Revisiting Kwiatkowska et al. on probabilistic model-checking for systems biology. Moving from models of a single protein to slightly larger populations, still with symbolic model-checking.
The problem of state-space explosion, and the use of simulation. Gillespie’s algorithm for stochastic simulation. I’m using the slides from Gillespie’s invited talk at CMSB 2007 in Edinburgh. So far we have covered the approximation from precise dynamic simulation of all positions and velocities, down to stochastic simulation of populations through modelling only reactive molecular collisions. This gives the exact SSA; next are various tau-leaping methods for efficient approximation.
Wilkinson’s book on stochastic modelling covers the Gillespie algorithm in §§6.2–6.5, with Chapter 8 then going on to deal with approximation strategies.
Links: Slides; Gillespie on Stochastic Chemical Kinetics; All CMSB 2007 talks.