Computational methods for the structural alignment of molecules

Similarity is an important concept for the comparison of molecular structures. There are a number of different definitions of molecular similarity. In the context of molecular recognition, which is one of the basic principles of life on a subcellular level, structural similarity in 3D space may be considered the most important. The relative orientation of the molecules plays a key role in comparing molecular structures being objects with volume, shape and a specific distribution of physicochemical properties. Since molecules are flexible objects, the conformation of the molecules is also crucial. In this study we present algorithms that allow meaningful relative orientations and conformations (i.e. structural alignments) to be determined and used as the basis for calculating molecular similarity. Unfortunately, the task of determining the structural alignment of molecules is extremely difficult. Firstly, no manageable model exists that describes the process of molecular recognition in its entirety. Furthermore, while molecular recognition is based on the interaction of (at least) two complementary molecules, in structural alignment only half of the data is available. Secondly, it is necessary to consider a high number of degrees of freedom for the underlying optimization problem. We present a novel approach to modeling the structural alignment problem, employing both combinatorial and numerical techniques for tackling various variants of this problem. In addition, we have developed algorithms that enable us to best possibly balance the weight of different parameters of a scoring function on the basis of a training set of examples. This then allows us to quantify similarity on the basis of the determined alignment