Generalized distance and its application in protein folding

The concept of Euclidean distance between two points can be generalized to extended objects. The generalized distance $\cal D$ can be used as a reaction coordinate in protein folding process. Here $\cal D$ is compared and contrasted with some well-known reaction coordinates, Q and RMSD and is applied to protein fragments such as alpha helix and beta hairpin. The non-crossing constraint in utilizing $\cal D$ is also discussed.