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
Biosystems 01/2007; 90:161-178. DOI: 10.1007/11764298_23
Source: DBLP


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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Available from: Bhaskar Dasgupta
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    • "Hence the paradigm of monotonicity has gained some momentum in recent years and there is by now a consistent literature on using these properties to study biological networks (DasGupta et al., 2007; Iacono & Altafini, 2010; Iacono et al., 2010; Ma'ayan et al., 2008; Sontag, 2007). "
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    • "An influence graph is a signed graph where the signs may have the already mentioned meaning of activatory/inhibitory action, or may simply represent the signature of the Jacobian linearization of a nonlinear vector field which is unknown but sign constant over the entire state space (common forms of the kinetics , such as mass-action and Michaelis-Menten, normally obey to this condition), see [3] [5]. In choosing this level of detail for our networks, we are guided by an abundant literature [5] [9] [15] [18] [22] [23] [30], and inspired in particular by a series of papers by E. Sontag and colleagues [1] [3] [17] [28] who showed monotone subsystems are obtained in one case, and a single large strongly monotone subnetwork in the other. Depending on the context, each of these approaches may be of help in better understanding the global structure of large systems and in investigating more properly their dynamical properties. "
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