Single-gene tuning of Caulobacter cell cycle period and noise, swarming motility, and surface adhesion

Super-exponential growth and stochastic size dynamics in rod-like bacteria

Proliferating bacterial cells exhibit stochastic growth and size dynamics, but the regulation of noise in bacterial growth and morphogenesis remains poorly understood. A quantitative understanding of morphogenetic noise control, and how it changes under different growth conditions, would provide better insights into cell-to-cell variability and intergenerational fluctuations in cell physiology. Using multigenerational growth and width data of single Escherichia coli and Caulobacter crescentus cells, we deduce the equations governing growth and size dynamics of rod-like bacterial cells. Interestingly, we find that both E. coli and C. crescentus cells deviate from exponential growth within the cell cycle. In particular, the exponential growth rate increases during the cell cycle irrespective of nutrient or temperature conditions. We propose a mechanistic model that explains the emergence of super-exponential growth from autocatalytic production of ribosomes coupled to the rate of cell elongation and surface area synthesis. Using this new model and statistical inference on large datasets, we construct the Langevin equations governing cell growth and size dynamics of E. coli cells in different nutrient conditions. The single-cell level model predicts how noise in intragenerational and intergenerational processes regulate variability in cell morphology and generation times, revealing quantitative strategies for cellular resource allocation and morphogenetic noise control in different growth conditions.

A one-dimensional three-state run-and-tumble model with a 'cell cycle'

We study a one-dimensional three-state run-and-tumble model motivated by the bacterium Caulobacter crescentus which displays a cell cycle between two non-proliferating mobile phases and a proliferating sedentary phase. Our model implements kinetic transitions between the two mobile and one sedentary states described in terms of their number densities, where mobility is allowed with different running speeds in forward and backward direction. We start by analyzing the stationary states of the system and compute the mean and squared-displacements for the distribution of all cells, as well as for the number density of settled cells. The latter displays a surprising super-ballistic scaling [Formula: see text] at early times. Including repulsive and attractive interactions between the mobile cell populations and the settled cells, we explore the stability of the system and employ numerical methods to study structure formation in the fully nonlinear system. We find traveling waves of bacteria, whose occurrence is quantified in a non-equilibrium state diagram.

Absolute Measurements of mRNA Translation in Caulobacter crescentus Reveal Important Fitness Costs of Vitamin B12 Scavenging

Caulobacter crescentus is a model system of the bacterial cell cycle culminating in asymmetric cell division, with each daughter cell inheriting a distinct set of proteins. While a genetic network of master transcription factors coordinates the cell cycle timing of transcription for nearly 20% of Caulobacter genes, we lack knowledge of how many of each protein “part” encoded in the genome are synthesized. Therefore, to determine the absolute production rates across the genome, we performed ribosome profiling, providing, for the first time, a quantitative resource with measurements of each protein “part” needed to generate daughter cells. This resource furthers the goal of a systems-level understanding of the genetic network controlling asymmetric cell division. To highlight the utility of this data set, we probe the protein synthesis cost of a B₁₂ utilization pathway and provide new insights into Caulobacter’s adaptation to its natural environments.

Caulobacter crescentus is a model for the bacterial cell cycle which culminates in asymmetric cell division, yet little is known about the absolute levels of protein synthesis of the cellular parts needed to complete the cell cycle. Here we utilize ribosome profiling to provide absolute measurements of mRNA translation in C. crescentus, providing an important resource with quantitative genome-wide measurements of protein output across individual genes. Analysis of protein synthesis rates revealed ∼4.5% of cellular protein synthesis is for genes related to vitamin B₁₂ import (btuB) and B₁₂-independent methionine biosynthesis (metE) when grown in common growth media lacking B₁₂. While its facultative B₁₂ lifestyle provides a fitness advantage in the absence of B₁₂, we find that it provides a fitness disadvantage of the cells in the presence of B₁₂, potentially explaining why many Caulobacter species have lost the metE gene and become obligates for B₁₂.

IMPORTANCECaulobacter crescentus is a model system of the bacterial cell cycle culminating in asymmetric cell division, with each daughter cell inheriting a distinct set of proteins. While a genetic network of master transcription factors coordinates the cell cycle timing of transcription for nearly 20% of Caulobacter genes, we lack knowledge of how many of each protein “part” encoded in the genome are synthesized. Therefore, to determine the absolute production rates across the genome, we performed ribosome profiling, providing, for the first time, a quantitative resource with measurements of each protein “part” needed to generate daughter cells. This resource furthers the goal of a systems-level understanding of the genetic network controlling asymmetric cell division. To highlight the utility of this data set, we probe the protein synthesis cost of a B₁₂ utilization pathway and provide new insights into Caulobacter’s adaptation to its natural environments.

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Beyond the bulk: disclosing the life of single microbial cells

Microbial single cell analysis has led to discoveries that are beyond what can be resolved with population-based studies. It provides a pristine view of the mechanisms that organize cellular physiology, unbiased by population heterogeneity or uncontrollable environmental impacts. A holistic description of cellular functions at the single cell level requires analytical concepts beyond the miniaturization of existing technologies, defined but uncontrolled by the biological system itself. This review provides an overview of the latest advances in single cell technologies and demonstrates their potential. Opportunities and limitations of single cell microbiology are discussed using selected application-related examples.

Spatiotemporal Models of the Asymmetric Division Cycle of Caulobacter crescentus

The spatial localization of proteins within the cytoplasm of bacteria is an underappreciated but critical aspect of cell cycle regulation for many prokaryotes. In Caulobacter crescentus-a model organism for the study of asymmetric cell reproduction in prokaryotes-heterogeneous localization of proteins has been identified as the underlying cause of asymmetry in cell morphology, DNA replication, and cell division. However, significant questions remain. Firstly, the mechanisms by which proteins localize in the organelle-free prokaryotic cytoplasm remain obscure. Furthermore, how variations in the spatial and temporal dynamics of cell fate determinants regulate signaling pathways and orchestrate the complex programs of asymmetric cell division and differentiation are subjects of ongoing research. In this chapter, we review current efforts in investigating these two questions. We describe how mathematical models of spatiotemporal protein dynamics are being used to generate and test competing hypotheses and provide complementary insight about the control mechanisms that regulate asymmetry in protein localization and cell division.

A stochastic spatiotemporal model of a response-regulator network in the Caulobacter crescentus cell cycle

The asymmetric cell division cycle in Caulobacter crescentus is controlled by an elaborate molecular mechanism governing the production, activation and spatial localization of a host of interacting proteins. In previous work, we proposed a deterministic mathematical model for the spatiotemporal dynamics of six major regulatory proteins. In this paper, we study a stochastic version of the model, which takes into account molecular fluctuations of these regulatory proteins in space and time during early stages of the cell cycle of wild-type Caulobacter cells. We test the stochastic model with regard to experimental observations of increased variability of cycle time in cells depleted of the divJ gene product. The deterministic model predicts that overexpression of the divK gene blocks cell cycle progression in the stalked stage; however, stochastic simulations suggest that a small fraction of the mutants cells do complete the cell cycle normally.

Dynamical Localization of DivL and PleC in the Asymmetric Division Cycle of Caulobacter crescentus: A Theoretical Investigation of Alternative Models

Cell-fate asymmetry in the predivisional cell of Caulobacter crescentus requires that the regulatory protein DivL localizes to the new pole of the cell where it up-regulates CckA kinase, resulting in a gradient of CtrA~P across the cell. In the preceding stage of the cell cycle (the "stalked" cell), DivL is localized uniformly along the cell membrane and maintained in an inactive form by DivK~P. It is unclear how DivL overcomes inhibition by DivK~P in the predivisional cell simply by changing its location to the new pole. It has been suggested that co-localization of DivL with PleC phosphatase at the new pole is essential to DivL's activity there. However, there are contrasting views on whether the bifunctional enzyme, PleC, acts as a kinase or phosphatase at the new pole. To explore these ambiguities, we formulated a mathematical model of the spatiotemporal distributions of DivL, PleC and associated proteins (DivJ, DivK, CckA, and CtrA) during the asymmetric division cycle of a Caulobacter cell. By varying localization profiles of DivL and PleC in our model, we show how the physiologically observed spatial distributions of these proteins are essential for the transition from a stalked cell to a predivisional cell. Our simulations suggest that PleC is a kinase in predivisional cells, and that, by sequestering DivK~P, the kinase form of PleC enables DivL to be reactivated at the new pole. Hence, co-localization of PleC kinase and DivL is essential to establishing cellular asymmetry. Our simulations reproduce the experimentally observed spatial distribution and phosphorylation status of CtrA in wild-type and mutant cells. Based on the model, we explore novel combinations of mutant alleles, making predictions that can be tested experimentally.

Intergenerational continuity of cell shape dynamics in Caulobacter crescentus

We investigate the intergenerational shape dynamics of single Caulobacter crescentus cells using a novel combination of imaging techniques and theoretical modeling. We determine the dynamics of cell pole-to-pole lengths, cross-sectional widths, and medial curvatures from high accuracy measurements of cell contours. Moreover, these shape parameters are determined for over 250 cells across approximately 10000 total generations, which affords high statistical precision. Our data and model show that constriction is initiated early in the cell cycle and that its dynamics are controlled by the time scale of exponential longitudinal growth. Based on our extensive and detailed growth and contour data, we develop a minimal mechanical model that quantitatively accounts for the cell shape dynamics and suggests that the asymmetric location of the division plane reflects the distinct mechanical properties of the stalked and swarmer poles. Furthermore, we find that the asymmetry in the division plane location is inherited from the previous generation. We interpret these results in terms of the current molecular understanding of shape, growth, and division of C. crescentus.

Scaling laws governing stochastic growth and division of single bacterial cells

Uncovering the quantitative laws that govern the growth and division of single cells remains a major challenge. Using a unique combination of technologies that yields unprecedented statistical precision, we find that the sizes of individual Caulobacter crescentus cells increase exponentially in time. We also establish that they divide upon reaching a critical multiple (≈ 1.8) of their initial sizes, rather than an absolute size. We show that when the temperature is varied, the growth and division timescales scale proportionally with each other over the physiological temperature range. Strikingly, the cell-size and division-time distributions can both be rescaled by their mean values such that the condition-specific distributions collapse to universal curves. We account for these observations with a minimal stochastic model that is based on an autocatalytic cycle. It predicts the scalings, as well as specific functional forms for the universal curves. Our experimental and theoretical analysis reveals a simple physical principle governing these complex biological processes: a single temperature-dependent scale of cellular time governs the stochastic dynamics of growth and division in balanced growth conditions.

Potential role of a bistable histidine kinase switch in the asymmetric division cycle of Caulobacter crescentus

The free-living aquatic bacterium, Caulobacter crescentus, exhibits two different morphologies during its life cycle. The morphological change from swarmer cell to stalked cell is a result of changes of function of two bi-functional histidine kinases, PleC and CckA. Here, we describe a detailed molecular mechanism by which the function of PleC changes between phosphatase and kinase state. By mathematical modeling of our proposed molecular interactions, we derive conditions under which PleC, CckA and its response regulators exhibit bistable behavior, thus providing a scenario for robust switching between swarmer and stalked states. Our simulations are in reasonable agreement with in vitro and in vivo experimental observations of wild type and mutant phenotypes. According to our model, the kinase form of PleC is essential for the swarmer-to-stalked transition and to prevent premature development of the swarmer pole. Based on our results, we reconcile some published experimental observations and suggest novel mutants to test our predictions.

Phase resetting reveals network dynamics underlying a bacterial cell cycle

Genomic and proteomic methods yield networks of biological regulatory interactions but do not provide direct insight into how those interactions are organized into functional modules, or how information flows from one module to another. In this work we introduce an approach that provides this complementary information and apply it to the bacterium Caulobacter crescentus, a paradigm for cell-cycle control. Operationally, we use an inducible promoter to express the essential transcriptional regulatory gene ctrA in a periodic, pulsed fashion. This chemical perturbation causes the population of cells to divide synchronously, and we use the resulting advance or delay of the division times of single cells to construct a phase resetting curve. We find that delay is strongly favored over advance. This finding is surprising since it does not follow from the temporal expression profile of CtrA and, in turn, simulations of existing network models. We propose a phenomenological model that suggests that the cell-cycle network comprises two distinct functional modules that oscillate autonomously and couple in a highly asymmetric fashion. These features collectively provide a new mechanism for tight temporal control of the cell cycle in C. crescentus. We discuss how the procedure can serve as the basis for a general approach for probing network dynamics, which we term chemical perturbation spectroscopy (CPS).

During the cell cycle, the cell progresses through a series of stages that are associated with various cell cycle events such as replication of genetic materials. Genetic and molecular dissections have revealed that the cell cycle is regulated by a network of interacting molecules that produces oscillatory dynamics. The major cell cycle regulators have been identified previously in different species and the activity of these regulators oscillates. However, the question of how cell cycle regulators coordinate different cell cycle events during the cell cycle remains controversial. Here, we investigate this question in a model bacterial system for cell cycle, Caulobacter crescentus. We perturb the expression of the master cell cycle regulator ctrA in a pulsatile fashion and quantify the response of the cell cycle to such perturbations. The measured response is contradictory to the existing mechanism of Caulobacter cell cycle control, which views the cell cycle progression as a sequential activation/inhibition process. We propose a new model that involves coupling of multiple oscillators and show the quantitative agreement between this new model and our measurements. We expect this procedure to be generalized and applied to a broad range of systems to obtain information that complements that obtained from other methods.

The conserved polarity factor podJ1 impacts multiple cell envelope-associated functions in Sinorhizobium meliloti

Although diminutive in size, bacteria possess highly diverse and spatially confined cellular structures. Two related alphaproteobacteria, Sinorhizobium meliloti and Caulobacter crescentus, serve as models for investigating the genetic basis of morphological variations. S. meliloti, a symbiont of leguminous plants, synthesizes multiple flagella and no prosthecae, whereas C. crescentus, a freshwater bacterium, has a single polar flagellum and stalk. The podJ gene, originally identified in C. crescentus for its role in polar organelle development, is split into two adjacent open reading frames, podJ1 and podJ2, in S. meliloti. Deletion of podJ1 interferes with flagellar motility, exopolysaccharide production, cell envelope integrity, cell division and normal morphology, but not symbiosis. As in C. crescentus, the S. meliloti PodJ1 protein appears to act as a polarity beacon and localizes to the newer cell pole. Microarray analysis indicates that podJ1 affects the expression of at least 129 genes, the majority of which correspond to observed mutant phenotypes. Together, phenotypic characterization, microarray analysis and suppressor identification suggest that PodJ1 controls a core set of conserved elements, including flagellar and pili genes, the signalling proteins PleC and DivK, and the transcriptional activator TacA, while alternative downstream targets have evolved to suit the distinct lifestyles of individual species.