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

Process Calculi Abstractions for Biology

Several approaches have been proposed to model biological systems by means of the formal techniques and tools available in computer science. To mention just a few of them, some representations are inspired by Petri Nets theory, and some other by stochastic processes. A most recent approach consists in interpreting the living entities as terms of process calculi where the behavior of the represented systems can be inferred by applying syntax-driven rules. A comprehensive picture of the state of the art of the process calculi approach to biological modeling is still missing. This paper goes in the direction of providing such a picture by presenting a comparative survey of the process calculi that have been used and proposed to describe the behavior of living entities. This is the preliminary version of a paper that was published in Algorithmic Bioprocesses. The original publication is available at http://www.springer.com/computer/foundations/book/978-3-540-88868-

A Software Interface Between the Narrative Language and Bio-PEPA

AbstractWe present a software tool for the automatic translation of models from the Narrative Language, a semi-formal language for biological modelling, into the Bio-PEPA process algebra. This provides biologists with an easy way to describe systems and at the same time gives them access to the simulation and analysis techniques provided by Bio-PEPA. We present details of the translation algorithm and its integration into existing software, and discuss ways in which this idea could be further explored

Aspirin-dependent effects on purinergic P2Y1 receptor express

Chronic treatment with aspirin in healthy volunteers (HVs) is associated with recovery of adenosine diphosphate (ADP)-induced platelet activation. The purinergic P2Y1 receptor exerts its effects via a Gq-protein, which is the same biochemical pathway activated by thromboxane-A2 receptor. We hypothesized that recovery of ADP-induced platelet activation could be attributed to increased P2Y1 expression induced by chronic aspirin exposure. We performed a multi-phase investigation which embraced both in vitro and in vivo experiments conducted in (1) human megakaryoblastic DAMI cells, (2) human megakaryocytic progenitor cell cultures, (3) platelets obtained from HVs treated with aspirin and (4) platelets obtained from aspirin-treated patients. DAMI cells treated with aspirin or WY14643 (PPARα agonist) had a significant up-regulation of P2Y1 mRNA, which was shown to be a PPARα-dependent process. In human megakaryocytic progenitors, in the presence of aspirin or WY14643, P2Y1 mRNA expression was higher than in mock culture. P2Y1 expression increased in platelets obtained from HVs treated with aspirin for 8 weeks. Platelets obtained from patients who were on aspirin for more than 2 months had increased P2Y1 expression and ADP-induced aggregation compared with patients on aspirin treatment for less than a month. Overall, our results suggest that aspirin induces genomic changes in megakaryocytes leading to P2Y1 up-regulation and that PPARα is the nuclear receptor involved in this regulation. Since P2Y1 is coupled to the same Gq-protein of thromboxane-A2 receptor, platelet adaptation in response to pharmacological inhibition seems not to be receptor specific, but may involve other receptors with the same biochemical pathway

Narrative-based computational modelling of the Gp130/JAK/STAT signalling pathway.

BACKGROUND: Appropriately formulated quantitative computational models can support researchers in understanding the dynamic behaviour of biological pathways and support hypothesis formulation and selection by "in silico" experimentation. An obstacle to widespread adoption of this approach is the requirement to formulate a biological pathway as machine executable computer code. We have recently proposed a novel, biologically intuitive, narrative-style modelling language for biologists to formulate the pathway which is then automatically translated into an executable format and is, thus, usable for analysis via existing simulation techniques. RESULTS: Here we use a high-level narrative language in designing a computational model of the gp130/JAK/STAT signalling pathway and show that the model reproduces the dynamic behaviour of the pathway derived by biological observation. We then "experiment" on the model by simulation and sensitivity analysis to define those parameters which dominate the dynamic behaviour of the pathway. The model predicts that nuclear compartmentalisation and phosphorylation status of STAT are key determinants of the pathway and that alternative mechanisms of signal attenuation exert their influence on different timescales. CONCLUSION: The described narrative model of the gp130/JAK/STAT pathway represents an interesting case study showing how, by using this approach, researchers can model biological systems without explicitly dealing with formal notations and mathematical expressions (typically used for biochemical modelling), nevertheless being able to obtain simulation and analysis results. We present the model and the sensitivity analysis results we have obtained, that allow us to identify the parameters which are most sensitive to perturbations. The results, which are shown to be in agreement with existing mathematical models of the gp130/JAK/STAT pathway, serve us as a form of validation of the model and of the approach itself

Stochastic properties of the plant circadian clock

Circadian clocks are gene regulatory networks whose role is to help the organisms to cope with variations in environmental conditions such as the day/night cycle. In this work, we explored the effects of molecular noise in single cells on the behaviour of the circadian clock in the plant model species Arabidopsis thaliana. The computational modelling language Bio-PEPA enabled us to give a stochastic interpretation of an existing deterministic model of the clock, and to easily compare the results obtained via stochastic simulation and via numerical solution of the deterministic model. First, the introduction of stochasticity in the model allowed us to estimate the unknown size of the system. Moreover, stochasticity improved the description of the available experimental data in several light conditions: noise-induced fluctuations yield a faster entrainment of the plant clock under certain photoperiods and are able to explain the experimentally observed dampening of the oscillations in plants under constant light conditions. The model predicts that the desynchronization between noisy oscillations in single cells contributes to the observed damped oscillations at the level of the cell population. Analysis of the phase, period and amplitude distributions under various light conditions demonstrated robust entrainment of the plant clock to light/dark cycles which closely matched the available experimental data

Complementary approaches to understanding the plant circadian clock

Circadian clocks are oscillatory genetic networks that help organisms adapt to the 24-hour day/night cycle. The clock of the green alga Ostreococcus tauri is the simplest plant clock discovered so far. Its many advantages as an experimental system facilitate the testing of computational predictions. We present a model of the Ostreococcus clock in the stochastic process algebra Bio-PEPA and exploit its mapping to different analysis techniques, such as ordinary differential equations, stochastic simulation algorithms and model-checking. The small number of molecules reported for this system tests the limits of the continuous approximation underlying differential equations. We investigate the difference between continuous-deterministic and discrete-stochastic approaches. Stochastic simulation and model-checking allow us to formulate new hypotheses on the system behaviour, such as the presence of self-sustained oscillations in single cells under constant light conditions. We investigate how to model the timing of dawn and dusk in the context of model-checking, which we use to compute how the probability distributions of key biochemical species change over time. These show that the relative variation in expression level is smallest at the time of peak expression, making peak time an optimal experimental phase marker. Building on these analyses, we use approaches from evolutionary systems biology to investigate how changes in the rate of mRNA degradation impacts the phase of a key protein likely to affect fitness. We explore how robust this circadian clock is towards such potential mutational changes in its underlying biochemistry. Our work shows that multiple approaches lead to a more complete understanding of the clock

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