To estimate the influence of the applied approximations on the
description of protein structure and dynamics, we have extracted
the following observables from the long time simulations.
As a measure for the temporal evolution of protein structure
we have chosen the *rms* deviations
of the intermediate configurations from the
initial structure.
If are the atomic positions obtained after the
equilibration phase, the *rms*
deviations of the set of heavy backbone atoms
() and of
the corresponding set of side chain atoms
() are given by

where denotes the number of atoms in the set
.

To estimate approximation effects on protein dynamics we monitor
correlations between the motions of atoms *i* and
*j* by the
normalized covariance matrix

where the averages are taken over trajectory sections specified
further below.

Subsequently we compare covariance matrices and
from simulations
*A* and
*B*, respectively, both by
a graphical method and by a single numerical observable.
The latter is the *rms* difference of the cross correlations,
i.e.,

whereas the former is an overlay of certain contour plots pertaining
to the .
These contour plots visualize histograms representing the frequencies
of values as functions of atomic distances
and will be called covariance plots.

As a technical point we would like to note that comparisons of the type sketched above require, that the trajectories refer to one and the same conformational substate of the protein considered. The reason is, that dynamical correlations may vary from substate to substate, such that differences of these correlations, which are caused by the application of different algorithms, may be obscured.

Wed Apr 30 15:40:09 MET DST 1997