Take the shot!

Dimitri Rascalov runs for his life, as he must, because he has angered the wrong man. Niko Bellic, a former soldier and incredibly efficient killer, has sworn to avenge his cousin Roman's murder on Rascalov's orders, and has tracked his enemy to this dilapidated casino on the edge of town. Now Dimitri's only hope is to escape in his helicopter. Niko pursues him across the roof, sees him about to escape, then races halfway across the building to grab hold of the landing skid. Moments later, he is shaken off into the water next to a speedboat. Now there will be a spectacular chase, by boat and helicopter, across Liberty City, culminating in a confrontation at its most famous landmark. But it is a chase that should not be happening, because Niko Bellic, trained killer, had a rocket launcher, and a clear shot he should have taken. That he did not is a signpost to one of Grand Theft Auto IV's central flaws.

A video game, particularly of the kind GTA IV is, poses a challenge for the creator because the experience of the work that ultimately emerges depends strongly on the input of the player. In order to define the parameters of the experience the creator must exert authorship in a variety of ways. The display of cutscenes, the presentation of incidental dialogue, and the occurrence of scripted events are authorial influences familiar from other media. The developer also constrains the experience through the design of spaces, the placement of enemies, and the programming of artificial intelligence. Beyond this, the conditions for "victory" also define the player's experience because of his assumed desire to complete the game. The key is to use all these authoring steps so that they work coherently. It's not enough to make sure the characters behave consistently across all their cutscenes — every aspect of the game must be considered in light of the characters and their goals.

A reasonably intelligent criminal who knows he will be fleeing from police shortly would not, given any choice at all, take a slow and clumsy vehicle to escape from a crime scene. Nor would the player, for whom the victory condition involves escaping his pursuers. To this point, authorship has succeeded in bringing the player's perspective into line with the criminal's. The developer, desiring that the player/character should use an unwieldy vehicle anyway, has some options. One (good) option would be to arrange the mission in such a way that the heavy van is the only vehicle close to hand. An alternative approach is to make using the van a requirement of success for some obvious reason — say, something valuable is in the van and cannot be removed. A game starts to run into trouble if it requires the player to use the van, for no apparent reason, when a more suitable vehicle is immediately available. This final approach breaks the fiction, using an arbitrary, externally imposed requirement to force the player and characters to act in ways at odds with their goals and personalities.

GTA IV uses this approach all the time, both in and out of actual missions. At one point, Niko receives a call from Packie McCreary, telling him to go visit Packie's brother Gerry in the penitentiary in a remote corner of the city. It is arguably a problem to even mention prison in a game where you can kill a dozen cops, get arrested, and undergo no greater inconvenience than the trip to the police station and the loss of your considerable arsenal of assault weapons. It is certainly a problem to have Niko Bellic — a wanted illegal immigrant, drug runner, and prolific murderer — walk into that prison. And it simply implodes the fiction to have him go to that prison so that Gerry can tell him to call Packie, who — you will recall — set this whole trek into motion with a phone call in the first place. The long, credulity-stretching detour to the prison leads the story precisely nowhere, and what is most troubling about this is that it's not the worst use of authorship in the game.

Consider, for example, the mission "A Long Way to Fall", in which Niko, in a cutscene, walks up to a door and leans his head towards it, allowing a drug dealer on the other side to bang the door into Niko's face. For Niko, ostensibly a hardened soldier, to approach a door this way under these circumstances would be problematic for any kind of narrative. Of course, if Niko had walked peacefully into the building, accepting fresh-baked cookies from little old ladies, the scene would be a reasonable continuation of the fiction. But the immediately preceding gameplay emphatically warned against carelessness. Prior to encountering this door, the player has climbed through a housing complex full of the dealer's hostile posse. Because of the game's difficulty, this is only possible by advancing cautiosly, with judicious use of cover. Moreover, when the player first enters the apartment, he must use a doorway as cover against the well-armed thugs waiting in the main room. The importance of approaching a door carefully will therefore be at the front of the player's (and ostensibly Niko's) mind. In order to serve their dramatic end, the developers use a cutscene to force Niko to act in ways counter not only to the way the character should act, but also to the way the game has been encouraging the player to behave.

For me, this is the defining flaw of GTA IV — so many of the missions, cutscenes, and incidental moments actively undermine the propositions the game is trying to sell you on. Niko is an unstoppable trained killer until the developers' plan for a mission requires him to act like a man who has never fought inside a building, or to choose an obviously inappropriate vehicle, or not to kill a man until he reaches Alderney. Rascalov is a nervous wimp constantly concerned about playing by the "rules" until the developers' plot requires him to kill all his business partners and allies. The characters act not from the internal motivations arising in a fully-imagined personality, but from the external motivation of the developers' desire to move along to the next set-piece.

GTA IV has been hailed as a new gold standard in video-game storytelling, and if that is true then we should double-check the purity of our ingots. The character who is always precisely as smart or as foolish, as competent or helpless as the plot requires at a given moment is a consistent staple of poorly-written action flicks and romantic comedies. GTA IV operates entirely on that same wavelength, except that the authoring of mission objectives and cutscenes means that Rockstar attempts to make the player be as smart or stupid as their dramatic purpose requires. But Rockstar can only constrain action, not thought. They can make me chase Rascalov all around the city, but they can't make me forget Niko Bellic's rocket launcher, or the shot he should have taken.

Read the rest...

What's the word, Slim?

Tuesday saw the widely-expected unveiling of Sony's new hardware model: a slimmer, lighter, and less energy-hungry Playstation 3. They also debuted a new, $299 price, meant to make the PS3 more competitive with the XBox 360 and Wii. At the same time, my PS2 has started to sputter; it had a tough time chewing through Persona 4, and since then has only gotten more feeble. This would be a great time for Sony to sell me a brand-new PS3 with a reduced form factor and lower energy consumption, but Sony has chosen not to include backwards compatibility with PS2 games in the feature set of their new hardware. In the end, that turns out to be a minor problem for me, and perhaps a larger one for Sony.

Don't get me wrong, I'm not a Sony "hater". Obviously I have and love a PS2, and much of my home theater is Sony electronics. And I'm not going to say that the PS3 Slim is a great huge terrible waste of time because it doesn't have backwards compatibility. Nothing could be further from the truth — the Slim answers most of the demands of the average consumer and the game developers Sony needs to keep happy. I personally think this particular change is too little, too late to fundamentally change the balance of power. Nonetheless, the lower price, in combination with Blu-Ray, makes the PS3 a much more solid choice, and arguably the best choice, for anyone buying his or her first HD console.

But I'm not buying my first HD console. I have an XBox 360, and that means I already have access to nearly all of the games I'm interested in. I don't need a Blu-Ray player, though I might use it if I had one, and while I'm fascinated by some of the games I've seen available for the PS3, I don't need those either. Not even for the new, low price of $299. What I do need is a way to keep playing my PS2 games, and Sony is still selling new PS2s for $100. Sales of the PS2, though they've declined dramatically, have still been bringing in much-needed money for Sony, and their pronouncements that backwards compatibility is never coming are probably meant to prop those sales up. But it seems to me that continuing to sell the PS2 is a dead end.

If I buy one, the executives at Sony will think they gained $100, but they're wrong. The sale of a PS2 is a loss of at least $199, because it's a lost opportunity to sell a PS3. Sure, the profit margin on the PS2 is higher, but the guy who buys a PS2 is going to use it to play PS2 games he already owns, or to play used games, and none of this will earn Sony a dime. These players won't be playing PS3 games that earn royalties for Sony, or supporting the Blu-Ray market that Sony is invested in. That means that the sale of a PS2 is a lost opportunity, not a net benefit. What Sony should be striving to do is find a way to turn any would-be PS2 buyers into PS3 buyers. Now that the PS3 Slim offers a more competitive price, they should leverage their existing, unbelievably massive PS2 install base into new buyers for PS3 by presenting that console as an upgrade that possesses all the capabilities of the console those users have already invested in (some substantially), plus exciting new capabilities and games.

Why hasn't Sony done this? Some initial offerings of the PS3 (back when it cost too much for me) had a hardware solution, but this seems to have been uneconomical, and anyway would probably be at odds with their goal of shrinking things down for the PS3 Slim. The answer, then, is software emulation, which seems to have been pretty difficult to implement for even some titles, and given the size of the PS2 library, would represent a QA nightmare. I understand that problem, and if Sony feels that the investment required to make emulation possible on their sole SKU going forward is not worth the (considerable) reward, then I'll accept that, though I feel their cost-benefit analysis has been suspect in the past (e.g. Home).

But what I would like to see is all the cards laid out on the table. Those recent comments from Sony reps that backwards compatibility is never coming carry as much weight for me as the ranting of some random fanboy, because Sony's communication with their customers this console generation has been an endless cycle of dissembling and outright lying (in which they are admittedly not alone). They did this with rumble functionality, and with the Slim itself, so why wouldn't they do it with backwards compatibility? There's no reason to trust what they say, especially when it takes the form of some slick marketing director spewing nonsense about surveys. The simple fact is that used backwards-compatible PS3s are selling for more than the new console price right now, a sure sign of continued interest and demand. What Sony should do is come out with the tech guys and say, "Look, here's the problem, here's what we've tried to do, here's why it hasn't worked, here's how much it would cost to make it work, and that's why we're not doing it." Or, if they really do have plans to try, come out and say that's happening, but they don't know how it will turn out. That may not do much for the corporate ego, but it would go a long way towards establishing some credibility.

As it stands, I feel like I'll get burned whatever I choose to do. If I buy a PS3 in hopes that BC is coming, and it doesn't, then all I'm really getting out of those $300 is access to a set of exclusives that mostly don't excite me. I could see myself paying up to $50 to play Flower, but not more than $300. I'm willing to opt for the PS2 and maybe eventually get a PS3 when its case is strong enough, but I'm not so wealthy that the $100 means nothing to me. If I replace my PS2, will Sony screw me by introducing backwards compatibility shortly thereafter? I don't know, and until Sony chooses forthrightness over the ability to make a big splash by holding back secrets, I can't possibly trust what they'll say. So until my PS2 gives up the ghost permanently, what I'm buying from Sony is nothing, which from their perspective should be the worst outcome of all.

Read the rest...

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

Read the rest...

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

Read the rest...

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

Read the rest...

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

Read the rest...

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.

Read the rest...

Capsule: Lost Odyssey

Final Status: ~3/4 complete, and that's it for me

Put this on your box: Loading, please wait...

Most intriguing idea: Subverting some boss battles into a game of protecting your putative opponent.

Best design decision: The ring system alleviates many of the attentional problems that come with the limited interactivity of round-based combat.

Worst design decision: The irritatingly high proportion of idiot mazes in the dungeons.

Summary: Lost Odyssey is a fairly interesting tale about an immortal, amnesiac (ugh), vaguely effeminate (hruagh) man named Kaim who is trying to find his family and prevent a cruel, selfish sorcerer from conquering the other cruel, selfish rulers of the world. The game has several good ideas built in it — in addition to those mentioned above, I liked its skill system and the lightly-interactive text stories that reveal Kaim's life story. The score was also pleasant. The key issue is that the flow of the game is constantly broken up by loading screens and long battle introductions. This is a particular problem on the third disc, where the party is split up into 3-4 groups and long pauses for loading seem to occur every 30 seconds. The delays get to be quite frustrating, especially in timed sequences where the countdown continues as you engage in a meaningless survey of the completely non-interactive battle space. Penalizing the player for the developer's delays is kind of insulting, an emotion accentuated by idiot mazes such as the Prototype Staff, where shallow cart tracks somehow become an impenetrable barrier blocking Kaim's path. Eventually I got to a point where I just wasn't willing to put up with the crap anymore.

If you can't say something nice... Lost Odyssey shows off a number of really sharp decisions, which might have made it a classic if someone had come up with a way to cut out the dead time.

Read the rest...