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FiniteStateProjection.jl

Finite State Projection [1] algorithms for chemical reaction networks based on Catalyst.jl and ModelingToolkit.jl. Converts descriptions of reaction networks into ODEProblems and SteadyStateProblems for use with DifferentialEquations.jl.

Features:

Built on top of Catalyst.jl
FSP equations are generated as ODEFunction/ODEProblems and can be solved with DifferentialEquations.jl, with on-the-fly generation of targeted functions for improved performance
The Chemical Master Equation can be represented as a SparseMatrixCSC

More information is available in the documentation. Please feel free to open issues and submit pull requests!

Examples

Birth-Death System

using FiniteStateProjection
using OrdinaryDiffEq

rn = @reaction_network begin
    σ, 0 --> A
    d, A --> 0
end

sys = FSPSystem(rn)

# Parameters for our system
ps = [ :σ => 10.0, :d => 1.0 ]

# Initial distribution (over 1 species)
# Here we start with 0 copies of A
u0 = zeros(50)
u0[1] = 1.0

prob = ODEProblem(sys, u0, (0, 10.0), ps)
sol = solve(prob, Vern7())

Visualisation

Telegraph Model

using FiniteStateProjection
using OrdinaryDiffEq

rn = @reaction_network begin
    σ_on * (1 - G_on), 0 --> G_on
    σ_off, G_on --> 0
    ρ, G_on --> G_on + M
    d, M --> 0
end

sys = FSPSystem(rn)

# Parameters for our system
ps = [ :σ_on => 0.25, :σ_off => 0.15, :ρ => 15.0, :d => 1.0 ]

# Initial distribution (over two species)
# Here we start with 0 copies of G_on and M
u0 = zeros(2, 50)
u0[1,1] = 1.0

prob = ODEProblem(sys, u0, (0, 10.0), ps)
sol = solve(prob, Vern7())

Visualisation

References

<a id="1">[1]</a> B. Munsky and M. Khammash, "The Finite State Projection algorithm for the solution of the Chemical Master Equation", Journal of Chemical Physics 124, 044104 (2006). https://doi.org/10.1063/1.2145882