Thesis Title: Subtitle - NMR Spectroscopy Research Group

Computational study of proteins with paramagnetic NMR: Automatic 

assignments of spectral resonances, determination of protein-protein and 

protein-ligand complexes, and structure determination of proteins 

Christophe Schmitz 

A thesis submitted for the degree of Doctor of Philosophy at 

The University of Queensland in December 2009 

School of Chemistry and Molecular Biosciences

ii 

Declaration by author 

This thesis is composed of my original work, and contains no material previously published 

or written by another person except where due reference has been made in the text. I have clearly 

stated the contribution by others to jointly-authored works that I have included in my thesis. 

I have clearly stated the contribution of others to my thesis as a whole, including statistical 

assistance, survey design, data analysis, significant technical procedures, professional editorial 

advice, and any other original research work used or reported in my thesis. The content of my 

thesis is the result of work I have carried out since the commencement of my research higher 

degree candidature and does not include a substantial part of work that has been submitted to 

qualify for the award of any other degree or diploma in any university or other tertiary institution. I 

have clearly stated which parts of my thesis, if any, have been submitted to qualify for another 

award. 

I acknowledge that an electronic copy of my thesis must be lodged with the University 

Library and, subject to the General Award Rules of The University of Queensland, immediately 

made available for research and study in accordance with the Copyright Act 1968. 

I acknowledge that copyright of all material contained in my thesis resides with the 

copyright holder(s) of that material. 

Statement of Contributions to Jointly Authored Works Contained 

in the Thesis 

John M, Schmitz C, Park AY, Dixon NE, Huber T and Otting G (2007) Sequence-specific and 

stereospecific assignment of methyl groups using paramagnetic lanthanides. J Am Chem 

Soc 129:13749-13757. 

John designed new NMR experiments, recorded and assigned the spectra, and wrote the 

corresponding paragraphs in the paper. Schmitz designed and implemented the software to 

automate the assignment procedure, ran the calculations, and wrote the paragraphs ―The Program 

Possum‖ and the ―Automatic Assignments without EXSY Data‖. Park made the protein samples. 

Dixon coordinated the protein sample preparation and corrected aspects of the paper. Huber was 

responsible for the computational aspects of the project and the writing of corresponding sections 

of the paper, Otting coordinated the overall project and was responsible for the writing of the paper.

iii 

Schmitz C, Stanton-Cook MJ, Su XC, Otting G and Huber T (2008) Numbat: an interactive 

software tool for fitting Δχ-tensors to molecular coordinates using pseudocontact shifts. J 

Biomol NMR 41:179-189 

Schmitz designed and implemented the software to automate the determination of the Δχ- 

tensor and wrote most of the paper except for the ―study case‖ section. Stanton-Cook was 

responsible of the calculation, the protein-protein modelling, the writing of the ―study case‖ and 

improvements of the paper. Su was responsible for improving the design of the software from an 

―end-user‖ perspective. Otting and Huber were responsible for the overall project and the writing of 

the manuscript. 

Schmitz C, Vernon R, Otting G, Baker D and Huber T Protein structure determination from 

pseudocontact shifts using ROSETTA. Proc Natl Acad Sci U S A submitted. 

Schmitz designed and implemented the PCS-score into the software ROSETTA, collected 

experimental data sets, performed computations, and was responsible for writing the manuscript. 

Vernon guided the implementation of the PCS-score, ran calculations, interpreted the results, and 

improved the manuscript. Otting gathered experimental data sets, set up the overall project, and 

corrected versions of the manuscript. Baker was responsible for guiding the overall project, and for 

the overall manuscript. Huber designed the PCS-score, guided the overall project, and improved the 

paper. 

Statement of Contributions by Others to the Thesis as a Whole 

No contributions by others. 

Statement of Parts of the Thesis Submitted to Qualify for the 

Award of Another Degree 

None. 

Published Works by the Author Incorporated into the Thesis 

John M, Schmitz C, Park AY, Dixon NE, Huber T and Otting G (2007) Sequence-specific and 

stereospecific assignment of methyl groups using paramagnetic lanthanides. J Am Chem 

Soc 129:13749-13757. Incorporated as Chapter 2.

iv 


software tool for fitting Δχ-tensors to molecular coordinates using pseudocontact shifts. J 

Biomol NMR 41:179-189. Incorporated as Chapter 3. 

Schmitz C, Vernon R, Otting G, Baker D and Huber T Protein structure determination from 

pseudocontact shifts using ROSETTA. Proc Natl Acad Sci U S A submitted. Incorporated 

as Chapter 4. 

Additional Published Works by the Author Relevant to the Thesis 

but not Forming Part of it 

Su XC, Man B, Beeren S, Liang H, Simonsen S, Schmitz C, Huber T, Messerle BA and Otting G 

(2008) A dipicolinic acid tag for rigid lanthanide tagging of proteins and paramagnetic 

NMR spectroscopy. J Am Chem Soc 130:10486-10487

v 

Acknowledgements 

I would like to thank my advisors Dr Thomas and Prof. Gottfried for their scientific and 

moral support that made this thesis so enjoyable. In particular, I really appreciated their door 

constantly opened for discussions; their communicative scientific enthusiasm; their exemplary - if 

not legendary - efficiency; their honesty and encouragement in whatever I tried to accomplish, and 

of course their constant and reliable good humor. 

Thanks to the people who put me on track to postgraduate studies, in particular Denis 

Barthou for his amazing teaching, Philippe Pucheral and Luc Bouganim for introducing me to 

research, and of course Prof. Guido for somehow bringing me into the field of structural biology. 

Thanks to the past and present members / visitors of the BMMG / MD group for those 3.5 

years of fun, I appreciated their company whether it was for a discussion, ―une boue‖, a tea break, a 

beer or two, or three, a meal, a game of tennis / squash, or a dance, so thanks to Matt, Itamar, 

David, Mitchel, Ying, Zrinka, Daniela, Michael, Kim, Liz, Alpesh, Prof. Alan Mark and all the 

others. 

It has always been a pleasure to visit ANU in Canberra thanks to Michael, Xun-Cheng, 

Hiromasa, Kiyoshi, Karin and Laura. 

I also would like to thank Prof. David Baker and his lab for welcoming me for a couple of 

months for a fructiferous collaboration, and many many thanks to Robert for so much help with 

that project, and for being a great illustration of how friendly Canadian people are. 

My apologizes to my family for being away so far for so long, I know you understood my 

decision. Thanks for all your support. Thank you Chantel for your patience, love, support and 

patience.

vi 

Abstract 

Understanding biological phenomena at atomic resolution is one of the keys to modern drug 

design. In particular, knowledge of 3D structures of proteins and their interactions with other 

macromolecules are necessary for designing chemical compounds that modify biological processes. 

Conventional methods for protein structure determinations comprise X-ray crystallography and 

nuclear magnetic resonance (NMR) spectroscopy. These techniques can also determine the binding 

mode of chemical compounds. Either technique can be slow and costly, making it highly relevant 

to explore alternative strategies. Paramagnetic NMR spectroscopy is emerging as such an 

alternative technique. In order to measure the paramagnetic effects, two NMR spectra are compared 

that have been measured with and without a bound paramagnetic metal ion. In particular, 

pseudocontact shifts (PCS) of nuclear spins are easily measured as the difference (in ppm) of the 

chemical shifts between the two spectra. PCSs provide long range and orientation dependent 

restraints, allowing positioning of the spin with respect to the magnetic susceptibility tensor 

anisotropy (Δχ-tensor) of the metal ion. 

In this thesis, I used the PCS effect to computationally extract information from NMR 

spectra. I developed (i) a tool (called Possum) to automatically assign diamagnetic and 

paramagnetic spectra of the methyl groups of amino acid side chains, given structural information 

of the protein studied and prior knowledge of the Δχ-tensor; (ii) I designed a comprehensive 

software package (called Numbat) to extract Δχ-tensor parameters from assigned PCS values and 

the available 3D structure; and (iii) I incorporated PCS-based restraints into the protein structure 

prediction software CS-ROSETTA and demonstrated that this combination (PCS-ROSETTA) 

presents a significant improvement for de novo structure determination. The three projects serve 

different purposes at different stages of protein NMR studies. They could be combined in the 

following manner: Starting from assigned backbone PCSs, PCS-Rosetta could be used to determine 

the 3D structure of the protein. Possum can then be used to automatically assign the NMR 

resonances of the methyl groups using PCSs. Finally, Numbat can be used to fit improved Δχ- 

tensors to all the PCS data, analyze the quality of the Δχ-tensors and identify possible wrong 

assignments. Iterative repetition of this protocol would give a 3D structural model of the protein 

with a minimum of data. Alternatively, the Δχ-tensor parameters and PCSs could be used as input 

for a traditional software package such as Xplor-NIH to compute a 3D structure of the protein.

vii 

Keywords 

paramagnetic nmr, pseudocontact shift, lanthanide, magnetic susceptibility tensor, protein, 

structure determination, resonance assignment, protein folding 

Australian and New Zealand Standard Research Classifications 

(ANZSRC) 

060112 (40%), 080301 (30%), 030406 (30%)

viii 

Table of Contents 

Declaration by author ......................................................................................................................... ii 

Statement of Contributions to Jointly Authored Works Contained in the Thesis .............................. ii 

Statement of Contributions by Others to the Thesis as a Whole ....................................................... iii 

Statement of Parts of the Thesis Submitted to Qualify for the Award of Another Degree ............... iii 

Published Works by the Author Incorporated into the Thesis ........................................................... iii 

Additional Published Works by the Author Relevant to the Thesis but not Forming Part of it ........ iv 

Acknowledgements .............................................................................................................................. v 

Abstract .............................................................................................................................................. vi 

Keywords .......................................................................................................................................... vii 

Australian and New Zealand Standard Research Classifications (ANZSRC) .................................. vii 

Table of Contents ............................................................................................................................. viii 

List of Figures .................................................................................................................................... xi 

List of Tables ................................................................................................................................... xiv 

List of Abbreviations ......................................................................................................................... xv 

1. Introduction ................................................................................................................................ 1 

1.1 Liquid State Nuclear Magnetic Resonance .......................................................................... 1 

1.2 Paramagnetic NMR .............................................................................................................. 4 

1.2.1 The four paramagnetic effects in NMR ........................................................................ 4 

1.2.2 The pseudocontact shift as a restraint ........................................................................... 7 

1.3 Computational study of paramagnetic proteins .................................................................. 12 

1.3.1 The assignment problem ............................................................................................. 12 

1.3.2 The Δχ-tensor determination problem ........................................................................ 16 

1.3.3 De novo structure determination of proteins .............................................................. 19 

1.4 Scope of the thesis .............................................................................................................. 23 

1.5 References .......................................................................................................................... 24 

2. Possum: paramagnetically orchestrated spectral solver of unassigned methyls ...................... 27 

2.1 Abstract .............................................................................................................................. 28 

2.2 Introduction ........................................................................................................................ 28 

2.3 Experimental section .......................................................................................................... 30 

2.3.1 Sample preparation ..................................................................................................... 30 

2.3.2 NMR spectroscopy ..................................................................................................... 30

ix 

2.3.3 Manual resonance assignments from PCS ................................................................. 32 

2.3.4 The program Possum .................................................................................................. 32 

2.4 Results ................................................................................................................................ 36 

2.4.1 13 C-HSQC spectra of the cz- 186/ /Ln 3+ complexes ................................................. 36 

2.4.2 Methyl CZ-EXSY experiments ................................................................................... 38 

2.4.3 Resonance assignment of Met, Ala and Thr methyl groups ....................................... 39 

2.4.4 Assignments of Val, Leu, and Ile methyl groups ....................................................... 41 

2.4.5 Automatic assignments without EXSY data .............................................................. 44 

2.4.6 PCS and flexibility ..................................................................................................... 46 

2.5 Discussion .......................................................................................................................... 48 

2.6 Acknowledgement .............................................................................................................. 50 

2.7 Supporting Information Available ..................................................................................... 50 

2.8 References .......................................................................................................................... 51 

2.9 Supporting information ...................................................................................................... 56 

3. Numbat: new user-friendly method built for automatic Δχ-tensor determination ................... 75 

3.1 Abstract .............................................................................................................................. 76 

3.2 Keywords ........................................................................................................................... 76 

3.3 Abbreviations ..................................................................................................................... 76 

3.4 Introduction ........................................................................................................................ 77 

3.5 Algorithm ........................................................................................................................... 78 

3.6 Program Features ................................................................................................................ 80 

3.6.1 GUI ............................................................................................................................. 80 

3.6.2 Input files .................................................................................................................... 81 

3.6.3 Methyl group definition .............................................................................................. 81 

3.6.4 Optimization of the tensor parameters ....................................................................... 81 

3.6.5 Residual Anisotropic Chemical Shifts (RACS) ......................................................... 82 

3.6.6 Multiple PCS data sets ................................................................................................ 82 

3.6.7 PCS modification ........................................................................................................ 83 

3.6.8 PCS selection .............................................................................................................. 83 

3.6.9 Conventions ................................................................................................................ 83 

3.6.10 Error analysis ............................................................................................................ 84 

3.6.11 Visualization ............................................................................................................. 85 

3.6.12 Output ....................................................................................................................... 86 

3.7 Study case ........................................................................................................................... 86

x 

3.7.1 Subunit ε186 ............................................................................................................... 87 

3.7.2 Subunit θ ..................................................................................................................... 89 

3.7.3 Modelling the complex between ε186 and θ .............................................................. 90 

3.8 Conclusion .......................................................................................................................... 92 

3.9 Acknowledgment ............................................................................................................... 93 

3.10 References ........................................................................................................................ 93 

3.11 Supporting information .................................................................................................... 97 

4. Protein Structure Determination from Pseudocontact Shifts using ROSETTA ..................... 101 

4.1 Abstract ............................................................................................................................ 102 

4.2 Introduction ...................................................................................................................... 102 

4.3 Results .............................................................................................................................. 104 

4.3.1 Test set ...................................................................................................................... 104 

4.3.2 Capacity of the PCS Score to Identify Native-like Structures ................................. 105 

4.3.3 Comparison of PCS-ROSETTA with CS-ROSETTA ............................................. 106 

4.3.4 Successes and Limits of PCS-ROSETTA Calculations ........................................... 109 

4.4 Discussion ........................................................................................................................ 110 

4.5 Materials and Methods ..................................................................................................... 112 

4.5.1 PCS-ROSETTA Score. ............................................................................................. 112 

4.5.2 PCS-ROSETTA Algorithm ...................................................................................... 113 

4.5.3 Input for PCS-ROSETTA ......................................................................................... 113 

4.5.4 PCS-ROSETTA Protocol for Protein Structure Determination ............................... 114 

4.5.5 Computation of Structures to Evaluate the Effects of PCS Scoring ........................ 115 

4.6 Acknowledgments ............................................................................................................ 115 

4.7 References ........................................................................................................................ 115 

4.8 Supporting information .................................................................................................... 118 

5. Conclusion and perspectives .................................................................................................. 129 

5.1 The use of PCS for structure determination ..................................................................... 130 

5.1.1 Folding of proteins using only pseudocontact shifts ................................................ 130 

5.1.2 Uses of multiple lanthanide binding sites ................................................................. 132 

5.1.3 Development of a new PCS-ROSETTA protocol .................................................... 133 

5.2 The use of PCS for chemical shift assignment ................................................................. 134 

5.3 The use of PCS for protein docking ................................................................................. 135 

5.4 References ........................................................................................................................ 136

xi 

List of Figures 

Figure 1.1 NMR effects used for structure determination .................................................................. 3 

Figure 1.2 Representation of the distance and angular dependence of the four paramagnetic effects 

for the spin S, or system of spin S1-S2 (green) ...................................................................... 5 

Figure 1.3 Experimental measurement of the four paramagnetic effects with two 1D undecoupled 

spectra .................................................................................................................................... 5 

Figure 1.4 The PCS is less sensitive than RDC to small discrepancies between X-ray and solution 

structure ................................................................................................................................. 7 

Figure 1.4 The Δχ-tensor determination problem ............................................................................... 8 

Figure 1.5 Illustration of the three approaches of resonance assignment ........................................... 8 

Figure 1.6 Illustration of PCS restraints ........................................................................................... 11 

Figure 1.7 Protein complexes determined using PCSs ..................................................................... 11 

Figure 1.8 Flow-chart of the Echidna algorithm ............................................................................... 14 

Figure 1.9 Examples of the MAP problem ....................................................................................... 15 

Figure 1.10 Illustration of the task performed by the software Possum ........................................... 16 

Figure 1.11 Isosurface shapes calculated by equation (1.1) ............................................................. 16 

Figure 1.12 Sanson-Flamsteed projection for visualization of Δχ-tensor uncertainty ...................... 17 

Figure 1.13 Sanson-Flamsteed representations of Δχ-tensor axes orientation ................................. 19 

Figure 1.14 Illustration of the task performed by the software Numbat ........................................... 19 

Figure 1.15 Effect of the mobility of the tag on the PCS ................................................................. 22 

Figure 2.1 Methyl CZ-EXSY experiments ........................................................................................ 31 

Figure 2.2 Formulation of the assignment problem depending on the information available .......... 35 

Figure 2.3 Methyl region of constant-time 13 C-HSQC spectra of the cz- 186/ complex (containing 

13 C/ 15 N labeled cz- 186) in the presence of La 3+ (blue) and a 1:1 mixture of (a) La 3+ /Dy 3+ 

and (b) La 3+ /Yb 3+ (red) ........................................................................................................ 37 

Figure 2.4 Assignment of Met CH3 from PCS ................................................................................ 39 

Figure 2.5 PCS measurements in isopropyl groups of Val and Leu and use of PCS for 

stereospecific resonance assignments .................................................................................. 42 

Figure 2.6 Residues showing deviations between predicted and experimental PCS ........................ 47 

Figure S2.1 Pulse scheme of the 2D (H)C(C)H-TOCSY experiment used in this study ................. 56 

Figure S2.2 Assigned constant-time (28 ms) 13 C-HSQC spectrum of the cz- 186/ /La 3+ complex 

( 13 C/ 15 N labeled cz- 186) at pH 7.2 and 25 o C .................................................................... 57

xii 

Figure S2.3 Assigned constant-time 13 C-HSQC spectrum of the cz- 186/ /La 3+ complex, where cz- 

186 was biosynthetically fractionally 13 C-labeled using 20% uniformly 13 C-labeled 

glucose ................................................................................................................................. 58 

Figure S2.4 Assigned constant-time 13 C-HSQC spectrum of the cz- 186/ /La 3+ complex 

containing 13 C/ 15 N-Leu labeled cz- 186 (blue) superimposed onto a 2D (H)C(C)H- 

TOCSY spectrum of the same sample (red) ........................................................................ 59 

Figure S2.5 Comparisons of calculated and experimental PCS in the cz- 186/ /Dy 3+ complex for 

methyl groups of (a) Met, (b) Ala, (c) Thr, (d) Val, (e) Leu, and (f) Ile ............................. 60 

Figure S2.6 Comparisons of calculated and experimental 13 C and 1 H PCS as in Figure S2.5 but for 

the cz- 186/ /Yb 3+ complex. ............................................................................................... 62 

Figure 3.1 Screenshots of Numbat main windows ........................................................................... 80 

Figure 3.2 Euler angle definitions used by Numbat ......................................................................... 84 

Figure 3.3 Visualisation of the Δχ-tensor in MOLMOL and PyMOL, and display of its 

orientational uncertainty in a Sanson-Flamsteed projection plot ........................................ 85 

Figure 3.4 The four degenerate solutions arising from the symmetry of the Δχ-tensor around the x, 

y and z axes ......................................................................................................................... 92 

Figure 3.5 The complex between ε186 and θ determined by superimposition of Δχ-tensors .......... 92 

Figure 4.1 Fold identification by pseudocontact shifts ................................................................... 106 

Figure 4.2 Improved conformational sampling by PCS-ROSETTA .............................................. 108 

Figure 4.3 Energy landscapes generated by PCS-ROSETTA ........................................................ 108 

Figure 4.4 Superimpositions of ribbon representations of the backbones of the lowest energy 

structures calculated with PCS-ROSETTA (blue) onto the corresponding target structures 

(red) ................................................................................................................................... 110 

Figure S4.1 Fold identification by pseudocontact shift score and ROSETTA energy ................... 119 

Figure S4.2 Improved fragment assembly by PCS-ROSETTA ..................................................... 120 

Figure S4.3 Energy landscape generated by CS-ROSETTA and PCS-ROSETTA, with full atom 

ROSETTA energies and C α rmsd values being calculated using only the core residues as 

defined in Table S4.1 ......................................................................................................... 121 

Figure S4.4 Identification of successful calculations with PCS-ROSETTA .................................. 122 

Figure S4.5 Flow diagram of PCS-ROSETTA ............................................................................... 123 

Figure S4.6 Expected C α rmsd of the lowest energy structure calculated with PCS-ROSETTA .. 124 

Figure 5.1 Capacity of the PCS score, as the only energy term, to fold the protein ....................... 131 

Figure 5.2 The intersection of isosurfaces defines the position and orientation of peptide fragments 

in the protein structure ....................................................................................................... 131

xiii

xiv 

List of Tables 

Table 2.1 Automatic assignment of methyl groups by the program Possum a ................................. 45 

Table S2.1 13 C and 1 H chemical shifts (ppm) of methyl groups of cz- 186 in the cz- 186/ /Ln 3+ 

complexes used in this study a ............................................................................................. 64 

Table S2.2 Number of correctly assigned methyl groups of Met, Thr, and Ala residues of cz- 186 

using the program Possum a ................................................................................................ 69 

Table S2.3 Number of correctly assigned methyl groups of Val, Leu, and Ile residues of cz- 186 

using the program Possum with methyl connectivity information in the Yb 3+ complex a .. 71 

Table S2.4 Number of correctly assigned methyl groups of valine, leucine, and isoleucine residues 

of cz- 186 using the program Possum without methyl connectivity information in the Yb 3+ 

complex a ............................................................................................................................. 73 

Table 3.1 Δχ-tensors determined by Numbat in the frames of the ε186 and θ molecule .................. 87 

Table 3.2 Error analysis for the Dy 3+ Δχ-tensors fitted to PCS of ε186 and θ a ............................... 89 

Table S3.1 Experimentally determined 1 H N PCS for θ in complex with ε186 at pH 7.0 and 25°C a 97 

Table S3.2 Comparison of θ Δχ-tensor parameters when using only conformer 10 a or all 

conformers b of the NMR structure of . ............................................................................. 99 

Table 4.1 Protein structures used to evaluate the performance of PCS-ROSETTA ....................... 104 

Table S4.1 PCS data information and grid search parameters used. .............................................. 125 

Table S4.2 Protein structures used to evaluate the performance of PCS-ROSETTA. .................... 126

xv 

List of Abbreviations 

α Subunit α of the E. coli polymerase III 

ε186 N-terminal 185 residues of the E. coli polymerase III subunit ε 

θ Subunit θ of the E. coli polymerase III 

CCR Cross Correlated Relaxation 

CSA Chemical Shielding Anisotropy 

GUI Graphical User Interface 

HOT The bacteriophage P1-encoded homolog of θ 

MAP Multi-dimensional Assignment Problem 

NMR Nuclear Magnetic Resonances 

NOE Nuclear Overhauser Effect 

PCS Pseudocontact Shift 

ppm parts per million 

PRE Paramagnetic Relaxation Enhancement 

RACS Residual Anisotropic Chemical Shift 

RDC Residual Dipolar Coupling 

RMSD Root Mean Square Deviation 

UTR Unique Δχ-Tensor Representation

Chapter 1 

Introduction 

1. Introduction 

1.1 Liquid State Nuclear Magnetic Resonance 

In the last few decades Nuclear Magnetic Resonance (NMR) has been used routinely to 

investigate chemical compounds, proteins and complexes. The method relies on intrinsic spin 

properties of nuclei. Spins are first exposed to a strong and constant magnetic field delivered by the 

spectrometer. Then, they are excited by a radiofrequency pulse sequence. The precession of the 

spins is recorded during the free induction decay of the NMR experiment and converted into a 

frequency spectrum after Fourier transformation. Several parameters can be read from the spectra 

which provide information about the structure of the molecule. 

The chemical shift describes the dependence of nuclear magnetic energy levels on the 

electronic environment in a molecule. The chemical shift depends on the nature of the nucleus. It 

also strongly depends on its local neighborhood (up to 5 Å) due to the influence of the electron 

configuration. Hence, in a protein, almost all nuclei have different chemical shifts. This allows to 

distinguish them in the NMR spectrum by their specific resonance frequency. 

The dipole-dipole coupling is the direct magnetic interaction between two close spins. The 

effect is intra- and intermolecular, since it acts through space. The interaction energy is minimal 

when the two spins are aligned. This spin interaction is responsible for the Nuclear Overhauser 

Effect (NOE).

2 Chapter 1. Introduction. 

The scalar J-coupling results from an indirect magnetic interaction of two nuclear spins 

via their surrounding electrons. The effect is exclusively intramolecular because it is propagated 

through the bonds between two nuclei. Typically, it can be measured for nuclei separated by up to 

three bonds. In this case, it is referred as 3 J coupling. The 3 J-coupling constant yields angle 

information, as shown in Figure 1.1.b. 

NMR experiments measure the effects described above. One can classify NMR experiments 

in two groups: Those that yield structural information, and those that yield information to facilitate 

resonance assignment. The structural information comes mainly from direct dipole-dipole 

couplings providing short-range distance restraints between two spins, and from 3 J-couplings which 

offer dihedral angle restraints between the three bonds concerned. Some examples of NMR 

experiments that offer structural information are: 

1D proton experiment: It provides the chemical shifts of the protons. Each 1 H has a 

different chemical shift, and each corresponding signal may be split into multiplets due to scalar 

couplings. The spectrum gets more complex as the number of spins increases. To reduce spectral 

overlap, two- or multi-dimensional NMR spectra can be recorded. 

1D carbon experiment is equivalent to the 1D proton experiment, but measured on carbon. 

Only 1% of natural carbon is 13 C and often the protein has to be 13 C labeled in order to observe 

carbon chemical shifts because the natural isotope of carbon ( 12 C) has no nuclear spin. 

NOESY: This experiment correlates spins that are separated in space by a distance of up to 

6 Å. The NOE observed in the NOESY experiment is based on the direct dipole-dipole coupling 

and provides valuable inter-spin distance information for the structure determination of proteins. 

NOE restraints are measured from the peak intensity in the NOESY experiment and provide 

distance information (Figure 1.1.a). As the effect is through-space and independent of chemical 

bonds, it is also useful for investigations of protein-ligand and protein-protein interactions. 

A major task and challenge of structure determination is to assign resonances to their 

corresponding atoms in order to apply experimental restraints to the correct set of atoms. 

Additional correlation NMR experiments are routinely recorded to assist in the chemical shift 

assignment task. These include: 

2D 15 N-HSQC experiments correlate protons with nitrogens of a 15 N labeled protein. These 

correlations simplify the analysis of a 1D spectrum since the additional dimension allows the

1.1 Liquid State Nuclear Magnetic Resonance. 3 

separation of the resonances into cross-peaks observed in a 2D plane. The recording time of the 

experiment is however longer. 

3D 13 C- 15 N-correlation experiments are 3-dimensional heteronuclear experiments that 

correlate C, N and H atoms. The resulting spectrum is in particular beneficial for large proteins, 

because resonance overlap is reduced in 3D. The disadvantage of these experiments is, however, 

that they are less sensitive than the 15 N-HSQC experiment and usually require that the protein is 13 C 

and 15 N double labeled. 

COSY experiments correlate 1 H spins via scalar couplings. They are used to identify groups 

of spins connected by less than four bonds (spin systems). 

TOCSY experiments correlate 1 H resonances that belong to the same spin-system, where 

pairs of spins are separated by no more than three bonds. TOCSY spectra include the COSY 

information, and are used to identify connected spin systems. TOCSY spectra are useful for 

sequential resonance assignment. 

NOESY experiments can also be used in the assignment procedure. COSY and TOCSY 

experiment should provide the amino acid type information of the resonances, whereas the NOESY 

experiment allows the sequential piecing together of the assignment by exploiting the distance 

dependency of the NOE effect. 

Figure 1.1 NMR effects used for structure determination. (a) The NOE effect 

provides distance information (up to 0.6 nm) between two protons. The intensity of 

the NOE signal is proportional to 1/d 6 , where d is the interproton distance. (b) The 

3 J-coupling gives dihedral angle restraints. The relationship between the angle Φ 

and the 3 J-coupling is given by the Karplus equation (Karplus, 1959) and the 

allowed values for Φ is illustrated by the plot 3 J = f(Φ). Figures adapted from web 

resources.


In contrast to NOE or 3 J coupling effects that are short-range (measureable for distance 

below 6 Å) and local (each measurement concerns an independent group of atoms), paramagnetic 

NMR introduces new effects that are long-range (measured up to 40 Å), and global (i.e. their effect 

is described for all spins in a common frame centered on the paramagnetic lanthanide). 

1.2 Paramagnetic NMR 

1.2.1 The four paramagnetic effects in NMR 

When a paramagnetic centre with unpaired electrons, such as a lanthanide ion, is present in 

a protein, the observed NMR spectrum changes due to induced paramagnetic effects. By 

comparison of the diamagnetic and paramagnetic spectra, one can observe the following four 

paramagnetic effects: 

The pseudocontact shift (PCS): It is given by equation (1.1), where the spin of interest is 

described by its polar coordinate in an internal frame (the Δχ-tensor frame) centered on the 

paramagnetic center (Figure 1.2.a). 

(1.1) 

Δχax = χz – (χz + χy)/2 and Δχrh = (χx - χy) are respectively the axial and rhombic component 

that describe the anisotropic effect; r, θ and θ are the polar coordinate of the spin in the Δχ-tensor 

frame (Figure 1.2.a). The PCS is a long range effect (up to 40 Å) which decays with 1/r 3 , and is 

measured as the difference between the paramagnetic and diamagnetic chemical shift (Figure 1.3). 

The residual dipolar coupling (RDC): With an attached paramagnetic lanthanide, a 

protein weakly aligns with respect to the magnetic field. RDCs are manifested as increases or 

decreases of the magnitudes of multiplet splittings that can be observed in undecoupled NMR 

spectra (Figure 1.3). The RDC can also be back-calculated (equation (1.2)) provided that the 

orientation of the two spins with respect to the alignment tensor is known (Figure 1.2.b). 

with: 

(1.2)

1.2 Paramagnetic NMR. 5 

(1.3) 

B0 is the magnetic field, γH and γN are proton and nitrogen magnetogyric ratios, ћ Planck’s 

constant divided by 2π, S the order parameter of the molecular alignment, rNH the N-H distance, kB 

the Boltzmann constant, and T the absolute temperature. 

Figure 1.2 Representation of the distance and angular dependence of the four 

paramagnetic effects for the spin S, or system of spin S1-S2 (green). (a) PCSs and (b) 

RDCs are described in the χ-tensor frame centered on the lanthanide l (red). (c) 

PREs only yield distance dependence while (d) CCRs also yield angle dependence. 

Adapted from (Pintacuda et al., 2004). 

Figure 1.3 Experimental measurement of the four paramagnetic effects with two 1D undecoupled 

spectra. The figure shows the diamagnetic and paramagnetic antiphase doublets. PCS is measured


as the chemical shift difference. RDC is measured as the difference in line splitting. PRE and CCR 

can be determined from the differential line broadening. 

The paramagnetic relaxation enhancement (PRE): The PRE yields distance information 

between the paramagnetic lanthanide and the spin of interest (Figure 1.2.c). It depends on the 

distance r between the paramagnetic center and the nuclear spin with 1/r 6 (equation (1.4)) and 

accounts for the difference of line broadening between the paramagnetic and diamagnetic chemical 

shift (Figure 1.3). 

with: 

(1.4) 

(1.5) 

where ηr is the rotational correlation time, ωH the Larmor frequency of the proton, μ0 the 

vacuum permeability, gJ the g-factor, μB the Bohr magneton, and J the total spin moment. 

The cross correlated relaxation (CCR): This effect is also measured by the observed line 

broadening; more precisely by comparing the width between the two components of the antiphase 

doublet (Figure 1.3). This effect combines distance and angle dependence (equation (1.6) and 

Figure 1.2.d). 

with: 

(1.6) 

(1.7) 

All four paramagnetic effects can be used to study protein structure. Residual dipolar 

coupling has been widely used to help determining protein structures (Rohl et al., 2002), but when 

carefully comparing RDCs measured by NMR with RDCs predicted from a crystal structure, it was 

observed that small discrepancies between the N-H bond orientation in crystal and liquid state can


lead to large deviations between measurement and prediction. PCSs are less sensitive to the 

difference between the crystal model and the solution structure. The focus in my PhD has been on 

using PCS to study proteins and their interactions. 

Figure 1.4 The PCS is less sensitive than RDC to small discrepancies 

between X-ray and solution structure. A large change in the orientation 

of the N-H vector will considerably affect the calculation of the RDC 

(equation (1.2) and Figure 1.2.b). On the other hand, the PCS will be 

less affected as the relative position of the hydrogen with respect to the 

tensor frame is almost unchanged when PCS are measurable (d > 10 Å). 

1.2.2 The pseudocontact shift as a restraint 

PCSs can be calculated using equation (1.1) if the magnitude (two parameters: Δχax and 

Δχrh, Figure 1.5.a), location (three Cartesian coordinates x, y and z, Figure 1.5.b) and orientation 

(three Euler angles α, β and γ, Figure 1.5.c) of the Δχ-tensor are known, and if a structure is 

available. The paramagnetic chemical shift of a spin located close to the paramagnetic center is 

broadened beyond detection due to PRE, and consequently, its PCS cannot be observed. The cutoff 

radius is typically about 10 Å. 

The NMR resonances have first to be assigned in order to measure PCSs. Three kinds of 

assignment have to be distinguished (Figure 1.6): 

(i) The assignment of the diamagnetic NMR spectrum: it is routinely performed with 

conventional sequential assignment methods using one or a combination of COSY, 

TOCSY, NOESY NMR and triple resonance experiments.


Figure 1.5 The Δχ-tensor determination problem. The Δχ-tensor can be conveniently represented by 

isosurfaces. For a given ppm value p, all spins that have a PCS value equal to p would be located 

on a given isosurface (red for negative PCS, blue for positive PCS). (a) The Δχax and Δχrh 

parameters that have to be determined are responsible for the shape and size of the isosurfaces. (b) 

The location of the paramagnetic center is described by three Cartesian coordinates. (c) The three 

Euler angles α, β and γ relate the orientation of the Δχ-tensor to the protein frame. 

Figure 1.6 Illustration of the three approaches of resonance assignment. (a) The peaks of the 

diamagnetic spectrum (blue) are assigned to their corresponding amino acids. (b) The 

paramagnetic cross peaks (red) are assigned to their corresponding residues. (c) When the pairing


between diamagnetic and paramagnetic cross peak is already determined by a transfer experiment, 

the pairs of cross peaks can be assigned to their corresponding residues. 

(ii) The assignment of the paramagnetic NMR spectrum: sequential approaches are not 

suitable because the lanthanide induces PRE effects resulting in large line 

broadening for residues close to the paramagnetic center. Proposed experimental 

approaches use temperature dependence (Nguyen et al., 1999), magnetic field 

dependence (Bertini et al., 1998) or fast / slow exchange of the lanthanide (John et 

al., 2007) to transfer the chemical shift from the diamagnetic to the paramagnetic 

state. 

(iii) The assignment of the pseudocontact shift: One can pair the chemical shifts of 

diamagnetic and paramagnetic resonances when a transfer experiment can be 

performed, but the assignment to the individual atoms is still unknown. There is no 

direct method to assign experimental PCSs to the structure; the only way is to 

compare experimental and predicted PCSs to find the best match. 

Comparison between a calculated and measured PCS provides a restraint (Figure 1.7) that 

has been used for different purposes in the literature: 

Structure refinement: Allegrozzi et al. (Allegrozzi et al., 2000) showed how using PCS as 

restraints in structure refinement improved the quality of structures of calbindin. They compared 

the original NMR structures obtained from 1539 NOEs with structures refined using additional 

PCS restraints from three different lanthanides. The magnitude of the paramagnetic dipole moment 

differs between different paramagnetic metal ions. Hence, the cutoff radius and the distance for 

which PCSs can still be observed is lanthanide-dependent. The three lanthanides chosen in this 

study (Ce 3+ , Yb 3+ and Dy 3+ ) cover different regions of the 3D space in shells of 5-15 Å for Ce 3+ , 9- 

25 Å for Yb 3+ , and 13-40 Å for Dy 3+ . Each lanthanide used focuses on a different region of the 

protein, and provides additional independent information to the NOEs. The resulting ensemble of 

structures generated with each PCS data set separately shows better definition of the backbone in 

the area covered by the lanthanide used. In particular, the residues 56-59 have an RMSD above 1.5 

Å in the family of NMR structures. Inclusion of PCS restraints decreases the RMSD value to 0.75 

Å. What this study failed to show is the improvement in structure quality when all data (from all 

different lanthanides) are used simultaneously in the refinement procedure.


Protein-ligand interaction: John et al. (John et al., 2006) showed how PCS restraints can 

be used to determine the structure of protein-ligand complexes. The approach is of major interest 

for drug screening. In a first step, the Δχ-tensor is determined for the target protein. This is the most 

complicated task because the protein can be large, making the assignment of chemical shifts 

difficult. However, in the context of drug screening this step needs to be performed only once. Each 

ligand that is being screened is isotopically labeled, and a paramagnetic spectrum of the ligand in 

complex with the protein is recorded. The assignment of a ligand spectrum and the corresponding 

Δχ-tensor are swiftly and easily obtained. The two Δχ-tensors from ligand and protein being the 

same by definition, a simple superimposition of them leads to the rigid body structure of the 

complex. A molecular dynamics package is further used to locally refine the conformation of the 

protein on the contact surface. John and coworkers demonstrated the approach with the thymidine 

nucleotide as the ligand binding to the ε subunit of DNA polymerase III. The determined thymidine 

structure was found to have a very similar binding mode compared to the thymidine 

monophosphate present in the reference crystal structure. 

Protein-protein interaction: Pintacuda et al. (Pintacuda et al., 2006) described a protocol 

to solve the structure of a protein-protein complex using only PCSs and illustrated the protocol on 

the example of the N-terminal domain of the subunit ε and subunit θ of the E. coli DNA 

polymerase III. Again the method relies on the determination of the Δχ-tensors, first relative to one 

molecule (ε, Figure 1.8.a) and then relative to the second molecule (θ, Figure 1.8.b), followed by 

the superimposition of the Δχ-tensor frames (Figure 1.8.c). Such an approach is particularly 

relevant considering the difficulty to co-crystallize proteins in complexes, compared to the 

crystallization of the components separately. An alternative has been to use RDCs (McCoy et al., 

2002), but the relative orientation and location of the two rigid bodies obtained with PCSs is more 

accurate compared to what would result from a complex build from RDC data, since PCSs yield 

simultaneously orientation and distance information, while RDC data lack distance information and 

are sensitive to small fluctuations of NH bond orientation. The resulting rigid-body docked 

complex could exhibit sterical clashes that would need to be resolved with a molecular refinement 

package. The final result is valuable as input for docking refinement software considering that the 

most difficult part of docking two molecules in a complex is to obtain with confidence the 

approximate binding sites.


Figure 1.7 Illustration of PCS restraints. If the Δχ-tensor parameters are fully determined, one can 

accurately predict PCS values. The assignment of both diamagnetic and paramagnetic spectra 

provides experimental PCSs. Direct comparison of both offers a PCS-based restraint. 

Figure 1.8 Protein complexes determined using PCSs. Paramagnetic NMR 

experiments are performed on the complex, (a) firstly with only the first protein 

labeled, (b) secondly with only the second protein labeled. The two Δχ-tensors are 

fitted separately, according to the experimental PCSs. The two Δχ-tensors are 

theoretically the same, their superimposition provides the structure of the complex 

(c). Adapted from (Pintacuda et al., 2006).


1.3 Computational study of paramagnetic proteins 

1.3.1 The assignment problem 

Assigning the resonances of NMR spectra is a necessary step towards applying NMR 

restraints for protein computation. Although several software packages are capable of predicting 

chemical shifts, they require high-resolution 3D structures and lack accuracy especially for the 

unstructured parts of a protein (Shen et al., 2007). Their algorithms are not based on pure 

calculation from the 3D structure, but rather use statistical information extracted from the pdb data 

bank and from deposited chemical shifts. 

Pseudocontact shifts can be accurately predicted using equation (1.1). Consequently, it is 

possible to compare measured and calculated PCSs. The root mean square deviation between the 

calculated and the measured PCSs provides a score to minimize in order to yield the best possible 

assignment. This strategy has been applied to simultaneously assign measured PCSs and optimize 

the Δχ-tensor by a software package named ―Platypus‖ (Pintacuda et al., 2004). In this work, the 

protein was selectively labeled by residue type in order to simplify spectra. This led to the 

measurement of unassigned PCSs by unambiguous identification of the connectivity between a 

diamagnetic cross peak and its paramagnetic partner shifted along the diagonal in a 2D 15 N-HSQC 

spectrum. The diagonal shift is explained by the fact that in first approximation, hydrogen and 

nitrogen of an NH group have similar PCS values. This is due to the short distance between N and 

H atoms (approximately 1 Å) compared to the large distance (at least 10 Å) separating the NH bond 

from the lanthanide inducing the observed PCS. As a result, the polar coordinates within the Δχ- 

tensor frame are similar for the N and H spins and hence, both spins experience similar 

pseudocontact shifts. The second step of the protocol consists of combining a grid search over the 

Δχ-tensor parameters with an optimal assignment algorithm called the Hungarian method (Kuhn, 

1955): The grid search covers a large ensemble of possible combinations for the Δχ-tensor 

parameters. At each node of the grid search, it becomes possible to use the Hungarian method to 

obtain the optimal assignment in a polynomial time. A score can be calculated over each node to 

reflect the quality of the assignment, and compared to other nodes to extract the best assignment 

along with the best set of Δχ-tensor parameters. 

The ―diagonal rule‖ used in (Pintacuda et al., 2004) to manually measure PCSs has also 

been exploited in (Schmitz et al., 2006) to automatically assign paramagnetic chemical shifts of a 

full 15 N-HSQC spectrum, given a known 3D structure and the list of assigned diamagnetic

1.3 Computational study of paramagnetic proteins. 13 

resonances. The software Echidna was developed to overcome the difficulties of sequential 

assignment of cross peaks in a paramagnetic spectrum. It works as follow: 

Firstly, a small number n1 of paramagnetic peaks are paired with diamagnetic peaks by 

automatically screening unambiguous possibilities along the diagonal of a 2D 15 N-HSQC 

spectrum. 

Secondly, a Δχ-tensor is calculated to minimize the root mean square deviations between the n1 

experimental and calculated PCSs. 

Thirdly, the Δχ-tensor is used to predict for each diamagnetic cross peak the area of the 

spectrum where the paramagnetic partner is expected. This area is centered on the back- 

calculated PCS value, and defines a much smaller zone than the diagonal strip used in the first 

step. More paramagnetic peaks are unambiguously assigned. 

The two last steps are iterated until convergence. A final assignment is performed in order to 

yield the overall best assignment of all cross peaks after convergence of the method. This 

assignment uses the Hungarian method which finds in a polynomial time the optimal 

assignment among the n! possibilities, with n being the number of peaks to assign. A complete 

flow chart of the method is given in Figure 1.9.


Figure 1.9 Flow-chart of the Echidna algorithm. 

Both these two automatic NMR assignment techniques require partial initial assignments. In 

the case of Echidna, the whole diamagnetic spectrum needs to be assigned, while Platypus required 

the connectivity between the paramagnetic and the diamagnetic cross peak. In both cases, those 

prerequisites reduced the computational problem to a 2D Multi-dimensional Assignment Problem 

(MAP, Figure 1.10.a). A 2D-MAP is easily solved with the Hungarian method. More challenging 

and attractive would be to shortcut any initial manual assignment and start directly from the 

chemical shift lists of the diamagnetic and paramagnetic states. Such a method could be applied to 

automate the side chain assignment of a protein, once the preliminary and easier task of assigning 

the backbone chemical shifts and determining the Δχ-tensor has been done, for example with


Echidna. Computationally, the problem becomes a 3D-MAP (Figure 1.10.b) with the number of 

possibilities increasing by (n!) 2 . This problem can no longer be solved in a polynomial time since a 

MAP problem of dimension larger or equal to three is proven to be NP-hard 1 (Karp, 1972). Instead, 

a heuristic method has to be used to find a good assignment, but without any guarantee of reaching 

the optimal assignment. An approach that tries to cope with the computational challenges (by 

means of additional experimental information) led to the development of a software dubbed 

Possum (Figure 1.11), which is described in Chapter 2. 

Figure 1.10 Examples of the MAP problem. (a) When calculated and predicted PCSs have to be 

matched, the cost function c(i, j) can be defined as the square deviation of the two values. The aim 

is to minimize the sum Q. The binary variables xi,j are defined to ensure that each element i and j is 

chosen exactly once. (b) The experimental PCSs are not directly available, but the paramagnetic 

and chemical shifts are measured. Their differences give possible experimental PCSs. 

1 The time required to solve a NP-Hard problem drastically increases with the size of the problem 

which is, in this context, the number n of residue to assign. Some problems with low n value (< 12) 

could be easily solved in a few minutes. The same problem, with just one extra peak to assign, 

remained unsolved after days of calculation. This illustrates that, independently of the algorithm 

used, NP-Hard problem becomes practically and suddenly insolvable for a given size n.which is, in 

this context, the number n of residue to assign. Some problems with low n value (< 12) could be 

easily solved in a few minutes. The same problem, with just one extra peak to assign, remained 

unsolved after days of calculation. This illustrates that, independently of the algorithm used, NP- 

Hard problem becomes practically and suddenly insolvable for a given size n.


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 NMR 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


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


(Bugayevskiy et al., 1995) as shown in Figure 1.13. A Sanson-Flamsteed plot is a projection of a 

sphere on a plane, and is commonly used in geography to project the globe on a map. The axes of 

the Δχ-tensor penetrate the surface of a unitary sphere, and the penetration points can be identified 

on the projection. This representation is convenient to highlight how reliable the fit of a Δχ-tensor 

is in the context of the data and structure used for the calculation. For example, the Δχ-tensor found 

for the ε subunit of DNA polymerase III is particularly well defined (Figure 1.14.a), while the 

Sanson-Flamsteed plot corresponding to the fit for the θ subunit (in complex with ε) reveals more 

uncertainties (Figure 1.14.b). Those differences are mainly due to the large distance (>15 Å) that 

separates θ from the lanthanide bound to ε. 

When docking a small molecule compound such as a drug to a protein, it is likely that the 

Sanson-Flamsteed plot highlights large uncertainties because only a small number of PCSs can be 

measured. To improve the situation, an important and desired feature would be to use the 

information of the protein’s Δχ-tensor in order to improve the fit of the drug’s Δχ-tensor. The 

resulting enhancements are illustrated in Figure 1.14.c (compared to Figure 1.14.b) for the ε/θ 

protein-protein complex and are expected to be similar for small ligand-protein complexes. 

In order to address the presented issues, it is required to have an efficient software package 

to work with the Δχ-tensor. Chapter 3 presents the software package ―Numbat‖ (Figure 1.15) that 

tries to meet all those needs.


Figure 1.14 Sanson-Flamsteed representations of Δχ-tensor axes orientation. The error analysis 

used one thousand Monte-Carlo iterations that randomly selected 50% of the PCS data set. (a) The 

Δχ-tensors fitted for ε are very well defined. (b) As the lanthanide is 15 Å away from the θ subunit, 

the fitted Δχ-tensors are less accurate, as indicated by the large area each axis can spawn. (c) 

When keeping the relative orientation and magnitude of the two Δχ-tensors fixed (to the value 

determined for ε), the quality of the Δχ-tensor fitted increases, resulting in a more reliable complex 

of the two subunits. The well defined z-axis-area of the two Δχ-tensors (blue and brown) in (c) 

illustrates the reduced uncertainty around the z axes. 

Figure 1.15 Illustration of the task performed by the software 

Numbat. Given assigned PCSs, Numbat performs a structure 

based determination of the Δχ-tensor. 

1.3.3 De novo structure determination of proteins


The determination of protein structures is one of the main challenges of the post genomic 

era. The knowledge of structures at atomic detail is a prerequisite to understand how 

macromolecular complexes assemble and perform their tasks within living organisms. The 

established methods of X-ray crystallography and NMR spectroscopy still require significant 

human and financial resources to determine the structure of proteins of interest. Efforts are being 

focused on high-throughput methods to speed up the process of characterizing a large number of 

proteins (Kobe et al., 2008). 

De novo structure prediction software packages such as ROSETTA (Simons et al., 1997) 

are quite successful for small proteins (< 100 residues). The large size of the conformational space 

to explore makes it difficult, however, to tackle larger proteins. To overcome the ―sampling 

problem‖, one approach is to include additional experimental restraints that facilitate the three- 

dimensional reconstruction of protein structures. Those restraints must be easier to measure than it 

would be to obtain crystals of the target protein, or to measure and assign the NOEs required for the 

full determination of the structure. 

The pseudocontact shift effect is a candidate for this approach. PCSs can be measured 

swiftly and accurately as the chemical shift difference between two spectra, once a paramagnetic 

probe has been introduced into the protein. The use of lanthanide binding tags makes these 

techniques potentially available to any protein. Several lanthanide tags are now available. For a 

recent review, see (Su et al., 2009b). While it is not yet routine to attach lanthanide binding tags to 

a protein, several options are possible. Attachment by one or two disulfide bonds (Smith et al., 

1975), attachment at one of the termini of the protein (Donaldson et al., 2001), or even use of a 

non-covalent tag as demonstrated by (Su et al., 2009a) can be considered. It is expected that 

lanthanide attachment techniques will become routine in the future. 

Beyond the process of attachment, the second challenge is to have a tag that is not flexible. 

The physical model underlying equation (1.1) is accurate if the Δχ-tensor parameters are constant 

over time. This hypothesis could be questioned if small movements of the tag occur. Fluctuation of 

the tag produces two undesired effects: 

(i) It changes the electronic environment in the vicinity of the lanthanide and 

consequently, the orientation or magnitude of the Δχ-tensor. As equation (1.1) is 

linear with respect to the axial component, the rhombic component, and the three 

Euler angles, changes over time of those five parameters will not affect the way 

PCSs are predicted. More precisely, n conformations of the Δχ-tensor occurring


within the protein (and sharing the same center coordinate) can be equally explained 

by one single conformation. To demonstrate this, let’s take a spin i of measured 

pseeudocontact shift PCSi. PCSi is the sum of the contribution of the n states of the 

Δχ-tensor. 

For the state j, an alternative formula of the pseudocontact shift in a given frame f is: 

With 

(1.8) 

(1.9) 

(1.10) 

Where x, y, z are the Cartesian coordinates of the spin i in the frame f, and r the distance 

between the lanthanide and the spin i. Equation (1.8) becomes: 

With 

(1.11) 

(1.12) 

The traceless and symmetric matrix D contains the effective Δχ-tensor parameters that are 

necessary and sufficient to describe the PCS experienced by the spin i.


(ii) It could displace the position of the paramagnetic center with respect to the protein 

frame. The amplitude of those movements depends on the size and rigidity of the tag 

used. Small displacements have mostly small impact on the value of the PCS 

because PCSs are usually observable only more than ten Angstroms from the 

lanthanide. To assess this principle further, the comparison between a static metal 

ion and a mobile one following a realistic trajectory is illustrated in Figure 1.16. 

Figure 1.16 Effect of the mobility of the tag on the PCS. (a) Twelve tensors are being used to 

represent a realistic trajectory of the tag. They have random orientation, random axial and 

rhombic values, and are located three Angstroms away from the anchor point (black dot). The 

range of angles covers 110 degrees, in steps of 10 degrees. (b) The isosurfaces resulting from the 

ensemble of tensors in (a). The red surface represents the isolevel of 5.0 ppm, the blue one 

corresponds to -5.0 ppm. The shapes are distorted compared to the typical shape of an isosurface 

shown in Figure 1.12. (c) PCSs cannot be measured closer than 10 Angstroms from the 

paramagnetic center. The cutoff area is shown in grey. (d) Surfaces of isolevel 1.0 ppm and -1.0 

ppm are shown superimposed to (b). They exhibit a classical profile as seen in Figure 1.12. (e) 

The cutoff of 10 Angstroms is superimposed on figure (d).

1.4 Scope of the thesis. 23 

Once the PCSs have been measured, the next step is to use them appropriately in order to 

extract structural information. Using the PCSs to filter the correct structure(s) (by comparing 

calculated and experimental values) among a large ensemble of generated structures would not be 

enough. The PCS-based restraint needs to be directly incorporated into the process of structure 

generation to bias the outputted conformations towards the native one. Several options are to be 

considered: incorporating a PCS-restraint into a molecular dynamics software, a molecular 

refinement package that employs simulated annealing routines, or into a molecular fragment 

replacement software. The main question is which one of those approaches is the most suited to 

capture the global nature of the PCS effect. 

The merit of the PCS for de novo structure determination in the context of a molecular 

fragment replacement is described in Chapter 4. A PCS score function has been added to the 

package CS-ROSETTA (Shen et al., 2008). The ability of the PCS to drive CS-ROSETTA 

calculations towards the native conformation and to identify native like structures is discussed. 

1.4 Scope of the thesis 

This thesis covers different aspects of paramagnetic NMR from a computational point of 

view. This includes the use of PCSs for NMR resonance assignment, for Δχ-tensor determination in 

preparation of rigid body complex calculations, and de novo structure determinations of proteins. 

The rest of the thesis is organized as follow: 

In Chapter 2 is described an experimental and a computational approach to assign chemical 

shifts of methyl groups from the paramagnetic and diamagnetic NMR spectra. The computational 

route is supported by the development of the software Possum which was tested on artificial data 

first before being applied to experimental data. 

In Chapter 3 is presented a newly developed software that works specifically with 

pseudocontact shifts. The possibilities offered by the software are discussed and illustrated by the 

rapid reconstruction of the complex between the subunit ε and θ of the DNA polymerase III. 

In Chapter 4 is reported the incorporation of the PCS into the molecular fragment 

replacement software CS-ROSETTA, and the development of a new protocol to perform, for the 

first time, de novo protein structure determination using only PCSs and chemical shifts as 

experimental restraints.


Chapters 5 concludes this thesis by presenting some perspective of further development to 

better exploit PCS information in structural biology. 

1.5 References 

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pseudocontact shifts for solution structure refinements of macromolecules in shells up to 40 

angstrom from the metal ion. J Am Chem Soc 122:4154-4161 

Banci L, Bertini I, Savellini GG, Romagnoli A, Turano P, Cremonini MA, Luchinat C and Gray 

HB (1997) Pseudocontact shifts as constraints for energy minimization and molecular 

dynamics calculations on solution structures of paramagnetic metalloproteins. Proteins 

29:68-76 

Bertini I, Felli IC and Luchinat C (1998) High magnetic field consequences on the NMR hyperfine 

shifts in solution. J Magn Reson 134:360-364 

Bugayevskiy LM and Snyder JP (1995). Map projections: A reference manual. Taylor & Francis, 

London. 

Clore GM, Gronenborn AM and Bax A (1998) A robust method for determining the magnitude of 

the fully asymmetric alignment tensor of oriented macromolecules in the absence of 

structural information. J Magn Reson 133:216-221 

Donaldson LW, Skrynnikov NR, Choy WY, Muhandiram DR, Sarkar B, Forman-Kay JD and Kay 

LE (2001) Structural characterization of proteins with an attached ATCUN motif by 

paramagnetic relaxation enhancement NMR spectroscopy. J Am Chem Soc 123:9843-9847 

John M, Headlam MJ, Dixon NE and Otting G (2007) Assignment of paramagnetic 15 N-HSQC 

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Karp RM (1972) Reducibility Among Combinatorial Problems. Complexity of Computer 

Computations. New York: Plenum, R. E. Miller and J. W. Thatcher. 

Karplus M (1959) Contact electron-spin coupling of nuclear magnetic moments. J Chem Phys 

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Kobe B, Guss M and Huber T (2008). Structural Proteomics: High Throughput Methods. Humana 

Press, Totowa, NJ, USA.

1.5 References. 25 

Kuhn HW (1955) The Hungarian Method for the assignment problem. Naval Res Logistics Quart 

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McCoy MA and Wyss DF (2002) Structures of protein-protein complexes are docked using only 

NMR restraints from residual dipolar coupling and chemical shift perturbations. J Am 

Chem Soc 124:2104-2105 

Nguyen BD, Xia ZC, Yeh DC, Vyas K, Deaguero H and La Mar GN (1999) Solution NMR 

determination of the anisotropy and orientation of the paramagnetic susceptibility tensor as 

a function of temperature for metmyoglobin cyanide: Implications for the population of 

excited electronic states. J Am Chem Soc 121:208-217 

Pintacuda G, Keniry MA, Huber T, Park AY, Dixon NE and Otting G (2004) Fast structure-based 

assignment of 15 N HSQC spectra of selectively 15 N-labeled paramagnetic proteins. J Am 

Chem Soc 126:2963-2970 

Pintacuda G, Park AY, Keniry MA, Dixon NE and Otting G (2006) Lanthanide labeling offers fast 

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NMR in press

Chapter 2 

Possum: paramagnetically 

orchestrated spectral solver of 

unassigned methyls 

2. Possum: paramagnetically orchestrated spectral solver of unassigned methyls

28 Chapter 2. Possum: paramagnetically orchestrated spectral solver of unassigned methyls. 

2.1 Abstract 

Pseudocontact shifts (PCS) induced by a site-specifically bound paramagnetic lanthanide 

ion are shown to provide fast access to sequence-specific resonance assignments of methyl groups 

in proteins of known three-dimensional structure. Stereospecific assignments of Val and Leu 

methyls are obtained as well as the resonance assignments of all other methyls, including Met CH3 

groups. No prior assignments of the diamagnetic protein are required, nor are experiments that 

transfer magnetization between the methyl groups and the protein backbone. Methyl Cz-exchange 

experiments were designed to provide convenient access to PCS measurements in situations where 

a paramagnetic lanthanide is in exchange with a diamagnetic lanthanide. In the absence of 

exchange, simultaneous 13 C-HSQC assignments and PCS measurements are delivered by the newly 

developed program Possum. The approaches are demonstrated with the complex between the N- 

terminal domain of the subunit and the subunit of the Escherichia coli DNA polymerase III. 

2.2 Introduction 

Methyl groups are excellent probes for the study of proteins by NMR spectroscopy due to 

their favorable relaxation properties and intense 1 H NMR signals. When buried, they report on the 

packing of side chains in the protein core and thus provide important restraints for protein fold 

determination (Zwahlen et al., 1998). On the protein surface, they can serve as hydrophobic probes 

of protein-protein (Janin et al., 1988, Gross et al., 2003) and protein-ligand (Hajduk et al., 2000) 

interactions. Methyl groups have also been established as probes of protein dynamics (Nicholson et 

al., 1992, Muhandiram et al., 1995, Wand et al., 1996, Liu et al., 2003, Korzhnev et al., 2004, 

Tugarinov et al., 2005a, Tugarinov et al., 2005b) which, in contrast to amide protons, are inert with 

regard to solvent exchange. 

The resonance assignment of methyl groups in 13 C labeled proteins is usually achieved by 

magnetization transfers from sequentially assigned backbone resonances (Montelione et al., 1992). 

While this approach works well for proteins up to 30 kDa, it is impeded by fast transverse 

relaxation for proteins of high molecular weight or for paramagnetic proteins. Recent advances use 

tailored isotope labeling schemes (Tugarinov et al., 2003a, Tugarinov et al., 2003b) which are 

expensive and not generally applicable to any type of methyl group. In particular, the methyl 

groups of methionine residues are hard to assign since any scalar couplings with the CH3 group 

are small (Bax et al., 1994).

2.2 Introduction. 29 

As a further drawback, experiments that transfer magnetization between methyl groups and 

backbone resonances usually do not afford stereospecific discrimination between the prochiral 

methyl groups in Val and Leu residues. In this situation, stereospecific assignments require 

additional, stereospecifically labeled samples (Neri et al., 1989, Senn et al., 1989, Ostler et al., 

1993, Kainosho et al., 2006) or more complicated NMR experiments that often entail cumbersome 

data analysis (Zuiderweg et al., 1985, Sattler et al., 1992, Karimi-Nejad et al., 1994, Tugarinov et 

al., 2004, Tang et al., 2005). 

In the case where the three-dimensional structure of the protein is known prior to the NMR 

studies, it would be attractive to use the structure to facilitate the NMR resonance assignments. In 

favorable situations, structure-based resonance assignments can be achieved from NOE data 

(Grishaev et al., 2002). In addition, structure-based assignments of backbone resonances have been 

achieved using residual dipolar couplings (RDCs) measured with different alignment media (Jung 

et al., 2004) or using the combined information from pseudocontact shifts (PCS), RDCs, 

paramagnetic relaxation enhancements (PREs) and cross-correlated relaxation (CCR) induced by 

paramagnetic metal ions (Pintacuda et al., 2007). The structural interpretation of PCS has been used 

earlier to support resonance assignments of ligand residues in heme proteins (Senn et al., 1985). 

Recent advances in site-specific attachment of single lanthanide ions to proteins (Ma et al., 2000, 

Dvoretsky et al., 2002, Wöhnert et al., 2003, Ikegami et al., 2004, Prudêncio et al., 2004, Leonov et 

al., 2005, Haberz et al., 2006, Rodriguez-Castañeda et al., 2006, Su et al., 2006) extend this 

approach to long-range paramagnetic effects, with the possibility of tuning the range of focus by 

choice of a particular lanthanide (Allegrozzi et al., 2000, Balayssac et al., 2006, Pintacuda et al., 

2007). 

Here we show that the analysis of PCS induced by lanthanide ions presents a powerful tool 

for the assignment of methyl resonances, which by reference to the 3D structure of the protein, 

works even in situations when connectivities to the backbone resonances are difficult to establish or 

the backbone resonance assignment is incomplete. Stereospecific assignments of Val and Leu 

methyls are obtained as well as the assignments of any other methyl resonances, including those of 

Met CH3 groups. We present two Cz-EXSY experiments for the convenient measurement of PCS 

in situations where a paramagnetic lanthanide is in exchange with a diamagnetic lanthanide. In 

addition, an algorithm was developed to assign the 13 C-HSQC cross-peaks of methyl groups in the 

situation where no exchange information is available. The approaches are demonstrated with the 30 

kDa complex between the N-terminal exonuclease domain 186 and the subunit of Escherichia


coli DNA polymerase III. The active site of 186 binds two divalent ions (Hamdan et al., 2002b) 

that can be replaced by a single Ln 3+ ion (Pintacuda et al., 2004). 

2.3 Experimental section 

2.3.1 Sample preparation 

A cyclized version of 186, cz- 186, was designed for enhanced stability of the protein in 

unrelated crystallographic experiments (Park, 2006). Using an intein-based strategy (Williams et 

al., 2002), the N-terminal Ser2 and C-terminal Ala186 of 186 were linked by the nonapeptide 

TRESGSIEF (numbered 187-195). Apart from the N- and C-terminal residues that are structurally 

disordered in 186 (Hamdan et al., 2002b),the amide proton chemical shifts of the linear protein are 

conserved in cz- 186 within ±0.05 ppm, indicating that cyclization does not significantly affect the 

protein structure. The proteins cz- 186 and were prepared, and used to isolate samples of the cz- 

186/ complex, essentially as described previously (Hamdan et al., 2002a). NMR experiments 

made use of three different samples of complexes of unlabeled with isotope-labeled cz- 186: (i) a 

uniformly 13 C/ 15 N-labeled sample (0.5 mM), (ii) a biosynthetically directed fractional 13 C-labeled 

sample prepared from 20% 13 C-glucose (0.5 mM) (Neri et al., 1989, Senn et al., 1989), and (iii) a 

sample with 13 C/ 15 N-Leu (0.15 mM). Samples of 186/ were dialyzed against NMR buffer (20 

mM Tris, pH 7.2, 100 mM NaCl, 0.1 mM dithiothreitol, and 0.08% (w/v) NaN3 in 90% H2O/10% 

D2O). 

Lanthanides (Ln 3+ = La 3+ or 1:1 mixtures of La 3+ /Dy 3+ or La 3+ /Yb 3+ ) were added from 

LnCl3 stock solutions in the same buffer containing total Ln 3+ concentrations of 30 mM. The 1:1 

mixtures were added in slight molar excess to catalyze the metal ion exchange, resulting in 

exchange rates of a few s –1 (John et al., 2007a, John et al., 2007b).Restoration of the apo-complex 

was achieved by extensive dialysis against buffer containing 1 mM EDTA followed by dialysis 

against EDTA-free buffer. 

2.3.2 NMR spectroscopy 

All NMR experiments were performed at 25 o C on a Bruker AV 800 MHz NMR 

spectrometer equipped with a cryogenic TCI probe. Sequence-specific resonance assignments of

2.3 Experimental section. 31 

the methyl groups in the diamagnetic state were established by 3D HNCA and (H)CCH-TOCSY 

spectra of the uniformly 13 C/ 15 N labeled sample complexed with 1 equivalent of La 3+ (cz- 

186/ /La 3+ ), and by reference to the assignments reported for the linear 186 protein with Mg 2+ 

(DeRose et al., 2003). Stereospecific assignments of Val and Leu methyl groups were obtained 

from a constant-time (28 ms) 13 C-HSQC spectrum recorded of the fractionally 13 C labeled sample. 

Where possible, the rotameric states of the side chains of Val and Leu residues in the crystal 

structure of 186 (Hamdan et al., 2002b) were confirmed in solution by a 3D NOESY- 15 N-HSQC 

spectrum (mixing time 60 ms) recorded of the uniformly 13 C/ 15 N labeled sample. 

Sequence-specific resonance assignments of the methyl groups in the paramagnetic state 

were established by 2D and 3D methyl Cz-EXSY spectra recorded with the pulse schemes of Figure 

2.1 using a mixing period ( m) of 480 ms and spectral widths of 30 ppm ( 13 C) and 16 ppm ( 1 H). The 

2D spectra were acquired with 160 × 1024 complex data points and 32 scans in 10 h, while the 3D 

spectra were acquired with 80 × 64 × 1024 complex points and 4 scans in 40 h. For all spectra, the 

initial t1 delay was set to half the increment so that folded paramagnetic peaks could be identified 

by their inverted sign (Bax et al., 1991). 

The methyl group assignments obtained with these experiments provided the controls for 

the assignment methods described below. 

Figure 2.1 Methyl CZ-EXSY experiments. (a, b) Pulse schemes of the 2D and 3D versions, 

respectively. Narrow and wide bars represent radiofrequency pulses with flip angles of 90º 

and 180º, respectively, applied with phase x unless indicated otherwise. Selective 13 C pulses 

were applied as a 1.5 ms Q5 pulse prior to the delay C and as a 1.5 ms time-reversed Q5


pulse prior to the delay H, generating an excitation bandwidth of 20 ppm. 1 H saturation is 

achieved with 120º pulses applied every 5 ms, and the 3-9-19 sequence is used for water 

suppression. During m, 180 o ( 1 H) pulses are applied every 6 ms with a MLEV-16 supercycle 

to suppress cross relaxation between 1 H and 13 C spins. The phase cycle was 1(x, –x), 2(2x, 

2(–x)), 3(x), 4(4y, 4(–y)) and rec(x, 2(–x), x, –x, 2x, –x). States-TPPI was applied to 1 and 

3 for quadrature detection. Delays: T = 28 ms, = 3 ms, C = 0.75 ms, H = 1.7 ms. 

Gradients (Gi) were applied along the z-axis with strengths of 23.2, 14.5, 20.3, 17.5 and 11.6 

G/cm. (c-e) Simulated dipolar 13 C relaxation rates and NOE in isolated CH3 groups versus 

molecular rotational correlation time ( R) using eqs 1-4 in ref. 5. (c) Transverse relaxation 

rate R2, (d) longitudinal relaxation rate R1, and (e) steady-state 13 C{ 1 H} NOE. The dashed 

line reports the relaxation rates calculated for a static CH3 group, whereas the solid line 

takes into account a rapid rotation around the three-fold symmetry axis with a correlation 

time f = 25 ps and assuming tetrahedral geometry (Sf 2 = 0.111, rCH = 1.10 Å, rCC = 1.52 Å) 

(Wand et al., 1996). The dotted line represents the contribution from a neighboring 13 C spin 

to R2, R1, and cross-relaxation ( ), respectively. The vertical axis of the 13 C- 13 C cross- 

relaxation rate in (e) is in s –1 . Due to the small contribution of PRE to R1 (John et al., 2007a), 

the 13 C{ 1 H} NOE is similar for paramagnetic and diamagnetic proteins. 

2.3.3 Manual resonance assignments from PCS 

The PCS measured from EXSY spectra were used to evaluate the possibility of assigning 

the methyl peaks by comparison with back-calculated PCS. PCS were back-calculated using a 

Mathematica (Wolfram Research) script and the crystal structure of 186 (PDB entry 1J53, ref. 40). 

The -tensor parameters of Dy 3+ in complex with 186/ have been reported previously (Schmitz 

et al., 2006). The tensor parameters for Yb 3+ were determined from 15 N-HSQC spectra using the 

program Echidna (Schmitz et al., 2006) as: ax = –6.52 × 10 –32 m 3 , rh = 1.12 × 10 –32 m 3 , = 

24.4º, = 84.5º, and = –299.5º (using the zxz convention of Euler angle rotations). 1 H PCS of 

methyl groups were calculated for each of the three methyl protons individually and averaged. This 

average is largely insensitive to the rotational position of the methyl group. Residual CSA effects 

due to paramagnetic alignment (John et al., 2005) were disregarded since CSA tensors of methyl 

groups are small (Liu et al., 2003). 

2.3.4 The program Possum


The program Possum (paramagnetically orchestrated spectral solver of unassigned methyls) 

was developed to assign the cross-peaks of methyl groups in correlation spectra recorded with 

diamagnetic and paramagnetic metal ions by reference to the 3D structure of the protein and 

independently determined tensors. The program requires that the amino-acid type is known (e.g. 

by residue-type selective 13 C-labeling). Furthermore, it can accept information about methyl cross- 

peaks belonging to the same residue (―methyl connectivity‖ data for Ile, Leu, and Val, as provided 

by HCCH-TOCSY experiments) and stereospecific information (―methyl specificity‖ data 

distinguishing between 2 and 1 cross-peaks of Ile, 1 and 2 cross-peaks of Leu, and 1 and 2 

cross-peaks of Val, as provided by samples produced with biosynthetically directed fractional 13 C- 

labeling (Neri et al., 1989, Senn et al., 1989, Tugarinov et al., 2004) or stereoselective isotope 

labeling (Ostler et al., 1993, Kainosho et al., 2006)). In the present version of the program, the 

methyl connectivity information is always assumed to be available for the diamagnetic state. 

The program takes as input the 1 H and 13 C chemical shifts of methyl groups measured in 

13 C-HSQC spectra and the 13 C chemical shifts of methyl groups that are too close to the 

paramagnetic center to be directly observable in 1 H-detected NMR spectra. By comparing the 

chemical shifts in the diamagnetic and paramagnetic states, Possum attempts to find the resonance 

assignment with the lowest residual cost C(l) defined by: 

with: 

subject to: 

(2.1) 

(2.2)


(2.3) 

(2.4) 

where PCS S calc(k,l) is the predicted PCS value for the spin S (S = 13 C or 1 H) of the methyl 

group in residue k arising from the paramagnetism of the lanthanide l, para δ S exp(j,l) is the chemical 

shift of the resonance j in the presence of the lanthanide l for the spin S, and dia δ S exp(i) is the 

diamagnetic resonance i for the spin S. The cost function assigns smaller costs for deviations 

between calculated and observed PCS when the experimentally observed PCS is large, while the 

constant e(l) prevents a singularity in the cost function and accounts for the error in measurements 

when a spin experiences small paramagnetic effects far away from the paramagnetic center. e(l) 

scales with the magnitude of the tensor of the lanthanide l. Empirically determined values 

(e(Yb 3+ ) = 1/6 ppm and e(Dy 3+ ) = 1 ppm) were used here 2 . Equations (2.3) and (2.4) ensure that 

each calculated PCS and each experimental chemical shift are chosen exactly once within the 

global assignment. 

Equations (1.1), (2.3) and (2.4) present the formulation of the three-index assignment 

problem (Schell, 1955) which is the three-dimensional instance of the multidimensional assignment 

problem (MAP). With D being the number of dimensions of the MAP (D = 3 in the example above) 

and n being the size of each of the D sets of data, there are (n!) D-1 possible assignments. When D is 

strictly larger than 2, MAP has been proven to be NP-hard (Karp, 1972) and, as a result, no 

algorithm can guarantee the best solution to the problem in a polynomial time. An exhaustive 

2 The purpose of e(l) is to avoid degenerate cases where the experimental PCS is very close to zero. 

Its value is not critical for the success of the algorithm. E(l) has however been optimized to yield 

best possible results.


search through the (n!) 2 possibilities is impracticable for even the smallest problem sizes. An exact 

branch and bound algorithm that explores only a part of all possible assignments has been proposed 

(Balas et al., 1991) and works well for small problem sizes, especially when there is a good 

agreement between predicted and observed PCS. In the present context, a simulated annealing 

optimization scheme proved more efficient computationally. The dimensionality D of the 

assignment problem generated by Possum depends on the residue type, the availability of 

connectivity information, and the number of different lanthanides used. We have performed 

calculations with up to 6 dimensions. Examples of 3- and 4-dimensional problems are illustrated in 

Figure 2.2. 

Figure 2.2 Formulation of the assignment problem depending on the information available. The 

columns dia δ S exp and para δ S exp contain the chemical shifts (S = 13 C and S = 1 H as observed for 13 C- 

HSQC cross-peaks) measured in the presence of a diamagnetic or paramagnetic lanthanide, 

respectively. The column marked PCS S calc contains the 13 C and 1 H PCS calculated from the 

tensor and the 3D structure of the protein. (a) Assignment problem for residues with a single 

methyl group (Ala, Met, Thr). The indices i and j refer to the cross-peak number in the diamagnetic 

and paramagnetic state, respectively, and the index k is the residue number in the amino-acid 

sequence, as in equation (1.1). The assignment (i = 1, j = 3, k = 1) is illustrated by connecting 

lines. The associated cost can be calculated using equation (2.2). The other n-1 assignments 

necessary to calculate the total cost C(l) according to equation (1.1) are not shown. Overall, this 

assignment problem is three-dimensional. (b) Simultaneous use of the information from two 

samples containing the paramagnetic lanthanides l1 or l2 creates a four-dimensional assignment 

problem. (c) For amino acids with two methyl groups (Ile, Leu, Val), the columns dia δ S exp, para δ S exp, 

and PCS S calc embed the chemical shifts (and PCS) of two methyl groups (m1 and m2). If the methyl- 

specificity information is not available in the paramagnetic state (illustrated by m? in the column


para δ S exp), Possum will compute the two possible costs and only keep the lower one. (d) For Ile, Leu, 

and Val residues, the methyl-methyl connectivity information may be available in the diamagnetic 

state but not in the paramagnetic state. This situation creates a four-dimensional assignment 

problem for data from a single paramagnetic lanthanide. 

The program also takes into account the absence of paramagnetic peaks due to PRE by 

preventing the assignment of observable paramagnetic peaks to methyl groups located closer to the 

metal ion than a user-specified cutoff. In the present work, cutoffs of 6 and 9 Å were used for the 

Yb 3+ and Dy 3+ complexes, respectively. Paramagnetic peaks missing for any other reason (e.g. 

spectral overlap) are also tolerated. This is achieved by assigning a cost only to pairings of 

observable paramagnetic and diamagnetic peaks, whereas a zero cost is associated with any 

unassigned diamagnetic peak left over. Finally, the program allows for the possibility that 

paramagnetic shifts may have been observed only for either the 13 C or the 1 H resonance of a methyl 

group. 

The calculation of the assignment starting from the chemical shifts of Table S2.1 took less 

than 2 h on an AMD 64 4200+ processor, when using all available information, including methyl 

connectivity and methyl specificity information and the chemical shifts from the Yb 3+ and Dy 3+ 

complexes. 

2.4 Results 

2.4.1 13 C-HSQC spectra of the cz- 186/ /Ln 3+ complexes 

Constant-time 13 C-HSQC spectra of the uniformly 13 C labeled diamagnetic cz- 186/ /La 3+ 

complex and the paramagnetic cz- 186/ /Dy 3+ and cz- 186/ /Yb 3+ complexes illustrate the spectral 

complexity of the methyl region and the effect of the paramagnetism. The spectrum of the cz- 

186/ /La 3+ complex (blue peaks in Figure 2.3) contains approximately the number of methyl peaks 

expected for 19 Ala, 14 Thr, 6 Met, 12 Val, 17 Leu, and 14 Ile residues (125 methyl groups). The 

signals of Met CH3 groups are particularly well resolved and easily identified as they appear with 

opposite sign.

2.4 Results. 37 

Figure 2.3 Methyl region of constant-time 13 C-HSQC spectra of the cz- 186/ complex 

(containing 13 C/ 15 N labeled cz- 186) in the presence of La 3+ (blue) and a 1:1 mixture of (a) 

La 3+ /Dy 3+ and (b) La 3+ /Yb 3+ (red). Met CH3 and CH2 groups appear with inverted sign 

(light colors). The spectra were recorded using a constant time of 28 ms and t2max = 160 ms. 

The spectra of the mixed samples were acquired with 4 times as many scans to compensate 

for the halving of the effective concentrations. 

As Dy 3+ is one of the strongest paramagnetic lanthanide ions (Pintacuda et al., 2007), the 

methyl peaks of the cz- 186/ /Dy 3+ complex (red peaks in Figure 2.3a) are strongly shifted by PCS 

and affected by 1 H line broadening due to transverse paramagnetic relaxation enhancement (PRE). 

Thus, only 55 cross-peaks are observable corresponding to methyl groups with a distance from the 

Dy 3+ ion larger than 15 Å, many of them with intensities close to the noise level. Part of the 1 H line 

broadening is caused by unresolved RDCs, including intra-methyl RDCs (Kaikkonen et al., 2001), 

originating from the paramagnetically induced alignment of the protein with the magnetic field. 

In the cz- 186/ /Yb 3+ complex, the cutoff distance is reduced to about 9 Å due to the about 

6 times smaller paramagnetic moment of Yb 3+ so that only 10 methyl peaks are expected to be 

broadened beyond detection. Of the remaining 115 methyl resonances (red peaks in Figure 2.3b), 

only 14 peaks could not be analyzed due to overlap or very small PCS at larger distances from the 

metal ion. Figure 2.3 shows that for both paramagnetic lanthanides, it is nearly impossible to trace 

the paramagnetic shift of a 13 C-HSQC peak using the criterion that the PCS in the 13 C and 1 H 

dimensions of the spectrum must be similar. (In methyl groups, the distance between the carbon 

and the average position of the three protons is less than 0.4 Å.) Therefore, without prior 

knowledge of resonance assignments, PCS measurements cannot be made manually from 13 C- 

HSQC spectra alone.


2.4.2 Methyl CZ-EXSY experiments 

In order to measure PCS data conveniently and with high sensitivity, we designed an 

experiment applicable to samples prepared with a 1:1 mixture of paramagnetic and diamagnetic 

metal ions, where chemical exchange between the metal ions leads to exchange of the protein 

between paramagnetic and diamagnetic states. By generating exchange cross-peaks between methyl 

peaks of the diamagnetic and paramagnetic lanthanide complexes, the experiment allows the 

measurement of 1 H and 13 C PCS from a single spectrum. Figure 2.1 shows 2D and 3D versions of 

the methyl Cz-EXSY experiment. The pulse sequences are related to previously published Nz- 

exchange experiments (Farrow et al., 1994, John et al., 2007a). 

During a mixing period m, magnetization is stored as relatively slowly relaxing CZ 

magnetization. Simulations indicate that, owing to rapid rotation around the 3-fold symmetry axis, 

longitudinal relaxation rates R1 of methyl 13 C spins are fairly insensitive with respect to molecular 

size, and barely exceed 2 s –1 even for very small proteins (Figure 2.1d). In the cz- 186/ /La 3+ 

complex ( C = 17 ns), we measured R1( 13 C) rates of about 1.6 s –1 for the majority of methyl groups. 

Only a group of highly mobile Thr residues relaxed somewhat faster (2 s –1 ), whereas the R1( 13 C) 

relaxation in Met CH3 groups was much slower (about 0.7 s –1 ). In contrast to transverse relaxation 

rates R2, R1 rates in macromolecules are barely affected by the paramagnetism of lanthanides(John 

et al., 2007a). 

The experiment yields auto-peaks for the diamagnetic and paramagnetic states (dd and pp 

peaks, respectively) and exchange peaks arising from magnetization exchange from the 

paramagnetic to the diamagnetic state and vice versa (pd and dp peaks, respectively). 

Since the experiment starts from 13 C polarization rather than using an INEPT transfer, pd 

peaks can be detected even for methyl groups that are strongly affected by 1 H PRE in the 

paramagnetic state and thus invisible in the 13 C-HSQC spectrum. Combined with the dd peaks, this 

allows 13 C PCS measurements that are limited only by the (16-fold smaller) 13 C PRE (John et al., 

2007b). As indicated previously 13 and illustrated by the simulations of Figure 2.1e, 13 C polarization 

in methyl groups of proteins can be very efficiently enhanced using the { 1 H} 13 C NOE. This holds 

irrespective of paramagnetism. We observed an about two-fold increase in 13 C polarization in the 

cz- 186/ /La 3+ complex using 1 s of 1 H irradiation between subsequent scans. 

For improved resolution in the 13 C dimension and measurement of small 13 C PCS, the 2D 

experiment is implemented as a constant-time experiment in the t1 dimension. The 3D experiment 

additionally records the 13 C frequency of the protein state after the mixing time. Real-time


evolution periods in both indirect dimensions yield superior sensitivity for residues with substantial 

13 C PRE that commonly also have larger PCS. Selective 13 C pulses select the spectral window of 

the methyl 13 C resonances of the diamagnetic complex in order to limit the spectral width required 

in the F1 dimension. 

2.4.3 Resonance assignment of Met, Ala and Thr methyl groups 

Figure 2.4a shows the spectral region of the Met CH3 cross-peaks of the 2D methyl Cz- 

exchange spectrum, recorded with a sample of cz- 186/ containing La 3+ and Dy 3+ in a 1:1 ratio. 

Out of six Met residues, four are observed in the 13 C-HSQC spectrum of the cz- 186/ /Dy 3+ 

complex (the cross-peak of Met178 in the paramagnetic state appears with very weak intensity at 

2( 1 H) = 5.33 ppm). For these residues, both auto and both exchange peaks become visible in the 

exchange spectrum, forming a rectangle that allows straightforward identification of dd-pp peak 

pairs, yielding 13 C PCS of 3.28, 1.31, 0.49 and –0.65 ppm. A fifth residue only yields a pd 

exchange peak with a 13 C PCS value of –3.39 ppm. 

Figure 2.4 Assignment of Met CH3 from PCS. (a) 2D methyl Cz-EXSY spectrum of cz- 186/ 

(containing 13 C/ 15 N-labeled cz- 186) loaded with a 1:1 mixture of La 3+ and Dy 3+ (red), overlaid 

with the 13 C-HSQC spectrum (blue). The diamagnetic auto-peaks (dd) are labeled with the 

assignment and connected to the paramagnetic auto-peaks (pp) and the exchange peaks (pd and 

dp) with dashed rectangles. The dp and pp peaks of Met178 are outside the selected spectral region


at 2 = 5.53 ppm. Met107 only shows a pd exchange peak (vertical dashed line), and neither pp- 

peak nor exchange peaks are observed for Met18. The spectrum was recorded with a mixing time 

of 480 ms. (b) Comparison of predicted (top) and measured (bottom) PCS of Met CH3 groups. 13 C 

PCS and 1 H PCS are plotted with filled and open bars, respectively, and sorted according to the 

predicted 13 C PCS. The distances rC-Ln are given in Å in the center. 3 

The measured PCS can be compared with values predicted from the known structure of 

186 (Park, 2006) and the previously determined tensor of Dy 3+ (Figure 2.4b) (Schmitz et al., 

2006). Only five Met residues belong to the structured part of the protein with predicted 13 C PCS of 

3.74 (Met178), 1.30 (Met137), –0.56 (Met87), –1.68 (Met18) and –2.87 ppm (Met107). Met185 is 

located in the flexible cyclizing loop of cz- 186 and can be immediately assigned to the very 

intense and narrow resonance with a 13 C PCS of 0.49 ppm, in agreement with the PCS of 0.53 ppm 

observed for the amide proton of this residue. Met18 is the residue closest to the metal ion (rC-Dy = 

12.0 Å) and can be assigned to the methyl group that does not show any exchange peak. As Met18 

lines the active site this assignment is independently confirmed by its sensitivity to titration with 

nucleotides (unpublished results). Met107 is the second closest residue (rC-Dy = 14.2 Å) and 

displays a pd but no dp exchange peak; the assignment of all other Met residues follows in a 

straightforward manner from the PCS data. 

The data show that it is possible to assign a limited number of methyl groups using PCS 

only. The situation is more complex for the methyl groups of the other amino acids since with the 

exception of Ile CH3 groups, the amino acid type cannot be identified from 13 C-HSQC spectra 

alone. This information would have to be provided either by the use of residue-specific labeling or 

additional NMR experiments (in the cz- 186/ /La 3+ complex, the amino acid type can readily be 

identified from a 3D (H)CCH-TOCSY spectrum). In addition, important information is provided by 

(i) the relative size of 13 C and 1 H PCS and (ii) whether the paramagnetic 1 H resonance can be 

observed (rC-Dy > 15 Å) or only pd exchange peaks (rC-Dy > 10 Å, Figure S2.4 and Figure S2.5). 

3 Experimental PCS have an error below 0.1 ppm. Errors in the calculated PCS depend on the 

quality of the 3D structures used. Residues 87, 107, 137 and 178 belong to structured part. The 

error on their calculated PCS can be considered below 10% of their absolute value.

2.4.4 Assignments of Val, Leu, and Ile methyl groups 


Val, Leu, and Ile are amino acids with two methyl groups that can easily be linked by 

correlations observed in TOCSY spectra; combining the PCS data for both methyl groups greatly 

facilitates the resonance assignment of these residues. This is illustrated in Figure 2.5 with the cz- 

186/ complex containing 1:1 mixtures of Yb 3+ /La 3+ (a, b) and Dy 3+ /La 3+ (c, d), respectively. 

Whereas a 2D (H)C(C)H-TOCSY experiment (Figure S2.1, Supporting Information) recorded with 

short mixing time (12 ms) strongly favors intra-residual methyl-methyl correlations (Figure 2.5a) 

(Eaton et al., 1990), the 2D methyl CZ-EXSY spectrum yields predominantly exchange peaks and 

only weak 1- 2 correlations arising from 13 C- 13 C NOE (Fischer et al., 1996). We have also applied 

the (H)C(C)H-TOCSY experiment to a sample of the pure cz- 186/ /La 3+ complex containing 

selectively 13 C/ 15 N-Leu labeled cz- 186, where all 1- 2 methyl pairs could be identified (Figure 

S2.4).


Figure 2.5 PCS measurements in isopropyl groups of Val and Leu and use of PCS for 

stereospecific resonance assignments. (a) Selected spectral region from a 2D (H)C(C)H TOCSY 

spectrum (red) of cz- 186/ loaded with a 1:1 mixture of La 3+ and Yb 3+ , showing the methyl cross- 

peaks of Val96. The spectrum is overlaid with the 13 C-HSQC spectrum (blue). Intraresidual 

correlations between the cross-peaks of the 1CH3 and 2CH3 groups are identified by dotted lines. 

The TOCSY spectrum was recorded with 12 ms mixing time. (b) Same spectral region as in (a) 

taken from the 2D methyl Cz-EXSY spectrum of the same sample recorded with a mixing time of 

480 ms. (c) Selected strips from the 3D methyl CZ-EXSY spectrum of cz- 186/ loaded with a 1:1 

mixture of La 3+ and Dy 3+ (right panels) aligned with corresponding spectral regions from the 2D 

methyl CZ-EXSY spectrum (left panels). The strips display the methyl group correlations of Val10 

and Leu113. The arrows point from the chemical shifts of the diamagnetic auto-peaks (dd) to the 

chemical shifts of the exchange peaks (pd), indicating the 13 C PCS. Horizontal lines identify the


positions of the dd- and pd-peaks in the 1( 13 C) dimension. The line at 26.35 ppm identifies the 13 C- 

13 C NOEs with the CH group of Leu113. (d) Assignment of methyl resonances from the 

comparison of predicted with experimental PCS. For each Val residue, the distances from the 

lanthanide in Å are indicated for both methyl carbons in the center of the plot. 13 C PCS and 1 H 

PCS are displayed as filled and open bars, respectively. The residues are sorted according to the 

predicted 13 C-PCS and the PCS are plotted in the sequence C 1 /H 1 /C 2 /H 2 . 

Figure 2.5c compares the measurement of 13 C PCS for two residues from strips of 2D and 

3D methyl CZ-EXSY spectra. The two experiments are complementary, showing better frequency 

resolution in the 2D spectrum and generally less cross-peak overlap in the 3D spectrum. The 

example of Leu113 shows that one- and two-bond 13 C- 13 C NOE correlations are visible, but 

generally of much smaller intensity than the exchange peaks. Through-bond correlations can again 

be identified from TOCSY spectra. From the combined use of the 2D and 3D Cz-EXSY spectra, all 

13 C-HSQC cross-peaks observable for any of the methyl groups of the cz- 186/ /Dy 3+ and cz- 

186/ /Yb 3+ complexes could readily be correlated with the corresponding 13 C-HSQC cross-peaks 

of the cz- 186/ /La 3+ complex, yielding the PCS. Compared to the 13 C-HSQC spectrum, the methyl 

Cz-EXSY spectra yielded the 13 C chemical shifts in the paramagnetic state for a further 47 methyl 

groups of the cz- 186/ /Dy 3+ complex with rC-Dy distances as short as 10 Å, leaving only 11 methyl 

groups completely unobservable due to excessive PRE. For the cz- 186/ /Yb 3+ complex, the 

methyl Cz-EXSY spectra yielded the 13 C chemical shifts for 7 additional methyl groups with rC-Yb 

distances as short as 6 Å, leaving only 1 methyl group unobservable. 

Figure 2.5d compares the predicted and measured PCS for Val methyl groups in the cz- 

186/ /Dy 3+ complex. Each residue is characterized by up to 4 PCS values, resulting in the 

straightforward assignment of 10 out of 12 residues. Only Val39 did not yield unambiguous PCS 

data due to resonance overlap, and Val65 is too close to the Dy 3+ ion. The assignment of Val65 

could be made in the 186/ /Yb 3+ complex, where this residue yields large PCS (Supporting 

Information). The methyl cross-peaks of Leu residues can be assigned in an analogous way (see 

below). 

Importantly, this approach automatically yields the stereospecific assignment of Val and 

Leu methyl peaks, as long as different PCS are observed for the two prochiral methyl groups. Since 

the methyl carbons in an isopropyl group are separated by 2.5 Å, this is almost always the case


(Figure 2.5d). A rare exception is Val50, where the predicted 13 C and 1 H PCS of the 1 and 2 

methyl groups are indistinguishable in both the Dy 3+ and Yb 3+ complex. 

The methyl groups of Ile residues are particularly easy to assign by PCS, since the spectral 

ranges of the 13 C-NMR signals of 2 and 1 methyl groups are clearly separated, while intra- 

residual methyl-methyl connectivity can still be obtained from TOCSY spectra. 

2.4.5 Automatic assignments without EXSY data 

Cz-EXSY spectra provide an exceptionally simple way of measuring PCS. For situations 

where the metal exchange is too slow for exchange spectra and spectral crowding prevents the 

straightforward pairing between diamagnetic and paramagnetic 13 C-HSQC peaks (Figure 2.3), we 

have devised the program Possum which determines the correct peak pairings, their resonance 

assignments, and their PCS, using the 3D structure of the protein and the tensor (that can readily 

be obtained from, e.g. , 15 N-HSQC spectra (Pintacuda et al., 2004, Schmitz et al., 2006)). 

The performance of the program was initially tested with simulated data, replacing the 

experimental paramagnetic shifts of Table S2.1 by shifts back-calculated from the crystal structure 

of 186 (Hamdan et al., 2002b) and using the crystal structure, the experimental diamagnetic 

chemical shifts, and the tensors of Dy 3+ and Yb 3+ as input. In all calculations, it was assumed 

that the residue types of all methyl resonances were known and the methyl connectivity information 

of Val, Leu, and Ile residues was available for the diamagnetic state. Except for extreme cases of 

spectral overlap, the program yielded 100% correct assignments. In a second step, structural 

uncertainties were simulated by randomly displacing the methyl groups, following a Maxwell- 

Boltzmann distribution with maxima at 0.35 and 0.7 Å (resulting in maximal atom displacements of 

0.75 and 1.5 Å, respectively, always using the same direction of displacement). Even in the case 

with the maximum structural noise, using only paramagnetic data from the Yb 3+ complex and 

neither methyl specificity nor methyl connectivity information in the paramagnetic state, Possum 

yielded >75% correct assignments of the diamagnetic methyl resonances (Table S2.2 and Table 

S2.4). The score increased to >90% when paramagnetic data from the Dy 3+ complex, methyl 

specificity information in all complexes, and methyl connectivity information in the Yb 3+ complex 

(but not the Dy 3+ complex) were included (Table S2.2 and Table S2.3). 

The program was subsequently applied to the experimental data of the methyl groups of cz- 

186/ loaded with La 3+ , Yb 3+ and Dy 3+ . Table 2.1 summarizes the results. Using both 

paramagnetic lanthanides, the assignment is complete and correct for all diamagnetic 13 C-HSQC


cross-peaks that have observable paramagnetic partners. The only exceptions are swapped 

assignments for Met18 and Met107 and Val65 and Val82. The first arises from a side-chain 

conformation that is different in solution than in the single crystal and the second from differences 

in the predicted and experimental PCS observed for the peptide segment near Val65 (John et al., 

2007b).The assignments of the methyl groups of the Yb 3+ complex are similarly reliable, whereas 

the methyl signals of the Dy 3+ complex are harder to assign (in the absence of methyl connectivity 

information). Using only data from the Yb 3+ complex and omitting any methyl specificity 

information or connectivity information in the paramagnetic state still results in >70% correct 

assignments of the diamagnetic methyl resonances (Table S2.2 and Table S2.4) 4 . 

Table 2.1 Automatic assignment of methyl groups by the program Possum a 

Residue type Occurrence b La c observable Yb d assigned Dy d assigned La e assigned 

Met 6 (1) 5 3/5 4/4 3/5 

Thr 14 (4) 8 7/7 7/7 7/7 

Ala 19 (2) 17 13/13 11/13 14/14 

Ile 14 (2) 24 24/24 21/23 24/24 

Val 12 (0) 24 20/20 17/20 18/22 

Leu 17 (0) 34 34/34 19/25 34/34 

a Obtained using the data reported in Table S2.1, the crystal structure of 186 (Hamdan et al., 

2002b) and tensors determined from 15 N-HSQC spectra as described in the experimental 

section. The paramagnetic data measured with Yb 3+ and Dy 3+ were combined to derive the 

assignments. 

b Total number of residues in cz- 186. The number in brackets refers to residues not observed in 

the crystal structure; these were excluded from the calculation. 

c Number of methyl groups with coordinates reported in the crystal structure for which cross-peaks 

were observed in the cz- 186/ /Ln 3+ sample. Their unassigned chemical shifts were available for 

the program. 

4 It is the responsibility of the user to inspect and optimize the assignment provided by Possum; in 

particular to untangle areas of the spectrum with overlapping peaks.


d Fraction of correct assignments for the paramagnetic cz- 186/ /Yb 3+ and cz- 186/ /Dy 3+ 

complexes, as indicated. The number in the denominator is the number of methyl groups for which 

cross-peaks were observed in the presence of Yb 3+ or Dy 3+ . 

e Fraction of correct assignments for the diamagnetic cz- 186/ /La 3+ complex. The number in the 

denominator is the number of methyl groups for which cross-peaks were observed in at least one of 

the paramagnetic complexes. 

2.4.6 PCS and flexibility 

Structural differences between the crystal structure of 186 determined under cryogenic 

conditions (Hamdan et al., 2002b) and the solution structure of the cz- 186/ complex become 

apparent as differences between measured and predicted PCS. In a few cases, the structural 

differences interfere with the resonance assignment. Figure 2.6a illustrates the situation for the cz- 

186/ /Dy 3+ complex, where the measured PCS of Leu161 are smaller than predicted and would 

more closely match the values predicted for Leu131. This can be explained by a small displacement 

of the peptide segment comprising residues 151-161 that decreases the PCS of both methyls of 

Leu161. Smaller PCS than expected were also observed for the backbone amides of this segment. 45 

The correct assignment would be obtained by focusing on the difference in 13 C PCS between both 

methyl groups rather than their magnitude (Figure 2.6a) or by using the data of the cz- 186/ /Yb 3+ 

complex which are less strongly distance dependent in the 11 Å distance range (Figure 2.6b).


Figure 2.6 Residues showing deviations between predicted and experimental PCS. Comparison of 

calculated and experimental PCS of Leu131, Leu95, Leu161, Leu11 and Ile154 in the cz- 

186/ /Dy 3+ complex. The data are plotted in the sequence C 1 /H 1 /C 2 /H 2 and C 2 /H 2 /C 1 /H 1 / for 

the Leu residues and Ile154, respectively. (b) Same as (a), but for the cz- 186/ /Yb 3+ complex. (c) 

Predicted 13 C PCS of the prochiral methyl groups of Val82 in cz- 186/ /Dy 3+ versus sidechain 

dihedral angle. The values predicted from the crystal structure of 186 40 are marked. (d) Same as 

(c), but for the CH3 groups of Leu95. 

In the cases of Val82 and Leu95 in the Dy 3+ complex, the comparison of experimental and 

predicted 13 C-PCS data yields the wrong stereospecific assignment. The 1 and 2 angles of these 

residues are –47º and 172º, respectively, in the crystal structure (Hamdan et al., 2002b). Adjusting 

these angles to –60º and 180º, respectively, inverts the relative size of the 13 C PCS predicted for the 

two methyl groups, leads to much better agreement between predicted and experimental PCS, and 

results in the correct stereospecific assignments (Figure 2.6c and d). This observation is most 

simply explained by a small difference between the crystal and solution structures. Note that the


correct assignment could have been obtained for Leu95 in the Yb 3+ complex (Figure 2.6b). None of 

the other Val and Leu residues swapped their stereospecific assignment when we changed their 1 

angles ( 2 angles in the case of Leu) by ±10º. 

In the case of Leu11, different NMR criteria suggest that its side chain undergoes dynamic 

conformational averaging. (i) The 13 C-PCS values predicted from the structure are -7.0 and -11.9 

ppm, whereas the experimental value found for both methyl groups is -8.4 ppm. (ii) In the crystal 

structure, the two methyl groups are 9.2 and 11.1 Å from the metal ion, but the 13 C-NMR line 

widths observed for the methyl groups in the cz- 186/ /Dy 3+ complex are indistinguishable. (iii) 

Both methyl resonances overlap with each other in the 13 C-HSQC spectrum, indicating similar 

chemical environments, and their line shapes are narrower than those of most other methyl groups. 

Remarkably, however, Leu11 is located in the hydrophobic core of the protein and is very well 

defined in the crystal structure, 40 although the side chain forms no steric contacts and could access 

different rotameric states without introducing van der Waals violations with neighboring atoms. 

Conceivably, the low temperature used in the X-ray experiment may have frozen out a single 

conformation, whereas a much larger conformational space is accessible at room temperature. 

Ile154 presents an example where partial motional averaging may be indicated by a smaller 

difference observed between the PCS of the 1 and 2 carbon atoms than predicted. The side chain 

heavy atoms of this residue shows enhanced B-factors in the crystal structure, in agreement with its 

location at the protein surface. 

2.5 Discussion 

The present work shows that methyl resonances of 13 C-labeled proteins can be assigned 

solely from PCS with reference to the 3D structure of the protein, yielding both sequence- and 

stereo-specific resonance assignments without having to establish connectivities to backbone 

resonances. This presents a significant advance over our previous strategy for the assignment of 

15 N-HSQC spectra, which relied on PCS, PRE, CCR, and RDCs measured on selectively labeled 

samples (Pintacuda et al., 2004). 

Clearly, any resonance assignment based on comparison of experimental and back- 

calculated PCS critically depends on the accuracy of the 3D structure of the protein and is expected 

to fail for flexible protein segments. Yet, this problem is much less severe than in the case of RDCs

2.5 Discussion. 49 

(Sibille et al., 2002), since PCS are far less affected by local mobility as long as the spins are not 

very close to the paramagnetic center. The robustness of PCS with regard to structural variations is 

particularly beneficial for the assignment of Met CH3 groups that are notoriously difficult to 

assign by conventional methods. The potential of PCS for their assignment has been noted 

previously (Bose-Basu et al., 2004). 

The assignment strategy presented here requires the determination of the tensor, which 

can readily be achieved from 15 N- 1 H correlation spectra by the Platypus algorithm (Pintacuda et al., 

2004). Obtaining resonance assignments of methyl groups in this way is attractive because 15 N- 1 H 

correlation spectra of backbone amides and 13 C- 1 H correlation spectra of methyl groups can be 

recorded even for high-molecular weight systems (Fiaux et al., 2002, Sprangers et al., 2007). 

Alternatively, the -tensor parameters can be determined from assigned diamagnetic NMR 

resonances and a set of PCS identified by comparison with the paramagnetic NMR spectrum, either 

manually or automatically using the Echidna algorithm (Schmitz et al., 2006). Initial sequence- 

specific resonance assignments can, if necessary, be achieved by site-directed mutagenesis (Siivari 

et al., 1995, Bose-Basu et al., 2004), for example by mutation of Ile to Val (Wu et al., 2007). 

Assignments by PCS are not limited to metal-binding proteins as different techniques have 

recently become available that achieve site-specific attachment of lanthanide-tags to proteins 

devoid of natural metal binding sites (Ma et al., 2000, Dvoretsky et al., 2002, Wöhnert et al., 2003, 

Ikegami et al., 2004, Prudêncio et al., 2004, Leonov et al., 2005, Haberz et al., 2006, Rodriguez- 

Castañeda et al., 2006, Su et al., 2006). The use of different tags or attachment at different sites 

readily generates very different tensors (Rodriguez-Castañeda et al., 2006) that can highlight 

inconsistencies between experimental and back-calculated PCS. 

If the exchange between paramagnetic and diamagnetic metal ions is too slow to measure 

exchange spectra, the program Possum can be used to assign the methyl groups in the diamagnetic 

and paramagnetic state. As expected, the robustness of Possum with regard to small differences 

between the atomic coordinates of the protein and its actual structure in solution increases with the 

amount of additional data available. In this respect, data from two paramagnetic metal ions are 

particularly beneficial, but also information about intraresidual methyl-methyl connectivities or 

stereospecific identities of methyl groups in Val, Leu, and Ile residues. 

The robustness of assignments made by Possum can further be enhanced by the increased 

spectral resolution afforded by 3D NMR spectra which would greatly facilitate the identification of 

the corresponding NMR resonances in the diamagnetic and paramagnetic state based on the


criterion that all correlated spins are close in space and therefore experience similar PCS. For 

example, 3D (H)CCH-TOCSY or NOESY- 13 C-HSQC spectra would resolve several cross-peaks 

for each methyl group, which can simultaneously be compared with the 3D structure of the protein 

and the predicted PCS to obtain resonance assignments. For methyl groups in the vicinity of the 

paramagnetic ion, the observation of correlations can be aided by protonless experiments (Bermel 

et al., 2006). 

Conceivably, assignments by PCS can also be achieved for perdeuterated proteins of 

increased molecular weight containing selectively protonated methyl groups (Rosen et al., 1996). 

The best spectral resolution in the methyl region of the 13 C-HSQC spectrum would be obtained for 

CD2H groups (Kainosho et al., 2006).Notably, however, the Cz-EXSY experiments described here 

allowed us to measure all PCS data in the uniformly 13 C/ 15 N-labeled and fully protonated sample, 

i.e. the improved spectral resolution of selectively labeled samples was not necessary for our 

system. 

In conclusion, resonance assignments of the 13 C-HSQC cross-peaks of methyl groups by 

PCS induced by a site-specifically attached lanthanide ion present a versatile and convenient 

technique which can open many opportunities for NMR studies of proteins of known three- 

dimensional structure. It is anticipated that resonance assignments by this technique will be 

particularly useful in ligand screening applications. 

2.6 Acknowledgement 

The authors thank Don A. Grundel for source codes of the MAP solver and for useful 

discussions. M.J. thanks the Humboldt Foundation for a Feodor-Lynen Fellowship. Financial 

support from the Australian Research Council for project grants, a Federation Fellowship for G.O. 

and the 800 MHz NMR spectrometer at the ANU is gratefully acknowledged. This work was 

supported by an award under the Merit Allocation Scheme of the National Facility of the Australian 

Partnership for Advanced Computing. 

2.7 Supporting Information Available


Pulse scheme of a (H)C(C)H-TOCSY experiment for correlations between isopropyl methyl 

groups, 13 C-HSQC spectra of uniformly, fractionally, and selectively isotope labeled cz- 186/ , 

diagrams comparing experimental and predicted PCS, a table with the chemical shifts of the methyl 

groups cz- 186 observed in the presence of La 3+ , Yb 3+ , or Dy 3+ , and tables reporting the number of 

methyl groups assigned by Possum. This material is available free of charge via the Internet at 

http://pubs.acs.org. 




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2.9 Supporting information 

Figure S2.1 Pulse scheme of the 2D (H)C(C)H-TOCSY experiment 

used in this study. Parameters are as for the pulse schemes of Figure 

2.1. Efficient magnetization transfer between the methyl groups of 

isopropyl groups was obtained by applying DIPSI3 mixing for 12 ms 

with a radiofrequency amplitude of 8.6 kHz. The Bruker pulse 

programs of this pulse sequence and of the pulse sequences of Figure 

2.1 can be downloaded from http://rsc.anu.edu.au/~go/.

2.9 Supporting information. 57 

Figure S2.2 Assigned constant-time (28 ms) 13 C-HSQC spectrum of the cz- 186/ /La 3+ complex 

( 13 C/ 15 N labeled cz- 186) at pH 7.2 and 25 o C. Only the region containing the methyl cross-peaks is 

shown. Cross-peaks from methyl groups of Val, Leu, Ile, Ala and Thr appear as positive peaks 

(blue), whereas cross-peaks from Met CH3 and all CH2 groups appear as negative peaks (red).


Figure S2.3 Assigned constant-time 13 C-HSQC spectrum of the cz- 186/ /La 3+ complex, where cz- 

186 was biosynthetically fractionally 13 C-labeled using 20% uniformly 13 C-labeled glucose. 

Parameters and plot region as in Figure S2.2. Cross-peaks from Val 1, Leu 1, and Ala methyl 

groups are positive (blue). Cross-peaks from Val 2, Leu 2, Thr 2 and Met methyl groups are 

negative (red). Cross-peaks from Ile 1 and 2 methyl groups are mostly invisible due to 

scrambling of 13 C during Ile biosynthesis.


Figure S2.4 Assigned constant-time 13 C-HSQC spectrum of the cz- 186/ /La 3+ complex containing 

13 C/ 15 N-Leu labeled cz- 186 (blue) superimposed onto a 2D (H)C(C)H-TOCSY spectrum of the 

same sample (red). The assignments of the 13 C-HSQC cross-peaks are indicated. The three mobile 

residues Leu11, Leu43 and Leu145 also show one-bond correlations between CH3 and CH 

groups.


Figure S2.5 Comparisons of calculated and experimental PCS in the cz- 186/ /Dy 3+ complex for 

methyl groups of (a) Met, (b) Ala, (c) Thr, (d) Val, (e) Leu, and (f) Ile. The distances rC-Ln are 

indicated in Å at the top of each plot. For residues with two methyl groups, the distance value 

shown at the top refers to the C 1 (Val), C 1 (Leu), or C 1 (Ile) atom.

Figure S2.5 continued 

2.9 Supporting information. 61


Figure S2.6 Comparisons of calculated and experimental 13 C and 1 H PCS as in Figure S2.5 but for 

the cz- 186/ /Yb 3+ complex.

Figure S2.6 continued 

2.9 Supporting information. 63


Table S2.1 13 C and 1 H chemical shifts (ppm) of methyl groups of cz- 186 in the cz- 186/ /Ln 3+ 

complexes used in this study a 

Group rC-Ln cz- 186/ /La 3+ cz- 186/ /Dy 3+ cz- 186/ /Yb 3+ 

Methionine 

(Å) 

13 C 

1 H 

M18 12.0 17.78 2.06 18.04 2.34 

M87 22.5 15.97 1.53 15.32 0.93 16.05 1.63 

M107 14.2 16.23 2.04 12.84 16.77 2.64 

M137 20.7 16.69 2.05 18.00 3.38 16.41 1.78 

M178 15.4 15.39 2.22 18.67 5.53 14.69 1.53 

M185 16.83 2.07 17.32 2.55 16.75 1.98 

Alanine 

A4 19.14 1.35 

13 C 

A23 20.2 17.15 0.62 17.35 

A35 11.5 24.14 1.57 17.70 25.47 2.79 

A62 10.9 18.72 1.55 30.88 16.97 -0.24 

A69 16.2 23.77 1.61 26.74 23.15 

A80 22.3 18.68 1.46 19.04 1.84 18.66 1.39 

A83 20.1 19.35 1.29 18.97 1.00 

A93 19.2 20.74 1.21 19.78 0.22 20.90 1.39 

A100 13.3 19.85 1.41 16.19 21.22 1.77 

A101 15.1 18.20 1.45 15.48 -1.16 18.58 1.82 

A132 17.6 17.89 1.60 17.16 

A134 15.8 18.44 1.79 20.16 3.58 17.96 1.30 

A147 14.8 18.49 1.28 20.54 18.01 0.86 

A150 17.2 17.57 1.42 20.22 3.91 17.12 0.99 

A164 5.2 18.93 1.21 

A168 7.5 17.24 1.42 18.52 

A172 12.5 18.54 1.38 24.10 17.77 0.73 

A177 18.5 16.75 0.92 20.11 4.39 16.17 0.34 

A186 19.07 1.39 19.45 1.77 19.02 1.32 

1 H 

13 C 

1 H

Threonine 

T3 2 

T6 2 21.50 1.20 21.53 1.25 

T13 2 8.0 

T15 2 9.0 19.45 -0.13 34.77 17.36 


T16 2 13.8 23.64 1.28 31.65 22.35 0.04 

T44 2 21.0 22.65 1.34 22.64 1.35 22.67 1.39 

T78 2 21.1 22.40 1.42 23.44 2.48 22.19 1.21 

T121 2 17.4 21.07 0.66 19.34 -1.07 21.31 0.83 

T123 2 25.0 21.48 1.09 20.80 0.50 21.66 1.26 

T128 2 16.9 21.93 1.10 

T160 2 12.9 

T179 2 19.6 20.56 0.66 22.15 2.28 20.25 0.35 

T183 2 21.44 1.21 22.16 1.91 21.33 1.08 

T187 2 21.57 1.19 21.88 1.51 21.50 1.13 

Valine 

V10 1 10.4 22.52 0.91 28.21 21.70 -0.07 

V10 2 12.8 19.56 0.66 22.13 19.19 0.31 

V36 1 11.2 21.16 0.75 

V36 2 12.3 21.09 0.67 21.97 

V38 1 18.5 22.09 0.83 23.20 2.03 21.92 0.67 

V38 2 16.2 20.58 0.82 22.08 2.42 20.43 0.64 

V39 1 24.1 21.08 0.89 21.14 1.00 

V39 2 22.0 22.03 0.95 22.06 1.01 

V50 1 14.9 22.32 0.58 19.95 22.70 0.94 

V50 2 13.2 20.00 0.68 17.80 20.26 0.97 

V58 1 12.7 21.64 1.29 30.67 20.19 -0.24 

V58 2 13.5 22.31 1.18 30.02 21.00 -0.16 

V65 1 6.4 20.72 0.90 22.51 

V65 2 8.8 21.14 0.93 21.74 1.65


V82 1 17.7 20.81 0.82 20.09 0.08 

V82 2 16.6 20.37 0.72 19.79 0.10 

V96 1 13.3 19.60 0.23 21.73 19.08 -0.32 

V96 2 15.0 19.04 0.29 19.83 1.04 18.87 0.13 

V127 1 15.8 21.62 0.78 19.64 -1.32 21.84 1.05 

V127 2 17.2 20.59 0.72 19.02 -0.93 20.89 0.95 

V133 1 17.9 21.22 0.97 22.43 2.24 20.92 0.67 

V133 2 18.4 21.99 1.16 22.69 1.76 21.77 0.95 

V174 1 13.3 22.88 0.95 31.40 21.37 -0.49 

V174 2 12.5 24.96 0.97 35.55 23.21 -0.83 

Leucine 

L11 1 11.1 27.14 1.00 18.89 28.30 2.40 

L11 2 9.2 26.90 0.99 18.65 28.30 2.39 

L43 1 16.1 25.49 0.96 27.78 3.35 25.24 0.69 

L43 2 15.6 25.52 0.94 27.63 3.15 25.26 0.72 

L52 1 13.6 26.18 0.65 25.88 0.34 

L52 2 15.0 24.99 0.56 25.93 24.81 0.39 

L57 1 21.4 25.94 0.72 28.07 2.74 25.61 0.39 

L57 2 20.4 21.82 0.85 24.23 3.21 21.40 0.44 

L73 1 13.8 25.49 0.96 24.36 -0.30 

L73 2 13.4 21.30 0.97 25.98 20.34 -0.02 

L74 1 22.4 26.03 0.99 27.27 2.17 25.78 0.75 

L74 2 21.8 22.44 0.85 23.95 2.39 22.12 0.55 

L95 1 15.2 25.21 0.75 22.60 25.64 1.20 

L95 2 14.6 23.20 0.78 20.84 -1.73 23.72 1.21 

L113 1 20.2 24.42 0.34 25.63 1.59 24.22 0.15 

L113 2 22.3 21.37 0.64 22.17 1.45 21.27 0.53 

L114 1 21.6 26.00 1.22 26.00 1.24 

L114 2 22.0 22.35 1.01 22.33 0.95 

L131 1 13.3 22.74 0.79 21.14 22.69 0.70 

L131 2 12.5 25.78 0.71 21.89 26.09 1.07

L145 1 8.9 23.96 0.70 16.25 

L145 2 6.5 24.01 0.62 14.34 


L148 1 13.2 26.21 0.92 31.96 25.03 -0.32 

L148 2 15.4 23.33 1.14 27.21 22.59 0.42 

L161 1 11.3 24.89 0.72 23.66 25.39 1.18 

L161 2 10.6 21.78 0.83 19.26 22.39 1.42 

L165 1 10.1 24.05 0.89 17.02 25.60 2.34 

L165 2 11.0 26.53 1.03 19.74 27.83 2.26 

L166 1 8.8 22.89 0.74 

L166 2 7.7 24.99 0.86 26.66 

L171 1 10.1 21.06 0.82 36.23 18.23 -2.00 

L171 2 8.9 26.65 0.99 23.97 

L176 1 17.6 24.89 0.72 27.48 3.25 24.51 0.36 

L176 2 18.5 21.98 0.70 24.08 2.64 21.66 0.40 

Isoleucine 

I5 2 17.94 0.95 17.86 0.87 17.96 0.97 

I5 1 12.76 0.82 12.66 0.71 

I9 2 13.9 18.78 0.77 16.02 19.39 1.35 

I9 1 16.6 10.64 0.31 9.09 -1.20 11.00 0.64 

I21 2 23.8 17.24 0.85 17.29 0.91 17.24 0.87 

I21 1 24.3 12.79 0.85 12.86 0.93 

I30 2 10.4 17.96 0.82 23.37 17.09 -0.06 

I30 1 12.0 13.35 0.64 15.00 13.15 0.55 

I31 2 11.9 18.45 0.75 28.85 16.71 -0.92 

I31 1 9.8 14.65 0.34 33.74 11.31 -2.95 

I33 2 10.6 17.24 0.71 8.89 18.77 2.26 

I33 1 12.2 12.24 0.08 9.89 12.65 0.45 

I68 2 11.4 19.25 0.79 28.19 17.44 -0.91 

I68 1 8.4 13.87 0.56 9.07 

I90 2 15.6 18.42 0.41 15.93 -2.28 18.93 0.92 

I90 1 16.7 12.90 0.53 10.88 -1.52


I97 2 9.1 18.43 1.01 8.34 19.69 2.37 

I97 1 11.4 14.99 0.88 9.50 15.78 1.68 

I104 2 16.0 17.84 0.90 15.86 -2.05 18.13 1.19 

I104 1 14.4 10.34 0.71 7.50 10.70 1.14 

I118 2 22.6 15.96 0.66 15.47 0.17 16.02 0.75 

I118 1 23.0 13.16 0.86 12.89 0.58 13.23 0.91 

I154 2 13.7 16.96 0.76 23.43 15.97 -0.23 

I154 1 16.3 11.78 0.73 17.48 6.40 10.94 -0.16 

I170 2 9.5 18.41 0.71 40.65 15.06 -2.55 

I170 1 8.6 12.88 0.68 32.52 10.26 -1.98 

I193 2 17.46 0.81 17.55 0.91 17.42 0.78 

I193 1 13.04 0.83 13.15 0.94 13.00 0.80 

a Conditions: 25 ºC, pH 7.2. The chemical shifts in the cz- 186/ /La 3+ complex were measured 

from 13 C-HSQC spectra of the sample containing 13 C/ 15 N labeled cz- 186 in the presence of 1 

equivalent La 3+ . Whenever possible, chemical shifts of the cz- 186/ /Dy 3+ and cz- 186/ /Yb 3+ 

complexes were measured from 13 C-HSQC spectra of samples prepared with 1:1 mixtures of La 3+ 

and Dy 3+ , or La 3+ and Yb 3+ , respectively. 13 C chemical shifts of methyl groups for which no 1 H 

chemical shift is reported were measured from the pd exchange peaks in 2D or 3D methyl Cz-EXSY 

spectra, whichever gave better resolution. When neither 13 C nor 1 H chemical shifts are indicated, 

the expected cross-peak could not be identified either because of spectral overlap (e.g. in the case 

of vanishing PCS) or strong PRE.


Table S2.2 Number of correctly assigned methyl groups of Met, Thr, and Ala residues of cz- 186 

using the program Possum a 

a Calculations were performed using the experimental data of Table S2.1 and simulated data, 

where the paramagnetic chemical shifts of Table S2.1 were replaced by chemical shifts back- 

calculated from the crystal structure of 186 and the tensors used in the present study. Two 

additional sets of simulated data were generated by addition of structural noise to the PDB 

coordinates of 186. The structural noise followed a Gaussian distribution of 0.25 and 0.5 Å 

standard deviation, resulting in a Maxwell-Boltzmann distribution of atomic displacements with 

maxima at 0.35 and 0.7 Å, respectively. The columns marked “Dy max”, “Yb max”, and “La max” 

report the number of methyl groups for which data in the paramagnetic state were available to the 

program. (Additional peaks observed in the diamagnetic state remained unassigned.) The results 

are reported for calculations where the diamagnetic chemical shifts were supplemented only with 

data from Dy 3+ (light yellow), Yb 3+ (light blue) or both (grey). The rows marked with the % symbol


display the percentage of correctly assigned methyl groups for all three residues. The program 

Possum is available from http://compbio.chemistry.uq.edu.au/bmmg/christophe.


Table S2.3 Number of correctly assigned methyl groups of Val, Leu, and Ile residues of cz- 186 

using the program Possum with methyl connectivity information in the Yb 3+ complex a


a Calculations were performed using the experimental data of Table S2.1 and simulated data as 

described in the footnote of Table S2.2. As each Val, Leu and Ile residue contains two methyl 

groups, methyl specificity and methyl connectivity information can be used as additional 

information to support the resonance assignment. (Methyl specificity information refers to 

stereospecific assignments of the methyl groups of Val and Leu and the a priori distinction of 2 

and 1 methyl groups of Ile. Methyl connectivity information refers to the knowledge of which peaks 

arise from the same residue.) The results of four different combinations are shown, with and 

without methyl specificity information in the paramagnetic complexes, and with and without methyl 

specificity information in the diamagnetic complex. It was assumed that no methyl connectivity 

information can be established for the Dy 3+ complex because of strong PRE. The data are 

presented in the same format as in Table S2.2. Assignments were counted as correct whenever a 

methyl cross-peak was assigned to the correct residue, disregarding the stereospecific correctness 

of the assignment. Note that the maximum number of assignable methyl groups reported in the 

column marked “La max” can vary when both Dy 3+ and Yb 3+ data are used, because Possum has 

the freedom not to assign every HSQC cross-peak observed for the Dy 3+ complex to a peak 

observed for the Yb 3+ complex. This results in a small variation of the number of residues for which 

the program has paramagnetic information available and can attempt an assignment of the 

diamagnetic data.


Table S2.4 Number of correctly assigned methyl groups of valine, leucine, and isoleucine residues 

of cz- 186 using the program Possum without methyl connectivity information in the Yb 3+ complex 

a 

a The data are presented as in Table S2.3.

Chapter 3 

Numbat: new user-friendly 

method built for automatic Δχ- 

tensor determination 

3. Numbat: new user-friendly method built for automatic Δχ-tensor determination

76 Chapter 3. Numbat: new user-friendly method built for automatic Δχ-tensor determination. 

3.1 Abstract 

Pseudocontact shift (PCS) effects induced by a paramagnetic lanthanide bound to a protein 

have become increasingly popular in NMR spectroscopy as they yield a complementary set of 

orientational and long-range structural restraints. PCS are a manifestation of the χ-tensor 

anisotropy, the Δχ-tensor, which in turn can be determined from the PCS. Once the Δχ-tensor has 

been determined, PCS become powerful long-range restraints for the study of protein structure and 

protein-ligand complexes. Here we present the newly developed package Numbat (New User- 

friendly Method Built for Automatic Δχ-Tensor determination). With a Graphical User Interface 

(GUI) that allows a high degree of interactivity, Numbat is specifically designed for the 

computation of the complete set of Δχ-tensor parameters (including shape, location and orientation 

with respect to the protein) from a set of experimentally measured PCS and the protein structure 

coordinates. Use of the program is illustrated by building a model of the complex between the E. 

coli DNA polymerase III subunits ε186 and θ using PCS. 

3.2 Keywords 

paramagnetic NMR · pseudocontact shift · magnetic susceptibility tensor · software · 

program · unique tensor representation 

3.3 Abbreviations 

α Subunit α of the E. coli polymerase III 

ε186 N-terminal 185 residues of the E. coli polymerase III subunit ε 

θ Subunit θ of the E. coli polymerase III 

CSA Chemical shielding anisotropy 

GUI Graphical user interface 

HOT The bacteriophage P1-encoded homolog of θ 

PCS Pseudocontact shift 

RACS Residual anisotropic chemical shift 

RDC Residual dipolar coupling 

UTR Unique Δχ-tensor representation



Paramagnetic lanthanide ions bound to the natural metal-binding site of a metalloprotein or 

introduced via a lanthanide tag provide a number of paramagnetic effects that can be distance 

dependent (i.e. paramagnetic relaxation enhancement), orientation dependent (i.e. residual dipolar 

couplings, RDC), or a combination of both, like cross-correlated relaxation effects and 

pseudocontact shifts (PCS;(Bertini et al., 2002, Pintacuda et al., 2004)). PCS present particularly 

valuable structural restraints, as they are easy to measure and provide long-range information that 

would be difficult to obtain by other techniques. PCS originate from unpaired electron spins which 

lead to an anisotropic magnetic susceptibility tensor (χ-tensor). PCS restraints induced by 

lanthanide ions have been used to investigate structural and dynamical properties of proteins 

(Allegrozzi et al., 2000, Bertini et al., 2001, Bertini et al., 2004, Gaponenko et al., 2004, Jensen et 

al., 2006, Eichmüller et al., 2007, Wang et al., 2007) and protein-ligand complexes (John et al., 

2006, Pintacuda et al., 2007). 

In order to apply PCS restraints, eight variables have to be determined. These comprise the 

lanthanide position (three Cartesian coordinates), three angles (e.g. Euler angles) that relate the 

molecular frame to the χ-tensor frame, and the axial and rhombic anisotropy parameters of the χ- 

tensor. (Since PCS depend only on the χ-tensor anisotropy Δχ rather than the absolute magnitude of 

the χ-tensor, it is sufficient to determine the anisotropy parameters represented by the Δχ-tensor.) 

Several integrated software tools are available for the determination and study of the alignment 

tensor using RDCs (Dosset et al., 2000, Zweckstetter et al., 2000, Valafar et al., 2004, Wei et al., 

2006). For the situation where the 3D structure of the protein is known a priori, corresponding 

tools for the determination of the Δχ-tensor from PCS have been developed but are more limited in 

scope. The program Fantasia (Banci et al., 1996) and its extension Fantasian (Banci et al., 1997) 

can fit the magnitude and Euler angles of the Δχ-tensor using a set of experimental PCS but 

requires prior knowledge of the metal coordinates. The program Platypus (Pintacuda et al., 2004) 

can simultaneously fit the Δχ-tensor and assign the signals of 15 N-HSQC spectra of samples 

containing diamagnetic and paramagnetic lanthanides, but assumes that the 15 N-HSQC peaks are 

sufficiently well resolved such that the paramagnetic peaks can be unambiguously associated with 

their diamagnetic partners. The program Echidna (Schmitz et al., 2006) uses assigned diamagnetic 

15 N-HSQC cross-peaks of a uniformly 15 N-labelled protein to determine the magnitude and Euler 

angles of the Δχ- tensor and, simultaneously, the assignment of the paramagnetic 15 N-HSQC cross- 

peaks. It also requires prior knowledge of the approximate metal ion position. In principle, the 

structure refinement packages Xplor-NIH (Schwieters et al., 2003, Schwieters et al., 2006) with the


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.


3.6 Program Features 

3.6.1 GUI 

The graphical user interface (GUI) of Numbat was built with the GTK+ library (Krause, 

2007) that is part of standard installations of recent Linux systems. Figure 3.1 shows two 

screenshots of the main interface of Numbat illustrating the intuitive and flexible user interface. 

Figure 3.1 Screenshots of Numbat main windows. (a) Graphical User Interface for the 

selection Structure and Data. Four PCS data sets can be loaded simultaneously under 

the tabs PCS1 to PCS4. The list of all atoms is displayed in the main frame and can be 

filtered with the Display tab to show only the atom or residue types of interest. The 

experimental PCS and the tolerance can be directly modified, and only atoms that are 

selected (see the column labelled “use?”) are taken into account in the calculations. 

The distance between the respective atom to the metal ion, the calculated PCS and the 

deviation between experimental and predicted PCS are calculated and displayed after

3.6 Program Features. 81 

each fitting procedure. (b) Graphical User Interface for Tensor Calculation. A Δχ- 

tensor can be fitted for each of the data sets PCS1 to PCS4. An additional tab 

(Multiple PCS) is for fitting different data sets that share the same metal-ion centre. 

The frame PDB selector allows the choice of the model(s) to be used from a family of 

conformers loaded. The Tensor search restraints frame allows the individual selection 

of each of the eight variables to be free, fixed or constrained between two values. The 

computed Δχ-tensor values are displayed with error estimates from the GSL 

implementation of the Levenberg-Marquardt algorithm and the corresponding unique 

tensor representation (“UTR”) is reported. 

3.6.2 Input files 

Numbat reads atomic coordinates from protein data bank (PDB; (Berman et al., 2000)) files. 

In the case of NMR structures, the entire ensemble of conformers is loaded and any subset can be 

selected for subsequent calculations. When optimizing the Δχ-tensor, PCS are back-calculated for 

each selected structure and averaged for the computation of the cost function c (equation (3.2)). 

PCS data can be read either in the Xplor-NIH format or in a format specific to Numbat. For test 

purposes, Numbat also allows the generation of PCS data (optionally with addition of Gaussian 

noise) for a user-specified Δχ-tensor. 

3.6.3 Methyl group definition 

The 1 H chemical shift of a rotating methyl group can be described as the average of the 

chemical shifts of the three 1 H spins. The selection ―methyl association‖ in the GUI allows 

definition of pseudoatom names for any methyl group for which the experimental PCS value is to 

be treated as the average of the PCS of the three 1 H nuclei. The pseudoatom names can be used to 

identify the experimental PCS values of methyl groups in the input file. Alternatively, the PCS 

values of methyl groups can be interactively entered via the user-interface. 

3.6.4 Optimization of the tensor parameters 

In order to give the user a maximum of flexibility, any subset of the eight Δχ-tensor 

variables can be optimized with the remaining ones fixed to user-specified values. Such a situation 

occurs, for example, when a protein-ligand complex is studied where the protein is tagged with a 

lanthanide. First, the Δχ-tensor can be determined using the PCS measured for the protein. Fitting 

of the position and orientation of the Δχ-tensor with respect to the ligand can subsequently be


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


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 NMR 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


Different conventions have been used in the literature to report Δχ-tensor parameters, 

including different definitions of Euler angles, choice of principal and secondary axis of the Δχ- 

tensor, and units of Δχ-tensor magnitudes. Numbat can report the Δχ-tensor parameters in many 

different conventions but uses as a default the following conventions: (i) The axes of the Δχ-tensor 

frame are labelled such that |Δχzz| ≥ |Δχyy| ≥ |Δχxx| in analogy to alignment tensor conventions 

(Clore et al., 1998). This ensures that axial and rhombic components are always of the same sign. 

(ii) The Euler angles α, β and γ are expressed in the ―ZYZ‖ convention, i.e., the first rotation of 

angle α is around the z axis of the protein frame, the second rotation of angle β is around the new y’ 

axis and the last rotation of angle γ is around the new z’’ axis (Figure 3.2). While for an 

asymmetric object the Euler angles are uniquely defined if the angles α, β and γ are taken in the 

intervals [0, 2π[, [0, π[, [0, 2π[, respectively, ambiguities arise for symmetric objects. Therefore, we 

chose the interval [0, π[ for all three angles, eliminating the potential ambiguities arising from the 

four symmetry-related Δχ-tensors that generate the same PCS values. In the case of β = 0, an 

infinite number of combinations of and would produce the same overall rotation. In this case, 

we set γ = 0. These two rules ensure that any Δχ-tensor is unambiguously reported as a single set of 

parameters which is referred to in the GUI as UTR (Unique Δχ-Tensor Representation). 

Figure 3.2 Euler angle definitions used by Numbat. The relative orientation of the Δχ- 

tensor frame with respect to the protein frame is defined by Euler rotations of angle α, β 

and γ in the ZYZ convention. (a) A right-handed rotation of angle α around the z axis is 

applied to the protein frame xyz to give the frame x’y’z’. (b) A second rotation of angle 

β around the new axis z’ is applied to the frame x’y’z’ to give x’’y’’z’’. (c) The last 

rotation of angle γ around the z’’ axis gives the Δχ-tensor frame. 

3.6.10 Error analysis 

The Levenberg-Marquardt algorithm is used to minimize the cost c (equation (3.2)), but the 

quality of the fit cannot be assessed without further error analysis. Therefore, in addition to the 

uncertainty values provided by the GSL implementation of the minimiser, Numbat embeds a Monte


Carlo protocol with random Gaussian noise added either to the atomic coordinates of the molecule 

or to the experimental PCS values. The robustness of the Δχ-tensor fit with respect to the PCS data 

set can also be tested by random subset selection of the PCS values used. Resulting Δχ-tensor 

orientations are displayed in a Sanson-Flamsteed projection (Bugayevskiy et al., 1995) using the 

plotting utility gnuplot. 

3.6.11 Visualization 

Graphical visualization of the Δχ-tensor frame and isosurfaces of PCS values in the 

structure of the molecule presents a convenient way to assess the similarity of the principal axes of 

multiple Δχ-tensors and the similarity of their respective isosurfaces. To this end Numbat interfaces 

with the molecular viewers MOLMOL (Koradi et al., 1996) and PyMOL (DeLano, 2002) by 

generating suitable macro files and displaying the Δχ-tensor frame and corresponding PCS 

isosurfaces in superimposition with the protein studied, as illustrated in Figure 3.3. The files of the 

macros, PCS potential and PDB file containing the coordinates of the protein together with 

coordinates of the metal ion and Δχ-tensor axes can also be saved for later use. 

Figure 3.3 Visualisation of the Δχ-tensor in MOLMOL and PyMOL, and display of 

its orientational uncertainty in a Sanson-Flamsteed projection plot. Numbat can 

directly call MOLMOL and PyMOL to display the axes of the fitted Δχ-tensor and 

PCS isosurfaces at user-defined contour levels. The orientational uncertainty of the 

Δχ-tensor frame can be evaluated by a Monte-Carlo protocol with random additions 

of noise to the structure coordinates and/or PCS data, with optional random


selection of subsets of data. Numbat calls gnuplot to display the results in a Sanson- 

Flamsteed projection plot. 

3.6.12 Output 

The list of PCS can be saved in Xplor-NIH format and in a Numbat-specific format. The 

weak molecular alignment in the magnetic field resulting from a non-vanishing Δχ-tensor can be 

described by an alignment tensor with principal axes parallel to those of the Δχ-tensor and axial and 

rhombic components that are directly proportional to Δχax and Δχrh, respectively (Tolman et al., 

1995). Numbat calculates the RDC between two spins A and B for the situation of a completely 

rigid molecule, using (Bertini et al., 2002) 

(3.5) 

where γA and γB are the magnetogyric ratios of spins A and B, respectively, ħ the Planck 

constant divided by 2π, S the order parameter, rAB the internuclear distance, and AB, AB, AB the 

coordinates of the vector AB expressed in the Δχ-tensor frame. The RDC values are reported in 

Xplor-NIH (Schwieters et al., 2003, Schwieters et al., 2006) and Pales (Zweckstetter et al., 2000) 

format. 

Finally, Numbat can generate PDB files where the Δχ-tensor is reported in a format ready 

for use with MOLMOL or PyMOL for rigid-body docking alignment, or for further refinement by 

Xplor-NIH. 

3.7 Study case 

The proteins ε and θ are subunits of the complex of proteins constituting E. coli DNA 

polymerase III. The complex between the N-terminal domain of ε (ε186) and θ has been 

extensively studied using PCS data (Pintacuda et al., 2006, Pintacuda et al., 2007). In light of the 

recent crystal structure of the complex between ε186 and the θ homolog HOT (Kirby et al., 2006), 

we illustrate in the following the features of Numbat by revisiting the NMR structure of the 

complex between ε186 and θ which was derived from PCS induced by Dy 3+ and Er 3+ ions bound to 

the natural metal-binding site of ε186 (Pintacuda et al., 2006).

3.7 Study case. 87 

The coordinates of the A chain in the PDB deposition 2IDO (Kirby et al., 2006) was used as 

the structural model for ε186. The structural model of θ was conformer 10 of the NMR structure of 

θ in complex with ε186 (PDB accession code 2AXD; (Keniry et al., 2006)). This conformer was 

chosen because it has the lowest backbone RMSD to the HOT protein (2.1 Å) for residues 9-66 (the 

structurally defined region for which meaningful PCS could be measured). The experimentally 

determined PCS values of ε186 have been reported previously (Schmitz et al., 2006) and the PCS 

values of θ are provided in the Supporting Information. All Δχ-tensor optimizations were performed 

using Numbat including the RACS correction term and a tolerance value toli of zero for all spins. 

3.7.1 Subunit ε186 

Table 3.1 presents the results of the Δχ-tensor fit to the PCS measured for ε186. Initially, 

individual eight-variable Δχ-tensor optimizations were performed using the PCS data of each 

lanthanide (Table 3.1, columns 1 and 2). Next, the Numbat GUI was updated to display the 

deviations between the experimental and back-calculated PCS for the Δχ-tensors found. Several 

atoms showed deviations > 0.15 ppm between the experimental and back-calculated PCS (15 out of 

199 and 8 out of 255 atoms in the case of Dy 3+ and Er 3+ , respectively. Without the RACS 

correction, deviations > 0.15 ppm where observed for 36 and 7 atoms, respectively). Assuming that 

these outliers were due to problematic measurements or inaccuracies of the 3D structure, these PCS 

were removed interactively using the GUI. Re-calculation of the Δχ-tensor was found not to change 

the fitted Δχ-tensor parameters significantly for any of the lanthanide ions (results not shown). This 

can be explained by the high quality and large number of experimental PCS data available for each 

lanthanide (backbone 13 C’, 15 N and 1 H N spins), resulting in robust fits of the Δχ-tensors. 

Table 3.1 Δχ-tensors determined by Numbat in the frames of the ε186 and θ molecule 

ε186 a θ b 

Individual c Combined d Individual c Combined d Fixed e 

Dy 3+ Er 3+ Dy 3+ Er 3+ Dy 3+ Er 3+ Dy 3+ Er 3+ Dy 3+ Er 3+ 

Δχax f 42.3 -10.6 42.3 -10.7 40.1 -13.0 40.2 -10.0 42.3 -10.7 

Δχrh f 5.3 -5.1 5.3 -5.1 14.8 -6.5 14.9 -4.8 5.3 -5.1 

α g 169.5 144.2 169.5 143.9 27.7 23.7 27.7 19.9 42.2 34.9 

β g 30.2 29.1 30.2 29.2 114.6 108.8 113.9 118.2 119.2 121.5 

γ g 134.6 126.9 134.7 126.8 28.4 170.6 27.3 177.7 44.7 177.4 

mx h 29.4 29.3 29.4 29.4 6.2 9.5 6.4 6.4 4.3 4.3 

my h 31.9 32.0 31.9 31.9 -7.5 -7.2 -7.5 -7.5 -5.5 -5.5


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


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


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.


can be used to align the Δχ-tensors. Numbat reports the coordinate system of the Δχ-tensor in such 

a way that all four degenerate solutions arising from the symmetry of the Δχ-tensor about the x, y 

and z axes (Figure 3.4) can easily be visualised. Identification of the correct solution requires 

additional information, such as proper steric interactions, chemical shift perturbation data or 

knowledge of the biological function of the complex. The most objective way, however, is by 

simultaneous evaluation of the Δχ-tensors of different lanthanides (Pintacuda et al., 2006). 

In the case of the complex between ε186 and θ, the Δχ-tensor frames of Dy 3+ and Er 3+ share 

a common origin for both proteins. Seven coordinates are necessary to define two Δχ-tensor frames 

sharing the same origin. Because of the second Δχ-tensor, the degeneracy of Figure 3.4 is broken. 

There are exactly 16 possibilities to align two pairs of Δχ-tensor. The lowest RMSD value resulting 

from all 16 possible 7-coordinate alignments between the two combined Δχ-tensors identified a 

single relative orientation of the two proteins as the best solution. The position of θ relative to ε186 

derived from PCS data in this way was also the correct solution. It agreed with a model of the 

complex obtained by superimposition of θ onto HOT in the ε186/HOT complex, with a backbone 

RMSD of 4.4 Å. Similarly for the Δχ-tensor of θ calculated with fixed Δχax and Δχrh values, a 

backbone RMSD of 4.3 Å was calculated relative to HOT. When PCS data from only Dy 3+ or Er 3+ 

were used, the backbone RMSD values were, respectively, 4.2 Å and 4.4 Å for the best fit to the 

ε186/HOT complex. The model of the ε186/θ complex derived from the fixed, Dy 3+ and Er 3+ data 

sets is displayed in Figure 3.5.


3.8 Conclusion 

Figure 3.4 The four degenerate solutions arising from the symmetry of the 

Δχ-tensor around the x, y and z axes. All four possibilities result in the same 

calculi of PCS, hence in the same isosurfaces. 

Figure 3.5 The complex between ε186 and θ determined by superimposition 

of Δχ-tensors. The ε186/HOT complex (PDB accession code 2IDO) is shown 

for reference, with ε186 coloured in silver and HOT (residues 9-66) in 

orange. The isosurfaces correspond to the PCS induced by the Dy 3+ ion 

(from individual optimisation) contoured at +/-1.5 ppm and +/-0.5 ppm. 

Blue and red isosurfaces represent regions with positive and negative PCS, 

respectively. Residues 9-66 of θ are shown as a thin ribbon in the position 

defined by the fixed Dy 3+ and Er 3+ data (brown). 

The program Numbat is the first software package for fitting Δχ-tensors from PCS data with 

a user-friendly graphical user interface (GUI). Numbat calculations are fast, as it was written with 

open-source Linux routines in C. While the main task of Numbat is the fit of the eight Δχ-tensor

3.9 Acknowledgment. 93 

variables, the intuitive GUI combined with convenient data handling, including Monte-Carlo error 

analysis and links to the molecular viewers MOLMOL and PyMOL, offer high flexibility of use. 

The study case of the complex formed between the subunits ε186 and θ of E. coli DNA polymerase 

III illustrates the simplicity of use of Numbat. 

The program is freely available under the GNU General Public License (GPL) upon request 

(see also http://compbio.chemistry.uq.edu.au/bmmg/christophe/numbat.html). 

3.9 Acknowledgment 

Financial support from the Australian Research Council for project grants to G.O and T.H. 

is gratefully acknowledged. 




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3.11 Supporting information 

Table S3.1 Experimentally determined 1 H N PCS for θ in complex with ε186 at pH 7.0 and 25°C a 

Residue PCS Dy 3+ (ppm) PCS Er 3+ (ppm) 

ASP 9 -1.28 0.31 

GLN 10 -1.19 0.3 

THR 11 -1.11 0.25 

GLU 12 -1.24 0.27 

MET 13 -1.84 0.38 

ASP 14 -2 0.32 

LYS 15 -1.5 

VAL 16 -1.97 0.13 

VAL 18 -1.91 0.14 

ASP 19 -1.32 -0.03 

LEU 20 -1.29 -0.03 

ALA 21 -1.37 -0.14 

ALA 22 -0.57 -0.18 

ALA 23 0.15 -0.38 

GLY 24 0.37 -0.46 

VAL 25 0.29 -0.26 

ALA 26 0.54 -0.3 

PHE 27 1.21 

LYS 28 0.85 -0.31 

GLU 29 0.68 -0.19 

ARG 30 0.81 -0.23 

ASN 32 0.72


MET 33 0.6 

VAL 35 0.02 

ILE 36 -0.29 0.08 

ALA 37 -0.12 0 

GLU 38 -0.22 0.04 

ALA 39 -0.4 

VAL 40 -0.55 

GLU 41 -0.51 -0.06 

ARG 42 -0.56 0.09 

GLU 43 -0.84 0.12 

GLU 46 -0.66 0.11 

LEU 48 -0.71 -0.01 

ARG 49 -0.58 0.08 

SER 50 -0.45 0.05 

TRP 51 -0.5 

PHE 52 -0.58 

ARG 53 -0.38 

GLU 54 -0.26 -0.01 

ARG 55 -0.23 -0.07 

LEU 56 -0.15 -0.09 

ILE 57 0.02 -0.09 

ALA 58 0.14 -0.11 

HIS 59 0.3 -0.18 

ARG 60 0.39 -0.17 

LEU 61 0.42 -0.15 

SER 63 0.8 -0.27 

VAL 64 0.71 -0.19 

ASN 65 0.8 -0.21 

LEU 66 -0.26 

a Experimental conditions as described in Pintacuda et al. (2006) J. Am. Chem. Soc. 128, 3696- 

3702


Table S3.2 Comparison of θ Δχ-tensor parameters when using only conformer 10 a or all 

conformers b of the NMR structure of . 

Fixed a Fixed(Family) b 

Dy 3+ Er 3+ Dy 3+ Er 3+ 

Δχax c 42.3 -10.7 42.3 -10.7 

Δχrh c 5.3 -5.1 5.3 -5.1 

α d 42.2 34.9 40.5 34.5 

β d 119.2 121.5 118.9 121.2 

γ d 44.7 177.4 38.1 174.8 

mx e 4.3 4.3 4.7 4.7 

my e -5.5 -5.5 -5.8 -5.8 

mz e -19.8 -19.8 -19.7 -19.7 

a The Δχ-tensor determined using the fixed optimisation scheme relative to θ conformer 10 

b The Δχ-tensor determined using the fixed optimisation scheme relative to simultaneously all 12 

deposited θ conformers 

c In units of 10 -32 m 3 

d Euler rotations in the ZYZ convention (degrees) 

e Metal ion coordinate (Å) in the protein frame (PDB data set 2AXD)

Chapter 4 

Protein Structure 

Determination from 

Pseudocontact Shifts using 

ROSETTA 

4. Protein Structure Determination from Pseudocontact Shifts using ROSETTA 

Christophe Schmitz a , Robert Vernon b , Gottfried Otting c , David Baker b and Thomas Huber a 

a School of Chemistry and Molecular Biosciences, University of Queensland, Brisbane, QLD 4072, 

Australia 

b Department of Biochemistry, University of Washington, University of Washington, Seattle, WA 

98195 

c Research School of Chemistry, Australian National University, Canberra, ACT 0200, Australia 

Manuscript submitted to the Proceedings of the National Academy of Sciences of the United States 

of America.

102 Chapter 4. Protein Structure Determination from Pseudocontact Shifts using ROSETTA. 

4.1 Abstract 

Pseudocontact shifts (PCS) arise from paramagnetic metal ions bound to proteins and are 

manifested as large changes in chemical shifts detected in nuclear magnetic resonance (NMR) 

spectra. PCS data constitute long-range restraints on the positions of nuclear spins relative to the 

coordinate system of the magnetic susceptibility anisotropy tensor ( -tensor) of the metal ion. 

Protein structure determination using PCS data only, however, is hampered by the difficulty to 

determine the -tensor and metal position without knowledge of the protein structure. We have 

circumvented this problem in the program PCS-ROSETTA by using the structure prediction 

program ROSETTA to generate the models required for fitting of the -tensor parameters. PCS 

restraints implemented in the fragment assembly step of PCS-ROSETTA proved highly efficient in 

biasing the sampling of the conformational space towards the correct target structure. The results 

show that using a combination of chemical shift and PCS data, ROSETTA can determine structures 

accurately for proteins of up to 150 residues. Lanthanides can be incorporated into proteins quite 

generally through metal binding tags, and the combination of these data with the PCS-ROSETTA 

method provides a powerful new approach to protein structure determination. 


The three-dimensional (3D) structure of proteins is a prerequisite for understanding protein 

function, protein-ligand interactions and rational drug design. Protein structures can be readily 

determined by NMR spectroscopy. The most difficult part of an NMR structure determination 

typically is the assignment of sidechain chemical shifts and NOESY peaks. This bottleneck can 

potentially be avoided if methods for computing high accuracy structures from backbone-only 

NMR experiments can be developed. 

PCSs are a potentially rich source of structural information that are manifested as large 

changes in chemical shifts in the NMR spectrum caused by a non-vanishing magnetic susceptibility 

anisotropy tensor ( -tensor) of a paramagnetic metal ion. The PCS (in ppm) of a nuclear spin i 

depends on the polar coordinates ri, i, and i of the nuclear spin with respect to the -tensor 

frame of the metal ion and the axial and rhombic components of the -tensor:


(4.1) 

The -tensor defines a coordinate system in the molecule that is centered on the metal ion 

and is fully described by eight parameters ( ax, rh, three Euler angles relating the orientation of 

the Δχ-tensor to the protein frame, and the coordinates of the metal ion). Therefore, the Δχ-tensor 

can be determined using PCS data from at least eight nuclear spins, provided the coordinates of the 

spins are known. 

As PCSs can be measured for nuclear spins 40 Å away from the metal, they present long- 

range structure restraints exquisitely suited to characterize the global structural arrangement of a 

protein. PCSs have thus been used very successfully to refine protein structures (Bertini et al., 

2001, Gaponenko et al., 2004, Arnesano et al., 2005), dock protein molecules of known 3D 

structures (Ubbink et al., 1998, Pintacuda et al., 2006) and determine the structure of small 

molecules bound to a protein of known 3D structure (John et al., 2006, Pintacuda et al., 2007, 

Zhuang et al., 2008). The need for atom coordinates to determine the Δχ-tensor parameters, 

however, makes it more difficult to use PCSs in de novo determinations of protein 3D structures. 

All presently available protein structure determination software that uses PCS data to supplement 

conventional NMR restraints requires estimates of ax and rh as input parameters (Banci et al., 

1998, Banci et al., 2004). These are often difficult to estimate accurately, as they depend on the 

chemical environment of the metal ion and the mobility of the paramagnetic center with respect to 

the protein. 

The ROSETTA structure prediction methodology (Simons et al., 1997) is well suited for 

taking advantages of the rich source of information inherent in PCSs. ROSETTA de novo structure 

prediction has two stages —first a low resolution phase in which conformational space is searched 

broadly using a coarse grained energy function, and second, a high resolution phase in which 

models generated in the first phase are refined in a physically realistic all atom force field. The 

bottleneck in structure prediction using ROSETTA is conformational sampling; close to native 

structures almost always have lower energies than non native structures. For small proteins ( < 100 

residues), ROSETTA has produced models with atomic level accuracy in blind prediction 

challenges (Raman et al., 2009). For larger proteins, however, structures close enough to the native 

structure to fall into the deep native energy minimum are generated seldom or not at all. This 

sampling problem can be overcome if even very limited experimental data is available to guide the 

initial low resolution search. For example, CS-ROSETTA uses NMR chemical shifts to guide


fragment selection and constrain backbone torsion angles, greatly improving the final yield of 

correctly folded protein models (Shen et al., 2008). As ROSETTA in favorable cases is capable of 

generating protein structures very close to experimentally determined structures from sequence 

information alone (Bradley et al., 2005), it is of great interest to combine ROSETTA with readily 

accessible experimental data to determine protein structures. 

In this paper we describe the incorporation of PCS data into ROSETTA. We show that this 

new PCS-ROSETTA method can generate accurate structures for proteins of up to 150 amino acids 

in length even from quite limited data sets. 

4.3 Results 

4.3.1 Test set 

We tested the new PCS-ROSETTA method (see Methods) on a benchmark of nine proteins 

for which chemical shifts and PCSs have been published. ArgN repressor was determined twice 

with PCS data measured from paramagnetic metal ions at two different sites. The proteins were 

between 56 to 186 amino acid residues in size, had different folds and had between 82 and 1169 

PCSs measured from one to eleven different metal ions located at a single metal binding site [Table 

4.1 and supporting information (SI) Table S4.1]. Fragments for each protein were selected with CS- 

ROSETTA using available chemical shift data and were used for all calculations. Structures of 

proteins with significant sequence similarity to the target proteins were explicitly excluded from the 

CS-ROSETTA database. 

Table 4.1 Protein structures used to evaluate the performance of PCS-ROSETTA 

Targets PDB ID Nres a NM b c PCS-ROSETTA 

Npcs 

run d 

CS-ROSETTA 

run e 

rmsd f conv g Q h rmsd f conv g 

protein G (A) 3GB1 56 3 158 0.61 0.92 0.06 0.80 0.88 (Wilton et al., 2008) 

Refcs i Refpcs j 

calbindin (B) 1KQV 75 11 1169 1.46 2.04 0.16 4.96 4.37 (Balayssac et al., 2006) 

θ subunit (C) 2AE9 76 2 91 1.65 4.35 0.07 8.90 8.75 (Mueller et al., 2005) 

(Saio et al., 

2009) 

(Bertini et al., 

2001) 

(Schmitz et al., 

2008) 

ArgN k (D) 1AOY 78 3 222 0.98 2.38 0.08 6.93 5.32 (Su et al., 2008) (Su et al., 2008) 

ArgN l (E) 1AOY 78 2 82 1.03 2.25 0.09 8.01 6.64 (Su et al., 2008) (Su et al., 2009a) 

N-calmodulin 

(F) 

1SW8 79 2 125 2.34 1.85 0.09 4.69 3.68 (Bertini et al., 2004) 


2004)

thioredoxin (G) 1XOA 108 1 90 2.58 2.64 0.23 

parvalbumin 

(H) 

4.98 6.06 

(Lemaster et al., 1988, 

Chandrasekhar et 

al., 1991) 

1RJV 110 1 106 11.26 10.42 0.20 11.80 11.20 (Baig et al., 2004) 

calmodulin (I) 2K61 146 4 408 2.80 2.12 0.14 6.35 5.55 (Bertini et al., 2009) 

ε186 m (J) 1J54 186 3 738 20.57 17.54 0.36 15.46 17.23 (DeRose et al., 2002) 

a Number of residues. 

b Number of metal ions for which PCS data were measured. 

c Total number of PCSs measured. 


(Jensen et al., 

2006) 

(Baig et al., 

2004) 


2009) 

(Schmitz et al., 

2006) 

d The structures used to calculate the rmsds were identified using the combined PCS-score and 

ROSETTA full atom energy on the whole protein sequence. 

e The structures used to calculate the rmsds were identified by the ROSETTA full-atom energy on 

the whole protein sequence. 

f C α rmsd (with respect to the native structure) of the structure of lowest score, in Å. All C rmsd 

values were calculated using the core residues defined in SI Table S4.2. 

g Average C α rmsd calculated between the lowest score structure and the next four lowest scoring 

structure, in Å. The rmsd values were calculated on the whole protein sequence. 

h Quality factor Q = rms(PCSi cal – PCSi exp ) / rms(PCSi exp ) calculated on the structure of lowest 

PCS-ROSETTA score. 

i Reference for the experimental chemical shifts. 

j Reference for the experimental PCSs. 

k PCSs measured with a covalent tag attached to the N-terminal domain of the E. coli arginine 

repressor (ArgN). 

l PCSs measured with a non-covalent tag bound to ArgN. 

m N-terminal 186 residues of the subunit of the E. coli polymerase III. 

4.3.2 Capacity of the PCS Score to Identify Native-like Structures 

The PCS score describes a model’s agreement with observed PCS data by calculating the 

expected PCS data given the structure. To calculate this, a three dimensional grid search is used to 

determine the metal coordinates and Δχ-tensor components necessary for producing an optimal 

match between calculated and observed data (see Materials and Methods). The capacity of the PCS 

score to identify native like models was tested on sets of 3000 CS-ROSETTA structures for each of 

the nine test proteins. These test structures were produced using a reduced fragment set and


included native fragments to ensure that some of the models were similar to the target structure. 

The C rmsd of the decoy with the lowest PCS score was always small (below 2.3 Å) with respect 

to the target protein (Figure 4.1). In addition, for all target proteins for which PCSs were available 

from two or more paramagnetic metal ion, low C rmsd values correlated with low PCS scores. 

This indicates that the PCS score can be used not only to identify near-native structures, but also to 

bias conformational sampling towards the native structure during the fragment assembly. 

Comparisons between the ROSETTA low resolution energy function and PCS score are shown in 

SI Figure S4.1. 

Figure 4.1 Fold identification by pseudocontact shifts. 3000 decoys were generated using CS- 

ROSETTA. In order to ensure the presence of decoys with low rmsd values to the target structure, 

the starting set of peptide fragments was reduced and included fragments from the known target 

structures. PCS scores are plotted versus the C rmsd to the target structure. The targets are 

labeled A-J as in Table 4.1. The PCS score correlates strongly with the C rmsd. 

PCSs from eleven different lanthanides were available for calbindin. In order to explore the 

value of using PCSs from multiple lanthanides, we rescored the structures using PCSs from both 

individual and multiple lanthanides. Linear regressions of PCS score versus rmsd had slopes 

ranging from 0.03 to 5.17 (average 2.26) for single data sets. Pairwise combination of PCS sets 

resulted in increased regression slopes ranging from 0.15 to 7.42 (average 3.84). Using all PCS sets 

resulted in a slope greater than 11, showing that PCSs from multiple metal ions greatly facilitate 

identification of native-like protein folds. 

4.3.3 Comparison of PCS-ROSETTA with CS-ROSETTA


10000 decoys each were generated with CS-ROSETTA and PCS-ROSETTA. Both 

computations used the same fragment set, taking into account secondary structure information from 

chemical shift measurements. Figure 4.2 illustrates the ability of the PCS score to bias sampling 

towards the native structure. For seven out of the ten structure calculations, the PCSs dramatically 

increased the frequency with which decoys with low C rmsd to the reference structure were found. 

The effect was particularly pronounced for protein targets with larger PCS data sets. For example, 

more than a third of the decoys found for calmodulin had a C rmsd of less than 4 Å to the target 

structure, whereas fewer than 3% met this criterion in the absence of PCS data. Similar results were 

obtained for the θ subunit, protein G, and both ArgN repressor calculations. The PCS data did not 

significantly improve the results for thioredoxin and parvalbumin for which only PCS data from a 

single paramagnetic metal ion were available. No native-like structures were found for 186 which 

may be attributed to its larger size (186 residues). To evaluate the influence of the PCS score during 

the fragment assembly, we performed an additional calculation with the PCS score as the only 

energy term (SI Text S4.1). 

The low resolution models were subjected to full atom relaxation refinement in the last step 

of the calculation, using the full atom ROSETTA force field (without inclusion of the PCS score). 

The additional minimization step did not significantly change the overall shape of the distributions, 

but tended to improve the C rmsd of native-like decoys (SI Figure S4.2) and, most importantly, 

allows recognition of the best models based on their energies. 

Rescoring full atom relaxed structures with a weighted combination of the ROSETTA and 

PCS scores further improved the recognition of near-native structures as measured by the C rmsd 

of the lowest energy structure [Table 4.1-f, PCS-ROSETTA run; Figure 4.3], with PCS-ROSETTA 

identifying low C rmsd (< 3 Å) structures in eight out of ten cases. With the exception of target C, 

for all successful targets a population of the five lowest energy structures converge to less than 3 Å 

, while the two failed targets do not improve beyond 10 Å [Table 4.1-g]. Convergence is a signal 

that the protocol has found a topology that reliably satisfies the combined score, which in the case 

of PCS-ROSETTA clearly identifies the failed models as unreliable, allowing for their rejection 

(Shen et al., 2008). In the case of target C large disordered termini prevent a clear identification of 

convergence, but convergence becomes apparent when only the core residues are considered (Table 

S4.2-g). Results with CS-ROSETTA and PCS-ROSETTA are compared in SI Figure S4.3.


Figure 4.2 Improved conformational sampling by PCS-ROSETTA. 10000 independent low 

resolution trajectories were carried out with (black) or without (red) PCS information. The plots 

show the density of C rmsd values to the target structure after the fragment assembly step. The 

targets are labeled as in Table 4.1. Corresponding plots of structures calculated with full atom 

relaxation for positioning the amino acid side chains are shown in SI Figure S4.2. The library used 

for fragment selection explicitly excluded any protein with sequence similarity to the target protein. 

The figure shows that PCS scores efficiently guide fragment assembly towards the correct target 

structure. 

Figure 4.3 Energy landscapes generated by PCS-ROSETTA. Combined ROSETTA energy and PCS 

score (using the weighting factor w(c)) are plotted versus the C rmsd to the target structure for 

structures calculated using PCS-ROSETTA. The lowest energy structures are indicated in red. The 

targets are labeled as in Table 4.1. The results show that PCS-ROSETTA is likely to generate and 

identify the correct fold.


Agreement of the structures with the experimental data can also be directly assessed by the 

quality factor Q = rms(PCSi cal – PCSi exp ) / rms(PCSi exp ), where PCSi exp is the experimental PCS 

value for the nuclear spin i 7 . A quality factor above 25% indicates failure to find a correct structure 

and a quality factor below 20% indicates that the computed structure is in good agreement with the 

experimental PCSs (Table 4.1), as in other definitions of quality factors (Cornilescu et al., 1998). 

The low quality factor of the θ subunit (7%) establishes the success of the calculation despite the 

lack of clear convergence. 

4.3.4 Successes and Limits of PCS-ROSETTA Calculations 

The results of PCS-ROSETTA calculations are summarized in Table 4.1. The structures of 

small proteins (< 80 residues, targets A to F) are easily solved by PCS-ROSETTA: the lowest PCS- 

ROSETTA energy are consistently below 2.4 Å in C rmsd relative to the native structure and have 

quality factor below 16%. For these proteins, the generation of 10000 models was ample (Figure 

4.2 A to F). The same number of decoys calculated with CS-ROSETTA did not lead to satisfactory 

convergence for targets B-C-D-E-F (Table 4.1-g), though targets C and D partially recover if 

flexible termini are removed at the full atom rescoring step (SI Text S4.2). The tag used to 

paramagnetically label ArgN (D) produced Δχ-tensor axes of significantly different orientation with 

different lanthanides (Su et al., 2008) which may explain why the PCS-ROSETTA calculations 

performed particular well with these data. 

PCS-ROSETTA succeeded in calculating the structure of a protein with 146 residues and 

PCSs from multiple lanthanides (target I). More than 62% of calculated structures had a C RMSD 

below 5 Å, while only 6.2% met that criterion for CS-ROSETTA calculation (Figure 4.2 I). This 

indicates that the PCS data score will effectively guide the sampling towards the correct fold also 

for larger proteins. While calculations on target J (186 residues) did not converge despite a large 

PCS data set, this can be attributed to a sampling problem associated with large proteins of 

complex topology (Bradley et al., 2005) which may be overcome with a modified protocol. 

Importantly, the success of a calculation can be ascertained from calculating the quality factor Q. 

Combined with the convergence criterion (Shen et al., 2008), the quality factor is an effective way 

7 Rms stands for Root Mean Square. Not to be confused with Rmsd (Root Mean Square Deviation).


to assert the success of a calculation (SI Figure S4.4). For each of the eight targets for which the 

PCS-ROSETTA calculations converged, the structure with the lowest energy is shown 

superimposed with the native structure in Figure 4.4. 

Figure 4.4 Superimpositions of ribbon representations of the backbones of the lowest energy 

structures calculated with PCS-ROSETTA (blue) onto the corresponding target structures (red). 

The protein targets are (A) protein G, (B) calbindin, (C) the θ subunit of E. coli DNA polymerase 

III, (D) the N-terminal domain of the E. coli arginine repressor (ArgN; with covalent lanthanide 

tag), (E) ArgN with non-covalent lanthanide tag, (F) the N-terminal domain of calmodulin, (G) 

thioredoxin, (H) parvalbumin, (I) calmodulin and (J) the globular domain of the ε subunit of E. coli 

DNA polymerase III. Flexible termini were omitted as described in SI Table S4.1. Only the target 

structure is shown for parvalbumin (H) and the ε subunit (J), as the calculations could not 

reproduce the correct fold for these proteins. 

4.4 Discussion 

The structural information content of the PCS effect has long been recognized, but initial 

attempts to determine the 3D structures of biomolecules by the use of PCSs were hampered by the 

difficulty to determine -tensor and structure simultaneously (Barry et al., 1971). Subsequently, 

the first 3D structure determinations of proteins relied on nuclear Overhauser effect data (Wüthrich, 

1986). Full structure determination of proteins from PCS data alone continues to be regarded as 

difficult (Bertini et al., 2002a). Owing to its modeling capabilities, PCS-ROSETTA makes it

4.4 Discussion. 111 

possible, for the first time, to determine 3D structures using PCSs as the only restraints while 

simultaneously determining all Δχ-tensor parameters and integrating PCSs from different metal 

ions. In addition, a PCS quality factor can be calculated that is highly indicative of the correctness 

of the final structure. The effect of the PCSs on improving convergence of the calculations towards 

the correct target structures is particularly remarkable if one considers that PCS data mostly were 

available only for backbone amides. 

The success of PCS-ROSETTA is based on the fact that, in contrast to scoring functions 

using chemical shift data, the PCS score is much more sensitive to global than local structure. 

Therefore, PCS data can guide the search in the low resolution fragment assembly step, greatly 

increasing the yield of near-native structures compared to CS-ROSETTA. PCSs thus present an 

ideal complement to chemical shift information that is most important in the preceding fragment 

selection step. The improved convergence alleviates the need to compute large numbers of decoys. 

It would be possible to accelerate the computations further by using the PCS score to select decoys 

with low rmsd values to the target structure prior to the computationally expensive refinement of 

amino acid side chain conformations. 

Many protein specific factors, including fold complexity, number and quality of PCS data, 

and metal site play roles in the success of PCS-ROSETTA fragment assembly and their relative 

importance is difficult to disentangle. In general, PCS data from two or more lanthanides are 

expected to assist identification of decoys with low rmsd to the target structure. While the structure 

of calmodulin, a protein with 146 residues, was successfully determined by PCS-ROSETTA, the 

structure of ε186 (186 residues) was not found by the program despite the availability of many 

PCSs overall (Table 4.1). The scarcity of PCS values for residues near the lanthanide binding site 

may have contributed to this effect. As the PCS-ROSETTA protocol did not sample structures 

below 10 Å rmsd (Figure 4.3 J) and the PCS scores of native-ε186 like structures only show a 

funnel-like energy landscape below 10 Å rmsd (Figure 4.1 J), this could also be a case where 

structures explored by the basic ROSETTA sampling protocol do not form enough native features 

for the PCS score to discriminate between them. An alternative sampling protocol, such as broken 

chain sampling (Bradley et al., 2006) or iterative refinement (Qian et al., 2007), may be the key to 

accurately modeling the structure of ε186 using PCS data. 

The present calculations were performed with proteins containing single metal binding sites. 

Clearly, data from multiple metal ions using different metal binding sites will greatly enhance the 

information content of PCS data. In particular, lanthanide ions display very different paramagnetic 

properties while their chemical similarity allows all lanthanides to bind at a given lanthanide


binding site. Several metal binding tags have recently been developed to tag proteins site- 

specifically with a paramagnetic lanthanide; for a recent review, see (Su et al., 2009b). We note that 

PCSs were as useful for targets devoid of natural metal binding sites (targets A, C, D and E) as for 

metalloproteins (Figure 4.2). 

We propose a new approach to protein structure determination in which PCS data are 

collected from natural or engineered metal binding sites, and then used to guide ROSETTA 

conformational search along with backbone chemical shift data. The accuracy and reliability of the 

lowest energy models is assessed based on the convergence of the calculation and the PCS quality 

factor. With multiple independent lanthanide datasets and improved conformational search 

methods, the approach should be extendable to proteins greater than 150 amino acids. 

4.5 Materials and Methods 

4.5.1 PCS-ROSETTA Score. 

et al., 2002b) 

The PCS (in ppm) induced by a metal ion M on a nuclear spin can be calculated as (Bertini 

(4.2) 

where ri is the distance between the spin i and the paramagnetic centre M, xi, yi, zi are the 

Cartesian coordinates of the vector between the metal ion and the spin i in an arbitrary frame f and 

Δχxx, Δχyy, Δχzz, Δχxy, Δχxz, Δχyz are the Δχ-tensor components in the frame f (as Δχzz = -Δχxx -Δχyy, 

there are only five independent parameters). The Δχ-tensor components and the metal coordinates 

are initially unknown and must be redetermined each time the PCS score c is evaluated. c is 

calculated over all metal ions Mj as 

(4.3) 

where PCSi calc (Mj) and PCSi exp (Mj) are the calculated and experimental PCS values of spin 

i induced by the metal ion Mj, respectively. The determination of the Δχ-tensor components and the

4.5 Materials and Methods. 113 

metal coordinates presents a non-linear least square fitting problem. In order to avoid local minima 

and speed up the calculation, we split the problem into its linear and non-linear part. Equation (4.2) 

shows that PCSi calc is linear with respect to the five Δχ-tensor components. Using a three- 

dimensional grid search over the Cartesian coordinates xM, yM, zM of the paramagnetic centre, 

singular value decomposition optimizes the five Δχ-tensor parameters efficiently and without 

ambiguity for lowest residual score c at each node of the grid. The grid node with the lowest c score 

is then used as the starting point for optimization of the three metal coordinates along with the five 

Δχ-tensor components to reach the minimal cost c. 

The PCS score was added to the ROSETTA low resolution energy function using a different 

weighting factor w(c) for each structure calculation. w(c) was determined by first generating 1000 

decoys with ROSETTA and calculating w(c) as 

(4.4) 

where ahigh and alow are the average of the highest and lowest 10% of the values of the 

ROSETTA ab initio score, and chigh and clow are the average of the highest and lowest 10% of the 

values of the PCS score c upon rescoring each of the 1000 decoys with the PCS. The weights used 

for the ten structure calculations performed in the present work are given in SI Table S4.1. 

4.5.2 PCS-ROSETTA Algorithm 

PCS-ROSETTA uses the ROSETTA de novo structure prediction methodology to build low 

resolution models, followed by all atom refinement using the ROSETTA high resolution Monte 

Carlo minimization protocol. The additions to the standard ROSETTA structure prediction methods 

are: the use of chemical shifts to guide fragment selection as in CS-ROSETTA, the use of PCS data 

to guide the initial low resolution search and the use of PCS data for final model selection. A flow 

diagram of the computational protocol of PCS-ROSETTA is shown in SI Figure S4.5. 

4.5.3 Input for PCS-ROSETTA 

The chemical shifts of all protein targets were taken from the literature or from the 

BioMagResBank. CS-ROSETTA was used for fragment selection. CS-ROSETTA reports the 

difference between experimental and expected chemical shifts. Chemical shifts with very large 

deviations from expectations (often attributable to errors in the deposited data) were removed from 

the input. CS-ROSETTA also suggests corrections in the chemical shift referencing. We only


corrected 13 C chemical shifts, except for thioredoxin where 15 N chemical shift were corrected (SI 

Table S4.1). CS-ROSETTA aims to generate 200 9-residue fragments and 200 3-residue fragments 

centered on each residue of the polypeptide chain for use in the ab initio fragment assembly 

protocol of ROSETTA. In cases where CS-ROSETTA failed to generate 200 fragments, we 

generated additional fragments using the conventional ROSETTA protocol in order to make 200 

fragments available. For each of the target proteins, we removed any protein with recognizable 

sequence similarity (BLAST E-value below 0.05) from the CS-ROSETTA protein database. (For 

example, the structure of ε186 is present in the CS-ROSETTA database, but was explicitly 

excluded when fragments were generated.) In order to accelerate the grid search for the metal 

position, PCS-ROSETTA allows a precise description of the space to be searched, including the 

center of the grid search (cg), the step size between two nodes (sg), an outer cutoff radius (co) to 

limit the search to a minimal distance from cg, and an inner cutoff radius (ci) to avoid a search too 

close to cg. A moderately large step size (sg) was chosen to speed up computations during low 

resolution sampling (Table S4.1), and reduced to 25% of its value during the final high resolution 

scoring step to ensure maximum accuracy. For each target, the grid parameters cg, co and ci were 

chosen in accordance to prior knowledge about the approximate metal binding site. For example, 

for a covalent tag attached to the protein, we used the known geometric information of the tag to set 

cg, co, and ci, whereas for proteins with a natural metal binding site, a highly conserved negatively 

charged residue was picked as a reference point for cg. In the absence of prior biochemical 

information, the nuclear spin with the largest absolute PCS value was chosen as the center of the 

grid. SI Table S4.1 summarizes the grid parameters used for the different protein targets. In order to 

assess the impact of the initial grid parameters on the structures calculated, a set of PCS-ROSETTA 

calculations was performed for each target, where cg was centered at the nuclear spin of the largest 

PCS observed and the cutoff radius co was set to 15 Å. No change in the quality of the results was 

observed but in most cases the calculations took longer. 

4.5.4 PCS-ROSETTA Protocol for Protein Structure Determination 

Chemical shifts of the proteins were prepared in Talos format (Cornilescu et al., 1999) and 

used by CS-ROSETTA for fragment selection. Chemical shift corrections, fragment selection, and 

determination of the weights w(c) were performed as described above. 10000 protein structures 

were computed with PCS-ROSETTA and subjected to the full atom relaxation protocol of 

ROSETTA to model the side chain conformations. The final structures were rescored using the 

ROSETTA full atom energy function combined with the PCS scores c, using the weighting factors 

w(c) (Equation (4.4)) with ahigh and alow calculated against the ROSETTA full atom energy, and

4.6 Acknowledgments. 115 

with a total weight multiplied by 2 to give a larger contribution to the PCS score than in the 

fragment assembly. The best scoring structures can be assessed by the PCS quality factor Q = 

rms(PCS cal – PCS exp ) / rms(PCS exp ). Computation of 10000 PCS-ROSETTA structures took on 

average 137 CPU days per target and was run on a local cluster. SI Figure S4.6 shows a posteriori 

that 1000 structures per targets would have been enough for convergence of the protocol. 

4.5.5 Computation of Structures to Evaluate the Effects of PCS Scoring 

3000 decoys with a wide range of rmsd values to the target structure were generated by 

including the native fragment and limiting the number of alternatives fragments in the fragment 

generation step of the ROSETTA calculations. 1000 decoys each were calculated using two, five 

and ten fragments per residue, respectively. The presence of the native fragments in a small pool of 

fragments ensured the generation of structures very similar to the target structure. 

4.6 Acknowledgments 

C.S. thanks the University of Queensland for a Graduate School Research Travel Grant to 

undertake this collaborative research project. T.H. thanks the Australian Research Council for a 

Future Fellowship. Financial support from the Australian Research Council for project grants to 

G.O. and T.H. is gratefully acknowledged. D.B. thanks the Howard Hughes Medical Institutes. 


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4.8 Supporting information


Figure S4.1 Fold identification by pseudocontact shift score and ROSETTA energy. 3000 decoys 

were generated using CS-ROSETTA. In order to ensure that some decoys with small rmsd to the 

target structure were obtained, the starting set of peptide fragments was reduced and included the 

fragments from the known target structures. A to J: ROSETTA energies plotted versus the C rmsd 

to the target structure. A’ to J’: PCS scores plotted versus the C rmsd to the target structure. The 

targets are labeled A-J as in Table 4.1.


Figure S4.2 Improved fragment assembly by PCS-ROSETTA. Fragments were assembled in 10000 

different runs of CS-ROSETTA (red), 10000 different runs of PCS-ROSETTA (black), and 10000


different runs using exclusively the PCS score of PCS-ROSETTA (blue). The plots show the 

frequency with which structures of different C rmsd values to the target structure were found. The 

red and black solid lines reproduce the data of Figure 4.2. The dashed lines show the 

corresponding data obtained in independent calculations that included the full atom refinement 

step. The same colors were used for calculations with and without the full atom refinement step. 

The full atom refinement step does not significantly change the C rmsd of the structures produced 

in the fragment assembly step with respect to the target structure. The targets are labeled A-J as in 

Table 4.1. 

Figure S4.3 Energy landscape generated by CS-ROSETTA and PCS-ROSETTA, with full atom 

ROSETTA energies and C α rmsd values being calculated using only the core residues as defined in 

Table S4.1. A to J: full atom ROSETTA energies plotted versus the C α rmsd to the target structure 

for structures calculated using CS-ROSETTA. A’ to J’: Combined ROSETTA energy and PCS score 

plotted versus the C rmsd to the target structure for structures calculated using PCS-ROSETTA. 

The lowest energy structures are indicated in red. The targets are labeled A-J as in Table 4.1.


Figure S4.4 Identification of successful calculations with PCS-ROSETTA. The quality factor Q 

reports on the agreement between the experimental and calculated PCS. A value below 20% 

usually indicates that the calculated structure satisfy the PCS restraint. Above 25%, the quality of 

the structure is poor. On the y axis are the average C α rmsd calculated between the lowest scored 

structure and the next four lowest scoring structures. Rmsd below 3 Å are indicative of the 

convergence of the protocol. Convergence criterion and quality factor can be combined to further 

ascertain the success of the calculations for the targets A-B-C-D-E-F-I-G., and reject targets H and 

J. The targets are labeled A-J as in Table 4.1. The values are those of Table 4.1-h for the x axis, 

and Table 4.1-g for the y axis.


Figure S4.5 Flow diagram of PCS-ROSETTA. (a) Fragments are selected by their chemical shifts 

using CS-ROSETTA. (b) The PCS weight is calculated using equation (4.4) on 1000 decoys 

generated with CS-ROSETTA. (c) Structures are produced by the classical fragment assembly of 

ROSETTA with addition of the PCS-score. (d) Side chains are added to the structures and 

subjected to a full atom minimization. (e) Resulting structures are rescored using a combination of 

the ROSETTA full atom energy score and the PCS score. (f) Best structures are selected by their 

lowest score.


Figure S4.6 Expected C α rmsd of the lowest energy structure calculated with PCS-ROSETTA. A 

given number n of structures (x axis) was randomly chosen 5000 times from the total of 10 000 

generated structures and the averaged C α rmsd of the lowest energy (over the 5000 trials) is 

graphed. The curves show a posteriori that 1000 structures calculated for all the targets would 

have been ample to ensure convergence of PCS-ROSETTA calculations. The targets are labeled A- 

J as in Table 4.1. The curve for the target parvalbumin (H) and ε (J) are not shown.

Table S4.1 PCS data information and grid search parameters used. 


Protein name Residues a Metal ions used Atom types cs corr b w(c) cg c sg d co d ci d 

protein G (A) 1-56 Tb 3+ Tm 3+ Er 3+ H N Ce 

0.53 15.5 E19 CA 6 17 7 

calbindin (B) 2-75 

3+ Dy 3+ Er 3+ 

Eu 3+ Ho 3+ Nd 3+ 

Pr 3+ Sm 3+ Tb 3+ 

Tm 3+ Yb 3+ 

H N , N, C’ 2.72 48.9 D54 CA 6 8 4 

θ subunit (C) 10-64 Dy 3+ Er 3+ H N -0.16 7.1 D14 CA 6 25 15 

ArgN (D) 8-70 Tb 3+ Tm 3+ Yb 3+ H N , N 2.09 13.5 C68 CB 6 10 4 

ArgN (E) 8-70 Tb 3+ Tm 3+ H N 2.09 48.9 K12 CB 6 15 0 

N-calmodulin (F) 3-79 Tb 3+ Tm 3+ H N , CA, CB 0.00 4.7 D60 CA 6 8 4 

thioredoxin (G) 2-108 Ni 2+ H N 1.23 106.3 S1 N 3.8 4 0 

parvalbumin (H) 2-109 Dy 3+ H N , N 2.65 2.86 D93 CA 6 8 4 

calmodulin (I) 3-146 

Tb 3+ Tm 3+ Yb 3+ 

Dy 3+ H N 0.59 5.1 D60 CA 6 8 4 

ε186 (J) 7-180 Tb 3+ Dy 3+ Er 3+ H N , N, C’ 0.53 8.2 D12 CA 6 8 4 

a Ordered residues 

b Uniform offset used for 13 C chemical shifts (in ppm) compared to published values. In the case of 

thioredoxin, the offset was applied to 15 N chemical shifts 

c Residue and atom name defining the center of the grid search to position the paramagnetic center. 

d In Ångstrom


Table S4.2 Protein structures used to evaluate the performance of PCS-ROSETTA. 

Targets PCS-ROSETTA run a CS-ROSETTA run b 

rmsd c convergence d rmsd c convergence d 

protein G (A) 0.61 0.92 0.80 0.88 

calbindin (B) 1.46 2.09 4.96 4.72 

θ subunit (C) 1.30 0.55 1.56 2.25 

ArgN e (D) 1.00 0.77 1.31 2.21 

ArgN f (E) 0.83 0.94 1.65 5.43 

N-calmodulin (F) 1.74 1.49 4.69 4.49 

thioredoxin (G) 2.58 2.44 4.61 5.55 

parvalbumin (H) 11.26 10.25 11.80 11.30 

calmodulin (I) 2.80 2.12 6.35 2.94 

ε186 g (J) 20.57 18.03 17.07 17.74 

a The structures used to calculate the rmsds were identified using the combined PCS-score and 

ROSETTA full atom energy across only the core residues defined in SI Table S4.1. 

b The structures used to calculate the rmsds were identified by the ROSETTA full-atom energy 

across only the core residues defined in SI Table S4.1. 

c C α rmsd (with respect to the native structure) of the structure of lowest score, in Å. All C rmsd 

values were calculated using the core residues defined in SI Table S4.1. 

d Average C α rmsd calculated between the lowest score structure and the next four lowest scoring 

structure, in Å. The rmsd values were calculated using the core residues defined in SI Table S4.1. 

e PCSs measured with a covalent tag attached to the N-terminal domain of the E. coli arginine 

repressor (ArgN). 

f PCSs measured with a non-covalent tag bound to ArgN. 

g N-terminal 186 residues of the ε subunit of the E. coli polymerase III. 

Text S4.1 Fragment Assembly Using PCSs Only. 

In order to gain a better understanding of the merit of PCS data, we generated 10000 decoys 

per protein with all ROSETTA force field components turned off except for the PCS score. In 

seven of the ten protein structure calculations, the PCS score alone produced decoys with a C rmsd 

of less than 2.5 Å to the target structure (Figure S4.2, solid blue line). Control calculations without


any scoring function produced not a single useful decoy. This highlights the power of PCS data to 

define the overall topology of a protein at the fragment assembly stage. The effect was particularly 

pronounced for the target proteins θ and ArgN (Figure S4.2 C and D). 

The second set of PCS data of ArgN (Table 4.1; structure E) yielded worse decoys in the 

PCS-only computations with PCS-ROSETTA than CS-ROSETTA. Remarkably, however, using 

the PCS score in combination with the ROSETTA force field yielded much better structures than 

when used separately (Figure S4.3 E). This shows that the PCS score adds information that is not 

captured by the ROSETTA energy score alone. 

Text S4.2 Scoring over Core Residues. 

Disordered residues can add noise to the ROSETTA energy, and this noise can prevent 

identification of low rmsd structures. Notably, three of the targets that succeeded under the PCS- 

ROSETTA protocol and failed under the CS-ROSETTA protocol have disordered termini 

accounting for ten or more residues each (Table S4.2-d: Targets C, D & E). In practice it is possible 

to experimentally determine the disordered character of a residue, so to compare the effect of 

disorder on the two protocols we produced an additional set of structures by removing disordered 

residues during the final rescoring step (cores defined in Table S4.1). When the core residues are 

perfectly defined, in this case by observation of the solved structures, the CS-ROSETTA protocol 

identifies low rmsd structures in four of the ten cases (including C, D & E), and shows convergence 

to a low rmsd structure in three of the ten cases [Table S4.2-c, d, CS-ROSETTA run]. In contrast, 

removing the disordered residues has little effect on PCS-ROSETTA’s rmsd values, suggesting that 

the combined PCS and ROSETTA score is less sensitive to disorder. The remaining targets had 

little disorder and removal of disordered terminal residues had little effect on the results.

Chapter 5 

Conclusion and perspectives 

5. Conclusion and perspectives

130 Chapter 5. Conclusion and perspectives. 

5.1 The use of PCS for structure determination 

Structure determination of proteins remains a major challenge of the post genomic era. 

Conventional techniques such as X-ray crystallography and NMR spectroscopy are slow. Hence, 

the gap between known protein sequences and known protein structures remains large. Alternative 

experimental methods are required to speed up the process. Those methods have to present an 

attractive compromise between the efforts required to measure the desired data, and the merit that 

data can bring in assisting de novo determination of proteins. 

In Chapter 4, it has been demonstrated that PCS data are a potential candidate. It has been 

shown that combining a molecular fragment approach with the PCS score leads to the correct 

folding of proteins smaller than 146 residues. A benchmark of ten data sets has been compiled for 

this work, and the PCS-ROSETTA approach showed success in eight out of the ten cases. The first 

case where PCS did not lead to the correct folding concerned a protein having only one data set of 

PCS. The importance to measure multiple data sets with different lanthanides has already been 

shown in Chapter 2 (to increase the quality of the resonance assignment) and Chapter 3 (to increase 

the quality of the fitted Δχ-tensor). It was not surprising that PCS-ROSETTA had difficulties when 

working with a single data set. The second case where the fold was incorrect was for the largest 

protein of the benchmark: the subunit ε, 186 residues. The size of the protein might be a limiting 

factor for the current approach. It is well known that for proteins larger than 150 residues, the size 

of the conformational space explodes in the molecular fragment replacement protocol of 

ROSETTA. The question whether PCS-ROSETTA is facing the same problem is legitimate. Some 

elements of responses to that question are presented in the following sections. 

5.1.1 Folding of proteins using only pseudocontact shifts 

In order to gain a better understanding of the merit of the PCS, structure calculations with 

PCS-ROSETTA have been made with all energy terms switched off, except the PCS score. The 

fragment assembly within ROSETTA is hence guided purely by the PCS. While turning off the 

normal force field of ROSETTA presents no practical interest, the theoretical results presented in 

the following explanations remain interesting. 

The protocol generated and identified (by the lowest score) attractive folding for four out of 

the ten structure calculations (Figure 5.1). The term ―attractive folding‖ has to be defined in that 

context. Obviously, without energy terms such as van der Waals terms or hydrogen bonding, the 

resulting structures can exhibit steric clashes (Figure 5.1 a, c, d), or poor β-sheet pairing (Figure 5.1

5.1 The use of PCS for structure determination. 131 

a and c). However, the C α rmsd against the native structure was found to be reasonably low (2.25 Å 

for protein G, 1.89 Å for θ, 2.39 Å for ArgN, 5.03 Å for calmodulin). This provides proof of 

principle that the PCS alone can direct the correct folding of a protein at the fragment assembly 

level. The conditions of success remain unclear and should be further analyzed. It could be a 

combination of the complexity or size of the protein, the number and quality of data sets, the 

relative orientation of each Δχ-tensor, and the location of the paramagnetic center. 

Figure 5.1 Capacity of the PCS score, as the only energy term, to fold the 

protein. The lowest PCS energy structure (blue) is superimposed onto the 

native structure (white). (a) protein G, (b) θ subunit, (c) ArgN, (d) calmodulin. 

Figure 5.2 The intersection of isosurfaces defines the position and orientation of peptide 

fragments in the protein structure. (a) Three PCS of the spin (black) measured with three


different lanthanides can be depicted as three isosurfaces (red, blue and yellow) where the 

spin must be located. In order to fulfill all three PCS data simultaneously, the spin must be 

located at the intersection of the three isosurfaces, helping to define the orientation and 

position of the fragment (purple) in the protein structure (white). (b) The same principle 

holds, if PCS from different lanthanide binding sites are available, in which case the 

intersection of the three isosurfaces is even better defined. 

A direct consequence of those results is the theoretical demonstration that it is possible to 

apply the PCS score in a ―divide and conquer‖ approach in order to overcome the sampling 

problem typically encountered with proteins larger than 120 residues. If a large protein was 

composed of the four proteins present in Figure 5.1, a protocol to obtain the folding of the large 

protein could be (i) to cut the protein in four pieces (Figure 5.1 a-b-c-d), (ii) to reassemble the 

pieces separately, and (iii) to reconstitute the whole proteins by superimposition of the four 

separately determined (sets of) Δχ-tensors. The proof of principle holds as no energy term (that 

would report on interactions between the four parts of the proteins) is used. A more efficient way 

however, could be to work with smaller overlapping fragments. The size of the fragments would 

need to be large enough to make it possible to optimize the Δχ-tensor (larger than 20 residues), but 

not too small to prevent running into the sampling problem (smaller than 80 residues). 

Clearly, the PCS-score would benefit favorably from additional energy terms, starting from 

the van der Waals term that would strongly penalize conformations with steric clashes, thus 

favoring the sampling of the correct fold. In particular, the symmetric shape of the isosurfaces 

implies the existence of symmetrical folds that could be discriminated with the help of the van der 

Waals term, as theoretically demonstrated in (Bertini et al., 2002). 

5.1.2 Uses of multiple lanthanide binding sites 

Erstwhile limited to metalloproteins, paramagnetic NMR is increasingly enjoying a wider 

playground since the arrival of lanthanide binding tags. These tags can be attached to the protein 

via a disulfide bond or at the termini of the protein. A non-covalent tag can also be used, although 

the disadvantage is the loss of control over whether (and where) the tags bind. Attaching metal tags 

to a protein of interest site-specifically is one of the current challenges of paramagnetic NMR. 

Several groups are developing new tags, for a recent review, see (Su et al., 2009). While those tags 

are engineered to simplify as much as possible the process of tag attachment, a consequence of this

5.1 The use of PCS for structure determination. 133 

quest will hopefully be the possibility to attach them at different positions on the surface of the 

target protein. 

All work outlined in this thesis has greatly benefited from the availability of multiple data 

sets measured with different lanthanides. The magnitude of the paramagnetic dipole moment differs 

between different paramagnetic metal ions. The orientation of the Δχ-tensor varies too. The 

advantage is that those differences provide additional information that can be used to improve the 

quality of the fitted Δχ-tensor (Chapter 3) or the quality of the automated assignment (Chapter 2). 

PCS-ROSETTA calculations can take advantage of that fact. Especially the calculations done on 

calbindin greatly improved when all available lanthanide data were used compared to test 

calculations using PCS from only one or two lanthanides simultaneously. It can be expected that 

the use of tags attached at different locations on the protein will enhance the PCS-ROSETTA 

calculations further. In particularly, the location and the orientation of fragments with respect to the 

rest of the protein structure would be defined more accurately by isosurfaces intersecting at steeper 

angles (Figure 5.2). The current implementation of PCS-ROSETTA would make it straightforward 

to design such a protocol. The benefits of using two different lanthanide binding sites could be 

explored already using the arginine repressor as a test case, were PCS data measured for two 

different lanthanide binding sites are available. 

5.1.3 Development of a new PCS-ROSETTA protocol 

The way structures are calculated by PCS-ROSETTA is similar to the standard protocol of 

ROSETTA. The only difference is the calculation of a PCS-score during the fragment assembly 

stage (which requires fitting of a Δχ-tensor and metal position). The weight of the PCS-score 

compared relative to the standard centroid score of ROSETTA is chosen so that both have an equal 

influence. While ROSETTA benefits from additional experimental restraints such as PCSs, it is 

important to bear in mind that the original goal of ROSETTA is to generate a wide variety of 

protein-like structures in a first step (fragment assembly) and identify the native one in a second 

step (full atom score). Considering that the PCS have proven to drive the sampling towards the 

native structure with great efficiency, it can be questioned whether it is necessary to enforce 

diversity in the generated structures. Several thousands of structures (using a large amount of CPU 

time) are usually generated by ROSETTA to cover a wide range of possible structures. It may be 

more profitable to generate, at equal CPU time, a smaller number of structures for which more time 

is spent for the fragment assembly.


Clearly, a larger benchmark containing proteins of different topology and size is necessary 

to gain a better understanding of the merit of the pseudocontact shift. We are in the process of 

creating an artificial one, since PCS can easily be predicted. The parameters that would impact the 

success of calculation, and that we have to explore are: the level of noise within the data PCS- 

ROSETTA can tolerate, the influence of the position of the paramagnetic center relative to the 

protein, and the influence of the relative orientations of different Δχ-tensors. 

5.2 The use of PCS for chemical shift assignment 

The work of Chapter 2 provides proof of principle that PCS can be used for automatic 

chemical shift assignment when a 3D structure is available. Chemical shifts are sensitive to the 

local environment. Small variations in the surrounding electronic configuration can have a large 

impact on the chemical shift values. This makes it extremely difficult to predict chemical shifts 

accurately. In contrast, the PCS of a spin i is much less affected by similar variations, as the PCS 

only depends on the spherical coordinates of i with respect to the Δχ-tensor frame. 

While the program Possum presented in Chapter 2 is limited to methyl groups, the approach 

used to automatically assign the chemical shifts could be applied to any atom type for which PCS 

can be measured. The simulated annealing protocol used to solve the multi-dimensional assignment 

problem has proven to be highly efficient at sampling the possible assignment space and find a 

solution of lower energy than manual assignments. The scoring scheme used to optimize the 

assignment is also efficient; only few misassignments were present when multiple lanthanide data 

sets were available. Even more interesting may be to obtain the Δχ-tensor parameters directly from 

unassigned chemical shifts. The program Echidna (Schmitz et al., 2006) is capable of 

simultaneously getting the Δχ-tensor parameters and assigning the paramagnetic NMR spectrum, 

provided that the diamagnetic spectrum is already assigned. This raises the question whether both 

the diamagnetic and the paramagnetic spectrum can be assigned, while determining the Δχ-tensor at 

the same time. A software package for this purpose is currently under development. The idea is to 

handle various kinds of input information (partial assignment for some residues in the diamagnetic 

or paramagnetic state, measurement of some unassigned pseudocontact shifts, selective isotope 

labeling of some amino acids) and use this partial information in a simulated annealing protocol to 

optimize the assignment while determining the Δχ-tensor parameters. The challenge of this 

approach is to use the right combination of methods: simulated annealing for the assignment, grid

5.3 The use of PCS for protein docking. 135 

search for the coordinates of the paramagnetic center, and singular value decomposition for the 

determination of the remaining Δχ-tensor parameters. 

5.3 The use of PCS for protein docking 

At present, structural biology groups are investing much effort in producing models of 

proteins by NMR or X-ray crystallography. Currently more than 48000 crystal structures and 

almost 7000 NMR structures of proteins have been deposited in the protein data bank. In contrast, 

the number of protein-protein complexes solved by any of those methods remains low (less than 

2500). For X-ray crystallography, the difficulty to co-crystallize a complex is much greater than to 

obtain crystal structures of the individual proteins. For NMR spectroscopy, the larger molecular 

weight of complexes presents a problem, making it more difficult to obtain and analyze data. 

Additionally, the most useful information of intermolecular NOEs often involves amino acid side 

chains the resonances of which are much harder to assign than the backbone resonances of the 

protein. 

For a better insight of the molecular basis of life, the challenge is to understand how 

individual macromolecules come together to fulfill their tasks in DNA replication, gene expression 

and regulation, etc. Construction of models for protein-protein, protein-DNA and protein-ligand 

complexes are necessary. An angle to tackle the problem is the use of a docking program that 

predicts the binding mode of the complex given the structures of the individual components. The 

major difficulty of this approach is to comprehensively explore the 6-dimensional space that 

describes the relative orientation and position of two rigid bodies in space. This presents a 

challenging sampling problem. Shortage of experimental information to support any model 

generated is another drawback of the docking approach. Therefore, alternative techniques to 

provide more experimental information would be important. Measurements of residual dipolar 

couplings are an efficient way to obtain orientational information between two macromolecules: the 

macromolecules are weakly aligned using an alignment media. Independent determination of the 

alignment tensor with respect to the two macromolecules gives direct access to the relative 

orientation of the two rigid bodies. More interestingly, PCS measurements provide, in addition to 

orientational information, information on the distance between the two bodies. Determination of the 

Δχ-tensor with respect to the two molecules and superimposition of the two Δχ-tensor frames yields 

the relative orientation and position of the two macromolecules, as illustrated in Figure 1.8


(Chapter 1). Pseudocontact shifts therefore present particularly powerful experimental data to 

construct a model of the complex between two molecules by rigid body docking, and to shortcut 

the computationally expensive task of sampling the conformational space. PCS cannot, however, 

provide the high resolution accuracy that crystallography achieves and more detailed models will 

still require structural refinement software that optimizes the intermolecular packing and any other 

structural adjustments. At least, however, the computational effort of protein docking can focus on 

the atomic details when starting from a valid rigid body model. 

Another challenge facing the modeling of a protein-protein complex arises when one of the 

proteins undergoes a large conformational change. Protein docking software can tackle the problem 

to some extent by adapting the conformations of the side chains and the backbone close to the 

complex interface. As this approach greatly increases the conformational space to search, it is 

computationally challenging. Paramagnetic NMR and PCS could assist the modeling of large 

conformational changes by directing the conformational alterations toward the correct 

conformation. A protein that undergoes a large conformational change due to motions about a 

hinge that separates two rigid domains would present an attractive example. In a situation, where 

such a hinge motion occurs as a result of association with a binding partner, a technique for rigid 

body docking with the help of PCS as presented in this thesis could be particularly fruitfully 

applied to assist the modeling of the complex. 


Bertini I, Longinetti M, Luchinat C, Parigi G and Sgheri L (2002) Efficiency of paramagnetism- 

based constraints to determine the spatial arrangement of α-helical secondary structure 

elements. J Biomol NMR 22:123-136 



87 

Su XC and Otting G (2009) Paramagnetic labelling of proteins and oligonucleotides. J Biomol 

NMR in press

Thesis Title: Subtitle - NMR Spectroscopy Research Group

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