Experimenting the Simulation Strategy of Membrane Computing with Gillespie Algorithm by Using Two Biological Case Studies

Abstract

<b>Problem statement:</b> The evolution rules of membrane computing have been applied in a nondeterministic and maximally parallel way. In order to capture these characteristics, Gillespie’s algorithm has been used as simulation strategy of membrane computing in simulating biological systems. <b>Approach:</b> This study was carried to discuss the simulation strategy of membrane computing with Gillespie algorithm in comparison to the simulation approach of ordinary differential equation by analyzing two biological case studies: prey-predator population and signal processing in the Ligand-Receptor Networks of protein TGF-&#946;. <b>Results:</b> Gillespie simulation strategy able to confine the membrane computing formalism that used to represent the dynamics of prey-predator population by taking into consideration the discrete character of the quantity of species in the system. With Gillespie simulation of membrane computing model of TGF-&#946;, the movement of objects from one compartment to another and the changes of concentration of objects in the specific compartments at each time step can be measured. <b>Conclusion:</b> The simulation strategy of membrane computing with Gillespie algorithm able to preserve the stochastic behavior of biological systems that absent in the deterministic approach of ordinary differential equation. However the performance of the Gillespie simulator should be improved to capture complex biological characteristics as well as to enhance the simulation processes represented by membrane computing model

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

“…The biological case studies modeled in membrane computing by Muniyandi and Abdullah (2010) are translated into PRISM formalism. This translation technique from membrane computing into PRISM applied in this research is proposed by .…”

“…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). Simulation strategies based on membrane computing such as Gillespie Algorithm are also used to proof this claim.…”

“…Meanwhile, through simulations the operation of the model can be studied and consequently, the properties concerning the behavior of the biological system can be inferred as shown by Muniyandi and Abdullah (2010). However, although simulation outlines some key features, the preservations of other properties of model such as computability, understandability, extensibility and relevancy also need to be checked to make sure essential properties, dynamic behaviors, informal concepts and higher levels extensible capabilities of specific biological system are captured as well (Regev and Shapiro, 2004).…”

“…In this study, 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.…”

“…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). (Kwiatkowska et al, 2002) is probabilistic model checker that represent a technique for formally verifying quantitative properties of a stochastic system.…”