Geometry Dynamics of α-Helices in Different Class I Major Histocompatibility Complexes

Figure 13

Curvature integral as a function of hinge movement. The relative error in retrieving the correct hinge angle is plotted against helix hinge angle and polynomial degree. To model the hinge motion, a kink of varying angle was introduced to an ideal linear helix comprising only atoms (31 atoms). Images (a), (b), and (c) show the same data for different positions of the kink in the helix. We refer to the kink angle as the signal we want to measure. We compared the signal to the curvature integral of the polynomial fitted to the helical axis by calculating the relative error. An ideal method would show a linear correlation between signal and the measured value. We see that polynomials of higher order show a higher relative error and overestimate the magnitude of the kink. We also see that the position of the kink modulates the relative error. Second-order polynomials have a nearly linear dependency and were therefore adopted to model α-helices of MHCs.

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