Using alpha shapes to characterize protein flexibility

There are only limited methods available to study the global motions of the protein such as their hinge motions and shear motions. These motions take place over a broad range of time scales, from microseconds to seconds; however, molecular dynamics methods can only model easily the motions occurring on the time scale from picoseconds to microseconds, and in addition, such simulations require that replicas be run. Thus, extracting the meaningful slow motions is difficult. Hence, there is a need to model the global motions of the protein. The important motions depend on a multiscale phenomenon known as protein packing. In this study, we have explored alpha shapes (a subset of Delaunay tessellations) for the protein backbone coordinates as a model of protein packing. We demonstrate that the method can predict the protein hinges which are responsible for the global motions of the proteins.