The differential geometry of proteins and its applications to structure determination

Understanding the three-dimensional structure of proteins is critical to understand their function. While great progress is being made in understanding the structures of soluble proteins, large classes of proteins such as membrane proteins, large macromolecular assemblies, and partially organized or heterogeneous structures are being comparatively neglected. Part of the difficulty is that the coordinate models we use to represent protein structure are discrete and static, whereas the molecules themselves are flexible and dynamic. In this article, we review methods to develop a continuous description of proteins more general than the traditional coordinate models and which can describe smooth changes in form. This description can be shown to be strictly equivalent to the traditional atomic coordinate description.