Blur removal is an important problem in signal and image processing. The blurring matrices obtained by using the zero boundary condition (corresponding to assuming dark background outside the scene) are Toeplitz matrices for one-dimensional problems and block-Toeplitz-Toeplitzblock matrices for two-dimensional cases. They are computationally intensive to invert especially in the block case. If the periodic boundary condition is used, the matrices become (block) circulant and can be diagonalized by discrete Fourier transform matrices. In this paper, we consider the use of the Neumann boundary condition (corresponding to a reflection of the original scene at the boundary). The resulting matrices are (block) Toeplitz-plus-Hankel matrices. We show that for symmetric blurring functions, these blurring matrices can always be diagonalized by discrete cosine transform matrices. Thus the cost of inversion is significantly lower than that of using the zero or periodic boundary conditions. We also show that the use of the Neumann boundary condition provides an easy way of estimating the regularization parameter when the generalized cross-validation is used. When the blurring function is nonsymmetric, we show that the optimal cosine transform preconditioner of the blurring matrix is equal to the blurring matrix generated by the symmetric part of the blurring function. Numerical results are given to illustrate the efficiency of using the Neumann boundary condition.

Inclusion body myopathy associated with Paget's disease of bone and frontotemporal dementia (IBMPFD) is a dominantly inherited degenerative disorder caused by mutations in the valosin-containing protein (VCP7) gene. VCP (p97 in mouse, TER94 in Drosophila melanogaster, and CDC48 in Saccharomyces cerevisiae) is a highly conserved AAA ϩ (ATPases associated with multiple cellular activities) ATPase that regulates a wide array of cellular processes. The mechanism of IBMPFD pathogenesis is unknown. To elucidate the pathogenic mechanism, we developed and characterized a Drosophila model of IBMPFD (mutant-VCP-related degeneration). Based on genetic screening of this model, we identified three RNA-binding proteins that dominantly suppressed degeneration; one of these was TBPH, the Drosophila homolog of TAR (trans-activating response region) DNA-binding protein 43 (TDP-43). Here we demonstrate that VCP and TDP-43 interact genetically and that disease-causing mutations in VCP lead to redistribution of TDP-43 to the cytoplasm in vitro and in vivo, replicating the major pathology observed in IBMPFD and other TDP-43 proteinopathies. We also demonstrate that TDP-43 redistribution from the nucleus to the cytoplasm is sufficient to induce cytotoxicity. Furthermore, we determined that a pathogenic mutation in TDP-43 promotes redistribution to the cytoplasm and enhances the genetic interaction with VCP. Together, our results show that degeneration associated with VCP mutations is mediated in part by toxic gain of function of TDP-43 in the cytoplasm. We suggest that these findings are likely relevant to the pathogenic mechanism of a broad array of TDP-43 proteinopathies, including frontotemporal lobar degeneration and amyotrophic lateral sclerosis.

Summary The cytochrome bc1 complex (bc1) is the mid-segment of the cellular respiratory chain of mitochondria and many aerobic prokaryotic organisms; it is also part of the photosynthetic apparatus of non-oxygenic purple bacteria. The bc1 complex catalyzes the reaction of transferring electrons from the low potential substrate ubiquinol to high potential cytochrome c. Concomitantly, bc1 translocates protons across the membrane, contributing to the proton-motive force essential for a variety of cellular activities such as ATP synthesis. Structural investigations of bc1 have been exceedingly successful, yielding atomic resolution structures of bc1 from various organisms and trapped in different reaction intermediates. These structures have confirmed and unified results of decades of experiments and have contributed to our understanding of the mechanism of bc1 functions as well as its inactivation by respiratory inhibitors.

Edited by Norma AllewellP-glycoprotein (P-gp) is a polyspecific ATP-dependent transporter linked to multidrug resistance in cancer; it plays important roles in determining the pharmacokinetics of many drugs. Understanding the structural basis of P-gp, substrate polyspecificity has been hampered by its intrinsic flexibility, which is facilitated by a 75-residue linker that connects the two halves of P-gp. Here we constructed a mutant murine P-gp with a shortened linker to facilitate structural determination. Despite dramatic reduction in rhodamine 123 and calcein-AM transport, the linker-shortened mutant P-gp possesses basal ATPase activity and binds ATP only in its N-terminal nucleotide-binding domain. Nine independently determined structures of wild type, the linker mutant, and a methylated P-gp at up to 3.3 Å resolution display significant movements of individual transmembrane domain helices, which correlated with the opening and closing motion of the two halves of P-gp. The open-andclose motion alters the surface topology of P-gp within the drugbinding pocket, providing a mechanistic explanation for the polyspecificity of P-gp in substrate interactions.The association of multidrug resistance (MDR) 3 in cancer treatment with expression of human ABC transporters on the cell surface has raised the possibility that overcoming MDR might be achieved by inhibiting these transporters (1). One transporter in particular, the human P-glycoprotein (P-gp), has been well characterized; it is able to confer MDR by transporting numerous structurally unrelated drugs at the expense of hydrolyzing ATP (2, 3). In addition, P-gp plays important roles in drug distribution in normal physiology and is an essential component of many physiological barriers (4, 5).Long-standing efforts have been devoted to understanding the mechanism of P-gp function by various experimental approaches. Among them, structural studies of P-gp from various organisms have been reported (6 -8). In particular, a number of structures for the mouse P-gp (mP-gp) were obtained (8 -10). However, the diffraction limits of "near-native," inhibitor-bound, and nanobody-associated mP-gp crystals were relatively low, mostly near 4 Å resolution. The methylated protein gave higher resolution structures (11), but the impact of reductive methylation on the structure and function of P-gp was not addressed. The low resolution diffraction of P-gp crystals has been attributed in part to the intrinsic flexibility of the molecule (12-14).Mouse P-gp is a 1276-residue polypeptide and bears 87% sequence identity to human P-gp; it consists of two homologous halves connected by a flexible linker of ϳ75 residues. Each half is made of a transmembrane domain (TMD) implicated in drug recognition and transport and a nucleotide-binding domain (NBD). Each NBD is able to bind and hydrolyze ATP (15, 16), which is, however, dependent on the other NBD being functional (17,18). The two NBDs of P-gp are highly homologous, each featuring a consensus nucleotide-binding site with full-fledged Walker...