A fourier fingerprint-based method for protein surface representation

A crucial enabling technology for structural genomics is the development of algorithms that can predict the putative function of novel protein structures: the proposed functions can subsequently be experimentally tested by functional studies. Testable assignments of function can be made if it is possible to attribute a putative, or indeed probable, function on the basis of the shapes of the binding sites on the surface of a protein structure. However the comparison of the surfaces of 3D protein structures is a computationally demanding task. Here we present four surface representations that can be used locally to describe the global shape of specifically bounded local region models. The most successful of these representations is obtained by a Fourier analysis of the distribution of surface curvature on concentric spheres around a surface point and summarizes a 24 A diameter spherically clipped region of protein surface by a fingerprint of 18 Fourier amplitude values. Searching experiments using these fingerprints on a set of 366 proteins demonstrate that this provides an effective and an efficient technique for the matching of protein surfaces.     

The selective enhancement of band intensities in resonance Raman spectra of cobalt corrinoids

The role of point group symmetry in relation to localized-site cluster expansions is elucidated. Simple ways in which to accomplish symmetry adaptation are described, and new supersymmetries are found to arise for certain types of wave function ansätze. These new supersymmetries are shown to provide additional quantum numbers, which although often approximate are found in some model cases to be exact.     

Equation structure and the meaning of the equal sign: The impact of task selection in eliciting elementary students’ understandings

This paper reports results from a written assessment given to 290 third-, fourth-, and fifth-grade students prior to any instructional intervention. We share and discuss students’ responses to items addressing their understanding of equation structure and the meaning of the equal sign. We found that many students held an operational conception of the equal sign and had difficulty recognizing underlying structure in arithmetic equations. Some students, however, were able to recognize underlying structure on particular tasks. Our findings can inform early algebra efforts by highlighting the prevalence of the operational view and by identifying tasks that have the potential to help students begin to think about equations in a structural way at the very beginning of their early algebra experiences.     

Structural DNA profiles: single sequence queries

Structural DNA profiles use the structural properties of the constituent octamers either to observe any characteristics of a single sequence that are unusual (a single sequence query) or to visualize a pattern common to a set of sequences (a multiple sequence query). They are an aid in understanding structural reasons for functional DNA activity. Profiles that answer single sequence queries are introduced and Profile Manager (a software application developed to automate profile generation) is presented. Two sequences that are similar by their nucleotide composition but are known to be very different by structure are analyzed, resulting in useful illustrations that agree with the experimental nuclear magnetic resonance structures.     

Genomic data analysis using DNA structure: an analysis of conserved nongenic sequences and ultraconserved elements

Recent comparative studies of the human and mouse genomes have revealed sets of conserved nongenic sequences (CNGs) and sets of ultraconserved elements (UCEs). Both sets of sequences, which exhibit extremely high levels of conservation, extend over hundreds of bases and have no known function. Since there is no detectable sequence homology between paralogous CNGs or UCEs in either of the species, an alignment-free technique is needed for their analysis. We have previously compiled a database of the structural properties of all 32,896 unique DNA octamers, including information on stability, the minimum energy conformation, and flexibility. We have used Fourier techniques to analyze the UCEs and CNGs in terms of their octamer structural properties, to reveal structural correlations which may indicate possible functions for some of these sequences.     

Convex Hull Algorithms for Piecewise Linear-Quadratic Functions in Computational Convex Analysis

Computing the convex envelope is a core operation in nonsmooth analysis that bridges the convex with the nonconvex world. Although efficient algorithms to compute fundamental transforms of convex analysis have been proposed over the years, they are limited to convex functions until an efficient algorithm becomes available to compute the convex envelope of a piecewise linear-quadratic function (of one variable) efficiently. We present two such algorithms, one based on maximum and conjugate computation that is easy to implement but has quadratic time complexity, and another based on direct computation that requires more work to implement but has optimal (linear time) complexity. We prove their time (and space) complexity, and compare their performances.     

NMR‐Solution Structures of Fluoro‐Substituted β‐Peptides: A 314‐Helix and a Hairpin Turn. The First Case of a 90° OC?C?F Dihedral Angle in an α‐Fluoro‐Amide Group

To further study the preference of the antiperiplanar (ap) conformation in α‐fluoro‐amide groups, two β‐peptides, 1 and 2 , containing a (2‐F)‐β³hAla and a (2‐F)‐β²hPhe residue, have been synthesized. Their NMR‐solution structures in CD₃OH were determined and compared with those of non‐F‐substituted analogs, 3 and 4a . While we have found in a previous investigation (Helv. Chim. Acta 2005 , 88, 266) that a stereospecifically introduced F‐substituent in the central position of a β‐heptapeptide is capable of ‘breaking’ the 3₁₄‐helical structure by enforcing the F? C? C?O ap‐conformation, we could now demonstrate that the same procedure leads to a structure with the unfavorable ca. 90° F? C? C?O dihedral angle, enforced by the 3₁₄‐helical folding in a β‐tridecapeptide (cf. 1 ; Fig. 4). This is interpreted as a consequence of cooperative folding in the longer β‐peptide. A F‐substituent placed in the turn section of a β‐peptidic hairpin turn was shown to be in an ap‐arrangement with respect to the neighboring C?O bond (cf. 2 ; Fig. 7). Analysis of the non‐F‐substituted β‐tetrapeptides (with helix‐preventing configurations of the two central β²/β³‐amino acid residues) provides unusually tight hairpin structural clusters (cf. 3 and 4a ; Figs. 8 and 9). The skeleton of the β‐tetrapeptide H‐(R)β³hVal‐(R)β²hVal‐(R)β³hAla‐(S)β³hPhe‐OH ( 4a ) is proposed as a novel, very simple backbone structure for mimicking α‐peptidic hairpin turns.     

Raman studies of molten salt hydrates: the beryllium and aluminium nitrate-water systems

Raman spectra of the liquid systems Be(NO₃)₂ · 20H₂O, Be(NO₃)₂ · 4H₂O, Al(NO₃)₃·20H₂O, and Al(NO₃)₃ · 9H₂O have been recorded. The spectra are analysed in terms of vibrational modes arising from water, the nitrate ion, the aquated metal ions and hydrolysis products. For the concentrated beryllium system, though not for the aluminium system, the spectra suggest a significant degree of proton transfer from [Be(OH₂)₄]²⁺ to NO₃^?. Solvent-separated metal-nitrate ion pairs appear to be present in all the systems studied.