Abstract:

An Order (N ) technique, the phonon functional method, for the study of the low frequency mechanical modes of large molecular systems is developed where the displacement patterns are modeled with atomic detail. The method is based on ideas from electronic structure theory and uses an energy functional to find the lowest frequency phonon states of a classical dynamical matrix below a pseudo-Fermi level. The resulting method is iterative and requires only the operation of the dynamical matrix on a set of vectors.

An analysis of the low frequency motions of three viral capsids, the satellite tobacco necrosis virus, the cowpea chlorotic mottle virus, and the M13 bacteriophage are calculated using the technique. The Raman spectra of the viral capsids are calculated using the atomistic displacement patterns and an empirical bond polarizability model. In addition, the mechanical modes and Raman spectra of the M13 bacteriophage are also found with continuum elastic theory and an amorphous isotropic bond polarizability model which are then compared with the atomistic calculations.

The mechanical modes of an adenosine triphosphate binding cassette are also calculated using the phonon functional method. The results indicate two clear modes that are responsible for the transport process. Based on the two normal modes a transport cycle is hypothesized.

The possibility of viron destruction through a resonant excitation of its capsids mechanical modes is examined next. A recent impulsive stimulated Raman scattering experiment of the M13 bacteriophage capsid is theoretically modeled using classical molecular dynamics. The results are analyzed with a simple driven harmonic oscillator approach and indicate the existence of an "amplitude threshold" which causes the virus capsid to break apart once reached.

Finally, the activation relaxation technique is extended to atomistic systems with explicit water. A test of the extension is performed on a small single amino acid protein. The results reveal difficulty extending the technique to systems with explicit water.