Synchrony patterns in gene regulatory networks

Motivated by studying synchronization mechanisms in gene regulatory networks (GRNs) and their relation to evolutionary events such as genetic duplication redundancy, we consider two types of mathematical dynamical models GRNs that depict general additive (SUM model) or multiplicative (MULT regulations. By a synchrony pattern mean clusters synchronized genes whose states coincide for all time. The identification the each cluster network results into (smaller) quotient equations representing evolution original GRN restricted pattern. From perspective dynamics GRN, case functions core underlying example, if is globally attracting, could represent structural motif performs biological function, also known functional motif. Gene GNRs has its analog lifting process theory coupled cell networks, which reverse quotient: unfolding network, where those unfolded more genes, leads (bigger) lift network. In general, there are many lifts associated with fixed this paper, obtain on robust patterns SUM MULT inspired existing theoretical formalisms. Moreover, explore concepts context related phenomenon subfunctionalization an outcome divergence.