Anti‐cooperativity and cooperativity in hydrophobic interactions: Three‐body free energy landscapes and comparison with implicit‐solvent potential functions for proteins

Abstract

Potentials of mean force (PMFs) of three-body hydrophobic association are investigated to gain insight into similar processes in protein folding. Free energy landscapes obtained from explicit simulations of three methanes in water are compared with that predicted by popular implicit-solvent effective potentials for the study of proteins. Explicit-water simulations show that for an extended range of three-methane configurations, hydrophobic association at 25 degrees C under atmospheric pressure is mostly anti-cooperative, that is, less favorable than if the interaction free energies were pairwise additive. Effects of free energy nonadditivity on the kinetic path of association and the temperature dependence of additivity are explored by using a three-methane system and simplified chain models. The prevalence of anti-cooperativity under ambient conditions suggests that driving forces other than hydrophobicity also play critical roles in protein thermodynamic cooperativity. We evaluate the effectiveness of several implicit-solvent potentials in mimicking explicit water simulated three-body PMFs. The favorability of the contact free energy minimum is found to be drastically overestimated by solvent accessible surface area (SASA). Both the SASA and a volume-based Gaussian solvent exclusion model fail to predict the desolvation barrier. However, this barrier is qualitatively captured by the molecular surface area model and a recent "hydrophobic force field." None of the implicit-solvent models tested are accurate for the entire range of three-methane configurations and several other thermodynamic signatures considered.

Hydrophobicity within the three-dimensional Mercedes-Benz model: Potential of mean force

“…However, the qualitative aspects of the PMF as well as the temperature dependence of the enthalpic-entropic compensation discussed here are in agreement with previous work. 21,25,26,48,50 In summary, we used the three-dimensional MercedesBenz model for water and Monte Carlo simulations to study the structure and thermodynamics of the hydrophobic interaction. Radial distribution functions are used to classify different cases of the interaction, namely contact configurations, solvent separated configurations, and desolvation configurations.…”

“…[21][22][23][24] Also, the hydrophobic interaction between clusters of nonpolar solutes has been shown to be nonadditive. 23,[25][26][27] In this paper, our focus is on the qualitative temperature dependent features of the hydrophobic effect. We use the three-dimensional Mercedes-Benz model (3DMB) (Ref.…”

Hydrophobic interactions in the formation of secondary structures in small peptides

“…In this regard, it should be noted that hydrophobic interactions are in general not pairwise additive. Explicit-water simulations of aqueous solutions of methane molecules showed deviations from pairwise additivity in their interactions; but the deviations are mild [38,62,63]. For instance, for the interaction between a pair of polyalanine helices, the total potential based on an implicit-solvent model that assumes pairwise additivity [40] is similar to the corresponding PMF determined by explicit-water simulation [42].…”

The application of the integral equation theory to study the hydrophobic interaction

“…A lot can be learned from PMFs accompanying functions, namely, enthalpy, entropy, and heat capacity change for bringing two solutes from infinity to a certain distance. [13][14][15][16][17][18] The (anti)cooperativity of hydrophobic interaction due to its many-body nature has been studied by Shimizu,19,20 while others examined the effect of temperature, pressure, solute size, and salt on many-body interaction between the hydrophobes. 21,22 Most of the above-mentioned work has been done with molecular dynamics simulations of popular water models (SPC, TIP).…”