INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS: CONDENSED MATTERJ. Phys.: Condens. Matter 14 (2002) 9445–9460 PII: S0953-8984(02)36792-4Hydrophobic interactions: an overviewPieter Rein ten Wolde1,21Division of Physics and Astronomy, Vrije Universiteit, De Boelelaan 1081, 1081 HV,Amsterdam, The NetherlandsReceived 9 May 2002, in final form 23 May 2002Published 27 September 2002Onlineatstacks.iop.org/JPhysCM/14/9445AbstractWe present an overview of the recent progress that has been made inunderstanding the origin of hydrophobic interactions. We discuss the differentcharacter of the solvation behaviour of apolar solutes at small and large lengthscales. We emphasize that the crossoverinthesolvation behaviourarises from acollective effect, which means that implicit solvent models should be used withcare. We then discuss a recently developedexplicit solvent model, in which thesolvent is not described at the atomic level, but rather at the level of a densityfield. The model is based upon a lattice-gas model, which describes densityfluctuations in the solvent at large length scales, and a Gaussian model, whichdescribes density fluctuations at smaller length scales. By integrating out thesmall-length-scalefield,aHamiltonian is obtained, which is a function of thebinary, large-length-scale field only. This makes it possible to simulate muchlarger systems than was hitherto possibleasdemonstrated by the application ofthemodel to the collapse of an ideal hydrophobic polymer. The results showthat the collapse is dominated by the dynamics of the solvent, in particular theformation of a vapour bubble of critical size. Implications of these findings forthe understanding of pressure denaturation of proteins are discussed.(Some figures in this article are in colour only in the electronic version)1. IntroductionHydrophobic interactions are widely believed to play a dominant role in the formation oflarge biological structures [1, 2]. Yet, themechanism of the hydrophobic effect is still underdebate. The solvation of small apolar species is well understood [3–6]. However, the attractionbetween two such species in water is weak [3, 4, 6] andprobably not responsible for the stabilityof biological structures. On the other hand, strong and long-ranged attractions have beenmeasured between extended hydrophobic surfaces [7, 8]. But here, the origin of the effectis still being discussed. It has been suggested that the interaction arises from electrostatic2Address for correspondence: FOM-Instiute for Atomic and Molecular Physics (AMOLF), Kruislaan 407, 1098 SJ,Amsterdam, The Netherlands.0953-8984/02/409445+16$30.00 © 2002 IOP Publishing Ltd Printed in the UK 94459446 PRtenWoldefluctuations [9], changes in water structure [10], bridging (sub)microscopic bubbles [11, 12],and a ‘drying’ transition induced by the hydrophobic surfaces [13–15].Recently, Lum et al [15] have developed a theory of hydrophobicity which suggests thatthenature of the hydrophobic effect precisely arises from the interplay of density fluctuationsat both small and large length scales. Small apolar species only affect density fluctuationsin wateratsmall length scales. Concomitantly, water can only induce a relatively weak andshort-ranged attraction between small hydrophobic objects. In contrast, large hydrophobicspecies can affect density fluctuations at large length scales. At ambient conditions, water isclose to phase coexistence. A sufficiently large hydrophobic object or, more importantly, anassembly of several small apolar species, can therefore induce a depletion of water relative tothe bulk density [16, 17]. Recently, it has been demonstrated that this drying transition caninduce a strong attraction between hydrophobic objects and provide a strong driving force forprotein folding [18].In this paper, we give an overview of the recent progress that has been made inunderstanding the origin of the hydrophobic effect. In section 2 we discuss the statisticsof density fluctuations at small and large length scales. Understanding these fluctuations isimportant, because it provides insight not only into how the solvation free energy of solutesscales with their size, but also into which models are needed to describe their solvationbehaviour. In the next section, we briefly discuss a recently developed model. In section 4, wesee that this model gives a reasonable prediction of the solvation free energy of apolar solutes.In particular, it predicts that in the small-length-scale regime the solvation free energy scaleswith the size of the excluded volume of the solute, whereas in the large-length-scale regimeit scales with the area of the excluded volume. The model also shows that the crossover inthe solvation free energy arises from a collective effect in the solvent. Implicit solvent modelscannot conveniently describe this collective effect. It thus appears that explicit solvent modelsare needed. Explicit atomistic solvent models, however, are computationally demanding.The model discussed in section 3 lays the foundation for a scheme in which the solvent isnot described at the atomic level, but rather at the level of a coarse-grained density field. Thisscheme, which is discussed in section 5, allowsusto simulate the solvent much more efficiently.In section 6 we discuss the role of attractive interactions between the solutes and thesolvent. Most of the theoretical work on the hydrophobic effect has focused on the solvationbehaviour of ideal hydrophobic solutes [15, 19, 20]. These are objects that exclude solventfrom a certain region in space, but have no attractiveinteractions with the solvent. In section 6,however, it is seen that the presence of weak dispersive interactionsdoes not significantly affectthesolvation behaviour of hydrophobic solutes.Finally, in section 7 we apply the scheme discussed in section 5 to study the collapseof an ideal hydrophobic polymer. The simulations reveal that the dynamics of the collapsetransition is dominated by the dynamics of the solvent. In particular, the rate-limiting step isthe formation of a vapour bubble of critical size. In addition, we show that during the collapsethe chain and the solvent remain out of equilibrium. Both observations imply that implicitsolvent models should be used with great care. In the past, a statistically meaningful studyof protein folding using explicit solvent models seemed impractical. The current analysis,however, suggests that such studies become feasible by
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