  Protein representation and potential function are essential ingredients for
studying proteins folding and protein prediction. We introduce a novel
geometric representation of contact interactions using the edge simplices from
alpha shape of protein structure. This representation can eliminate implausible
neighbors not in physical contact, and can avoid spurious contact between two
residues when a third residue is between them. We develop statistical alpha
contact potential. A studentized bootstrap method is then introduced for
assessing the 95% confidence intervals for each of the 210 parameters. We found
with confidence that there is significant long range propensity (>30 residues
apart) for hydrophobic interactions. We test alpha contact potential for native
structure discrimination using several decoy sets, and found it often has
comparable performance with atom-based potentials requiring more parameters. We
also show that alpha contact potential has better performance than potential
defined by cut-off distance between geometric centers of side chains.
Clustering of alpha contact potentials reveals natural grouping of residues. To
explore the relationship between shape representation and physicochemical
representation, we test the minimum alphabet size for structure discrimination.
We found that there is no significant difference in discrimination when
alphabet size varies from 7 to 20, if geometry is represented accurately by
alpha simplicial edges. This result suggests that the geometry of packing plays
an important role, but the specific residue types are often interchangeable.
