Thesis Title: Subtitle - NMR Spectroscopy Research Group

90 Chapter 3. Numbat: new user-friendly method built for automatic Δχ-tensor determination.
Er 3+ ). Like for ε186, removal of these PCS from the optimization did not significantly change the
parameters of the fitted Δχ-tensors. While the Δχax and Δχrh values of Er 3+ determined from the PCS
observed for θ and 186 were very similar, the Δχrh value of the Dy 3+ tensor found for θ was almost
three times larger than that found for ε186 6 . We subsequently performed an error analysis for θ as
for the ε186 subunit, introducing either random variations into the atomic positions of θ according
to a Gaussian distribution with a standard deviation ζ of 0.5 Å or using a random selection of only
80% of the measured PCS. In either case, the Δχ-tensor parameters of θ proved to be less well
defined than those of ε186 (Table 3.2) and Figure 1.14.b. As θ samples a relatively small and
remote volume of the Δχ-tensors due to its spatial separation from the metal ion, one would expect
a less accurate determination of the Δχ-tensors from the θ data. The effect could be exacerbated by
inaccuracies of the NMR structure.
In order to compensate for the smaller number of experimentally determined PCS available
for θ (only 1 H N spins) and the poorer quality of the Δχ-tensors fitted, we performed another fit with
Δχax and Δχrh fixed to the values determined for ε186 (Table 3.1, columns 9 and 10). Analysis of
the experimental versus back-calculated PCS, both for the eight- and six-variable fits of the Δχ-
tensor to θ, showed that the PCS deviations were similar in magnitude and trends. Therefore,
constraining Δχax and Δχrh did not significantly deteriorate the quality of the fit, despite considerable
changes of the Δχ-tensor parameters (Table 3.1). The variability of the Δχ-tensor parameters over
all the 12 deposited θ conformers in 2AXD using the fixed optimisation scheme is provided in the
Supporting Information.
3.7.3 Modelling the complex between ε186 and θ
Numbat facilitates the modelling of protein-protein complexes by listing coordinates of the
Δχ-tensor axes together with the protein coordinates in files in PDB format. Superimposition of the
Δχ-tensors fitted to ε186 and θ for each lanthanide ion yields the three-dimensional structure of the
ε186/θ complex by straightforward rigid-body docking. Standard PyMOL or MOLMOL commands
6 The discrepancy of the Rhombic component would not necessarily affect the rigid body docking
of the complex, as only the orientation of the Δχ-tensors and the coordinates of the paramagnetic
center are used.