FUNCTIONAL PRINCIPAL COMPONENTS MODEL FOR HIGH-DIMENSIONAL BRAIN IMAGING

We establish a fundamental equivalence between singular value decomposition (SVD) and functional principal components analysis (FPCA) models. The constructive relationship allows to deploy the numerical efficiency of SVD to fully estimate the components of FPCA, even for extremely high-dimensional functional objects, such as brain images. As an example, a functional mixed effect model is fitted to high-resolution morphometric (RAVENS) images. The main directions of morphometric variation in brain volumes are identified and discussed.

Three-dimensional consensus structure of sst2-selective somatostatin (SRIF) antagonists by NMR

The three-dimensional NMR structures of seven octapeptide analogs of somatostatin (SRIF), based on octreotide, with the basic sequence H-Cpa/Phe2-c[DCys3-Xxx7-DTrp/DAph(Cbm)8-Lys9-Thr10-Cys14]-Yyy-NH2 (the numbering refers to the position in native SRIF), with Xxx7 being Aph(Cbm)/Tyr/Agl(NMe,benzoyl) and Yyy being Nal/DTyr/Thr, are presented here. Most of these analogs exhibit potent and highly selective binding to sst2 receptors, and all of the analogs are antagonists inhibiting receptor signaling. Based on their consensus 3D structure, the pharmacophore of the sst2-selective antagonist has been defined. The pharmacophore involves the side chains of Cpa2, DTrp/DAph(Cbm)8, and Lys9, with the backbone for most of the sst2-selective antagonists comprised a Type-II' beta-turn. Hence, the sst2-selective antagonist pharmacophore is very similar to the sst2-selective agonist pharmacophore previously described.

Preservation of high resolution protein structure by cryo-electron microscopy of vitreous sections

We have quantitated the degree of structural preservation in cryo-sections of a vitrified biological specimen. Previous studies have used sections of periodic specimens to assess the resolution present, but preservation before sectioning was not assessed and so the damage due particularly to cutting was not clear. In this study large single crystals of lysozyme were vitrified and from these X-ray diffraction patterns extending to better than 2.1A were obtained. The crystals were high pressure frozen in 30% dextran, and cryo-sectioned using a diamond knife. In the best case, preservation to a resolution of 7.9A was shown by electron diffraction, the first observation of sub-nanometre structural preservation in a vitreous section.

On low-dimensional projections of high-dimensional distributions

Let P be a probability distribution on q -dimensional space. The so-called Diaconis-Freedman effect means that for a fixed dimension d<

Similarity Mapplet: Interactive Visualization of the Directory of Useful Decoys and ChEMBL in High Dimensional Chemical Spaces

An Internet portal accessible at www.gdb.unibe.ch has been set up to automatically generate color-coded similarity maps of the ChEMBL database in relation to up to two sets of active compounds taken from the enhanced Directory of Useful Decoys (eDUD), a random set of molecules, or up to two sets of user-defined reference molecules. These maps visualize the relationships between the selected compounds and ChEMBL in six different high dimensional chemical spaces, namely MQN (42-D molecular quantum numbers), SMIfp (34-D SMILES fingerprint), APfp (20-D shape fingerprint), Xfp (55-D pharmacophore fingerprint), Sfp (1024-bit substructure fingerprint), and ECfp4 (1024-bit extended connectivity fingerprint). The maps are supplied in form of Java based desktop applications called “similarity mapplets” allowing interactive content browsing and linked to a “Multifingerprint Browser for ChEMBL” (also accessible directly at www.gdb.unibe.ch) to perform nearest neighbor searches. One can obtain six similarity mapplets of ChEMBL relative to random reference compounds, 606 similarity mapplets relative to single eDUD active sets, 30 300 similarity mapplets relative to pairs of eDUD active sets, and any number of similarity mapplets relative to user-defined reference sets to help visualize the structural diversity of compound series in drug optimization projects and their relationship to other known bioactive compounds.

Definition of a metal-dependent/Li(+)-inhibited phosphomonoesterase protein family based upon a conserved three-dimensional core structure.

Inositol polyphosphate 1-phosphatase, inositol monophosphate phosphatase, and fructose 1,6-bisphosphatase share a sequence motif, Asp-Pro-(Ile or Leu)-Asp-(Gly or Ser)-(Thr or Ser), that has been shown by crystallographic and mutagenesis studies to bind metal ions and participate in catalysis. We compared the six alpha-carbon coordinates of this motif from the crystal structures of these three phosphatases and found that they are superimposable with rms deviations ranging from 0.27 to 0.60 A. Remarkably, when these proteins were aligned by this motif a common core structure emerged, defined by five alpha-helices and 11 beta-strands comprising 155 residues having rms deviations ranging from 1.48 to 2.66 A. We used the superimposed structures to align the sequences within the common core, and a distant relationship was observed suggesting a common ancestor. The common core was used to align the sequences of several other proteins that share significant similarity to inositol monophosphate phosphatase, including proteins encoded by fungal qa-X and qutG, bacterial suhB and cysQ (identical to amtA), and yeast met22 (identical to hal2). Evolutionary comparison of the core sequences indicate that five distinct branches exist within this family. These proteins share metal-dependent/Li(+)-sensitive phosphomonoesterase activity, and each predicted tree branch exhibits unique substrate specificity. Thus, these proteins define an ancient structurally conserved family involved in diverse metabolic pathways including inositol signaling, gluconeogenesis, sulfate assimilation, and possibly quinone metabolism. Furthermore, we suggest that this protein family identifies candidate enzymes to account for both the therapeutic and toxic actions of Li+ as it is used in patients treated for manic depressive disease.

Cluster analysis of high-dimensional data: A case study

Normal mixture models are often used to cluster continuous data. However, conventional approaches for fitting these models will have problems in producing nonsingular estimates of the component-covariance matrices when the dimension of the observations is large relative to the number of observations. In this case, methods such as principal components analysis (PCA) and the mixture of factor analyzers model can be adopted to avoid these estimation problems. We examine these approaches applied to the Cabernet wine data set of Ashenfelter (1999), considering the clustering of both the wines and the judges, and comparing our results with another analysis. The mixture of factor analyzers model proves particularly effective in clustering the wines, accurately classifying many of the wines by location.

A principled approach to interactive hierarchical non-linear visualization of high-dimensional data

Hierarchical visualization systems are desirable because a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex high-dimensional data sets. We extend an existing locally linear hierarchical visualization system PhiVis [1] in several directions: bf(1) we allow for em non-linear projection manifolds (the basic building block is the Generative Topographic Mapping -- GTM), bf(2) we introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree, bf(3) we describe folding patterns of low-dimensional projection manifold in high-dimensional data space by computing and visualizing the manifold's local directional curvatures. Quantities such as magnification factors [3] and directional curvatures are helpful for understanding the layout of the nonlinear projection manifold in the data space and for further refinement of the hierarchical visualization plot. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. We demonstrate the visualization system principle of the approach on a complex 12-dimensional data set and mention possible applications in the pharmaceutical industry.

Computational mechanics of molecular systems:quantifying high-dimensional dynamics by distribution of Poincaré recurrence times

A framework that connects computational mechanics and molecular dynamics has been developed and described. As the key parts of the framework, the problem of symbolising molecular trajectory and the associated interrelation between microscopic phase space variables and macroscopic observables of the molecular system are considered. Following Shalizi and Moore, it is shown that causal states, the constituent parts of the main construct of computational mechanics, the e-machine, define areas of the phase space that are optimal in the sense of transferring information from the micro-variables to the macro-observables. We have demonstrated that, based on the decay of their Poincare´ return times, these areas can be divided into two classes that characterise the separation of the phase space into resonant and chaotic areas. The first class is characterised by predominantly short time returns, typical to quasi-periodic or periodic trajectories. This class includes a countable number of areas corresponding to resonances. The second class includes trajectories with chaotic behaviour characterised by the exponential decay of return times in accordance with the Poincare´ theorem.

Generation of infrared surface plasmon resonances with high refractive index sensitivity utilizing tilted fiber Bragg gratings

We demonstrate the use of tilted fiber gratings to assist the generation of localized infrared surface plasmons with short propagation lengths and a sensitivity of d lambda/dn = 3365 nm in the aqueous index regime. It was also found that the resonances could be spectrally tuned over 1000 nm at the same spatial region with high coupling efficiency (in excess of 25 dB) by altering the polarization of the light illuminating the device.

Optic sensors of high refractive-index responsivity and low thermal cross sensitivity that use fiber Bragg gratings of >80° tilted structures

For the first time to the authors' knowledge, fiber Bragg gratings (FBGs) with >80° tilted structures have been fabricated and characterized. Their performance in sensing temperature, strain, and the surrounding medium's refractive index was investigated. In comparison with normal FBGs and long-period gratings (LPGs), >80° tilted FBGs exhibit significantly higher refractive-index responsivity and lower thermal cross sensitivity. When the grating sensor was used to detect changes in refractive index, a responsivity as high as 340nm/refractive-index unit near an index of 1.33 was demonstrated, which is three times higher than that of conventional LPGs.

High refractive index plastic optical materials

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Generation of infrared surface plasmon resonances with high refractive index sensitivity utilizing tilted fiber Bragg gratings

We demonstrate the use of tilted fiber gratings to assist the generation of localized infrared surface Plasmons with short propagation lengths and a sensitivity of dλ/dn = 3365 nm in the aqueous index regime. It was also found that the resonances could be spectrally tuned over 1000 nm at the same spatial region with high coupling efficiency (in excess of 25 dB) by altering the polarization of the light illuminating the device. © 2007 Optical Society of America.