Tension-induced vesicle fusion: pathways and pore dynamics

Size-dependent properties of small unilamellar vesicles formed by model lipids

The size-dependent behavior of small unilamellar vesicles is explored by dissipative particle dynamics, including the membrane characteristics and mechanical properties. The spontaneously formed vesicles are in the metastable state and the vesicle size is controlled by the concentration of model lipids. As the vesicle size decreases, the bilayer gets thinner and the area density of heads declines. Nonetheless, the area density in the inner leaflet is higher than that in the outer. The packing parameters are calculated for both leaflets. The result indicates that the shape of lipid in the outer leaflet is like a truncated cone but that in the inner leaflet resembles an inverted truncated cone. Based on a local order parameter, our simulations indication that the orientation order of lipid molecules decreases as the size of the vesicle reduces and this fact reveals that the bilayer becoming thinner for smaller vesicle is mainly attributed to the orientation disorder of the lipids. The membrane tension can be obtained through the Young-Laplace equation. The tension is found to grow with reducing vesicle size. Therefore, small vesicles are less stable against fusion. Using the inflation method, the area stretching and bending moduli can be determined and those moduli are found to grow with reducing size. Nonetheless, a general equation with a single numerical constant can relate bending modulus, area stretching modulus, and bilayer thickness irrespective of the vesicle size. Finally, a simple metastable model is proposed to explain the size-dependent behavior of bilayer thickness, orientation, and tension.

Forming transmembrane channels using end-functionalized nanotubes

Using dissipative particle dynamics (DPD) simulations, we examine the interaction between amphiphilic nanotubes and lipid bilayer membranes. The nanotubes are represented by a hydrophobic shaft that is end-functionalized with hydrophilic groups. Nanotubes that are capped by a monolayer of hydrophilic beads or also encompass hydrophilic "hairs" on just one end of the shaft are found to spontaneously penetrate and assume a transmembrane position; the process, however, depends critically on the membrane tension. On the other hand, nanotubes that include hydrophilic hairs at both ends of the hydrophobic shaft are not observed to spontaneously self-organize into the bilayer. When the membrane is stretched to form a pore, the nanotubes with two hairy ends adsorb on the edge of the pore and become localized in the membrane, thus forming a transmembrane channel. The findings from these studies provide guidelines for creating biomimetic nanotube channels that are capable of selectively transporting molecules through the membrane in response to changes in the local environment.

Direct simulation of protein-mediated vesicle fusion: lung surfactant protein B

We simulated spontaneous fusion of small unilamellar vesicles mediated by lung surfactant protein B (SP-B) using the MARTINI force field. An SP-B monomer triggers fusion events by anchoring two vesicles and facilitating the formation of a lipid bridge between the proximal leaflets. Once a lipid bridge is formed, fusion proceeds via a previously described stalk - hemifusion diaphragm - pore-opening pathway. In the absence of protein, fusion of vesicles was not observed in either unbiased simulations or upon application of a restraining potential to maintain the vesicles in close proximity. The shape of SP-B appears to enable it to bind to two vesicles at once, forcing their proximity, and to facilitate the initial transfer of lipids to form a high-energy hemifusion intermediate. Our results may provide insight into more general mechanisms of protein-mediated membrane fusion, and a possible role of SP-B in the secretory pathway and transfer of lung surfactant to the gas exchange interface.

Cluster formation of anchored proteins induced by membrane-mediated interaction

Computer simulations were used to study the cluster formation of anchored proteins in a membrane. The rate and extent of clustering was found to be dependent upon the hydrophobic length of the anchored proteins embedded in the membrane. The cluster formation mechanism of anchored proteins in our work was ascribed to the different local perturbations on the upper and lower monolayers of the membrane and the intermonolayer coupling. Simulation results demonstrated that only when the penetration depth of anchored proteins was larger than half the membrane thickness, could the structure of the lower monolayer be significantly deformed. Additionally, studies on the local structures of membranes indicated weak perturbation of bilayer thickness for a shallowly inserted protein, while there was significant perturbation for a more deeply inserted protein. The origin of membrane-mediated protein-protein interaction is therefore due to the local perturbation of the membrane thickness, and the entropy loss-both of which are caused by the conformation restriction on the lipid chains and the enhanced intermonolayer coupling for a deeply inserted protein. Finally, in this study we addressed the difference of cluster formation mechanisms between anchored proteins and transmembrane proteins.

Dynamics of multicomponent vesicles in a viscous fluid

We develop and investigate numerically a thermodynamically consistent model of two-dimensional multicomponent vesicles in an incompressible viscous fluid. The model is derived using an energy variation approach that accounts for different lipid surface phases, the excess energy (line energy) associated with surface phase domain boundaries, bending energy, spontaneous curvature, local inextensibility and fluid flow via the Stokes equations. The equations are high-order (fourth order) nonlinear and nonlocal due to incompressibil-ity of the fluid and the local inextensibility of the vesicle membrane. To solve the equations numerically, we develop a nonstiff, pseudo-spectral boundary integral method that relies on an analysis of the equations at small scales. The algorithm is closely related to that developed very recently by Veerapaneni et al. [81] for homogeneous vesicles although we use a different and more efficient time stepping algorithm and a reformulation of the inextensibility equation. We present simulations of multicomponent vesicles in an initially quiescent fluid and investigate the effect of varying the average surface concentration of an initially unstable mixture of lipid phases. The phases then redistribute and alter the morphology of the vesicle and its dynamics. When an applied shear is introduced, an initially elliptical vesicle tank-treads and attains a steady shape and surface phase distribution. A sufficiently elongated vesicle tumbles and the presence of different surface phases with different bending stiffnesses and spontaneous curvatures yields a complex evolution of the vesicle morphology as the vesicle bends in regions where the bending stiffness and spontaneous curvature are small.

The fusion of membranes and vesicles: pathway and energy barriers from dissipative particle dynamics

The fusion of lipid bilayers is studied with dissipative particle dynamics simulations. First, to achieve control over membrane properties, the effects of individual simulation parameters are studied and optimized. Then, a large number of fusion events for a vesicle and a planar bilayer are simulated using the optimized parameter set. In the observed fusion pathway, configurations of individual lipids play an important role. Fusion starts with individual lipids assuming a splayed tail configuration with one tail inserted in each membrane. To determine the corresponding energy barrier, we measure the average work for interbilayer flips of a lipid tail, i.e., the average work to displace one lipid tail from one bilayer to the other. This energy barrier is found to depend strongly on a certain dissipative particle dynamics parameter, and, thus, can be adjusted in the simulations. Overall, three subprocesses have been identified in the fusion pathway. Their energy barriers are estimated to lie in the range 8-15 k(B)T. The fusion probability is found to possess a maximum at intermediate tension values. As one decreases the tension, the fusion probability seems to vanish before the tensionless membrane state is attained. This would imply that the tension has to exceed a certain threshold value to induce fusion.

Phase-field modeling of the dynamics of multicomponent vesicles: Spinodal decomposition, coarsening, budding, and fission

We develop a thermodynamically consistent phase-field model to simulate the dynamics of multicomponent vesicles. The model accounts for bending stiffness, spontaneous curvature, excess (surface) energy, and a line tension between the coexisting surface phases. Our approach is similar to that recently used by Wang and Du [J. Math. Biol. 56, 347 (2008)] with a key difference. Here, we concentrate on the dynamic evolution and solve the surface mass conservation equation explicitly; this equation was not considered by Wang and Du. The resulting fourth-order strongly coupled system of nonlinear nonlocal equations are solved numerically using an adaptive finite element numerical method. Although the system is valid for three dimensions, we limit our studies here to two dimensions where the vesicle is a curve. Differences between the spontaneous curvatures and the bending rigidities of the surface phases are found numerically to lead to the formation of buds, asymmetric vesicle shapes and vesicle fission even in two dimensions. In addition, simulations of configurations far from equilibrium indicate that phase separation via spinodal decomposition and coarsening not only affect the vesicle shape but also that the vesicle shape affects the phase separation dynamics, especially the coarsening and may lead to lower energy states than might be achieved by evolving initially phase-separated configurations.

Lipids on the move: simulations of membrane pores, domains, stalks and curves

In this review we describe the state-of-the-art of computer simulation studies of lipid membranes. We focus on collective lipid-lipid and lipid-protein interactions that trigger deformations of the natural lamellar membrane state, showing that many important biological processes including self-aggregation of membrane components into domains, the formation of non-lamellar phases, and membrane poration and curving, are now amenable to detailed simulation studies.