Physical Principles of Membrane Shape Regulation by the Glycocalyx.

Cells bend their plasma membranes into highly curved forms to interact with the local environment, but how shape generation is regulated is not fully resolved. Here, we report a synergy between shape-generating processes in the cell interior and the external organization and composition of the cell-surface glycocalyx. Mucin biopolymers and long-chain polysaccharides within the glycocalyx can generate entropic forces that favor or disfavor the projection of spherical and finger-like extensions from the cell surface. A polymer brush model of the glycocalyx successfully predicts the effects of polymer size and cell-surface density on membrane morphologies. Specific glycocalyx compositions can also induce plasma membrane instabilities to generate more exotic undulating and pearled membrane structures and drive secretion of extracellular vesicles. Together, our results suggest a fundamental role for the glycocalyx in regulating curved membrane features that serve in communication between cells and with the extracellular matrix.

Curving Cells Inside and Out: Roles of BAR Domain Proteins in Membrane Shaping and Its Cellular Implications.

Many cellular processes rely on precise and timely deformation of the cell membrane. While many proteins participate in membrane reshaping and scission, usually in highly specialized ways, Bin/amphiphysin/Rvs (BAR) domain proteins play a pervasive role, as they not only participate in many aspects of cell trafficking but also are highly versatile membrane remodelers. Subtle changes in the shape and size of the BAR domain can greatly impact the way in which BAR domain proteins interact with the membrane. Furthermore, the activity of BAR domain proteins can be tuned by external physical parameters, and so they behave differently depending on protein surface density, membrane tension, or membrane shape. These proteins can form 3D structures that mold the membrane and alter its liquid properties, even promoting scission under various circumstances.As such, BAR domain proteins have numerous roles within the cell. Endocytosis is among the most highly studied processes in which BAR domain proteins take on important roles. Over the years, a more complete picture has emerged in which BAR domain proteins are tied to almost all intracellular compartments; examples include endosomal sorting and tubular networks in the endoplasmic reticulum and T-tubules. These proteins also have a role in autophagy, and their activity has been linked with cancer. Here, we briefly review the history of BAR domain protein discovery, discuss the mechanisms by which BAR domain proteins induce curvature, and attempt to settle important controversies in the field. Finally, we review BAR domain proteins in the context of a cell, highlighting their emerging roles in cell signaling and organelle shaping.

Protein-membrane interactions: sensing and generating curvature.

Biological membranes are integral cellular structures that can be curved into various geometries. These curved structures are abundant in cells as they are essential for various physiological processes. However, curved membranes are inherently unstable, especially on nanometer length scales. To stabilize curved membranes, cells can utilize proteins that sense and generate membrane curvature. In this review, we summarize recent research that has advanced our understanding of interactions between proteins and curved membrane surfaces, as well as work that has expanded our ability to study curvature sensing and generation. Additionally, we look at specific examples of cellular processes that require membrane curvature, such as neurotransmission, clathrin-mediated endocytosis (CME), and organelle biogenesis.

Curvature-mediated rapid extravasation and penetration of nanoparticles against interstitial fluid pressure for improved drug delivery.

Elevated interstitial fluid pressure (IFP) within pathological tissues (e.g., tumors, obstructed kidneys, and cirrhotic livers) creates a significant hindrance to the transport of nanomedicine, ultimately impairing the therapeutic efficiency. Among these tissues, solid tumors present the most challenging scenario. While several strategies through reducing tumor IFP have been devised to enhance nanoparticle delivery, few approaches focus on modulating the intrinsic properties of nanoparticles to effectively counteract IFP during extravasation and penetration, which are precisely the stages obstructed by elevated IFP. Herein, we propose an innovative solution by engineering nanoparticles with a fusiform shape of high curvature, enabling efficient surmounting of IFP barriers during extravasation and penetration within tumor tissues. Through experimental and theoretical analyses, we demonstrate that the elongated nanoparticles with the highest mean curvature outperform spherical and rod-shaped counterparts against elevated IFP, leading to superior intratumoral accumulation and antitumor efficacy. Super-resolution microscopy and molecular dynamics simulations uncover the underlying mechanisms in which the high curvature contributes to diminished drag force in surmounting high-pressure differentials during extravasation. Simultaneously, the facilitated rotational movement augments the hopping frequency during penetration. This study effectively addresses the limitations posed by high-pressure impediments, uncovers the mutual interactions between the physical properties of NPs and their environment, and presents a promising avenue for advancing cancer treatment through nanomedicine.

Multistability of segmented rings by programming natural curvature.

Multistable structures have widespread applications in the design of deployable aerospace systems, mechanical metamaterials, flexible electronics, and multimodal soft robotics due to their capability of shape reconfiguration between multiple stable states. Recently, the snap-folding of rings, often in the form of circles or polygons, has shown the capability of inducing diverse stable configurations. The natural curvature of the rod segment (curvature in its stress-free state) plays an important role in the elastic stability of these rings, determining the number and form of their stable configurations during folding. Here, we develop a general theoretical framework for the elastic stability analysis of segmented rings (e.g., polygons) based on an energy variational approach. Combining this framework with finite element simulations, we map out all planar stable configurations of various segmented rings and determine the natural curvature ranges of their multistable states. The theoretical and numerical results are validated through experiments, which demonstrate that a segmented ring with a rectangular cross-section can show up to six distinct planar stable states. The results also reveal that, by rationally designing the segment number and natural curvature of the segmented ring, its one- or multiloop configuration can store more strain energy than a circular ring of the same total length. We envision that the proposed strategy for achieving multistability in the current work will aid in the design of multifunctional, reconfigurable, and deployable structures.

Molecular basis for curvature formation in SepF polymerization.

The self-assembly of proteins into curved structures plays an important role in many cellular processes. One good example of this phenomenon is observed in the septum-forming protein (SepF), which forms polymerized structures with uniform curvatures. SepF is essential for regulating the thickness of the septum during bacteria cell division. In Bacillus subtilis, SepF polymerization involves two distinct interfaces, the ß-ß and α-α interfaces, which define the assembly unit and contact interfaces, respectively. However, the mechanism of curvature formation in this step is not yet fully understood. In this study, we employed solid-state NMR (SSNMR) to compare the structures of cyclic wild-type SepF assemblies with linear assemblies resulting from a mutation of G137 on the ß-ß interface. Our results demonstrate that while the sequence differences arise from the internal assembly unit, the dramatic changes in the shape of the assemblies depend on the α-α interface between the units. We further provide atomic-level insights into how the angular variation of the α2 helix on the α-α interface affects the curvature of the assemblies, using a combination of SSNMR, cryo-electron microscopy, and simulation methods. Our findings shed light on the shape control of protein assemblies and emphasize the importance of interhelical contacts in retaining curvature.

Magnetochiral tunneling in paramagnetic Co1/3NbS2.

Electric currents have the intriguing ability to induce magnetization in nonmagnetic crystals with sufficiently low crystallographic symmetry. Some associated phenomena include the non-linear anomalous Hall effect in polar crystals and the nonreciprocal directional dichroism in chiral crystals when magnetic fields are applied. In this work, we demonstrate that the same underlying physics is also manifested in the electronic tunneling process between the surface of a nonmagnetic chiral material and a magnetized scanning probe. In the paramagnetic but chiral metallic compound Co1/3NbS2, the magnetization induced by the tunneling current is shown to become detectable by its coupling to the magnetization of the tip itself. This results in a contrast across different chiral domains, achieving atomic-scale spatial resolution of structural chirality. To support the proposed mechanism, we used first-principles theory to compute the chirality-dependent current-induced magnetization and Berry curvature in the bulk of the material. Our demonstration of this magnetochiral tunneling effect opens up an avenue for investigating atomic-scale variations in the local crystallographic symmetry and electronic structure across the structural domain boundaries of low-symmetry nonmagnetic crystals.

Tetraspanin proteins in membrane remodeling processes.

Membrane remodeling is a fundamental cellular process that is crucial for physiological functions such as signaling, membrane fusion and cell migration. Tetraspanins (TSPANs) are transmembrane proteins of central importance to membrane remodeling events. During these events, TSPANs are known to interact with themselves and other proteins and lipids; however, their mechanism of action in controlling membrane dynamics is not fully understood. Since these proteins span the membrane, membrane properties such as rigidity, curvature and tension can influence their behavior. In this Review, we summarize recent studies that explore the roles of TSPANs in membrane remodeling processes and highlight the unique structural features of TSPANs that mediate their interactions and localization. Further, we emphasize the influence of membrane curvature on TSPAN distribution and membrane domain formation and describe how these behaviors affect cellular functions. This Review provides a comprehensive perspective on the multifaceted function of TSPANs in membrane remodeling processes and can help readers to understand the intricate molecular mechanisms that govern cellular membrane dynamics.

Topological and geometric analysis of cell states in single-cell transcriptomic data.

Single-cell RNA sequencing (scRNA-seq) enables dissecting cellular heterogeneity in tissues, resulting in numerous biological discoveries. Various computational methods have been devised to delineate cell types by clustering scRNA-seq data, where clusters are often annotated using prior knowledge of marker genes. In addition to identifying pure cell types, several methods have been developed to identify cells undergoing state transitions, which often rely on prior clustering results. The present computational approaches predominantly investigate the local and first-order structures of scRNA-seq data using graph representations, while scRNA-seq data frequently display complex high-dimensional structures. Here, we introduce scGeom, a tool that exploits the multiscale and multidimensional structures in scRNA-seq data by analyzing the geometry and topology through curvature and persistent homology of both cell and gene networks. We demonstrate the utility of these structural features to reflect biological properties and functions in several applications, where we show that curvatures and topological signatures of cell and gene networks can help indicate transition cells and the differentiation potential of cells. We also illustrate that structural characteristics can improve the classification of cell types.

Biophysical aspects of migrasome organelle formation and their diverse cellular functions.

The transient cellular organelles known as migrasomes, which form during cell migration along retraction fibers, have emerged as a crutial factor in various fundamental cellular processes and pathologies. These membrane vesicles originate from local membrane swellings, encapsulate specific cytoplasmic content, and are eventually released to the extracellular environment or taken up by recipient cells. Migrasome biogenesis entails a sequential membrane remodeling process involving a complex interplay between various molecular factors such as tetraspanin proteins, and mechanical properties like membrane tension and bending rigidity. In this review, we summarize recent studies exploring the mechanism of migrasome formation. We emphasize how physical forces, together with molecular factors, shape migrasome biogenesis, and detail the involvement of migrasomes in various cellular processes and pathologies. A comprehensive understanding of the exact mechanism underlying migrasome formation and the identification of key molecules involved hold promise for advancing their therapeutic and diagnostic applications.

Curvature sensing as an emergent property of multiscale assembly of septins.

The ability of cells to sense and communicate their shape is central to many of their functions. Much is known about how cells generate complex shapes, yet how they sense and respond to geometric cues remains poorly understood. Septins are GTP-binding proteins that localize to sites of micrometer-scale membrane curvature. Assembly of septins is a multistep and multiscale process, but it is unknown how these discrete steps lead to curvature sensing. Here, we experimentally examine the time-dependent binding of septins at different curvatures and septin bulk concentrations. These experiments unexpectedly indicated that septins' curvature preference is not absolute but rather is sensitive to the combinations of membrane curvatures present in a reaction, suggesting that there is competition between different curvatures for septin binding. To understand the physical underpinning of this result, we developed a kinetic model that connects septins' self-assembly and curvature-sensing properties. Our experimental and modeling results are consistent with curvature-sensitive assembly being driven by cooperative associations of septin oligomers in solution with the bound septins. When combined, the work indicates that septin curvature sensing is an emergent property of the multistep, multiscale assembly of membrane-bound septins. As a result, curvature preference is not absolute and can be modulated by changing the physicochemical and geometric parameters involved in septin assembly, including bulk concentration, and the available membrane curvatures. While much geometry-sensitive assembly in biology is thought to be guided by intrinsic material properties of molecules, this is an important example of how curvature sensing can arise from multiscale assembly of polymers.

Membrane remodeling properties of the Parkinson's disease protein LRRK2.

Mutations in Leucine-rich repeat kinase 2 (LRRK2) are responsible for late-onset autosomal dominant Parkinson's disease. LRRK2 has been implicated in a wide range of physiological processes including membrane repair in the endolysosomal system. Here, using cell-free systems, we report that purified LRRK2 directly binds acidic lipid bilayers with a preference for highly curved bilayers. While this binding is nucleotide independent, LRRK2 can also deform low-curvature liposomes into narrow tubules in a guanylnucleotide-dependent but Adenosine 5'-triphosphate-independent way. Moreover, assembly of LRRK2 into scaffolds at the surface of lipid tubules can constrict them. We suggest that an interplay between the membrane remodeling and signaling properties of LRRK2 may be key to its physiological function. LRRK2, via its kinase activity, may achieve its signaling role at sites where membrane remodeling occurs.

Engineering contact curved interface with high-electronic-state active sites for high-performance potassium-ion batteries.

Potassium-ion batteries (PIBs) have attracted ever-increasing interest due to the abundant potassium resources and low cost, which are considered a sustainable energy storage technology. However, the graphite anodes employed in PIBs suffer from low capacity and sluggish reaction kinetics caused by the large radius of potassium ions. Herein, we report nitrogen-doped, defect-rich hollow carbon nanospheres with contact curved interfaces (CCIs) on carbon nanotubes (CNTs), namely CCI-CNS/CNT, to boost both electron transfer and potassium-ion adsorption. Density functional theory calculations validate that engineering CCIs significantly augments the electronic state near the Fermi level, thus promoting electron transfer. In addition, the CCIs exhibit a pronounced affinity for potassium ions, promoting their adsorption and subsequently benefiting potassium storage. As a result, the rationally designed CCI-CNS/CNT anode shows remarkable cyclic stability and rate capability. This work provides a strategy for enhancing the potassium storage performance of carbonaceous materials through CCI engineering, which can be further extended to other battery systems.

Computing geodesic paths encoding a curvature prior for curvilinear structure tracking.

In this paper, we introduce an efficient method for computing curves minimizing a variant of the Euler-Mumford elastica energy, with fixed endpoints and tangents at these endpoints, where the bending energy is enhanced with a user-defined and data-driven scalar-valued term referred to as the curvature prior. In order to guarantee that the globally optimal curve is extracted, the proposed method involves the numerical computation of the viscosity solution to a specific static Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE). For that purpose, we derive the explicit Hamiltonian associated with this variant model equipped with a curvature prior, discretize the resulting HJB PDE using an adaptive finite difference scheme, and solve it in a single pass using a generalized fast-marching method. In addition, we also present a practical method for estimating the curvature prior values from image data, designed for the task of accurately tracking curvilinear structure centerlines. Numerical experiments on synthetic and real-image data illustrate the advantages of the considered variant of the elastica model with a prior curvature enhancement in complex scenarios where challenging geometric structures appear.

Consensus, controversies, and conundrums of P4-ATPases: The emerging face of eukaryotic lipid flippases.

The cryo-EM resolution revolution has heralded a new era in our understanding of eukaryotic lipid flippases with a rapidly growing number of high-resolution structures. Flippases belong to the P4 family of ATPases (type IV P-type ATPases) that largely follow the reaction cycle proposed for the more extensively studied cation-transporting P-type ATPases. However, unlike the canonical P-type ATPases, no flippase cargos are transported in the phosphorylation half-reaction. Instead of being released into the intracellular or extracellular milieu, lipid cargos are transported to their destination at the inner leaflet of the membrane. Recent flippase structures have revealed multiple conformational states during the lipid transport cycle. Nonetheless, critical conformational states capturing the lipid cargo "in transit" are still missing. In this review, we highlight the amazing structural advances of these lipid transporters, discuss various perspectives on catalytic and regulatory mechanisms in the literature, and shed light on future directions in further deciphering the detailed molecular mechanisms of lipid flipping.

A human septin octamer complex sensitive to membrane curvature drives membrane deformation with a specific mesh-like organization.

Septins are cytoskeletal proteins interacting with the inner plasma membrane and other cytoskeletal partners. Being key in membrane remodeling processes, they often localize at specific micrometric curvatures. To analyze the behavior of human septins at the membrane and decouple their role from other partners, we used a combination of bottom-up in vitro methods. We assayed their ultrastructural organization, their curvature sensitivity, as well as their role in membrane reshaping. On membranes, human septins organize into a two-layered mesh of orthogonal filaments, instead of generating parallel sheets of filaments observed for budding yeast septins. This peculiar mesh organization is sensitive to micrometric curvature and drives membrane reshaping as well. The observed membrane deformations together with the filamentous organization are recapitulated in a coarse-grained computed simulation to understand their mechanisms. Our results highlight the specific organization and behavior of animal septins at the membrane as opposed to those of fungal proteins.

Tetraspanner-based nanodomains modulate BAR domain-induced membrane curvature.

The topography of biological membranes is critical for formation of protein and lipid microdomains. One prominent example in the yeast plasma membrane (PM) are BAR domain-induced PM furrows. Here we report a novel function for the Sur7 family of tetraspanner proteins in the regulation of local PM topography. Combining TIRF imaging, STED nanoscopy, freeze-fracture EM and membrane simulations we find that Sur7 tetraspanners form multimeric strands at the edges of PM furrows, where they modulate forces exerted by BAR domain proteins at the furrow base. Loss of Sur7 tetraspanners or Sur7 displacement due to altered PIP2 homeostasis leads to increased PM invagination and a distinct form of membrane tubulation. Physiological defects associated with PM tubulation are rescued by synthetic anchoring of Sur7 to furrows. Our findings suggest a key role for tetraspanner proteins in sculpting local membrane domains. The maintenance of stable PM furrows depends on a balance between negative curvature at the base which is generated by BAR domains and positive curvature at the furrows' edges which is stabilized by strands of Sur7 tetraspanners.

Transmembrane proteins tetraspanin 4 and CD9 sense membrane curvature.

Multiple membrane-shaping and remodeling processes are associated with tetraspanin proteins by yet unknown mechanisms. Tetraspanins constitute a family of proteins with four transmembrane domains present in every cell type. Prominent examples are tetraspanin4 and CD9, which are required for the fundamental cellular processes of migrasome formation and fertilization, respectively. These proteins are enriched in curved membrane structures, such as cellular retraction fibers and oocyte microvilli. The factors driving this enrichment are, however, unknown. Here, we revealed that tetraspanin4 and CD9 are curvature sensors with a preference for positive membrane curvature. To this end, we used a biomimetic system emulating membranes of cell retraction fibers and oocyte microvilli by membrane tubes pulled out of giant plasma membrane vesicles with controllable membrane tension and curvature. We developed a simple thermodynamic model for the partitioning of curvature sensors between flat and tubular membranes, which allowed us to estimate the individual intrinsic curvatures of the two proteins. Overall, our findings illuminate the process of migrasome formation and oocyte microvilli shaping and provide insight into the role of tetraspanin proteins in membrane remodeling processes.

Robotic swimming in curved space via geometric phase.

Locomotion by shape changes or gas expulsion is assumed to require environmental interaction, due to conservation of momentum. However, as first noted in [J. Wisdom, Science 299, 1865-1869 (2003)] and later in [E. Guéron, Sci. Am. 301, 38-45 (2009)] and [J. Avron, O. Kenneth, New J. Phys, 8, 68 (2006)], the noncommutativity of translations permits translation without momentum exchange in either gravitationally curved spacetime or the curved surfaces encountered by locomotors in real-world environments. To realize this idea which remained unvalidated in experiments for almost 20 y, we show that a precision robophysical apparatus consisting of motors driven on curved tracks (and thereby confined to a spherical surface without a solid substrate) can self-propel without environmental momentum exchange. It produces shape changes comparable to the environment's inverse curvatures and generates movement of [Formula: see text] cm per gait. While this simple geometric effect predominates over short time, eventually the dissipative (frictional) and conservative forces, ubiquitous in real systems, couple to it to generate an emergent dynamics in which the swimming motion produces a force that is counter-balanced against residual gravitational forces. In this way, the robot both swims forward without momentum and becomes fixed in place with a finite momentum that can be released by ceasing the swimming motion. We envision that our work will be of use in a broad variety of contexts, such as active matter in curved space and robots navigating real-world environments with curved surfaces.

Membrane insertion mechanism of the caveola coat protein Cavin1.

Caveolae are small plasma membrane invaginations, important for control of membrane tension, signaling cascades, and lipid sorting. The caveola coat protein Cavin1 is essential for shaping such high curvature membrane structures. Yet, a mechanistic understanding of how Cavin1 assembles at the membrane interface is lacking. Here, we used model membranes combined with biophysical dissection and computational modeling to show that Cavin1 inserts into membranes. We establish that initial phosphatidylinositol (4, 5) bisphosphate [PI(4,5)P2]-dependent membrane adsorption of the trimeric helical region 1 (HR1) of Cavin1 mediates the subsequent partial separation and membrane insertion of the individual helices. Insertion kinetics of HR1 is further enhanced by the presence of flanking negatively charged disordered regions, which was found important for the coassembly of Cavin1 with Caveolin1 in living cells. We propose that this intricate mechanism potentiates membrane curvature generation and facilitates dynamic rounds of assembly and disassembly of Cavin1 at the membrane.