Sensing the shape of a surface by intracellular filaments

Understanding the mechanisms that dictate the localization of cytoskeletal filaments is crucial for elucidating cell shape regulation in prokaryotes. The actin homolog MreB plays a pivotal role in maintaining the shape of many rod-shaped bacteria such as Escherichia coli by directing cell-wall synthesis according to local curvature cues. However, the basis of MreBs curvature-dependent localization has remained elusive. Here, we develop a biophysical model for the energetics of filament binding to a surface that integrates the complex interplay between filament twist and bending and the two-dimensional surface geometry. Our model predicts that the spatial localization of a filament like MreB with substantial intrinsic twist is governed by both the mean and Gaussian curvatures of the cell envelope, which strongly covary in rod-shaped cells. Using molecular dynamics simulations to estimate the mechanical properties of MreB filaments, we show that their thermodynamic preference for regions with lower mean and Gaussian curvatures matches experimental observations for physiologically relevant filament lengths of [~]50 nm. We find that the experimentally measured statistical curvature preference is maintained in the absence of filament motion and after a cycle of depolymerization, repolymerization, and membrane rebinding, indicating that equilibrium energetics can explain MreB localization. These findings provide critical insights into the physical principles underlying cytoskeletal filament localization, and suggest new design principles for synthetic shape sensing nanomaterials. Significance statementThe protein MreB, a homolog of eukaryotic actin, regulates the shape of bacteria like Escherichia coli by guiding new cell-wall insertion based on local curvature cues. However, the mechanism by which a nanometer-scale MreB filament "senses" the micron-scale curvature of the cell wall has remained a mystery. We introduce a biophysical model of the energetics of twisted and bent filaments bound to curved surfaces, which predicts that localization of filaments like MreB is sensitive to both mean and Gaussian curvature. The model captures experimentally measured curvature enrichment patterns and explains how MreB naturally localizes to saddle-shaped regions without energy-consuming processes. Beyond cell shape regulation, our work suggests design principles for synthetic systems that can sense and respond to surface shape.