Algebraic connectivity may explain the evolution of gene regulatory networks

Gene expression is a result of the interplay between the structure, type, kinetics, and specificity of gene regulatory interactions, whose diversity gives rise to the variety of life forms. As the dynamic behavior of gene regulatory networks depends on their structure, here we attempt to determine structural reasons which, despite the similarities in global network properties, may explain the large differences in organismal complexity. We demonstrate that the algebraic connectivity, the smallest non-trivial eigenvalue of the Laplacian, of the directed gene regulatory networks decreases with the increase of organismal complexity, and may therefore explain the difference between the variety of analyzed regulatory networks. In addition, our results point out that, for the species considered in this study, evolution favours decreasing concentration of strategically positioned feed forward loops, so that the network as a whole can increase the specificity towards changing environments. Moreover, contrary to the existing results, we show that the average degree, the length of the longest cascade, and the average cascade length of gene regulatory networks cannot recover the evolutionary relationships between organisms. Whereas the dynamical properties of special subnetworks are relatively well understood, there is still limited knowledge about the evolutionary reasons for the already identified design principles pertaining to these special subnetworks, underlying the global quantitative features of gene regulatory networks of different organisms. The behavior of the algebraic connectivity, which we show valid on gene regulatory networks extracted from curated databases, can serve as an additional evolutionary principle of organism-specific regulatory networks.