Calcium-Binding Protein Protocols Calcium-Binding Protein Protocols

292 Werner et al.
Fig. 3. (A) Rotational diffusion anisotropy of cbEGF32-33. The diffusion tensor
of each of the 22 structures in the family was calculated and the angle α between the
N–H bond vector and the largest principal component of the diffusion tensor was
determined. (T 1/T 2) –1 ratios are plotted as a function of the averages and standard
deviations of the angles α. The linear least-squares fit to the data is shown for illustration
of Eq. 10. (B) Orientation of the unique axis of the diffusion tensor D || in the
molecular frame of cbEGF32-33 depicted using an arrow and a ribbon diagram of
the average structure. The coordinate system of the inertia tensor and approximate
shape of the molecule are provided as references. The figure was produced using the
program MOLMOL (25).
10. Quantitative data analysis employs similar statistical reasoning at three stages: in
derivation of the relaxation time-constants and their associated uncertainties, in
determination of a global diffusion model, using a given a set of T 1 and T 2 values,
and in selection of models of internal dynamics for each residue.
In each case, parameters, a 1…a M, are obtained by a least-squares fit of the
model data, y(x i;a 1…a M), to the experimental data y i with errors σ i by minimizing
χ 2
χ2 = N
∑[yi – y(xi;a1…aM) / σi] i
2 (7)
The uncertainties of the parameters are determined by Monte Carlo simulations
of the fitted values, using the experimental errors. Concomitantly a χ2 distribution
is generated and a fit is deemed adequate, if the χ2 of the best fit is within a
chosen percentile (usually the ninety-fifth percentile) of the distribution (39).