Gene Duplication Models and Reconstruction of Gene Regulatory Network Evolution from Network Structure

Abstract

In this paper we study evolution of gene regulatory networks from the graph-theoretic perspective. We consider two gene duplication models that are based on those studied before, but are more general and/or mathematically more precise than previously published schemes. Our aims are to assess the biological appropriateness of the proposed models and to study the possibilities of reconstruction of the evolution history of networks solely on the basis of network topology. For one of the proposed models, which is fully deterministic, we provide an exact algorithm for reconstruction of evolutionary history of the network. The algorithm is applicable in real time to networks with up to 200 genes, which is comparable to sizes of real biological networks. The other proposed model involves random deletions of gene interactions. In this case a heuristic modification of the algorithm can be used to identify a large subset of genes that have been duplicated during the last duplication event. The methods have been tested for analysis of yeast gene regulatory network and have been able to identify several biologically confirmed pairs of duplicated genes. Similarity between inferred pairs of gene duplicates is shown to be above average, thus indicating that traces from gene duplications, which have occurred long time ago, can still be detected from the network topology alone.