Comparing membrane computing simulation strategies of Metabolic and Gillespie algorithms with Lotka-Voltera Population as a case study

Abstract

Membrane computing enriches the model of molecular computing by providing a spatial structure for molecular computation, inspired by the structure of living cell. The fundamental features that are used in this computing model are a membrane structure where objects evolve discretely according to specified evolution rules. The evolution rules are applied in a non-deterministic and maximally parallel way, which means all the objects that can evolve, must evolve. Implementing a membrane system on an existing electronic computer cannot be a real implementation, it is merely a simulation. Metabolic and Gillespie algorithms have been used as simulation strategies for membrane computing models. Both algorithms implement discrete evolution approach but Metabolic algorithm is deterministic and Gillespie algorithm is stochastic in its evolution procedures. The Lotka-Volterra population is frequently used to describe the dynamics of biological systems in which two objects interact, one is a predator and another is its prey. The objects, reactions and parameters extracted from the system of Ordinary Differential Equation of Lotka-Volterra population are used in defining membrane computing model. This paper compares the two simulation strategies by using membrane computing model of Lotka Voltera Population. The experiments show that number of objects, initial multisets, rules, volume of the system, reactivity rates, and numbers of simulation steps are essential elements in differentiating the simulation strategies. These elements are also being characterized according to the features offered by the simulation strategies. The results show that membrane computing simulation strategy of Gillespie Algorithm is an approach to preserve the stochastic behaviours of biological systems that absent in the deterministic approach of Metabolic Algorithm.