Model Checking the Biological Model of Membrane Computing with Probabilistic Symbolic Model Checker by Using Two Biological Systems

Muniyandi Muniyandi

doi:10.3844/jcssp.2010.669.678

Abstract

Problem statement: Membrane computing formalism has provided better modeling capabilities for biological systems in comparison to conventional mathematical models. Model checking could be used to reason about the biological system in detail and with precision by verifying formally whether membrane computing model meets the properties of the system. Approach: This study was carried to investigate the preservation of properties of two biological systems that had been modeled and simulated in membrane computing by a method of model checking using PRISM. The two biological systems were prey-predator population and signal processing in the legend-receptor networks of protein TGF-β. Results: The model checking of membrane computing model of the biological systems with five different properties showed that the properties of the biological systems could be preserved in the membrane computing model. Conclusion: Membrane computing model not only provides a better approach in representing and simulating a biological system but also able to sustain the basic properties of the system.

Highlights

Membrane computing provides a hierarchical structure for molecular computation in which embraces play an essential role for objects to pass in a regulated fashion within and across the membranes
The biological description of membrane computing formalism has been utilized to characterize and preserve the elements in biological systems. The research in this line shows that biological system can be modeled better using membrane computing than the conventional methods using mathematical representation such as Ordinary Differential Equation (ODE) (Bernardini et al, 2006; Muniyandi and Abdullah, 2009; 2010)
Model checking of prey predator population: The membrane computing model of prey-predator population translated into PRISM formalism as follows: ctmc

Summary

INTRODUCTION

Membrane computing provides a hierarchical structure for molecular computation in which embraces play an essential role for objects to pass in a regulated fashion within and across the membranes. We investigate whether the properties of two biological case studies modeled using membrane computing and simulated by Muniyandi and Abdullah (2010) are preserved by using the PRISM model checker. The two biological case studies are preypredator population and signal processing in the legendreceptor Networks of protein TGF-β These two case studies have been modeled in membrane computing formalism and simulated with simulation strategy of membrane computing with Gillespie Algorithm (Muniyandi and Abdullah, 2009; 2010). The assumptions for the model are the rate at which predators encounter prey is jointly proportional to the sizes of the two populations and a fixed proportion of encounters lead to the death of the prey Based on these behaviors, three rules are formulated in membrane computing as follows (k1, k2 and k3 are kinetic constants): R1:[X] k 1 →[X, Y]. The graph is analyzed to verify whether the identified properties are preserved or not

RESULTS

DISCUSSION

CONCLUSION