Van der Waals (vdW) volumes ( V w,x ) of 117 molecular fragments ( X ) have been calculated by numerical integration of the van der Waals envelope using the hard-sphere approximation, standard geometries, and effective atomic van der Waals radii which were determined by comparison of their effects on the predicted sterically allowed conformations of peptides with observed crystal structures. vdW volume fragmental constants give accurate estimates of molecular, vdW volume as sum of approximate V w,x s.
A pattern recognition quantitative structure-activity relationship (QSAR) study has been performed to determine the molecular features of carbamate anticonvulsants which influence biological activity. Although carbamates, such as felbamate, have been used to treat epilepsy, their mechanisms of efficacy and toxicity are not completely understood. Quantum and classical mechanics calculations have been exploited to describe 46 carbamate drugs. Employing a principal component analysis and multiple linear regression calculations, five crucial structural descriptors were identified which directly relate to the bioactivity of the carbamate family. With the resulting mathematical model, the biological activity of carbamate analogues can be predicted with 85-90% accuracy.
We prove that groups acting geometrically on delta-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero.