title: Long-time mean-square displacements in proteins.
abstract: We propose a method for obtaining the intrinsic, long-time mean square displacement (MSD) of atoms and molecules in proteins from finite-time molecular dynamics (MD) simulations. Typical data from simulations are limited to times of 1 to 10 ns, and over this time period the calculated MSD continues to increase without a clear limiting value. The proposed method consists of fitting a model to MD simulation-derived values of the incoherent intermediate neutron scattering function, I(inc)(Q,t), for finite times. The infinite-time MSD, <r(2)>, appears as a parameter in the model and is determined by fits of the model to the finite-time I(inc)(Q,t). Specifically, the <r(2)> is defined in the usual way in terms of the Debye-Waller factor as I(Q,t=∞)=exp(-Q(2)<r(2)>/3). The method is illustrated by obtaining the intrinsic MSD <r(2)> of hydrated lysozyme powder (h=0.4 g water/g protein) over a wide temperature range. The intrinsic <r(2)> obtained from data out to 1 and to 10 ns is found to be the same. The intrinsic <r(2)> is approximately twice the value of the MSD that is reached in simulations after times of 1 ns which correspond to those observed using neutron instruments that have an energy resolution width of 1 μeV.
authors: Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716-2570, USA.
authors: Derya
authors: D
authors: Vural
authors: Center for Molecular Biophysics, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA and Department of Biochemistry and Cellular and Molecular Biology, University of Tennessee, Knoxville, Tennessee 37996, USA.
authors: Liang
authors: L
authors: Hong
authors: Center for Molecular Biophysics, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA and Department of Biochemistry and Cellular and Molecular Biology, University of Tennessee, Knoxville, Tennessee 37996, USA.
authors: Jeremy C
authors: JC
authors: Smith
authors: Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716-2570, USA.
authors: Henry R
authors: HR
authors: Glyde
mesh_terms: D056004:Molecular Dynamics Simulation; D011506:Proteins / Q000737:chemistry*; D013997:Time Factors
chemical_list: D011506:Proteins