Abstract Interpretation for Probabilistic Termination of Biological Systems

In a previous paper the authors applied the Abstract Interpretation approach for approximating the probabilistic semantics of biological systems, modeled specifically using the Chemical Ground Form calculus. The methodology is based on the idea of representing a set of experiments, which differ only for the initial concentrations, by abstracting the multiplicity of reagents present in a solution, using intervals. In this paper, we refine the approach in order to address probabilistic termination properties. More in details, we introduce a refinement of the abstract LTS semantics and we abstract the probabilistic semantics using a variant of Interval Markov Chains. The abstract probabilistic model safely approximates a set of concrete experiments and reports conservative lower and upper bounds for probabilistic termination

A Global Occurrence Counting Analysis for Brane Calculi

We propose a polynomial static analysis for Brane Calculi, based on Abstract Interpretation techniques. The analysis provides a description of the possible hierarchical structure of membranes and of the processes possibly associated to each membrane, together with global occurrence counting information. Our analysis can be applied in the biological setting to investigate systems in which the information on the number of membranes occurring in the system plays a crucial role

Causal static analysis for Brane Calculi

We present here a static analysis, based on Abstract Interpretation, obtained by defining an abstract version of the causal semantics for the Mate/Bud/Drip (MBD) version of Brane Calculi, proposed by Busi. Our analysis statically approximates the dynamic behaviour of MBD systems. More precisely, the analysis is able to describe the essential behaviour of the represented membranes, in terms of their possible interactions. Furthermore, our analysis is able to statically capture the possible causal dependencies among interactions, whose determination can be exploited to better understand the modelled biological phenomena. Finally, we apply our analysis to an abstract specification of the receptor-mediated endocytosis mechanism

A static analysis for Brane Calculi providing global occurrence counting information

In this paper we propose a static analysis for Brane Calculi [1], based on Abstract Interpretation [2] techniques. Our analysis statically approximates the dynamic behaviour of Brane systems, by providing a description of the possible hierarchical structure of membranes and of the processes possibly associated to each membrane, together with global occurrence counting information. Our analysis can be computed in polynomial time. We apply it to investigate several biological systems in which occurrence counting information plays a crucial role. In particular, our case study concerns the formation of the haemoglobin polymer in presence of alterations and investigate the influence that such alterations have on the ability of the haemoglobin polymer to bind oxygen molecules