Calcium-Binding Protein Protocols Calcium-Binding Protein Protocols

310 Boyd et al.
total and NOE energies. D a was incremented from 22.5 to 25.0 Hz in steps of
0.5 Hz, and R was incremented from 0.12 to 0.20 in steps of 0.02. For the LDLR-
AB pair, optimal agreement was found with D a 23–23.5 Hz and R 0.16–0.18.
These values are consistent with the estimates obtained based on analysis of the
histogram shown in Fig. 3.
4. Introduction of residual dipolar coupling-derived restraints may result in violation
of a subset of the NOE restraints. This is caused by inaccuracies in the NOEderived
distances because of spin diffusion, time averaging, or spectral overlap.
In this case, the NOE restraint list may be refined iteratively against the residual
dipolar coupling restraints, until the structures satisfy selection criteria. For the
LDLR-AB pair, structures shown in Fig. 5 were chosen with no NOE restraint
violated by more than 0.5 Å, no dihedral angle restraint violated by more than 5°,
and | 1 D NH,calc – 1 D NH,exp| < 2 Hz.
3.6. Validation of Structure Refinement
1. Although chemical shifts are dependent on molecular alignment, changes in 13C’ chemical shifts (∆δ13C’), which are particular sensitive to this effect, have been
used to evaluate protein structures before and after refinement against residual
dipolar coupling-derived restraints via use of a quality (Q) factor defined as:
Q = rms(∆δmeas – ∆δpred )/rms(∆δmeas ) (6)
where ∆δ is the change in chemical shift observed when shifting from an isotropic
to an aligned medium (28). In the absence of 13C chemical shift data for the
LDLR-AB pair, we have chosen instead to evaluate the improvement in structures
based on T1/T2 ratios, which were not incorporated into the structure refinement.
The T1/T2 ratio depends on the angle that NH bond vector angle with respect
to the the diffusion tensor (see Chapter 22 in this volume). Therefore a comparison
of (T1/T2) calc – (T1/T2) meas , via analysis of χ2 values for the structural
ensembles computed before and after refinement against the residual dipolar coupling-derived
restraints, should directly probe changes in the accuracy of the
structure determination. χ2 is defined as:
χ 2 = i
∑ {[(T 1/T 2) meas – (T 1/T 2) calc ] i / err [(T 1/T 2) meas ] i} 2 (7)
where i is summed over values for residues that do not manifest large amplitude
internal motions or conformational exchange line broadening. For the LDLR-AB
pair, this subset of residues was defined as those localized to β-strands excluding
residues affected by either fast or slow motions ({ 1 H}– 15 N-NOE > 0.7 and T 2 >
90 ms). As expected, the LDLR-AB families of structures were best-fit using a
prolate ellipsoid model with D // = D zz and D ⊥ = D xx = D yy and D //> D ⊥, where D is
defined as the molecular rotational diffusion tensor. Twenty structures were
selected from ensembles calculated before and after residual dipolar coupling
based refinement based on total energies and agreement with experimental constraints.
The average χ 2 for each family dropped from and average value of 120 to
109 upon refinement, an approx 9% improvement.