Topological analysis of complex molecular surfaces

An algorithm for the calculation of local and global curvatures of molecular surfaces is presented. The analysis is based on a surface representation as a set of points in 3-D space (“dotted surface” representation). The surface data are used to subdivide the surfac into domains with different curvatures. All domains are characterized by a reference point with a corresponding curvature profile specifiying the topological properties in its neighborhood. The curvature profiles provide a method for a systematic comparison of the shapes of different molecules. Such a strategy is important for the treatment of molecular recognition problems. The enzyme-inhibitor complex trypsin/BPTI was chosen to demonstrate the scopes of the method.     

The interdeparture-time distribution for each class in the ∑ i M i /G i /1 queue

A stationary queueing system is described in which a single server handles several competing Poisson arrival streams on a first-come first-served basis. Each class has its own generally distributed service time characteristics. The principal result is the Laplace-Stieltjes transform, for each class, of the interdeparture time distribution function. Examples are given and applications are discussed.     

Determining the geometry of hydrogen bonds in solids with picometer accuracy by quantum-chemical calculations and NMR spectroscopy.

The structure of multiply hydrogen-bonded systems is determined with picometer accuracy by a combined solid-state NMR and quantum-chemical approach. On the experimental side, advanced 1H-15N dipolar recoupling NMR techniques are capable of providing proton-nitrogen distances of up to about 250 pm with an accuracy level of +/-1 pm for short distances (i.e., around 100 pm) and +/-5 pm for longer ones (i.e., 180 to 250 pm). The experiments were performed under fast magic-angle spinning, which ensures sufficient dipolar decoupling and spectral resolution of the 1H resonance lines. On the quantum-chemical side, the structures of the hydrogen-bonded systems were computationally optimised, yielding complete sets of nitrogen-proton and proton-proton distances, which are essential for correctly interpreting the experimental NMR data. In this way, nitrogen-proton distances were determined with picometer accuracy, so that vibrational averaging effects on dipole-dipole couplings need to be considered. The obtained structures were finally confirmed by the complete agreement of computed and experimental 'H and '5N chemical shifts. This demonstrates that solid-state NMR and quantum-chemical methods ideally complement each other and, in a combined manner, represent a powerful approach for reliable, high-precision structure determination whenever scattering techniques are inapplicable.