Maria Luisa Guerriero

Modelling Biological Compartments in Bio-PEPA

Compartments and membranes play an important role in cell biology. Therefore it is highly desirable to be able to represent them in modelling languages for biology. Bio-PEPA is a language for the modelling and analysis of biochemical networks; in its present version compartments can be defined but they are only used as labels to express the location of molecular species. In this work we present an extension of Bio-PEPA with some features in order to represent more details about locations of species and reactions. With the term location we mean either a membrane or a compartment. We describe how models involving compartments and membranes can be expressed in the language and, consequently, analysed. We limit our attention to static locations (i.e. with a fixed structure) whose size can depend on time. We illustrate our approach via a classical model used to represent intracellular Ca^2^+ oscillations.

An automated translation from a narrative language for biological modelling into process algebra

The aim of this work is twofold. First, we propose an high level textual modelling language, which is meant to be biologically intuitive and hence easily usable by life scientists in modelling intracellular systems. Secondly, we provide an automatic translation of the proposed language into Beta-binders, a bio-inspired process calculus, which allows life scientists to formally analyse and simulate their models. We use the Gp130 signalling pathway as a case study.

The Bio-PEPA Tool Suite

Bio-PEPA is a timed process algebra designedspecifically for the description of biological phenomena and theiranalysis through quantitative methods such asstochastic simulation and probabilistic model-checking.Two software tools are available for modelling with Bio-PEPA, theBio-PEPA Workbench and the Bio-PEPA Eclipse Plugin. The Bio-PEPAWorkbench is the research prototype tool which allows us to try outnew language features and new types of analysis through rapidprototyping. The Bio-PEPA Eclipse Plugin is a polished modellingenvironment which targets end-users who wish to do Bio-PEPA modellingsupported by a comprehensive integrated development environment. Bothmodelling tools allow the user to analyse their model both in thediscrete stochastic regime and in the sure continuous regime whilemaintaining only a single source in the Bio-PEPA language.

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 di erent analysis techniques, such as ordinary di erential equations, stochastic simulation algorithms and model-checking. The small number of molecules reported for this system tests the limits of the continuous approximation underlying di erential equations. We investigate the di erence 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 a ect 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.

Query-based verification of qualitative trends and oscillations in biochemical systems

We investigate the application of query-based verification to the analysis of behavioural trends of stochastic models of biochemical systems. We derive temporal logic properties which address specific behavioural questions, such as the likelihood for a species to reach a peak/deadlock state, or to exhibit monotonic/oscillatory trends. We introduce a specific modelling convention through which stochastic models of biochemical systems are made suitable to verification of the behavioural queries we define. Based on the queries we identify, we define a classification procedure which, given a stochastic model, allows for identifying meaningful qualitative behavioural trends. We illustrate the proposed query-based classification on a number of simple abstract models of biochemical systems.

Modelling Biological Clocks with Bio-PEPA: Stochasticity and Robustness for the Neurospora crassa Circadian Network

Circadian clocks are biochemical networks, present in nearly all living organisms, whose function is to regulate the expression of specific mRNAs and proteins to synchronise rhythms of metabolism, physiology and behaviour to the 24 hour day/night cycle. Because of their experimental tractability and biological significance, circadian clocks have been the subject of a number of computational modelling studies. In this study we focus on the simple circadian clock of the fungus Neurospora crassa . We use the Bio-PEPA process algebra to develop both a stochastic and a deterministic model of the system. The light on/off mechanism responsible for entrainment to the day/night cycle is expressed using discrete time-dependent events in Bio-PEPA. In order to validate our model, we compare it against the results of previous work which demonstrated that the deterministic model is in agreement with experimental data. Here we investigate the effect of stochasticity on the robustness of the clocks function in biological timing. In particular, we focus on the variations in the phase and amplitude of oscillations in circadian proteins with respect to different factors such as the presence/absence of a positive feedback loop, and the presence/absence of light. The time-dependent sensitivity of the model with respect to some key kinetic parameters is also investigated.

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 others by stochastic processes.

A model of flux regulation in the cholesterol biosynthesis pathway: Immune mediated graduated flux reduction versus statin-like led stepped flux reduction

The cholesterol biosynthesis pathway has recently been shown to play an important role in the innate immune response to viral infection with host protection occurring through a coordinate down regulation of the enzymes catalysing each metabolic step. In contrast, statin based drugs, which form the principle pharmaceutical agents for decreasing the activity of this pathway, target a single enzyme. Here, we build an ordinary differential equation model of the cholesterol biosynthesis pathway in order to investigate how the two regulatory strategies impact upon the behaviour of the pathway. We employ a modest set of assumptions: that the pathway operates away from saturation, that each metabolite is involved in multiple cellular interactions and that mRNA levels reflect enzyme concentrations. Using data taken from primary bone marrow derived macrophage cells infected with murine cytomegalovirus or treated with IFNγ, we show that, under these assumptions, coordinate down-regulation of enzyme activity imparts a graduated reduction in flux along the pathway. In contrast, modelling a statin-like treatment that achieves the same degree of down-regulation in cholesterol production, we show that this delivers a step change in flux along the pathway. The graduated reduction mediated by physiological coordinate regulation of multiple enzymes supports a mechanism that allows a greater level of specificity, altering cholesterol levels with less impact upon interactions branching from the pathway, than pharmacological step reductions. We argue that coordinate regulation is likely to show a long-term evolutionary advantage over single enzyme regulation. Finally, the results from our models have implications for future pharmaceutical therapies intended to target cholesterol production with greater specificity and fewer off target effects, suggesting that this can be achieved by mimicking the coordinated down-regulation observed in immunological responses.