Arginine Kinase: Joint Crystallographic and NMR RDC Analyses Link

Contents lists available at www.sciencedirect.com

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

doi:10.1016/j.jmb.2010.11.007 J. Mol. Biol. (2011) 405, 479–496

Arginine Kinase: Joint Crystallographic and NMR RDCAnalyses Link Substrate-Associated Motions toIntrinsic Flexibility

Xiaogang Niu1, Lei Bruschweiler-Li1, Omar Davulcu2, Jack J. Skalicky3,Rafael Brüschweiler1 and Michael S. Chapman2⁎1Department of Chemistry and Biochemistry, Florida State University, Tallahassee, FL 32306, USA2Department of Biochemistry and Molecular Biology, School of Medicine, Oregon Health and Science University,Portland, OR 97239-3098, USA3Department of Biochemistry, University of Utah School of Medicine, Salt Lake City, UT 8412-5650, USA

Received 20 July 2010;received in revised form21 September 2010;accepted 1 November 2010Available online12 November 2010

Edited by A. G. Palmer III

Keywords:induced fit;conformational selection;protein dynamics;conformational change;residual dipolar coupling

*Corresponding author. E-mail [email protected] used: AK, arginine

difference distance matrix; RDC, rescoupling; 3D, three-dimensional; PDPEG, polyethylene glycol; TROSY, toptimized spectroscopy; HSQC, hetquantum coherence; TLS, translation

0022-2836/$ - see front matter © 2010 E

The phosphagen kinase family, including creatine and arginine kinases(AKs), catalyzes the reversible transfer of a “high-energy” phosphatebetween ATP and a phosphoguanidino substrate. They have become amodel for the study of both substrate-induced conformational change andintrinsic protein dynamics. Prior crystallographic studies indicated largesubstrate-induced domain rotations, but differences among a recent set ofAK structures were interpreted as a plastic deformation. Here, the structureof Limulus substrate-free AK is refined against high-resolution crystallo-graphic data and compared quantitatively with NMR chemical shifts andresidual dipolar couplings (RDCs). This demonstrates the feasibility of thistype of RDC analysis of proteins that are large by NMR standards (42 kDa)and illuminates the solution structure, free from crystal-packing constraints.Detailed comparison of the 1.7 Å resolution substrate-free crystal structureagainst the 1.7 Å transition-state analog complex shows large substrate-induced domain motions that can be broken down into movements ofsmaller quasi-rigid bodies. The solution-state structure of substrate-free AKis most consistent with an equilibrium of substrate-free and substrate-bound structures, with the substrate-free form dominating, but withvarying displacements of the quasi-rigid groups. Rigid-group rotationsevident from the crystal structures are about axes previously associatedwith intrinsic millisecond dynamics using NMR relaxation dispersion.Thus, “substrate-induced” motions are along modes that are intrinsicallyflexible in the substrate-free enzyme and likely involve some degree ofconformational selection.

© 2010 Elsevier Ltd. All rights reserved.

ess:

kinase; DDM,idual dipolarB, Protein Data Bank;ransverse relaxationeronuclear single, libration, and screw.

lsevier Ltd. All rights reserve

Introduction

Protein motions are intrinsically more difficult tostudy than their time-averaged structures, but as theirpotential relevance to function has come into light, thecharacterization of dynamics has become one of thecentral challenges in structural biochemistry.1–6 Thenotion of induced fit, introduced by Koshland,7,8

helped a generation understand how conformational

d.

mailto:[email protected]

http://dx.doi.org/

480 Crystallographic and NMR Analysis of AK Flexibility

changes, required for catalysis or needed in regula-tion, could be driven by specific substrate or ligandinteractions. Implicit was the premise that suchconformational changes were driven by the freeenergy of new substrate/ligand interactions. Thispremise has been questioned with increasing indica-tions that, at least in some systems, the ligand mightbe more accurately represented as capturing orstabilizing one of the conformational variants sam-pled with intrinsic motions, even in the absence ofligand.9–12 In the emerging paradigm of conforma-tional selection, substrate/ligand binding is proposedto shift a preexisting equilibrium in favor of a boundconfiguration. It is proposed to be at work in thesubstrate-associated conformational changes of anumber of enzymes.9,11,13–16 For other enzymes, amore classical induced-fit mechanism is still consid-ered to be more appropriate.17 Induced fit andconformational selection represent the extremes on acontinuum, where a mixture might be common.17

Selection of a particular conformation implies stabili-zation, presumably with energy coming from sub-strate/ligand association. It is also possible thatselection of a conformation closer to the bound formis followed by an induced change that is driven by theenergy of ligand binding. There is very little under-standing of how much of the substrate-associatedconformational change exists intrinsically within anenzyme's ensemble of conformational variants.Phosphagen kinases, such as creatine kinase,

catalyze the reversible transfer of a phosphatebetween a phosphoguanidino substrate (such asphosphocreatine) and ADP to generate ATP.18

Phosphagen kinases function in cellular energyhomeostasis, maintaining near-constant levels ofATP in spite of transient fluctuations in demand.They have long been a model system for classicalenzymology.Arginine kinase (AK) is usually a 42-kDamonomer in contrast to the dimeric or octamericforms of creatine kinase and is chosen for itsamenability to both X-ray crystallography andNMR spectroscopy. Structures first became availablefor creatine kinase in its “open” form, eithersubstrate-free or with ADP bound,19,20 and then forthe “closed” transition-state analog (TSA) form ofAK21 containing substrates arginine, ADP, and anitrate mimicking the trigonal-planar phosphatebeing transferred. Subsequently, transition-statestructures of creatine kinase22 have become avail-able, as have substrate-free structures of LimulusAK.23,24 These structures have revealed substantialconformational changes upon substrate binding thatappear to be fundamentally similar throughout theenzyme family and consistent with previouslymeasured solution scattering.25–28 The conforma-tional changes were characterized crystallographi-cally as rotations inward by up to 18° of three quasi-rigid dynamic domains.23 Dynamic domains aredefined as groups of residues that are contiguous in

three-dimensional (3D) space (but not necessarily inlinear sequence) whose displacement is predomi-nantly rigid group.29,30 It was proposed that therigid-group movements, together with the reorder-ing of two flexible active-site loops, not only movedamino acids into their catalytic configuration but alsoexcluded solvent from the active site (as proposed forother kinases),minimizing awasteful hydrolytic sidereaction.31,32

Recently, structures of the distantly related Sticho-pus dimeric AK have been used to re-characterizethe motion as an inward bending with the confor-mational changes occurring everywhere.24 Thestructures were determined in substrate-free formand as a Michaelis-like complex with substratearginine and analog AMPPNP at 1.75 and 2.45 Åresolutions, respectively. The authors found littleevidence of a rigid-group rotation between N- andC-terminal domains but did not report any attemptto subdivide the C-terminal region as in the priorwork23 (see also related comments33). Support forsegmented rotation between quasi-rigid groups inAK has come from NMR relaxation dispersionanalysis. The sites of chemical exchange correlatedapproximately with the rigid-group boundaries,indicating intrinsic flexibility (in the absence ofsubstrates) roughly where the hinge points wouldbe expected.34 These experiments also revealed thatthe exchange rate for conformational changes in aflexible loop, and at the interface between N- and C-terminal domains, was commensurate with enzymeturnover (∼135 s− 1).35–37 This emphasizes thepotential functional significance in that the proteinconformational changes may be rate limiting on theenzyme.In the work reported here, a crystallographic

structure of substrate-free LimulusAK is extended to1.7 Å resolution, such that comparison with the 1.2Å resolution TSA structure can be used for a robustand detailed appraisal of the rigid-group approxi-mation. Due to the size of AK (42 kDa), determina-tion of the 3D structure of AK in solution bystandard Nuclear Overhauser enhancement NMRmethods would be very challenging. Instead,residual dipolar coupling (RDC), measured fromweakly aligned protein and interpreted with thecrystal structures was used to understand thesolution structure.38,39

Results and Discussion

Detailed analysis of the NMR results is based onthe crystallographic structures, which are presentedfirst. However, the NMR and crystallographicrefinements proceeded in parallel, facilitating eachother. In fact, it was greater consistency of the NMRchemical shifts for the substrate-free enzyme withthe TSA crystal structure that motivated higher-

Table 1. Summary of diffraction data and refinementstatistics

Space group P21Unit cell dimensionsa (Å) 60.2b (Å) 90.4c (Å) 70.6β (°) 111Subunits per asymmetric unit 2Resolution range (Å)a 27–1.73

(1.77–1.73)Rmerge

b 0.069 (0.517)Completeness (%) 95 (98)Rcryst 0.19 (0.26)Rfree 0.24 (0.29)RMSD bond lengths (Å)/RMSD bond angles (°) 0.005/0.856No. of protein atoms 5562Wilson/mean protein B-factor (Å2)

(isotropic equivalent)17.6/26.7

Estimated error (maximum likelihood, Å) 0.23a Numbers in parentheses are values in highest-resolution shell.b Rmerge=∑hkl∑i|Ii(hkl)− ⟨I(hkl)⟩|/∑hkl∑iIi(hkl), where Ii(hkl) is

the ith observation of a symmetry equivalent of reflection hkl.

481Crystallographic and NMR Analysis of AK Flexibility

resolution refinement of the substrate-free crystalstructure.

Crystallographic structure refinement

The current analysis extends the resolution of thesubstrate-free structure to 1.7 Å. Refinement statis-tics are presented in Table 1. Overall, the structure issimilar to that refined at 2.4 Å resolution23 [ProteinData Bank (PDB) ID 1M80]. A good indicator ofmodel improvement is the decrease in the unre-strained Cα RMSD between A and B chains from0.57 Å in the 2.4-Å structure to 0.36 Å here, a numberconsistent with the estimated overall coordinateerror of ±0.23 Å.

Fig. 1. Superposition of 15N–1H TROSY (red) and HSQC (blrecoded at 800 MHz. The inset shows half of the one-bond 15Nbetween 15N frequency in the TROSY and HSQC spectra.

Local improvements to the structure include theredesignation of residues 136–140, 192–197, and289–292 as short α-helices and the extension ofseveral secondary structural elements as hydrogenbonding became clearer. Most noteworthy is theextension of a helix (previously residues 298–304) tonow include residues 293–304. The prior tracingthrough weak density was incorrect, involving alocal single-residue frameshift error, and the higher-resolution density showed the correct path clearly.All the changes improve the local agreement withthe 1.2 Å TSA structure.40 Thus, it is now apparentthat there is no partial unfolding of the 293–304 helixupon substrate binding.23 It is emphasized that eventhough the changes improve the local agreement ofsubstrate-free and substrate-bound structures, theoverall difference between the two structuresremains substantial at 2.9 Å (Cα RMSD) due todomain-sized rotations. However, improvement inthe local consistency of the two structures hasallowed more precise analysis of the conformationalchanges (below).

Solution structure by NMR RDC

Two independent sets of RDCs of apo-AK weremeasured in polyethylene glycol (PEG) alkyl etherand Pf1 Phage alignment media in solution by15N–1H transverse relaxation optimized spectroscopy(TROSY) and heteronuclear single quantum coher-ence (HSQC) spectra (Fig. 1). RDCs allow directvalidation of a 3D structural model of a protein.The two sets of RDCs were fit to the crystalstructures of substrate-free AK (3M10) and theTSA (1M15). Figure 2 shows the correlationsbetween RDCs calculated from the substrate-freecrystal structure (open form) and the experimental

ack) spectrum of substrate-free AK in 10 mg/ml Pf1 phage–1H splittings (JNH+DNH)/2 measured from the difference

Fig. 2. Correlation plot between the back-calculated 15N–1H RDCs and the experimental RDCs of substrate-free AKfrom PEG (a and c) and Pf1 phage (b and d). For (a) and (b), the experimental RDCs were fit to the substrate-free crystalstructure of AK (open form). For (c) and (d), the experimental RDCs were fit to the transition-state crystal structure of AK(closed form). Parenthetical Q-values were calculated without loop 310–320, which is not visible in the substrate-freecrystal structure.


RDCs measured in PEG (Fig. 2a) and Pf1 phage(Fig. 2b). For comparison, Fig. 2c and d show theRDCs calculated from TSA (closed form)40 versusthe experimental RDCs measured in PEG (Fig. 2c)and Pf1 phage (Fig. 2d).The level of agreement between the experimental

RDCs and the calculated RDCs is expressed in termsof a Q-value.38 The substrate-free crystal structureyields significantly lower Q-values (0.34 and 0.39),that is, better agreement, than the transition-statecrystal structure (0.49 and 0.46) for RDCs from PEGand Pf1 phage, which indicates that, following high-resolution refinement, the substrate-free crystalstructure is a better model for solution-state sub-strate-free AK.

Crystallographic analysis of conformationalchanges upon substrate binding

Regions with pseudo-rigid conformational transi-tions between substrate-free and TSA crystal struc-tures of AK were identified by analysis of thedifference distance matrices (DDMs) using the

program ESCET.41 Quasi-rigid segments of thebackbone can be recognized as blocks along thediagonal with consistently low values (gray in Fig. 3).Qualitatively, there is good correspondence betweenour DDM for the Limulus TSA and one for theStichopus AMPPNP·Arg·AK complex determinedrecently.24 However, the higher-precision Limulusstructures give a cleaner DDM, from which it is clearthat the conformational change is not an even plasticdeformation as described for the Stichopus complex.24

When the DDM is viewed with a high threshold(1.5 Å or 8 σ), it is apparent that the N-terminaldomain of∼100 residues is the largest andmost rigidof the blocks. It closes upon substrate binding by∼12 Å relative to the ∼85 C-terminal residues, asindicated by the intensely shaded regions in thebottom left and top right of the DDM (Fig. 3). Withinthe ∼200 middle residues, a series of blocks on thediagonal indicates segmented motions that the off-diagonal terms show are intermediate between theN- and C-terminal regions. One has to look at alower threshold (0.7 Å or 3 σ) to see, in detail, howthe 260 C-terminal residues are segmented into at

image of Fig. 2


least 12 diagonal blocks. Thesemake sense onlywhenone searches for combinations of noncontiguoussegments of the sequence that behave like rigidgroups (see below).Both ESCET41 and DynDom44 were used to

determine sets of residues that behaved as quasi-rigid bodies. The methods employ different algo-rithms. ESCET looks for near-zero off-diagonalregions in the DDM that indicate correlated dis-placement, while DynDom looks for regions in 3Dspace in which the residues from one structure mapto the second with similar rotational transforma-tions. Both methods favor five rigid bodies betweenwhich most of the residues of the structure areallocated. In spite of each method's sensitivity toinput parameters, the two methods have 79%agreement in the allocation of residues to each rigidgroup. About half of the remaining discrepanciesinvolve choice in the exact boundary between rigidand flexible parts. The other discrepancies resultfrom different sorting of backbone fragments intofour rigid groups within the 257-residue C-terminalpart. The challenge is apparent when the DDM isviewed at 3 σ or ±0.7 Å. Near-zero cross-terms allowsome of the fragments to be combined unambigu-ously, but for others, the choice between two of thegroups seems equally plausible, and the programshave not always made the same choice. In construct-ing a consensus designation (Table S1 and Table 2),locally, one of the two solutions, or a compromise,was chosen to minimize the fragmentation insequence and 3D space.The substrate-free and substrate-bound structures

differ by 2.9 Å (Cα RMSD) when superimposed assingle rigid groups. When superimposed as the fiverigid groups, the Cα RMSD drops to 0.7 Å. This isabout twice the deviation between the chemicallyidentical A and B chains of the substrate-freestructure; hence, the rigid-group approximationleaves some local changes unaccounted for.However,the decrease in RMSD from 2.9 to 0.7 Å correspondsto 94% of the mean-square deviation (variance),indicating that the rigid-group designation is anexcellent first-order approximation for the actualconformational changes, especially considering thatcrystal-packing interactions likely have some effect.The remaining 0.7 Å residual may also reflectuncertainties in the exact boundaries of the quasi-rigid groups. It also reflects the extent to which theactual structure bends gradually through hingepoints, as opposed to the sharp transition impliedin a rigid-group approximation.Rigid-group rotations between the substrate-free

and transition-state structures are robustly deter-mined and not sensitive to residual coordinateerrors. When superimpositions of the transition-state rigid groups to the A and B chains of thesubstrate-free form are compared, the directions ofrotation axes have a maximum discrepancy of 13°

(between groups 1 and 2) and a mean discrepancy of5°. The average discrepancy in the magnitude of therotations is only 2°.The rotational component of the rigid-group trans-

formations accounts for more than 80% of the totalmovement between substrate-free and substrate-bound forms. For group 3, up to half of the motionis translation, but for all other groups, rotationdominates (Table 2). The rotations are predominantlyclosure, except for group 3, which is more balanced inclosure and twist components. Not only are the axesoriented consistently with closure (or opening), butthe off-diagonal elements of the DDM show predom-inantly reductions of intergroup distances on sub-strate binding (Fig. 3, below), consistent with physicalclosure.Several points are noteworthy about the quasi-rigid-

group interpretation of substrate-associated confor-mational changes: (1) When mapped to the 3Dstructure (Fig. 4), disparate regions of the sequence,grouped together by ESCET or DynDom, are broughtinto close proximity. One example is the grouping ofloops 193–201 and 269–276 with the N-terminaldomain (1–102) (green in Fig. 4). (2) In the middle ofthe sequence, short stretches are alternately assignedto groups 2 and 4 (red and teal). The alternatingsegments correspond to opposite ends of the strandsof the β-sheet, which is divided by a hinge runningdiagonally across the strands (Fig. 4a and b).Flexibility in a β-sheet might seem counterintuitive,but supporting evidence will be provided below. (3)With the exception of group 3 (blue), the combinedeffect of the hinges (Fig. 4b) is a segmented bendingthat brings rigid groups 1 and 5 (green and orange)towards each other. The intergroup rotation axes arenot fully parallel but constitute a spiral. (4) Relativeto the transition-state form, rotation of group 5(orange) in the substrate-free form points the ends offlexible loop 311–319 away from the active site andtowards exterior solvent (or crystal contacts). In thesubstrate-free form, the loop would form fewerintramolecular interactions, explaining its apparentflexibility in both crystal and NMR structures (seebelow). In our substrate-free crystals, this puts theloop in contact with a neighboring molecule that isnot related by lattice symmetry such that the twochains would have different configurations. Interac-tions with neighbors may account for the conforma-tional diversity of this loop in the homologues wherethe structures can be resolved.The largest displacement between substrate-free

and substrate-bound forms is of group 5 (6.9 Å;orange) as it rotates 30° with respect to the rest of theprotein. Relative to its immediate neighbor (group 4,teal), the rotation is 18° (Table 2); thus, the totalrotation has contributions from the other intergrouphinges. Group 5 brackets the 311–319 flexible loopthat is unseen in the substrate-free form and,therefore, not part of any of the assigned groups.

Fig. 3. (a and b) DDMs for AK calculated with the program ESCET.41 The intensity of the color is proportional to thechange in distance. Error weighting makes little difference; thus, angstroms are used rather than σ. Residue numbers areshown along the axes. The secondary structure is designated underneath with open boxes for α-helices and filled boxes forβ-strands. Red pixels indicate residues that are closer in the transition-state form than in the substrate-free form. There aremore red regions than blue, because, overall, the enzyme closes upon substrate binding. Segments of backbone that aremoving as quasi-rigid groups will appear as mostly gray boxes along the diagonal. If disparate regions of the sequencehave the same rigid transformation, the off-diagonal cross-terms will be close to zero (gray). Assignments to the consensusrigid groups are shown to the right of each panel. (a) Substrate-free minus the TSA complex structures (PDB IDs 3M10 and1M15, respectively). The top right half uses a high (1.5 Å) threshold to highlight features that are rigid in crudeapproximation. The bottom-left half reveals the intradomain segment structure at lower threshold (0.7 Å). (b) Differencesamong the ensemble fit to the NMR data for the substrate-free enzyme. Unlike (a) that examined systematic differencesbetween open and closed states, the NMR structures are distributed about an average; hence, there should be near-equalpositive (red) and negative (blue) terms. The amplitude of the intrinsic variation in panel b is smaller than the amplitudeof the substrate-induced change in panel a, so the DDM is less clear, but the distribution of rigid and flexible regions issimilar to that in (a). (c) Delta matrix calculated from the anisotropic individual B-factors of the 1.2 Å resolution structureof the TSA complex.40,42 Darkness signifies deviation from Hirshfeld's rigid-body postulate43 for the paired groups ofatoms. Light regions indicate groups whose displacements are substantially rigid in the cryo-frozen structure:approximately residues 2–107, 112–286, and 300–353. This is in approximate agreement with the high-threshold DDM (a).


image of Fig. 3

Fig. 3 (legend on previous page)


However, it likely plays a critical role in the transition-state configuration of group 5, with interactions toboth of the substrates: Thr311 hydrogen-bondedto the ribose, Arg309 salt-bridged to the α- andγ-phosphates, and Glu314 had a backbone hydrogenbond to the α-phosphate and side-chain interactionswith the substrate guanidinium.It is when this is combined with the 17° rotation of

the mostly N-terminal group 1 that the enzymeclosure is achieved. The motions of groups 1 and 5(green and orange) are mostly in opposite directionssuch that the 5.5 and 6.9 Å movements bring thegroups 10.4 Å closer. The rotations of group 1relative to 3D neighbors, groups 2 and 4 (red andteal), and to group 3 (blue) are 11°, 21°, and 37°,respectively; the effects of segmented rotation areonce again apparent. There are several interactions

that could stabilize the closed state. Residues 65through 68, part of the substrate-specificity loop,45,46

hydrogen bondwith the guanidinium substrate. Theimmediate neighbor of the specificity loop, andmoving as part of group 1 (green), is the loopcontaining the active-site Cys271 that interacts withthe substrate guanidinium.21The next most obvious change (Fig. 4) is in group 3

(blue), containing helix 174–185. One component ofthe motion is along the helix axis towards the activesite, bringing His185 into hydrogen-bondingdistance with the substrate ribose. This motionhelps to close the active site but does not appearlinked to other changes. There is also a swingingout of the N-terminal end of the helix that can beseen in Fig. 4a and which seems to be coupledwith the bending of the β-sheet (below).

Fig. 3 (legend on page 484)

Table 2. Large rotations and small translations between the quasi-rigid groups in going from the substrate-free to thetransition state form of AK

Rigid group(no. of residues) Residues 1 2 3 4 5

1 (118) 2–102, 193–201, 269–276 Rotation (°): 10.9 45.6 21.1 36.6Translation (Å): 0.3 3.4 0.2 0.7Movement (RMS) (Å): 2.7 6.5 7.5 10.4Closure (%): 96 88 91 71

2 (57) 129–155, 167–173, 202–213,221–229, 258–259

Rotation (°): 36.4 13.7 31.1Translation (Å): 1.3 0.2 0.4Movement (RMS) (Å): 3.4 4.2 8.4Closure (%): 100 100 99

3 (14) 174–187 Rotation (°): 34.4 44.4Translation (Å): 4.1 1.7Movement (RMS) (Å): 10.1 13.8Closure (%): 48 86

4 (121) 103–128, 156–166, 216–220, 230–257,260–268, 277–290, 330–357

Rotation (°): 18.0Translation (Å): 0.5Movement (RMS) (Å): 2.9Closure (%): 100

Residues are assigned according to the consensus designation. Transformations were calculated using the DomSelect program44 andmalign.py.


Fig. 4. (a) The crystallographic structures of the open (substrate-free) form (opaque) and closed (transition state) form(transparent) have been superimposed within the largest rigid group (#4). Regions are colored according to the consensusrigid-group designation: 1, green; 2, red; 3, blue; 4, teal; 5, orange. Flexible regions are colored gray, except for the active-site loop (311–319; pink), which is seen only when substrates (ball-and-stick) are bound. (b) Correlation of rigid-grouphinge axes with sites of intrinsic dynamics. On top of the substrate-free (opaque) and TSA (translucent) structures areoverlaid the axes of rotation between the different rigid groups. (With the exception of group 3, all of the transformationsare predominantly rotations with small translational components.) Residues exhibiting NMR relaxation exchange, oftenindicative of local dynamics, were identified earlier34 and are highlighted here with a wider ribbon. Residues for which nodetermination was possible (missing or degenerate resonances) are colored light brown.


Groups 2 and 4 (red and teal) form the core of theC-terminal domain. It is here that the newly refinedstructure has helped most in understanding theperhaps surprising flexing of the β-sheet spanningboth groups. The rotation between groups 2 and 4 is14° (a 4-Åmovement, Table 2), and it is visible in Fig.4a where group 4 (teal) has been superimposed andgroup 2 (red) is clearly rotated. From Fig. 4a, it isdifficult to distinguish a hinged motion between rigidgroups from a gradual deformation through the sheet.

The reality is likely to be neither one exclusively, butsome combination. However, there is evidence that ahinged motion is a good first approximation. Firstly,the fitting of two rigid groups accounts for 4.2 Å of the4.3 Å RMSD in the superimposed coordinates. Theremaining residual of only 0.8 Å includes experimen-tal error as well as the deviations from rigid behavior,which are therefore quite small. Later, evidence ofintrinsic conformational variation at the residues atthe interface of these rigid groups will be presented.

image of Fig. 4


Comparison of the NMR solution structure to thecrystal structures

Optimizations of atomic models against the NMRRDC and chemical shift observations were stableonly with restraints to the crystallographic struc-tures. The number of NMR observables is insuffi-cient for independent analysis at the amino acidlevel. However, insights are possible through thefitting of an ensemble of atomic models followed byanalysis of the ensemble variance in ways that arenot sensitive to the exact restraints employed.Distance-dependent matrices offer such an oppor-tunity. While the overall magnitude of the termsdepends on the strength of structural restraints to acrystallographic target, the spatial distribution ofsmall and large terms shows where the NMR dataindicate flexibility and deviation from the restrainttarget.The DDM calculated from the NMR ensemble

shows features that are strikingly similar to thosecalculated between the open (substrate-free) and

Fig. 5. Q-values between the experimental RDCs from PEGthe open (substrate-free) and closed (TSA) structures are rapidthe substrate-free form, Papo, and the transition-state form, 1found between the two crystal states. (c and d) The RMSD ofshifts predicted from the two state model using SHIFTX (c) an

closed (transition state) crystal structures (Fig. 3).The magnitudes of the terms differ, due to differ-ences between intrinsic (NMR) and induced (crys-tallographic) conformational changes and due to thestructural restraints used in NMR refinement. Thesigns (red/blue coloring) may also be inverted,because the DDM of an (NMR) ensemble is theaverage of all possible pairwise comparisons wherethe reference structures of each pair are chosenconsistently, but the program makes an arbitrarychoice whether the reference state of the first pair isthe more open or closed form. The NMR DDMclearly indicates that loops 170–196 and 307–320are weakly restrained by the NMR data and/orthe most flexible of the structure. This is fullyconsistent with atomic displacement parametersand disorder in the crystal structures, as well asprior NMR relaxation characterization ofdynamics.34 Even more noteworthy is the similar-ity of the NMR and crystallographic DDMs intheir distribution of low-value (gray) blocks alongthe diagonal (Fig. 3), which indicate that similar

(a) and phage (b) and RDCs calculated by assuming thatly interconverting. Q-values vary with the populations of−Papo, used to build the model. The lowest Q-values areexperimental Cα and Cβ chemical shifts and the chemicald SPARTA (d).

image of Fig. 5

Table 3. Qsubj values showing the agreement between

experimental and calculated NMR RDCs for each rigidgroup using the substrate-free and transition-state crystalstructures

Rigidgroup

Substrate-free Transition-state analog

PEG Phage PEG Phage

1 0.38 (0.38) 0.35 (0.36) 0.35 (0.44) 0.33 (0.36)2 0.16 (0.20) 0.20 (0.23) 0.21 (0.29) 0.21 (0.32)3 0.37 (0.78) 0.19 (0.72) 0.22 (1.3) 0.37 (1.2)4 0.33 (0.35) 0.47 (0.49) 0.29 (0.37) 0.26 (0.30)5 0.35 (0.43) 0.31 (0.34) 0.28 (0.75) 0.31 (0.55)

Each quasi-rigid group was assumed to have an independentalignment tensor during the RDC fitting. The parenthetical values(Qpart

j) were calculated using a single alignment tensor for thewhole structure.


groups of residues are moving as quasi-rigidbodies.

NMR RDC analysis of rigid-group reorientation

Figure 5a and b show the variation of RDCQ-value with respect to populations of substrate-free(Papo) and transition-state (1−Papo) forms in a mixedmodel. (The mixed model is composed of thecrystallographic atomic structures, neither of whichhas been optimized against the NMR data.) Thelowest Q-values lie between those of the two crystalstructures, indicating that the solution structure isintermediate between the substrate-free and TSAcrystal structures. The optimum is closer to thesubstrate-free crystal structure. However, the varia-tion in Q is very small, the optimal value being only0.01 lower than that of the substrate-free crystalstructure for the PEG RDCs and 0.05 lower than thatfor the Pf1 phage RDCs.For the above mixed-model Q-value calculations,

a two-state dynamic equilibrium was assumed.Previously reported NMR relaxation dispersionexperiments had suggested intrinsic conformationalexchange in substrate-free AK.34 Thus, the calcula-tions tested whether the deviation between solution-state NMR data and crystal structures resulted fromconformational exchange between rapidly intercon-verting open- and closed-form structures. Analternative to a dynamic equilibrium would be anaverage static structure model. This was tested bycalculating RDCs from the population-weightedaverage orientations of N–H vector orientationstaken from the two crystal structures (see Materialsand Methods). The static and dynamic equilibriummodels yield very similar Q-values, which makes itimpossible to differentiate, based on RDCs alone,between the two possibilities. Cα and Cβ chemicalshifts were predicted from the substrate-free andTSA crystal structures and compared with theexperimental chemical shifts reported previouslyto further explore the static versus dynamic models.Based on a two-state dynamic equilibrium model,the RMSDs between experimental and predicted Cα

and Cβ chemical shifts were plotted against thepopulation of the substrate-free crystal structure(Papo) used in the model (Fig. 5c and d). The optimalfit to the solution-state NMR data comes from anear-equal mixture of solution-state and TSA crystalstructures, SHIFTX (Fig. 5c) and SPARTA (Fig. 5d),giving consistent results. The RMSD variations ofthe Cα and Cβ chemical shifts are remarkably smallthroughout the structure. The optimum in thechemical shift analysis (Papo=0.4–0.5) is somewhatlower than that for the RDC analysis (Papo=0.6–0.8).Cα and Cβ chemical shifts are sensitive primarily tolocal secondary structure and less dependent on theorientations that are important in RDC analysis. Thelower Papo for chemical shift analysis may therefore

reflect better consistency of the NMR data withthe higher-resolution secondary structure of thetransition-state crystal structure. Although therecan be several reasons for differences betweenobserved and modeled chemical shifts, they aremostly (five of eight) at the same flexible sites in bothTSA and substrate-free forms, either at sites under-going NMR relaxation exchange34 or immediateneighbors. Although the changes in RDC Q-valueversus Papo are modest, they are statistically signif-icant. The excess of RDC observations (N≈250) overmodel degrees of freedom (five alignment tensorparameters plus a population parameter for thepopulation-weighted model) makes even a smallreduction in χ2-value (and hence Q-value) highlysignificant. The magnitude of χ2 indicates thatdifferences between predicted and experimentalRDCs cannot be explained by an estimated RDCerror of ∼1–2 Hz and that the combination ofresidual coordinate error in the crystal structuresand systematic differences between the solutionand crystalline structures translates into RDCchanges that exceed the experimental error in RDCmeasurement.At this point, it is fair to conclude that the solution

structure is perturbed slightly from the substrate-free crystal structure, but there is no constraint thatmovement towards the transition-state form need beuniform in all parts of the protein. Using thecrystallographically determined rigid-group assign-ments, we determined Q-values separately for eachof the five rigid groups by individually fitting analignment tensor to the RDC data. The level ofagreement was expressed as Qsub

,j for subdo-main j. For comparison, Qpart values for the fivegroups were also determined using single alignmenttensors fit to the crystal structures of substrate-freeor transition-state forms as single rigid bodies(Table 3). All the Qsub values turn out to be smallerthan the corresponding Qpart values, supporting theapplicability of this rigid-group approximation to the


solution state. Improved fitting of individual rigidgroups indicates that the global conformation for thesolution structure of AK deviates somewhat fromboth crystal structures. It is interesting that the Qsub

values of the TSA crystal structure are smaller thanthat of the substrate-free crystal structure exceptfor rigid group 2 (57 residues) and rigid group 3(14 residues). This indicates that in solution, eventhough the substrate-free crystal structure is abetter match overall, the internal structures of theindividual rigid groups are better matched by theTSA crystal structure, perhaps because the 1.2 ÅTSA crystal structure is of higher precision. It isalso interesting to note that the amount ofimprovement differs between the rigid groups, anindication that the rigid groups are reorientednonuniformly in the solution state, and that thesolution state should be regarded as more than justa linear combination of the two crystal structures.

Indications of rigid-group displacementsthrough anisotropic thermal parameters

With a crystallographic structure of sufficientlyhigh resolution (better than 1.2 Å), such as the AKtransition-state structure,40 anisotropic atomic dis-placement parameters can be refined providing adescription for the direction of preferred displace-ments. For the lower-resolution 1.7 Å substrate-freeform, it is possible to refine parameters for the rigidtranslation, libration, and screw (TLS) translationcorrelation motions of assumed rigid groups,47–49

which here are taken to be the quasi-rigid groupsinferred from the substrate-associated conformation-al changes (Table 2).With the higher-resolution ADPrefinement of the transition-state form, rigid groupsdo not need to be predefined but can be inferred fromthe Delta matrix (Fig. 3c).42,43,48 Conceptually,interpretation is similar to the DDM (Fig. 3a); regionsapproximating rigid bodies should have low values.However, close agreement should not be expectedbetween the DDM and Delta matrix, because theformer represents substrate-associated changes andthe latter represents intrinsic disorder as constrainedby the crystal lattice. Even though less detail isapparent (Fig. 3), it is remarkable that the principalfeatures of the DDM can be discerned in the Deltamatrix with three quasi-rigid blocks. The first(residues 2–107) corresponds closely to rigid group1. The last (residues∼300–353) includesmost of rigidgroup 5 and some of rigid group 4. A middle block(residues ∼112–286) combines most of rigid groups2–4. Thus, the Delta matrix of the TSA complexcrystal structure provides a hint of intrinsic motionsthat are consistent with the substrate-associateddomain closure.Both high-resolution ADP analysis for the

transition-state form and TLS refinement for thesubstrate-free crystals provide descriptions of the

directionality of rigid-group displacements.48,49

Generally, the correlation is unimpressive betweenthe principal axes of thermal displacement libra-tions and either librations between NMR ensemblemembers or crystallographically observed substrate-associated group rotations. This is expected—coherent intramolecular motions of functionalinterest are just one small component of crystallo-graphic disorder;50–52 crystal-packing and experi-mental temperatures have disparate impacts; andthe experiments probe motions in very differenttimescales. The most impressive agreement is in theprincipal axes of librations for group 3, wherevariation between NMR ensemble members isaligned 9° and 36° from librations in the substrate-free and transition-state crystal structures, respec-tively. Group 3 undergoes a large (37°, blue in Fig. 4)rotation upon substrate binding. It is also the mostprominent region in the intrinsic milliseconddynamics probed by relaxation dispersionanalysis.34 Here, we add that crystallographic andNMR RDC analyses provide consistent evidence ofintrinsic dynamics both in the presence and in theabsence of substrates.

Correlations with NMR relaxation dispersionanalysis

There is intriguingly good agreement whencomparing the axes of rotation between rigid groupsand the distribution of amino acids exhibiting NMRrelaxation dispersion, indicative of millisecond-to-microsecond motions. The prior relaxation disper-sion experiments had indicated that 35 residues, orroughly 10% of the enzyme, undergo microsecond-to-millisecond timescale dynamics in the absence ofsubstrates.34 These residues cluster into four distinctregions of the enzyme: (1) the interface and (2) thehinge between the N- and C-terminal domains;(3) a segment running through the middle ofthe C-terminal domain β-sheet; and (4) the loopspanning residues I182–G209. Assuming two-state exchange, summed forward and reverseexchange rates (kex) and minor state populations(pB) had been determined collectively for allresidues in any given cluster. For the interface,kex=800±100 s−1 and pB=1.1±0.1%; for the inter-domain hinge, kex=1930±350 s−1 and pB=0.4±0.1%;for the β-sheet, kex=790±70 s−1 and pB=0.4±0.1%;and for the I182–G209 loop, kex=790±60 s−1 andpB=2.6±0.6%. The applicability of unified parametersfor all residues in each cluster suggests, but does notprove, a concerted motion. Similar rate constantssuggest that there may be some coupling between theclusters, but it was not possible to fit a single set ofparameters to all clusters, suggesting that it is not arigidly coupled, fully concerted global motion. (Inpassing, it is noted that the relaxation dispersion dataindicate that in the absence of substrates, the low-


energy form, presumably an open conformation,dominates at N97%.)Returning to the current comparison of the

substrate-free and TSA crystal structures, axes ofrotation were calculated by Cα superposition for allpossible pairs of the consensus rigid groups. Withthe exception of rigid group 3, which has asignificant translational component (up to 4 Å), allof the motions are primarily rotational, predomi-nantly (70–100%) closure rather than twist (Table 2),as evaluated by DomSelect.44 The rotation axes thatrelate neighboring rigid groups are overlaid uponthe open- and closed-form structures in Fig. 4b. Twonearly parallel axes near the group 3 helix (darkblue) can be thought of as the same—relating group3 to its two neighboring groups. The other axesnearly intersect, forming a spiral through which theenzyme undergoes a segmented bending uponsubstrate binding. Particularly unexpected is theaxis between groups 1 and 4 that passes nearly in theplane of the β-sheet, orthogonal to its strands. Thissuggests that a hinge runs across the middle of thesheet, an observation that is unexpected, butsupported by the NMR relaxation dispersion data(above).First, some caveats should be noted. Firstly, the

determination of hinge points is at bestapproximate44 and is only as good as the underlyingrigid-group assumption. Secondly, one would ex-pect the group 1/4 rotation axis to be more reliablewhere the two groups come into contact (green andteal) than where they are separated by group 2 (red).Thirdly, the group 1/4 axis bisects the intersectingand nearly orthogonal 2/4 and 1/2 axes, meaningthat apparent rotations in the 1/4 axis couldapproximate coordinated compound rotations ofthe 2/4 and 1/2 axes.Notwithstanding these caveats, two observations

lend credence to the hypothesis that the axesapproximate real hinges. Firstly, all of the axesdetermined this way pass very close to theinterfaces between rigid groups (colored differentlyin Fig. 4b). Secondly, there is very strong spatialcorrelation between the rotation axes (hypotheticalhinges) and residues that are observed by NMRrelaxation dispersion as undergoing exchange inthe millisecond-to microsecond regime (shown asthickened ribbon in Fig. 4b).34 It is usually assumedthat the underlying changes in NMR chemical shiftare the result of local changes in conformation or intertiary contacts. We now see that the vast majorityof the residues exhibiting relaxation exchange are inclose proximity to one of the rotation axes and/orare at an interface between rigid groups wherecontacts would be changing. Thus, the NMRrelaxation dispersion provides independent exper-imental evidence that the residues close to therotation axes are flexible and actually exhibitintrinsic dynamics.

In passing, it is noted that the only proposed hingepoint where relaxation dynamics is not observed isbetween groups 5 and 4. It was within group 4, andthe flexible loop (311–319) only crystallographicallyresolved in the transition-state form, that fast(nanosecond/picosecond) internal dynamics wereidentified through NMR R1/R2/nuclear Overhauserenhancement measurements and Lipari–Szaboanalysis.34 Thus, this region is also dynamic, buton a faster timescale than accessible to the relaxationdispersion analysis.Returning to the juxtaposition of rigid-group

hinges and residues exhibiting relaxation exchange,four important conclusions can be drawn. Firstly, itis emphasized that the rigid-group analysis is basedon crystallographic structures of substrate-free andsubstrate-bound structures and thus pertains tosubstrate-associated changes. In contrast, the NMRdata, obtained in the absence of substrates, pertainsto intrinsic dynamics. This includes the prior NMRrelaxation dispersion analysis implicating dynamichinge points34 and the current NMR RDC analysisshowing structural perturbation towards thesubstrate-bound form. The consistency of thesedifferent data supports the hypothesis that onbinding substrates, at least some of the conforma-tional change is achieved by selecting conformationsthat are part of an intrinsic dynamic equilibrium inthe absence of substrates.Secondly, nearly all of the residues exhibiting

relaxation dynamics are close to intergroup rotationaxes. This suggests that much of the total intrinsic(substrate-free) backbone dynamics at millisecondtimescales might result from motions betweenquasi-rigid groups. In an earlier paper,34 this wasapparent for motions of the N-terminal domain.Now, particularly with the refined designations ofgroups 3 and 2, it appears more generally true.Thirdly, there are multiple data pointing to the

flexibility of the β-sheet. Both the 1/4 and 2/4rotation axes run across the β-sheet nearly ortho-gonal to the strands; thus, rigid-group motionsapparently require flexibility the β-sheet. It isunexpected that a β-sheet, which one mightanticipate to be relatively rigid, exhibits flexingcentral to the enzyme's conformational changes. InFig. 4a, it certainly appears as if the sheet bendssubstantially on substrate binding. Furthermore,from Fig. 4b, we see that where both the 1/4 and2/4 axes pass through the β-strands, local NMRrelaxation dispersion provides evidence of intrinsicconformational dynamics. Much of the β-sheet fallsbetween or near these two putative hinge axes, andmuch of it exhibits the relaxation dynamics. Theextent to which the axes should be regardedliterally as discrete hinges between segments ofβ-sheet, or as the best rigid-group approximationto a more evenly distributed flexing of the wholesheet, is not clear.


Fourthly, the relaxation dynamics established thatthe motions of at least some of the residues werecommensurate with the enzyme turnover rate (evenin the absence of substrates) and could potentially berate limiting.34 Given the high correlation betweenthe relaxation dynamics and the rigid-group analysishere, it is likely that the long-range conformationaldynamics analyzed here is critically relevant to theenzyme's function.

Conclusion

High-resolution refinement has improved the localconsistency of the substrate-free crystal structure ofAK with the 1.2 Å TSA form, enabling more precisedetermination of which parts of the molecule remaincongruent in the two states. The application of twodifferent algorithms gives an improved designationof five quasi-rigid groups whose transformation,predominantly closure rotations, can account formost of the differences between the substrate-freeand substrate-bound crystal structures. Thus, arigid-group description offers an excellent first-order approximation in the characterization ofconformational changes.Overall closure is achieved by segmented 11–18°

rotations between groups 1 and 2, between groups 2and 4, and between groups 4 and 5,where the groupsare numbered from N- to C-termini. The groupscontain noncontiguous and sometimes alternatingregions of the linear sequence that come together inthe 3D structure. Newly apparent is the 14° rotationbetween groups 2 and 4 (red and teal in Fig. 4)around one of two axes that (perhaps surprisingly)run across the β-sheet. Group 3 (blue), containinghelix 174–185 plus a subsequent loop, is newlyrecognized as a group rotating 40° about anindependent axis. The loop is prominent in theNMR relaxation dispersion analysis of the substrate-free enzyme, indicating that it undergoes intrinsicmotion as well as substrate-associated changes.Comparison of the observed NMR RDCs with the

two crystallographic models indicates that the solu-tion state overall is most faithfully represented by amixed population of the substrate-free and substrate-bound crystal structures. The molar fractions of eachremain an open question with the population of thesubstrate-free form estimated as ∼0.5 using chemicalshifts, ∼0.7 using RDCs (this article), and N0.97 byrelaxation dispersion.34 Each focuses on differentcharacteristics of the structure, and its dynamics, andis subject to its own biases. RDCs and chemical shiftsreflect conformational averaging in the picosecond/millisecond timescales and give a consistent popula-tion (Papo=0.5–0.7). By contrast, relaxation dispersionreports on small populations of excited states in thelow-millisecond regime that might be differentsubstates from those probed by RDC/chemicalshift. Nevertheless, all three approaches support the

qualitative conclusion that the solution structurecontains elements of the substrate-bound form.The solution-state NMR RDCs provide evidence

that the adoption of substrate-associated structuralcharacteristics in the substrate-free solution state isnot uniform throughout the structure: the use ofindependent alignment tensors for each rigidgroup markedly improves the fit of calculatedand observed RDCs, but by different degrees.The NMR RDC data do not indicate the degree to

which the intermediate nature of the solution staterepresents a perturbation of a single structure and/or a dynamic equilibrium between multiple states.However, the prior NMR relaxation dispersion dataindicate that there is at least some intrinsic dynamicexchange.34 Furthermore, spatial correlation be-tween the sites of relaxation dispersion and thehinge axes inferred from the two crystal structuresmakes a strong circumstantial case that the solutionstate represents, at least in part, a dynamic exchangebetween open and partially or substantially closedenzyme configurations.Finally, it has been argued that for lid-closing

enzymes that exclude solvent from the active site,conformational selection is insufficient, and that theenergy of substrate binding is needed to change theenergy landscape and drive the conformationalchange.17 The phosphagen kinases are such lid-closing enzymes. The results here by no means ruleout traditional induced fit in final loop closure butemphasize that intrinsic dynamics, and possiblyconformational selection, could also have importantroles in the lid-closing paradigms of induced fit.

Materials and Methods

Crystal structure determination for substrate-free AK

Protein expression, crystallization, diffraction datacollection, and molecular replacement structure determi-nation are as described for the prior 2.4 Å resolutionstructure23 (PDB ID 1M80). In the prior work, serialtransfer to a number of commonly used cryo-protectantshad proved problematic, yielding only 3 Å diffraction. The2.4 Å data had been obtained by using 26% PEG 5000monomethyl ether as a joint crystallizing agent and cryo-protectant, avoiding changes upon serial transfer. Whenlarger crystals were grown by macroseeding, the PEG5000 monomethyl ether was no longer sufficient tocompletely inhibit ice formation. The highest-resolutiondata set (1.73 Å) was compromised by the presence ofdiffraction from cubic ice. The current analysis takesadvantage of recently developed methods to integratediffraction data in the presence of ice rings.53

Refinement was performed using Phenix,54 alternatedwith interactive rebuilding using Coot.55 Atomic displace-ment parameters (B-factors) were modeled with aniso-tropic components coming from the TLS tensors47 initiallyfit to four rigid bodies per subunit and with additional


restrained individual isotropic atomic displacement para-meters. The rigid groups were taken initially from thework of Yousef et al.23 The test set for the 1.7 Å refinementwas selected as a super set of that used for the 2.4 Årefinement to avoid bias in cross-validation. The diffrac-tion data and an atomic model were deposited with PDBID 3M15. Following analysis of the conformationaldifferences between the newly refined substrate-freestructure and the TSA form, we adjusted the TLS rigidgroups and expanded them to five per subunit, and themodel was subject to an additional round of refinement.While this provided TLS parameters consistent with therigid groupings described below, there was no furtherimprovement in the refinement statistics.

RDC and NMR chemical shift analysis

Uniformly 15N- and 2H-enriched Limulus polyphemusAK was prepared as described previously.56 The finalNMR sample was concentrated to about 1 mM in a buffercontaining 10 mM sodium citrate, 50 μM sodium azide,90% H2O, and 10% D2O (pH 6.5). For RDCmeasurements,AK was aligned in two different alignment media: PEGalkyl ether liquid crystalline medium (3% C12E5/hexanolat a molar ratio, r, of 0.85)57 and 10 mg/ml Pf1 phage.58

Due to the large size of AK (42 kDa), the RDCs cannot bemeasured by the standard IPAP technique,59 because ofsignificant line broadening of the anti-TROSY component.Thus, RDCs were determined from the differences in peakpositions of the 15N resonances measured in the aniso-tropic and isotropic samples using HSQC and TROSYspectra.60 For the isotropic sample, the peak displacementis JNH/2, whereas for the aligned sample, it is (JNH+DNH)/2. Hence, their difference multiplied by 2 yields thedesired dipolar couplings DNH (Fig. 1). Experiments wereperformed at 298 K on a Bruker 800-MHz spectrometerequipped with a TCI cryoprobe. Chemical shift assign-ments for the apo state AK have been reported.56 Spectrawere processed by NMRPipe61 and analyzed withSPARKY.62

RDCs were fit to the substrate-free (open) and TSA(closed) crystal structures (PDB codes: 3M10 and 1M15)via singular value decomposition63 using the MATLABsoftware. The calculation of the alignment tensor wasinitially performed with all the available residues and thenthe calculation was repeated for individual subdomains.The experimental RDCs were also fit to a two-state

dynamic equilibrium model in which the open (substrate-free) and closed (TSA) structures are assumed to be rapidlyinterconverting. The two X-ray structures (substrate-freeand TSA) were alignedwith respect to each other using thebackbone Cα atoms and the backbone N–H bond unitvectors v=(x,y,z) were extracted from the two structures.The six bilinear terms ⟨x2⟩, ⟨y2⟩, ⟨z2⟩, ⟨xy⟩, ⟨xz⟩, and ⟨yz⟩ arepopulation averages:64

hx2i = p1hx21i + p2hx22ihy2i = p1hy21i + p2hy22ihz2i = p1hz21i + p2hz22i

hxyi = p1hx1y1i + p2hx2y2ihxzi = p1hx1z1i + p2hx2z2ihyzi = p1hy1z1i + p2hy2z2i

ð1Þ

where p1=Papo and p2=1−Papo.

A static average structure was also tested. In this model,a new set of N–H bond vectors ⟨v⟩ is built by populationaveraging the vectors extracted from the substrate-freeand TSA crystal structures:

x = p1x1 + p2x2; y = p1y1 + p2y2; z = p1z1 + p2z2 ð2Þwhere p1=Papo and p2=1−Papo.After normalization of the average vector orientations

(x, y, z) to unity, we fitted RDCs by systematically varyingPapo between 0 and 1, and the level of agreement betweenthe experimental and calculated RDCs is expressed interms of a Q-value.Experimental Cα and Cβ chemical shifts (δexp) were

compared with the chemical shifts predicted fromindividual structures and the two-state model (δcalc).Chemical shifts were predicted from substrate-free (δcalc

apo)and transition-state (δcalc

TSA) crystal structure usingSHIFTX 4.365 and SPARTA.66 The two-state model wasalso used for back-calculation of an average chemicalshift (assuming that the states exchange rapidly on thechemical shift timescale):

ycalc = Papo × yapocalc + 1 − Papo

� �× yTSAcalc ð3Þ

NMR solution structure determination

The solution structure of substrate-free AK was deter-mined by combining NMR RDC and chemical shiftobservations with restraints from the crystallographicstructures. Due to the sparseness of the NMR observa-tions, restraints from the crystallographic structures arenecessary, but the resulting structures show bias in theirdetailed features. Therefore, the NMR ensemble (Fig. S1)was analyzed only with regard to the distributions offlexible and rigid parts, which are independent ofrestraints to a particular structure. Restraints were ofseveral forms. Local Cα–Cα distances (b10 Å) wererestrained within the range spanned by the substrate-free and transition-state crystals, and the ϕ, ψ backbonetorsion angles were weakly restrained towards the TSAstructure. The effect of the dihedral angle constraints isprimarily the conservation of secondary structure withminimal impact on the relative orientations of thesubdomains. O–N hydrogen-bond distance restraintswere also used for conserved secondary structuralelements. For the NMR restraints, two independent setsof backbone N–H RDCs from PEG and Pf1 phage wereused in addition to the Cα, Cβ chemical shift restraints.Structures were optimized using torsion angle dyna-

mics, followed by Cartesian coordinate refinement, start-ing with either the transition-state crystal structure or thesubstrate-free crystal structure. Simulated annealing andoptimization were carried out using the IVM internalvariable module within the molecular structure determi-nation package of Xplor-NIH.67,68 From an ensemble sizeof 50, the 25 best structures were used for further analysis.

Analysis of conformational changes

Conformational changes between the substrate-free andtransition analog complex forms were analyzed first usingDDMs calculated with the ESCET program.41 With high-


precision structures (estimated coordinate errors of 0.03and 0.14 Å for 1M15 and 3M10, respectively69), and largeconformational changes (up to∼15 Å), initial analysis wasat the 8 σ level, corresponding to differences of 1.25 Å.Quasi-rigid groups were identified two ways. One wasthrough clustering of near-zero terms in the DDM (b8 σor b1.25 Å) using ESCET.41 DynDom44 was also used tofind clusters of residues that mapped from one structureto another with similar rotations (window≥11 residues;interdomain fluctuation/intradomain fluctuation≥1.0).The designation was somewhat sensitive to the choiceof parameters, but good consistency was obtainedbetween DynDom, ESCET, and the sub-8 σ regions ofthe DDM. Both programs found five quasi-rigid groups,and there was 79% agreement in the residues allocated toeach. Discrepancies were of two types. About half weredifferences in the exact boundaries between rigid andflexible regions and are unlikely to be of greatconsequence (Table S1). The other half were due toslightly different groupings of ∼15 quasi-rigid backbonesegments into rigid groups 2 and 4. A consensusdesignation was obtained manually, choosing a compro-mise that minimized fragmentation of the sequence,consolidated regions within the 3D structure, and wasvisually consistent with the 3 σ DDM (Table S1 andTable 2).Relationships between the rigid groups were analyzed

using DomSelect†,44 LsqKab,70 and malign.py. The latterwas written to extend the functionality of phenix.superpose_pdbs (Zwart et al.‡). In all cases, theconsensus rigid-group assignments were explicitlyinput rather than relying on automatically generatedassignments. Malign.py determines domain reorienta-tions using the same approach as DomSelect. It firstperforms least-squares rigid-body superposition of twostructures based on a reference selection of atoms andthen a subsequent alignment of a second selection of“moving atoms” to their corresponding targets. Anyintergroup change is then given by the transformationbetween the reference and second superpositions.Malign.py extended the functionality of prior programsby supporting statistical analysis of multi-chain andensemble (NMR) models and comparison with TLSlibrations. The similarity of rotational (and librational)operators was assessed from the magnitude of rotation(square root of mean square libration), as well as themagnitudes of the dot products between unit vectorsalong the rotational (principal librational) axes. For thesecomparisons, the TLS tensors were first decomposedusing the CCP4 program TLSANL.71 Graphical analysiswas performed with PyMOL.72

The Delta matrix (Fig. 4) was used for identification ofquasi-rigid groups from the individually refined atomicdisplacement parameters of the transition-statestructure.40 It was calculated using the CCP4 programANISOANL.42,73 Residues were binned into themaximum100 bins. The output matrix was inverted horizontally forconsistency with ESCET.

†http://fizz.cmp.uea.ac.uk/dyndom/domainSelect.do‡http://www.phenix-online.org/documentation/

superpose_pdbs.htm

Accession numbers

Coordinates and structure factors have been depositedin the PDB with accession number 3M10.

Acknowledgements

Crystallographic data were collected with theassistance of Mohammad Yousef, Shawn Clark,and T. Somasundaram. We thank Dr. Charles. D.Schwieters for help with using Xplor-NIH. Thiswork was supported by National Institutes ofHealth–National Institute of General MedicalSciences grant R01GM077643 (M.S.C.). The NMRRDC experiments were conducted at the NationalHigh Magnetic Field Laboratory supported bycooperative agreement DMR 0654118 between theNational Science Foundation and the State ofFlorida.

Supplementary Data

Supplementary data associated with this articlecan be found, in the online version, at doi:10.1016/j.jmb.2010.11.007

References

1. Jardetzky, O. (1996). Protein dynamics and conforma-tional transitions in allosteric proteins. Prog. Biophys.Mol. Biol. 65, 171–219.

2. Boehr, D. D. & Wright, P. E. (2008). Biochemistry.How do proteins interact? Science, 320, 1429–1430.

3. Hammes-Schiffer, S. & Benkovic, S. J. (2006). Relatingprotein motion to catalysis. Annu. Rev. Biochem. 75,519–541.

4. Henzler-Wildman, K. & Kern, D. (2007). Dynamicpersonalities of proteins. Nature, 450, 964–972.

5. Pisliakov, A. V., Cao, J., Kamerlin, S. C. & Warshel, A.(2009). Enzyme millisecond conformational dynamicsdo not catalyze the chemical step. Proc. Natl Acad. Sci.USA, 106, 17359–17364.

6. Smock, R. G. & Gierasch, L. M. (2009). Sending signalsdynamically. Science, 324, 198–203.

7. Koshland, D. E. (1958). Application of a theory ofenzyme specificity to protein synthesis. Proc. NatlAcad. Sci. USA, 44, 98–104.

8. Koshland, D. E. (1994). The key-lock theory and theinduced-fit theory. Angew. Chem., Int. Ed. Engl. 33,2375–2378.

9. Boehr, D. D., Dyson, H. J. & Wright, P. E. (2006). AnNMR perspective on enzyme dynamics. Chem. Rev.106, 3055–3079.

10. Bahar, I., Chennubhotla, C. & Tobi, D. (2007). Intrinsicdynamics of enzymes in the unbound state andrelation to allosteric regulation. Curr. Opin. Struct.Biol. 17, 633–640.

http://dx.doi.org/10.1016/j.jmb.2010.11.007

http://dx.doi.org/10.1016/j.jmb.2010.11.007


11. Henzler-Wildman, K. A., Thai, V., Lei, M., Ott, M.,Wolf-Watz, M., Fenn, T. et al. (2007). Intrinsic motionsalong an enzymatic reaction trajectory. Nature, 450,838–844.

12. Ma, B., Kumar, S., Tsai, C. J. & Nussinov, R. (1999).Folding funnels and bindingmechanisms. Protein Eng.12, 713–720.

13. Osborne, M. J., Schnell, J., Benkovic, S. J., Dyson, H. J.& Wright, P. E. (2001). Backbone dynamics indihydrofolate reductase complexes: role of loopflexibility in the catalytic mechanism. Biochemistry,40, 9846–9859.

14. Wang, C., Karpowich, N., Hunt, J. F., Rance, M. &Palmer, A. G. (2004). Dynamics of ATP-bindingcassette contribute to allosteric control, nucleotidebinding and energy transduction in ABC transporters.J. Mol. Biol. 342, 525–537.

15. Beach, H., Cole, R., Gill, M. L. & Loria, J. P. (2005).Conservation of mus-ms enzyme motions in theapo- and substrate-mimicked state. J. Am. Chem. Soc.127, 9167–9176.

16. Lange, O. F., Lakomek, N. A., Farès, C., Schröder,G. F., Walter, K. F., Becker, S. et al. (2008).Recognition dynamics up to microseconds revealedfrom an RDC-derived ubiquitin ensemble in solution.Science, 320, 1471–1475.

17. Sullivan, S. M. & Holyoak, T. (2008). Enzymes withlid-gated active sites must operate by an induced fitmechanism instead of conformational selection. Proc.Natl Acad. Sci. USA, 105, 13829–13834.

18. Ellington, W. R. (2001). Evolution and physiologicalroles of phosphagen systems. Annu. Rev. Physiol. 63,289–325.

19. Fritz-Wolf, K., Schnyder, T., Wallimann, T. & Kabsch,W. (1996). Structure of mitochondrial creatine kinase.Nature, 381, 341–345.

20. Rao, J. K., Bujacz, G. & Wlodawer, A. (1998). Crystalstructure of rabbit muscle creatine kinase. FEBS Lett.439, 133–137.

21. Zhou, G., Somasundaram, T., Blanc, E., Parthasarathy,G., Ellington, W. R. & Chapman, M. S. (1998).Transition state structure of arginine kinase: implica-tions for catalysis of bimolecular reactions. Proc. NatlAcad. Sci. USA, 95, 8449–8454.

22. Lahiri, S. D., Wang, P. F., Babbitt, P. C., McLeish,M. J., Kenyon, G. L. & Allen, K. N. (2002). The2.1 Å structure of Torpedo californica creatinekinase complexed with the ADP–Mg2+–NO3

−–creatinetransition-state analogue complex. Biochemistry, 41,13861–13867.

23. Yousef,M. S., Clark, S. A., Pruett, P. K., Somasundaram,T., Ellington,W.R.&Chapman,M. S. (2003). Induced fitin guanidino kinases—comparison of substrate-freeand transition state analog structures of arginine kinase.Protein Sci. 12, 103–111.

24. Wu, X., Ye, S., Guo, S., Yan, W., Bartlam, M. & Rao, Z.(2010). Structural basis for a reciprocating mechanismof negative cooperativity in dimeric phosphagenkinase activity. FASEB J. 24, 242–252.

25. Dumas, C. & Janin, J. (1983). Conformational changesin arginine kinase upon ligand binding seen by small-angle X-ray scattering. FEBS Lett. 153, 128–130.

26. Forstner, M., Kriechbaum, M., Laggner, M. P. &Wallimann, T. (1996). Changes of creatine kinase

structure upon ligand binding as seen by small-anglescattering. J. Mol. Struct. 383, 217–227.

27. Forstner,M., Kriechbaum,M., Laggner, P. &Wallimann,T. (1998). Structural changes of creatine kinase uponsubstrate binding. Biophys. J. 75, 1016–1023.

28. Zhou, G., Ellington, W. R. & Chapman, M. S. (2000).Induced fit in arginine kinase.Biophys. J. 78, 1541–1550.

29. Hayward, S. (1999). Structural principles governingdomain motions in proteins. Proteins, 36, 425–435.

30. Berendsen, H. J. & Hayward, S. (2000). Collectiveprotein dynamics in relation to function. Curr. Opin.Struct. Biol. 10, 165–169.

31. Bennett, W. S. & Steitz, T. A. (1980). Structure of acomplex between yeast hexokinase A and glucose II.Detailed comparisons of conformation and active siteconfiguration with the native hexokinase B monomerand dimer. J. Mol. Biol. 140, 211–230.

32. Bennett, W. S. & Huber, R. (1984). Structural andfunctional aspects of domainmotions in proteins. CRCCrit. Rev. Biochem. 15, 291–384.

33. Wallimann, T. & Schlattner, U. (2010). Creatinekinases: a cornerstone for structural research in thephosphagen kinase family. FASEB J. 24, 7.

34. Davulcu, O., Flynn, P. F., Chapman, M. S. & Skalicky,J. J. (2009). Intrinsic domain and loop dynamicscommensurate with catalytic turnover in an induced-fit enzyme. Structure, 17, 1356–1367.

35. Blethen, S. L. (1972). Kinetic properties of the argininekinase isoenzymes of Limulus polyphemus. Arch.Biochem. Biophys. 149, 244–251.

36. Pruett, P. S., Azzi, A., Clark, S. A., Yousef, M., Gattis,J. L., Somasundaram, T. et al. (2003). The putativecatalytic bases have, at most, an accessory role in themechanism of arginine kinase. J. Biol. Chem. 29,26952–26957.

37. Gattis, J. L., Ruben, E., Fenley, M. O., Ellington, W. R.& Chapman, M. S. (2004). The active site cysteine ofarginine kinase: structural and functional analysis ofpartially active mutants. Biochemistry, 43, 8680–8689.

38. Bax, A. (2003). Weak alignment offers new NMRopportunities to study protein structure and dynamics.Protein Sci. 12, 1–16.

39. Blackledge, M. (2005). Recent progress in the study ofbiomolecular structure and dynamics in solution fromresidual dipolar couplings. Prog. Nucl. Magn. Reson.Spectrosc. 46, 24–61.

40. Yousef, M. S., Fabiola, F., Gattis, J. L., Somasundaram,T. & Chapman, M. S. (2002). Refinement of thearginine kinase transition-state analogue complexat 1.2 Å resolution: mechanistic insights. ActaCrystallogr., Sect. D: Biol. Crystallogr. 58, 2009–2017.

41. Schneider, T. R. (2002). A genetic algorithm for theidentification of conformationally invariant regions inprotein molecules. Acta Crystallogr., Sect. D: Biol.Crystallogr. 58, 195–208.

42. Winn, M. (2001). ANISOANL—analysing anisotropicdisplacement parameters. In CCP4 Newsletter, Vol.39. CCP4.

43. Rosenfield, R. E., Trueblood, K. N. & Dunitz, J. D.(1978). A test for rigid-body vibrations, based on ageneralisation of Hirshfeld's ‘rigid-bond’ postulate.Acta Crystallogr., Sect. A, 34, 828–829.

44. Hayward, S. & Berendsen, H. J. (1998). Systematicanalysis of domain motions in proteins from


conformational change: new results on citratesynthase and T4 lysozyme. Proteins, 30, 144–154.

45. Suzuki, T., Kawasaki, Y., Furukohri, T. & Ellington,W. R. (1997). Evolution of phosphagen kinase. VI.Isolation, characterization and cDNA-derived aminoacid sequence of lombricine kinase from the earth-worm Eisenia foetida, and identification of a possiblecandidate for the guanidine substrate recognition site.Biochim. Biophys. Acta, 1343, 152–159.

46. Uda, K. & Suzuki, T. (2004). Role of amino acidresidues on the GS region of Stichopus arginine kinaseand Danio creatine kinase. Protein J. 23, 53–64.

47. Schomaker, V. & Trueblood, K. N. (1968). On therigid-body motion of molecules in crystals. ActaCrystallogr., Sect. B, 24, 63–76.

48. Howlin, B., Moss, D. S. & Harris, G. W. (1989).Segmented anisotropic refinement of bovine ribonu-clease A by the application of the rigid-body TLSmodel. Acta Crystallogr., Sect. A: Found. Crystallogr. 45,851–861.

49. Winn, M. D., Isupov, M. N. & Murshudov, G. N.(2001). Use of TLS parameters to model anisotropicdisplacements in macromolecular refinement. ActaCrystallogr., Sect. D: Biol. Crystallogr. 57, 122–133.

50. Caspar, D. L., Clarage, J., Salunke, D. M. & Clarage,M. (1988). Liquid-like movements in crystallineinsulin. Nature, 332, 659–662.

51. Clarage, J. B., Clarage, M. S., Phillips, W. C., Sweet,R. M. & Caspar, D. L. (1992). Correlations of atomicmovements in lysozyme crystals. Proteins, 12,145–157.

52. Moore, P. B. (2009). On the relationship betweendiffraction patterns and motions in macromolecularcrystals. Structure, 17, 1307–1315.

53. Chapman,M. S. & Somasundaram, T. (2010). De-icing:recovery of diffraction intensities in the presence of icerings. Acta Crystallogr., Sect. D: Biol. Crystallogr. 66,741–744.

54. Adams, P. D., Afonine, P. V., Bunkoczi, G., Chen, V. B.,Davis, I. W., Echols, N. et al. (2010). PHENIX: acomprehensive Python-based system for macromolec-ular structure solution. Acta Crystallogr., Sect. D: Biol.Crystallogr. 66, 213–221.

55. Emsley, P., Lohkamp, B., Scott, W. G. & Cowtan, K.(2010). Features and development of Coot. ActaCrystallogr., Sect. D: Biol. Crystallogr. 66, 486–501.

56. Davulcu, O., Clark, S. A., Chapman, M. S. & Skalicky,J. J. (2005). Main chain (1)H, (13)C, and (15)Nresonance assignments of the 42-kDa enzyme argininekinase. J. Biomol. NMR, 32, 178.

57. Ruckert, M. & Otting, G. (2000). Alignment ofbiological macromolecules in novel nonionic liquidcrystalline media for NMR experiments. J. Am. Chem.Soc. 122, 7793.

58. Hansen, M. R., Mueller, L. & Pardi, A. (1998). Tunablealignment of macromolecules by filamentous phage

yields dipolar coupling interactions. Nat. Struct. Biol.5, 1065–1074.

59. Ottiger, M., Delagio, F. & Bax, A. (1998). Measurementof J and dipolar couplings from simplified two-dimensional NMR spectra. J. Magn. Reson. 131,373–378.

60. Kontaxis, G., Clore, G. M. & Bax, A. (2000). Evaluationof cross-correlation effects and measurement of one-bond couplings in proteins with short transverserelaxation times. J. Magn. Reson. 143, 184–196.

61. Delaglio, F., Grezesiek, S., Vuister, G. W., Zhu, G.,Pfeifer, J. & Bax, A. (1995). NMRPipe: a multidimen-sional spectral processing system based on UNIXpipes. J. Biomol. NMR, 6, 277–293.

62. Goddard, T. D. & Kneller, D. G. (2004). SPARKY 3,University of California, San Francisco.

63. Losonczi, J. A., Andrec, M., Fischer, M. W. F. &Prestegard, J. H. (1999). Order matrix analysis ofresidual dipolar couplings using singular valuedecomposition. J. Magn. Reson. 138, 334.

64. Showalter, S. A. & Brüschweiler, R. (2007). Quantita-tive molecular ensemble interpretation of NMRdipolar couplings without restraints. J. Am. Chem.Soc. 129, 4158–4159.

65. Neal, S., Nip, A. M., Zhang, H. &Wishart, D. S. (2003).Rapid and accurate calculation of protein 1H, 13C and15N chemical shifts. J. Biomol. NMR, 26, 215–240.

66. Shen, Y. & Bax, A. (2007). Protein backbone chemicalshifts predicted from searching a database for torsionangle and sequence homology. J. Biomol. NMR, 38,289–302.

67. Schwieters, C. D. & Clore, G. M. (2001). Internalcoordinates for molecular dynamics andminimizationin structure determination and refinement. J. Magn.Reson. 152, 288–302.

68. Schwieters, C. D., Kuszewski, J. J. & Clore, G. M.(2006). Using Xplor-NIH for NMRmolecular structuredetermination. Prog. Nucl. Magn. Reson. Spectrosc. 48,47–62.

69. Cruickshank, D. W. (1999). Remarks about proteinstructure precision. Acta Crystallogr., Sect. D: Biol.Crystallogr. 55, 583–601.

70. Kabsch, W. (1976). A solution for the best rotation torelate two sets of vectors. Acta Crystallogr., Sect. A, 32,922–923.

71. Howlin, B., Butler, S. A., Moss, D. S., Harris, G. W. &Driessen, H. P. C. (1993). TLSANL: TLS parameteranalysis program for segmented anisotropic refine-ment ofmacromolecular structures. J. Appl. Crystallogr.26, 622–624.

72. DeLano, W. L. (2002). The PyMOL Molecular GraphicsSystem. DeLano Scientific, San Carlos, CA.

73. Collaborative Computational Project, Number 4(1994). The CCP4 suite: programs for protein crystal-lography.Acta Crystallogr., Sect. D: Biol. Crystallogr. 50,760–763.

Arginine Kinase: Joint Crystallographic and NMR RDC Analyses Link

Documents

Transcript of Arginine Kinase: Joint Crystallographic and NMR RDC Analyses Link