Approximate Analysis of Homeostasis of Gene Networks by Linear Temporal Logic using Network Motifs

We proposed a novel framework to analyse homeostasis of gene networks using linear temporal logic. We formulate a kind of homeostasis as strong satisfiability of reactive system specifications. Both behaviours and properties of gene networks are specified in linear temporal logic and homeostasis of the network is checked by strong satisfiability checkers. Though this framework is simple and applicable for many networks, the computational complexity is heavy and large networks cannot be directly analysed. In this paper we present an approximate analysis method to mitigate this computational difficulty. We approximately specify a network specification using fewer propositions such that approximated specifications guarantee homeostasis of the network. However it is difficult to find such safely approximated specifications for any gene network. Thus we present approximate specifications for network motifs, which are common patterns appearing in many gene networks. We demonstrate our approximate method and see that our approximate method is quite efficient in analysing large networks.