P systems with reaction maps

Some recent types of membrane systems have shown their potential in the modelling of specific processes governing biological cell behavior. These models represent the cell as a huge and complex dynamical system in which quantitative aspects, such as biochemical concentrations, must be related to the discrete informational nature of the DNA and to the function of the organelles living in the cytosol. In an effort to compute dynamical (especially oscillatory) phenomena—so far mostly treated using differential mathematical tools—by means of rewriting rules, we have enriched a known family of membrane systems (P systems), with rules that are applied proportionally to the values expressed by real functions called reaction maps. Such maps are designed to model the dynamic behavior of a biochemical phenomenon and their formalization is best worked out inside a family of P systems called PB systems. The overall rule activity is controlled by an algorithm that guarantees the system to evolve consistently with the available resources (i.e., objects). Though radically different, PB systems with reaction maps exhibit very interesting, often similar dynamic behavior as compared to systems of differential equations. Successful simulations of the Lotka-Volterra population dynamics, the Brusselator, and the Protein Kinase C activation foster potential applications of these systems in computational systems biology.