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Long Time Observables


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 tex2html_wrap_inline1435 of the intermediate configurations from the initial structure. If tex2html_wrap_inline1437 are the atomic positions obtained after the equilibration phase, the rms deviations of the set tex2html_wrap_inline1439 of heavy backbone atoms (tex2html_wrap_inline1441) and of the corresponding set tex2html_wrap_inline1443 of side chain atoms (tex2html_wrap_inline1445) are given by
where tex2html_wrap_inline1447 denotes the number of atoms in the set tex2html_wrap_inline1449.

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 tex2html_wrap_inline1455 and tex2html_wrap_inline1457 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 tex2html_wrap_inline1463. These contour plots visualize histograms representing the frequencies of values tex2html_wrap_inline1465 as functions of atomic distances tex2html_wrap_inline1467 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.

Helmut Grubmueller
Wed Apr 30 15:40:09 MET DST 1997