Mechanical collapse of confined fluid membrane vesicles.

Compact cylindrical and spherical invaginations are common structural motifs found in cellular and developmental biology. To understand the basic physical mechanisms that produce and maintain such structures, we present here a simple model of vesicles in confinement, in which mechanical equilibrium configurations are computed by energy minimization, balancing the effects of curvature elasticity, contact of the membrane with itself and the confining geometry, and adhesion. For cylindrical confinement, the shape equations are solved both analytically and numerically by finite element analysis. For spherical confinement, axisymmetric configurations are obtained numerically. We find that the geometry of invaginations is controlled by a dimensionless ratio of the adhesion strength to the bending energy of an equal area spherical vesicle. Larger adhesion produces more concentrated curvatures, which are mainly localized to the "neck" region where the invagination breaks away from its confining container. Under spherical confinement, axisymmetric invaginations are approximately spherical. For extreme confinement, multiple invaginations may form, bifurcating along multiple equilibrium branches. The results of the model are useful for understanding the physical mechanisms controlling the structure of lipid membranes of cells and their organelles, and developing tissue membranes.

Dimensional analysis and parametric studies for designing artificial nacre.

Nacre, the iridescent material found in Abalone shells, exhibits remarkable strength and toughness despite its composition of over 95% brittle ceramic. Its hierarchical structure over multiple length scales gives rise to its increase in toughness despite its material composition. In this work we develop a computational model of composites incorporating key morphological features of nacre's microstructure. By conducting a parametric analysis we are able to determine an optimal geometry that increases energy dissipation over 70 times. We discuss the contribution of varying ceramic strengths and size effect to see how this affects the overall performance of the composite. We then compare our simulations to experiments performed on a material possessing the same microstructure investigated computationally. For both simulations and experiments we show that our optimal geometry corresponds to that of natural nacre indicating the importance of specifically incorporating nacre's key morphological and constituent features. This combination of simulations and experiments gives great insight to the delicate interplay between material parameters and microstructure showing that if we optimally combine all aspects, we can develop novel synthetic materials with superior performance.

Multiscale modeling framework of transdermal drug delivery.

This study addresses the modeling of transdermal diffusion of drugs to better understand the permeation of molecules through the skin, especially the stratum corneum, which forms the main permeation barrier to percutaneous permeation. In order to ensure reproducibility and predictability of drug permeation through the skin and into the body, a quantitative understanding of the permeation barrier properties of the stratum corneum (SC) is crucial. We propose a multiscale framework of modeling the multicomponent transdermal diffusion of molecules. The problem is divided into subproblems of increasing length scale: microscopic, mesoscopic, and macroscopic. First, the microscopic diffusion coefficient in the lipid bilayers of the SC is found through molecular dynamics (MD) simulations. Then, a homogenization procedure is performed over a model unit cell of the heterogeneous SC, resulting in effective diffusion parameters. These effective parameters are the macroscopic diffusion coefficients for the homogeneous medium that is "equivalent" to the heterogeneous SC, and thus can be used in finite element simulations of the macroscopic diffusion process. The resulting drug flux through the skin shows very reasonable agreement to experimental data.

Electric field-induced direct delivery of proteins by a nanofountain probe.

We report nanofabrication of protein dot and line patterns using a nanofountain atomic force microscopy probe (NFP). Biomolecules are continuously fed in solution through an integrated microfluidic system, and deposited directly onto a substrate. Deposition is controlled by application of an electric potential of appropriate sign and magnitude between the probe reservoir and substrate. Submicron dot and line molecular patterns were generated with resolution that depended on the magnitude of the applied voltage, dwell time, and writing speed. By using an energetic argument and a Kelvin condensation model, the quasi-equilibrium liquid-air interface at the probe tip was determined. The analysis revealed the origin of the need for electric fields in achieving protein transport to the substrate and confirmed experimental observations suggesting that pattern resolution is controlled by tip sharpness and not overall probe aperture. As such, the NFP combines the high-resolution of dip-pen nanolithography with the efficient continuous liquid feeding of micropipettes while allowing scalability to 1- and 2D probe arrays for high throughput.

Using the method of homogenization to calculate the effective diffusivity of the stratum corneum with permeable corneocytes.

The stratum corneum is the outermost layer of the skin, which acts as a barrier membrane against the penetration of molecules into and out of the body. It has a biphasic structure consisting of keratinized cells (corneocytes) that are embedded in a lipid matrix. The macroscopic transport properties of the stratum corneum are functions of its microstructure and the transport properties of the corneocytes and the lipid matrix, and are of considerable interest in the context of transdermal drug delivery and quantifying exposure to toxins, as well as for determining the relation of skin disorders to disruption of the stratum corneum barrier. Due to the complexity of the tissue and the difference in length scales involved in its microstructure, a direct analysis of the mass transport properties of the stratum corneum is not feasible. In this study, we undertake an approach where the macroscopic diffusion tensor of the stratum corneum is obtained through homogenization using the method of asymptotic expansions. The biphasic structure of the stratum corneum is fully accounted for by allowing the corneocytes to be permeable and considering the partitioning between the corneocytes and the lipid phases. By systematically exploring the effect of permeable corneocytes on the macroscopic transport properties of the stratum corneum, we show that solute properties such as lipophilicity and relative permeabilities in the two phases have large effects on its transdermal diffusion behavior.

Finite element modeling of coupled diffusion with partitioning in transdermal drug delivery.

The finite element method is employed to simulate two-dimensional (axisymmetric) drug diffusion from a finite drug reservoir into the skin. The numerical formulation is based on a general mathematical model for multicomponent nonlinear diffusion that takes into account the coupling effects between the different components. The presence of several diffusing components is crucial, as many transdermal drug delivery formulations contain one or more permeation enhancers in addition to the drug. The coupling between the drug and permeation enhancer(s) results in nonlinear diffusion with concentration-dependent diffusivities of the various components. The framework is suitable for modeling both linear and nonlinear, single- and multicomponent diffusions, however, as it reduces to the correct formulation simply by setting the relevant parameters to zero. In addition, we show that partitioning of the penetrants from the reservoir into the skin can be treated in a straightforward manner in this framework using the mixed method. Partitioning at interface boundaries poses some difficulty with the standard finite element method as it creates a discontinuity in the concentration variable at the interface. To our knowledge, nonlinear (concentration-dependent) partitioning in diffusion problems has not been treated numerically before, and we demonstrate that nonlinear partitioning may have an important role in the effect of permeation enhancers. The mixed method that we adopt includes the flux at the interface explicitly in the formulation, allowing the modeling of concentration-dependent partitioning of the permeants between the reservoir and the skin as well as constant (linear) partitioning. The result is a versatile finite element framework suitable for modeling both linear and nonlinear diffusions in heterogeneous media where the diffusivities and partition coefficients may vary in each subregion.