Thesis Title: Subtitle - NMR Spectroscopy Research Group

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78 Chapter 3. Numbat: new user-friendly method built for automatic Δχ-tensor determination. module PARArestraint for Xplor-NIH (Banci et al., 2004), GROMACS (Van der Spoel et al., 2005) with an implementation of orientation restraints (Hess et al., 2003) or DYANA (Güntert et al., 1997) with the module PSEUDYANA (Banci et al., 1998) could be used for Δχ-tensor determination from PCS but the protocols would be cumbersome. Considering that simultaneous determination of the Δχ-tensor and metal ion position relative to a known protein structure is a commonly required task, we set out to design a tool to achieve this in an easier and user-friendly way. While the metal coordinates of metalloproteins can be accurately determined by crystallography, the metal position must be fitted when no crystal structure is available, e.g., when the lanthanide is introduced via a lanthanide tag. None of the reported tools addresses this issue. Here we present the newly developed program Numbat (New User-friendly Method Built for Automatic Δχ-Tensor determination), which can simultaneously fit the Δχ-tensor and lanthanide coordinates using experimental PCS values and the coordinates of the protein. Furthermore, the program encompasses a number of useful tools for multiple data sets recorded with different paramagnetic lanthanides, for rigid-body docking using PCS, and for analysis and visualization of the results. Following a description of the algorithm on which the program builds and a presentation of the graphical user interface, we illustrate the use of Numbat for building the model of a complex in a rigid-body docking approach using PCS. 3.5 Algorithm The Δχ-tensor can be determined and refined by the comparison between experimentally determined PCS values and PCS values back-calculated from the atomic coordinates of the molecular structure (Sherry et al., 1977, Lee et al., 1983, Emerson et al., 1990, Veitch et al., 1990, Banci et al., 1992, Capozzi et al., 1993). The pseudocontact shift of a nuclear spin i, PCSi calc , is given by (Bertini et al., 2002): (3.1) where i, i, i are the Cartesian coordinates of the nuclear spin i in the Δχ-tensor frame, ri is the distance between the spin i and the paramagnetic centre, and Δχax and Δχrh are the axial and
3.5 Algorithm. 79 rhombic components of the Δχ-tensor. The orientation of the Δχ-tensor frame with respect to the protein frame can be specified, e.g., by three Euler angles α, β and γ 5 . To quantify the difference between experimental and back-calculated PCS values we define a quadratic cost c: (3.2) where PCSi exp is the experimental PCS for the spin i, and toli is its associated tolerance. The tolerance values can be used to reflect different uncertainties in the measurement of different PCS. When the lanthanide position is known, only five Δχ-tensor parameters have to be optimized. In this case, the least square fitting problem is linear, as can be seen from an alternate formulation of the PCS (Bertini et al., 2002): (3.3) where xi, yi, zi are the Cartesian coordinates of the spin i in an arbitrary frame f and Δχxx, Δχyy, Δχzz, Δχxy, Δχxz, Δχyz are the Δχ-tensor components in this frame. The Singular Value Decomposition (SVD) algorithm, which is commonly used to determine an alignment tensor from a set of experimental RDC (Valafar et al., 2004, Wei et al., 2006), would be a good candidate to minimize the cost c. The least square fitting, or the Simplex algorithm (Nelder et al., 1965) has been applied in previous work (Emerson et al., 1990, Capozzi et al., 1993). However the most general problem one has to solve is non-linear since the metal ion position may be unknown. We consequently chose for the non-linear least square fitting procedure in Numbat the Levenberg- Marquardt algorithm (Marquardt, 1963) as implemented in the GNU Scientific Library (Galassi et al., 2006). 5 The parameters that are fitted by the software Numbat are: i, i, i, Δχax, Δχrh, α, β, and γ.
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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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10 Chapter 1. Introduction. Protein
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26 Chapter 1. Introduction. Su XC,
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Page 109 and 110: 3.9 Acknowledgment. 93 variables, t
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Chapter 5 Conclusion and perspectiv
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5.1 The use of PCS for structure de
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5.1 The use of PCS for structure de
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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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