Noise propagation in an integrated model of bacterial gene expression and growth

Abstract

In bacterial cells, gene expression, metabolism, and growth are highly interdependent and tightly coordinated. As a result, stochastic fluctuations in expression levels and instantaneous growth rate show intricate cross-correlations. These correlations are shaped by feedback loops, trade-offs and constraints acting at the cellular level; therefore a quantitative understanding requires an integrated approach. To that end, we here present a mathematical model describing a cell that contains multiple enzymes that are each expressed stochastically and jointly limit the growth rate. Conversely, metabolism and growth affect protein synthesis and dilution. Thus, expression noise originating in one gene propagates to metabolism, growth, and the expression of all other genes. Nevertheless, under a small-noise approximation many statistical quantities can be calculated analytically. We identify several routes of noise propagation, illustrate their origins and scaling, and establish important connections with metabolic control analysis. We then present a many-protein model parameterized by previously measured protein abundance data and demonstrate that the predicted cross-correlations between gene expression and growth rate are in broad agreement with published measurements.

Abundant proteins contribute strongly to noise in the growth rate of optimally growing bacteria

“…To quantify how fluctuations in a the expression of protein affect growth rate , we use Growth Control Coefficients (20):…”

“…In earlier work, our group proposed a mathematical framework to describe these experimental results. In it, noise in the expression of all proteins in the cell together caused cellular fluxes to fluctuate and, therewith, also propagated to the growth rate (20). We introduced so-called Growth Control Coefficients (GCCs) that quantify, to first order, the sensitivity of the cellular growth rate to changes in the expression of a particular protein species -how much "control" this protein species exerts over the growth rate.…”

“…We introduced so-called Growth Control Coefficients (GCCs) that quantify, to first order, the sensitivity of the cellular growth rate to changes in the expression of a particular protein species -how much "control" this protein species exerts over the growth rate. Using this theory and the underlying GCCs, we were able to reproduce the characteristics of the observed noise propagation (20).…”

Segregostat: a novel concept to control phenotypic diversification dynamics on the example of Gram‐negative bacteria

“…These mechanisms have been the focus of intensive researches during the last decade and have led to a coherent mathematical and experimental framework of molecular stochasticity in prokaryotic and eukaryotic systems (Kaern et al ., ; Eldar and Elowitz, ). This framework has been notably used in order to decipher the impact of regulatory network structure on the propagation (Blake et al ., ; Kleijn et al ., ) and control of phenotypic diversification (Milias‐Argeitis et al ., ; Briat and Khammash, ; Briat et al ., ), as well as on the possible functionality of such diversification (Eldar and Elowitz, ; Levine et al ., ; Ackermann, ). However, most of these researches have been conducted at low spatio‐temporal resolution, i.e.…”

“…Nutrient stress is a strong trigger of phenotypic diversification that can be eventually used for controlling the degree of diversification of a bacterial population. Previous studies have shown that such phenotypic diversification mechanisms are governed by a complex set of physiological mechanisms involving noise in gene expression, metabolism and growth (Kiviet et al ., ; Kleijn et al ., ; Patange et al ., ), these three mechanisms being highly cross‐correlated and being controlled through mutual feedback loops. Ultimately, the superimposition of these three mechanisms leads to population phenotypic heterogeneity that can in turn confer interesting functionalities to the whole population (e.g.…”