Abstract
Although noisy gene expression is widely accepted, its mechanisms are subjects of debate, stimulated largely by single-molecule experiments. This work is concerned with one such study, in which Choi et al., 2008, obtained real-time data and distributions of Lac permease in E. coli. They observed small and large protein bursts in strains with and without auxiliary operators. They also estimated the size and frequency of these bursts, but these were based on a stochastic model of a constitutive promoter. Here, we formulate and solve a stochastic model accounting for the existence of auxiliary operators and DNA loops. We find that DNA loop formation is so fast that small bursts are averaged out, making it impossible to extract their size and frequency from the data. In contrast, we can extract not only the size and frequency of the large bursts, but also the fraction of proteins derived from them. Finally, the proteins follow not the negative binomial distribution, but a mixture of two distributions, which reflect the existence of proteins derived from small and large bursts.
Highlights
Data from many independent experiments show that the abundance of any given protein varies among individual cells of isogenic populations growing under identical conditions [1,2,3]
Even though l%1 (Table 2), we cannot neglect the transcription from the bound state, since it captures the effect of the small transcriptional bursts, which can account, as we show later, for almost 80% of the mRNAs synthesized per cell cycle
Based on a comparison of our expressions for the Fano factor, noise, and protein distribution of strains SX701 and SX703 with those proposed by Choi et al, we arrive at the following conclusions: 1. The physical interpretations of the Fano factor F and reciprocal noise g{2 for strain SX703 are identical to those proposed by Choi et al, namely F and g{2 represent the size and frequency of transcriptional bursts
Summary
Data from many independent experiments show that the abundance of any given protein varies among individual cells of isogenic populations growing under identical conditions [1,2,3]. Cai et al [9] and Yu et al [10] developed two different methods for measuring the number of proteins in single cells. The real-time data of both studies showed that protein synthesis was bursty, and the burst size was exponentially distributed. Under this condition, the steady state protein distribution follows the Gamma distribution, pn~na{1e{n=b=baC(a), where a and b denote the mean burst frequency and burst size [11]. Cai et al and Yu et al showed that the Gamma distribution could fit their steady state data, and the values of the mean burst frequency and size derived from the steady state data agreed well with those obtained from real-time measurements
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