Universal Protein Fluctuations in Populations of Microorganisms

Abstract

The copy number of any protein fluctuates among cells in a population; characterizing and understanding these fluctuations is a fundamental problem in biophysics. We show here that protein distributions measured under a broad range of biological realizations collapse to a single non-Gaussian curve under scaling by the first two moments. Moreover in all experiments the variance is found to depend quadratically on the mean, showing that a single degree of freedom determines the entire distribution. Our results imply that protein fluctuations do not reflect any specific molecular or cellular mechanism, and suggest that some buffering process masks these details and induces universality.The protein content of a cell is a primary determinant of its phenotype. However, protein copy number is subject to large cell-to-cell variation even among genetically identical cells grown under uniform conditions ([1-3] and references therein). This variation has been the subject of intensive research in recent years ([4-7] and references therein). Much of this previous work was devoted to characterizing the stochastic properties of various processes underlying gene expression, such as transcription and translation [8], or different stages of the cell cycle [9], and understanding their effect on protein variation. However, gene expression is generally coupled to all aspects of cell physiology, such as growth [10], metabolism [11], aging [12], division [13,14] and epigenetic processes [15,16], as well as gene location and function [17], all of which were shown to affect protein variation. The emerging picture is of a plethora of correlated mechanisms at different levels of organization; how they integrate to shape the total protein variation in a dividing population remains an open question [11,14].In this work we addressed this question by a phenomenological approach. We measured distributions of highly expressed proteins in proliferating clonal populations of bacteria and yeast under natural conditions, where gene expression is coupled to other cellular processes. By designing an array of different metabolic and regulatory conditions as well as growth environments, we collected a compendium of measurements which systematically covers the major processes of gene expression and 2 cell division, and compared the measured distributions in a wide range of biological realizations. More specifically, our comparisons included: (a) Two archetypical microorganisms, bacteria and yeast, with two well-studied regulatory systems of essential metabolic pathways: the LAC operon in E. coli [18] and the GAL system in S. cerevisiae [19]. Both systems were studied under environmental conditions in which expression is strongly coupled to metabolism, namely they control the utilization of an essential sugar (lactose and galactose, respectively) as the sole carbon The spectrum of our experiments spans an array of "control parameters" p which covers many of the essential processes affecting protein content in cells. The two organisms used, E. coli an...

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“…The magnitude of these fluctuations is expected to increase not linearly but as the square root of the mean number of molecules. A linear scaling similar to ours has been reported for proteins produced in high copy numbers (31,32), however, and has been attributed to sources of extrinsic noise. In the Pvd system, this high level of noise may be due to fluctuations in the number of efflux pumps and transporters.…”

Mechanical bounds to transcriptional noise

“…Although the resulting universal curve is not identical to the one found in ref. 9, there is strong agreement with only moderate deviation at large expression levels. Additional effects such as more complex translational mechanisms, copy number variation, and variable decay likely contribute to the observed disagreement.…”

“…2 illustrate the collapse where the mean and SD are a function of the parameters whereas the rescaled and shifted form of the PDFs is universal. This form of universal collapse is noteworthy as its occurrence was first observed for protein expression levels (9). Such a collapse is not a generic property of PDFs derived from simple single-or two-state (10) models of gene expression.…”

Universal protein distributions in a model of cell growth and division

“…Given that the universal statistical properties described above were found for a range of experimental conditions for various proteins in bacteria [4], such a model should rely only on general coarse-grained processes. We therefore start by assuming as little as possible given the experimental data:…”

“…Protein content depends on a complex interplay of genetic, epigenetic and metabolic processes, with numerous cell-specific regulatory mechanisms and feedback loops. However, recent experiments [4] have demonstrated that for two different types of microorganism (yeast and bacteria), each under a broad range of conditions, the distribution of highly expressed protein copy number appears universal : under rescaling by mean and standard deviation, all such distributions collapse onto a single skewed curve [5]. In the same experiments variances were found to depend quadratically on their means, a trend displayed also by all highly expressed proteins in E. coli in a genome-wide study [6] (see also [7]).…”