Petri Net modelling approach for analysing the behaviour of Wnt/[inline-formula removed] -catenin and Wnt/Ca 2+ signalling pathways in arrhythmogenic right ventricular cardiomyopathy.

Arrhythmogenic right ventricular cardiomyopathy (ARVC) is an inherited heart muscle disease that may result in arrhythmia, heart failure and sudden death. The hallmark pathological findings are progressive myocyte loss and fibro fatty replacement, with a predilection for the right ventricle. This study focuses on the adipose tissue formation in cardiomyocyte by considering the signal transduction pathways including Wnt/[inline-formula removed]-catenin and Wnt/Ca2+ regulation system. These pathways are modelled and analysed using stochastic petri nets (SPN) in order to increase our comprehension of ARVC and in turn its treatment regimen. The Wnt/[inline-formula removed]-catenin model predicts that the dysregulation or absence of Wnt signalling, inhibition of dishevelled and elevation of glycogen synthase kinase 3 along with casein kinase I are key cytotoxic events resulting in apoptosis. Moreover, the Wnt/Ca2+ SPN model demonstrates that the Bcl2 gene inhibited by c-Jun N-terminal kinase protein in the event of endoplasmic reticulum stress due to action potential and increased amount of intracellular Ca2+ which recovers the Ca2+homeostasis by phospholipase C, this event positively regulates the Bcl2 to suppress the mitochondrial apoptosis which causes ARVC

Modeling biological systems with delays in Bio-PEPA

Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed, or to provide abstraction of some behavior of the system resulting more compact models. In this paper we enrich the stochastic process algebra Bio-PEPA, with the possibility of assigning delays to actions, yielding a new non-Markovian process algebra: Bio-PEPAd. This is a conservative extension meaning that the original syntax of Bio-PEPA is retained and the delay specification which can now be associated with actions may be added to existing Bio-PEPA models. The semantics of the firing of the actions with delays is the delay-as-duration approach, earlier presented in papers on the stochastic simulation of biological systems with delays. These semantics of the algebra are given in the Starting-Terminating style, meaning that the state and the completion of an action are observed as two separate events, as required by delays. Furthermore we outline how to perform stochastic simulation of Bio-PEPAd systems and how to automatically translate a Bio-PEPAd system into a set of Delay Differential Equations, the deterministic framework for modeling of biological systems with delays. We end the paper with two example models of biological systems with delays to illustrate the approach.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005

On Modeling Signal Transduction Networks

Signal transduction networks are very complex processes employed by the living cell to suitably react to environmental stimuli. Qualitative and quantitative computational models play an increasingly important role in the representation of these networks and in the search of new insights about these phenomena. In this work we analyze some graph-based models used to discover qualitative properties of such networks. In turn, we show that MP systems can naturally extend these graph-based models by adding some qualitative elements. The case study of integrins activation during the lymphocyte recruitment, a crucial phenomenon in inflammatory processes, is described, and a first MP graph for this network is designed. Finally, we discuss some open problems related to the qualitative modeling of signaling networks

Descriptive Timed Membrane Petri Nets for Modelling of Parallel Computing

In order to capture the compartmentation and behaviour of membrane systems for modelling of parallel computing, we introduce the descriptive dynamic rewriting Descriptive Membrane Timed Petri Nets (DM-nets) that can at in run-time modify their own structure by rewriting some of their descriptive expression components. Furthermore, this descriptive approach facilitates the understanding of complex models and their component-based construction as well as the application of modern computer engineering concepts