Authors:
Sohei Ito
1
;
2
;
Kenji Osari
3
;
Shigeki Hagihara
4
and
Naoki Yonezaki
5
;
6
Affiliations:
1
National Fisheries University, Japan
;
2
Silesian University in Opava, Czech Republic
;
3
Yahoo Japan Corporation, Japan
;
4
Tokyo Institute of Technology, Japan
;
5
Tokyo Denki University, Japan
;
6
The Open University of Japan, Japan
Keyword(s):
Gene Regulatory Network, Systems Biology, Homeostasis, Temporal Logic, Realisability.
Abstract:
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 i
n 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.
(More)