Gas-liquid transfer data used to analyze hydrophobic hydration and find the nature of the Kauzmann-Tanford hydrophobic factor

Abstract

Hydrophobic free energy for protein folding is currently measured by liquid-liquid transfer, based on an analogy between the folding process and the transfer of a nonpolar solute from water into a reference solvent. The second part of the analogy (transfer into a nonaqueous solvent) is dubious and has been justified by arguing that transfer out of water probably contributes the major part of the free energy change. This assumption is wrong: transfer out of water contributes no more than half the total, often less. Liquidliquid transfer of the solute from water to liquid alkane is written here as the sum of 2 gas-liquid transfers: (i) out of water into vapor, and (ii) from vapor into liquid alkane. Both gas-liquid transfers have known free energy values for several alkane solutes. The comparable values of the two different transfer reactions are explained by the values, determined in 1991 for three alkane solutes, of the cavity work and the solute-solvent interaction energy. The transfer free energy is the difference between the positive cavity work and the negative solute-solvent interaction energy. The interaction energy has similar values in water and liquid alkane that are intermediate in magnitude between the cavity work in water and in liquid alkane. These properties explain why the transfer free energy has comparable values (with opposite signs) in the two transfers. The current hydrophobic free energy is puzzling and poorly defined and needs a new definition and method of measurement. solvation free energy | hydrophobicity | protein energetics | Ostwald coefficient | Pratt-Chandler analysis E ver since Kauzmann's revolutionary proposal (1) in 1959, the hydrophobic factor has been widely acknowledged as a major factor in protein folding energetics (1-3). In the widely used Kauzmann-Tanford approach to measuring it, hydrophobic free energy is synonymous with hydrophobic hydration and is measured by the preference of a nonpolar solute for a reference solvent over water, based on the solute's relative solubility in the two solvents. This approach is still the standard one, although it has been criticized. Much of the current research into the nature of the hydrophobic factor is based on computer simulations (4). The basic criticism of the liquid-liquid transfer approach is that gasliquid transfer (which is better understood) is used to determine the solvation free energy of the nonpolar solute. Moreover, the choice of a reference solvent ought not to change the apparent hydrophobic free energy, but it does (5). The purpose here is to investigate these criticisms with the aid of gas-liquid transfer results and their interpretation.The 1971 paper by Nozaki and Tanford (2) is often cited as the starting point of quantitative work on measuring hydrophobic hydration. However, as ref. 2 emphasizes, it was based on the protocol developed in the Cohn and Edsall laboratory at Harvard by McMeekin, et al. (6) who used it to investigate the water solubility of polar as well as nonpolar protein side chains. The latter au...

The new view of hydrophobic free energy

“…Chandler [28,29] argued persuasively, however, that the cavity work in water is not proportional to surface area in the small-size regime (see below) but instead scales linearly with molar volume. Until now, the controversy has been based on data for liquid-liquid transfer, which is more complex than gas-liquid transfer because DG LL depends on the values of DG c and E a in both liquid alkane and water [5].…”

“…1 to plot DG c (water) against molar volume (V) for 4 linear alkanes. McAuliffe [12] showed that a plot of this kind should be limited to hydrocarbons of a single type, such as linear or cyclic, because [4] (see [5]). DG GL is the sum of E a and DG c .…”

“…Thus, he argued, a similar DG should help to fold a protein when a non-polar side chain is buried by folding. The analogy breaks down, however, when the liquid-liquid transfer is divided into two gas-liquid transfers [5], because the ''hydrophobic'' transfer from water into vapor has less than half of the total DG. and the second transfer, from vapor to liquid alkane, is not obviously related to the protein folding process.…”

“…Kauzmann [1] and Tanford [2] expected that removing the hydrocarbon solute from water would account for most of the free energy change in liquid-liquid transfer but this expectation was not correct: data are available for the DG values of both gas-liquid transfers, which show that the ''hydrophobic'' transfer from water to vapor accounts for less than half of the total DG (5)(6)(7). This disconcerting fact was realized as early as 1976 when Wolfenden and Lewis [6] studied why water is a poor solvent for liquid hydrocarbons.…”

“…When an alkane solute is transferred from water through vapor to the liquid alkane, the liquid-liquid transfer may be written as two successive gas-liquid transfers [5]: first from water into vapor and then from vapor into liquid alkane. Kauzmann [1] and Tanford [2] expected that removing the hydrocarbon solute from water would account for most of the free energy change in liquid-liquid transfer but this expectation was not correct: data are available for the DG values of both gas-liquid transfers, which show that the ''hydrophobic'' transfer from water to vapor accounts for less than half of the total DG (5)(6)(7).…”