Potentials of mean force for protein structure prediction vindicated, formalized and generalized

Thomas Hamelryck; Mikael Borg; Martin Paluszewski; Jonas Paulsen; Jes Frellsen; Christian Andreetta; Wouter Krogh Boomsma; Sandro Bottaro; Jesper Ferkinghoff-Borg

doi:10.1371/journal.pone.0013714

Potentials of mean force for protein structure prediction vindicated, formalized and generalized

Thomas Hamelryck, Mikael Borg, Martin Paluszewski, Jonas Paulsen, Jes Frellsen, Christian Andreetta, Wouter Krogh Boomsma, Sandro Bottaro, Jesper Ferkinghoff-Borg

Computational and RNA Biology

46 Citations (Scopus)

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Abstract

Understanding protein structure is of crucial importance in science, medicine and biotechnology. For about two decades, knowledge-based potentials based on pairwise distances--so-called "potentials of mean force" (PMFs)--have been center stage in the prediction and design of protein structure and the simulation of protein folding. However, the validity, scope and limitations of these potentials are still vigorously debated and disputed, and the optimal choice of the reference state--a necessary component of these potentials--is an unsolved problem. PMFs are loosely justified by analogy to the reversible work theorem in statistical physics, or by a statistical argument based on a likelihood function. Both justifications are insightful but leave many questions unanswered. Here, we show for the first time that PMFs can be seen as approximations to quantities that do have a rigorous probabilistic justification: they naturally arise when probability distributions over different features of proteins need to be combined. We call these quantities "reference ratio distributions" deriving from the application of the "reference ratio method." This new view is not only of theoretical relevance but leads to many insights that are of direct practical use: the reference state is uniquely defined and does not require external physical insights; the approach can be generalized beyond pairwise distances to arbitrary features of protein structure; and it becomes clear for which purposes the use of these quantities is justified. We illustrate these insights with two applications, involving the radius of gyration and hydrogen bonding. In the latter case, we also show how the reference ratio method can be iteratively applied to sculpt an energy funnel. Our results considerably increase the understanding and scope of energy functions derived from known biomolecular structures.

Original language	English
Article number	e13714
Journal	PLoS ONE
Volume	5
Issue number	11
Number of pages	11
ISSN	1932-6203
DOIs	https://doi.org/10.1371/journal.pone.0013714
Publication status	Published - 2010

Keywords

Algorithms
Computational Biology
Hydrogen Bonding
Models, Molecular
Protein Conformation
Protein Folding
Reproducibility of Results
Thermodynamics

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Potentials of Mean Force for Protein...Final published version, 582 KBLicence: CC BY

Cite this

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title = "Potentials of mean force for protein structure prediction vindicated, formalized and generalized",

abstract = "Understanding protein structure is of crucial importance in science, medicine and biotechnology. For about two decades, knowledge-based potentials based on pairwise distances--so-called {"}potentials of mean force{"} (PMFs)--have been center stage in the prediction and design of protein structure and the simulation of protein folding. However, the validity, scope and limitations of these potentials are still vigorously debated and disputed, and the optimal choice of the reference state--a necessary component of these potentials--is an unsolved problem. PMFs are loosely justified by analogy to the reversible work theorem in statistical physics, or by a statistical argument based on a likelihood function. Both justifications are insightful but leave many questions unanswered. Here, we show for the first time that PMFs can be seen as approximations to quantities that do have a rigorous probabilistic justification: they naturally arise when probability distributions over different features of proteins need to be combined. We call these quantities {"}reference ratio distributions{"} deriving from the application of the {"}reference ratio method.{"} This new view is not only of theoretical relevance but leads to many insights that are of direct practical use: the reference state is uniquely defined and does not require external physical insights; the approach can be generalized beyond pairwise distances to arbitrary features of protein structure; and it becomes clear for which purposes the use of these quantities is justified. We illustrate these insights with two applications, involving the radius of gyration and hydrogen bonding. In the latter case, we also show how the reference ratio method can be iteratively applied to sculpt an energy funnel. Our results considerably increase the understanding and scope of energy functions derived from known biomolecular structures.",

keywords = "Algorithms, Computational Biology, Hydrogen Bonding, Models, Molecular, Protein Conformation, Protein Folding, Reproducibility of Results, Thermodynamics",

author = "Thomas Hamelryck and Mikael Borg and Martin Paluszewski and Jonas Paulsen and Jes Frellsen and Christian Andreetta and Boomsma, {Wouter Krogh} and Sandro Bottaro and Jesper Ferkinghoff-Borg",

year = "2010",

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T1 - Potentials of mean force for protein structure prediction vindicated, formalized and generalized

AU - Hamelryck, Thomas

AU - Borg, Mikael

AU - Paluszewski, Martin

AU - Paulsen, Jonas

AU - Frellsen, Jes

AU - Andreetta, Christian

AU - Boomsma, Wouter Krogh

AU - Bottaro, Sandro

AU - Ferkinghoff-Borg, Jesper

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N2 - Understanding protein structure is of crucial importance in science, medicine and biotechnology. For about two decades, knowledge-based potentials based on pairwise distances--so-called "potentials of mean force" (PMFs)--have been center stage in the prediction and design of protein structure and the simulation of protein folding. However, the validity, scope and limitations of these potentials are still vigorously debated and disputed, and the optimal choice of the reference state--a necessary component of these potentials--is an unsolved problem. PMFs are loosely justified by analogy to the reversible work theorem in statistical physics, or by a statistical argument based on a likelihood function. Both justifications are insightful but leave many questions unanswered. Here, we show for the first time that PMFs can be seen as approximations to quantities that do have a rigorous probabilistic justification: they naturally arise when probability distributions over different features of proteins need to be combined. We call these quantities "reference ratio distributions" deriving from the application of the "reference ratio method." This new view is not only of theoretical relevance but leads to many insights that are of direct practical use: the reference state is uniquely defined and does not require external physical insights; the approach can be generalized beyond pairwise distances to arbitrary features of protein structure; and it becomes clear for which purposes the use of these quantities is justified. We illustrate these insights with two applications, involving the radius of gyration and hydrogen bonding. In the latter case, we also show how the reference ratio method can be iteratively applied to sculpt an energy funnel. Our results considerably increase the understanding and scope of energy functions derived from known biomolecular structures.

AB - Understanding protein structure is of crucial importance in science, medicine and biotechnology. For about two decades, knowledge-based potentials based on pairwise distances--so-called "potentials of mean force" (PMFs)--have been center stage in the prediction and design of protein structure and the simulation of protein folding. However, the validity, scope and limitations of these potentials are still vigorously debated and disputed, and the optimal choice of the reference state--a necessary component of these potentials--is an unsolved problem. PMFs are loosely justified by analogy to the reversible work theorem in statistical physics, or by a statistical argument based on a likelihood function. Both justifications are insightful but leave many questions unanswered. Here, we show for the first time that PMFs can be seen as approximations to quantities that do have a rigorous probabilistic justification: they naturally arise when probability distributions over different features of proteins need to be combined. We call these quantities "reference ratio distributions" deriving from the application of the "reference ratio method." This new view is not only of theoretical relevance but leads to many insights that are of direct practical use: the reference state is uniquely defined and does not require external physical insights; the approach can be generalized beyond pairwise distances to arbitrary features of protein structure; and it becomes clear for which purposes the use of these quantities is justified. We illustrate these insights with two applications, involving the radius of gyration and hydrogen bonding. In the latter case, we also show how the reference ratio method can be iteratively applied to sculpt an energy funnel. Our results considerably increase the understanding and scope of energy functions derived from known biomolecular structures.

KW - Algorithms

KW - Computational Biology

KW - Hydrogen Bonding

KW - Models, Molecular

KW - Protein Conformation

KW - Protein Folding

KW - Reproducibility of Results

KW - Thermodynamics

U2 - 10.1371/journal.pone.0013714

DO - 10.1371/journal.pone.0013714

M3 - Journal article

C2 - 21103041

SN - 1932-6203

VL - 5

JO - PLoS Computational Biology

JF - PLoS Computational Biology

IS - 11

M1 - e13714

ER -

Potentials of mean force for protein structure prediction vindicated, formalized and generalized

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Keywords

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