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"## Comparing the dynamics of the reaction `A <-> B` , with and without an enzyme\n",
"\n",
"LAST REVISED: Dec. 3, 2023"
]
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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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"source": [
"from src.modules.chemicals.chem_data import ChemData\n",
"from src.modules.reactions.reaction_dynamics import ReactionDynamics"
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"# 1. WITHOUT ENZYME\n",
"### `A` <-> `B`"
]
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"id": "23c15e66-52e4-495b-aa3d-ecddd8d16942",
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"name": "stdout",
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"Number of reactions: 1 (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",
"Set of chemicals involved in the above reactions: {'A', 'B'}\n"
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"# Initialize the system\n",
"chem_data = ChemData(names=[\"A\", \"B\"])\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 part 2, below\n",
"chem_data.add_reaction(reactants=\"A\", products=\"B\",\n",
" forward_rate=1., delta_G=-3989.73)\n",
"\n",
"chem_data.describe_reactions()"
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"id": "0e771dda-1c0f-4fc0-ab21-049740643897",
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"### Set the initial concentrations of all the chemicals"
]
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"SYSTEM STATE at Time t = 0:\n",
"2 species:\n",
" Species 0 (A). Conc: 20.0\n",
" Species 1 (B). Conc: 0.0\n",
"Set of chemicals involved in reactions: {'A', 'B'}\n"
]
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"dynamics = ReactionDynamics(chem_data=chem_data)\n",
"dynamics.set_conc(conc={\"A\": 20., \"B\": 0.},\n",
" snapshot=True)\n",
"dynamics.describe_state()"
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"id": "651941bb-7098-4065-a598-e50c0b641ab3",
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"### Take the initial system to equilibrium"
]
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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 0.5 (set to 0.05) [Step started at t=0, and will rewind there]\n",
"30 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=1.5, downshift=0.5, abort=0.5)\n",
"dynamics.set_error_step_factor(0.5)\n",
"\n",
"dynamics.single_compartment_react(reaction_duration=3.0,\n",
" initial_step=0.1, variable_steps=True, explain_variable_steps=False)"
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"#dynamics.explain_time_advance()"
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",
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"metadata": {},
"output_type": "display_data"
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],
"source": [
"dynamics.plot_history(colors=['darkorange', 'green'], show_intervals=True, title_prefix=\"WITHOUT enzyme\")"
]
},
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"cell_type": "markdown",
"id": "ef7ed670-39dd-4e44-afec-82dbd6e6a431",
"metadata": {},
"source": [
"#### Note how the time steps get automatically adjusted, as needed by the amount of change - including a complete step abort/redo at time=0"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "550dc065-6f3a-4961-b1ea-d52e0aa0baff",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Min abs distance found at data row: 18\n"
]
},
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"source": [
"dynamics.curve_intersection(\"A\", \"B\", t_start=0, t_end=1.0)"
]
},
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"execution_count": 9,
"id": "19e66cfc-8e1c-4332-b85d-2b8ced01d4b3",
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"text": [
"0: A <-> B\n",
"Final concentrations: [A] = 3.398 ; [B] = 16.6\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.88533\n",
" Formula used: [B] / [A]\n",
"2. Ratio of forward/reverse reaction rates: 5.00000519021548\n",
"Discrepancy between the two values: 2.293 %\n",
"Reaction IS in equilibrium (within 3% tolerance)\n",
"\n"
]
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"source": [
"# Verify that the reaction has reached equilibrium\n",
"dynamics.is_in_equilibrium(tolerance=3)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "6517c7bd-3243-4326-9c7e-0ca04da6d812",
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"source": []
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"cell_type": "markdown",
"id": "27401e5d-8f3e-4c27-8438-129d3e3408a2",
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"source": [
"# 2. WITH ENZYME `E`\n",
"### `A` + `E` <-> `B` + `E`"
]
},
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"cell_type": "markdown",
"id": "878edb65-e2f9-46d0-b3ba-3a82c064243b",
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"source": [
"### Note: for the sake of the demo, we'll completely ignore the concomitant (much slower) direct reaction A <-> B\n",
"This in an approximation that we'll drop in later experiments"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "ffaef48b-e95b-4cb9-ab9f-c526a159222e",
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"text": [
"Number of reactions: 1 (at temp. 25 C)\n",
"0: 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"
]
}
],
"source": [
"# Initialize the system\n",
"chem_data = ChemData(names=[\"A\", \"B\", \"E\"])\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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"### Notice how, while the ratio kF/kR is the same as it was without the enzyme (since it's dictated by the energy difference), the individual values of kF and kR now are each 10 times bigger than before"
]
},
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"### Set the initial concentrations of all the chemicals (to what they originally were)"
]
},
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"execution_count": 11,
"id": "e80645d6-eb5b-4c78-8b46-ae126d2cb2cf",
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"text": [
"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: 30.0\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 = ReactionDynamics(chem_data=chem_data)\n",
"dynamics.set_conc(conc={\"A\": 20., \"B\": 0., \"E\": 30.},\n",
" snapshot=True) # Plenty of enzyme `E`\n",
"dynamics.describe_state()"
]
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"### Take the initial system to equilibrium"
]
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"\n",
"*** CAUTION: negative concentration in chemical `A` in step starting at t=0. It will be AUTOMATICALLY CORRECTED with a reduction in time step size, as follows:\n",
" INFO: the tentative time step (0.1) leads to a NEGATIVE concentration of `A` from reaction A + E <-> B + E (rxn # 0): \n",
" Baseline value: 20 ; delta conc: -600\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.25 (set to 0.025) [Step started at t=0, and will rewind there]\n",
"\n",
"*** CAUTION: negative concentration in chemical `A` in step starting at t=0. It will be AUTOMATICALLY CORRECTED with a reduction in time step size, as follows:\n",
" INFO: the tentative time step (0.025) leads to a NEGATIVE concentration of `A` from reaction A + E <-> B + E (rxn # 0): \n",
" Baseline value: 20 ; delta conc: -150\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.25 (set to 0.00625) [Step started at t=0, and will rewind there]\n",
"\n",
"*** CAUTION: negative concentration in chemical `A` in step starting at t=0. It will be AUTOMATICALLY CORRECTED with a reduction in time step size, as follows:\n",
" INFO: the tentative time step (0.00625) leads to a NEGATIVE concentration of `A` from reaction A + E <-> B + E (rxn # 0): \n",
" Baseline value: 20 ; delta conc: -37.5\n",
" -> will backtrack, and re-do step with a SMALLER delta time, multiplied by 0.25 (set to 0.0015625) [Step started at t=0, and will rewind there]\n",
"* INFO: the tentative time step (0.0015625) 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 0.000625) [Step started at t=0, and will rewind there]\n",
"* INFO: the tentative time step (0.000625) 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 0.00025) [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",
"43 total step(s) taken\n"
]
}
],
"source": [
"dynamics.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n",
"\n",
"# All of these settings are currently close to the default values... but subject to change; set for repeatability\n",
"dynamics.set_thresholds(norm=\"norm_A\", low=0.5, high=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",
"dynamics.single_compartment_react(reaction_duration=0.1,\n",
" initial_step=0.1, variable_steps=True, explain_variable_steps=False)"
]
},
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"source": [
"#### Note how the (proposed) initial step - kept the same as the previous run - is now _extravagantly large_, given the much-faster reaction dynamics. However, the variable-step engine intercepts and automatically corrects the problem!"
]
},
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"source": [
"#dynamics.explain_time_advance()"
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Reaction `A + E <-> B + E` . Changes in concentrations with time (time steps shown in dashed lines)"
},
"xaxis": {
"anchor": "y",
"autorange": true,
"domain": [
0,
1
],
"range": [
-9.174058431160702e-05,
0.1059603748799061
],
"title": {
"text": "SYSTEM TIME"
},
"type": "linear"
},
"yaxis": {
"anchor": "x",
"autorange": true,
"domain": [
0,
1
],
"range": [
-1.6666666666666665,
31.666666666666668
],
"title": {
"text": "concentration"
},
"type": "linear"
}
}
},
"image/png": 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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 enzyme\")"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "2cf77dd1-040e-4e3a-9867-678479a3dda6",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Min abs distance found at data row: 16\n"
]
},
{
"data": {
"text/plain": [
"(0.0024674107137523833, 10.000000000000002)"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dynamics.curve_intersection(\"A\", \"B\", t_start=0, t_end=0.02)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "c3afbcc8-bdae-4938-a3f1-ce00d62816f2",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0: A + E <-> B + E\n",
"Final concentrations: [A] = 3.334 ; [B] = 16.67 ; [E] = 30\n",
"1. Ratio of reactant/product concentrations, adjusted for reaction orders: 4.99958\n",
" Formula used: ([B][E]) / ([A][E])\n",
"2. Ratio of forward/reverse reaction rates: 5.00000519021548\n",
"Discrepancy between the two values: 0.008546 %\n",
"Reaction IS in equilibrium (within 1% tolerance)\n",
"\n"
]
},
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Verify that the reaction has reached equilibrium\n",
"dynamics.is_in_equilibrium()"
]
},
{
"cell_type": "markdown",
"id": "97efd24d-c771-4354-a924-eb21bc3d070c",
"metadata": {},
"source": [
"## Thanks to the (abundant) enzyme, the reaction reaches equilibrium roughly around t=0.02, far sooner than the roughly t=3.5 without enzyme\n",
"The concentrations of `A` and `B` now become equal (cross-over) at t=0.00246 , rather than t=0.740"
]
},
{
"cell_type": "code",
"execution_count": 17,
"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",
" 30.0 | \n",
" Initial state | \n",
"
\n",
" \n",
" | 1 | \n",
" 0.000250 | \n",
" 18.500000 | \n",
" 1.500000 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 2 | \n",
" 0.000375 | \n",
" 17.817500 | \n",
" 2.182500 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 3 | \n",
" 0.000500 | \n",
" 17.165712 | \n",
" 2.834288 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 4 | \n",
" 0.000625 | \n",
" 16.543255 | \n",
" 3.456745 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 5 | \n",
" 0.000750 | \n",
" 15.948809 | \n",
" 4.051191 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 6 | \n",
" 0.000875 | \n",
" 15.381112 | \n",
" 4.618888 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 7 | \n",
" 0.001000 | \n",
" 14.838962 | \n",
" 5.161038 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 8 | \n",
" 0.001125 | \n",
" 14.321209 | \n",
" 5.678791 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 9 | \n",
" 0.001250 | \n",
" 13.826755 | \n",
" 6.173245 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 10 | \n",
" 0.001375 | \n",
" 13.354551 | \n",
" 6.645449 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 11 | \n",
" 0.001525 | \n",
" 12.813405 | \n",
" 7.186595 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 12 | \n",
" 0.001675 | \n",
" 12.301481 | \n",
" 7.698519 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 13 | \n",
" 0.001855 | \n",
" 11.720345 | \n",
" 8.279655 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 14 | \n",
" 0.002071 | \n",
" 11.068171 | \n",
" 8.931829 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 15 | \n",
" 0.002330 | \n",
" 10.346417 | \n",
" 9.653583 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 16 | \n",
" 0.002589 | \n",
" 9.692012 | \n",
" 10.307988 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 17 | \n",
" 0.002900 | \n",
" 8.980003 | \n",
" 11.019997 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 18 | \n",
" 0.003274 | \n",
" 8.221264 | \n",
" 11.778736 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 19 | \n",
" 0.003647 | \n",
" 7.564476 | \n",
" 12.435524 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 20 | \n",
" 0.004095 | \n",
" 6.882233 | \n",
" 13.117767 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 21 | \n",
" 0.004543 | \n",
" 6.309997 | \n",
" 13.690003 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 22 | \n",
" 0.004991 | \n",
" 5.830030 | \n",
" 14.169970 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 23 | \n",
" 0.005528 | \n",
" 5.346939 | \n",
" 14.653061 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 24 | \n",
" 0.006066 | \n",
" 4.957322 | \n",
" 15.042678 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 25 | \n",
" 0.006711 | \n",
" 4.580248 | \n",
" 15.419752 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 26 | \n",
" 0.007485 | \n",
" 4.232821 | \n",
" 15.767179 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 27 | \n",
" 0.008413 | \n",
" 3.932073 | \n",
" 16.067927 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 28 | \n",
" 0.009528 | \n",
" 3.691843 | \n",
" 16.308157 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 29 | \n",
" 0.010865 | \n",
" 3.519230 | \n",
" 16.480770 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 30 | \n",
" 0.012470 | \n",
" 3.411824 | \n",
" 16.588176 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 31 | \n",
" 0.014396 | \n",
" 3.357403 | \n",
" 16.642597 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 32 | \n",
" 0.016707 | \n",
" 3.337375 | \n",
" 16.662625 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 33 | \n",
" 0.019480 | \n",
" 3.333337 | \n",
" 16.666663 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 34 | \n",
" 0.022808 | \n",
" 3.333329 | \n",
" 16.666671 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 35 | \n",
" 0.026802 | \n",
" 3.333331 | \n",
" 16.666669 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 36 | \n",
" 0.031594 | \n",
" 3.333330 | \n",
" 16.666670 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 37 | \n",
" 0.037345 | \n",
" 3.333331 | \n",
" 16.666669 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 38 | \n",
" 0.044245 | \n",
" 3.333330 | \n",
" 16.666670 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 39 | \n",
" 0.052526 | \n",
" 3.333332 | \n",
" 16.666668 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 40 | \n",
" 0.062463 | \n",
" 3.333327 | \n",
" 16.666673 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 41 | \n",
" 0.074388 | \n",
" 3.333341 | \n",
" 16.666659 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 42 | \n",
" 0.088697 | \n",
" 3.333285 | \n",
" 16.666715 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
" | 43 | \n",
" 0.105869 | \n",
" 3.333568 | \n",
" 16.666432 | \n",
" 30.0 | \n",
" | \n",
"
\n",
" \n",
"
\n",
"