Dynamics fast and slow

How do motions of a peptide chain depend on those of water molecules in the hydration shell? It's clear enough that the solvent dynamics can span a wide range of timescales, depending on how the water molecules interact with the protein. But in unfolded and molten-globule states, it has been suggested that there are rapid fluctuations between various helical and beta-sheet-like states that are 'lubricated' by picosecond rearrangements of the hydrogen-bonding network in water. This lubrication, enabled by the rapidity of H-bond making and breaking, is presumed to enable protein folding. Neil Hunt and coworkers at the University of Strathclyde now say that they've seen such motions, with timescales of a few tenths of a picosecond, in the alpha-helix-to-random-coil transition of a homo-polypeptide (poly-L-lysine) using optical Kerr-effect spectroscopy. The paper is here.

Motions in the hydration shell that are one or two orders of magnitude slower have been studied by Dongping Zhong and colleagues at Ohio State, in a paper here. They're looking at apomyoglobin, and specifically at the water dynamics around a tryptophan group (Trp7), which serves as a convenient fluorescent chromophore. Through both experiment and simulation, they find slow relaxation on timescales of 5-87 ps. Previous studies of such slow dynamics have offered divergent interpretations. Ahmed Zewail and coworkers have suggested that these dynamics are due to the effect of the protein's potential field on the hydration water (J. Phys. Chem. B 107, 13218; 2003). Bertil Halle thinks that these water dynamics close to a protein aren't so different from those in the bulk (PNAS 102, 13867; 2005). Zhong and colleagues say that the slow relaxation is due to strongly coupled water-protein motions. If either the water or the protein is frozen in the simulations, the slow component disappears. I guess that supports the contention of Bizzarri and Cannistraro that the dynamics of the protein and solvent are so strongly coupled that they ‘should be conceived as a single entity' (J. Phys. Chem. B 106, 6617-6633; 2002).

Quantum hydrophobicity, and water in drug design

A paper in PNAS by Ned Wingreen at Princeton uses first-principles quantum molecular dynamics to look at the hydrophobic interaction of two hydrated methane molecules. I’d say this is primarily a methodological paper – that’s pretty much the angle Guilia Galli takes in her accompanying commentary – in that it aims to establish how well classical simulation approaches do in capturing the nature of the interaction. The answer is: not particularly. Classical force fields predict two free-energy minima, one at methane-methane contact and a second, rather shallow, at a small separation corresponding to one intervening solvent layer. But the relative stability of these minima is rather sensitive to the precise force-field parameters and can be reversed for some values. The quantum simulations reveal a deeper potential well at contact – this is always the stable configuration. But there is a succession of shallow minima at several other methane-methane separations, implying the existence of several relatively stable hydration cages. The authors talk about these configurations in terms of ‘clathrate-like cages’, but in fact it seems that they don’t have any well-defined hydrogen-bonding arrangements: two independent simulations at a specific methane-methane separation gave water structures that could not be superimposed. (There was, however, apparently some consistency in the ‘hydrogen-bonded rings’ in between the two methanes.) Wingreen and colleagues suggest that the shallow minima are the result of relatively well packed configurations for water in the hydration shells. But I don’t really know what this means. Normally, considerations of molecular packing in liquids are governed by the short-ranged repulsion between molecules. But ‘well packed’ is an ambiguous term for water, where optimal hydrogen bonding means that the waters sit rather further apart than equivalent spherical molecules would do. I’m assuming ‘well packed’ here refers to unbroken, unstrained H-bonding configurations…?
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“Until a few years ago it was common practice to ignore water molecules in protein binding sites”, say Jonathan Essex and colleagues at Southampton University in an interesting paper in JACS. But now, they point out, there is increasing interest in designing ligands that will displace particular water molecules in drug binding. Conceivably, this might make the ligands more selective and the binding energy more favourable.

But it’s not clear whether that will necessarily be so. Despite the entropic advantage of expelling bound water from a binding cleft, one can’t generalize about the consequent free energy change. Whether or not it is advantageous to incorporate a water molecule at the binding interface hinges on a delicate balance. Confining a water molecule clearly has an entropic penalty, but this might be repaid by the enthalpic gains of hydrogen-bond formation – an issue that must itself be weighed against the average number of hydrogen bonds that a bulk water molecule engages in. Jack Dunitz (Science 264, 670 (1994); Chem. Biol. 2, 709-712 (1995)) has estimated that transferring a water molecule from an ordered binding site where it is bound by an ‘average’ hydrogen bond to the bulk involves an overall free-energy change that is close to zero. So it is not obvious which way the scales will tip in any instance. John Ladbury and his coworkers (D. A. Renzoni, M. J. J. M. Zvelebil, T. Lundbäck & J. E. Ladbury, in J. E. Ladbury & P. R. Connelly (eds), Structure-Based Drug Design: Thermodynamics, Modeling and Strategy 161-180, Landes Bioscience (1997)) have thought about the implications for drug design.

The message is illustrated in the binding of various inhibitors of HIV-1 protease, one of the key targets in AIDS therapies. Crystal structures show that some of these, such as KNI-272, bind to the enzyme via a bridging water molecule. Other inhibitors, such as DMP450, have been designed specifically to exclude this water molecule while mimicking its hydrogen-bonding capacity, and have found to bind more strongly. Li and Lazaridis (JACS 125, 6636-6637 (2003)) have calculated that displacement of the bound water by DMP450 is in itself unfavourable relative to KNI-272, but that this cost is outweighed by the lower cost of desolvating DMP450 to form the bound complex. So the consequences of eliminating the water molecule are both highly specific and not obvious.

With all this in mind, Essex and colleagues have sought a way of classifying water molecules in protein binding sites according to how easily displaced they are by ligands. By studying the thermodynamics of six proteins complexed with a variety of ligands, they say that the water molecules in the binding sites seem to come in two classes: those that are readily displaced (by at least some ligands), and those that never are. The latter, unsurprisingly, turn out to be more tightly bound according to MC simulations. All the same, the authors say that “no linear correlation exists between the binding free energies of water molecules and the change in binding affinity of ligands displacing the water molecules.” Yet they conclude that if we can identify the ‘conserved’ water molecules – those that do not get displaced come what may – then these can be usefully used in the design of drug docking: in effect, they serve as ‘part of the protein’, available for hydrogen bonding to the ligand. This paper supplies some heuristics for deciding which water molecules are conserved or displacable.

Why does water do that?

Following on from the suggestion that the ‘glass transition’ of hydrated proteins at around 220 K is in fact a change in the dynamical state of the water of hydration, related to the second critical point of water in the supercooled, high-pressure state (see the previous post below), Gene Stanley and his coworkers have now released a preprint that aims to relate this behaviour to the molecular structure of the liquid. To recap, the idea is that the ‘transition’ corresponds to the crossing of the so-called Widom line, the locus of the maximum in the correlation length that extends like a ‘ghost’ of the liquid-liquid phase transition beyond the critical point at which this transition vanishes. (At the critical point itself, this correlation length diverges.) What does this mean for the nature of the hydrogen-bonded network? Well, it’s subtle. In thermodynamic terms, the crossover corresponds to a change from non-Arrhenius dynamics at high temperature (the activation energy for water diffusion depends on temperature) to Arrhenius dynamics at low temperature (temperature-independent activation energy). The simulations by Stanley and colleagues now suggest that this crossover shows up in terms of the tendency to form non-bifurcated hydrogen bonds. Bifurcated H-bonds are fairly common in the liquid state at ambient conditions, and seem to be the defects that make diffusion facile. The Widom line corresponds to the point at which the derivative of the probability of forming non-bifurcated bonds with respect to temperature is maximal. Hmm, not an easy quantity to visualize. But it does mean that above the Widom line, supercooled water has fewer non-bifurcated hydrogen bonds, and so is less ‘tetrahedral’ and denser (like the high-density liquid phase), than below this line. That’s intuitive enough – crossing the Widom line as temperature decreases corresponds to the supercooled liquid becoming less dense, more structured and changing from a high-density-liquid-like to a low-density-liquid-like state: a ghost of the liquid-liquid phase transition itself, but with no abrupt change of thermodynamic variables.

Lawrence Pratt at Los Alamos and his coworkers have posted a preprint entitled ‘What is special about water as a matrix of life?’. This, as I recall, is basically the paper that Lawrence presented at the Varenna meeting, convened to discuss that very question in early 2005. The paper aims to address the title question in general, and hydrophobic effects in particular, by moving away from an emphasis on structure (for example, the classic Kauzmann model of entropically driven hydrophobic attraction due to the release of ‘structured water’ in the space between hydrophobes) and focusing instead on what the authors call the ‘engineering characteristics of the liquid’, such as its equation of state. The key message seems to be that, as a solvent for life, water represents a safe bet: the liquid state exists over a wide temperature range (compared with other simple small-molecule solvents), and within that range there is rather little variation in thermodynamic variables: response functions such as the compressibility and thermal expansion coefficient, as well as the nature of the solvophobic effect, vary little. It seems to me that this raises several questions (which are not objections), such as: does life require a wide temperature range, or does it just fill up whatever niches are available? (Thermophiles seem very ancient; would life have happily persisted if all Earth’s water was warm?) Does the ‘structured’ character of water play any necessary role in this scheme? (It does seem to be biologically important that water forms directional H-bonds.) And what does underlie the hydrophobic attraction, and how general is it?

Speaking of which, more evidence for the role of nanobubbles in the long-range hydrophobic attraction is provided in a study of nanoparticle adsorption onto a quartz microbalance in gassed and degassed water by Sangmin Jeon and colleagues in Korea (Langmuir 23, 1623-1625 (2007)).