Abstract
BackgroundFeed-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.ResultsFeed-forward motif dynamics were studied using cellular automata and compared with differential equation modeling. The number of cellular automata iterations needed for a 100% conversion of a substrate into a target product was used as an inverse measure of the transformation rate. Several basic topological patterns were identified that order the specific feed-forward constructions according to the rate of dynamics they enable. At the same number of network nodes and constant other parameters, the bi-parallel and tri-parallel motifs provide higher network efficacy than single feed-forward motifs. Additionally, a topological property of isodynamicity was identified for feed-forward motifs where different network architectures resulted in the same overall rate of the target production.ConclusionIt was shown for classes of structural motifs with feed-forward architecture that network topology affects the overall rate of a process in a quantitatively predictable manner. These fundamental results can be used as a basis for simulating larger networks as combinations of smaller network modules with implications on studying synthetic gene circuits, small regulatory systems, and eventually dynamic whole-cell models.
Highlights
Feed-forward motifs are important functional modules in biological and other complex networks
There was no need to use a more sophisticated numerical method as we considered the special case in which all rate constants are equal, and the system is not stiff (the eigenvalues of the Jacobian matrices associated with these systems of Ordinary Differential Equations (ODE) are (i) all negative and (ii) are of the same order of magnitude)
The essential element in such applications is the extraction of useful topological-dynamic patterns, which identify specific effects of topological structure on the dynamics of network processes while keeping all kinetic parameters constant
Summary
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. Modeling is a means of making predictions and testing our understanding. The quantitative nature of mathematical modeling has the benefit of yielding detailed, objective descriptions and predictions of processes. An accurate mathematical model can help clarify the roles of individual components within a process and generate specific, testable hypotheses and predictions. The quantitative results of a mathematical model provide an objective basis for evaluating the accuracy of a model when compared to experimental results and can enable iterative improvement of a model [7,8]
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