Modular Verification of Biological Systems

Systems of interest in systems biology (such as metabolic pathways, signalling pathways and gene regulatory networks) often consist of a huge number of components interacting in different ways, thus exhibiting very complex behaviours. In biology, such behaviours are usually explored by means of simulation techniques applied to models defined on the basis of system observation and of hypotheses on its functioning. Model checking has also been recently applied to the analysis of biological systems. This analysis technique typically relies on a state space representation whose size, unfortunately, makes the analysis often intractable for realistic models. A method for trying to avoid the state space explosion problem is to consider a decomposition of the system, and to apply a modular verification technique. In particular, properties to be verified often concern only a small portion of the modelled system rather than the system as a whole. Hence, for each property it would be useful to be able to isolate a minimal fragment of the model that is necessary to verify such a property. In this thesis we introduce a modular verification technique in which the system of interest is described by means of an automata-based formalism, called sync-programs, that supports modular construction. Our modular verification technique is based on results of Grumberg et al.~and on their application to the theory of concurrent systems proposed by Attie and Emerson. In particular, we adapt Attie and Emerson's approach to deal with biological systems by allowing automata to synchronise by performing transitions simultaneously. Modular verification allows qualitative aspects of systems to be analysed with the guarantee that properties proved to hold in a suitable model fragment also hold in the whole model. The correctness of the verification technique is proved. The class of properties preserved is ACTL$^{-}$, the universal fragment of temporal logic CTL. The preservation holds only for positive answers and negative answers are not necessarily preserved. In order to verify properties we use the NuSMV model checker, which is a well-established and efficient instrument. We provide a formal translation of sync-programs to simpler automata, which can be given as input to NuSMV. We prove the correspondence of the verification problems. We show the application of our verification technique in some biological case studies. We compare the time required to verify the property on the whole model with the time needed to verify the same property by only considering those modules which are involved in the behaviour of the system related to the property. In order to handle modelling and verification of more realistic biological scenarios, we propose also a dynamic version of our formalism. It allows entities to be created dynamically, in particular by other already running entities, as it often happens in biological systems. Moreover, multiple copies of the same entities can be present at the same time in a system. We show a correspondence of our model with Petri Nets. This has a consequence that tools developed for Petri Nets could be used also for dynamic sync-programs. Modular verification allows properties expressed as DACTL- formulae (dynamic version of ACTL-) to be verified on a portion of the model. The results of analysis of the case study of the MAP kinase cascade activated by surface and internalised EGF receptors, which consists of 143 species and 80 reactions, suggest applicability and scalability of the approach. The results raise the prospect of rendering tractable problems that are currently intractable in the verification of biological systems. In addition, we expect that the techniques developed in the thesis could be applied with profit not only to models of biological systems, but more generally to models of concurrent systems

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

QUALITATIVE AND QUANTITATIVE FORMAL MODELING OF BIOLOGICAL SYSTEMS

Nella tesi si sviluppa un formalismo basato su riscrittura di termini e lo si propone come strumento per la descrizione di sistemi biologici. Tale formalismo, chiamato calculus of looping sequences (cls) consente di descrivere proteine, dna e membrane come termini, e interazioni tra questi elementi come regole di riscrittura. Diverse varianti di cls sono studiate al fine di descrivere diversi aspetti dei sistemi biologici, inoltre vengono definite equivalenze sul comportamento dei sistemi (bisimulazioni) e una versione stocastica del formalismo che consente di sviluppare strumenti di simulazione

Hands-on Science: brightening our future

Light, either sunlight or coming from the moon or the stars, emitted by the fireflies or the bulbs in our room or coming out of our TV screen, is not only one of the first main vehicles of contact with the world around us but also adds beauty and fascination to our lives. Blessing all of us, it is definitely one of the corner stones of the structure of our modern world and crucial to its development. The book herein aims to contribute to an effective implementation of a sound widespread scientific literacy and effective Science Education in our schools and at all levels of society

Meta-stochastic simulation for systems and synthetic biology using classification

PhD ThesisTo comprehend the immense complexity that drives biological systems, it is necessary to generate hypotheses of system behaviour. This is because one can observe the results of a biological process and have knowledge of the molecular/genetic components, but not directly witness biochemical interaction mechanisms. Hypotheses can be tested in silico which is considerably cheaper and faster than “wet” lab trialand- error experimentation. Bio-systems are traditionally modelled using ordinary differential equations (ODEs). ODEs are generally suitable for the approximation of a (test tube sized) in vitro system trajectory, but cannot account for inherent system noise or discrete event behaviour. Most in vivo biochemical interactions occur within small spatially compartmentalised units commonly known as cells, which are prone to stochastic noise due to relatively low intracellular molecular populations. Stochastic simulation algorithms (SSAs) provide an exact mechanistic account of the temporal evolution of a bio-system, and can account for noise and discrete cellular transcription and signalling behaviour. Whilst this reaction-by-reaction account of system trajectory elucidates biological mechanisms more comprehensively than ODE execution, it comes at increased computational expense. Scaling to the demands of modern biology requires ever larger and more detailed models to be executed. Scientists evaluating and engineering tissue-scale and bacterial colony sized biosystems can be limited by the tractability of their computational hypothesis testing techniques. This thesis evaluates a hypothesised relationship between SSA computational performance and biochemical model characteristics. This relationship leads to the possibility of predicting the fastest SSA for an arbitrary model - a method that can provide computational headroom for more complex models to be executed. The research output of this thesis is realised as a software package for meta-stochastic simulation called ssapredict. Ssapredict uses statistical classification to predict SSA performance, and also provides high performance stochastic simulation implementations to the wider community.Newcastle University & University of Nottingham Computing Science department

Exploration of scalable industrial platforms for the commercial production of active molecules from microalgae cell walls

Food, nutraceutical, cosmeceutical, pharmaceutical and biomedical industries are putting significant effort into looking for new natural ingredients [1,2]. Microalgae have been recognised as potential sources of high-value chemicals, with most attention focused on antioxidants, pigments and specialty oils [3]. An under-exploited group of biochemicals produced by microalgae are extracellular polymeric substances (EPS) with hyaluronan (HA) representing one of them. Current industrial production methodologies for HA leave opportunities for the establishment of improved routes with higher molecular mass, enhanced biophysical properties, lower production costs and non-bacterial nor animal origins as key unique selling points. At present, incumbent platforms are either based upon Streptococcus spp. (pathogen) bacterial fermentation, modified (GM) Bacillus subtilis or derived from animal tissues. Furthermore, the extraction of various economically exploitable cell components from microalgal biomass is at the core of a successful microalgal biorefinery approach, and it remains a current bottleneck for the economic feasibility of microalgal biotechnological processes [4]. Cell disruption is often required to break down the hard and complicated microalgal cell walls in order to retrieve microalgal constituents such as proteins, lipids, and polysaccharides. Viral enzymes may play a beneficial role in this scenario and might be used to facilitate genetic engineering by overcoming the cell wall barrier or for biorefinery purposes. This project's hypothesis was that it was feasible for microalgae to produce HA. The objectives included investigating a stress-induced platform for the possible production of HA, learning how Chlorovirus/C. varibilis infection leads to HA formation, improving the HA production for the latter platform and looking into intriguing enzymes that can break down polysaccharides. This PhD project focused on exploring, characterizing and developing new platforms in order to achieve profitable industrial production of valuable compounds from microalgae and identify viral enzymes that could help with the processing of Chlorella cells for multiple applications. Two platforms were successfully explored for the production of valuable polysaccharides, and multiple enzymes were identified, produced, characterised and evaluated for Chlorella cell wall digestion to enable possible biorefinery approaches of a non-domesticated Chlorella vulgaris strain

A novel approach to dynamic flux balance analysis that accounts for the dynamic transfer of information by internal metabolites

Understanding the dynamics of information feedback amongst components of complex biological systems is crucial to the success of engineering desirable metabolic phenotypes. Flux Balance Analysis (FBA) is a structural metabolic modelling procedure that allows for local topological constraints to be related to steady-state global behaviors of metabolic systems. A vast majority of biological systems of interest, such as microbial communities, however do not exist under steady-state conditions. Therefore, extending FBA methods to the dynamical setting has been a major challenge to metabolic modelling. In dynamic FBA (dFBA), the representation of feedback dynamics is made possible by combining the methods of FBA with those of Ordinary Differential Equations (ODE). Although numerous dFBA models have been constructed to date, very little effort has gone into the theoretical analysis of how static FBA models and dynamic ODE models should be combined in dFBA. To develop a better understanding of the mathematical structure of dFBA, we investigate the properties of FBA. In order to predict time-derivatives of population growth, every dFBA model must make the assumption that the underlying metabolic network modeled via FBA optimizes a phenotypic function of growth rate. We show however, that under certain circumstances, this requirement introduces a rigid correspondence between growth rate, and a related quantity, the growth yield. The consequence of this is that the dFBA models become rigid in its predictions, effectively becoming a near-static representation of metabolism. In this thesis, we show that this tight correspondence between yield and rate may be broken by combining two inversely related approaches to formulating the FBA problem

Classification and detection of Critical Transitions: from theory to data

From population collapses to cell-fate decision, critical phenomena are abundant in complex real-world systems. Among modelling theories to address them, the critical transitions framework gained traction for its purpose of determining classes of critical mechanisms and identifying generic indicators to detect and alert them (“early warning signals”). This thesis contributes to such research field by elucidating its relevance within the systems biology landscape, by providing a systematic classification of leading mechanisms for critical transitions, and by assessing the theoretical and empirical performance of early warning signals. The thesis thus bridges general results concerning the critical transitions field – possibly applicable to multidisciplinary contexts – and specific applications in biology and epidemiology, towards the development of sound risk monitoring system