Tight frames of k-plane ridgelets and the problem of representing objects that are smooth away from d-dimensional singularities in Rn

For each pair (n, k) with 1 ≤ k < n, we construct a tight frame (ρλ : λ ∈ Λ) for L2 (Rn), which we call a frame of k-plane ridgelets. The intent is to efficiently represent functions that are smooth away from singularities along k-planes in Rn. We also develop tools to help decide whether k-plane ridgelets provide the desired efficient representation. We first construct a wavelet-like tight frame on the X-ray bundle χn,k—the fiber bundle having the Grassman manifold Gn,k of k-planes in Rn for base space, and for fibers the orthocomplements of those planes. This wavelet-like tight frame is the pushout to χn,k, via the smooth local coordinates of Gn,k, of an orthonormal basis of tensor Meyer wavelets on Euclidean space Rk(n−k) × Rn−k. We then use the X-ray isometry [Solmon, D. C. (1976) J. Math. Anal. Appl. 56, 61–83] to map this tight frame isometrically to a tight frame for L2(Rn)—the k-plane ridgelets. This construction makes analysis of a function f ∈ L2(Rn) by k-plane ridgelets identical to the analysis of the k-plane X-ray transform of f by an appropriate wavelet-like system for χn,k. As wavelets are typically effective at representing point singularities, it may be expected that these new systems will be effective at representing objects whose k-plane X-ray transform has a point singularity. Objects with discontinuities across hyperplanes are of this form, for k = n − 1.

Chimeric anti-angiogenin antibody cAb 26–2F inhibits the formation of human breast cancer xenografts in athymic mice

Angiogenin (Ang), an inducer of neovascularization, is secreted by several types of human tumor cells and appears critical for their growth. The murine anti-Ang monoclonal antibody (mAb) 26–2F neutralizes the activities of Ang and dramatically prevents the establishment and metastatic dissemination of human tumor cell xenografts in athymic mice. However, for use clinically, the well-documented problem of the human anti-globulin antibody response known to occur with murine antibodies requires resolution. As a result, chimeric as well as totally humanized antibodies are currently being evaluated as therapeutic agents for the treatment of several pathological conditions, including malignancy. Therefore, we have constructed a chimeric mouse/human antibody based on the structure of mAb 26–2F. Complementary DNAs from the light and heavy chain variable regions of mAb 26–2F were cloned, sequenced, and genetically engineered by PCR for subcloning into expression vectors that contain human constant region sequences. Transfection of these vectors into nonproducing mouse myeloma cells resulted in the secretion of fully assembled tetrameric molecules. The chimeric antibody (cAb 26–2F) binds to Ang and inhibits its ribonucleolytic and angiogenic activities as potently as mAb 26–2F. Furthermore, the capacities of cAb 26–2F and its murine counterpart to suppress the formation of human breast cancer tumors in athymic mice are indistinguishable. Thus cAb 26–2F, with its retained neutralization capability and likely decreased immunogenicity, may be of use clinically for the treatment of human cancer and related disorders where pathological angiogenesis is a component.

Anti-CD14 mAb treatment provides therapeutic benefit after in vivo exposure to endotoxin

The presence of endotoxin from Gram-negative bacteria signals the innate immune system to up-regulate bacterial clearance and/or killing mechanisms. Paradoxically, such responses also contribute to septic shock, a clinical problem occurring with high frequency in Gram-negative septicemia. CD14 is a receptor for endotoxin (lipopolysaccharide, LPS) and is thought to have an essential role in innate immune responses to infection and thereby in the development of septic shock. Using a novel rabbit model of endotoxic shock produced by multiple exposures to endotoxin, we show that anti-rabbit CD14 mAb, which blocks LPS-CD14 binding, protects against organ injury and death even when the antibody is administered after initial exposures to LPS. In contrast, anti-rabbit tumor necrosis factor mAb treatment fails to protect when administered after LPS injections. These results support the concept that anti-CD14 treatment provides a new therapeutic window for the prevention of pathophysiologic changes that result from cumulative exposures to LPS during septic shock in man.