Polar collective motion commonly arises from alignment interactions, particle anisotropy, or an imposed directional bias. Here we identify a distinct route to polar order that does not rely on alignment interactions between the active particles. We show that non-aligning active Brownian particles embedded in a dense passive medium can develop polar coherence when confined to a compact curved surface. Persistent active motion redistributes stress through the host and creates passive-depleted regions. When the stress-spreading length becomes comparable to the sphere radius, these regions merge into elongated scars that channel active motion and, through feedback with the active flux, promote a common direction of motion. Removing the passive host suppresses polar coherence even though the active particles continue to cluster on the same sphere. Our results establish an environment-mediated route to collective polarity in which symmetry breaking emerges from the coupling between active motion, passive stress redistribution, and compact geometry.
Endocytosis is an essential biological process for the trafficking of macromolecules (cargo) and membrane proteins in cells. In yeast cells, this involves the invagination of a tubular structure on the membrane and the formation of endocytic vesicles. Bin/Amphiphysin/Rvs (BAR) proteins holding a crescent-shape are generally assumed to be the active player to squeeze the tubular structure and pinch off the vesicle by forming a scaffold on the side of the tubular membrane. Here we use the extended Helfrich model to theoretically investigate how BAR proteins help drive the formation of vesicles v…
The adhesive and frictional response of an AFM tip connected to a substrate through supramolecular host-guest complexes is investigated by dynamic Monte Carlo simulations. The variation of the pull-off force with the unloading rate recently observed in experiments is here unraveled by evidencing a simultaneous (progressive) break of the bonds at fast (slow) rates. The model reveals the origin of the observed plateaus in the retraction force as a function of tip-surface distance, showing that they ensue from the tip geometrical features. In lateral sliding, the model exhibits a wide range of dy…
Plasma membrane tubes are ubiquitous in cellular membranes and in the membranes of intracellular organelles. They play crucial roles in trafficking, ion transport, and cellular motility. The formation of plasma membrane tubes can be due to localized forces acting on the membrane or by curvature-induced by membrane-bound proteins. Here, we present a mathematical framework to model cylindrical tubular protrusions formed by proteins that induce anisotropic spontaneous curvature. Our analysis revealed that the tube radius depends on an effective tension that includes contributions from the bare me…
Particles in soft matter often interact through the deformation field they create, as in the "cheerios" effect or the curvature-mediated interactions of membrane proteins. Using a simple model for field-mediated interactions between passive particles, or active particles that switch conformation randomly or synchronously, we derive generic results concerning multibody interactions, activity driven patterns, and retardation effects.
The shapes of cell membranes are largely regulated by membrane associated, curvature active, proteins. We use a numerical model of the membrane with elongated membrane inclusions, recently developed by us, which posses spontaneous directional curvatures that could be different along and perpendicular to its long axis. We show that, due to membrane mediated interactions these curvature inducing membrane nematogens can oligomerize spontaneously, even at low concentrations, and change the local shape of the membrane. We demonstrate that for a large group of such inclusions, where the two spontane…
We investigate the phenomenon of protein induced tubulation of lipid bilayer membranes within a continuum framework using Monte Carlo simulations coupled with the Widom insertion technique to compute excess chemical potentials. Tubular morphologies are spontaneously formed when the density and the curvature-field strength of the membrane bound proteins exceed their respective thresholds and this transition is marked by a sharp drop in the excess chemical potential. We find that the planar to tubular transition can be described by a micellar model and that the corresponding free energy barrier …
Particles embedded in a fluctuating interface experience forces and torques mediated by the deformations and by the thermal fluctuations of the medium. Considering a system of two cylinders bound to a fluid membrane we show that the entropic contribution enhances the curvature-mediated repulsion between the two cylinders. This is contrary to the usual attractive Casimir force in the absence of curvature-mediated interactions. For a large distance between the cylinders, we retrieve the renormalization of the surface tension of a flat membrane due to thermal fluctuations.
The interplay of membrane proteins is vital for many biological processes, such as cellular transport, cell division, and signal transduction between nerve cells. Theoretical considerations have led to the idea that the membrane itself mediates protein self-organization in these processes through minimization of membrane curvature energy. Here, we present a combined experimental and numerical study in which we quantify these interactions directly for the first time. In our experimental model system we control the deformation of a lipid membrane by adhering colloidal particles. Using confocal m…
Torques on interfaces can be described by a divergence-free tensor which is fully encoded in the geometry. This tensor consists of two terms, one originating in the couple of the stress, the other capturing an intrinsic contribution due to curvature. In analogy to the description of forces in terms of a stress tensor, the torque on a particle can be expressed as a line integral along any contour surrounding the particle. Interactions between particles mediated by a fluid membrane are studied within this framework. In particular, torque balance places a strong constraint on the shape of the mem…
Cellular membranes exhibit a large variety of shapes, strongly coupled to their function. Many biological processes involve dynamic reshaping of membranes, usually mediated by proteins. This interaction works both ways: while proteins influence the membrane shape, the membrane shape affects the interactions between the proteins. To study these membrane-mediated interactions on closed and anisotropically curved membranes, we use colloids adhered to ellipsoidal membrane vesicles as a model system. We find that two particles on a closed system always attract each other, and tend to align with the…
Nematic colloids exhibit a large diversity of topological defects and structures induced by colloidal particles in the orientationally ordered liquid crystal host fluids. These defects and field configurations define elastic interactions and medium-mediated self-assembly, as well as serve as model systems in exploiting the richness of interactions between topologies and geometries of colloidal surfaces, nematic fields, and topological singularities induced by particles in the nematic bulk and at nematic-colloidal interfaces. Here we demonstrate formation of quarter-strength surface-pinned disc…
We study the collective behavior of inclusions inducing local anisotropic curvatures in a flexible fluid membrane. The N-body interaction energy for general anisotropic inclusions is calculated explicitly, including multi-body interactions. Long-range attractive interactions between inclusions are found to be sufficiently strong to induce aggregation. Monte Carlo simulations show a transition from compact clusters to aggregation on lines or circles. These results might be relevant to proteins in biological membranes or colloidal particles bound to surfactant membranes.
A very recent observation on the membrane mediated attraction and ordered aggregation of colloidal particles bound to giant phospholipid vesicles (I. Koltover, J. O. Rädler, C. R. Safinya, Phys. Rev. Lett. {\bf 82}, 1991(1999)) is investigated theoretically within the frame of Helfrich curvature elasticity theory of lipid bilayer fluid membrane. Since the concave or waist regions of the vesicle possess the highest local bending energy density, the aggregation of colloidal beads on these places can reduce the elastic energy in maximum. Our calculation shows that a bead in the concave region low…
Biological membranes are shaped by various proteins that either generate inward or outward membrane curvature. In this article, we investigate the membrane morphologies induced by mixtures of arc-shaped particles with coarse-grained modeling and simulations. The particles bind to the membranes either with their inward, concave side or their outward, convex side and, thus, generate membrane curvature of opposite sign. We find that small fractions of convex-binding particles can stabilize three-way junctions of membrane tubules, as suggested for the protein lunapark in the endoplasmic reticulum …
Directed assembly of colloids is an exciting field in materials science to form structures with new symmetries and responses. Fluid interfaces have been widely exploited to make densely packed ordered structures. We have been studying how interface curvature can be used in new ways to guide structure formation. On a fluid interface, the area of the deformation field around adsorbed microparticles depends on interface curvature; particles move to minimize the excess area of the distortions that they make in the interface. For particles that are sufficiently small, this area decreases as particl…
We analytically study membrane mediated interactions between inclusions embedded in a tubular membrane. We model inclusions as constraints coupled to the curvature tensor of the membrane tube. First, as special test cases, we analyze the interaction between ring and rod shaped inclusions. Using Monte Carlo simulations, we further show how point-like inclusions interact to form linear aggregates. Our results reveal that depending on the hard-core radius of the inclusions, they arrange into either lines or rings to globally minimize the curvature energy of the membrane.
In many biological systems, the curvature of the surfaces cells live on influence their collective properties. Curvature should likewise influence the behavior of active colloidal particles. We show using molecular simulation of self-propelled active particles on surfaces of Gaussian curvature (both positive and negative) that curvature sign and magnitude can alter the system's collective behavior. Curvature acts as a geometrical lens and shifts the critical density of motility-induced phase separation (MIPS) to lower values for positive curvature and higher values for negative curvature, whic…
The assembly of banana-shaped rodlike proteins on membranes, and the associated membrane shape transformations, are investigated by analytical theory and coarse-grained simulations. The membrane-mediated interactions between two banana-shaped inclusions are derived theoretically using a point-like formalism based on fixed anisotropic curvatures, both for zero surface tension and for finite surface tension. On a larger scale, the interactions between assemblies of such rodlike inclusions are determined analytically. Meshless membrane simulations are performed in the presence of a large number o…
