Formation of protein-mediated bilayer tubes is governed by a snapthrough transition

Biophysical modeling of membrane curvature generation and curvature sensing by the glycocalyx

Generation of membrane curvature is fundamental to cellular function. Recent studies have established that the glycocalyx, a sugar-rich polymer layer at the cell surface, can generate membrane curvature. While there have been some theoretical efforts to understand the interplay between the glycocalyx and membrane bending, there remain open questions about how the properties of the glycocalyx affect membrane bending. For example, the relationship between membrane curvature and the density of glycosylated proteins on its surface remains unclear. In this work, we use polymer brush theory to develop a detailed biophysical model of the energetic interactions of the glycocalyx with the membrane. Using this model, we identify the conditions under which the glycocalyx can both generate and sense curvature. Our model predicts that the extent of membrane curvature generated depends on the grafting density of the glycocalyx and the backbone length of the polymers constituting the glycocalyx. Furthermore, when coupled with the intrinsic membrane properties such as spontaneous curvature and a line tension along the membrane, the curvature generation properties of the glycocalyx are enhanced. These predictions were tested experimentally by examining the propensity of glycosylated transmembrane proteins to drive the assembly of highly curved filopodial protrusions at the plasma membrane of adherent mammalian cells. Our model also predicts that the glycocalyx has curvature-sensing capabilities, in agreement with the results of our experiments. Thus, our study develops a quantitative framework for mapping the properties of the glycocalyx to the curvature generation capability of the membrane.

Glycocalyx-induced formation of membrane tubes

Tubular membrane structures are ubiquitous in cells and in the membranes of intracellular organelles such as the Golgi complex and the endoplasmic reticulum. Tubulation plays essential roles in numerous biological processes, including filopodia growth, trafficking, ion transport, and cellular motility. Understanding the fundamental mechanism of the formation of membrane tubes is thus an important problem in the fields of biology and biophysics. Though extensive studies have shown that tubes can be formed due to localized forces acting on the membrane or by the curvature induced by membrane-bound proteins, little is known about how membrane tubes are induced by glycocalyx, a sugar-rich layer at the cell surface. In this work, we develop a biophysical model that combines polymer physics theory and the Canham-Helfrich membrane theory to investigate how the glycocalyx generates cylindrical tubular protrusions on the cell membrane. Our results show that the glycocalyx alone can induce the formation of tubular membrane structures. This tube formation involves a first-order shape transition without any externally applied force or other curvature-inducing mechanisms. We also find that critical values of glycocalyx grafting density and glycopolymer length are needed to induce the formation of tubular structures. The presence of vertical actin force, line tension, and spontaneous curvature reduces the critical grafting density and length of polymer that triggers the formation of membrane tube, which suggests that the glycocalyx makes tube formation energetically more favorable when combined with an actin force, line tension, and spontaneous curvature.

Significance Statement

In many cells, the existence of glycocalyx, a thick layer of polymer meshwork comprising proteins and complex sugar chains coating the outside of the cell membrane, regulates the formation of membrane tubes. Here, we propose a theoretical model that combines polymer physics theory and the Canham-Helfrich membrane theory to study the formation of cylindrical tubular protrusions induced by the glycocalyx. Our findings indicate that glycocalyx plays an important role in the formation of membrane tubes. We find that there exists critical grafting density and length of polymer that triggers the formation of membrane tubes, and the glycocalyx-induced tube formation is facilitated when combined with actin forces, line tension, and spontaneous curvature. Our theoretical model has implications for understanding how biological membranes may form tubular structures.

Dynamins combine mechano-constriction and membrane remodeling to enable two-step mitochondrial fission via a 'snap-through' instability

Mitochondrial fission is controlled by dynamin proteins, the dysregulation of which is correlated with diverse diseases. Fission dynamins are GTP hydrolysis-driven mechanoenzymes that self-oligomerize into helical structures that constrict membrane to achieve fission, but details are not well understood. However, dynamins can also remodel membranes by inducing negative Gaussian curvature, the type of curvature required for completion of fission. Here, we examine how these drastically different mechanisms synergistically exert their influences on a membrane, via a mechanical model calibrated with small-angle X-ray scattering structural data. We find that free dynamin can trigger a "snap-through instability" that enforces a shape transition from an oligomer-confined cylindrical membrane to a drastically narrower catenoid-shaped neck within the spontaneous hemi-fission regime, in a manner that depends critically on the length of the confined tube. These results indicate how the combination of dynamin assembly, and paradoxically disassembly, can lead to diverse pathways to scission.

Dynamic framework for large-scale modeling of membranes and peripheral proteins

In this chapter, we present a novel computational framework to study the dynamic behavior of extensive membrane systems, potentially in interaction with peripheral proteins, as an alternative to conventional simulation methods. The framework effectively describes the complex dynamics in protein-membrane systems in a mesoscopic particle-based setup. Furthermore, leveraging the hydrodynamic coupling between the membrane and its surrounding solvent, the coarse-grained model grounds its dynamics in macroscopic kinetic properties such as viscosity and diffusion coefficients, marrying the advantages of continuum- and particle-based approaches. We introduce the theoretical background and the parameter-space optimization method in a step-by-step fashion, present the hydrodynamic coupling method in detail, and demonstrate the application of the model at each stage through illuminating examples. We believe this modeling framework to hold great potential for simulating membrane and protein systems at biological spatiotemporal scales, and offer substantial flexibility for further development and parametrization.

Inferring biophysical properties of membranes during endocytosis using machine learning

Endocytosis is a fundamental cellular process in eukaryotic cells that facilitates the transport of molecules into the cell. With the help of fluorescence microscopy and electron tomography, researchers have accumulated extensive geometric data of membrane shapes during endocytosis. These data contain rich information about the mechanical properties of membranes, which are hard to access via experiments due to the small dimensions of the endocytic patch. In this study, we propose an approach that combines machine learning with the Helfrich theory of membranes to infer the mechanical properties of membranes during endocytosis from a dataset of membrane shapes extracted from electron tomography. Our results demonstrate that machine learning can output solutions that both match the experimental profile and satisfy the membrane shape equations derived from Helfrich theory. The learning results show that during the early stage of endocytosis, the inferred membrane tension is negative, indicating the presence of strong compressive forces at the boundary of the endocytic invagination. Our method presents a generic framework for extracting membrane information from super-resolution imaging.

Cristae formation is a mechanical buckling event controlled by the inner mitochondrial membrane lipidome

Cristae are high-curvature structures in the inner mitochondrial membrane (IMM) that are crucial for ATP production. While cristae-shaping proteins have been defined, analogous lipid-based mechanisms have yet to be elucidated. Here, we combine experimental lipidome dissection with multi-scale modeling to investigate how lipid interactions dictate IMM morphology and ATP generation. When modulating phospholipid (PL) saturation in engineered yeast strains, we observed a surprisingly abrupt breakpoint in IMM topology driven by a continuous loss of ATP synthase organization at cristae ridges. We found that cardiolipin (CL) specifically buffers the inner mitochondrial membrane against curvature loss, an effect that is independent of ATP synthase dimerization. To explain this interaction, we developed a continuum model for cristae tubule formation that integrates both lipid and protein-mediated curvatures. This model highlighted a snapthrough instability, which drives IMM collapse upon small changes in membrane properties. We also showed that cardiolipin is essential in low-oxygen conditions that promote PL saturation. These results demonstrate that the mechanical function of cardiolipin is dependent on the surrounding lipid and protein components of the IMM.