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

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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Available from: Bhaskar Dasgupta, Aug 30, 2015
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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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    Journal of Computational Biology 10/2007; 14(7):927-49. DOI:10.1089/cmb.2007.0015 · 1.67 Impact Factor
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    • "The algorithm in [53] provides a CD of 43. In other words, deleting a mere 4% of edges makes the network consistent. "
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    ABSTRACT: This paper (parts I and II) provides an expository introduction to monotone and near-monotone dynamical systems associated to biochemical networks, those whose graphs are consistent or near-consistent. Many conclusions can be drawn from signed network structure, associated to purely stoichiometric information and ignoring fluxes. In particular, monotone systems respond in a predictable fashion to perturbations and have robust and ordered dynamical characteristics, making them reliable components of larger networks. Interconnections of monotone systems may be fruitfully analyzed using tools from control theory, by viewing larger systems as interconnections of monotone subsystems. This allows one to obtain precise bifurcation diagrams without appeal to explicit knowledge of fluxes or of kinetic constants and other parameters, using merely "input/output characteristics" (steady-state responses or DC gains). The procedure may be viewed as a "model reduction" approach in which monotone subsystems are viewed as essentially one-dimensional objects. The possibility of performing a decomposition into a small number of monotone components is closely tied to the question of how "near" a system is to being monotone. We argue that systems that are "near monotone" may be more biologically more desirable than systems that are far from being monotone. Indeed, there are indications that biological networks may be much closer to being monotone than random networks that have the same numbers of vertices and of positive and negative edges.
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