Abstract: In cell signaling, competition between messenger RNAs (mRNAs) for shared microRNA (miRNA) regulators plays a crucial role in post-transcriptional gene regulation. This study examines mathematical models of such competition, focusing on both continuous resource sharing and pulsed interactions.

We first developed a model where two mRNAs compete for a common miRNA regulator under continuous interaction. Then, we introduced a time-sharing strategy by periodically modulating the binding constant, kon, using a square pulse to simulate pulsed interactions.

Next, we designed a simplified system consisting of a single miRNA and mRNA, where miRNA synthesis was periodically pulsed. During the miRNA synthesis phase, the mRNA interacts with the miRNA, while a competing mRNA utilizes the miRNA when synthesis is inactive. This model captures the symmetry of competition: when miRNA is being synthesized, one mRNA uses it, and when synthesis pauses, the other mRNA takes over. This approach broadens the range of experimental conditions for future studies.

The three models were compared using a metric called "fold repression," which quantifies the degree of translational inhibition exerted by miRNAs on mRNAs. Our results highlight conditions under which pulsed interactions outperform continuous competition in terms of regulatory efficiency.

These findings suggest that dynamic, pulsatile miRNA interactions can enhance regulatory outcomes compared to constant competition, providing new insights into the complex regulatory strategies at play in cellular environments.

Keywords: cell signaling, mRNA competition, microRNA, time-sharing, fold repression, dynamic modeling