Studies of membrane proteins have revealed a direct link between the lipid environment and the structure and function of some of these proteins. Although some of these effects involve specific chemical interactions between lipids and protein residues, many can be understood in terms of protein-induced perturbations to the membrane shape. The free-energy cost of such perturbations can be estimated quantitatively, and measurements of channel gating in model systems of membrane proteins with their lipid partners are now confirming predictions of simple models.

The intensive reduced efficiency eta(r) is derived for thermoelectric power generation (in one dimension) from intensive fields and currents, giving eta(r)=(E x J) divided by (- inverted Delta)T x J(S). The overall efficiency is derivable from a thermodynamic state function, Phi=1 divided by u + alphaT, where we introduce u=J divided by kappa (inverted Delta)T as the relative current density. The method simplifies the computation and clarifies the physics behind thermoelectric devices by revealing a new materials property s=(sqrt[1+zT]-1) divided by (alphaT), which we call the compatibility factor. Materials with dissimilar compatibility factors cannot be combined by segmentation into an efficient thermoelectric generator because of constraints imposed on u. Thus, control of the compatibility factor s is, in addition to z, essential for efficient operation of a thermoelectric device, and thus will facilitate rational materials selection, device design, and the engineering of functionally graded materials.

Cells typically maintain characteristic shapes, but the mechanisms of self-organization for robust morphological maintenance remain unclear in most systems. Precise regulation of rod-like shape in Escherichia coli cells requires the MreB actin-like cytoskeleton, but the mechanism by which MreB maintains rod-like shape is unknown. Here, we use time-lapse and 3D imaging coupled with computational analysis to map the growth, geometry, and cytoskeletal organization of single bacterial cells at subcellular resolution. Our results demonstrate that feedback between cell geometry and MreB localization maintains rod-like cell shape by targeting cell wall growth to regions of negative cell wall curvature. Pulsechase labeling indicates that growth is heterogeneous and correlates spatially and temporally with MreB localization, whereas MreB inhibition results in more homogeneous growth, including growth in polar regions previously thought to be inert. Biophysical simulations establish that curvature feedback on the localization of cell wall growth is an effective mechanism for cell straightening and suggest that surface deformations caused by cell wall insertion could direct circumferential motion of MreB. Our work shows that MreB orchestrates persistent, heterogeneous growth at the subcellular scale, enabling robust, uniform growth at the cellular scale without requiring global organization.bacterial cytoskeleton | biophysical modeling | morphogenesis H ow cells maintain stable and defined morphologies is a fundamental question in all branches of life. Building cellularscale structures with the correct spatial architecture and mechanical properties requires that nanometer-scale proteins have the ability to detect and alter cell shape across multiple length scales. In walled organisms such as plants (1-5), fungi (6), and bacteria (7-10), morphogenesis is often achieved through an interplay between the cytoskeleton and cell wall synthesis. A central challenge in bacterial physiology is to understand the feedback between cell shape and the coordination of wall growth by the cytoskeleton.The cell wall plays a critical mechanical role in balancing turgor stress in virtually all bacteria and is both necessary and sufficient to define cell shape (11). The bacterial cell wall is a mesh-like network of sugar strands cross-linked by peptides (11,12). In rod-shaped Escherichia coli cells, cell wall growth occurs along the cylindrical body. Biophysical modeling has suggested that a random pattern of insertion cannot preserve cell shape (13), indicating that spatial coordination of the growth machinery is necessary for cell shape maintenance. Several lines of evidence demonstrate that the actin homolog MreB (14, 15) plays a major role in this coordination in most rod-shaped bacteria. The small molecule A22 depolymerizes MreB and causes a gradual transition from a rod-like to a spherical shape (15)(16)(17). This observation suggests that the disruption of MreB changes the patterning of new material insertion, although the nature of this...

Biological membranes are elastic media in which the presence of a transmembrane protein leads to local bilayer deformation. The energetics of deformation allow two membrane proteins in close proximity to influence each other's equilibrium conformation via their local deformations, and spatially organize the proteins based on their geometry. We use the mechanosensitive channel of large conductance (MscL) as a case study to examine the implications of bilayer-mediated elastic interactions on protein conformational statistics and clustering. The deformations around MscL cost energy on the order of 10 kBT and extend ∼3 nm from the protein edge, as such elastic forces induce cooperative gating, and we propose experiments to measure these effects. Additionally, since elastic interactions are coupled to protein conformation, we find that conformational changes can severely alter the average separation between two proteins. This has important implications for how conformational changes organize membrane proteins into functional groups within membranes.

Cellular membranes are a heterogeneous mix of lipids, proteins and small molecules. Special groupings enriched in saturated lipids and cholesterol form liquid-ordered domains, known as "lipid rafts," thought to serve as platforms for signaling, trafficking and material transport throughout the secretory pathway. Questions remain as to how the cell maintains small fluid lipid domains, through time, on a length scale consistent with the fact that no large-scale phase separation is observed. Motivated by these examples, we have utilized a combination of mechanical modeling and in vitro experiments to show that membrane morphology plays a key role in maintaining small domain sizes and organizing domains in a model membrane. We demonstrate that lipid domains can adopt a flat or dimpled morphology, where the latter facilitates a repulsive interaction that slows coalescence and helps regulate domain size and tends to laterally organize domains in the membrane.bilayer mechanics | lipid rafts | membrane morphology T he plasma and organelle membranes of cells are composed of a host of different lipids, lipophilic molecules, and membrane proteins (1). Together, they form a heterogeneous layer capable of regulating the flow of materials and signals into and out of the cell. Lipid structure and sterol content play a key role in bilayer organization, where steric interactions and energetically costly mismatch of lipid hydrophobic thickness result in a line tension that induces lateral phase separation (2). Saturated lipids and cholesterol are sequestered into liquid-ordered (L o ) domains, often known as "lipid rafts," distinct from an unsaturated liquid-disordered (L d ) phase (3-5). Domains whose lipids include saturated sphingolipids and cholesterol, with sizes in the range of ≈50-500 nm, have been implicated in a range of biological processes from lateral protein organization and virus uptake to signaling and plasma-membrane tension regulation (6-18). In the biological setting, maintenance of small domain size is thought to arise from a combination of lipid recycling and energetic barriers to domain coalescence (19)(20)(21) [potentially provided by transmembrane proteins (22)], ostensibly resulting in a stable distribution of domain sizes. These biological examples serve as a motivation to better understand the biophysical mechanisms that maintain small lipid domains over time and pose challenges to the classical theories of phase-separation and "domain ripening" [such as Cahn-Hilliard kinetics (23)].A simple physical model that describes the evolution of lipid domain size and position predicts that domains diffuse and coalesce, such that the number of domains constantly decreases, whereas the average domain size constantly increases (23). Indeed, models of 2D phase separation have been studied in detail for many physical systems (24-27), and where the phase boundary is unfavorable and characterized by an energy per unit length (28), the domain size grows continuously (23,29,30). However, membranes can adopt 3D morphologi...

BackgroundThe determination and regulation of cell morphology are critical components of cell-cycle control, fitness, and development in both single-cell and multicellular organisms. Understanding how environmental factors, chemical perturbations, and genetic differences affect cell morphology requires precise, unbiased, and validated measurements of cell-shape features.ResultsHere we introduce two software packages, Morphometrics and BlurLab, that together enable automated, computationally efficient, unbiased identification of cells and morphological features. We applied these tools to bacterial cells because the small size of these cells and the subtlety of certain morphological changes have thus far obscured correlations between bacterial morphology and genotype. We used an online resource of images of the Keio knockout library of nonessential genes in the Gram-negative bacterium Escherichia coli to demonstrate that cell width, width variability, and length significantly correlate with each other and with drug treatments, nutrient changes, and environmental conditions. Further, we combined morphological classification of genetic variants with genetic meta-analysis to reveal novel connections among gene function, fitness, and cell morphology, thus suggesting potential functions for unknown genes and differences in modes of action of antibiotics.Conclusions Morphometrics and BlurLab set the stage for future quantitative studies of bacterial cell shape and intracellular localization. The previously unappreciated connections between morphological parameters measured with these software packages and the cellular environment point toward novel mechanistic connections among physiological perturbations, cell fitness, and growth.Electronic supplementary materialThe online version of this article (doi:10.1186/s12915-017-0348-8) contains supplementary material, which is available to authorized users.

Summary In virtually all bacteria, the cell wall is crucial for mechanical integrity and for determining cell shape. Escherichia coli’s rod-like shape is maintained via the spatiotemporal patterning of cell-wall synthesis by the actin homologue MreB. Here, we transiently inhibited cell-wall synthesis in E. coli to generate cell-wall-deficient, spherical L-forms, and found that they robustly reverted to a rod-like shape within several generations after inhibition cessation. The chemical composition of the cell wall remained essentially unchanged during this process, as indicated by liquid chromatography. Throughout reversion, MreB localized to inwardly curved regions of the cell, and fluorescent cell wall labelling revealed that MreB targets synthesistothose regions. When exposed to the MreB inhibitor A22, reverting cells regrew a cell wall but failed to recover a rod-like shape. Our results suggest that MreB provides the geometric measure that allows E. coli to actively establish and regulate its morphology.

Assembly of protein complexes is a key mechanism for achieving spatial and temporal coordination in processes involving many enzymes. Growth of rod-shaped bacteria is a well-studied example requiring such coordination; expansion of the cell wall is thought to involve coordination of the activity of synthetic enzymes with the cytoskeleton via a stable complex. Here, we use singlemolecule tracking to demonstrate that the bacterial actin homolog MreB and the essential cell wall enzyme PBP2 move on timescales orders of magnitude apart, with drastically different characteristic motions. Our observations suggest that PBP2 interacts with the rest of the synthesis machinery through a dynamic cycle of transient association. Consistent with this model, growth is robust to large fluctuations in PBP2 abundance. In contrast to stable complex formation, dynamic association of PBP2 is less dependent on the function of other components of the synthesis machinery, and buffers spatially distributed growth against fluctuations in pathway component concentrations and the presence of defective components. Dynamic association could generally represent an efficient strategy for spatiotemporal coordination of protein activities, especially when excess concentrations of system components are inhibitory to the overall process or deleterious to the cell.