Alternative side-chain structures from methyl CPMG

As I have mentioned before on this blog, the use of tools like CS-ROSETTA holds the promise of determining protein structures using only the chemical shifts of its backbone atoms. In addition to potentially making NOEs and RDCs redundant, this technology allows biologists to determine the conformations of minor members of the structural ensemble, which are very difficult to obtain using conventional approaches in population-dominated techniques like NMR and X-ray crystallography. There are two limitations here, however. First, we only gain insight into the backbone, and as we know, the positions of side chains in minor states can be critical for function. In addition, backbone chemical shifts are not always available due to relaxation problems. Both weaknesses could, in principle, be addressed by extracting conformational information from the chemical shifts of methyl groups, which report on side-chain behavior and continue to give good signal even in very large proteins. This is the rationale behind a series of recent papers from the Kay lab [1-3] intended to determine changes in side-chain rotameric state from methyl relaxation-dispersion data.

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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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Apparently, the moon hit their eyes like a big pizza pie

This post continues my series about selected articles from the dynamics-focused topical issue of JBNMR.

It is helpful, in examining some NMR articles, to understand that NMR spectroscopists have a long and resilient tradition of giving their pulse sequences silly names. You can think of it as the biophysical equivalent of fly geneticist behavior. From the basic COSY and NOESY experiments (pronounced "cozy" and "nosy") to the INEPT spin-echo train, to more complicated pulse trains such as AMNESIA and DIPSI (which, I am not making this up, is used in an experiment sometimes called the HOHAHA), the field is just littered with ludicrous acronyms (look upon our words, ye mighty, and despair). A team from Josh Wand's lab now joins this club by developing a multiple optimization for radially enhanced NMR-based hydrogen exchange (AMORE-HX) approach. The name is ridiculous, but the experiment fills an important role and illustrates a very active area of technical development in NMR.

The experiment they developed is intended to measure the rate of hydrogen/deuterium exchange at amide groups on the backbone of the protein. This sort of exchange reaction proceeds pretty quickly for most residue types, and can be either acid- or base- catalyzed. For it to happen, however, two things must be true. One of them is that the amide proton must not be in a hydrogen bond already. Also, the site of the reaction must be accessible to water. These requirements should indicate to you that HX measures the rate of local unfolding and can therefore be interpreted as a measure of fold stability at each NH group on the backbone. This data is of obvious interest to researchers studying protein folding. In addition, because some structural transitions are proposed to involve an unfolded state this may have explanatory power for protein interactions and regulation.

A typical HX experiment involves taking your protein, switching it rapidly into >75% D₂O buffer, then placing it in the magnet and taking a series of HSQC or HMQC spectra that separate signals from backbone NH groups by the proton and nitrogen chemical shift. These spectra can be taken with very high time resolution (<2 min each), and the rate of exchange can then be measured by the decay of peak intensity as hydrogen is replaced by deuterium. Assuming that the chemical step occurs significantly faster than the rate of local unfolding and refolding, this decay can be directly interpreted as a local unfolding rate. This works quite well, but as proteins get larger there is a significant likelihood of signal overlap. It would be nice, with these large proteins, to separate the hydrogen signals using an additional chemical shift — say, that of the adjacent carbonyl. Unfortunately, taking these decay curves using 3-dimensional spectra like the HNCO turns out to be impossible because of the way these experiments are collected.

Multidimensional NMR spectra rely on a series of internal delays during which a coherence acquires the frequency characteristics of a particular nucleus. In a typical experiment, the delays are multiples of a set dwell time, the length of which is determined by the frequency range one wishes to examine. Typically the collection proceeds linearly through the array, so for m y dwell times and n z dwell times you would collect 1D spectra with the delays:

0,0 0,y 0,2y 0,3y ... 0,my

then

z,0 z,y z,2y z,3y ... z,my

and so on until

nz,0 nz,y nz,2y nz,3y ... nz,my

This is called Cartesian sampling, and it has some advantages. The numerous data points typically do a good job of specifying resonance frequencies, and processing this data is a fairly straightforward proposition. The glaringly obvious disadvantage is time, of which a great deal is required. Completely sampling either one of these dimensions separately can take less than 30 minutes, but sampling both can push a triple-resonance experiment into the 60 hour range. Most annoyingly, because triple-resonance spectra can be really rather sparse, this extremely long experiment often over-specifies the resonance frequencies. That is, much of this time is spent collecting data you don't need.

Because spectrometer availability and sample stability are not infinite, there is considerable interest in making this process more efficient. One of the methods for doing so is called radial sampling. In this approach, the spectrum is built up from a series of "diagonal" spectra that lie along a certain defined angle with respect to the two time domains (imagine the above array as a rectangle with sides of my and nz to get a rough idea of what this means). If these angles are judiciously chosen, the spectrum can then be rebuilt from just a few of them with only modest losses in resolution. Gledhill et al. apply this approach as a means of addressing their time-resolution problem. Guided by a selection algorithm, they use just four angles (at 500 MHz) to resolve more than 90% of the peaks possible in myelin basic protein. As a result, they were able to collect HNCO-based HX data with 15-minute resolution. This isn't enough to catch the fastest-exchanging peaks, but it's more than sufficient to catch core residues.

Gledhill et al. used some additional tricks to gain extra speed in the experiment, however. Using band-selective excitation, they cut down the experiment's relaxation delay to 0.6 s, which is important because this delay is a considerable portion of the duration of each transient. Having done this, they started to get really clever. Because this experiment is being used to measure the intensities of known frequencies, it is possible to significantly reduce the amount of processing required by employing the 2D-FT only for those regions that contained actual peak intensity. Moreover, they could extract peak intensities from each individual angle plane. Because they did not interleave the collection, this enabled them to substantially increase the time-resolution when necessary.

For peaks that exchanged quickly Gledhill et al. took relaxation data from the individual angle spectra, to maximize the time-sensitivity of the data. For slowly-exchanging peaks, they averaged the data from the angle spectra to maximize the signal-to-noise ratio. The resulting intensity curve seems a bit noisy, but this is an acceptable price to access new peaks. More importantly, the precision of the overall rate (as opposed to the instantaneous intensity) appears to be on par with simpler methods of measuring HX.

Successful use of the AMORE-HX experiment will depend on a wise selection of acquisition angles, a process that may benefit from further optimization. Because the HNCO has relatively good dispersion, the pulse sequence should enable HX measurements for just about any protein that is suitable for NMR. This would allow for a direct assessment of large enzymes and complexes, as well as a measurement of local stabilities in domain-domain interfaces.

Gledhill, J., Walters, B., & Wand, A. (2009). AMORE-HX: a multidimensional optimization of radial enhanced NMR-sampled hydrogen exchange Journal of Biomolecular NMR DOI: 10.1007/s10858-009-9357-4

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Mesodynamics, field cycling, and SARS: an explanation

Part of the motivation for my previous post about the spectral density was the recent appearance online (and upcoming appearance in print) of my paper in the Journal of Biomolecular NMR, which is open access, so you can open it up from home and read along as I tell you about it. The obscure-sounding title "Mesodynamics in the SARS nucleocapsid measured by NMR field cycling" means that we were able to characterize an interesting fluctuation in a protein from the SARS coronavirus, and that we used a cool technique to do it.

In the previous post, I mentioned that NMR dynamics studies ought to use data collected at multiple static magnetic field strengths. This is typically accomplished by increasing the strength, because of clear advantages in sensitivity and resolution at high and ultra-high field. Corresponding author Alfred Redfield, however, created a device (left) to capture information about relaxation at lower magnetic field strengths while retaining the advantages of, say, a 500 MHz magnet. This is accomplished by field-cycling, which in this case means physically moving the sample from the center of the magnet's superconducting coil to a spot several centimeters away. If one has carefully measured the magnetic field gradient with respect to distance, one can reproducibly measure relaxation at a desired (lower) field within the bore of the 500 MHz magnet.

As you might surmise from the photograph, Al built the field-cycling device himself, often jury-rigged from whatever parts were convenient. For instance, as you can see at right, the push-rod that connects the sample in the tube to the motor assembly was made from an arrow purchased at a sporting goods store. I'll count myself lucky if I'm half as creative and active in my 50s as Al is in his 70s. Al has used this device to investigate the dynamics of nucleic acids and lipids, but he was interested to see what we could learn about proteins by examining relaxation at low magnetic fields. Relatively low, at any rate — the weakest magnetic field I used is higher than you would typically encounter in, say, a clinical MRI. In his ³¹P research, however, Al has gone near zero field during the relaxation period.

Elan Eisenmesser, now a professor at the University of Colorado Health Sciences Center, did some initial investigations using this technique on cyclophilin A, and edited the pulse sequences so they could control the field-cycling device. Unfortunately, the results in CypA were kind of boring because for that protein the dynamics on the ps-ns timescale are relatively homogeneous. At this time, Elan was also working on the N-terminal domain of the SARS nucleocapsid protein (henceforth SARSN). As you can see from the structure at left (explore it at the PDB), SARSN has a long β-hairpin (sticking out to the right) which is known to be flexible. The hairpin is thought to interact with RNA as part of the viral assembly process, as well as binding to several host proteins during the process of infection. As Elan prepared to move on, he passed the project to me, and with Wladimir Labeikovsky assisting for the first couple of months, I took a bunch of spectra under various conditions.

You can see what a low-field spectrum looks like at right: this is an HSQC from an R₁ experiment where excitation and acquisition were performed at 50.7 MHz (¹⁵N) and the relaxation period took place at ~17 MHz (blue). I've also overlayed a spectrum collected entirely at 50.7 MHz (red). The peaks are all in the same place and the sensitivity is good, but the signal/noise ratio is clearly lower for the 17 MHz spectrum, and we get some sidebands from the water on the right side of the spectrum. Getting the water signal to behave was a significant challenge for these experiments and took several tries to get right.

Besides the experiments I performed personally, spectra were collected by Elan and Geoffrey Armstrong at the Rocky Mountain magnet facility (the 900 MHz R₁ and NOE) and Karl Koshlap at the UNC Pharmacy School (500 MHz data). Karl's involvement was necessitated by a change in sample conditions and the unfortunate incident our spectrometer had with an HDTV channel (chronicled here, here, and here).

In the end I managed to gather relaxation data from four high fields (using standard equipment) and two low fields (using the field cycler). The R₁ data are shown in Figure 2, and if you read the previous post then they shouldn't surprise you very much. For most of the protein, R₁ decreases steeply as the strength of the static magnetic field is increased, but for a subset of amides this field dependence is substantially reduced. Most of these residues fall into a continuous stretch encompassing the β-hairpin of SARSN and an adjacent loop (shown on the structure in Figure 1). In addition, the heteronuclear NOE measurements for these residues show a very large R_NOE/R₁ ratio at 50 MHz that decreases substantially as the field increases (Figure 3). As I discussed in the last post, these patterns of field dependence are characteristic of flexible regions in a protein, but more specifically they indicate flexibility with an internal correlation time of around a nanosecond or so.

One might expect a large, relatively unconstrained feature like the hairpin to have flexibility on multiple timescales. In particular, it seems like the sort of structural element that might move with a time constant of microseconds or milliseconds. These slower motions can't be fit with great accuracy using the experiments performed here, but evidence of their absence can be found in the R₂ experiments performed at 500 and 600 MHz (Fig. 4). Assuming that they are correlated with changes in chemical shift, we would expect motions on this timescale to increase the R₂, but in the hairpin this relaxation rate is substantially reduced, consistent with high flexibility on the nanosecond timescale (low S²).

In order to gain a more complete picture of the dynamics, I fit the relaxation data to model-free formulations of the spectral density. For most residues, the classic Lipari-Szabo formalism worked quite well, although the S² are generally higher than I like. An analysis of the fits, however, indicated that many residues needed to be fit to a more complex model, called extended model-free or model 5. In this model the spectral density is given as:

where S²_f and S²_s are order parameters for a fast and slow internal motion, respectively, and τ_s is the internal correlation time for the slow motion (τ_f is assumed to be ~0). The residues that were fit to this alternative model happened to be those with anomalous R₁ and NOE dispersions, meaning they mostly belonged to the β-hairpin and the loop incorporating residues 60-65.

Ultimately I didn't include the low-field data in the quantitative fits. The large random errors in these rates (error bars in Fig. 2) meant that the more precise high-field data would dominate the fits, for one thing. For another, the low-field data were not entirely consistent with the high-field results. Although the general features of the relaxation at 17 and 30 MHz agree with predictions from high field, the observed low-field R₁ differ substantially from predictions. This could be due to a number of error sources, the two biggest being positioning error and interference between the CSA and dipolar relaxation mechanisms (because we cannot suppress this interference in the fringe field). Al also thinks some of the error may be due to the influence of a low-amplitude fluctuation in the globular portion of SARSN. Qualitatively the R₁ behave much as we would expect, but bringing them into line quantitatively will take more work.

The upshot of all of this effort to fit the dynamics is that the residues in the hairpin have an interesting duality. On very short timescales (< 10 ps or so) they are quite rigid, much like the rest of the protein. On a slightly longer timescale, however, they are very flexible, with S²_s of around 0.6, and similar internal correlation times across the entire feature in the range of 600-800 ps (Fig. 5). Because the correlation time of this fluctuation is significantly faster than molecular tumbling but much slower than typical backbone fluctuations, Al called them "mesodynamic", a word Dorothee seems to like. At any rate, these observations led us to propose that the hairpin fluctuates widely (based on S²_s and τ_s) as a coherent structural unit (based on S²_f), rather than having its strands fall apart and flop around randomly. The hairpin is both ordered and disordered, depending on the timescale of analysis and frame of reference.

The physical plausibility of this dynamic model was assessed using a pair of 15 ns all-atom molecular dynamics simulations performed by Ming Lei. What these found, shown in Fig. 7, was that the hairpin maintained its internal structure while moving freely with respect to the globular portion of the protein. In addition, the simulations suggested a reason the 60-65 loop had similar dynamics to the hairpin — transient hydrogen bonds formed between side chains in the hairpin and residues in the loop, causing their motions to be correlated.

The qualitative agreement between the low-field and high-field data supports our contention that this technique can be made to work and to give valuable data about certain kinds of fluctuations. Future work on proteins with this technique will require a rigorous approach to control for the systematic bias we observed. Additionally, this study re-emphasizes the value of taking relaxation data at many fields in order to fully characterize biomolecular dynamics.

As for the dynamics of SARSN, the finding is interesting but doesn't yet provide any specific insight. Disordered regions of a protein are often associated with promiscuous binding activity, and this hairpin is no exception. However, the existence of multiple binding sites in one of these regions is usually attributed to a significant ability to restructure itself. Here, that possibility would seem to be limited by the apparent persistence of the hairpin's intrinsic structure. The ability of the hairpin to move freely while maintaining a particular internal arrangement may have advantages in capsid construction, an idea that could potentially be tested by inserting prolines or glycines in the β-strands, which should disrupt the hydrogen bonding that preserves the hairpin.

Al and his collaborator Mary Roberts are currently continuing their investigations of ³¹P dynamics in nucleic acids and lipids using low field. They're even advertising:


Clarkson, M., Lei, M., Eisenmesser, E., Labeikovsky, W., Redfield, A., & Kern, D. (2009). Mesodynamics in the SARS nucleocapsid measured by NMR field cycling Journal of Biomolecular NMR DOI: 10.1007/s10858-009-9347-6 OPEN ACCESS

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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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Urea binds to the peptide group

I've mentioned urea and guanidinium (Gdm) before on this blog, usually with reference to questions about their mechanism of action. These small molecules cause proteins to denature, or lose their higher levels of structure and become unfolded chains. The complete unfolding of a protein typically requires a fairly high concentration of denaturant, almost always more than 1M, and the explanation for this is that the denaturant molecules preferentially associate with the polypeptide chain with low affinity. In a recent issue of PNAS, a paper from Walter Englander argues that urea, but not guanidinium, associates with the backbone of the protein via hydrogen-bonding interactions.

Lim et al. reached this conclusion using hydrogen-exchange experiments. Amide nitrogens in proteins freely exchange their covalently-bound hydrogens (protons) with the surrounding water. The rate of this process can be measured (among other ways), by placing a protonated amide group into a deuterated solvent and tracking the decline in proton signal by NMR; this is called an HX experiment. In the case of a folded protein chain the observed rate will depend on the intrinsic chemistry of the particular amide and the stability of the protein structure, because this structure excludes water from the backbone and makes hydrogen bonds that lock the protons in place. Rather than deal with all of that, the authors used a small peptide mimic that (probably) has no complex structure. This had the additional advantage that the simple spectrum could be tracked by 1-D NMR, substantially increasing the time-resolution of the measurements. The authors measured the rates as they varied the pH — because we're talking about D₂O, it's called the pD instead — and added various cosolutes that are known to denature or stabilize protein folds.

As expected, the dialanine itself had a V-shaped rate profile in these HX experiments, with a minimum at a pD of 4. The hydrogen exchange reaction can be catalyzed by acid or base, so the rate increases as you go up or down in pD from this minimum. When urea was added to the solution, the authors found that acid-catalyzed HX accelerated while base-catalyzed HX decelerated. The most reasonable explanation for the latter result is that a hydrogen bond between the carbonyl of urea and the amide proton protects it from water attack. The authors do some mathematical modeling to establish that the effect on rate reflects a bonding association between the peptide and urea, not just random collisions or thermodynamically neutral associations.

The acid-catalyzed result is interesting, because in theory one would expect that urea would accelerate acid-catalyzed HX more than it actually does, because under acidic conditions it can accept a hydrogen from the amide nitrogen. While there are some confounding factors, the most likely explanation for this result is that the NH₂ groups of urea form hydrogen bonds to the carbonyl of the peptide. Because acid catalysis of HX hinges on the favorability of protonating this carbonyl, a hydrogen bond would be expected to reduce the HX rate. The authors argue that the ability of urea to serve as an acid catalyst is therefore mitigated by its propensity to bind to the carbonyl.

The formation of hydrogen bonds between urea and the peptide group meshes well with evidence that it denatures proteins through interactions with the backbone, some of which I have mentioned before. From HX experiments under native conditions we know that even a folded protein chain regularly undergoes excursions from its water-excluded, hydrogen-bonded state. Urea may bind to the backbone during these fluctuations, preventing or slowing a return to the folded structure.

Lim et al. also tested a number of other cosolutes, and found that none of them had a similar effect on the HX rate. In the case of the stabilizing molecules (glycerol, sorbitol) this is entirely expected, as their action cannot be explained in terms of a preferential association with the backbone anyway. The surprise concerns guanidinium, which is a more powerful denaturant than urea. The authors noted that Gdm has a small effect on the rate, but not in a pD-dependent way, and one that was little different from an equivalent concentration of NaCl (ordinary table salt). Gdm has no groups that can hydrogen bond to the amide, so the absence of an effect on base-catalyzed HX is expected. However, it should be possible for guanidinium to hydrogen-bond to the carbonyl, so it should seemingly have an effect on acid catalysis. This is not in fact the case.

The authors note that existing evidence does not support the idea that Gdm forms hydrogen bonds with water (although urea is known to do so). Lim et al. suggest instead that the planar Gdm molecule forms favorable stacking interactions with other planar groups. These include the peptide bond and several side chains. They argue that the stacking of Gdm with these groups pries the protein apart without requiring hydrogen bonds.

As a means to investigate diseases that result from protein misfolding, many groups are now trying to structurally characterize the unfolded state of protein molecules. Many of these experiments model the in vivo denatured state by using chemical denaturants such as urea or Gdm. The possibility that direct interactions between the denaturant and the protein will give rise to experimental artifacts should be taken seriously. Urea's promiscuous formation of hydrogen bonds with the backbone, itself, and water, may give rise to loose networks of hydrogen-bonded molecules that act to condense the chain. By contrast, Gdm's stacking effect will likely act to artificially extend the chain by steric obstruction. Because of the difference in these mechanisms, it may be of value to cross-validate findings from structural studies on unfolded states by repeating experiments with alternative denaturants.

Lim, W., Rosgen, J., & Englander, S. (2009). Urea, but not guanidinium, destabilizes proteins by forming hydrogen bonds to the peptide group Proceedings of the National Academy of Sciences, 106 (8), 2595-2600 DOI: 10.1073/pnas.0812588106

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High resolution protein structure from a living cell

Virtually everything we know about protein conformation comes from experiments performed in environments that do not resemble the biological context of proteins in action. Our data generally come from solutions that lack the significant array of salts, sugars, and metabolites that fill the cytosol of living cells, and often these data are acquired at a pH far removed from cytosolic. In addition, the dilute solution conditions used in almost all structural biology experiments do not capture the crowding and excluded volume effects that are likely to play a role in determining protein conformation in densely-packed cellular environments. As techniques in biology and NMR have advanced, however, the determination of protein structures in living organisms has become possible, despite the significant challenges. This week in Nature, a research team from several institutions in Japan and Germany reports that they have solved a high-resolution NMR structure of a protein in the cytosol of living E. coli bacteria (1).

The authors chose a relatively small and simple protein to work out their technique, in this case a 66-residue metal-binding protein from a thermophilic organism. They expressed the protein in E. coli using standard methods, exchanging the bacteria into isotopically-enriched media once they reached the appropriate density for induction. At the end of the induction period, the bacteria were gently centrifuged, resuspended into a thick slurry, and put in an NMR tube. Samples produced in this way were stable for about 6 hours, which is generally not enough time to perform the kinds of 3-dimensional experiments necessary for NMR structure determination.

To get around this problem, the authors used non-linear sampling and maximum entropy processing. This approach allowed them to reduce the number of data points they took, without losing much of the frequency discrimination that is vital to successful NMR. In this way they were able to compress the essential assignment and structural experiments to about 3 hours, although they found it necessary to repeat experiments and add them together in order to get enough signal to proceed. In order to ensure that the data were not contaminated by sample degradation, they ran short two-dimensional experiments to check sample quality in between the 3-D spectra. With this approach they managed to take 9 assignment spectra, several relaxation spectra, and several NOESY spectra for structural data. Apparently, each spectrum required its own, new sample due to the short lifetime of the bacteria under these conditions.

The authors performed control experiments in order to address some of the problems that affected previous research on proteins in living E. coli. They found that removing the cells from the NMR tube eliminated most of the protein signal, and that lysates of the bacteria contained protein signal. These experiments showed that the data collected in their experiments genuinely came from protein inside the bacteria rather than protein that had leaked out.

After all this work, the authors were eventually able to solve a structure of TTHA1718 in live E. coli, which you can see to the right (explore this structure at the PDB). This result would not have been possible, however, had the authors not employed specific methyl labeling in order to get additional long-range restraints, a technique typically used for very large proteins. As you can see in the supplementary information, attempts to solve the structure without the methyl NOEs gave rise to a fairly disordered ensemble. Even this ensemble is nowhere near as tight as the in vitro structure that the authors also solved. Because the in vivo structure used many fewer NOEs than the one from dilute solution it is difficult to tell whether differences between these ensembles reflect real conformational changes or simple uncertainty. The loop near the metal-binding cysteines (shown as fat sticks in this image) is a case in point — it looks quite different from the solution structure, especially in the positioning of the critical side chains, but there are almost no NOE restraints for this loop in the in vivo structure (Figure 4e). Chemical shifts support the idea of a conformational change, and inside the cells many of the signals in that region are too broad to detect. This, in conjunction with some metal-enrichment experiments the authors performed, suggests that the protein is regularly binding to metals in vivo, but the structure of this bound state is essentially a mystery. There are also a few clear structural differences in well-defined regions of the protein, but their significance is also unclear at this time.

This experiment serves as proof of principle, but NMR spectroscopists weary of years of promising experiments that turn out to only work on ubiquitin might rightly question whether this approach has any further applicability. In order to address this, the authors expressed the protein to a lower level in order to demonstrate that the procedure could still work for less-concentrated proteins. In addition, they show spectra from calmodulin in the supplementary data, suggesting that this approach will at least be applicable to proteins up to the 20 kilodaltons. However, the relaxation data the authors show in the supplementary data indicate that tumbling in the bacteria is significantly slower than in dilute solution, and the T₂ of the protein is 5-6 times shorter in vivo. If this result is general, then structural work on larger proteins may not be possible.

Why did this experiment work when other experiments on globular proteins in E. coli have led to leaking protein or an absence of signal (2)? Part of this may be that not all E. coli are created equal: the authors of this study used the JM109(DE3) rather than the popular BL21(DE3) strain. Genetic differences between the cells used may be responsible for the altered outcome. This will be a difficult thing to nail down, however, as overexpression typically involves the introduction of foreign DNA, an antibiotic, and an exotic activator of some kind, not to mention that isotopic labeling requires nutrient-poor minimal media. The difference between CI-2 that leaks out of cells and TTHA1718 that stays in may be as simple as the amount of magnesium sulfate in the M9. Until the factors causing the excretion of overexpressed proteins are more fully understood, careful controls will be an absolute necessity of in vivo experiments.

Because of the difficulty and expense this is clearly not an approach to be taken up lightly. For the time being, at least, you want to save this sort of experiment for systems where there is a real inconsistency between structural data from dilute solutions and results in vivo. As we improve the NMR approaches and increase our ability to manipulate E. coli behavior, however, this technique will grow more powerful and broadly applicable. Moreover, the Japanese part of the team reports in the same issue of Nature that they have managed to acquire spectra from proteins transferred into cultured human cells (3). This suggests the possibility of purifying labeled proteins at high yield, transferring them into living human cells, and then monitoring their structural and dynamic properties in their biological context.

1) Daisuke Sakakibara, Atsuko Sasaki, Teppei Ikeya, Junpei Hamatsu, Tomomi Hanashima, Masaki Mishima, Masatoshi Yoshimasu, Nobuhiro Hayashi, Tsutomu Mikawa, Markus Wälchli, Brian O. Smith, Masahiro Shirakawa, Peter Güntert, Yutaka Ito (2009). Protein structure determination in living cells by in-cell NMR spectroscopy Nature, 458 (7234), 102-105 DOI: 10.1038/nature07814

2) 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

3) Kohsuke Inomata, Ayako Ohno, Hidehito Tochio, Shin Isogai, Takeshi Tenno, Ikuhiko Nakase, Toshihide Takeuchi, Shiroh Futaki, Yutaka Ito, Hidekazu Hiroaki, Masahiro Shirakawa (2009). High-resolution multi-dimensional NMR spectroscopy of proteins in human cells Nature, 458 (7234), 106-109 DOI: 10.1038/nature07839

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Allostery in the CBP KIX domain

Classically, allosteric and cooperative effects have been identified with large complexes of multiple protein subunits, in which the binding of a ligand to one subunit enhances ligand binding in a different subunit. While some features of the models developed to deal with these systems do not translate well to cases of allostery within a single protein or domain, many of their core ideas continue to illuminate these single-subunit systems. In an upcoming paper in the Journal of the American Chemical Society, a team of European researchers examine an allosteric effect based on population shifts in a transcriptional activator, comparing it to a famous model for explaining allostery in hemoglobin (1).

The CREB binding protein (CBP) is a large molecular scaffold that brings pieces of the transcriptional machinery together in order to turn on a gene. Like many scaffold proteins it contains several protein-protein interaction domains linked together by large unfolded regions. One of these domains is KIX, a small bundle of helices that binds other proteins at two distinct sites. In one case, a protein called MLL binds to one site while a protein called c-Myb binds at the other. What is so interesting about this is that KIX is much more likely to bind c-Myb when it is already bound to MLL. Brüschweiler et al. used NMR techniques to try and understand how this happens.

In order to pull this off they performed relaxation-dispersion experiments on the amide nitrogen, α-carbon, and some methyl carbon atoms of the KIX domain bound to a peptide derived from MLL. Many of the amino acids in the protein showed a significant contribution to R₂ from exchange, suggesting a global conformational switch between two states. In order to cover their bases, the authors performed experiments to prove that this behavior was not related to the unfolding of the protein. Satisfied that the protein was stable, they used standard methods to calculate the rate of the conformational change, the population of the two states, and the chemical shift difference between them. They found that the minor state of the KIX-MLL complex is 7% of the total population of protein molecules. They also noticed that the chemical shift difference between the two states correlates very well with the chemical shift difference between the KIX-MLL complex and the KIX-MLL-c-Myb complex. Assuming that the conformation of KIX is the primary determinant of chemical shift in the bound state, this suggests that the dynamics are sensing a switch between a state that doesn't bind c-Myb and a state that does.

In order to determine whether MLL binding gave rise to this conformational switching behavior, the authors measured relaxation dispersion in KIX at several different concentrations of MLL. Excluding residues highly sensitive (by chemical shift) to MLL binding, they found that the exchange contribution to relaxation increases as MLL is added. Although Brüschweiler et al. were unable to fit this small number of residues quantitatively, these results strongly suggest that the addition of MLL increases the population of the c-Myb binding state. Moreover, under conditions where KIX forms a saturated complex with MLL and a peptide from another protein (pKID), the chemical exchange contribution to relaxation vanishes, suggesting that the protein has been pushed completely to the binding-competent state.

In order to identify the pathway by which the MLL binding site communicates to the c-Myb binding site, the authors examined the residues in KIX that had the largest chemical shift change associated with the chemical exchange behavior. As it happens, residues satisfying these criteria cluster in a region stretching from the MLL site to the c-Myb site, as you can see to the right (explore this structure at the PDB). Here, KIX is blue, the MLL peptide is red, and the c-Myb peptide is green. The side chains of the residues Brüschweiler et al. identify are shown as sticks inside the pink atomic surface. As you can see, these residues constitute a contiguous body stretching from one site to the other. Presumably, this set of residues provides a pathway for communication between the two sites. A trio of isoleucines at the core of this region (I 611, 660, and 657) are present in KIX domains from many different species (supporting information), suggesting that this communication pathway is evolutionarily conserved. Mutational studies centered on this trio of residues may teach us more about the mechanism of information flow in this domain.

Although this allosteric pathway is known to work in reverse (binding of c-Myb enhances the binding of MLL), the authors were unable to detect any exchange contribution to R₂ when only c-Myb or pKID was bound. While this may suggest that communication in the opposite direction uses a completely different mechanism, such that KIX has two unidirectional allosteric pathways, that's not a necessary conclusion from this result. Alteration of R₂ due to conformational exchange is dependent on the populations of the two states, the difference in chemical shift between them, and the rate of the switch. Actually detecting a dispersion curve requires that all these parameters lie within a 'sweet spot' that allows observation. This doesn't always happen, even when a dynamic process is occurring with a μs-ms rate. Because the chemical shift changes that result from MLL binding appear to be quite large (2) the exchange process may be slow on the NMR timescale.

One minor concern I have with the paper is that the experiments were carried out at a pH of 5.8, which is lower than the pH of cytosol (7.2). The only groups likely to change their charge over that range are histidines, but one of the key residues for this paper is H651 in the KIX domain. The experiments that established the allosteric effect of MLL on c-Myb binding (2) were performed at pH 7.0 so it is formally possible that the dynamics and allostery are a coincidence (although the chemical shift data argue against this). It would probably be worthwhile to perform HMQC experiments to clarify the protonation state of the histidine, or to repeat the binding experiments at a lower pH. The latter might be preferable; I assume that mildly acidic conditions are used for the NMR experiments because KIX has undesirable spectral characteristics nearer neutral pH. Additionally, it might be interesting to perform experiments that explore the effects MLL has on the kinetics of binding, seeing as this appears to be a dynamic process.

Brüschweiler et al. identify their results with the Monod-Wyman-Changeux model of allostery. Although this model was formally developed for systems with multiple subunits, what the authors really wish to emphasize is the idea from the MWC model that proteins in solution exist in an equilibrium of high-affinity and low-affinity forms. The evidence from the relaxation-dispersion experiments indicates that a very small proportion of free KIX exists in a (unfavorable) conformation that's ready to bind c-Myb. The binding of MLL enhances KIX affinity for c-Myb by stabilizing this structure — the allosteric effect arises because MLL binding defrays the energetic cost of adopting this fold. This manifests as a shift in the population of KIX proteins towards the binding-competent state. This kind of binding cooperativity may play a significant role in CBP's transcriptional activation function.

(1) Sven Brüschweiler, Paul Schanda, Karin Kloiber, Bernhard Brutscher, Georg Kontaxis, Robert Konrat, Martin Tollinger (2009). Direct Observation of the Dynamic Process Underlying Allosteric Signal Transmission Journal of the American Chemical Society DOI: 10.1021/ja809947w

(2) N. K. Goto, T. Zor, M. Martinez-Yamout, H. J. Dyson, P. E. Wright (2002). Cooperativity in Transcription Factor Binding to the Coactivator CREB-binding Protein (CBP). Journal of Biological Chemistry, 277 (45), 43168-43174 DOI: 10.1074/jbc.M207660200

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How media resemble real life in your head

How does the human brain react to the communication of emotion? Does the observation or imagination of emotions have anything in common with the personal experience of them? It is possible that the brain uses a setup in which seeing a person experience an emotion, imagining that emotion, and feeling that same emotion all use completely independent circuitry. Yet since all of these experiences make references to the same emotional state, it is also reasonable to think that some of the pathways are shared. In a recent article from PLoS ONE, a team of researchers uses functional Magnetic Resonance Imaging (fMRI) to determine similarities and differences in the patterns of brain activation following various means of communicating disgust. PLoS ONE is open access, so go ahead and open the article up in another window.

First, a word about fMRI, for those unfamiliar with it. As the name would suggest, fMRI is an elaboration of the standard MRI techniques used image the interior of your body without the use of potentially harmful radioactivity. Neuronal activity in the brain causes a local depletion of oxygen from the blood, followed by a localized increase in blood flow. Because the magnetic properties of iron in the blood change with its oxygenation state, it is possible to detect these hemodynamics using magnetic resonance imaging. Thus, fMRI is able to indirectly detect neural activity, although the fMRI signal lags behind activity by a few seconds. A given fMRI signal also encompasses a large number of individual neurons and therefore can only serve as a rough map to where things are happening in the brain. These temporal and spatial limitations limit the conclusions that can be drawn reliably from fMRI, but the observed correlations can provide valuable insights.

Jabbi et al. used fMRI to map the neural response of subjects to various encounters with disgust. Previous research had shown that a particular region of the brain (the IFO) showed increased activity when subjects either tasted something disgusting, or viewed a short clip of someone else tasting something disgusting. For this study, Jabbi et al. had participants read short scripts (samples can be found in the supplementary materials) intended to make the reader imagine being disgusted, pleased, or not feeling anything. They found that reading disgusting passages induced a neural response in this region of interest, just as it had for the cases of tasting or observing disgust.

While this may seem completely unsurprising, it bears some consideration. The experience of personal disgust differs significantly from the experience of observing disgust in others. Similarly, imagining or reading about disgust creates a very different subjective experience than, say, drinking quinine. Given that these are all quite different feelings, it is somewhat surprising that a single area is activated by all three.

Of course, there is a fine line to consider here -- the passages meant to make the subjects imagine disgust may have actually disgusted them. The paragraphs that the authors make available in the supplementary materials are written in second person and involve things like accidentally ingesting animal waste. Because the subjects are reading passages that ask them to imagine themselves being disgusted, and the passages are themselves disgusting, the act of imagination may be contaminated by an immediate personal experience of disgust. In a more elaborate experiment it might be of value to use passages written in the third person. Additionally, it might be useful to employ passages in which the characters, because of particular phobias or personal experiences, are disgusted by items or actions the reader is likely to find innocuous.

Whether the readers where themselves disgusted or not, the overall response in the brain differed for each of the stimuli, as shown by a map of correlated activity (Figure 2). While the area outside the IFO activated by observation was relatively small, both the disgusting taste and the disgusting scripts produced widespread activity relative to a neutral taste or script. In general there was not much overlap between the networks, except for a small region shared by the imagination and experience groups. The authors propose that the similarities of imagining, observing, and experiencing emotion are due to the common activation of the IFO, while the differences between these are due to the largely distinct networks of correlated activity. Different modes of exposure to disgust may therefore act in complementary, rather than independent, ways.

Additionally, this result appears to be consistent with the view that our recognition of observed disgust and our imagination of disgust rely on an internal simulation of our own feelings of disgust. However, these experiments cannot establish exactly what a particular region of the brain is doing, so this remains an open question.

While this research does not indicate whether these results can be generalized to other emotional states, this finding may interest developers of media that make use of multiple modes of communication, specifically video games. Games often rely on video cutscenes to convey story and emotion, but this approach may be wasting a significant amount of potential. The participatory nature of games makes it possible to approach emotional communication not only through the observational route, but also the experiential route.

Consider the case of Agro's fall in Shadow of the Colossus. Observing the cutscene, and hearing the voice of Wander, the player can understand that Wander feels grief at this event, in much the same way that anyone watching a movie could understand it. Additionally, the emptiness of the game's landscape and the forced collaboration between the player and the Agro AI has helped to create a relationship between the player and the horse. Thus, in observing Agro's fall, the player may feel his own sense of grief at the event, increasing the emotional resonance of the moment.

This suggests a possible, if lengthy, experiment. It would be interesting to compare the fMRI profile of a subjects observing Agro's fall under two conditions: one in which they have actually played the game up to that point, and another in which they have watched the game as a movie, with exploration and battles recorded previously from an expert player's run. Would the first group have activity in both the observational and experiential networks, or would each group activate a different network? What implications might these outcomes have for the development of emotionally fulfilling games?

Of course fMRI studies are not some holy grail that makes everything clear. The work of Jabbi et al. has given us a rough map to where things are happening, but understanding exactly what is happening and how it is happening will require additional experiments and possibly new investigative techniques. Nonetheless, this is an interesting piece of the puzzle, and perhaps some food for thought.

Mbemba Jabbi, Jojanneke Bastiaansen, Christian Keysers (2008). A Common Anterior Insula Representation of Disgust Observation, Experience and Imagination Shows Divergent Functional Connectivity Pathways PLoS ONE, 3 (8) DOI: 10.1371/journal.pone.0002939

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