Simultaneous Definition of High Resolution Protein Structure and Backbone Conformational Dynamics using NMR Residual Dipolar Couplings

Transcription

1 DOI: /cphc Simultaneous Definition of High Resolution Protein Structure and Backbone Conformational Dynamics using NMR Residual Dipolar Couplings Guillaume Bouvignies, Phineus R. L. Markwick, and Martin Blackledge* [a] Despite the importance of molecular dynamics for biological activity, most approaches to protein structure determination, whether based on crystallographic or solution studies, propose three-dimensional atomic representations of a single configuration that take no account of conformational fluctuation. Nonaveraged anisotropic NMR interactions, such as residual dipolar couplings, that become measurable under conditions of weak alignment, provide sensitive probes of both molecular structure and dynamics. Residual dipolar couplings are becoming increasingly powerful for the study of proteins in solution. In this minireview we present their use for the simultaneous determination of protein structure and dynamics. Introduction Molecular motions, enabling changes in protein backbone or sidechain conformation, are thought to play a crucial role in both protein stability and function. [1 4] Despite the recognized importance ofdynamics for biochemical activity, most approaches to protein structure determination, whether based on crystallographic or solution studies, propose three dimensional atomic representations ofa single configuration, that takes little or no account ofconformational fluctuation. Motional properties are routinely measured in solution, most commonly using nuclear magnetic resonance (NMR) spin relaxation, [5 8] where rapid fluctuations, up to the range of the characteristic rotational correlation time ofthe molecule (around 10 ns for medium-size proteins in aqueous solution at room temperature) can be characterised, [9 11] or using rotating frame relaxation dispersion experiments that can detect conformational exchange occurring on slower timescales. [12 13] However, the ability to elucidate both structural and dynamic aspects would provide direct access to the conformational space sampled by the native protein, as well as leading to more accurate average conformations. NMR is uniquely suited to this purpose, with experimental techniques routinely probing time and ensemble-averaged conformation-dependent observables. These observables are generally used to extract a single conformation, but inherently encode, albeit in some potentially complex way, detailed information on conformational dynamics occurring on multiple timescales up to the millisecond range. These slower timescales are ofparticular interest, firstly because they are not probed routinely by spin relaxation, and secondly because functionally important biological processes, including enzyme catalysis, [14] signal transduction, [15] ligand binding or allosteric regulation, [16] requiring collective motions involving groups ofatoms or amino acids, are expected to occur in this time range. The quest to use NMR data to determine average molecular structure and to simultaneously describe the associated conformational dynamics about this mean, has thus been the subject ofconsiderable interest over the last 20 years, fostering a number ofremarkable methodological developments. NMR spectroscopy is established as the method ofchoice for the study of the structure and dynamics of proteins in solution. [17] The success ofnmr as a tool for structural biology has relied on the ability to measure a large number ofcross-relaxation (nuclear Overhauser, noe) effects between proton spins close together in space (< 5 6 Š), providing approximate distance restraints mapping inter-proton proximity throughout the molecule ofinterest and thereby allowing reconstruction ofthe three-dimensional model. [18] These data have regularly been combined with through-bond scalar couplings, and the dependence ofcarbon chemical shifts on the presence ofregular secondary structure, both reporting on dihedral angle ranges along the backbone and sidechains ofthe protein. Despite the large volume ofexperimental data, they can often be mutually redundant, such that NMR-based structure elucidation may be under-determined, leading to different local conformations that are in equal agreement with available experimental data. This local imprecision is commonly presented in terms of the differences between equivalent solutions to the same repeated calculation, and is strongly related to the local density ofconstraints. The direct effects of true dynamic averaging on solution state NMR spectra can be separated into two broad categories: Conformational exchange occurring on frequencies slower [a] G. Bouvignies, Dr. P. R. L. Markwick, Dr. M. Blackledge Institut de Biologie Structurale 41 Rue Jules Horowitz, Grenoble (France) Fax: (+ 33) martin.blackledge@ibs.fr ChemPhysChem 0000, 00, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim &1& These are not the final page numbers! ÞÞ

2 M. Blackledge et al. than the difference in chemical shifts of the interchanging species Dd (generally less than tens to hundreds ofmilliseconds) can be relatively easily identified, with significantly populated species giving rise to distinct chemical shifts. Conformational equilibria with exchange rates faster than Dd on the other hand still give rise to a single peak representing all exchanging species. This case is therefore far more difficult to identify, and is commonly ignored in standard structure determination protocols. Such difficulties are compounded because cross-relaxation effects giving rise to the noe are also strongly dependent on the nature and timescale of fast (ps ns) motional fluctuations ofthe two interacting nuclei. [19] These dynamic-averaging effects may however vary throughout the molecule, due to the different motional properties of diverse sites in the protein, that can result in different effective cross-relaxation rates for similar average distances. This possibility is also very difficult to allow for during structure refinement, as the necessary information cannot be known a priori and is in general too complex to be determined from the available data. Measured cross relaxation rates are thus dependent on dynamic events occurring on very different timescales, whose effects on the measured interaction will depend strongly on the nature and the timescale ofthe motion, rather than a simple and unique dependence on distance. In combination with additional sources ofuncertainty in measured relaxation rates, such as spin diffusion, [20] it has long been accepted that precise determination ofdistances from standard noe measured in proteins is unrealistic. This has led to the development ofthe successful adoption of pragmatic procedures based on the measurement ofa very large number ofimprecise distances. These are then used in combination with classical molecular mechanics approaches, to triangulate a unique molecular conformation in agreement with the experimental data. Despite the prevalence, and obvious success ofsingle copy structure determination approaches, the dual dependence of NMR data, coding for both structure and dynamics, has been recognised ever since the very early applications ofnmr to structural biology. In most cases this occurred when measured experimental data, from small protein fragments or cyclic peptides, could not be explained in terms ofa single conformation. [21,22] In one such study conformational space was extensively sampled by creating conformers in agreement with subsets ofexperimentally determined distances and an equilibrium proposed in agreement with all measured noe and rotating frame relaxation measurements. [23] A number ofmethods were proposed to modify restrained molecular dynamic simulations to allow the evolution of different conformations that on average reproduce the measured data. Slightly differing techniques for averaging over time and ensemble were proposed, exploiting either multiple parallel trajectories (ensemble-averaged restrained molecular dynamics EARMD) over which the restraint must be fulfilled on average, or a restraint integral applied over the length ofthe trajectory (time-averaged restrained molecular dynamics TARMD). [24 27] The efficiency ofthese approaches to describe the diverse degrees of motion present throughout the molecule depends to an extent on the chosen number ofcopies (EARMD) or the length of the memory function chosen before the restraint must be reapplied (TARMD). As mentioned above NMR structure calculation can be locally under-determined, even for single-copy approaches, implying that the extent ofadditional conformational space explored when using multiple copies or time-averaging is not easily defined. Recently motional amplitudes derived from spin-relaxation rates were used to define this ensemble conformational disorder, allowing the ensemble average to sample configurations that could give rise to observed fast motional characteristics of backbone and sidechains. [28] Combination ofsuch constraints with noe that may be averaged over slowly exchanging conformers faces the problem of mixing effective timescales for the different phenomena. The authors have therefore developed additional procedures to average over different populations for different experimental observables. [29] More recently Nilges and co-workers have also used extensive conformational sampling, in combination with a Bayesian analysis, to reproduce experimental data from ensembles ofstructures selected on the basis oftheir ability to reproduce experimental data. [30] As discussed above however, the major difficulties of simultaneously extracting structural and dynamic information from proteins using NMR data are incurred because the principal restraint, the noe, is susceptible to additional dynamic averaging phenomena that cannot easily be accounted for, even using time or ensemble averaging ofrestraints. Herein, we describe how residual dipolar couplings (RDCs), measured under conditions ofpartial molecular alignment, [31,32] can be used to overcome many ofthese di ficulties, and to provide access to direct, analytical determination ofboth structural and dynamic components ofprotein behaviour in solution. Residual DipolarCouplings The dipolar coupling between two spins 1/2 (i,j) is described by the time and ensemble average ofthe dipolar Hamiltonian over all sampled orientations [Eq. (1)]: D ij ¼ g ig j m 0 h 8p 3 P 2 ½cos qðtþš r 3 ij rij is the distance between the two nuclei, gi and gj are the gyromagnetic ratios ofthe two spins, h is Planck s constant and m 0 the permittivity offree space. Note that the dipolar Hamiltonian depends on the orientation q ofthe internuclear vector between the coupled spins, relative to the magnetic field, following a second order Legendre polynomial dependence (P 2 cosq). Time and ensemble averaging ofthis function, denoted by the angular brackets, reduces the measured coupling to zero under the conditions oforientational averaging found in isotropic solution. In order to measure a residual coupling (RDC) in solution it is necessary to induce partial alignment, or order, in the sample. It has been shown over ten years ago [31] that simple dissolution ofa protein in a dilute liquid crystal solution ofphospholipid bicelle, would allow the measurement oflarge (tens ofhertzs) couplings, while retaining the high ð1þ &2& Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim ChemPhysChem 0000, 00, 1 10 ÝÝ These are not the final page numbers!

3 Protein Structure and Backbone Conformational Dynamics quality spectra necessary for high resolution protein NMR. Very rapidly additional solvent systems were developed to provide partial alignment. [33 39] In the case ofa macromolecule whose shape does not change significantly, the average in Equation (1) can be described as a convolution ofthe restricted motion ofthe solute molecules, defined by the average over all orientations of the molecule relative to the magnetic field, and the orientation of the interspin vector relative to the molecule (see Figure 1). The Figure 1. Orientation ofthe internuclear vector in the principle axis system ofthe molecular alignment tensor. The angles are those described in Equation (3). preferential orientational averaging of the molecule is commonly described in terms ofan alignment tensor A whose units are dimensionless, and whose trace is zero, reflecting its probabilistic nature. [40] It is convenient to describe the measured couplings in terms oftheir orientation relative to this alignment tensor or principal axis system (PAS) common to the whole molecule. The orientation ofthe PAS or alignment tensor with respect to the coordinate frame of the molecule can in return be defined simply via a three-dimensional Euler rotation RACHTUNGTRENUNG{a,b,g}. One can describe the measured coupling in terms of{q,f}, the polar angles ofthe inter-spin vector in the eigenframe of the alignment tensor, with eigenvalues A xx, A yy and A zz as in Equation (2): D ij ðq;þ¼ g ig j m 0 h 8p 3 r 3 ij or as defined in Equation (3) A zz cos 2 q þ A xx sin 2 q cos 2 þ A yy sin 2 D ij ðq;þ¼ g ig j m 0 h A 16p 3 rij 3 a ð3cos 2 q 1Þþ 3 2 A r sin 2 q cos 2 where A a =A zz /2 is the axial component ofthe alignment tensor and A r =(1/3)ACHTUNGTRENUNG(A xx A yy ) is the rhombic component. The available orientations ofan interaction vector for a single measured RDC in the presence ofa known tensor are depicted in cartoon form in Figure 2 on the surface of a sphere. ð2þ ð3þ Protein Structure Determination Using RDCs Alone A number ofstudies have shown the utility ofcombining RDCs with sparse distance and dihedral angle constraints derived from noe, scalar coupling and chemical shift data to determine low resolution folds of small proteins. [41 44] Two approaches have also been developed using only RDCs as experimental constraints. One ofthese, Molecular fragment replacement, [45] searches databases for peptide strands present in proteins ofknown structure, and combines these segments to propose a complete protein fold. In parallel we attempted a de novo approach that places oriented peptide planes and tetrahedral junctions sequentially, as a function of the measured RDCs, in order to define the polypeptide fold. [46] The approach was named meccano (molecular engineering calculations using coherent association ofnonaveraged orientations), and its feasibility was initially demonstrated using the dataset from ubiquitin in bicelles and charged bicelles measured by the Bax group, [47, 48] and applied to the determination ofthe backbone conformation ofthe active site ofa larger molecule, methionine sulfoxide reductase (27 kd). [49] The initial step ofthe approach is to calibrate the alignment tensors, using no information concerning the molecular fold. This requires optimization of7 parameters (A 1 a, A 1 r, A 2 a, A 2 r, a, b, g), where a, b, g describe the orientation of A 2 with respect to A 1, taken to be diagonal in the calculation frame. Simultaneously, the orientation ofeach peptide plane is determined with respect to the calculation frame. This algorithm reliably finds the global minimum ofthe target function [Eq. (4)]; c 2 ¼ X n n o 2. D exp ij D calc ij s 2 ij Figure 2. Cartoon representation ofthe dependence of measured dipolar couplings on the orientation ofthe internuclear vector. Dipolar coupling isocontours are shown as shaded bands: black/dark grey: positive coupling, white: intermediate and zero coupling, light grey: negative coupling. The axes represent the axes ofthe alignment tensor. over all measured couplings (s ij is the experimental uncertainty), requiring no a priori estimation ofthe alignment tensors. The second stage ofthe algorithm constructs the molecule. The orientation ofany planar element has a twofold degeneracy with respect to the possible couplings in the presence of two different alignment media, introducing an orientational ambiguity between the correct alignment and the mirror image that must be solved for each planar element. RDCs measured in the tetrahedral junction ( a C i 1 a H i 1, a C i 1 b C i 1 ) and the geometry ofthe junctions allow unambiguous positioning. The final Ubiquitin backbone conformation compares closely with the structure determined using an extensive noe data set, in combination with RDCs, 3 J couplings and hydrogen ð4þ ChemPhysChem 0000, 00, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim &3& These are not the final page numbers! ÞÞ

4 M. Blackledge et al. bonding restraints (2.0 Š backbone rmsd, and 1.0 Š following refinement with a standard force field). Protein Dynamics from RDCs So far we have considered only the structural dependence of dipolar couplings and their application for determining static structures, but it is in terms ofmolecular dynamics that a second, equally powerful aspect of RDCs, is revealed. RDCs are averaged over all orientations ofthe magnetic dipolar interaction vector sampled up to a timescale defined by the inverse ofthe alignment-induced coupling, thus reporting on averages up to the millisecond range under conditions ofpartial molecular alignment. [50] Expressing the dependence ofthe dipolar coupling on the vector orientation with respect to the alignment tensor as in Equation (3), we implicitly assume that the inter-spin vector is static with respect to the alignment tensor. In the presence of local internal motion the measured coupling is better represented by incorporating local conformational averaging over both time and ensemble [Eq. (5)]: g i g j m 0 h D ij ðq;þ ¼ A 16p 3 rij 3 a h3 cos 2 q 1iþ 3 2 A rhsin 2 q cos 2i The angular brackets indicate conformational averaging. This provides access to information that is potentially highly complementary to the dynamic parameters routinely extracted from spin relaxation measurements. [51] Comparison ofmotional averaging on the two timescales provides information on dynamics in the nano- to millisecond range. This relevance is particularly evident for first order averaging of dipolar interactions whose rapid reorientation also dominates experimental spin relaxation rates (for example 15 N 1 H couplings). The ability of RDCs to describe local conformational fluctuations over the nano to millisecond time range in proteins has been studied by a number ofgroups in recent years. The effects ofintramolecular motion on the dynamic averaging ofrdcs is represented in Figure 3. In the presence ofdi ferent alignment tensors the averaging will sample dipolar couplings isocontours (shown as shaded bands in Figure 3) differently and give rise to differential averaging effects. A number of methods have been developed that attempt to extract the extent and shape ofthe motional envelope ofinternuclear vectors from dipolar couplings measured in differently aligning media. Prestegard and co-workers interpreted local motions in terms oflocal alignment characteristics, and expressed these as a site-specific generalized degree of order (GDO), [52] while Griesinger and co-workers used a very large number ofdatasets measured on Ubiquitin [53 56] to determine the shape and size ofthe orientational averaging envelope for each N H N vector in the protein. Tolman has independently proposed and applied related approaches. [57,58] In an alternative approach, Bax and co-workers have attempted to define the limits of possible local dynamic amplitudes in protein GB3 by using refined static models, and comparing the ability ofthese models to ð5þ Figure 3. Representation of the effects of intramolecular motion on the dynamic averaging ofresidual dipolar couplings. In the presence ofmotion the effective measured coupling reports on all orientations sampled in the motional envelope (shown as an ensemble ofvectors and as black circles). If the motional envelope is anisotropic, as shown here, the effective averaging depends on the orientation ofthe motional anisotropy with respect to the alignment tensor. In the presence of different alignment tensors the averaging will sample dipolar couplings isocontours (shown as shaded bands). describe the experimental data. [59] Finally, with reference to earlier discussion, Clore et al. have used ensemble averaging of RDCs to describe the conformational space available to both Ubiquitin and protein GB3. [60] We have explored the possibility ofusing specific geometric models to describe local motional averaging ofrdcs. Initial studies used a one-dimensional gaussian axial fluctuation (GAF) model for peptide plane reorientation about the C a i 1 C a i axis, identifying a common anisotropic component of protein backbone dynamics from 15 N 1 H RDCs. [61 63] This simple approach demonstrated that statistically significant improvements could be made to the accuracy ofthe description ofthe overall molecular alignment tensor by taking into account local motions, even in the absence ofsite-specific details. In the light ofvigorous debate concerning the nature and extent ofslow motions present in soluble proteins, and the ability of RDCs to describe these dynamics, we undertook a detailed study ofthe presence ofslow motions in protein GB3, interpreting an extensive set ofrdcs [59,64] measured in multiple differently aligning media, in terms of the three dimensional gaussian axial fluctuation model (3D-GAF, see Figure 4). This general model ofpeptide plane dynamics allows for stochastic motions around three orthogonal axes attached to the peptide plane, [65] and our interpretation assumed a fixed time- and ensemble-averaged model ofthe average structure. The study delivered a site-specific motional description of each peptide plane in the protein, and provided a quantitative estimate ofthe nature and extent ofdynamics present on the protein backbone. [66] We identified a heterogeneous distribution ofslower motions in the protein in comparison to 15 N spin relaxation data, [67] with local motions in some regions ofthe protein that are quantitatively the same as those detected using spin relaxation, for example in the a-helix and some sur- &4& Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim ChemPhysChem 0000, 00, 1 10 ÝÝ These are not the final page numbers!

5 Protein Structure and Backbone Conformational Dynamics Figure 4. Three-dimensional Gaussian axial fluctuation (GAF) model of peptide plane reorientation used for the modelling of dynamic reorientation. One-dimensional GAF models imply rotations about any one ofthe three axes. face loops and turns. We can therefore detect no additional (ns ms) slow motions in these regions. In the b-sheet, and one ofthe surface loops, however, slower motions are observed, in particular in the region where the protein interacts with its physiological partner (b-strand II). The presence ofthese dynamic modes is verified using extensive cross validation of data that are not used in the analysis, and the dependence on the structural model is tested against two crystal conformations and an RDC refined structure, all of which gave similar motional distributions. Analysis oftrans-hydrogen bond scalar couplings in terms of these local dynamic amplitudes and directions also found strong evidence that the motion was correlated and that the collective motion transmitted across the b-sheet was propagated via the inter-strand hydrogen bonds. Although this kind of transmission ofdynamics has been proposed, it has never been observed by other experimental methods, and is computationally challenging to simulate. The existence ofthese slow motional modes extending across the entire b-sheet carries clear implications for understanding the mechanisms of longrange signal propagation in proteins. In the case ofprotein G, these findings illustrate how the protein harnesses thermal motions via specific dynamic networks to enable molecular function at the interaction site (see Figure 5). This parameterisation ofmolecular motion in terms ofa simple dynamic model led us to explore the possibility of using extended sampling molecular dynamics based approaches to develop a more explicit molecular description of the slower timescale motions present in GB3. [68] Accelerated molecular dynamics (AMD) [69] simulations were shown to accurately reproduce the amplitude and distribution ofslow motional modes characterized using RDCs and the 3D GAF model. In agreement with experiment, larger amplitude slower motions were localized in the b-strand/loop-motifspanning residues and in loop Principal component analysis showed these fluctuations dominating the lowest energy eigenmode, substantiating the existence ofa correlated motion traversing the b-sheet that culminates in maximum excursions at the active site ofthe molecule. Interestingly fast dynamics were simulated using extensive standard MD simulations and compared to order parameters extracted from 15 N relaxation. Sixty 2 ns fully-solvated MD simulations exploring the different Figure 5. Representation ofthe collective motion traversing the b-sheet of protein GB3. The ribbon is coloured as a function ofthe amplitude ofthe component ofthe motion about the gamma axis shown in Figure 4. Blue indicates little motion, yellow regions have higher amplitude motion while red indicates the highest amplitude motions. The highest amplitude motions are clearly located in the interaction site ofthe protein that forms a complete b-sheet with FAB (shown in sky blue). conformational sub-states sampled from AMD resulted in significantly better reproduction of order parameters compared to the same number ofsimulations starting from the relaxed crystal structure, illustrating the inherent dependence ofprotein dynamics on local conformational topology. The results provide rare insight into the complex hierarchy ofdynamics present in proteins and allow us to develop a picture ofthe conformational landscape native to the protein. Recent results from Showalter and Brüschweiler [70] have also demonstrated that free MD simulations using the most recent force fields [71] provide very close reproduction ofexperimental RDCs from Ubiquitin, substantiating the conclusions drawn from our study. We have also used standard and accelerated molecular dynamics simulations to determine the accuracy of3d GAF-based approaches to characterising the nature and extent oflocal molecular motions. The results demonstrate the robustness of the 3D GAF analysis even in the presence oflarge-scale motions, and illustrate the remarkably quantitative nature ofextracted amplitudes. These observations suggest that the approach can generally be employed for the study of functionally interesting biomolecular motions. Simultaneous Determination of Protein Structure and Dynamics from RDCs It appears therefore that RDCs can be used both to determine high resolution protein structure, and to accurately describe the nature and extent oflocal molecular motions, clearly illustrating the dual dependence ofthese parameters, and underlining their remarkable potential for studying biomolecular behaviour in solution. In comparison to noe, experimental RDCs are sensitive to relatively few sources of uncertainty, and as we have seen, are averaged over all conformations sampled up to the millisecond range, simplifying their interpretation in terms ofboth structure and dynamics. This means that dynamic effects can in principle be analytically incorporated into the con- ChemPhysChem 0000, 00, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim &5& These are not the final page numbers! ÞÞ

6 M. Blackledge et al. formational definition of the coupling, suggesting these data as optimal candidates for simultaneous determination of protein structure and dynamics. In a recent study we therefore attempted to use peptide plane RDCs alone to simultaneously determine the backbone structure and conformational dynamics of protein GB3. [72] A version ofthe meccano approach was developed, using analytical descriptions ofthe structural and dynamic dependence of RDCs. In particular we exploit the dependence ofmeasured RDCs on the orientation and a single anisotropic motion about each ofthe 3D GAF axes [Eq. (6)]: D ij 1D GAF ¼ m 0 g i g j h 8p 2 rij D a½s 1 ð3 cos 2 b 1Þþ3s 2 sin 2b cos a þ 3s 3 sin 2 b cos 2aŠþ 3 8 D r þ2s 3 s 1 sin 2 b cos 2g 2s 2 sin b cosða þ 2gÞcos b 2 cos a 2g 2 ð b Þsin2 2 cosð2a þ 2gÞcos b 4 þ cos 2a 2g 2 ð b Þsin4 2 ð6þ where s 1 = 2ð3 cos 2 q 1Þ, s 2 =2 sin 2q expð s 2 =2Þ, s 3 = 2 sin 2 q expð 2s 2 Þ and r ij is the internuclear distance, s the motional amplitude, RACHTUNGTRENUNG{a, b, g} the Euler rotation transforming the alignment tensor principal axis system into the local peptide plane frame defined with its z axis along the rotational axis and its x axis so that the internuclear vector lies in the x z plane. {q} is the azimuthal angle between the rotational axis and the internuclear vector. This relationship was used to determine both the average peptide plane orientation and the amplitude ofthe major mode ofdynamic reorientation for each peptide plane in the protein. Three coplanar RDCs measured in five alignment media are used, comprising N 1 H N, 13 C 13 C a and 15 N (i) 13 C (i 1) RDCs. Only peptide plane RDCs are used in this study, as these are the structural units for which we have an analytical model ofreorientational dynamics. The only a priori knowledge ofthe protein structure used here is an assumed common, perfectly flat, peptide plane conformation derived from a database of ultra-high resolution X-ray crystallographic structures. As in the case ofthe static-meccano approach, the first step in the dynamic-meccano protocol is to determine the components (D a, D r, q,f, y) ofall five tensors. This entails the determination ofthe average orientation ofeach plane (a, b, g) i,aparameter s i accounting for dynamic fluctuation of each plane and the 22 parameters defining the tensors. A total of 238 parameters are therefore optimized in this step. Dynamic reorientation was incorporated using the best-fitting model for each peptide plane from 3 orthogonal one dimensional Gaussian axial fluctuations (1D GAF) or a common scaling factor for all RDCs in the plane. In the interests ofcomparison molecular alignment tensors were also determined using the static model, in Equation (3). Some motion may in this case be absorbed into the fitted average tensor components D av a and D av r. [63] The backbone conformation is sequentially built by positioning the average conformations of the peptide planes of fixedinternal geometry to best reproduce the experimental data by minimizing Equation (4). Intervening tetrahedral junction geometries were also weakly imposed. Optimisation ofthe plane orientation is accompanied by selection ofone ofthe four dynamic modes described above (amplitudes s a, s b, s g ofthe GAF motions, or an order parameter S, ofan axially symmetric motion) on the basis of the target function for this plane. Once the structure has been determined on the basis ofthis algorithm a complete 3D GAF analysis ofthe dynamic disorder present along the chain was applied. The advantage ofsuch a study is the ability to directly compare the quality ofoptimally performed static and dynamic descriptions ofthe protein in solution, without resorting to the use ofmolecular mechanical force fields and in the near absence of spurious contributions to the experimental data. In this respect the results are remarkable. The dynamic-meccano structure (pdb accession code 2 nmq) directly resulting from this procedure is shown in Figure 6 in comparison to the 1.1 Š crystal structure (1igd: backbone rmsd 0.55 Š) and to the crystal structure refined with respect to the same RDCs (1p7e: backbone rmsd 0.34 Š). The dynamic-meccano structure is clearly very close to these conformations. The main differences between the dynamic-meccano structure and the X-ray structure occur in the loop region 14 20, where our previous 3D GAF study revealed the presence ofslow dynamics. The static-meccano structure also finds the global fold correctly, but is significantly further from 1igd and 1p7e (rmsd of 1.15 Š and 1.10 Š respectively) than the dynamic model. Of Figure 6. Comparison ofdynamic-meccano and static-meccano structures (red) with known conformations (blue) [left: 1igd the crystal structure, right: 1p7e the RDC-refined crystal structure]. Static meccano gives structures whose rmsds are 1.15 Š and 1.10 Š respectively, while dynamic meccano gives structures that are 0.55 Š and 0.34 Š respectively. &6& Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim ChemPhysChem 0000, 00, 1 10 ÝÝ These are not the final page numbers!

7 Protein Structure and Backbone Conformational Dynamics course this does not immediately tell us which ofthese models is more accurate, as both the crystal and the RDC-refined crystal structures may actually be different to the true solution average conformation. Structure determination using only peptide plane RDCs however can address this issue and tell us whether the dynamic-meccano description is actually better than the static-meccano structure. Using classical cross validation approaches, five calculations were performed for both static and dynamic-meccano calculations, with all data from one of the media removed from the analysis in each case. Predicted values were compared to experimental values for both static and dynamic cases. The dynamic-meccano structure was found to reproduce experimental data significantly better than the static-meccano structure (reduced c 2 of 0.8 compared to 1.7), even for the most linearly independent alignment medium (c 2 red of0.6 compared to 2.6), with largest discrepancies in the static case corresponding to the most dynamic sites in the protein. Interestingly the dynamic-meccano average conformation is further validated by 250 C a H a RDCs that were not used in the calculation but are reproduced significantly better from this structure than by 1igd (reduced c 2 of 7.8 compared to 14.4) (Figure 7). Although the C a H a RDCs are Figure 7. Cross validation of250 C a H a RDCs that were not used in the meccano structure calculations. The average structure ofthe dynamic model (right) reproduces the data significantly better than the static calculation (right) performed on the crystal structure (reduced c 2 of7.8 compared to 14.4). Figure 8. Dynamic amplitudes extracted from dynamic-meccano. Top: Comparison of s g determined using 3D GAF analysis ofexperimental RDCs with 1p7e and the dynamic-meccano structure (dashed). Bottom: Comparison of S 2 order parameters determined for the N H vector using dynamic-meccano (dotted), following 3DGAF analysis of the dynamic-meccano structure (dashed) and the crystal structure 1p7e. interpreted in a static way in both cases, the average dynamic meccano structure still provides an improved average conformation as measured by the orientation ofthese vectors present in the tetrahedral C a centres. Anisotropic dynamic parameters extracted from the 3D GAF analysis ofthe dynamic-meccano structure compare closely to values determined with respect to 1p7e, and to those predicted using the recent accelerated molecular dynamics study of protein G (Figure 8). Importantly motion about the g-axis (C a C a direction) and the effective order parameter S 2 NH RDC are similarly distributed along the chain and ofsimilar amplitude. Alternation ofanisotropic motions in the b-strand, indicative ofa complex correlated motion across the b-sheet, is again observed. [68] The S 2 NH RDC values are in general closely reproduced between analyses ofthe dynamic-meccano and 1p7e structures, and are similarly distributed to those from a recent study using EARMD ofthe same RDCs. [27] The distribution and amplitude ofdynamics determined here are therefore very similar to those recently evaluated using the 3D GAF model applied to both 1p7e and 1igd. This study also allowed us to address the remaining questions concerning structural noise for interpreting RDCs using an existing conformation. [73] Dynamic-meccano constructs the backbone conformation ab initio, so that this source of error is not a concern. The similarity ofthese results with 1p7e, where peptide units are not all flat ( deviation) also implies that this effect does not strongly influence extracted dynamic amplitudes. Recent comparisons ofdata simulated from accelerated molecular dynamics trajectories demonstrates that the dynamic-meccano protocol closely reproduces the average coordinates ofthe trajectory even in the case ofbroad conformational sampling. This result substantiates conclusions ofour previous study; including the observation that slow motions are not uniformly distributed through the protein backbone, but are present only in certain regions, and affirms the independence ofthe previous results on the structural model. This important result also demonstrates the accuracy and robustness ofthese GAF-based approaches, that appear to allow quantitative estimates ofthe extent ofslow motions in proteins at ambient temperature. This quantitative analysis relies on a careful treatment ofthe level ofmolecular alignment with respect to which the dynamic amplitudes are estimated. It is interesting to piece together the information derived from these related studies of protein GB3 in order to better understand the conformational landscape of this small model protein. The evidence from RDC analysis and molecular dynamics simulation both suggest that the protein lies in a ChemPhysChem 0000, 00, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim &7& These are not the final page numbers! ÞÞ

8 M. Blackledge et al. steep-sided conformational energy potential, whose stippled base is relatively shallow and apparently harmonic, and comprises multiple local minima. The average solution structure determined using only RDCs, and accounting for significant levels ofdynamic sampling as described above turns out to be very close to the single-copy RDC refined structure determined by Ulmer et al. This may not be a general result, but in this case supports the model ofa simple harmonic potential well. The crystal conformation on the other hand is slightly different and probably lies in distinct conformational minimum on the potential-energy landscape. The apparent resolution ofthe dynamic-meccano structure as measured using cross validation is remarkable in view ofthe simplicity ofthe approach. These results, in addition to a recent study ofthe structure ofperdeuterated protein GB1 using extensive RDCs from two alignment media, including 1 H 1 H RDCs, [74] suggest that this level ofstructural precision is inherent to RDCs. Use ofthese constraints alone provides access to ultra-high resolution structure ofapparent precision comparable to that from high resolution X-ray crystallography as measured by independent cross-validation and structure comparison. This is apparently due both to the fact that dynamic averaging is relatively well-understood and well-suited to incorporation into structure calculation by analytical methods, and to the lack ofadditional phenomena that can contribute to the precision ofthe experimentally measured coupling. We find that the dynamically averaged structure provides a significantly better description of the conformational properties in solution than a bias-free static approach performed in parallel. The accuracy ofthe mean structure also significantly improves using a dynamic interpretation. Conclusions and Oulook In summary we have demonstrated the capacity ofrdcs to simultaneously quantify slow motions probed by native proteins and their average conformations to high resolution. One of the most promising aspects ofthis work may result from the combination ofconformational analysis ofrdcs with the results of molecular dynamics simulation as shown by recent simulation on Ubiquitin [70] and protein GB3. [68] RDCs can be used to guide molecular dynamics sampling methods, and provide a complete description ofconformational behaviour ofproteins in solution. Acknowledgements G.B. and P.R.L. M. receive grants from the CEA. This work was supported by the EU through EU-NMR JRA3 and French Research Ministry through ANR NT The authors would like to thank the Centre de Calcul Recherche et Technologie (CCRT) (CEA, BruyØres-le-Châtel). 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10 MINIREVIEWS G. Bouvignies, P. R. L. Markwick, M. Blackledge* && && Simultaneous Definition of High Resolution Protein Structure and Backbone Conformational Dynamics using NMR Residual DipolarCouplings The whole story: In NMR data the nuclear overhauser effect is susceptible to additional dynamic averaging phenomena. Residual dipolar couplings measured under conditions ofpartial molecular alignment overcome theses difficulties and provide access to direct, analytical determination ofboth structural and dynamics components ofprotein behaviour (see figure) in solution. &10& Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim ChemPhysChem 0000, 00, 1 10 ÝÝ These are not the final page numbers!