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Recent analysis demonstrates that the HIV-1 Long Terminal Repeat (HIV LTR) promoter exhibits a range of possible transcriptional burst sizes and frequencies for any mean-expression level. However, these results have also been interpreted as demonstrating that cell-to-cell expression variability (noise) and mean are uncorrelated, a significant deviation from previous results. Here, we re-examine the available mRNA and protein abundance data for the HIV LTR and find that noise in mRNA and protein expression scales inversely with the mean along analytically predicted transcriptional burst-size manifolds. We then experimentally perturb transcriptional activity to test a prediction of the multiple burst-size model: that increasing burst frequency will cause mRNA noise to decrease along given burst-size lines as mRNA levels increase. The data show that mRNA and protein noise decrease as mean expression increases, supporting the canonical inverse correlation between noise and mean.

Protein noise measurements are increasingly used to elucidate biophysical parameters. Unfortunately noise analyses are often at odds with directly measured parameters. Here we show that these inconsistencies arise from two problematic analytical choices: (i) the assumption that protein translation rate is invariant for different proteins of different abundances, which has inadvertently led to (ii) the assumption that a large constitutive extrinsic noise sets the low noise limit in gene expression. While growing evidence suggests that transcriptional bursting may set the low noise limit, variability in translational bursting has been largely ignored. We show that genome-wide systematic variation in translational efficiency can-and in the case of E. coli does-control the low noise limit in gene expression. Therefore constitutive extrinsic noise is small and only plays a role in the absence of a systematic variation in translational efficiency. These results show the existence of two distinct expression noise patterns: (1) a global noise floor uniformly imposed on all genes by expression bursting; and (2) high noise distributed to only a select group of genes.

Gene expression occurs either as an episodic process, characterized by pulsatile bursts, or as a constitutive process, characterized by a Poisson-like accumulation of gene products. It is not clear which mode of gene expression (constitutive versus bursty) predominates across a genome or how transcriptional dynamics are influenced by genomic position and promoter sequence. Here, we use time-lapse fluorescence microscopy to analyze 8,000 individual human genomic loci and find that at virtually all loci, episodic bursting--as opposed to constitutive expression--is the predominant mode of expression. Quantitative analysis of the expression dynamics at these 8,000 loci indicates that both the frequency and size of the transcriptional bursts varies equally across the human genome, independent of promoter sequence. Strikingly, weaker expression loci modulate burst frequency to increase activity, whereas stronger expression loci modulate burst size to increase activity. Transcriptional activators such as trichostatin A (TSA) and tumor necrosis factor α (TNF) only modulate burst size and frequency along a constrained trend line governed by the promoter. In summary, transcriptional bursting dominates across the human genome, both burst frequency and burst size vary by chromosomal location, and transcriptional activators alter burst frequency and burst size, depending on the expression level of the locus.

Steady-state behavior and bistability have been proposed as mechanisms for decision making in gene circuits. However, transient gene expression has also been proposed to control cell fate, with the decision arbitrated by the duration of a transient gene expression pulse. Here, using an HIV-1 model system, we directly quantify transcriptional feedback strength and its effects on both the duration of HIV-1 Tat transcriptional pulses and the fate of HIV-infected cells. By measuring shifts in the autocorrelation of noise inherent to gene expression, we found that transcriptional positive feedback extends the single-cell Tat expression lifetime two- to sixfold for both minimal Tat circuits and full length, actively replicating HIV-1. Notably, artificial weakening of Tat positive feedback shortened the duration of Tat expression transients and biased the probability in favor of latency. Thus, transcriptional positive feedback can modulate transient expression lifetime to a greater extent than protein half-life modulation, and it has a critical role in the cell-fate decision in HIV.

Recent advances in single cell methods have spurred progress in quantifying and analyzing stochastic fluctuations, or noise, in genetic networks. Many of these studies have focused on identifying the sources of noise and quantifying its magnitude, and at the same time, paying less attention to the frequency content of the noise. We have developed a frequency domain approach to extract the information contained in the frequency content of the noise. In this article we review our work in this area and extend it to explicitly consider sources of extrinsic and intrinsic noise. First we review applications of the frequency domain approach to several simple circuits, including a constitutively expressed gene, a gene regulated by transitions in its operator state, and a negatively autoregulated gene. We then review our recent experimental study, in which time-lapse microscopy was used to measure noise in the expression of green fluorescent protein in individual cells. The results demonstrate how changes in rate constants within the gene circuit are reflected in the spectral content of the noise in a manner consistent with the predictions derived through frequency domain analysis. The experimental results confirm our earlier theoretical prediction that negative autoregulation not only reduces the magnitude of the noise but shifts its content out to higher frequency. Finally, we develop a frequency domain model of gene expression that explicitly accounts for extrinsic noise at the transcriptional and translational levels. We apply the model to interpret a shift in the autocorrelation function of green fluorescent protein induced by perturbations of the translational process as a shift in the frequency spectrum of extrinsic noise and a decrease in its weighting relative to intrinsic noise.

We present a frequency domain Langevin approach for stochastic analysis that remains valid for many important gene circuit elements even as molecular populations approach zero. We begin by considering the case of low-rate transcription and show that the previously reported shot noise representation is exact at all mRNA population levels for a constant transcription rate. Next, we consider transcriptional control through protein-DNA interactions at an operator site within the gene promoter region. This analysis results in expressions for the dynamics and noise behavior of this important gene sub-circuit, including the spectral density of the intrinsic operator noise and the processing of extrinsic noise by this transcriptional regulation system. This analysis shows that mRNA synthesis noise is composed of wideband shot noise and band-limited operator binding generated noise components. We find that the bandwidth of operator noise and its ultimate effect on total mRNA and protein noise is controlled by operator binding and unbinding dynamics. The most substantial impact of the operator noise is seen at transcription rates just above basal expression. This analysis captures the full behavior of this transcriptional regulation system, and points to potentially serious flaws in simplified mathematical relationships often used to model transcriptional regulation.