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Bacterial populations typically exhibit exponential growth under resource-rich conditions, yet individual cells often deviate from this pattern. Recent work has shown that the elongation rates of and increase throughout the cell cycle (super-exponential growth), while displays a midcycle minimum (convex growth), and grows linearly. Here, we develop a single-cell model linking gene expression, proteome allocation, and mass growth to explain these diverse growth trajectories. By calibrating model parameters with experimental data, we show that DNA-proportional mRNA transcription produces near-exponential growth, whereas deviations from this proportionality yield the observed non-exponential growth patterns. Analysis of gene expression perturbations reveals that ribosome expression primarily controls dry mass growth rate, whereas cell envelope protein expression more strongly affects cell elongation rate. We show that cell-cycle-dependent transcription dynamics give rise to convex, super-exponential, and linear modes of cell elongation observed experimentally, demonstrating how the timing of cell envelope and ribosomal protein expressions drive cell-cycle-specific behaviors. These findings provide a mechanistic basis for non-exponential single-cell growth and offer insights into how bacterial cells dynamically regulate elongation rates within each generation.
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Cellular perception of growth rate and the mechanistic origin of bacterial growth law
Many cellular activities in bacteria are organized according to their growth rate. The notion that ppGpp measures the cell’s growth rate is well accepted in the field of bacterial physiology. However, despite decades of interrogation and the identification of multiple molecular interactions that connects ppGpp to some aspects of cell growth, we lack a system-level, quantitative picture of how this alleged “measurement” is performed. Through quantitative experiments, we show that the ppGpp pool responds inversely to the rate of translational elongation in Escherichia coli . Together with its roles in inhibiting ribosome biogenesis and activity, ppGpp closes a key regulatory circuit that enables the cell to perceive and control the rate of its growth across conditions. The celebrated linear growth law relating the ribosome content and growth rate emerges as a consequence of keeping a supply of ribosome reserves while maintaining elongation rate in slow growth conditions. Further analysis suggests the elongation rate itself is detected by sensing the ratio of dwelling and translocating ribosomes, a strategy employed to collapse the complex, high-dimensional dynamics of the molecular processes underlying cell growth to perceive the physiological state of the whole.
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- Award ID(s):
- 1818384
- PAR ID:
- 10376713
- Date Published:
- Journal Name:
- Proceedings of the National Academy of Sciences
- Volume:
- 119
- Issue:
- 20
- ISSN:
- 0027-8424
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Bacterial growth is remarkably robust to environmental fluctuations, yet the mechanisms of growth-rate homeostasis are poorly understood. Here, we combine theory and experiment to infer mechanisms by which Escherichia coli adapts its growth rate in response to changes in osmolarity, a fundamental physicochemical property of the environment. The central tenet of our theoretical model is that cell-envelope expansion is only sensitive to local information, such as enzyme concentrations, cell-envelope curvature, and mechanical strain in the envelope. We constrained this model with quantitative measurements of the dynamics of E. coli elongation rate and cell width after hyperosmotic shock. Our analysis demonstrated that adaptive cell-envelope softening is a key process underlying growth-rate homeostasis. Furthermore, our model correctly predicted that softening does not occur above a critical hyperosmotic shock magnitude and precisely recapitulated the elongation-rate dynamics in response to shocks with magnitude larger than this threshold. Finally, we found that, to coordinately achieve growth-rate and cell-width homeostasis, cells employ direct feedback between cell-envelope curvature and envelope expansion. In sum, our analysis points to cellular mechanisms of bacterial growth-rate homeostasis and provides a practical theoretical framework for understanding this process.more » « less
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ABSTRACT Across species and environments, the ribosome content of cell populations correlates with population growth rate. The robustness and universality of this correlation have led to its classification as a “growth law.” This law has fueled theories about how evolution selects for microbial organisms that maximize their growth rate based on nutrient availability, and it has informed models about how individual cells regulate their growth rates and ribosomal content. However, due to methodological limitations, this growth law has rarely been studied at the level of individual cells. Whilepopulationsof fast-growing cells tend to have more ribosomes thanpopulationsof slow-growing cells, it is unclear whether individual cells tightly regulate their ribosome content to match their environment. Here, we employ recent groundbreaking single-cell RNA sequencing techniques to study this growth law at the single-cell level in two different microbes,S. cerevisiae(a single-celled yeast and eukaryote) andB. subtilis(a bacterium and prokaryote). In both species, we observe significant variation in the ribosomal content of single cells that is not predictive of growth rate. Fast-growing populations include cells exhibiting transcriptional signatures of slow growth and stress, as do cells with the highest ribosome content we survey. Broadening our focus to non-ribosomal transcripts reveals subpopulations of cells in unique transcriptional states suggestive that they have evolved to do things other than maximize their rate of growth. Overall, these results indicate that single-cell ribosome levels are not finely tuned to match population growth rates or nutrient availability and cannot be predicted by a Gaussian process model that assumes measurements are sampled from a normal distribution centered on the population average. This work encourages the expansion of growth law and other models that predict how growth rates are regulated or how they evolve to consider single-cell heterogeneity. To this end, we provide extensive data and analysis of ribosomal and transcriptomic variation across thousands of single cells from multiple conditions, replicates, and species.more » « less
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null (Ed.)Abstract The alarmone nucleotides guanosine tetraphosphate and pentaphosphate, commonly referred to as (p)ppGpp, regulate bacterial responses to nutritional and other stresses. There is evidence for potential existence of a third alarmone, guanosine-5′-monophosphate-3′-diphosphate (pGpp), with less-clear functions. Here, we demonstrate the presence of pGpp in bacterial cells, and perform a comprehensive screening to identify proteins that interact respectively with pGpp, ppGpp and pppGpp in Bacillus species. Both ppGpp and pppGpp interact with proteins involved in inhibition of purine nucleotide biosynthesis and with GTPases that control ribosome assembly or activity. By contrast, pGpp interacts with purine biosynthesis proteins but not with the GTPases. In addition, we show that hydrolase NahA (also known as YvcI) efficiently produces pGpp by hydrolyzing (p)ppGpp, thus modulating alarmone composition and function. Deletion of nahA leads to reduction of pGpp levels, increased (p)ppGpp levels, slower growth recovery from nutrient downshift, and loss of competitive fitness. Our results support the existence and physiological relevance of pGpp as a third alarmone, with functions that can be distinct from those of (p)ppGpp.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1073/pnas.2201585119
