Water's Hydrogen Bonds in the Hydrophobic Effect:  A Simple Model

Abstract

We propose a simple analytical model to account for water's hydrogen bonds in the hydrophobic effect. It is based on computing a mean-field partition function for a water molecule in the first solvation shell around a solute molecule. The model treats the orientational restrictions from hydrogen bonding, and utilizes quantities that can be obtained from bulk water simulations. We illustrate the principles in a 2-dimensional Mercedes-Benz-like model. Our model gives good predictions for the heat capacity of hydrophobic solvation, reproduces the solvation energies and entropies at different temperatures with only one fitting parameter, and accounts for the solute size dependence of the hydrophobic effect. Our model supports the view that water's hydrogen bonding propensity determines the temperature dependence of the hydrophobic effect. It explains the puzzling experimental observation that dissolving a nonpolar solute in hot water has positive entropy.

Interaction of Bile Salts with Model Membranes Mimicking the Gastrointestinal Epithelium: A Study by Isothermal Titration Calorimetry

“…1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Large positive variations in the system entropy are usually considered a fingerprint for the removal of non-polar surfaces from water due to the hydrophobic effect. 45,46 The results obtained may therefore be interpreted as the hydrophobic effect not being the main driving force for the interaction. In fact, the enthalpy variation observed upon transfer of a non-polar molecule from water to a non-polar media depends on the interactions established between the molecule being transferred and the non-polar media and is partially compensated by a variation in the system entropy.…”

Analytical theory of the hydrophobic effect of solutes in water

“…4) [12]. We compute the Gibbs free energy of transferring a hydrophobic solute into water using [43]…”

“…The main difference between the two models is that in ours, energy is a continuous function of the relative orientation θ of two water molecules, while in the other the hydrogen-bonding (HB) energy is a discontinuous function of the relative configurations, but both models possess similar features. For hydrophobic hydration, Xu and Dill [43] proposed a very simple analytical theory of the hydrophobic effect in two dimensions which builds on a 2D MB model of water. Starting from the statistical partition functions for a water molecule in the bulk and a water in the first solvation shell around a hydrophobe, the theory reproduces the main characteristics of the hydrophobic effect and accounts for different solute size effects.…”

“…The theory in Ref. [43] required the results of a reference Monte Carlo simulation of pure bulk water phase. That approach was improved by Luksic et al [12], which is simpler and circumvents any computer simulation steps by using an analytical model of the pure phase of water.…”

Simple Model of Hydrophobic Hydration

“…Whereas equation (19) gives the average energy, 〈ε〉 b , of water molecule in the bulk, the average energy 〈ε〉 h of molecule of water in the first solvation shell will be $${true\langle \epsilon false(\zeta false(\varphi false)false)true\rangle }_{\mathrm{h}}=\frac{1}{2}false\{\zeta false(\varphi false)false[true\langle u_{\mathrm{normalH}\mathrm{normalB}}true\rangle f_{\mathrm{normalH}\mathrm{normalB}}+true\langle u_{\mathrm{S}}true\rangle f_{\mathrm{S}}false]+3true\langle u_{\mathrm{normalL}\mathrm{normalJ}}true\rangle f_{\mathrm{normalL}\mathrm{normalJ}}-{\epsilon }_{\mathrm{normalS}\mathrm{normalW}}false\},$$ where ε SW is the energy of interaction between the solute and a water molecule. Based on these energies, the partition function for a bulk water can be approximated, by treating interactions between waters only in averaged way, as 11 $$q_{\mathrm{b}}={\int }_0^{\pi /3}\text{exp }true(-\frac{{true\langle \epsilon true\rangle }_{\mathrm{b}}+p{\upsilon }_{\text{mol}}^{\mathrm{b}}}{kT}true)\mathrm{normald}\varphi =\frac{\pi }{3}\text{exp }true(-\frac{{true\langle \epsilon true\rangle }_{\mathrm{b}}+p{\upsilon }_{\text{mol}}^{\mathrm{b}}}{kT}true),$$ whereas the partition function for a water molecule in the first shell around a solute molecule can be written as 11 $$q_{\mathrm{h}}={\int }_0^{\pi /3}\text{exp }true(-\frac{{true\langle \epsilon false(\zeta false)true\rangle }_{\mathrm{h}}+p{\upsilon }_{\text{mol}}^{\mathrm{h}}}{kT}true)\mathrm{normald}\varphi =true\{\begin{array}{c}left(\frac{\pi }{3}-{\varphi }_{\mathrm{normalc}})\text{ exp }(-\frac{{\langle \epsilon (\zeta =3)\rangle }_{\mathrm{normalh}}+p{\upsilon }_{\text{mol}}^{\mathrm{normalh}}}{kT})+{\varphi }_{\mathrm{normalc}}\text{ exp }\end{array}$$…”