Subnetwork analysis reveals dynamic features of complex (bio)chemical networks

Abstract

In analyzing and mathematical modeling of complex (bio)chemical reaction networks, formal methods that connect network structure and dynamic behavior are needed because often, quantitative knowledge of the networks is very limited. This applies to many important processes in cell biology. Chemical reaction network theory allows for the classification of the potential network behavior-for instance, with respect to the existence of multiple steady states-but is computationally limited to small systems. Here, we show that by analyzing subnetworks termed elementary flux modes, the applicability of the theory can be extended to more complex networks. For an example network inspired by cell cycle control in budding yeast, the approach allows for model discrimination, identification of key mechanisms for multistationarity, and robustness analysis. The presented methods will be helpful in modeling and analyzing other complex reaction networks.reaction network ͉ structure ͉ elementary flux mode ͉ bistability

Subnetwork analysis for multistationarity in mass action kinetics

“…Thus, in the context of this paper, when a subnetwork is analysed using the toolbox [16] one can either establish S sub -and thus S-multistationarity or exclude S sub -, not S-multistationarity. As discussed in [6] multistationarity can be established for the subnetworks defined by the generators E 9 , E 10 and E 11 of network N 1 , while one fails to establish S sub -multistationarity for any of the subnetworks of network N 2 . But, using the ideas described in [5,4], one can establish S-multistationarity for the subnetworks defined by generators E 9 and E 12 .…”

“…(5.4)). As described in the main text and in [6], the shaded networks can exhibit S sub -and thus, trivially, S-multistationarity.…”

Functional similarities of reaction sets in metabolic pathways

“…If this number is similar for the reactions of two reaction sets we compare, then they are considered to have similar functions by the UP/UC measure. The last existing approach is Reaction participation similarity [5,16]. Reaction participation uses the number of EFMs that a reaction participates in to measure the importance of that reaction for the pathway.…”

“…Analyzing and quantifying the impacts of these components provide a better understanding of the pathway. When the reactions of a pathway are of interest, several existing approaches measure the impact of a reaction as the number of its neighbors (centrality) [14], the number of compounds it uniquely produces or consumes (UP/UC) [17] and the number of EFMs that it participates in (participation) [5,16]. However, none of these methods characterize the biological functions of a reaction set as a function of the steady states of its pathway.…”

Algebraic connectivity may explain the evolution of gene regulatory networks

“…The elucidation of complete network of regulatory interactions parametrized with kinetic information leading to a particular type of gene expression is, at present, still a challenging task even for the well-studied model organisms whose networks have been partially assembled for few selected processes, conditions or on the level of the entire genome (Davidson et al, 2002;Shen-Orr et al, 2002;Zhang et al, 2006). Nevertheless, recent theoretical investigations have established that the qualitative behavior of dynamic processes on complex networks is closely related to the structural network properties (Conradi et al, 2007;Craciun et al, 2006;Elowitz and Leibler, 2000;Feinberg, 1987;Madan Babu et al, 2006). Consequently, the existing studies of gene regulatory networks have attempted to determine unifying design principles in order to understand and make biologically relevant conclusions solely from the network structure.…”