  We investigate the relation between backbone and side-chain ordering in a
small protein. For this purpos e we have performed multicanonical simulations
of the villin headpiece subdomain HP-36, an often used to y model in protein
studies. Concepts of circular statistics are introduced to analyze side-chain
fluctuations. In contrast to earlier studies on homopolypeptides (Wei et al.,
J. Phys. Chem. B, 111 (2007) 4244) we do not find collective effects leading to
a separate transition. Rather, side-chain ordering is spread over a wide
temperature range. Our results indicate a thermal hierarchy of ordering events,
with side-chain ordering appearing at temperatures below the helix-coil
transition but above the folding transition. We conjecture that this thermal
hierarchy reflects an underlying temporal order, and that side-chain ordering
facilitates the search for the correct backbone topology.
