The hydrophobic effect: is water afraid, or just not that interested?

Abstract

Our understanding of the hydrophobic effect has advanced greatly since 1990, with the help of experimental, theoretical, and computer simulation results. The key hydrophobic signature of positive ∆C°_P and negative ∆S° at room temperature has been interpreted in light of the importance of solvent cavity creation, solvent-excluded volume, and solute–water intermolecular forces, along with some unusual thermodynamic properties of pure water. Application of the hydrophobic effect to the hydration of small nonpolar solutes, protein folding stability, and protein–ligand binding is discussed in detail in this review, with an emphasis on thermodynamic analyses and interpretations.

Appendices

Appendix

Table 8 Unfolding thermodynamic parameters for curves plotted in Figs. 7 and 8

Enthalpy, entropy convergence for hydrophobic hydration

In his massive and influential 1979 review of protein stability [112], one of the observations that Privalov made was that at about 100–110 °C, compact globular proteins converged on the same value of specific enthalpy of unfolding (cal/g). He found a similar convergence for the specific entropy of unfolding around 110 °C, although the effect was not nearly as clear.

In 1986, Robert Baldwin published a keystone paper [116] in which he compared the thermodynamics of liquid hydrocarbon neat transfer to the unfolding of the enzyme lysozyme. He found that for six hydrocarbons (benzene, toluene, ethylbenzene, cyclohexane, n-pentane, and n-hexane), T_H and T_S were approximately the same: T_H = 22 ± 5 °C, and T_S = 113 ± 3 °C.⁷ Baldwin then applied these values to the temperature-dependent unfolding of hen lysozyme by splitting protein stability into a hydrophobic effect (HE) and a non-hydrophobic effect (NHE, ∆X_obs = ∆X_HE + ∆X_NHE), and assuming that (1) ∆C°_P(U) is entirely due to the HE, and (2) for the effect of hydrophobicity on protein unfolding, T_H and T_S are identical to the liquid hydrocarbon neat transfer values. Using Eqs. (4) and (6) (main text), Baldwin calculated HE ∆H°₂₉₈ and ∆S°₂₉₈, and then by subtracting from the net observed ∆H°₂₉₈ and ∆S°₂₉₈, he calculated the NHE values. Both NHE values were temperature-independent: ∆H°₂₉₈(U, NHE) =  + 217.8 ± 0.7 kJ/mol, and ∆S°₂₉₈(U, NHE) =  + 2294 ± 3 J/K/mol. The former value was interpreted as the cost, upon unfolding, of breaking polar interactions (e.g., H-bonds), and the latter the increase in conformational entropy, i.e., the release of polypeptide chain positioning constraints.

In 1990, Murphy and Gill took this analysis a step further, defining the notion of “convergence” temperatures for enthalpy and entropy [10, 13, 114, 115]. They started by applying Baldwin’s HE/NHE breakdown to the temperature dependence of enthalpy, considering a series of homologous compounds (e.g., noble gases, alkanes, alcohols, amines) which shared the same functional group and differed only in their hydrophobicity (e.g., size of noble gas or number of carbons). The hydration enthalpy can then be envisioned as comprising a hydrophobic term that increases with solute hydrophobicity, and a non-hydrophobic term that is independent of hydrophobicity. Enthalpy convergence would then occur at some temperature, T_H,conv, at which all of the homologous compounds in the series have the same hydration enthalpy, ∆H_conv. Thus, at the convergence temperature, ∆H° of hydration depends only on the nature of the series (i.e., the functional group), and not on the individual compound. With this in mind, the temperature dependence of ∆H (main text Eq. 2), can be cast as

$$ \begin{aligned} \Delta H^\circ (T) & = \Delta H^\circ (T_{{{\text{ref}}}} ) \, + \, \Delta C^\circ_{P} (T{-}T_{{{\text{ref}}}} ) \\ & = \Delta H^\circ (T_{{H{\text{,conv}}}} ) \, + \, \Delta C^\circ_{P} (T{-}T_{{H,{\text{conv}}}} ). \\ \end{aligned} $$

(19)

Normally, one would use Eq. (19) along with measured values of ∆H° at various temperatures to determine ∆C°_P. If, however, one already knows ∆C°_P for each compound in the series, then measured values of ∆H° at a specific reference temperature (e.g., 298 K) can be used in the following version of Eq. (19):

$$ \Delta H^\circ_{298} = \Delta H^\circ (T_{{H,{\text{conv}}}} ) + \Delta C^\circ_{P} (298 \, {-}T_{{H,{\text{conv}}}} ). $$

(20)

Thus, a plot of ∆H°₂₉₈ vs. ∆C°_P for each compound in the series will give a straight line with slope = (298 − T_conv) and intercept = ∆H°(T_conv). This is sometimes referred to as an MPG (Murphy–Privalov–Gill) plot. Because ∆H°(T_conv) characterizes the entire series, it must apply to what remains the same in the series, i.e., the non-hydrophobic component of the observed net ∆H°; thus, it would be different for a series of alkanes vs. alcohols vs. amines. On the other hand, T_conv should be the same for alkanes, alcohols, and amines because they all differ by the same hydrophobic parameter, i.e., the number of carbons.

A similar analysis of entropy leads to this adaptation of Eq. (3) in the main text:

$$ \Delta S^\circ_{298} = \Delta S^\circ (T_{{S,{\text{conv}}}} ) + \Delta C^\circ_{P} \cdot \ln (298/T_{{S,{\text{conv}}}} ). $$

(21)

The MPG plot here would be ∆S°₂₉₈ vs. ∆C°_P, with slope = ln(298/T_S,conv), and intercept = ∆S°(T_S,conv). As with enthalpy, ∆S°(T_conv) characterizes the entire series, so it must apply to the non-hydrophobic component of the observed net ∆S°.

For example, MPG plots of Baldwin’s liquid hydrocarbon neat transfer data [116] do show a linear correlation (Fig. 11), although the relationship is not very strong for ∆H (R² = 0.6). From the slopes, the convergence temperatures are calculated to be T_S,conv = 106 ± 5 °C; T_H,conv = 40 ± 6 °C. Note that these temperatures are close to, but not identical to T_S and T_H.

Fig. 11

Data from ref. [116]

MPG plots of liquid hydrocarbon neat transfer. a Entropy; b enthalpy; liquids are benzene, toluene, ethylbenzene, cyclohexane, n-pentane, and n-hexane

Figure 11a, with its excellent linearity, suggests that entropy convergence for the neat transfer of this series of liquid hydrocarbons does occur. The relative uncertainty in the convergence temperature is good, at only 4% (= 100 × 4.7/106). (For ∆S°(T_S,conv), however, it is 70%!) Thus, we might expect to see a fairly robust isosbestic point in the ∆S° vs. T plot for neat transfer (Fig. 12). Sadly, that is not actually the case.

Fig. 12

Data from ref. [116]

Temperature dependence of the entropy of neat transfer of liquid hydrocarbons

The first thing to note from Fig. 12 is that for all six liquids, T_S, the temperature at which each curve crosses the T-axis, lies between 382 and 390 K; this matches the average value reported above (113 ± 3 °C). Most of the curves cross each other (shared values of ∆S°) between about 360 and 390 K; this also matches the calculated convergence temperature from the MPG plot, 106 ± 5 °C. However, there are several intersections below 360 K, and several more above 400 K. The lack of a clear isosbestic point suggests that the entropic convergence behavior is not nearly as robust as one might have expected from the MPG plot. A similar “smeared” isosbestic is observed in the ∆H° vs. T curve intersections, stretching from 300 to 345 K (data not shown). At least some of this “blurring” of the expected isosbestic point has been shown to be due to the temperature dependence of ∆C_P [117]. Beyond this though, one may question the assumptions in the convergence derivation, namely, that the hydrophobic and non-hydrophobic contributions can be separated out and that the former really are identical for every member of the homologous series of compounds. Graziano [32] and Pratt [117] have supported the existence of entropy convergence for families of small solutes, but rejected enthalpy convergence (Graziano, personal communication).

Murphy, Privalov, and Gill published an extremely influential paper in 1990 in which they compared MPG plots of Baldwin’s liquid hydrocarbon data with nonpolar gas hydration, solid → water transfer of nonpolar cyclic peptides, and protein unfolding [10]. They found that the slopes of all four of the ∆S° vs. ∆C°_P plots were nearly identical, ranging from − 0.23 ± 0.04 to − 0.28 ± 0.01. Thus T_S,conv for all four of these sets of compounds lie in a fairly narrow range between 102 ± 15 and 121 ± 6 °C; this pointed to the “dominant role that water [and the hydrophobic effect] play in determining the [entropy] of hydration of [all of] these compounds” [10].

Murphy, Privalov, and Gill drew another interesting conclusion from the intercepts of their MPG plots [10]. They determined ∆S°(T_S,conv) to be − 78.5 ± 2.5 J/K/mol for nonpolar gas hydration vs. − 6 ± 4 J/K/mol for liquid neat transfer; this is expected, because gases lose much more freedom of motion upon transfer to the aqueous phase than liquids do. Meanwhile, ∆S°(T_S,conv) was quite similar for protein unfolding (18 ± 1 J/K/mol) and the transfer of solid nonpolar cyclic peptides into water (16 ± 1 J/K/mol). This corroborated previous findings that in terms of packing and freedom of motion, the protein interior is best modeled as a solid organic compound, rather than a liquid [118,119,120].

To give some idea of the linearity of the MPG plots in the 1990 Science paper, Fig. 13 plots the nonpolar gas hydration and protein unfolding results. Note that once again, the linear fits are good (R² = 0.89 for gas hydration, 0.96 for protein unfolding), and the slopes are fairly close (− 0.068 and − 0.077). In light of how influential the 1990 Murphy, Privalov, and Gill paper was, it is surprising that no one seems to have checked to see whether these gases and proteins actually demonstrated isosbestic behavior in their ∆H° vs. T plots. In Fig. 14 I have plotted the five members of each series that lie closest to the linear fit line in the MPG plots. As with liquid hydrocarbon neat transfer (Fig. 12), many of the crossings lie in a fairly narrow range of temperature (355–365 K for A and 370–380 K for B), but a number of crossings occur far outside this range.

Fig. 13

MPG enthalpy plots of a nonpolar gas hydration; and b protein unfolding; data from ref. [101]. Without giving any reason, MPG omitted the parvalbumin unfolding data point (red) from their published plot

Fig. 14

Data from ref. [101]

Temperature dependence of the enthalpy of a nonpolar gas hydration, and b protein unfolding

Perhaps the most interesting part of this story about convergence came to light in the years after 1990, as more protein unfolding thermodynamic data became available. Twelve proteins were originally tabulated in Privalov and Gill’s 1988 review [101], 11 of which were included in their 1990 MPG plot [10]. It turned out that not only was the omitted point (suspiciously?) far off the fit line (Fig. 14b), but the 11 points included were extraordinarily unusual in their linearity.

This was discovered in 1997, when Robertson and Murphy published a review in which they tabulated unfolding thermodynamic data for 65 globular proteins of known structure [102]. The MPG plots in this paper had R² values of only 0.36 and 0.33; unsurprisingly, the convergence temperatures calculated from the slopes of these plots (66 °C for enthalpy, 65 °C for entropy) were much different from those in the 1990 paper (102 °C for enthalpy, 106 °C for entropy).⁸ Robertson and Murphy’s conclusion from these disappointing MPG plots was that the convergence behavior for this much larger set of unfolded proteins was “not very compelling.” Huang and Chandler [121], using Lum–Chandler–Weeks theory [18], showed that the convergence temperature should decrease with increasing protein size, thus “one may not expect to observe a convergence temperature for the entropy of unfolding for all proteins.” Considering the diversity of protein groups that are exposed to water upon unfolding, as well as the change in shape, it is not surprising that proteins do not behave like a set of homologous compounds all with the same functional group. (And as we have seen, the convergence behavior even in this best of cases is not as clear as one might hope.) This failure to observe convergence behavior in the larger data sets has been recognized by some authors [20], but has been ignored by others [99].

It is important to conclude this discussion by stressing that enthalpy and entropy convergence do not generally exist for protein unfolding, and the existence of enthalpy convergence for hydrophobic hydration can be questioned as well.

Entropy is a measure of freedom of motion

One way to measure entropy is given by Boltzmann’s entropy equation,

$$ S = R \cdot \ln (W), $$

(22)

where R is the gas law constant, 8.314 J/K/mol, and W is the number of ways that a system can be arranged. For an ideal gas, W can be a measure of positions within a volume of space available to the particle. Excluding the particle from a portion of the volume will lower W and thus decrease entropy.

We can demonstrate this by combining the first and second laws of thermodynamics to get, for a fully reversible reaction,

$$ {\text{d}}U\left( {{\text{internal}}\;{\text{energy}}} \right) = T \cdot {\text{d}}S - P \cdot {\text{d}}V. $$

(23)

Furthermore, since dU = C_V·dT, Eq. (23) becomes

$$ {\text{d}}S = C_{V} \left( {\frac{{{\text{d}}T}}{T}} \right) + \left( \frac{P}{T} \right){\text{d}}V. $$

(24)

Using the ideal gas law (PV = nRT → P/T = R/$\overline{V}$), we get

$$ {\text{d}}S = C_{V} \left( {\frac{{{\text{d}}T}}{T}} \right) + R \cdot \frac{{{\text{d}}V}}{{\overline{V}}}. $$

(25)

For an isothermal process, dT = 0, so

$$ {\text{d}}S = R \cdot \frac{{{\text{d}}V}}{{\overline{V}}}. $$

(26)

For the reversible isothermal compression of an ideal gas, dV is negative and thus dS would be negative as well. In other words, restricting the available space curtails freedom of motion, which in turn lowers entropy.

Although the situation is more complex in the liquid (and solid) phase, the general conclusion remains the same: excluding solvent from a volume of space (e.g., a cavity) decreases the entropy of the solvent.