Optimal control of gene expression for fast proteome adaptation to environmental change

Abstract

Bacterial populations growing in a changing world must adjust their proteome composition in response to alterations in the environment. Rapid proteome responses to growth medium changes are expected to increase the average growth rate and fitness value of these populations. Little is known about the dynamics of proteome change, e.g., whether bacteria use optimal strategies of gene expression for rapid proteome adjustments and if there are lower bounds to the time of proteome adaptation in response to growth medium changes. To begin answering these types of questions, we modeled growing bacteria as stoichiometrically coupled networks of metabolic pathways. These are balanced during steady-state growth in a constant environment but are initially unbalanced after rapid medium shifts due to a shortage of enzymes required at higher concentrations in the new environment. We identified an optimal strategy for rapid proteome adjustment in the absence of protein degradation and found a lower bound to the time of proteome adaptation after medium shifts. This minimal time is determined by the ratio between the Kullback-Leibler distance from the pre-to the postshift proteome and the postshift steady-state growth rate. The dynamics of optimally controlled proteome adaptation has a simple analytical solution. We used detailed numerical modeling to demonstrate that realistic bacterial control systems can emulate this optimal strategy for rapid proteome adaptation. Our results may provide a conceptual link between the physiology and population genetics of growing bacteria.bacterial adaptation | protein synthesis | control theory | on-off control A challenging problem in bacterial physiology is to understand how bacteria adapt to changes in nutritional supply to grow rapidly in different environments (1). More than 50 y ago, the remarkable observation was made that the cell mass and intracellular composition of protein, RNA, and DNA appeared to be determined by the steady-state growth rate of bacterial population rather than by the nutritional composition of the growth medium (2). The work of Schaechter et al. (2) and subsequent seminal works on DNA replication (e.g., ref.3) led to the concept of growth rate-dependent control of physiological parameters (4), later shown to be an approximation (1, 5). These early observations along with later determinations of the varying components of bacterial cells growing in changing environments (e.g., ref. The linear relation between growth rate and RNA content found by Schaechter et al. (2) implies that the growth rate is a linear function of the ribosome content of growing bacteria (4, 5). To this first "growth law" have recently been added complementary growth laws (6), suggesting partitioning of the bacterial proteome in three functionally distinct sectors: (i) ribosomal proteins and auxiliary translation factors, (ii) enzymes for nutrient uptake and metabolism, and (iii) a fixed fraction independent of growth condition (6).Bacterial cells continually import nutrients from the environm...

Escherichia coli translation strategies differ across carbon, nitrogen and phosphorus limitation conditions

“…4a, Supplementary Fig. 9 and details in the Supplementary Information) 4,35 . We experimentally tested this prediction by measuring the growth rates of slow-growing (0.1 h −1 ) E. coli immediately after being shifted to rich media (Luria-Bertani media (LB) + 0.4% glucose) 36 .…”

Determinants of the Rate of mRNA Translocation in Bacterial Protein Synthesis

“…Regarding systems biology modeling of growing bacteria with implications for optimal physiology of growth [46,47], growth inhibition by antibiotics [48], fitness loss by drug resistance mutations and improved fitness by compensatory mutations [49], quantitative assessment of the kinetic properties of the protein synthesis machinery is essential. One reason is that ribosomes and their factor proteins occupy a significant fraction of the bacterial proteome [46,47], making cell growth and fitness hypersensitive to ribosome performance so that calibration of the biochemistry of protein synthesis to ribosome performance in vivo is a prerequisite for realistic systems biology modeling of bacterial cell growth.…”

“…One reason is that ribosomes and their factor proteins occupy a significant fraction of the bacterial proteome [46,47], making cell growth and fitness hypersensitive to ribosome performance so that calibration of the biochemistry of protein synthesis to ribosome performance in vivo is a prerequisite for realistic systems biology modeling of bacterial cell growth. Such a calibration is a multiple parameter problem, but the present and earlier [18,29,50] work suggest that the concentration of free Mg 2+ ions plays such an important role that adjustment of this parameter is the natural starting point for such a calibration.…”

Mechanistic links between cellular trade-offs, gene expression, and growth

“…A whole-cell model has been proposed as one way to make such predictions (11), but its level of detail may sometimes obscure the core biochemistry that underlies the observed phenotypes and potentially complicates further analyses. We instead adopt a complementary coarse-grained approach (12)(13)(14) and try to find minimal descriptions that highlight the mechanisms generating the in silico phenotypes we observe. In contrast to other approaches (13,14), we emphasize that we do not optimize either growth rate or any other physiological variable.…”

“…We instead adopt a complementary coarse-grained approach (12)(13)(14) and try to find minimal descriptions that highlight the mechanisms generating the in silico phenotypes we observe. In contrast to other approaches (13,14), we emphasize that we do not optimize either growth rate or any other physiological variable.…”