A time-dependent extension of gillespie algorithm for biochemical stochastic π-calculus

Realistic simulations of the biological systems evolution require a mathematical model of the stochasticity of the involved processes and a formalism for specifying the concurrent nature of the biochemical interactions. The Gillespie algorithm is a well-established stochastic algorithm satisfying the first requirement. The second requirement can be satisfied by the π-calculus, a process algebra used in computer science for describing interactions between simultaneously running processes. Its stochastic variant has been recently applied to the specification of the biological systems.This paper shows how to generalize the Gillespie algorithm by letting the reaction propensity be a function of time. In particular, the work formulates those modifications necessary when the time dependence of the reaction propensity is due to changes either of volume or temperature. This re-formulation has been then adapted to be incorporated in the framework of stochastic π-calculus and has been applied to a sample simulation in biology: the passive glucose cellular transport.

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