A VIBRATIONAL EIGENFUNCTION OF A PROTEIN - ANHARMONIC COUPLED-MODE GROUND AND FUNDAMENTAL EXCITED-STATES OF BPTI

We present detailed methodology and results for the approximate calcul ation of the anharmonic vibrational wave functions for a given structu re of a protein. The ground state and the fundamental vibrationally ex cited states of hydrated BPTI are computed with an approach that is of very good accuracy for low-lying states. The eigenfunctions are used to predict quantum properties such as vibrational excitation frequenci es and IR intensities as well as atomic mean square displacements at T = 0 K. The method treats diagonal anharmonic effects exactly up to fo urth order in normal mode coordinates, while using a mean-field approx imation, the vibrational self-consistent field (SCF) approximation for the mode-mode couplings. The inclusion of the diagonal effects (exact in fourth order) makes the potentials stiffer than quadratic. When th e mode-mode coupling is included as a mean field, the system becomes e ven stiffer. These effects produce significant modifications of such o bservables as the vibrational spectrum and Debye-Waller factors. The r esults presented here should be considered essentially exact except fo r potentially important approximations: (a) that the potential energy used bears some resemblance to reality, (b) that the system is restric ted to a single minimum in the potential energy surface, and (c) that the quartic expansion in normal modes, when truncated to fourth order, provides a good description of the potential. These issues will be ad dressed in the main text. The results show that the vibrational absorp tion spectrum is strongly affected by anharmonic and mode-mode couplin g effects. Deviations from the corresponding harmonic absorption inten sities are very large. Unlike our previous study that found only weak mode-mode coupling effects for the lowest 100 modes, the SCF correctio ns calculated here for the intermediate frequency modes are seen to be very significant. The results have important implications for the vib rational spectroscopy and other properties of proteins at low temperat ures.