Morphology, growth, and size limit of bacterial cells

Energy allocation theory for bacterial growth control in and out of steady state

Efficient allocation of energy resources to key physiological functions allows living organisms to grow and thrive in diverse environments and adapt to a wide range of perturbations. To quantitatively understand how unicellular organisms utilize their energy resources in response to changes in growth environment, we introduce a theory of dynamic energy allocation which describes cellular growth dynamics based on partitioning of metabolizable energy into key physiological functions: growth, division, cell shape regulation, energy storage and loss through dissipation. By optimizing the energy flux for growth, we develop the equations governing the time evolution of cell morphology and growth rate in diverse environments. The resulting model accurately captures experimentally observed dependencies of bacterial cell size on growth rate, superlinear scaling of metabolic rate with cell size, and predicts nutrient-dependent trade-offs between energy expended for growth, division, and shape maintenance. By calibrating model parameters with available experimental data for the model organism E. coli, our model is capable of describing bacterial growth control in dynamic conditions, particularly during nutrient shifts and osmotic shocks. The model captures these perturbations with minimal added complexity and our unified approach predicts the driving factors behind a wide range of observed morphological and growth phenomena.

Quantifying turgor pressure in budding and fission yeasts based upon osmotic properties

Walled cells, such as plants, fungi, and bacteria cells, possess a high internal hydrostatic pressure, termed turgor pressure, that drives volume growth and contributes to cell shape determination. Rigorous measurement of turgor pressure, however, remains challenging, and reliable quantitative measurements, even in budding yeast are still lacking. Here, we present a simple and robust experimental approach to access turgor pressure in yeasts based upon the determination of isotonic concentration using protoplasts as osmometers. We propose three methods to identify the isotonic condition - three-dimensional cell volume, cytoplasmic fluorophore intensity, and mobility of a cytGEMs nano-rheology probe - that all yield consistent values. Our results provide turgor pressure estimates of 1.0 ± 0.1 MPa for Schizosaccharomyces pombe, 0.49 ± 0.01 MPa for Schizosaccharomyces japonicus, 0.5 ± 0.1 MPa for Saccharomyces cerevisiae W303a and 0.31 ± 0.03 MPa for Saccharomyces cerevisiae BY4741. Large differences in turgor pressure and nano-rheology measurements between the Saccharomyces cerevisiae strains demonstrate how fundamental biophysical parameters can vary even among wild-type strains of the same species. These side-by-side measurements of turgor pressure in multiple yeast species provide critical values for quantitative studies on cellular mechanics and comparative evolution.

Pressure-induced shape-shifting of helical bacteria

Many bacterial species are helical in shape, including the widespread pathogen H. pylori. Motivated by recent experiments on H. pylori showing that cell wall synthesis is not uniform [J. A. Taylor, et al., eLife, 2020, 9, e52482], we investigate the possible formation of helical cell shape induced by elastic heterogeneity. We show, experimentally and theoretically, that helical morphogenesis can be produced by pressurizing an elastic cylindrical vessel with helical reinforced lines. The properties of the pressurized helix are highly dependent on the initial helical angle of the reinforced region. We find that steep angles result in crooked helices with, surprisingly, a reduced end-to-end distance upon pressurization. This work helps explain the possible mechanisms for the generation of helical cell morphologies and may inspire the design of novel pressure-controlled helical actuators.

Cellular resource allocation strategies for cell size and shape control in bacteria

Bacteria are highly adaptive microorganisms that thrive in a wide range of growth conditions via changes in cell morphologies and macromolecular composition. How bacterial morphologies are regulated in diverse environmental conditions is a long-standing question. Regulation of cell size and shape implies control mechanisms that couple the growth and division of bacteria to their cellular environment and macromolecular composition. In the past decade, simple quantitative laws have emerged that connect cell growth to proteomic composition and the nutrient availability. However, the relationships between cell size, shape, and growth physiology remain challenging to disentangle and unifying models are lacking. In this review, we focus on regulatory models of cell size control that reveal the connections between bacterial cell morphology and growth physiology. In particular, we discuss how changes in nutrient conditions and translational perturbations regulate the cell size, growth rate, and proteome composition. Integrating quantitative models with experimental data, we identify the physiological principles of bacterial size regulation, and discuss the optimization strategies of cellular resource allocation for size control.

Antibiotic Resistance via Bacterial Cell Shape-Shifting

Bacteria have evolved to develop multiple strategies for antibiotic resistance by effectively reducing intracellular antibiotic concentrations or antibiotic binding affinities, but the role of cell morphology in antibiotic resistance remains poorly understood. By analyzing cell morphological data for different bacterial species under antibiotic stress, we find that bacteria increase or decrease the cell surface-to-volume ratio depending on the antibiotic target. Using quantitative modeling, we show that by reducing the surface-to-volume ratio, bacteria can effectively reduce the intracellular antibiotic concentration by decreasing antibiotic influx. The model further predicts that bacteria can increase the surface-to-volume ratio to induce the dilution of membrane-targeting antibiotics, in agreement with experimental data. Using a whole-cell model for the regulation of cell shape and growth by antibiotics, we predict shape transformations that bacteria can utilize to increase their fitness in the presence of antibiotics. We conclude by discussing additional pathways for antibiotic resistance that may act in synergy with shape-induced resistance.

Bacterial Targets of Antibiotics in Methicillin-Resistant Staphylococcus aureus

Methicillin-resistant Staphylococcus aureus (MRSA) is one of the most prevalent bacterial pathogens and continues to be a leading cause of morbidity and mortality worldwide. MRSA is a commensal bacterium in humans and is transmitted in both community and healthcare settings. Successful treatment remains a challenge, and a search for new targets of antibiotics is required to ensure that MRSA infections can be effectively treated in the future. Most antibiotics in clinical use selectively target one or more biochemical processes essential for S. aureus viability, e.g., cell wall synthesis, protein synthesis (translation), DNA replication, RNA synthesis (transcription), or metabolic processes, such as folic acid synthesis. In this review, we briefly describe the mechanism of action of antibiotics from different classes and discuss insights into the well-established primary targets in S. aureus. Further, several components of bacterial cellular processes, such as teichoic acid, aminoacyl-tRNA synthetases, the lipid II cycle, auxiliary factors of β-lactam resistance, two-component systems, and the accessory gene regulator quorum sensing system, are discussed as promising targets for novel antibiotics. A greater molecular understanding of the bacterial targets of antibiotics has the potential to reveal novel therapeutic strategies or identify agents against antibiotic-resistant pathogens.

Measurement of the interconnected turgor pressure and envelope elasticity of live bacterial cells

Turgor pressure and envelope elasticity of bacterial cells are two mechanical parameters that play a dominant role in cellular deformation, division, and motility. However, a clear understanding of these two properties is lacking because of their strongly interconnected mechanisms. This study established a nanoindentation method to precisely measure the turgor pressure and envelope elasticity of live bacteria. The indentation force-depth curves of Klebsiella pneumoniae bacteria were recorded with atomic force microscopy. Through combination of dimensional analysis and numerical simulations, an explicit expression was derived to decouple the two properties of individual bacteria from the nanoindentation curves. We show that the Young's modulus of bacterial envelope is sensitive to the external osmotic environment, and the turgor pressure is significantly dependent on the external osmotic stress. This method can not only quantify the turgor pressure and envelope elasticity of bacteria, but also help resolve the mechanical behaviors of bacteria in different environments.

Ag3PO4 decorated black urchin-like defective TiO2 for rapid and long-term bacteria-killing under visible light

Both phototherapy via photocatalysts and physical puncture by artificial nanostructures are promising substitutes for antibiotics when treating drug-resistant bacterial infectious diseases. However, the photodynamic therapeutic efficacy of photocatalysts is seriously restricted by the rapid recombination of photogenerated electron–hole pairs. Meanwhile, the nanostructures of physical puncture are limited to two-dimensional (2D) platforms, and they cannot be fully used yet. Thus, this research developed a synergistic system of Ag₃PO₄ nanoparticles (NPs), decorated with black urchin-like defective TiO₂ (BU–TiO_2-X/Ag₃PO₄). These NPs had a decreased bandgap compared to BU-TiO_2-X, and BU-TiO_2-X/Ag₃PO₄ (3:1) exhibited the lowest bandgap and the highest separation efficiency for photogenerated electron–hole pairs. After combination with BU-TiO_2-X, the photostability of Ag₃PO₄ improved because the oxygen vacancy of BU-TiO_2-X retards the reduction of Ag⁺ in Ag₃PO₄ into Ag⁰, thus reducing its toxicity. In addition, the nanospikes on the surface of BU-TiO_2-X can, from all directions, physically puncture bacterial cells, thus assisting the hybrid's photodynamic therapeutic effects, alongside the small amount of Ag⁺ released from Ag₃PO₄. This achieves synergy, endowing the hybrid with high antibacterial efficacy of 99.76 ± 0.15% and 99.85 ± 0.09% against Escherichia coli and Staphylococcus aureus, respectively, after light irradiation for 20 min followed by darkness for 12 h. It is anticipated that these findings may bring new insight for developing synergistic treatment strategies against bacterial infectious diseases or pathogenic bacterial polluted environments.

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BU-TiO_2-X/Ag₃PO₄ (3:1) hybrid improved the photostability of Ag₃PO₄.

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BU-TiO_2-X/Ag₃PO₄ (3:1) hybrid exhibited outstanding photodynamic therapeutic effects.

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The nanospikes from all directions on the BU-TiO_2-X physically punctured bacterial cells.

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The physical puncture combined with the Ag⁺ released by Ag₃PO₄ had long-term bacteriostatic efficacy.

Beading of injured axons driven by tension- and adhesion-regulated membrane shape instability

The formation of multiple beads along an injured axon will lead to blockage of axonal transport and eventually neuron death, and this has been widely recognized as a hallmark of nervous system degeneration. Nevertheless, the underlying mechanisms remain poorly understood. Here, we report a combined experimental and theoretical study to reveal key factors governing axon beading. Specifically, by transecting well-developed axons with a sharp atomic force microscope probe, significant beading of the axons was triggered. We showed that adhesion was not required for beading to occur, although when present strong axon–substrate attachments seemed to set the locations for bead formation. In addition, the beading wavelength, representing the average distance between beads, was found to correlate with the size and cytoskeleton integrity of axon, with a thinner axon or a disrupted actin cytoskeleton both leading to a shorter beading wavelength. A model was also developed to explain these observations which suggest that axon beading originates from the shape instability of the membrane and is driven by the release of work done by axonal tension as well as the reduction of membrane surface energy. The beading wavelength predicted from this theory was in good agreement with our experiments under various conditions. By elucidating the essential physics behind axon beading, the current study could enhance our understanding of how axonal injury and neurodegeneration progress as well as provide insights for the development of possible treatment strategies.

Targeting Mannitol Metabolism as an Alternative Antimicrobial Strategy Based on the Structure-Function Study of Mannitol-1-Phosphate Dehydrogenase in Staphylococcus aureus

Mannitol-1-phosphate dehydrogenase (M1PDH) is a key enzyme in Staphylococcus aureus mannitol metabolism, but its roles in pathophysiological settings have not been established. We performed comprehensive structure-function analysis of M1PDH from S. aureus USA300, a strain of community-associated methicillin-resistant S. aureus, to evaluate its roles in cell viability and virulence under pathophysiological conditions. On the basis of our results, we propose M1PDH as a potential antibacterial target. In vitro cell viability assessment of ΔmtlD knockout and complemented strains confirmed that M1PDH is essential to endure pH, high-salt, and oxidative stress and thus that M1PDH is required for preventing osmotic burst by regulating pressure potential imposed by mannitol. The mouse infection model also verified that M1PDH is essential for bacterial survival during infection. To further support the use of M1PDH as an antibacterial target, we identified dihydrocelastrol (DHCL) as a competitive inhibitor of S. aureus M1PDH (SaM1PDH) and confirmed that DHCL effectively reduces bacterial cell viability during host infection. To explain physiological functions of SaM1PDH at the atomic level, the crystal structure of SaM1PDH was determined at 1.7-Å resolution. Structure-based mutation analyses and DHCL molecular docking to the SaM1PDH active site followed by functional assay identified key residues in the active site and provided the action mechanism of DHCL. Collectively, we propose SaM1PDH as a target for antibiotic development based on its physiological roles with the goals of expanding the repertory of antibiotic targets to fight antimicrobial resistance and providing essential knowledge for developing potent inhibitors of SaM1PDH based on structure-function studies.IMPORTANCE Due to the shortage of effective antibiotics against drug-resistant Staphylococcus aureus, new targets are urgently required to develop next-generation antibiotics. We investigated mannitol-1-phosphate dehydrogenase of S. aureus USA300 (SaM1PDH), a key enzyme regulating intracellular mannitol levels, and explored the possibility of using SaM1PDH as a target for developing antibiotic. Since mannitol is necessary for maintaining the cellular redox and osmotic potential, the homeostatic imbalance caused by treatment with a SaM1PDH inhibitor or knockout of the gene encoding SaM1PDH results in bacterial cell death through oxidative and/or mannitol-dependent cytolysis. We elucidated the molecular mechanism of SaM1PDH and the structural basis of substrate and inhibitor recognition by enzymatic and structural analyses of SaM1PDH. Our results strongly support the concept that targeting of SaM1PDH represents an alternative strategy for developing a new class of antibiotics that cause bacterial cell death not by blocking key cellular machinery but by inducing cytolysis and reducing stress tolerance through inhibition of the mannitol pathway.

Distribution of mechanical stress in the Escherichia coli cell envelope

The cell envelope in Gram-negative bacteria comprises two distinct membranes with a cell wall between them. There has been a growing interest in understanding the mechanical adaptation of this cell envelope to the osmotic pressure (or turgor pressure), which is generated by the difference in the concentration of solutes between the cytoplasm and the external environment. However, it remains unexplored how the cell wall, the inner membrane (IM), and the outer membrane (OM) effectively protect the cell from this pressure by bearing the resulting surface tension, thus preventing the formation of inner membrane bulges, abnormal cell morphology, spheroplasts and cell lysis. In this study, we have used molecular dynamics (MD) simulations combined with experiments to resolve how and to what extent models of the IM, OM, and cell wall respond to changes in surface tension. We calculated the area compressibility modulus of all three components in simulations from tension-area isotherms. Experiments on monolayers mimicking individual leaflets of the IM and OM were also used to characterize their compressibility. While the membranes become softer as they expand, the cell wall exhibits significant strain stiffening at moderate to high tensions. We integrate these results into a model of the cell envelope in which the OM and cell wall share the tension at low turgor pressure (0.3 atm) but the tension in the cell wall dominates at high values (>1 atm).

A model of cell-wall dynamics during sporulation in Bacillus subtilis

To survive starvation, Bacillus subtilis forms durable spores. After asymmetric cell division, the septum grows around the forespore in a process called engulfment, but the mechanism of force generation is unknown. Here, we derived a novel biophysical model for the dynamics of cell-wall remodeling during engulfment based on a balancing of dissipative, active, and mechanical forces. By plotting phase diagrams, we predict that sporulation is promoted by a line tension from the attachment of the septum to the outer cell wall, as well as by an imbalance in turgor pressures in the mother-cell and forespore compartments. We also predict that significant mother-cell growth hinders engulfment. Hence, relatively simple physical principles may guide this complex biological process.

Shape Transformation of the Nuclear Envelope during Closed Mitosis

The nuclear envelope (NE) in lower eukaryotes such as Schizosaccharomyces pombe undergoes large morphology changes during closed mitosis. However, which physical parameters are important in governing the shape evolution of the NE, and how defects in the dividing chromosomes/microtubules are reflected in those parameters, are fundamental questions that remain unresolved. In this study, we show that improper separation of chromosomes in genetically deficient cells leads to membrane tethering or asymmetric division in contrast to the formation of two equal-sized daughter nuclei in wild-type cells. We hypothesize that the poleward force is transmitted to the nuclear membrane through its physical contact with the separated sister chromatids at the two spindle poles. A theoretical model is developed to predict the morphology evolution of the NE where key factors such as the work done by the poleward force and bending and surface energies stored in the membrane have been taken into account. Interestingly, the predicted phase diagram, summarizing the dependence of nuclear shape on the size of the load transmission regions, and the pole-to-pole distance versus surface area relationship all quantitatively agree well with our experimental observations, suggesting that this model captures the essential physics involved in closed mitosis.

Shape dynamics of growing cell walls

We introduce a general theoretical framework to study the shape dynamics of actively growing and remodeling surfaces. Using this framework we develop a physical model for growing bacterial cell walls and study the interplay of cell shape with the dynamics of growth and constriction. The model allows us to derive constraints on cell wall mechanical energy based on the observed dynamics of cell shape. We predict that exponential growth in cell size requires a constant amount of cell wall energy to be dissipated per unit volume. We use the model to understand and contrast growth in bacteria with different shapes such as spherical, ellipsoidal, cylindrical and toroidal morphologies. Coupling growth to cell wall constriction, we predict a discontinuous shape transformation, from partial constriction to cell division, as a function of the chemical potential driving cell wall synthesis. Our model for cell wall energy and shape dynamics relates growth kinetics with cell geometry, and provides a unified framework to describe the interplay between shape, growth and division in bacterial cells.

Origins of Escherichia coli growth rate and cell shape changes at high external osmolality

In Escherichia coli, a sudden increase in external concentration causes a pressure drop across the cell envelope, followed by an active recovery. After recovery, and if the external osmolality remains high, cells have been shown to grow more slowly, smaller, and at reduced turgor pressure. Despite the fact that the active recovery is a key stress response, the nature of these changes and how they relate to each other is not understood. Here, we use fluorescence imaging of single cells during hyperosmotic shocks, combined with custom made microfluidic devices, to show that cells fully recover their volume to the initial, preshock value and continue to grow at a slower rate immediately after the recovery. We show that the cell envelope material properties do not change after hyperosmotic shock, and that cell shape recovers along with cell volume. Taken together, these observations indicate that the turgor pressure recovers to its initial value so that reduced turgor is not responsible for the reduced growth rate observed immediately after recovery. To determine the point at which the reduction in cell size and turgor pressure occurs after shock, we measured the volume of E. coli cells at different stages of growth in bulk cultures. We show that cell volume reaches the same maximal level irrespective of the osmolality of the media. Based on these measurements, we propose that turgor pressure is used as a feedback variable for osmoregulatory pumps instead of being directly responsible for the reduction in growth rates. Reestablishment of turgor to its initial value might ensure correct attachment of the inner membrane and cell wall needed for cell wall biosynthesis.

Bacterial growth and form under mechanical compression

A combination of physical and chemical processes is involved in determining the bacterial cell shape. In standard medium, Escherichia coli cells are rod-shaped, and maintain a constant diameter during exponential growth. Here, we demonstrate that by applying compressive forces to growing E. coli, cells no longer retain their rod-like shapes but grow and divide with a flat pancake-like geometry. The deformation is reversible: deformed cells can recover back to rod-like shapes in several generations after compressive forces are removed. During compression, the cell elongation rate, proliferation rate, DNA replication rate, and protein synthesis are not significantly altered from those of the normal rod-shaped cells. Quantifying the rate of cell wall growth under compression reveals that the cell wall growth rate depends on the local cell curvature. MreB not only influences the rate of cell wall growth, but also influences how the growth rate scales with cell geometry. The result is consistent with predictions of a mechanochemical model, and suggests an active mechanical role for MreB during cell wall growth. The developed compressive device is also useful for studying a variety of cells in unique geometries.

Cell size modulates oscillation, positioning and length of mitotic spindles

Mitotic spindle is the main subcellular structure that accomplishes the chromosome segregation between daughter cells during cell division. However, how mitotic spindles sense and control their size, position and movement inside the cell still remains unclear. In this paper, we focus on the size effects of mitotic spindles, i.e., how cell size controls various interesting phenomena in the metaphase, such as oscillation, positioning and size limit of mitotic spindles. We systematically studied the frequency doubling phenomenon during chromosome oscillation and found that cell size can regulate the period and amplitude of chromosome oscillation. We found that the relaxation time of the positioning process increases exponentially with cell size. We also showed that the stabler microtubule-kinetochore attachments alone can directly lead to an upper limit of spindle size. Our work not only explains the existing experimental observations, but also provides some interesting predictions that can be verified or rejected by further experiments.

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.

Bactericidal activity of black silicon

Black silicon is a synthetic nanomaterial that contains high aspect ratio nanoprotrusions on its surface, produced through a simple reactive-ion etching technique for use in photovoltaic applications. Surfaces with high aspect-ratio nanofeatures are also common in the natural world, for example, the wings of the dragonfly Diplacodes bipunctata. Here we show that the nanoprotrusions on the surfaces of both black silicon and D. bipunctata wings form hierarchical structures through the formation of clusters of adjacent nanoprotrusions. These structures generate a mechanical bactericidal effect, independent of chemical composition. Both surfaces are highly bactericidal against all tested Gram-negative and Gram-positive bacteria, and endospores, and exhibit estimated average killing rates of up to ~450,000 cells min⁻¹ cm⁻². This represents the first reported physical bactericidal activity of black silicon or indeed for any hydrophilic surface. This biomimetic analogue represents an excellent prospect for the development of a new generation of mechano-responsive, antibacterial nanomaterials.

The topographical features of insect wings result in some interesting surface properties, including hydrophobicity and antibacterial activity. Here the authors identify the surface of black silicon as a mimic of dragonfly wings and show that it too possesses antibacterial activity.

How and why cells grow as rods

The rod is a ubiquitous shape adopted by walled cells from diverse organisms ranging from bacteria to fungi to plants. Although rod-like shapes are found in cells of vastly different sizes and are constructed by diverse mechanisms, the geometric similarities among these shapes across kingdoms suggest that there are common evolutionary advantages, which may result from simple physical principles in combination with chemical and physiological constraints. Here, we review mechanisms of constructing rod-shaped cells and the bases of different biophysical models of morphogenesis, comparing and contrasting model organisms in different kingdoms. We then speculate on possible advantages of the rod shape, and suggest strategies for elucidating the relative importance of each of these advantages.

Universality in stochastic exponential growth

Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.

Response of Escherichia coli growth rate to osmotic shock

It has long been proposed that turgor pressure plays an essential role during bacterial growth by driving mechanical expansion of the cell wall. This hypothesis is based on analogy to plant cells, for which this mechanism has been established, and on experiments in which the growth rate of bacterial cultures was observed to decrease as the osmolarity of the growth medium was increased. To distinguish the effect of turgor pressure from pressure-independent effects that osmolarity might have on cell growth, we monitored the elongation of single Escherichia coli cells while rapidly changing the osmolarity of their media. By plasmolyzing cells, we found that cell-wall elastic strain did not scale with growth rate, suggesting that pressure does not drive cell-wall expansion. Furthermore, in response to hyper- and hypoosmotic shock, E. coli cells resumed their preshock growth rate and relaxed to their steady-state rate after several minutes, demonstrating that osmolarity modulates growth rate slowly, independently of pressure. Oscillatory hyperosmotic shock revealed that although plasmolysis slowed cell elongation, the cells nevertheless "stored" growth such that once turgor was reestablished the cells elongated to the length that they would have attained had they never been plasmolyzed. Finally, MreB dynamics were unaffected by osmotic shock. These results reveal the simple nature of E. coli cell-wall expansion: that the rate of expansion is determined by the rate of peptidoglycan insertion and insertion is not directly dependent on turgor pressure, but that pressure does play a basic role whereby it enables full extension of recently inserted peptidoglycan.

Getting into shape: How do rod-like bacteria control their geometry?

Rod-like bacteria maintain their cylindrical shapes with remarkable precision during growth. However, they are also capable to adapt their shapes to external forces and constraints, for example by growing into narrow or curved confinements. Despite being one of the simplest morphologies, we are still far from a full understanding of how shape is robustly regulated, and how bacteria obtain their near-perfect cylindrical shapes with excellent precision. However, recent experimental and theoretical findings suggest that cell-wall geometry and mechanical stress play important roles in regulating cell shape in rod-like bacteria. We review our current understanding of the cell wall architecture and the growth dynamics, and discuss possible candidates for regulatory cues of shape regulation in the absence or presence of external constraints. Finally, we suggest further future experimental and theoretical directions which may help to shed light on this fundamental problem.

Escherichia coli peptidoglycan structure and mechanics as predicted by atomic-scale simulations

Bacteria face the challenging requirement to maintain their shape and avoid rupture due to the high internal turgor pressure, but simultaneously permit the import and export of nutrients, chemical signals, and virulence factors. The bacterial cell wall, a mesh-like structure composed of cross-linked strands of peptidoglycan, fulfills both needs by being semi-rigid, yet sufficiently porous to allow diffusion through it. How the mechanical properties of the cell wall are determined by the molecular features and the spatial arrangement of the relatively thin strands in the larger cellular-scale structure is not known. To examine this issue, we have developed and simulated atomic-scale models of Escherichia coli cell walls in a disordered circumferential arrangement. The cell-wall models are found to possess an anisotropic elasticity, as known experimentally, arising from the orthogonal orientation of the glycan strands and of the peptide cross-links. Other features such as thickness, pore size, and disorder are also found to generally agree with experiments, further supporting the disordered circumferential model of peptidoglycan. The validated constructs illustrate how mesoscopic structure and behavior emerge naturally from the underlying atomic-scale properties and, furthermore, demonstrate the ability of all-atom simulations to reproduce a range of macroscopic observables for extended polymer meshes.

The structure of the bacterial cell wall has been a point of controversy and contention since it was first discovered. Although the basic chemical composition of peptidoglycan, the key constituent of the cell wall, is now well established, its long-range organization is not. This dearth of information at the mesoscopic scale is a result of the inability of experimental imaging techniques to simultaneously visualize both the atomic-level detail of the peptidoglycan network and its macroscopic arrangement around the bacterium. Now, using molecular dynamics (MD) simulations, we have carefully constructed and validated models of sections of the Escherichia coli cell wall in full atomic detail. By comparing various properties of these models, including elasticity, pore size, and thickness with experiments, we can discriminate between them, resolving which best represents the native wall structure. In doing so, our study provides approaches for connecting measurements made in atomic-scale MD simulations with large-scale and even macroscopic properties.

Elasticity and biochemistry of growth relate replication rate to cell length and cross-link density in rod-shaped bacteria

In rod-shaped bacteria, cell morphology is correlated with the replication rate. For a given species, cells that replicate faster are longer and have less cross-linked cell walls. Here, we propose a simple mechanochemical model that explains the dependence of cell length and cross-linking on the replication rate. Our model shows good agreement with existing experimental data and provides further evidence that cell wall synthesis is mediated by multienzyme complexes; however, our results suggest that these synthesis complexes only mediate glycan insertion and cross-link severing, whereas recross-linking is performed independently.

Deformation of filamentous Escherichia coli cells in a microfluidic device: a new technique to study cell mechanics

The mechanical properties of bacterial cells are determined by their stress-bearing elements. The size of typical bacterial cells, and the fact that different time and length scales govern their behavior, necessitate special experimental techniques in order to probe their mechanical properties under various spatiotemporal conditions. Here, we present such an experimental technique to study cell mechanics using hydrodynamic forces in a microfluidic device. We demonstrate the application of this technique by calculating the flexural rigidity of non-growing Escherichia coli cells. In addition, we compare the deformation of filamentous cells under growing and non-growing conditions during the deformation process. We show that, at low forces, the force needed to deform growing cells to the same extent as non-growing cells is approximately two times smaller. Following previous works, we interpret these results as the outcome of the difference between the elastic response of non-growing cells and the plastic-elastic response of growing cells. Finally, we observe some heterogeneity in the response of individual cells to the applied force. We suggest that this results from the individuality of different bacterial cells.

Association of a D-alanyl-D-alanine carboxypeptidase gene with the formation of aberrantly shaped cells during the induction of viable but nonculturable Vibrio parahaemolyticus

Vibrio parahaemolyticus is a halophilic Gram-negative bacterium that causes human gastroenteritis. When the viable but nonculturable (VBNC) state of this bacterium was induced by incubation at 4°C in Morita minimal salt solution containing 0.5% NaCl, the rod-shaped cells became coccoid, and various aberrantly shaped intermediates were formed in the initial stage. This study examined the factors that influence the formation of these aberrantly shaped cells. The proportion of aberrantly shaped cells was not affected in a medium containing D-cycloserine (50 μg/ml) but was lower in a medium containing cephalosporin C (10 μg/ml) than in the control medium without antibiotics. The proportion of aberrantly shaped cells was higher in a culture medium that contained 0.5% NaCl than in culture media containing 1.0 or 1.5% NaCl. The expression of 15 of 17 selected genes associated with cell wall synthesis was enhanced, and the expression of VP2468 (dacB), which encodes D-alanyl-D-alanine carboxypeptidase, was enhanced the most. The proportion of aberrantly shaped cells was significantly lower in the dacB mutant strain than in the parent strain, but the proportion was restored in the presence of the complementary dacB gene. This study suggests that disturbance of the dynamics of cell wall synthesis by enhanced expression of the VP2468 gene is associated with the formation of aberrantly shaped cells in the initial stage of induction of VBNC V. parahaemolyticus cells under specific conditions.

The molecular origins of chiral growth in walled cells

Cells from all kingdoms of life adopt a dizzying array of fascinating shapes that support cellular function. Amoeboid and spherical shapes represent perhaps the simplest of geometries that may minimize the level of growth control required for survival. Slightly more complex are rod-shaped cells, from microscopic bacteria to macroscopic plants, which require additional mechanisms to define a cell's longitudinal axis, width, and length. Recent evidence suggests that many rod-shaped, walled cells achieve elongated growth through chiral insertion of cell-wall material that may be coupled to a twisting of the cell body. Inspired by these observations, biophysical mechanisms for twisting growth have been proposed that link the mechanics of intracellular proteins to cell shape maintenance. In this review, we highlight experimental and theoretical work that connects molecular-scale organization and structure with the cellular-scale phenomena of rod-shaped growth.

Growth of curved and helical bacterial cells

A combination of cell wall growth and cytoskeletal protein action gives rise to the observed bacterial cell shape. Aside from the common rod-like and spherical shapes, bacterial cells can also adopt curved or helical geometries. To understand how curvature in bacteria is developed or maintained, we examine how Caulobacter crescentus obtains its crescent-like shape. Caulobacter cells with or without the cytoskeletal bundle crescentin, an intermediate filament-like protein, exhibit two distinct growth modes, curvature maintenance that preserves the radius of curvature and curvature relaxation that straightens the cell (Fig. 1). Using a proposed mechanochemical model, we show that bending and twisting of the crescentin bundle can influence the stress distribution in the cell wall, and lead to the growth of curved cells. In contrast, after crescentin bundle is disrupted, originally curved cells will slowly relax towards a straight rod over time. The model is able to quantitatively capture experimentally observed curvature dynamics. Furthermore, we show that the shape anisotropy of the cross-section of a curved cell is never greater than 4%, even in the presence of crescentin.

Physics of bacterial morphogenesis

Bacterial cells utilize three-dimensional (3D) protein assemblies to perform important cellular functions such as growth, division, chemoreception, and motility. These assemblies are composed of mechanoproteins that can mechanically deform and exert force. Sometimes, small-nucleotide hydrolysis is coupled to mechanical deformations. In this review, we describe the general principle for an understanding of the coupling of mechanics with chemistry in mechanochemical systems. We apply this principle to understand bacterial cell shape and morphogenesis and how mechanical forces can influence peptidoglycan cell wall growth. We review a model that can potentially reconcile the growth dynamics of the cell wall with the role of cytoskeletal proteins such as MreB and crescentin. We also review the application of mechanochemical principles to understand the assembly and constriction of the FtsZ ring. A number of potential mechanisms are proposed, and important questions are discussed.

From the regulation of peptidoglycan synthesis to bacterial growth and morphology

How bacteria grow and divide while retaining a defined shape is a fundamental question in microbiology, but technological advances are now driving a new understanding of how the shape-maintaining bacterial peptidoglycan sacculus grows. In this Review, we highlight the relationship between peptidoglycan synthesis complexes and cytoskeletal elements, as well as recent evidence that peptidoglycan growth is regulated from outside the sacculus in Gram-negative bacteria. We also discuss how growth of the sacculus is sensitive to mechanical force and nutritional status, and describe the roles of peptidoglycan hydrolases in generating cell shape and of D-amino acids in sacculus remodelling.

Mechanical control of bacterial cell shape

In bacteria, cytoskeletal filament bundles such as MreB control the cell morphology and determine whether the cell takes on a spherical or a rod-like shape. Here we use a theoretical model to describe the interplay of cell wall growth, mechanics, and cytoskeletal filaments in shaping the bacterial cell. We predict that growing cells without MreB exhibit an instability that favors rounded cells. MreB can mechanically reinforce the cell wall and prevent the onset of instability. We propose that the overall bacterial shape is determined by a dynamic turnover of cell wall material that is controlled by mechanical stresses in the wall. The model affirms that morphological transformations with and without MreB are reversible, and quantitatively describes the growth of irregular shapes and cells undergoing division. The theory also suggests a unique coupling between mechanics and chemistry that can control organismal shapes in general.

Direct measurement of cell wall stress stiffening and turgor pressure in live bacterial cells

We study intact and bulging Escherichia coli cells using atomic force microscopy to separate the contributions of the cell wall and turgor pressure to the overall cell stiffness. We find strong evidence of power-law stress stiffening in the E. coli cell wall, with an exponent of 1.22±0.12, such that the wall is significantly stiffer in intact cells (E=23±8  MPa and 49±20  MPa in the axial and circumferential directions) than in unpressurized sacculi. These measurements also indicate that the turgor pressure in living cells E. coli is 29±3  kPa.

Mechanisms for maintaining cell shape in rod-shaped Gram-negative bacteria

For the rod-shaped Gram-negative bacterium Escherichia coli, changes in cell shape have critical consequences for motility, immune system evasion, proliferation and adhesion. For most bacteria, the peptidoglycan cell wall is both necessary and sufficient to determine cell shape. However, how the synthesis machinery assembles a peptidoglycan network with a robustly maintained micron-scale shape has remained elusive. To explore shape maintenance, we have quantified the robustness of cell shape in three Gram-negative bacteria in different genetic backgrounds and in the presence of an antibiotic that inhibits division. Building on previous modelling suggesting a prominent role for mechanical forces in shape regulation, we introduce a biophysical model for the growth dynamics of rod-shaped cells to investigate the roles of spatial regulation of peptidoglycan synthesis, glycan-strand biochemistry and mechanical stretching during insertion. Our studies reveal that rod-shape maintenance requires insertion to be insensitive to fluctuations in cell-wall density and stress, and even a simple helical pattern of insertion is sufficient for over sixfold elongation without significant loss in shape. In addition, we demonstrate that both the length and pre-stretching of newly inserted strands regulate cell width. In sum, we show that simple physical rules can allow bacteria to achieve robust, shape-preserving cell-wall growth.

The domain organization of the bacterial intermediate filament-like protein crescentin is important for assembly and function

Crescentin is a bacterial filament-forming protein that exhibits domain organization features found in metazoan intermediate filament (IF) proteins. Structure-function studies of eukaryotic IFs have been hindered by a lack of simple genetic systems and easily quantifiable phenotypes. Here we exploit the characteristic localization of the crescentin structure along the inner curvature of Caulobacter crescentus cells and the loss of cell curvature associated with impaired crescentin function to analyze the importance of the domain organization of crescentin. By combining biochemistry and ultrastructural analysis in vitro with cellular localization and functional studies, we show that crescentin requires its distinctive domain organization, and furthermore that different structural elements have distinct structural and functional contributions. The head domain can be functionally subdivided into two subdomains; the first (amino-terminal) is required for function but not assembly, while the second is necessary for structure assembly. The rod domain is similarly required for structure assembly, and the linker L1 appears important to prevent runaway assembly into nonfunctional aggregates. The data also suggest that the stutter and the tail domain have critical functional roles in stabilizing crescentin structures against disassembly by monovalent cations in the cytoplasm. This study suggests that the IF-like behavior of crescentin is a consequence of its domain organization, implying that the IF protein layout is an adaptable cytoskeletal motif, much like the actin and tubulin folds, that is broadly exploited for various functions throughout life from bacteria to humans.