### 2007 week 03: Articles in Maths

Interaction geometry involving planar groups in protein-protein interfaces

The geometry of interactions of planar residues is nonrandom in protein tertiary structures and gives rise to conventional, as well as nonconventional (XH···, XH···O, where X = C, N, or O) hydrogen bonds. Whether a similar geometry is maintained when the interaction is across the protein-protein interface is addressed here. The relative geometries of interactions involving planar residues, and the percentage of contacts giving rise to different types of hydrogen bonds are quite similar in protein structures and the biological interfaces formed by protein chains in homodimers and protein-protein heterocomplexes - thus pointing to the similarity of chemical interactions that occurs during protein folding and binding. However, the percentage is considerably smaller in the nonspecific and nonphysiological interfaces that are formed in crystal lattices of monomeric proteins. The CH···O interaction linking the aromatic and the peptide groups is quite common in protein structures as well as the three types of interfaces. However, as the interfaces formed by crystal contacts are depleted in aromatic residues, the weaker hydrogen bond interactions would contribute less toward their stability. Proteins 2007; © 2007 Wiley-Liss, Inc.

Science's breakthrough of the year -- The Poincaré Theorem

Science honors the top 10 research advances of 2006

In 2006, researchers closed a major chapter in mathematics, reaching a consensus that the elusive Poincaré Conjecture, which deals with abstract shapes in three-dimensional space, had finally been solved. Science and its publisher AAAS, the nonprofit society, now salute this development as the Breakthrough of the Year and also give props to nine other of the year’s most significant scientific accomplishments.

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The Poincaré Conjecture is part of a branch of mathematics called topology, informally known as "rubber sheet geometry" because it involves surfaces that can undergo arbitrary amounts of stretching. The conjecture, proposed in 1904 by Henri Poincaré, describes a test for showing that a space is equivalent to a "hypersphere," the three-dimensional surface of a four-dimensional ball.

Partial least squares: a versatile tool for the analysis of high-dimensional genomic data

Partial least squares (PLS) is an efficient statistical regression technique that is highly suited for the analysis of genomic and proteomic data. In this article, we review both the theory underlying PLS as well as a host of bioinformatics applications of PLS. In particular, we provide a systematic comparison of the PLS approaches currently employed, and discuss analysis problems as diverse as, e.g. tumor classification from transcriptome data, identification of relevant genes, survival analysis and modeling of gene networks and transcription factor activities.

Multivariate Distribution Function

Multivariate distribution functions are typically found in probability theory, and especially in statistics. An example of a commonly used multivariate distribution function is the multivariate Gaussian distribution function.

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The attempt here is to study a class of functions that can be used as models for distributions of distances between points in a “probabilistic metric space”.

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Labels: dimension, geometry, hydrogen, probability, protein, proteome, statistics, topology

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