Evidence for C?Cl/C?Br⋅⋅⋅π Interactions as an Important Contribution to Protein–Ligand Binding Affinity

Attractive chlorine : Noncovalent interactions between chlorine or bromine atoms and aromatic rings in proteins open up a new method for the manipulation of molecular recognition. Substitution at distinct positions of two factor Xa inhibitors improves the free energy of binding by interaction with a tyrosine unit. The generality of this motif was underscored by multiple crystal structures as well as high‐level quantum chemical calculations (see picture).

     

Suitability of infrared spectroscopic imaging as an intraoperative tool in cerebral glioma surgery

Infrared spectroscopic imaging is a promising intraoperative tool which enables rapid, on-site diagnosis of brain tumors during neurosurgery. A classification model was recently developed using infrared spectroscopic images from thin tissue sections to grade malignant gliomas, the most frequent class of primary brain tumor. In this study the model was applied to 54 specimens from six patients with inhomogeneous gliomas composed of regions with different tumor density and morphology. The resection was controlled using neuronavigation which transfers the findings obtained by preoperative magnetic resonance imaging (MRI) into the operating field. For comparison, all specimens were independently evaluated by histopathology after hematoxylin and eosin staining. The infrared-derived grading agreed with histopathology and MRI findings for almost all specimens. With regard to histopathological assessment, sensitivities of 100% (22/22) and 93.1% (27/29) and specificities of 96.9% (31/32) and 88.0% (22/25) were achieved, depending on whether the classification was based on the predominant or maximal tumor grade, respectively, in the specimen. Altogether, in 98% (53/54) of all specimens the decision to continue or not continue tumor resection could have been made according to the infrared spectroscopic classification. This retrospective study clearly demonstrates that infrared spectroscopic imaging may help to define tumor margins intraoperatively and to detect high-grade tumor residues for achieving more radical tumor resection. MRT-guided tumor resection (left) is combined with infrared spectroscopy-based tissue classification (middle, right). With regard to histopathological assessment, sensitivities of 100% and 93.1% and specificities of 96.9% and 88.0% were achieved for 54 specimens. (TIF 47.1 KB)     

Edge irregular total labellings for graphs of linear size

As an edge variant of the well-known irregularity strength of a graph G=(V,E) we investigate edge irregular total labellings, i.e. functions f:V∪E→{1,2,…,k} such that f(u)+f(uv)+f(v)≠f(u^′)+f(u^′v^′)+f(v^′) for every pair of different edges uv,u^′v^′∈E. The smallest possible k is the total edge irregularity strength of G. Confirming a conjecture by Ivan?o and Jendrol’ for a large class of graphs we prove that the natural lower bound is tight for every graph of order n, size m and maximum degree Δ with m>111000Δ. This also implies that the probability that a random graph from G(n,p(n)) satisfies the Ivan?o-Jendrol’ Conjecture tends to 1 as n→∞ for all functions p∈[0,1]^N. Furthermore, we prove that is an upper bound for every graph G of order n and size m≥3 whose edges are not all incident to a single vertex.     

The incidence game chromatic number

We introduce the incidence game chromatic number which unifies the ideas of game chromatic number and incidence coloring number of an undirected graph. For k-degenerate graphs with maximum degree Δ, the upper bound 2Δ+4k−2 for the incidence game chromatic number is given. If Δ≥5k, we improve this bound to the value 2Δ+3k−1. We also determine the exact incidence game chromatic number of cycles, stars and sufficiently large wheels and obtain the lower bound for the incidence game chromatic number of graphs of maximum degree Δ.     

Infinite-Dimensional Quadrature and Approximation of Distributions

We study numerical integration of Lipschitz functionals on a Banach space by means of deterministic and randomized (Monte Carlo) algorithms. This quadrature problem is shown to be closely related to the problem of quantization and to the average Kolmogorov widths of the underlying probability measure. In addition to the general setting, we analyze, in particular, integration with respect to Gaussian measures and distributions of diffusion processes. We derive lower bounds for the worst case error of every algorithm in terms of its cost, and we present matching upper bounds, up to logarithms, and corresponding almost optimal algorithms. As auxiliary results, we determine the asymptotic behavior of quantization numbers and Kolmogorov widths for diffusion processes.      

Solution of inverse problems to detect permissible design spaces

In many engineering applications, a structural design is determined by way of a multi-stage design process. Thereby, the information of previous simulations, e.g. sensitivity analysis, should be used for further investigations. In special, the aim is to improve the reliability as early as possible. Therefore, an approach is presented to determine alternative permissible design spaces on the basis of arbitrary point sets. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fully implicit time discretization for a free surface flow problem

One of the challenges in the numerics of free surface flows is the coupling of the flow field to the geometry of the domain. The most simple approach is an explicit decoupling, i.e. computing the flow field with geometrical information of a prior time step and then updating the geometry. This widely used approach leads to a severe CFL condition of the type , which may prescribe infinitesimally small time step sizes in the interesting case of a small Weber number (i.e. high surface tension). A semi-implicit approach utilizing the fact that , where x^k is a parametrization of the capillary boundary Γ, is also available [1]. This approach can be proven to be unconditionally stable but is of first order only. It also suffers from relatively strong numerical dissipation. We present a fully implicit approach using a backward differentiation formula to achieve a time discretization method that is of second order and only minimally dissipative. A numerical example of an oscillating drop showing very low numerical dissipation and second order convergence as well as numerical evidence for the stability of the method is presented. Since the method requires the solution of a highly nonlinear coupled system, possible preconditioners for this system are discussed, including a lower order decoupling. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Photoinduced cycloadditions of N-methyl-1,8-naphthalenedicarboximides with alkynes

Photoinduced cycloadditions of N-methyl-1,8-naphthalenedicarboximide 1 with phenylacetylenes 2a-2c, cyclopropylacetylene 2d, diphenylacetylenes 2e-2f and 1-phenylpropyne 2g were investigated. In the case of phenylacetylenes 2a, 2b and cyclopropylacetylene 2c, photoreaction with 1 takes place at the naphthalene C(1)C(2) bond to give the cyclobutene products. For 4-methoxyphenylacetylene 1c, the cyclobutene 3c is obtained together with the 4-benzo[a]thebenidinone 4c derived from a primary oxetene product formed by [2+2] addition of the imide carbonyl with the alkyne. Similar to 2c, photocycloaddition of 1 with 2e and 2f gave the cyclobutenes 7e, 7f, 8f and the 4-benzo[a]thebenidinone products 9e, 9f and 10f, respectively, derived from the corresponding oxetenes. Photoreaction of 1 with 2g gave cyclobutene 7g and benzo[a]thebenidinone 9g. Sensitization experiment and internal heavy atom effect study showed that these reactions proceed from the ππ* singlet excited state of 1. Estimation of the free energy change for electron transfer between ¹1* and the alkynes and the calculation of charge and spin density distribution in the anion radical of 1 and the cation radical of the alkynes suggested that the cyclobutene products are formed by direct [2+2] cycloaddition of ¹1* with the alkyne, while the formation of the oxetene products is the result of electron transfer interaction between ¹1* and the alkyne. The regioselectivity in the oxetene formation is accounted for by charge and spin density distribution in the anion radical of 1 and the cation radical of the alkyne.     

Raman and surface enhanced Raman microscopy of microstructured polyethylenimine/DNA multilayers

We analyze microstructured multilayer films of poly(ethyleneimine) (PEI) and DNA by employing Raman and surface enhanced Raman spectroscopy (SERS). The microstructuring of the samples allows a simultaneous measurement of signal and reference in a single analytic process. Silver nanoparticles are implemented in the microstructured multilayers for SERS measurements. The recorded SERS spectra of PEI/DNA are dominated by the Raman bands of the DNA bases which show a larger mean enhancement than bands belonging to DNA backbone vibrations. Our results show that the combination of SERS and microstructured multilayer films provides an adapted way to characterize the polyelectrolytes as well as to measure the enhancement factor and the distance dependence for the SERS active silver nanoparticles. Furthermore, microstructured polyelectrolyte films containing SERS active nanoparticles are used for sensing molecules.