  Using a time-dependent perturbation theory, vibrational energy relaxation
(VER) of isotopically labeled amide I modes in cytochrome c solvated with water
is investigated. Contributions to the VER are decomposed into two contributions
from the protein and water. The VER pathways are visualized using radial and
angular excitation functions for resonant normal modes. Key differences of VER
among different amide I modes are demonstrated, leading to a detailed picture
of the spatial anisotropy of the VER. The results support the experimental
observation that amide I modes in proteins relax with sub picosecond
timescales, while the relaxation mechanism turns out to be sensitive to the
environment of the amide I mode.
