Finite State Projection [1] algorithms for chemical reaction networks based on Catalyst.jl and ModelingToolkit.jl. Converts descriptions of reaction networks into ODEProblems for use with DifferentialEquations.jl.
- 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 - Automatic dimensionality reduction for systems with conserved quantities
More information is available in the documentation. Please feel free to open issues and submit pull requests!
using FiniteStateProjection
using OrdinaryDiffEq
@parameters σ d
rn = @reaction_network begin
σ, 0 --> A
d, A --> 0
end σ d
sys = FSPSystem(rn)
# Parameters for our system
ps = [ 10.0, 1.0 ]
# Initial values
u0 = zeros(50)
u0[1] = 1.0
prob = ODEProblem(sys, u0, (0, 10.0), ps)
sol = solve(prob, Vern7(), atol=1e-6)
using FiniteStateProjection
using OrdinaryDiffEq
@parameters ρ σ_on σ_off d
rn = @reaction_network begin
ρ, G_on --> G_on + M
(σ_on, σ_off), G_off <--> G_on
d, M --> 0
end ρ σ_on σ_off d
# This automatically reduces the dimensionality of the
# network by exploiting conservation laws
ih = ReducingIndexHandler(rn)
sys = FSPSystem(rn, ih)
# There is one conserved quantity: G_on + G_off
cons = conservedquantities([1, 0, 0], sys)
# Parameters for our system
ps = [ 15.0, 0.25, 0.15, 1.0 ]
# In the reduced model, G_off = 1 - G_on does not have to be tracked
u0 = zeros(2, 50)
u0[1,1] = 1.0
prob = ODEProblem(sys, u0, (0, 10.0), (ps, cons))
sol = solve(prob, Vern7(), atol=1e-6)
- Add bursty reactions
- Add stationary FSP support
- Add support for sparse Jacobians
[1] 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