Biomedical Engineering Reference
In-Depth Information
interactions between spins (often
15
N-
1
H) can provide precise information
about the presence of dynamics in the picosecond to millisecond range.
Numerous approaches have been proposed over the last 15 years to determine
local protein backbone dynamics from RDCs.
46-64
These techniques can be
classed into two generic approaches; the first exploits a direct determination of
dynamic amplitudes and motional modes of individual bond vectors or structural
elements from multiple RDCs. These approaches are independent of molecular
models, and do not suffer from the potential bias incurred when potential energy
force fields and experimental target functions are combined in an arbitrary way.
There are, however numerous disadvantages—the motional parameters are
generally expressed in an abstract form that is not easily converted into a format
accessible to a structural or molecular biologist. Common to many fitting
procedures, the possibility that motional parameters are fitted to noise rather
than signal must also be carefully monitored. The second generic method takes a
very different approach to the problem, exploiting molecular dynamics
simulation to construct a description of the protein ensemble that reproduces
the experimental data. The advantages of this kind of approach are diametrically
opposed to those of the mathematical modeling based approaches—in this case
an explicit molecular description of the ensemble is determined, holding immense
potential for understanding the mechanistic basis of biomolecular interaction and
function. The disadvantage is that the Boltzmann weighting of the ensemblemay
not be properly described when terms that are used to drive the ensemble into
agreement with the experimental data are combined, in a more or less arbitrary
way, with the potential energy term.
8.4.2.1 Model-Free Approaches
The analytical approaches generally determine the average spherical harmonics
that define the orientational sampling of each vector relative to a common
molecular alignment frame, using the expression in eqn (8.2).
55,65,66
The
measurement of RDCs in the presence of different alignment media changes
the way the same dynamics average the measured RDC, as shown in
Figure 8.2. The spherical harmonics can be mathematically determined from
more than five independent experimental data sets averaged in the different
tensorial frames using Wigner rotation matrices. We can consider these
approaches as 'model-free' when considering a single dipolar interactionor
internuclear vector, because, as for relaxation data analysis, the motional
averaging is described without invoking a specific physical model, thereby
avoiding bias due to incorrect motional models. Two different model-free
approaches were developed to extract dynamic information from RDCs
measured in different alignment media based on the determination of the
sampling characteristics defined by the spherical harmonic terms shown ineqn
(8.2).
55,65
In both cases the quantitative determination of the dynamics is
dependent on an accurate determination of the alignment tensors (j), and in
particular the amplitude term for each tensor [A
j
in eqn (8.2)]. When only
