A Logical Paradigm for Systems Biology (Invited Talk)

François Fages, Marc Herbstritt
2010 International Conference on Logic Programming  
Biologists use diagrams to represent complex systems of interaction between molecular species. These graphical notations encompass two types of information: interactions (e.g. protein complexation, modification, binding to a gene, etc.) and regulations (of an interaction or a transcription). Based on these structures, mathematical models can be developed by equipping such molecular interaction networks with kinetic expressions leading to quantitative models of mainly two kinds: ordinary
more » ... tial equations for a continuous interpretation of the kinetics, and continuous-time Markov chains for a stochastic interpretation of the kinetics. The Systems Biology Markup Language (SBML) [7] uses a syntax of reaction rules with kinetic expressions to define such reaction models in a precise way. Nowadays, an increasing collection of models of various biological processes is available in this format in model repositories, such as for instance www.biomodels.net [8] . Since 2002, we investigate the transposition of programming concepts and tools to the analysis of living processes at the cellular level. Our approach relies on a logical paradigm for systems biology which consists in making the following identifications: biological model = quantitative state transition system biological properties = temporal logic formulae biological validation = model-checking model inference = constraint solving Our modelling software platform BioCham [6] (implemented in Prolog) is founded on this paradigm. An SBML model can be interpreted in BioCham at three abstraction levels: • the Boolean semantics (asynchronuous Boolean state transitions on the presence/absence of molecules), • the continuous semantics (ODE on molecular concentration), • the stochastic semantics (CTMC on numbers of molecules). These semantics have been related in the framework of abstract interpretation in [5] , showing for instance that the Boolean semantics is an abstraction of the stochastic semantics, i.e. that the possible stochastic behaviors can be checked in the Boolean semantics, and that if a Boolean behavior is not possible, it cannot be achieved in the quantitative semantics for any kinetics. The temporal logics used to formalize the properties of the behavior of the system are respectively the Computation Tree Logic (CTL) for the Boolean semantics, 1998 ACM Subject Classification: algorithm, theory,verification.
doi:10.4230/lipics.iclp.2010.2 dblp:conf/iclp/Fages10 fatcat:j2p4jn3lfrczhnbrj6nmd72ogu