Acceleration and suppression of banana-shaped-protein-induced tubulation by addition of small membrane inclusions of isotropic spontaneous curvatures

Which Coverages of Arc-Shaped Proteins Are Required for Membrane Tubulation?

Arc-shaped BIN/Amphiphysin/Rvs (BAR) domain proteins generate curvature by binding to membranes and induce membrane tubulation at sufficiently large protein coverages. For the amphiphysin N-BAR domain, Le Roux et al., Nat. Commun. 2021, 12, 6550, measured a threshold coverage of 0.44 ± 0.097 for nanotubules emerging from the supported lipid bilayer. In this article, we systematically investigate membrane tubulation induced by arc-shaped protein-like particles with coarse-grained modeling and simulations and determine the threshold coverages at different particle-particle interaction strengths and membrane spontaneous curvatures. In our simulations, the binding of arc-shaped particles induces a membrane shape transition from spherical vesicles to tubules at a particle threshold coverage of about 0.5, which is rather robust to variations of the direct attractive particle interactions or spontaneous membrane curvature in the coarse-grained model. Our study suggests that threshold coverages of around or slightly below 0.5 are a general requirement for membrane tubulation by arc-shaped BAR domain proteins.

Membrane domain formation induced by binding/unbinding of curvature-inducing molecules on both membrane surfaces

The domain formation of curvature-inducing molecules, such as peripheral or transmembrane proteins and conical surfactants, is studied in thermal equilibrium and nonequilibrium steady states using meshless membrane simulations. These molecules can bind to both surfaces of a bilayer membrane and also move to the opposite leaflet by a flip-flop. Under symmetric conditions for the two leaflets, the membrane domains form checkerboard patterns in addition to striped and spot patterns. The unbound membrane stabilizes the vertices of the checkerboard. Under asymmetric conditions, the domains form kagome-lattice and thread-like patterns. In the nonequilibrium steady states, a flow of the binding molecules between the upper and lower solutions can occur via flip-flop.

Modulation of self-organizing circuits at deforming membranes by intracellular and extracellular factors

Mechanical forces exerted to the plasma membrane induce cell shape changes. These transient shape changes trigger, among others, enrichment of curvature-sensitive molecules at deforming membrane sites. Strikingly, some curvature-sensing molecules not only detect membrane deformation but can also alter the amplitude of forces that caused to shape changes in the first place. This dual ability of sensing and inducing membrane deformation leads to the formation of curvature-dependent self-organizing signaling circuits. How these cell-autonomous circuits are affected by auxiliary parameters from inside and outside of the cell has remained largely elusive. Here, we explore how such factors modulate self-organization at the micro-scale and its emerging properties at the macroscale.

A Review of Mechanics-Based Mesoscopic Membrane Remodeling Methods: Capturing Both the Physics and the Chemical Diversity

Specialized classes of proteins, working together in a tightly orchestrated manner, induce and maintain highly curved cellular and organelles membrane morphology. Due to the various experimental constraints, including the resolution limits of imaging techniques, it is non-trivial to accurately elucidate interactions among the various components involved in membrane deformation. The spatial and temporal scales of the systems also make it formidable to investigate them using simulations with molecular details. Interestingly, mechanics-based mesoscopic models have been used with great success in recapitulating the membrane deformations observed in experiments. In this review, we collate together and discuss the various mechanics-based mesoscopic models for protein-mediated membrane deformation studies. In particular, we provide an elaborate description of a mesoscopic model where the membrane is modeled as a triangulated sheet and proteins are represented as either nematics or filaments. This representation allows us to explore the various aspects of protein-protein and protein-membrane interactions as well as examine the underlying mechanistic pathways for emergent behavior such as curvature-mediated protein localization and membrane deformation. We also put forward current efforts in the field towards back-mapping these mesoscopic models to finer-grained particle-based models-a framework that could be used to explore how molecular interactions propagate to physical scales and vice-versa. We end the review with an integrative-modeling-based road map where experimental imaging micrograph and biochemical data are combined with mesoscopic and molecular simulations methods in a theoretically consistent manner to faithfully recapitulate the multiple length and time scales in the membrane remodeling processes.

Membrane Remodeling Due to a Mixture of Multiple Types of Curvature Proteins

We present an extension of the Monte Carlo based mesoscopic membrane model, where the membrane is represented as a dynamically triangulated surface and the proteins are modeled as anisotropic inclusions formulated as in-plane nematic field variables adhering to the deformable elastic sheet. In the extended model, we have augmented the Hamiltonian to study membrane deformation due to a mixture of multiple types of curvature generating proteins. This feature opens the door for understanding how multiple kinds of curvature-generating proteins may be working in a coordinated manner to induce desired membrane morphologies. For example, among other things, we study membrane deformations and tubulation due to a mixture of positive and negative curvature proteins as mimics of various proteins from BAR domain family. We also study the effect of membrane anisotropy that manifests as differential binding affinity and organization of curvature proteins, leading to insights into the tightly regulated cargo sorting and transport processes. Our simulation results show different morphology of deformed vesicles that depend on membrane tension, the curvatures and number of the participating proteins as well as on protein-protein and membrane-protein interactions.

Membrane shape deformation induced by curvature-inducing proteins consisting of chiral crescent binding and intrinsically disordered domains

Curvature-inducing proteins containing a bin/amphiphysin/Rvs domain often have intrinsically disordered domains. Recent experiments have shown that these disordered chains enhance curvature sensing and generation. Here, we report on the modification of protein–membrane interactions by disordered chains using meshless membrane simulations. The protein and bound membrane are modeled together as a chiral crescent protein rod with two excluded-volume chains. As the chain length increases, the repulsion between them reduces the cluster size of the proteins. It induces spindle-shaped vesicles and a transition between arc-shaped and circular protein assemblies in a disk-shaped vesicle. For flat membranes, an intermediate chain length induces many tubules owing to the repulsion between the protein assemblies, whereas longer chains promote perpendicular elongation of tubules. Moreover, protein rods with zero rod curvature and sufficiently long chains stabilize the spherical buds. For proteins with a negative rod curvature, an intermediate chain length induces a rugged membrane with branched protein assemblies, whereas longer chains induce the formation of tubules with periodic concave-ring structures.

Binding of anisotropic curvature-inducing proteins onto membrane tubes

Bin/Amphiphysin/Rvs superfamily proteins and other curvature-inducing proteins have anisotropic shapes and anisotropically bend biomembranes. Here, we report how the anisotropic proteins bind the membrane tube and are orientationally ordered using mean-field theory including an orientation-dependent excluded volume. The proteins exhibit a second-order or first-order nematic transition with increasing protein density depending on the radius of the membrane tube. The tube curvatures for the maximum protein binding and orientational order are different and varied by the protein density and rigidity. As the external force along the tube axis increases, a first-order transition from a large tube radius with low protein density to a small radius with high density occurs once, and subsequently, the protein orientation tilts to the tube-axis direction. When an isotropic bending energy is used for the proteins with an elliptic shape, the force-dependence curves become symmetric and the first-order transition occurs twice. This theory quantitatively reproduces the results of meshless membrane simulation for short proteins, whereas deviations are seen for long proteins owing to the formation of protein clusters.

Binding of curvature-inducing proteins onto tethered vesicles

A tethered vesicle, which consists of a cylindrical membrane tube and a spherical vesicle, is produced by a mechanical force that is experimentally imposed by optical tweezers and a micropipette. This tethered vesicle is employed for examining the curvature sensing of curvature-inducing proteins. In this study, we clarify how the binding of proteins with a laterally isotropic spontaneous curvature senses and generates the membrane curvatures of the tethered vesicle using mean-field theory and meshless membrane simulation. The force-dependence curves of the protein density in the membrane tube and the tube curvature are reflection symmetric and point symmetric, respectively, from the force point, in which the tube has a sensing curvature. The bending rigidity and spontaneous curvature of the bound proteins can be estimated from these force-dependence curves. First-order transitions can occur between low and high protein densities in the tube at both low and high force amplitudes. The simulation results of the homogeneous phases agree very well with the theoretical predictions. In addition, beaded-necklace-like tubes with microphase separation are found in the simulation.

Vesicle budding induced by binding of curvature-inducing proteins

Vesicle budding induced by protein binding that generates an isotropic spontaneous curvature is studied using a mean-field theory. Many spherical buds are formed via protein binding. As the binding chemical potential increases, the proteins first bind to the buds and then to the remainder of the vesicle. For a high spontaneous curvature and/or high bending rigidity of the bound membrane, it is found that a first-order transition occurs between a small number of large buds and a large number of small buds. These two states coexist around the transition point. The proposed scheme is simple and easily applicable to many interaction types, so we investigate the effects of interprotein interactions, the protein-insertion-induced changes in area, the variation of the saddle-splay modulus, and the area-difference-elasticity energy. The differences in the preferred curvatures for curvature sensing and generation are also clarified.

Membrane morphologies induced by mixtures of arc-shaped particles with opposite curvature

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 of cells. For comparable fractions of concave-binding and convex-binding particles, we observe lines of particles of the same type, and diverse membrane morphologies with grooves and bulges induced by these particle lines. The alignment and segregation of the particles is driven by indirect, membrane-mediated interactions.

Detachment of a fluid membrane from a substrate and vesiculation

The detachment dynamics of a fluid membrane with isotropic spontaneous curvature from a flat substrate are studied by using meshless membrane simulations. The membrane is detached from an open edge leading to vesicle formation. With strong adhesion, the competition between the bending and adhesion energies determines the minimum value of the spontaneous curvature for the detachment. In contrast, with weak adhesion, detachment occurs at smaller spontaneous curvatures due to the membrane thermal undulation. When parts of the membrane are pinned on the substrate, the detachment becomes slower and a remaining membrane patch forms straight or concave membrane edges. The edge undulation induces vesiculation of long strips and disk-shaped patches. Therefore, membrane rolling is obtained only for membrane strips shorter than the wavelength for deformation into unduloids. This suggests that the rolling observed for Ca²⁺-dependent membrane-binding proteins annexins A3, A4, A5, and A13 results from the anisotropic spontaneous curvature induced by the proteins.

Shape transition from elliptical to cylindrical membrane tubes induced by chiral crescent-shaped protein rods

Proteins often form chiral assembly structures on a biomembrane. However, the role of the chirality in the interaction with an achiral membrane is poorly understood. Here, we report how chirality of crescent-shaped protein rods changes their assembly and tubulation using meshless membrane simulations. The achiral rods deformed the membrane tube into an elliptical shape by stabilizing the edges of the ellipse. In contrast, the chiral rods formed a helical assembly that generated a cylindrical membrane tube with a constant radius in addition to the elliptical tube. This helical assembly could be further stabilized by the direct side-to-side attraction between the protein rods. The chirality also promotes the tubulation from a flat membrane. These results agree with experimental findings of the constant radius of membrane tubules induced by the Bin/Amphiphysin/Rvs (BAR) superfamily proteins.

Theoretical study of vesicle shapes driven by coupling curved proteins and active cytoskeletal forces

Eukaryote cells have a flexible shape, which dynamically changes according to the function performed by the cell. One mechanism for deforming the cell membrane into the desired shape is through the expression of curved membrane proteins. Furthermore, these curved membrane proteins are often associated with the recruitment of the cytoskeleton, which then applies active forces that deform the membrane. This coupling between curvature and activity was previously explored theoretically in the linear limit of small deformations, and low dimensionality. Here we explore the unrestricted shapes of vesicles that contain active curved membrane proteins, in three-dimensions, using Monte-Carlo numerical simulations. The activity of the proteins is in the form of protrusive forces that push the membrane outwards, as may arise from the cytoskeleton of the cell due to actin or microtubule polymerization occurring near the membrane. For proteins that have an isotropic convex shape, the additional protrusive force enhances their tendency to aggregate and form membrane protrusions (buds). In addition, we find another transition from deformed spheres with necklace type aggregates, to flat pancake-shaped vesicles, where the curved proteins line the outer rim. This second transition is driven by the active forces, coupled to the spontaneous curvature, and the resulting configurations may shed light on the formation of sheet-like protrusions and lamellipodia of adhered and motile cells.

Binding constant of membrane-anchored receptors and ligands that induce membrane curvatures

Cell adhesion is crucial for immune response, tissue formation, and cell locomotion. The adhesion process is mediated by the specific binding of membrane-anchored receptor and ligand proteins. These adhesion proteins are in contact with the membranes and may generate curvature, which has been shown for a number of membrane proteins to play an important role in membrane remodeling. An important question remains of whether the local membrane curvatures induced by the adhesion proteins affect their binding. We've performed Monte Carlo simulations of a mesoscopic model for membrane adhesion via the specific binding of curvature-inducing receptors and ligands. We find that the curvatures induced by the adhesion proteins do affect their binding equilibrium constant. We presented a theory that takes into account the membrane deformations and protein-protein interactions due to the induced curvatures, and agrees quantitatively with our simulation results. Our study suggests that the ability to induce membrane curvatures represents a molecular property of the adhesion proteins and should be carefully considered in experimental characterization of the binding affinity.

Tubulation pattern of membrane vesicles coated with biofilaments

Narrow membrane tubes are commonly pulled out from the surface of phospholipid vesicles using forces applied either through laser or magnetic tweezers or through the action of processive motor proteins. Recent examples have emerged in which an array of such tubes grows spontaneously from vesicles coated with bioactive cytoskeletal filaments (e.g., FtsZ, microtubule) in the presence GTP or ATP. We show how a soft vesicle deforms as a result of the interplay between its topology, local curvature, and the forces due to filament bundles. We present results from dynamically triangulated Monte Carlo simulations of a closed membrane vesicle coated with a nematic field (the filaments), and we show how the intrinsic curvature of the filaments and their bundling interactions drive membrane tubulation. We predict interesting patterns consisting of a large number of nematic defects that accompany tubulation. A common theme emerges: defect locations on vesicle surfaces are hot spots of membrane deformation activity, which could be useful for vesicle origami. Although our equilibrium model is not applicable to the nonequilibrium shape dynamics exhibited by active microtubule-coated vesicles, we show that some of the features, such as the size-dependent vesicle shape and the number of tubes, can still be understood from our equilibrium model.

Controlling Cargo Trafficking in Multicomponent Membranes

Biological membranes typically contain a large number of different components dispersed in small concentrations in the main membrane phase, including proteins, sugars, and lipids of varying geometrical properties. Most of these components do not bind the cargo. Here, we show that such "inert" components can be crucial for the precise control of cross-membrane trafficking. Using a statistical mechanics model and molecular dynamics simulations, we demonstrate that the presence of inert membrane components of small isotropic curvatures dramatically influences cargo endocytosis, even if the total spontaneous curvature of such a membrane remains unchanged. Curved lipids, such as cholesterol, as well as asymmetrically included proteins and tethered sugars can, therefore, actively participate in the control of the membrane trafficking of nanoscopic cargo. We find that even a low-level expression of curved inert membrane components can determine the membrane selectivity toward the cargo size and can be used to selectively target membranes of certain compositions. Our results suggest a robust and general method of controlling cargo trafficking by adjusting the membrane composition without needing to alter the concentration of receptors or the average membrane curvature. This study indicates that cells can prepare for any trafficking event by incorporating curved inert components in either of the membrane leaflets.

Organizing membrane-curving proteins: the emerging dynamical picture

Lipid membranes play key roles in cells, such as in trafficking, division, infection, remodeling of organelles, among others. The key step in all these processes is creating membrane curvature, typically under the control of many anchored, adhered or included proteins. However, it has become clear that the membrane itself can mediate the interactions among proteins to produce highly ordered assemblies. Computer simulations are ideally suited to investigate protein organization and the dynamics of membrane remodeling at near-micron scales, something that is extremely challenging to tackle experimentally. We review recent computational efforts in modeling protein-caused membrane deformation mechanisms, specifically focusing on coarse-grained simulations. We highlight work that exposed the membrane-mediated ordering of proteins into lines, meshwork, spirals and other assemblies, in what seems to be a very generic mechanism driven by a combination of short and long-ranged forces. Modulating the mechanical properties of membranes is an underexplored signaling mechanism in various processes deserving of more attention in the near future.