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We begin our development with the hNM family of hinge predictors. The name suggests
its relationship to HingeMaster (the integrated hinge predictor) and its reliance on
Normal Mode information. As mentioned, this family has four members, designated
hNMa to hNMe, of which hNMb, through hNMe are novel. The output of hNMa is
simply the normalized squared fluctuations due to the first normal mode, with the idea
that the minima of this quantity coincide with the hinge location.
Normal modes describe the oscillations of elastic bodies. We obtain them by
representing the body as a set of identical point masses connected by linear springs, and
using a harmonic ansatz to solve the equations of motion. Obtaining the form of the 3N
normal modes reduces to the eigenvalue problem:
2
(m" i [ I]
# [ K])
r
x i = 0
Where I is the identity matrix, K is the Kirchoff or stiffness matrix, " i is the frequency of
oscillation corresponding to mode i, and
displacements due to mode i.
r
x i is the eigenvector describing the
Under the Gaussian Network Model,
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the protein is simplified to consist of identical point
masses at the location of the Cα atoms, which are connected by identical linear springs to
all other such masses within a 7Å radius. Further adjustments are made to K to account
for interactions between residues adjacent in sequence, and to suppress large
displacements in the middle of the chain. The simplifications mean that only one
parameter (the spring constant) needs to be determined, and this is done by fitting to
experimentally observed thermal motions. The eigenvalue problem simplifies to:
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