Efficient solutions to robust, semi-implicit discretizations of the immersed boundary method

The immersed boundary method is a versatile tool for the investigation of flow-structure interaction. In a large number of applications, the immersed boundaries or structures are very stiff and strong tangential forces on these interfaces induce a well-known, severe time-step restriction for explicit discretizations. This excessive stability constraint can be removed with fully implicit or suitable semi-implicit schemes but at a seemingly prohibitive computational cost. While economical alternatives have been proposed recently for some special cases, there is a practical need for a computationally efficient approach that can be applied more broadly. In this context, we revisit a robust semi-implicit discretization introduced by Peskin in the late 1970s which has received renewed attention recently. This discretization, in which the spreading and interpolation operators are lagged. leads to a linear system of equations for the inter-face configuration at the future time, when the interfacial force is linear. However, this linear system is large and dense and thus it is challenging to streamline its solution. Moreover, while the same linear system or one of similar structure could potentially be used in Newton-type iterations, nonlinear and highly stiff immersed structures pose additional challenges to iterative methods. In this work, we address these problems and propose cost-effective computational strategies for solving Peskin`s lagged-operators type of discretization. We do this by first constructing a sufficiently accurate approximation to the system`s matrix and we obtain a rigorous estimate for this approximation. This matrix is expeditiously computed by using a combination of pre-calculated values and interpolation. The availability of a matrix allows for more efficient matrix-vector products and facilitates the design of effective iterative schemes. We propose efficient iterative approaches to deal with both linear and nonlinear interfacial forces and simple or complex immersed structures with tethered or untethered points. One of these iterative approaches employs a splitting in which we first solve a linear problem for the interfacial force and then we use a nonlinear iteration to find the interface configuration corresponding to this force. We demonstrate that the proposed approach is several orders of magnitude more efficient than the standard explicit method. In addition to considering the standard elliptical drop test case, we show both the robustness and efficacy of the proposed methodology with a 2D model of a heart valve. (C) 2009 Elsevier Inc. All rights reserved.

Structure, Dynamics, and RNA Interaction Analysis of the Human SBDS Protein

Shwachman-Bodian-Diamond syndrome is an autosomal recessive genetic syndrome with pleiotropic phenotypes, including pancreatic deficiencies, bone marrow dysfunctions with increased risk of myelodysplasia or leukemia, and skeletal abnormalities. This syndrome has been associated with mutations in the SBDS gene, which encodes a conserved protein showing orthologs in Archaea and eukaryotes. The Shwachman-Bodian-Diamond syndrome pleiotropic phenotypes may be an indication of different cell type requirements for a fully functional SBDS protein. RNA-binding activity has been predicted for archaeal and yeast SBDS orthologs, with the latter also being implicated in ribosome biogenesis. However, full-length SBDS orthologs function in a species-specific manner, indicating that the knowledge obtained from model systems may be of limited use in understanding major unresolved issues regarding SBDS function, namely, the effect of mutations in human SBDS on its biochemical function and the specificity of RNA interaction. We determined the solution structure and backbone dynamics of the human SBDS protein and describe its RNA binding site using NMR spectroscopy. Similarly to the crystal structures of Archaea, the overall structure of human SBDS comprises three well-folded domains. However, significant conformational exchange was observed in NMR dynamics experiments for the flexible linker between the N-terminal domain and the central domain, and these experiments also reflect the relative motions of the domains. RNA titrations monitored by heteronuclear correlation experiments and chemical shift mapping analysis identified a classic RNA binding site at the N-terminal FYSH (fungal, Yhr087wp, Shwachman) domain that concentrates most of the mutations described for the human SBDS. (C) 2010 Elsevier Ltd. All rights reserved.