Thesis Title: Subtitle - NMR Spectroscopy Research Group

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82 Chapter 3. Numbat: new user-friendly method built for automatic Δχ-tensor determination. performed with a minimal number of adjustable parameters by keeping the axial and rhombic components of the Δχ-tensor fixed at the values determined for the protein. The Δχ-tensors determined for the protein and the ligand can finally be superimposed to derive a model of the protein-ligand complex (Pintacuda et al., 2007). Numbat also offers the option of restricting the Δχ-tensor variables within user-defined boundaries. This is useful if the magnitude, position and/or orientation of the Δχ-tensor is approximately known from previous studies (Su et al., 2008). Depending on the quality and quantity of PCS measurements available, the Δχ-tensor variables (especially the lanthanide coordinates) may only reach a local minimum during the optimization procedure. Therefore the starting values of all Δχ-tensor variables used to initialize the minimiser can be changed interactively within Numbat. 3.6.5 Residual Anisotropic Chemical Shifts (RACS) Paramagnetic lanthanides bound to the protein weakly align the molecule in the magnetic field resulting in an incomplete averaging of the anisotropic chemical shifts. This can affect the PCS by a shift of up to 0.2 ppm for backbone 15 N and 13 C’ spins at a magnetic field of 18.8 T (John et al., 2005). The RACS correction term Δδ RACS for 1 H N , backbone 15 N and 13 C’ spins can be calculated given the Δχ-tensor and the chemical shielding anisotropic tensor (CSA-tensor) using (John et al., 2005): (3.4) where B0 is the magnetic field, μ0 the induction constant, k the Boltzmann constant, T the temperature, ζii CSA the principal components of the CSA-tensor, cos θij the nine direction cosines between pairs of the principal axis of the Δχ-tensor and the CSA-tensor, and Δχjj the principal components of the Δχ-tensor. Numbat optionally uses the RACS correction term when generating PCS data and fitting Δχ-tensors. The orientations of the principal component axes of the nuclear CSA-tensors and the ζii CSA values for 1 H N , backone 15 N and 13 C’ are taken from (Cornilescu et al., 2000). 3.6.6 Multiple PCS data sets
3.6 Program Features. 83 A new PCS data set can be obtained by replacing one paramagnetic lanthanide with another paramagnetic lanthanide. Multiple PCS data sets obtained in this way share a conserved lanthanide position, but different orientations and magnitudes of the Δχ-tensors must be fitted to each individual PCS data set. Numbat can perform a simultaneous fit of the Δχ-tensors and the shared lanthanide position. This feature is of particular interest when only a limited number of PCS can be measured for each lanthanide ion, as fewer variables in the Δχ-tensor fit will facilitate the determination of accurate Δχ-tensor parameters. For example, a limited set of unambiguously measured PCS can be used to determine initial Δχ-tensor parameters from which the PCS of unassigned paramagnetic cross-peaks can be back-calculated, leading to assignments of additional paramagnetic cross-peaks and improved Δχ-tensor parameters. Similarly, applications to small ligand molecules with a small number of <strong>NMR</strong> signals are aided by limiting the number of adjustable variables to a minimum. 3.6.7 PCS modification Once an initial Δχ-tensor has been fitted, Numbat computes and displays PCS values for all atoms. Doubtful assignments can easily be detected at this stage by inspection of the deviation between experimental and calculated values. Numbat allows interactive modification of PCSi exp and toli as well as the input of additional PCS data. 3.6.8 PCS selection The experimental PCS values to be used for the Δχ-tensor fit can be selected according to three criteria: A list of (i) residue types or (ii) atom types can be provided by the user. This is convenient in the case of selectively isotope-labelled proteins and allows a quick assessment of the amount of information necessary in order to retrieve a robust Δχ-tensor. (iii) Each individual PCS can be selected or deselected interactively via the GUI interface. This is particularly convenient if, after initial optimisation of the Δχ-tensor, some of the back-calculated PCS consistently show large deviations with respect to the experimental values, which may be due to erroneous assignments or discrepancies between the atomic coordinates of the PDB file and the actual structure of the protein, as is often the case for flexible polypeptide segments. Deselecting the corresponding atoms is likely to improve the Δχ-tensor fit in the next iteration. 3.6.9 Conventions
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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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xv List of Abbreviations α Subunit
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2 Chapter 1. Introduction. The scal
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5.3 The use of PCS for protein dock
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Thesis Title: Subtitle - NMR Spectroscopy Research Group

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