August 20, 2015

# PISKa

Figure 1: Diagram of the SSA.

Stochastic simulation is an increasingly important method used to solve problems in biological sciences. We develop PISKa as a simulation software which allows the modeling of reaction-diffusion systems and its execution on distributed computing architectures. PISKa makes profitable use of the spatial properties of biological systems and approximate the sequential Stochastic Simulation Algorithm (SSA)[1] (see fig. 1) using the MPI paradigm.

We have proposed a new algorithm where the vector state of system $X$ is partitioned in compartments, such there is no reaction $R_i$ with reactants in two different partitions. Reactions that have reactants and products in different compartments provoke diffusion events, which generate perturbations. It is easy to calculate how to apply these perturbation in the system and preserve the accuracy of SSA. However, to achieve a better performance, PISKa implements a distributed algorithm which use a synchronization process based on the $\tau$-leaping assumption[2] of the diffusion process.

Figure 2: Example of spatial instructions of Compartmental Kappa

Models need to be written in an expanded version of Kappa Language called Compartmental Kappa, a rule-based language that allows to model reactive systems using agent patterns in rules to fight combinatorial explosion of species. This version is based on Spatial Kappa[3] and allows to explicitly define compartments, grids and diffusion. An example of its spatial instructions can be seen in figure 2.

For now, a first version of PISKa can be found here. The tutorial for its use is still in preparation.

References

[1] D.T. Gillespie (1976). A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comp. Phys. 22(4):403-434
[2] D.T. Gillespie (2001). Approximate accelerated stochastic simulation of chemically reacting systems. J. Chem. Phys. 115 (4): 1716
[3] O. Sorokina, A. Sorokin, J. Douglas Armstrong, and V. Danos (2013). A simulator for spatially extended kappa models. Bioinformatics (Oxford, England), 29(23):3105–6.