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, Oct 04, 2015
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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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    ABSTRACT: Given a large-scale biological network represented as an influence graph, in this article we investigate possible decompositions of the network aimed at highlighting specific dynamical properties. The first decomposition we study consists in finding a maximal directed acyclic subgraph of the network, which dynamically corresponds to searching for a maximal open-loop subsystem of the given system. Another dynamical property investigated is strong monotonicity. We propose two methods to deal with this property, both aimed at decomposing the system into strongly monotone subsystems, but with different structural characteristics: one method tends to produce a single large strongly monotone component, while the other typically generates a set of smaller disjoint strongly monotone subsystems. Original heuristics for the methods investigated are described in the article.
    Bioinformatics 11/2011; 28(1):76-83. DOI:10.1093/bioinformatics/btr620 · 4.98 Impact Factor
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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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    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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    • "The first step of our method is to distill experimental conclusions into qualitative regulatory relations between cellular components. Following [8] [22], we distinguish between positive and negative regulation, usually denoted by the verbs " promote " and " inhibit " and represented graphically as → and ⊣. Biochemical and pharmacological evidence is represented as component-to-component relationships, such as " A promotes B " , and is incorporated as a directed arc from A to B. Arcs corresponding to direct interactions are marked as such. Genetic evidence leads to double causal inferences of the type " C promotes the process through which A promotes B " . "
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    ABSTRACT: In this paper, we introduce a new method of combined synthesis and inference of biological signal transduction networks. A main idea of our method lies in representing observed causal relationships as network paths and using techniques from combinatorial optimization to find the sparsest graph consistent with all experimental observations. Our contributions are twofold: (a) We formalize our approach, study its computational complexity and prove new results for exact and approximate solutions of the computationally hard transitive reduction substep of the approach (Sections 2 and 5). (b) We validate the biological usability of our approach by successfully applying it to a previously published signal transduction network by Li et al. (2006) and show that our algorithm for the transitive reduction substep performs well on graphs with a structure similar to those observed in transcriptional regulatory and signal transduction networks.
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