Bow-tie architecture of gene regulatory networks in species of varying complexity

The gene regulatory network (GRN) architecture plays a key role in explaining the biological differences between species. We aim to understand species differences in terms of some universally present dynamical properties of their gene regulatory systems. A network architectural feature associated with controlling system-level dynamical properties is the bow-tie, identified by a strongly connected subnetwork, the core layer, between two sets of nodes, the in and the out layers. Though a bow-tie architecture has been observed in many networks, its existence has not been extensively investigated in GRNs of species of widely varying biological complexity. We analyse publicly available GRNs of several well-studied species from prokaryotes to unicellular eukaryotes to multicellular organisms. In their GRNs, we find the existence of a bow-tie architecture with a distinct largest strongly connected core layer. We show that the bow-tie architecture is a characteristic feature of GRNs. We observe an increasing trend in the relative core size with species complexity. Using studied relationships of the core size with dynamical properties like robustness and fragility, flexibility, criticality, controllability and evolvability, we hypothesize how these regulatory system properties have emerged differently with biological complexity, based on the observed differences of the GRN bow-tie architectures.