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The string will have a nodal point in the middle which remains stationary. A drum head
(effectively two dimensional) similarly will have nodal lines, depending on which mode
is excited. A three dimensional object such as a tuning fork or a protein will have a
surface which describes the locus of points that remain stationary when the object
vibrates at one of its normal frequencies. The displacements of points on opposite sides
of this nodal surface have opposite sign.[74] If the structure in question is composed of
two rigid regions connected by a flexible region, then points within each rigid region will
move in a correlated fashion, and points in different regions will tend to be anticorrelated
to conserve center of mass motion. The velocities change sign at the nodal surface, and
therefore the latter might be expected to coincide with the flexible region or hinge[47, 61,
64, 76]. This leads to the following two ideas:
The HAG set consists of proteins with two domains separated by a single (possibly multi-
stranded) flexible region. This single hinge should correspond to a single nodal surface.
The lowest order mode has the smallest number of nodes and (assuming the equipartition
theorem applies) the largest displacements and therefore the coincidence of nodal surface
with hinge should be strongest for this mode.
There may be multiple degrees of freedom about the hinge, and therefore to some degree
the second, third, and higher modes might also coincide with the hinge.
To test these ideas, we extracted the mobility score,
!
166
M ik for each residue i in the
mode, for k = 1 to 7. This quantity is the square fluctuation of residue i in mode k,
!
normalized such that the most mobile residue has mobility Mik =1 for mode k. We then
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k th