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Cells often migrate on curved surfaces inside the body, such as curved tissues, blood vessels, or highly curved protrusions of other cells. Recent in vitro experiments provide clear evidence that motile cells are affected by the curvature of the substrate on which they migrate, preferring certain curvatures to others, termed "curvotaxis." The origin and underlying mechanism that gives rise to this curvature sensitivity are not well understood. Here, we employ a "minimal cell" model which is composed of a vesicle that contains curved membrane protein complexes, that exert protrusive forces on the membrane (representing the pressure due to actin polymerization). This minimal-cell model gives rise to spontaneous emergence of a motile phenotype, driven by a lamellipodia-like leading edge. By systematically screening the behavior of this model on different types of curved substrates (sinusoidal, cylinder, and tube), we show that minimal ingredients and energy terms capture the experimental data. The model recovers the observed migration on the sinusoidal substrate, where cells move along the grooves (minima), while avoiding motion along the ridges. In addition, the model predicts the tendency of cells to migrate circumferentially on convex substrates and axially on concave ones. Both of these predictions are verified experimentally, on several cell types. Altogether, our results identify the minimization of membrane-substrate adhesion energy and binding energy between the membrane protein complexes as key players of curvotaxis in cell migration., Competing Interests: Competing interests statement:The authors declare no competing interest.

Phagocytosis is the process of engulfment and internalization of comparatively large particles by cells, and plays a central role in the functioning of our immune system. We study the process of phagocytosis by considering a simplified coarse grained model of a three-dimensional vesicle, having a uniform adhesion interaction with a rigid particle, and containing curved membrane-bound protein complexes or curved membrane nano-domains, which in turn recruit active cytoskeletal forces. Complete engulfment is achieved when the bending energy cost of the vesicle is balanced by the gain in the adhesion energy. The presence of curved (convex) proteins reduces the bending energy cost by self-organizing with a higher density at the highly curved leading edge of the engulfing membrane, which forms the circular rim of the phagocytic cup that wraps around the particle. This allows the engulfment to occur at much smaller adhesion strength. When the curved membrane-bound protein complexes locally recruit actin polymerization machinery, which leads to outward forces being exerted on the membrane, we found that engulfment is achieved more quickly and at a lower protein density. We consider spherical and non-spherical particles and found that non-spherical particles are more difficult to engulf in comparison to the spherical particles of the same surface area. For non-spherical particles, the engulfment time crucially depends on the initial orientation of the particles with respect to the vesicle. Our model offers a mechanism for the spontaneous self-organization of the actin cytoskeleton at the phagocytic cup, in good agreement with recent high-resolution experimental observations.

Membrane deformations induced by attached BAR superfamily domains could trigger or facilitate the growth of plasma membrane protrusions. The BAR domain family consists of BAR, F-BAR and I-BAR domains, each enforcing a different local curvature when attached to the membrane surface. Our theoretical study mainly focuses on the role of I-BAR in the membrane tubular deformations generated or stabilised by actin filaments. The influence of the area density of membrane attached BAR domains and their intrinsic curvature on the closed membrane shapes (vesicles) was investigated numerically. We derived an analytical approximative expression for the critical relative area density of BARs at which the membrane tubular protrusions on vesicles are most prominent. We have shown that the BARs with a higher intrinsic curvature induce thinner and longer cylindrical protrusions. The average orientation of the membrane attached BARs is altered when the vesicle shape is subjected to external force of growing actin rod-like structure inside a vesicle. The average orientation angle of membrane attached BARs may indicate whether the actin filaments are just stabilising the protrusion or generating it by stretching the vesicle., (Copyright © 2016 Elsevier B.V. All rights reserved.)

The detergent (Triton X-100, 4°C)-resistant membrane (DRM)-associated membrane proteins stomatin, sorcin, and synexin (anexin VII) exposed on the cytoplasmic side of membrane were investigated for their lateral distribution in relation to induced ganglioside(M1) (GM1) raft patches in flat (discocytic) and curved (echinocytic) human erythrocyte membrane. In discocytes, no accumulation of stomatin, sorcin, and synexin in cholera toxin subunit B (CTB) plus anti-CTB-induced GM1 patches was detected by fluorescence microscopy. In echinocytes, stomatin, sorcin, and synexin showed a similar curvature-dependent lateral distribution as GM1 patches by accumulating to spiculae induced by ionophore A23187 plus calcium. Stomatin was partly and synexin and sorcin were fully recruited to the spiculae. However, the DRM-associated proteins only partially co-localized with GM1 and were frequently distributed into different spiculae than GM1. The study indicates that stomatin, sorcin, and synexin are echinophilic membrane components that mainly locate outside GM1 rafts in the human erythrocyte membrane. Echinophilicity is suggested to contribute to the DRM association of a membrane component in general., (Copyright © 2010 Elsevier Inc. All rights reserved.)

Protrusions at the leading-edge of a cell play an important role in sensing the extracellular cues during cellular spreading and motility. Recent studies provided indications that these protrusions wrap (coil) around the extracellular fibers. However, the physics of this coiling process, and the mechanisms that drive it, are not well understood. We present a combined theoretical and experimental study of the coiling of cellular protrusions on fibers of different geometry. Our theoretical model describes membrane protrusions that are produced by curved membrane proteins that recruit the protrusive forces of actin polymerization, and identifies the role of bending and adhesion energies in orienting the leading-edges of the protrusions along the azimuthal (coiling) direction. Our model predicts that the cell's leading-edge coils on fibers with circular cross-section (above some critical radius), but the coiling ceases for flattened fibers of highly elliptical cross-section. These predictions are verified by 3D visualization and quantitation of coiling on suspended fibers using Dual-View light-sheet microscopy (diSPIM). Overall, we provide a theoretical framework, supported by experiments, which explains the physical origin of the coiling phenomenon. The leading edges of cellular protrusions coil around extracellular fibers and other fibrous structures such as axons. Combining 3D imaging with theoretical models, the authors show that coiling occurs naturally on curved surfaces due to energy minimization. [ABSTRACT FROM AUTHOR]

Migratory cells use distinct motility modes to navigate different microenvironments, but it is unclear whether these modes rely on the same core set of polarity components. To investigate this, we disrupted actin-related protein 2/3 (Arp2/3) and the WASP-family verprolin homologous protein (WAVE) complex, which assemble branched actin networks that are essential for neutrophil polarity and motility in standard adherent conditions. Surprisingly, confinement rescues polarity and movement of neutrophils lacking these components, revealing a processive bleb-based protrusion program that is mechanistically distinct from the branched actin-based protrusion program but shares some of the same core components and underlying molecular logic. We further find that the restriction of protrusion growth to one site does not always respond to membrane tension directly, as previously thought, but may rely on closely linked properties such as local membrane curvature. Our work reveals a hidden circuit for neutrophil polarity and indicates that cells have distinct molecular mechanisms for polarization that dominate in different microenvironments. [ABSTRACT FROM AUTHOR]

Abstract: Positively charged proteins can attach themselves to the negatively charged outer surface of biological cell membranes and liposomes. In this work, the influence of the intrinsic shape of the membrane-attached proteins on the elastic properties of the membrane is considered theoretically. It is shown that attachment of anisotropic proteins to the outer surface of biological membranes may induce tubulation of the membrane. The attachment of semi-flexible rod-like proteins increases the local bending constant, while the attachment of semi-flexible plate-like anisotropic proteins may also reduce the local bending constant of the membrane. The role of the hydrophobic protrusion of the attached protein which is embedded in the outer membrane layer is also discussed. [Copyright &y& Elsevier]

The distribution of raft markers in curved membrane exvaginations and invaginations, induced in human erythrocytes by amphiphile-treatment or increased cytosolic calcium level, was studied by fluorescence microscopy. Cholera toxin subunit B and antibodies were used to detect raft components. Ganglioside GM1 was enriched in membrane exvaginations (spiculae) induced by cytosolic calcium and amphiphiles. Stomatin and the cytosolic proteins synexin and sorcin were enriched in spiculae when induced by cytosolic calcium, but not in spiculae induced by amphiphiles. No enrichment of flotillin-1 was detected in spiculae. Analyses of the relative protein content of released exovesicles were in line with the microscopic observations. In invaginations induced by amphiphiles, the enrichment of ganglioside GM1, but not of the integral membrane proteins flotillin-1 and stomatin, was observed. Based on the experimental results and theoretical considerations we suggest that membrane skeleton-detached, laterally mobile rafts may sort into curved or flat membrane regions dependent on their intrinsic molecular shape and/or direct interactions between the raft elements. [ABSTRACT FROM AUTHOR]

Tunneling nanotubes (TNTs) are thin membranous tubes that interconnect cells, representing a novel route of cell-to-cell communication and spreading of pathogens. TNTs form between many cell types, yet their inception mechanisms remain elusive. We review in this study general concepts related to the formation and stability of membranous tubular structures with a focus on a deviatoric elasticity model of membrane nanodomains. We review experimental evidence that tubular structures initiate from local membrane bending facilitated by laterally distributed proteins or anisotropic membrane nanodomains. We further discuss the numerical results of several theoretical and simulation models of nanodomain segregation suggesting the mechanisms of TNT inception and stability. We discuss the coupling of nanodomain segregation with the action of protruding cytoskeletal forces, which are mostly provided in eukaryotic cells by the polymerization of f-actin, and review recent inception mechanisms of TNTs in relation to motor proteins. [ABSTRACT FROM AUTHOR]

Abstract: Recent studies have demonstrated that actin filaments are not crucial for the short-term stability of tubular membrane protrusions originating from the cell surface. It has also been demonstrated that prominin nanodomains and curvature inducing I-BAR proteins could account for the stability of the membrane protrusion. Here we constructed an axisymmetric model of a membrane protrusion that excludes actin filaments in order to investigate the contributions of prominin nanodomains (rafts) and I-BAR proteins to the membrane protrusion stability. It was demonstrated that prominin nanodomains and I-BAR proteins can stabilize the membrane protrusion only over a specific range of spontaneous curvature. On the other hand, high spontaneous curvature and/or high density of I-BAR proteins could lead to system instability and to non-uniform contraction in the radial direction of the membrane protrusion. In agreement with previous studies, it was also shown that the isotropic bending energy of lipids is not sufficient to explain the stability of the observed tubular membrane protrusion without actin filaments. [Copyright &y& Elsevier]

Abstract: The detergent (Triton X-100, 4°C)-resistant membrane (DRM)-associated membrane proteins stomatin, sorcin, and synexin (anexin VII) exposed on the cytoplasmic side of membrane were investigated for their lateral distribution in relation to induced gangliosideM1 (GM1) raft patches in flat (discocytic) and curved (echinocytic) human erythrocyte membrane. In discocytes, no accumulation of stomatin, sorcin, and synexin in cholera toxin subunit B (CTB) plus anti-CTB-induced GM1 patches was detected by fluorescence microscopy. In echinocytes, stomatin, sorcin, and synexin showed a similar curvature-dependent lateral distribution as GM1 patches by accumulating to spiculae induced by ionophore A23187 plus calcium. Stomatin was partly and synexin and sorcin were fully recruited to the spiculae. However, the DRM-associated proteins only partially co-localized with GM1 and were frequently distributed into different spiculae than GM1. The study indicates that stomatin, sorcin, and synexin are echinophilic membrane components that mainly locate outside GM1 rafts in the human erythrocyte membrane. Echinophilicity is suggested to contribute to the DRM association of a membrane component in general. [ABSTRACT FROM AUTHOR]