Can water stand the heat of a hydrophobic carbon nanotube?

"If you cannot stand the lipophilia, get out of the nanotube"- Anon

Yes. And this sort of ties in with the recent discussions of water in hydrophobic channels and cavities that I have been reading , discussions that can have a direct impact on ligand design (and also "rational" drug design). At least in once case, a simulation of water inside a carbon nanotube, the authors find that water does indeed get inside this greasy den. This study if part of many recent studies which I believe challenge our basic notions of "hydrophobicity" of surfaces and cavities.

I was not aware of this CNT paper, which was published in Nature in 2001 (Nature | Vol 414 | 8 November 2001 | pg. 188-190). The paper involved simulating water around a CNT. The researchers found that a few water molecules do enter the CNT in single file and exit, as the CNT is wide enough to accomodate only the diameter of a water. The interesting explanation for why the waters can ever get inside such an unwelcome environment is given by the energetics; apparently the waters can form two hydrogen bonds inside the nanotube, but fluctuations in the number of hydrogen bonds even in bulk means that they are incompletely hydrogen bonded even in bulk. Part of the explanation also may be that the Hbonds inside the tube have better geometrical characteristics, although I am not sure how much enthalpic advantage such slight changes in geometry provide to a Hbond.

This is a very significant fact in my opinion, and does not completely tie in with the study of Friesner et al. where they say that expelling a water molecule from a protein cavity into bulk may be enthalpically favourable because in bulk water is assumed to form its full complement of hydrogen bonds. I think the verdict may be still out there, as far as the enthalpic gain of waters expelled from hydrophobic protein active sites is concerned. On the other hand, in the nanotube study, it's clear that since the waters are certainly entropically constrained inside the tube, which means that the enthalpic advantage is what drives them in, even if they don't stay there forever.

However, the flags which are always raised in my mind when I read such a study pertain to the method dependence of the results. After all, any model is as good as the parameters in it. For example, the very reason why people do simulations of water under confinement is because they cannot study it by experiment, but at the same time, they are using bulk or gas phase parameters to represent the water molecules. In this study, the authors use Bill Jorgensen's TIP3P water model, which is a very good model that nonetheless represents bulk and gas-phase properties. The fact that the simulation results depend on model parametrization becomes clear when the authors change the depth of the energy well of the Lennard-Jones potential by a mere 0.05 kcal/mol, they observe a drastic change in the wetting event, with a two-step wetting-dewetting transition in a a nanosecond. The question arises is; what if they had used another value for the well depth? Would they have then observed no wetting at all? And would this then have been a representation of the real world? As usual, the question here is of the transferability of parameters, in this case whether the parameters from bulk apply under confinement. Unless there is a better hypothesis and reason, there may be some good reason to believe this transferability, but as usual, with what confidence does the model represent the "real world" is another question.

On a related note, is anyone aware of studies in which such confined-water parameters have been experimentally obtained?

How much water does it hold?

The last couple of days, in connection with the behaviour of water in protein active sites, I have been reading about water and the hydrophobic effect in general, and I found it fascinating how little we really know about both of these in general. For one thing, we still seem to have miles to go in understanding ice, bulk water, and the transition between the two. There was a debate between Richard Saykally of Cal Berkeley and Anders Nilsson of Stanford about the number of hydrogen bonds that a water molecule makes in bulk water. One would think that something as simple as this would have been unraveled by now. But nothing about water is simple. Nilsson published the pretty amazing contention that many water molecules in bulk liquid water at room temperature form only two hydrogen bonds. This would mean that those hydrogen bonds are unusually strong. This paper sparked heated debate, and Saykally was a vocal opponent, countering with his own experiments, and contending that it would be a walk across the street to Stockholm if Nilsson's viewpoint turned out to be true. I am no water expert, but the best value for the energy of an average hydrogen bond in bulk water that I have come across seems to be 1.5 kcal/mol (determined by Saykally), which can definitely be less than that in a protein active site. At least for now, this discussion of "average" hydrogen bonds generally sounds a little slippery to me.

I think that this whole issue of how much a hydrogen bond in bulk water is worth could affect how much gain in energy a water molecule displaced from a protein active site might gain. Friesner et al. in their recent publications indicate that water molecules which cannot form their full complement of hydrogen bonds in a protein active site because of confinement could get an enthalpic advantage if they are pushed out into solvent. I think there's much less ambiguity about the entropic advantage that such a water molecule could have. Then there's also Dunitz's whole argument about entropy-enthalpy compenstation (see previous post) which could factor in...I am still really groping about for coherence in this landscape.

As far as hydrophobic interactions are concerned, while the general idea that the hydrophobic effect is entropically driven seems correct, it also seems situation dependent, especially varying with the temperature. One of those basic important things to note is that the enthalpy of transfer for a nonpolar solute to water is close to zero, and can even be slightly favourable. But when two nonpolar surfaces in water aggregate, it's the entropy of disordering waters clustered around the solute that is very favourable. As usual, even these seemingly simple issues are draped in subtleties. Among others, Themis Lazaridis has explored this very interestingly in a review (2001), in which he cements the "classical" view of the hydrophobic effect. He also counters arguments about the similar energy of cavity creation in water compared to some other solvents by saying that while this may be true, the decomposition of factors contributing to the energy might be different for the two cases.

And finally, and I should have posted about this a long time back, Water In Biology, a great blog all about the molecular intricacies of water, from Philip Ball, staff writer for Nature and author of many excellent books, including H2O: A biography of water.

Water really seems like a testament to that quote by T.S. Eliot about coming back to the beginning again and again, and newly getting to know a place every time. There are just so many things about it we don't understand.

Nature adores a vacuum?

Well, ok, nature does not actually adore a vacuum, but what are we then to make of Bruce Berne's newest PNAS piece, in which he talks about water molecules in protein active sites that are so horribly unhappy that they would almost let a vacuum take their place?

The article comes on the heels of Friesner et al.'s comprehensive JMC 06 Glide XP article, which was an impressively comprehensive instance of how computational chemists can take into consideration the detailed physical chemistry of protein-ligand/drug interactions. As usual, electrostatics, van der Waals interactions, and desolvation among other things are taken care of. As usual, it turns out that in most earlier studies, the 'other half'-water-had not been considered. No wonder attempts to explain diabolically strong interactions like that of streptavidin-biotin (the strongest protein-ligand interaction known) resulted in drastic underestimates of the binding energy. With their latest framework, Berne et al. seek to remedy this situation. They make a couple of elementary sounding but oft neglected and important points:

1. Water is not going to be happy in a place in a protein where it is surrounded by a hydrophobic enclosure.

2. It is not going to be happy if it cannot make its full complement of hydrogen bonds with the protein/with other water molecules.

3. Even if it can make such bonds, it is not going to be happy if there are only one or two configurations in which it can do so.

4. Clearly, such water molecules are going to be more than happy to be kicked out by ligand atoms which can form their full complement of h-bonds with protein residues. These bonds, if they form part of a ring or if they are in close vicinity, have been called correlated hydrogen bonds. As per the authors' interpretation, its is these correlated hydrogen bonds that give special binding stability to examples like the streptavidin-biotin complex.

Obviously, like all life forms, water aspires to that highest ideal- freedom.

In the PNAS article, Berne et al. examine three cases, including streptavidin and COX 2 binding, in which water seems to be simply aching to get of the protein cavity. In the case of streptavidin, five water molecules form a metastable ring as depicted above. They do manage to form bonds with each other and with protein residues, but they are hopelessly trapped on top and bottom by hydrophobic parts. In this case, as explained in the JMC piece, the atom-atom pairwise addition principle does not work for hydrophobic enclosures. Clearly, the sum of the parts is not equal to the whole here, and the effect of two hydrophobic atoms, one each on top and bottom, is different from the calculated pairwise sum of effects for two atoms .

The word "metastable" is the best word I can think of for describing this unhappy situation for water. Surreal, simmering, patient, but waiting to become free.

In the case of COX 2, I saw a few statements which neither me nor my advisor could make sense of at first. Aristotle notwithstanding, it seems that there are actually some solvation situations which are almost as bad as a vacuum. Or even worse? Consider what the authors have to say:

The Cox-2 active site was found to contain no persistent hydration sites and is in fact entirely devoid of solvent in 80% of the simulation, despite the cavity sterically accommodating approximately seven water molecules. The high excess chemical potential of the binding-cavity solvent is due to an inability of the water molecules to make hydrogen bonds with the surrounding hydrophobic protein residues and other water molecules...An extreme case of hydrophobic enclosure is observed in the Cox-2 binding cavity, where no energetically stable solvent configurations appear to exist; insertion of ligand hydrophobic groups into such a region of persistent vacuum will result in substantially larger free-energy liberation than would be expected if the binding cavity were treated as solvated.

Well...I second the study; water, that humble but amazingly complex liquid, has often been neglected and underestimated in studies of protein-drug-ligand interactions.

Almost concomitantly, Essex et al. have published a report in JACS, in which they examined the nature of water molecules in active sites. They find that most of the water molecules are displaceable. Not surprisingly, they conclude that the binding affinity of the ligand depends upon the nature and environment of the water molecules. It's a good statistical study.

A central point that is coming to light through such studies is that the absolute hydrophobicity/hydrophilicity of a ligand certainly does not constitute the whole story. This may well be kept in mind by medicinal chemists who aim at modulating these properties of drug-like molecules from SAR studies. Sometimes, a single well-positioned ligand atom which displaces one or two extremely metastable water molecules can lead to orders of magnitude of binding affinity, which cannot be predicted from absolute characteristics of the ligand.

As usual, quality, not quantity, matters.

Addendum:
Another nice 3 page review I found in the rarely read Chemical Biology and Drug Design again makes the case. The review explores the thermodynamic aspects of drug-protein binding, and says among other things:

As the major contributors to the binding enthalpy are polar groups, a common misconception is that enthalpically driven compounds must be highly polar and that consequently their bioavailability will be compromised. In fact, what is often observed experimentally is that compounds with the same number of polar groups have vastly different binding enthalpies...To generate a favorable binding enthalpy, it is not the number of polar groups that matters but the quality of their interactions with the target. It is better to have few groups that establish strong interactions than a large number of groups mostly paying the desolvation penalty.

Again, by a "few groups", all that is needed is two functional groups that can kick out a metastable water molecule, and your job might be done.