The dynamics of phase separation in multicomponent bilayer fluid vesicles is investigated by means of large-scale dissipative particle dynamics. The model explicitly accounts for solvent particles, thereby allowing for the very first numerical investigation of the effects of hydrodynamics and area-to-volume constraints. We observed regimes corresponding to coalescence of flat patches, budding and vesiculation, and coalescence of caps. We point out that the area-to-volume constraint has a strong influence on crossovers between these regimes.

We present a method for simulating fluid vesicles with in-plane orientational ordering. The method involves computation of local curvature tensor and parallel transport of the orientational field on a randomly triangulated surface. It is shown that the model reproduces the known equilibrium conformation of fluid membranes and work well for a large range of bending rigidities. Introduction of nematic ordering leads to stiffening of the membrane. Nematic ordering can also result in anisotropic rigidity on the surface leading to formation of membrane tubes.

A systematic investigation of the phase separation dynamics in self-assembled multi-component bilayer fluid vesicles and open membranes is presented. We use large-scale dissipative particle dynamics to explicitly account for solvent, thereby allowing for numerical investigation of the effects of hydrodynamics and area-to-volume constraints. In the case of asymmetric lipid composition, we observed regimes corresponding to coalescence of flat patches, budding, vesiculation and coalescence of caps. The area-to-volume constraint and hydrodynamics have a strong influence on these regimes and the crossovers between them. In the case of symmetric mixtures, irrespective of the area-tovolume ratio, we observed a growth regime with an exponent of 1/2. The same exponent is also found in the case of open membranes with symmetric composition.

Biological membranes constitute boundaries of cells and cell organelles. These membranes are soft fluid interfaces whose thermodynamic states are dictated by bending moduli, induced curvature fields, and thermal fluctuations. Recently, there has been a flood of experimental evidence highlighting active roles for these structures in many cellular processes ranging from trafficking of cargo to cell motility. It is believed that the local membrane curvature, which is continuously altered due to its interactions with myriad proteins and other macromolecules attached to its surface, holds the key to the emergent functionality in these cellular processes. Mechanisms at the atomic scale are dictated by protein-lipid interaction strength, lipid composition, lipid distribution in the vicinity of the protein, shape and amino acid composition of the protein, and its amino acid contents. The specificity of molecular interactions together with the cooperativity of multiple proteins induce and stabilize complex membrane shapes at the mesoscale. These shapes span a wide spectrum ranging from the spherical plasma membrane to the complex cisternae of the Golgi apparatus. Mapping the relation between the protein-induced deformations at the molecular scale and the resulting mesoscale morphologies is key to bridging cellular experiments across the various length scales. In this review, we focus on the theoretical and computational methods used to understand the phenomenology underlying protein-driven membrane remodeling. Interactions at the molecular scale can be computationally probed by all atom and coarse grained molecular dynamics (MD, CGMD), as well as dissipative particle dynamics (DPD) simulations, which we only describe in passing. We choose to focus on several continuum approaches extending the Canham - Helfrich elastic energy model for membranes to include the effect of curvature-inducing proteins and explore the conformational phase space of such systems. In this description, the protein is expressed in the form of a spontaneous curvature field. The approaches include field theoretical methods limited to the small deformation regime, triangulated surfaces and particle-based computational models to investigate the large-deformation regimes observed in the natural state of many biological membranes. Applications of these methods to understand the properties of biological membranes in homogeneous and inhomogeneous environments of proteins, whose underlying curvature fields are either isotropic or anisotropic, are discussed. The diversity in the curvature fields elicits a rich variety of morphological states, including tubes, discs, branched tubes, and caveola. Mapping the thermodynamic stability of these states as a function of tuning parameters such as concentration and strength of curvature induction of the proteins is discussed. The relative stabilities of these self-organized shapes are examined through free-energy calculations. The suite of methods discussed here can be tailored to applications in specific cellular set...

The shapes of cell membranes are largely regulated by membrane-associated, curvature-active proteins. Herein, we use a numerical model of the membrane, recently developed by us, with elongated membrane inclusions possessing spontaneous directional curvatures that could be different along, and perpendicular to, the membrane's long axis. We show that, due to membrane-mediated interactions, these curvature-inducing membrane-nematogens can aggregate 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 spontaneous curvatures have equal sign, the tubular conformation and sometimes the sheet conformation of the membrane are the common equilibrium shapes. We elucidate the factors necessary for the formation of these protein lattices. Furthermore, the elastic properties of the tubes, such as their compressional stiffness and persistence length, are calculated. Finally, we discuss the possible role of nematic disclination in capping and branching of the tubular membranes.

The phase behavior of the coarse-grained MARTINI model for three-component lipid bilayers composed of dipalmytoyl-phosphatidylcholine (DPPC), cholesterol (Chol), and an unsaturated phosphatidylcholine (PC) was systematically investigated by molecular dynamics simulations. The aim of this study is to understand which types of unsaturated PC induce the formation of thermodynamically stable coexisting phases when added to mixtures of DPPC and Chol and to unravel the mechanisms that drive phase separation in such three-component mixtures. Our simulations indicate that the currently used MARTINI force field does not induce such phase separation in mixtures of DPPC, Chol, and unsaturated PCs with a low unsaturation level, such as palmitoyl-oleoyl-phosphatidylcholine (POPC) or dioleoyl-phosphatidylcholine (DOPC). Also, we found that phase separation does occur in mixtures of DPPC, Chol, and polyunsaturated PCs, such as dilinoleyl-phosphatidylcholine (DUPC) and diarachidonoyl-phosphatidylcholine (DAPC). Through systematic tweaking of the interactions between the hydrophobic groups of the PC molecules, we show that the appearance of phase separation in three-component lipid bilayers, as modeled through the MARTINI force field, is primarily due to the interactions between the coarse-grained molecules, i.e., the beads, rather than due to the differences between the conformations of saturated and unsaturated lipid acyl chains, namely entropy driven.

We investigate the behavior of flexible two-component bilayer and three-component monolayer membranes. The components are assumed to have different spontaneous curvatures, and to mutually phase separate in planar membranes. As a function of temperature, lateral tension and bending rigidity, a rich phase behavior is obtained. In particular, we find three different types of modulated phases. In symmetric bilayers, the excess component assembles at the boundary between oppositely curved domains; in sufficiently asymmetric bilayers, the excess component is found to preferentially assemble in a single layer, with no tendency for segregation to the domain boundaries. We show that the phase behavior of three-component monolayer strongly resembles the behavior of two-component bilayers. In fact, in a certain, restricted region of parameter space, the two models can be shown to be equivalent.

Recent developments in biology seems to indicate that the Fluid Mosaic model of membrane proposed by Singer and Nicolson, with lipid bilayer functioning only as medium to support protein machinery, may be too simple to be realistic. Many protein functions are now known to depend on the composition of the membrane. Experiments indicate that biomembranes of eukaryotic cells may be laterally organized into small nanoscopic domains. This inplane organization is expected to play an important role in a variety of physiological functions such as signaling, recruitment of specific proteins and endocytosis. However, mainly because of their complexity, the precise in-plane organization of lipids and proteins and their stability in biological membranes remain difficult to elucidate. This has reiterated the importance of understanding the equilibrium phase behavior and the kinetics of fluid multicomponent lipid membranes. Current increase in interest in the domain formation in multicomponent membranes also stems from the experiments demonstrating liquid ordered-liquid disordered coexistence in mixtures of lipids and cholesterol and the success of several computational models in predicting their behavior. This review includes basic foundations on membrane model systems and experimental approaches applied in the membrane research area, stressing on recent advances in the experimental and computational techniques.