Article

Algorithmic and complexity results for decompositions of biological networks into monotone subsystems.

Department of Computer Science, University of Illinois at Chicago, Chicago, IL 60607, United States; Mathematical Biosciences Institute, 250 Mathematics Building, 231 W 18th Avenue, Columbus, OH 43210, United States; Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, United States; Received 23 January 2006. Revised 3 August 2006. Accepted 3 August 2006. Available online 12 August 2006.
Biosystems 01/2007; 90:161-178. DOI: 10.1007/11764298_23
Source: DBLP

ABSTRACT A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions which are optimal in an appropriate sense. In graph-theoretic language, the problems can be recast in terms of maximal sign-consistent subgraphs. The theoretical results include polynomial-time approximation algorithms as well as constant-ratio inapproximabil- ity results. One of the algorithms, which has a worst-case guarantee of 87.9% from optimality, is based on the semidefinite programming relaxation approach of Goemans- Williamson (23). The algorithm was implemented and tested on a Drosophila segmen- tation network and an Epidermal Growth Factor Receptor pathway model, and it was found to perform close to optimally.

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    ABSTRACT: In this paper we propose three different graph-theoretical decompositions of large-scale biologi-cal networks, all three aiming at highlighting specific dynamical properties of the system. The first consists in finding a maximal directed acyclic subgraph in the network, which dynamically cor-responds to searching for the maximal open-loop subsystem of the given system. The other two decompositions deal with the strong monotonicity property, and aim at decomposing the system into strongly monotone components with different structural characteristics: a single large strongly con-nected monotone subsystem in one case, and a set of smaller disjoint monotone subsystems in the other. For all three decompositions we provide original heuristic algorithms.
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