275109 | \n",
" 3.341490 | \n",
" 16.658510 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 33 | \n",
" 0.277677 | \n",
" 3.333922 | \n",
" 16.666078 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 34 | \n",
" 0.280758 | \n",
" 3.333264 | \n",
" 16.666736 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 35 | \n",
" 0.284456 | \n",
" 3.333353 | \n",
" 16.666647 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 36 | \n",
" 0.288893 | \n",
" 3.333317 | \n",
" 16.666683 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 37 | \n",
" 0.294218 | \n",
" 3.333343 | \n",
" 16.666657 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 38 | \n",
" 0.300608 | \n",
" 3.333314 | \n",
" 16.666686 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
"
\n",
"