  We present a study on the near equilibrium dynamics of two small proteins in
the family of truncated hemoglobins, developed under the framework of a
Gaussian network approach. Effective beta carbon atoms are taken into account
besides C-alphas for all residues but glycines in the coarse-graining
procedure, without leading to an increase in the degrees of freedom
(betaGaussian Model). Normalized covariance matrix and deformation along
slowest modes with collective character are analyzed, pointing out
anti-correlations between functionally relevant sites for the proteins under
study. In particular we underline the functional motions of an extended
tunnel-cavity system running inside the protein matrix, which provide a pathway
for small ligands binding with the iron in the heme group. We give a rough
estimate of the order of magnitude of the relaxation times of the slowest two
overdamped modes and compare results with previous studies on globins.
