An O(N log N) algorithm for shape modeling.

We present a shape-recovery technique in two dimensions and three dimensions with specific applications in modeling anatomical shapes from medical images. This algorithm models extremely corrugated structures like the brain, is topologically adaptable, and runs in O(N log N) time, where N is the total number of points in the domain. Our technique is based on a level set shape-recovery scheme recently introduced by the authors and the fast marching method for computing solutions to static Hamilton-Jacobi equations.

Periodic variation in side-chain polarities of T-cell antigenic peptides correlates with their structure and activity.

We present an analysis that synthesizes information on the sequence, structure, and motifs of antigenic peptides, which previously appeared to be in conflict. Fourier analysis of T-cell antigenic peptides indicates a periodic variation in amino acid polarities of 3-3.6 residues per period, suggesting an amphipathic alpha-helical structure. However, the diffraction patterns of major histocompatibility complex (MHC) molecules indicate that their ligands are in an extended non-alpha-helical conformation. We present two mutually consistent structural explanations for the source of the alpha-helical periodicity, based on an observation that the side chains of MHC-bound peptides generally partition with hydrophobic (hydrophilic) side chains pointing into (out of) the cleft. First, an analysis of haplotype-dependent peptide motifs indicates that the locations of their defining residues tend to force a period 3-4 variation in hydrophobicity along the peptide sequence, in a manner consistent with the spacing of pockets in the MHC. Second, recent crystallographic determination of the structure of a peptide bound to a class II MHC molecule reveals an extended but regularly twisted peptide with a rotation angle of about 130 degrees. We show that similar structures with rotation angles of 100-130 degrees are energetically acceptable and also span the length of the MHC cleft. These results provide a sound physical chemical and structural basis for the existence of a haplotype-independent antigenic motif which can be particularly important in limiting the search time for antigenic peptides.

Quantitative analysis of senile plaques in Alzheimer disease: observation of log-normal size distribution and molecular epidemiology of differences associated with apolipoprotein E genotype and trisomy 21 (Down syndrome).

The discovery that the epsilon 4 allele of the apolipoprotein E (apoE) gene is a putative risk factor for Alzheimer disease (AD) in the general population has highlighted the role of genetic influences in this extremely common and disabling illness. It has long been recognized that another genetic abnormality, trisomy 21 (Down syndrome), is associated with early and severe development of AD neuropathological lesions. It remains a challenge, however, to understand how these facts relate to the pathological changes in the brains of AD patients. We used computerized image analysis to examine the size distribution of one of the characteristic neuropathological lesions in AD, deposits of A beta peptide in senile plaques (SPs). Surprisingly, we find that a log-normal distribution fits the SP size distribution quite well, motivating a porous model of SP morphogenesis. We then analyzed SP size distribution curves in genotypically defined subgroups of AD patients. The data demonstrate that both apoE epsilon 4/AD and trisomy 21/AD lead to increased amyloid deposition, but by apparently different mechanisms. The size distribution curve is shifted toward larger plaques in trisomy 21/AD, probably reflecting increased A beta production. In apoE epsilon 4/AD, the size distribution is unchanged but the number of SP is increased compared to apoE epsilon 3, suggesting increased probability of SP initiation. These results demonstrate that subgroups of AD patients defined on the basis of molecular characteristics have quantitatively different neuropathological phenotypes.