arXiv:cond-mat/0305204v2 [cond-mat.soft] 25 Jun 2004 qeu ei 4 ,6 ,8 9]. 8, 7, 6, 5, in ability [4, solubility effect. media the solute aqueous influence kosmotropic on to the cosolvents focused kosmotropic of have of investigations origin in- recent physical growing Many a the generated for in has cells, importance terest in their balance osmotic and of the aggregates particles, and solute proteins hydrophobic for maker). function order re- = stabilising therefore (‘kosmo-trope’ Their are kosmotropes and as structure to water ferred the known of are cosolvents promoters the Such as enhancing aggregates. and their solubility of formation their dangerous decreasing neutralise by cosolvents solutes These ‘compatible 3]. as concen- [2, to high osmolytes’) referred very also at are even they cell (therefore trations the of of metabolism concentrations compatible the high [1]. with remain which solution relatively (cosolvents), from solutes by stabilising solutes modified undesirable is way a the Water such exclude in water, to usually prop- environments. is the as which hostile modify solvent, the to in of is erties exist strategy and adaptation common kind survive One this systems of living to many stresses expected Nevertheless, generally life. are preclude concentra- substances, high dangerous as of condi- such tions physiological deviations, of important range and limited tions, rather a in function omtoe n horps oeln rfrnilexclu preferential modelling chaotropes: and Kosmotropes ntttd heredsp´nmee hsqe,Eoepol ph´enom`enes th´eorie Ecole des de physiques, Institut ntttd heredsp´nmee hsqe,Eoepol ph´enom`enes th´eorie Ecole des de physiques, Institut feulitrs n motnei h blt of ability the is importance and interest equal Of to adjusted are organisms living in processes Most ASnmes 47.g 12.p 71.e 64.70.Ja 87.10.+e, 61.20.-p, 64.75.+g, numbers: ch PACS sodium of effect kosmotropic the cosolven qualitatively o structure-changing modelling enhancement of influence consequent the the illustrate o and We binding particles, or hydrophobic exclusion preferential of Mo the use We level molecular cont particles. the hydrophobic By preferential of solvation themselves aggregates. to are of contribute structure, stabilisation water con hydropho a of The of to formation shell leads structure. solvation dominan solution water the the the of from contains formation molecules the cosolvent model of enhance This to is t particles. which th of solute of description version small complete adapted a for desta provides an which to water, within for act phenomena model cosolvents these for chaotropic mechanism while particles, solute omtoi oovnsaddt nauosslto promot solution aqueous an to added cosolvents Kosmotropic .INTRODUCTION I. ´ preetd hsqe nvri´ eFior,CH-170 Fribourg, Universit´e de Physique, D´epartement de NMUR-Pltcio os uadgiArzi2,119To 10129 24, Abruzzi degli Duca Corso Politecnico, - UdR INFM Dtd ac 9 2018) 19, March (Dated: al eLsRios Los De Paolo uan Moelbert Susanne tcnqefe´rl eLuan,C-05Luan,Swit Lausanne, f´ed´erale CH-1015 ytechnique Lausanne, de .Normand B. stability tcnqefe´rl eLuan,C-05Luan,Swit Lausanne, f´ed´erale CH-1015 ytechnique Lausanne, de sfeunl sdi ihycnetae ( concentrated which highly urea, species) in solute used of frequently majority is the for condi- most and sub- (under tions of notably number property, significant this denat- A display complete stances function. a of to 18], loss solutions, and protein 17, uration of aggregates be case [16, solute the may of in magnitude destabilisation and, solubility complete of the a 12, orders to systems leading 11, several certain [10, For by solutions enhanced 15]. non- aqueous 14, of in 13, solubility particles the solute increase polar to cosolvents chaotropic fahdohbcmlcl ed oadsrcino lo- of destruction a to insertion leads the molecule Although hydrophobic 1). a (Fig. of ordered highly be- coming networks, form liquid hydrogen-bonded pure, extended to form and ability may water bonds, the aque- hydrogen have the descrip- intermolecular molecules of microscopic strong, Water properties a unique medium. the 24], ous with co- 23, begin between must [22, interactions the tion solute on direct and influence in their solvent than in rather primarily lie solvent, to appears effects fully not present at is destabilising cosolvents, consequent understood. chaotropic the of for 21]. changes action and the 20, structure, for water 19, mechanism in physical [5, exact formation the However, structure water molecules, water between suppressing bonds hydrogen water break than thus polar and less cosolvents are Chaotropic order-breaking) = denaturant. (‘chao-tropic’ protein a as solutions eas h rgno h omtoi n chaotropic and kosmotropic the of origin the Because yecue rmteslto,adthereby and solution, the from excluded ly so ffciehdohbcitrcin by interactions hydrophobic effective on ts oovn oeue nteslainshell solvation the in molecules cosolvent f iiesc grgts edsusthe discuss We aggregates. such bilise i atce n fteeprilsfrom particles these of and particles bic enr ae/oovn/ouesystem water/cosolvent/solute ternary e oieadtecatoi ffc furea. of effect chaotropic the and loride t al iuain odmntaeat demonstrate to simulations Carlo nte at horpcsbtne irp the disrupt substances chaotropic rast, upeso fageaeformation. aggregate of suppression r ffc faksorpcsubstance, kosmotropic a of effect t eun rfrnilecuinboth exclusion preferential sequent etosaeMuller-Lee-Graziano two-state he h grgto fhydrophobic of aggregation the e rbug Switzerland Fribourg, 0 in idn n aggregate and binding sion, io Italy. rino, c .-0M) 0.5-10 . eln and zerland zerland 2

FIG. 1: Schematic illustration of water structure as a conse- quence of the formation of more or less extended networks of hydrogen bonds. cal hydrogen-bond structure, at low temperatures water molecules are found to rearrange in a cage-like config- uration around small solute particles and around high- curvature regions of larger ones. The orientation imposed FIG. 2: Schematic representation of preferential phenomena on the water molecules at the interface with the particle in a mixture of water and hydrophobic solute particles in the results in the cage hydrogen bonds being slightly stronger presence of chaotropic (left) and kosmotropic (right) cosol- than before, and causing a net reduction of energy dur- vents (after Ref. [24]). ing the insertion process [25, 26, 27, 28, 29]. However, at higher temperatures the free energy of the system is de- creased by reducing the local restructuring of water, thus systems, are less polar than water, so that their presence increasing the entropy of the solvent molecules, which in solution leads to an energetically unfavourable disrup- drives the aggregation of hydrophobic particles through tion of water structure. Such cosolvents are therefore ex- a minimisation of their total surface exposed to water. cluded from bulk water, an effect known as “preferential This competition between enthalpic and entropic effects binding” to the solute particles [11, 24], although it relies in the solvent is fundamental to the phenomenology of less on any direct binding of cosolvent to solute (which liquid-liquid demixing processes. The effective hydropho- would enhance the effect) than on the fact that the cosol- bic interaction between small, non-polar solute particles vent molecules are pushed from the solvent into the shell is thus thought to be primarily solvent-induced, i.e. to regions of the solute. Preferential binding and exclusion be a consequence of changes in the ordering of water of cosolvent molecules are depicted in Fig. 2. In the for- molecules rather than being controlled by direct water- mer case, the smaller number of water molecules in con- solute interactions [30, 31, 32, 33, 34]. In this descrip- tact with the surface of non-polar solute particles leads to tion, the primary contribution to the action of structure- a weaker effective interaction between solute and solvent, changing cosolvents, which are generally highly soluble such that a larger mutual interface becomes favourable. and uncharged in physiological conditions, then depends The addition of chaotropic cosolvents to aqueous solu- on their ability to alter this local ordering of liquid water. tions therefore results in an increase in solvent-accessible Kosmotropic cosolvents, such as sucrose and betaine, surface area which destabilises hydrophobic aggregates, are more polar than water and act to enhance its struc- micelles and native protein structures [10, 11, 24, 35]. ture due to their ability to form hydrogen bonds [5]. The essential phenomenology of the kosmotropic and For the same reason they interact with water molecules chaotropic effects may be explained within a solvent- rather than with non-polar solute particles, which leads based model founded on the concept of two physically to an effective preferential exclusion from the solvation distinct types of solvent state, namely ordered and dis- shell of hydrophobic molecules [1, 6, 24], and thus to a ordered water [4, 5] (Fig. 1). In Sec. II we review stronger net repulsion between solute and solvent. In this model, described in detail in Ref. [36], and fo- the presence of kosmotropic cosolvents, structural ar- cus on the adaptations which represent the structure- rangement of the water-cosolvent mixture is enthalpically changing effects of the cosolvents. Sec. III presents favourable compared to a cage-like organisation around the results of Monte Carlo simulations for kosmotropic hydrophobic solute particles. Solute molecules are thus substances, which illustrate their stabilising effect on pushed together to minimise their total exposed surface, hydrophobic aggregation, the decrease in solubility of which results in an enhancement of hydrophobic aggre- non-polar molecules in water-cosolvent mixtures and the gation. The same process leads to a stabilisation of na- underlying preferential exclusion of cosolvent molecules tive protein configurations, in spite of the fact that kos- from the solvation shell of hydrophobic particles. We con- motropic substances have no net charge and do not in- sider the inverse phenomena of the chaotropic effect in teract directly with the proteins [5, 7, 8]. Sec. IV. In Sec. V we illustrate these results by compar- Chaotropic cosolvents, such as urea in most ternary ison with available experimental data for a kosmotropic 3 and a chaotropic cosolvent, and discuss the extent of the symmetry between the two effects in the context of the E model description for weakly or strongly active agents. Sec. VI contains a summary and conclusions. Eds,qds Edb,qdb

II. MODEL

A. Hydrophobic-Polar Model Eob,qob Eos,qos The driving force in the process of solvation and ag- gregation is the effective hydrophobic interaction between polar water and the non-polar solute [23, 30]. As noted in FIG. 3: Energy levels of a water site in the bimodal MLG Sec. I, the origin of this interaction is the rearrangement model. The energy levels of shell water are different from bulk of water around the solute particle. For solute surfaces of water due to breaking and rearrangement of hydrogen bonds sufficiently high curvature to permit (partial) cage forma- in the proximity of a solute particle. The solid arrows rep- tion, this process decreases the enthalpy due to reinforced resent the effect of a kosmotropic cosolvent in creating more hydrogen bonds between water molecules in the solvation ordered states, and the dashed arrows the opposite effect of shell of the hydrophobic particle in comparison to those chaotropic species. in bulk water, but reduces simultaneously the number of degenerate states of the solvent. These physical features are described by the model of Muller, Lee and Graziano shown that this framework yields a successful description (MLG), where the energy levels and respective degenera- of preferential binding, and of the resulting destabilisa- cies of water molecules are determined by the local water tion of aggregates of solute particles as a consequence of structure [37, 38]. the role of chaotropic cosolvents in reducing the forma- Because solute particles are relatively large compared tion of water structure. We begin with a brief review of with single water molecules, we use an adapted version of the model to summarise its physical basis and to explain the MLG model in which each site contains a group of wa- the modifications required for the inclusion of cosolvent ter molecules. The distinction between solvent molecules effects. and non-polar solute particles lies in their ability to form The microscopic origin of the energy and degener- hydrogen bonds. The continuous range of interaction en- acy parameters for the four different types of water ergies within a partially hydrogen-bonded water cluster site (ordered/disordered and shell/bulk) is discussed in may be simplified to two discrete states of predominantly Refs. [36, 41, 42], in conjunction with experimental intact or broken hydrogen bonds [39]. The water sites in and theoretical justification for the considerations in- the coarse-grained model may then be characterised by volved. Here we provide only a qualitative explanation two states, where an “ordered” site represents a water of their relative sizes, which ensure the competition of cluster with mostly intact hydrogen bonds, while a “dis- enthalpic and entropic contributions underlying the fact ordered” site contains relatively fewer intact hydrogen that the model describes a closed-loop aggregation re- bonds (Fig. 1). The use of a bimodal distribution in the gion bounded by upper and lower critical temperatures adapted model is not an approximation, but a natural and densities [40]. Considering first the energies of wa- consequence of the two-state nature of the pure MLG ter sites (groups of molecules), the strongest hydrogen model [36]. In the presence of a non-polar solute a fur- bonding arises not in ordered bulk water, but in the ther distinction is required, between “bulk” water sites shell sites of hydrophobic particles due to the cage for- undisturbed by the solute particles and “shell” sites in mation described in Sec. I (which can be considered as their vicinity whose hydrogen bonding is altered. As ex- a result of the orientational effect of a hydrophobic sur- plained in more detail below, this adaptation of the MLG face). Both types of ordered water cluster are enthalpi- model contains the essential features required to encap- cally much more favourable than disordered groups of sulate the enthalpy/entropy balance which is the basis molecules, for which the presence of a non-polar parti- for the primary phenomena of hydrophobic aggregation cle serves only to reduce hydrogen bonding still further, in two-component water/solute mixtures. The model has making the disordered shell energy the highest of all. As been used to reproduce the appearance of upper (UCST) regards the site degeneracies, which account for the en- and lower (LCST) critical solution temperatures and a tropy of the system, cage formation permits very few closed-loop coexistence regime [40], demonstrating that different molecular configurations, and has a low degen- the origin of the hydrophobic interaction lies in the al- eracy. Water molecules in ordered clusters have signif- teration of water structure. icantly reduced rotational degrees of freedom compared The adapted MLG model has been extended to provide to disordered ones, with the result that the degeneracy of a minimal model for the study of chaotropic phenomena the latter is considerably higher. Finally, the degeneracy in ternary water/solute/cosolvent systems [36]. It was of a disordered shell site is still higher than that of a bulk 4 site because the relative reduction of hydrogen bonding for the (partial) formation of hydrogen-bonded cages be- due to the non-polar surface admits a higher amount of come inappropriate for larger curvatures, on the order rotational freedom. of 1 nm, where a crossover occurs to “depletion” or Figure 3 summarises the energy levels of a water site, “dangling-bond” models in which hydrogen-bond forma- which are arranged in the sequence Eds > Edb > Eob > tion is frustrated [50]. While the adapted MLG model be- Eos. Their respective degeneracies are qds > qdb > qob > comes inapplicable for such particles at the point where a qos, where the states are denoted ds = disordered shell, clathrate description breaks down, we note [46] that most db = disordered bulk, ob = ordered bulk and os = or- solute species, and in particular proteins, are atomically dered shell (cage conformation). We stress that these rough, in that they composed of chains and side-groups sequences are neither an assuption of the model nor may with high local curvatures on the order of 0.3-0.5 nm. they be altered if the model is to represent a system As a consequence the model may remain valid for solute exhibiting the closed-loop form of the coexistence curve particles of considerably greater total dimension. For for aggregation: only these specific sequences reproduce the purposes of the present analysis, we note that a sig- appropriately the competition of enthalpic and entropic nificant quantity of the available data concerning cosol- contributions to the free energy. From the microscopic vent effects has been obtained for protein solutions, and considerations of the previous paragraph these sequences that the majority of this data is consistent with our ba- are entirely plausible, and they have been confirmed by sic picture of the dominance of water structure effects in a range of experimental measurements; the exact values dictating solute solubility. However, while most proteins of the parameters are not important for the qualitative may indeed fall in the class of systems well described by a properties of the system while the order of energies and clathrate picture, we stress that the adapted MLG model degeneracies is maintained. We return in Sec. V to the cannot be expected to provide a complete description for issue of departure from these sequences. large solute molecules containing many amino-acids of In the calculations to follow we have used the en- different local hydrophobicity and chemical interactions. ergy values Eds = 1.8, Edb = 1.0, Eob = −1.0 and Eos = −2.0, which are thought to be suitably represen- tative for aqueous solutions, and which have been suc- B. Cosolvent Addition cessful in describing a number of different types of so- lution [40, 41, 43]. Their corresponding degeneracies, In comparison with the hydrophobic solute particles, normalised to a non-degenerate ordered shell conforma- cosolvent molecules are generally small and polar, and tion, are taken as qds = 49, qdb = 40, qob = 10 and are therefore included directly in water sites by changing qos = 1 [41]. We remind the reader that these energy and the number of states of these sites. A site containing wa- degeneracy parameters are independent of temperature ter molecules and a cosolvent particle is referred to as a and solute density. Their relative values have been found cosolvent site. Kosmotropic cosolvents, being more polar to be appropriate for reproducing the primary qualitative than water, increase the number of intact hydrogen bonds features of hydrophobic interactions [40, 41], swelling of at a site [19]. In the bimodal MLG framework their addi- biopolymers [43], protein denaturation [44, 45], and mi- tion to weakly hydrogen-bonded, disordered clusters may celle formation [46]. The essential behaviour obtained be considered to create ordered clusters with additional within this model is indeed found to be rather insensitive intact hydrogen bonds. The creation of ordered states to the precise parameter values, which may, however, be from disordered ones in the presence of a kosmotropic refined by comparison with experimental measurements cosolvent increases the degeneracy of the former at the to yield semi-quantitative agreement for different solu- expense of the latter. This feature is incorporated by tions [40, 41, 43]. The energy scale is correlated directly raising the number of possible ordered states compared to −1 with a temperature scale, which we define as kBT ≡ β . the number of disordered states (solid arrows in Fig. 3), We conclude this subsection by qualifying the range of validity of the adapted MLG model, including what is qob,k = qob + ηb, qdb,k = qdb − ηb, meant above by “small” solute particles. The model is qos,k = qos + ηs, qds,k = qds − ηs, (1) not appropriate for solute species smaller than a group of water molecules with intercluster hydrogen-bonding, where k denotes the states of water clusters containing which necessitates a linear cluster (and solute) size of kosmotropic cosolvent molecules, and the total number at least 2 water molecules. The model will also fail to of states is kept constant. capture the physics of large, uniform systems where the The effect of chaotropic cosolvents on the state de- linear cluster size exceeds perhaps 10 water molecules, generacies is opposite to that of kosmotropic substances, because in this case the majority of the water molecules and may be represented by inverting the signs in eq. 1. in a “shell site” would correspond effectively to bulk Chaotropic cosolvents are less strongly polar than wa- water. Most molecular-scale treatments of water struc- ter, acting in an aqueous solution of hydrophobic parti- ture in the vicinity of non-polar solute particles assume cles to reduce the extent of hydrogen bonding between a spherical and atomically flat solute surface. These water molecules in both shell and bulk sites [23, 51]. analyses [47, 48, 49] indicate that “clathrate” models Within the adapted MLG framework, this effect is re- 5 produced by the creation of disordered states, with addi- where a = k,c denotes sites containing water and a kos- tional broken hydrogen bonds and higher enthalpy, from motropic or chaotropic cosolvent molecule. The site vari- the more strongly bonded ordered clusters (dashed ar- able λi is defined as the product of the nearest neigh- 2 rows in Fig. 3), whence bours, λi = Qhi,ji nj , and takes the value 1 if site i is completely surrounded by water and cosolvent or 0 oth- q = q − η , q = q + η , ob,c ob b db,c db b erwise. The first sum defines the energy of pure water qos,c = qos − ηs, qds,c = qds + ηs. (2) sites and the second the energy of cosolvent sites. Be- We stress three important qualitative points. First, cause a water site i may be in one of q different states, ˜ the cosolvent affects only the number of intact hydrogen δi,σos is 1 if site i is occupied by water in one of the qos ˜ bonds, but not their strength [23], as a result of which, ordered shell states and 0 otherwise, and δi,σds is 1 if it is also in the bimodal distribution of the coarse-grained occupied by pure water in one of the qds disordered shell model, the energies of the states remain unchanged. Co- states and 0 otherwise. Analogous considerations apply solvent effects are reproduced only by the changes they for the bulk states and for the states of cosolvent sites. cause in the relative numbers of each type of site [eqs. (1) A detailed description of the mathematical structure of and (2)]. Secondly, cosolvent effects on the relative de- the model is presented in Refs. [40] and [36]. generacy parameters are significantly stronger in the bulk The canonical partition function of the ternary N-site than in the shell, because for obvious geometrical reasons system, obtained from the sum over the state configura- related to the orientation of water molecules around a tions {σi}, is non-polar solute particle [36, 41], many more hydrogen- ni(ni+1) ni(ni+1) 2 (1−λi) 2 λi bonded configurations are possible in the bulk. Finally, ZN = Zs Z P{ni} Qi b as suggested in Sec. I, our general framework does not n n − n n − i( i 1) (1−λ ) i( i 1) λ include the possibility of cosolvent-solute interactions, 2 i 2 i × Zs,a Zb,a , (4) which have been found to be important in certain ternary −βEoσ −βEdσ systems, specifically those containing urea [52, 53]. where Zσ = qoσe + qdσe for the shell (σ = The illustrative calculations in Secs. III and IV are per- s) and bulk (σ = b) states both of pure-water and of formed with ηb =9.0 and ηs =0.1 in eqs. (1) and (2). In cosolvent sites (σ = s,a and σ = b,a). the analysis of Ref. [36] these values were found to pro- When the number of particles may vary, a chemical vide a good account of the qualitative physics of urea as a potential is associated with the energy of particle addi- chaotropic cosolvent; in Sec. V we will return to a more tion or removal. The grand canonical partition function quantitative discussion of the role of these parameters. of the system for variable particle number becomes By using the same values for a hypothetical kosmotropic gc cosolvent we will demonstrate that a symmetry of model βµNw+β(µ+∆µ)Na −βHeff [{ni}] Ξ= X e ZN = X e . (5) degeneracy parameters does not extend to a quantitative, N {ni} or even qualitative, symmetry in all of the relevant phys- ical phenomena caused by structure-changing cosolvents. Nw denotes the number of pure water sites, Na the num- We comment briefly that the fractional value of ηs arises ber of cosolvent sites and Np the number of solute par- only from the normalisation convention qos = 1. 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 C. Mathematical Formulation ∆µ the chemical potential for the insertion of a cosolvent molecule at a water site. From the role of the two cosol- To formulate a description of the ternary solution vent types in enhancing or disrupting water structure, at within the framework of statistical mechanics, we begin constant solute particle density ∆µ is expected to be neg- by associating with each of the N sites of the system, ative for kosmotropic agents and positive for chaotropic labelled i, a variable ni, which takes the values ni = 1 ones. if the site contains either pure water, ni = 0 if the site contains a hydrophobic particle, or ni = −1 if the site contains a water cluster including one or more cosolvent D. Monte Carlo Simulations molecules. This system is described by the Hamiltonian

N We describe only briefly the methods by which the n (n +1) H[{n }, {σ }]= i i [(E δ˜ +E δ˜ )λ model may be analyzed; full technical details may be i i X 2 ob i,σob db i,σdb i i=1 found in Ref. [40]. Because our primary interest is in the local solute and cosolvent density variations which +(E δ˜ + E δ˜ )(1 − λ )] os i,σos ds i,σds i demonstrate aggregation and preferential phenomena, we N n (n − 1) focus in particular on Monte Carlo simulations at the + i i [(E δ˜ + E δ˜ )λ X 2 ob i,σob,a db i,σdb,a i level of individual solute molecules. Classical Monte i=1 Carlo simulations allow the efficient calculation of ther- ˜ ˜ +(Eosδi,σos,a + Edsδi,σds,a )(1 − λi)], (3) mal averages in many-particle systems with statistical 6

fluctuations [40], such as that represented by eq. (5). We work 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, pure water or a water-cosolvent mixture. The results are un- affected by changes in lattice size. We have implemented a Metropolis algorithm for sampling of the configuration space. After a sufficiently large number (100000) of re- laxation steps, the system achieves thermal equilibrium and averages are taken over a further 500000 measure- ments to estimate thermodynamic quantities. Coexis- tence lines in the µ-T phase diagram are obtained from the transitions determined by increasing the temperature at fixed chemical potential µ (grand canonical sampling), which results in a sudden density jump at the transition temperature. The solute particle densities ρp correspond- FIG. 4: Closed-loop coexistence curves for a ternary system ing to these jumps yield closed-loop coexistence curves of water, kosmotropic cosolvent and hydrophobic particles for in the ρp-T phase diagram. Despite the rather crude ap- two different cosolvent densities ρk, obtained by mean-field proximation to a continuum system offered by the use calculation with degeneracy parameters ηb = 9.0 and ηs = of a cubic lattice, we have found quantitative agreement 0.1 in eq. (1). On the outside of each curve the solution with other theoretical approaches, which is why we focus is homogeneous, whereas on the inside it separates into two primarily on Monte Carlo simulations here. In Sec. V we phases. The dashed arrow represents the heating process of a ρ0 ρ 2 will also demonstrate remarkable qualitative, and in some system with particle density and cosolvent density k = 0.61 from temperature T0 in the homogeneous region to T1 in cases semi-quantitative, agreement with experiment, sug- the two-phase region. At T1 the system is separated into two gesting that the adapted MLG framework may indeed phases of different densities ρ1 (nearly pure water-cosolvent form a suitable basis for more sophisticated modelling. mixture) and ρ2 (hydrophobic aggregates). For the macroscopic properties of the system, such as aggregation and phase coexistence, the results of the Monte Carlo simulations may be interpreted with the aid and for intermediate particle concentrations, a phase sep- of a mean-field analysis. If the densities at each site are aration is found into a pure solvent phase (meaning a approximated by their average values in the solution, ρ p water-cosolvent mixture) and an aggregated phase with for hydrophobic particles, ρ for pure water and ρ for w a fixed solute density. cosolvent, where ρ + ρ + ρ = 1, the mean value hn i p w a i The hydrophobic repulsion between water and non- at site i is given by hnii = Pσ ni,σρσ = ρw − ρa and analogously hn2i = n2 ρ = ρ + ρ . The equilib- polar solute particles, developed as a result of the forma- i Pσ i,σ σ w a tion of water structure, increases in the presence of kos- rium densities are obtained by minimisation of the grand canonical mean-field free energy per site, motropic cosolvents (this result may be shown by rewrit- ing the partition function (eq. 5) in terms of the par- −1 −1 f = (µ − β ln Zs)ρw + (µ + ∆µ − β ln Zs,a)ρa ticle sites [36]). As shown in Fig. 4, the temperature and density ranges of the aggregation region indeed rise +β−1(ln Z − ln Z )ρ (ρ + ρ )z s b w a w with increasing cosolvent concentration, illustrating the −1 z +β (ln Zs,a − ln Zb,a)ρa(ρa + ρw) stabilising effect of kosmotropic agents. Further, the par- −1 +β (ρw ln ρw + ρa ln ρa + ρp ln ρp), (6) ticle density of the aggregate phase in the two-phase re- gion increases when adding cosolvent, demonstrating in where z denotes the number of nearest neighbours of each addition the strengthening of effective hydrophobic in- site. teractions between solute particles due to the growing water-solute repulsion. This is illustrated by the process of heating a system at constant density: the dashed ar- III. KOSMOTROPIC EFFECT row in Fig. 4 represents a solution with particle density ρ0, which is heated from temperature T0 in the homo- We begin our analysis of the kosmotropic effect by dis- geneous region to a temperature between the LCST and cussing the mean-field ρp-T phase diagram for different the UCST. In the heterogeneous region (T1), the solu- cosolvent concentrations, shown in Fig. 4. As expected tion separates into two phases of densities ρ1 (almost from Sec. IIA the system exhibits a closed-loop coex- pure solvent) and ρ2 (hydrophobic aggregates) under the istence curve, forming a homogeneous particle-solvent- constraint ρ0(V1 + V2) = ρ1V1 + ρ2V2, where Vi is the cosolvent mixture below a LCST and above an UCST for volume occupied by phase i. An increase in cosolvent all concentrations, whereas between these temperatures, density leads to a higher density ρ2 of hydrophobic ag- 7

FIG. 5: Closed-loop coexistence curves obtained by Monte FIG. 6: µ-T phase diagram of hydrophobic solute in an aque- Carlo simulations for an aqueous solution of hydrophobic par- ous cosolvent mixture for two different kosmotropic cosol- ticles with the same parameters as in Fig. 4. vent concentrations ρk, obtained by Monte Carlo simulations. The endpoints of the finite transition lines correspond to the UCST and LCST. gregates and a lower value ρ1, which may be interpreted as a strengthening of the hydrophobic interactions gen- erated between solute particles. of finite length terminated by the UCST and LCST de- However, the mean-field approximation neglects fluc- marcate the aggregation phase transition. An increase in tuations in the density, and consequently is unable to cosolvent density leads to a larger separation of UCST detect intrinsically local phenomena such as preferential and LCST as a direct result of the expansion of the ag- exclusion of cosolvent particles from the solvation shell of gregation regime (Fig. 5). The transition line is shifted a hydrophobic particle (Fig. 2). Because the kosmotropic to higher values of µ, indicating an increased resistance effect is strongly dependent upon local enhancement of of the system to addition of water at constant volume water structure, a full analysis is required of the spatial in the presence of cosolvent. This is a consequence of density fluctuations in the system. We thus turn to the the fact that the resistance to addition of hydrophobic results of Monte Carlo simulations, which at the macro- particles depends on both µ and ∆µ: with increasing co- scopic level show the same enhancement of hydrophobic solvent concentration, ∆µ decreases (i.e. becomes more aggregation (Fig. 5) as indicated in the mean-field anal- negative) and hence µ must increase for the critical par- ysis. Below the LCST and above the UCST, one homo- ticle density to remain constant. geneous mixture is found where the hydrophobic parti- By inspection of the energy levels, and of the alteration cles are dissolved, while between these temperatures they in their relative degeneracies caused by a kosmotropic form aggregates of a given density. The LCST and the cosolvent (Fig. 3), it is energetically favourable to max- critical aggregate densities determined by the mean-field imise the cosolvent concentration in bulk water with re- calculation do not differ strongly from the numerical re- spect to shell water. Thus one expects a preferential sults, but the UCST lies at a temperature higher than exclusion, also known as preferential hydration, as repre- that determined by Monte Carlo simulations. This is to sented schematically in the right panel of Fig. 2. Except be expected because mean-field calculations neglect fluc- at the lowest temperatures, an increased number of water tuation effects, generally overestimating both transition molecules in the solvation shell of non-polar solute par- temperatures. The agreement of the mean-field result for ticles increases the repulsion between solute and solvent, small ρk with the simulated value for the LCST suggests resulting in a reduction of solubility, in an enhanced ef- a predominance of local effects at low temperatures, and fective attraction between solute particles due to the de- that density fluctuations between sites are small. We creased interface with water as they approach each other, note, however, that a cosolvent concentration ρk = 0.61 and thus in aggregate stabilisation. is required in the mean-field approximation to produce Monte Carlo simulations confirm the expectation that an expansion of the aggregated phase similar to that ob- the cosolvent concentration is lower in shell water than served in the Monte Carlo results for ρk =0.25, demon- in bulk water. Figure 7 shows the cosolvent shell con- strating the growing importance of fluctuation effects at centration compared to the overall cosolvent concentra- higher cosolvent concentrations. tion in the solution, where preferential exclusion of the The µ-T phase diagram of the ternary system obtained kosmotropic cosolvent from the solvation shell of the hy- by Monte Carlo simulations is presented in Fig. 6. Lines drophobic solute particles is observed. At constant chem- 8

2.5 ρ c=0.02 ρ c=0.3 2 ρ c=0.4 ρ c=0.5 ρ c=0.53 T 1.5

1

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

FIG. 8: Closed-loop miscibility curves of an aqueous solution of hydrophobic particles for different chaotropic cosolvent con- FIG. 7: Relative concentration of kosmotropic cosolvent in the centrations ρc, obtained by Monte Carlo simulations using the solvation shell of hydrophobic particles, obtained from Monte degeneracy parameters ηb = 9.0 and ηs = 0.1 in eq. (2). On Carlo simulations at chemical potential µ = 2.5, exhibiting the outside of the curves is the homogeneous, dissolved state preferential exclusion. The effect is most pronounced for low while inside them is the aggregated state. As the cosolvent cosolvent densities. concentration grows, particle solubility increases, leading to a reduced coexistence regime. ical potential µ, a sharp drop occurs at the phase tran- sition temperature (Fig. 6), which is due to the sudden mation of disordered bulk water states into energetically change in solute particle density. At very low particle favourable ordered bulk states by the kosmotropic cosol- density, a clear exclusion of the cosolvent from the solva- vent. Preferential hydration is a further manifestation of tion shell appears. However, at high particle density (for this exclusion. temperatures below the aggregation phase transition) the effect is only marginal, because here the number of parti- cle sites becomes substantial, most solvent and cosolvent IV. CHAOTROPIC EFFECT sites are shell sites and thus the total cosolvent density is almost identical to the shell cosolvent density. The com- A detailed study of chaotropic cosolvent effects within paratively strong fluctuations in relative cosolvent shell the adapted MLG model for a hydrophobic-polar mixture concentration at temperatures above the phase transition was presented in Ref. [36]. Here we provide only a brief may be attributed to the very low particle density in the review of the results of this analysis, with emphasis on system. Small, thermal fluctuations in the number of the differences and similarities in comparison with the shell sites occupied by cosolvent molecules result in large kosmotropic effect, which we have discussed at greater fluctuations in the cosolvent shell concentration. length in Sec. III. Figure 8 shows the coexistence curves Considering next the effect of the cosolvent concentra- demarcating the aggregated state for a range of cosolvent tion, the system shows a substantially stronger preferen- concentrations, computed by Monte Carlo simulations. tial exclusion for low than for high cosolvent densities. The general features of the phase diagram are those of This is again largely a consequence of considering the Sec. III (Figs. 4 and 5), with the obvious exception of the relative, as opposed to absolute, decrease in cosolvent shrinking of the coexistence regime as cosolvent concen- concentration in the shell. Preferential exclusion is less tration is increased. However, it appears that for the q pronounced for high cosolvent densities because a smaller and η parameters used in the analysis (Sec. IIB) the ef- proportion of cosolvent sites can contribute to the effect. fect of high chaotropic cosolvent concentrations is rather At high temperatures, entropy, and therefore mixing, ef- stronger than that obtained with the kosmotropic cosol- fects become dominant and the preferential exclusion of vent, an issue to which we return in Sec. V. Figure 8 sug- cosolvent particles shows a slight decrease. gests that sufficiently high concentrations of chaotropic We conclude this section by commenting also on the cosolvent may cause complete aggregate destabilisation phenomenon shown in Figs. 4 and 5, that for tempera- at any temperature and solute particle density. tures where no aggregation is possible in the pure water- Figure 9 shows the corresponding µ-T phase diagram. solute solution (below the LCST), it can be induced only As in Fig. 6, the lines representing the discontinuous by the addition of a cosolvent. Aggregation is driven by jump in density from the low- to the high-ρp phase move exclusion of solute from the solution in this intermediate to higher µ with increasing cosolvent concentration, again regime, and is thus an indirect result of the transfor- reflecting the increased cost of adding water to the sys- 9

3 2 ρ c=0.02 2.5 ρ c=0.3 ρ = 0.03 ρ 1.8 c, total c=0.4 ρ 2 c=0.5 ρ = 0.28 1.6 c, total

low particle density c,total ρ T = 0.35 1.5 ρ c, total / high particle density low particle density

1.4c,shell

1 ρ high particle density ρ = 0.55 0.5 1.2 c, total

ρ = 0.71 0 c, total 0 1 2 3 4 5 6 7 1 µ 0 0.5 1 1.5 2 2.5 T FIG. 9: µ-T phase diagram of hydrophobic solute in an aque- FIG. 10: Preferential binding effect, illustrated by the relative ous cosolvent mixture for different chaotropic cosolvent con- concentration of chaotropic cosolvent in the solvation shell of centrations ρc, obtained by Monte Carlo simulation. The fi- hydrophobic particles, for different cosolvent concentrations nite transition lines terminate at an UCST and a LCST, which at fixed µ = 3.0, obtained by pair approximation. approach each other with increasing cosolvent concentration. tem in the presence of cosolvent. However, in this case tween the opposing effects of kosmotropic and chaotropic the endpoints of the lines, which represent the UCST and substances on hydrophobic aggregation of a given solute LCST for each cosolvent concentration, become closer as species. Indeed, the competition of the two effects has been studied for solutions of the protein HLL with the ρc increases until they approach a singularity (Fig. 8), which we discuss in detail in Sec. V. (denaturing) chaotrope guanidine hydrochloride and the Figure 10 shows as a function of temperature the co- (native-structure stabilising) kosmotrope betaine [8]. We solvent concentration in the shell of a solute particle nor- remark, however, that the same cosolvent may have a different effect for solutions of different types and sizes malised by the total ρc. This demonstration of prefer- ential binding of chaotropic agents to non-polar solute of solute (Sec. II), and for this reason a global charac- particles was obtained from the model of eq. (3) within terisation of the effectiveness of any one agent may be a pair approximation, which was shown in Ref. [36] to misleading. provide a semi-quantitative reproduction of the Monte At low cosolvent concentration, the stabilising or Carlo results. As in Fig. 7, the sharp step at the phase destabilising effects of the two cosolvent types on ag- transition is due to the sudden change in particle density. gregate formation are rather small, and appear almost At low particle densities (below the transition) the effect symmetrical in the expansion or contraction of the coex- is clear, whereas at high densities it is small because the istence region (Figs. 5 and 8, Figs. 6 and 9). For weakly majority of solvent and cosolvent sites have become shell kosmotropic and chaotropic agents, by which is meant sites. For low cosolvent concentrations, preferential bind- those causing only small enhancement or suppression of aggregation even at high concentrations, such qualitative ing can lead to a strong increase in ρc on the shell sites (80% in Fig. 10), but the relative enhancement becomes symmetry might be expected as a general feature of the less significant with increasing total cosolvent concentra- coexistence curves. With the same caveats concerning tion. Finally, in counterpoint to the discussion at the low concentrations or weak cosolvent activity, this state- end of Sec. III, we comment that for chaotropic agents, ment is also true for preferential exclusion and binding of which in bulk water transform ordered states into disor- cosolvent to the solute particles, as shown by comparing dered ones, preferential binding (cosolvent exclusion) is Figs. 7 and 10. However, differing phenomena emerge for favoured and solute exclusion decreases. Thus a regime strongly kosmotropic and chaotropic agents. exists in the ρp-T phase diagram where at fixed temper- ature and particle density, aggregates of solute particles may be made to dissolve simply by the addition of cosol- A. Urea as a Strong Chaotrope vent. Chaotropic cosolvents act to suppress the formation of water structure and, because the latter is already dis- V. STRONG AND WEAK COSOLVENTS rupted by the presence of a non-polar solute particle, are more efficient for bulk than for shell sites. Within the As indicated in Sec. II and illustrated by the results adapted MLG model, a maximally chaotropic agent is of Secs. III and IV, there is a qualitative symmetry be- one which causes sufficient disruption that the number 10

3 Such singular behaviour is well known in many aque- (a) ous solutions containing urea, and indeed frequent use ρ = 0.8 2.5 c is made of the destabilising properties of this cosolvent ρ = 0.75 c (Sec. I). We stress at this point that the chaotropic ac- 2 ρ c= 0.65 tion of urea is by no means universal: in a number of T ρ = 0.5 systems, such as the ultra-small solute methane [20, 54], 1.5 c * ρ and proteins with variable hydrophobicity [49] or signifi- T c= 0.33 ρ = 0.03 cant interactions between chain segments and the cosol- 1 c vent molecules [52, 53], its effect may in fact be inverted. However, because of its ubiquity as a solubilising agent 0.5 for most binary systems, we continue to consider urea as 0 a generic example of a strong chaotrope. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ρ* The aggregation singularity was reproduced in the p ρ p qualitative analysis of urea as a chaotropic agent per- formed in Ref. [36], and is illustrated in Fig. 11. Because of the discrete nature of the Monte Carlo simulations, the 3 exact parameters for the critical point cannot be found ρ using this technique; these were instead obtained only c=0.03 (b) 2.5 ρ c=0.33 within the mean-field approximation, and as a result ρ =0.5 c cannot be considered to be quantitatively accurate for 2 ρ =0.65 c ρ ρ* the parameters of the system under consideration. Fig- ρ =0.75 p< p T c ure 11(a) shows the shrinking of the coexistence curves ρ =0.8 1.5 c ρ =0.81 with increasing cosolvent concentration until they vanish c ∗ ∗ at a critical value ρc =0.81 (cf. ρc ≈ 0.55 expected from 1 inspection of the Monte Carlo results in Fig. 8). The ρ >ρ* p p corresponding evolution of the transition line in the µ-T 0.5 phase diagram is shown in Fig. 11(b). With the canonical choice of degeneracy parameters 0 0 2 4 6 8 (Sec. IIB) q = 49, q = 40, q = 10 and q = 1 [41], µ ds db ob os the values ηb = 9.0 and ηs = 0.1 required in eq. (2) to reproduce this critical vanishing are indeed such that FIG. 11: (a) Coexistence curves for ternary water/cosol- qob,c = 1 and qos,c = 0.9 become very close. The level vent/solute systems with different cosolvent concentrations of “fine-tuning” of the underlying parameters required in ρc, obtained by mean-field calculation. At a critical cosolvent ∗ the adapted MLG model reflects not a weakness of the concentration of ρc = 0.81, the LCST and UCST coincide, at ∗ framework but rather of the strongly chaotropic proper- a critical temperature T = 1.35 and critical particle density ∗ ties of urea in water: the destruction of hydrogen-bonded ρp = 0.14, where the aggregation regime is reduced to a single point. For still higher cosolvent concentrations the solution networks is almost complete at high concentrations. In is homogeneous over the full range of temperature and par- practice, concentrated urea is used to destabilise aque- ticle density. (b) Mean-field µ-T phase diagram for different ous solutions of many folded proteins, micelles and ag- cosolvent concentrations. As ρc increases, the separation of gregates of hydrophobic particles. While we are unaware ∗ LCST and UCST decreases until for ρc = ρc they meet at the of systematic experimental studies of the effects of urea ∗ ∗ ∗ temperature TL = TU = T , where the value µL = µU = 7.05 ∗ on the extent of the coexistence regime, aggregate desta- determines ρp = 0.14. bilisation has been achieved at high concentrations in certain systems. At room temperature, the solubility of the highly hydrophobic amino-acid phenylalanin is dou- bled in an 8M urea solution (a solution with equal volume of ordered bulk states is reduced to its hypothetical min- fractions of urea and water) [16]. imum value, which is equal to the number of ordered shell states; by the definition based on hydrogen-bond forma- tion, it is not possible to have fewer ordered bulk than or- B. Sodium Chloride as a Weak Kosmotrope dered shell states, so qob ≥ qos. When qob and qos become similar, the entropic gain of creating ordered bulk states by aggregation (removal of shell sites) is largely excluded, Kosmotropic cosolvents increase the extent of water and thus a strongly chaotropic agent raises the solubility structure formation, raising the number of ordered bulk of hydrophobic particles very significantly. With a suffi- and shell sites. While this process may be more efficient cient concentration of such cosolvents, aggregation may for ordered shell states, their degeneracy cannot exceed be completely prevented at all temperatures and den- that of ordered bulk states. A maximally kosmotropic sities, and the coexistence regime vanishes at a critical agent is one which causes sufficient structural enhance- value of cosolvent concentration. ment that the number of ordered bulk states rises to the 11

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 a significantly greater temperature range. Although the data do not extend to sufficiently high temperatures to discuss the full extension of the aggregation regime in density (Fig. 12, inset), the qualitative similarity of Figs. 4 and 5 to the experimentally determined coexis- tence curves (Fig. 12, main panel) suggests that sodium chloride 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 of sodium sulphate, investigated by the same authors [55], at maximal concentrations it appears that the aggre- gation singularity is not reached and the closed-loop FIG. 12: Coexistence curve measured in the experimentally form of the miscibility curve is preserved. Here we note accessible temperature range for N,N-Diethylmethylamine in that, while the kosmotropic action of sodium chloride is water in the presence and in the absence of the kosmotropic due to its ionic nature in solution, the considerations of cosolvent sodium chloride, reproduced from Ref. [55]. The the adapted MLG framework (Sec. IIB) remain valid to ◦ ◦ LCST is reduced from 51 C in the salt-free case to −0.6 C in model this effect. A more detailed comparison of the the saturated cosolvent solution. model results with the data is precluded by the fact that the cosolvent concentration in the saturated solu- tion changes with both temperature and solute density. point where it is equal to the number of disordered bulk Measurements of different solutions are required to char- states, q = q . Singular behaviour for a strongly kos- ob db acterise the dependence of aggregation enhancement on motropic cosolvent (the counterpart to the vanishing of the molecular properties of the solute and on both solute aggregation caused by chaotropic cosolvents) is then the and cosolvent concentrations in the system. perfect aggregation of the system with densities ρ = 0 1 Finally, preferential exclusion of kosmotropic cosol- and ρ = 1 (Fig. 4), i.e. extension of the coexistence 2 vents from the immediate vicinity of hydrophobic par- regime across the entire phase diagram. Only at the low- ticles in aqueous solutions is measured only for very high est temperatures, where entropy effects are irrelevant, cosolvent concentrations. Concentrations of compatible would the mechanism of cage formation allow solution of osmolytes, such as sucrose and betaine in the cytoplasm, the solute particles. For a sufficiently strong kosmotropic typically reach values well in excess of 0.5M. The stabil- effect (high concentrations of a strong agent) there is no ity of the protein lactate dehydrogenase against thermal reason why q should not exceed q , a situation which ob db denaturation increases by approximately 90% in a 1M represents the breakdown of the sequence of energies and sucrose solution at room temperature, and by 100% for degeneracies characteristic of a system with a closed-loop the same concentration of hydroxyecotine [1], classifying miscibility curve (Sec. IIA). Complete aggregation is the these cosolvents as being strongly kosmotropic. In the hallmark of this breakdown. current model it is difficult to specify the exact cosolvent The “symmetrical” parameters η = 9.0 and η = 0.1 b s concentration because one site contains a group of water used in the analysis of Sec. III give the values q = 19 ob molecules, but the results are nevertheless qualitatively and q = 31 [eq. (1)]. These are clearly not suffi- db consistent with observation. We have found that, except ciently close to represent a strongly kosmotropic cosol- for specifically chosen values of the parameters q and vent, which would explain both the rather modest ex- σ η , cosolvent concentrations well in excess of 10% are re- pansion of the coexistence regime even with relatively σ quired to show a clear stabilising effect on hydrophobic high cosolvent concentrations (ρ ) and the small values k aggregates (Fig. 5). of the upper particle density ρ2 < 1 (Figs. 4, 5). One may thus conclude that quantitative symmetry between kosmotropic and chaotropic effects cannot be expected for any temperatures or densities, except in the event of VI. SUMMARY very carefully chosen degeneracy parameters. To our knowledge, rather little data is presently avail- We have discussed the physical mechanism underlying able concerning the phase diagram of hydrophobic solute the action of kosmotropic and chaotropic cosolvents on particles in cosolvent solutions. However, Ting et al. [55] hydrophobic aggregates in aqueous solutions. The aggre- have measured the lower coexistence curves for N,N- gation phenomena arise from a balance between enthalpic Diethylmethylamine both in pure water and in a mixture and entropic contributions to the solvent free energy, of water and the cosolvent sodium chloride (Fig. 12), which is fully contained within an adapted version of the 12 bimodal model of Muller, Lee and Graziano. This model tween solute particles, thus stabilising their aggregates; considers two populations of water molecules with differ- similarly, the preferential binding of chaotropic agents ing physical properties, and generates indirectly the ef- to solute particles reduces the hydrophobic interaction, fective hydrophobic interaction between solute particles. causing the particles to remain in solution. The essen- Such a description, based on the microscopic details of tial cosolvent phenomena may thus be explained purely water structure formation around a solute particle, is ex- by the propensity of these agents to promote or suppress pected to be valid for small solute species, characterised water structure formation, and the effectiveness of a co- by lengthscales below 1 nm, and for those larger solute solvent is contained in a transparent way in the micro- particles whose solubility is dominated by the atomically scopic degeneracy parameters of the solvent states. rough (highly curved) nature of their surfaces. In the adapted MLG framework, one may include Our focus on water structure is intended to extract one the ability of kosmotropic cosolvents to enhance and of of the primary factors determining aggregation and co- chaotropic cosolvents to disrupt the structure of liquid solvent activity, and is not meant to imply that other in- water simply by altering the state degeneracies [eqs. (1) teractions are not important. The range of solute species and (2)] associated with the two populations characteris- and additional contributions which are beyond the scope ing this structure. As a consequence only of these changes of our analysis includes extremely small solutes, large, in the properties of the solvent, the model reproduces all atomically flat solute surfaces, solutes with differing sur- of the physical consequences of cosolvents in solution: face hydrophobicity (such as polar side-groups) and sur- for kosmotropes the stabilisation of aggregates, expan- faces undergoing specific chemical (or other) interactions sion of the coexistence regime and preferential cosolvent with the cosolvent. However, from the qualitative trends, exclusion from the hydration shell of hydrophobic solute and even certain quantitative details, observed in a wide particles; for chaotropes the destabilisation of aggregates, variety of aqueous systems it appears that the adapted a contraction of the coexistence regime and preferential MLG model is capable of capturing the essential phe- binding to solute particles. nomenology of cosolvent activity on aggregation and sol- The microscopic origin of these preferential effects lies ubility for solutes as diverse as short hydrocarbons and in the energetically favourable enhancement of hydrogen- large proteins. bonded water structure in the presence of a kosmotropic Acknowledgments cosolvent, and conversely the avoidance of its disruption in the presence of a chaotrope. In a more macroscopic in- terpretation, the preferential hydration of solute particles We thank the Swiss National Science Foundation for by kosmotropic agents can be considered to strengthen financial support through grants FNRS 21-61397.00 and the solvent-induced, effective hydrophobic interaction be- 2000-67886.02.

[1] E.A. Galinski, Compatible solutes of halophilic eubacte- natural selection of a thermodynamic force in protein ria: molecular principles, water-solute interaction, stress folding, J. Mol. Biol. 310 (2001), 955-963. protection, Experientia 49 (1993) 487-496. [10] J.A. Schellman, Selective binding and solvent denatura- [2] P.H. Yancey, M.E. Clark, S.C. Hand, R.D. Bowlus and tion, Biopolymers 26 (1987) 549-559; A simple model for G.N. Somero, Living with water stress: evolution of os- solvation in mixed solvents, Biophys. Chem. 37 (1990) molyte systems, Science 217 (1982) 1214-1222. 121-140; The relation between the free energy of interac- [3] G.N. Somero, Protons, osmolytes, and fitness of internal tion and binding, Biophys. Chem. 45 (1993) 273-279. milieu for protein function, Am. J. Physiol. 251 (1986) [11] S.N. Timasheff, Thermodynamic binding and site occu- R197-R213. pancy in the light of the Schellman exchange concept, [4] P.M. Wiggins, Role of water in some biological processes, Biophys. Chem. 101-102 (2002) 99-111. Microbiol. Rev. 54 (1990) 432-449. [12] A. Tovchigrechko, M. Rodnikova and J. Barthel, Com- [5] E. A. Galinski, M. Stein, B. Amendt and M. Kinder, The parative study of urea and tetramethylurea in water by kosmotropic (structure-forming) effect of compensatory molecular dynamics simulations, J. Mol. Liq. 79 (1999) solutes, Comp. Biochem. Physiol. 117A (1997) 357-365. 187-201. [6] T. Arakawa and S.N. Timasheff, Mechanism of [13] J.R. De Xammar Oro, Role of co-solute in biomolecular poly(ethylene glycol) interaction with proteins, Biochem- stability: glucose, urea and the water structure, J. Biol. istry 24 (1985) 6756-6762. Phys. 27 (2001) 73-79. [7] S.N. Timasheff, in: Water and life, ed. G.S. Somero [14] Y. Feng, Z.-W. Yu and P.J. Quinn, Effect of urea, (Springer Verlag, Berlin, 1992) p. 70. dimethylurea, and tetramethylurea on the phase behav- [8] T. S¨oderlund, K. Zhu, A. Jutila and P.K.J. Kinnunen, ior of dioleoylphosphatidylethanolamine, Chem. Phys. Effects of betaine on the structural dynamics of Ther- Lipids 114 (2002) 149-157. momyces (Humicola) lanuginosa lipase, Coll. Surf. B: [15] T.H. Plumridge and R.D. Waigh, Water structure theory Biointerfaces 26 (2003) 75-83. and some implications for drug design, J. Pharm. Phar- [9] D.W. Bolen and I.V. Baskakov, The osmophobic effect: macol. 54 (2002) 1155-1179. 13

[16] Y. Nozaki and C. Tanford, The solubility of amino acids [38] B. Lee and G. Graziano, A two-state model of hydropho- and related compounds in aqueous urea solutions, J. Biol. bic hydration that produces compensating enthalpy and Chem. 238 (1963) 4074-4081. entropy changes, J. Am. Chem. Soc. 22 (1996) 5163-5168. [17] Y. Nozaki and C. Tanford, The solubility of amino acids, [39] K.A.T. Silverstein, A.D.J. Haymet and K.A. Dill, The diglycine, and triglycine in aqueous guanidine hydrochlo- strength of hydrogen bonds in liquid water and around ride solutions, J. Biol. Chem. 245 (1970) 1648-1652. non-polar solute, J. Am. Chem. Soc. 122 (2000) 8037- [18] P.K. Nandi and D.R. Robinson, Effects of urea and guani- 8041. dine hydrochloride on peptide and non-polar groups, Bio- [40] S. Moelbert and P. De Los Rios, Hydrophobic interaction chemistry 23 (1984) 6661-6668. model for upper and lower critical solution temperatures, [19] G.E. Walrafen, Raman spectral studies of the effects of Macromolecules 36 (2003) 5845-5853. urea and sucrose on water structure, J. Chem. Phys. 44 [41] K.A.T. Silverstein, A.D.J. Haymet and K.A. Dill, Molec- (1966) 3726-3727. ular model of hydrophobic solvation, J. Chem. Phys. 111 [20] D.B. Wetlaufer, S.K. Malik, L. Stoller and R.L. Coffin, (1999) 8000-8009. Nonpolar group participation in the denaturation of pro- [42] D. Paschek, Temperature dependence of the hydrophobic teins by urea and guanidinium salts, J. Am. Chem. Soc. hydration and interaction of simple solutes: an examina- 86 (1967) 508-514. tion of five popular water models, J. Chem. Phys. 120 [21] M. Roseman and W.P. Jencks, Interactions of urea and (2004) 6674-6690; Heat capacity effects associated with other polar compounds in water, J. Am Chem. Soc. 97 the hydrophobic hydration and interaction of simple so- (1975) 631-640. lutes: a detailed structural and energetical analysis based [22] Y. Kita, T. Arakawa, T.-Y. Lin and S.N. Timasheff, on molecular dynamics simulations, J. Chem. Phys. 120 Contribution of the surface free energy perturbation (2004) 10605-10617. to protein-solvent interactions, Biochemistry 33 (1994) [43] P. De Los Rios and G. Caldarelli, Cold and warm swelling 15178-15189. of hydrophobic polymers, Phys. Rev. E 63 (2001) 031802- [23] F. Franks, Protein stability: the value of ’old litera- 1-5. ture’, Biophys. Chem. 96 (2002) 117-127, and references [44] P. De Los Rios and G. Caldarelli, Putting proteins back therein. into water, Phys. Rev. E 62 (2000) 8449-8452. [24] S.N. Timasheff and T. Arakawa, in: Protein structure: a [45] G. Caldarelli and P. De Los Rios, Cold and warm denat- practical approach, ed. T.E. Creighton (IRL Press, Ox- uration of proteins, J. Biol. Phys. 27 (2001) 229-241. ford, 1997) p. 331. [46] S. Moelbert, B. Normand and P. De Los Rios, Solvent- [25] H.S. Frank and M.W. Evans, Free volume and entropy in induced micelle formation in a hydrophobic interaction condensed systems, J. Chem. Phys. 13 (1945) 507-532. model, Phys. Rev. E 69 (2004) 061924-1-11. [26] M. Yaacobi and A. Ben-Naim, Solvophobic interaction, [47] C.Y. Lee, J.A. McCammon and P.J. Rossky, The struc- J. Phys. Chem. 78 (1974) 175-178. ture of liquid water at an extended hydrophobic surface, [27] P.L. Privalov and S.J. Gill, Stability of protein struc- J. Chem. Phys. 80 (1984) 4448-4453. ture and hydrophobic interaction, Adv. Protein Chem. [48] X. Huang, C.J. Margulis and B.J. Berne, Do molecules 39 (1988) 191-234. as small as neopentane induce a hydrophobic response [28] P.H.K. De Jong, J.E. Wilson and G.W. Neilson, Hy- similar to that of large hydrophobic surfaces ? J. Phys. drophobic hydration of methane, Mol. Phys. 91 (1997) Chem. B 107 (2003) 11742-11748. 99-103. [49] S. Shimizu and H.S. Chan, Origins of protein denatured [29] A. Perstemilidis, A.M. Saxena, A.K. Soper, T. Head- states compactness and hydrophobic clustering in aque- Gordon and R.M. Glaeser, Direct evidence for modi- ous urea: inferences from nonpolar potentials of mean fied solvent structure within the hydration shell of a hy- force, Proteins: Struct. Funct. Genet. 49 (2002) 560-566. drophobic amino acid, Proc. Natl. Acad. Sci. USA 93 [50] K. Lum, D. Chandler and J.D. Weeks, Hydrophobicity at (1996) 10769-10774. small and large length scales, J. Phys. Chem. 103 (1999), [30] W. Kauzmann, Some factors in the interpretation of pro- 4570-4577. tein denaturation, Adv. Protein Chem. 14 (1959) 1-63. [51] E.G. Finer, F. Franks and M.J. Tait, Nuclear mag- [31] C. Tanford, The hydrophobic effect: formation of mi- netic resonance studies of aqueous urea solutions, J. Am. celles and biological membranes (Wiley, New York, Chem. Soc. 94 (1972) 4424-4427. 1980). [52] J.M. Scholtz, D. Barrick, E.J. York, J.M. Stewart and [32] F.H. Stillinger, Water revisited, Science 209 (1980) 451- R.L. Baldwin, Urea unfolding of peptide helices as a 457. model for interpreting protein unfolding, Proc. Natl. [33] A. Ben-Naim, Water and aqueous solutions: introduction Acad. Sci. USA 92 (1995) 185-189. to a molecular theory (Plenum Press, New York, 1974). [53] R.A. Kuharski and P.J. Rossky, Solvation of hydrophobic [34] R. Ludwig, Water: from clusters to the bulk, Angew. species in aqueous urea solution: a molecular dynamics Chem. Int. Ed. Engl. 40 (2001) 1808-1827. study, J. Am. Chem. Soc. 106 (1984) 5794-5800. [35] S.N. Timasheff, Protein-solvent preferential interactions, [54] G. Graziano, On the solubility of aliphatic hydrocarbons protein hydration, and the modulation of biochemical re- in 7 M aqueous urea, J. Phys. Chem. B 105 (2001) 2632- actions by solvent components, Proc. Natl. Acad. Sci. 99 2637. (2002) 9721-9726. [55] A.M. Ting, S. Lynn and J.M. Prausnitz, Liquid- [36] S. Moelbert and P. De Los Rios, Chaotropic effect and liquid equilibria for aqueous systems containing N,N- preferential binding in a hydrophobic interaction model, Diethylmethylamine and sodium chloride or sodium sul- J. Chem. Phys. 119 (2003) 7988-8001. fate, J. Chem. Eng. Data 37 (1992) 252-259. [37] N. Muller, Search for a realistic view of hydrophobic ef- fects, Acc. Chem. Res. 23 (1990) 23-28.