  The main chain dihedral angles play an important role to decide the protein
conformation. The native states of a protein can be regard as an ensemble of a
lot of similar conformations, in different conformations the main chain
dihedral angles vary in a certain range. Each dihedral angle value can be
described as a distribution, but only using the distribution can't describe the
real conformation space. The reason is that the dihedral angle has correlation
with others, especially the neighbor dihedral angles in primary sequence. In
our study we analysis extensive molecular dynamics (MD) simulation trajectories
of eleven proteins with different sizes and folds, we found that in stable
second structure the correlations only exist between the dihedrals near to each
other in primary sequence, long range correlations are rare. But in unstable
structures (loop) long range correlations exist. Further we observed some
characteristics of the short range correlations in different second structures
({\alpha}-helix, {\beta}-sheet) and we found that we can approximate good high
order dihedral angle distribution good only use three order distribution in
stable second structure which illustrates that high order correlations (over
three order) is small in stable second structure.
