Generating reaction systems programmatically

Generating reaction systems programmatically#

There are two ways to create a reaction for a ReactionSystem:

  • Reaction() function

  • @reaction macro

using Catalyst
using ModelingToolkit

@parameters α K n δ γ β μ
@variables t
@species m₁(t) m₂(t) m₃(t) P₁(t) P₂(t) P₃(t)
\[\begin{split} \begin{equation} \left[ \begin{array}{c} \mathtt{m_1}\left( t \right) \\ \mathtt{m_2}\left( t \right) \\ \mathtt{m_3}\left( t \right) \\ \mathtt{P_1}\left( t \right) \\ \mathtt{P_2}\left( t \right) \\ \mathtt{P_3}\left( t \right) \\ \end{array} \right] \end{equation} \end{split}\]

Reaction function#

The Reaction(rate, substrates, products) function builds reactions. To allow for other stoichiometric coefficients we also provide a five argument form: Reaction(rate, substrates, products, substrate_stoichiometries, product_stoichiometries)

rxs = [
    Reaction(hillr(P₃, α, K, n), nothing, [m₁]),
    Reaction(hillr(P₁, α, K, n), nothing, [m₂]),
    Reaction(hillr(P₂, α, K, n), nothing, [m₃]),
    Reaction(δ, [m₁], nothing),
    Reaction(γ, nothing, [m₁]),
    Reaction(δ, [m₂], nothing),
    Reaction(γ, nothing, [m₂]),
    Reaction(δ, [m₃], nothing),
    Reaction(γ, nothing, [m₃]),
    Reaction(β, [m₁], [m₁, P₁]),
    Reaction(β, [m₂], [m₂, P₂]),
    Reaction(β, [m₃], [m₃, P₃]),
    Reaction(μ, [P₁], nothing),
    Reaction(μ, [P₂], nothing),
    Reaction(μ, [P₃], nothing)
]

15-element Vector{Catalyst.Reaction{Any, Int64}}:
 Catalyst.hillr(P₃(t), α, K, n), ∅ --> m₁
 Catalyst.hillr(P₁(t), α, K, n), ∅ --> m₂
 Catalyst.hillr(P₂(t), α, K, n), ∅ --> m₃
 δ, m₁ --> ∅
 γ, ∅ --> m₁
 δ, m₂ --> ∅
 γ, ∅ --> m₂
 δ, m₃ --> ∅
 γ, ∅ --> m₃
 β, m₁ --> m₁ + P₁
 β, m₂ --> m₂ + P₂
 β, m₃ --> m₃ + P₃
 μ, P₁ --> ∅
 μ, P₂ --> ∅
 μ, P₃ --> ∅

Use ReactionSystem(reactions, indenpendeent_variable) to collect these reactions. @named macro is used because every system in ModelingToolkit needs a name. @named x = System(...) is a short hand for x = System(...; name=:x)

@named repressilator = ReactionSystem(rxs, t)
\[\begin{split} \begin{align*} \varnothing &\xrightarrow{\frac{K^{n} \alpha}{K^{n} + \mathtt{P_3}^{n}}} \mathrm{\mathtt{m_1}} \\ \varnothing &\xrightarrow{\frac{K^{n} \alpha}{\mathtt{P_1}^{n} + K^{n}}} \mathrm{\mathtt{m_2}} \\ \varnothing &\xrightarrow{\frac{K^{n} \alpha}{K^{n} + \mathtt{P_2}^{n}}} \mathrm{\mathtt{m_3}} \\ \mathrm{\mathtt{m_1}} &\xrightleftharpoons[\gamma]{\delta} \varnothing \\ \mathrm{\mathtt{m_2}} &\xrightleftharpoons[\gamma]{\delta} \varnothing \\ \mathrm{\mathtt{m_3}} &\xrightleftharpoons[\gamma]{\delta} \varnothing \\ \mathrm{\mathtt{m_1}} &\xrightarrow{\beta} \mathrm{\mathtt{m_1}} + \mathrm{\mathtt{P_1}} \\ \mathrm{\mathtt{m_2}} &\xrightarrow{\beta} \mathrm{\mathtt{m_2}} + \mathrm{\mathtt{P_2}} \\ \mathrm{\mathtt{m_3}} &\xrightarrow{\beta} \mathrm{\mathtt{m_3}} + \mathrm{\mathtt{P_3}} \\ \mathrm{\mathtt{P_1}} &\xrightarrow{\mu} \varnothing \\ \mathrm{\mathtt{P_2}} &\xrightarrow{\mu} \varnothing \\ \mathrm{\mathtt{P_3}} &\xrightarrow{\mu} \varnothing \end{align*} \end{split}\]

The @reaction macro provides the same syntax in the @reaction_network to build reactions. Note that @reaction macro only allows one-way reaction; reversible arrows are not allowed.

@variables t
@species P₁(t) P₂(t) P₃(t)

rxs = [
    (@reaction hillr($P₃, α, K, n), ∅ --> m₁),
    (@reaction hillr($P₁, α, K, n), ∅ --> m₂),
    (@reaction hillr($P₂, α, K, n), ∅ --> m₃),
    (@reaction δ, m₁ --> ∅),
    (@reaction γ, ∅ --> m₁),
    (@reaction δ, m₂ --> ∅),
    (@reaction γ, ∅ --> m₂),
    (@reaction δ, m₃ --> ∅),
    (@reaction γ, ∅ --> m₃),
    (@reaction β, m₁ --> m₁ + P₁),
    (@reaction β, m₂ --> m₂ + P₂),
    (@reaction β, m₃ --> m₃ + P₃),
    (@reaction μ, P₁ --> ∅),
    (@reaction μ, P₂ --> ∅),
    (@reaction μ, P₃ --> ∅)
]

@named repressilator2 = ReactionSystem(rxs, t)
\[\begin{split} \begin{align*} \varnothing &\xrightarrow{\frac{K^{n} \alpha}{K^{n} + \mathtt{P_3}^{n}}} \mathrm{\mathtt{m_1}} \\ \varnothing &\xrightarrow{\frac{K^{n} \alpha}{\mathtt{P_1}^{n} + K^{n}}} \mathrm{\mathtt{m_2}} \\ \varnothing &\xrightarrow{\frac{K^{n} \alpha}{K^{n} + \mathtt{P_2}^{n}}} \mathrm{\mathtt{m_3}} \\ \mathrm{\mathtt{m_1}} &\xrightleftharpoons[\gamma]{\delta} \varnothing \\ \mathrm{\mathtt{m_2}} &\xrightleftharpoons[\gamma]{\delta} \varnothing \\ \mathrm{\mathtt{m_3}} &\xrightleftharpoons[\gamma]{\delta} \varnothing \\ \mathrm{\mathtt{m_1}} &\xrightarrow{\beta} \mathrm{\mathtt{m_1}} + \mathrm{\mathtt{P_1}} \\ \mathrm{\mathtt{m_2}} &\xrightarrow{\beta} \mathrm{\mathtt{m_2}} + \mathrm{\mathtt{P_2}} \\ \mathrm{\mathtt{m_3}} &\xrightarrow{\beta} \mathrm{\mathtt{m_3}} + \mathrm{\mathtt{P_3}} \\ \mathrm{\mathtt{P_1}} &\xrightarrow{\mu} \varnothing \\ \mathrm{\mathtt{P_2}} &\xrightarrow{\mu} \varnothing \\ \mathrm{\mathtt{P_3}} &\xrightarrow{\mu} \varnothing \end{align*} \end{split}\]

This notebook was generated using Literate.jl.