INELASTIC NEUTRON-SCATTERING ANALYSIS OF LOW-FREQUENCY MOTIONS IN PROTEINS - HARMONIC AND DAMPED HARMONIC MODELS OF BOVINE PANCREATIC TRYPSIN-INHIBITOR

Inelastic neutron scattering spectra are calculated from harmonic and damped harmonic models of the internal dynamics of a small protein, the bovine pancreatic trypsin inhibitor (BPTI). Numerical Fourier transformation of the intermediate scattering function Fincvib (q, t) is used to calculate the inelastic scattering. This permits the inclusion of multiphonon scattering and frictional damping effects. Although for a typical experimental configuration, the multiphonon contribution does not significantly alter the form of the scattering at frequencies below about 30 cm-1, it does have a significant effect on the scattering intensity at higher frequencies. Frictional damping is introduced into the harmonic model by assuming that each mode acts as an independent damped Langevin oscillator. With this model and the assumption that the lowest frequency modes are overdamped while the higher frequency modes are underdamped, improved agreement with the experimental BPTI powder results is obtained. The measured scattering from BPTI in solution shows increased intensity at frequencies below 50 cm-1 relative to the powder results. The solution scattering profile can be reproduced approximately by the addition of overdamped Langevin oscillator normal modes to the dynamic model in best agreement with the powder data. Several other aspects of neutron scattering from proteins are examined. Anisotropy in the harmonic resolution broadened scattering is demonstrated. Spectra calculated assuming classical equations of motion are shown to agree with those calculated with the full quantum-mechanical dynamical model. Translational diffusion broadening is found to be small compared to the instrumental resolution broadening for the range of scattering wave vectors of interest. The contribution of the coherent scattering to the measured intensity is calculated for the case of a partially hydrated protein. Under typical experimental conditions, the measured cross sections are dominated by the incoherent scattering and the self part of the coherent scattering, a result that justifies the comparison of experimental data with calculated incoherent scattering spectra. © 1990 American Institute of Physics.