Hydrophobic interactions between methane and a nanoscopic pocket: Three dimensional distribution of potential of mean force revealed by computer simulations

Tailoring the Variational Implicit Solvent Method for New Challenges: Biomolecular Recognition and Assembly

Predicting solvation free energies and describing the complex water behavior that plays an important role in essentially all biological processes is a major challenge from the computational standpoint. While an atomistic, explicit description of the solvent can turn out to be too expensive in large biomolecular systems, most implicit solvent methods fail to capture “dewetting” effects and heterogeneous hydration by relying on a pre-established (i.e., guessed) solvation interface. Here we focus on the Variational Implicit Solvent Method, an implicit solvent method that adds water “plasticity” back to the picture by formulating the solvation free energy as a functional of all possible solvation interfaces. We survey VISM's applications to the problem of molecular recognition and report some of the most recent efforts to tailor VISM for more challenging scenarios, with the ultimate goal of including thermal fluctuations into the framework. The advances reported herein pave the way to make VISM a uniquely successful approach to characterize complex solvation properties in the recognition and binding of large-scale biomolecular complexes.

Molecular Shape and the Hydrophobic Effect

This review focuses on papers published since 2000 on the topic of the properties of solutes in water. More specifically, it evaluates the state of the art of our understanding of the complex relationship between the shape of a hydrophobe and the hydrophobic effect. To highlight this, we present a selection of references covering both empirical and molecular dynamics studies of small (molecular-scale) solutes. These include empirical studies of small molecules, synthetic hosts, crystalline monolayers, and proteins, as well as in silico investigations of entities such as idealized hard and soft spheres, small solutes, hydrophobic plates, artificial concavity, molecular hosts, carbon nanotubes and spheres, and proteins.

Hydrophobicity of proteins and nanostructured solutes is governed by topographical and chemical context

Hydrophobic interactions drive many important biomolecular self-assembly phenomena. However, characterizing hydrophobicity at the nanoscale has remained a challenge due to its nontrivial dependence on the chemistry and topography of biomolecular surfaces. Here we use molecular simulations coupled with enhanced sampling methods to systematically displace water molecules from the hydration shells of nanostructured solutes and calculate the free energetics of interfacial water density fluctuations, which quantify the extent of solute-water adhesion, and therefore solute hydrophobicity. In particular, we characterize the hydrophobicity of curved graphene sheets, self-assembled monolayers (SAMs) with chemical patterns, and mutants of the protein hydrophobin-II. We find that water density fluctuations are enhanced near concave nonpolar surfaces compared with those near flat or convex ones, suggesting that concave surfaces are more hydrophobic. We also find that patterned SAMs and protein mutants, having the same number of nonpolar and polar sites but different geometrical arrangements, can display significantly different strengths of adhesion with water. Specifically, hydroxyl groups reduce the hydrophobicity of methyl-terminated SAMs most effectively not when they are clustered together but when they are separated by one methyl group. Hydrophobin-II mutants show that a charged amino acid reduces the hydrophobicity of a large nonpolar patch when placed at its center, rather than at its edge. Our results highlight the power of water density fluctuations-based measures to characterize the hydrophobicity of nanoscale surfaces and caution against the use of additive approximations, such as the commonly used surface area models or hydropathy scales for characterizing biomolecular hydrophobicity and the associated driving forces of assembly.

Practical Aspects of Free-Energy Calculations: A Review

Free-energy calculations in the framework of classical molecular dynamics simulations are nowadays used in a wide range of research areas including solvation thermodynamics, molecular recognition, and protein folding. The basic components of a free-energy calculation, that is, a suitable model Hamiltonian, a sampling protocol, and an estimator for the free energy, are independent of the specific application. However, the attention that one has to pay to these components depends considerably on the specific application. Here, we review six different areas of application and discuss the relative importance of the three main components to provide the reader with an organigram and to make nonexperts aware of the many pitfalls present in free energy calculations.

Water repellency in hydrophobic nanocapsules--molecular view on dewetting

The hydrophobic effect plays a major role in a variety of important phenomena in chemistry, materials science and biology, for instance in protein folding and protein-ligand interactions. Studies--performed within cavities of the unique metal oxide based porous capsules of the type {(pentagon)12(linker)30}≡{(W)W5}12{Mo2(ligand)}30 with different acetate/water ligand ratios--have provided unprecedented results revealing segregation/repellency of the encapsulated "water" from the internal hydrophobic ligand walls of the capsules, while the disordered water molecules, interacting strongly with each other via hydrogen bonding, form in all investigated cases the same type of spherical shell. The present results can be (formally) compared--but only regarding the repellency effect--with the amazing "action" of the (super)hydrophobic Lotus (Nelumbo) leaves, which are self-cleaning based on water repellency resulting in the formation of water droplets picking up dirt. The present results were obtained by constructing deliberately suitable hydrophobic interiors within the mentioned capsules.

Dynamics and energetics of hydrophobically confined water

The effects of water confined in regions between self-assembling entities is relevant to numerous contexts such as macromolecular association, protein folding, protein-ligand association, and nanomaterials self-assembly. Thus assessing the impact of confined water, and the ability of current modeling techniques to capture the salient features of confined water is important and timely. We present molecular dynamics simulation results investigating the effect of confined water on qualitative features of potentials of mean force describing the free energetics of self-assembly of large planar hydrophobic plates. We consider several common explicit water models including the TIP3P, TIP4P, SPC/E, TIP4P-FQ, and SWM4-NDP, the latter two being polarizable models. Examination of the free energies for filling and unfilling the volume confined between the two plates (both in the context of average number of confined water molecules and "depth" of occupancy) suggests TIP4P-FQ water molecules generally occupy the confined volume at separation distances larger than observed for other models under the same conditions. The connection between this tendency of TIP4P-FQ water and the lack of a pronounced barrier in the potential of mean force for plate-plate association in TIP4P-FQ water is explored by artificially, but systematically, populating the confined volume with TIP4P-FQ water at low plate-plate separation distances. When the critical separation distance [denoting the crossover from an unoccupied (dry) confined interior to a filled (wet) interior] for TIP4P-FQ is reduced by 0.5 Å using this approach, a barrier is observed; we rationalize this effect based on increased resistant forces introduced by confined water molecules at these low separations. We also consider the dynamics of water molecules in the confined region between the hydrophobes. We find that the TIP4P-FQ water model exhibits nonbulklike dynamics, with enhanced lateral diffusion relative to bulk. This is consistent with the reduced intermolecular water-water interaction indicated by a decreased molecular dipole moment in the interplate region. Analysis of velocity autocorrelation functions and associated power spectra indicate that the interplate region for TIP4P-FQ at a plate separation of 14.4 Å approaches characteristics of the pure water liquid-vapor interface. This is in stark contrast to the other water models (including the polarizable SWM4-NDP model).

Water in cavity-ligand recognition

We use explicit solvent molecular dynamics simulations to estimate free energy, enthalpy, and entropy changes along the cavity-ligand association coordinate for a set of seven model systems with varying physicochemical properties. Owing to the simplicity of the considered systems we can directly investigate the role of water thermodynamics in molecular recognition. A broad range of thermodynamic signatures is found in which water (rather than cavity or ligand) enthalpic or entropic contributions appear to drive cavity-ligand binding or rejection. The unprecedented, nanoscale picture of hydration thermodynamics can help the interpretation and design of protein-ligand binding experiments. Our study opens appealing perspectives to tackle the challenge of solvent entropy estimation in complex systems and for improving molecular simulation models.

Drainage, rupture, and lifetime of deionized water films: effect of dissolved gases?

Gas bubbles coalesce in deionized (DI) water because the water (foam) films between the bubbles are not stable. The so-called hydrophobic attraction has been suggested as the cause of the film instability and the bubble coalescence. In this work, microinterferometry experiments show that foam films of ultrapure DI water can last up to 10 s and the contact time between the two gas bubble surfaces at close proximity (approximately 1 microm separation distance) significantly influences the film drainage, rupture, and lifetime. Specifically, when the two bubbles were first brought into contact, the films instantly ruptured at 0.5 microm thickness. However, the film drainage rate and rupture thickness sharply decreased and the film lifetime steeply increased with increasing contact time up to 10 min, but then they leveled off. The constant thickness of film rupture was around 35 nm. Possible contamination was vigorously investigated and ruled out. It is argued that migration of gases inherently dissolved in water might cause the transient behavior of the water films at the short contact time. The film drainage rate and instability at the long contact time were analyzed employing Eriksson et al.'s phenomenological theory of long-range hydrophobic attraction (Eriksson, J. C.; Ljunggren, S.; Claesson, P. M., J. Chem. Soc., Faraday Trans. 2 1989, 85, 163-176) and the hypothesis of water molecular structure modified by dissolved gases, and the extended Stefan-Reynolds theory by incorporating the mobility of the air-DI-water interfaces.

Interfaces and hydrophobic interactions in receptor-ligand systems: A level-set variational implicit solvent approach

A model nanometer-sized hydrophobic receptor-ligand system in aqueous solution is studied by the recently developed level-set variational implicit solvent model (VISM). This approach is compared to all-atom computer simulations. The simulations reveal complex hydration effects within the (concave) receptor pocket, sensitive to the distance of the (convex) approaching ligand. The ligand induces and controls an intermittent switching between dry and wet states of the hosting pocket, which determines the range and magnitude of the pocket-ligand attraction. In the level-set VISM, a geometric free-energy functional of all possible solute-solvent interfaces coupled to the local dispersion potential is minimized numerically. This approach captures the distinct metastable states that correspond to topologically different solute-solvent interfaces, and thereby reproduces the bimodal hydration behavior observed in the all-atom simulation. Geometrical singularities formed during the interface relaxation are found to contribute significantly to the energy barrier between different metastable states. While the hydration phenomena can thus be explained by capillary effects, the explicit inclusion of dispersion and curvature corrections seems to be essential for a quantitative description of hydrophobically confined systems on nanoscales. This study may shed more light onto the tight connection between geometric and energetic aspects of biomolecular hydration and may represent a valuable step toward the proper interpretation of experimental receptor-ligand binding rates.

Standard Free Energy of Binding from a One-Dimensional Potential of Mean Force

A practical approach that enables one to calculate the standard free energy of binding from a one-dimensional potential of mean force (PMF) is proposed. Umbrella sampling and the weighted histogram analysis method are used to generate a PMF along the reaction coordinate of binding. At each point, a restraint is applied orthogonal to the reaction coordinate to make possible the determination of the volume sampled by the ligand. The free energy of binding from an arbitrary unbound volume to the restrained bound form is calculated from the ratio of the PMF integrated over the bound region to that of the unbound. Adding the free energy changes from the standard-state volume to the unbound volume and from the restrained to the unrestrained bound state gives the standard free energy of binding. Exploration of the best choice of binding paths is also made. This approach is first demonstrated on a model binding system and then tested on the benzamidine-trypsin system for which reasonable agreement with experiment is found. A comparison is made with other methods to obtain the standard free energy of binding from the PMF.