On algorithmic analysis of transcriptional regulation by LTL model checking

Studies of cells in silico can greatly reduce the need for expensive and prolonged laboratory experimentation. The use of model checking for the analysis of biological networks has attracted much attention recently. The practical limitations are still the size of the model, and the time needed to generate the state space. This paper is focused on the model checking approach for analysis of piecewise-linear deterministic models of genetic regulatory networks. Firstly, the qualitative simulation algorithm of de Jong et al. that builds the heart of Genetic Network Analyzer (GNA) is revisited and its time complexity is studied in detail. Secondly, a novel algorithm that reduces the state space generation time is introduced. The new algorithm is developed as an abstraction of the original GNA algorithm. Finally, a fragment of linear time temporal logic for which the provided abstraction is conservative is identified. Efficiency of the new algorithm when implemented in the parallel model checking environment is demonstrated on a set of experiments performed on randomly modified biological models. In general, the achieved results bring a new insight into the field of qualitative simulation emerging in the context of systems biology.