Long-range energetic coupling in a PDZ domain

Despite its relative ease and proven utility, mutagenesis is a frustrating way to dissect the energetics of a protein domain. No matter how carefully you choose the position to be altered or the residue to swap in, unexpected results or unusable protein are frequent. Even when you get relatively clean data, the interpretation of the results is usually difficult because mutations are classic violators of ceteris paribus assumptions. Proteins are in general quite flexible, and this mobility means that the effects of a mutation can often be moderated by compensating deformations. Thus it is difficult to pin down energetic coupling by double mutant cycle analysis. However, in the course of an attempt to assess the usefulness of a computational method, a group from Sweden has shown an energetic coupling that correlates with some NMR dynamics results (1).

So, what exactly are Chi et al. assessing? Well, as I've discussed before on this blog, almost a decade ago Rama Ranganathan published an algorithm that used co-conservation of residues in a protein sequence to identify an energetic pathway in PDZ domains (2). The linkage between residues was defined in terms of a "statistical coupling energy" or ΔΔG^stat. As the authors of the present study note, several subsequent papers have criticized the computational approach employed by Lockless and Ranganathan. Chi et al. aim to re-examine this network prediction in the context of the PSD95 PDZ3 domain, which was used by Lockless and Ranganathan in some of their non-computational work. Chi et al. performed double mutant cycle analysis involving several residues in PSD95 PDZ3, some of them predicted to be coupled by Ranganathan's procedure and some of them not.

I should note that when these groups look at identical cycles (K380A, A376V) they generally get different results. Just judging off the raw data shown I am inclined to trust Chi et al., but a detailed inspection of all the raw data would be necessary to judge which approach was more accurate (Lockless and Ranganathan used FRET while Chi et al. used fluorescent emission).

No project of this kind can definitively address the quality of Ranganathan's algorithm. Although the statistical coupling is expressed as an energy, it is best interpreted as a probability. That is, the prediction of Ranganathan's algorithm is not that any protein will display precisely the calculated ΔΔG^stat, even assuming we knew what kind of observable to measure that reflected the observed statistical coupling (ligand binding? folding? mechanical disruption?). Rather, ΔΔG^stat reflects a predicted probability over the set of all PDZ domains that two sites will be energetically coupled. Thus, finding or not finding energetic coupling in a particular PDZ domain is not evidence for or against the accuracy of the algorithm, just as rolling 6 ones in a row is not evidence that the probability of rolling one on a fair die is anything other than 1/6. Nor is dissimilarity between the energetic network in any PDZ domain (or even in all PDZ domains) and the algorithmic prediction evidence that the algorithm is wrong. To find out if the algorithm is wrong using mutant cycle experiments, you must determine coupling energies in a number of PDZ domains and compare those results back to the prediction.

So, Chi et al. cannot establish whether the algorithm is right, but they can at least tell us whether the predictions of the algorithm are accurate in this particular case. They assert that the predictions are not very good in this instance, and judging on a linear correlation plot they provide this seems to be true. Before we draw any conclusions, however, let's take a look at the results in the context of the structure.

The figure I've made for us on the right is pretty busy, so you may find it helpful to open it in a new window. You can also explore this structure at the PDB. The key residue for this study, H372, is in red, and the peptide ligand is in purple. The backbone and side chains are colored for other residues that were mutated in this study. Residues with blue side chains were not predicted to be part of the energetic network by Lockless and Ranganathan (green side-chains were). Note that G329 was also predicted to be on the network, but of course it has no side chain for me to color. If the detected coupling energy for a mutation was larger than the error (based on Chi et al. Fig. 3A), I painted the backbone ribbon gold; otherwise it is blue. You will note that every mutation producing a coupling energy larger than the error in the measurement lies on the network predicted by Lockless and Ranganathan.

To be fair, an A376V mutation did not produce a coupling while A376G did, so the results are equivocal at this residue. Because G has a very low helix propensity it may be significantly altering local secondary structure (ceteris paribus violation). Therefore, the A376V result may be more representative. This highlights a significant weakness of mutational experiments. Because of glycine's quirks, there is no such thing as a conservative mutation of an alanine. Also, because glycine and proline have unusual properties with respect to secondary structure, mutations that have a G or P on either end are virtually impossible to interpret without careful structural studies.

The Ranganathan method gave a substantial number of false positives in this study. It bears mentioning that Lockless and Ranganathan saw substantial correlation between experimental couplings and ΔΔG^stat in this domain, though they used different mutations, which if I recall correctly were chosen based on the second most common residue for a given site. However, even in these results, the Ranganathan algorithm did accurately identify a distal residue (V362) which displays a significant coupling energy even though the β carbons of it and H372 are 14.0 Å apart. It is very odd for the authors to say in light of this that the domain has no coupling other than a straightforward distance relationship. From the data they show it is evident that distance from H372 would not be an accurate predictor of coupling. The absence of a coupling at both V428 and A376 (for the V mutation) indicates that very close residues may have no coupling at all. Also, given the A376V results, it seems premature to designate V428A as an outlier.

Of further interest, previous NMR experiments regularly identified a homologous residue (V61) of hPTP1e PDZ2 as having a dynamic response to peptide binding (3). A shamelessly stolen figure to the right shows some of these results. Ligand binding induced a decrease in the S² and an increase in τ_e on the side chain of V61. While mutational studies did not indicate a substantial effect of a V61A mutation on ligand binding (4), it would be interesting to check whether non-additivity between H71Y and V61A mutations is observed in hPTP1e. Similarly, it would be of great interest to examine the dynamic response of PSD95 PDZ3 to ligand binding.

The data in the Chi et al. paper indicate that there is, in fact, at least one long-range energetic coupling in the PSD95 PDZ3 domain. This coupling, between H372 and V362, was predicted by Ranganathan's algorithm. Moreover, NMR experiments have shown that the homologous residue in hPTP1e experiences dynamic changes in response to ligand binding, further strengthening the case for a functional connection. Clearly, Ranganathan's algorithm produces a substantial number of false positives in the case of this particular domain, supporting the author's contention that it poorly predicts the energetic behavior of any single domain.

Nonetheless, the demonstration of a long-range energetic coupling between H372 and V362, when most other core residues tested showed no coupling, strongly suggests the existence of some sparse energetic network within PSD95 PDZ3, consistent with the findings of Fuentes et al. and the predictions of Lockless and Ranganathan. It is to be hoped that Jemth's group will undertake further studies, perhaps guided by the existing structural and dynamic results, to identify the precise pathway by which energy is transmitted from V362 to H372.

1. Chi, C.N., Elfstrom, L., Shi, Y., Snall, T., Engstrom, A., Jemth, P. (2008). Reassessing a sparse energetic network within a single protein domain. Proceedings of the National Academy of Sciences, 105(12), 4679-4684. DOI: 10.1073/pnas.0711732105

2. Lockless, S.W., and Ranganathan, R. (1999). Evolutionarily Conserved Pathways of Energetic Connectivity in Protein Families. Science, 286(5438), 295-299. DOI: 10.1126/science.286.5438.295

3. Fuentes, E.J., Der, C.J., and Lee, A.L. (2004). Ligand-dependent Dynamics and Intramolecular Signaling in a PDZ Domain. Journal of Molecular Biology, 335(4), 1105-1115. DOI: 10.1016/j.jmb.2003.11.010

4. Fuentes, E.J., Gilmore, S.A., Mauldin, R.V., and Lee, A.L. (2006). Evaluation of Energetic and Dynamic Coupling Networks in a PDZ Domain Protein. Journal of Molecular Biology, 364(3), 337-351. DOI: 10.1016/j.jmb.2006.08.076

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It's quenchin' time!

In one of the very first posts on this blog I related the story of how television ruined our 500 MHz spectrometer, at least when it came to pesky things like low-sensitivity spectra of biomolecules. That's right, folks. Television not only rots your brain, it bricks your enormously expensive magnetic resonance spectrometer, at least if your proton Larmor frequency overlaps the broadcast band of the home shopping network. It turns out that this problem is actually rather difficult to fix: blocking out the television signal well enough to actually get reasonable spectra would have required lining the room with a considerable quantity of copper, an expensive proposition and one unlikely to be supported given that there are plans to tear that building down anyway. Instead it was proposed that we move the spectrometer to a room lined with a significant quantity of rock, i.e. the basement.

Unfortunately, the particular basement in question already had a spectrometer and rather a lot of other equipment and was anyway in need of some serious remodeling. The school managed to gather up the money for this, and just a few days ago the 500 was brought down from field and moved. Here (courtesy of Sara) is a picture of the old 500 in its new digs. This week was spent getting it down there and getting it back on its legs (obviously, they were removed for the trip). Tomorrow and Friday will be spent bringing it up to field. This will probably entail a quench.

For those of you who are not familiar with NMR spectrometers, these instruments have a superconducting coil to produce the magnetic field, and like most superconductors this must be kept extremely cold by some cryogen, in this case liquid helium. The liquid helium, in turn, is kept cold by being surrounded by liquid nitrogen. And the liquid nitrogen is insulated by a vacuum, just as in a thermos. When something goes wrong and the superconductivity is lost, an enormous amount of heat gets dumped into these cryogens and all that liquid gas turns into normal gaseous gas and emerges from the magnet with a sound resembling a freight train running over your ear. This video of a much smaller magnet quenching under controlled conditions should give you an idea of what's to come.



A quench is dangerous, especially in a small space, because all this extra nitrogen and helium can lower the percentage of oxygen in the local area to below what can be tolerated by human beings. Because the particular basement room in question is so enormous this will likely not be a serious problem. Anyway, our 500 apparently has a history of quenching when it is brought to field, so it will likely be several more days before we are actually back to using it again. Or at least, we will once we get through with the referencing, calibrations, etc. that are necessary to actually get anything to work.

UPDATE: The magnet quenched on the afternoon of 3/31. Regrettably there wasn't time to get the lab downstairs for a "Wizard of Oz" re-enactment.

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Two folds for lymphotactin

While reports of my man-crush on Brian Volkman are in general much exaggerated, it is true that I adore one of the systems he studies, the bizarre chemokine lymphotactin. In case you couldn't guess from past posts here, I am endlessly fascinated by this protein, and so I was very happy to finally see his latest paper on the subject in today's feed-dump from PNAS. Previously published research out of Brian's group indicated that lymphotactin adopted two totally different structures under different solution conditions. The new paper provides high-resolution structures of the non-chemokine fold and demonstrates that the structures have distinct activities, both of which are essential for full lymphotactin function in vivo.

Lymphotactin is a chemokine, a small protein which has the property of binding to molecules in the extracellular matrix (ECM) such as long polysaccharides, and also of activating certain G-protein coupled receptors (GPCRs). A previously-solved structure of lymphotactin (left) displayed a normal chemokine fold (explore this structure at the PDB), which is designated Ltn10. However, in order to get this structure by NMR, the Volkman lab had to either engineer in a second disulfide bond (as in this structure), or acquire their data under very specific conditions (10 °C, 200 mM NaCl). The reason for this is that at under reasonable biological conditions (37 °C, 150 mM NaCl), their spectra showed evidence of an alternate conformation. At higher temperature and lower salt, the peaks corresponding to the structure at left disappeared entirely and were replaced by peaks corresponding to an alternate conformation.

You can see that alternate conformation, called Ltn40, at right (explore this structure at the PDB). As you can see, this structure is dimeric, taking the form of a β-sandwich. The β-sheets themselves have a sort of Greek key meander arrangement. You can learn more about β elements, protein topology, and protein structure at Larry Moran's Sandwalk. This new fold buries a substantial number of hydrophobic side-chains between the β-sheets. At the same time, a preponderance of positively-charged residues is exposed to solution. The α-helices of the chemokine structure appear to unfold completely, a new β-strand forms at the N-terminus, and the existing sheets shift their hydrogen-bonding register by one residue, meaning that β1 and β3 are rotated 180° along their lengthwise axes.

The existence of two native folds under reasonable physiological conditions (K_eq near one at 37 °C) poses two questions. The first is whether and how fast the structures interconvert. The fact that the equilibrium of a given sample can be shifted with temperature and ionic strength implies that this is an active equilibrium, i.e. that the energy barrier is low enough to cross using just thermal energy. Tuinstra et al. used an NMR experiment to establish that interconversion takes place on a timescale of about 100 ms.

The second question that naturally comes to mind is whether the two structures have different functions, and what those functions are. With a few clever experiments in which they used mutations to stabilize one fold or the other, Tuinstra et al. demonstrated that only the Ltn10 fold activates the partner GPCR, and only the Ltn40 fold binds to heparin, a polysaccharide often found in the ECM. Thus, neither fold possesses the full range of biological functions of lymphotactin; in order to fulfill its biological role it must switch between these structures in vivo. Moreover, the exclusivity of these functions between folds naturally suggests a switching mechanism for regulation.

This is an interesting and important finding because it is (so far) the only example of a protein adopting two completely different stable folds with no hydrogen bonds in common at equilibrium. Trivially, natively disordered proteins adopt multiple conformations under physiological solution conditions, and many proteins alter their conformations in response to ligand binding while keeping most of their hydrogen bond network intact. In this case, however, an existing network of stabilizing bonds is completely disrupted in order to form a new fold with a totally different function. I've already discussed some of the implications of this with respect to protein folding, and in regards to the recent transitive homology studies out of the Cordes group. Lymphotactin offers lessons and ideas for protein folding and evolution that must be taken into account. In particular, the fact that point mutations can significantly stabilize one or the other of these structures implies that there may be previously unsuspected shortcuts through structural space between folded states that avoid unproductive or energetically unfavorable molten globules.

In addition, these results signify that the Anfinsen paradigm that dominates our understanding of protein structure ought not be taken for granted. In many cases it is true that a peptide sequence uniquely determines a single structure under all physiological conditions. Of course we have known for some time that certain peptide sequences do not produce ordered structural ensembles at all. What the lymphotactin example makes crystal clear is that a given sequence can yield an ensemble with multiple energetic minima that reflect related but topologically distinct structures. Tuinstra et al. suspect that this phenomenon has not been noted previously because structures of this kind would not be amenable to crystallization, or would only crystallize in one (of many) structures. If this is so, then as more and more proteins are studied using solution techniques under physiological conditions we may find multiple structural minima in a variety of proteins. Such discoveries may significantly enhance our understanding of the protein regulation, function, and evolution.

1. Tuinstra, R.L., Peterson, F.C., Kutlesa, S., Elgin, E.S., Kron, M.A., Volkman, B.F. (2008). Interconversion between two unrelated protein folds in the lymphotactin native state. Proceedings of the National Academy of Sciences 105 (13) 5057-5062. DOI: 10.1073/pnas.0709518105

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Enzymes almost as good as Ma Nature used to make

Biological systems have the interesting property that most of the reactions enabling life processes are, when left to their own devices, exceedingly slow. To reach the timescales that we associate with "living", these reactions must be sped up, which requires the presence of enzymes. Because they significantly enhance reaction rates under conditions that can be encountered almost anywhere, the design of artificial enzymes is an active area of research. In two papers this month, David Baker's lab describes notable success in designing enzymes in silico to have specific activities with significant (10⁶-fold) rate enhancement.

As a graduate student at UNC, I was fortunate to interact frequently with Richard Wolfenden, who did a great deal of work to find out just how good enzymes are at what they do (1). The fact is that there is a wide range of activities and rate enhancements. The proline isomerase cyclophilin, for instance, achieves a modest 10⁶-fold rate increase, depending on the substrate. In contrast, arginine decarboxylase achieves an amazing rate enhancement of about 10¹⁹. Many reactions we think nothing of, such as hydrolysis of a phosphodiester bond (found in nucleic acids) would take millions of years in pure neutral water at 25° C. Of course, deviations from neutral pH and the presence of other molecules greatly enhance these rates, and obviously the same is true of changes in temperature, but this is a useful starting point for comparing enzymes to basal rates.

In the works at hand, collaborative teams involving several labs coordinated by David Baker designed enzymes to perform a novel retro-aldol reaction (2) and the Kemp elimination from 5-nitro-benzisoxazole (3) (a proton abstraction causing a ring to open). The retro-aldol paper is fascinating, particularly because of the multi-step nature of the reaction, but I'm going to focus on the Nature paper because its results are more complete, in that they implemented an appropriate wet-lab extension to the computational procedure.

The fundamental strategy of both papers is the same. For most enzymes it is believed that catalysis occurs because the transition state, the moment when the chemical reaction has the highest energy, is stabilized by the functional groups of the enzyme (see (1), among others). Using their knowledge of chemistry, the researchers of these groups predicted a transition state, and then positioned functional groups of side chains in such a way that they would stabilize this predicted state. They also placed potential bases in an appropriate geometry to attack protons as necessary. This done, they used a program based on Baker's ROSETTA to predict sequences that would fold to produce this geometry. This required a somewhat more complicated process in the case of the retro-aldol reaction due to its multiple steps.

One interesting outcome was that TIM barrels were a popular choice of this algorithm in both papers. The final results in the Röthlisberger paper are all based on backbones identified by CATH as TIM-barrel folds (explore these scaffolds at the PDB: 1thf, 1a53, 1h61, 1jcl). As the authors note, the TIM barrel is a very common catalytic scaffold in nature, in part because the central β-strands provide a convenient way to orient side-chains towards the catalytic pocket. In both papers, the structures predicted using the ROSETTA algorithm were shown to be very close to the actual result, although they only checked successful catalysts. A comparison of the failed designs to their predicted structures may be of great use in refining the computational approach.

As the above paragraph implies, the groups did in fact succeed in designing enzymes that achieved significant rate enhancements. In the case of the Kemp elimination, the eight enzymes reported had ~5x10³ - 2x10⁵ -fold increases in rate over the spontaneous reaction in a very slightly basic solution. This amounted to actual k_cat (reaction rate) values of 0.006 - 0.29 s^-1, which is significantly slower than is common for enzymes.

In order to improve these results, Röthlisberger et al. turned to the process that produced our own prodigious enzymes in the first place, i.e. evolution. Using a relatively standard in vitro evolution approach, they altered one of the early successes, KE07, which had a k_cat of 0.018 s^-1. Keep in mind, this was not the best computational design result, just one of the first that worked. This in vitro evolution procedure, in just a few rounds, produced an enzyme with a k_cat of 1.37 s^-1. While this is still slow for an enzyme, it represents a rate enhancement of ~1x10⁶ over the spontaneous reaction in solution, an acceleration comparable to that of a modest enzyme like cyclophilin.

This is nowhere near a complete journey. I've already mentioned that the enzymes produced in these experiments are still quite slow in comparison to the genuine article, and the rate enhancements are still modest. The specificity of the enzymes also has yet to be proven—can these proteins distinguish their targets from a sea of similar molecules, or are they promiscuous catalysts? A further dissection of the failed designs is essential to refining the computational approach employed. More careful consideration of effects beyond the secondary shell, and (as the authors note) backbone dynamics and loop positioning may prove particularly helpful in future iterations.

So, we are not all the way to the creation of a truly proficient man-made enzyme, but this is a tremendous step in that direction. The combination of wet lab and computational approaches proved to be very successful in this case. In principle, it should be possible to incorporate all that was learned in the in vitro evolution experiments into the design algorithm from the start. We will not be designing custom catalysts for biofuel production and bioremediation tomorrow or next week. These results, however, demonstrate substantial promise for the future.

In particular, the retro-aldol paper suggests that this approach will work for multi-step reactions. However, provided that the intermediates are stable and soluble this will not be strictly necessary. So long as efficient catalysts can be designed for each step, the ability of ROSETTA to design protein-protein interfaces will make it possible to assemble functional synthetic or catabolic enzyme cassettes to achieve very complex chemistry with tremendous accelerations over basal rates.

1. Wolfenden, R., Snider, M. (2001). The Depth of Chemical Time and the Power of Enzymes as Catalysts. Accounts of Chemical Research, 34 (12), 938-945. DOI: 10.1021/ar000058i

2. Jiang, L., Althoff, E.A., Clemente, F.R., Doyle, L., Rothlisberger, D., Zanghellini, A., Gallaher, J.L., Betker, J.L., Tanaka, F., Barbas, C.F., Hilvert, D., Houk, K.N., Stoddard, B.L., Baker, D. (2008). De Novo Computational Design of Retro-Aldol Enzymes. Science, 319(5868), 1387-1391. DOI: 10.1126/science.1152692

3. Röthlisberger, D., Khersonsky, O., Wollacott, A.M., Jiang, L., DeChancie, J., Betker, J., Gallaher, J.L., Althoff, E.A., Zanghellini, A., Dym, O., Albeck, S., Houk, K.N., Tawfik, D.S., Baker, D. (2008). Kemp elimination catalysts by computational enzyme design. Nature DOI: 10.1038/nature06879

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Arthur C. Clarke dead at 90

It's a sad day for lovers of science fiction, as Sir Arthur C. Clarke has passed away. Clarke has always been one of my favorite authors, mostly on the strength of Rendezvous with Rama. Of course, I'm also a huge fan of his more famous work, 2001: A Space Odyssey. More than Asimov's misbehaving robots, Clarke and Kubrick's HAL with its baleful red eye fixed in the public imagination the dangers of creating machines that can think for themselves. Clarke is also credited with popularizing the idea of placing telecommunications satellites in geosynchronous orbit (often called "Clarke orbits") in order to allow rapid global communication worldwide. Clarke was a man full of visions of the future. Some of them, like the satellites and a visit to the moon, have come to fruition already. Others, like the space elevator, functioning colony ships, or Pan-Am jets in space are somewhat further from reality.

Much modern science fiction is pessimistic, suffused with the idea that technology will always be misused, will always turn on its creators. Clarke certainly was not free of this idea: HAL is a cultural icon of advancement gone awry. Yet Clarke was always fundamentally optimistic about the possibilities that science opened for human beings. His worlds were ones in which imperfect people using imperfect technologies nonetheless managed to do great, amazing things. That's a possibility we ought to keep in mind for ourselves, too.

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It's the most wonderful tiiiiime of the yeeeear!

My post rate, never among the most prodigious on the intertubes, will drop off a bit for the next month or so as a significant portion of my post-writing time will be consumed by one of my favorite sports—college basketball. The ACC tournament starts tomorrow, and the Big Dance soon after, which means that I will be watching the television and trying to ignore Dick Vitale, Billy Packer, and Bill Raftery, or at least hate them to death.

Since my beloved, hapless 'Hoos have essentially zero chance of playing their way into the tournament at this point, I'll have to settle for keeping an eye on these three teams:

UNC—Having defeated the hated Dookies at Cameron once again, I'm hoping that my 'Heels can turn their momentum and improving health into a national championship. This guy to the left will have a lot to do with that, I'm sure.

Mississippi State—It's that family loyalty thing. I hope the Bulldogs don't end up in a region with UNC; that way I can still root for them to make the Final Four. The SEC West champions haven't picked up much buzz in what seems to be widely perceived as a down year for the conference, but they might be able to put together a good tournament run.

UAB—It's not looking so good after that terrible loss in the rematch with Memphis. Still, if the Blazers play their way into the C-USA Championship Game and don't get blown out by Memphis then they have a pretty good chance of making it in. As long as Vaden is hot, they have a chance to make some noise, though I doubt they'll go farther than the Sweet Sixteen.

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I continue to beat this horse because it is a zombie

I know, I know... you're pretty darn sick of seeing me beat up on corn ethanol in this space. To be honest, I'm a little sick of it, too. However, the idea is so appealing on its surface, so desirable to the agricultural lobbies, and so pernicious in its environmental effects that I feel I have no choice but to do whatever I can to publicize the very good research indicating its flaws and dangers. Increasing awareness of the problems associated with corn ethanol mandates is the only way to kill that horse and make it stay dead. The corn ethanol lunacy of our would-be Presidents was most clearly on display before the Iowa caucuses, but don't think just because the politicians aren't talking about it that the issue has gone away.

So that's why I'm talking about a paper (now in PNAS preprints) by Simon Donner and Christopher Kucharik on the effect of corn ethanol on the oceans (1). Given that we do not actually grow corn in the ocean, this might seem like a bit of a stretch. But the existence of rain and rivers means that what we put in the soil almost always ends up in the sea, where it often has significant effects.

The problem corn causes for the ocean is hypoxia. As you should be aware, there is an enormous (>22,000 km²) seasonal hypoxic region or "dead zone" in the Gulf of Mexico. Fresh water efflux from the Mississippi bearing significant concentrations of nitrogen-rich fertilizer is believed to cause the hypoxia primarily through eutrophication. Beyond being undesirable on its own merits, the dead zone puts fisheries at risk, and eutrophication can contribute to toxic algal blooms. So whether you care about the environment or the economy of coastal regions you have good cause to want to mitigate nitrogen fertilizer pollution.

But that's a problem, because corn is a pretty fertilizer-intensive crop. Given that making ethanol for transportation from corn starch will probably require a significant increase in corn production, Donner and Kucharik asked what effect the changes in agriculture would have on the amount of dissolved inorganic nitrogen (DIN) exported to the Gulf of Mexico. I have shamelessly stolen the figure to the left for your benefit. As you can see, they tested their forecasting model against several scenarios. The control was just to check export for the years 2004-2006 using the model against known data. The 2007 column is a prediction for last year. Then they get to the models forecasting export in the case of 15 billion gallons of production under two land-use scenarios, and a situation where radical changes in land use allow the production of all 36 billion gallons of mandated biofuels as ethanol from corn. As you can see, none of these situations even come close to reducing DIN to desired levels, though arguably the "optimistic" (left) 15 billion gallon scenario isn't too much worse than the status quo.

Of course, there is that last one, which reflects a Panglossian possibility in which red meat production is cut in half, the corn once destined for feed is repurposed for ethanol, and wetlands that filter out 35% of DIN are created around all corn and soybean farming land. Basically, this plan depends on a dramatic increase in the popularity of vegetarianism, as well as some extremely unrealistic behavior by farmers and federal land planners. The upshot of it all is that reaching biofuel production goals through corn ethanol is almost certain to increase the amount of nitrogen reaching the Gulf. Of course, this is a computer model of future outcomes, and as such, the results reflect the assumptions made in the construction of the model. However, the authors generally appear to err on the side of favoring ethanol. In the "optimistic" 15 billion gallon model, for instance, annual yields continue to increase without any additional fertilizer use per plot.

Of course, this will be a problem for other biofuels as well. Switchgrass can be grown on marginal lands with decent yields. However, biofuel demand will create an economic incentive to improve output; one convenient way to do this is to fertilize. Even if a relatively small amount of fertilizer is used on every switchgrass plot, that will still be an enormous increase over the amount of fertilizer used on those plots previously (i.e. zero). The ill effects of poorly-conceived biofuel initiatives will not be limited to economic disruptions and increases in greenhouse gases—enormous tracts of biofuel monocultures will have pronounced effects on ecosystems nearby and downstream. Before we take the plunge on massive initiatives we need to study the outcomes, and ask whether what we are doing achieves more harm than good. Too bad our would-be leaders only seem interested in pandering for votes and campaign funding.

1. Donner, S.D., Kucharik, C.J. (2008). Corn-based ethanol production compromises goal of reducing nitrogen export by the Mississippi River. Proceedings of the National Academy of Sciences DOI: 10.1073/pnas.0708300105

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Protein Structure from Chemical Shifts Alone

Unless you have extremely good luck or a lot of supporting information, deriving a protein structure from NMR data is an enormous pain in the ass. First, you have to assign the resonances of the protein—that is, you must determine the chemical shifts of most or all of the protons in the protein, which in turn entails figuring out the chemical shifts of most of the carbon and nitrogen atoms as well. Then you have to acquire nuclear Overhauser effect (NOE) and/or residual dipolar coupling (RDC) data to figure out how far the atoms are from each other and how some of the bonds are oriented. Automated NOE assignment programs make the analysis of all this data less onerous than it once was, but particularly if your protein has non-ideal relaxation characteristics, scraping together enough data to derive a structure can be a tough task. The most irksome thing about it is that in principle, all the structural information you could ever want is contained in the chemical shifts you figured out in the very first step. What if you had a technique that could figure out a structure just from them?

First, a little more explanation about chemical shift. The local chemical structure dominates the chemical shift in most cases—you expect to find a proton in a particular place based on whether it's in a methyl group or bound to a nitrogen. Additionally, the chemical shift is sensitive to local bond angles. Surrounding groups (especially aromatic rings and paramagnetic atoms) can also alter the chemical shift substantially. However, the chemical shift is an ensemble averaged property. We cannot receive NMR data from a single molecule; as a result the observed chemical shift reflects every conformation in the ensemble and also (to some extent) the interconversions between those conformations. Because it should be possible to reconstruct an entire protein structure just knowing the local information about bond angles, it should in principle be possible to use chemical shifts to reconstruct the average conformation. The problem is that all these different factors get mashed up into a single number, often in contradictory ways. Parsing the purely structural factors (bond angles) out from this single number has proven difficult. Dihedral angle restraints based on chemical shifts have been used for many years, but only as a component of a more complete structural determination using NOEs or RDCs.

However, a series of publications over the past year or so has pointed towards some steady progress towards developing structures from chemical shifts alone, with a paper from the labs of Ad Bax and David Baker now in PNAS preprints showing some of the best progress yet (1). The approach used much resembles the CHESHIRE method described last year by Michele Vendruscolo (2), in that both are based on fragment replacement. The Vendruscolo group's paper explicitly compares CHESHIRE to David Baker's ROSETTA program. So it seems only natural for Shen et al. to incorporate refinements based on chemical shift directly into the ROSETTA program to create CS-ROSETTA.

The standard ROSETTA approach is to break the protein up into small overlapping fragments of several peptides. A library of structures (the PDB) is then searched with these fragments to obtain a set of about 200 potential conformations based on sequence similarity. ROSETTA then attempts to assemble low-energy (stable) structures out of these potential fragment conformations. CS-ROSETTA uses chemical shift data at two distinct steps. First, chemical shift data are used to select the most appropriate potential conformations from the library, theoretically improving the "building materials" for ROSETTA. In later stages, the consistency between the ROSETTA-predicted structures and the known chemical shifts is used to re-score their energy.

That this can significantly improve the ROSETTA output can be seen from the part of Shen et al.'s Figure 2 that I have shamelessly stolen for your benefit. These are predictions for calbindin (B) and HPr (C), with the ROSETTA predictions on top and the rescored energies on the bottom. As you can see, the calbindin structures do not have a well-defined energy minimum in the ROSETTA prediction, and the HPr structure has three minima which are not all close to the actual structure as measured by Cα root mean square deviations (RMSDs). Rescoring, however, produces funnel-shaped distributions of energy with respect to RMSD, such that low energies reliably indicate structures close to reality.

Shen et al. optimized CS-ROSETTA against 16 known structures. I checked their results back against the CHESHIRE results. Five proteins were predicted in both papers, and CS-ROSETTA did a better job in terms of backbone atom RMSD for four of them. On average, CS-ROSETTA produced a 24% reduction in this RMSD relative to CHESHIRE. Also, Shen et al. tested CS-ROSETTA blindly against nine proteins whose structures had been recently solved by the Northeast Structural Genomics Consortium, with favorable results.

This isn't the end of the road by a long shot. Backbone RMSDs for these predictions are generally <2 Å, which is easily good enough for picking out general characteristics of a fold. Identifying subtle features, however, will probably require higher precision and thus more rigorous refinement. However, having these predicted conformations in hand may significantly accelerate the assignment and refinement of structures using NOE data. Combining fragment-replacement approaches based on RDC data and chemical shift may also produce significant improvements.

There were other limitations. Shen et al. were not able to converge structures for every protein attempted. CS-ROSETTA is presently limited to proteins smaller than many routinely solved by NMR, and proteins with unusual or complicated topologies may not be solvable using this approach. And, of course, the presence of cofactors that significantly alter local chemical shifts will significantly complicate analyses of this kind, if not render them impossible. Obviously, a great deal of work remains to be done before computational approaches will be capable of tackling the large, highly degenerate systems where they would have the most power to resolve problems. However, the excellent results of CHESHIRE and CS-ROSETTA suggest that our ability to derive structures from limited NMR data will improve dramatically in the next few years.

1. Shen, Y., Lange, O., Delaglio, F., Rossi, P., Aramini, J.M., Liu, G., Eletsky, A., Wu, Y., Singarapu, K.K., Lemak, A., Ignatchenko, A., Arrowsmith, C.H., Szyperski, T., Montelione, G.T., Baker, D., Bax, A. (2008). Consistent blind protein structure generation from NMR chemical shift data. Proceedings of the National Academy of Sciences, 105 (12), 4685-4690. DOI: 10.1073/pnas.0800256105

2. Cavalli, A., Salvatella, X., Dobson, C.M., Vendruscolo, M. (2007). Protein structure determination from NMR chemical shifts. Proceedings of the National Academy of Sciences, 104(23), 9615-9620. DOI: 10.1073/pnas.0610313104

POSTSCRIPT: You can read another take on this paper at Plausible Accuracy.

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Why are Xfaso and Pfl Cro so different?

A few weeks ago, when I posted on the transitive homology studies performed by the Cordes group, I promised a closer look at the structures when they became available. If you'll recall, one of the central findings of the Roessler et al. paper (1) was that the Xfaso and Pfl 6 Cro proteins, though they had 40% sequence identity, as well as an identical function, had very different structures and dimerization characteristics. The Pfl6 Cro structure is now available in the PDB, and Dr. Cordes was kind enough to send me the Xfaso Cro structure, which has been held up by some technicalities. I made the overlay of the structures to the left, with Xfaso in dark green and Pfl 6 in crimson. As you can see, the N-terminal helix-turn-helix motifs of the two molecules overlay very precisely, with some slight differences in orientation in the context helices. The C-terminal portions, of course, are completely different. How did they get to be this way?

Well, I have a few thoughts. To achieve a significant change in structure like we have here, two possibilities suggest themselves. We can destablilize one structure, or we can stabilize the other. So let's try to look at this from both angles. First, the Xfaso structure, which is on the left. The ribbon is orange for residues that don't change between the two proteins, green for mutated sites, and red over a deleted range. I've also drawn in a couple of the mutated side chains that might have an effect. For instance, at the upper right you can see a glutamate of Xfaso Cro that becomes a glycine in Pfl cro. The presence of the glycine may destabilize the helix. Lower on the helix, a solvent-exposed arginine becomes a hydrophobic leucine in Pfl; likely the structure will change to reduce the contact of the leucine with water. By the same token, a partially-buried threonine at the base of the helix gets mutated to glutamate. Not only might this put an unsolvated negative charge inside a hydrophobic region, but favorable helix-capping interactions of the threonine might be broken. Roessler et al. also point out that a pair of cysteines in the Xfaso structure are in a favorable position to form a disulfide bond; both are absent from the Pfl6 sequence.

On the other side of things, what mutations are stabilizing the new fold of Pfl 6 Cro? Check out the image below, color-coded the same way as the previous structure:
There are a couple of things going on here. First, the hydrophobic residues. The leucine that was an arginine in Xfaso Cro has indeed been buried, up at the top of the structure. Nearby, the glutamate that was a partially-buried threonine in Xfaso is now fully solvent-exposed. In the same vein, an aspartate has become an isoleucine near the middle. This new isoleucine appears to pack into the core of the companion protein near a conserved isoleucine (and a new methionine), and probably accounts to some degree for the stability of the dimer. There are a wealth of minor effects too—an alanine to arginine mutation has created a charged group that is solvent stabilized on one of the strands; down near the bottom a proline-to-arginine change probably has allowed the extension of a helix. Some other side-chains are drawn that I was taking a look at, but probably aren't critical, and of course I've probably missed a few that matter.

The R→L, T→E, and D→I mutations probably do a great deal to change the most stable conformation from all-α to α/β and strengthen dimerization in solution. However, just from looking you can never be sure what mutations are the most important. Doubtless the Cordes lab is already examining which residues are critical in altering the conformation. It will be interesting to see whether point mutations tend to move Xfaso from the all-α to the mixed structure, or whether they produce molten globules.

1. Roessler, C.G., Hall, B.M., Anderson, W.J., Ingram, W.M., Roberts, S.A., Montfort, W.R., Cordes, M.H. (2008). Transitive homology-guided structural studies lead to discovery of Cro proteins with 40% sequence identity but different folds. Proceedings of the National Academy of Sciences, 105(7), 2343-2348. DOI: 10.1073/pnas.0711589105

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Allostery without conformational change

Allostery is a strange-looking word for a relatively simple idea: regulation at a distance. Binding events at one location on a protein can influence binding events that are relatively far away. It is allostery—in the form of cooperative binding in hemoglobin—that makes our oxygen-delivery system work. Because it provides an alternative way to attack drug targets, allosteric regulation is an attractive possibility for new medicines; recent results suggest that allosteric inhibitors may have promise in the treatment of diseases related to hormone receptor activation. Yet, as interest increases in the therapeutic potential of allosteric drugs, structural biologists are re-evaluating what allostery really means.

In the classic view of allostery, binding of one ligand at one site provokes a large conformational change that alters the affinity of another site for its ligand. Without denying that this conception of remote regulation has proven phenomenally successful, we can still ask whether models of this kind cover the full breadth of possibilities. Chung-Jung Tsai, Antonio del Sol, and Ruth Nussinov ask precisely that in their article now in press at the Journal of Molecular Biology (1). They find, based on an allosteric protein "benchmark", that significant backbone deformations are not an essential characteristic of allosteric effects. They therefore state that allostery might arise not only from large conformational changes, but also from changes in dynamics.

This is not a new concept—the possibility that allostery could be driven by entropic effects was articulated as early as 1984 by Cooper and Dryden (2). It seems like an odd idea, in part (I believe) because most of the analogies we use to describe allostery involve obvious changes of shape. But even stably folded proteins undergo significant fluctuations—at a fundamental level, especially when it comes to side chains, their shape is fluid. This imparts a substantial configurational entropy, which could be important in regulating binding.

Almost any binding event, irrespective of the structural dynamics of the protein or ligand, results in a decrease in the entropy of the system because the translational and rotational degrees of freedom of the protein and ligand are no longer independent. It is normal, although not always the case, that binding a ligand also significantly reduces the configurational entropy of the protein. These entropic costs are offset by energetic benefits of binding.


So, let us consider a protein that binds two ligands at different sites (see my figure cave drawing at right; CE = configurational entropy), such that neither binding event significantly alters the overall conformation. Binding of ligand A, however, might still be expected to decrease the fluctuations in the immediate vicinity of the binding site. If that's all that happens, then binding of ligand A does not alter the binding of ligand B (case I). Let us imagine, however, that the rigidification spreads from the "A site" to the "B site" (case II). Such a rigidification might pre-organize the B site; in this case the entropic cost of binding B is reduced. Thus, the binding is enhanced. Obviously, this could work the opposite way as well. It is known that binding a ligand sometimes increases the configurational entropy of a protein. If this increased entropy is communicated to the B site, then the entropic penalty for binding B and rigidifying that site is increased (case III). So depending on the system, either positive or negative allostery is possible. Tsai et al. discuss these and other models in greater detail.

Is it in fact possible for dynamic effects to be "transmitted" through a protein? As Tsai, et al. point out, previous research indicates that it is, even in relatively small globular domains. Ernesto Fuentes demonstrated that peptide binding to a PDZ domain induced changes in side-chain dynamics on the back side of the protein (3). As I discussed previously, this communication pathway has been associated with an allosteric interaction between two PDZ domains in PTP-BL. Moreover, Andrew Lee and some weirdo demonstrated that similar effects occurred in a protein of the potato inhibitor I family that lacked any discernible allosteric behavior whatsoever (4). Beyond proving that dynamic effects are transmissible, results of this kind support the idea that allosteric potential is a property of proteins generally (5).

The Tsai et al. paper is meant to reinforce and develop the concept that allostery is not solely a feature of proteins or complexes that undergo large conformational rearrangements in response to particular ligand-binding events. Small changes in backbone conformation or altered dynamics may also be responsible for allosteric effects. This may sound significantly different from present views of allostery, but in a sense it does not alter the classic interpretation. Rather, this new view points to a deficiency in the classic understanding of "conformational change". A genuine understanding of a protein's structure is not captured by a single conformation, but rather by the structural dynamics of a conformational ensemble. In some cases, i.e. the classic examples, the structural effects of ligand binding take the form of a change in the energy distribution: a particular subset of conformations becomes lower in energy and thus becomes more populated. In others, however, binding results in an elimination of possible sub-states of a given backbone conformation. Both outcomes significantly change the conformational ensemble, and both of them can produce allosteric effects.

1. Tsai, C., del Sol, A., Nussinov, R. (2008). Allostery: Absence of a change in shape does not imply that allostery is not at play. Journal of Molecular Biology DOI: 10.1016/j.jmb.2008.02.034

2. Cooper, A., Dryden, D.T. (1984). Allostery without conformational change. European Biophysics Journal, 11(2), 103-109. DOI: 10.1007/BF00276625 OPEN ACCESS

3. Fuentes, E., Der C.J., and Lee A.L. (2004). Ligand-dependent Dynamics and Intramolecular Signaling in a PDZ Domain. Journal of Molecular Biology, 335(4), 1105-1115. DOI: 10.1016/j.jmb.2003.11.010

4. Clarkson, M., Gilmore, S., Edgell, M., Lee, A. (2006). Dynamic coupling and allosteric behavior in a nonallosteric protein. Biochemistry, 45(25), 7693-7699. DOI: 10.1021/bi060652l

5. Gunasekaran, K., Ma, B., Nussinov, R. (2004). Is allostery an intrinsic property of all dynamic proteins?. Proteins: Structure, Function, and Bioinformatics, 57(3), 433-443. DOI: 10.1002/prot.20232

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Thoughts on game critiques

That last post was actually extremely difficult to write. I had the ideas for it quite a long time ago, and I think I did a pretty good job of explaining how the various aspects of the presentation and gameplay produced a gestalt related to the Prince's maturation process. But when I wrote a draft of that post yesterday morning, it sucked. It may have been the worst thing I ever wrote. For one thing, it had a completely awful structure. Also, it was about three times as long as what I eventually published. I ended up excising a lot of points that I really liked because they didn't add to the critique. I'm not going to print any of those here, but I want to make a few points about game critiques in general, and about games themselves. Your responses are of course welcome; indeed I eagerly request them.

1. "Critique" versus "Review" posts

This was really the hardest thing to nail down. I had all sorts of points about the crispness of controls, character and enemy design, navigability, sound balance, and so on, and I ultimately excised almost all of them. Essentially technical items like these would have been really great to discuss in a review, but they didn't belong in the piece I was writing, which I wanted to be something different. A review is just a piece of writing that tells you what it's like to play the game, and that's important. But what I was after was not technical aspects but rather an exploration of theme and meaning, and an analysis of how the various features of the game—from writing to presentation to mechanics—served that meaning. I felt this tension when writing the FFXII post too, and because I didn't resolve it, that one didn't turn out as well as I would have liked. It would be nifty to do both at the same time, but especially when handling a trilogy like the Prince of Persia games that produces a piece that's simply too long, and it interferes with structure.

So I probably will never write anything that's both a review and an artistic critique. My Persona 3, Phantom Hourglass, Revenant Wings, and Professor Layton posts fall in the former category, while the posts on Silent Hill 2, Final Fantasy XII, and Prince of Persia better fit the latter. And, I think, since there are a ton of game sites writing reviews, I'm probably not going to put any more straight reviews up here, though I will probably write a few on accessible games for Love Camel. What I put up here, though, I want to be focused on artistic criticism. So expect more posts like that last one and less that are like the Revenant Wings one.

2. "Stuff" versus "People" stories

One thought that occurred to me as I was writing the Prince of Persia post was that there are two main ways to think about stories, both of which showed up in that trilogy. The most common way to encounter a story in a video game is as a recounting of stuff that happens (this is the approach of Warrior Within). There are characters in the story, but very little about them matters to it, and seemingly little about it matters to them. The characters are just part of the stuff that's happening. Alternately, the story can be viewed as people that happen. Stuff happens as well, but what the story is really about is not the stuff, but the way the characters interpret and respond to the stuff. Moreover, the people "happen" not just in that they are, but in that they become. The strength of Sands of Time and The Two Thrones is not just that the characters are fully realized and interact charmingly, but that the Prince changes and grows. I think that this sort of transition is a critical part of successful stories, especially in games where the player can be brought along for the change.

3. Expressive versus Narrative games

Thinking about games strictly as narratives is obviously too constricting. The approach I used in the critiques I've already written clearly relies on this mode of understanding, which may be an intrinsic limitation. One thing I think I need to try is to do one of these critiques for a purely (or nearly so) expressive game, that is, one that tries to induce an emotion rather than convey a story. I'm leaning towards trying a critique of Katamari Damacy, just to see if I can do it.

4. Art versus Entertainment

I made this point in my previous rant, too. There are games that really aren't intended to mean anything, that exist purely to be entertainment. They are the potato chips of gaming: tasty, filling, and fun to consume, but without lasting nutrition for body or mind. And there are also games that have nutritional value, but aren't expressive or narrative (i.e. Brain Age). I don't think this is a problem for games as art: nobody denies that Citizen Kane is art on the basis that Predator and classroom film reels aren't. I am, however, not certain of the value of trying, as film critics do, to interpret the pure entertainments in the same way as I do the meatier fare. I'm just one guy, after all, and the internet has plenty of sites that can tell you that dual-wielding is awesome.

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"Time is an ocean in a storm..."

The modern Prince of Persia trilogy begins almost inexplicably—a man stands on a balcony that looks out into a thick jungle. All he can do is enter a palatial building through swaying drapes. Then come the images—a drop of water, the desert, a beautiful woman—and the story begins:

Most people think Time is like a river that flows swift and sure in one direction. But I have seen the face of Time, and I can tell you, they are wrong. Time is an ocean in a storm. You may wonder who I am, or why I say this. Come, sit down, and I will tell you a tale like none you have ever heard...

Impressively, this is true; more impressively, the tale is actually good.

Megaspoilers below the fold.

The man telling the story is the Prince himself, and the game in which he tells it, Sands of Time, is deliberately constructed to evoke the feel of the 1001 Nights. As the game progresses, the Prince's narration occasionally explains where you are or what he's feeling. When the player dies, the Prince steps in to correct him: "No, no, no, that's not what happened."

The characters are also evocative of the 1001 Nights. The Prince himself is the main character, accompanied by the Maharajah's daughter Farah. His opponent, the treacherous Vizier, first betrayed the Maharajah to the Persians, and then betrayed his new master by tricking the Prince into opening the Sands of Time. This mystical substance has destroyed the palace of Azad and infected its inhabitants. In order to "undo what he has done", the Prince must traverse the crumbling ruins to confront the Vizier and re-seal the Sands in their Hourglass. Along the way, he must mature from a sarcastic young charmer fixated on honor and glory into a responsible adult who properly understands his duty as a person.

To do this, he must use an array of acrobatic skills. The Prince can run up or across walls, jump great distances, balance on beams, swing on poles, and cling to precarious ledges. The challenge of the Prince of Persia games is to figure out which route to use through a landscape, and which skills must be used. Then, precise timing is often required to make it through. Mistakes are inevitable, but the Prince can survive them using the Dagger of Time which he finds early in the game. With this, he can rewind time back to a moment before his failure, or slow down time to make evading a trap easier, or even freeze his opponents in time.

The Prince's first confrontation with the Vizier ends in failure. Despite the bond that has grown between him and Farah on their journey through the ruins, he distrusts her at the critical moment and the Vizier casts them down into a tomb. They escape, but the price of his failure is that Farah steals the Dagger. But because she is not a warrior, she dies en route to the Hourglass. Filled with remorse and aware of the futility of fighting for honor and glory, the Prince at last heeds her words and plunges the Dagger into the Hourglass. The effect is to rewind time all the way back to before the Vizier betrayed the Maharajah. As the story ends, it becomes clear that the whole game that was played was the story the Prince was telling to Farah to warn her of the Vizier's treachery.

The final combat with the Vizier is a rather mundane sequence; properly viewed as an epilogue rather than the final boss. The true final boss of the game, as others have noted, is the Tower of Dawn, which the Prince must climb using all his skill but without the Dagger. This is a critically important key to understanding what the Prince of Persia games are really about. The platforming, motion, and timing are the essence of the game. Farah's criticism of fighting as futile is also important to this point.

Yet the developers themselves did not understand it. In the sequel, Warrior Within, the focus is on combat. Because Sands of Time was criticized for its repetitive and excessive fighting, the developers attempted to address this by creating more unique fighting moves. This was an attempt to solve the wrong problem. The fundamental flaw with the combat was not that it was dull or there was too much of it, though both these things were true. The problem was that the combat had nothing to do with the rest of the game.

The platforming and combat aspects of gameplay in Sands of Time did not interface well, to the point where it felt like you were playing two different games. One of them was a magnificent platformer, and the other was a mediocre hack-and-slash game. The careful timing, exhilarating acrobatics, and understanding of the environment that were the core of the platforming were abandoned when the swords came out. Thus, the player had to shift gears every time a battle started. Jerry Holkins likened the feeling to ordering a pizza and getting a free walrus. Any step to "fix" the combat that did not recognize this divide was doomed to failure.

In Warrior Within The Prince, pursued by the demonic Dahaka for the crime of opening the Sands, flees to the Isle of Time to prevent their creation. He fundamentally does not change his behavior—when he accidentally creates the Sands of Time by killing the Empress Kaileena, his answer is to go back in time to fix his error. He succeeds in doing this, and also kills the Dahaka. The Prince's failure to change as a human being is accompanied by an intellectual regression in the game itself. Farah's rejection of violence is cast aside, and in a way she is ridiculed from afar by the game's glorification of violence and puerile, chauvinistic sexuality (best evinced in Shahdee's outfit). Granted, a chauvinistic viewpoint (the Prince's) was also present in Sands of Time, but there it was used to ridicule the Prince and demonstrate his childishness. In Warrior Within the chauvinist's view is celebrated. Moreover, every aspect of the 1001 Nights influence vanishes, replaced by generic architectural and musical elements; the narration is excised completely. As a cumulative effect of these decisions the game is an artistic failure.

Warrior Within alienated many fans of Sands of Time, but all the errors were fixed in the finale, The Two Thrones (or Rival Swords in its Wii incarnation). The Prince returns to Babylon with Kaileena, who narrates the tale, recovering this part of the atmosphere. The classic characters also return, for the Prince finds the city ravaged by the Vizier, who has overthrown the Maharajah, imprisoned Farah, and invaded the Prince's kingdom, with the intention of seizing Kaileena. He succeeds in doing this, and the Prince, still acting as he did in Warrior Within, attacks recklessly and fails to save her. She dies, releasing the destruction of the Sands of Time within the city, and also into the Prince. He comes away from his failure with nothing other than the Dagger.

The Sands give rise to an alter ego—the Dark Prince, who in form resembles a sand monster, and whose personality is the purest articulation of the man the Prince was in Warrior Within. As the Prince works his way back to the Vizier for a final confrontation, the Dark Prince constantly urges him into combat and seduces him with promises of bloody vengeance. Farah once more argues against this path, ultimately convincing the Prince himself. For the Prince, hearing his dark half's eulogy of the bloodthirsty warrior, replies, "...what you describe is not a man, but a beast..." Implicit here is a criticism of the very kind of game Warrior Within was, and of what it celebrated.

This is more than just a passing note from the writers, for the game itself constantly de-emphasizes the sword-based combat that dominated the earlier entries. While the Prince can fight in this way, the best approach to combat is always to use the stealth-based "speed kill" system. In this sense, "stealth" means moving through the environment to a point above or behind the target, waiting for the right moment, and then engaging in a timing-critical attack sequence. Bloody, violent combat becomes less a part of play, while platforming begins to inform every aspect of the game. The boss fights, once purely combat experiences, become fusions of combat with platforming or timing. The "two games" problem is thus put to rest.

This evolution is best articulated in the fight against the Vizier, which has three phases. The first is a straight-up fight that might have come directly out of Sands of Time. In the second, the Prince must engage three speed kills, and the combat of Warrior Within vanishes. In the last segment, the Prince must navigate a floating maze to reach the Vizier—with this, the death of fighting is nearly complete. Combat has been supplanted by platforming.

Yet the final articulation of the Prince's agreement with Farah comes in the game's epilogue. Here the Prince confronts the Dark Prince in the realm of the mind. To defeat the Dark Prince, platforming is necessary, but the amount of combat needed declines throughout the sequence. In the end, to triumph over the Dark Prince, the player must choose not to fight him, and instead to follow Farah's voice, casting the "warrior within" aside forever. Thus the player's gameplay transition matches the Prince's maturation process.

This is true in another connection as well. Throughout the trilogy, the Prince and the player fix mistakes by manipulating time. This is fundamentally childish, akin to putting a broken lamp back together using Elmer's glue in an attempt to make it seem as if an accident never happened. Yet each repair the Prince performs causes a new problem. Undoing his error at Azad provokes the Dahaka. Going back in time to kill the Empress creates the Sands. Traversing time again to rescue Kaileena from himself and destroy the Dahaka only brings the Empress into the grasp of the Vizier. Near the end of The Two Thrones, when the Vizier has captured Farah and cast the Prince down into the Palace catacombs, he comes across the greatest sign of this failure: the body of his dead father. As the voice of the Dark Prince mocks him, the Prince casts aside the idea of "undoing" his mistakes. He will not rewind time; rather, he will confront his mistakes and their consequences.

The player, who knows all too well (from three games) the attraction of rewinding time to reverse one's errors, is implicitly invited to this kind of maturity. And, by giving up the dagger after the confrontation with the Vizier, but before the game ends, the player is made a part of the Prince's decision. This could have been accentuated more powerfully, as in Sands of Time, by giving up the Dagger when the Prince finds his father, but for story reasons the Dagger must be with him at the top of the tower after the Vizier's defeat. Nonetheless, by playing the final stage (within the mind) without the dagger, the player and Prince are united in confronting the outcome of their mistakes (in this case, the Dark Prince) without trying to "undo" them.

The Prince of Persia trilogy is very uneven; Warrior Within was a significant artistic failure, devoid of the atmosphere and meaning that informed Sands of Time and The Two Thrones. Sands of Time itself was seriously flawed, because of its divided gameplay. Its story and atmosphere, however, more than compensated for that imperfection. These were preserved in The Two Thrones, and moreover that game achieved a gestalt in which the two primary gameplay aspects were unified with each other, and then brought into alignment with the thematic rejection of violence and of "undoing" mistakes. When the Prince repeats his introduction from Sands of Time at the end of The Two Thrones, the story comes full circle, but his enormous growth as a person is undeniable, for the player has participated in it.

Prince of Persia: Sands of Time (highly recommended) and Prince of Persia: Warrior Within (not so highly recommended) can both be played at GameTap. Prince of Persia: The Two Thrones and its Wii counterpart Prince of Persia: Rival Swords are still available for purchase at video game retailers (as of 3/2008). I would regard any video game library as incomplete without The Two Thrones.

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