Computational Intractability Law Molds the Topology of Biological Networks

Abstract

Virtually all molecular interaction networks (MINs), irrespective of organism or physiological context, have a majority of loosely-connected 'leaf' genes interacting with at most 1-3 genes, and a minority of highly-connected 'hub' genes interacting with at least 10 or more other genes. Previous reports proposed adaptive and non-adaptive hypotheses describing sufficient but not necessary conditions for the origin of this majority-leaves minority-hubs (mLmH) topology. We modeled the evolution of MINs as a computational optimization problem which describes the cost of conserving, deleting or mutating existing genes so as to maximize (minimize) the overall number of beneficial (damaging) interactions network-wide. The model 1) provides sufficient and, assuming P = N P, necessary conditions for the emergence of mLmH as an adaptation to circumvent computational intractability, 2) predicts the percentage number of genes having d interacting partners, and 3) when employed as a fitness function in an evolutionary algorithm, produces mLmH-possessing synthetic networks whose degree distributions match those of equal-size MINs.Author Summary: Our results indicate that the topology of molecular interaction networks is a selected-for adaptation that minimizes the evolutionary cost of re-wiring the network in response to an evolutionary pressure to conserve, delete or mutate existing genes and interactions.

KISL: knowledge-injected semi-supervised learning for biological co-expression network modules

“…It is important in SFT networks to identify the dominant hub nodes because they usually have significant influence on the network. In the case of biological networks it may mean that the genes, proteins or metabolites represented by these nodes are biologically important (Albert, 2005;Andrecut et al, 2008;Nafis et al, 2015;Atiia et al, 2020). Therefore, we investigate the SFT of the two correlation coefficients for the eight datasets.…”