Thesis Title: Subtitle - NMR Spectroscopy Research Group

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88 Chapter 3. Numbat: new user-friendly method built for automatic Δχ-tensor determination. mz h 26.7 26.7 26.7 26.7 -18.9 -19.0 -18.8 -18.8 -19.8 -19.8 a Δχ-tensor parameters determined relative to chain A in the PDB coordinate set 2IDO b Δχ-tensor parameters determined relative to model 10 in the PDB data set 2AXD c Δχ-tensors determined from PCS induced by Dy 3+ or PCS induced by Er 3+ (individual optimization) d Δχ-tensors determined by using the PCS data of Dy 3+ and Er 3+ simultaneously and optimizing for a single metal ion position (combined optimization) e Δχ-tensors determined by using the PCS data of Dy 3+ and Er 3+ simultaneously, optimizing for a single metal ion position and fixing the Δχax and Δχrh at the values determined from the PCS data of ε186 (fixed optimization) f In units of 10 -32 m 3 g Euler rotations in the ZYZ convention (degrees) h Metal ion coordinate (Å) relative to chain A in the PDB coordinate set 2IDO Since the coordinates of the Dy 3+ and Er 3+ found in the individual fits were very similar (Table 3.1, columns 1 and 2), we subsequently assumed that the Δχ-tensors induced by each lanthanide are centered at the same position relative to ε186. The results obtained by simultaneously fitting the distinct Δχ-tensors while restraining their metal coordinate to a common centre (Table 3.1, columns 3 and 4) show little difference to the Δχ-tensor parameters found when performing the individual optimizations. For comprehensive error analysis, we introduced a random error into the structure coordinates of ε186, where the atomic coordinates were varied according to a Gaussian distribution with a standard deviation ζ of 0.5 Å, resulting in a mean atom displacement of 0.8 Å. The resulting uncertainty in Δχ-tensor parameters was approximately equivalent to the uncertainty introduced by a random variation added to the measured PCS data sampled from a Gaussian distribution with a standard deviation ζ of 0.15 ppm. The Δχ-tensor parameters of ε186 were well defined, as the values of all eight Δχ-tensor variables determined by 1000 randomized pseudo-replicates of the structure were in good agreement with the Δχ-tensors fitted to the original structure (Table 3.2, column 1). To eliminate the possibility that the quality of the Δχ-tensor fit was significantly affected by the number of PCS measured, the error analysis for the Δχ-tensors fitted to ε186 was recalculated with random selection of only 20% of the measured PCS. The results (Table 3.2, column 2) show that the Δχ-tensor parameters of ε186 were still well defined. Figure 1.14.a
3.7 Study case. 89 illustrates how well the Δχ-tensor axis are defined, even when randomly disregarding 50% of the data. Table 3.2 Error analysis for the Dy 3+ Δχ-tensors fitted to PCS of ε186 and θ a ε186 θ Structure variation Subset of PCS Structure variation Subset of PCS Δχax b 42.0 (0.8) 42.4 (1.1) 41.9 (4.3) 40.3 (3.1) Δχrh b 5.3 (0.5) 5.4 (0.8) 15.0 (4.5) 15.3 (2.8) α c 169.5 (0.7) 169.7 (0.9) 29.3 (6.1) 27.6 (3.2) β c 30.2 (0.3) 30.2 (0.5) 114.5 (4.3) 114.4 (3.3) γ c 134.0 (2.6) 134.7 (4.0) 29.2 (10.6) 28.9 (7.9) mx d 29.4 (0.1) 29.4 (0.2) 6.1 (1.3) 6.2 (0.9) my d 31.9 (0.1) 31.9 (0.2) -7.4 (1.0) -7.6 (0.7) mz d 26.7 (0.1) 26.7 (0.1) -19.1 (0.8) -18.9 (0.4) a The average values of the Δχ-tensors and their standard deviations (in brackets) are reported. Average values and standard deviations were calculated from 1000 sets of randomised atom coordinates (where the extent of randomisation followed a Gaussian distribution with a standard deviation ζ of 0.5 Å) or from randomly picked subsets of the PCS data (20% in the case of ε186 and 80% in the case of θ where much fewer PCS were available) b In units of 10 -32 m 3 c Euler rotations in the ZYZ convention (degrees) d Metal ion coordinate (Å) in the protein frame (A chain of the PDB coordinates 2IDO and model 10 in the PDB data set 2AXD, respectively) 3.7.2 Subunit θ The results of the Δχ-tensor determination in the molecular frame of θ are presented in Table 3.1. There was only a small number of spins for which the back-calculated PCS deviated from the experimental PCS by more than 0.15 ppm (4 out of 50 in the case of Dy 3+ , 0 out of 41 for
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Computational study of proteins wit
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iii Schmitz C, Stanton-Cook MJ, Su
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v Acknowledgements I would like to
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vii Keywords paramagnetic nmr, pseu
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ix 2.3.3 Manual resonance assignmen
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xi List of Figures Figure 1.1 NMR e
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xiii
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xv List of Abbreviations α Subunit
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2 Chapter 1. Introduction. The scal
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28 Chapter 2. Possum: paramagnetica
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Page 95 and 96: 3.5 Algorithm. 79 rhombic component
Page 97 and 98: 3.6 Program Features. 81 each fitti
Page 99 and 100: 3.6 Program Features. 83 A new PCS
Page 101 and 102: 3.6 Program Features. 85 Carlo prot
Page 103: 3.7 Study case. 87 The coordinates
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Page 109 and 110: 3.9 Acknowledgment. 93 variables, t
Page 111 and 112: 3.10 References. 95 Galassi M, Davi
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Thesis Title: Subtitle - NMR Spectroscopy Research Group

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