In order to estimate the quality of the numerous approximations utilized by FAMUSAMM and to measure the gain of computational efficiency we have carried out a series of test simulations. We have applied two versions of our method, one employing the linear extrapolation, which we call FAMUSAMM/linear, and one using the DC-1d extrapolation scheme, which we correspondingly denote by FAMUSAMM/DC-1d. To enable comparisons with established methods, we have also performed test simulations using a cutoff method , the fast SAMM algorithm  and the slow but exact evaluation of the Coulomb sum, eq. (1), which we use as the reference method.
As discussed in the introduction, the complicated and chaotic nature of protein dynamics renders quality assessments of approximate MD algorithms a non-trivial task. For example, comparisons of system trajectories or of other atomic details obtained from simulations carried out with different approximation schemes are useless for that purpose, since possible observed deviations merely reflect the chaotic character of these details and thus do not allow to derive accuracy measures. Instead, following the arguments and suggestions in refs.  and , we will apply a set of so-called ``relevant'' statistical observables for our intended estimates of algorithmic quality. These observables have been selected according to the conditions, that they should exhibit regular, i.e., non-chaotic temporal behavior and that they should refer to functionally important properties of proteins [16, 20]