Dynamics conservation in the Ras superfamily

The proposition that general fold architecture is preserved within a family of evolutionarily-related proteins is not controversial. The amino acid sequence of a protein determines its structure, and countless studies have substantiated the idea that proteins with similar sequences will adopt similar folded conformations. Because structure and dynamics are intrinsically linked, one could reasonably assume that many features of a protein's dynamics get conserved along with the fold. A growing number of experiments show that this is indeed the case, including a recent paper in Structure (1).

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Non-native hydrogen bonds mediate structural transitions

A 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.

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The role of dynamics in catalysis

For 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 k_chem:

Pisliakov et al. (1) ask whether the closing process can accelerate k_chem. 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 k_chem. 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 k_cat. This is why the concordance between k_cat and k_open 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

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Filling the donut hole in dynamics

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.

Standard 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 (S²_rdc) 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 S²_rdc is roughly anticorrelated with the number of dihedral angles between a given methyl group and the peptide backbone. The anisotropy of motion (η_rdc) 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 S²_rdc to order parameters determined using other approaches. As one would expect, for most methyls the S²_rdc, 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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A step towards incorporating dynamics data into drug design

My field-cycling article (previous post) is part of a dynamics-focused topical issue of JBNMR. In my next few science posts I'll describe some of the other contributions.

Research into the interplay between protein structural dynamics and function is a window into important fundamental knowledge about biochemistry, but the general justification for public funding of these studies by medical agencies is that they will have the ultimate effect of improving our ability to design and optimize drugs. However, even though our ability to characterize macromolecular dynamics has increased dramatically in the past few decades, there are few, if any, cases in which this knowledge has been applied successfully to the design of therapeutic agents. In part this is because incorporating data on fluctuations into the design algorithms poses a significant challenge. It's also true, though, that we understand only part of each system, i.e. the dynamics of the protein target, not the small molecules it binds. If dynamics studies are to make the maximum possible contribution to pharmaceutical sciences, the motions of the ligand must be characterized. In their article in Journal of Biomolecular NMR, Jeffrey Peng and students from Notre Dame attempt to address this shortcoming in the case of a substrate for the phosphorylation-directed prolyl isomerase Pin1.

Pin1 is implicated in a number of regulatory and signaling pathways, which seems strange because it doesn't possess any intrinsic transcriptional regulation ability, nor does it covalently add or remove phosphate groups. Instead, Pin1 has an enzymatic activity that accelerates, generally without altering the relative populations, the conversion of prolines from their cis- to trans- state and vice versa. This activity is specifically targeted to prolines that are adjacent to phosphorylated serines or threonines. In addition to the catalytic domain that does this work, Pin1 possesses a WW domain that has identical specificity. Because Pin1 does not alter the balance between cis- and trans- Pro, only the rate at which one changes to the other, its role in signaling has been difficult to ascertain, although there is intense interest in this area.

You don't need to understand an entire pathway to design an effective inhibitor. What you do need to understand is the relationship between specific chemical groups and binding affinity. Getting that knowledge can be very difficult if the proposed drug is flexible. In that case, refinement methods that focus only on the particular chemical groups rather than their dynamic properties could go badly astray. Unfortunately, the dynamics of protein-bound drug molecules are difficult to measure. Their proton signals are likely to be swamped by the protein, and small molecules are often difficult to label with isotopes convenient for NMR. Peng et al. propose to address this by studying ¹³C relaxation at natural abundance.

A little less than 99% of the world's carbon is in the form of NMR-inactive ¹²C, which is a problem for NMR because carbon is very abundant in proteins and drugs. Of the rest, most (about 1% of all carbon) is dipolar, NMR-detectable ¹³C, which is usually not enough to accomplish anything in terms of protein NMR. As a result, NMR researchers typically adopt the strategy of expressing their proteins using bacteria grown in media containing ¹³C₆ D-glucose. Such enrichment of drug molecules probably could not be carried out for pharmaceutical research due to the cost and the limited availability of properly labeled reagents. Fortunately, advances such as magnets stronger than 17 T and cryoprobes make sensitive detection of natural-abundance ¹³C a plausible approach. Because natural-abundance measurements also simplify the experiments and analysis considerably, Peng et al. adopt this approach in their study.

Peng et al. measure μs-ms fluctuations in a 10-residue peptide in the presence and absence of Pin1. Keeping in mind that such motions can only be detected when they are associated with a change of chemical shift, it is reasonable that no such motions are detected when the peptide is all by itself. In the presence of Pin1, however, methyl groups on phospho-Thr 5 and Val 7 experience some kind of chemical exchange process on the order of several 100 /s (at 278 K), as does a methylene group in Pro 6.

Peng et al. rationalize their observations with reference to a previously-determined structure of the Pin1 WW domain in complex with this peptide (explore it at the PDB). As you can see from the lowest-energy member of this NMR ensemble (left), the residues where they detect these fluctuations in the methyls and methylenes are those that are most involved in the binding interaction. The WW domain is represented as blue ribbons, while the peptide is shown as sticks down at the bottom. That the Pro and pThr form part of the interface is unsurprising, as they constitute the specific binding sequence, while the Val side chain appears to be in position to make some hydrophobic contacts. Everything makes sense, but that doesn't mean it's telling us what we want to know.

The structure above shows us the interaction of the peptide with the WW domain, while what we're really interested in getting at is the catalytic domain. Using an exchange spectroscopy experiment, Peng et al. determined that the ms dynamics they were observing probably reflected the binding of the peptide to the WW domain. To avoid this interaction, they created an artificial Pin1 that contained only the catalytic domain, and found that this also caused chemical exchange in the methyls and methylenes. Cross-checking against the exchange spectroscopy rates suggested that the ms dynamics in this case reflect the result of Pin1 catalytic activity, namely the interconversion from cis to trans and vice versa.

Unfortunately, this experiment did not report the most desired data, i.e. the dynamics of the ligand on the enzyme. On-enzyme fluctuations certainly contribute to the exchange experienced by the ligand, but because the on-enzyme population is so small (at most 2.5% of ligand) this would only be detectable in the case of an extremely large change in chemical shift. In principle one could deconvolute the dynamics from a partial-occupancy system where 50% or more of the ligand is bound to enzyme, but reliably fitting all the parameters for a two-state chemical exchange system from CPMG data is an already-dicey proposition. Fitting a four-state process from data like these is unlikely to be practical. So, in order to observe on-enzyme dynamics the drug of interest will need be saturated with its target protein, which would require millimolar protein concentrations for most ligands. Under those conditions, the spectra will also contain significant signal from the protein. The 70% deuteration used in this experiment, combined with ¹³C depletion, will probably be enough to suppress this, although these isotopes will increase the cost of the technique (and diminish protein yields).

Nevertheless, this paper establishes that the natural-abundance approach to measuring ligand dynamics on the µs-ms timescale is feasible. Because methylenes and methyls are common moieties in drugs and small molecules this technique may have broad applicability. Investigating the motions of small molecules bound to large proteins poses a unique problem because these systems don't have the advantages of either small molecules (low R₂) or proteins (exotic labeling schemes). The ongoing work of Peng et al. suggests that this problem is tractable, which may have positive consequences for our ability to design and optimize drugs.

Peng, J., Wilson, B., & Namanja, A. (2009). Mapping the dynamics of ligand reorganization via ¹³CH₃ and ¹³CH₂ relaxation dispersion at natural abundance Journal of Biomolecular NMR DOI: 10.1007/s10858-009-9349-4

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Let's explore the spectral density!

The model-free formalism of Lipari and Szabo is a way to convert experimental NMR data into a limited number of generalized parameters describing the internal dynamics of a protein. However, the relaxation rates that are typically measured by NMR — the R₁, the R₂, and the steady-state nuclear Overhauser effect (nOe) — do not themselves appear in the model-free formulas. Instead we see a term, J(ω), and this constitutes the interface between the data and the model. This term refers to the spectral density, which is a measure of the power available to relax spins at a given angular frequency. The relaxation rates measured by NMR spectroscopists interrogate this density at known frequencies, which means that we can use those rates to assess general information about the shape of the spectral density function and thus constrain the model-free parameters.

In biomolecular NMR, these rates are most frequently measured on the nitrogen of a backbone amide group, in which case they fundamentally depend on the spectral density at three frequencies: 0, the Larmor frequency of nitrogen (ω_N), and the larmor frequency of the proton (ω_H). The precise relationships are as follows:

R₁ = D [3J(ω_N) + 6J(ω_N+ω_H) + J(ω_N-ω_H)] + C [3J(ω_N)]
R₂ = D/2 [4J(0) + 3J(ω_N) + 6J(ω_H)+ 6J(ω_N+ω_H) + J(ω_N-ω_H)] + C/6[J(0) + 3J(ω_N)]
steady-state nOe = 1 + R_NOE γ_H / R₁ γ_N
R_NOE = D [6J(ω_N+ω_H) - J(ω_N-ω_H)]
D = μ₀²ℏ²γ_N²γ_H²/64π²r_NH⁶
C = Δσ²ω_N²/3

where γ_H and γ_N are the gyromagnetic ratios of these nuclei, ℏ is the reduced Planck constant, and μ₀ is the magnetic constant (or vacuum permeability, if you prefer), and Δσ is the chemical shift anisotropy of the ¹⁵N nucleus (typically -160 - -170ppm).

I'm not going to cover precisely why they have these relationships today; instead I want to focus on how these relationships connect certain dynamic behaviors to particular observations about relaxation rates. The key to this is to think about how the spectral density looks. At right I have a simplified spectral density calculated for a rigid protein of reasonable NMR size (I only show the positive side of the function, the negative is a mirror image). While the particular shape of the spectral density function will depend strongly on the internal dynamics and overall size, certain general features will be the same for most proteins. It should be immediately evident, for instance, that J(0) >> J(ω_N) >> J(ω_H) (shown on the figure for a 500 MHz magnet). This implies that each relaxation rate reports on just one spot in the spectral density. R₂ should be proportional to J(0), R₁ to J(ω_N), and R_NOE to J(ω_H), keeping in mind that ω_H >> ω_N.

The shape of this curve derives in a fairly obvious way from the Lorentzian used to calculate it, in this case the Lipari-Szabo formalism, which if you'll recall is:


Where τ_m is the time it takes the protein to tumble through one radian in solution, S² is the order parameter for the bond in question, and τ_e is the correlation time of internal motions. The Lipari-Szabo model is not the only model of the spectral density, but most of the alternatives just add more Lorentzians or scaling factors. These models differ in the fine structure of the spectral density, but the overall shape (and the features I'm about to describe) is generally not affected.

It should be clear from examining this (and given that τ_m >> τ_e) that the point where ωτ_m = 1 divides the spectral density into two regions. Where ωτ_m <= 1, the first term dominates, and the spectral density is determined by S² and τ_m. Where ωτ_m >> 1, the second term dominates and the spectral density is essentially dependent on (1-S²) and τ_e. This being the case, you would expect highly flexible moieties (low S²) to have inefficient R₂ and R₁ relaxation and highly efficient NOE relaxation, and this we generally find to be the case.

Similarly, you would predict that increasing τ_m would cause R₂ to increase. The graph at right simulates relaxation rates for a typical, rigid backbone amide nitrogen (at 500 MHz) as the τ_m increases (note log scale on x). As you can see, the R₂ (red) does in fact get continuously higher as τ_m is increased; this is one of the reasons NMR spectroscopy of very large molecules is so difficult. Also note that R₁ (blue) goes through a maximum and then declines. This is because as τ_m increases, the point where ωτ_m = 1 shifts to lower and lower frequency. When |ω_N| > 1/τ_m, the spectral density at ω_N starts to fall off, reducing R₁. This might sound advantageous, but in fact it is another reason that spectroscopy on large molecules is difficult — their inefficient R₁ relaxation means that additional time must be scheduled after each transient to create a sufficiently sensitive steady state. Because even a simple spectrum can have 2048 transients, adding just a few fractions of a second per transient can rapidly amount to a significant increase in experiment time.

It's obvious that it would be questionable to map the spectral density based on just three relaxation rates, if for no other reason than that we have four unknowns and three pieces of data. This is typically addressed in three ways, which are often used in combination. The first is to reduce the spectral density, by making some general assumptions about the nature of the spectral density around ω_H and collapsing the J(ω_N +/- ω_H) terms into 0.87*J(ω_H). Another approach is to increase the number of relaxation rates measured, by incorporating R_1zz or other measurements, but many of these rates incorporate additional factors (such as ρ_HH) that must also be fit, so that their ability to reduce the dimensionality of the problem is sometimes limited.

The third approach is to take data at several fields. The Larmor frequencies ω_H and ω_N depend on the strength of the magnetic field in the spectrometer, while J(0) is obviously field-independent. As a result, each additional field of data taken improves the ratio between data and unknowns. This improvement is valuable even when the relaxation is being fit to a simplified representation such as the model-free formalism, and therefore dynamics experiments should always include measurements at more than one field if at all possible. Moreover, the field-dependence of relaxation rates can be very informative, in general terms, about the dynamics of the system.

In the simplified view it might seem that R₂ should be essentially independent of field strength, but observations show this not to be the case. R₂ increases at high fields primarily because of the chemical shift anisotropy contribution, which has a square field dependence and therefore increases with field to a greater degree than ω_N declines. As a result, R₂ has a sort of chevron appearance as you vary the field, with differences in dynamics primarily affecting the magnitude rather than the shape. This means that for R₂ the field-dependence is not particularly informative about the dynamics. However, if a residue has anomalous R₂ field-dependence with respect to the rest of the protein, this can be an indicator of a chemical exchange process on the μs - ms timescale.

Because relaxation due to chemical shift anisotropy makes a lesser contribution to R₁ (and depends entirely on J(ω_N) for this rate) the behavior of R₁ with respect to field is generally much simpler — for proteins, the R₁ almost always decreases as field increases. The degree to which this occurs, however, can be quite different depending on the dynamics behavior that is going on. The reason for that can be seen in the sample spectral densities to the left, calculated for a typical backbone amide (blue) and a flexible one (red). As you can see, the more flexible residue has a lower J(0) and a smaller slope between the flat portions of the spectral density than the rigid one. This means that the R₁ will be lower at high field and higher at low field, decreasing the field-dependence of the residue's relaxation. The exact magnetic field where this crossover occurs depends on the correlation times of the internal motion and global tumbling.

The gyromagnetic ratios of the hydrogen and nitrogen nuclei have opposite signs, so the heteronuclear NOE measured for these nuclei should be less than one. How much less depends on the relative ratio between J(ω_H) and J(ω_N). For flexible residues, the spectral density at large ω will be high (and that at lower ω will be low), this ratio will be large, and a low value will be measured in the hetNOE experiment. R_NOE typically has a steep field-dependence for flexible residues, and because this rate dominates the ratio, one tends to see greater field-dependence of the hetNOE for flexible residues. However, the situation for the hetNOE is more complex than for the other two rates because the spectral density around ω_H defines the relaxation. As a result, the internal correlation time (particularly if it's on the order of 100 ps - 1 ns) starts to dictate the shape of the spectral density, and hence the magnetic field-dependence of relaxation. For certain τ_e, the hetNOE will have no apparent field dependence, whether the residue is flexible or not.

Actually parameterizing the dynamics of a given group requires numerical fitting of the relaxation data, but for many questions a qualitative estimate will suffice. In these cases just examining the field-dependence of one or two relaxation rates (especially R₁ or NOE) can provide valuable insight into the heterogeneous dynamics of a given protein. In the next post I'll describe an example of a case in which this turns out to be true.

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Drugs disrupt DHFR dynamics

One of the most-studied cases of the relationship between dynamics and catalysis is the bacterial dihydrofolate reductase (DHFR). DHFR catalyzes the reduction of dihydrofolate to tetrahydrofolate while oxidizing the cofactor nicotinamide adenine dinucleotide phosphate (NADPH). As part of this catalytic process, a region of the protein called the "Met 20 loop" switches from a "closed" state that shields the active site from solvent to an "occluded" state that separates the substrate from the cofactor. NMR studies of DHFR structural dynamics have correlated the protein motions with the chemical changes. In a recent study appearing in Structure, researchers from the University of North Carolina show that the binding of inhibitors such as methotrexate (MTX) and trimethoprim (TMP) appears to uniquely disrupt the dynamic networks of DHFR.

Previously, seminal work from the lab of Peter Wright surveyed the dynamics of DHFR in every step of its reaction pathway. Boehr et al. determined that structural fluctuations in each complex represented motions towards the next step in the reaction. The conformational exchange rates they obtained from their relaxation-dispersion experiments closely resembled the rate constants that had been independently determined for the chemical steps. In almost every complex the conformational exchange was widespread, affecting residues in both the substrate and cofactor binding sites, as well as important distal locations such as the Met 20 loop.

Because the existing work from the Wright lab hewed as close to the natural substrates and products as possible, Mauldin et al. chose to examine the dynamic effects of inhibitor binding to DHFR. Like Wright's group, they used relaxation-dispersion experiments to identify conformational changes taking place on the μs-ms timescale. In the NADPH:DHFR complex the motions are widespread, encompassing the substrate binding site, the Met 20 loop, and distal locations. Binding of either inhibitor eliminates about half of this dynamic network and dramatically reduces the fluctuation rates of those residues for which conformational exchange continues to occur.

Based on their fits of the exchange rates, Mauldin et al. conclude that the substrate binding pocket moves in a way that mimics the enzyme's normal motions in the transition from its closed state to its occluded state. The long-range conformational changes that actually complete this transition, however, have been completely quenched. With the inhibitors bound, DHFR is like a car that's turning over but won't start. Part of the enzyme is still moving in exactly the right way to proceed along the reaction coordinate, but for some reason this motion doesn't catch on throughout the protein.

In order to gain a more complete understanding of the dynamic effects, Mauldin et al. performed experiments to identify the motion of the protein on the ps-ns timescale. Analyzing the dynamics of methyl and amide resonances using the Lipari-Szabo model-free formalism, the authors realized that inhibitor binding did cause long-range changes in dynamics, just in a faster regime. Where the natural substrate complexes have motions that occur hundreds or thousands of times per second, the inhibitor-bound forms have (smaller) motions that occur millions of times per second. Because these altered motions encompass the Met 20 loop and surrounding residues, the authors argue that they reflect abortive attempts by the protein to transition into the occluded state.

Although these inhibitors do not appear to change the protein's overall conformation, they produce long-range dynamic effects on short timescales and quench distal motions on intermediate timescales. The binding pocket appears to still be experiencing fluctuations related to the transition between the closed and occluded conformational states, but the mechanism that couples the binding site dynamics to the motion of the loop that defines these two states appears to be broken.

The million-dollar question is this: do drugs alter DHFR dynamics because they inhibit the chemistry, or do these drugs inhibit the chemistry because they alter DHFR dynamics? Quenching dynamics costs energy in the form of conformational entropy, and it may be possible to tune a drug for improved efficiency by blocking the binding site without altering the dynamics. This is only true, however, if the dynamics don't matter to successful inhibition. On the other hand, if blocking the conformational switching of the Met 20 loop inhibits the enzyme, then drugs can be designed for that angle of attack as well. In the case of a protein like DHFR, where the bacterial enzyme has similar activity but a very different structure from its human equivalent, drugs that target regions other than the active site may significantly reduce side-effects. As a result, protein targets that were previously off-limits due to shared chemistry may become tractable due to divergent dynamics and structure.

Mauldin, R., Carroll, M., & Lee, A. (2009). Dynamic Dysfunction in Dihydrofolate Reductase Results from Antifolate Drug Binding: Modulation of Dynamics within a Structural State Structure, 17 (3), 386-394 DOI: 10.1016/j.str.2009.01.005

Boehr, D., McElheny, D., Dyson, H., & Wright, P. (2006). The Dynamic Energy Landscape of Dihydrofolate Reductase Catalysis Science, 313 (5793), 1638-1642 DOI: 10.1126/science.1130258

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A conformational equilibrium controls the Vav DH domain

One emerging view of allostery, and protein behavior generally, describes function in terms of pre-existing equilibria. In this view, proteins are not like switches that get turned on and off, but rather are like dials that are turned "more on" or "more off" depending on the conditions. In this view, regulatory modifications such as phosphorylation do not enforce an active conformation so much as promote it. Because some relaxation measurements are sensitive to conformational exchange, NMR is well-suited to examine systems with this behavior. In the most recent edition of Nature Structural and Molecular Biology, a group from Michael Rosen's lab discover that this kind of equilibrium is governing the behavior of the DH domain from the Vav protein.

Vav activates Rho GTPases by inducing the exchange of GDP for GTP, making it a Guanine nucleotide Exchange Factor (GEF). This activity is performed by the DH domain, and is inhibited by a small neighboring element called the acidic region (Ac). As you can see from the figure of the combined Ac and DH domains (AD) at right, Ac (red) inhibits the DH domain (blue) by forming a helix that binds to the active site (explore this structure at the PDB, noting that the numbering is off by 167). Phosphorylation of Y174 (red side chain) unfolds the helix and exposes the active site, which would be a nice model except for two things. First, as you can see, Y174 is pretty well buried in this structure, which would make it difficult to phosphorylate. Second, mutation of Y174 to phenylalanine, a residue that cannot be phosphorylated, activates DH domain activity. How can Y174 get phosphorylated? What is phosphorylation actually doing?

One possible answer is that the existing structure doesn't tell the whole story. A protein, after all, doesn't have just a single structure, but rather an ensemble of structures across a population or time. While AD may spend most most of its time in this inhibited state, it's possible that sometimes it adopts an alternate conformation that allows Y174 phosphorylation. Li et al. set out to assess this possibility using measurements of R₂ relaxation dispersion. Residues that have a large field-dependence of transverse relaxation (ΔR₂) are undergoing some sort of conformational exchange process that changes their chemical shift between two or more states.

Using CPMG experiments on methyl-bearing side chains, Li et al. identified two groups of residues engaged in conformational exchange processes, shown at left. The first group (orange side chains) have a large ΔR₂ that vanishes once Y174 is phosphorylated. The second group (green side chains) have high ΔR₂ in both the phosphorylated and unphosphorylated states, but the rates are slightly higher in the former. Residues that were observed to have low ΔR₂ are shown with gray side chains. All of this indicates that there are two dynamic processes occuring on the microsecond-millisecond timescale. The first encompasses some change in the chemical shift of the acidic helix, while the second involves some unknown process. However, because the Group 2 residues react to the phosphorylation state, these processes are likely linked in some way. I notice that the Group 2 residues are clustered around loops and joints in the upper half of the domain (in this view), while residues not adjacent to loops or joints do not appear to have significant ΔR₂. It is possible that the observed dispersion represents some flexing of the domain around these loops, and that the rate of this motion increases slightly when the binding site is unoccupied.

That's all very interesting, but it's also bad news for the analysis, because it means the observed relaxation dispersion would have to be fit to a four-state model in order to obtain populations and kinetic parameters. Previous analysis by several groups has shown this to be a dubious proposition, so Li et al. take an alternative approach. Rather than try to fit out populations from the dispersion data, they make a series of mutations to AD to push the populations of the two states in one direction or the other. They find a number of states where the methyl peaks lie on a line between the open (phosphorylated) and bound (unmodified) states. The Y174F mutation lies very close to the phosphorylated state, interestingly enough, implying that the phosphate group itself is not a significant determinant of chemical shifts in the open state. Using a combination of HSQC peak positions and ΔR₂ measurements, Li et al. determine for each mutant or modification what population of the ensemble is in the open state. They find that this NMR-assigned population correlates with the rate constant (k_cat/K_M) for phosphorylation.

This implies a model in which regulation of DH by Ac involves an equilibrium between the bound and open states. In the bound state, Ac forms a helix in the binding site, an effect strongly dependent on a hydrogen bond to the OH of the Y174 (R332 may be the partner here). However, in this state Ac samples the open state about 10% of the time. While in the unbound state, Ac can be phosphorylated, a modification that prevents helix formation or binding; probably by steric interference in the binding site. This stabilization of the open state dramatically increases the chances that the Vav DH domain will be in an active state when it encounters a target. Thus, DH regulation depends on a population shift of an underlying equilibrium, not a singular on/off switch. This model has the advantage of accounting for how Y174 gets phosphorylated and why a mutation that prevents phosphorylation nonetheless leads to a constitutively activated state.

In vivo, Vav consists of many other domains in addition to the AD construct used here. These domains are known to contribute to the inhibition of DH; given these results it is probable that they do so by stabilizing the bound state. Because Ac binding causes the formation of a negatively-charged surface on one side of the helix, charge stabilization is a likely mechanism. Further research will hopefully identify these mechanisms, as well as the origin of the second conformational exchange process revealed by the experiments in this paper. This study is a good example of scientists making the best use of limited data to describe an instance of this important, but difficult to characterize, regulatory mechanism.

1. Li, P., Martins, I.R., Amarasinghe, G.K., Rosen, M.K. (2008). Internal dynamics control activation and activity of the autoinhibited Vav DH domain. Nature Structural & Molecular Biology, 15(6), 613-618. DOI: 10.1038/nsmb.1428

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Structural dynamics of PDZ allostery

If Michele Vendruscolo were trying to get me to blog about one of his papers, he could hardly have assembled a more perfect lure than his upcoming paper in JACS. It brings together all sorts of things I've been talking about on this webpage: NMR dynamics, MD simulations, and dynamics-driven allostery (in the PDZ domain, no less). Previous investigations of this PDZ domain indicated the existence of a network of residues that had a dynamic response to ligand binding. Dhuselia et al. extend this work using molecular dynamics simulations constrained by the existing dynamics results. This leads them to discover not one, but two networks in the PDZ domain, with different properties.

NMR experiments have enormous power to sensitively detect changes in dynamics resulting from a perturbation, but they are also quite limited. Because of the models we use, the parameters we can fit out of relaxation data only give us information about the magnitude and timescale of fluctuations. Chemical shift overlap and interference caused by nearby dipoles limit the number of probes. Moreover, because NMR can only measure an ensemble, it is practically impossible to extract anything other than the most general information about correlated motions. MD has answers to all of these problems, but as a general rule has done poorly at reproducing NMR data about side-chain motions, calling the validity of the conclusions into question. Vendruscolo has taken some interesting strides in this regard by employing the limited experimental dynamics data as a component of the energy function. By constraining the simulation to mimic the known dynamics, we can hopefully learn more about the sites to which we are blind, as well as what kinds of motions the experiment is sensing and how they are linked.

In this instance, the authors make use of the PDZ domain previously studied by Ernesto Fuentes in Drew Lee's lab (there was also some hack working there at the time). Ernie's research followed on previous evolutionary studies indicating a network of communication in PDZ domains (local summary here), and Ernie found, by comparing the dynamics of the free and ligand-bound states, that changes in motions propagated away from the binding site to two distal surfaces. The pathways of communication compared pretty well with the evolutionary results. Dhulesia et al. aim to extend these results by determining which motions are correlated and identifying the mechanisms by which energy is transmitted. They accomplished this by running multiple parallel simulations of the free and ligand-bound states of the PDZ domain constrained by Ernie's dynamics results, as well as NOE and ³J data.

They find that two regions of the protein have correlated motions internally and move in an anticorrelated fashion relative to each other (Figure 3A). One of these regions consists of part of the binding site and all of distal surface 2 (DS2), while the other includes the other half of the binding site and all of distal surface 1 (DS1). When the ligand binds, something interesting happens. The motions of DS2 become more tightly correlated to the motion of an area around V30. The tight correlation between the motions of DS1 and α2 (an element of the binding cleft) switch to a slight anticorrelation.

When a ligand binds to a protein we expect a broad increase in rigidity of the complex so that the proper orientations of bonding pairs are maintained. For the most part, the simulations affirm this expectation, but not for all regions. For the binding site and DS2, the backbone mobility decreases, as expected, but the backbone mobility of DS1 increases (I am going off the text and Table 3 here, rather than Figure 3). The side chains have a similar response. This agrees with other studies indicating that the change in conformational entropy upon binding a ligand need not be homogeneous. What is more interesting is that these results imply that opposite coherent responses can be induced in a small domain by a single stimulus.

Although (as far as I know) this PDZ domain has no allosteric behavior in vivo, one can imagine that the binding of a ligand at the cleft could alter the binding of other modules to this domain. The entropic penalty for binding to DS2 would be lower in this case, while the penalty for binding to DS1 would be higher. The opposed nature of the dynamic responses may be related to the broad regional anticorrelation of free-state motions; disruption of this mode (by linking the motion of β2 and α2) may shunt that energy into DS1.

The authors also find, using a series of structural parameters, that a set of residues have clear structural changes. Some of them appear to be associated with coupled changes in rotameric states; the authors map out one pathway in Figure 5. Because it is a rotameric pathway, it should be possible to test whether it is essential to communication experimentally—mutation of the intermediary residues should abolish the linkage. The authors also carry out a network analysis to identify the most connected residues, a prediction that may also be testable by mutagenesis. These "structural network" residues overlap only slightly with the dynamic network, and indeed do not generally intersect with the evolutionary network either. In the absence of identified allosteric behaviors or clear energetic connectivities it's difficult to say what this disjunction means. However, the residues undergoing structural changes surround most of the residues undergoing dynamic changes. It is possible that these changes in structure provide the context that allows the changes in dynamics (or vice-versa); the two properties are inextricably linked.

Although communication between the binding site and distal surfaces is proven in this PDZ domain, and appears to be a general feature of the fold, the absence of a known function for the propagation in this instance makes it tough to assess the quality of these results. However, the findings of Dhulesia et al. make it clear that this approach can produce testable predictions and explanations. Hopefully this approach will be employed in the near future to study PDZ domains known to possess allosteric properties.

1. Dhulesia, A., Gsponer, J., Vendruscolo, M. (2008). Mapping of Two Networks of Residues That Exhibit Structural and Dynamical Changes upon Binding in a PDZ Domain Protein. Journal of the American Chemical Society DOI: 10.1021/ja0752080

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Is in-cell NMR feasible?

As I mentioned in my last post, it is sometimes difficult to tell if a protein structural model matches the physiologically-active form. One way to address this problem would be to take structural data under physiological conditions, i.e. in the cell. While this obviously isn't a viable approach for crystallography, it seems possible with other techniques such as FRET or NMR. Existing NMR structures are solved under solution conditions, and the cytoplasm is a kind of solution. So we would expect to be able to solve structures, or at least get spectra, in vivo. However, the success of NMR strongly depends on what kind of solution you have, and a forthcoming paper in JACS suggests that the bacterial cytoplasm may not be amenable to NMR.

This paper has a bit of history behind it. A few years ago, Gary Pielak's lab attempted to determine the dynamic behavior of chymotrypsin inhibitor 2 (CI2) and apocytochrome-b5 in living E. coli (1),(2). They found in these experiments that the dynamics of these proteins did not differ significantly between in vivo and dilute solution conditions. A later experiment, however, showed that most or all of the signals that had been observed arose from protein that had leaked out of the cells and into the surrounding medium in which they were suspended. This wasn't true for all proteins: cells expressing α-synuclein (αSN) and FlgM did not leak protein. Subsequently the first two papers were retracted (3), while Gary and his folks tried to figure out just what was going on.

Li et al. encapsulated E. coli cells that were producing either CI2 or αSN in alginate microcapsules to prevent protein leakage and took some basic NMR spectra. Samples of the surrounding fluid proved that neither protein was leaking into the surrounding medium. Nonetheless, although normal spectra of αSN were observed, the cells expressing CI2 did not produce any CI2 spectral signals at all (normal metabolite signals were observed). Experiments showed that these cells did contain CI2 (4). What happened to the signal?

Li et al. hypothesize that this is an effect of the viscosity of the cytoplasm. The intensity of an NMR signal depends on the concentration of the atoms giving rise to the signal, and also the relaxation properties of these atoms, i.e. the rate at which the polarization induced by radio-frequency pulses returns to equilibrium levels. For larger molecules and viscous solutions, the rate at which detectable polarization decays (R₂) is higher, and the rate at which polarization returns to equilibrium (R₁) is lower. The behavior of R₂ is one of the chief obstacles to performing NMR on proteins or complexes that have high molecular weight.

In order to establish that this cytoplasmic viscosity is a reasonable cause of the invisibility of CI2, Li et al. measure the NMR relaxation of αSN and CI2 in a solution doped with poly(vinylpyrrolidone) (PVP), which increases the viscosity significantly. They find that the R₁ of αSN is essentially unchanged, while that of CI2 decreases significantly. The R₂ of αSN resonances increases 2-6 fold relative to dilute solution, but for CI2 this increase is much more significant, up to 40-fold. You can see these features in the graph at right. These results indicate that the relaxation behavior of resonances in a stably folded protein like CI2 is dominated by the global rotational diffusion, while the relaxation of resonances in a disordered protein like αSN is dominated by the significant local fluctuations. Because these latter motions involve less surface area and hence less drag (as compared to the folded protein), the viscosity of the solution has relatively less of an effect. Thus, the vanishing CI2 peaks could conceivably be the result of differential relaxation responses to viscosity.

However, other groups have managed to acquire NMR spectra of folded proteins in E. coli before. These experiments may have experienced the same leakage problem that affected the previous CI2 results, and some control experiments addressing this possibility are likely to be forthcoming. At the same time, the PVP solutions here are supposedly 5 times as viscous as E. coli cytoplasm, and yet CI2 resonances are apparently still visible. This suggests that the complete obliteration of these resonances in cells cannot be chalked up entirely to viscosity. One possibility is that CI2 overexpresses so significantly that it massively increases the effective viscosity of the cell. It may also be possible that the vast quantities of CI2 expressed in these experiments are crammed into a small volume somehow, perhaps as relatively loose inclusions in the cytoplasm or loaded in the periplasmic space, where interactions with peptidoglycan may rotationally lock them. It is also possible that PVP does not capture some important aspect of cellular crowding. For instance, the washing-out of the CI2 signal may be an effect of transient protein-protein interactions. Fluorescence and electron microscopy experiments may be able to address this concern.

If the observations of CI2 are really a result of some unique localization or a consequence of the significant overexpression then it is possible that NMR of different proteins on somewhat less active promoters may yet be viable. In addition, in vivo studies of proteins in systems such as X. laevis oocytes or cultured eukaryotic cells may not be subject to the same difficulties, due to differences in cytoplasmic viscosity. The major implication of this work, however, is that in vivo NMR results cannot be taken at face value. Careful controls will be required in order to ensure that the experiments actually measure protein within the cell, and in the absence of such controls the results should be interpreted cautiously.

1. Bryant, J., Lecomte, J., Lee, A., Young, G., Pielak, G. (2005). Protein Dynamics in Living Cells. Biochemistry, 44(26), 9275-9279. DOI: 10.1021/bi050786j

2. Bryant, J., Lecomte, J., Lee, A., Young, G., Pielak, G. (2006). Cytosol has a small effect on protein dynamics. Biochemistry, 45(33), 10085-10091. DOI: 10.1021/bi060547b

3. Bryant, J., Lecomte, J., Lee, A., Young, G., Pielak, G. (2007). Retraction. Biochemistry, 46(27), 8206-8206. DOI: 10.1021/bi700744h

4. Li, C., Charlton, L.M., Lakkavaram, A., Seagle, C., Wang, G., Young, G.B., Macdonald, J.M., Pielak, G.J. (2008). Differential Dynamical Effects of Macromolecular Crowding on an Intrinsically Disordered Protein and a Globular Protein: Implications for In-Cell NMR Spectroscopy. Journal of the American Chemical Society DOI: 10.1021/ja801020z

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Does flexibility increase protein stability?

Since my favorite physicist of the blogosphere put up a great post on the basics of NMR in preparation for a geeky post on the subject, I figure I'll add in a geeky post of my own. As Chad mentions in his post, the dependence of the resonance frequency on local chemical structure allows us to get a great deal of information about covalent bonds and their conformation from NMR spectra. In addition, certain NMR experiments can provide us with detailed information about the motions of atoms with respect to one another. Although the various approaches differ in the level of detail they offer, the sum of NMR dynamics experiments fairly effectively cover the range from picosecond motions to month-long fluctuations. My particular interest in these approaches is in their use to dissect intramolecular signaling in proteins.

The major part of my graduate studies at UNC under Andrew Lee was devoted to understanding the pathways by which changes in dynamics are propagated in eglin c (explore this protein at the PDB). Eglin c is an excellent subject for this kind of study because it has very good spectroscopic properties, and because it has no discernable allosteric properties at all. This means we can do a lot of different experiments on it, and also that our observations about long-range dynamic interactions are likely to be generalizable to any protein that has a hydrophobic core, not just allosteric ones.

My work with eglin c involved making mutations to the protein and determining what dynamic changes resulted. In the course of this I discovered several mutants that caused significant changes in the motions of amino acid side chains on the timescale of picoseconds to nanoseconds (1,2). This is the range covered by the Lipari-Szabo model-free formalism (3). One mutation in particular, V54A (read: valine 54 to alanine), caused almost universal rigidification of the core of eglin c on this timescale. However, the protein was significantly less stable.

This is curious because a lack of stability is known to correlate with an increased frequency of localized unfolding of the backbone. In elements of secondary structure, hydrogens attached to amide nitrogens tend to be caught in hydrogen bonds. When placed in a solution of deuterated water, these hydrogens can only be replaced by deuterium when the hydrogen bond breaks (this is called hydrogen-deuterium exchange or HX). This process can be monitored by NMR (and less specifically by mass spectrometry), and is known to speed up when the structural elements are less stable. So the V54A mutant is more flexible on this slower timescale, and less flexible with respect to some faster processes.

The significant caveat here is that we only looked at some groups in the protein. For reasons that are a bit too complex to discuss in this post, it was only feasible to observe the dynamics of methyl groups. This is a problem because the core of eglin c has a substantial number of aromatic side chains in it. Any picture of dynamic behavior would be incomplete without examining these side chains and quantifying the changes in HX behavior, which I did not do.

In an upcoming article in Biochemistry, Josh Boyer and Andrew Lee address these deficiencies (4). In order to look at the aromatic side chains, they employ a clever biosynthetic labeling scheme devised by Akke's group (5). While this only allowed them to look directly at δ-carbons of these residues, the general rigidity of aromatic rings meant that they could generalize the observations to essentially the whole side chain. They found using this approach that the dynamic response of aromatic side chains to the V54A mutation was more heterogeneous than that of the methyl side chains. As you can see in the figure I have shamelessly stolen from their paper, the central portion of the core appears to have rigidified across all residue types, while the edges of the core and the outward-facing residues of the protein all appear to have become somewhat more flexible. The location of V54 is shown here in black.

This heterogeneity of the dynamic response was also observed when the HX results were taken into account. The distribution of responses, however, is very unexpected. The top portion of the figure at left shows rigidified side chains as a transparent surface, and destabilized backbone amides (as measured by HX) as solid surfaces. Note that the two regions of destabilized amides are linked by contiguous side chains. The lower figure shows side chains that have become more flexible as transparent pink surfaces. The solid backbone surface indicates a region of the protein that has become more stable. You will notice that this stabilized region lies a significant distance from the mutation site (though as the figure above shows it is connected to it by a network of contiguous side chains), and that it corresponds with a bundle of aromatic sidechains that have become more flexible. A significant portion of the protein is clearly destabilized, as was expected from the previous results on V54A. However, the co-localization of side-chain rigidity and backbone instability (and vice-versa) doesn't jive with our expectations.

Our physical intuitions suggest that rigid things are stable and flexible things are not, and in many cases these intuitions have been borne out—in studies of backbone dynamics of proteins from thermophilic organisms, for example. However, the present results can be rationalized if one supposes that conformational entropy makes a significant contribution to stability. Indeed, because the structure of V54A is known to be essentially unchanged from wild-type (2), the enthalpic contributions (hydrogen bonds, charge-charge interactions, etc.) will not be altered. Entropic contributions will therefore dominated the observed changes in stability.

Rigid regions of a protein may have no place to disperse thermal energy other than localized unfolding, while flexible regions may have the option to dump some of that energy into side-chain fluctuations. When mutations increase the available space for those fluctuations, therefore, stability may be expected to increase, and vice versa. Obviously, the benefits of flexibility to ordered backbone structure will diminish as the fluctuations approach a magnitude that permits solvent to permeate the site.

Boyer and Lee's results, though probably expected by those who have followed previous research in eglin c, do not mesh with our macroscopic understanding of the relationship between rigidity and stability. However, they are not so outlandish that they can't be rationalized in terms of what we already know about proteins. An investigation of this anticorrelation in other eglin c mutants (promised in the paper) would be welcome. In addition, it will be interesting to see if this phenomenon is observed in other proteins (especially thermophilic proteins). As new labeling techniques and experimental approaches expand the range of molecules that can be effectively investigated using NMR, we may learn significantly more about the role of conformational entropy in the stabilization of protein folds.

1. Clarkson, M.W., Lee, A. (2004). Long-Range Dynamic Effects of Mutations Propagate Through Side Chains in the Serine Protease Inhibitor Eglin C. Biochemistry, 43(39), 12448-12458. DOI: 10.1021/bi0494424

2. Clarkson, M., Gilmore, S., Edgell, M., Lee, A. (2006). Dynamic Coupling and Allosteric Behavior in a Non-Allosteric Protein. Biochemistry, 45(25), 7693-7699. DOI: 10.1021/bi060652l

3. Lipari, G., Szabo, A. (1982). Model-free approach to the interpretation of nuclear magnetic resonance relaxation in macromolecules. 1. Theory and range of validity. Journal of the American Chemical Society, 104(17), 4546-4559. DOI: 10.1021/ja00381a009

4. Boyer, J.A., Lee, A.L. (2008). Monitoring Aromatic Picosecond to Nanosecond Dynamics in Proteins via 13C Relaxation: Expanding Perturbation Mapping of the Rigidifying Core Mutation, V54A, in Eglin c. Biochemistry DOI: 10.1021/bi702330t

5. Teilum, K., Brath, U., Lundstrom, P., Akke, M. (2006). Biosynthetic ¹³C Labeling of Aromatic Side Chains in Proteins for NMR Relaxation Measurements. Journal of the American Chemical Society, 128(8), 2506-2507. DOI: 10.1021/ja055660o

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