R.R. Gabdoulline &
R.C. Wade. Analytically defined surfaces to analyze molecular interaction
properties, J. Mol. Graph. (1996) 14, 341-353.
Molecular surfaces are widely used for characterizing
molecules and displaying and quantifying their interaction properties.
Here we consider molecular surfaces defined as iso-contours of a function
(a sum of exponential functions centred on each atom) that approximately
represents electron density. The smoothness is advantageous for surface
mapping of molecular properties (e.g. electrostatic potential). By varying
parameters, these surfaces can be constructed to represent the van der
Waals or solvent accessible surface of a molecule with any accuracy.
We describe numerical algorithms to operate on
the analytically defined surfaces. Two applications are considered. (1)
We define and locate extremal points of molecular properties on the surfaces.
The extremal points provide a compact representation of a property on a
surface obviating the necessity to compute values of the property on an
array of surface points as is usually done. (2) A molecular surface patch
or interface is projected onto a flat surface (by introducing curvilinear
coordinates) with approximate conservation of area for analysis purposes.
Applications to studies of protein-protein interactions are described.
Razif Gabdoulline Rebecca Wade