Adaptive spectral clustering with application to tripeptide conformation analysis.

A decomposition of a molecular conformational space into sets or functions (states) allows for a reduced description of the dynamical behavior in terms of transition probabilities between these states. Spectral clustering of the corresponding transition probability matrix can then reveal metastabilities. The more states are used for the decomposition, the smaller the risk to cover multiple conformations with one state, which would make these conformations indistinguishable. However, since the computational complexity of the clustering algorithm increases quadratically with the number of states, it is desirable to have as few states as possible. To balance these two contradictory goals, we present an algorithm for an adaptive decomposition of the position space starting from a very coarse decomposition. The algorithm is applied to small data classification problems where it was shown to be superior to commonly used algorithms, e.g., k-means. We also applied this algorithm to the conformation analysis of a tripeptide molecule where six-dimensional time series are successfully analyzed.

Conformational analysis of alternariol on the quantum level.

With the help of theoretical calculations we explain the phenomenon of nonplanarity of crystalline alternariol. We find out that the different orientations of the hydroxyl groups of alternariol influence its planarity and aromaticity and lead to different twists of the structure. The presence of the intramolecular hydrogen bond stabilizes the planar geometry while the loss of the bond results in a twist of over 14°. This effect is thought to be involved while cutting DNA strands by alternariol.