FiniteStateProjection.jl

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FiniteStateProjection.jl

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Finite State Projection algorithms for chemical reaction networks

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# FiniteStateProjection.jl

[![Dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://docs.sciml.ai/FiniteStateProjection/dev/)

Finite State Projection [[1]](#1)  algorithms for chemical reaction networks based on [Catalyst.jl](https://github.com/SciML/Catalyst.jl) and [ModelingToolkit.jl](https://github.com/SciML/ModelingToolkit.jl). Converts descriptions of reaction networks into `ODEProblem`s and `SteadyStateProblem`s for use with [DifferentialEquations.jl](https://github.com/SciML/DifferentialEquations.jl).

## Features:

- Built on top of [Catalyst.jl](https://github.com/SciML/Catalyst.jl)
  - FSP equations are generated as `ODEFunction`/`ODEProblem`s and can be solved with [DifferentialEquations.jl](https://github.com/SciML/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](https://kaandocal.github.io/FiniteStateProjection.jl/dev/). Please feel free to open issues and submit pull requests!

## Examples

### Birth-Death System

```julia
using FiniteStateProjection
using Catalyst
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](https://raw.githubusercontent.com/SciML/FiniteStateProjection.jl/main/docs/src/assets/birth_death.png)

### Telegraph Model

```julia
using FiniteStateProjection
using Catalyst
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](https://raw.githubusercontent.com/SciML/FiniteStateProjection.jl/main/docs/src/assets/telegraph.png)

## 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

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