Multivariate rational data fitting: general data structure,maximal accuracy and object orientation

Sections 1 and 2 discuss the advantages of an object-oriented implementation combined with higher floating-point arithmetic, of the algorithms available for multivariate data fitting using rational functions. Section 1 will in particular explain what we mean by higher arithmetic. Section 2 will concentrate on the concepts of object orientation. In sections 3 and 4 we shall describe the generality of the data structure that can be dealt with: due to some new results virtually every data set is acceptable right now, with possible coalescence of coordinates or points. In order to solve the multivariate rational interpolation problem the data sets are fed to different algorithms depending on the structure of the interpolation points in then-variate space.This text is a preparatory publication for the development of a scientific expert system for multivariate rational interpolation. The issues addressed are relevant to the implementation of such a system.     

Metallic stripe in two dimensions: stability and spin-charge separation

The problems of charge stripe formation, spin-charge separation, and stability of the antiphase domain wall (ADW) associated with a stripe are addressed using an analytical approach to the t- J(z) model. We show that a metallic stripe together with its ADW is the ground state of the problem in the low doping regime. The stripe is described as a system of spinons and magnetically confined holons strongly coupled to the two dimensional spin environment with holon-spin-polaron elementary excitations filling a one-dimensional band.     

Potential and limitations of ensemble docking

A major problem in structure-based virtual screening applications is the appropriate selection of a single or even multiple protein structures to be used in the virtual screening process. A priori it is unknown which protein structure(s) will perform best in a virtual screening experiment. We investigated the performance of ensemble docking, as a function of ensemble size, for eight targets of pharmaceutical interest. Starting from single protein structure docking results, for each ensemble size up to 500,000 combinations of protein structures were generated, and, for each ensemble, pose prediction and virtual screening results were derived. Comparison of single to multiple protein structure results suggests improvements when looking at the performance of the worst and the average over all single protein structures to the performance of the worst and average over all protein ensembles of size two or greater, respectively. We identified several key factors affecting ensemble docking performance, including the sampling accuracy of the docking algorithm, the choice of the scoring function, and the similarity of database ligands to the cocrystallized ligands of ligand-bound protein structures in an ensemble. Due to these factors, the prospective selection of optimum ensembles is a challenging task, shown by a reassessment of published ensemble selection protocols.     

An adeno-associated viral vector transduces the rat hypothalamus and amygdala more efficient than a lentiviral vector

Background  

This study compared the transduction efficiencies of an adeno-associated viral (AAV) vector, which was pseudotyped with an AAV1 capsid and encoded the green fluorescent protein (GFP), with a lentiviral (LV) vector, which was pseudotyped with a VSV-G envelop and encoded the discosoma red fluorescent protein (dsRed), to investigate which viral vector transduced the lateral hypothalamus or the amygdala more efficiently. The LV-dsRed and AAV1-GFP vector were mixed and injected into the lateral hypothalamus or into the amygdala of adult rats. The titers that were injected were 1 × 10⁸ or 1 × 10⁹ genomic copies of AAV1-GFP and 1 × 10⁵ transducing units of LV-dsRed.     

Exploring multivariate Padé approximants for multiple hypergeometric series

We investigate the approximation of some hypergeometric functions of two variables, namely the Appell functions F _i , i = 1,...,4, by multivariate Padé approximants. Section 1 reviews the results that exist for the projection of the F _i onto ϰ=0 or y=0, namely, the Gauss function ₂ F ₁(a, b; c; z), since a great deal is known about Padé approximants for this hypergeometric series. Section 2 summarizes the definitions of both homogeneous and general multivariate Padé approximants. In section 3 we prove that the table of homogeneous multivariate Padé approximants is normal under similar conditions to those that hold in the univariate case. In contrast, in section 4, theorems are given which indicate that, already for the special case F ₁(a, b, b′; c; x; y) with a = b = b′ = 1 and c = 2, there is a high degree of degeneracy in the table of general multivariate Padé approximants. Section 5 presents some concluding remarks, highlighting the difference between the two types of multivariate Padé approximants in this context and discussing directions for future work. This revised version was published online in June 2006 with corrections to the Cover Date.     

Synthesis of strained cyclic peptides via an aza-Michael-acyl-transfer reaction cascade

A new method is presented to prepare strained lactams. Esterification of the C-terminus of a dipeptide with β-nitrostyrene or quinoline-type auxiliaries is followed by lactam formation by an intramolecular aza-Michael-acyl-transfer reaction cascade. Ultimately, the cyclic tetrapeptide cyclo[Phe-Tyr-Ala-Gly] has been prepared.     

The consequences of translational and rotational entropy lost by small molecules on binding to proteins

When a small molecule binds to a protein, it loses a significant amount of rigid body translational and rotational entropy. Estimates of the associated energy barrier vary widely in the literature yet accurate estimates are important in the interpretation of results from fragment-based drug discovery techniques. This paper describes an analysis that allows the estimation of the rigid body entropy barrier from the increase in binding affinities that results when two fragments of known affinity and known binding mode are joined together. The paper reviews the relatively rare number of examples where good quality data is available. From the analysis of this data, we estimate that the barrier to binding, due to the loss of rigid-body entropy, is 15–20 kJ/mol, i.e. around 3 orders of magnitude in affinity at 298 K. This large barrier explains why it is comparatively rare to observe multiple fragments binding to non-overlapping adjacent sites in enzymes. The barrier is also consistent with medicinal chemistry experience where small changes in the critical binding regions of ligands are often poorly tolerated by enzymes.     

Magnetic ordering below 10K in the high-Tc superconductor YBa2(Cu0.985Fe0.015)3O7−σ

The high-temperature superconductor with the nominal composition YBa₂Cu₃O_7?σ has been doped with iron 93% enriched in⁵⁷Fe. When 1.5 at % Fe substitutes for Cu, the transition temperature is reduced by about 30° K with full ac shielding (X′=?1/4π) achieved by ≈40 K. At room temperature the Mössbauer spectrum consists of three overlapping doublets. Below 10 K, hyperfine-field splitting is observed; relaxation still takes place at T=1.8 K.