Multi-sample cluster analysis using Akaike's Information Criterion

Summary Multi-sample cluster analysis, the problem of grouping samples, is studied from an information-theoretic viewpoint via Akaike's Information Criterion (AIC). This criterion combines the maximum value of the likelihood with the number of parameters used in achieving that value. The multi-sample cluster problem is defined, and AIC is developed for this problem. The form of AIC is derived in both the multivariate analysis of variance (MANOVA) model and in the multivariate model with varying mean vectors and variance-covariance matrices. Numerical examples are presented for AIC and another criterion calledw-square. The results demonstrate the utility of AIC in identifying the best clustering alternatives. This research was supported by Office of Naval Research Contract N00014-80-C-0408, Task NR042-443 and Army Research Office Contract DAAG 29-82-K-0155, at the University of Illinois at Chicago.     

3D composition of epitaxial nanocrystals by anomalous X-ray diffraction: observation of a Si-rich core in Ge domes on Si(100)

Three-dimensional composition maps of nominally pure Ge domes grown on Si(001) at 600 degrees C were obtained from grazing incidence anomalous x-ray scattering data at the Ge K edge. The data were analyzed in terms of a stack of layers with laterally varying concentration. The results demonstrated that the domes contained a Si-rich core covered by a Ge-rich shell and were independently supported by selective etch experiments. The composition profile resulted from substrate Si alloying into the Ge during growth to partially relax the stress in and under the domes.     

Automatic Symmetrization and Energy Estimates Using Local Operators for Partial Differential Equations

We develop a method for automatically symmetrizing Petrowsky well-posed Cauchy problems for constant coefficient linear partial differential equations. The method is rooted in the Sturm sequence technique for establishing the location of the roots of a complex polynomial and can be automated using standard symbolic computation tools. In the special case of homogeneous strictly hyperbolic scalar equations, we show that the resulting estimates are strong enough to control all principal order derivatives and thus can be used in place of the Leray energies. We also illustrate the method by applying it to various problems of mixed type.     

AssignFit: a program for simultaneous assignment and structure refinement from solid-state NMR spectra

AssignFit is a computer program developed within the XPLOR-NIH package for the assignment of dipolar coupling (DC) and chemical shift anisotropy (CSA) restraints derived from the solid-state NMR spectra of protein samples with uniaxial order. The method is based on minimizing the difference between experimentally observed solid-state NMR spectra and the frequencies back calculated from a structural model. Starting with a structural model and a set of DC and CSA restraints grouped only by amino acid type, as would be obtained by selective isotopic labeling, AssignFit generates all of the possible assignment permutations and calculates the corresponding atomic coordinates oriented in the alignment frame, together with the associated set of NMR frequencies, which are then compared with the experimental data for best fit. Incorporation of AssignFit in a simulated annealing refinement cycle provides an approach for simultaneous assignment and structure refinement (SASR) of proteins from solid-state NMR orientation restraints. The methods are demonstrated with data from two integral membrane proteins, one α-helical and one β-barrel, embedded in phospholipid bilayer membranes.     

Comprehensive inter‐laboratory calibration of reference materials for δ18O versus VSMOW using various on‐line high‐temperature conversion techniques

Internationally distributed organic and inorganic oxygen isotopic reference materials have been calibrated by six laboratories carrying out more than 5300 measurements using a variety of high‐temperature conversion techniques (HTC) a in an evaluation sponsored by the International Union of Pure and Applied Chemistry (IUPAC). To aid in the calibration of these reference materials, which span more than 125‰, an artificially enriched reference water (δ¹⁸O of +78.91‰) and two barium sulfates (one depleted and one enriched in ¹⁸O) were prepared and calibrated relative to VSMOW2 b and SLAP reference waters. These materials were used to calibrate the other isotopic reference materials in this study, which yielded:

Dual quartz crystal microbalance compensation using a submerged reference crystal. Effect of surface roughness and liquid properties

Absolute resonant frequency measurements were made on gold-coated AT-cut quartz crystals with one face in contact with a series of liquids. The effect of surface roughness and liquid properties (viscosity and density) was analyzed in terms of a “trapped liquid” model. In this model, liquid present in surface imperfections is viewed as rigidly coupled mass. In some of the literature this density-dependent, but not viscosity-dependent, term is viewed as being additive to the hydrodynamic shift seen for a smooth surface. Data obtained using 1 μm and 5 μm surface finish crystals are inconsistent with the predictions of the trapped liquid model. This suggests hydrodynamic coupling between liquid internal and external to the crevices. Despite the lack of a theoretical model for the liquid motion, it is possible to compensate for frequency variations resulting from changing liquid properties and for roughness effects by making direct measurements of the resonant frequency difference between two crystals exposed to the same solution. This novel procedure works to the extent that the two crystals have similar surface topographies. Compensation is excellent for 1 μm finish crystals and good for 5 μm finish crystals.     

Structure determination of a membrane protein with two trans-membrane helices in aligned phospholipid bicelles by solid-state NMR spectroscopy

The structure of the membrane protein MerFt was determined in magnetically aligned phospholipid bicelles by solid-state NMR spectroscopy. With two trans-membrane helices and a 10-residue inter-helical loop, this truncated construct of the mercury transport membrane protein MerF has sufficient structural complexity to demonstrate the feasibility of determining the structures of polytopic membrane proteins in their native phospholipid bilayer environment under physiological conditions. PISEMA, SAMMY, and other double-resonance experiments were applied to uniformly and selectively (15)N-labeled samples to resolve and assign the backbone amide resonances and to measure the associated (15)N chemical shift and (1)H-(15)N heteronuclear dipolar coupling frequencies as orientation constraints for structure calculations. (1)H/(13)C/(15)N triple-resonance experiments were applied to selectively (13)C'- and (15)N-labeled samples to complete the resonance assignments, especially for residues in the nonhelical regions of the protein. A single resonance is observed for each labeled site in one- and two-dimensional spectra. Therefore, each residue has a unique conformation, and all protein molecules in the sample have the same three-dimensional structure and are oriented identically in planar phospholipid bilayers. Combined with the absence of significant intensity near the isotropic resonance frequency, this demonstrates that the entire protein, including the loop and terminal regions, has a well-defined, stable structure in phospholipid bilayers.     

Self-assembled monolayers on Pt(111): molecular packing structure and strain effects observed by scanning tunneling microscopy

Self-assembled monolayers (SAMs) of octanethiol and benzeneethanethiol were deposited on clean Pt(111) surfaces in ultrahigh vacuum (UHV). Highly resolved images of these SAMs produced by an in situ scanning tunneling microscope (STM) showed that both systems organize into a super-structure mosaic of domains of locally ordered, closely packed molecules. Analysis of the STM images indicated a (square root 3 x square root 3)R30 degrees unit cell for the octanethiol SAMs and a 4(square root 3 x square root 3)R30 degrees periodicity based on 2 x 2 basic molecular packing for the benzeneethanethiol SAMs under the coverage conditions investigated. SAMs on Pt(111) exhibited differences in molecular packing and a lower density of disordered regions than SAMs on Au(111). Electron transport measurements were performed using scanning tunneling spectroscopy. Benzeneethanethiol/Pt(111) junctions exhibited a higher conductance than octanethiol/Pt(111) junctions.     

Two-Photon Excitation of 4'-Hydroxymethyl-4,5',8-Trimethylpsoralen

Abstract— Psoralens are a class of pharmaceutical agents commonly used to treat several cutaneous disorders. When irradiated with a mode-locked titanium: sapphire (Ti: sapphire) laser tuned to 730 nm, an aqueous solution of 4'-hydroxymethyl-4,5',8-trimethylpsoralen (HMT) emits blue light. The emission spectrum is centered at 452 nm and is identical to that obtained by one-photon excitation with UVA excitation, and its magnitude depends quad-ratically on the intensity of laser excitation. These results suggest that two-photon excitation occurs to a potentially photochemically active state. To estimate the two-photon absorption cross section, it was first necessary to measure the emission quantum yield of HMT using 365 nm excitation at room temperature that resulted in a value of 0.045 ± 0.007. The two-photon absorption cross section of HMT at 730 nm is therefore estimated to be 20 ± 10⁻⁵⁰ cm⁴ s (20 Göppert-Mayer). The excited-state photophysics and photochemistry of psoralens suggest potential applications to cutaneous phototherapy in diseases such as psoriasis and dystrophic epidermolysis bullosa.