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Neutron Frequency Windows and the Protein Dynamical Transition

Torsten Becker ^*, Jennifer A. Hayward ^*, John L. Finney , Roy M. Daniel  and Jeremy C. Smith ^*

^* Computational Molecular Biophysics, Interdisciplinary Center for Scientific Computing, Universität Heidelberg, Heidelberg, Germany; Department of Physics and Astronomy, University College London, London, United Kingdom; and Department of Biological Sciences, University of Waikato, Hamilton, New Zealand

Correspondence: Address reprint requests to J.C. Smith, Interdisciplinary Center for Scientific Computing (IWR), Universität Heidelberg, Im Neuenheimer Feld 368, D-69120 Heidelberg, Germany. Tel.: 49-6-221-548857; E-mail: biocomputing{at}iwr.uni-heidelberg.de.

Proteins undergo an apparent dynamical transition on temperature variation that has been correlated with the onset of function. The transition in the mean-square displacement, r², that is observed using a spectrometer or computer simulation, depends on the relationship between the timescales of the relaxation processes activated and the timescale accessible to the instrument or simulation. Models are described of two extreme situations—an "equilibrium" model, in which the long-time dynamics changes with temperature and all motions are resolved by the instrument used; and a "frequency window" model, in which there is no change in the long-time dynamics but as the temperature increases, the relaxation frequencies move into the instrumental range. Here we demonstrate that the latter, frequency-window model can describe the temperature and timescale dependences of both the intermediate neutron scattering function and r² derived from molecular dynamics simulations of a small protein in a cryosolution. The frequency-window model also describes the energy-resolution and temperature-dependences of r² obtained from experimental neutron scattering on glutamate dehydrogenase in the same solvent. Although equilibrium effects should also contribute to dynamical transitions in proteins, the present results suggests that frequency-window effects can play a role in the simulations and experiments examined. Finally, misquotations of previous findings are discussed in the context of solvent activation of protein dynamics and the possible relationship of this to activity.

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