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"## Coupled pair of reactions: `S <-> P` , and `S + E <-> P + E`\n",
"A direct reaction and the same reaction, catalyzed\n",
"### Re-run from same initial concentrations of S (\"Substrate\") and P (\"Product\"), for various concentations of the enzyme `E`: from zero to hugely abundant\n",
"\n",
"LAST REVISED: Dec. 3, 2023"
]
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"id": "cbb1af2e-3564-460e-a4ae-41e4ec4f719f",
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"name": "stdout",
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"text": [
"Added 'D:\\Docs\\- MY CODE\\BioSimulations\\life123-Win7' to sys.path\n"
]
}
],
"source": [
"import set_path # Importing this module will add the project's home directory to sys.path"
]
},
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"id": "087c0d08",
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"from src.modules.chemicals.chem_data import ChemData\n",
"from src.modules.reactions.reaction_dynamics import ReactionDynamics\n",
"from src.modules.movies.movies import MovieTabular\n",
"\n",
"import pandas as pd\n",
"import plotly.express as px"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "23c15e66-52e4-495b-aa3d-ecddd8d16942",
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"name": "stdout",
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"Number of reactions: 2 (at temp. 25 C)\n",
"0: S <-> P (kF = 1 / kR = 0.2 / delta_G = -3,989.7 / K = 5) | 1st order in all reactants & products\n",
"1: S + E <-> P + 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): {'S', 'P'}\n",
"Set of enzymes involved in the above reactions: {'E'}\n"
]
}
],
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"# Initialize the system\n",
"chem_data = ChemData(names=[\"S\", \"P\", \"E\"])\n",
"\n",
"# Reaction S <-> P , 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=\"S\", products=\"P\",\n",
" forward_rate=1., delta_G=-3989.73)\n",
"\n",
"# Reaction S + E <-> P + 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=[\"S\", \"E\"], products=[\"P\", \"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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"cell_type": "code",
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"id": "919280b2-fd0f-4557-9008-e154b64a2b66",
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"source": []
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"# 1. 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 (S). Conc: 20.0\n",
" Species 1 (P). Conc: 0.0\n",
" Species 2 (E). Conc: 0.0\n",
"Set of chemicals involved in reactions (not counting enzymes): {'S', 'P'}\n",
"Set of enzymes involved in reactions: {'E'}\n"
]
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"dynamics = ReactionDynamics(chem_data=chem_data)\n",
"dynamics.set_conc(conc={\"S\": 20., \"P\": 0., \"E\": 0.},\n",
" snapshot=True) # Initially, no enzyme `E`\n",
"dynamics.describe_state()"
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"### Advance the reactions (for now without enzyme) to equilibrium"
]
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"execution_count": 5,
"id": "76f24d9a-a788-41d8-90a4-db87386f91aa",
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"* INFO: the tentative time step (0.1) leads to a least one norm value > its ABORT threshold:\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.4 (set to 0.04) [Step started at t=0, and will rewind there]\n",
"35 total step(s) taken\n"
]
}
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"dynamics.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n",
"\n",
"# All of these settings are currently close to the default values... but subject to change; set for repeatability\n",
"dynamics.set_thresholds(norm=\"norm_A\", low=0.5, high=0.8, abort=1.44)\n",
"dynamics.set_thresholds(norm=\"norm_B\", low=0.08, high=0.5, abort=1.5)\n",
"dynamics.set_step_factors(upshift=1.2, downshift=0.5, abort=0.4)\n",
"dynamics.set_error_step_factor(0.25)\n",
"\n",
"# Perform the reactions\n",
"dynamics.single_compartment_react(reaction_duration=4.0,\n",
" initial_step=0.1, variable_steps=True, explain_variable_steps=False)"
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"#dynamics.explain_time_advance()"
]
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",
"text/html": [
""
]
},
"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": "code",
"execution_count": 8,
"id": "7b253509-903b-4c1a-8771-cd283e7fbf4c",
"metadata": {},
"outputs": [],
"source": [
"# To save up snapshots of crossover times at various Enzyme concentrations\n",
"crossover_points = MovieTabular(parameter_name=\"Enzyme concentration\")"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "4677fcaa-e90b-4975-a567-cb55b66f91f2",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Min abs distance found at data row: 20\n"
]
},
{
"data": {
"text/plain": [
"(0.7435259497128707, 9.999999999999996)"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"new_crossover = dynamics.curve_intersection(\"S\", \"P\", t_start=0, t_end=1.0)\n",
"crossover_points.store(par=dynamics.get_chem_conc(\"E\"), \n",
" data_snapshot = {\"crossover time\": new_crossover[0]})\n",
"new_crossover"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "d684e2c3-c717-4c95-8852-62729914e48f",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0: S <-> P\n",
"Final concentrations: [S] = 3.372 ; [P] = 16.63\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.93068\n",
" Formula used: [P] / [S]\n",
"2. Ratio of forward/reverse reaction rates: 5.00000519021548\n",
"Discrepancy between the two values: 1.387 %\n",
"Reaction IS in equilibrium (within 2% tolerance)\n",
"\n",
"1: S + E <-> P + E\n",
"Final concentrations: [S] = 3.372 ; [P] = 16.63 ; [E] = 0\n",
"Reaction IS in equilibrium because it can't proceed in either direction due to zero concentrations in both some reactants and products!\n",
"\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"D:\\Docs\\- MY CODE\\BioSimulations\\life123-Win7\\src\\modules\\reactions\\reaction.py:468: RuntimeWarning:\n",
"\n",
"invalid value encountered in double_scalars\n",
"\n"
]
},
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Verify that the reaction has reached equilibrium\n",
"dynamics.is_in_equilibrium(tolerance=2)"
]
},
{
"cell_type": "code",
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"# 2. Re-start all the reactions from the same initial concentrations - except for now having a tiny amount of enzyme (two orders of magnitude less than the starting [S])"
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"dynamics = ReactionDynamics(chem_data=chem_data) # A brand-new simulation "
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"dynamics.set_conc(conc={\"S\": 20., \"P\": 0., \"E\": 0.2},\n",
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"SYSTEM STATE at Time t = 0:\n",
"3 species:\n",
" Species 0 (S). Conc: 20.0\n",
" Species 1 (P). Conc: 0.0\n",
" Species 2 (E). Conc: 0.2\n",
"Set of chemicals involved in reactions (not counting enzymes): {'S', 'P'}\n",
"Set of enzymes involved in reactions: {'E'}\n"
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"### Re-take the new system (now with a tiny amount of enzyme) to equilibrium"
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"* INFO: the tentative time step (0.05) leads to a least one norm value > its ABORT threshold:\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.4 (set to 0.02) [Step started at t=0, and will rewind there]\n",
"Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n",
"33 total step(s) taken\n"
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_history(colors=['darkorange', 'green', 'violet'], show_intervals=True, title_prefix=\"With a tiny amount of enzyme\")"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "e4632751-75db-40d8-95ee-6ddede100b41",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Min abs distance found at data row: 17\n"
]
},
{
"data": {
"text/plain": [
"(0.24710707675961718, 10.0)"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"new_crossover = dynamics.curve_intersection(\"S\", \"P\", t_start=0, t_end=0.5)\n",
"crossover_points.store(par=dynamics.get_chem_conc(\"E\"), \n",
" data_snapshot = {\"crossover time\": new_crossover[0]})\n",
"new_crossover"
]
},
{
"cell_type": "markdown",
"id": "3171fd78-a103-4523-8c43-6e29695f49d2",
"metadata": {},
"source": [
"## Notice how even a tiny amount of enzyme (1/100 of the initial [A]) makes a very pronounced difference!"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "c3afbcc8-bdae-4938-a3f1-ce00d62816f2",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0: S <-> P\n",
"Final concentrations: [S] = 3.34 ; [P] = 16.66\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.98745\n",
" Formula used: [P] / [S]\n",
"2. Ratio of forward/reverse reaction rates: 5.00000519021548\n",
"Discrepancy between the two values: 0.2511 %\n",
"Reaction IS in equilibrium (within 1% tolerance)\n",
"\n",
"1: S + E <-> P + E\n",
"Final concentrations: [S] = 3.34 ; [P] = 16.66 ; [E] = 0.2\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.98745\n",
" Formula used: ([P][E]) / ([S][E])\n",
"2. Ratio of forward/reverse reaction rates: 5.00000519021548\n",
"Discrepancy between the two values: 0.2511 %\n",
"Reaction IS in equilibrium (within 1% tolerance)\n",
"\n"
]
},
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Verify that the reaction has reached equilibrium\n",
"dynamics.is_in_equilibrium()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "b116cbea-f62a-4072-9255-24e109f894a2",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "fe1c77c1-0e3e-4f6a-b774-d86398cde6aa",
"metadata": {},
"source": [
"# 3. Re-start all the reactions from the same initial concentrations - except for now having a more substantial amount of enzyme"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "7c3d57f9-00cc-4377-ad12-a3d9af0fac18",
"metadata": {},
"outputs": [],
"source": [
"dynamics = ReactionDynamics(chem_data=chem_data) # A brand-new simulation "
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "61deddc2-1435-4261-8e40-66043b73365e",
"metadata": {},
"outputs": [],
"source": [
"dynamics.set_conc(conc={\"S\": 20., \"P\": 0., \"E\": 1.},\n",
" snapshot=True) # A more substantial amount of enzyme `E`"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "b4377e1a-8c8e-41a3-8087-2f4d617a2c2e",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SYSTEM STATE at Time t = 0:\n",
"3 species:\n",
" Species 0 (S). Conc: 20.0\n",
" Species 1 (P). Conc: 0.0\n",
" Species 2 (E). Conc: 1.0\n",
"Set of chemicals involved in reactions (not counting enzymes): {'S', 'P'}\n",
"Set of enzymes involved in reactions: {'E'}\n"
]
}
],
"source": [
"dynamics.describe_state()"
]
},
{
"cell_type": "markdown",
"id": "4c4616a5-4cd6-44b9-82bf-2e46689f512b",
"metadata": {
"tags": []
},
"source": [
"### Re-take the new system (now with a more substantial amount of enzyme) to equilibrium"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "a4dd3c4e-06b3-4823-9c62-7528460f7d4a",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"* INFO: the tentative time step (0.02) leads to a least one norm value > its ABORT threshold:\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.4 (set to 0.008) [Step started at t=0, and will rewind there]\n",
"* INFO: the tentative time step (0.008) leads to a least one norm value > its ABORT threshold:\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.4 (set to 0.0032) [Step started at t=0, and will rewind there]\n",
"Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n",
"39 total step(s) taken\n"
]
}
],
"source": [
"dynamics.single_compartment_react(reaction_duration=0.5, \n",
" initial_step=0.02, variable_steps=True, explain_variable_steps=False)"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "12ed7017-11b0-460d-8c53-34dd3962d9a7",
"metadata": {},
"outputs": [],
"source": [
"#dynamics.explain_time_advance()"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "50c6521a-7c67-437d-9666-fef5782cf4ef",
"metadata": {},
"outputs": [
{
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_history(colors=['darkorange', 'green', 'violet'], show_intervals=True, title_prefix=\"With a more substantial amount of enzyme\")"
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "11d21c1a-bf34-4572-a5ff-d360617380c0",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Min abs distance found at data row: 21\n"
]
},
{
"data": {
"text/plain": [
"(0.06769827987210066, 10.0)"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"new_crossover = dynamics.curve_intersection(\"S\", \"P\", t_start=0, t_end=0.5)\n",
"crossover_points.store(par=dynamics.get_chem_conc(\"E\"), \n",
" data_snapshot = {\"crossover time\": new_crossover[0]})\n",
"new_crossover"
]
},
{
"cell_type": "markdown",
"id": "f01eaeb0-e3e6-40fc-9e3e-c79a9fe54285",
"metadata": {},
"source": [
"## Notice the continued - and substantial - speedup of the reaction, over the earlier runs"
]
},
{
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"# 4. Re-start all the reactions from the same initial concentrations - except for now having a good amount of enzyme"
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"dynamics.set_conc(conc={\"S\": 20., \"P\": 0., \"E\": 5.},\n",
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"SYSTEM STATE at Time t = 0:\n",
"3 species:\n",
" Species 0 (S). Conc: 20.0\n",
" Species 1 (P). Conc: 0.0\n",
" Species 2 (E). Conc: 5.0\n",
"Set of chemicals involved in reactions (not counting enzymes): {'S', 'P'}\n",
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"### Re-take the new system to equilibrium"
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"* INFO: the tentative time step (0.01) leads to a least one norm value > its ABORT threshold:\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.4 (set to 0.004) [Step started at t=0, and will rewind there]\n",
"* INFO: the tentative time step (0.004) leads to a least one norm value > its ABORT threshold:\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.4 (set to 0.0016) [Step started at t=0, and will rewind there]\n",
"Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n",
"36 total step(s) taken\n"
]
}
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_history(colors=['darkorange', 'green', 'violet'], show_intervals=True, title_prefix=\"With a good amount of enzyme\")"
]
},
{
"cell_type": "code",
"execution_count": 33,
"id": "193fcaa3-b936-4221-bedc-d4c0e516b1ac",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Min abs distance found at data row: 15\n"
]
},
{
"data": {
"text/plain": [
"(0.014494267066104415, 10.000000000000002)"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"new_crossover = dynamics.curve_intersection(\"S\", \"P\", t_start=0, t_end=0.5)\n",
"crossover_points.store(par=dynamics.get_chem_conc(\"E\"), \n",
" data_snapshot = {\"crossover time\": new_crossover[0]})\n",
"new_crossover"
]
},
{
"cell_type": "markdown",
"id": "9c8cc734-7144-4a60-bdfe-a1e707a8899d",
"metadata": {},
"source": [
"## Notice the continued - and substantial - speedup of the reaction, over the earlier runs"
]
},
{
"cell_type": "code",
"execution_count": 34,
"id": "8bc8ff02-307d-4842-a34a-58b458850264",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Verify that the reaction has reached equilibrium\n",
"dynamics.is_in_equilibrium(explain=False)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "ff8b0763-358c-4765-a134-274a843b959a",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "711d3422-71b5-42dc-a121-5c4fba686ea3",
"metadata": {},
"source": [
"# 5. Re-start all the reactions from the same initial concentrations - except for now having a lot of enzyme (same as the initial [A])"
]
},
{
"cell_type": "code",
"execution_count": 35,
"id": "bbae7051-3d61-45ea-b4be-a79dad90342a",
"metadata": {},
"outputs": [],
"source": [
"dynamics = ReactionDynamics(chem_data=chem_data) # A brand-new simulation "
]
},
{
"cell_type": "code",
"execution_count": 36,
"id": "a1abec42-c74c-4adf-8580-914df5188021",
"metadata": {},
"outputs": [],
"source": [
"dynamics.set_conc(conc={\"S\": 20., \"P\": 0., \"E\": 20.},\n",
" snapshot=True) # A lot of enzyme `E`"
]
},
{
"cell_type": "code",
"execution_count": 37,
"id": "52260372-0585-4c38-abf8-c4764cb45368",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SYSTEM STATE at Time t = 0:\n",
"3 species:\n",
" Species 0 (S). Conc: 20.0\n",
" Species 1 (P). Conc: 0.0\n",
" Species 2 (E). Conc: 20.0\n",
"Set of chemicals involved in reactions (not counting enzymes): {'S', 'P'}\n",
"Set of enzymes involved in reactions: {'E'}\n"
]
}
],
"source": [
"dynamics.describe_state()"
]
},
{
"cell_type": "markdown",
"id": "c3e69edd-0089-4135-be74-01d88c06bda5",
"metadata": {
"tags": []
},
"source": [
"### Re-take the new system (now with a lot of enzyme) to equilibrium"
]
},
{
"cell_type": "code",
"execution_count": 38,
"id": "29c08e79-d275-41b1-a2a0-c4db6521dfe7",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"* INFO: the tentative time step (0.005) leads to a least one norm value > its ABORT threshold:\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.4 (set to 0.002) [Step started at t=0, and will rewind there]\n",
"* INFO: the tentative time step (0.002) leads to a least one norm value > its ABORT threshold:\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.4 (set to 0.0008) [Step started at t=0, and will rewind there]\n",
"* INFO: the tentative time step (0.0008) leads to a least one norm value > its ABORT threshold:\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.4 (set to 0.00032) [Step started at t=0, and will rewind there]\n",
"Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n",
"39 total step(s) taken\n"
]
}
],
"source": [
"dynamics.single_compartment_react(reaction_duration=0.05, \n",
" initial_step=0.005, variable_steps=True, explain_variable_steps=False)"
]
},
{
"cell_type": "code",
"execution_count": 39,
"id": "b0c435d2-4cb9-438c-8c21-1f4eea081b99",
"metadata": {},
"outputs": [],
"source": [
"#dynamics.explain_time_advance()"
]
},
{
"cell_type": "code",
"execution_count": 40,
"id": "f05b1cff-a69e-439e-870f-5ede95c9a69c",
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.plotly.v1+json": {
"config": {
"plotlyServerURL": "https://plot.ly"
},
"data": [
{
"hovertemplate": "Chemical=S
SYSTEM TIME=%{x}
concentration=%{y}",
"legendgroup": "S",
"line": {
"color": "darkorange",
"dash": "solid"
},
"marker": {
"symbol": "circle"
},
"mode": "lines",
"name": "S",
"orientation": "v",
"showlegend": true,
"type": "scatter",
"x": [
0,
0.00032,
0.00048000000000000007,
0.00064,
0.0008,
0.00096,
0.0011200000000000001,
0.00128,
0.00144,
0.0016,
0.00176,
0.0019520000000000002,
0.002144,
0.0023744,
0.00265088,
0.00292736,
0.0032591359999999997,
0.0036572671999999997,
0.004135024639999999,
0.004708333567999999,
0.0052816424959999985,
0.005854951423999998,
0.006542922137599998,
0.007230892851199998,
0.007918863564799997,
0.008744428421119997,
0.009735106248703997,
0.010725784076287997,
0.011914597469388798,
0.013341173541109757,
0.015053064827174908,
0.01710733437045309,
0.019572457822386907,
0.022530605964707486,
0.026080383735492183,
0.030340117060433817,
0.03545179705036378,
0.04158581303827974,
0.04894663222377889,
0.05777961524637786
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"xaxis": "x",
"y": [
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",
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]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_history(colors=['darkorange', 'green', 'violet'], show_intervals=True, title_prefix=\"With a lot of enzyme\")"
]
},
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"execution_count": 41,
"id": "e0869320-aee5-4273-a6e3-dd46d173d80d",
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"name": "stdout",
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"text": [
"Min abs distance found at data row: 17\n"
]
},
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"data": {
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"(0.003687634618431487, 9.999999999999996)"
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"source": [
"new_crossover = dynamics.curve_intersection(\"S\", \"P\", t_start=0, t_end=0.5)\n",
"crossover_points.store(par=dynamics.get_chem_conc(\"E\"), \n",
" data_snapshot = {\"crossover time\": new_crossover[0]})\n",
"new_crossover"
]
},
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"cell_type": "markdown",
"id": "ae56f399-c58b-4c2c-b994-5ef3e7d498ac",
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"source": [
"## Notice the continued - and substantial - speedup of the reaction, over the earlier runs"
]
},
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"id": "6594d68a-ff8b-428c-b42f-f1b5fa22b5d2",
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"source": [
"# Verify that the reaction has reached equilibrium\n",
"dynamics.is_in_equilibrium(explain=False)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "5f165e29-6c26-47f7-9f0c-143305a11c67",
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"source": []
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"source": [
"# 6. Re-start all the reactions from the same initial concentrations - except for now having a very large amount of enzyme (more than the initial substrate concentration [S])"
]
},
{
"cell_type": "code",
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"source": [
"dynamics = ReactionDynamics(chem_data=chem_data) # A brand-new simulation "
]
},
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"dynamics.set_conc(conc={\"S\": 20., \"P\": 0., \"E\": 30.},\n",
" snapshot=True) # A very large amount of enzyme `E`"
]
},
{
"cell_type": "code",
"execution_count": 45,
"id": "5ba56162-8c48-47b4-b105-5fe2376d1797",
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"name": "stdout",
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"text": [
"SYSTEM STATE at Time t = 0:\n",
"3 species:\n",
" Species 0 (S). Conc: 20.0\n",
" Species 1 (P). Conc: 0.0\n",
" Species 2 (E). Conc: 30.0\n",
"Set of chemicals involved in reactions (not counting enzymes): {'S', 'P'}\n",
"Set of enzymes involved in reactions: {'E'}\n"
]
}
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"### Re-take the new system to equilibrium"
]
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"* INFO: the tentative time step (0.001) leads to a least one norm value > its ABORT threshold:\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.4 (set to 0.0004) [Step started at t=0, and will rewind there]\n",
"* INFO: the tentative time step (0.0004) leads to a least one norm value > its ABORT threshold:\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.4 (set to 0.00016) [Step started at t=0, and will rewind there]\n",
"Some steps were backtracked and re-done, to prevent negative concentrations or excessively large concentration changes\n",
"36 total step(s) taken\n"
]
}
],
"source": [
"dynamics.single_compartment_react(reaction_duration=0.02, \n",
" initial_step=0.001, variable_steps=True, explain_variable_steps=False)"
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},
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"source": [
"#dynamics.explain_time_advance()"
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tu726n4tjhUWnnQy1yqr91Prq0ezXveoDympf9I5jLZ/UJ3szfbPqj1PtygfntP/9LV6dtxRyCoK6D/LMrZKD/JV2dlYmxj/4DESay3VX98K4B57C/oNHIGLz4O9uxeP/nB2wK9dXxs3oq/x9B/Mkm3fffh1uGHR5wIVIcNU6eSmPHfG5ko1VH1rkNsKoex+XmglXBLt1gnVCBKl9VdoM51uAcGfwwrkO66U6aJ1z5PPLXyePxUNTZ+DHDdukJvXOT+qUhXM7tkZewfHTxng4fst1IimQvSbcIzFWlfE3e51RxisSYzXWhLuekDVK69O7Xk+dPBaffvmD9C2i/BI64ZyObTDlyZeDrjNaqXNmztehjjn1dVB5LQh1jZTTc9VpznpaQVxLL7u4S+BaIXzSOl9qpU2HShlU9i1UX0Q5s9pAtqk8BsV76pQ3rSyQUN9KPf/KgsA3yEa+eFa4ywPdbFD0LpBad1FiME99dg4m33NLYOZF66RvxabejYbWgSwPPuXAVAdZK8BWLkx6JwIhMJXtWrnL1OujsCEEmlhvoDVYQ/XXjD9m2jXDVD44hTBVHmR6B5PeSVh5MlRf4IStJ1+Yi1tu6B9YW2A1lloMI8FV74StJ1LC8cEpsa70VY51OOJCq8+REEFOCfhIiKFQN+Vmxq6oL18EtW7q1Os2tL45jURqY6jUSjs3BKKuV4S7G2M1XAEfibEaS8Ld6PpslCqjXE+ljLNSAynFp/p99Xoss9dEvWNDff3Tim+oGXet417NQHktVV4rQl1rlP02q1/M9EXWnGa0gdY3K2rNqrVWQu6XYK5cfyj8O3AoP7AGx8gXTwt35R2I0YlX70Jg5cBXL+iyYlMNXvZXbTPUwhfl4Mo/Wqg56yrqr1rznWEaQKgZd61ZXKPdHcx8DW3lxG2WrZV2tRYzqjnoHehaF2Yj4a61sNSsGDaT4y7PuEeCa6jjSYuFEz4YHcNWPteawbK6yE8pUCJxg2F0k2BmUkKPu/z+rn2Hwk5tMMvbyrGhdw4VM4fyRgKiXSvnZbN+Ku3K3wDIde3G1wnhrvZJ9s3MuI3GWLXaZiTGqt1xEs7iVCvjTVnW6GY0HOGuPm7kNozeN6sz9FLGQl2flq5ci8t7dJW2mtW7Rur5qbYbqh21bb22fvplO9LTUnU34TDbF7PawIrP6vOh+PvDT76Whs2A3hdK36hrjXEjX2qNcNcSWVpf9ShnkIzEpWwzVCDNXsjUszpyOoY42Zu5wKtPNlaFu5EINXMCDVVGfYdqlW2oGwu9k4TWTFmoA0KkdBjNYijFQShmRsLSinCPBFerwt0JH8K9IIaqp/66UpQ1I4REOavCJJQwNHuM6s2k6fUx1LdB4utzs+1aYW80doWtUCkBWl/5qne3MnM+seKzVlmt87sZAa+XMqTVhhl7RjOxZvoZzljV64fZlC2rbToxVo2EtszKbC6+2RlZMzEwKhPqOiTquincrVwTtfqljH2o8RLqPKC3pa9ykrOktDSQdqreXU3NSx4bVr9pNdsXs9ogFFu1DeUNf27jhlJ6U48LOkvI16xbL82wy6mxypsxI188LdxFSoPZC5NZISiAyWXVOwxYnXGXhVuoO221Tb2tLbVmX7Ty08yesJwW7kazCUqu6txsrc/MxstMu1aYGh0QdoW7HLO8/GNBX4WpZ+ysCPdQDNSfmeVqVbg74YPRhc+Jz2U/rTyAyI30A2UbZoWT+uZCycfsecAKU7Nj14pwN/rWyuibPiv+G5WVhbzZa4rSnhMz7kaTI0b+K8+jIsXQzE2DGZvqMnZTZdRbl9oZq3Zv8GqrcLdyTTSaNFDGUz0pond8a900K9uRxXco4a51zGnd2Jk5n2rdxKr7YlYbhFqArP5MOX7PO7sdHp46A3+ZPFZCIf+eX3AcT02fF/TNqZEvnhXu8oXO7F7WVgSL2btEszZDnVyszLgbnWSt5PY6LdzNnECdmJXV+yot3Bl3NVOjA8KucDf6ikueebQi3CPB1apwd8IHo/Ht1Oeh8i5DtREJAR+uYJf9NJMq5hQ3s2PXinBXn/9kX82cT5zql2zHzCSAXpteEe7qvjgp4MMV7JEcq3bHSTSEu9bElWDklRn3cI8rrQlPs1pKr02jbIVQ6dJ21rRo9cWsNrAy465MWWrVoklgll3wkGffd+w+EJTfHmqsyBrQs8JdvjiEeoiQMt/brMg2ytVVfr0TCZtmvzYVbReXlOKcDq2DxrxZUeK0cA/FTfa17ZnNpMEoXurHrasPCifYyu02a9JQ9+s2O8LdSHTopV9pPbRJfeEPlYOoZmM0ZpUnN7NcrQp3J3wI94KhridyLNu1bq6Z0+iE0HVCwDthQ/Tbif6Y5a53brGa464cj3qzU3YFmVafhE15e2Ctz0PNlBkx8ppwd1LAKwWQndnxSIxVu+PETeFudG0PNYb0rtdGuezqcSCXN/LFaLyL+iJN9/Ie5wUV1Upf0UqJMXushfJTvW5QmVtv5WbcSl+0bhT0ZtHNXv9lZg0b1MPQX/UN7BQn3lfnu8v9MrqJ8LRwD3VHJcM0egCT1sDQgiJ/BRNOjruArTVQ5ffUJ0O178pZKHm3G63FqVYORqeFu/BR61sQ9d2nVhkrq9u1+mimXTNMxUIcowNCOeNuJDq0DtxQ48Ds14xa4jsSXK3OLtr1wehiYfZzvVxH+Xyh9WAms7aV5ax+6yfX1RuL4fgQCTEUKu7qdR5yX8yOXfXxpeW/2ZxTq7yUqYVGD+yzaturwl0tYMx+Q6285oitbcXrhcfvs7y/vZJjJMZqLAl3wSLUxFqob3ycFu5KTaJOqRJM1bvqqY8HreuwVnxDCXS91DRRR2xxKXLa9TSNfI43+gbczI2Z2b6Eow3UO/RppXfLcReMlWt99N4X5Yx88bRwV18I1YNLGVSrM43qXCkRAPEKZ8Zdz09xwIivR7TuSJUXGWW/lANBK0/NTD6X1gnEKh+9C5uW32qftMqoL6RW/Qm3XdEPM9tf6p2AlONEax939YIa5QlTZijGgdijVv2odnXenZz359Q+7lq7B5nJsw0lUuzE1qpYClVeL4czUnm/TvpuxVYkxJAVrnpj1+ziVNGWepyL40jMDIq8Tqdz3PUWZJpdsBzqpkZ9/JqNo965Xq5v1zezfkS6XCTGqhPCXf1cCiUHp88XRjPN6vOWfF2MhHAX/TSjM/TGhfJbQ+W1TGsRqcxYPZa1ztPKMnr+aR0TWse22W+IzPTFSCzraRiRriZeesex3MeWuY2CMhHk/mjtDGbkS0wI90ifcCJpX/11TyTbom0SIAESIAESIIHoEIjEzUt0euJOq1ayCNzxKDZaoXB3KE7ijm7O/GWYNH64tL+peIVaxOBQszRDAiRAAiRAAiTgEQJ2FkF7pAuuuUHhHh5qCvfwuJ1WS+urmHj5CtQhRDRDAiRAAiRAAnFPQE6xdDoVJ97AUbiHF1EK9/C4sRYJkAAJkAAJkAAJkAAJuEqAwt1V3GyMBEiABEiABEiABEiABMIjQOEeHjfWIgESIAESIAESIAESIAFXCVC4u4qbjZEACZAACZAACZAACZBAeAQo3MPjxlokQAIkQAIkQAIkQAIk4CoBCndXcbMxEiABEiABEiABEiABEgiPAIV7eNxYiwRIgARIgARIgARIgARcJUDh7ipuNkYCJEACJEACJEACJEAC4RGgcA+PG2uRAAmQAAmQAAmQAAmQgKsEKNxdxc3GSIAESIAESIAESIAESCA8AhTu4XFjLRIgARIgARIgARIgARJwlQCFu6u42RgJkAAJkAAJkAAJkAAJhEeAwj08bqxFAiRAAiRAAiRAAiRAAq4SoHB3FTcbIwESIAESIAESIAESIIHwCFC4h8eNtUiABEiABEiABEiABEjAVQIU7q7iZmMkQAIkQAIkQAIkQAIkEB4BCvfwuLEWCZAACZAACZAACZAACbhKgMLdVdxsjARIgARIgARIgARIgATCI0DhHh431iIBEiABEiABEiABEiABVwlQuLuKm42RAAmQAAmQAAmQAAmQQHgEKNzD48ZaJEACJEACJEACJEACJOAqAQp3V3GzMRIgARIgARIgARIgARIIjwCFe3jcWIsESIAESIAESIAESIAEXCVA4e4qbjZGAiRAAiRAAiRAAiRAAuERoHAPjxtrkQAJkAAJkAAJkAAJkICrBCjcHcBdWFyBwpPlDliiiXghkFMvFSeKy1FaXhUvXWI/HCBQNz0JCT4fjvN84QDN+DGRnOhDVt0UHD5WGj+dYk8cIdAkOx2HCopR5XfEXESM5OakR8QujWoToHB3YGQI0S7EO18kIBOgcOdY0CJA4c5xoUWAwp3jQo8AhTvHhpoAhbsDY4LC3QGIcWaCwj3OAupQdyjcHQIZZ2Yo3OMsoA52h8LdQZhxYorC3WYgH3vsMUyc9FBgxn3p+++g09nnoWXrdgHLa1avQJ269XBu1wsx8/m/Y/RdE7F54084eGAfLu93Nea/+Qp697saZWVlWLd2NQZfPwLLlyxA63Yd0TS3Od6ZOwu3jpmAb9Z+BvFt2QXde+K1mc/h5pFjkJaegbfmzMSVg4Ygq0EOPnh3Ls7vfilym7VEZWUlXnlpGsaMvz/gy+erlqF+VjbO7tJNeu9E4XEsnP86Rtx+VxCJBW/PRo9e/dC4SW7Q+1s2rcfuHdvQd8BgTXKy323addAlu/7Hb1GQn4eeva/ULXMk7xBWLluEG4ePMoxQUdEJLJj3KkaOvtuwrN/vl2Jwx4RJhmVFgVdnPItht92J1NQ0U+VFoU+WL0b7tq3Run1n06ky27duwtZN69F/4BDT7SgLivG0d88u9Ok/KKz6G37+HkcOHUCvvleFVV9Zaf/e3YFxbNuYysC+PTvx7ddrcM2QYU6bDns8W3EkHOG+euWHyG7YCJ3P6WqlKdfKzn11Oq4ZMhyZ9eq71qZTDeUdOoBPP16K64fd7pTJsOxEWrjPeO4JjP3tA2H5Fo+V7J4v3WTideEuxtaUKVPcRFLr26JwB/D09HmY+caiwGCYNe1BXNS1Y+Dv+YtW4dEnXpb+vuaKHnhs0hikp6VIf1O4Bx9DFO4U7hTu+tcVCndvXXMp3L0VD7e8oXB3jjSFu3MszVqq9cK94Fgh/jN3McbfPkQS41t37sPDU2fgL5PHou2Zufjqu414avo8vPD4fWhQP1MS+eI1cdxQCneNUUbhTuFO4U7hbvYCFO1yFO7RjkB02qdwd447hbtzLM1aqvXCXQ1KCPnxDz6D+8cNlWbdhVBv1aIJbhh0uVRULeTFe8xxNzvcak855rjXnlhb6Wk4M+5W7LNsbBKIdKpMbFKh14KA11NlhI/cVcbdsUrhruIthPnkqTMw/Yn7kdu4IaY8+TJ6XNA5INzVM/IU7u4O2FhpjcI9ViLlrp8U7u7yjpXWKNxjJVLu+0nhDoh05TXr1gelKbsfCfstqieGw7VI4V5DTgjycQ88hf0Hj0DOcS8uKZOE+83X9gnkvKuFe/EnxShZVRIuf9YjARIgARIgARIggZgkkHBpCupfUceW70r9JRtq2jhHmkAVKcvRFO6i7XkLVwbSpe10lMLdDr0QdZVgz+nYxnDGXSxOvSfhnoDFhf6FOAfnoLWvdeC9T/2foi7q4nzf+Xiu6jnc7bsbG7AB+/370T+hP96oegP9ff1R5ivDmqo1uDHhRiz2L0Y7tEMzXzO8XvU67ki4A1/6v5RsXuy7GDOqZuBW361I96VjdtVsDPINQrYvG/P989Ed3dHc1xyVqMSLVS9iQsKEgC+f+D9BFrJwnu886b1CFOLtqrcxOmF0EJV5VfNwme8yNPU1DXr/F/8v2OHfgasStHcfkf1u72uvS/kH/w/I9+ejT0If3TJ5yMOHVR9iZMJIw0ifwAkIf8ckjDEs64dfisHvEn5nWFYUmF41HaN8o5DqSzVVXhRa5l+GXOSis6+z6Tpb/Fuwyb8JgxLC3BXGvwF7/HtwZYL+Tj2hnPmeYANQAAAgAElEQVTJ/xMO+Q+hX0I/0z7rFdyLvYFxbNuYysBu/2587f8a1ydc77RpTXtmxnOkHfnY/zEaoiHO9Z0b6abCsj+rahZu8N2Aer56YdWPZqVDOIQVVSswPGF4NN2IeNvPVj0bdJ2KeIMeb2CDzfOlx7vnqntibNnZVUbe/EO9KYjIfnhr4Uppln3xijWccVdElTPuGkNcmddulOPOXWWCAXJxKhencnGq/nUznFQZbgcZOR3CxamRY+tly1yc6lx07CxOlWfap04eG7STn9o7ecZ98JWXSGsQxUs5Iy+XV8/c/2bEoMBGIvL6xNHDrsbEPz0fZOP7n7cEdg48t1OboNl1rdl+5U6DwpDcjtY3B39+YEwg1Zoz7g6NOwF6+afrcOet10oW1QOJu8pwH3fu427tYKNwp3C3NmKiV5rCPXrso9kyhbtz9O0Id7NpKLJQVgpxMal64FB+IO/9tDTmmlTnJo2yJfEutNyoex8PiGxBQN4KXG1XfCbvHKgW7mqfRUr1Ox98ghuv6Y19B/NC6kkKd4fGnZzH/sHyNQGLVvZxF5W4q4xDwYgjM1ycGkfBdLAr4cy4O9g8TXmUABenejQwHnArnhenqsW3Hm6tWW+tSVXlDoDClrLMlu17g7b2Vn8utvvWek/ZdklpadCug2aGhzJrg8LdDDGXylC4uwQ6hpqhcI+hYLnoKoW7i7BjqCkK9xgKlsuuUrhr7yqjFOVpqanSekTlBKwcJjn1xQnhLmbUn3x+LqY+NFZ6ro/WS57ZV34mz+hTuLt88IRqjsLdQ8HwiCsU7h4JhMfcoHD3WEA84g6Fu0cC4UE34lm4W0mVUW8HqSXclVt3q0Op9QweM+8pZ9yNhLuYXV+04svAbjjCB+VDOyncPXKAcXFqcCC4OJWLU5njrn9yCke4c3Fq5E72zHGPHFsvW2aOu3PRsZPjHmpxqjJ3XGtXGaP1h5EQ7qFSZbS2D6dwd26cOWqJwp3CXT2gPlm+GO3btkbr9p1RWl5larxt37oJWzetR/+BQ0yVVxeyeyHa8PP3OHLoAHr11d7m04pTFO4U7lbGSzTLUrhHk3702rZ7vnTTc6/PuNsR7oKj1naQ8sx0y9xGuttBqoW7nKKi3sXlP3MXY/ztQ/DTxm22c9zT01KkGfS1320M7Dwj32AMuuISPP7P2ZAXw4q+qRfEcsbdzSMnRFsU7hTuFO7BBCjcKdw9cno2dIPC3RBRXBagcHcurHaFu/BEaxtF5U4vZhan6tmRhbyZtBhZbD81fV5AmGu1Le9GI1NU57D/uGGb9JF4X36JXWoo3J0bd7YtMcfdNsK4M8Ac97gLqSMdCidVxpGGacTTBJjj7unwRNU5r8+4Czi5OelRZVTbGucDmByIOIW7AxDjzASFe5wF1KHuULg7BDLOzFC4x1lAHewOhbuDMOPEFIW7A4GkcHcAYpyZoHCPs4A61B0Kd4dAxpkZCvc4C6iD3aFwdxBmnJiicLcZSOa4BwPkrjLcVYY57vonlXCEO3eVsXmSDlGdOe6RY+tly8xxdy46TuS4O+dN7bBE4W4zzhTuFO7qIcRdZXZj3drVGHz9CJtH1+nV9+3ZiW+/XoNrhgxz3LaWQTM3olYcoXC3QivyZSncI8/Yiy1QuDsXFQp351iatUThbpaUTjkKdwp3CvdgApxx54y7zdOqa9Up3F1D7amGKNydCweFu3MszVqicDdLKkQ55rg7ADHOTDDHPc4C6lB3wplxd6hpmvEwAea4ezg4UXaNOe5RDoAHm6dwdyAoFO4OQIwzExTucRZQh7pD4e4QyDgzQ+EeZwF1sDsU7g7CjBNTFO4OBJLC3QGIcWaCwj3OAupQdyjcHQIZZ2Yo3OMsoA52h8LdQZhxYorC3WYgmeMeDNDMYr71P36Lgvw89Ox9pS79I3mHsHLZItw4fJRhhIqKTmDBvFcxcvTdhmX9fj9mPv933DFhkmFZUeDVGc9i2G13IjU1zVR5UYiLU7k4VW+whCPcuauM6UPPckHmuFtGFhcVmOPuXBiZ4+4cS7OWKNzNktIpR+FO4a4eGhTuFO4U7jZPrC5Vp3B3CbTHmqFwdy4g8Src5y9ahUefeDkI1KxpD+Kirh2dgxemJQr3MMHJ1SjcKdwp3IMJcFcZ/ZMKZ9xtnnAdrk7h7jDQGDFH4e5coOJRuH/13UY8NX0eXnj8PjSonynB2rpzH5Z/ug533nqtc/DCtEThHiY4ZTXmuDsAMc5MMMc9zgLqUHfCEe4ONU0zHibAHHcPByfKrjHH3f0APD19ntToxHFD3W/cRIsU7iYgGRWhcDciVPs+p3CvfTE302MKdzOUal8ZCvfaF3OzPa4Vwr1wD3B0i1kkzpXLbA5ktTvNnpwm45XUGLWDFO4ODAEKdwcgxpkJCvc4C6hD3aFwdwhknJmhcI+zgDrYnVoh3Nc9A6yc6CA1k6YuuA/o87RmYXWO+7md2gSlzphsISLFKNxtYmWOezBA7irDXWWY465/UglHuHNXGZsn6RDVmeMeObZetswcd+ei40iO+6a3ge/+5ZxTZi2ddRPQdYJh6eKSMkx5snqh6mOTxiA9LcWwTiQLULjbpEvhTuGuHkLcVYa7yuidVijcbZ5wHa5O4e4w0BgxR+HuXKAcEe7OuRMxS1oLViPWmIFhCneb5CncKdwp3IMJcMadM+42T6uuVadwdw21pxqicHcuHPEo3MXi1Msu7hK09aOXFqxSuDswfpnj7gDEODPBHPc4C6hD3Qlnxt2hpmnGwwSY4+7h4ETZtVqR4x5lxurmxez6qHsfD3r7NyMGeWaXGQp3BwYMhbsDEOPMBIV7nAXUoe5QuDsEMs7MULjHWUAd7A6Fu4Mw48QUhbsDgaRwdwBinJmgcI+zgDrUHQp3h0DGmRkK9zgLqIPdoXB3EGacmKJwtxlI5rgHA+SuMtxVhjnu+ieVcIQ7d5WxeZIOUZ057pFj62XLzHF3LjrxmOPuHJ3IWKJwt8mVwp3CXT2EuKsMd5XRO61QuNs84TpcncLdYaAxYo7C3blAUbg7x9KsJQp3s6R0ylG4U7hTuAcT4Iw7Z9xtnlZdq07h7hpqTzVE4e5cOCjcnWNp1hKFu1lSIcoxx90BiHFmgjnucRZQh7oTzoy7Q03TjIcJMMfdw8GJsmvMcY9yADzYfFSFe8GxQox/8Bn8uGHbaWi89HhZo7hRuBsRqn2fU7jXvpib6TGFuxlKta8MhXvti7nZHlO4myVVe8pFVbh7aUN7OyGncLdDLz7rUrjHZ1zt9orC3S7B+KxP4R6fcXWiVxTuTlCMLxtRE+5itn3yX2dg0t3D0fbM3Jilyhz34NBxVxnuKsMcd/3TWTjCnbvKRO7ywBz3yLH1smXmuDsXHea4O8fSrCUKd7OkdMpRuFO4q4cGd5XhrjJ6pxUKd5snXIerU7g7DDRGzFG4OxcoCnfnWJq1FDXhLhwUqTKtWjTBDYMuN+uv58pRuFO4U7gHE+CMO2fcPXei1nGIwj1WIuWsnxTuzvGMR+H+1XcbMerexwOQmjbOwfQn7vdMdkhUhfvWnfswZ/4yTBo/HOlpKc6NJJctMcfdZeAx0Bxz3GMgSFFwMZwZ9yi4ySZdJsAcd5eBx1BzzHF3P1hCuD81fR5eePw+NKifCfH35KkzPCPeoybcQ+0oI8LEXWXcH6xs0TkCFO7OsYwnSxTu8RRN5/pC4e4cy3izROHufkTVwr24pAxTnnwZN1/bBxd17ei+Q6oWoybco95zBx3gjLuDMOPEFIV7nATS4W5QuDsMNE7MUbjHSSAj0I3aINz3HN+DLflbIkAvtMnm9ZqjXXa70wqphbs80Xz/uKEU7q5HKQINMsc9GCp3leGuMsxx1z/RhCPcuatMBE7cNSaZ4x45tl62zBx356LjRI77M2uewcSlE51zyqSl+3rch6evetpQuM9ftArzFq4MpM6YNB+xYlGfcVcvAhA9nTXtQU/c1ZihTuFO4a4eJ9xVhrvK6J07KNzNnFXdK0Ph7h5rL7VE4e5cNJwQ7m+vfxv/+upfzjll0tJNnW/ChIsmaAp35eJUr6VuR1W4q7+OEPTEgtVxDzyFu2+/LiZ2m6Fwp3CncA8mwBl3zribvG5GvRiFe9RDEBUHKNydw+6EcHfOG2csaWlTZyw7YyVqwj1Usr+A9tbClXhs0piY2G2GOe7ODMZ4ssIc93iKpnN9CWfG3bnWacmrBJjj7tXIRN+v2pDjHn3KwR5QuOtEJNSTU8Ws+5PPz8XUh8ZKW/F4/UXh7vUIue8fhbv7zGOhRQr3WIiS+z5SuLvPPFZapHB3P1IU7jrMOePu/mBki+4RoHB3j3UstUThHkvRcs9XCnf3WMdaSxTusRaxyPsbtVQZ0TWtlbrMcV+NwdePgLw7S9Pc5nhn7izcOmYCvln7GfwALujeE6/NfA43jxyDtPQMvDVnJq4cNARZDXLwwbtzcX73S5HbrCUqKyvxykvTMGb8/YGR9PmqZaiflY2zu3ST3jtReBwL57+OEbffFTTaFrw9Gz169UPjJrlB72/ZtB67d2xD3wGDNUcnd5XhrjLMcdc/cYcj3LmrTOQuhMxxjxxbL1tmjrtz0YnHHHfn6ETGUlSFu+hStHeVkWf+P1i+JkBYvauNuMF49ImXpc+vuaJHUO49F6cGD0wKdwp3CncK98hcrpy3SuHuPNNYsEjh7lyUKNydY2nWUtSFu1lHI1VO5Nr/Z+5ijL99iLQQVv1oW3Wu09PT50muTBw3VPpJ4U7hrh6b3A6S20Hqna844x6pM3l4dincw+MW67Uo3J2LIIW7cyzNWqr1wl0NSv2ELCHUW7VoEtiaUmvRAhenmh1utaccc9xrT6yt9DQc4W7FPsvGJgHmuMdm3NzwmjnublCOrTYo3FXxEjn2D0+dgb9MHovcxg0x5cmX0eOCzgHhrvy87ZnV+d8U7rE16N3wlsLdDcqx1waFe+zFzA2PKdzdoBybbVC4x2bcIum168JdntEePexq/OfNJfhxwzbN/kXjSVVyvrss1LV2vjlNuB/fiYqtS1Dc8TeRjBNtxxiBjNRElJVXoaJKLCfmiwSqCaQkJcDnA0rLq4iEBAIEEn1AWkoiikorSYUEggiIm/2i4gppYwqvvjLTk7zqWlz65bpwlymG2sc9Gg9gkkV6k0bZgfx1tZAXvquFu8hxn1L3Tyi56k2Ut7ke/53/Frqc1xVt2rYPDJiVHy9Dvcx66HZhd0x76nHcc98DWP/zj9i3dw8GXH0NZr8yEwMGDkZZaSk+/2wVhg6/Fe+/9y7O6tARzZu3xKuz/o27JvweX3z+KcTRe0nPy/DCv6Zh1Og7kZ6RgVkvv4RfXXcDsnMa4q0356DHJb3QouWZ0q4yz/3j7/j9xD8GfPl4+YfIapCN87tdKL13/PgxzHtjNu4YF/zY3zfmvII+ffujaW6zoIG/Yf3P2L59CwZdc53mASH7fVaHTroHzHffrkP+kTz063+VbpnDhw9hyQfv4dej7jA88E6cKMTrr83CneN/Z1jW7/dLMbjvD5MNy4oCz//zaYwZezfS0tJMlReFli5+H61bt0Kns89FZaW50+3mTRuxccN6XHvdDabbURYU42nXzh24etC1YdX/4ftvcejgAfQfMDCs+spKe3bvCoxj28ZUBkQf1375OW4aOtJp02GPZyuOpCQnwAcfSsvNC7TlHy1BwzMa4byu1TtBee0186XncdOwkahfP8trrhn6c/DgASxbugi33DbGsGwkCyQk+CThfrKkIiLNPP3kXzFx0kMRsR2LRu2eL93sc930ZBSVlMNv7lLipmtSW2JsTZkyxfV2a3ODnhTubj+ASUu0y4PCKMddFu7+hFTkDVqO99dsR6ezz0PL1u0C42rN6hWoU7cezu16IWY+/3eMvmsixOKYgwf24fJ+V2P+m6+gd7+rUVZWhnVruR2kAHck7xBWLluEG4ePMjw+i4pOYMG8VzFy9N2GZYVwFzG4Y8Ikw7KiwKsznsWw2+5Eaqp54c7FqVycqje4wkmV4XaQpg7VsApxcWpY2GK+EhenOhdCLk51jqVZS54U7mL7xTXr1gdtu2i2Q1bLac2qK22Y2VXm4c5rkLRrCapSc/BqxlR07NKDwr1dB91QrP/xWxTk56Fn7yt1y1C4WxvJdi9EG37+HkcOHUCvvvrfgpj1iNtB6pOicDc7itwpR+HuDmevtWL3fOlmf7ye407h7uZoqG7LdeEuP2Bp/8Ejur1t2jgH05+4H/Liz0hi0fPnNyMGBVJmQu3jLnwrPH4cae/0RnL+d6jIbIfDv/oM/uTMSLpN2x4nwMWpHg9QlNwLR7hHyVU26yIBLk51EXaMNeV14S5w5uakxxjV0O5qPV9I1PjzA2MCG5VEs8OuC3e5s6Fy3KMJJJy2xa4yRUcP4oyFPZF4YhdKG1+G/Kvehz8hORxzrBMHBCjc4yCIEegChXsEoMaBSQr3OAhihLpA4R4hsCHMam377b4X+i1GTbh7CYJdX+TtIJMKt6LhwsuQUHYUxa2HoqD3LLumWT9GCVC4x2jgIuw2hXuEAceoeQr3GA2cC25TuLsAWdUEhbv7zF1tUf3k1I/mz0SPghfQIXE9jnd7DCe6TAIXpwaHhDnupw/R7Vs3Yeum9eg/cEhY49duziZz3LWxL1+yAK3bdUSbEGs2rAQsHOHOxalWCFsryxx3a7zipbTd86WbHLwu3J3Ica86XoWqAve3yE3ITEBCdsJp4aRwDzHCQ+W7R2Mf93AORrVwX/r+OzivUSm6rR8rmSvoMwcf76nHXWUUcCncKdzDOdZEnX17duLbr9fgmiHDwjVhqR6FuzGuua9OxzVDhiOzXn3jwh4rQeHusYC45A6Fu3OgnRDuJWtKUPxRsXNOmbSUenEqMgZkaAr3Ufc+ftr7tT7HXbmby3lnt8Oc+cswafxwpKelQGzBeNnFXXBR144m8UevmJZwF9tBdi56H/W+fghim8gFTV9A+hntuB1kTZgo3Cncwz1iKdzDJRe5ehTu9tlGOlVGiKuxv33AvqNxYoHC3blAOiHcyzeUo+SrEuecMmkppVMKUi9K1RTuT02fhxcevw8N6ntvo5Go5bgrF6cKak8+PxdTHxorQYrGA5hMxlmzmJzjrv6w/ue/RZ1NL0vbRB7+1WpU1jnTTjOsG0MEmOMeQ8Fy0dVwUmVcdI9NRYlApIV7lLrFZh0g4PVUGdHFeNxVhsJdY/AqhXt2ViamPjsHk++5RRLubj+Aye6xpSfc4a9C9rIbkbZ3KbeJtAs5xupTuMdYwFxyl8LdJdAx1gyFe4wFzEV3KdxdhF3TFHPcdZirH3ykfEKpmw9gcmJI6Ap3sVF+ZTEafnCFtMc7t4l0gnZs2KBwj404ue0lhbvbxGOjPQr32IhTNLykcHefOvdxN8lczMCPf/AZ/LhhG9x8AJNJ93SL6eW4t2zdLlBnzSeL0GTHv3Gpfwn+XDQFo8dPgsixO3hgHy7vdzXmv/kKeve7GmVlZVi3djUGXz8C8qK4prnN8c7cWbh1zAR8s/Yz+AFc0L0nXpv5HG4eOQZp6Rl4a85MXDloCLIa5OCDd+fi/O6XIrdZS1RWVuKVl6ZhzPj7A758vmoZ6mdl4+wu3aT3ThQex8L5r2PE7XcF9XHB27PRo1c/NG6SG/T+lk3rsXvHNvQdMFiTiZnFfMxxPx0dd5UxdyQyx90cJzdLMcfdPu1IC3fmuAfHiDnu9sesbMGJHHfnvKkdlqKW4x4veE0J99UrUC+pFP22/QZ/yb8H93f4Gl82+x8K995X6g6DI3mHsHLZItw4fJThUCkqOoEF817FyNF3G5b1+/2Y+fzfcceESYZlRYFXZzyLYbfdidTUNFPlRaFPli9G+7at0bp9Z5SWm9viisLdHF4Kd3Oc3CxF4W6fNoW7fYZWLFC4W6EVuiyFu3MszVqKmnCPlyenmhXuderWwwW5ZXhh3io8XOf/8FWDsdhe7yrOuOuMVAp3s4dwdTm7FyLu467N28w3SFYiFU6qDPdxt0LYWlluB2mNV7yUtnu+dJOD11NlKNzdHA3VbVG4O8A8VI672nza3o+Q/dF10tuF505C4QWPOeABTXiNAHPcvRYRb/gTjnD3huf0IpIEIj3jHknfaTuyBLwu3EXv421XmchG1L71qAl34Xos7dceCrUV4S7spO16H9krhkomizqMxbFL/mE/krTgKQIU7p4Kh2ecoXD3TCg85QiFu6fC4SlnKNw9FQ5POBNV4S62fVQ+eMkTRMJwwqpwF02k73wXDT6+RWqtuPVQFPSeFUbLrOJVAhTuXo1MdP3yinA/WVGE8spylFWVobyyDGWVpSirLEe5/Lf0s/rv0srSmvcV5QP1ylBeVY7Kygr4xT+/H1WoCvzu91f/XuWv/qz69ypA/O6r/l35vvy7VE+jTPX7CNgJ1BVtig9q7GvarCkj+1BdRrhS7ZdkuOZV/Un1q9ruqVfQZ8pyZusE2au27fMBiQk+lFecWhOj54PyfbV/If326fXJZF+D+Ch4hOKjw7QG7CnGOr6F3VedWATZC9Nv3fiH6GvwGArF+3SuYmyI48fMeCytdP8hRn+4+FE8efX/RvfEWstaj5pwV+4io8X83E5tPPvUKqW/VnLcz+16obQwcvRdE6Wc5Lxt63BTwQN4qfDXGNh8H/K6/RVff/Uld5UBwBx3a2ciuzmbzHHX5m01x11cOE8XwGWSQC6rLENSUiUqqspx9GRxQCRLwrhGJIsyQizLNkorSpC2MxElKWU4mn1csiF9XlFtU4huZXnxd2mVyp6qjCScHXzdi3sxC7NwFEcdtOqOqVzkYjAG4yW85E6DUWrlT6j+x1c1ga7oilZohf/iv0Rik4AYV1OmTLFphdWtEIiacLfipJfL2hHuYjvIK7o2xfx5s3Fd8js4kdUNKzAEg2+8ldtBclcZS8Oewl0fV2HZcRSVn0BReRFOSv9P4GTFSem9k+UnUVQmflZ/dkJ6r/p38Xm7g62wO3UvdqfsPiWaxUy1JLZl8VyOkspiS/GyUlgIywM4gK/xtZVqIcumJaYjOTEZKQkpSE5MqfmZjJTEVKQkpiBZfj8xOfB7akKqVEd8dqpMMhr+nImTnSqBVB98Ph8SfAnw1fwTv0P8Lr1f866ijJhqTkBNeWVdUVa2o1Gm2iZOtRVUJkFqT/yTfFH8Lir5/KfeLz16Evu+2452fbsEeAm78kvY0Pog6H1pxvxUOeVnp5VT2FPWSU5MQN30ZBw9URZkq7pthW2ddqRSej74fPjsjcXoOWKgxET5Cqrj127HrA9KW8Feh/YtyB+zvJVMwuCzZ8s25O0/gPMv63kabzMxP72vJuMfIkbKUadkIlJlDh8tQZVfORKCmVbzNh4nqYnmd0cze7Lh4lSzpJwrFzXhHmpXGbH5/VsLV+KxSWOQnpbiXG8jYMmucBf7uL/7+ksY4nsFFScLsKJqEAb++iF8tPJTtG7XEdzHndtBmhm28Sjcj5UeRUHJEeQXH0F+yREUlOSj4MAhVOwswYHW+SoBLoR2EYorqn8K0X20pMAMupBlhmIofsJPWI/1pm3VSa5bI4qVIrhaJKclpyItKQ0+JJ4mgMXnQjhXC+MagZyUiowdSUjITEJys4wgwXxKdNe0oxLVKUmyID8lzIVgd/rF7SDtE410jjv3cQ+Okd3zpf2Im7fg9Rx3CnfzsXSqpCeFu8h9f/L5uZj60Fg0qJ/pVF8jZiecHHe1Mwklh5GzZBCSj/6Misy2ODLoI1SmN4mYzzQcWQLMcQ/me7z0GPJL8iQRXlCaXyPG83C0uAB5xYdPCfOaMuI9p15CSGck10FGUh3USRb/6yIjJQMZ4mdShvS39H5KJjKSM2rKVdepm5IpiWVZJAeJavG+ENqJyVIdMy+v5Lib8ZVl3CMQaeHuXk/YktMEvC7cRX+5q4zTUQ9tz5PCff6iVVizbn1MzLgLvE4Id2HHV34COR9eh5TDX6CyTnMcuXqxJOL5ij0C8SzcZREuZsDFTLgkxsWMeHF+QISL2e78ksPSZ+GKcCGoG6RlIzstR/rfID0HDcTv6TmS0BbCWpRJT8pAZko9pCelIyOl+n1ZpIvPvPSicPdSNLzjC4W7d2LhNU8o3L0Wkej747pwF7Pp4x54CvsPHtHtfdPGOZj+xP1oe2Zu9AmZ8MAp4S6J96pSNFgxEml7FqMqNRtHBi5FedbZJrxgES8RiCXhLoT47sKdOFC0TxLfYmb8SHGelJoipahI7x2Wfh4uPhQWZiGkheCWhHh6jRBPaxj4XbyXk34GstIaSCK9SZ3YOPatwqBwt0qsdpSncK8dcQ6nlxTu4VCL7zquC3cZZ218cqp6VxmxOFXkuM9/8xX07nc1ysrKsG7tagweMgyr5vwJXUoWoWVqHl4o/T1uueM+fLP2M2mTqwu698RrM5/DzSPHIC09A2/NmYkrBw1BVoMcfPDuXJzf/VLkNmuJyspKvPLSNIwZf39gFH++ahnqZ2Xj7C7dpPdOFB7HwvmvY8TtdwWN9AVvz0aPXv3QuEmwgNqyaT1279iGvgMGax4ZZnbhWP/jtyjIz0PP3lfqHl3cVcbaiSdUzqYszHcf34k9hTux61j1T/G3EOxi8eaFuBBN0ATv433DhsUstiy+JTGeWi3EszMaSj/rFGegdFshzr+yFxqkZqNp3WaGNs0W2LdnJ779eg2uGTLMbBVb5cyMZysNhCPc+eRUK4StleWTU63xipfSzHF3LpLMcXeOpVlLURPuZh30ejknFqeeJtyvHyHtKtM54Qd03PtPvHDyLowe0htf7E2jcNcYEEVFJ7Bg3qsYOfpuw+Ei9tMVW3LeMWGSYVlR4NUZz2LYbXciNdX8avxPli9G+7at0bp9Z5SWm9t6b/vWTdi6aT36Dxxiyi91oVVff4jdu7ejuE25pjAPZX0vpxEAACAASURBVFTsNNAvtR+a+5rjcO5RNEjPlma/5dnxnLRTM+FmRPj+vburb0CvHxFWX0JVonB3HKltg1ycahshIj3jzsWpwTGicLc/ZmULFO7OsTRricLdLCmdcpEU7mJXmbYlqzHnk534Q91pWJI7DeX1O3DGXRWL2iLcxZaDm/I3Ykv+L/glfz22FPwi/b3t6OaQ+xILYd48swVa1GuF5pkt0VL8rFfzM7MlzshoDO7jrn2Ac8bd+ARJ4W7MyKgEhbsRIWc/p3B3jieFu3MszVqKqnAP9RCmWHkAkwDtZI67VuDSd7yDBit/LX1UeO4kFF7wmNn4slyUCNjJcRepK5vyN2BTwUZsPrIxINL3FO7S7U1u3eY4q0FHNK93Js6s3xrNMltUC/QaYR4lDGxWRSCcVBlCjH8CkRbu8U8wfnvIHPf4jW24PYuqcH96+jzJ74njhobrvyfqRVq4i06m7l+J7GU3wVd5EqW5VyC/3xvwJ9X1RP/pxOkEzAh3sdBTzJ4Lkb65YGP1z/xfcOjkAU2kib5EtKzXGu2zO6B9dkd0yO6Mdg3E7x1Mb0fIWEWXAIV7dPl7tXUKd69GJvp+UbhHPwZe8yBqwj1eFqdKs+Any1FYXBHx2CYXrEf2h4ORWHwA5VmdkXftp/BH4IEqEe9ILWhAKdz3Fu7G5qO/YLOYRT+yEZvzN2Lz0Y26DwgST7Jsk9UO7bM64qzsjmifI352kt5LSUitBfTit4sU7vEbWzs9o3C3Qy++61K4x3d8w+kdhXs41BR1Ip3jrn5yqtjrfUDe/2DanoEYn/UGSvtNx+wVW7mrjEcWp67d/zm++/QLHEzehy/K12Bz/iacrCjSHGXiKZbtGpwlzZ539nVGvWN1cUn//mib1d7yqLSbs8kcd23kzHE3HorMcTdmZFQi0sKdi1ODI2D3fGkUTyc/97pwZ467k9E2Zytqwl24J1JlWrVoghsGXW7OWw+Wclu4i+0gL+x2Hmb/+1lMSH0aGb6T+Gfl/+CKG8ZyO0iXd5U5WLQfX+7/DN/s/wpfHfgC3x38WhqhQzAEO7AD3+E76W/xcCAhzkUO+lk5ndC+QUe0y+6AlpmtAiPa7q4ydi9EFO4U7uGeXincwyV3qh6Fu32GVizYPV9aactuWQp3uwTjr35Uhbt4GNOc+cswafxwpKelxCTdaAh3eR/32y9OQ+NvHsDzJ+7ADbkb4bv631i4eAX3cQ8xkuxsB/nNgbX45uBarN33BdYd+FJ6YJH6dWa9Nhjiuw5NmjdBh05d0CrzLDSu09RwbFO4GyKSCnA7SHOc3CxF4W6fNoW7fYZWLFC4W6EVuixn3J1jadZS1IR7qB1lhPPcVcZcCJOPbkCDZTcj6cQ2VKXmoKDvHJQ2id1vMMz12p1Sq3avwKe7l0tC/esDa05rVGyzeF6jbriw6cW4oEkPXJR7CXLSGkrlzCxOdacXbMVLBJjj7qVoeMeXSAt37/SUnlgl4PUZd9Gf3Jx0q91ieRsEoibcbfjsuapuLU7V67jYaSZr1Tik73wHQAIKuzyAwvMfAXwJnmPlZYe2H9uClTuXYcXOpfh8zyqIfdOVryZ1cnGhJNB74IImF+P8xhfpdofC3cuRjp5vFO7RY+/llincvRyd6PpG4R5d/l5sncLdgahEW7jLXcjY/Arqr5kIX2Uxyhpdivx+r6MqrZEDPYxPE8UVJ7F6z0qs2rkcy3Yuwa7j24M6Kp4S2r/VQPRq0QfdGneH2Cvd7IvC3Syp2lWOwr12xdtsbynczZKqfeUo3GtfzI16HFXhXlxShilPvowPlq9B08Y5mP7E/cht3FB6r8cFnWNi0Wo0c9xvHjkGaekZeGvOzMCuMove/g/6lr+OtqWfoTylEf52dALG3D0pMA4+X7UM9bOycXaXbtJ7JwqPY+H81zHi9ruCxsqCt2ejR69+aNwkN+j9LZvWY/eObeg7YLDm2DKzC8f6H79FQX4eeva+Und8Hsk7hJXLFuHG4aOMxjCsPDl1w5Gf8Okbi7Cs+cdYu/8LlFeWBeyL1JcezXqi75kD0LflVdKOL6/OeBbDbrsTqalphn7IBT5Zvhjt27ZG6/adUVpeZaoec9xNYWKOuzlMrpZijrt93JEW7txVJjhGzHG3P2ZlC8xxd46lWUtRFe7yrjID+/XAky/MxS039EfbM3Px1Xcb8dbClXhs0hjPL1r1mnD/4N256HbBhei89TGk7FyAqScexO8vLUfh+Y9KqTO1TbifKD+Blbs+xMc7PsTKXctwqOgAHsEj+F/8r3SMtMlqjz4tr0S/VgNwSbPLILZoVL4o3M2eSk6V2793N9atXY3B14+wXtmgBhenOo7UtkEKd9sIQeFun6EVCxTuVmiFLkvh7hxLs5aiJtyVD2ASs+xK4S52m3ny+bmY+tBYNKifabYvUSnnReF+fvdLkdusJVI3v4YXlu7GI3X/L5A6s3rtD3E94+6HHz8c+gYf7/pIEuvfHvwKlf7KwNiok1QXf6i4H6m9G6BvqwFBWzJqDSAKd+uHFYW7PrNwUmVWr/wQ2Q0bofM5Xa0Hw4UaFO72IVO422doxQKFuxVaFO7O0XLGkieFeyzNuIsweCXHXWtIJB3bjOzlNyHp+Oa43XWmsOw4lu1YgiVb38One1bgWOnRIBQds89GnzP7o0/LAbisRV9njhwDK8xxdwVzzDUSjnCPuU7SYcsEIi3cLTvECp4hwBx3z4TCM45ETbgLAvMXrcKadesx+Z5b8M+X35VSZbKzMjH+wWcw9No+MZHj7nXhLvzzVZag3pqJqLN5ljTwilvdjOPdp6IyIzh/3TOj0qQjS7a9h7c2zsGSbQuDamSmZOKyFlegf+uB6N3iCojdYNx+Ubi7TTw22qNwj404ue0lhbvbxGOnPQr32ImVW55GVbiLTorZ9VH3Ph7U31nTHsRFXTu6xcB2O16ecVd2LmPbm6j/2d3SrjP+5Ewc7/43FLU3XvxpG5CDBr7ctxpvbXwd7295B4VlhQHL7Rt0wMA210npL92bXupgi+GZonAPj1u816Jwj/cIh9c/CvfwuNWGWhTutSHK1voYdeFuzV3vlfZyjntlZSVeeWkaxoy/PwDui+XvoumhBbi0dJ703qEzBuK1w1dgxKi7g+B6aVeZzQW/4O2Nc/Dupjext3B3wM8zMhpjSPuhuPbMG/DL8nUYOTq4D1qjxc6TU82OPu4qw8WpemMlHOHOHHezR571cnmHDuDTj5fi+mG3W6/sYI1IC3fuKhMcLOa4Ozd4uTjVOZZmLUVVuItdZQ4cyg/aPUbeIpLbQS5A63Yd0TS3Od6ZOwu3jpmAb9Z+Bj+AC7r3xGszn4PWdpBiVxl5caqWcJd3lbk4eQ0yv3oExyvT8J/i32DUVZ1xsu2pXUCiLdy37duEZUsXYH7Gu/jx8HeB8ZyelIEBra/BsE63oXfLK6T3rWwHSeGufWrY8PP3OHLoAHr1vcrsuUO3HBen6iOkcLc9vBw1QOHuKM6YMUbh7lyoKNydY2nWUtSEuyzQb762z2lpMbG0ODXWZtyV20EmFu1EwrIJmLOnC+6tMw3l2V1xtOfzKM/pimgJdzG7/uI3z2Dlhg8xBEPwIl6UxvLlLfphWOfbcHWba0/bspHCHbB7IaJw1z5lmnkugdmTrShH4W6FVuTLUrhHnrEXW7B7vnSzT15PlaFwd3M0VLcVNeGu3A5S7N2ufMXSdpDC71jJcdceXn5kbJmNel89goTSwwASUNT+dhRe8GdUpWW7NiJX7V6Bl759Fh/v+jDQpshbH3n2aFx/1jCItJhYejHHPZai5Z6v4Qh397xjS9EiEOlUmWj1i+3aJ+B14S56mJsT/PwT+72mhVAEoibc42XGPfaFe80dXPkJZK77E+r+8hLgr0BVShYKuz2Gog6/kR7cFImXeGrpO5vm4qXvnsUvR9ZX30nCJz0Q6Y7zf4s+LfpHollXbFK4u4I55hqhcI+5kLniMIW7K5hjshEK95gMW0SdjppwF70SKTGTp87A9Cful56YKl5itn3cA0/h7tuv43aQEQ29tvGkY5uQtXo8Ug5/IRUozzoHx3o9j7KGFzrmTUFJPmb9OB2v/DAdh4sPSXbrJNfF0E634s6uv0PLeq0daytahijco0Xe2+1SuHs7PtHyjsI9WuS93y6Fu/dj5LaHURXuSqG+/+CRQN9jaTvIWM5xF8BPFB7HwvmvY8TtdwWNvYVz/oGr8SbOLBcLQ3042W4kjl80FZt2HsLuHdvQd8BgzbEaKid469HNePGbadix8RdkVWVhERZJIn3MeXdhROfRqJtcN2DzSN4hrFy2CDcON96ukjnuzHGP1ImTOe7GZPnkVGNGRiUiLdy5q0xwBJjjbjQizX/OHHfzrJwqGXXh7lRHnLAjdrlp1aLJaTP94kFRjz7xstTENVf0CNoFJ16Fu1icesmll6LtvpdRd/1z8FWVoSq5Hr7OnYzN5W3Qd8C1poX7p7s/xvRv/4GVuz6CH350R3ecU6cLevUZIO0QI9Jj1C8Kd2sj2u6FiItTtXlTuBuPQwp3Y0ZGJSjcjQg5+7nd86Wz3oS25vUZdwp3N0dDdVsU7jVPcJWF+Z8fGBMk3EU6z1PT5+GFx+9Dg/qZEOJevCaOGyr9jGfh3qNXPzRukouk41tQf81EpO5bhh8ruuCXpEvQr/9VKGl+9WkjVhY6LVq3xvzNb+Klb57FxvyfpXJpiem4vsMwXFv3OiQVJ6Bn7yt1RzyFu7WTgd0LEYU7hbu1EXeqNIV7uORO1aNwt8/QigW750srbdktS+Ful2D81Y+qcBc7y4x/8Bn8uGHbaWTP7dQmIJbdwq41465+Ty3khW+xvauMebppuxai/toHkHhip1Sp7IzuOH7RX1HW6NSTSkX++is/vYRZ378YyF9vWrcZRp07DredMxb1UuubbzCGSzLHPYaDF0HXmeMeQbgxbDrSwj2G0dR6170u3EWAuKuMu8M0qsJdPXvtbtdPb00t0rUeBiUWzz48dQb+MnlsYEFtbRHugpivsgx1Ns1A3e+fREJJ9cLS0tx+2NXlj5i2bSn+88OLKK44Kb1/YZMeuKPrBAxscx2SEpKiHV5X26dwdxV3zDRG4R4zoXLVUQp3V3HHVGMU7jEVLlecjZpwD7WPuys912hET7grHxKlJdxLy6tQVlEVLbej0q6v4iRSfvwXitc9iWlFBXiyFCiq8eTmTsNxT/eJOK/x+VHxzQuNZqQmoqy8ChVV4lm3fJFANYGUpAT4fIA4Z/BFAjKBRB+QlpKIotJKQiGBIALiZr+ouEJ6arpXX5nptWtiLtpxoHBXRCCcGXeR4/7gQ49IIk28/jv/LXQ5ryvatG0fsLzy42Wol1kP3S7sjmlPPY577nsA63/+Efv27sGAq6/B7FdmYsDAwSgrLcXnn63C0OG34v333sVZHTqiefOWeHXWv3HXhN/ji88/hTh6L+l5GV741zSMGn0n0jMyMOvll/Cr625Adk5DvPXmHPS4pBdatDwTlZWVeO4ff8fvJ/4x4MvHyz9EVoNsnN+tenvH48ePYd4bs3HHuAlBY/GNOa+gT9/+aJrbLOj9Det/xvbtW9B3wJV48Zt/Ydrav6OgpEAqMyQJGOwfiovaNEO7nsNReYa2cP/u23XIP5In5cnrvQ4fPoQlH7yHX4+6w/AYOXGiEK+/Ngt3jv+dYVm/3y/F4L4/TDYsKwo8/8+nMWbs3UhLSzNVXhRauvh9tG7dCp3OPheVleZOt5s3bcTGDetx7XU3mG5HWVCMp107d+DqQdqLho2M/vD9tzh08AD6DxhoVNTw8z27dwXGsWFhiwVEH9d++TluGjrSYs3wisvH4VkdOoVnQFUrJTlBWoxdWm5eoC3/aAkantEI53Xt5ogPThuZ+dLzuGnYSNSvn+W06YjbO3jwAJYtXYRbbhsT8bZCNZCQ4JOE+8mSioj48fSTf8XESQ9FxHYsGrV7vnSzz3XTk1FUUg6/uUuJm65JbYmxNWXKFNfbrc0NRk24SwHX2cUlWgEJJ8e9NixOVcZj48Yf8On3H+G5E88ir1g8aRW4vEU/PHrRH9Fj3xIsXncAZyd+j85J61F2Rg8UnT0BxS2vAxSpMut//BYF+XlcnKoAu33rJmzdtB79Bw4Ja/jbXWzFxana2LmrjPFw5OJUY0ZGJSKdKsPtIIMjYPd8aRRPJz/3eqoMd5VxMtrmbEVVuIu0kznzl2HS+OFIT0sx53EES2kJd+4qU/1gLPFasm0hZq+YjgYlWZiP+ejWpDse7flXdG96anHq8g/eQufUrTg/78VADnxlRjOc7HQXijrcgaqU+qBwP30QU7ibO7D37dmJb79eg2uGDDNXwWYpCndjgBTuxoyMSlC4GxFy9nMKd+d4Urg7x9KspagJ91A7ygjn3dxVRrlPu2i7aeOcoKe5htrHXZSP98Wp249twSMrJ2Ll7mXSuOqQ0xkPX/p/uOLM07eDlAeeWMSavv1N1PnpWSQfrd4O0p+YjpNthqHonPtQUf9UKpHZwRpL5bg4NZai5Z6vXJzqHutYainSwj2WWNDXYAJen3EX3nJXGXdHbdSEu7vdjGxr8Srcxe4wT6/9K2Z8/xzKK8uQmVIPf7j4EYzuMh6JvkTTUFP3rUCdn/6BtH1C+Fcn6pU26Y2is3+LkhaDpCezxtuLwj3eIupMfyjcneEYb1Yo3OMtos71h8LdOZbxYonC3YFIxqNw/+/mefjz6odwoGiftJjupo4j8WivqchJaxg2saRjm1Hnp2nI2PoGfFUlkp2Kuq1xsvN4FLUfBX9y3bBte60ihbvXIuINfyjcvREHr3lB4e61iHjHHwp378TCK55EXbiLHPJR9z4exGPWtAdxUdeOXmEU0o94W5y6pWAT/rB8PM47cDaWYAkyc7Lw937Po2vj6l1otmxaj907tqHvgMGaXMzkBG/4ZjVObF+Na8teQEJp9QJXf1JdnGz3axSd81tJzPPJqdaGv92cTS5O1eZtZjxbiVQ4wn31yg+R3bAROp/T1UpTrpVljrt91JEW7lycGhwju+dL+xE3b8Hrwp057uZj6VTJqAp3raeQigWr4x54Cnfffh1uGHS5U/2MmJ14Ee7XjrwVf/t8ivTU00p/JcYljEPLrmfhtkvGIcGXEODnhHCXF6f26tUb6dvnSmk0yUc31LThQ0mzAdjZ7Df48Ic83Dh8lGHsiopOYMG8VzFy9N2GZcV2kDOf/zvumDDJsKwo8OqMZzHstjuRmmp+O8hPli9G+7at0bp9Z9P7dXNxqqlwgItTzXFysxSFu33aFO72GVqxQOFuhVboshTuzrE0aylqwl1+Kqny4Uay00LQv7VwJR6bNMYTu82Eghnrwr2w8BjefPPfeBb/wJGSPEmkD+90Oy7Juwg9Lx+Axk1O7SojODgp3Hv2vjKAVsqD//lZpO39UHrvYFUTzK8YiVsua4riVjehMr2xbhgo3AG7FyLOuGsPL864G19KKNyNGRmVoHA3IuTs53bPl856E9oaZ9zdpB0bbUVNuId6cqqYdX/y+bmY+tBYNKif6XmSsZrjvrtwJ363dAy+OvCFxFikwzze51mce0b0vpIXM+9iBj5jy6tBcS/N7YfiNiNQ3GoI/El1PD8mmOPu+RBFxcFwUmWi4igbdZVApIW7q51hY44S8LpwF53lrjKOhtzQWNSEe7zMuAvCsSjcX/7hefzfZ4+gtLJE2i1mymV/w4hOtxsOGLcKJJQcRsaW15G+9Q0kF/wQaNafkCaJ95K2I1DS7NSMvVt+mW2Hwt0sqdpVjsK9dsXbbG8p3M2Sqn3lKNxrX8yNehw14S4cE/ujz1u4Ei88fl9gZj3WctxjTbirZ9kva9EX/+j/bzSu09RorETt86Tjm5G++TVkbHsTiUW7A35UpjVGcZuhKG47AuU50fuWQAsMhXvUhounG6Zw93R4ouYchXvU0Hu+YQp3z4fIdQejKtxFb7mrzNWY/+Yr6N3vapSVlWHd2tUYfP0IyLm1TXOb4525s3DrmAn4Zu1n0i7oF3TviddmPoebR45BWnoG3pozE1cOGoKsBjn44N25OL/7pcht1hKVlZV45aVpGDP+fmlgvbflbSz+8B0cqNqPDSkb8Njlf8c1za7DwvmvY8TtdwUNvgVvz0aPXv1cy3FXj3y9XWVSD65G2pbXkbHjHfjKC6Vqhf56mFFyN8b2Skdp454oa3TqSa5qu1ycqn2OYY67NhfmuBtfk5jjbszIqESkhTt3lQmOAHPcjUak+c+5ONU8K6dKRl24O9WRaNmJhcWpt9w5AQ9/MhFvrJ+FQRiExg2b4bfX/hFN6uTiROHxmBLuyjin7/gv0re9gfKdn2DGyTswsc7T0sf+5EyU5F6BsmZXoqT5VajMOLXAlsKdwt3KuYLC3ZgWhbsxI6MSFO5GhJz9nMLdOZ4U7s6xNGspqsL96enzcOBQftDuMXLue48LOnM7yHYdYXfGfdb0Z/BKvdew9ehmZKfl4E+5f0HH5ufg7C7dpDESy8JdHuTFBfvx37dfx91n/YjUfcuQUJofNP7LszqjtPkAlDYbgJImvbkdpMbZgTPunHE3e9FQl6NwD5fcqXoU7vYZWrFA4W6FVuiyFO7OsTRrKWrCnYtTzYYo/HLzNs7GQyvvRXHFSXRr0h0vXzMPZ6Q3Ct9gTNT0IyXvG6Tu/Qipez5ESt5XgL8y4Ll40FNpk8tR2vyq6tn4ui0j0ivmuEcEa8wbZY57zIcwIh2ItHCPiNM06goB5ri7gjmmGomacOd2kJEbJ0Ko37dsHBZueUfal/13F0zC/Rc/gkRfYuQa9ajlhLLjSN2/DKm7P5Rm4xNP7gvytKJee5TkXomyFlehtEkv+BPTHekJhbsjGOPOCIV73IXUkQ5RuDuCMS6NULjHZVhtdSpqwp0z7rbipltZpMT8+r3rsfP4Nik1ZvrAObi0mfefQBsZGqdbTT76M1L3iNn4pUg59AV8VWWnZuMT0lDWpJeUViOe3lpR/6yw3aJwDxtdXFekcI/r8IbdOQr3sNHFfUUK97gPseUORk24C0/FjjKTp87A9CfuR9szqxcQxtp2kF5anLp4/0Ks//hrrPCvQKOmuXjxqtfwwWuvB3aVEXw/X7UM9bOy4yrHPdwnp/oqipC6fyVS9y6T0mqSTmwPOoAq67TA34+Mwa8HdUdiTntU1mlu6gD7ZPlitG/bGq3bd0ZpeZWpOtu3bsLWTevRf+AQU+XVhezmbDLHXRs7F6caD0fmuBszMioRaeHOXWWCI2D3fGkUTyc/97pwZ467k9E2Zyuqwl0p1PcfPBLweNa0B3FR147mehDlUl4Q7vPmzMBnmV/i7V2vYxRGoWGHXPy+/0PwV/mDtoOkcAdC7SqTdGxzTVrNUqQe+BS+ymL8rehB/D5jGtJ8JahMb4KyRpegvMmlKDvjYpQ1vFBz9FG47w5sa+r04blvz058+/UaXDNkmNOmNe1RuBtjpnA3ZmRUgsLdiJCzn1O4O8eTwt05lmYtRV24m3XUq+WiLdx3Fe/EgrmzMbvqNVSl+TE582H06TVIcx93CvfQwl09xlL3Lse/F36N8bkrUC//09OGoHiKa3nDbihtfAnKhZBvdCmq0rJB4U7hrne+CidVZvXKD5HdsBE6n+Oth4zJfaRwt391onC3z9CKBQp3K7RCl6Vwd46lWUsU7mZJhShXeLIchcUVDliyZuK1n/6NKZ8+gNLKEnRveileGvR6Ldg1xhojJ0unHP4KKYe/RPLBL6Sf6oWuoq2Kum1Q1vhiJHcZjeKKRBSnt0JlhnefSuskH9oyJhCOcDe2yhKxTiDSwj3W+dRm/72eKiNik5vjzKYOtTnOVvpO4W6Flk5Zt4X7yYoi3PPRHVi8dYHk0cSLHpJ2jeHLXQKJJ/cj5fAXSD74JVIOfY6UvHWaDogHQom95Cvqd0BFg06oyOqI8vodUFm3lbsOs7WoE6Bwj3oIPOkAhbsnw+IJpyjcPREGTzlB4e5AONwU7oeLD+GWBb/Cz3k/oEFaNqZfPQc9m/d2oBc04QQBScAf+gp1TvwMf97PSCzYBF9lkbagT0yXdq4pz+qIygadUVGvA8qzOqGifnsnXKENDxKgcPdgUDzgEoW7B4LgURco3D0amCi6ReFuE76bOe5LP3kX72x8Ax+Uv4/JCZMxZPhtaJ59Jt6aMxNXDhqCrAY5+ODduTi/+6XMcdeJa6jFqVpVXp3xLIbddidSU9NMjxR1jnviid1IOv4Lko9uQGLBRiQf3Yik4xuRUFoQsLmhojN+LD8HQ9PnwZ+Qgop67VBRv6M0Oy/P0ldktoc/MUXTD7s5m9xVRju8XJxqPOyZ427MyKhEpIU7d5UJjoDd86VRPJ383OvCnTnuTkbbnC0Kd3OcdEu5JdzbXtUF0997CuWVZahqkYCBh6/C0Ft+g7T0DAr3ohNYMO9VjBx9t2E0oyHc9ZxKKDmE5KO/IOnoBmzbvgO/HCjDzRnzkVh8QLuKLxEVdVtXp9pkdUBlVmdptr4iqwM2bd6GvXt2oU//QYYMtApQuFO4hzVwAFC4h0vuVD0Kd/sMrVigcLdCK3RZCnfnWJq1ROFulpROOTeE++uzX8T/lD2KPuiDi3N74p4bHsZrM5/DzSPHULgDCHcfdzOhd2LG3Uw7yn3cxdNehZhPOrYRSWJ2vmA9ko//gsQTu3RNfZvQD1uTL8JVHROBpAxU1G0h5dBX1m2JyvTGhi5QuFO4Gw4SnQIU7uGSo3C3Ty48CxTu4XHTqkXh7hxLs5Yo3M2SClEukjnur6//Dx5Y8VskJiRKD1Qa2PY6BzymiUgTiMSTU8W+8kLIi1n6xKMbkCwL++ObQ3ZHbFtZWbcFKmqEfFVm64Cwr8g8E1VpjSKNg/ZrCDDHnUNBi0CkZ9xJPXYJeD1VRpDlrjLuji8Kdwd4KILnAgAAHFhJREFUR0q4P7HmMfzj678hJSEVswa/jd4tr3DAW5pwg0AkhHsov5MLfkJi4XYkndiJhMKd0s/Emv8J5ceNhX1mS5Q0Hwh/Up3qsglJqEptgKq0HFSlnlH9e2oOKus0cwNf3LZB4R63obXVMQp3W/jiujKFe1yHN6zOUbiHhS24ktPCvcpfhYnLx+GtjXNQN7kuZl+3ABc1ucQBT2nCLQJuC/dQ/UooOxYQ8eEIe7Vtf2JGjaDPOfUzNQdV6Q0lcS8eQlWV2jDwWWVGrlvYPd8OhbvnQxQVBynco4I9JhqlcI+JMLnqJIW7TdxO57h/9eUqvJMyH9k7MrE9eQf+fO3T+H7JF7h1zAR8s/Yz+AFc0L0nc9wVcYu3HPdwhqSdnE0h7Dd+txpHDh3AFR3TkVCaB19JvvQzofQIEkqOSD8Txc+SQ4bu7axshY/L+mBU+qxAWX9iHVSli9l78V8I+xxUpjaEP+MMVKXIM/tC7Nd8piP29+3ZiW+/XoNrhgwz9MOJAtxVxpgic9yNGRmViLRw564ywRGwc740iqXTn3tduDPH3emIG9ujcDdmFLKEk8L9WPExzFvyMv5Z9ixuS7odQy4dji7tLsQ7c2dRuIeIAoU7YPdCZGVxqhD6SkEvC3tJ7Jccxt6CUnx24Az8uuFSJBQL0X84rKPMn1Q3IOQloZ+Wgx0lTbEmPxfX9TnvNJv+xFT4k+ugKqmOlPIjfhffDth5Ubgb06NwN2ZkVILC3YiQs5/bPV86601oaxTubtKOjbYo3G3GySnh3qXnxXh0xUS0Od4KK+t/ioeyH0GnDl3RNLc5hbtBjCjc3RXuRofM/r27sW7tagy+fkSgaLXYz6uZvRcCXwh6MbNfIIl96UagNB+JokwIsb+9sg0+LeuF29JfNXLj1Gy/uAFQivnkevAnpaEquS78SRkQNwiSyE/OrPlbCP+6qEqug8Xf5uHMsy9Fm3YdTLcXqmA4qTKrV36I7IaN0Pmcro744LQRCnf7RCnc7TO0YoHC3Qqt0GU54+4cS7OWKNzNkgpRzm6O+45jWzF8wWDsPr4THbPPxts3LJWeispX7BLwUo57rFJMKD2KhLJTqTryLL+v9Bh85YXwVRQhobwIvooT0u/S3+JnzXvKB1y5yUC6EUhMhj8hFUhMgd+XIv2NhBQkJKUCSamo8CdJD9pSfy59ayC9nyzVE2VFPfHgLel98bv0dzIg2RV/17Qj16kpKz2sq6Zuddlk+BPT3UTBtkwSiLRwN+kGi3mQgNdn3AUy7irj7sChcHeAtx3h/lPe9xj+32tQUJIvLUAVC1HFglS+YpsAhbt34if2xZfEvSTohbgXQv9kjeA/CV/ZCUnwQ3xeXn0TUH0DUHNDUFkKX1UZUFkGn1/8LIevqhS+yjKgqgy+qnKIrTpj6SUEvD+h+mZCEviysJdvAuT3E8QNSE2ZhNRq8S9uKOSbA2EjMQ1ISADgq/7vSwB8PsBf/btf/C69r/gpysBX85lGXemzGjuS3ZoywoawKdkTJhTv+6vLS/Xk9pS/o8aXGr9O+SPKK17CbuB16g+pTfkl9UWnkvIz0VZQMeXfp35PSkpA3fRkHD1RVsPxVCX9ds3Zru5nwHF9f5S+qvoX5IMuB7U/JvgobYniinZD8g7iqheXcPhITgQcrx67GuxCxT8ER6VtvbgEtwk0bpCOw0dLUCUWuOmMTclD3Tgr+iOO1Qi8KNwjADWESQp3B3iHK9w/37sKty+8EScriqStHsWWj2LrR75inwCFe+zHMJwe+CpLACHkhaAXwt5f/dNXWQ5UlSIjqRIJ/nKcPFl8qox0E1Bec1MgbgTEDUG1DVSU1Nw0BH8euGkIupmoqSvdaNTUF59LNxenbjggLXHniwRIgATsEyjs+jAyr/g/+4ZowTQBCnfTqLQLhpvj/vaqV/DxT0vxHt7DH1MfxC1DxqGsrCyQGywvimOO+yjDCDHH3fs57oZBNFmAu8qYBGVQTEotEjcT8o1FVWnNNwnyjUP1zUa14C+Vbiqqbz4UNyQV1d9AzPyyCjd1LkP9tCrAL24KqiBuDnz+6p/Se9L78u9VYj69+m9RNvDZqd+luuJ9n6hzyk61TVFV8b7CjmRXriv/XtOur8YvZd0DpZlYcqgDRjVfC5/kh/xS/B70vtS4djnl+ybryG2KydLEBB8qKmv6J/fRqj86ffjrnpvxUPN5mn5Xx+L/27v/ICnKO4/j3+QSC004ECwhBg8QRFxi3BI0W5U72IJEZVfErOWCSUUQg6BelSwI54q6cpRZZIPBqgC12YBSFY+4KBYh/EqigJKqLQlBQ51Y4RD3SPHLiNlaS3bxgKunSY8zvTPdT/fTPTM9/Z6/YOfp53n69TzT85mep3v+8XDrd4/n/G6T+YExw1uNc0j7mpofLvX9ufsa+eDMFTK59+s59j3XGLuMf6754xhLd+90hgt9sL680q37XFc4BwgftSz65ClpaGjwsQVFTQUI7oaCQYL712+5RlZsfUYGySDp+40BcuOJG2Tc+FsJ7mlj8dHfTsrO32+RO6cS3HWmqOnFVn7uKuPVn2wXp3pto/s8wV1XKn/luDjV3DrqNe7cDjJzjEyPl+Yjrl9Dsa9x5+JU/bEMqyTB3VDSb3D/xcomWXRukZRLuVReOkHm/WCRbHhpLcHdMQ4Ed38T0/SNiOCe3ZvbQXrPQ4K7t5FXCYK7l1C4z5seL8PtjXttBPd8asejLYJ7COOku8b9j8fbZPLL460WvzeiVn528+c/UBNCN6iiiARY415Eg1FEXQlyO8gi6j5diUgg6uAeUbepNg8CxR7cFQEXp+ZhIqQ1QXAPwVsnuB/u+B+pbh0rHd1/l1uvmiSrq14KoWWqKFYBgnuxjkxh+0VwL6x/sbZOcC/WkSl8vwjuhR+DYusBwT2EEfEK7qe6PpKJL31b/tr5v5xpD8E7DlUQ3OMwSvnvI8E9/+ZxaJHgHodRKkwfCe6FcS/mVgnuhqPjtca96+xpefKFOXLo9EH5bOB5mXyyWu6dPdf6ifoTx4/K2PG3ssY9yxiwxt3fxDRds8ka9+zerHH3noescfc28ioRdXDn4tTMETA9XnqNZ5jPF3tw5+LUMEdbry6Cu55TzlJuwf3c+XMy7Td3ykXtX5Av9vqS/OSHP5eXV/+C4L5/n3x86m/y7XHfzelKcPc3MU3fiAjuBHd/M+7z0gT3oHKfb0dwNzf0U4Pp8dJPW6ZlCe6mgqW3PcHdcEzdgvuCHf8uL/73Grn9nybL92+4V/7tWzfL6pU/IbgT3HvMusOH/iKH/vKufGfiHYFmpOkbEcGd4B5o4okIwT2oHMHdXC5YDabHy2CtBtuK4B7MrZS3IriHMLrZ1rg373tO/vMP9dYvob5cs01GD/xWCC1RRVwEWOMel5HKbz9Z455f77i0FvUZ97g40M+eAsUe3FWPuatMfmcuwT0Eb2dw3/b+r+VHW+6W83JeWib+l1QNC3YWNYSuUUWBBAjuBYIv8mYJ7kU+QAXqHsG9QPAxaJbgHoNBynMXCe4hgKcH9z8df0tqXr1ZPjt7RhZUNMjDY/4jhBaoIm4CBPe4jVh++ktwz49z3FohuMdtxPLXX4J7/qzj0hLB3XCk0te4f9BxSJpfbJK2c20yakR56geW2na/Ll/56j/LdeVjWOMuIu+yxr3HrGONu94L8ehf22XfH9uk+o4pehsYluKuMt6ArHH3NvIqEXVw564ymSPAGnevGan/PHeV0bcKqyTBXUNyw5Y35Imla6yS1RMqZNH8GXJxr4us/9vBvf3jE9a92sd2/qt09vtUfjZ1rXzpi1+2yhDcM5EJ7j0nHcFd44UoIgR3Pad8liK4m2sT3M0N/dRAcPej5V6W4B6epW5NBHcPqT1vvyfLmltl1ZI6ubRPb3m2udXaYu6s2lRwf6CuTr7zy3Gy/8O35b4v/0i+P36mjLz6ulTNBHeCu9cLkuDuJXTheYK7nlM+SxHczbUJ7uaGfmoguPvRIriHpxVOTQR3D0cV1IdcOVBqqsZaJZ1BXt2rfeIvq+W372+Tfr36y5Ypu+XK3oPDGR1qia0Aa9xjO3SRdpw17pHyxrbyqIN7bGHouLDGnUngFCC4u8yJ011npKFpjVSMLksF90PtR2VhY4s8XT9Thg2+Quq218nytuVWLVtqd8v1l9/ALENACO5MgmwCBHfmRTYBgjvzIpcAwZ25QXD3MQfs4H7XpEq5sXyktaUzuA9ZPkTaO9rlldpXpObaGh+1UxQBBBBAAAEEEEAAAX0BzrgbnnFXF6cOqB4gs8fMtmpat26djB49WkaMGJGqefv27dKnTx+pqKiQxYsXy8KFC+Wdd96RI0eOyO233y7Nzc0yefJk6e7ulh07dsj06dNl/fr1MmrUKBk8eLCsWrVKHnnkEdm1a5ecP39eKisrpampSR566CG55JJLZMWKFTJlyhS57LLLZO3atTJu3DgZMmSInD17VhobG+Xxxx9P9WXr1q3Sv39/uemmm6y/dXR0yPPPPy9z5szJkFi9erXccsstMmjQoIy/79+/Xw4ePCg1Ndk/pNj9Lisryym7Z88e+fDDD6WqqipnmRMnTsirr74qs2dfcHV7dHZ2SktLi8ydO9erqOWnxuDJJ5/0LKsKPPPMM/Lwww9Lr169tMqrQhs3brTGrby8XHubAwcOiLKtrb1w7YTfh5pPhw8fljvuCPabAXv37pVjx47Jbbfd5rfpHuXb29tT89i4MkcFah/ffPNNueeee8KuOmt9OvM56o5s3rxZBgwYIGPGjIm6qUD1P/fcczJt2jTp27dvoO0LuZGa85s2bZL777+/kN2IvG31PtXQ0BB5O3FpwPR4GZf9zEc/mVv5UM5sg+DuYe61xj39dpCqqu2/eUWuHXW9/MvQ4amauTg1E5m7yvScdFycqnfw4+JUPad8luLiVHPtqJfKcDvIzDHi4lTzOWvXwF1lwrPUrYng7iGlc1eZufMfk87T/2fVRHDfKEOHj5Srhl+TU5bgTnDXPUA5yxHcg8pFtx3B3dyW4G5u6KcGgrsfLfeyBPfwLHVrIrhrSLndx11tnv7LqRrVUSQBAlycmoBBDrCLXJwaAC0Bm0Qd3BNAWLK7yMWpJTu0gXeM4B6Y7vMNCe4hIJZYFQT3EhvQkHaH4B4SZIlVQ3AvsQENcXcI7iFilkhVBPcQBpLgHgJiiVVBcC+xAQ1pdwjuIUGWWDUE9xIb0BB3h+AeImaJVEVwNxxILk7NBHxtG2vcd722Va4eNlSGXl0m3Z+d05phXJyqxcQvp+ox5bUUa9zNuaMO7lycmjlGrHE3n7N2DaxxD89StyaCu65UjnIEd4K7c2oQ3I/I3rd2y23fu9vw1dVzcy5ODZ3UuEKCuzGhENzNDf3UQHD3o+VeluAenqVuTQR3XSm34L5goXWBqnpwVxnOuBPcCe65DitBlsrs3vlb6XfZ5VL2Df3fBTA8rPnanODuiytrYYK7uaGfGgjufrQI7uFphVMTwT0cR2pBAAEEEEAAAQQQQCBSAYJ7pLxUjgACCCCAAAIIIIBAOAIE93AcqQUBBBBAAAEEEEAAgUgFCO6R8lI5AggggAACCCCAAALhCBDcAzp+3NEpDzz6U9l/4H2rhheWPyo3lo8MWBubFaOA1y/mOvvsVv501xlpaFojm19rszZbvGCG1FSNtf7tnEvqb18b0F+al86TYYOvKEYa+pQmsOft92T6nCXWX6679ipZtaROLu3TO6eRTnk1lz44clzmzqrFOiYCft8TdMqrMvU/bpH5D07NOBakH2tsnvvurmK+xGCuuL0XZOu+W/lD7Udl1oJlcuzER9rHnxgQ0UUPAYJ7gCliv5AqRpdZ4Uu9eBY2tsjT9TMJWgE8i3ETFa6WNbemQtizza1WN3MFKa/y6dvbb9jzZtVaH/ac/y9GD/qUXcD52leBqm3vu7Jo/gy5uNdFPTbyKp8e6gli8Zl1ft8TvMqnh7VsH+K95ll85JLXU7f3gmwabuXV8eLI0ZOpk0Cq7PGTp3Ief5KnXZp7THAPMK7qzbdp5a+k8bGZ1pk150E4QJVsUmQC6gA45MqBqQOiM5g7u+tWXpV1njXze/AuMh668w8B55lxrw/xuuU54x6vKeb3PUG3vNsZd7cPiPHSS05vs42n20khv+W93qeSI13ae0pwDzC+2V4cXmdkAzTDJgUSyPZBzC2QeZVXu+H8Rib9jFlXd3fGsiuWyRRo4AM063zde317olue4B5gMAq4id/3BN3yuktl+HamgIPvo+ls7yNu3574Lc83MT4GI8ZFCe4BBk8ddNdv2pnxdRTBPQBkkW5iB/G7JlWmrlvQCe65yqvdTP+GRv3f7QCrnmvdtNNzrXSR8iWqW85vWnSCe/o3ObnKE9zjNY38vifols8V3NN17DlUO6ky9Q1hvPSS01vnNy1e7wV+ynt925cc5dLfU4J7gDHWPVsSoGo2KQIBrzPozgtGvcp7nXF3roXWebMuAia6ICK6Z9BtLN3yBPd4TS+/7wm65XWPBcyXeMwXv2fQdcvbF6k21s/kJhnxmApGvSS4B+DTXZ8YoGo2KRKBfK5xd+6y7pt1kVAluhu6a9ZtJN3yBLF4TSu/7wm65XWPBcyXeMwXv2vWdcoT2uMx9mH2kuAeQNPrjgABqmSTIhPwukuMczmLV3mvOwOo3bdvJ8o6xSKbDC7d8bpLjHOeeJXPFfDjI5LMnnq9JziXs3iVtxWzBTe17Subd8md1eOsOxd5Lc9K5ogU717r3GEsfdmTW3mWxxTvOEfZM4J7QF2de/AGrJrNikTA7b7s2dahB72PO/fiLZIBD9gNt/uyZ5snbuXTn7O7w29EBByYPG/m9p6QbR26W3nnvbvVrlRPqEhdV6XC3Op1W1J7mP67EHnebZrzKaDzmx7pwd2tfLb7+avucMzwOSgxK05wj9mA0V0EEEAAAQQQQACBZAoQ3JM57uw1AggggAACCCCAQMwECO4xGzC6iwACCCCAAAIIIJBMAYJ7MsedvUYAAQQQQAABBBCImQDBPWYDRncRQAABBBBAAAEEkilAcE/muLPXCCCAAAIIIIAAAjETILjHbMDoLgIIIIAAAggggEAyBQjuyRx39hoBBBBAAAEEEEAgZgIE95gNGN1FAAEEEEAAAQQQSKYAwT2Z485eI4AAAggggAACCMRMgOAeswGjuwgggAACCCCAAALJFCC4J3Pc2WsEEEAAAQQQQACBmAkQ3GM2YHQXAQQQQAABBBBAIJkCBPdkjjt7jQACCCCAAAIIIBAzAYJ7zAaM7iKAAAIIIIAAAggkU4DgnsxxZ68RQAABBBBAAAEEYiZAcI/ZgNFdBBBAAAEEEEAAgWQKENyTOe7sNQIIIIAAAggggEDMBAjuMRswuosAAuELfNzRKQ88+lPZf+D9jMoXL5ghE8dXSEPTGuvvi+bPkIt7XZQqc6j9qMxasEwenDZZaqrGils96vlnm1tl9botOXfgumuvkmefekiW/3y9bH6trUe56gkVVh/UQ/VJlXlh+aNyY/nIVNnTXWdyPmcX2rDlDXli6YV9yvb42oD+svSJ2bJ0xbqUierbqiV1cmmf3qn9UD5qv9If9j7az6X3x9mWvT/ppuGPLjUigAACpSNAcC+dsWRPEEAggIAzfNtVqL+/uOH3Mv+BqdLV3W0F+9pJlRlBVYVU9Zg7q1Z06kkPqHbInzerNmvwHnh5P6vebI/0MHzf3VUZ5fa8/Z5Mn7PE2swZ6t3qqhhd1iOE2+04+2KHc2fwtg2OnfhInMHdbX8CDBubIIAAAokUILgnctjZaQQQsAXU2efWTTtTZ5NzyahAXN/YIs1L58mwwVeI+v+y5tbUdrr12PWHEdyHD/26/Gn/QZn/4FSrT3bQ/mbZMHmhdZs01s/M+FAQZnD/5NMu+eSTT+WuSZWpNlSg/+pXLpbX/7Av9SEnV/hnBiKAAAII+BcguPs3YwsEECghAWcgd9s1FUyPnzwldfffJXVPrcg4A++nHtVGGMFdnSX/4Mhxq8v2Wf+mlb8SdRZefciIMrirNodcOVDa9r5rLd9R30rU/7jFalt9oLG/nSC4l9CLhV1BAIGCCxDcCz4EdAABBAopkG0Ndra126qP6UtBnMtE/NSjE9x11rir4H79qOGysLFFnq6fKRu37bbCtPqbWnsfdXC/d+pEawmRWu5z5OhJ60OE/TdncHfbH9a4F/IVQNsIIBAnAYJ7nEaLviKAQKQC6evDVUPO9ePqb2pJzMq1G1NLZrJ1SKeesM642xe9vrXvgPTt01saH5spp/7emZfgrs7yW0uEfr3DYlAfHvr17Z1xPQBn3COdslSOAAIJEyC4J2zA2V0EENATyLX0xbm23au2XPWEGdydF8ba/4/6jLsK7vZ+3FQ+0lquY/+fpTJeM4PnEUAAAf8CBHf/ZmyBAAIlJPBG2zuibnWobnOY/lDh116Coi78tB+5grvfesIM7qpvL274nVRNqLD2I5/BXbW9fedbMnzoIOsCWYJ7Cb042BUEECg6AYJ70Q0JHUIAgXwK2Pc0T791or28Q/XDee/2XMHdbz1hB3fnh458rHHPdrtKgns+Zy9tIYBA0gQI7kkbcfYXAQR6CGT7QaJs69vVhm5LZfzU4xXcdS9Odf4AkupjGGfcnT8m5fwBJtWOn+DOxam88BBAAAFzAYK7uSE1IIAAAggggAACCCAQuQDBPXJiGkAAAQQQQAABBBBAwFyA4G5uSA0IIIAAAggggAACCEQuQHCPnJgGEEAAAQQQQAABBBAwFyC4mxtSAwIIIIAAAggggAACkQsQ3CMnpgEEEEAAAQQQQAABBMwFCO7mhtSAAAIIIIAAAggggEDkAgT3yIlpAAEEEEAAAQQQQAABcwGCu7khNSCAAAIIIIAAAgggELkAwT1yYhpAAAEEEEAAAQQQQMBcgOBubkgNCCCAAAIIIIAAAghELkBwj5yYBhBAAAEEEEAAAQQQMBcguJsbUgMCCCCAAAIIIIAAApELENwjJ6YBBBBAAAEEEEAAAQTMBQju5obUgAACCCCAAAIIIIBA5AIE98iJaQABBBBAAAEEEEAAAXMBgru5ITUggAACCCCAAAIIIBC5AME9cmIaQAABBBBAAAEEEEDAXIDgbm5IDQgggAACCCCAAAIIRC5AcI+cmAYQQAABBBBAAAEEEDAXILibG1IDAggggAACCCCAAAKRCxDcIyemAQQQQAABBBBAAAEEzAUI7uaG1IAAAggggAACCCCAQOQCBPfIiWkAAQQQQAABBBBAAAFzAYK7uSE1IIAAAggggAACCCAQuQDBPXJiGkAAAQQQQAABBBBAwFyA4G5uSA0IIIAAAggggAACCEQuQHCPnJgGEEAAAQQQQAABBBAwFyC4mxtSAwIIIIAAAggggAACkQsQ3CMnpgEEEEAAAQQQQAABBMwFCO7mhtSAAAIIIIAAAggggEDkAgT3yIlpAAEEEEAAAQQQQAABcwGCu7khNSCAAAIIIIAAAgggELkAwT1yYhpAAAEEEEAAAQQQQMBcgOBubkgNCCCAAAIIIIAAAghELkBwj5yYBhBAAAEEEEAAAQQQMBcguJsbUgMCCCCAAAIIIIAAApELENwjJ6YBBBBAAAEEEEAAAQTMBQju5obUgAACCCCAAAIIIIBA5AL/D38XiLmldDQZAAAAAElFTkSuQmCC",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_history(colors=['darkorange', 'green', 'violet'], show_intervals=True, title_prefix=\"With a very large amount of enzyme\")"
]
},
{
"cell_type": "code",
"execution_count": 49,
"id": "1fde8290-ac8a-4d02-80c3-14a5ee801b5a",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Min abs distance found at data row: 18\n"
]
},
{
"data": {
"text/plain": [
"(0.002465868124424963, 10.0)"
]
},
"execution_count": 49,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"new_crossover = dynamics.curve_intersection(\"S\", \"P\", t_start=0, t_end=0.5)\n",
"crossover_points.store(par=dynamics.get_chem_conc(\"E\"), \n",
" data_snapshot = {\"crossover time\": new_crossover[0]})\n",
"new_crossover"
]
},
{
"cell_type": "markdown",
"id": "d69fe48c-8f70-43ad-9cdf-4c2530bd6c49",
"metadata": {},
"source": [
"## Yet more speedup of the reaction, over the previous run"
]
},
{
"cell_type": "code",
"execution_count": 50,
"id": "b49cc4ba-b349-43c1-9e0d-9b5969653d88",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 50,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Verify that the reaction has reached equilibrium\n",
"dynamics.is_in_equilibrium(explain=False)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "50b3aa69-81a6-4cfb-8de6-a88d4e64470a",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "e998b386-e0ae-4342-a18b-493fc80695b9",
"metadata": {},
"source": [
"# 7. Finally, re-start all the reactions from the same initial concentrations - except for now having a huge amount of enzyme (far more than the initial [A])"
]
},
{
"cell_type": "code",
"execution_count": 51,
"id": "7979df61-ab06-4a86-ae67-62a12561e4bd",
"metadata": {},
"outputs": [],
"source": [
"dynamics = ReactionDynamics(chem_data=chem_data) # A brand-new simulation "
]
},
{
"cell_type": "code",
"execution_count": 52,
"id": "9fa2865e-ccf0-4f3f-8f63-3c54692c541f",
"metadata": {},
"outputs": [],
"source": [
"dynamics.set_conc(conc={\"S\": 20., \"P\": 0., \"E\": 100.},\n",
" snapshot=True) # A lavish amount of enzyme `E`"
]
},
{
"cell_type": "code",
"execution_count": 53,
"id": "f430f845-821d-4e35-b015-cb3e09012d7d",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SYSTEM STATE at Time t = 0:\n",
"3 species:\n",
" Species 0 (S). Conc: 20.0\n",
" Species 1 (P). Conc: 0.0\n",
" Species 2 (E). Conc: 100.0\n",
"Set of chemicals involved in reactions (not counting enzymes): {'S', 'P'}\n",
"Set of enzymes involved in reactions: {'E'}\n"
]
}
],
"source": [
"dynamics.describe_state()"
]
},
{
"cell_type": "markdown",
"id": "2ffda9ba-42c0-40fa-bd3f-fabb689a43f6",
"metadata": {
"tags": []
},
"source": [
"### Re-take the new system to equilibrium"
]
},
{
"cell_type": "code",
"execution_count": 54,
"id": "9bdb8454-4e1d-4a04-ae00-c178a0a799b7",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"* INFO: the tentative time step (0.0005) leads to a least one norm value > its ABORT threshold:\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.4 (set to 0.0002) [Step started at t=0, and will rewind there]\n",
"* INFO: the tentative time step (0.0002) leads to a least one norm value > its ABORT threshold:\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.4 (set to 8e-05) [Step started at t=0, and will rewind there]\n",
"40 total step(s) taken\n"
]
}
],
"source": [
"dynamics.single_compartment_react(reaction_duration=0.02, \n",
" initial_step=0.0005, variable_steps=True, explain_variable_steps=False)"
]
},
{
"cell_type": "code",
"execution_count": 55,
"id": "a30fa6b8-d788-43bf-8203-0fe90ab853cf",
"metadata": {},
"outputs": [],
"source": [
"#dynamics.explain_time_advance()"
]
},
{
"cell_type": "code",
"execution_count": 56,
"id": "5bcb8653-ebf6-41da-9b68-298931d91359",
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.plotly.v1+json": {
"config": {
"plotlyServerURL": "https://plot.ly"
},
"data": [
{
"hovertemplate": "Chemical=S
SYSTEM TIME=%{x}
concentration=%{y}",
"legendgroup": "S",
"line": {
"color": "darkorange",
"dash": "solid"
},
"marker": {
"symbol": "circle"
},
"mode": "lines",
"name": "S",
"orientation": "v",
"showlegend": true,
"type": "scatter",
"x": [
0,
8e-05,
0.00012000000000000002,
0.00016,
0.0002,
0.00024,
0.00028000000000000003,
0.00032,
0.00036,
0.0004,
0.00044,
0.00048800000000000004,
0.0005456,
0.0006032,
0.00067232,
0.000755264,
0.0008547968,
0.00097423616,
0.00109367552,
0.00121311488,
0.0013325542399999998,
0.0014758814719999997,
0.0016192087039999996,
0.0017912013823999995,
0.0019631940607999993,
0.0021695852748799993,
0.0024172547317759994,
0.0027144580800511995,
0.0030711020979814394,
0.003499074919497727,
0.004012642305317273,
0.004628923168300727,
0.005368460203880872,
0.006255904646577046,
0.0073208379778124544,
0.008598757975294946,
0.010132261972273935,
0.011972466768648722,
0.014180712524298466,
0.016830607431078157,
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"xaxis": "x",
"y": [
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_history(colors=['darkorange', 'green', 'violet'], show_intervals=True, title_prefix=\"With a huge amount of enzyme\")"
]
},
{
"cell_type": "code",
"execution_count": 57,
"id": "05d1e5d7-b21e-4fba-bd2a-fd020dac6711",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Min abs distance found at data row: 15\n"
]
},
{
"data": {
"text/plain": [
"(0.0007383445224719487, 10.0)"
]
},
"execution_count": 57,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"new_crossover = dynamics.curve_intersection(\"S\", \"P\", t_start=0, t_end=0.5)\n",
"crossover_points.store(par=dynamics.get_chem_conc(\"E\"), \n",
" data_snapshot = {\"crossover time\": new_crossover[0]})\n",
"new_crossover"
]
},
{
"cell_type": "markdown",
"id": "122ce249-db1a-439b-b7ac-51999895bb5c",
"metadata": {},
"source": [
"## Yet more speedup of the reaction, over the previous run"
]
},
{
"cell_type": "code",
"execution_count": 58,
"id": "d73a6b89-2b43-4ca2-b8fd-56d04c39de5c",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 58,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Verify that the reaction has reached equilibrium\n",
"dynamics.is_in_equilibrium(explain=False)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "bf097a1e-4741-4301-b723-f73ff7297972",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "eff43c80-0f3a-4c40-8993-f619978a7a16",
"metadata": {},
"source": [
"# 8. Finally, re-start all the reactions from the same initial concentrations - except for now having a LAVISH amount of enzyme (two orders of magnitude more than the starting substrate concentration [S])"
]
},
{
"cell_type": "code",
"execution_count": 59,
"id": "ba4e3803-839e-48b6-ac06-0b29b0863101",
"metadata": {},
"outputs": [],
"source": [
"dynamics = ReactionDynamics(chem_data=chem_data) # A brand-new simulation "
]
},
{
"cell_type": "code",
"execution_count": 60,
"id": "19d037f7-7fc2-4f1f-b9fe-3e9b22bf5f8c",
"metadata": {},
"outputs": [],
"source": [
"dynamics.set_conc(conc={\"S\": 20., \"P\": 0., \"E\": 2000.},\n",
" snapshot=True) # A lavish amount of enzyme `E`"
]
},
{
"cell_type": "code",
"execution_count": 61,
"id": "932e7c3e-0a39-40ca-a66d-d94277b09c1f",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"SYSTEM STATE at Time t = 0:\n",
"3 species:\n",
" Species 0 (S). Conc: 20.0\n",
" Species 1 (P). Conc: 0.0\n",
" Species 2 (E). Conc: 2000.0\n",
"Set of chemicals involved in reactions (not counting enzymes): {'S', 'P'}\n",
"Set of enzymes involved in reactions: {'E'}\n"
]
}
],
"source": [
"dynamics.describe_state()"
]
},
{
"cell_type": "markdown",
"id": "eb327388-65a3-4e61-ba7e-11e5206a203d",
"metadata": {
"tags": []
},
"source": [
"### Re-take the new system (now with a lavish amount of enzyme) to equilibrium"
]
},
{
"cell_type": "code",
"execution_count": 62,
"id": "1e470552-7588-4a8a-a3e2-b4ff6f4b24c1",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"* INFO: the tentative time step (5e-06) leads to a least one norm value > its ABORT threshold:\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.4 (set to 2e-06) [Step started at t=0, and will rewind there]\n",
"48 total step(s) taken\n"
]
}
],
"source": [
"dynamics.single_compartment_react(reaction_duration=0.0015, \n",
" initial_step=0.000005, variable_steps=True, explain_variable_steps=False)"
]
},
{
"cell_type": "code",
"execution_count": 63,
"id": "66abe729-adb3-4528-abd9-9d7fe0554185",
"metadata": {},
"outputs": [],
"source": [
"#dynamics.explain_time_advance()"
]
},
{
"cell_type": "code",
"execution_count": 64,
"id": "832c1130-a9d5-48bc-8327-414d3bcc9dab",
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.plotly.v1+json": {
"config": {
"plotlyServerURL": "https://plot.ly"
},
"data": [
{
"hovertemplate": "Chemical=S
SYSTEM TIME=%{x}
concentration=%{y}",
"legendgroup": "S",
"line": {
"color": "darkorange",
"dash": "solid"
},
"marker": {
"symbol": "circle"
},
"mode": "lines",
"name": "S",
"orientation": "v",
"showlegend": true,
"type": "scatter",
"x": [
0,
2.0000000000000003e-06,
4.4e-06,
5.600000000000001e-06,
6.800000000000001e-06,
8.000000000000001e-06,
9.200000000000002e-06,
1.0400000000000002e-05,
1.1600000000000002e-05,
1.2800000000000003e-05,
1.4000000000000003e-05,
1.5440000000000005e-05,
1.6880000000000004e-05,
1.8608000000000005e-05,
2.0336000000000007e-05,
2.2409600000000006e-05,
2.4897920000000006e-05,
2.7386240000000005e-05,
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3.825522176000001e-05,
4.341500211200001e-05,
4.857478246400001e-05,
5.476651888640001e-05,
6.095825530880001e-05,
6.714999173120001e-05,
7.458007543808001e-05,
8.201015914496001e-05,
9.092625959321601e-05,
9.984236004147202e-05,
0.00011054168057937921,
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dynamics.plot_history(chemicals=['S', 'P'],\n",
" colors=['darkorange', 'green', 'violet'], show_intervals=True, title_prefix=\"With a LAVISH amount of enzyme (NOT shown)\")"
]
},
{
"cell_type": "markdown",
"id": "7faa3d9f-f2b3-4031-9bb5-ebb18dfb5345",
"metadata": {},
"source": [
"_Note: NOT showing the enzyme (concentration 2,000) in the graph, to avoid squishing down the other curves!_"
]
},
{
"cell_type": "code",
"execution_count": 65,
"id": "fb5f2c87-acbe-42e7-867f-15a42e0c726e",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Min abs distance found at data row: 20\n"
]
},
{
"data": {
"text/plain": [
"(3.7174487975074336e-05, 10.0)"
]
},
"execution_count": 65,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"new_crossover = dynamics.curve_intersection(\"S\", \"P\", t_start=0, t_end=0.5)\n",
"crossover_points.store(par=dynamics.get_chem_conc(\"E\"), \n",
" data_snapshot = {\"crossover time\": new_crossover[0]})\n",
"new_crossover"
]
},
{
"cell_type": "markdown",
"id": "7cf81e1a-dd35-4075-95d0-a7f014dc02e5",
"metadata": {},
"source": [
"## Yet more speedup of the reaction, over the previous run"
]
},
{
"cell_type": "code",
"execution_count": 66,
"id": "859e65f6-873e-4126-88f3-24ef0cfb8030",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0: S <-> P\n",
"Final concentrations: [S] = 3.313 ; [P] = 16.69\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 5.03748\n",
" Formula used: [P] / [S]\n",
"2. Ratio of forward/reverse reaction rates: 5.00000519021548\n",
"Discrepancy between the two values: 0.7496 %\n",
"Reaction IS in equilibrium (within 1% tolerance)\n",
"\n",
"1: S + E <-> P + E\n",
"Final concentrations: [S] = 3.313 ; [P] = 16.69 ; [E] = 2,000\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 5.03748\n",
" Formula used: ([P][E]) / ([S][E])\n",
"2. Ratio of forward/reverse reaction rates: 5.00000519021548\n",
"Discrepancy between the two values: 0.7496 %\n",
"Reaction IS in equilibrium (within 1% tolerance)\n",
"\n"
]
},
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 66,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Verify that the reaction has reached equilibrium\n",
"dynamics.is_in_equilibrium()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "5de0f238-e027-42ca-bbed-a4a7b3e54e79",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
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"## Now, let's look at the time of the crossover points (for the [S] and [P] curves to intersect), as a function of the Enzyme concentration"
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Let's plot just the first 6 data points, to avoid squishing the curve\n",
"px.line(data_frame=df.loc[0:5],\n",
" x=\"Enzyme concentration\", y=[\"crossover time\"],\n",
" title=\"Time of crossover of [S] and [P] , as a function of Enzyme concentration (first 6 points)\",\n",
" labels={\"value\":\"Crossover time\"},\n",
" line_shape=\"spline\")"
]
},
{
"cell_type": "code",
"execution_count": 69,
"id": "42894206-49cb-4880-857c-e831fd8800bb",
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.plotly.v1+json": {
"config": {
"plotlyServerURL": "https://plot.ly"
},
"data": [
{
"hovertemplate": "variable=crossover time
Enzyme concentration=%{x}
Crossover time=%{y}",
"legendgroup": "crossover time",
"line": {
"color": "#636efa",
"dash": "solid",
"shape": "spline"
},
"marker": {
"symbol": "circle"
},
"mode": "lines",
"name": "crossover time",
"orientation": "v",
"showlegend": true,
"type": "scatter",
"x": [
0,
0.2,
1,
5,
20,
30,
100,
2000
],
"xaxis": "x",
"y": [
0.7435259497128707,
0.24710707675961718,
0.06769827987210066,
0.014494267066104415,
0.003687634618431487,
0.002465868124424963,
0.0007383445224719487,
3.7174487975074336e-05
],
"yaxis": "y"
}
],
"layout": {
"autosize": true,
"legend": {
"title": {
"text": "variable"
},
"tracegroupgap": 0
},
"template": {
"data": {
"bar": [
{
"error_x": {
"color": "#2a3f5f"
},
"error_y": {
"color": "#2a3f5f"
},
"marker": {
"line": {
"color": "#E5ECF6",
"width": 0.5
},
"pattern": {
"fillmode": "overlay",
"size": 10,
"solidity": 0.2
}
},
"type": "bar"
}
],
"barpolar": [
{
"marker": {
"line": {
"color": "#E5ECF6",
"width": 0.5
},
"pattern": {
"fillmode": "overlay",
"size": 10,
"solidity": 0.2
}
},
"type": "barpolar"
}
],
"carpet": [
{
"aaxis": {
"endlinecolor": "#2a3f5f",
"gridcolor": "white",
"linecolor": "white",
"minorgridcolor": "white",
"startlinecolor": "#2a3f5f"
},
"baxis": {
"endlinecolor": "#2a3f5f",
"gridcolor": "white",
"linecolor": "white",
"minorgridcolor": "white",
"startlinecolor": "#2a3f5f"
},
"type": "carpet"
}
],
"choropleth": [
{
"colorbar": {
"outlinewidth": 0,
"ticks": ""
},
"type": "choropleth"
}
],
"contour": [
{
"colorbar": {
"outlinewidth": 0,
"ticks": ""
},
"colorscale": [
[
0,
"#0d0887"
],
[
0.1111111111111111,
"#46039f"
],
[
0.2222222222222222,
"#7201a8"
],
[
0.3333333333333333,
"#9c179e"
],
[
0.4444444444444444,
"#bd3786"
],
[
0.5555555555555556,
"#d8576b"
],
[
0.6666666666666666,
"#ed7953"
],
[
0.7777777777777778,
"#fb9f3a"
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",
"text/html": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Same plot, but with log scales on both axes (all data points used this time, \n",
"# but the value E = 0 is automatically dropped by the graphic function because of the log scale)\n",
"px.line(data_frame=df,\n",
" x=\"Enzyme concentration\", y=[\"crossover time\"],\n",
" log_x=True, log_y=True,\n",
" title=\"Time of crossover of [S] and [P] , as a function of Enzyme conc (log scales on both axes)\",\n",
" labels={\"value\":\"Crossover time\"},\n",
" line_shape=\"spline\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "1bb12fdd-1c93-4cf3-a302-13da5339e82a",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"jupytext": {
"formats": "ipynb,py:percent"
},
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.10"
}
},
"nbformat": 4,
"nbformat_minor": 5
}