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Differentiable, multi‐dimensional, knowledge‐based energy terms for torsion angle probabilities and propensities
Author(s) -
Amir ElAd David,
Kalisman Nir,
Keasar Chen
Publication year - 2008
Publication title -
proteins: structure, function, and bioinformatics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.699
H-Index - 191
eISSN - 1097-0134
pISSN - 0887-3585
DOI - 10.1002/prot.21896
Subject(s) - differentiable function , dihedral angle , torsion (gastropod) , computer science , algorithm , mathematics , statistical physics , mathematical analysis , physics , medicine , hydrogen bond , surgery , quantum mechanics , molecule
Rotatable torsion angles are the major degrees of freedom in proteins. Adjacent angles are highly correlated and energy terms that rely on these correlations are intensively used in molecular modeling. However, the utility of torsion based terms is not yet fully exploited. Many of these terms do not capture the full scale of the correlations. Other terms, which rely on lookup tables, cannot be used in the context of force‐driven algorithms because they are not fully differentiable. This study aims to extend the usability of torsion terms by presenting a set of high‐dimensional and fully‐differentiable energy terms that are derived from high‐resolution structures. The set includes terms that describe backbone conformational probabilities and propensities, side‐chain rotamer probabilities, and an elaborate term that couples all the torsion angles within the same residue. The terms are constructed by cubic spline interpolation with periodic boundary conditions that enable full differentiability and high computational efficiency. We show that the spline implementation does not compromise the accuracy of the original database statistics. We further show that the side‐chain relevant terms are compatible with established rotamer probabilities. Despite their very local characteristics, the new terms are often able to identify native and native‐like structures within decoy sets. Finally, force‐based minimization of NMR structures with the new terms improves their torsion angle statistics with minor structural distortion (0.5 Å RMSD on average). The new terms are freely available in the MESHI molecular modeling package. The spline coefficients are also available as a documented MATLAB file. Proteins 2008. © 2008 Wiley‐Liss, Inc.