Expected Distributions of Root-Mean-Square Positional Deviations in Proteins

The
atom positional root-mean-square deviation (RMSD) is a standard
tool for comparing the similarity of two molecular structures. It
is used to characterize the quality of biomolecular simulations, to
cluster conformations, and as a reaction coordinate for conformational
changes. This work presents an approximate analytic form for the expected
distribution of RMSD values for a protein or polymer fluctuating about
a stable native structure. The mean and maximum of the expected distribution
are independent of chain length for long chains and linearly proportional
to the average atom positional root-mean-square fluctuations (RMSF̅). To approximate the
RMSD distribution
for random-coil or unfolded ensembles, numerical distributions of
RMSD were generated for ensembles of self-avoiding and non-self-avoiding
random walks. In both cases, for all reference structures tested for
chains more than three monomers long, the distributions have a maximum
distant from the origin with a power-law dependence on chain length.
The purely entropic nature of this result implies that care must be
taken when interpreting stable high-RMSD regions of the free-energy
landscape as “intermediates” or well-defined stable
states.