Petri nets for multiscale Systems Biology

Computational modelling and analysis of biochemical networks contribute to a better understanding of biological systems in terms of both the ability to explain behaviours and mechanisms as well as being able to predict the behaviour of a system under different conditions. Such approaches are at the core of Systems Biology, which attempts to understand biological systems by modelling the interaction of their components, and is a crucial discipline in the life sciences. Multiscale modeling is the field of solving physical problems which have important features at multiple scales, particularly multiple spatial and(or) temporal scales. In this proposal, we will focus on spatial aspects, with an application to biological systems.

Petri nets are a natural and established notation for describing reaction networks because they can easily represent reactions and biochemical components, have a formal semantics and are particularly attractive to biologists. The intuitive visualization that is a consequence of the graphical formalism is complemented by a rich set of sophisticated analysis techniques, which are supported by reliable tools.
A drawback of current modelling approaches, including Petri nets, are their limitation to relatively small networks. Biological systems can be represented as networks which themselves typically contain regular (network) structures, and/or repeated occurrences of network patterns. Moreover, this organisation occurs in a hierarchical manner, reflecting the physical and spatial organisation of the organism, from the intracellular to the intercellular level and beyond (tissues, organs etc.).

Although network models can be designed using standard Petri nets, so far there is no support for such structuring, it becomes impractical as the size of the networks to be modelled increases. Besides the purely technical aspect due to the impracticality of handling large flat nets, humans need some hierarchy and organisation in what they are designing in order to be able to conceptualise the modelled object. Thus, models should explicitly reflect the organisation in complex biological systems.

Hierarchical Petri nets reuse the well-established engineering principle of hierarchical decomposition to manage the design of large-scale systems. Sub-networks are hidden as building blocks within macro nodes, and the comprehension of the whole network builds upon the understanding of all building blocks and the interconnection of their interfaces

Coloured Petri nets allow the description of similar network structures in a concise and well-founded way, providing a flexible template mechanism for network designers. In coloured Petri nets, tokens can be distinguished via their colours. This allows for the discrimination of species (molecules, metabolites, proteins, secondary substances, genes, etc.). In addition, colours can be used to distinguish between sub-populations of a species in different locations (cytosol, nucleus and so on).

Although Hierarchical and Coloured Petri nets have been extensively deployed in modelling technical systems, the use of neither approach has gained popularity so far in Systems Biology. Their combination is potentially extremely powerful, and but has not been explored systematically so far in any area of application.

Specifically, the goal of this project is to develop approaches to support the modelling of large and complex biological systems by the use of a novel integrative combination of hierarchy and colour in Petri nets, which promises to be particularly helpful in investigating spatial aspects of biochemical network behaviour, such as communication at the intra and intercellular levels. Our concrete contribution to the area will be the development of a suitable methodology to underpin the process of engineering robust and useful models for such complex biological systems.

This research will initially benefit biomodel engineers, and impact on the process of designing, constructing and analysing models of complex biological systems. The advantage will be both in a sound framework to support reasoning, as well as in the tools that that can be constructed on its basis. It will also benefit experimental bioscientists, impacting on the process of planning and carrying out biological experimentation, because it will provide a means to clearly describe a system that is subject to experimental investigation, as well as providing a sound basis for procedures that explore in-silico the experimental space of in-vitro/in-vivo assays. Thus overall the research will benefit systems biologists, and positively impact the sound development of systems biology, where modeling and laboratory experimentation are connected in a tight loop; it will do this by enabling fruitful interactions between modelers and experimental life-scientists.

At a wider level, the research will benefit a wide range of modelers - not just biosystem modelers, impacting on the science of modeling, because currently colour and hierarchy exist as separate concepts, which can at best be used side-by-side in existing approaches. This applies equally to the object-oriented variations of colouring. Our proposal entails a true integration of both colour and hierarchy giving an increased power in the ability to model multiscale dynamic systems in general where hierarchical structuring is important. Although our research focuses on biological systems, other applications include transport, manufacturing and health.

There will also be an impact on basic computer science, because the integration of colour and hierarchy is a non-trivial task that has yet to be achieved in a sound and robust manner, and this project will contribute a framework to underpin this.

The research will also benefit lecturers due to its impact in the area of teaching, because the outputs from the project can be used to contribute to courses in systems biology. These outputs include the standard set of biological examples, the theory of spatial information, the algorithms for automatic detection of motifs and hierarchy levels, and their automatic assignation of hierarchically structured colour in Petri net systems.