An enzyme with a monkey's tail

It is rare, but not unheard of, for a human baby to be born with a tail. Atavism of this kind is generally understood to be the result of mutations in regulatory genes that cause an ancestral pattern of development to re-emerge. A physiological step backwards through the path of descent is often easy to recognize, because many of the evolutionary relationships are known. It should also be possible to identify atavistic events in particular molecules. For instance, one can imagine that a mutation to CLC-0 might result in a reversion to the ancestral transporter function. In a recent article in PLoS Biology, researchers from Florida State University and Brandeis University identify just such a relationship in the bi-functional enzyme inosine monophosphate dehydrogenase (IMPDH). PLoS Biology is an open-access journal, so open it up and follow along.

IMPDH plays a critical role in the synthesis of guanine nucleotides, an essential component of DNA. Two reactions take place in the active site — first, the inosine ring is oxidized to xanthosine, forming a covalent linkage with the enzyme, and then this bond is broken by a hydrolysis. The enzyme active site changes shape to carry out the reaction, bringing a catalytic arginine (R418) into position to activate the water for nucleophilic attack. Any time you see a complicated mechanism like this, it's natural to wonder how such a system could have evolved. Min et al. performed simulations and experiments to find out.

Using a crystal structure of IMPDH as a starting point, Min et al. performed hybrid QM/MM simulations in which the atoms taking direct part in the reaction were treated with quantum mechanics, and the rest of the protein was simulated using molecular mechanics. As one would expect given the enormous reduction in catalytic rate that occurs when R418 is mutated, the reaction proceeded through the arginine when the simulation had a neutral R418 side chain. The water is stabilized by two additional side chains from T321 and Y419, and reacts almost instantaneously, without the formation of a stable hydroxide intermediate. Although this is unusual, this prediction of the simulation is consistent with isotope effect experiments.

When the arginine was replaced by a glutamine in the simulation, the mechanism changed, naturally. Under these conditions, it was Y419 that activated the water for the hydrolysis, although the energy barrier was much higher (leading to a slower reaction). Again, the characteristics of the reaction indicated by the simulation line up pretty well with the results of biochemical experiments. Of course, Y419 enters the active site the same way R418 does, so the question of how the hydrolase activity could have evolved remains open.

Something very interesting, however, happens when the simulation is performed with R418 in a charged state. A fully protonated arginine will have a very hard time activating water for a nucleophilic attack. The simulation indicated that under these conditions, T321 performed this role, after being activated by a nearby glutamate (E431). T321 is adjacent to cysteine 319, which is essential for the oxidation reaction, and is not located on the mobile flap. If T321 really can catalyze hydrolysis, this would mean that it is possible that IMPDH possessed an (inefficient) hydrolysis activity before it evolved the mobile flap.

Because T321 only plays a signficant role in catalysis when R418 is protonated, blocking this pathway should result in decreased IMPDH activity at low pH. This is precisely what Min et al. observe in enzymatic assays (Figure 5) on a mutant in which E431 is mutated to glutamine. There is other experimental support as well: IMPDH enzymes that have been mutated at R418 usually have large isotope effects, which makes sense in light of the fact that the alternative T321 pathway involves the simultaneous transfer of two protons (rather than just one).

Things get even more interesting when IMPDH is compared to one of its cousins, GMP reductase. Although GMPR catalyzes a very different reaction, the C319/T321/E431 triad is also present there. This, along with other data from sequence alignment, suggests that these three residues were also present in a similar configuration in the ancestor of these modern proteins. Over time, progressive optimization of the two proteins resulted in the T321 pathway being supplanted by the more effective R418 in IMPDH, while remaining essential in GMPR.

If T321 really is a remnant of an earlier water-activating pathway, why is it conserved now that IMPDH has a much more efficient catalytic residue available? T321 is probably preserved because it stabilizes the water while it is being activated by R418. However, the other essential residue of that activating pathway (E431) is usually an inactive glutamine in eukaryotic forms of IMPDH (and some prokaryotes, as well). In these species the T321 activation pathway has been completely supplanted by the arginine pathway. Yet in the other forms of IMPDH this alternative mechanism still lingers, perhaps because of the additional activity it affords at low pH, or because it confers resistance to a particular inhibitor of the enzyme. In that sense, IMPDH's "tail" might provide an adaptive advantage quite different from that which gave rise to hydrolytic activity in the first place.

Donghong Min, Helen R. Josephine, Hongzhi Li, Clemens Lakner, Iain S. MacPherson, Gavin J. P. Naylor, David Swofford, Lizbeth Hedstrom, Wei Yang, Daniel Herschlag (2008). An Enzymatic Atavist Revealed in Dual Pathways for Water Activation PLoS Biology, 6 (8) DOI: 10.1371/journal.pbio.0060206 OPEN ACCESS
Disclaimer: Although I have little contact with Dr. Hedstrom's group, I am also working at Brandeis.

Read the rest...

How to help an enzyme crack cocaine

In addition to the adverse consequences of addiction and the inconvenience of serving several years of jail time for possessing it, cocaine can cause a fatal overdose. Although this condition can be treated, no therapy presently exists that attacks the overdose by removing cocaine from the bloodstream. One possible approach to eliminating cocaine from a patient would be to accelerate the process by which it is degraded. Unfortunately, the enzymes that perform this activity in the human body are not very efficient. In an upcoming article in the Journal of the American Chemical Society, however, a group from the University of Kentucky (assisted by researchers at the University of Michigan) have remodeled the active site of butyrylcholinesterase (BChE) to achieve a 2000-fold increase in rate. This raises the possibility of producing therapeutic enzymes as a treatment for cocaine overdose.

A cocaine overdose typically results in an elevated pulse rate, seizures, and hyperthermia, among other possibilities. The usual course of treatment involves addressing the symptoms — diazepam to reduce the heart rate, cooling protocols to address hyperthermia. These steps are proven to work, but they don't address the core problem: there's still a lot of cocaine floating around in the bloodstream. Treating with sedatives amounts to using one giant truck to stop another giant truck... both trucks will probably stop, but there might be a lot of collateral damage. Instead, it would be advantageous to either block the receptors that cocaine binds, or clear cocaine from the bloodstream somehow.

Plasma butylcholinesterase does most of the work in metabolizing cocaine, by cleaving it into two products that no longer exert the same pharmacological effects. If BChE was a highly efficient enzyme it's unlikely that people would experience cocaine overdoses at all, but it breaks down the main form of cocaine quite slowly, with a catalytic rate (k_cat) of 4.1 /min, resulting in a very long half-life for this substrate. The chemical mechanism of BChE (Figure 1) will be familiar to anyone who has taken biochemistry, being basically the same as a serine protease. Instead of a peptide bond, however, it is the ester linkage of cocaine that undergoes nucleophilic attack from an activated serine, while hydrogen bonds stabilize the evolving negative charge in an oxyanion hole.

Previous efforts to optimize the activity of BChE by mutation focused on eliminating steric clashes, but Zheng et al. noted that the hydrogen bond lengths in the oxyanion hole were not optimal for stabilizing the putative transition state. They therefore decided to focus their efforts on improving the energetics of this region. To do so, they used combined quantum mechanics/ molecular mechanics (QM/MM) simulations to determine the energy barriers in simulated reaction coordinates for a number of different mutants. This has the advantage of screening potential mutants for a specific effect, which may be quicker than wet lab work, but it requires the researcher to know the catalytic mechanism and to define a region of interest in advance.

By working through a series of mutations, Zheng et al. arrived at one multiple mutant of BChE that had favorable interaction energy for every residue in the oxyanion hole. When they generated this mutant in the lab, they found that it had a vastly increased catalytic rate towards cocaine, with k_cat now about 5700 /min. Based on these in vitro results they decided to test the mutant BChE in vivo using mice. They found that injecting mice with 30 µg of BChE protected them from seizure and death due to cocaine overdose. While the n for this experiment is small, and the BChE was injected prior to cocaine exposure rather than after, these results suggest that the mutant BChE has potential as a therapy for cocaine overdose in humans.

Obviously, further improvement would be needed before these protective effects could be realistically equaled in humans. To match the dose used in this experiment, a 180-pound man would need to be injected with 82 mg of the protein, which is a rather large amount. However, if used in conjunction with existing treatments, the required dose of BChE may be lower. If not, then translating these results into a useful therapy will require either further catalytic optimization or an enormous production effort. A significant amount of additional clinical research is required before this or any other mutant of BChE is introduced as a therapy for overdose or addiction. Nonetheless, these results illustrate the promise of enzyme optimization and design as a tool for medicine in the future.

Fang Zheng, Wenchao Yang, Mei-Chuan Ko, Junjun Liu, Hoon Cho, Daquan Gao, Min Tong, Hsin-Hsiung Tai, James H. Woods, Chang-Guo Zhan (2008). Most Efficient Cocaine Hydrolase Designed by Virtual Screening of Transition States Journal of the American Chemical Society DOI: 10.1021/ja803646t

Read the rest...

Do conformational changes precede or follow binding?

The binding of a ligand to a protein rarely occurs with the simplicity of a block sliding into an appropriately-shaped hole. Protein and ligand often engage in complementary conformational changes to adapt their shapes to each other. As a result, the structure of a protein bound to its target may differ substantially from the structure of the free protein. Unfortunately, it is virtually impossible to view the binding process in fine structural detail; as a result, most of our knowledge comes from the relatively stable bound and free states. Improving biophysical techniques, however, have brought a change in the way we view some binding events.

Most alterations of conformation during a binding event have historically been interpreted using the induced fit model. In this view, the protein stably maintains the free or "open" structure until it comes into contact with a ligand molecule. This encounter stimulates a conformational change so that the protein adopts the "closed" conformation that tightly holds onto the ligand. Thus, the ligand induces the conformational change necessary to form the bound, closed (BC) structure from the unbound, open (UO) structure, and the intermediate on this path is some kind of bound, open (BO) structure. This model is physically reasonable and has been very successful in interpreting many systems.

However, for the past few decades an increasing amount of evidence has suggested that this is not the whole story. NMR investigations indicated that instead of remaining in a single, well-defined backbone conformation most of the time, many proteins experienced significant changes in their structure while floating free in solution. These results suggested an alternative mechanism of population shift. In this view, the protein actually samples the "closed" conformation (or something very similar) while unbound, and it is this conformation that binds to the ligand. We still go from UO to BC, but now the intermediate is an unbound, closed (UC) structure.

This sounds very arcane, but it is not without functional relevance. Consider, for instance, a protein that is activated by a particular ligand. If we wish to make a drug that binds exclusively to the BC form, then we may experience unforeseen side-effects if our target protein occasionally samples a UC state. It would be useful to have a general idea of what kinds of circumstances are likely to favor a population shift model vs. an induced fit model. That is precisely what Kei-Ichi Okazaki and Shoji Takada aim to provide in an upcoming paper in Proceedings of the National Academy of Sciences (1).

Okazaki and Takada performed a coarse-grained molecular dynamics simulation of glutamine binding protein. In the bound and unbound states they employed a double-well Gō model, a simplified representation of molecular forces, to represent "opening" and "closing". To switch between these states (i.e. to represent binding) they used a Monte Carlo algorithm. This approach has the advantage of being quick and relatively inexpensive from a computational standpoint, but the results must be interpreted cautiously because the physics of the model are greatly simplified. They observe UO ↔ UC and UC ↔ BC events in this system, but they also observe UO ↔ BO and BO ↔ BC events. This suggests that the simulation will be able to make predictions about both population-shift and induced-fit mechanisms.

In order to try to make some predictions about the circumstances in which a particular mechanism is favored, Okazaki and Takada varied the strength and range of the binding interaction. By monitoring whether the simulated system entered the BC state from BO or UC, they could tell whether the system obeyed the induced-fit or population-shift mechanisms, respectively. They find that as either the strength or the range increase, the induced-fit mechanism is increasingly favored (Figure 4). These results make sense. If the protein regularly samples the closed state while unbound, then the amount of energy needed to reach that state is probably small, so it makes sense to see a population-shift mechanism associated with low-energy binding. Similarly, if a ligand is to associate productively with a non-optimal protein conformation, it makes sense that key interactions will be effective at long range.

From these results Okazaki and Takada suggest that the binding of small hydrophobic ligands is generally likely to proceed via population shift, while the binding of large, charged ligands (such as DNA) will likely proceed via induced fit. They acknowledge, however, that the simulation is limited, particularly in its view of conformational change. Unitary transitions in which the whole protein changes its structure simultaneously are probably not the norm, particularly in the case of very large conformational changes. These changes may instead be stepwise or hierarchical. For instance, a protein or complex recognizing multiple features of a DNA strand may proceed by an apparently induced-fit mechanism, even though each individual binding event more closely resembles population-shift behavior.

An additional limitation of this study is that it considers only one protein, but mechanisms of binding and conformational change may be idiosyncratic properties of particular folds. One could consider the behavior of lymphotactin, which displays clear hallmarks of the population-shift mechanism despite binding to macromolecules (heparin and a GPCR) much larger than itself, as a counterpoint to the predictions developed here. Similarly, the population shift of NtrC involves a charged phosphate group likely to have long-range interactions, although this is a post-translational modification and not a strict ligand-binding event. While the authors point to some examples that match their expectations, overall the data are not unanimously in support of their predictions. Still, the general rules laid out here provide a starting point for experimental work.

Despite the limitations of the simulation, it provides a relatively efficient tool for assessing these processes in other proteins. While no simulation can yet replace experimental data, coarse-grained models like this can serve as a means to formulate testable hypotheses about the energetics of protein-ligand systems.

1. Okazaki, K., Takada, S. (2008). Dynamic energy landscape view of coupled binding and protein conformational change: Induced-fit versus population-shift mechanisms. Proceedings of the National Academy of Sciences 105(32) 11182-11187. DOI: 10.1073/pnas.0802524105

Read the rest...

Structural dynamics of PDZ allostery

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

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

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

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

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

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

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

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

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

Read the rest...

What do we learn from the Protein Ensemble Method?

Anonymous left a comment on my post on Bruschweiller's work, referencing a couple of papers by Amarda Shehu, Cecilia Clementi, and Lydia Kavraki, the cites for which you can find at the bottom of this post. The most fascinating thing about these papers is the remarkable fidelity with which their Protein Ensemble Method (PEM) reproduces NMR-derived order parameters, 3-bond J couplings, and residual dipolar couplings. The authors demonstrate excellent correlations for ubiquitin, eglin c, Fyn SH3, Fnf10, and CI-2, and while all of these are relatively small proteins this is still a major accomplishment. Nonetheless, it is striking how little we learn from the exercise.

Keep in mind that one of the key goals of a structural biology research program is to get a veridical ensemble, i.e. an ensemble of structures that closely resembles those actually sampled by a protein under equilibrium conditions. We can learn important information from other kinds of ensembles, but the one that contains the information we are really after is the veridical ensemble.

The limitation here is intrinsic to the technique, so the technique bears some explanation. PEM utilizes an algorithm derived from robotics to move pieces of the protein. Initially, the approach was designed to map the ensemble of structures available to a loop, and I want to stress that with regards to that task I have no complaints. When given the task of mapping out the range of likely conformations of these regions this seems like an excellent approach, and the second figure of the 2006 paper seems to put this usage on fairly solid footing. The overall idea is that positioning the ends of a loop next to their anchor points is similar to solving a problem for getting a robotic arm with some number of degrees of freedom to adopt a particular pose. The authors' algorithm solves this inverse kinematic problem with a coarse-grained view of the backbone. At this point the backbone is frozen, the side chains are added back and their conformations are sampled randomly. The conformations thus generated are then subjected to energy refinement using a conventional force field. For a loop with no surroundings, this is all well and good.

The problem arises when the whole protein is subjected to the technique. This is done by using a rolling window of residues: the fragment is chosen, an ensemble defined for it while the rest of the protein is held rigid, and then the window moves to the next overlapping fragment. The various structures determined in this phase are all stored; the dynamic properties of a given residue are derived from a weighted average of all snapshots of all fragments that include that residue, with the exception that the first and last few residues of any fragment are out of bounds due to artificial restraints.

The ensemble of structures derived is therefore not veridical. Because of the fragment-replacement approach, only a single part of the protein is ever actually departing from the equilibrium or minimum-energy structure—it is unlikely that motions are actually distributed this way. Moreover, because the endpoints of all snapshots cannot be simultaneously resolved, it is not possible to assemble whole-protein conformational ensembles from the individual fragment ensembles. So, no individual snapshot is likely to reflect a significantly populated member of the ensemble, and also there is no way to collate the snapshots in such a way that the energetics of the real ensemble are accurately sampled. We thus end up with an ensemble of structures that does not reflect the set of structures actually sampled by the protein at equilibrium.

As a result, the structure that is produced can give us only limited information about the protein. For instance, this might be a reasonably reliable way to predict what sorts of deformations are possible or likely in a binding interaction. Also, PEM probably does a good job of reporting at least the lower limit of the range of the structural ensemble. However, because it does not allow for significant compensating deformations outside of the modeled region the conformations obtained probably do not cover the entire solution ensemble even for a particular fragment.

A clear implication of this work is the idea that the data are dominated by local fluctuations. That is, dynamics information derived from NMR relaxation experiments, quantitative J-coupling analysis, and RDCs primarily reflects short-range motions that do not involve major excursions from the overall structure. If this were not the case, it is unlikely that an intrinsically short-range method such as PEM could reproduce the data so well. This is not exactly a surprise, however, and the nature of PEM for the most part prevents us from learning how local motions in one region of the protein affect local motions in a distal region.

In a larger sense, however, this work reinforces the idea that the ideal approach to constructing a veridical ensemble will involve some combination of coarse-grained and all-atom approaches. The key problem here is not the computational method but the windowing. If the inverse kinematics approach used here can be extended to treat the whole protein—or at least multiple regions of the protein—simultaneously, then I think the situation improves. The question is whether this kind of algorithm will be any more efficient than MD if the whole system is in motion; I suspect at least some part of the computational savings (after what comes automatically with the coarse-graining during step one) arises from having rigid context for the fragment motions. However, this approach is also likely to be more amenable to parallelism than standard MD simulations, and because of the coarse-graining it has the ability to sample structures accessible on a timescale longer than MD can treat.

The authors of these studies imply that their future focus will be on extending this approach to larger structures; I would urge them instead to prioritize developing a way to employ PEM or a similar method without relying on fragment replacement.

Shehu, A., Kavraki, L.E., Clementi, C. (2006). On the Characterization of Protein Native State Ensembles. Biophysical Journal, 92(5), 1503-1511. DOI: 10.1529/biophysj.106.094409

Shehu, A., Clementi, C., Kavraki, L.E. (2006). Modeling protein conformational ensembles: From missing loops to equilibrium fluctuations. Proteins: Structure, Function, and Bioinformatics, 65(1), 164-179. DOI: 10.1002/prot.21060

Read the rest...

Can MD match model-free?

As I mentioned in my last post, a major challenge in the interpretation of protein motion has been the poor correlation between dynamics information arising from computer molecular dynamics simulations and NMR relaxation experiments. MD simulations complement the order parameters of the model-free formalism by providing detailed descriptions of motions that model-free parameters describe in a general way. However, the output of an MD simulation is only to be trusted if its specific model matches the experimental observations from NMR. Historically this has not been the case, especially when it comes to the description of side-chain motions.

Rafael Brüschweiller's lab has for several years been engaged, with some success, in an effort to improve MD simulations to the point where they can predict S² values that match NMR results for side chains. While a cold-eyed analysis of the correlations they've obtained so far (r values near 0.6) might not be very favorable, the comparisons aren't that bad. Their most recent communication to JACS (citation at the end of the post), appearing online last week, displays a marked improvement in the correlations between simulation and experiment. The r values are still not that close to 1, but the current results appear to be a significant step forward.

So, what was done differently? Showalter et al. use an altered version of the AMBER99 forcefield that has a modified dihedral angle potential. This had good results in simulating the dynamics of backbone amide moieties, although MD has historically done a reasonably good job with these anyway. In this communication they simulated the side-chain motions of calbindin and compared them to experimental values. They calculated spectral densities J(ω) from their simulated correlation functions, though they are required in this case to make use of experimentally determined molecular correlation times. They do a strikingly good job of predicting the J(ω) at the Larmor frequency of deuterium and also at twice that frequency (figure filched from paper):
This really is an amazingly good job. Yet, as you can see from their figure 2 (a part of it is at right), the S² values they obtain aren't very close to those that are derived from NMR experiments. This is also reflected in the relatively poor agreement at J(0) (r=0.86). This seems to be very odd, because the magnitude of the spectral density at J(0) is very strongly dependent on τ_m, which they took from an NMR experiment. As is evident from the model-free expression for J(ω), the order parameter scales this term. Keep in mind that τ_m is typically on the order of 10^-9 seconds while τ_e is on the order of 10^-11 seconds—this means that the second term in the spectral density expression is negligible at J(0). Because they took their τ_m from experimental data, the decreased correlation at J(0) indicates that their correlation functions converged to inaccurate values.

Giving the data a once-over, it appears that their fitted order parameters were mostly high. It's not clear to me why this should be so, except that over-constraint of the backbone may be affecting the side chains. From the supplementary information it appears that fits of backbone order parameters were also slightly higher in MD than experiment.

The most notable failure is not much help because it missed low. The significant outlier in the J(0) plot is threonine 45, shown in orange at right—this figure is made from PDB structure 3ICB, which was used in this simulation. The correlation function for this residue fails to converge, largely due to sampling of an alternate ψ angle. This behavior is consistent with the observations of low order parameters in that particular loop of the protein. From the crystal structure it appears that the hydroxyl moiety of Thr 45 is capping a helix (blue). It's possible that the misbehavior of this particular residue is due to some miscalibration of the force-field that doesn't accurately capture this capping interaction. The altered backbone dihedral angle potential may be overwhelming the hydrogen bonding interaction, resulting in the aberrantly low J(0) fit for this methyl group.

In general, the simulations for threonines and valines were not as accurate as those for other types of residues, which seems a little strange. These were also unusual in that they missed low, while, as I mentioned, on average residues tended to miss high. The branched nature of these amino acids causes some steric interactions with the backbone, so one would expect an improved potential to help these residues the most. However, if the altered potential is causing unwarranted excursions from the equilibrium structure, as seems to be the case with Thr 45, then valines and threonines, whose motions are at least partially controlled by steric interactions with the backbone, might be the most strongly affected.

I should stress that it's not necessary for the simulation to produce too much backbone motion to get this result. If the backbone dynamics are the wrong kind of motion that could have this effect even if the model-free parameters for the backbone derived from the simulation appear to be accurate.

It isn't terribly clear why an improved backbone potential should increase the correlation of side-chain order parameters between MD and NMR. Showalter et al. venture no explanation, and my own research and that of others hasn't shown any particular linkage between backbone dynamics and side-chain dynamics, except in the case of alanine residues. It may be that a more accurate depiction of backbone motions contributes to a more accurate dynamic environment generally. Or, the motions of the backbone and side chains could be related in unexpected ways. An in-depth analysis of the simulation probing for these correlations could be very instructive. Regardless, these results are a significant, encouraging step towards using MD simulations to interpret the findings of NMR dynamics experiments.

Showalter, S. A.; Johnson, E.; Rance, M.; Bruschweiler, R. "Toward Quantitative Interpretation of Methyl Side-Chain Dynamics from NMR by Molecular Dynamics Simulations" J. Am. Chem. Soc. (Communication); 2007;ASAP Article.

Read the rest...

The evolution of watches

PZ Myers is one the internet's most sarcastic and unapologetic atheists, and occasionally this leads him to say things I find extremely disagreeable. His lightning-rod status, however, means that he occasionally picks up some very interesting stuff from the interwebs. By this I do not mean his regular e-mails from the religious fringe, but instead the stuff he finds in support of evolution. As a case in point, this post where he gets an interesting video in which watches are evolved in silico from random parts. You should go check it out; it will take about 10 minutes for an entertaining explanation. Particularly note the way that the evolution plays out—relatively stable forms persist for huge numbers of generations and then rapidly change into completely different forms. Apply this knowledge the next time someone trots out the "no transitional fossils" argument.

Also, RIP Arthur Kornberg, Nobel Prize winner and great biochemist. Despite his gifts, his own research might be his secondary contribution, as his biological and scientific progeny may prove the greater. They already include another Nobelist. As scientists, we are always tempted to see our own work as being of paramount importance, but the training we give to our students and the spirit of enquiry we impart to our children are truly our greatest gift. Any scientist who neglects these aspects of his or her legacy is a failure, no matter how many splashy publications decorate his or her CV.

Read the rest...

Mr. Deeds goes to town

I hate the idea of submitting a paper to Proceedings of the National Academy of Sciences because if you get rejected you feel especially bad. Despite its relatively high impact factor, PNAS puts out a fair amount of garbage, and sometimes you feel like you're reading a dumping ground for the bad ideas of big names. Case in point is a paper from the lab of Eugene Shaknovich that just showed up in pre-publication form. Shaknovich is famous for performing simulations of proteins that rely on a reduced or "lattice" representation, and in the interest of full disclosure I'll admit that I'm highly dubious of this method. In this case, however, I'm relatively certain that the simulation produced a correct answer, for reasons that should become obvious as we go along.

Deeds et al. are out to address what seems like a fairly interesting problem of specificity in protein interactions. Most experiments performed in biomolecular laboratories make use of highly overexpressed proteins in relatively pure environments. This allows us to obtain quality information about the details of particular proteins and their interactions. However, what happens when we put these proteins into the cell at relatively dilute concentrations? If we consider a particular pair of interacting proteins, A and B, we know that their specific binding is strongly energetically favored. However, A and B probably have the potential to interact nonspecifically with many other proteins. If A and B are at relatively low concentration, and the cellular milieu is crowded with millions of these potential nonspecific interactions, can we be sure A and B will find one another?

To address this question, Deeds et al. construct their typical lattice models with two "proteins" that have a designed interaction, and simulated a situation in which up to 90% of a 3d space is populated by random "proteins" that have a small potential to interact with the targets. They let the systems equilibrate, and then take a look at the kind of interactions that are occurring. The findings are truly revolutionary, as you can see from the figure below. At low temperatures (A), the random interactions (blue) predominate when nonspecific-binding proteins are the larger component of the system. As the temperature increases slightly, to a point above the 'melting temperature' of random complexes, the designed, 'specific' interactions (black) begin to play a larger role, even at low 'concentrations' of interacting proteins. Finally, as the temperature really climbs, the specific interactions start to dominate the milieu.


So basically what Deeds et al. have discovered is that when the energy available from heat is enough to break random interactions but not specific interactions, then at equilibrium specific interactions are highly favored even if there is an awful lot of opportunity to bind randomly. On the other hand, if the temperature of the system is too low to break up random-binding events, then random binding dominates when most of the proteins are nonspecific binders. This is not a surprise, and hardly qualifies as a conclusion at all, even less so when you consider that this is a simulation (and thus that unsurprising results are likely to result directly from the assumptions used) and not an experiment on real proteins. This seems more like a control for some other experiment using this same system that derives some surprising conclusion.

Deeds et al. go on to make some important predictions from their discovery that energetics dictate binding (who knew kT could be so important?). For instance, they point out that in crowded protein-protein interaction experiments like the yeast two-hybrid screen there may be a lot of false positives, which must come as shocking news to any yeast two-hybrid researchers who have never read any papers or protocols about yeast two-hybrid screens, nor even Wikipedia. They also recommend using techniques that don't rely on overexpression, but the fact is that almost any molecular biologist would prefer it if he could answer questions using experiments that involved no overexpression. None of this is new, and to treat the insight as novel because some simulation showed it is just insulting.

In the end, this is a paper about a control, and not even a particularly well-written one. Don't get me wrong; it isn't bad for what it is, and I don't blame Shaknovich for trying to get it published in the best journal he could find for it. This is not bad science, but it doesn't tell us anything new, doesn't present a novel technique with wide application, or really provide any other reason to appear in a broad-based journal. I can and do blame PNAS for allowing in something that really ought to have been relegated to a specialized journal. And I will blame Shaknovich for the condescending tone of the discussion, in which he descends from his lofty computational height to tell us poor experimentalists "interesting implications" that we already knew. Too often, simulations get a bad rap from experimentalists, but this sort of paper, which will leave a bad taste in the mouth of anyone unfortunate enough to spend time reading it, makes that attitude seem justified.

Read the rest...