Qualitative analysis of gene regulatory networks by temporal logic

In this article we propose a novel formalism to model and analyse gene regulatory networks using a well-established formal verification technique. We model the possible behaviours of networks by logical formulae in linear temporal logic (LTL). By checking the satisfiability of LTL, it is possible to check whether some or all behaviours satisfy a given biological property, which is difficult in quantitative analyses such as the ordinary differential equation approach. Owing to the complexity of LTL satisfiability checking, analysis of large networks is generally intractable in this method. To mitigate this computational difficulty, we developed two methods. One is a modular checking method where we divide a network into subnetworks, check them individually, and then integrate them. The other is an approximate analysis method in which we specify behaviours in simpler formulae which compress or expand the possible behaviours of networks. In the approximate method, we focused on network motifs and presented approximate specifications for them. We confirmed by experiments that both methods improved the analysis of large networks.