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"# Enzymatic\n",
"\n",
"For slightly more complex example,\n",
"`SimBio` contains compound reactions,\n",
"consisting of many single or compound reactions.\n",
"For instance,\n",
"from `simbio.reactions.enzymatic`\n",
"we can import a `MichaelisMenten` reaction,\n",
"which binds a substrate $S$ to an enzyme $E$\n",
"creating an intermediate bound species $E:S$,\n",
"before converting to the product $P$ species:\n",
"\n",
"$$ S + E ↔ E:S → P + E $$\n",
"\n",
"It consists of a `ReversibleSynthesis` ($ S + E ↔ E:S$)\n",
"and a `Dissociation` ($E:S → P + E$) reaction.\n",
"In turn,\n",
"`ReversibleSynthesis` is also a compound reaction,\n",
"consisting of a `Synthesis` ($ S + E → E:S$)\n",
"and `Dissociation` ($ E:S → S + E$) reactions."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "4382e3e9",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"\n",
"from simbio.components import EmptyCompartment, Species\n",
"from simbio.reactions.enzymatic import MichaelisMenten\n",
"from simbio.simulator import Simulator"
]
},
{
"cell_type": "markdown",
"id": "342a6873",
"metadata": {},
"source": [
"When defining a model,\n",
"we do not need to explicitly create every species.\n",
"For instance,\n",
"the intermediate species `ES`,\n",
"is created inside the reaction\n",
"by assigning it to a number."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "c7c5d961",
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"source": [
"class Model(EmptyCompartment):\n",
" enzyme: Species = 1\n",
" subtrate: Species = 1\n",
" product: Species = 0\n",
"\n",
" catalyze = MichaelisMenten(\n",
" E=enzyme,\n",
" S=subtrate,\n",
" ES=0, # \"nameless\" intermediate species\n",
" P=product,\n",
" forward_rate=1,\n",
" reverse_rate=1,\n",
" catalytic_rate=1,\n",
" )"
]
},
{
"cell_type": "markdown",
"id": "09ea7bf1",
"metadata": {},
"source": [
"To simulate it,\n",
"we feed the model into `Simulator`,\n",
"and use the `.run()` method.\n",
"It will compile and integrate an `ODE`-based simulation,\n",
"returning a `pandas.DataFrame` with the result:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "44b4b71b",
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"outputs": [
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"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" enzyme | \n",
" subtrate | \n",
" catalyze.ES | \n",
" product | \n",
"
\n",
" \n",
" | time | \n",
" | \n",
" | \n",
" | \n",
" | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0.00000 | \n",
" 1.000000 | \n",
" 1.000000 | \n",
" 0.000000 | \n",
" 0.000000 | \n",
"
\n",
" \n",
" | 0.10101 | \n",
" 0.916804 | \n",
" 0.912323 | \n",
" 0.083196 | \n",
" 0.004481 | \n",
"
\n",
" \n",
" | 0.20202 | \n",
" 0.860984 | \n",
" 0.845092 | \n",
" 0.139016 | \n",
" 0.015891 | \n",
"
\n",
" \n",
" | 0.30303 | \n",
" 0.823633 | \n",
" 0.791686 | \n",
" 0.176367 | \n",
" 0.031947 | \n",
"
\n",
" \n",
" | 0.40404 | \n",
" 0.798962 | \n",
" 0.747866 | \n",
" 0.201038 | \n",
" 0.051096 | \n",
"
\n",
" \n",
"
\n",
"