Mechanical Bounds to Transcriptional Noise

Timing is essential for many cellular processes, from cellular responses to external stimuli to the cell cycle and circadian clocks. Many of these processes are based on gene expression. For example, an activated gene may be required to reach in a precise time a threshold level of expression that triggers a specific downstream process. However, gene expression is subject to stochastic fluctuations, naturally inducing an uncertainty in this threshold-crossing time with potenti...

Recently, several studies have investigated the transcription process associated to specific genetic regulatory networks. In this work, we present a stochastic approach for analyzing the dynamics and effect of negative feedback loops (FBL) on the transcriptional noise. First, our analysis allows us to identify a bimodal activity depending of the strength of self-repression coupling D. In the strong coupling region D>>1, the variance of the transcriptional noise is found to be...

Stochasticity in gene expression can give rise to fluctuations in protein levels and lead to phenotypic variation across a population of genetically identical cells. Recent experiments indicate that bursting and feedback mechanisms play important roles in controlling noise in gene expression and phenotypic variation. A quantitative understanding of the impact of these factors requires analysis of the corresponding stochastic models. However, for stochastic models of gene expr...

{\it Transcription} is the process whereby RNA molecules are polymerized by molecular machines, called RNA polymerase (RNAP), using the corresponding DNA as the template. Recent {\it in-vivo} experiments with single cells have established that transcription takes place in "bursts" or "pulses". In this letter we present a model that captures not only the mechano-chemistry of individual RNAPs and their steric interactions but also the switching of the gene between the ON and OF...

In early development, regulation of transcription results in precisely positioned and highly reproducible expression patterns that specify cellular identities. How transcription, a fundamentally noisy molecular process, is regulated to achieve reliable embryonic patterning remains unclear. In particular, it is unknown how gene-specific regulation mechanisms affect kinetic rates of transcription, and whether there are common, global features that govern these rates across a ge...

We study the response of an autoregulated gene to a range of concentrations of signal molecules. We show that transcriptional leakage and noise due to translational bursting have the opposite effects. In a positively autoregulated gene, increasing the noise converts the response from graded to binary, while increasing the leakage converts the response from binary to graded. Our findings support the hypothesis that, being a common phenomenon, leaky expression may be a relative...

The canonical model of mRNA expression is the telegraph model, describing a gene that switches on and off, subject to transcription and decay. It describes steady-state mRNA distributions that subscribe to transcription in bursts with first-order decay, referred to as super-Poissonian expression. Using a telegraph-like model, I propose an answer to the question of why gene expression is bursty in the first place, and what benefits it confers. Using analytics for the entropy p...

Due to the stochastic nature of biochemical processes, the copy number of any given type of molecule inside a living cell often exhibits large temporal fluctuations. Here, we develop analytic methods to investigate how the noise arising from a bursting input is reshaped by a transport reaction which is either linear or of the Michaelis-Menten type. A slow transport rate smoothes out fluctuations at the output end and minimizes the impact of bursting on the downstream cellular...

A stochastic model of autoregulated bursty gene expression by Kumar et al. [Phys. Rev. Lett. 113, 268105 (2014)] has been exactly solved in steady-state conditions under the implicit assumption that protein numbers are sufficiently large such that fluctuations in protein numbers due to reversible protein-promoter binding can be ignored. Here we derive an alternative model that takes into account these fluctuations and hence can be used to study low protein number effects. The...

Gene expression is inherently a noisy process which manifests as cell-to-cell variability in time evolution of proteins. Consequently, events that trigger at critical threshold levels of regulatory proteins exhibit stochasticity in their timing. An important contributor to the noise in gene expression is translation bursts which correspond to randomness in number of proteins produced in a single mRNA lifetime. Modeling timing of an event as a first-passage time (FPT) problem,...