Biomedical Engineering Reference
In-Depth Information
The correct level of acceleration, and therefore conformational space, is
directly estimated by comparing the experimental RDCs to predicted values
from ensembles calculated at different levels of acceleration. Both experimental
scalar and dipolar couplings represent a population-weighted average over all
conformers contributing to the measurement and are therefore treated using
the same ensemble average. The method was used to describe conformational
dynamics in ubiquitin.
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Figure 8.3 shows order parameters at different acceleration levels, identify-
ing the optimal AMD molecular ensemble that best reproduces both RDCs
and scalar J-couplings. The average backbone structure of the AMD ensemble
is very similar to that of the experimentally refined 1D3Z structure (using over
2500 experimental restraints), showing that while the ensemble samples more
conformational space, it is distributed about a mean that resembles the
experimentally determined time- and ensemble-averaged structure. This result
is all the more remarkable when we consider that no structural restraints were
applied, and the conformational space is only defined via global agreement
with all data. The free-energy-weighted ensemble reproduces experimental
NMR observables substantially better than a control set of 5 ns standard MD
simulations and provides significantly better results compared to the static X-
ray crystal structure (1UBQ).
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Enhanced sampling from AMD is thus capable
of defining a representative molecular ensemble for solution-state protein
conformational dynamics. Perturbation of statistical mechanical sampling that
may be associated with incorporation of non-physical terms into a potential
energy force field is avoided by using restraint-free trajectories seededat
different points in the conformational space that are sampled by the
accelerated MD. Accuracy of predicted RDCs is hardly compromised,
resulting in a similar level of reproduction compared to state-of-the-art
single-structure or restrained-ensemble approaches.
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Crucially, the level of
acceleration, and therefore the extent of sampling, is the only variable
parameter, and this is determined directly from the measured couplings, with
no direct fitting to experimental data.
RDCs provide a powerful theoretical and analytical framework with which
to address the level of disorder present in biomolecules at equilibrium. Two
very different approaches have been presented in more detail here: in one case
analytical expressions are used in a least-squares fitting approach, to determine
the amplitude and modes of local dynamics along the backbone. This requires
no structural model, is independent of physical assumptions except for the
average geometry of the peptide plane, and determines overall alignment, local
dynamics and average conformation, in a single algorithm. In the second case,
the experimental data are removed, and enhanced sampling of conformational
space is exploited to develop a statistical mechanical description of the rapidly
exchanging structural ensemble. The comparison is quite remarkable,
exhibiting a level of agreement that strongly substantiates the results found
in both cases.
