doi:10.1016/j.jmb.2011.12.056 J. Mol. Biol. (2012) 416, 668–677

Contents lists available at www.sciencedirect.com

Journal of Molecular Biologyj ourna l homepage: ht tp : / /ees .e lsev ie r.com. jmb

Protein Structure Determination from PseudocontactShifts Using ROSETTA

Christophe Schmitz 1†, Robert Vernon 2†, Gottfried Otting 3,David Baker 2⁎ and Thomas Huber 3⁎1School of Chemistry and Molecular Biosciences, University of Queensland, Brisbane, QLD 4072, Australia2Department of Biochemistry, University of Washington, University of Washington, Seattle, WA 98195, USA3Research School of Chemistry, Australian National University, Canberra, ACT 0200, Australia

Received 21 October 2011;received in revised form16 December 2011;accepted 27 December 2011Available online18 January 2012

Edited by A. G. Palmer III

Keywords:pseudocontact shift;protein structuredetermination;NMR spectroscopy;PCS-ROSETTA;lanthanides

*Corresponding authors. E-mail adddabaker@u.washington.edu; t.huberPresent address: C. Schmitz, Bijvoe

Biomolecular Research, Science FaculPadualaan 8, 3584 CH Utrecht, The N

† C.S. and R.V. contributed equalAbbreviations used: PCS, pseudo

three-dimensional; NOE, nuclear Ovenhancement.

0022-2836/$ - see front matter © 2011 P

Paramagnetic metal ions generate pseudocontact shifts (PCSs) in nuclearmagnetic resonance spectra that are manifested as easily measurablechanges in chemical shifts. Metals can be incorporated into proteins throughmetal binding tags, and PCS data constitute powerful long-range restraintson the positions of nuclear spins relative to the coordinate system of themagnetic susceptibility anisotropy tensor (Δχ-tensor) of the metal ion. Weshow that three-dimensional structures of proteins can reliably bedetermined using PCS data from a single metal binding site combinedwith backbone chemical shifts. The program PCS-ROSETTA automaticallydetermines the Δχ-tensor and metal position from the PCS data during thestructure calculations, without any prior knowledge of the proteinstructure. The program can determine structures accurately for proteins ofup to 150 residues, offering a powerful new approach to protein structuredetermination that relies exclusively on readily measurable backbonechemical shifts and easily discriminates between correctly and incorrectlyfolded conformations.

© 2011 Published by Elsevier Ltd.

Introduction

The three-dimensional (3D) structure of proteinsis a prerequisite for understanding protein func-tion, protein–ligand interactions and rational drug

resses:@uq.edu.au.t Center forty, Utrecht University,etherlands.ly to this work.contact shift; 3D,erhauser

ublished by Elsevier Ltd.

design. Protein structures can be readily deter-mined by nuclear magnetic resonance (NMR)spectroscopy.1 The most difficult part of an NMRstructure determination typically is the assignmentof side-chain chemical shifts and nuclear Over-hauser enhancement spectroscopy (NOESY) peaks.This bottleneck can potentially be avoided ifmethods for computing high-accuracy structuresfrom backbone-only NMR experiments can bedeveloped.2

Pseudocontact shifts (PCSs) are a rich source ofstructural information that are manifested as largechanges in chemical shifts in the NMR spectrumcaused by a nonvanishing magnetic susceptibilityanisotropy tensor (Δχ-tensor) of a paramagneticmetal ion. The PCS (in parts per million) of a nuclearspin i depends on the polar coordinates ri, Θi and Φiof the nuclear spin with respect to the Δχ-tensor

669Protein Structure Determination using PCS-ROSETTA

frame of the metal ion and the axial and rhombiccomponents of the Δχ-tensor:

PCScalci =1

12k r3i

hDmax 3 cos2 Qi − 1

� �+

32Dmrh sin

2 Qi � cos 2Ai

ið1Þ

The Δχ-tensor defines a coordinate system in themolecule that is centered on the metal ion and isfully described by eight parameters (Δχax, Δχrh,three Euler angles relating the orientation of the Δχ-tensor to the protein frame and the coordinates ofthe metal ion). Therefore, the Δχ-tensor can bedetermined using PCS data from at least eightnuclear spins, provided that the coordinates of thespins are known.As PCSs can be measured for nuclear spins 40 Å

away from the metal, they present long-rangestructure restraints exquisitely suited to characterizethe global structural arrangement of a protein. Thus,PCSs have been used very successfully to refineprotein structures,3–5 dock protein molecules ofknown 3D structures6–8 and determine the structureof small molecules bound to a protein of known 3Dstructure.9–11 The need for atom coordinates todetermine the Δχ-tensor parameters, however,makes it more difficult to use PCSs in de novodeterminations of protein 3D structures. All pres-ently available protein structure determinationsoftware that uses PCS data to supplement conven-tional NMR restraints requires estimates of effectiveΔχax and Δχrh as input parameters.12–15 These areoften difficult to estimate accurately, as they dependon the chemical environment of the metal ion andthe mobility of the paramagnetic center with respectto the protein.The ROSETTA structure prediction methodology16

is well suited for taking advantages of the richsource of information inherent in PCSs. ROSETTAde novo structure prediction has two stages—first, alow-resolution phase in which conformationalspace is searched broadly using a coarse-grainedenergy function and, second, a high-resolutionphase in which models generated in the firstphase are refined in a physically realistic all-atomforce field. The bottleneck in structure predictionusing ROSETTA is conformational sampling; close-to-native structures almost always have lowerenergies than nonnative structures. For small pro-teins (b100 residues), ROSETTA has producedmodels with atomic level accuracy in blind predic-tion challenges.17 For larger proteins, however,structures close enough to the native structure tofall into the deep native energy minimum aregenerated seldom or not at all. This samplingproblem can be overcome if even very limitedexperimental data are available to guide the initial

low-resolution search. For example, CS-ROSETTAuses NMR chemical shifts to guide fragmentselection and constrain backbone torsion angles,greatly improving the final yield of correctly foldedprotein models.18 As ROSETTA in favorable cases iscapable of generating protein structures very close toexperimentally determined structures from se-quence information alone,19 it is of great interest tocombine ROSETTA with readily accessible experi-mental data to determine protein structures.In this paper, we describe the incorporation of

PCS data into ROSETTA. We show that this newPCS-ROSETTA method can generate accurate struc-tures for proteins of up to 150 amino acids in lengtheven from quite limited data sets.

Results

Test set

We tested the new PCS-ROSETTA method (seeMaterials and Methods) on a benchmark of nineproteins for which chemical shifts and PCSs havebeen published. ArgN repressor was independentlydetermined twice with PCS data measured fromparamagnetic metal ions at two different sites. Theproteins were between 56 and 186 amino acidresidues in size, had different folds and had between82 and 1169 PCSs measured from one to elevendifferent metal ions located at a single metal bindingsite (Table 1 and Supporting Information Table 1).Fragments for each protein were selected with CS-ROSETTA using available chemical shift data andwere used for all calculations. Structures of proteinswith significant sequence similarity to the targetproteins were explicitly excluded from the CS-ROSETTA database. The exclusion threshold weused was significantly stricter than that used in theoriginal CS-ROSETTA study,18 and in the caseswhere distant homologs were removed, the finalmodel quality in our CS-ROSETTA calculations wasworse than previously reported.

Capacity of the PCS score to identify native-likestructures

The PCS score describes a model's agreement withobserved PCS data by calculating the expected PCSdata given the structure. To calculate this, we used a3D grid search for the metal coordinates coupledwith singular value decomposition for the Δχ-tensor components to find the optimal matchbetween calculated and observed data (see Materialsand Methods). The capacity of the PCS score toidentify native-like models was assessed on sets of3000 CS-ROSETTA structures for each of the ninetest proteins. These test structures were produced

Table 1. Protein structures used to evaluate the performance of PCS-ROSETTA

TargetsProtein DataBank ID Nres

a NMb NPCS

c

PCS-ROSETTA rund CS-ROSETTA rune

RefCSf RefPCS

grmsdh Convegencei Qj rmsdh Convergencei

Protein G (A) 3GB1 56 3 158 0.61 0.92 0.06 0.80 0.88 33 34Calbindin (B) 1KQV 75 11 1169 1.46 2.04 0.16 4.96 4.37 35 4θ subunit (C) 2AE9 76 2 91 1.65 4.35 0.07 8.90 8.75 36 37ArgNk (D) 1AOY 78 3 222 0.98 2.38 0.08 6.93 5.32 21 21ArgNl (E) 1AOY 78 2 82 1.03 2.25 0.09 8.01 6.64 21 38N-Calmodulin (F) 1SW8 79 2 125 2.34 1.85 0.09 4.69 3.68 39 39Thioredoxin (G) 1XOA 108 1 90 2.58 2.64 0.23 4.98 6.06 40, 41 42Parvalbumin (H) 1RJV 110 1 106 11.26 10.42 0.20 11.80 11.20 43 43Calmodulin (I) 2K61 146 4 408 2.80 2.12 0.14 6.35 5.55 44 44ɛ186m (J) 1J54 186 3 738 20.57 17.54 0.36 15.46 17.23 45 46

a Number of residues.b Number of metal ions for which PCS data were measured.c Total number of PCSs measured.d The structures used to calculate the rmsd values were identified using the combined PCS score and ROSETTA full-atom energy on

the whole protein sequence.e The structures used to calculate the rmsd values were identified by the ROSETTA full-atom energy on the whole protein sequence.f Reference to source of chemical shifts in diamagnetic state of the protein.g Reference to source of PCS data of the protein.h Cα rmsd (with respect to the native structure) of the structure of lowest score, in angstroms. All Cα rmsd values were calculated using

the core residues defined in Supplementary Table 1.i Average Cα rmsd calculated between the lowest-score structure and the next four lowest-scoring structure, in angstroms. The rmsd

values were calculated on the whole protein sequence.j Quality factor Q=rms(PCSi

calc−PCSiexp)/rms(PCSiexp) calculated on the structure of lowest PCS-ROSETTA score.

k PCS measured with covalently attached dipicolinic acid tag.l PCS measured with non-covalently bound [Ln(DPA)3]

3−.m N-terminal 186 residues of the ɛ subunit of the E. coli polymerase III.

670 Protein Structure Determination using PCS-ROSETTA

using a reduced fragment set and included nativefragments to ensure that some of the models weresimilar to the target structure. The Cα rmsd of thedecoy with the lowest PCS score was always small(below 2.3 Å) with respect to the target protein (Fig.1). In addition, for all target proteins for which PCSswere available from two or more paramagneticmetal ions, low Cα rmsd values correlated with lowPCS scores. This indicates that the PCS score can beused not only to identify near-native structures but

Fig. 1. Fold identification by PCSs. We generated 3000 decodecoys with low rmsd values to the target structure, we redfragments from the known target structures. PCS scores are plo(a–j) are as in Table 1. The PCS score correlates with the Cα rm

also to bias conformational sampling toward thenative structure during fragment assembly. Com-parisons between the ROSETTA low-resolutionenergy function and PCS score are shown inSupporting Information Fig. 1.PCSs from 11 different lanthanides were available

for calbindin. In order to explore the value of usingPCSs from multiple lanthanides, we rescored thestructures using PCSs from both individual andmultiple lanthanides. Spearman rank correlation of

ys using CS-ROSETTA. In order to ensure the presence ofuced the starting set of peptide fragments and includedtted versus the Cα rmsd to the target structure. The targetssd.

671Protein Structure Determination using PCS-ROSETTA

PCS score versus rmsd had coefficients ranging from0.060 to 0.569 (average, 0.377) for single data sets.Pairwise combination of PCS sets resulted inincreased coefficients ranging from −0.080 to 0.574(average, 0.459). Using all PCS sets resulted in a rankcorrelation coefficient greater than 0.6, showing thatPCSs from multiple metal ions greatly facilitateidentification of native-like protein folds.

Comparison of PCS-ROSETTAwithCS-ROSETTA

We generated 10,000 decoys each with CS-ROSETTA and PCS-ROSETTA. Both computationsused the same fragment set, taking into accountsecondary structure information from chemical shiftmeasurements. Figure 2 illustrates the ability of thePCS score to bias sampling toward the nativestructure. For seven out of the ten structurecalculations, the PCSs dramatically increased thefrequency with which decoys with low Cα rmsd tothe reference structure were found. The effect wasparticularly pronounced for protein targets withlarger PCS data sets. For example, more than a thirdof the decoys found for calmodulin had a Cα rmsdof less than 4 Å to the target structure, whereasfewer than 3% met this criterion in the absence ofPCS data. Similar results were obtained for the θsubunit, protein G and both ArgN repressorcalculations. The PCS data did not significantlyimprove the results for thioredoxin and parvalbu-min for which only PCS data from a singleparamagnetic metal ion were available. No native-like structures were found for ɛ186, which may beattributed to its larger size (186 residues). Toevaluate the influence of the PCS score during thefragment assembly, we performed an additionalcalculation with the PCS score as the only energyterm (Supporting Information Text 1).

Fig. 2. Improved conformational sampling by PCS-ROSEtrajectories with (black) or without (red) PCS information. Thstructure after the fragment assembly step. The targets arecalculated with full-atom relaxation for positioning the amino2. The library used for fragment selection explicitly excludedThe figure shows that PCS scores efficiently guide fragment a

The low-resolution models were subjected to full-atom relaxation refinement in the last step of thecalculation, using the full-atom ROSETTA force field(without inclusion of the PCS score). The additionalminimization step did not significantly change theoverall shape of the distributions but tended toimprove the Cα rmsd of native-like decoys (Sup-porting Information Fig. 2) and, most importantly,allows recognition of the best models based on theirenergies.Rescoring full-atom relaxed structures with a

weighted combination of the ROSETTA and PCSscores further improved the recognition of near-native structures as measured by the Cα rmsd of thelowest-energy structure (Table 1, PCS-ROSETTArun; Fig. 3), with PCS-ROSETTA identifying low Cα

rmsd (b3 Å) structures in eight out of ten cases. Withthe exception of target C, for all successful targets, apopulation of the five lowest-energy structuresconverge to less than 3 Å, while the two failedtargets do not improve beyond 10 Å (Table 1).Convergence is a signal that the protocol has found atopology that reliably satisfies the combined score,which, in the case of PCS-ROSETTA, clearlyidentifies the failed models as unreliable, allowingfor their rejection.18 In the case of target C, largedisordered termini prevent a clear identification ofconvergence, but convergence becomes apparentwhen only the core residues are considered (Sup-porting Information Table 2). Results with CS-ROSETTA and PCS-ROSETTA are compared inSupporting Information Fig. 3.Agreement of the structures with the experimental

data can also be directly assessed by the qualityfactor Q= rms(PCSi

calc −PCSiexp)/rms(PCSi

exp),where PCSi

exp is the experimental PCS value for thenuclear spin i. A quality factor above 25% indicatesfailure to find a correct structure, and a quality factor

TTA. We carried out 10,000 independent low-resolutione plots show the density of Cα rmsd values to the targetlabeled as in Table 1. Corresponding plots of structuresacid side chains are shown in Supporting Information Fig.any protein with sequence similarity to the target protein.ssembly toward the correct target structure.

Fig. 3. Energy landscapes generated by PCS-ROSETTA. Combined ROSETTA energy and PCS score [using theweighting factorw(c)] are plotted versus the Cα 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 1. The results show that PCS-ROSETTA is likely to generate and identify the correct fold.

672 Protein Structure Determination using PCS-ROSETTA

below 20% indicates that the computed structure isin good agreement with the experimental PCSs(Table 1), as in other definitions of quality factors.20

The low quality factor of the θ subunit (7%)establishes the success of the calculation despite thelack of clear convergence.

Successes and limits of PCS-ROSETTAcalculations

The results of PCS-ROSETTA calculations aresummarized in Table 1. The structures of small

Fig. 4. Superimpositions of ribbon representations of the bPCS-ROSETTA (blue) onto the corresponding target structure(c) the θ subunit of Escherichia coli DNA polymerase III, (d) thewith covalent lanthanide tag), (e) ArgN with non-covalent lanthioredoxin, (h) parvalbumin, (i) calmodulin and (j) the globuFlexible termini were omitted as described in Supporting Infparvalbumin (h) and the ɛ subunit (j), as the calculations coul

proteins (b80 residues, targets A to F) are easilysolved by PCS-ROSETTA: the lowest PCS-ROSET-TA energy is consistently below 2.4 Å in Cα rmsdrelative to the native structure and has a qualityfactor below 16%. For these proteins, the generationof 10,000 models was ample (Fig. 2a–f). The samenumber of decoys calculated with CS-ROSETTA didnot lead to satisfactory convergence for targets B to F(Table 1), though targets C and D partially recover ifflexible termini are removed at the full-atomrescoring step (Supporting Information Text 2).The tag used to paramagnetically label ArgN (D)

ackbones of the lowest-energy structures calculated withs (red). The protein targets are (a) protein G, (b) calbindin,N-terminal domain of the E. coli arginine repressor (ArgN;thanide tag, (f) the N-terminal domain of calmodulin, (g)lar domain of the ɛ subunit of E. coli DNA polymerase III.ormation Table 1. Only the target structure is shown ford not reproduce the correct fold for these proteins.

673Protein Structure Determination using PCS-ROSETTA

produced Δχ-tensor axes of significantly differentorientation with different lanthanides,21 which mayexplain why the PCS-ROSETTA calculations per-formed particular well with these data.PCS-ROSETTA succeeded in calculating the

structure of a protein with 146 residues and PCSsfrom multiple lanthanides (target I). More than 62%of calculated structures had a Cα rmsd below 5 Å,while only 6.2% met that criterion for CS-ROSETTAcalculation (Fig. 2i). This indicates that the PCS datascore can effectively guide the sampling toward thecorrect fold also for larger proteins. While calcula-tions on target J (186 residues) did not convergedespite a large PCS data set, this can be attributed toa sampling problem associated with large proteinsof complex topology,19 which may be overcomewith a modified protocol. Importantly, the successof a calculation can be ascertained from calculatingthe quality factor Q. Combined with the conver-gence criterion,18 the quality factor is an effectiveway to assert the success of a calculation (Support-ing Information Fig. 4). For each of the eight targetsfor which the PCS-ROSETTA calculations con-verged, the structure with the lowest energy isshown superimposed with the native structure inFig. 4.

Discussion

The structural information content of the PCSeffect has long been recognized, but initial attemptsto determine the 3D structures of biomolecules bythe use of PCSs were hampered by the difficulty todetermine Δχ-tensor and structure simulta-neously.22 Subsequently, the first 3D structuredeterminations of proteins relied on nuclear Over-hauser effect (NOE) data.1 Later attempts to solve aprotein structure without the use of NOEs reliedheavily on a blend of restraints from paramagneticNMR effects, including residual dipolar coupling,cross-correlated relaxation and PCS restraints, andadditional experimental secondary structurerestraints.23 Full structure determination of proteinsfrom PCS data alone continues to be regarded asdifficult.24 Owing to its modeling capabilities, PCS-ROSETTA makes it possible, for the first time, todetermine 3D structures using PCSs as the onlyrestraints while simultaneously determining all Δχ-tensor parameters and integrating PCSs from differ-ent metal ions. In addition, a PCS quality factor thatis highly indicative of the correctness of the finalstructure can be calculated. The effect of the PCSs onimproving convergence of the calculations towardthe correct target structures is particularly remark-able if one considers that PCS data mostly wereavailable 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 toglobal than local structure. Therefore, PCS data canguide the search in the low-resolution fragmentassembly step, greatly increasing the yield of near-native structures compared to CS-ROSETTA. PCSsthus present an ideal complement to chemical shiftinformation that is most important in the precedingfragment selection step. The improved convergencealleviates the need to compute large numbers ofdecoys. It would be possible to accelerate thecomputations further by using the PCS score toselect decoys with low rmsd values to the targetstructure prior to the computationally expensiverefinement of amino acid side-chain conformations.Many protein specific factors including fold

complexity, number and quality of PCS data andmetal site play roles in the success of PCS-ROSETTAfragment assembly, and their relative importance isdifficult to disentangle. In general, PCS data fromtwo or more lanthanides are expected to assistidentification of decoys with low rmsd to the targetstructure. While the structure of calmodulin, aprotein with 146 residues, was successfully deter-mined by PCS-ROSETTA, the structure of ɛ186 (186residues) was not found by the program despite theavailability of many PCSs overall (Table 1). Thescarcity of PCS values for residues near thelanthanide binding site may have contributed tothis effect. As the PCS-ROSETTA protocol did notsample structures below 10 Å rmsd (Fig. 3j) and asthe energy landscape defined by the PCS scoresbecame funnel-like only for structures with less thanabout 10 Å rmsd to the native structure (Fig. 1j), it isalso conceivable that the conformational spaceexplored by the basic ROSETTA sampling protocolneeds to be much larger for larger proteins. Toexplore the performance of PCS-ROSETTA for largeproteins and proteins that converge poorly with CS-ROSETTA, we performed test calculations usingsimulated PCS data. The results show consistentlyimproved convergence and identification of correct-ly folded substructures by PCS-ROSETTA, eventhough convergence to structures close to the targetstructure remained difficult (Supporting Informa-tion). An alternative sampling protocol, such asbroken chain sampling25 or iterative refinement,26

may be required for accurate PCS-assisted modelingof difficult proteins such as ɛ186.The present calculations were performed with

proteins containing single metal binding sites.Clearly, data from multiple metal ions usingdifferent metal binding sites will greatly enhancethe information content of PCS data. In particular,lanthanide ions display very different paramagneticproperties, while their chemical similarity allows alllanthanides to bind at a given lanthanide bindingsite. Several metal binding tags have recently beendeveloped to tag proteins site-specifically with aparamagnetic lanthanide; for a recent review, see

674 Protein Structure Determination using PCS-ROSETTA

Refs. 27 and 28. We note that PCSs were as useful fortargets devoid of natural metal binding sites (targetsA, C, D and E) as for metalloproteins (Fig. 2). Rigidattachment of lanthanides to the protein can beimportant as tag mobility may introduce errors inthe computed structure due to the averaging of thePCS effect, but we note that excellent fits of PCSs toprotein structures can also be obtained in thepresence of substantial tag mobility.29

In conclusion, we propose a new approach toprotein structure determination in which PCS dataare collected from natural or engineered metalbinding sites and then used to guide ROSETTAconformational search along with backbone chem-ical shift data. Although ROSETTA calculations arecomputationally demanding particularly for largerproteins, the PCS-ROSETTA method shows im-proved convergence and is applicable without theneed of time-consuming side-chain resonance as-signments and NOE measurements. The approachfurther allows reliable assessment of the accuracyand reliability of the lowest-energy models based onthe convergence of the calculation and the PCSquality factor. In view of the increasing rate withwhich specific lanthanide tags are being developedand commercialized for proteins,30 with multipleindependent lanthanide data sets and improvedconformational search methods, the approachshould be extendable to proteins greater than 150amino acids when backbone PCS data sets fromthree or more lanthanides are available. PCS-ROSETTA is available free of charges as a moduleof the academic release of the ROSETTA programfor protein modeling‡.

Materials and Methods

PCS-ROSETTA score

The PCS (in ppm) induced by ametal ionM on a nuclearspin can be calculated as31

PCScalci =1

12kr5i� Trace½ð 3x2i − r2i 3xiyi 3xizi

3xiyi 3y2i − r2i 3yizi3xizi 3yizi 3z2i − r2i

Þ�ðDmxx Dmxy Dmxz

Dmxy Dmyy DmyzDmxz Dmyz Dmzz

Þ� ð2Þ

where ri is the distance between the spin i and theparamagnetic center M; xi, yi and zi are the Cartesiancoordinates of the vector between the metal ion and thespin i in an arbitrary frame f; and Δχxx, Δχyy, Δχzz, Δχxy,Δχxz andΔχyz are theΔχ-tensor components in the framef (as Δχzz=−Δχxx−Δχyy, there are only five independent

‡The design is available at http://www.rosettacommons.org/

parameters). The Δχ-tensor components and the metalcoordinates are initially unknown and must be redeter-mined each time the PCS score c is evaluated. c iscalculated over all metal ions Mj as

c =Xj

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXi

PCScalci Mj� �

−PCSexpi Mj� �� �2

sð3Þ

where PCSicalc (Mj) and PCSi

exp (Mj) are the calculated andexperimental PCS values of spin i induced by the metal ionMj, respectively. The determination of the Δχ-tensorcomponents and the metal coordinates presents a non-linear least-square fitting problem. In order to avoid localminima and speed up the calculation, we split the probleminto its linear and nonlinear parts. Equation (2) shows thatPCSi

calc is linear with respect to the five Δχ-tensorcomponents. With the use of a 3D grid search over theCartesian coordinates xM, yM and zM of the paramagneticcenter, singular value decomposition optimizes the fiveΔχ-tensor parameters efficiently and without ambiguityfor lowest residual score c at each node of the grid. Thegrid node with the lowest c score is then used as thestarting point for optimization of the three metal co-ordinates along with the five Δχ-tensor components toreach the minimal cost c.The PCS score was added to the ROSETTA low-

resolution energy function using a different weightingfactor w(c) for each structure calculation. w(c) wasdetermined by first generating 1000 decoys with ROSET-TA and calculating w(c) as

w cð Þ = ahigh − alowchigh − clow

ð4Þ

where ahigh and alow are the average of the highest andlowest 10% of the values of the ROSETTA ab initio score,and chigh and clow are the average of the highest and lowest10% of the values of the PCS score c upon rescoring each ofthe 1000 decoys with the PCS. The weights used for the 10structure calculations performed in the present work aregiven in Supporting Information Table 1.

PCS-ROSETTA algorithm

PCS-ROSETTA uses the ROSETTA de novo structureprediction methodology to build low-resolution models,followed by all-atom refinement using the ROSETTAhigh-resolution Monte Carlo minimization protocol. Theadditions to the standard ROSETTA structure predictionmethods are as follows: the use of chemical shifts to guidefragment selection as in CS-ROSETTA, the use of PCS datato guide the initial low-resolution search and the use ofPCS data for final model selection. A flow diagram of thecomputational protocol of PCS-ROSETTA is shown inSupporting Information Fig. 5.

Input for PCS-ROSETTA

The backbone 1H, 13C and 15N diamagnetic chemicalshifts of all protein targets, with exception of thioredoxinfor which only 1H and 15N chemical shifts were available,were taken from the literature or from the BiologicalMagnetic Resonance Bank (Table 1 and Supporting

675Protein Structure Determination using PCS-ROSETTA

Information Table 0). CS-ROSETTA was used for frag-ment selection. CS-ROSETTA reports the differencebetween experimental and expected chemical shifts.Chemical shifts with very large deviations from expecta-tions (often attributable to errors in the deposited data)were removed from the input. CS-ROSETTA also suggestscorrections in the chemical shift referencing. We onlycorrected 13C chemical shifts, except for thioredoxinwhere 15N chemical shift was corrected (SupportingInformation Table 1). CS-ROSETTA aims to generate 200nine-residue fragments and 200 three-residue fragmentscentered on each residue of the polypeptide chain for usein the ab initio fragment assembly protocol of ROSETTA.In cases where CS-ROSETTA failed to generate 200fragments, we generated additional fragments using theconventional ROSETTA protocol in order to make 200fragments available. For each of the target proteins, weremoved any protein with recognizable sequence similar-ity (BLAST E-value below 0.05) from the CS-ROSETTAprotein database. E-values were computed against the CS-ROSETTA sequence database, which is approximately 500times smaller than the nonredundant database used byShen et al.18 Since E-values scale with database size, thisresults in a much stricter homology threshold and isequivalent to an E-value of approximately 25 if thenonredundant database of Shen et al. had been used. Inorder to accelerate the grid search for the metal position,PCS-ROSETTA allows a precise description of the space tobe searched, including the center of the grid search (cg),the step size between two nodes (sg), an outer cutoffradius (co) to limit the search to a minimal distance from cgand an inner cutoff radius (ci) to avoid a search too close tocg. A moderately large step size (sg) was chosen to speedup computations during low-resolution sampling (Sup-porting Information Table 1) and reduced to 25% of itsvalue during the final high-resolution scoring step toensure maximum accuracy. For each target, the gridparameters cg, co and ciwere chosen in accordance to priorknowledge about the approximate metal binding site. Forexample, for a covalent tag attached to the protein, weused the known geometric information of the tag to set cg,co and ci, whereas for proteins with a natural metalbinding site, a highly conserved negatively chargedresidue was picked as a reference point for cg. In theabsence of prior biochemical information, the nuclear spinwith the largest absolute PCS value was chosen as thecenter of the grid. Supporting Information Table 1summarizes the grid parameters used for the differentprotein targets. In order to assess the impact of the initialgrid parameters on the structures calculated, we per-formed a set of PCS-ROSETTA calculations for each target,where cg was centered at the nuclear spin of the largestPCS observed and where the cutoff radius co was set to15 Å. No change in the quality of the results was observed,but in most cases, the calculations took longer.

PCS-ROSETTA protocol for protein structuredetermination

Chemical shifts of the proteins were prepared in Talosformat32 and used by CS-ROSETTA for fragment selection.Chemical shift corrections, fragment selection and determi-nation of the weights w(c) were performed as describedabove. We computed 10,000 protein structures with PCS-

ROSETTA and subjected them to the full-atom relaxationprotocol of ROSETTA to model the side-chain conforma-tions. The final structures were rescored using the ROSET-TA full-atom energy function combinedwith the PCS scoresc, using the weighting factors w(c) [Eq. (4)] with ahigh andalow calculated against the ROSETTA full-atom energy andwith a total weight multiplied by 2 to give a largercontribution to the PCS score than in the fragment assembly.The best scoring structures can be assessed by the PCSquality factor Q=rms(PCScalc−PCSexp)/rms(PCSexp).Computation of 10,000 PCS-ROSETTA structures took onaverage 137CPUdaysper target (approximately three timeslonger than CS-ROSETTA calculations) and was run on alocal cluster. Supporting Information Fig. 6 shows a poster-iori that 1000 structures per targetswould have been enoughfor convergence of the protocol.

Computation of structures to evaluate the effects ofPCS scoring

We generated 3000 decoys with a wide range of rmsdvalues to the target structure by including the nativefragment and limiting the number of alternatives frag-ments in the fragment generation step of the ROSETTAcalculations. We calculated 1000 decoys each using two,five and ten fragments per residue, respectively. Thepresence of the native fragments in a small pool offragments ensured the generation of structures verysimilar to the target structure.

Acknowledgements

C.S. thanks the University of Queensland for aGraduate School Research Travel Grant to under-take this collaborative research project. T.H. thanksthe Australian Research Council for a FutureFellowship. Financial support from the AustralianResearch Council for project grants to G.O. and T.H.is gratefully acknowledged. D.B. thanks the HowardHughes Medical Institutes.

Supplementary Data

Supplementary data to this article can be foundonline at doi:10.1016/j.jmb.2011.12.056

References

1. Wüthrich, K. (1986).NMR of Proteins and Nucleic Acids.Wiley, New York, NY.

2. Raman, S., Lange, O. F., Rossi, P., Tyka, M., Wang, X.,Aramini, J. et al. (2010). NMR structure determinationfor larger proteins using backbone-only data. Science,327, 1014–1018.

3. Arnesano, F., Banci, L. & Piccioli, M. (2005). NMRstructures of paramagnetic metalloproteins. Q. Rev.Biophys. 38, 167–219.

676 Protein Structure Determination using PCS-ROSETTA

4. Bertini, I., Donaire, A., Jiménez, B., Luchinat, C.,Parigi, G., Piccioli, M. & Poggi, L. (2001). Paramagne-tism-based versus classical constraints: an analysis ofthe solution structure of Ca Ln calbindin D9k. J.Biomol. NMR, 21, 85–98.

5. Gaponenko, V., Sarma, S. P., Altieri, A. S., Horita,D. A., Li, J. & Byrd, R. A. (2004). Improving theaccuracy of NMR structures of large proteins usingpseudocontact shifts as long-range restraints. J. Biomol.NMR, 28, 205–212.

6. Pintacuda, G., Park, A. Y., Keniry, M. A., Dixon, N. E.& Otting, G. (2006). Lanthanide labeling offers fastNMR approach to 3D structure determinations ofprotein–protein complexes. J. Am. Chem. Soc. 128,3696–3702.

7. Ubbink, M., Ejdebäck, M., Karlsson, B. G. & Bendall,D. S. (1998). The structure of the complex ofplastocyanin and cytochrome f, determined by para-magnetic NMR and restrained rigid-body moleculardynamics. Structure, 6, 323–335.

8. Keizers, P. H. J., Mersinli, B., Reinle, W., Donauer, J.,Hiruma, Y., Hannemann, F. et al. (2010). A solutionmodel of the complex formed by adrenodoxin andadrenodoxin reductase determined by paramagneticNMR spectroscopy. Biochemistry, 49, 6846–6855.

9. John, M., Pintacuda, G., Park, A. Y., Dixon, N. E. &Otting, G. (2006). Structure determination of protein–ligand complexes by transferred paramagnetic shifts.J. Am. Chem. Soc. 128, 12910–12916.

10. Pintacuda, G., John, M., Su, X. C. & Otting, G. (2007).NMR structure determination of protein–ligand com-plexes by lanthanide labeling. Acc. Chem. Res. 40,206–212.

11. Zhuang, T., Lee, H. S., Imperiali, B. & Prestegard, J. H.(2008). Structure determination of a galectin-3-carbo-hydrate complex using paramagnetism-based NMRconstraints. Protein Sci. 17, 1220–1231.

12. Banci, L., Bertini, I., Cavallaro, G., Giachetti, A.,Luchinat, C. & Parigi, G. (2004). Paramagnetism-basedrestraints for Xplor-NIH. J. Biomol. NMR, 28, 249–261.

13. Banci, L., Bertini, I., Cremonini, M. A., Savellini, G. G.,Luchinat, C., Wüthrich, K. & Güntert, P. (1998).PSEUDYANA for NMR structure calculation ofparamagnetic metalloproteins using torsion anglemolecular dynamics. J. Biomol. NMR, 12, 553–557.

14. Banci, L., Bertini, I., Savellini, G. G., Romagnoli, A.,Turano, P., Cremonini, M. A. et al. (1997). Pseudo-contact shifts as constraints for energy minimizationand molecular dynamics calculations on solutionstructures of paramagnetic metalloproteins. Proteins:Struct., Funct., Genet. 29, 68–76.

15. Hus, J. C., Marion, D. & Blackledge, M. (2000).De novodetermination of protein structure by NMR usingorientational and long-range order restraints. J. Mol.Biol. 298, 927–936.

16. Simons, K. T., Kooperberg, C., Huang, E. & Baker, D.(1997). Assembly of protein tertiary structures fromfragments with similar local sequences using simulat-ed annealing and Bayesian scoring functions. J. Mol.Biol. 268, 209–225.

17. Raman, S., Vernon, R., Thompson, J., Tyka, M.,Sadreyev, R., Pei, J. et al. (2009). Structure predictionfor CASP8 with all-atom refinement using Rosetta.Proteins: Struct., Funct., Bioinformatics, 77, 89–99.

18. Shen, Y., Lange, O., Delaglio, F., Rossi, P., Aramini,J. M., Liu, G. H. et al. (2008). Consistent blind proteinstructure generation from NMR chemical shift data.Proc. Natl Acad. Sci. USA, 105, 4685–4690.

19. Bradley, P., Misura, K. M. S. & Baker, D. (2005).Toward high-resolution de novo structure predictionfor small proteins. Science, 309, 1868–1871.

20. Cornilescu, G., Marquardt, J. L., Ottiger, M. & Bax, A.(1998). Validation of protein structure from anisotrop-ic carbonyl chemical shifts in a dilute liquid crystallinephase. J. Am. Chem. Soc. 120, 6836–6837.

21. Su, X. C., Man, B., Beeren, S., Liang, H., Simonsen, S.,Schmitz, C. et al. (2008). A dipicolinic acid tag forrigid lanthanide tagging of proteins and paramag-netic NMR spectroscopy. J. Am. Chem. Soc. 130,10486–10487.

22. Barry, C. D., North, A. C. T., Glasel, J. A., Williams,R. J. P. & Xavier, A. V. (1971). Quantitative determi-nation of mononucleotide conformations in solutionusing lanthanide ion shift and broadening NMRprobes. Nature, 232, 236–245.

23. Brunger, A. T., Adams, P. D., Clore, G. M., DeLano,W. L., Gros, P., Grosse-Kunstleve, R. W. et al. (1998).Crystallography & NMR system: a new software suitefor macromolecular structure determination. ActaCrystallogr., Sect. D: Biol. Crystallogr. 54, 905–921.

24. Bertini, I., Longinetti, M., Luchinat, C., Parigi, G. &Sgheri, L. (2002). Efficiency of paramagnetism-basedconstraints to determine the spatial arrangement of α-helical secondary structure elements. J. Biomol. NMR,22, 123–136.

25. Bradley, P. & Baker, D. (2006). Improved beta-proteinstructure prediction by multilevel optimization ofnonlocal strand pairings and local backbone confor-mation. Proteins, 65, 922–929.

26. Qian, B., Raman, S., Das, R., Bradley, P., McCoy, A. J.,Read, R. J. & Baker, D. (2007). High-resolutionstructure prediction and the crystallographic phaseproblem. Nature, 450, 259–264.

27. Su, X. C. &Otting, G. (2010). Paramagnetic labelling ofproteins and oligonucleotides for NMR. J. Biomol.NMR, 46, 101–112.

28. Keizers, P. H. & Ubbink, M. (2011). Paramagnetictagging for protein structure and dynamics analysis.Prog. Nucl. Magn. Reson. Spectrosc. 58, 88–96.

29. Graham, B., Loh, C. T., Swarbrick, J. D., Ung, P., Shin,J., Yagi, H. et al. (2011). A DOTA-amide lanthanide tagfor reliable generation of pseudocontact shifts inprotein NMR spectra. Bioconjug. Chem. 22, 2118–2125.

30. Jia, X., Maleckis, A., Huber, T. & Otting, G. (2011).4,4′-Dithiobisdipicolinic acid: a small and convenientlanthanide binding tag for protein NMR spectroscopy.Chem. Eur. J. 17, 6830–6836.

31. Bertini, I., Luchinat, C. & Parigi, G. (2002). Magneticsusceptibility in paramagnetic NMR. Prog. Nucl.Magn. Reson. Spectrosc. 40, 249–273.

32. Cornilescu, G., Delaglio, F. & Bax, A. (1999). Proteinbackbone angle restraints from searching a databasefor chemical shift and sequence homology. J. Biomol.NMR, 13, 289–302.

33. Wilton, D. J., Tunnicliffe, R. B., Kamatari, Y. O.,Akasaka, K. & Williamson, M. P. (2008). Pressure-induced changes in the solution structure of the GB1domain of protein G. Proteins, 71, 1432–1440.

677Protein Structure Determination using PCS-ROSETTA

34. Saio, T., Ogura, K., Yokochi, M., Kobashigawa, Y. &Inagaki, F. (2009). Two-point anchoring of a lantha-nide-binding peptide to a target protein enhances theparamagnetic anisotropic effect. J. Biomol. NMR, 44,157–166.

35. Balayssac, S., Jiménez, B. & Piccioli, M. (2006).Assignment strategy for fast relaxing signals: com-plete aminoacid identification in thulium substitutedcalbindin D9K. J. Biomol. NMR, 34, 63–73.

36. Mueller, G. A., Kirby, T. W., DeRose, E. F., Li, D.,Schaaper, R. M. & London, R. E. (2005). Nuclearmagnetic resonance solution structure of the Escher-ichia coli DNA polymerase III θ subunit. J. Bacteriol.187, 7081–7089.

37. Schmitz, C., Stanton-Cook, M. J., Su, X. C., Otting, G.& Huber, T. (2008). Numbat: an interactive softwaretool for fitting Δχ-tensors to molecular coordinatesusing pseudocontact shifts. J. Biomol. NMR, 41,179–189.

38. Su, X. C., Liang, H., Loscha, K. V. & Otting, G. (2009).[Ln(DPA)3]

3− is a convenient paramagnetic shiftreagent for protein NMR studies. J. Am. Chem. Soc.131, 10352–10353.

39. Bertini, I., Del Bianco, C., Gelis, I., Katsaros, N.,Luchinat, C., Parigi, G. et al. (2004). Experimentallyexploring the conformational space sampled bydomain reorientation in calmodulin. Proc. Natl Acad.Sci. USA, 101, 6841–6846.

40. Chandrasekhar, K., Krause, G., Holmgren, A. &Dyson, H. J. (1991). Assignment of the 15N NMR

spectra of reduced and oxidized Escherichia colithioredoxin. FEBS Lett. 284, 178–183.

41. Lemaster, D. M. & Richards, F. M. (1988). NMRsequential assignment of Escherichia coli thioredoxinutilizing random fractional deuteriation. Biochemistry,27, 142–150.

42. Jensen, M. R. & Led, J. J. (2006). Metal–proteininteractions: structure information from Ni2+-inducedpseudocontact shifts in a native nonmetalloprotein.Biochemistry, 45, 8782–8787.

43. Baig, I., Bertini, I., Del Bianco, C., Gupta, Y. K., Lee,Y. M., Luchinat, C. & Quattrone, A. (2004). Para-magnetism-based refinement strategy for the solutionstructure of human α-parvalbumin. Biochemistry, 43,5562–5573.

44. Bertini, I., Kursula, P., Luchinat, C., Parigi, G.,Vahokoski, J., Wilmanns, M. & Yuan, J. (2009).Accurate solution structures of proteins from X-raydata and a minimal set of NMR data: calmodulin–peptide complexes as examples. J. Am. Chem. Soc. 131,5134–5144.

45. DeRose, E. F., Li, D.W., Darden, T., Harvey, S., Perrino,F. W., Schaaper, R. M. & London, R. E. (2002). Modelfor the catalytic domain of the proofreading epsilonsubunit of Escherichia coliDNApolymerase III based onNMR structural data. Biochemistry, 41, 94–110.

46. Schmitz, C., John, M., Park, A. Y., Dixon, N. E., Otting,G., Pintacuda, G. & Huber, T. (2006). Efficient χ-tensor determination and NH assignment of para-magnetic proteins. J. Biomol. NMR, 35, 79–87.