  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).
