Cellular automata simulation of topological effects on the dynamics of feed-forward motifs

Abstract

Background: Feed-forward motifs are important functional modules in biological and other complex networks. The functionality of feed-forward motifs and other network motifs is largely dictated by the connectivity of the individual network components. While studies on the dynamics of motifs and networks are usually devoted to the temporal or spatial description of processes, this study focuses on the relationship between the specific architecture and the overall rate of the processes of the feed-forward family of motifs, including double and triple feed-forward loops. The search for the most efficient network architecture could be of particular interest for regulatory or signaling pathways in biology, as well as in computational and communication systems.

Network motif frequency vectors reveal evolving metabolic network organisation

“…This is perhaps not too surprising as both of these patterns are considered to play important functional roles in many biological networks. The addition of a feed forward loop to a linear cascade of biochemical reactions, for example, has been hypothesised to accelerate the metabolic process 39 . Importantly, we found the number of significant motifs to be greatest in those metabolic networks exposed to more variable environments: 2/212 for specialised and 6/212 for varied (see Table 3).…”

Cellular Automata Modeling of Biomolecular Networks

“…The ordering of the ten directed 4-node motifs in Fig. 9 was found to follow several topological transformation patterns (Apte et al, 2008). The acceleration of the S → T conversion might be predicted in part by conjecturing that every graph transformation that reduces the distance or, alternatively reduces the average path length, between the source and target vertices S and T, accelerates the process.…”

“…A different approach was also pioneered in our Center for the Study of Biological Complexity (Bonchev et al, 2006, Apte et al, 2008, Taylor et al, 2010. It was aimed to search for answers to a fundamental problem: "How structure affects the dynamics of processes in networks?".…”

“…The asterisks in motifs D, E, and J, stand for the edge, which changes its direction in a subsequent transformation. (Courtesy of Journal of Biological Engineering (Apte et al, 2008) (Apte et al, 2008)). …”

“…The performance of all directed 4-node feed-forward motifs having a single source and a single target node (S1T1 class) was evaluated and compared to that of the directed linear motif of the same size. The parallel ODE simulation was carried out in several approximations (Apte et al, 2008). The simplest way to construct an ODE model is to treat each feed-forward link A→B without regard to the underlying biochemical processes (e.g., neglecting the formation of substrate-enzyme and enzyme-product complex and the subsequent dissociation of the latter).…”