Formal Method for Biological Systems Modelling

Dear Colleagues,

The field of system biology poses many challenges to computer scientists. Regulatory networks, intra- and extra-cellular signalling pathways, metabolic networks and whole cells models suffer both from high conceptual difficulties and from a huge combinatorial complexity.  From the description of these models, by organising and collecting facts based on knowledge representation databases, to the execution of these models, through the abstraction of their main properties, formal methods offer promising potential approaches. While existing formal frameworks can be adapted to cope with the specific kinds of problems, new formal methods emerge from the confrontation with this new field of application. 

Besides the intrinsic combinatorial complexity, biological systems are characterised by the fact that they have not been humanly designed. Their dynamics are driven by competition for shared resources, time- and concentration-scale separation, and non-linear feedback loops. Many components have antagonistic effects according to the context. It is impossible to understand from which mechanisms the collective behaviour of these models come from.

Mainstream quantitative approaches (based on ODEs) suffer from various limitations. To cope with the combinatorial complexity, series of simplifications are usually required. This results in several drawbacks: not only does it usually restrict the context of the application of the models, but also, it is likely to skew the model in the direction of what is intended by the modeller. Moreover, their results are specific for particular sets of parameters and they are difficult to generalize. As a consequence, they usually offer an unsatisfying level of confidence.

Formal methods provide various means to increase confidence in models and to compute their properties. Formal languages provide hierarchical constructions to collect information about mechanistic interactions, in a more goal agnostic manner. Formal methods also assist the modeller to gradually refine/abstract information about a given process by including more/fewer details from the literature. Symbolic static analyses not only enhance confidence in models, but also provide new perspectives on models by efficiently computing informative invariants. Causal analyses provide explanations for the potential scenarios for events of interest to occur. The behaviour of models can be captured while avoiding the exploration of the different interleaving of these massively distributed agent-centric models. Lastly, model reduction provides new systems while identifying the elements that mainly drive the dynamics of these models.

This Special Issue is dedicated to formal methods developed for the analysis of biological systems and their application to current open questions in biology. Its scope covers the design of specific language and modelling tools, the design of static analyses, causal analyses, model reduction techniques. We are also interested in feedback on the usage of formal approaches in the design and the analysis of models to address biological issues. 

Dr. Jérôme Feret
Prof. Cédric Lhoussaine
Guest Editors

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• Systems biology
• Formal methods
• Static analysis
• Logic