A combined BIE-FE method for the Stokes equations

A numerical algorithm for the biharmonic equation in domains with piecewise smooth boundaries is presented. It is intended for problems describing the Stokes flow in the situations where one has corners or cusps formed by parts of the domain boundary and, due to the nature of the boundary conditions on these parts of the boundary, these regions have a global effect on the shape of the whole domain and hence have to be resolved with sufficient accuracy. The algorithm combines the boundary integral equation method for the main part of the flow domain and the finite-element method which is used to resolve the corner/cusp regions. Two parts of the solution are matched along a numerical ‘internal interface’ or, as a variant, two interfaces, and they are determined simultaneously by inverting a combined matrix in the course of iterations. The algorithm is illustrated by considering the flow configuration of ‘curtain coating’, a flow where a sheet of liquid impinges onto a moving solid substrate, which is particularly sensitive to what happens in the corner region formed, physically, by the free surface and the solid boundary. The ‘moving contact line problem’ is addressed in the framework of an earlier developed interface formation model which treats the dynamic contact angle as part of the solution, as opposed to it being a prescribed function of the contact line speed, as in the so-called ‘slip models’. Keywords: Dynamic contact angle; finite elements; free surface flows; hybrid numerical technique; Stokes equations.

Fas ligand-induced apoptosis is regulated by nitric oxide through the inhibition of fas receptor clustering and the nitrosylation of protein kinase Cepsilon

Apoptosis induced by the death-inducing ligand FasL (CD95L) is a major mechanism of cell death. Trophoblast cells express the Fas receptor yet survive in an environment that is rich in the ligand. We report that basal nitric oxide (NO) production is responsible for the resistance of trophoblasts to FasL-induced apoptosis. In this study we demonstrate that basal NO production resulted in the inhibition of receptor clustering following ligand binding. In addition NO also protected cells through the selective nitrosylation, and inhibition, of protein kinase Cepsilon (PKCepsilon) but not PKCalpha. In the absence of NO production PKCepsilon interacted with, and phosphorylated, the anti-apoptotic protein cFLIP. The interaction is predominantly with the short form of cFLIP and its phosphorylation reduces its recruitment to the death-inducing signaling complex (DISC) that is formed following binding of a death-inducing ligand to its receptor. Inhibition of cFLIP recruitment to the DISC leads to increased activation of caspase 8 and subsequently to apoptosis. Inhibition of PKCepsilon using siRNA significantly reversed the sensitivity to apoptosis induced by inhibition of NO synthesis suggesting that NO-mediated inhibition of PKCepsilon plays an important role in the regulation of Fas-induced apoptosis.