An algorithm to relate protein surface roughness with local geometry of protein exterior shape

Changes in the extent of local concavity along with changes in surface roughness of binding sites of proteins have long been considered as useful markers to identify functional sites of proteins. However, an algorithm that describes the connection between the simultaneous changes of these important parameters - eludes the students of structural biology. Here a simple yet general mathematical scheme is proposed that attempts to achieve the same. Instead of n-dimensional random vector description, protein surface roughness is described here as a system of algebraic equations. Such description resulted in the construction of a generalized index that not only describes the shape-change-vs-surface-roughness-change process but also reduces the estimation error in local shape characterization. Suitable algorithmic implementation of it in context-specific macromolecular recognition can be attempted easily. Contemporary drug discovery studies will be enormously benefited from this work because it is the first algorithm that can estimate the change in protein surface roughness as the local shape of the protein is changing (and vice-versa).