Shear-driven release of a bud from a multicomponent vesicle

Dynamics of a multicomponent vesicle in shear flow

We study the fully nonlinear, nonlocal dynamics of two-dimensional multicomponent vesicles in a shear flow with matched viscosity of the inner and outer fluids. Using a nonstiff, pseudo-spectral boundary integral method, we investigate dynamical patterns induced by inhomogeneous bending for a two phase system. Numerical results reveal that there exist novel phase-treading and tumbling mechanisms that cannot be observed for a homogeneous vesicle. In particular, unlike the well-known steady tank-treading dynamics characterized by a fixed inclination angle, here the phase-treading mechanism leads to unsteady periodic dynamics with an oscillatory inclination angle. When the average phase concentration is around 1/2, we observe tumbling dynamics even for very low shear rate, and the excess length required for tumbling is significantly smaller than the value for the single phase case. We summarize our results in phase diagrams in terms of the excess length, shear rate, and concentration of the soft phase. These findings go beyond the well known dynamical regimes of a homogeneous vesicle and highlight the level of complexity of vesicle dynamics in a fluid due to heterogeneous material properties.

An introduction to dissipative particle dynamics

Dissipative particle dynamics (DPD) is a particle-based mesoscopic simulation method, which facilitates the studies of thermodynamic and dynamic properties of soft matter systems at physically interesting length and time scales. In this method, molecule groups are clustered into the dissipative beads, and this coarse-graining procedure is a very important aspect of DPD as it allows significant computational speed-up. In this chapter, we introduce the DPD methodology, including its theoretical foundation and its parameterization. With this simulation technique, we can study complex behaviors of biological systems, such as the formation of vesicles and their fusion and fission processes, and the phase behavior of lipid membranes.

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.

Shape deformation and fission route of the lipid domain in a multicomponent vesicle

In this paper, the curvature changes and fission routes of the lipid domains in a multicomponent vesicle are studied by dissipative particle dynamics. Under different conditions of asymmetric distribution of lipids in two leaflets of lipid bilayer and area-to-volume ratio of the vesicle, we obtained different configurations of the domain in the vesicle: three typical curvature characters of the lipid domain, namely, positive, negative, and invariable curvatures compared to the vesicle are observed. Furthermore, some other morphologies of the domain and two vesicle fission routes (i.e., exocytic and endocytic fissions) are also obtained in our simulations. Particular emphasis is put on the formation of the negative curvature domain and on the behavior of endocytic fission. Based on our simulations, it is indicated that water plays an important role in the invagination and endocytic fission processes of the domain in a vesicle. For endocytic fission, domains of different sizes are evolved according to different routes under the effect of the water. Additionally, we find that both the spontaneous curvature of lipid molecules and area-to-volume ratio can promote or restrain the shape deformation of the lipid domain. Under the competition of these two factors, another possible route of endocytic fission is observed in our simulations, in that only a part of the lipid domain invaginates into the interior of the vesicle to complete the endocytic fission. Our study is helpful for understanding the possible mechanism of the shape transformation of the cellular membrane and the difference of several kinds of routes of vesicle fission.

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.

Modeling the phase separation in binary lipid membrane under externally imposed oscillatory shear flow

By adding external velocity terms, the two-dimensional time-dependent Ginzburg-Landau (TDGL) equations are modified. Based on this, the phase separation in binary lipid membrane under externally imposed oscillatory shear flow is numerically modeled employing the Cell Dynamical System (CDS) approach. Considering shear flows with different frequencies and amplitudes, several aspects of such a phase evolving process are studied. Firstly, visualized results are shown via snapshot figures of the membrane shape. And then, the simulated scattering patterns at typical moments are presented. Furthermore, in order to more quantitatively discuss this phase-separation process, the time growth laws of the characteristic domain sizes in both directions parallel and perpendicular to the flow are investigated for each case. Finally, the peculiar rheological properties of such binary lipid membrane system have been discussed, mainly the normal stress difference and the viscoelastic complex shear moduli.