Isometrically invariant and allosterically aware description of deformable macromolecular surfaces: Application to the viral neuraminidase

Motivation: The macromolecular surfaces associated with proteins and macromolecules play a key role in determining their functionality and interactions, and are also of importance in structural analysis and classification. As a result of their interaction with their environment, the macromolecular surfaces experience random conformational deformations. Consequently, a realistic description of the molecular surface must be invariant under these deformations. Further, the motion associated with disconnected regions on the molecular surface may be correlated. This property is known as the allosteric effect. In this paper, we address these two requirements. To this end, we propose an approach based on discrete differential geometry and the fractional Fokker-Planck equation which provides an isometrically invariant and allosteric aware description of macromolecular surfaces. Our method is applied to the influenza neuraminidase.