ABSTRACT
We show that statistics of observed events in evolving finite biological systems cannot be formally fitted and mechanistically explained in the terms of so-called “scale-free” network approach. However, the families of skewed size-dependent probability distribution functions could be used. In particular, we demonstrate that statistics of the number of domain-to-protein links in the proteomes of 90 species representing all of three super-kingdoms of life (archea, bacteria, eukaryotes) fit well to the Markov birth-death random process models the steady-state solution of which is approached by size-dependent Generalized Pareto function. A parameterization of this model allows us to associate the complexities of prokaryotic and eukaryotic organisms with two distinct network statistics, respectively. We also discuss new applications of the size-dependent skewed probabilistic models to de-noise the large-scale experiment data and to identify the underlying probability functions of gene expression levels and of avidity of transcription binding sites in genome by available incomplete data.
