Abstract
Experiments with cells reveal the existence of a lower bound for protein noise, the noise floor, in highly expressed genes. Its origins are still debated. We propose a minimal model of gene expression in a proliferating bacterial cell population. The model predicts the existence of a noise floor and it semi-quantitatively reproduces the curved shape of the experimental noise vs. mean protein concentration plots. When the cell volume increases in a different manner than does the mean protein copy number, the noise floor level is determined by the cell population’s age structure and by the dependence of the mean protein concentration on cell age. Additionally, the noise floor level may depend on a biological limit for the mean number of bursts in the cell cycle. In that case, the noise floor level depends on the burst size distribution width but it is insensitive to the mean burst size. Our model quantifies the contributions of each of these mechanisms to gene expression noise.
Highlights
Experimental data for b acteria[1,2,3] and yeast[4,5,6,7] show that, for proteins of low abundance, the coefficient of variation of protein molecule copy number or concentration is a decreasing function of average protein copy number or concentration
In a proliferating cell population, the noise floor is always present if the mean protein concentration in cells depends on their cell cycle age τ, i.e., if the mean protein copy number increases in a different manner than the cell volume
We have proposed a model of gene expression in a population of dividing cells which reproduces in a semiquantitative manner the experimental data of Ref.[1]
Summary
Experimental data for b acteria[1,2,3] and yeast[4,5,6,7] show that, for proteins of low abundance, the coefficient of variation (variance divided by mean squared) of protein molecule copy number or concentration is a decreasing function of average protein copy number or concentration. We show that the increase in the r-th cumulant κr(τ ) of the protein copy number probability density function p(x|τ )during the cell cycle depends solely on the time evolution of the r-th moment mr(τ ) of the burst size probability density function ν(u|τ ) .
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