On attracting sets in artificial networks: cross activation

Mathematical models of artificial networks can be formulated in terms of dynamical systems describing the behaviour of a network over time. The interrelation between nodes (elements) of a network is encoded in the regulatory matrix. We consider a system of ordinary differential equations that describes in particular also genomic regulatory networks (GRN) and contains a sigmoidal function. The results are presented on attractors of such systems for a particular case of cross activation. The regulatory matrix is then of particular form consisting of unit entries everywhere except the main diagonal. We show that such a system can have not more than three critical points. At least n–1 eigenvalues corresponding to any of the critical points are negative. An example for a particular choice of sigmoidal function is considered.

Conservation patterns’ analysis of 18,364 candidate human-specific regulatory sequences revealed two distinct pathways of the human regulatory DNA divergence

Thousands of candidate human-specific regulatory sequences (HSRS) have been identified, supporting the idea that unique to human phenotypes result from human-specific alterations of genomic regulatory networks. Here, conservation patterns analysis of 18,364 regulatory DNA segments comprising candidate HSRS was carried out using the most recent releases of the reference genomes’ databases of humans and nonhuman primates (NHP) and defining the sequence conservation threshold as the minimum ratio of bases that must remap of 1.00. Present analyses identified 5,535 candidate HSRS defined by either the acceleration of mutation rates on the human lineage or the functional divergence from chimpanzee that are highly conserved in NHP and appear to evolve by the exaptation of ancestral DNA pathway. This pathway seems mechanistically distinct from the evolution of regulatory DNA driven by the species-specific expansion of transposable elements. It is proposed that phenotypic divergence of Homo sapiens is driven by the evolution of human-specific genomic regulatory networks via at least two mechanistically distinct pathways of creation of divergent sequences of regulatory DNA: i) exaptation of the highly conserved ancestral regulatory DNA segments; ii) human-specific insertions of transposable elements.