Structure-based identification and clustering of protein families and superfamilies

Summary We describe an approach to protein structure comparison designed to detect distantly related proteins of similar fold, where the procedure must be sufficiently flexible to take into account the elasticity of protein folds without losing specificity. Protein structures are represented as a series of secondary structure elements, where for each element a local environment describes its relations with the elements that surround it. Secondary structures are then aligned by comparing their features and local environments. The procedure is illustrated with searches of a database of 468 protein structures in order to identify proteins of similar topology to porcine pepsin, porphobilinogen deaminase and serum amyloid P-component. In all cases the searches correctly identify protein structures of similar fold as the search proteins. Multiple cross-comparisons of protein structures allow the clustering of proteins of similar fold. This is exemplified with a clustering of /- and -class protein structures. We discuss applications of the comparison and clustering of three-dimensional protein structures to comparative modelling and structure-based protein design.     

A molecular filter based velocimetry technique for high speed flows

A molecular absorption filter-based diagnostic technique has been developed to obtain instantaneous, planar velocity measurements in high speed flows. This paper presents the details of the technique and its application in high Reynolds number compressible mixing layers with convective Mach numbers of 0.51 and 0.86. Pressure broadening was used to tune the absorption profile of the filter to a given flow field/optical arrangement. It is shown that two filters can be used when background scattering is significant: one as the velocity-discriminating filter, the other to eliminate unwanted background light from the reference camera. Collected images show instantaneous variations in velocity within both the highly organized roller type structures of the M _c = 0.51 mixing layer and the unorganized structures found in both mixing layers. An uncertainty analysis showed that the measurement uncertainty was ±8.6% for the current measurements, but improvements to reduce the uncertainty to ±3% are suggested.The authors would like to acknowledge support for this research from NASA Lewis Research Center under Dr. K. B. M. Q. Zaman (NAG3-764) the Air Force Office of Scientific Research under Dr. L. Sakell (AFOSR-91-0412), and an equipment grant from NSF (CTS-9006879). A fellowship from NSF to S. A. Arnette is gratefully acknowledged. The authors also wish to thank the AARL staff and graduate students M.F. Reeder and V.M. Belovich for their help. Thanks go to Prof. R.B. Miles and J.N. Forkey of Princeton University for their cooperation in obtaining measurements of the absorption profiles.     

Asymptotics of heavy atoms in high magnetic fields: II. Semiclassical regions

The ground state energy of an atom of nuclear chargeZe in a magnetic fieldB is exactly evaluated to leading order asZ in the following three regions:BZ ^4/3,BZ ^4/3 andZ ^4/3BZ³. In each case this is accomplished by a modified Thomas-Fermi (TF) type theory. We also analyze these TF theories in detail, one of their consequences being the nonintuitive fact that atoms are spherical (to leading order) despite the leading order change in energy due to theB field. This paper complements and completes our earlier analysis [1], which was primarily devoted to the regionsBZ ³ andBZ³ in which a semiclassical TF analysis is numerically and conceptually wrong. There are two main mathematical results in this paper, needed for the proof of the exactitude of the TF theories. One is a generalization of the Lieb-Thirring inequality for sums of eigenvalues to include magnetic fields. The second is a semiclassical asymptotic formula for sums of eigenvalues that isuniform in the fieldB.Work partially supported by U.S. National Science Foundation grant PHY90-19433 A02Work partially supported by U.S. National Science Foundation grant DMS 92-03829Work partially supported by the Heraeus Stiftung and the Research Fund of the University of Iceland.     

Absence of renormalization group pathologies near the critical temperature. Two examples

We consider real-space renormalization group transformations for Ising-type systems which are formally defined by $$\exp \left[ { - H'(\sigma ')} \right] = \sum\limits_\sigma {T(\sigma ,\sigma ')} \exp \left[ { - H(\sigma )} \right]$$ whereT(σ, σ′) is a probability kernel, i.e., ∑_σ′ T(σ,σ′) = 1 for every configuration σ. For each choice of the block spin configuration σ′, let σ′, let μ_σ′ be the measure on spin configurations σ which is formally given by taking the probability of σ to be proportional toT(σ, σ′) exp[?H(σ)]. We give a condition which is sufficient to imply that the renormalized HamiltonianH′ is defined. Roughly speaking, the condition is that the collection of measures μ_σ′ is in the high-temperature phase uniformly in the block spin configuration σ′. The proof of this result uses methods of Olivieri and Picco. We use our theorem to prove that the first iteration of the renormalization group transformation is defined in the following two examples: decimation with spacingb = 2 on the square lattice with β < 1.36β _c and the Kadanoff transformation with parameterp on the trian gular lattice in a subset of the β,p plane that includes values of β greater than β _c .     

Simultaneous determination of propranolol and pindolol by synchronous spectrofluorimetry

A completely automated method to determine the most common parameters in cured meat products is proposed. The approach to full automation is based on the coupling of a robotic station for development of preliminary operations (namely weighing of the sample, grinding, leaching, filtration and transport to the aspiration zone) and a continuous unsegmented manifold for derivatisation and spectrophotometric monitoring of the reaction coloured products. This assembly works in an unattended fashion thus eliminating the bottleneck produced by the determination of these parameters in routine laboratories. The good agreement between results obtained by the proposed method and those from conventional methods for target analytes confirms its excellent performance and usefulness.     

Mixing automorphisms of compact groups and a theorem of Schlickewei

Summary We prove that every mixing ^d by automorphisms of a compact, connected, abelian group is mixing of all orders.Oblatum 5-II-1992The second author gratefully acknowledges support from NSF grant DMS-91-03056 at the Ohio State University