An Attempt to Explore the Similarity of Two Proteins by Their Surface Shapes

Protein structure comparison is one of the most important problems in Bioinformatics. In this paper, we develop a convex hull expression of a protein and propose a grid method to evaluate similarity between two convex hulls. The purpose of introducing the convex hull expression is to investigate the relationship between the surface shape similarity and the protein function similarity. Extensive numerical experiments shows that proteins in a family do have surface shape similarity and proteins in different families have their shapes in quite large difference. To explore the shape similarity of proteins in different families, we observe the possible local shape similarity by reorganizing the convex hull’s supporting plane information into a set of local shape information. And comparing the local shape information of two proteins leads us to find some local shape similarity for some pairs of proteins whose structure similarity is difficult to evaluate by traditional comparison methods. The biological meaning of local shape similarity remains unclear.