Biomedical Engineering Reference
In-Depth Information
15
N-
1
H
N
dipolar couplings are used in the analysis, it is difficult to distinguish
between changes in overall alignment and uniform changes in local dynamics.
For this reason these analyses scaled the effective order parameters to be lower
than or equal to the levels determined from spin relaxation. This is justified on
the basis that amplitudes of motions occurring on all timescales up to the
millisecond must be equal to or greater than motions occurring up to the
nanosecond, that are sampled by spin relaxation for essentially the same
dipolar interactions. Diverse versions of these model-free approaches were
applied to the protein ubiquitin using data measured using many alignment
media. This resulted in the description of slow dynamics, ranging from
pervasive slow motional order parameters of 0.8 to 0.9, depending on the
combination of data sets used in the analysis and the exact determination of
the level of molecular alignment (vide infra). An important advance was made
with the application of the SECONDA analysis
67,68
to a collection of over 30
data sets. SECONDA uses a principal component analysis of the RDC
covariance matrix to identify data sets that are self-consistent, and therefore
show no evidence of perturbing interaction with any media or that are
incompatible due to excessive noise. The application of model-free approaches
to a pruned subset of data measured in 23 different alignment media provided
a better behaved mathematical description of the dynamics in ubiquitin.
8.4.2.2
Gaussian Axial Fluctuation Approaches
Related approaches have been developed that combine the dynamic averaging
properties of different bond vectors within a known structural motif. Suchan
approach was proposed to determine local alignment tensors providing a
generalised degree of order (GDO) for units of local structure comprising each
C
a
junction in the protein.
56
Further developments based on a similar idea
consider multiple RDCs oriented in different directions in a single-peptide plane
and exploit the principle that anisotropic re-orientational motion of the peptide
plane averages differently oriented RDCs in a different manner (Figure 8.2).
69-72
These approaches reduce the peptide chain to a series of identical peptide planes,
characterising the backbone dynamics of the protein using multiple RDCs
measured in each plane of a
13
C,
15
N-labelled protein using the Gaussian axial
fluctuation (GAF) model. The GAF model was originally developed for the
interpretation of spin relaxation data, and allows for diffusive motions around
three orthogonal axes attached to each plane (Figure 8.2). The relevance ofthis
model to the averaging properties of backbone RDCs in proteins was initially
demonstrated with statistical certainty, using common amplitudes for the c-
motion for peptide planes in secondary structural elements of a series of high-
resolution protein structures. This evidence that anisotropy of peptide plane
motion can help determine absolute levels of backbone dynamics in proteinswas
then exploited more fully as described below.
Motional amplitudes around all three axes (3D-GAF) were determined
using an extensive set of RDCs from the third immunoglobin binding domain
