A preceding study analysed how the topology of network motifs affects the overall rate of the underlying biochemical processes. Surprisingly, it was shown that topologically non-isomorphic motifs can still be isodynamic in the sense that they exhibit the exact same performance rate. Because of the high prevalence of feed-forward functional modules in biological networks, one may hypothesize that evolution tends to favour motifs with faster dynamics. As a step towards ranking the efficiency of feed-forward network motifs, we use a linear flow model to prove theorems establishing that certain classes of motifs are isodynamic. In partitioning the class of all motifs on n nodes into equivalence classes based upon their dynamics, we establish a basis for comparing the efficiency/performance rates of different motifs. The potential biological importance of the theorems is briefly discussed and is the subject of an ongoing large-scale project.
Copyright © 2010 Taylor & Francis. This article first appeared in Journal of Biological Dynamics 4:2 (2010), 196-211.
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Taylor, Dewey T., John W. Cain, Danail G. Bonchev, Stephen S. Fong, Advait A. Apte, and Lauren E. Pace. "Toward a Classification of Isodynamic Feed-forward Motifs." Journal of Biological Dynamics 4, no. 2 (2010): 196-211. doi:10.1080/17513750903144461.