In the last decade, different computing paradigms and modelling frameworks for the description and simulation of biochemical systems based on stochastic modelling have been proposed. From a computational point of view, many simulations of the model are necessary to identify the behaviour of the system. The execution of thousands of simulation can require huge amount of time, therefore the parallelization of these algorithms is highly desirable. In this work we discuss the different strategies that can be implemented for the parallelization of a space aware τ -DPP variant, that is proving a C-MPI implementation of the system and discussing its performances according to the simulation of a particle diffusion in a crowded environment.
I. INTRODUCTIONMembrane systems, also called P systems, are computing devices inspired to the structure and operation of living cells as well as from the way the cells are organized in tissues and higher order structures.The properties of this class of systems make them suitable also for modelling biological systems , in which the different sets of objects represent molecular species and the rewriting rules represent chemical reactions that describe the evolution of the system in the time. However, some features of P systems as non-determinism and maximal parallelism have to be mitigated, while other properties, as physicalbased procedure to describe the time evolution, have to be considered more carefully to ensure the accurateness of the results. Moreover, stochastic methods have gained a great attention since many biological processes are controlled by noisy mechanisms. This is particularly true when the molecular quantities involved are small, as in this case.A membrane system variant which relies on these considerations is called τ -DPP , where Dynamical Probabilistic P systems have been coupled with a modified version of the τ leaping stochastic simulation method , in order to obtain a quantitative time streamline. A novel variant of τ -DPP, called Sτ -DPP , , has been introduced to consider the size of volumes and objects involved in a system, in order to better describe systems where the space plays an important role in the dynamics, such as crowded systems.The algorithm can be used in the modelling and simulation of reaction-diffusion (RD) systems in crowded environ-