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

Figure 12

Curvature integral as a function of helical bending. In order to model a bending motion, an ideal linear helix comprising 31 atoms is distorted by bending its imaginary, linear axis along a cosine function. The curvature of the imaginary axis is known and its integral serves as the reference for the amount of bending. We compare this reference curvature integral with that derived via our fragment-fitting method by calculating the relative error. An ideal method would show a very close to linear correlation between the reference and the measured value. Polynomials of third and fifth degree show the highest relative error, especially for large magnitudes of bending. Sixth-order polynomials or polynomials of higher order look quite promising regarding relative error. Polynomials of higher order were ruled out because of overfitting and the fact that spurious terminal oscillations might occur. Second-order polynomials show a well behaved, close to linear dependence and were therefore adopted to model α-helices of MHCs.