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
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.

Download full-text

Full-text

Available from: Bhaskar Dasgupta, Aug 30, 2015
0 Followers
 · 
102 Views
  • Source
    • "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. "
    [Show abstract] [Hide abstract]
    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.
  • Source
    • "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 " . "
    [Show abstract] [Hide abstract]
    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.
    Journal of Computational Biology 10/2007; 14(7):927-49. DOI:10.1089/cmb.2007.0015 · 1.67 Impact Factor
  • Source
    • "The algorithm in [53] provides a CD of 43. In other words, deleting a mere 4% of edges makes the network consistent. "
    [Show abstract] [Hide abstract]
    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.
Show more