A framework to compute the MFPT of inherently stochastic biochemical reaction networks. Traditional methods to estimate the MFPT rely on numerical integration of deterministic models, however, these ignore intrinsic noise and hence their predictions may be inaccurate. Here we provide an accurate and efficient computational framework to compute the MFPT for reaction networks in the presence of (intrinsic) noise.
To compute MFPTs numerically, we use an adaptation of FiniteStateProjection.jl to construct the transition matrix of a stochastic reaction network and solve a modified system of equations using the standard sparse solvers in Julia. For more details see the supplementary material for The timing of cellular events: a stochastic vs deterministic perspective, specifically the section "Finite State Projection for the modified CME".
The script mfpt_functions.jl contains the core functions to compute the MFPT for any chemical reaction network and the script telegraph_example.jl implements a working example of computing MFPTs for a telegraph process. The script FPTD_extraction.jl shows how to obtain the full time-dependant FPTD using the telegraph model as an example.
For more details on the method and additional examples please refer to the associated paper: The timing of cellular events: a stochastic vs deterministic perspective