Topographical Properties of Molecular Surfaces

Two molecules of complex structure may form a stable complex only when those parts that are important for the binding can come into close contact. From the point of view of the molecular surfaces, this means that both surfaces have to be complementary to some extent in the binding area. This surface complementarity can be identified in simple cases just by inspection of the computer-generated images, although this technique is not very useful for systematic searches. To achieve the latter, a formal classification is necessary. Several methods for the characterization of surfaces in topological terms have been proposed.Mezey and co-workers have established a method for topological analysis of contour 

The comparison of two given molecular surfaces on the basis of curvature can be done interactively by the use of two-dimensional texture maps, with color coding of the two canonical curvatures calculated for different selection distances along the x and y coordinate of the texture map. However, the information from the curvature profile can be further reduced by introducing a surface topography index STI as demonstrated by 

Heiden and Brickmann. The surface topography index s may be defined on the basis of two global curvatures, c, and C2, as follows  

The STI values vary within the interval 0 5 4. When calculated from the relation of both global curvatures [each of which can be either concave ( + ), flat (0), or convex (-)], where c, C2, the STI gives an expression for the regional shape of every surface point. The shape varies continuously among five basic shape descriptors, namely, bag ( + / + ), cleft (+ /O), saddle ( + /-), ridge (0/ - ), knob (-/-), and as a special case, plateau (0/0). However, information about the absolute curvature is lost during the process of STI calculation. 

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