Fast calculation of the infrared spectra of large biomolecules
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ORIGINAL PAPER
Fast calculation of the infrared spectra of large biomolecules A. J. Mott • S. P. Thirumuruganandham M. F. Thorpe • P. Rez
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Received: 27 April 2013 / Revised: 25 July 2013 / Accepted: 21 August 2013 / Published online: 14 September 2013 European Biophysical Societies’ Association 2013
Abstract Vibrational spectra of proteins potentially give insight into biologically significant molecular motion and the proportions of different types of secondary structure. Vibrational spectra can be calculated either from normal modes obtained by diagonalizing the mass-weighted Hessian or from the time autocorrelation function derived from molecular dynamics trajectories. The Hessian matrix is calculated from force fields because it is not practical to calculate the Hessian from quantum mechanics for large molecules. As an alternative to molecular dynamics the spectral response can be calculated from a time autocorrelation derived from numerical solution of the harmonic equations of motion, resulting in calculations at least 4 times faster. Because the calculation also scales linearly with number of atoms, N, it is faster than normal-mode calculations that scale as N3 for proteins with more then 4,700 atoms. Using this method it is practical to perform all-atom calculations for large biological systems, for example viral capsids, with the order of 105 atoms. Keywords Infrared Molecular dynamics Proteins Equation of motion Macromolecules
A. J. Mott S. P. Thirumuruganandham M. F. Thorpe P. Rez (&) Department of Physics, Arizona State University, Tempe, AZ 85287, USA e-mail: [email protected] M. F. Thorpe Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, UK
Introduction There is substantial interest in the vibrational spectra of proteins and protein complexes. For example, the amide region from 1,300 to 1,800 cm-1 gives peaks that can be used to determine the proportions of different secondary structures, for example a helices and b sheets (Byler and Susi 1986). Much recent work has concentrated on the terahertz region, because these low-frequency vibrational modes could relate to biologically significant transformations in macromolecules (Markelz 2008; Tama and Sanejouand 2001). Several different methods have been used for calculation of the density of vibrational states or infrared (IR) spectra. The most straightforward method is normal-mode analysis. This involves calculating the Hessian matrix, the second derivative of potential energy with respect to atomic displacements, and then finding the eigenvalues and eigenvectors of the mass-weighted Hessian matrix (Bahar et al. 2010). The eigenvalues are the square of the vibration frequencies and the eigenvectors are the normal modes. The eigenvalues and eigenvectors can then be used to calculate IR absorption, density of states, or any other dynamical property of interest. Because proteins have a large number of atoms, it is not possible to calculate the Hessian from first principles using quantum mec
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