Thursday, January 14, 2016
Speaker: Luca Laurenti
Venue: IST Austria
The transient evolution of the stochastic process induced by a biochemical system is generally analysed through solving the Chemical Master Equation (CME). However, the solution of the CME is generally infeasible, because it requires solving a number of differential equations equal to the number of reachable states, which can be huge or even infinite. An interesting alternative is to consider continuous stochastic approximations of the discrete stochastic process. In this talk, I will introduce the Linear Noise Approximation (LNA) of the CME, and show how it enables scalable model checking of formulae of Stochastic Evolution Logic (SEL), a logic for probabilistic analysis of biochemical systems. I will demonstrate that the LNA achieves good accuracy for a large class of systems.
The LNA is known to be accurate if some conditions on the propensity rates of the reactions are satisfied. These conditions are always satisfied in the limit of high population. However, in biochemical systems, it is common that these conditions are satisfied only for a subset of species and reactions (i.e. stiff systems). This leads us to the derivation of a stochastic hybrid system where some species are treated with the LNA and others with the CME. I will present formal equations for the transient evolution of the resulting stochastic hybrid process. Finally, I will show how, for a large class of systems, this approach improves the accuracy of the LNA, while still ameliorating state space explosion.