beta-Arrestin1 modulates lymphoid enhancer factor transcriptional activity through interaction with phosphorylated dishevelled proteins.

One aspect of the function of the beta-arrestins is to serve as scaffold or adapter molecules coupling G-protein coupled receptors (GPCRs) to signal transduction pathways distinct from traditional second messenger pathways. Here we report the identification of Dishevelled 1 and Dishevelled 2 (Dvl1 and Dvl2) as beta-arrestin1 (betaarr1) interacting proteins. Dvl proteins participate as key intermediates in signal transmission from the seven membrane-spanning Frizzled receptors leading to inhibition of glycogen synthase kinase-3beta (GSK-3beta), stabilization of beta-catenin, and activation of the lymphoid enhancer factor (LEF) transcription factor. We find that phosphorylation of Dvl strongly enhances its interaction with betaarr1, suggesting that regulation of Dvl phosphorylation and subsequent interaction with betaarr1 may play a key role in the activation of the LEF transcription pathway. Because coexpression of the Dvl kinases, CK1epsilon and PAR-1, with Dvl synergistically activates LEF reporter gene activity, we reasoned that coexpression of betaarr1 with Dvl might also affect LEF-dependent gene activation. Interestingly, whereas betaarr1 or Dvl alone leads to low-level stimulation of LEF (2- to 5-fold), coexpression of betaarr1 with either Dvl1 or Dvl2 leads to a synergistic activation of LEF (up to 16-fold). Additional experiments with LiCl as an inhibitor of GSK-3beta kinase activity indicate that the step affected by betaarr1 is upstream of GSK-3beta and most likely at the level of Dvl. These results identify betaarr1 as a regulator of Dvl-dependent LEF transcription and suggest that betaarr1 might serve as an adapter molecule that can couple Frizzled receptors and perhaps other GPCRs to these important transcription pathways.

A New Method for Modeling Free Surface Flows and Fluid-structure Interaction with Ocean Applications

The computational modeling of ocean waves and ocean-faring devices poses numerous challenges. Among these are the need to stably and accurately represent both the fluid-fluid interface between water and air as well as the fluid-structure interfaces arising between solid devices and one or more fluids. As techniques are developed to stably and accurately balance the interactions between fluid and structural solvers at these boundaries, a similarly pressing challenge is the development of algorithms that are massively scalable and capable of performing large-scale three-dimensional simulations on reasonable time scales. This dissertation introduces two separate methods for approaching this problem, with the first focusing on the development of sophisticated fluid-fluid interface representations and the second focusing primarily on scalability and extensibility to higher-order methods.

We begin by introducing the narrow-band gradient-augmented level set method (GALSM) for incompressible multiphase Navier-Stokes flow. This is the first use of the high-order GALSM for a fluid flow application, and its reliability and accuracy in modeling ocean environments is tested extensively. The method demonstrates numerous advantages over the traditional level set method, among these a heightened conservation of fluid volume and the representation of subgrid structures.

Next, we present a finite-volume algorithm for solving the incompressible Euler equations in two and three dimensions in the presence of a flow-driven free surface and a dynamic rigid body. In this development, the chief concerns are efficiency, scalability, and extensibility (to higher-order and truly conservative methods). These priorities informed a number of important choices: The air phase is substituted by a pressure boundary condition in order to greatly reduce the size of the computational domain, a cut-cell finite-volume approach is chosen in order to minimize fluid volume loss and open the door to higher-order methods, and adaptive mesh refinement (AMR) is employed to focus computational effort and make large-scale 3D simulations possible. This algorithm is shown to produce robust and accurate results that are well-suited for the study of ocean waves and the development of wave energy conversion (WEC) devices.