@TechReport{Dartmouth:TR2003-474,
author = {Anthony K. Yan and Christopher J. Langmead and Bruce Randall Donald},
title = {{A Probability-Based Similarity Measure for Saupe Alignment Tensors with Applications to Residual Dipolar Couplings in NMR Structural Biology}},
institution = {Dartmouth College, Computer Science},
address = {Hanover, NH},
number = {TR2003-474},
year = {2003},
month = {October},
URL = {ftp://ftp.cs.dartmouth.edu/TR/TR2003-474.pdf},
comment = {
A revised and expanded version of this paper has been accepted at a
journal and will appear as: "A Probability-Based Similarity Measure
for Saupe Alignment Tensors with Applications to Residual Dipolar
Couplings in NMR Structural Biology", in The *International Journal
of Robotics Research* Special Issue on Robotics Techniques
Applied to Computational Biology, 2004.
},
abstract = {
High-throughput NMR structural biology and NMR structural genomics
pose a fascinating set of geometric challenges. A key bottleneck in
NMR structural biology is the resonance assignment problem. We seek to
accelerate protein NMR resonance assignment and structure
determination by exploiting *a priori* structural information. In
particular, a method known as Nuclear Vector Replacement (NVR) has
been proposed as a method for solving the assignment problem given a
priori structural information [24,25]. Among several
different kinds of input data, NVR uses a particular type of NMR data
known as *residual dipolar couplings (RDCs)*. The basic physics
of residual dipolar couplings tells us that the data should be
explainable by a structural model and set of parameters contained
within the *Saupe alignment tensor*.
In the NVR algorithm, one estimates the Saupe alignment tensors and
then proceeds to refine those estimates. We would like to quantify
the accuracy of such estimates, where we compare the estimated Saupe
matrix to the correct Saupe matrix. In this work, we propose a way to
quantify this comparison. Given a correct Saupe matrix and an
estimated Saupe matrix, we compute an upper bound on the probability
that a randomly rotated Saupe tensor would have an error smaller than
the estimated Saupe matrix. This has the advantage of being a
quantified upper bound which also has a clear interpretation in terms
of geometry and probability. While the specific application of our
rotation probability results is given to NVR, our novel methods can be
used for any RDC-based algorithm to bound the accuracy of the
estimated alignment tensors. Furthermore, they could also be used in
X-ray crystallography or molecular docking to quantitate the accuracy
of calculated rotations of proteins, protein domains, nucleic acids,
or small molecules.
}
}