A new method for mapping macromolecular topography

A new method, using circular variance, is introduced for mapping macromolecular topography. Circular variance, generally used to measures angular spread, can be used to characterize of molecular structures based on a simple idea. It will be shown that the circular variance of vectors drawn from some origin to a set of points is well correlated with the degree to which that origin is inside/outside the chosen points. In addition, it has continuous derivatives that are also easy to compute. This concept will be shown to be useful for: (i) distinguishing between atoms near the surface of a macromolecule and those in either the deep interior or remote exterior; (ii) identifying invaginations (even shallow ones); and (iii) detecting linker regions that interconnect two domains.