Thesis Title: Subtitle - NMR Spectroscopy Research Group

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16 Chapter 1. Introduction. Figure 1.11 Illustration of the task performed by the software Possum. The software package requires the Δχ-tensor parameters to perform a structure based automatic assignment of the <strong>NMR</strong> resonances. 1.3.2 The Δχ-tensor determination problem The Δχ-tensor determination problem consists of obtaining the eight parameters characterizing the Δχ-tensor such that the discrepancy between the observed and calculated PCS is minimal. These comprise the determination of the paramagnetic center location, of the Δχ-tensor orientation, and of the axial and rhombic component. The last two parameters characterize the shape of PCS effects that ranges between two extremes as illustrated in Figure 1.12. Figure 1.12 Isosurface shapes calculated by equation (1.1). The positive isolevel is shown in blue, the negative is shown in red. Both isolevels have the same absolute value. (a) When the rhombic component is equal to zero, the isosurface is axially symmetric (dotted line). (b) Isosurface when
1.3 Computational study of paramagnetic proteins. 17 the axial and rhombic components are equal. Three planar symmetries remain for the three planes orthogonal to the three main axes. (c) For an axial value of zero, the isosurface presents two additional planar symmetries due to an ambiguous main axis. While the axial and rhombic value “decide” the isosurface shape, equation (1.1) constrains any isosurfaces to be shaped between the two extremes shown in (a) and (c). Figure 1.13 Sanson-Flamsteed projection for visualization of Δχ- tensor uncertainty. The axes of the Δχ-tensor are projected on a 2D surface. The uncertainty of the axes orientation can be reflected by the size and shape of the colored area used for each axis, as done in Figure 1.14. The Δχ-tensor is similar to the alignment tensor used to compute RDCs. The alignment tensor parameters are easily determined by singular value decomposition, as equation (1.2) is linear with respect to the alignment tensor parameters. The axial and rhombic component of the alignment tensor can also be estimated without the requirement of protein coordinates, by exploiting the isotropic distribution of the NH bond orientation in space (Clore et al., 1998). The equation that governs the PCS is non-linear because no assumption of the isotropic distribution of PCS values can be made. Consequently, the way to determine the Δχ-tensor relies on a minimization of a cost comparing predicted and experimental PCS. A few existing computational software packages could be used to get the Δχ-tensor parameters, such as Fantasian (Banci et al., 1997), or Xplor-NIH (Schwieters et al., 2003, Schwieters et al., 2006). However, they can be cumbersome to use and have poor interactivity with the user. Another important feature that existing approaches fail to provide is the possibility to estimate the quality of the fit and directly visualize it in a Sanson-Flamsteed representation
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Page 3 and 4: iii Schmitz C, Stanton-Cook MJ, Su
Page 5 and 6: v Acknowledgements I would like to
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Page 9 and 10: ix 2.3.3 Manual resonance assignmen
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Chapter 3 Numbat: new user-friendly
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3.4 Introduction 3.4 Introduction.
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3.5 Algorithm. 79 rhombic component
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3.6 Program Features. 81 each fitti
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3.6 Program Features. 85 Carlo prot
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3.7 Study case. 87 The coordinates
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3.7 Study case. 89 illustrates how
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3.9 Acknowledgment. 93 variables, t
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3.10 References. 95 Galassi M, Davi
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Chapter 5 Conclusion and perspectiv
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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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