Proteins are involved either directly or indirectly in all biological processes in living organisms. It is now widely accepted that conformational changes of proteins can critically affect their ability to bind other molecules and that any progress in modeling protein motion and flexibility will contribute to the understanding of key biological functions. However, modeling protein flexibility has proven a very difficult task. Experimental laboratory methods such as X-ray crystallography produce rather few structures, while computational methods such as Molecular Dynamics are too slow for routine use with large systems. A medium sized protein typically has a few thousands of degrees of freedom. This paper shows how to obtain a reduced basis representation of protein flexibility. We use the Principal Component Analysis method, a dimensionality reduction technique, to transform the original high dimensional representation of protein motion into a lower dimensional representation that captures the dominant modes of motions of the protein. Although there is inevitably some loss in accuracy, we show that we can obtain conformations that have been observed in laboratory experiments, starting from different initial conformations and working in a drastically reduced search space.

This paper reports on the problem of docking a highly flexible small molecule to the pocket of a highly flexible receptor macromolecule. The prediction of the intermolecular complex is of vital importance for the development of new therapeutics as docking can alter the chemical behavior of the receptor macromolecule. We first present current methods for docking, which have several limitations. Some of these methods consider only the flexibility of the ligand solving a problem with a few tens of degrees of freedom. When the receptor flexibility is taken into account several hundreds or even thousands of degrees of freedom need to be considered. Most methods take into account only a small number of these degrees of freedom by using chemical knowledge specific to the problem. We show how to use a singular value decomposition of molecular dynamics trajectories to automatically obtain information about the global flexibility of the receptor and produce interesting conformations that can be used for docking purposes.