Comparison of feedback strategies for noise suppression in protein level

Stochastic variation in the level of 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. Recent studies have revealed the role of unspliced, precursor mRNA versus stable, cytoplasmic mRNA in gene-expression regulation and noise. Our work takes advantage of this distinction and creates a model describing mRNA as two separate species: pre-mRNA inside the nucleus and cytoplasmic mRNA outside the nucleus. Each gene synthesizes pre-mRNAs in transcriptional bursts. Then, each pre-mRNA transcript is exported to the cytoplasm and is subsequently translated into protein molecules. In this setup, three feedback architectures are implemented: protein inhibiting transcription of its own gene (I), protein enhancing the nuclear pre-mRNA degradation 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 feedback architectures. For example, when the pre-mRNA export rate is greater than its degradation rate, then feedback architecture I provides the best noise attenuation. In contrast, when mRNA is highly unstable, feedback architecture III is superior to both II and I. We finally discuss biological relevance of these findings in context of precursor mRNA and noise suppression in HIV.