Estimation of absolute solvent and solvation shell entropies via permutation reduction

Despite its prominent contribution to the free energy of solvated macromolecules such as proteins or DNA, and although principally contained within molecular dynamics simulations, the entropy of the solvation shell is inaccessible to straightforward application of established entropy estimation methods. The complication is twofold. First, the configurational space density of such systems is too complex for a sufficiently accurate fit. Second, and in contrast to the internal macromolecular dynamics, the configurational space volume explored by the diffusive motion of the solvent molecules is too large to be exhaustively sampled by current simulation techniques. Here, we develop a method to overcome the second problem and to significantly alleviate the first one. We propose to exploit the permutation symmetry of the solvent by transforming the trajectory in a way that renders established estimation methods applicable, such as the quasiharmonic approximation or principal component analysis. Our permutation-reduced approach involves a combinatorial problem, which is solved through its equivalence with the linear assignment problem, for which O(N3) methods exist. From test simulations of dense Lennard-Jones gases, enhanced convergence and improved entropy estimates are obtained. Moreover, our approach renders diffusive systems accessible to improved fit functions.     

A Variational Approach to Obstacle Problems for Shearable Nonlinearly Elastic Rods

We use variational methods to study obstacle problems for geometrically exact (Cosserat) theories for the planar deformation of nonlinearly elastic rods. These rods can suffer flexure, extension, and shear. There is a marked difference between the behavior of a shearable and an unshearable rod. The set of admissible deformations is not convex, because of the exact geometry used. We first investigate the fundamental question of describing contact forces, which we necessarily treat as vector‐valued Borel measures. Moreover, we introduce techniques for describing point obstacles. Then we prove existence for a very large class of problems. Finally, using nonsmooth analysis for handling the obstacle, we show that the Euler‐Lagrange equations are satisfied almost everywhere. These equations provide very detailed structural information about the contact forces. Accepted June 3, 1996     

Quantification of Saquinavir from Lysates of Peripheral Blood Mononuclear Cells Using Microarrays and Standard MALDI-TOF-MS

Drug monitoring is usually performed by liquid chromatography coupled with optical detection or electrospray ionization mass spectrometry. More recently, matrix-assisted laser desorption/ionization (MALDI) in combination with triple quadrupole or Fourier-transform (FT) mass analyzers has also been reported to allow accurate quantification. Here, we present a strategy that employs standard MALDI time-of-flight (TOF) mass spectrometry (MS) for the sensitive and accurate quantification of saquinavir from an extract of blood peripheral mononuclear cells. Unambiguous identification of saquinavir in the mass spectra was possible because of using internal mass calibration and by an overall low chemical noise in the low mass range. Exact mass determination of the constant background peaks of the cell extract, which were used for recalibration, was performed by an initial MALDI-FT-MS analysis. Fast and multiplexed sample analysis was enabled by microarray technology, which provided 10 replicates in the lower nL range for each sample in parallel lanes on a chip. In order to validate the method, we employed various statistical tests, such as confidence intervals for linear regressions, three quality control samples, and inverse confidence limits of the estimated concentration ratios.

Reprogramming Nonribosomal Peptide Synthetases for “Clickable” Amino Acids

Nonribosomal peptide synthetases (NRPSs) are multifunctional enzymes that produce a wide array of bioactive peptides. Here we show that a single tryptophan‐to‐serine mutation in phenylalanine‐specific NRPS adenylation domains enables the efficient activation of non‐natural aromatic amino acids functionalized with azide and alkyne groups. The resulting 10⁵‐fold switch in substrate specificity was achieved without appreciable loss of catalytic efficiency. Moreover, the effective communication of the modified A domains with downstream modules in dipeptide synthetases permitted incorporation of O‐propargyl‐L ‐tyrosine into diketopiperazines both in vitro and in vivo, even in the presence of competing phenylalanine. Because azides and alkynes readily undergo bioorthogonal click reactions, reprogramming NRPSs to accept non‐natural amino acids that contain these groups provides a potentially powerful means of isolating, labeling, and modifying biologically active peptides.     

Magnetische Ladungen oder, warum es manchmal sinnvoll ist, etwas mathematisch zu modellieren, was es gar nicht gibt

Es kann in der Praxis sinnvoll sein, für physikalische Vorg?nge mathematische Modelle zu betrachten, die mehr enthalten als die Realit?t. Dies gilt insbesondere dann, wenn das Modell für Computersimulationen verwendet wird. Als Beispiel werden elektromagnetische Wellen gezeigt, deren Simulation tats?chlich besser gelingt, wenn man magnetische Ladungen ins mathematische Modell einführt.