Limiting the Number of Potential Binding Modes by Introducing Symmetry into Ligands: Structure‐Based Design of Inhibitors for Trypsin‐Like Serine Proteases

In the absence of X‐ray data, the exploration of compound binding modes continues to be a challenging task. For structure‐based design, specific features of active sites in different targets play a major role in rationalizing ligand binding characteristics. For example, dibasic compounds have been reported as potent inhibitors of various trypsin‐like serine proteases, the active sites of which contain several binding pockets that can be targeted by cationic moieties. This results in several possible orientations within the active site, complicating the binding mode prediction of such compounds by docking tools. Therefore, we introduced symmetry in bi‐ and tribasic compounds to reduce conformational space in docking calculations and to simplify binding mode selection by limiting the number of possible pocket occupations. Asymmetric bisbenzamidines were used as starting points for a multistage and structure‐guided optimization. A series of 24 final compounds with either two or three benzamidine substructures was ultimately synthesized and evaluated as inhibitors of five serine proteases, leading to potent symmetric inhibitors for the pharmaceutical drug targets matriptase, matriptase‐2, thrombin and factor Xa. This study underlines the relevance of ligand symmetry for chemical biology.     

On the nuclear density distribution for nucleus-nucleus scattering. II

We investigate the effect of the antisymmetrization on the density distribution for nucleus-nucleus scattering. In contrast to an earlier paper¹ the motion of the nuclei is now taken into account. For experimentally available energies we find no pronounced density compression in the overlap region. For very high energies a superposition of the densities is justified.     

Lattice dynamics in RbCN

The dispersion of acoustic and optical phonons of rubidium cyanide has been measured at 300 K. The acoustic branches are affected by rotation-translation coupling in a way similar to the findings in KCN. The data are explained by a model which combines a shell model and rotation-translation coupling.     

Absolute triple differential cross sections for electron impact ionization of helium: Comparison between experimental and theoretical results at 256 eV collision energy

Triple differential cross sections have been measured for electron impact ionization of helium at 256 eV collision energy, 3 eV energy of the slow outgoing electrons and scattering angles of the fast outgoing electrons of 4°, 6°, 8°, and 10°. The data have been put on absolute scale by extrapolating the generalized oscillator strength to zero momentum transfer. In this optical limit the triple differential cross sections can be normalized by using the well-known cross sections for photoionization. The experimental data are compared with results of different theoretical approaches. For nearly all calculated curves rather good agreement with the measurements is obtained for the relative shape of the binary peak, while often its absolute cross section is overestimated. Concerning the recoil peak, larger discrepancies are found with respect to both, relative shapes and cross sections. A perceptible improvement can be stated for calculations which have been performed in a distorted wave approximation and in second Born approximation.     

Parallel Calculation of Accurate Path Lines in Virtual Environments through Exploitation of Multi-Block CFD Data Set Topology

The use of Virtual Reality (VR) techniques for the investigation of complex flow phenomena offers distinct advantages in comparison to conventional visualization techniques. Especially for unsteady flows, VR methodology provides an intuitive approach for the exploration of simulated fluid flows. However, the visualization of Computational Fluid Dynamics (CFD) data is often too time-consuming to be carried out in real-time, and thus violates essential constraints concerning real-time interaction and visualization. To overcome this obstacle, we make use of the fact that typically a multi-block approach is employed for domain decomposition, and we use the corresponding data structures for the computation of path lines and for parallelization. In this paper, we present the synthesis of fragmented multi-block data sets and our implementation of an accurate path line integration scheme in order to speed up path line computations. We report on the results of our efforts and describe a combination of this algorithm with a highly efficient visualization approach of large amounts of particle traces, thus considerably improving interactivity when exploring large scale CFD data sets.Mathematics Subject Classifications (2000) 76Mxx, 76M27, 76M28, 65M55, 65L05, 65L06, 65D05, 65Y05, 68U05.     

Invertibility theory for Toeplitz plus Hankel operators and singular integral operators with flip

It is well known that a Toeplitz operator is invertible if and only if its symbols admits a canonical Wiener-Hopf factorization, where the factors satisfy certain conditions. A similar result holds also for singular integral operators. More generally, the dimension of the kernel and cokernel of Toeplitz or singular integral operators which and Fredholm operators can be expressed in terms of the partial indices of an associated Wiener-Hopf factorization problem.In this paper we establish corresponding results for Toeplitz plus Hankel operators and singular integral operators with flip under the assumption that the generating functions are sufficiently smooth (e.g., Hölder continuous). We are led to a slightly different factorization problem, in which pairs , instead of the partial indices appear. These pairs provide the relevant information about the dimension of the kernel and cokernel and thus answer the invertibility problem.     

Stochastic gain in population dynamics

We introduce an extension of the usual replicator dynamics to adaptive learning rates. We show that a population with a dynamic learning rate can gain an increased average payoff in transient phases and can also exploit external noise, leading the system away from the Nash equilibrium, in a resonancelike fashion. The payoff versus noise curve resembles the signal to noise ratio curve in stochastic resonance. Seen in this broad context, we introduce another mechanism that exploits fluctuations in order to improve properties of the system. Such a mechanism could be of particular interest in economic systems.