Emergent correlations in gene expression dynamics as footprints of resource competition

Genetic circuits need a cellular environment to operate in, which naturally couples the circuit function with the overall functionality of gene regulatory network. To execute their functions, all gene circuits draw resources in the form of RNA polymerases, ribosomes, and tRNAs. Recent experiments pointed out that the role of resource competition on synthetic circuit outputs could be immense. However, the effect of complexity of the circuit architecture on resource sharing dynamics is yet unexplored. In this paper, we employ mathematical modelling and in-silico experiments to identify the sources of resource trade-off and to quantify its impact on the function of a genetic circuit, keeping our focus on regulation of immediate downstream proteins, which are often used as protein read-outs. We show that estimating gene expression dynamics from readings of downstream protein data might be unreliable when the resource is limited and ribosome affinities are asymmetric. We focus on the impact of mRNA copy number and ribosome binding site (RBS) strength on the nonlinear isocline that emerges with two regimes, prominently separated by a tipping point, and study how correlation and competition dominate each other depending on various circuit parameters. Focusing further on genetic toggle circuit, we have identified major effects of resource competition in this model motif and quantified the observations. The observations are testable in wet-lab experiments, as all the parameters chosen are experimentally relevant