Autoregulation of pre-mRNA processing for buffering noisy gene expression

Stochastic variation in the level of a protein among cells of the same population is ubiquitous across cell types and organisms. These random variations are a consequence of low-copy numbers, amplified by the characteristically probabilistic nature of biochemical reactions associated with gene-expression. We systematically compare and contrast negative feedback architectures in their ability to regulate random fluctuations in protein levels. Our stochastic model consists of gene synthesizing pre-mRNAs in transcriptional bursts. Each pre-mRNA transcript is exported to the cytoplasm and is subsequently translated into protein molecules. In this setup, three feedbacks architectures are implemented: protein inhibiting transcription of its own gene (I), protein enhancing the nuclear pre-mRNA decay rate (II), and protein inhibiting the export of pre-mRNAs (III). Explicit analytic expressions are developed to quantify the protein noise levels for each feedback strategy. Mathematically controlled comparisons provide insights into the noise-suppression properties of these feedbacks. For example, when the protein half-life is long, or the pre-mRNA decay is fast, then feedback architecture I provides the best noise attenuation. In contrast, when the timescales of export, mRNA, and protein turnover are similar, then III is superior to both II and I. We finally discuss biological relevance of these findings in context of noise suppression in an HIV cell-fate decision circuit.