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generated one ROC curve for each mode k. This is based on taking all residues with
normal mode displacement lower than a certain threshold to be test positives and all
others to be test negatives. The ROC curves are generated by moving the threshold and
calculating sensitivity and specificity for each possible threshold.
We found that the first idea above was correct; regions of low first normal mode
displacement are likely to coincide with hinge location. (Figure 4.1). The second and
third normal mode displacements were not correlated with hinge location, as reflected by
areas under the curve near 0.5. Modes higher than 3 were also found to have very little
correlation with hinges (data not shown). Therefore the second idea is incorrect for
domain hinge bending motions involving two domains. From this we concluded that if
normal mode displacements alone are used for domain hinge prediction under such
circumstances then it is the first rather than higher modes that should be used. This is not
to say that the higher modes are not useful; in the next section we will show that the
correlation matrix is generated by summing the correlations due to all modes, and this
matrix can be used effectively for hinge prediction.
Motion correlation based methods (hNMb, hNMc, hNMd)
We now move on to describe applications of normal modes to hinge finding. To do this
we must first calculate the normal mode motional correlations between α-carbon atoms
in a protein. This is obtained by computing an expectation value in the Boltzmann
ensemble. The result is:
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