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Cited by 88Protein Structure and DynamicsAdvanced Physical and Chemical Molecular InteractionsAdvanced Mathematical Modeling in Engineering

Multiscale multiphysics and multidomain models—Flexibility and rigidity

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Xia, Kelin, Opron, Kristopher, Wei, Guo-Wei·2013·The Journal of Chemical Physics
DOI 10.1063/1.4830404PMC PMC3855066
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Abstract

The emerging complexity of large macromolecules has led to challenges in their full scale theoretical description and computer simulation. Multiscale multiphysics and multidomain models have been introduced to reduce the number of degrees of freedom while maintaining modeling accuracy and achieving computational efficiency. A total energy functional is constructed to put energies for polar and nonpolar solvation, chemical potential, fluid flow, molecular mechanics, and elastic dynamics on an equal footing. The variational principle is utilized to derive coupled governing equations for the above mentioned multiphysical descriptions. Among these governing equations is the Poisson-Boltzmann equation which describes continuum electrostatics with atomic charges. The present work introduces the theory of continuum elasticity with atomic rigidity (CEWAR). The essence of CEWAR is to formulate the shear modulus as a continuous function of atomic rigidity. As a result, the dynamics complexity of a macromolecular system is separated from its static complexity so that the more time-consuming dynamics is handled with continuum elasticity theory, while the less time-consuming static analysis is pursued with atomic approaches. We propose a simple method, flexibility-rigidity index (FRI), to analyze macromolecular flexibility and rigidity in atomic detail. The construction of FRI relies on the fundamental assumption that protein functions, such as flexibility, rigidity, and energy, are entirely determined by the structure of the protein and its environment, although the structure is in turn determined by all the interactions. As such, the FRI measures the topological connectivity of protein atoms or residues and characterizes the geometric compactness of the protein structure. As a consequence, the FRI does not resort to the interaction Hamiltonian and bypasses matrix diagonalization, which underpins most other flexibility analysis methods. FRI's computational complexity is of \documentclass[12pt]{minimal}\begin{document}${\cal O}(N^2)$\end{document}O(N2) at most, where N is the number of atoms or residues, in contrast to \documentclass[12pt]{minimal}\begin{document}${\cal O}(N^3)$\end{document}O(N3) for Hamiltonian based methods. We demonstrate that the proposed FRI gives rise to accurate prediction of protein B-Factor for a set of 263 proteins. We show that a parameter free FRI is able to achieve about 95% accuracy of the parameter optimized FRI. An interpolation algorithm is developed to construct continuous atomic flexibility functions for visualization and use with CEWAR.

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  • This method has also been successfully applied to the prediction of Debye-Waller factors.

    “This method has also been successfully applied to the prediction of Debye-Waller factors.20”

    From Persistent homology analysis of protein structure, flexibility, and folding (2014) · cites this paper as [20]

  • The FRI theory has been intensively validated by comparing with the experimental data, especially the Debye-Waller factors.

    “The FRI theory has been intensively validated by comparing with the experimental data, especially the Debye-Waller factors.20”

    From Persistent homology analysis of protein structure, flexibility, and folding (2014) · cites this paper as [20]

  • The location of the maximum accumulated bar length gives an accurate prediction of the optimal characteristic distance for the flexibility and rigidity index (FRI) analysis of protein temperature factors.

    “It is found that the location of the maximum accumulated bar length gives an accurate prediction of the optimal characteristic distance for the flexibility and rigidity index (FRI) analysis20 of protein temperature factors.”

    From Persistent homology analysis of protein structure, flexibility, and folding (2014) · cites this paper as [20]

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Research works printed but not linked: 6

  1. Xia, Opron, and Wei J. Chem. Phys. 139, 194109 (2013) 194109-5
  2. Xia, Opron, and Wei J. Chem. Phys. 139, 194109 (2013) 194109-10
  3. Xia, Opron, and Wei J. Chem. Phys. 139, 194109 (2013) 194109-15
  4. Xia, Opron, and Wei J. Chem. Phys. 139, 194109 (2013)
  5. Y. V. Kiselev, M. Leda, A. I. Lobanov, D. Marenduzzo, and A. B. Gory- achev, "Lateral dynamics of charged lipids and peripheral proteins in Reuse of AIP Publishing content is subject to the terms: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 155.69.24.171 On: Mon, 08 Aug 2016 07:49:09 194109-16
  6. Xia, Opron, and Wei J. Chem. Phys. 139, 194109 (2013)

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Authors
Xia, K., Opron, K., & Wei, G.-W.
Affiliations
Michigan State University (US)
ORCID
Venue
The Journal of Chemical Physics
Publisher
AIP Publishing
Published
2013-11-20
Volume
139
Issue
19
Pages
194109-194109
ISSN
  • 0021-9606 (ISSN-L)
  • 1089-7690
DOI
10.1063/1.4830404
PMC
PMC3855066
OpenAlex
W2049419548
Cited by
88
References
76
Citations by year
2026: 3 · 2025: 6 · 2024: 6 · 2023: 7 · 2022: 8 · 2021: 7 · 2020: 8 · 2019: 6 · 2018: 4 · 2017: 8 · 2016: 6 · 2015: 13 · 2014: 5 · 2013: 1
FWCI
3.73
Type
journal article
Language
en
Open access
Locations
  • The Journal of Chemical Physics (publishedVersion)
  • Europe PMC (PubMed Central) (publishedVersion)
  • PubMed Central (publishedVersion)
  • PubMed (publishedVersion)
  • DR-NTU (Nanyang Technological University) (submittedVersion)
Funders
  • National Science Foundation (1160352, 1302285)
  • National Institutes of Health (R01GM)
  • National Institute of General Medical Sciences (R01GM090208)
Topics
  • Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Protein Structure and Dynamics
  • Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Advanced Physical and Chemical Molecular Interactions
  • Physical Sciences › Computer Science › Computational Theory and Mathematics › Advanced Mathematical Modeling in Engineering
Keywords
macromolecular flexibility, protein rigidity, Poisson-Boltzmann equation, continuum electrostatics, total energy functional, solvation energy
MeSH terms
Models, Molecular, Protein Conformation, Proteins, Molecular Dynamics Simulation

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