P systems for biological dynamics

P systems have clear structural analogies with the cell. However, certain difficulties arise when one attempts to represent a biomolecular process using these systems. This chapter suggests some ways to overcome such difficulties and to provide P systems with further functionalities aimed at increasing their versatility in the modeling of biomolecular processes. Concepts from state transition dynamics are taken to put P systems in a general analysis framework for dynamical discrete systems. An explicit notion of environment is proposed to provide P systems with a regulatory and constraining agent, as real biomolecular processes must deal with. The chapter focuses on a new rewriting strategy inspired by biochemistry, in which reactivities play a central role in driving the rules as happens during biochemical reactions. Tests on an algorithm implementing rewriting with reactivities, realized on a simulator called Psim, show the capability of this algorithm to express several processes with precision, particularly those presenting oscillatory phenomena. Finally, an analysis of the process of leukocyte recruitment is also performed using Psim.