Identifying Similar Surface Patches on Proteins Using a Spin-Image Surface Representation

Our contribution in this work is a new measure of similarity between surface points based on a spin-image surface representation that allows efficient identification of corresponding points between two surfaces. We represent a molecular surface as a collection of two-dimensional (2D) spin images associated to Connolly's points [1]. Given a surface point P with normal n, its associated spin image is a 2D histogram of the positions of neighboring points of P , with respect to a reference frame formed by P and its tangent plane [2]. It is a local description, invariant to rigid transformations, of the shape of a 3D object. We have developed a matching procedure that consists of 1) establishing point correspondences between two surfaces based on the correlation between their associated spin images and 2) grouping the corresponding points into similar surface patches, that are likely to correspond to active sites of the two proteins [3]. Here we introduce new spin image descriptors that speed up the matching process considerably and are robust enough to guarantee good quality of the results. Furthermore, as we will see, they are useful in the second step of matching in identifying surface cavities, that occur at the binding site of receptor-ligand complexes. We label surface points as blocked or open depending on the shape of their spin images. A surface point P with normal n is labeled open if n does not intersect the surface at any other point lying above the tangent plane T at P perpendicular to n, otherwise is blocked. Next, we define the spin image profile for surface points. Briefly, the profile of a spin image at point P is a one-dimensional (1D) array of elements corresponding to the image columns, where each element counts the number of contiguous 0-pixels in that column starting at the image boundary until the first non 0-pixel (see Figure 1). Since a 0-pixel of the image represents empty space, i.e. space not occupied by the protein points, the profile is a descriptor of the empty space as seen from P. Once all spin images of a protein surface are created, labeling the points as blocked or open and determining their profiles is computationally very simple. One measure of similarity between points is given by the 1D correlation of their spin image profiles. A second more complex measure is the 2D correlation of the spin images. In establishing individual correspondences …