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Normal mode analysis of molecular motions in curvilinear coordinates on a non-Eckart body-frame: an application to protein torsion dynamics

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Abstract

Normal mode analysis (NMA) was introduced in 1930s as a framework to understand the structure of the observed vibration-rotation spectrum of several small molecules. During the past three decades NMA has also become a popular alternative to figuring out the large-scale motion of proteins and other macromolecules. However, the “standard” NMA is based on approximations, which sometimes are unphysical. Especially problematic is the assumption that atoms move only “infinitesimally”, which, of course, is an oxymoron when large amplitude motions are concerned. The “infinitesimal” approximation has the further unfortunate side effect of masking the physical importance of the coupling between vibrational and rotational degrees of freedom. Here, we present a novel formulation of the NMA, which is applied for finite motions in non-Eckart body-frame. Contrary to standard normal mode theory, our approach starts by assuming a harmonic potential in generalized coordinates, and tries to avoid the linearization of the coordinates. It also takes explicitly into account the Coriolis terms, which couple vibrations and rotations, and the terms involving Christoffel symbols, which are ignored by default in the standard NMA. We also computationally explore the effect of various terms to the solutions of the NMA equation of motions.

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Authors and Affiliations

  1. Department of Chemistry, University of Helsinki, P.O. Box 55, (A. I. Virtasen aukio 1), 00014, Helsinki, Finland

    Janne Pesonen

  2. Department of Physics, University of Helsinki, P.O. Box 43, (Pietari Kalmin katu 2), 00014, Helsinki, Finland

    Krister O. E. Henriksson

  3. Department of Biological Physical Chemistry, Rocasolano Physical Chemistry Institute, CSIC, Serrano 119, 28006, Madrid, Spain

    Jose Ramon López-Blanco & Pablo Chacón

Authors
  1. Janne Pesonen
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  2. Krister O. E. Henriksson
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  3. Jose Ramon López-Blanco
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  4. Pablo Chacón
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Correspondence to Janne Pesonen.

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Pesonen, J., Henriksson, K.O.E., López-Blanco, J.R. et al. Normal mode analysis of molecular motions in curvilinear coordinates on a non-Eckart body-frame: an application to protein torsion dynamics. J Math Chem 50, 1521–1549 (2012). https://doi.org/10.1007/s10910-012-9987-8

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  • DOI: https://doi.org/10.1007/s10910-012-9987-8

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