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

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

Modelling Non-linear Crowd Dynamics in Bio-PEPA

Emergent phenomena occur due to the pattern of non-linear and distributed local interactions between the elements of a system over time. Surprisingly, agent based crowd models, in which the movement of each individual follows a limited set of simple rules, often re-produce quite closely the emergent behaviour of crowds that can be observed in reality. An example of such phenomena is the spontaneous self-organisation of drinking parties in the squares of cities in Spain, also known as "El Botellon" [20]. We revisit this case study providing an elegant stochastic process algebraic model in Bio-PEPA amenable to several forms of analyses, among which simulation and fluid flow analysis. We show that a fluid flow approximation, i.e. a deterministic reading of the average behaviour of the system, can provide an alternative and efficient way to study the same emergent behaviour as that explored in [20] where simulation was used instead. Besides empirical evidence, also an analytical justification is provided for the good correspondence found between simulation results and the fluid flow approximation

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

Programmable models of growth and mutation of cancer-cell populations

In this paper we propose a systematic approach to construct mathematical models describing populations of cancer-cells at different stages of disease development. The methodology we propose is based on stochastic Concurrent Constraint Programming, a flexible stochastic modelling language. The methodology is tested on (and partially motivated by) the study of prostate cancer. In particular, we prove how our method is suitable to systematically reconstruct different mathematical models of prostate cancer growth - together with interactions with different kinds of hormone therapy - at different levels of refinement.Comment: In Proceedings CompMod 2011, arXiv:1109.104

Trend-based analysis of a population model of the AKAP scaffold protein

We formalise a continuous-time Markov chain with multi-dimensional discrete state space model of the AKAP scaffold protein as a crosstalk mediator between two biochemical signalling pathways. The analysis by temporal properties of the AKAP model requires reasoning about whether the counts of individuals of the same type (species) are increasing or decreasing. For this purpose we propose the concept of stochastic trends based on formulating the probabilities of transitions that increase (resp. decrease) the counts of individuals of the same type, and express these probabilities as formulae such that the state space of the model is not altered. We define a number of stochastic trend formulae (e.g. weakly increasing, strictly increasing, weakly decreasing, etc.) and use them to extend the set of state formulae of Continuous Stochastic Logic. We show how stochastic trends can be implemented in a guarded-command style specification language for transition systems. We illustrate the application of stochastic trends with numerous small examples and then we analyse the AKAP model in order to characterise and show causality and pulsating behaviours in this biochemical system

PEPA'd Oysters: Converting Dynamic Energy Budget Models to Bio-PEPA, illustrated by a Pacific oyster case study

We present a Bio-PEPA (Biochemical-Performance Evaluation Process Algebra) computational model for the Pacific oyster, derived from a DEB (Dynamic Energy Budget) mathematical model. Experience with this specific model allows us to propose a generic scheme for translation between the widely-used DEB theory and Bio-PEPA. The benefits of translation are that a range of novel analysis tools become available, therefore improving the potential to understand complex biological phenomena at a systems level. This work also provides a link between biology, mathematics and computer science: such interlinking of disciplines is the core of the systems approach to biology

Scalable context-dependent analysis of emergency egress models

Pervasive environments offer an increasing number of services to a large number of people moving within these environments, including timely information about where to go and when, and contextual information about the surrounding environment. This information may be conveyed to people through public displays or direct to a person's mobile phone. People using these services interact with the system but they are also meeting other people and performing other activities as relevant opportunities arise. The design of such systems and the analysis of collective dynamic behaviour of people within them is a challenging problem. We present results on a novel usage of a scalable analysis technique in this context. We show the validity of an approach based on stochastic process-algebraic models by focussing on a representative example, i.e. emergency egress. The chosen case study has the advantage that detailed data is available from studies employing alternative analysis methods, making cross-methodology comparison possible. We also illustrate how realistic, context-dependent human behaviour, often observed in emergency egress, can naturally be embedded in the models, and how the effect of such behaviour on evacuation can be analysed in an efficient and scalable way. The proposed approach encompasses both the agent modelling viewpoint, as system behaviour emerges from specific (discrete) agent interaction, and the population viewpoint, when classes of homogeneous individuals are considered for a (continuous)approximation of overall system behaviour

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