Efficient Analysis Of Homeostasis Of Gene Networks With Compositional Approach

Homeostasis is an important property of life. Thanks to this property, living organisms keep their cellular conditions within an acceptable range to function normally. To understand mechanisms of homeostasis and analyse it, the systems biology approach is indispensable. For this purpose, we proposed a qualitative approach to model gene regulatory networks with logical formulae and formulate the homeostasis in terms of a kind of logical property - called realisability of linear temporal logic. This concise formulation of homeostasis naturally yields the method for analysing homeostasis of gene networks using realisability checkers. However, the realisability problem is well-known for its high computational complexity - double-exponential in the size of a formula - and the applicability of this approach will be limited to small gene networks, since the size of formula increases as the network does. To overcome this limitation, we leverage a compositional method to check realisability in which a formula is divided into a few sub-formulae. The difficulty in compositional approach is that we do not know how we obtain a good division. To tackle this issue, we introduce a new clustering algorithm based on a characteristic function on formulae, which calculates the size of formulae and the variation of propositions. The experimental results show that our method gives a good division to benefit from the compositional method.