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

Abstract

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.

Geometric evolution of bilayers under the functionalized Cahn–Hilliard equation

“…and 17) and introduce the functions Φ j ∈ L ∞ (R) for j = 1, 2 which are the solutions of 18) which are orthogonal to the kernel of L.…”

“…Indeed, the De Giorgi conjecture, which concerns the Γ limit of the FCH energy for η 2 < 0 with an untilted well has been established [14]. Extensions of these models to address deformations of elastic vesicles subject to volume constraints [15,16], and multi-component models that incorporate a variable intrinsic curvature have been investigated [17,18]. However, the single-layer interface forms the essential underpinning of each of these models.…”

Extended smoothed boundary method for solving partial differential equations with general boundary conditions on complex boundaries

“…However, the method was only applicable to no-flux boundary conditions, and no further extensions to other types of equations or boundary conditions have been reported. Recently, Lowengrub and coworkers [27,28,29,30,31,32,33] developed an alternative formulation for solving partial differential equations with various boundary conditions, based on asymptotic analyses commonly conducted in phase field modeling, which is different from the general derivation of the smoothed boundary method presented in this paper. Although such an implementation for imposing boundary conditions differs from the 'formal' practice suggested by Cahn [17], it dramatically simplifies the formulation, provides a justification of the method, and increases the applicability of the approach.…”

Locomotion, wrinkling, and budding of a multicomponent vesicle in viscous fluids

“…see [11,28,53,16]. It has also been reported recently that a time-dependent flow with a switch in the direction of the velocity gradient can also lead to bud formation [6].…”