l - People

!
[ K]
= [ U]
"
[ ] 2
[ U]
T
Where U is an orthogonal matrix whose columns are
diagonal matrix whose elements are the frequencies " i .
!
!
The choice of first vs. second or higher modes as hinge predictors is the subject of much
debate in the community; we now address ! this issue.
165
r
x i , the eigenvectors of K.
" is a
Normal mode expansions provide the form of displacements of a structure at each of a
progressive series of resonant frequencies, or excitation frequencies to which an elastic
structure responds strongly. Various studies underscore the importance of low-order
modes in describing protein motion, but opinions vary as to which of these should be
used for hinge prediction. Alexandrov et al.[61] and Krebs et al. compared the
successive normal modes of poteins with the displacements observed from interpolated
(“morphed”) structural pairs of proteins, and found that the correlation was highest for
the lowest order mode, and decreased progressively for higher modes. Kundu et al.[74]
assigned residues of protein to one of two clusters depending on the sign of the lowest-
order nontrivial normal mode eigenvector. These domain assignments are then adjusted
by a series of physicochemically motivated postprocessing steps. Yang et al. showed that
catalytic sites tend to coincide with regions of minimal displacement of the first and
second nontrivial mode. Here we show that for the case of domain hinge bending, the
lowest-order nontrivial mode should be used for hinge prediction.
To do so we will make use of the concept of a nodal surface. To introduce this consider
the example of a one dimensional guitar string driven at its second harmonic frequency.