| 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.
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