Hydrophobicity at Small and Large Length Scales: Two Faces of Water

 

Computer rendered picture showing the disordered hydrogen bonding network typical of liquid water. The blue spheres are oxygen and the white spheres are hydrogen. The dotted lines show the hydrogen bonds with which the water molecules attract one another.

Oil and water molecules actually attract each other, but not nearly so strongly. Mixing enough oil with water therefore leads to a reduction in favorable bonding. Strong mutual attractions between water molecules induces segregation of oil from water and results in an effective oil-oil attraction in the same way that groups of people segregate when one subgroup prefers association with members of its same subgroup. This water-induced effective attraction between oil molecules is called the hydrophobic interaction.

Forty years ago, Princeton chemist Walter Kauzmann identified hydrophobic interactions as a primary source of protein stability [2]. Proteins are chemically-bound chains of amino acids. These chains fold into specific functioning three-dimensional structures. Each specific protein has a specific structure determined, in some way, by the specific sequence with which amino acids are linked together in that protein. Kauzmann reasoned that since amino acids are either water-like or oil-like, the concomitant folded structure of a given linear sequence would be the one that best segregates oil-like amio acids from water. When protein structures were later determined experimentally by x-ray crystallography, Kauzmann's general predictions were found to be correct.

In subsequent years, with more and more x-ray-determined structures solved, it sometimes appears that other factors are at work besides the hydrophobic interaction as imagined by Kauzmann. There seems to be little doubt that hydrophobic effects play an important role in protein structure, and in related phenomena. Basic theory for understanding such effects, and the extent to which they affect protein structure, however, has proved elusive.

Professor Chandler and his former student, Ka Lum, argue that at least part of the problem is an issue of length scales. Under the right conditions, hydrophobicity of the traditional Kauzmann sort can appear, but only for extended oily surfaces in water. When surfaces are too small (or the concentration of oil too low), the energetic cost is insufficient to cause segregation. Instead, a different hydrophobic interaction occurs, one that acts only weakly and on only small length scales.

Weak short-ranged hydrophobic effects have been understood for about twenty years, on the basis of a theory developed by Lawrence Pratt and David Chandler [3]. That theory, and its contemporary variant [4] are based on the idea that because mutual attractions between water are so favorable, water-water attractions will persist even in the presence of oily species. The bonding will simply go around the oily groups. For this picture to be geometrically plausible, the concentration or size of oily species must be small. Hydrogen bonds cannot go around a sufficiently extended oily surface.

The nature of hydrophobicity changes when the spatial extent of oily surfaces leads to a depletion of hydrogen bonds. It is this energetic effect, the loss of hydrogen bonding, that leads to the segregation of oil from water. This consequence of depletion was anticipated long ago by theorist Frank Stillinger [5]. Its quantitative analysis can be obtained by exploiting the statistical mechanical theory of non-uniform fluids developed over the last decade by John Weeks and his students at the University of Maryland. Weeks' theory compactly describes drying transitions in terms of an unbalancing force [6]. Chandler and Lum together with Weeks viewed the depletion of hydrogen bonding near extended oily surfaces in terms of this force [7].

 

Water density outside a cylinder of radius 0.7 nm, where half the cylinder is hydrophilic and half is hydrophobic [7].  The height of the wave indicates the average value of the density at a particular radius and angle of the cylindrical coordinate system.  Adjacent to the hydrophobic surface, the lower left portion of the figure, the density is depleted relative to bulk water.  Adjacent to the hydrophilic surface, the upper right portion of the figure, the density is enhanced relative to bulk water.  The depletion is a manifestation of the drying transition that lies at the heart of large length scale hydrophobicity.  As distance from the cylinder increases, on either the hydrophobic or hydrophilic sides, the average density of water oscillates.  These oscillations are manifestations of small length scale solvent molecularity.  Far from the cylinder, the density of water is simply that of the bulk liquid.  The picture illustrates a prediction from the theory hydrophobicity at small and large length scales derived by Ka Lum, David Chandler and John Weeks.  This prediction is in remarkable accord with the figure created by M. Gerstein and R. M. Lynden-Bell [J. Phys. Chem. 1993, 97, 2982] illustrating their molecular dynamics computer simulation result for water density around a model protein helix that is approximately cylindrical, with one side predominantly hydrophobic and one side predominantly hydrophilic.

A principal conclusion of their analysis: A cluster of oily groups of the order of 1 nm in radius is sufficiently large to induce the formation of a water vapor-liquid-like interface, and it is the difference between free energies with and without this interface that accounts for a hydrophobic driving force of assembly. In particular, solvation free energies of smaller clusters scale linearly with solute volume, whereas those for larger clusters scale linearly with solute surface area. The figure below, taken from Ref. 9, illustrates the significance of this difference.

Another important conclusion concerns the nature of dynamics during the course of hydrophobically induced assembly. Density fluctuations in water are usually small. Yet a large fluctuation must accommodate the assembly of large oily clusters. Such fluctuations are facilitated by the occurrence of a critical cluster. While still small, this nascent cluster is large enough to nucleate an interface akin to that between water and vapor. It is this interface that allows for larger density fluctuations and the clustering of further oily groups. Movement of water molecules therefore plays a significant role in the pathway to hydrophobic collapse. Reference [9] illustrates a case where the role is dominant, the transition between coal and globule states of a hydrophobic polymer.

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