Tunability enhancement of gene regulatory motifs through competition for regulatory protein resources

Gene regulatory networks (GRNs) orchestrate the spatiotemporal levels of gene expression, thereby regulating various cellular functions ranging from embryonic development to tissue homeostasis. Some patterns called "motifs" recurrently appear in the GRNs. Owing to the prevalence of these motifs they have been subjected to much investigation, both in the context of understanding cellular decision making and engineering synthetic circuits. Mounting experimental evidence suggests that (1) the copy number of genes associated with these motifs varies, and (2) proteins produced from these genes bind to decoy binding sites on the genome as well as promoters driving the expression of other genes. Together, these two processes engender competition for protein resources within a cell. To unravel how competition for protein resources affects the dynamical properties of regulatory motifs, we propose a simple kinetic model that explicitly incorporates copy number variation (CNV) of genes and decoy binding of proteins. Using quasi-steady-state approximations, we theoretically investigate the transient and steady-state properties of three of the commonly found motifs: Autoregulation, toggle switch, and repressilator. While protein resource competition alters the timescales to reach the steady state for all these motifs, the dynamical properties of the toggle switch and repressilator are affected in multiple ways. For toggle switch, the basins of attraction of the known attractors are dramatically altered if one set of proteins binds to decoys more frequently than the other, an effect which gets suppressed as the copy number of the toggle switch is enhanced. For repressilators, protein sharing leads to an emergence of oscillation in regions of parameter space that were previously nonoscillatory. Intriguingly, both the amplitude and frequency of oscillation are altered in a nonlinear manner through the interplay of CNV and decoy binding. Overall, competition for protein resources within a cell provides an additional layer of regulation of gene regulatory motifs.