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Exact Relation between Potential of Mean Force and Free-Energy Profile.

ABSTRACT: We apply concepts of covariant and contravariant vector space in differential geometry and general relativity to derive new, general, exact relations between potential of mean force and free-energy profile. These relations are immensely practical in free-energy simulations because a full Jacobian transformation (which is usually unknown) is not required; rather, only knowledge of the (constraint) coordinate of interest is needed. We reveal that in addition to the Jacobian determinant, the Jacobian scale factor and Leibnizian contributions must also be considered, as well a Fixman term with correct mass dependence. Our newly derived relations are verified with new non-trivial benchmark numerical examples for which exact results can be computed, and compared with relations available in the literature that turn out to exhibit significant deviations from the exact values.

SUBMITTER: Wong KY

PROVIDER: S-EPMC3505112 | biostudies-literature | 2012 Nov

REPOSITORIES: biostudies-literature

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Exact Relation between Potential of Mean Force and Free-Energy Profile.

Wong Kin-Yiu KY York Darrin M DM

Journal of chemical theory and computation 20120906 11

We apply concepts of covariant and contravariant vector space in differential geometry and general relativity to derive new, general, exact relations between potential of mean force and free-energy profile. These relations are immensely practical in free-energy simulations because a full Jacobian transformation (which is usually unknown) is not required; rather, only knowledge of the (constraint) coordinate of interest is needed. We reveal that in addition to the Jacobian determinant, the Jacobi ...[more]

PMID: 23185141

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Project description:BackgroundThe development and testing of functions for the modeling of protein energetics is an important part of current research aimed at understanding protein structure and function. Knowledge-based mean force potentials are derived from statistical analyses of interacting groups in experimentally determined protein structures. Current knowledge-based mean force potentials are developed at the atom or amino acid level. The evolutionary information contained in the profiles is not investigated. Based on these observations, a class of novel knowledge-based mean force potentials at the profile level has been presented, which uses the evolutionary information of profiles for developing more powerful statistical potentials.ResultsThe frequency profiles are directly calculated from the multiple sequence alignments outputted by PSI-BLAST and converted into binary profiles with a probability threshold. As a result, the protein sequences are represented as sequences of binary profiles rather than sequences of amino acids. Similar to the knowledge-based potentials at the residue level, a class of novel potentials at the profile level is introduced. We develop four types of profile-level statistical potentials including distance-dependent, contact, Phi/Psi dihedral angle and accessible surface statistical potentials. These potentials are first evaluated by the fold assessment between the correct and incorrect models generated by comparative modeling from our own and other groups. They are then used to recognize the native structures from well-constructed decoy sets. Experimental results show that all the knowledge-base mean force potentials at the profile level outperform those at the residue level. Significant improvements are obtained for the distance-dependent and accessible surface potentials (5-6%). The contact and Phi/Psi dihedral angle potential only get a slight improvement (1-2%). Decoy set evaluation results show that the distance-dependent profile-level potentials even outperform other atom-level potentials. We also demonstrate that profile-level statistical potentials can improve the performance of threading.ConclusionThe knowledge-base mean force potentials at the profile level can provide better discriminatory ability than those at the residue level, so they will be useful for protein structure prediction and model refinement.

Dataset Information

Exact Relation between Potential of Mean Force and Free-Energy Profile.

Publications

Exact Relation between Potential of Mean Force and Free-Energy Profile.

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