We examine the interaction of a lipid bilayer membrane with a spherical particle in solution using dissipative particle dynamics, with the aim of controlling the passage of foreign objects into and out of vesicles. Parameters are chosen such that there is a favorable adhesive interaction between the membrane and the particle. Under these conditions, the membrane wraps the particle in a process resembling phagocytosis in biological cells. We find that, for a homogeneous membrane with a uniform attraction to the particle, the membrane is unable to fully wrap the particle when the adhesion strength is below a certain value. This is observed even in the limit of zero membrane tension. When the adhesion strength is increased above the threshold value, the membrane fully wraps the particle. However, the wrapped particle remains tethered to the larger membrane. We next consider an adhesive domain, or raft, in an otherwise nonadhesive membrane. We find that, when the particle is wrapped by the raft, the line tension at the raft interface promotes fission, allowing the wrapped particle to detach from the larger membrane. This mechanism could be used to allow particles to cross a vesicle membrane.

Solis, Olvera de la Cruz, and Smith Reply: The growth rate of the characteristic domain size L with time T , L ϳ T z , during the coarsening of strongly segregated interconnected self-similar structures was recently associated with the relaxation of interfaces to perturbation of the same order of magnitude L [1]. The relaxation is driven by the surface tension force proportional to the curvature at the interface. The linearized Navier-Stokes equation analysis for the relaxation of stable perturbations gives an exponential decay that scales as L 21 in the viscous regime ͑L ! 0͒ and as L 27͞4 with an oscillation v ϳ L 23͞2 in the inviscid limit ͑L !`͒. This suggests that z 1 in the viscous (short time) limit, in agreement with previous scaling results [2], z 4͞7 in the inviscid (long time) limit, and that the previously derived exponent by dimensional analysis [3], z 2͞3, corresponds only to the frequency of the oscillation.Furukawa argues that the mode z 2͞3 is not an oscillatory mode in the nonlinear case [4]. Whether the nonlinearity of the system recovers the z 2͞3 exponent or preserves the z 4͞7 linear exponent cannot be decided a priori. We have studied this issue numerically by analyzing the nonlinear response of a flat interface to a perturbation A͑0͒ cos͑kx͒ with large initial amplitudes, A͑0͒ ϳ 1͞k ϳ L, in the inviscid ͑k ! 0͒ limit. The nonlinear Navier-Stokes equation solved by using the level set method to track the interface gives a response for the amplitude A͑t͒ ϳ exp͑ivt 2 t͞t͒. The best fit in the inviscid limit is [5] t 21 ϳ k 7͞4 and v ϳ k 3͞2 , in agreement with the analytical linear analysis [1].In nonlinear systems where perturbations grow, such as the domain growth in the time-dependent Ginzburg-Landau model with conserved ͑z 1͞3͒ and nonconserved ͑z 1͞2͒ order parameters, the linear analysis is not applicable because it gives an exponential growth for the unstable amplitudes. However, in systems where the perturbations are stable, such as perturbations of spheres or flat interfaces in immiscible liquids, the linear analysis is often accurate given that the perturbations decay in time.Recent attempts to restore the exponent z 2͞3 for the growth in the inviscid limit [4,6] assume that the liquid is homogeneous. However, coarsening by hydrodynamics is highly inhomogeneous given that it is driven by the curvature of the interface, which is very localized, inhomogeneous, and anisotropic, and is mathematically represented by a delta function at the interface. For example, the dissipation layer during the decay of a flat interface perturbation A͑0͒ cos͑kx͒ with 1͞k ϳ L is localized in a region that scales as L 3͞4 from the interface in the inertial regime and is L independent in the viscous regime [1]. The nonlinear numerical analysis of the flow close to the interface confirms the inhomogeneous nature of the curvature driven relaxation process [5].Numerical data for the interface driven coarsening growth process in two dimensions [7] supports our linear analysis results. If the data is forced to ...

This article appears in The Journal of Clinical Endocrinology & Metabolism, published December 30, 2010, 10.1210/jc.2010-2098

We examine the static and dynamic properties of polymer chains in a melt in the presence of a solid surface. A molecular dynamics simulation is carried out using a coarse-grained bead−spring model of polymer chains. Both attractive and repulsive interactions between surface and monomers are examined. Static conformations are characterized in terms of trains of attached monomers and detached loops and tails. We compare these conformations to a random walk model. Chain desorption rates are measured in order to calculate characteristic desorption times. We distinguish between chains which desorb rapidly after arriving at the surface and chains which reach a relaxed state at the surface and then desorb at a constant rate. A kinetic model is developed as a means to predict desorption rates and late time chain conformations.

We develop a projection method to treat the motion of multiple junctions (such as contact lines) in the level set formulation. Multiple junctions are relevant to many fields including fluid dynamics, foams, and semiconductor manufacture. In the level set method an interface is defined as the zero level set of a smooth function. For an N -phase system the location of all interfaces can be specified by N − 1 functions (hence only one level set function is needed for a two-phase system). For N > 2 we describe a symmetric projection of the N level set functions onto an N − 1 dimensional manifold. This reduction in phase space eliminates unacceptable values of the level set functions (such as cases where more than one is positive at a given point.) This prevents the formation of vacuums or overlaps at multiple junctions during interface evolution. Further, this method can be applied to any number of phases and spatial dimensions. We present two-and three-dimensional results showing that the method gives correct equilibrium contact angles and produces accurate dynamics in multi-phase fluids.