A critical analysis of Powell’s results on the interdivision time distribution

Quedeville, Vincent; Morchain, Jérôme; Villedieu, Philippe; Fox, Rodney O.

doi:10.1038/s41598-019-44606-4

Cited by 2 publications

(1 citation statement)

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“…( 21 ) is not the most general way to obtain the quantities referring to the whole cell population from those referring to a single cell line. A more general approach would involve other model parameters being random variables (e.g., cell volume, cell cycle length), so that the age structure or the Master equation for protein levels would be derived ’from scratch’ from the time evolution of these variables 28 – 30 .…”

Section: Modelmentioning

confidence: 99%

Contributions to the ‘noise floor’ in gene expression in a population of dividing cells

Jędrak

Ochab-Marcinek

2020

Sci Rep

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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. Experimental data for bacteria 1-3 and yeast 4-7 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. However, for highly expressed genes, the coefficient of variation tends to a constant level 1-8. This lower bound for protein noise is called noise floor. There is a debate in the literature over the origin of the noise floor 9 : It has been attributed to protein partitioning at cell division 7 or to the existence of some limits to the frequencies of transcriptional and translational bursting 10. In Ref. 1 , the noise floor was introduced by heuristic addition of extrinsic noise as an overlay to the existing model. Here, we introduce a model of gene expression combining the effects which, to date, have been studied separately: cell volume growth 11,12 , protein partitioning at cell division 12-16 , age structure of the cell population 11-13,15,16 , and dependence of protein production on cell age 17,18. These ingredients suffice to semi-quantitatively reproduce the 'boomerang' shape of the experimental plots of noise vs protein concentration. We show that, 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. This can be the case even if the transcription rate k is constant during the cell cycle: The mean protein copy number increases linearly in time but the cell volume may increase, e.g., exponentially. We also show that the dependence of k on τ can considerably increase the noise floor level. Model The model is based on a Master equation which describes the time evolution of the probability that there are x protein molecules present in a single cell at time t between cell divisions. This probability is given by the probability density function p(x, t). We assume that the protein cop...

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Section: Modelmentioning

confidence: 99%