Cell walls define a cell's shape in bacteria. The walls are rigid to resist large internal pressures, but remarkably plastic to adapt to a wide range of external forces and geometric constraints. Currently, it is unknown how bacteria maintain their shape. In this paper, we develop experimental and theoretical approaches and show that mechanical stresses regulate bacterial cell wall growth. By applying a precisely controllable hydrodynamic force to growing rod-shaped Escherichia coli and Bacillus subtilis cells, we demonstrate that the cells can exhibit two fundamentally different modes of deformation. The cells behave like elastic rods when subjected to transient forces, but deform plastically when significant cell wall synthesis occurs while the force is applied. The deformed cells always recover their shape. The experimental results are in quantitative agreement with the predictions of the theory of dislocation-mediated growth. In particular, we find that a single dimensionless parameter, which depends on a combination of independently measured physical properties of the cell, can describe the cell's responses under various experimental conditions. These findings provide insight into how living cells robustly maintain their shape under varying physical environments.cell shape | dislocation | defects | peptidoglycan | elasticity B iological systems exhibit many properties rarely found in condensed matter physics which are often caused by growth. When coupled to mechanical forces, growth can drive a wide range of cellular phenomena such as regulation of the eukaryotic cell morphology by actin networks (1), collective behavior in tissues (2), cell differentiation (3), and the shape and division of yeast and plant cells (4,5). Of fundamental interest as well as practical importance is understanding the relationship between growth, form, and structure of bacterial cell walls (6). Bacterial cell walls define a cell's morphology and maintain large internal (turgor) pressure. Many antibiotics target them to efficiently hamper cell growth and reproduction. As such, cell walls and their synthesis have been the subject of extensive biochemical (7) and biophysical (6) studies in the context of cell growth (8), cell shape (9), and cell division (10).Despite a long history (11), however, we are still far from being able to predict the shape or dimensions of any cells from first principles based on the information obtained from studies so far. Recent experimental work sheds new insights in this regard. For example, bacteria can significantly deform when grown with constraints (12, 13) and yet are able to recover their native shape (13). However, the mechanism underlying deformation and recovery, as well as the cues which regulate cell wall growth, have not been well-understood.We have developed combined experimental and theoretical methods to directly address how mechanical stresses are involved in the regulation of cell wall growth. Our experimental approach is illustrated in Fig. 1. Rod-shaped Escherichia coli or Bacillus ...

A polymer must reach a certain size to exhibit significant excluded-volume interactions and adopt a swollen random-walk configuration. We show that single-molecule measurements can sense the onset of swelling by modulating the effective chain size with force: as the force is reduced from a large value, the polymer is first highly aligned, then a Gaussian coil, then finally a swollen chain, with each regime exhibiting a distinct elasticity. We use this approach to quantify the structural parameters of poly(ethylene glycol) and show that they vary in the expected manner with changes in solvent.

The interactions of charged, flexible polymers with counterions of various valencies is a fundamental unsolved problem of polyelectrolyte physics, with specific applications to structure formation by nucleic acids, including RNA folding and DNA nanotechnology. We recently showed that single-molecule measurements of the elasticity of a model polyelectrolyte, denatured single-stranded DNA (d-ssDNA), can reveal details of the polymer’s electrostatic interactions on multiple length scales. Here, we explore the effects of various salts on d-ssDNA elasticity. In agreement with our prior results in NaCl, we find that d-ssDNA elastic response in KCl, MgCl2, and CaCl2 shows a low-force Pincus regime, with a weaker response at higher forces. The data in KCl are quantitatively identical to prior NaCl data, reflecting the universality of monovalent salt electrostatics. In contrast, the behavior of d-ssDNA in divalent salt solutions shows subtantial quantitative differences, including a nonlogarithmic high-force behavior and a heightened sensitivity of elasticity to changes in divalent salt concentration. We introduce a condensed-ion model that can quantitatively account for some aspects of this sensitivity.

Base-stacking is a key factor in the energetics that determines nucleic acid structure. We measure the tensile response of single-stranded DNA as a function of sequence and monovalent salt concentration to examine the effects of base-stacking on the mechanical and thermodynamic properties of single-stranded DNA. By comparing the elastic response of highly stacked poly(dA) and that of a polypyrimidine sequence with minimal stacking, we find that base-stacking in poly(dA) significantly enhances the polymer's rigidity. The unstacking transition of poly(dA) at high force reveals that the intrinsic electrostatic tension on the molecule varies significantly more weakly on salt concentration than mean-field predictions. Further, we provide a model-independent estimate of the free energy difference between stacked poly(dA) and unstacked polypyrimidine, finding it to be ∼-0.25 kBT/base and nearly constant over three orders of magnitude in salt concentration.

Single-molecule force-extension data are typically compared to ideal models of polymer behavior that ignore the effects of self-avoidance. Here, we demonstrate a link between single-molecule data and the scaling pictures of a real polymer. We measure a low-force elasticity regime where the extension L of chemically denatured single-stranded DNA grows as a power law with force f : L approximately f;{gamma} , with gamma approximately 0.60-0.69 . This compares favorably with the "tensile-blob" model of a self-avoiding polymer, which predicts gamma=2/3 . We show that the transition out of the low-force regime is highly salt dependent, and use the tensile-blob model to relate this effect to the salt dependence of the polymer's Kuhn length and excluded-volume parameter. We find that, contrary to the well-known Odijk-Skolnick-Fixman theory, the Kuhn length of single-stranded DNA is linearly proportional to the Debye length of the solution. Finally, we show that the low-force elasticity becomes linear (gamma=1) at approximately 3 M salt, and interpret this as a Theta point of the polymer. At this point, the force-extension data is best described by the wormlike chain model, from which we estimate the bare (nonelectrostatic) persistence length of the polymer to be approximately 0.6 nm .

Single-cell techniques have a long history of unveiling fundamental paradigms in biology. Recent improvements in the throughput, resolution, and availability of microfluidics, computational power, and genetically encoded fluorescence have led to a modern renaissance in microbial physiology. This resurgence in research activity has offered new perspectives on physiological processes such as growth, cell cycle, and cell size of model organisms such as Escherichia coli. We expect these single-cell techniques, coupled with the molecular revolution of biology’s recent half-century, to continue illuminating unforeseen processes and patterns in microorganisms, the bedrock of biological science. In this article we review major open questions in single-cell physiology, provide a brief introduction to the techniques for scientists of diverse backgrounds, and highlight some pervasive issues and their solutions.

We derive a thermodynamic identity that allows one to infer the change in the number of screening ions that are associated with a charged macromolecule as the macromolecule is continuously stretched. Applying this identity to force-extension data on both single-stranded and double-stranded DNA, we find that the number of polymer-associated ions depends nontrivially on both the bulk salt concentration and the bare rigidity of the polymer, with single-stranded DNA exhibiting a relatively large decrease in ion excess upon stretching. We rationalize these observations using simple models for polyelectrolyte extension.

Understanding of the conformational ensemble of flexible polyelectrolytes, such as single-stranded nucleic acids (ssNAs), is complicated by the interplay of chain backbone entropy and saltdependent electrostatic repulsions. Molecular elasticity measurements are sensitive probes of the statistical conformation of polymers and have elucidated ssNA conformation at low force, where electrostatic repulsion leads to a strong excluded volume effect, and at high force, where details of the backbone structure become important. Here, we report measurements of ssDNA and ssRNA elasticity in the intermediate-force regime, corresponding to 5-to 100-pN forces and 50-85% extension. These data are explained by a modified wormlike chain model incorporating an internal electrostatic tension. Fits to the elastic data show that the internal tension decreases with salt, from >5 pN under 5 mM ionic strength to near zero at 1 M. This decrease is quantitatively described by an analytical model of electrostatic screening that ascribes to the polymer an effective charge density that is independent of force and salt. Our results thus connect microscopic chain physics to elasticity and structure at intermediate scales and provide a framework for understanding flexible polyelectrolyte elasticity across a broad range of relative extensions.single-stranded nucleic acids | flexible polyelectrolytes | force spectroscopy | electrostatics S ingle-stranded nucleic acids (ssNAs) occur in many biological processes, such as RNA folding (1, 2) and DNA replication (3-5), generally in disordered conformations that fluctuate between various structures. These fluctuations create a significant entropic elasticity; thus, direct measurements of molecular elasticity (extension, X , as a function of applied force, fapp) constitute a powerful tool for studying the ssNA structural ensemble (6). In particular, measurements at a particular fapp are sensitive to the conformation within the corresponding tensile length, kB T /fapp (to within a scaling factor), where kB T is the thermal energy (7).ssNA structure-and that of flexible polyelectrolytes more generally-is complicated by the strong negative charge of the molecule. Multiple electrostatic and structural length scales share a similar magnitude (roughly 1 nm), disallowing models that consider only electrostatics or only backbone structure. In an uncharged flexible chain, the key structural scale is the persistence length, lp, defining the distance beyond which thermal fluctuations strongly bend the polymer. Electrostatic interactions introduce several competing length scales: the distance, b, between charged phosphates along the ssNA backbone; the distance over which electrostatic fields are screened in salty solution (the Debye length, κ −1 ); and the distance at which interactions between elementary charges in water have energy kB T (the Bjerrum length, lB ).Prior studies have elucidated ssNA elastic behavior in the lowand high-force limits. At low forces, corresponding to tensile lengths larger than κ −1 (i....