Correlation Analysis of Trp-Cage Dynamics in Folded and Unfolded States

A fundamental and still debated problem
is how folded structures
of proteins are related to their unfolded state. Besides the classical
view, in which a large number of conformations characterize the unfolded
state while the folded one is dominated by a single structure, recently
a reassessment of the denatured state has been suggested. A growing
amount of evidence indicates that not only the folded but also the
unfolded state is at least partially organized. Here, we try to answer
the question of how different protein dynamics is in folded and unfolded
states by performing all-atom molecular dynamics simulations on the
model protein Trp-cage. Random matrix theory inspired analysis of
the correlation matrices has been carried out. The spectra of these
correlation matrices show that the low rank modes of Trp-cage dynamics
are outside of the limit expected for a random system both in folded
and in unfolded conditions. These findings shed light on the nature
of the unfolded state of the proteins, suggesting that it is much
less random than previously thought.