Investigating modularity in the analysis of process algebra models of biochemical systems

Compositionality is a key feature of process algebras which is often cited as one of their advantages as a modelling technique. It is certainly true that in biochemical systems, as in many other systems, model construction is made easier in a formalism which allows the problem to be tackled compositionally. In this paper we consider the extent to which the compositional structure which is inherent in process algebra models of biochemical systems can be exploited during model solution. In essence this means using the compositional structure to guide decomposed solution and analysis. Unfortunately the dynamic behaviour of biochemical systems exhibits strong interdependencies between the components of the model making decomposed solution a difficult task. Nevertheless we believe that if such decomposition based on process algebras could be established it would demonstrate substantial benefits for systems biology modelling. In this paper we present our preliminary investigations based on a case study of the pheromone pathway in yeast, modelling in the stochastic process algebra Bio-PEPA

Some investigations concerning the CTMC and the ODE model derived from Bio-PEPA

<p>Bio-PEPA is a recently defined language for the modelling and analysis of biochemical networks. It supports an abstract style of modelling, in which discrete levels of concentration within a species are considered instead of individual molecules. A finer granularity for the system corresponds to a smaller concentration step size and therefore to a greater number of concentration levels. This style of model is amenable to a variety of different analysis techniques, including numerical analysis based on a CMTC with states reflecting the levels of concentration.</p> <p>In this paper we present a formal definition of the CTMC with levels derived from a Bio-PEPA system. Furthermore we investigate the relationship between this CTMC and the system of ordinary differential equations (ODEs) derived from the same model. Using Kurtz's theorem, we show that the set of ODEs derived from the Bio-PEPA model is able to capture the limiting behaviour of the CTMC obtained from the same system. Finally, we define an empirical methodology to find the granularity of the Bio-PEPA system for which the ODE and the CTMC with levels are in a good agreement. The proposed definition is based on a notion of distance between the two models. We demonstrate our approach on a model of the Repressilator, a simple biochemical network with oscillating behaviour.</p&gt

Beta-binders with Biological Transactions

In this work we propose an extension of Beta-binders with biological transactions, called TBeta-binders, in order to model a sequence of elementary actions atomically. This extension is useful when we need to specify multi-reactant multi-product reactions or when we use a sequence of actions to represent a single biological interaction. Some properties of these transactions are reported. Finally, some simple but explicative examples are described to validate our extension

Modelling co-transcriptional cleavage in the synthesis of yeast pre-rRNA

AbstractIn this paper we present a quantified model of the synthesis of pre-rRNAs in yeast. The chemical kinetics simulation software Dizzy has been used as both the modelling and simulation framework of our study. The simulations have been used to investigate the mechanism of co-transcriptional cleavage which can occur during the synthesis of pre-rRNAs.Throughout the paper we emphasise the strong role of experimental data both in shaping the model and in guiding the analysis which is carried out. Parameter estimation procedures have been used to fit the model to the data and we discuss the validation of the model against the available experimental data. Simulation based on Gillespie’s algorithm is considered to be the reference method for our analysis and a comparison with other simulators is reported. Finally, we define an extended model, that relaxes one of the assumptions of the initial model

Bio-PEPA for Epidemiological Models

AbstractMany models have been defined in order to describe the evolution of a disease in a population. The modelling of diseases is helpful to understand the mechanisms for their spread and to predict their future evolution. Most of the models in the literature are defined in terms of systems of differential equations and only a few of them propose stochastic simulation for the analysis.The main aim of this work is to apply the process algebra Bio-PEPA for the modelling and analysis of epidemiological models. As Bio-PEPA has been originally defined for biochemical networks, we define a variant of it suitable for representing epidemiological models. Some features of Bio-PEPA are useful in the context of epidemiology as well: location can abstract spatial structure and event can describe the introduction of prophylaxis in a population infected by a disease at a given day. Concerning the analysis, we can take advantage of the various kinds of analysis supported by Bio-PEPA, such as, for instance, stochastic simulation, model checking and ODE-based analyses. In particular, the modeller can select the most appropriate approach for the study of the model and analysis techniques can be used together for a better understanding of the behaviour of the system.In this paper we apply Bio-PEPA to the study of epidemiological models of avian influenza, based on different assumptions about the spatial structure and the possible kind of treatment. These models demonstrate that Bio-PEPA has several features that facilitate epidemiological modelling

A Process Calculus for Molecular Interaction Maps

We present the MIM calculus, a modeling formalism with a strong biological basis, which provides biologically-meaningful operators for representing the interaction capabilities of molecular species. The operators of the calculus are inspired by the reaction symbols used in Molecular Interaction Maps (MIMs), a diagrammatic notation used by biologists. Models of the calculus can be easily derived from MIM diagrams, for which an unambiguous and executable interpretation is thus obtained. We give a formal definition of the syntax and semantics of the MIM calculus, and we study properties of the formalism. A case study is also presented to show the use of the calculus for modeling biomolecular networks.Comment: 15 pages; 8 figures; To be published on EPTCS, proceedings of MeCBIC 200

Computational Modeling for the Activation Cycle of G-proteins by G-protein-coupled Receptors

In this paper, we survey five different computational modeling methods. For comparison, we use the activation cycle of G-proteins that regulate cellular signaling events downstream of G-protein-coupled receptors (GPCRs) as a driving example. Starting from an existing Ordinary Differential Equations (ODEs) model, we implement the G-protein cycle in the stochastic Pi-calculus using SPiM, as Petri-nets using Cell Illustrator, in the Kappa Language using Cellucidate, and in Bio-PEPA using the Bio-PEPA eclipse plug in. We also provide a high-level notation to abstract away from communication primitives that may be unfamiliar to the average biologist, and we show how to translate high-level programs into stochastic Pi-calculus processes and chemical reactions.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005

Integrated Simulation and Model-Checking for the Analysis of Biochemical Systems

Model-checking can provide valuable insight into the behaviour of biochemical systems, answering quantitative queries which are more difficult to answer using stochastic simulation alone. However, model-checking is a computationally intensive technique which can become infeasible if the system under consideration is too large. Moreover, the finite nature of the state representation used means that a priori bounds must be set for the numbers of molecules of each species to be observed in the system. In this paper we present an approach which addresses these problems by using stochastic simulation and the PRISM model checker in tandem. The stochastic simulation identifies reasonable bounds for molecular populations in the context of the considered experiment. These bounds are used to parameterise the PRISM model and limit its state space. A simulation pre-run identifies interesting time intervals on which model-checking should focus, if this information is not available from experimental data