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Kosmotropes and chaotropes: modelling preferential exclusion, binding and aggregate

stability

Susanne MoelbertInstitut de theorie des phenomenes physiques, Ecole polytechnique federale de Lausanne, CH-1015 Lausanne, Switzerland

B. NormandDepartement de Physique, Universite de Fribourg, CH-1700 Fribourg, Switzerland

Paolo De Los RiosInstitut de theorie des phenomenes physiques, Ecole polytechnique federale de Lausanne, CH-1015 Lausanne, Switzerland and

INFM UdR - Politecnico, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.(Dated: March 19, 2018)

Kosmotropic cosolvents added to an aqueous solution promote the aggregation of hydrophobicsolute particles, while chaotropic cosolvents act to destabilise such aggregates. We discuss themechanism for these phenomena within an adapted version of the two-state Muller-Lee-Grazianomodel for water, which provides a complete description of the ternary water/cosolvent/solute systemfor small solute particles. This model contains the dominant effect of a kosmotropic substance,which is to enhance the formation of water structure. The consequent preferential exclusion bothof cosolvent molecules from the solvation shell of hydrophobic particles and of these particles fromthe solution leads to a stabilisation of aggregates. By contrast, chaotropic substances disrupt theformation of water structure, are themselves preferentially excluded from the solution, and therebycontribute to solvation of hydrophobic particles. We use Monte Carlo simulations to demonstrate atthe molecular level the preferential exclusion or binding of cosolvent molecules in the solvation shellof hydrophobic particles, and the consequent enhancement or suppression of aggregate formation.We illustrate the influence of structure-changing cosolvents on effective hydrophobic interactions bymodelling qualitatively the kosmotropic effect of sodium chloride and the chaotropic effect of urea.

PACS numbers: 64.75.+g, 61.20.-p, 87.10.+e, 64.70.Ja

I. INTRODUCTION

Most processes in living organisms are adjusted tofunction in a rather limited range of physiological condi-tions, and important deviations, such as high concentra-tions of dangerous substances, are generally expected topreclude life. Nevertheless, many living systems survivestresses of this kind and exist in hostile environments.One common adaptation strategy is to modify the prop-erties of the solvent, which is usually water, in such a wayas to exclude the undesirable solutes from solution [1].Water is modified by relatively high concentrations ofstabilising solutes (cosolvents), which remain compatiblewith the metabolism of the cell even at very high concen-trations (therefore they are also referred to as ‘compatibleosmolytes’) [2, 3]. These cosolvents neutralise dangeroussolutes by decreasing their solubility and enhancing theformation of their aggregates. Such cosolvents are knownas promoters of the water structure and are therefore re-ferred to as kosmotropes (‘kosmo-trope’ = order maker).Their stabilising function for proteins and aggregates ofhydrophobic solute particles, and their importance forthe osmotic balance in cells, has generated a growing in-terest in the physical origin of the kosmotropic effect.Many recent investigations have focused on the abilityof kosmotropic cosolvents to influence solute solubility inaqueous media [4, 5, 6, 7, 8, 9].

Of equal interest and importance is the ability of

chaotropic cosolvents to increase the solubility of non-polar solute particles in aqueous solutions [10, 11, 12,13, 14, 15]. For certain systems the solubility may beenhanced by several orders of magnitude [16, 17, 18],leading to a complete destabilisation of solute aggregatesand, in the case of protein solutions, to a complete denat-uration and loss of function. A significant number of sub-stances display this property, notably (under most condi-tions and for the majority of solute species) urea, whichis frequently used in highly concentrated (c. 0.5-10 M)solutions as a protein denaturant. Chaotropic cosolvents(‘chao-tropic’ = order-breaking) are less polar than waterand thus break hydrogen bonds between water molecules,suppressing water structure formation [5, 19, 20, 21].However, the exact physical mechanism for the changesin water structure, and for the consequent destabilisingaction of chaotropic cosolvents, is at present not fullyunderstood.

Because the origin of the kosmotropic and chaotropiceffects appears to lie primarily in their influence on thesolvent, rather than in direct interactions between co-solvent and solute [22, 23, 24], a microscopic descrip-tion must begin with the unique properties of the aque-ous medium. Water molecules have the ability to formstrong, intermolecular hydrogen bonds, and pure, liquidwater may form extended hydrogen-bonded networks, be-coming highly ordered (Fig. 1). Although the insertionof a hydrophobic molecule leads to a destruction of lo-

2

FIG. 1: Schematic illustration of water structure as a conse-quence of the formation of more or less extended networks ofhydrogen bonds.

cal hydrogen-bond structure, at low temperatures watermolecules are found to rearrange in a cage-like config-uration around small solute particles and around high-curvature regions of larger ones. The orientation imposedon the water molecules at the interface with the particleresults in the cage hydrogen bonds being slightly strongerthan before, and causing a net reduction of energy dur-ing the insertion process [25, 26, 27, 28, 29]. However, athigher temperatures the free energy of the system is de-creased by reducing the local restructuring of water, thusincreasing the entropy of the solvent molecules, whichdrives the aggregation of hydrophobic particles througha minimisation of their total surface exposed to water.This competition between enthalpic and entropic effectsin the solvent is fundamental to the phenomenology ofliquid-liquid demixing processes. The effective hydropho-bic interaction between small, non-polar solute particlesis thus thought to be primarily solvent-induced, i.e. tobe a consequence of changes in the ordering of watermolecules rather than being controlled by direct water-solute interactions [30, 31, 32, 33, 34]. In this descrip-tion, the primary contribution to the action of structure-changing cosolvents, which are generally highly solubleand uncharged in physiological conditions, then dependson their ability to alter this local ordering of liquid water.

Kosmotropic cosolvents, such as sucrose and betaine,are more polar than water and act to enhance its struc-ture due to their ability to form hydrogen bonds [5].For the same reason they interact with water moleculesrather than with non-polar solute particles, which leadsto an effective preferential exclusion from the solvationshell of hydrophobic molecules [1, 6, 24], and thus to astronger net repulsion between solute and solvent. Inthe presence of kosmotropic cosolvents, structural ar-rangement of the water-cosolvent mixture is enthalpicallyfavourable compared to a cage-like organisation aroundhydrophobic solute particles. Solute molecules are thuspushed together to minimise their total exposed surface,which results in an enhancement of hydrophobic aggre-gation. The same process leads to a stabilisation of na-tive protein configurations, in spite of the fact that kos-motropic substances have no net charge and do not in-teract directly with the proteins [5, 7, 8].

Chaotropic cosolvents, such as urea in most ternary

FIG. 2: Schematic representation of preferential phenomenain a mixture of water and hydrophobic solute particles in thepresence of chaotropic (left) and kosmotropic (right) cosol-vents (after Ref. [24]).

systems, are less polar than water, so that their presencein solution leads to an energetically unfavourable disrup-tion of water structure. Such cosolvents are therefore ex-cluded from bulk water, an effect known as “preferentialbinding” to the solute particles [11, 24], although it reliesless on any direct binding of cosolvent to solute (whichwould enhance the effect) than on the fact that the cosol-vent molecules are pushed from the solvent into the shellregions of the solute. Preferential binding and exclusionof cosolvent molecules are depicted in Fig. 2. In the for-mer case, the smaller number of water molecules in con-tact with the surface of non-polar solute particles leads toa weaker effective interaction between solute and solvent,such that a larger mutual interface becomes favourable.The addition of chaotropic cosolvents to aqueous solu-tions therefore results in an increase in solvent-accessiblesurface area which destabilises hydrophobic aggregates,micelles and native protein structures [10, 11, 24, 35].The essential phenomenology of the kosmotropic and

chaotropic effects may be explained within a solvent-based model founded on the concept of two physicallydistinct types of solvent state, namely ordered and dis-ordered water [4, 5] (Fig. 1). In Sec. II we reviewthis model, described in detail in Ref. [36], and fo-cus on the adaptations which represent the structure-changing effects of the cosolvents. Sec. III presentsthe results of Monte Carlo simulations for kosmotropicsubstances, which illustrate their stabilising effect onhydrophobic aggregation, the decrease in solubility ofnon-polar molecules in water-cosolvent mixtures and theunderlying preferential exclusion of cosolvent moleculesfrom the solvation shell of hydrophobic particles. We con-sider the inverse phenomena of the chaotropic effect inSec. IV. In Sec. V we illustrate these results by compar-ison with available experimental data for a kosmotropic

3

and a chaotropic cosolvent, and discuss the extent of thesymmetry between the two effects in the context of themodel description for weakly or strongly active agents.Sec. VI contains a summary and conclusions.

II. MODEL

A. Hydrophobic-Polar Model

The driving force in the process of solvation and ag-gregation is the effective hydrophobic interaction betweenpolar water and the non-polar solute [23, 30]. As noted inSec. I, the origin of this interaction is the rearrangementof water around the solute particle. For solute surfaces ofsufficiently high curvature to permit (partial) cage forma-tion, this process decreases the enthalpy due to reinforcedhydrogen bonds between water molecules in the solvationshell of the hydrophobic particle in comparison to thosein bulk water, but reduces simultaneously the number ofdegenerate states of the solvent. These physical featuresare described by the model of Muller, Lee and Graziano(MLG), where the energy levels and respective degenera-cies of water molecules are determined by the local waterstructure [37, 38].Because solute particles are relatively large compared

with single water molecules, we use an adapted version ofthe MLG model in which each site contains a group of wa-ter molecules. The distinction between solvent moleculesand non-polar solute particles lies in their ability to formhydrogen bonds. The continuous range of interaction en-ergies within a partially hydrogen-bonded water clustermay be simplified to two discrete states of predominantlyintact or broken hydrogen bonds [39]. The water sites inthe coarse-grained model may then be characterised bytwo states, where an “ordered” site represents a watercluster with mostly intact hydrogen bonds, while a “dis-ordered” site contains relatively fewer intact hydrogenbonds (Fig. 1). The use of a bimodal distribution in theadapted model is not an approximation, but a naturalconsequence of the two-state nature of the pure MLGmodel [36]. In the presence of a non-polar solute a fur-ther distinction is required, between “bulk” water sitesundisturbed by the solute particles and “shell” sites intheir vicinity whose hydrogen bonding is altered. As ex-plained in more detail below, this adaptation of the MLGmodel contains the essential features required to encap-sulate the enthalpy/entropy balance which is the basisfor the primary phenomena of hydrophobic aggregationin two-component water/solute mixtures. The model hasbeen used to reproduce the appearance of upper (UCST)and lower (LCST) critical solution temperatures and aclosed-loop coexistence regime [40], demonstrating thatthe origin of the hydrophobic interaction lies in the al-teration of water structure.The adapted MLG model has been extended to provide

a minimal model for the study of chaotropic phenomenain ternary water/solute/cosolvent systems [36]. It was

EEds q, ds

Eos ,qos

,Edb qdb

Eob ,qob

FIG. 3: Energy levels of a water site in the bimodal MLGmodel. The energy levels of shell water are different from bulkwater due to breaking and rearrangement of hydrogen bondsin the proximity of a solute particle. The solid arrows rep-resent the effect of a kosmotropic cosolvent in creating moreordered states, and the dashed arrows the opposite effect ofchaotropic species.

shown that this framework yields a successful descriptionof preferential binding, and of the resulting destabilisa-tion of aggregates of solute particles as a consequence ofthe role of chaotropic cosolvents in reducing the forma-tion of water structure. We begin with a brief review ofthe model to summarise its physical basis and to explainthe modifications required for the inclusion of cosolventeffects.

The microscopic origin of the energy and degener-acy parameters for the four different types of watersite (ordered/disordered and shell/bulk) is discussed inRefs. [36, 41, 42], in conjunction with experimentaland theoretical justification for the considerations in-volved. Here we provide only a qualitative explanationof their relative sizes, which ensure the competition ofenthalpic and entropic contributions underlying the factthat the model describes a closed-loop aggregation re-gion bounded by upper and lower critical temperaturesand densities [40]. Considering first the energies of wa-ter sites (groups of molecules), the strongest hydrogenbonding arises not in ordered bulk water, but in theshell sites of hydrophobic particles due to the cage for-mation described in Sec. I (which can be considered asa result of the orientational effect of a hydrophobic sur-face). Both types of ordered water cluster are enthalpi-cally much more favourable than disordered groups ofmolecules, for which the presence of a non-polar parti-cle serves only to reduce hydrogen bonding still further,making the disordered shell energy the highest of all. Asregards the site degeneracies, which account for the en-tropy of the system, cage formation permits very fewdifferent molecular configurations, and has a low degen-eracy. Water molecules in ordered clusters have signif-icantly reduced rotational degrees of freedom comparedto disordered ones, with the result that the degeneracy ofthe latter is considerably higher. Finally, the degeneracyof a disordered shell site is still higher than that of a bulk

4

site because the relative reduction of hydrogen bondingdue to the non-polar surface admits a higher amount ofrotational freedom.

Figure 3 summarises the energy levels of a water site,which are arranged in the sequence Eds > Edb > Eob >Eos. Their respective degeneracies are qds > qdb > qob >qos, where the states are denoted ds = disordered shell,db = disordered bulk, ob = ordered bulk and os = or-dered shell (cage conformation). We stress that thesesequences are neither an assuption of the model nor maythey be altered if the model is to represent a systemexhibiting the closed-loop form of the coexistence curvefor aggregation: only these specific sequences reproduceappropriately the competition of enthalpic and entropiccontributions to the free energy. From the microscopicconsiderations of the previous paragraph these sequencesare entirely plausible, and they have been confirmed bya range of experimental measurements; the exact valuesof the parameters are not important for the qualitativeproperties of the system while the order of energies anddegeneracies is maintained. We return in Sec. V to theissue of departure from these sequences.

In the calculations to follow we have used the en-ergy values Eds = 1.8, Edb = 1.0, Eob = −1.0 andEos = −2.0, which are thought to be suitably represen-tative for aqueous solutions, and which have been suc-cessful in describing a number of different types of so-lution [40, 41, 43]. Their corresponding degeneracies,normalised to a non-degenerate ordered shell conforma-tion, are taken as qds = 49, qdb = 40, qob = 10 andqos = 1 [41]. We remind the reader that these energy anddegeneracy parameters are independent of temperatureand solute density. Their relative values have been foundto be appropriate for reproducing the primary qualitativefeatures of hydrophobic interactions [40, 41], swelling ofbiopolymers [43], protein denaturation [44, 45], and mi-celle formation [46]. The essential behaviour obtainedwithin this model is indeed found to be rather insensitiveto the precise parameter values, which may, however, berefined by comparison with experimental measurementsto yield semi-quantitative agreement for different solu-tions [40, 41, 43]. The energy scale is correlated directlywith a temperature scale, which we define as kBT ≡ β−1.

We conclude this subsection by qualifying the range ofvalidity of the adapted MLG model, including what ismeant above by “small” solute particles. The model isnot appropriate for solute species smaller than a groupof water molecules with intercluster hydrogen-bonding,which necessitates a linear cluster (and solute) size ofat least 2 water molecules. The model will also fail tocapture the physics of large, uniform systems where thelinear cluster size exceeds perhaps 10 water molecules,because in this case the majority of the water moleculesin a “shell site” would correspond effectively to bulkwater. Most molecular-scale treatments of water struc-ture in the vicinity of non-polar solute particles assumea spherical and atomically flat solute surface. Theseanalyses [47, 48, 49] indicate that “clathrate” models

for the (partial) formation of hydrogen-bonded cages be-come inappropriate for larger curvatures, on the orderof 1 nm, where a crossover occurs to “depletion” or“dangling-bond” models in which hydrogen-bond forma-tion is frustrated [50]. While the adapted MLGmodel be-comes inapplicable for such particles at the point where aclathrate description breaks down, we note [46] that mostsolute species, and in particular proteins, are atomicallyrough, in that they composed of chains and side-groupswith high local curvatures on the order of 0.3-0.5 nm.As a consequence the model may remain valid for soluteparticles of considerably greater total dimension. Forthe purposes of the present analysis, we note that a sig-nificant quantity of the available data concerning cosol-vent effects has been obtained for protein solutions, andthat the majority of this data is consistent with our ba-sic picture of the dominance of water structure effects indictating solute solubility. However, while most proteinsmay indeed fall in the class of systems well described by aclathrate picture, we stress that the adapted MLG modelcannot be expected to provide a complete description forlarge solute molecules containing many amino-acids ofdifferent local hydrophobicity and chemical interactions.

B. Cosolvent Addition

In comparison with the hydrophobic solute particles,cosolvent molecules are generally small and polar, andare therefore included directly in water sites by changingthe number of states of these sites. A site containing wa-ter molecules and a cosolvent particle is referred to as acosolvent site. Kosmotropic cosolvents, being more polarthan water, increase the number of intact hydrogen bondsat a site [19]. In the bimodal MLG framework their addi-tion to weakly hydrogen-bonded, disordered clusters maybe considered to create ordered clusters with additionalintact hydrogen bonds. The creation of ordered statesfrom disordered ones in the presence of a kosmotropiccosolvent increases the degeneracy of the former at theexpense of the latter. This feature is incorporated byraising the number of possible ordered states compared tothe number of disordered states (solid arrows in Fig. 3),

qob,k = qob + ηb, qdb,k = qdb − ηb,

qos,k = qos + ηs, qds,k = qds − ηs, (1)

where k denotes the states of water clusters containingkosmotropic cosolvent molecules, and the total numberof states is kept constant.The effect of chaotropic cosolvents on the state de-

generacies is opposite to that of kosmotropic substances,and may be represented by inverting the signs in eq. 1.Chaotropic cosolvents are less strongly polar than wa-ter, acting in an aqueous solution of hydrophobic parti-cles to reduce the extent of hydrogen bonding betweenwater molecules in both shell and bulk sites [23, 51].Within the adapted MLG framework, this effect is re-

5

produced by the creation of disordered states, with addi-tional broken hydrogen bonds and higher enthalpy, fromthe more strongly bonded ordered clusters (dashed ar-rows in Fig. 3), whence

qob,c = qob − ηb, qdb,c = qdb + ηb,

qos,c = qos − ηs, qds,c = qds + ηs. (2)

We stress three important qualitative points. First,the cosolvent affects only the number of intact hydrogenbonds, but not their strength [23], as a result of which,also in the bimodal distribution of the coarse-grainedmodel, the energies of the states remain unchanged. Co-solvent effects are reproduced only by the changes theycause in the relative numbers of each type of site [eqs. (1)and (2)]. Secondly, cosolvent effects on the relative de-generacy parameters are significantly stronger in the bulkthan in the shell, because for obvious geometrical reasonsrelated to the orientation of water molecules around anon-polar solute particle [36, 41], many more hydrogen-bonded configurations are possible in the bulk. Finally,as suggested in Sec. I, our general framework does notinclude the possibility of cosolvent-solute interactions,which have been found to be important in certain ternarysystems, specifically those containing urea [52, 53].The illustrative calculations in Secs. III and IV are per-

formed with ηb = 9.0 and ηs = 0.1 in eqs. (1) and (2). Inthe analysis of Ref. [36] these values were found to pro-vide a good account of the qualitative physics of urea as achaotropic cosolvent; in Sec. V we will return to a morequantitative discussion of the role of these parameters.By using the same values for a hypothetical kosmotropiccosolvent we will demonstrate that a symmetry of modeldegeneracy parameters does not extend to a quantitative,or even qualitative, symmetry in all of the relevant phys-ical phenomena caused by structure-changing cosolvents.We comment briefly that the fractional value of ηs arisesonly from the normalisation convention qos = 1.

C. Mathematical Formulation

To formulate a description of the ternary solutionwithin the framework of statistical mechanics, we beginby associating with each of the N sites of the system,labelled i, a variable ni, which takes the values ni = 1if the site contains either pure water, ni = 0 if the sitecontains a hydrophobic particle, or ni = −1 if the sitecontains a water cluster including one or more cosolventmolecules. This system is described by the Hamiltonian

H [{ni}, {σi}]=

N∑

i=1

ni(ni+1)

2[(Eobδi,σob

+Edbδi,σdb)λi

+(Eosδi,σos+ Edsδi,σds

)(1 − λi)]

+

N∑

i=1

ni(ni − 1)

2[(Eobδi,σob,a

+ Edbδi,σdb,a)λi

+(Eosδi,σos,a+ Edsδi,σds,a

)(1− λi)], (3)

where a = k, c denotes sites containing water and a kos-motropic or chaotropic cosolvent molecule. The site vari-able λi is defined as the product of the nearest neigh-bours, λi =

∏〈i,j〉 n

2j , and takes the value 1 if site i is

completely surrounded by water and cosolvent or 0 oth-erwise. The first sum defines the energy of pure watersites and the second the energy of cosolvent sites. Be-cause a water site i may be in one of q different states,δi,σos

is 1 if site i is occupied by water in one of the qos

ordered shell states and 0 otherwise, and δi,σdsis 1 if it is

occupied by pure water in one of the qds disordered shellstates and 0 otherwise. Analogous considerations applyfor the bulk states and for the states of cosolvent sites.A detailed description of the mathematical structure ofthe model is presented in Refs. [40] and [36].The canonical partition function of the ternary N -site

system, obtained from the sum over the state configura-tions {σi}, is

ZN =∑

{ni}

∏i Z

ni(ni+1)

2 (1−λi)s Z

ni(ni+1)

2 λi

b

×Zni(ni−1)

2 (1−λi)s,a Z

ni(ni−1)

2 λi

b,a , (4)

where Zσ = qoσe−βEoσ + qdσe

−βEdσ for the shell (σ =s) and bulk (σ = b) states both of pure-water and ofcosolvent sites (σ = s, a and σ = b, a).When the number of particles may vary, a chemical

potential is associated with the energy of particle addi-tion or removal. The grand canonical partition functionof the system for variable particle number becomes

Ξ =∑

N

eβµNw+β(µ+∆µ)NaZN =∑

{ni}

e−βHgceff [{ni}]. (5)

Nw denotes the number of pure water sites, Na the num-ber of cosolvent sites and Np the number of solute par-ticle sites, the total number being N = Nw + Na + Np.The variable µ represents the chemical potential associ-ated with the addition of a water site to the system and∆µ the chemical potential for the insertion of a cosolventmolecule at a water site. From the role of the two cosol-vent types in enhancing or disrupting water structure, atconstant solute particle density ∆µ is expected to be neg-ative for kosmotropic agents and positive for chaotropicones.

D. Monte Carlo Simulations

We describe only briefly the methods by which themodel may be analyzed; full technical details may befound in Ref. [40]. Because our primary interest is inthe local solute and cosolvent density variations whichdemonstrate aggregation and preferential phenomena, wefocus in particular on Monte Carlo simulations at thelevel of individual solute molecules. Classical MonteCarlo simulations allow the efficient calculation of ther-mal averages in many-particle systems with statistical

6

fluctuations [40], such as that represented by eq. (5). Wework on a cubic lattice of 30×30×30 sites (N = 27 000),with random initial particle distributions and with peri-odic boundary conditions to eliminate edge effects (al-though clearly we cannot eliminate finite-size effects).Each site is occupied by either a solute particle, purewater or a water-cosolvent mixture. The results are un-affected by changes in lattice size. We have implementeda Metropolis algorithm for sampling of the configurationspace. After a sufficiently large number (100 000) of re-laxation steps, the system achieves thermal equilibriumand averages are taken over a further 500 000 measure-ments to estimate thermodynamic quantities. Coexis-tence lines in the µ-T phase diagram are obtained fromthe transitions determined by increasing the temperatureat fixed chemical potential µ (grand canonical sampling),which results in a sudden density jump at the transitiontemperature. The solute particle densities ρp correspond-ing to these jumps yield closed-loop coexistence curvesin the ρp-T phase diagram. Despite the rather crude ap-proximation to a continuum system offered by the useof a cubic lattice, we have found quantitative agreementwith other theoretical approaches, which is why we focusprimarily on Monte Carlo simulations here. In Sec. V wewill also demonstrate remarkable qualitative, and in somecases semi-quantitative, agreement with experiment, sug-gesting that the adapted MLG framework may indeedform a suitable basis for more sophisticated modelling.For the macroscopic properties of the system, such

as aggregation and phase coexistence, the results of theMonte Carlo simulations may be interpreted with the aidof a mean-field analysis. If the densities at each site areapproximated by their average values in the solution, ρpfor hydrophobic particles, ρw for pure water and ρa forcosolvent, where ρp + ρw + ρa = 1, the mean value 〈ni〉at site i is given by 〈ni〉 =

∑σ ni,σρσ = ρw − ρa and

analogously 〈n2i 〉 =

∑σ n

2i,σρσ = ρw + ρa. The equilib-

rium densities are obtained by minimisation of the grandcanonical mean-field free energy per site,

f = (µ− β−1 lnZs)ρw + (µ+∆µ− β−1 lnZs,a)ρa

+β−1(lnZs − lnZb)ρw(ρa + ρw)z

+β−1(lnZs,a − lnZb,a)ρa(ρa + ρw)z

+β−1(ρw ln ρw + ρa ln ρa + ρp ln ρp), (6)

where z denotes the number of nearest neighbours of eachsite.

III. KOSMOTROPIC EFFECT

We begin our analysis of the kosmotropic effect by dis-cussing the mean-field ρp-T phase diagram for differentcosolvent concentrations, shown in Fig. 4. As expectedfrom Sec. IIA the system exhibits a closed-loop coex-istence curve, forming a homogeneous particle-solvent-cosolvent mixture below a LCST and above an UCST forall concentrations, whereas between these temperatures,

FIG. 4: Closed-loop coexistence curves for a ternary systemof water, kosmotropic cosolvent and hydrophobic particles fortwo different cosolvent densities ρk, obtained by mean-fieldcalculation with degeneracy parameters ηb = 9.0 and ηs =0.1 in eq. (1). On the outside of each curve the solutionis homogeneous, whereas on the inside it separates into twophases. The dashed arrow represents the heating process of asystem with particle density ρ0 and cosolvent density ρk2 =0.61 from temperature T0 in the homogeneous region to T1 inthe two-phase region. At T1 the system is separated into twophases of different densities ρ1 (nearly pure water-cosolventmixture) and ρ2 (hydrophobic aggregates).

and for intermediate particle concentrations, a phase sep-aration is found into a pure solvent phase (meaning awater-cosolvent mixture) and an aggregated phase withfixed solute density.

The hydrophobic repulsion between water and non-polar solute particles, developed as a result of the forma-tion of water structure, increases in the presence of kos-motropic cosolvents (this result may be shown by rewrit-ing the partition function (eq. 5) in terms of the par-ticle sites [36]). As shown in Fig. 4, the temperatureand density ranges of the aggregation region indeed risewith increasing cosolvent concentration, illustrating thestabilising effect of kosmotropic agents. Further, the par-ticle density of the aggregate phase in the two-phase re-gion increases when adding cosolvent, demonstrating inaddition the strengthening of effective hydrophobic in-teractions between solute particles due to the growingwater-solute repulsion. This is illustrated by the processof heating a system at constant density: the dashed ar-row in Fig. 4 represents a solution with particle densityρ0, which is heated from temperature T0 in the homo-geneous region to a temperature between the LCST andthe UCST. In the heterogeneous region (T1), the solu-tion separates into two phases of densities ρ1 (almostpure solvent) and ρ2 (hydrophobic aggregates) under theconstraint ρ0(V1 + V2) = ρ1V1 + ρ2V2, where Vi is thevolume occupied by phase i. An increase in cosolventdensity leads to a higher density ρ2 of hydrophobic ag-

7

FIG. 5: Closed-loop coexistence curves obtained by MonteCarlo simulations for an aqueous solution of hydrophobic par-ticles with the same parameters as in Fig. 4.

gregates and a lower value ρ1, which may be interpretedas a strengthening of the hydrophobic interactions gen-erated between solute particles.

However, the mean-field approximation neglects fluc-tuations in the density, and consequently is unable todetect intrinsically local phenomena such as preferentialexclusion of cosolvent particles from the solvation shell ofa hydrophobic particle (Fig. 2). Because the kosmotropiceffect is strongly dependent upon local enhancement ofwater structure, a full analysis is required of the spatialdensity fluctuations in the system. We thus turn to theresults of Monte Carlo simulations, which at the macro-scopic level show the same enhancement of hydrophobicaggregation (Fig. 5) as indicated in the mean-field anal-ysis. Below the LCST and above the UCST, one homo-geneous mixture is found where the hydrophobic parti-cles are dissolved, while between these temperatures theyform aggregates of a given density. The LCST and thecritical aggregate densities determined by the mean-fieldcalculation do not differ strongly from the numerical re-sults, but the UCST lies at a temperature higher thanthat determined by Monte Carlo simulations. This is tobe expected because mean-field calculations neglect fluc-tuation effects, generally overestimating both transitiontemperatures. The agreement of the mean-field result forsmall ρk with the simulated value for the LCST suggestsa predominance of local effects at low temperatures, andthat density fluctuations between sites are small. Wenote, however, that a cosolvent concentration ρk = 0.61is required in the mean-field approximation to producean expansion of the aggregated phase similar to that ob-served in the Monte Carlo results for ρk = 0.25, demon-strating the growing importance of fluctuation effects athigher cosolvent concentrations.

The µ-T phase diagram of the ternary system obtainedby Monte Carlo simulations is presented in Fig. 6. Lines

FIG. 6: µ-T phase diagram of hydrophobic solute in an aque-ous cosolvent mixture for two different kosmotropic cosol-vent concentrations ρk, obtained by Monte Carlo simulations.The endpoints of the finite transition lines correspond to theUCST and LCST.

of finite length terminated by the UCST and LCST de-marcate the aggregation phase transition. An increase incosolvent density leads to a larger separation of UCSTand LCST as a direct result of the expansion of the ag-gregation regime (Fig. 5). The transition line is shiftedto higher values of µ, indicating an increased resistanceof the system to addition of water at constant volumein the presence of cosolvent. This is a consequence ofthe fact that the resistance to addition of hydrophobicparticles depends on both µ and ∆µ: with increasing co-solvent concentration, ∆µ decreases (i.e. becomes morenegative) and hence µ must increase for the critical par-ticle density to remain constant.

By inspection of the energy levels, and of the alterationin their relative degeneracies caused by a kosmotropiccosolvent (Fig. 3), it is energetically favourable to max-imise the cosolvent concentration in bulk water with re-spect to shell water. Thus one expects a preferentialexclusion, also known as preferential hydration, as repre-sented schematically in the right panel of Fig. 2. Exceptat the lowest temperatures, an increased number of watermolecules in the solvation shell of non-polar solute par-ticles increases the repulsion between solute and solvent,resulting in a reduction of solubility, in an enhanced ef-fective attraction between solute particles due to the de-creased interface with water as they approach each other,and thus in aggregate stabilisation.

Monte Carlo simulations confirm the expectation thatthe cosolvent concentration is lower in shell water thanin bulk water. Figure 7 shows the cosolvent shell con-centration compared to the overall cosolvent concentra-tion in the solution, where preferential exclusion of thekosmotropic cosolvent from the solvation shell of the hy-drophobic solute particles is observed. At constant chem-

8

FIG. 7: Relative concentration of kosmotropic cosolvent in thesolvation shell of hydrophobic particles, obtained from MonteCarlo simulations at chemical potential µ = 2.5, exhibitingpreferential exclusion. The effect is most pronounced for lowcosolvent densities.

ical potential µ, a sharp drop occurs at the phase tran-sition temperature (Fig. 6), which is due to the suddenchange in solute particle density. At very low particledensity, a clear exclusion of the cosolvent from the solva-tion shell appears. However, at high particle density (fortemperatures below the aggregation phase transition) theeffect is only marginal, because here the number of parti-cle sites becomes substantial, most solvent and cosolventsites are shell sites and thus the total cosolvent density isalmost identical to the shell cosolvent density. The com-paratively strong fluctuations in relative cosolvent shellconcentration at temperatures above the phase transitionmay be attributed to the very low particle density in thesystem. Small, thermal fluctuations in the number ofshell sites occupied by cosolvent molecules result in largefluctuations in the cosolvent shell concentration.

Considering next the effect of the cosolvent concentra-tion, the system shows a substantially stronger preferen-tial exclusion for low than for high cosolvent densities.This is again largely a consequence of considering therelative, as opposed to absolute, decrease in cosolventconcentration in the shell. Preferential exclusion is lesspronounced for high cosolvent densities because a smallerproportion of cosolvent sites can contribute to the effect.At high temperatures, entropy, and therefore mixing, ef-fects become dominant and the preferential exclusion ofcosolvent particles shows a slight decrease.

We conclude this section by commenting also on thephenomenon shown in Figs. 4 and 5, that for tempera-tures where no aggregation is possible in the pure water-solute solution (below the LCST), it can be induced onlyby the addition of a cosolvent. Aggregation is driven byexclusion of solute from the solution in this intermediateregime, and is thus an indirect result of the transfor-

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1ρ

p

0.5

1

1.5

2

2.5

T

ρc=0.02

ρc=0.3

ρc=0.4

ρc=0.5

ρc=0.53

FIG. 8: Closed-loop miscibility curves of an aqueous solutionof hydrophobic particles for different chaotropic cosolvent con-centrations ρc, obtained by Monte Carlo simulations using thedegeneracy parameters ηb = 9.0 and ηs = 0.1 in eq. (2). Onthe outside of the curves is the homogeneous, dissolved statewhile inside them is the aggregated state. As the cosolventconcentration grows, particle solubility increases, leading to areduced coexistence regime.

mation of disordered bulk water states into energeticallyfavourable ordered bulk states by the kosmotropic cosol-vent. Preferential hydration is a further manifestation ofthis exclusion.

IV. CHAOTROPIC EFFECT

A detailed study of chaotropic cosolvent effects withinthe adapted MLG model for a hydrophobic-polar mixturewas presented in Ref. [36]. Here we provide only a briefreview of the results of this analysis, with emphasis onthe differences and similarities in comparison with thekosmotropic effect, which we have discussed at greaterlength in Sec. III. Figure 8 shows the coexistence curvesdemarcating the aggregated state for a range of cosolventconcentrations, computed by Monte Carlo simulations.The general features of the phase diagram are those ofSec. III (Figs. 4 and 5), with the obvious exception of theshrinking of the coexistence regime as cosolvent concen-tration is increased. However, it appears that for the qand η parameters used in the analysis (Sec. IIB) the ef-fect of high chaotropic cosolvent concentrations is ratherstronger than that obtained with the kosmotropic cosol-vent, an issue to which we return in Sec. V. Figure 8 sug-gests that sufficiently high concentrations of chaotropiccosolvent may cause complete aggregate destabilisationat any temperature and solute particle density.Figure 9 shows the corresponding µ-T phase diagram.

As in Fig. 6, the lines representing the discontinuousjump in density from the low- to the high-ρp phase moveto higher µ with increasing cosolvent concentration, againreflecting the increased cost of adding water to the sys-

9

0 1 2 3 4 5 6 7µ

0

0.5

1

1.5

2

2.5

3T

ρc=0.02

ρc=0.3

ρc=0.4

ρc=0.5

high particle density

low particle density

FIG. 9: µ-T phase diagram of hydrophobic solute in an aque-ous cosolvent mixture for different chaotropic cosolvent con-centrations ρc, obtained by Monte Carlo simulation. The fi-nite transition lines terminate at an UCST and a LCST, whichapproach each other with increasing cosolvent concentration.

tem in the presence of cosolvent. However, in this casethe endpoints of the lines, which represent the UCST andLCST for each cosolvent concentration, become closer asρc increases until they approach a singularity (Fig. 8),which we discuss in detail in Sec. V.Figure 10 shows as a function of temperature the co-

solvent concentration in the shell of a solute particle nor-malised by the total ρc. This demonstration of prefer-ential binding of chaotropic agents to non-polar soluteparticles was obtained from the model of eq. (3) withina pair approximation, which was shown in Ref. [36] toprovide a semi-quantitative reproduction of the MonteCarlo results. As in Fig. 7, the sharp step at the phasetransition is due to the sudden change in particle density.At low particle densities (below the transition) the effectis clear, whereas at high densities it is small because themajority of solvent and cosolvent sites have become shellsites. For low cosolvent concentrations, preferential bind-ing can lead to a strong increase in ρc on the shell sites(80% in Fig. 10), but the relative enhancement becomesless significant with increasing total cosolvent concentra-tion. Finally, in counterpoint to the discussion at theend of Sec. III, we comment that for chaotropic agents,which in bulk water transform ordered states into disor-dered ones, preferential binding (cosolvent exclusion) isfavoured and solute exclusion decreases. Thus a regimeexists in the ρp-T phase diagram where at fixed temper-ature and particle density, aggregates of solute particlesmay be made to dissolve simply by the addition of cosol-vent.

V. STRONG AND WEAK COSOLVENTS

As indicated in Sec. II and illustrated by the resultsof Secs. III and IV, there is a qualitative symmetry be-

0 0.5 1 1.5 2 2.5T

1

1.2

1.4

1.6

1.8

2

ρ c,sh

ell/ρ

c,to

tal

ρc, total

= 0.03

ρc, total

= 0.71

ρc, total

= 0.55

ρc, total

= 0.35

ρc, total

= 0.28

low particle densityhigh particle density

FIG. 10: Preferential binding effect, illustrated by the relativeconcentration of chaotropic cosolvent in the solvation shell ofhydrophobic particles, for different cosolvent concentrationsat fixed µ = 3.0, obtained by pair approximation.

tween the opposing effects of kosmotropic and chaotropicsubstances on hydrophobic aggregation of a given solutespecies. Indeed, the competition of the two effects hasbeen studied for solutions of the protein HLL with the(denaturing) chaotrope guanidine hydrochloride and the(native-structure stabilising) kosmotrope betaine [8]. Weremark, however, that the same cosolvent may have adifferent effect for solutions of different types and sizesof solute (Sec. II), and for this reason a global charac-terisation of the effectiveness of any one agent may bemisleading.

At low cosolvent concentration, the stabilising ordestabilising effects of the two cosolvent types on ag-gregate formation are rather small, and appear almostsymmetrical in the expansion or contraction of the coex-istence region (Figs. 5 and 8, Figs. 6 and 9). For weaklykosmotropic and chaotropic agents, by which is meantthose causing only small enhancement or suppression ofaggregation even at high concentrations, such qualitativesymmetry might be expected as a general feature of thecoexistence curves. With the same caveats concerninglow concentrations or weak cosolvent activity, this state-ment is also true for preferential exclusion and binding ofcosolvent to the solute particles, as shown by comparingFigs. 7 and 10. However, differing phenomena emerge forstrongly kosmotropic and chaotropic agents.

A. Urea as a Strong Chaotrope

Chaotropic cosolvents act to suppress the formation ofwater structure and, because the latter is already dis-rupted by the presence of a non-polar solute particle, aremore efficient for bulk than for shell sites. Within theadapted MLG model, a maximally chaotropic agent isone which causes sufficient disruption that the number

10

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1ρp

0

0.5

1

1.5

2

2.5

3

T

ρc= 0.03

ρc= 0.33

ρc= 0.5

ρc= 0.65

ρc= 0.75

ρc= 0.8

(a)

ρp*

T*

0 2 4 6 8µ

0

0.5

1

1.5

2

2.5

3

T

ρc=0.03

ρc=0.33

ρc=0.5

ρc=0.65

ρc=0.75

ρc=0.8

ρc=0.81

ρp<ρ

p*

ρp>ρ

p*

(b)

FIG. 11: (a) Coexistence curves for ternary water/cosol-vent/solute systems with different cosolvent concentrationsρc, obtained by mean-field calculation. At a critical cosolventconcentration of ρ∗c = 0.81, the LCST and UCST coincide, ata critical temperature T ∗ = 1.35 and critical particle densityρ∗p = 0.14, where the aggregation regime is reduced to a singlepoint. For still higher cosolvent concentrations the solutionis homogeneous over the full range of temperature and par-ticle density. (b) Mean-field µ-T phase diagram for differentcosolvent concentrations. As ρc increases, the separation ofLCST and UCST decreases until for ρc = ρ∗c they meet at thetemperature T ∗

L = T ∗

U = T ∗, where the value µL = µU = 7.05determines ρ∗p = 0.14.

of ordered bulk states is reduced to its hypothetical min-imum value, which is equal to the number of ordered shellstates; by the definition based on hydrogen-bond forma-tion, it is not possible to have fewer ordered bulk than or-dered shell states, so qob ≥ qos. When qob and qos becomesimilar, the entropic gain of creating ordered bulk statesby aggregation (removal of shell sites) is largely excluded,and thus a strongly chaotropic agent raises the solubilityof hydrophobic particles very significantly. With a suffi-cient concentration of such cosolvents, aggregation maybe completely prevented at all temperatures and den-sities, and the coexistence regime vanishes at a criticalvalue of cosolvent concentration.

Such singular behaviour is well known in many aque-ous solutions containing urea, and indeed frequent useis made of the destabilising properties of this cosolvent(Sec. I). We stress at this point that the chaotropic ac-tion of urea is by no means universal: in a number ofsystems, such as the ultra-small solute methane [20, 54],and proteins with variable hydrophobicity [49] or signifi-cant interactions between chain segments and the cosol-vent molecules [52, 53], its effect may in fact be inverted.However, because of its ubiquity as a solubilising agentfor most binary systems, we continue to consider urea asa generic example of a strong chaotrope.The aggregation singularity was reproduced in the

qualitative analysis of urea as a chaotropic agent per-formed in Ref. [36], and is illustrated in Fig. 11. Becauseof the discrete nature of the Monte Carlo simulations, theexact parameters for the critical point cannot be foundusing this technique; these were instead obtained onlywithin the mean-field approximation, and as a resultcannot be considered to be quantitatively accurate forthe parameters of the system under consideration. Fig-ure 11(a) shows the shrinking of the coexistence curveswith increasing cosolvent concentration until they vanishat a critical value ρ∗c = 0.81 (cf. ρ∗c ≈ 0.55 expected frominspection of the Monte Carlo results in Fig. 8). Thecorresponding evolution of the transition line in the µ-Tphase diagram is shown in Fig. 11(b).With the canonical choice of degeneracy parameters

(Sec. IIB) qds = 49, qdb = 40, qob = 10 and qos = 1 [41],the values ηb = 9.0 and ηs = 0.1 required in eq. (2)to reproduce this critical vanishing are indeed such thatqob,c = 1 and qos,c = 0.9 become very close. The levelof “fine-tuning” of the underlying parameters required inthe adapted MLG model reflects not a weakness of theframework but rather of the strongly chaotropic proper-ties of urea in water: the destruction of hydrogen-bondednetworks is almost complete at high concentrations. Inpractice, concentrated urea is used to destabilise aque-ous solutions of many folded proteins, micelles and ag-gregates of hydrophobic particles. While we are unawareof systematic experimental studies of the effects of ureaon the extent of the coexistence regime, aggregate desta-bilisation has been achieved at high concentrations incertain systems. At room temperature, the solubility ofthe highly hydrophobic amino-acid phenylalanin is dou-bled in an 8M urea solution (a solution with equal volumefractions of urea and water) [16].

B. Sodium Chloride as a Weak Kosmotrope

Kosmotropic cosolvents increase the extent of waterstructure formation, raising the number of ordered bulkand shell sites. While this process may be more efficientfor ordered shell states, their degeneracy cannot exceedthat of ordered bulk states. A maximally kosmotropicagent is one which causes sufficient structural enhance-ment that the number of ordered bulk states rises to the

11

FIG. 12: Coexistence curve measured in the experimentallyaccessible temperature range for N,N-Diethylmethylamine inwater in the presence and in the absence of the kosmotropiccosolvent sodium chloride, reproduced from Ref. [55]. TheLCST is reduced from 51◦C in the salt-free case to −0.6◦C inthe saturated cosolvent solution.

point where it is equal to the number of disordered bulkstates, qob = qdb. Singular behaviour for a strongly kos-motropic cosolvent (the counterpart to the vanishing ofaggregation caused by chaotropic cosolvents) is then theperfect aggregation of the system with densities ρ1 = 0and ρ2 = 1 (Fig. 4), i.e. extension of the coexistenceregime across the entire phase diagram. Only at the low-est temperatures, where entropy effects are irrelevant,would the mechanism of cage formation allow solution ofthe solute particles. For a sufficiently strong kosmotropiceffect (high concentrations of a strong agent) there is noreason why qob should not exceed qdb, a situation whichrepresents the breakdown of the sequence of energies anddegeneracies characteristic of a system with a closed-loopmiscibility curve (Sec. IIA). Complete aggregation is thehallmark of this breakdown.The “symmetrical” parameters ηb = 9.0 and ηs = 0.1

used in the analysis of Sec. III give the values qob = 19and qdb = 31 [eq. (1)]. These are clearly not suffi-ciently close to represent a strongly kosmotropic cosol-vent, which would explain both the rather modest ex-pansion of the coexistence regime even with relativelyhigh cosolvent concentrations (ρk) and the small valuesof the upper particle density ρ2 < 1 (Figs. 4, 5). Onemay thus conclude that quantitative symmetry betweenkosmotropic and chaotropic effects cannot be expectedfor any temperatures or densities, except in the event ofvery carefully chosen degeneracy parameters.To our knowledge, rather little data is presently avail-

able concerning the phase diagram of hydrophobic soluteparticles in cosolvent solutions. However, Ting et al. [55]have measured the lower coexistence curves for N,N-Diethylmethylamine both in pure water and in a mixtureof water and the cosolvent sodium chloride (Fig. 12),

which is usually considered to be weakly kosmotropic.A decrease of the LCST from 51◦C to −0.6◦C is ob-served for a solution saturated with sodium chloride, cor-responding to extension of the aggregation regime over asignificantly greater temperature range. Although thedata do not extend to sufficiently high temperaturesto discuss the full extension of the aggregation regimein density (Fig. 12, inset), the qualitative similarity ofFigs. 4 and 5 to the experimentally determined coexis-tence curves (Fig. 12, main panel) suggests that sodiumchloride would be appropriately classified as a “weak”kosmotrope in its effect on N,N-Diethylmethylamine.While its activity is significantly stronger (or its sat-uration concentration significantly higher) than that ofsodium sulphate, investigated by the same authors [55],at maximal concentrations it appears that the aggre-gation singularity is not reached and the closed-loopform of the miscibility curve is preserved. Here we notethat, while the kosmotropic action of sodium chloride isdue to its ionic nature in solution, the considerations ofthe adapted MLG framework (Sec. IIB) remain valid tomodel this effect. A more detailed comparison of themodel results with the data is precluded by the factthat the cosolvent concentration in the saturated solu-tion changes with both temperature and solute density.Measurements of different solutions are required to char-acterise the dependence of aggregation enhancement onthe molecular properties of the solute and on both soluteand cosolvent concentrations in the system.Finally, preferential exclusion of kosmotropic cosol-

vents from the immediate vicinity of hydrophobic par-ticles in aqueous solutions is measured only for very highcosolvent concentrations. Concentrations of compatibleosmolytes, such as sucrose and betaine in the cytoplasm,typically reach values well in excess of 0.5M. The stabil-ity of the protein lactate dehydrogenase against thermaldenaturation increases by approximately 90% in a 1Msucrose solution at room temperature, and by 100% forthe same concentration of hydroxyecotine [1], classifyingthese cosolvents as being strongly kosmotropic. In thecurrent model it is difficult to specify the exact cosolventconcentration because one site contains a group of watermolecules, but the results are nevertheless qualitativelyconsistent with observation. We have found that, exceptfor specifically chosen values of the parameters qσ andησ, cosolvent concentrations well in excess of 10% are re-quired to show a clear stabilising effect on hydrophobicaggregates (Fig. 5).

VI. SUMMARY

We have discussed the physical mechanism underlyingthe action of kosmotropic and chaotropic cosolvents onhydrophobic aggregates in aqueous solutions. The aggre-gation phenomena arise from a balance between enthalpicand entropic contributions to the solvent free energy,which is fully contained within an adapted version of the

12

bimodal model of Muller, Lee and Graziano. This modelconsiders two populations of water molecules with differ-ing physical properties, and generates indirectly the ef-fective hydrophobic interaction between solute particles.Such a description, based on the microscopic details ofwater structure formation around a solute particle, is ex-pected to be valid for small solute species, characterisedby lengthscales below 1 nm, and for those larger soluteparticles whose solubility is dominated by the atomicallyrough (highly curved) nature of their surfaces.In the adapted MLG framework, one may include

the ability of kosmotropic cosolvents to enhance and ofchaotropic cosolvents to disrupt the structure of liquidwater simply by altering the state degeneracies [eqs. (1)and (2)] associated with the two populations characteris-ing this structure. As a consequence only of these changesin the properties of the solvent, the model reproduces allof the physical consequences of cosolvents in solution:for kosmotropes the stabilisation of aggregates, expan-sion of the coexistence regime and preferential cosolventexclusion from the hydration shell of hydrophobic soluteparticles; for chaotropes the destabilisation of aggregates,a contraction of the coexistence regime and preferentialbinding to solute particles.The microscopic origin of these preferential effects lies

in the energetically favourable enhancement of hydrogen-bonded water structure in the presence of a kosmotropiccosolvent, and conversely the avoidance of its disruptionin the presence of a chaotrope. In a more macroscopic in-terpretation, the preferential hydration of solute particlesby kosmotropic agents can be considered to strengthenthe solvent-induced, effective hydrophobic interaction be-

tween solute particles, thus stabilising their aggregates;similarly, the preferential binding of chaotropic agentsto solute particles reduces the hydrophobic interaction,causing the particles to remain in solution. The essen-tial cosolvent phenomena may thus be explained purelyby the propensity of these agents to promote or suppresswater structure formation, and the effectiveness of a co-solvent is contained in a transparent way in the micro-scopic degeneracy parameters of the solvent states.

Our focus on water structure is intended to extract oneof the primary factors determining aggregation and co-solvent activity, and is not meant to imply that other in-teractions are not important. The range of solute speciesand additional contributions which are beyond the scopeof our analysis includes extremely small solutes, large,atomically flat solute surfaces, solutes with differing sur-face hydrophobicity (such as polar side-groups) and sur-faces undergoing specific chemical (or other) interactionswith the cosolvent. However, from the qualitative trends,and even certain quantitative details, observed in a widevariety of aqueous systems it appears that the adaptedMLG model is capable of capturing the essential phe-nomenology of cosolvent activity on aggregation and sol-ubility for solutes as diverse as short hydrocarbons andlarge proteins.

Acknowledgments

We thank the Swiss National Science Foundation forfinancial support through grants FNRS 21-61397.00 and2000-67886.02.

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