The temperature dependence of the Hofmeister series : thermodynamic fingerprints of cosolute – protein interactions †

The Hofmeister series is a universal homologous series to rank ion-specific effects on biomolecular properties such as protein stability or aggregation propensity. Although this ranking is widely used, outliers and exceptions are discussed controversially and a molecular level understanding is still lacking. Studying the thermal unfolding equilibrium of RNase A, we here show that this ambiguity arises from the oversimplified approach to determine the ion rankings. Instead of measuring salt effects on a single point of the protein folding stability curve (e.g. the melting point Tm), we here consider the salt induced shifts of the entire protein 'stability curve' (the temperature dependence of the unfolding free energy change, ΔGu(T)). We found multiple intersections of these curves, pinpointing a widely ignored fact: the Hofmeister cation and anion rankings are temperature dependent. We further developed a novel classification scheme of cosolute effects based on their thermodynamic fingerprints, reaching beyond salt effects to non-electrolytes.


Introduction
The native conformation of a protein is only marginally stable. 1 The low stability is expressed by the low Gibbs free energy of unfolding, DG u = DH u À TDS u , which can be dissected into its enthalpic and entropic contributions, DH u , and TDS u , respectively. DG u , forms the thermodynamic driving force of the transition from the native to the unfolded state and has to be positive for a stable conformation. The low DG u is founded in the mutual compensation of large enthalpic and entropic contributions, known as ''enthalpy-entropy compensation'', 2 which can be manipulated by adding cosolutes.
The characterization of these cosolute effects is crucial to understand the role of species in the inner of the cell, which is densely crowded with (bio)-macromolecules up to 300 mg mL À1 . 3 In general, cosolutes which are preferentially excluded from the protein surface favor the folded state because of its smaller solvent exposed surface. Cosolutes which preferentially bind to protein surfaces shift the equilibrium to the unfolded state.
Macromolecular crowders, such as polyethylene glycol or dextran, are thought to be excluded cosolutes. Proposed mechanisms range from entropic excluded volume effects 4,5 to enthalpic effects similar to osmolytes. 6,7 Osmolytes including polyols, sugars and amines stabilize proteins and protect the cellular proteome from environmental stresses. 8 They are excluded from protein surfaces and act mainly via an enthalpic stabilization mechanism. 5,7,9 On the other hand, chemical denaturants, such as guanidinium salts and urea, destabilize proteins by direct interactions which reduce DH u . 7,[10][11][12] Since Hofmeister's observation 13 that salts precipitate hen egg-white proteins in a highly ion-specific manner, salt effects on proteins have received particular attention. [14][15][16][17][18] The resulting anion and cation rankings, known as ''Hofmeister series'', are encountered in many fields of chemistry and biochemistry such as surface tension and potential, 19,20 orientational ordering of thermotropic liquid crystals at aqueous interfaces, 21 protein crystallization, 22 protein aggregation, 23 and enzymatic activity. 24,25 Anion and cation rankings for the effect of salts on protein stability are typically based on the propensity to stabilize/destabilize native proteins, using the ''melting temperature'', T m , of the protein as a criterion. 14,26,27 T m is defined as the midpoint of the unfolding transition, where DG u = 0. There are, however, striking exceptions from Hofmeister behavior, such as an inverse anion series observed for hen egg-white lysozyme at low pH 22,23,28 and some ions that are difficult to integrate into the Hofmeister scheme. 14,15 Moreover, the ion-specificity is concentration dependent: while electrostatic effects are expected to be most significant at low concentrations, 27,29,30 ion-specific effects were observed both at low and high concentrations. 31,32 Instead of focusing on the single state, where DG u = 0, the understanding of ion-specific effects is largely increased by determining DG u over a wide range of temperatures, obtaining the so-called ''stability curve'' DG u (T) of the protein. Standard thermodynamic procedures allow to dissect DG u (T) into its enthalpic and entropic parts, DH u (T) and TDS u (T). 33 Cosoluteinduced changes relative to the cosolute-free, buffered solution are then quantified by the excess functions: We use here differential scanning calorimetry (DSC) to determine the excess free energy DDG u and its contributions DDH u and TDDS u , which provide intriguing thermodynamic fingerprints of the different mechanisms of cosolute action. Such information is also crucial for developing and validating molecular level theories of ion-specific behavior. DDG u is less suited for this purpose because different values of DDH u (T) and TDDS u (T) can result in the same value of DDG u . Specifically, we explore here effects of salts and of some nonelectrolytes on the unfolding thermodynamics of ribonuclease A (RNase A, 124 residues, 13.7 kDa). The ionic cosolutes range from simple alkali halides to complex low-melting organic salts (''ionic liquids''), which enable the systematic variation of the cosolute properties of the ions 34 and possess a high potential for steering biomolecular processes. 35,36 We have recently explored the impact of ionic liquids on unfolding of RNase A, 37,38 and their propensity to steer protein aggregation. 39 Since many questions applying to salt effects also concern neutral cosolutes, one gets insight into these mechanism by comparative studies, here especially for alcohols and osmolytic polyols.

Materials and methods
Bovine pancreatic RNase A (type III-A) and the various cosolutes were obtained from different companies (see Table S1, ESI †). Stock solutions of RNase A in 50 mM citrate buffer at pH 5.0 were mixed with solutions containing the cosolute to obtain a protein concentration of 0.5 mg mL À1 , which was controlled by UV-VIS spectroscopy at 280 nm, using a NanoDrop 2000 c spectrometer (Thermo Scientific, Waltham, USA). The unfolding transition was characterized by recording DSC thermograms at a rate of 90 K h À1 by a VP-DSC instrument (MicroCal, Northampton, USA) and a Capillary-DSC apparatus (Malvern, Herrenberg, Germany). Our analysis also includes DSC thermograms of RNase A (5.0 mg mL À1 ) in 10 mM phosphate buffer at pH 5.5 in the presence of ionic liquids, 37 which were recorded at a scan rate of 60 K h À1 (Table S1,  At pH B 5.0 RNase A (pI = 9.6) forms monomers with a charge of about +7, 39 which undergo a reversible two-state process, characterized by the equilibrium constant where R is the gas constant and DG 0 u the Gibbs free energy of unfolding in the standard state (index ''0''). For simplicity this index ''0'' will be dropped throughout this paper. In DSC scans deviations from standard conditions are expected to be small.
The experimental observable is the partial heat capacity C exp p,pr of the protein obtained from the DSC thermogram after correction for the solvent contribution (see ESI, † S.1). Fits to the twostate model yielded T m , DH u (T m ), DS u (T m ) = DH u (T m )/T m , and the heat capacity change at T m , DC p (T m ). For most measurements (Table S1, ESI †) the caloric enthalpy DH u,cal agreed with the van't Hoff enthalpy DH u,vH calculated from the temperature dependence of DG u to within 5% or better, as required for a two-state model. 33 Three repeated measurements in buffer were used to estimate the systematic error of all scans (Table S1, ESI †). The temperature dependence of DG u , DH u and DS u is given by Kirchhoff's laws (eqn (3)-(5)). In agreement with previous findings 7 the cosolutes did not significantly influence DC p (T m ) (see Table S2 and ESI, † S.2), which allows to approximate DC p (T) by the result obtained for the buffer solution. 40 Excess functions DDG u , DDH u and TDDS u (DDX = X cosolute À X buffer ) relative to buffer scans at equal condition were then calculated at T m,buffer using eqn (3)-(5) and the temperature dependence of DC p (see ESI, † S.1). Different choices of buffer and variation of the pH in the range from 5 to 5.5 had only a small effect on T m and DH u which canceled in the excess functions DDG u , DDH u and TDDS u and in DT m .

Salt-induced changes of T m
In Fig. 1 (Fig. 2f), the stabilizing ion-specific effects are too strong to trace these minima. For LiCl (Fig. 2b) and NaBr (Fig. 2d) T m decreases, but an inflection point of the concentration dependence is still reminiscent of the minima in Fig. 2a. For stronger destabilizing agents, such as Na[ClO 4 ], T m decreases monotonously. Most ionic liquids destabilize proteins as well. As the alkyl chains of the cation increase in length, the destabilizing power of ionic liquids increases rapidly and leads to a largely negative DT m (Fig. 2c). However, strong destabilization can also be enforced by anions, such as [dca] À and [SCN] À (Fig. 2e).

Cosolute-induced changes of DG u
The proper thermodynamic driving force of the unfolding transition is the excess free energy DDG u . Fig. 3 shows DDG u for some alkali metal salts and ionic liquids at the temperature T m,buffer as a function of salt concentration. In dilute solutions (o0.25 M) electrostatic interactions result in DDG u o 0, while at higher salt concentrations stabilizing ion-specific effects (DDG u 4 0) or destabilizing effects (DDG u o 0) become dominant, in parallel to the behavior of DT m displayed in Fig. 2. Considering this parallelism in more detail, we find an apparent linear relationship between DDG u and DT m (even though it is a nonlinear relation). For details we refer to Fig. S1 (ESI †).
Cosolute-induced changes of DH u and DS u    both, DDH u and TDDS u initially increase and pass maxima. Their behavior parallels one another, but DDH u becomes considerably larger than TDDS u , leading to high values of DDG u . For destabilizing Na[ClO 4 ] the behavior is inverse. The curves initially decrease and pass minima at a concentration near 1 M. Both, DDH u and TDDS u , retain the same shape, but TDDS u increases more strongly than DDH u and eventually becomes positive, rendering DDG u strongly negative. Finally, for more hydrophobic salts, here exemplified by [bmim]Br, both DDH u and TDDS u increase with concentration, but TDDS u strongly dominates over DDH u . Further insight into these issues is gained by an entropyenthalpy compensation plot of TDDS u versus DDH u shown in Fig. 5. This diagram characterizes the mutual compensation of large enthalpic and entropic contributions, which tend to cancel in DG u . Different signs of the excess functions DDG u , DDH u and TDDS u , define eight different fields in this plot which are marked by different colors. The blue diagonal corresponds to full enthalpy-entropy compensation and separates the protein destabilizing region (DDG u o 0) from the stabilizing region (DDG u 4 0). Positive (negative) values of DDH u imply stabilization (destabilization) by the cosolute. The entropy term acts in the opposite direction: a positive TDDS u supports destabilization.
The sections I (magenta), and II (blue) and the sections V (yellow) and VI (orange) are most populated due to largely compensating enthalpic and entropic contributions. All hydrophobic ionic liquids (here the cations with butyl side chain or longer) fall into the magenta segment I, where DDH u is positive, but TDDS u , is even more positive, leading to entropic destabilization offset by enthalpic stabilization. Hydrophilic salts (e.g. alkali halides) populate states near the borderline between sections V (yellow) and VI (orange), where both, the enthalpic as well as the entropic contribution are negative. Depending on the magnitudes of TDDS u and DDH u , one obtains stabilizing salts (DDG u 4 0 in section V) or destabilizing salts (DDG u o 0 in section VI). The chemical denaturants [gdm]Cl and urea also fall in section VI. Some chlorides intersect the borderline from destabilizing to stabilizing behavior at high concentrations (see also Fig. 2 and 3).
As already observed in Fig. 2 shows a non-monotonous behavior as well, but is strongly destabilizing and covers the segments VI and VII.
In principle, DDH u and DDS u (here calculated at T m,buffer ) are temperature dependent, but the assumption DC p,cosolute (T) = DC p,buffer (T) used in our modellings renders DDH u temperature independent and simplifies the expression for DDS u to DDS u = TDC p ln(T s,buffer /T s,cosolute ), where T s is the temperature of maximum stability, DG u,max . Thus, DDH u does not change with temperature and DDS u does not change its sign.

Temperature dependence of DG u
Because conformational stability requires DG u 4 0, the temperature dependence of the stability curve DG u (T) represents a highly useful measure of the conformational stability. Fig. 6 pinpoints the basic features of DG u (T) and shows some typical examples for its response to added salts and neutral cosolutes. In general, DG u (T) resembles a parabola and intersects the zero line at high and low temperatures, defining T m and the cold denaturation temperature T c , respectively. For RNase A at pH 5-5.5 we extrapolate T c to be o200 K. Like for most other proteins, 42 T c falls largely below the liquid range of the solution. Between T c and T m the stability curve passes a maximum, which gives access to T s and DG u,max .  We have previously shown that the temperature dependence of DC p is crucial when calculating DDH u and TDDS u via eqn (3)-(5). 7 By contrast, the temperature dependence of DG u can be reliably estimated using a constant value for DC p (see Fig. S2, ESI †), which enables an estimate of DG u at temperatures at which measurement of DC p (T) are infeasible. Here we used DC p = 5.0 kJ K À1 mol À1 , resembling DC p of RNase A around room temperature. 40 If the cosolute does not alter DC p (T), DDG u (T) deduced from the stability curve reflects the correct temperature dependence, and the shape of the stability curve is not affected by the cosolute (q 2 DG u (T)/qT 2 = À DC p /T). The discussion of cosolute-induced changes of DG u (T) can therefore be reduced to the vertical and horizontal changes of the maximum protein stability, DG u (T s ) ( Fig. 7 and 8).

Maximum protein stability
In Fig. 7 and 8 we plot the vertical change of DG u (T s ), DDG u,max , versus the horizontal change, DT s , for all cosolutes. At the maximum of the stability curve qDG u (T)/qT is zero. Since qDG u (T)/qT = ÀDS u the maximum stabilization of a protein is purely enthalpic. Therefore, a vertical shift of the stability curve along the y-axis signals a purely enthalpic process (DDS u = 0), while a horizontal shift usually affects both, enthalpy and entropy.  The red dashed line in Fig. 7 and 8 corresponds to the special case of a purely entropic effect (i.e. DDH u = 0). There is a bundle of curves for alkali metal halides, which reduce DG u,max , but increase T s , thus falling into the lower right quarter of Fig. 7, where the cosolute mechanisms are characterized by enthalpic destabilization and entropic stabilization. In this regime, we also find the widely used denaturants urea and [gdm]Cl. While urea and [gdm]Cl are on the right hand side of the curves in the lower right quarter, the strong denaturant Na[ClO 4 ] is found on the left hand side close to purely enthalpic behavior. Another bundle of curves is associated with hydrophobic behavior of ionic liquids, which fall into the lower to the upper left quarter of Fig. 7. The two ionic liquids [bmim]Br and [Bu 4 N]Br cross the abscissa corresponding to stability curves, where the maximum free energy is larger than that of the buffer solution. The latter regime is also populated by the neutral cosolutes ethanol and ethylene glycol, which are more hydrophobic than the larger polyols considered.
Summarizing these results, Fig. 8 compares the impact of all cosolutes considered in our study on DG u,max at typical concentrations of 1-2 M. The major difference between hydrophilic salts (red symbols) and hydrophobic salts (blue symbols) is founded in a transition from entropic stabilization (DT s 4 0) to entropic destabilization (DT s o 0). The same is true for the neutral cosolutes, where glycerol marks the borderline between entropic stabilization and destabilization. Although we are not aware of cosolutes that exhibit a purely enthalpic or purely entropic mechanism, there is a band of salts of low hydrophobicity which are close to these limits (light blue symbols and Na[ClO 4 ]). In the latter cases destabilization seems substantially affected by the anion (e.g. [SCN] À , [dca] À , [ClO 4 ] À ).

Thermodynamic fingerprints
In general, the cosolute effect of salts on protein stability depends on the charge of the protein and is determined mainly by two effects. Electrostatic (coulombic) effects dominate at low concentrations and ion-specific (Hofmeister) effects at high concentrations. 27,29,30 Since the cosolutes effect of inorganic salts is largely influenced by specific salt-protein interactions the thermodynamic fingerprints of proteins in the presence of inorganic salts can be different. For positively charged RNase A in the presence of alkali halides we find enthalpic destabilization and entropic stabilization. The positively charged peptide met16 shows the same behavior of DDG u , but thermodynamics reveals a different mechanism: the peptide is stabilized enthalpically, but destabilized entropically. 30 Yet another type of behavior is exhibited by positively charged ubiquitin. In the latter case the protein is stabilized via an enthalpic mechanism even at low concentrations of alkali and alkaline earth halides, at which electrostatic effects should prevail. 7,43 While for positively charged RNase A in this study, anionic effects prevail over cationic effects, for negatively charged  Fig. 2. While the red line (DDG u,max (DT s ) = DC p Â DT s ) represents a pure entropic effect, the y-axis corresponds to a pure enthalpic effect. Error bars are omitted for clarity, but are given in Fig. 8   RNase T1 the salt effect seems to result mainly from the interaction with the cations. 44 However, anions can strongly affect negatively charged proteins, specifically in the case of an extended positively charged amino acid cluster 31 or the existence of specific anion binding sites. 45 For in sum uncharged proteins, the overall salt effect seems to be weakened. 7 For simple inorganic salts the variation of the cation has only a small effect on the stability of positively charged RNase A. On the other hand, cation variation of ionic liquids can lead to very strong effects (Fig. 2) because the thermodynamic mechanism depends on the hydrophobicity of the cation (Fig. 5a, 7 and 8). The longer the hydrophobic side chain of the cation, the stronger the destabilization at the high temperature end of the stability curve. These findings are not limited to RNase A. Actually, it seems that ionic liquids, at least the so-called aprotic ones, 34 destabilize proteins at the high temperature end of the stability curve. [46][47][48] The recently reported stabilization of a-chymotrypsin by benzyl-methyl-imidazolium chloride 49 does not contradict this observation: although the overall effect on DDG u is stabilizing, a-chymotrypsin shows the typical thermodynamic fingerprint exhibited by RNase A and BSA 47 in the presence of ionic liquids: the enthalpic contribution is stabilizing, the entropic contribution is destabilizing.
It is interesting to compare these findings with data for some OH-bonded neutral cosolutes. Osmolytes like sorbitol or glycerol are known to increase T m . According to the current opinion they stabilize proteins via an enthalpic mechanism. 5,7 For RNase A several studies report, however, a stabilization via an entropic pathway. [50][51][52] Our data for salts help to rationalize this discrepancy by comparing the enthalpy-entropy compensation of homologous alcohols and three polyols which differ in the number of OH-groups. We find that the nonelectrolytes reveal the same correlation between the hydrophobicity of the cosolute and the cosolute effects as observed for ionic liquids: the more hydrophobic the cosolute (e.g. ethanol) the stronger the reduction of T m (Fig. S3, ESI †). The same trend holds for the enthalpy and entropy contributions: the more hydrophobic the cosolute, the larger the destabilizing entropic and the stabilizing enthalpic contribution (Fig. 5d). While ethanol induces an entropic destabilization which is counteracted by an enthalpic stabilization, sorbitol stabilizes RNase A entropically and the enthalpic contribution is even destabilizing. For alcohols as cosolutes a positive DDH u and DDS u seems to be a general phenomenon. [53][54][55][56] Our analysis also implies that the cosolute effects of ethanol and typical excluded osmolytes are not as different as it might appear at a first glance from the reduction of T m . Ethanol shifts the stability curve upwards (Fig. 6a), which is typical for excluded cosolutes, 57,58 As shown in Fig. 8, the hydrophobicity/ hydrophilicity determines the horizontal position of the maximum (T s ). The more hydrophobic the cosolute, the larger the shift of T s to lower temperatures, resulting in the discussed enthalpy-entropy compensation. While for RNase A in 4 M ethanol DT s = À16 K, the addition of 2.5 M sorbitol shifts T s even to higher temperatures compared to the buffer solution (DT s = 6.9 K). Martin et al. have reported similar effects for yeast frataxin in alcohol solutions. 55 In summary, combining the results for alkali halides, ionic liquids and alcohols/polyols, the stability curve of RNase A can be shifted in all possible directions scaling with the hydrophobicity of the cosolute ( Fig. 7 and 8), which results in different thermodynamic fingerprints for these important classes of cosolutes. Thereby, the thermodynamic fingerprint of proteins in inorganic salt solution is a fingerprint of both, the protein and the salt, while the scaling of protein thermodynamics with hydrophobicity of the cosolutes is almost protein independent. Regarding protein stability, ionic liquids can be classified as a class of cosolutes in between inorganic salts and nonelectrolytes.

Generalized Hofmeister series
An intriguing question is, how our results affect the current picture of ion-specific (Hofmeister) effects. For this purpose we adopt the cation and anion series of Collins and Washabaugh 14 as a reference, which are mainly based on data for salt effects on DT m by von Hippel and Schleich. 26 This criterion reflects the correct thermodynamic driving force since, as shown above, DT m is correlated with DDG u (Fig. S1, ESI †). If DDG u is dissected into its enthalpic and entropic contributions, DDH u , and TDDS u , the appealing simplicity and universality of the Hofmeister series immediately gets lost indicating heterologous molecular mechanisms.
We now compare the ion rankings deduced from DT m , DDG u , DDH u , and TDDS u , respectively. Moreover, we expand this comparison to some complex ions, which are frequently used in the field of ionic liquids. As for most salts/ionic liquids the concentration dependence of DDG u , DDH u , and TDDS u is highly non-linear and often non-monotonous, we compare these properties at a given concentration of 1 M, which is high enough to ignore electrostatic contributions, 30 but not yet affected by the limited solubilities exhibited by some salts and ionic liquids. Ranking the ions at the melting temperature of the salt-free protein from their stabilizing to destabilizing propensity, the formulation of Collins and Washabaugh 14 predicts for the salts considered here the ''direct'' cation series: [Me 4 N] + , Cs + , K + , Na + , Li + , [gdm] + . There is, however, mounting evidence that at pH o pI, this sequence is reversed. 16,22,23,28,59 This reversal is well established for anions, but work by Boström et al. 28 + and Li + seem anomalous as well. Based on our dissection of DDG u into DDH u and TDDS u , we can come up with an explanation for [Me 4 N] + being out of order: the hydrophobic character of the four methyl groups causes an up-and left-shift of the stability curve of RNase A compared to its expected position from the Hofmeister ranking. As already suggested by Flores et al. 60 and Schwierz et al., 61 the anomalous behavior of Li + can be rationalized by the tight binding of water molecules in the first hydration shell to the Li + -ion which decreases the surface charge density. As a consequence, the ion appears to be more hydrophobic as suggested by the coincidence of the data points of LiCl and [Me 4 N]Cl in Fig. 8.
Turning to effects exerted by some complex anions, which are frequently used in the field of ionic liquids, the observed rankings are  34 the results for DT m and DDG u may conform to an extension of the direct series, while the results for TDDS u and DDH u are inconclusive and not in opposite direction. These observations are in line with previous bio-electrochemistry studies by Medda et al., who found that the apparent Hofmeister ranking gets lost upon dissection of the redox potential of cytochrome c into the enthalpic and entropic contributions. 62

Temperature dependence of Hofmeister effects
Our results clearly show that for a proper understanding of Hofmeister behavior it is crucial to account for the temperature dependence of the cosolute effects. Translation of the different excess functions into stability curves ( Fig. 6 and 9) reveals an important result which, according to our knowledge, has so far not been addressed in detail: the Hofmeister series is temperature dependent.
Using as typical examples the stability curves of RNase A in the presence of NaCl, CsCl, and [Me 4 N]Cl, Fig. 9 illustrates how temperature influences the order of the Hofmeister series. Depending on the temperature (see the vertical lines at 285 K, 315 K, 342 K) different rankings of the cations Na + , Cs + , and [Me 4 N] + are obtained. While [Me 4 N] + is the least stabilizing cation at high temperatures, it is the most stabilizing cation at low temperatures. The order of Na + and Cs + , which remains the same in the temperature range shown in Fig. 9, changes at high temperatures (around 395 K) as well. Similar temperature depending Hofmeister effects are obtained for the ionic liquids (Fig. 6b).
Ranking ions in a Hofmeister series therefore implies that the underlying cosolute-mechanisms reflect homologous effects. However, the salt-induced changes of the stability curves ( Fig. 6-9) and of DDH u and TDDS u (Fig. 4 and 5) show that this is not the case. Different kind of ions can induce qualitatively different shifts of the DG u (T)-curve, whichdepending on the temperature -alter the sequence of salts in the Hofmeister series. These crossovers become more important the less the ions have in common (at least in the structural sense). Examples are [gdm] + or [Me 4 N] + within a cation series and complex molecular anions such as [SCN] À or [ClO 4 ] À within the anion series. However, as discussed in the previous section, even a homologous series such as Li + , Na + , K + , and Cs + has outliers (Li + ) when the salt effect is dissected into its thermodynamic mechanisms. The temperature dependence of the Hofmeister series, so far not appreciated in the literature, may explain most outliers in the discussed literature. For example, the non-homologous effects of salt-protein interactions cause a loss of the Hofmeister series upon dissection of the redox potential of cytochrome c into the enthalpic and entropic contributions. 62 We suggest that this is due to heterogeneous molecular mechanisms causing the intersections of the respective temperature dependent redox potentials. 62 Towards a molecular mechanism Strictly speaking, thermodynamics cannot provide a molecular mechanism of a reaction. However, comparisons of the thermodynamics of cosolute effects to well characterized cosolutes such as [gdm]Cl or urea could give microscopic insights, although one has to be careful: DDH u and DDS u include protein as well as solvent terms. Even though the enthalpic and entropic contributions of the solvent terms exactly cancel each other, 63,64 they can be large in comparison to the protein terms and therefore significantly influence the temperature dependence of DG u . 65 Thus, similar excess thermodynamic functions or similar shifts of the stability curve can have different molecular origins. 5 Today, it is widely accepted that the commonly used protein denaturants urea and [gdm]Cl denature proteins via direct chemical interactions. 11,12 The thermodynamic fingerprint of all proteins in the presence of these chemical denaturants is a negative DDH u and TDDS u . 7,10,30 Based on the thermodynamic fingerprint, the destabilizing Hofmeister effect of NaBr and LiCl (Fig. 5, 7 and 8) could also be founded in chemical interactions of the ions with the protein.
In contrast, the ionic liquids are mainly located in field I of Fig. 5 indicating a different molecular mechanism compared to a typical protein denaturant. This is in accordance with the measurement of transfer free energies of amino acids showing that imidazolium-based ionic liquids interact unfavorably with the protein backbone similar to excluded cosolutes such as polyols and sugars, even so the interaction with the side chains of amino acids is favorable. 66 The increasing trend of DDH u and TDDS u with increasing hydrophobicity of the cation indicates a molecular mechanism which is directly related to the cosolute effect of alcohols on protein stability.
With increasing the hydrophobicity of the cosolutes, the destabilizing entropic contribution and the counteracting stabilizing enthalpic contribution increase. The effect of a hydrophobic cosolute on protein thermodynamics is thereby similar to the transfer thermodynamics of a hydrophobic cosolute into water in the observed temperature range. 65 A decrease of entropy is a hallmark of the transfer of a hydrophobic cosolute from the gaseous state into water at temperatures below 100 1C. A reduced entropy of water in an aqueous solution of a hydrophobic cosolute could therefore diminish the reduction of the entropy of water upon unfolding of the protein due to the solvation of exposed hydrophobic residues, since the entropy of water is already reduced due to the presence of the hydrophobic cosolute (Fig. 10). This effect is consistent with a DDS u 4 0 and DDH u 4 0 as experimentally observed by us. A direct binding mechanism (as in the case of [gdm]Cl or urea) which could also explain the reduction of T m in ethanol solutions is not likely because the direct interactions between protein and denaturant cause a downshift of the stability curve resulting in DG u,max,cosolute o DG u,max,buffer . In fact, the stability curve of RNase A in the presence of ethanol resembles a horizontally shifted stability curve of an excluded cosolute instead (Fig. 6a).

Conclusion
Here we present a novel thermodynamic analysis of cosolute effects on protein stability based on their different impact on the protein stability curve, DG u (T). As the shape of the curve remains the same for different cosolutes, we discussed the effects in terms of shifts of the maximum stability. Different classes of cosolutes shift the maximum differently based on their respective enthalpic (DDH u ) and entropic (TDDS u ) contributions to the excess free energy (DDG u ): the more hydrophobic the cosolute, the larger the destabilizing entropic and the stabilizing enthalpic contributions. This classification is valid for both, neutral cosolutes as well as ions and leads to a new understanding of the Hofmeister series. Multiple intersections of the respective DG u (T) curves, determined by their thermodynamic fingerprints, manifest themselves in temperature dependent ion rankings. The present thermodynamic analysis is a fundamental framework for future molecular studies and simulations of cosolute effects. Fig. 10 Schematic representation of the hydrophobicity surface (blue: hydrophobic, red: hydrophilic) of a protein in dilute solution and in the presence of solvated [bmim] + . The scheme illustrates a possible molecular mechanism of a hydrophobic cosolute. The gradient of the background color from blue to red indicates the reduction of water entropy due to the hydration of the hydrophobic groups of [bmim] + . The reduced entropy diminishes the loss of entropy due to solvation of hydrophobic groups of the protein which get solvent exposed upon unfolding. This diminished loss of water entropy upon unfolding causes the experimentally observed DDS u 4 0.