Inelastic neutron scattering analysis of low frequency motion in proteins: A normal mode study of the bovine pancreatic trypsin inhibitor

Abstract

An improved understanding of the function of macromolecules of biological interest requires the characterization of their low-frequency internal fluctuations (ℏw≪kBT where kBT∼200 cm−1 at room temperature), which dominate the atomic displacements. To explore the potential or inelastic neutron scattering for supplying information about such motions, we employ the formalism of Zemach and Glauber [A. C. Zemach and R. J. Glauber, Phys. Rev. 101, 118 (1956)] to calculate the one-phonon vibrational incoherent scattering function, Svibinc (q,w), of a small protein, BPTI. An in vacuo normal mode analysis of BPTI [B. Brooks and M. Karplus, Proc. Natl. Acad. Sci. U.S.A. 80, 6571 (1983)], is used for the calculation of Svibinc (q,w). The dependence of Svibinc (q,w) on energy transfer and momentum transfer is investigated and the results are placed in the context of present instrumental capabilities. Although the overall energy dependence of Svibinc (q,w) has a simple form, the variations in the hydrogen atom displacements in the different modes have a significant effect on the scattering. Mode anisotropy is strongly manifested in oriented spectra calculated without instrumental resolution broadening. Contributions from individual atoms and residues to the unbroadened whole molecule scattering are examined in detail. They are found to depend significantly on the atom or residue examined. This suggests that inelastic neutron scattering has considerable potential for the investigation of local dynamic variations in proteins by use of a deuterated protein with specifically protonated residues. Orientational averaging and instrumental resolution broadening of Svibinc (q,w) indicate that the one-phonon scattering detectable on the most suitable current instrument would show strong features arising principally from the frequency distribution of the vibrational modes. Multiphonon scattering is small at low momentum transfers in the low frequency range of most interest (<30 cm−1) but increases rapidly with increasing energy and momentum transfers. It is shown to originate from the lowest frequency modes. The momentum transfer dependence of the one-phonon Svibinc (q,w) is investigated. An expression is found which can be used to extrapolate the calculated one-phonon scattering to zero momentum transfer using experimentally obtainable ranges of momentum transfer. This permits the extraction of an amplitude-weighted frequency distribution function. At current resolutions this function is similar in form to the unweighted frequency distribution function, knowledge of which would be very useful for analysis of protein thermodynamics and dynamics.