Dec 112009
ResearchBlogging.orgA few weeks ago, I wrote that the goal of a structural biology research program ought to be to “characterize the conformation and energy of key, functionally-relevant members of the protein’s structural ensemble and identify the pathways between them.” The Nature paper last week, among other examples I mentioned in the preceding post, described functionally significant minor members of the native-state ensemble, and this is certainly an area where structural studies are making a lot of progress. But what about the other part of that statement, the transition pathways? How are we to study them, and what can we learn about them? Experiments alone are unlikely to tell us everything we want to know about the intermediates between different native structures. We can, however, use simulations validated by experiments to investigate the mechanisms of structural change. Today in Cell, research primarily performed by my coworkers Alexandra Gardino and Janice Velos demonstrates that the bacterial signaling protein NtrC  rapidly samples its active conformation even when it is not phosphorylated. Moreover, they confirm predictions that the intermediates between these two states are stabilized by hydrogen bonds not present in either one.

Phosphorylation, or the covalent addition of a phosphate group to a protein, frequently appears as a way of transferring information within a cell. Often this chemical modification is described as a “switch” that flips a protein from an “off” state to an “on” state. The receiver domain of the bacterial protein NtrC (part of the nitrogen-fixing pathway) gets phosphorylated on  aspartate 54 in response to environmental stimuli, causing a change in conformation.  This causes NtrC to switch from a dimer to a hexamer, with the result that it binds to DNA, and eventually activates transcription of target genes. As you can see from the figure on the right, the change from inactive (red, PDB: 1DC7) to active (green, PDB: 1DC8) phosphorylation causes significant changes in the ’3445 face’ of the protein (dark colors), involving changes in not only the position of the helices, but also their length. That means numerous hydrogen bonds are broken and formed during the process, which would naturally lead one to suspect that going from one form to the other takes a while and is difficult to do. Neither is true

That NtrC converts rapidly from its active to its inactive state has been known for some time. Volkman et al. showed in 2001 that the 3445 face experiences some kind of chemical exchange process (2). Moreover, mutations that cause NtrC to become active in the absence of phosphate do not cause it to adopt the active conformation. As shown in Fig. 2e in (1) and Fig. 4 in (2), the NMR spectra for these mutants show peaks that lie partway between the active and inactive chemical shifts. This indicates that the exchange process reflects conversion between the active and inactive conformations in the absence of phosphorylation, and that this process is fast on the NMR timescale. The activating mutations merely shift the relative populations of the active and inactive states. As Janice’s folding experiments in the current paper show, these mutations operate by destabilizing the inactive state, i.e. they make it less energetically favorable relative to the active conformation. By contrast, phosphorylation of D54 significantly stabilizes the active state. However, conformational exchange is still observed in the phosphorylated protein, indicating that the protein samples the inactive state even when it is presumably activated. NtrC is never “locked” into one state or the other.

This description obviously does not jive with the typical language describing phosphorylation as a “switch” that turns signaling pathways “on”. One might well wonder why phosphorylation matters if the unphosphorylated protein can sample the active conformation. Of course, the NtrC receiver domain might not behave the same in isolation as it does when it’s integrated into a whole protein. NtrC signaling in vivo involves communication from the receiver domain to the DNA binding domain, as well as changes in oligomeric state, neither of which are addressed by examining the receiver domain alone in solution. Given that D86N is functionally activating, it’s likely that these results translate to the whole protein, but phosphorylation may still be considered an effective “switch” because of the way it extends the lifetime of the active state. That is, the receiver domain samples the active state occasionally in solution but doesn’t stay there long enough for the full sequence of steps that are required to result in transcription. In this model, the effect of the phosphorylation is simply to hold the protein in its active conformation long enough for the full transcriptional activation to occur.

Talking about lifetimes is all well and good, but that’s a pretty nebulous discussion unless you have some idea of the rates at which these forms are interconverting. The dispersion traces in Fig. 2 show that the rate is fast, so fast, in fact, that a refocusing field of 1000 Hz has a negligible ability to suppress the effects of conformational exchange in the unphosphorylated protein. In order to fit these curves, Alex and Janice had to use an alternative approach to determine the intrinsic relaxation rate. Once they did that, they found that the rate of interconversion exceeded 104 /s for the unphosphorylated protein, but was only around 2000 for the phosphorylated form. How can such a complex process, requiring so many bonds to be broken, occur so quickly? The only way to know is to examine the pathway of transition between the inactive and active forms.

Identifying transition pathways between structural states is a tough problem, though, because the conformations of intermediates and transition states are poorly populated in the solution ensemble. Obtaining a high-resolution structure of one of these states through experiment is essentially impossible, which suggests that our best hope for getting detailed information about the transition pathway is by simulating the conformational changes in the protein. This also presents a problem, however, because these events occur on the microsecond to millisecond timescale, which means that a simulation would need to be on the order of a second long to really sample the relevant fluctuations. Even using hugely parallel computer nodes, however, simulating a protein at equilibrium for as little as a microsecond takes several months. You would need to run such a simulation for years to adequately sample even this rapid of a transition. To get around this time barrier, researchers perform various tricks with their simulations, simplifying the representation of molecules and forces or biasing them so that transitions happen more frequently.

The latter approach was used by Ming Lei in his targeted molecular dynamics simulation of this transition (3) — he applied an external force to the protein in that simulation that pushed it from one state to another. Here some rotation students put in some good work. Aleksandr (you may have noticed that the Kern lab attracts a lot of people named Alex) carefully examined Ming’s simulation to identify unusual interactions and noticed that a number of short-lived hydrogen bonds appeared to be forming, specifically hydrogen bonds that were not present in the active or inactive conformations. Of course, when you include a fictional force pushing a  protein one way or the other you may end up with artifacts in the simulation, so Janice, along with rotating students Ce Feng and Phillip, tested the simulation predictions by generating mutants that were incapable of forming these hydrogen bonds.

As you can see from Fig. 4, these mutations dramatically slowed the conformational fluctuation, confirming the importance of these bonds in lowering the energy barrier of the structural transition. Even though the bonds exist for only a few nanoseconds in the simulation, they appear to play a significant role in lowering the energy barrier. Note, however, that the effect of these mutations is not necssarily additive — the double S85D/Y101F mutant is no slower than either S85D or Y101F alone. This suggests that these hydrogen bonds stabilize the transition pathway at different points, so that different non-native bonds are responsible for lowering the energy barriers of multiple independent steps. This finding has significant implications for efforts to model structural transitions using simplified potentials based entirely on native-state contacts; it is possible, perhaps even likely, that such simulations will miss critical interactions that stabilize intermediates along these transition pathways.

Our ability to successfully design functional proteins will require that we consider not only the structural heterogeneity of the native state, but also how the movement of the protein between different conformational substates can be tuned by raising or lowering the energy barrier between them. Here, NMR experiments have shown how mutations and phosphorylation alter the energy landscape of NtrC and alter the balance between its inactive and active conformations. Moreover, this study validates the prediction from a targeted molecular dynamics simulation that NtrC uses short-lived, non-native hydrogen bonds to facilitate the transition between these two conformational states. Beyond expanding our knowledge of NtrC’s conformational energy landscape, these findings suggest possibilities for other proteins that are activated by phosphorylation, one of nature’s most pervasive signaling methods.

1) Gardino, A., Villali, J., Kivenson, A., Lei, M., Liu, C., Steindel, P., Eisenmesser, E., Labeikovsky, W., Wolf-Watz, M., Clarkson, M.W., & Kern, D. (2009). Transient Non-native Hydrogen Bonds Promote Activation of a Signaling Protein Cell, 139 (6), 1109-1118 DOI: 10.1016/j.cell.2009.11.022

2) Volkman, B.F., Lipson, D., Wemmer, D.E., and Kern, D. (2001) Two-State Allosteric Behavior in a Single-Domain Signaling Protein. Science, 291 (5512), 2429-2433. DOI: 10.1126/science.291.5512.2429

3) Lei, M., Velos, J., Gardino, A., Kivenson, A., Karplus, M., and Kern, D. (2009). Segmented Transition Pathway of the Signaling Protein Nitrogen Regulatory Protein C. Journal of Molecular Biology, 392 (3), 823-836 DOI: 10.1016/j.jmb.2009.06.065

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Dec 032009
ResearchBlogging.orgOf all the sources of structural variability in proteins, the hardest to pin down is side-chain conformational heterogeneity. Side chains aren’t always easy to model into their primary conformation in the first place — you need excellent crystal diffraction or NMR data to do it. Even if you pulled that off, it’s not always clear how (or if) side-chain fluctuations relate to a protein’s activity. If we carefully examine our data for the faintest signals, however, we can sometimes find evidence of secondary conformations that play an important role in function. In an article in this week’s Nature, James Fraser, myself, and others show that in the case of the proline isomerase cyclophilin A (CypA), alternative conformations of side chains play a key role in catalysis.

Previous experiments on CypA had established that the backbone amide groups of many residues were sensitive to a conformational fluctuation on the millisecond timescale. Under conditions where this enzyme is saturated with a peptide substrate, the fluctuation rate for some of these residues is very similar to the catalytic rate, suggesting that the dynamics and catalysis are linked in some way (2). Later experiments also showed that this fluctuation was an intrinsic property of the enzyme, continuing even in the absence of substrate (3). What we didn’t know, however, was how the dynamics of cyclophilin were related to catalysis. We couldn’t know, because we had no idea what the motion we were detecting was.

In the case of enzymes like adenylate kinase, there is a dramatic rearrangement of structural elements, and the population of conformations corresponding to the “end points” of that motion can be significantly enriched by altering the amount of substrate present in solution. In the case of CypA, neither of these things seems to be true. Supplementary Fig. 1a (freely accessible from the article page) neatly encapsulates the problem. For this figure, 48 structures of CypA, some with ligand and some without, were aligned, and the variation between them was determined. While there is some variability in the chain conformation, it is primarily limited to a group of residues known to undergo fluctuations that are not related with catalysis (blue chain). The residues involved in the catalysis-related dynamics don’t seem to have much variability, even across this fairly large group. So we can’t trap the unknown, minor state of CypA by adding substrate, and there’s no evidence of an alternate state that explains the NMR data.

Knowing this, we suspected that some kind of side-chain motion accounted for the observed dynamics, probably involving an aromatic group of some kind. Our efforts to gather evidence for this, however, ran into some typical NMR problems — resonance overlap and poor sensitivity exacerbated by chemical exchange. Fortunately, the crystallographers came to our rescue, in the form of Tom Alber and his super-talented grad student Jaime Fraser. Jaime had determined a crystal structure of CypA at cryogenic temperature and analyzed the data using their algorithm RINGER, which examines electron density below the threshold typically considered “noise” in order to identify possible alternative rotameric states of side chains. He found evidence of multiple conformations for a few residues, but nothing that would explain the NMR results. Jaime had the bright idea to redo the experiment at room temperature, which Tom was convinced would result in nothing more than a radiation-damaged crystal and bad diffraction data.

What actually happened was that when Jaime examined the electron density from that experiment he could identify a group of side chains that had more than one conformation in the crystal, which you can see in Fig. 1. These residues included serine 99, methionine 61, and the catalytic arginine 55. Right in the middle of this group was phenylalanine 113, a residue with an aromatic side chain capable of causing changes in chemical shift at relatively long range. For context, the image to the left shows a structure of cyclophilin (PDB code: 1RMH) in complex with the model substrate we used in our own experiments (succinyl-Ala-Ala-Pro-Phe-p-nitroaniline), with the side chains of S99, F113, M61, and R55 in red. As you can see, F113 and M61 form part of the floor of the binding pocket, with S99 rather remote.

So here we have an alternative structure of CypA, hidden below the threshold typically considered when determining a crystal structure. It was certainly plausible that fluctuations in this ensemble of side chains could give rise to the NMR observations, but plausibility isn’t proof. One way to address this would be to try and force CypA to adopt the less-populated conformation. If you look at Fig. 1d you can see that the two conformations of S99 lie at the standard rotameric positions, and that the less-populated rotamer of S99 would run into the more-populated rotamer of F113. So, if you replaced one of the side-chain hydrogens of S99 with a methyl group (i.e. mutated the serine to threonine), that might push the other residues of this group into their minor conformational state. So, that’s what we did.

To the right you can see an overlay of structures for wild-type (WT) CypA (red) and S99T (green), aligned using structural elements on the opposite side of the protein from the active site. As you can see, the backbone traces match very closely, except for the helix and loop on the right. These elements are involved in crystal contacts in the S99T structure, but not the WT; a lower-resolution structure of S99T shows no differences here. Another key difference between these structures, of course, is the position of the side chains (thick neon); as shown here (and more clearly in Fig. 2c) they seem to have adopted the minor conformation from the WT structures. Although this mutation inspires widespread chemical shift changes (Fig. 3a) consistent with the hypothesis that this concerted side-chain rotation gives rise to the NMR observations, the structures seem very similar. Yet, S99T CypA differs from WT in two important ways.

The first difference is that the conformational fluctuations are dramatically slower, but only for residues that showed catalysis-related dynamics in WT (Fig 3d). In fact, this rate is now so slow that due to a quirk of NMR we can only determine the slowest rate of the process. At 10 °C, this fluctuation in S99T is about 60 times slower than the slowest process in WT.

The second key difference between the mutant and the WT is that catalysis is dramatically slowed. Because CypA does not consume its substrate (it acts on both cis- and trans- proline bonds) its activity can be assayed by NMR, as you can see in Fig. 4. As with any enzymatic assay, the net activity is proportional to the amount of enzyme added, so just glancing at these spectra (and knowing the enzyme concentration) you can estimate that S99T has at least 40-fold lower activity than WT enzyme. If you actually perform the fits, it turns out that the reaction velocity for S99T is about 240 times lower than that for normal CypA, but this includes a contribution due to the fact that S99T does not bind its substrate as tightly either. If you correct for this, it turns out that S99T has about 70-fold less activity than the normal enzyme. Not only is this similar to the change in dynamics, it’s also quite comparable to another mutation, R55K, that removes a group that performs some of the chemistry.

These results indicate that a conformational change in a group of side chains including F113 is primarily responsible for the chemical exchange behavior observed in WT. The S99T mutation stabilizing the minor conformation dramatically and similarly reduces both the conformational fluctuation rate and the catalytic rate. This suggests that dynamics and catalysis are linked not by happenstance but by some direct relationship. Unfortunately, these experiments do not provide any direct insight into the mechanism by which dynamics contribute to catalysis. They do establish, however, that in CypA coherent fluctuations of side chains, barely detectable in protein crystals, nonetheless make a critical contribution to function.

1) Fraser, J.S., Clarkson, M.W., Degnan, S.C., Erion, R., Kern, D., & Alber, T. (2009). Hidden alternative structures of proline isomerase essential for catalysis Nature, 462 (7273), 669-673 DOI: 10.1038/nature08615

2) Eisenmesser, E.Z., Bosco, D.A., Akke, M., & Kern, D. (2002). Enzyme Dynamics During Catalysis Science, 295 (5559), 1520-1523 DOI: 10.1126/science.1066176

3) Eisenmesser, E., Millet, O., Labeikovsky, W., Korzhnev, D., Wolf-Watz, M., Bosco, D., Skalicky, J., Kay, L., & Kern, D. (2005). Intrinsic dynamics of an enzyme underlies catalysis Nature, 438 (7064), 117-121 DOI: 10.1038/nature04105

Oct 272009
ResearchBlogging.orgFor some enzymes, dynamics on the millisecond timescale play a critical role in catalysis. I don’t think this is a particularly controversial or unclear statement, but then, I know what I mean by it. In the process of communication, however, the intended meaning sometimes gets lost or transformed. A statement that addresses an entire catalytic cycle, for instance, might be interpreted as addressing only the chemical step. This seems to have happened in a pair of papers that concern the transfer of energy from conformational rearrangements to a chemical reaction.

Consider a reaction scheme in which an enzyme loosely associates with substrates (E.S), then “closes” to form a tight, catalytically-competent complex that then undergoes a reaction with the rate kchem:

Pisliakov et al. (1) ask whether the closing process can accelerate kchem. They ask this question primarily because a group from Harvard University proposed that this was possible in a paper printed last year in J. Phys. Chem. B (2). In that paper, Min et al. performed some simulations suggesting that such an acceleration was at least possible, and consistent with some enzymatic data. Pisliakov et al. approach the question with simulations of the reaction of the phosphotransfer enzyme Adk with 2 ADP molecules to form ATP and AMP. As part of the catalytic cycle, the enzyme goes from an open state (PDB: 4AKE) where the ATP and AMP binding sites are exposed to solvent, to a closed state (PDB: 1ANK) where the substrates are shielded from the surrounding solution by ATP and AMP “lids” that close down over the active site.

One can, perhaps, imagine that when the enzyme closes around the substrates, some motion will occur that promotes the transfer of a phosphate group from one molecule to another. Pisliakov et al. use a three-tiered system of simulations to address the question, as a way of trying to get around the difficulty of dealing with the long timescales required. Their simulations allow them to adjust the energy barrier to match the experimental rates or accelerate the reaction so that the whole pathway can be simulated. In general, they find that conformational fluctuations do not enhance the chemical reaction rate in this system.

I have two main concerns about the science that was performed here. The first is that the energy barriers in the long-timescale experiment appear to be improperly paramaterized. In estimating these barriers for the phosphotransfer reaction in Adk, Pisliakov et al. used 260 /s as kchem. However, although the actual reaction carried out by Adk follows an extremely complex scheme, the analysis performed by Wolf-Watz et al. utilized a simplified scheme that combined all post-association steps into a single kcat. This is why the concordance between kcat and kopen justifies the conclusion that lid-opening is rate-limiting. In principle, the experiments used for that paper are incapable of separating the opening and closing steps from the chemical step. Therefore we have no experimental knowledge of the phosphotransfer rate, except that it is greater than 260 /s. This perplexing error appears to have originated with Min et al., but I am surprised Warshel’s group did not catch it.

This is not a major problem because the bulk of the conclusions of the experiment were drawn from a different simulation in which the energy barriers were lower, but this leads to my second concern. If the structural transition involves a very smooth and coherent rearrangement of the protein, then simply manipulating energy barriers should not result in a serious error of analysis. In reality, however, ensemble motions of protein elements are not going to be so directed or uniform. Structural rearrangements are not highly singular steps, but involve a large number of intermediates and transition states. Motions in the late stages of the structural transition that promote catalysis may well be missed by simplified models, or accelerated beyond productivity by lowering the energy barrier.

That said, I’m not particularly surprised that Pisliakov et al. find that energy from the conformational coordinate does not transfer to the chemical coordinate, nor do I disagree with the finding. Despite what Pisliakov et al. appear to believe, the papers that have come out of Dorothee’s group don’t argue that the millisecond motions contribute directly to the chemistry. Doro doesn’t believe that for a second. Neither do I. The importance of dynamics has little to do with shoving the reaction along the chemistry coordinate, but everything to do with getting substrates bound and into a state where chemistry is possible.

Dynamics allow an enzyme to reconcile incompatible functional requirements. To efficiently function as a phosphotransfer enzyme (as opposed to a hydrolytic phosphatase), Adk must expel water from the active site during catalysis. If the active site is inaccessible to solution, however, there is no way for the substrates to diffuse into it. It is difficult to create a single, rigid fold that can accommodate both these demands, but by fluctuating between two states the problem is resolved quite easily. So yes, the dynamics are essential to catalysis, but that does not imply that the conformational and chemical energy coordinates are coupled.

More perplexing is the discussion of the hierarchy of motion, which Pisliakov et al. take to mean that nanosecond motions somehow contribute to the chemical coordinate. As I discussed when that paper was initially published, the question being addressed was whether and how motions on the fast timescale (ps-ns) in Adk were related to the slower (ms) motions of the lids. In a hierarchy of motion, fast timescale fluctuations enable or promote slow timescale dynamics. In the case of Adk, this means that nanosecond flexibility at structural hinges allow the millisecond motions of the ATP and AMP lids. It was not implied, then or since, that the nanosecond motions in question make a direct contribution to movement along the chemical coordinate. This is not to say that there are no researchers who believe that ns motions contribute to catalysis — I’ve previously mentioned some work on hydrogen tunneling that makes precisely this argument. In the specific case of Adk, however, the contribution of ns motions to catalysis consists entirely in their enabling of the slower ensemble motions of the nucleotide binding domains, and nobody but the Warshel group has suggested otherwise.

There is an ongoing disconnect in the literature concerning the role of dynamics in catalysis. While it is true that in many cases rates of structural transitions correlate with rates of catalysis, this does not imply that the conformational transition coordinate is linked to the chemical reaction coordinate by direct transfer of energy. It is more likely that the dynamics of the enzyme contribute to catalysis by generating reaction-competent states from reaction-incompetent states. This is not to say that dynamics cannot possibly make a contribution to phenomena such as hydrogen tunneling, but it strikes me as unlikely that motions on the millisecond timescale will contribute to a chemical coordinate. Experiments, rather than simulations, will be the ultimate test of the idea. However, in principle, this hypothesis can only be tested experimentally on enzymes where the conformational changes do not limit the chemical reaction rate. Because the rate of the chemical step is unknown in Adk, it may not be an appropriate model system for addressing this question.

1. Pisliakov, A., Cao, J., Kamerlin, S., & Warshel, A. (2009). Enzyme millisecond conformational dynamics do not catalyze the chemical step Proceedings of the National Academy of Sciences, 106 (41), 17359-17364 DOI: 10.1073/pnas.0909150106

2. Min, W., Xie, X., & Bagchi, B. (2008). Two-Dimensional Reaction Free Energy Surfaces of Catalytic Reaction: Effects of Protein Conformational Dynamics on Enzyme Catalysis The Journal of Physical Chemistry B, 112 (2), 454-466 DOI: 10.1021/jp076533c

3. Wolf-Watz, M., Thai, V., Henzler-Wildman, K., Hadjipavlou, G., Eisenmesser, E., & Kern, D. (2004). Linkage between dynamics and catalysis in a thermophilic-mesophilic enzyme pair Nature Structural & Molecular Biology, 11 (10), 945-949 DOI: 10.1038/nsmb821

Aug 202009
This is the last of my series of posts about the dynamics-focused topical issue of JBNMR. There are plenty of other excellent papers in it, and I encourage you to at least glance over all of them, especially if you’re an NMR person.

ResearchBlogging.orgStandard NMR dynamics experiments on isotropically tumbling proteins cover a wide, but not comprehensive, swath of fluctuation timescales. Limited information about motions that take milliseconds or more can be obtained from hydrogen exchange data; the AMORE-HX experiment is meant to obtain this kind of information. Fluctuations with time constants in the range of μs-ms can be measured by relaxation-dispersion experiments, as were used in the Peng lab’s paper. Motions that are faster than the rotational correlation time of the protein can be characterized using dipolar relaxation data of the kind I collected for the field-cycling experiment. There are additional kinds of data that also cover these areas, but the glaring hole lies between the correlation time of the protein (several ns) and the low end of the chemical exchange regime (several μs). Several teams, including that of Christian Griesinger, propose to fill this gap using data derived from residual dipolar couplings (RDCs). In the topical dynamics issue of the Journal of Biomolecular NMR, his group demonstrates the use of this technique in measuring the dynamics of side chains in the small protein ubiquitin. The article is open access, so feel free to open it up and read along.

The strength of the dipolar coupling between two nuclei depends on their magnetic properties (specifically their gyromagnetic ratio), the distance between them, and the angle between the internuclear vector and the vector describing the external magnetic field. For solution NMR this last component is typically not important because most proteins tumble randomly with respect to the magnetic field, causing this interaction to be averaged away. However, if you were to somehow introduce a tiny amount of bias into the tumbling, very slightly aligning the protein parallel or perpendicular to the magnetic field, a residual portion of this coupling could be recovered. The effect is considerable: a net alignment of less than a fraction of a percent generates couplings on the order of 30 Hz or more.

There are many ways of inducing this alignment. Large charged particles such as phage or DNA nanorods have been used, as have assemblies such as charged or polar lipid bicelles. In addition, proteins can be labeled with paramagnetic metals to induce fractional orientation. Even mechanically manipulated media, such as acrylamide gels, can be used to achieve alignment if they are stretched or compressed along the field axis. When a new method of alignment is introduced, it is typically tried out on a small, abundant protein with good relaxation characteristics, most often the regulatory protein ubiquitin. The upshot of this is that there is a fantastic amount of RDC data on this protein, and Griesinger’s group uses this data to model the motions of its methyl-bearing side-chains.

This may sound strange, because RDCs are typically employed for structure determination. The angle defined by the measured coupling results from the overall tumbling bias of the protein (an alignment tensor) that is the same for each coupled pair, and their angle within that frame of reference, which can be used to uniquely define a structure. However, the dipolar coupling cannot be measured in an instantaneous fashion. It must evolve over time, just like chemical shift or a J coupling. As such, the dipolar coupling reflects an averaged orientation over the evolution period. In principle, the degree of averaging can be modeled as some kind of order parameter, similar to the S2 of the Lipari-Szabo system, reflecting all these motions. This should encompass not only the fast dynamics that determine dipolar relaxation rates, but also motions slower than the global correlation time, up to near the ms range.

In order to derive dynamics data from their set of experiments in 13 different alignment media, the authors first scaled the RDCs from C-H methyl bonds. The reason they did this is that the three hydrogens in a methyl group rotate constantly around an axis passing through the adjacent C-C bond (cyan in the isoleucine side chain depicted at right). Because this rotation is typically very fast, simple to model mathematically, and pretty uninteresting, it can be deconvoluted from the dynamics data to give us what we’re really interested in, the behavior of the C-C bond. Using an alignment tensor derived from a separate dataset of N-H RDCs in 36 different alignment media, the calculated C-C RDCs are combined into a matrix, from which simplified parameters describing motion can be derived. Fig. 1 depicts this schematically (note, the legend has the variables m and i reversed in meaning).

The order parameter (S2rdc) reflects the rigidity of the bond and ranges from 0 (highly flexible) to 1 (perfectly rigid). The values measured for the methyl groups of ubiquitin cover almost this entire range (Fig. 2a), which is typical of side chains which tend to have less constrained motions than the backbone. It’s also evident from this figure that S2rdc is roughly anticorrelated with the number of dihedral angles between a given methyl group and the peptide backbone. The anisotropy of motion (ηrdc) is generally low, and appears to be roughly correlated with the number of intervening dihedrals. Both of these observations agree with previous data from other dynamics experiments, as well as reasonable expectations about the movements of these groups.

Farès et al. compare their S2rdc to order parameters determined using other approaches. As one would expect, for most methyls the S2rdc, which encompasses motions from a wide array of timescales, is lower than the S2 determined using a Lipari-Szabo model-free approach that is only sensitive to ps-ns motions. The most notable exceptions are three residues for which the RDC method fit order parameters greater than 1. Probably these represent some unanticipated failure of the model, although these violations occur at groups that are expected to be rigid (two are alanines) and which have high S2 from the Lipari-Szabo model. One potential culprit is the previously discussed scaling, which may need to be adjusted if the axial rotation is unusually slow. The best agreement with existing data comes from an approach that combined J-coupling data with less-specific RDC information, but only when those data are corrected for very fast motions using backbone order parameters.

Because the RDC fundamentally contains data about the orientation of a given bond, it should be possible, with a minimal degree of modeling, to extract specific information about the kinds of motions being made, data that cannot be obtained from methods such as the Lipari-Szabo model-free interpretation. The authors modeled side-chain motions around the dihedral angles χ1 and χ2 using the MFA data. The agreement between these results and the existing ensembles is not particularly good, but it’s not completely obvious where the fault for this lies. Similarly there was limited agreement between these order parameters and those derived from existing ensembles. Agreement with the EROS ensemble structure determined last year was good, but it is difficult to judge what this means, as that ensemble was calculated using the same or similar data to what was used in this paper.

It’s fair to ask whether this sort of data analysis will be possible in systems with less comprehensive data. Even this extremely rich dataset proved problematic, for instance in the cases of the alanines and the disagreement concerning rotameric states. It remains to be seen whether this approach will be practical in cases where significantly fewer alignment media can be used. However, it is also true that methyl groups have the best relaxation properties of any group in a protein, and that the experiments for the determination of RDCs are simple and sensitive. This means that if this approach can be made to work, it can provide important dynamic data even in the largest proteins studied by NMR. Farès et al. have performed an impressively comprehensive analysis of dynamics in a time regime that NMR has had difficulty accessing. Hopefully they will next bend their considerable talents towards reproducing as much of this analysis as possible in a more difficult system with sparser data.

Farès, C., Lakomek, N., Walter, K., Frank, B., Meiler, J., Becker, S., & Griesinger, C. (2009). Accessing ns–μs side chain dynamics in ubiquitin with methyl RDCs Journal of Biomolecular NMR, 45 (1-2), 23-44 DOI: 10.1007/s10858-009-9354-7 OPEN ACCESS

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