Topological and statistical analyses of gene regulatory networks reveal unifying yet quantitatively different emergent properties

<div><p>Understanding complexity in physical, biological, social and information systems is predicated on describing interactions amongst different components. Advances in genomics are facilitating the high-throughput identification of molecular interactions, and graphs are emerging as indispensable tools in explaining how the connections in the network drive organismal phenotypic plasticity. Here, we describe the architectural organization and associated emergent topological properties of gene regulatory networks (GRNs) that describe protein-DNA interactions (PDIs) in several model eukaryotes. By analyzing GRN connectivity, our results show that the anticipated scale-free network architectures are characterized by organism-specific power law scaling exponents. These exponents are independent of the fraction of the GRN experimentally sampled, enabling prediction of properties of the complete GRN for an organism. We further demonstrate that the exponents describe inequalities in transcription factor (TF)-target gene recognition across GRNs. These observations have the important biological implication that they predict the existence of an intrinsic organism-specific <i>trans</i> and/or <i>cis</i> regulatory landscape that constrains GRN topologies. Consequently, architectural GRN organization drives not only phenotypic plasticity within a species, but is also likely implicated in species-specific phenotype.</p></div

Framework for sampling and predicting properties of complete GRNs.

<p>The subnetwork on the left depicts a reduced GRN sampled from the observed GRN (center) whose properties can be used to infer the properties of complete GRN depicted on the right. Black and grey nodes denote TFs and non-TF-coding genes, respectively. Dashed lines represent possible PDIs in complete GRNs that are yet to be identified, but are predicted based on the scale-free property of observed GRNs.</p

<i>In silico</i> GRNs.

<p>(a) Histogram of the out degree distribution of an <i>in silico</i> GRN and of an observed GRN corresponding to <i>S</i>. <i>cerevisiae</i>. (b) Distribution of the exponents for each of 1000 <i>in silico</i> GRNs. (c) Distributions of KS <i>P-</i>values of sub-networks sampled from an <i>in silico</i> GRN. (d) Distribution of exponents of sub-networks sampled from <i>in silico</i> GRN.</p

Sampling subnetworks.

<p>Distribution of exponents of subnetworks sampled from observed GRNs.</p

GRNs are scale-free.

<p>GRNs are scale-free.</p

Lorenz curves.

<p>Simulated Lorenz curves for exponents ranging from 2 to 4.5 (a). Lorenz curves for out-degrees of observed GRNs (b). TGs: target genes.</p