Modulation of noisy gene expression by general sequestration mechanisms

Sequestration of gene products through diverse mechanisms forms a fundamental layer of regulation in intracellular biochemical processes, including post-translational modification, promiscuous binding to genomic decoy sites, and partitioning into membraneless compartments formed through phase separation. Here, we develop a unified stochastic framework to quantify how such sequestration-type processes, when coupled to noisy gene expression, modulate cell-to-cell variation in protein levels. In this model, protein molecules reversibly switch between active (free) and inactive (sequestered) states, whose switching rates are arbitrary functions of the molecular counts. Using exact analytical calculations and the linear noise approximation, we derive expressions for the Fano factor of the active-protein level and identify fluctuation attenuation regimes in terms of the logarithmic sensitivities of the switching rates to protein abundances. We show that inactive-protein-dependent switching, of which genomic decoy binding is a natural example, can preserve Poisson-level fluctuations in the active-protein level under appropriate conditions. Enzymatic inactivation, a type of post-translational modification, emerges as a special case of active-protein-dependent sequestration, where greater responsiveness of the inactivation propensity attenuates active-protein fluctuations. In both decoy binding and enzymatic inactivation, protecting the inactive protein from decay lowers active-protein fluctuations. Finally, a noise-buffering regime associated with intracellular phase separation is recovered when the inactive-to-active switching rate depends inversely on the inactive-protein level. Together, the examples of genomic decoy binding, enzymatic inactivation, and intracellular phase separation suggest that noise buffering observed across diverse intracellular processes is rooted in a broader class of reversible sequestration mechanisms that attenuate protein-level fluctuations.