Alpha complex potentials for proteins
(Guibas, Koehl; Zomorodian)

It is the ability of proteins to fold into unique three-dimensional structures that allows them to function. Hence understanding how the amino acid sequence of a protein defines its native conformation is essential to understanding all biological processes involving proteins. It has been shown that the properties of proteins are directly related to their potential energy surfaces, with the native structure corresponding to the minimum of this surface. One of the challenges for theoretical biology is therefore to obtain a good approximation of the true energy function that can be used to model protein folding, or at least that can serve as a scoring tool for identifying native like structural models of a protein, in a collection of non native conformations. Semi-empirical energy functions based on physical principles are routinely used in short biomolecular simulations at atomic resolutions. These potentials however are impractical for studying processes with long time scale, such as protein folding. As an alternative, putative energy functions have been derived from amino acid pairing frequencies observed in known protein structures. These energy functions are usually referred to as potential of mean forces. The basis on which these pairwise potentials are computed has been questioned. In particular, it has been shown that there are strong correlations among all pairs of residues in a folded protein structure, and that these correlations invalidate the hypothesis of independence of pairs that is required to define the potential. We propose to minimize this problem by only taking a subset of all pairs of residue. Our filtering of the pairs is based on the concept of alpha complexes. An alpha-complex is a sub-complex of the Delaunay complex built from points representing the atoms of the protein of interest. The alpha parameter controls the degree to which the complex captures local geometry.