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

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. Liquid-liquid 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.