Stochastic analysis of feedback control by molecular sequestration

Sequestration of a protein by another decoy molecule, such that the protein is no longer available to perform its biological function, forms a fundamental layer of regulation in biomolecular systems. To quantify how fluctuations in protein level is controlled by decoys, we formulate a model where both proteins and decoys are stochastically expressed, with fast binding/unbinding of the protein to the decoy. Our analysis reveals that when the noise in the decoy copy number is small, the noise in the free protein numbers (as quantified by the Fano factor) monotonically decreases to the Poisson limit with the increasing average number of decoys. In contrast, for a high noise in decoys production, the response becomes nonmonotonic - the noise level in protein counts is amplified at first with the increasing decoy numbers, before attenuating back to the Poisson limit. Motivated by recent biological examples, we next implement feedback control in the sequestration process by having the free proteins upregulate the decoy synthesis. Thus any random increase in the abundance of free proteins also results in higher decoy numbers, and hence more sequestered proteins. Intriguingly, our results show that as before, noise in free protein levels can get amplified with increasing decoys, albeit with a lesser magnitude as compared to the no feedback case. In summary, molecular decoys can play a key role in either amplifying or dampening the stochastic fluctuation of protein levels, and this study systematically quantifies this behavior across parameter regimes.