Statistical Analyses of Hydrophobic Interactions: A Mini-Review

How do water-mediated interactions and osmotic second virial coefficients vary with particle size?

We examine quantitatively the solute-size dependences of the effective interactions between nonpolar solutes in water and in a simple liquid. The potential w(r) of mean force and the osmotic second virial coefficients B are calculated with high accuracy from molecular dynamics simulations. As the solute diameter increases from methane's to C60's with the solute-solute and solute-solvent attractive interaction parameters fixed to those for the methane-methane and methane-water interactions, the first minimum of w(r) lowers from -1.1 to -4.7 in units of the thermal energy kT. Correspondingly, the magnitude of B (<0) increases proportional to σα with some power close to 6 or 7, which reinforces the solute-size dependence of B found earlier for a smaller range of σ [H. Naito, R. Okamoto, T. Sumi and K. Koga, J. Chem. Phys., 2022, 156, 221104]. We also demonstrate that the strength of the attractive interactions between solute and solvent molecules can qualitatively change the characteristics of the effective pair interaction between solute particles, both in water and in a simple liquid. If the solute-solvent attractive force is set to be weaker (stronger) than a threshold, the effective interaction becomes increasingly attractive (repulsive) with increasing solute size.

Insight into Thermodynamic and Kinetic Profiles in Small-Molecule Optimization

Structure-activity relationships (SARs) and structure-property relationships (SPRs) have been considered the most important factors during the drug optimization process. For medicinal chemists, improvements in the potencies and druglike properties of small molecules are regarded as their major goals. Among them, the binding affinity and selectivity of small molecules on their targets are the most important indicators. In recent years, there has been growing interest in using thermodynamic and kinetic profiles to analyze ligand-receptor interactions, which could provide not only binding affinities but also detailed binding parameters for small-molecule optimization. In this perspective, we are trying to provide an insight into thermodynamic and kinetic profiles in small-molecule optimization. Through a highlight of strategies on the small-molecule optimization with specific cases, we aim to put forward the importance of structure-thermodynamic relationships (STRs) and structure-kinetic relationships (SKRs), which could provide more guidance to find safe and effective small-molecule drugs.

Osmotic second virial coefficients for hydrophobic interactions as a function of solute size

To gain quantitative insight into how the overall strength of the hydrophobic interaction varies with the molecular size, we calculate osmotic second virial coefficients B for hydrophobic spherical molecules of different diameters σ in water based on molecular simulation with corrections to the finite-size and finite-concentration effects. It is shown that B (<0) changes by two orders of magnitude greater as σ increases twofold and its solute-size dependence is best fit by a power law B ∝ σ^α with the exponent α ≃ 6, which contrasts with the cubic power law that the second virial coefficients of gases obey. It is also found that values of B for the solutes in a nonpolar solvent are positive but they obey the same power law as in water. A thermodynamic identity for B derived earlier [K. Koga, V. Holten, and B. Widom, J. Phys. Chem. B 119, 13391 (2015)] indicates that if B is asymptotically proportional to a power of σ, the exponent α must be equal to or greater than 6.

Thermodynamics of Hydration from the Perspective of the Molecular Quasichemical Theory of Solutions

The quasichemical organization of the potential distribution theorem, molecular quasichemical theory (QCT), enables practical calculations and also provides a conceptual framework for molecular hydration phenomena. QCT can be viewed from multiple perspectives: (a) as a way to regularize an ill-conditioned statistical thermodynamic problem; (b) as an introduction of and emphasis on the neighborship characteristics of a solute of interest; or (c) as a way to include accurate electronic structure descriptions of near-neighbor interactions in defensible statistical thermodynamics by clearly defining neighborship clusters. The theory has been applied to solutes of a wide range of chemical complexity, ranging from ions that interact with water with both long-ranged and chemically intricate short-ranged interactions, to solutes that interact with water solely through traditional van der Waals interations, and including water itself. The solutes range in variety from monatomic ions to chemically heterogeneous macromolecules. A notable feature of QCT is that, in applying the theory to this range of solutes, the theory itself provides guidance on the necessary approximations and simplifications that can facilitate the calculations. In this Perspective, we develop these ideas and document them with examples that reveal the insights that can be extracted using the QCT formulation.

Quadrupole-mediated dielectric response and the charge-asymmetric solvation of ions in water

Treating water as a linearly responding dielectric continuum on molecular length scales allows very simple estimates of the solvation structure and thermodynamics for charged and polar solutes. While this approach can successfully account for basic length and energy scales of ion solvation, computer simulations indicate not only its quantitative inaccuracies but also its inability to capture some basic and important aspects of microscopic polarization response. Here, we consider one such shortcoming, a failure to distinguish the solvation thermodynamics of cations from that of otherwise-identical anions, and we pursue a simple, physically inspired modification of the dielectric continuum model to address it. The adaptation is motivated by analyzing the orientational response of an isolated water molecule whose dipole is rigidly constrained. Its free energy suggests a Hamiltonian for dipole fluctuations that accounts implicitly for the influence of higher-order multipole moments while respecting constraints of molecular geometry. We propose a field theory with the suggested form, whose nonlinear response breaks the charge symmetry of ion solvation. An approximate variational solution of this theory, with a single adjustable parameter, yields solvation free energies that agree closely with simulation results over a considerable range of solute size and charge.

Reference values for biochemical analytes in feral sheep from Socorro Island, Revillagigedo Archipelago, Mexico

ABSTRACT To establish reference values for biochemical analytes related to freshwater shortage adaptation, a total of 376 blood samples were collected from feral sheep at Socorro Island, Revillagigedo Archipelago. Year-round variation was assessed by sampling at the beginning of each season defined by the March equinox, June solstice, September equinox, and December solstice. The resulting data set was analyzed using Gaussian distribution and descriptive statistics. Confidence intervals of 95% were established. Analysis of variance was used to compare the mean values of each season. Total cholesterol, triglycerides, urea, albumin, total protein, sodium ion, anion gap, creatine kinase, arginine vasopressin, and aldosterone showed concentrations above the reference range for domestic sheep. Triglycerides, urea, albumin, sodium ion, and aldosterone showed concentrations within the reference range for domestic goats. Most biochemical analytes showed differences (P<0.05) between seasons, with the highest values occurring during winter, and the lowest during spring. Results could help improve the accuracy of metabolic profiles used as a tool for evaluating dehydration indicators, and to describe the physiological mechanisms employed by feral sheep to cope with seasonal availability of freshwater.

Hydrophilic Interactions Dominate the Inverse Temperature Dependence of Polypeptide Hydration Free Energies Attributed to Hydrophobicity

We address the association of the hydrophobic driving forces in protein folding with the inverse temperature dependence of protein hydration, wherein stabilizing hydration effects strengthen with increasing temperature in a physiological range. All-atom calculations of the free energy of hydration of aqueous deca-alanine conformers, holistically including backbone and side-chain interactions together, show that attractive peptide-solvent interactions and the thermal expansion of the solvent dominate the inverse temperature signatures that have been interpreted traditionally as the hydrophobic stabilization of proteins in aqueous solution. Equivalent calculations on a methane solute are also presented as a benchmark for comparison. The present study calls for a reassessment of the forces that stabilize folded protein conformations in aqueous solutions and of the additivity of hydrophobic/hydrophilic contributions.

Conformational Ensembles of Antibodies Determine Their Hydrophobicity

A major challenge in the development of antibody biotherapeutics is their tendency to aggregate. One root cause for aggregation is exposure of hydrophobic surface regions to the solvent. Many current techniques predict the relative aggregation propensity of antibodies via precalculated scales for the hydrophobicity or aggregation propensity of single amino acids. However, those scales cannot describe the nonadditive effects of a residue’s surrounding on its hydrophobicity. Therefore, they are inherently limited in their ability to describe the impact of subtle differences in molecular structure on the overall hydrophobicity. Here, we introduce a physics-based approach to describe hydrophobicity in terms of the hydration free energy using grid inhomogeneous solvation theory (GIST). We apply this method to assess the effects of starting structures, conformational sampling, and protonation states on the hydrophobicity of antibodies. Our results reveal that high-quality starting structures, i.e., crystal structures, are crucial for the prediction of hydrophobicity and that conformational sampling can compensate errors introduced by the starting structure. On the other hand, sampling of protonation states only leads to good results when combined with high-quality structures, whereas it can even be detrimental otherwise. We conclude by pointing out that a single static homology model may not be adequate for predicting hydrophobicity.

Influence of Ionic Strength on Hydrophobic Interactions in Water: Dependence on Solute Size and Shape

Hydrophobicity is a phenomenon of great importance in biology, chemistry, and biochemistry. It is defined as the interaction between nonpolar molecules or groups in water and their low solubility. Hydrophobic interactions affect many processes in water, for example, complexation, surfactant aggregation, and coagulation. These interactions play a pivotal role in the formation and stability of proteins or biological membranes. In the present study, we assessed the effect of ionic strength, solute size, and shape on hydrophobic interactions between pairs of nonpolar particles. Pairs of methane, neopentane, adamantane, fullerene, ethane, propane, butane, hexane, octane, and decane were simulated by molecular dynamics in AMBER 16.0 force field. As a solvent, TIP3P and TIP4PEW water models were used. Potential of mean force (PMF) plots of these dimers were determined at four values of ionic strength, 0, 0.04, 0.08, and 0.40 mol/dm³, to observe its impact on hydrophobic interactions. The characteristic shape of PMFs with three extrema (contact minimum, solvent-separated minimum, and desolvation maximum) was observed for most of the compounds for hydrophobic interactions. Ionic strength affected hydrophobic interactions. We observed a tendency to deepen contact minima with an increase in ionic strength value in the case of spherical and spheroidal molecules. Additionally, two-dimensional distribution functions describing water density and average number of hydrogen bonds between water molecules were calculated in both water models for adamantane and hexane. It was observed that the density of water did not significantly change with the increase in ionic strength, but the average number of hydrogen bonds changed. The latter tendency strongly depends on the water model used for simulations.

Cavity Particle in Aqueous Solution with a Hydrophobic Solute: Structure, Energetics, and Functionals

Endpoints density functional theory (DFT) provides a framework for calculating the excess chemical potential of a solute in solution using solvent distribution functions obtained from both physical endpoints of a hypothetical charging process which transforms the solvent density from that of the pure liquid to the solution state. In this work, the endpoints DFT equations are formulated in terms of the indirect (solvent-mediated) contribution ω(x) to the solute-solvent potential of mean force, and their connections are established with the conventional DFT expressions which are based on the use of direct correlation functions. ω actually corresponds to the free-energy cost to move a cavity particle (a tagged solvent molecule which interacts with the other solvent molecules but not the solute) from the bulk to the configuration x of a solvent molecule relative to the solute and is a suitable variable to describe the solvent effects on the solute-solvent interactions. HNC and PY type approximations are then used to integrate the DFT charging integral involved in the exact expression for the excess chemical potential. With these approximations, molecular simulations are to be performed at the two endpoints of solute insertion: pure solvent without the solute and the solution system with the fully coupled solute-solvent interaction. An endpoints method thus utilizes the ensembles of intermolecular configurations of physical interest, which are often readily accessible with MD simulations given the present computational power. To illustrate properties of the formulation, we perform simulations of model systems consisting of a cavity particle in an aqueous solution containing a spherical hydrophobic solute of three different sizes from which ω(x) and the solute chemical potential can be calculated using endpoints DFT expressions. These are compared with corresponding results obtained using the approximations needed in order to evaluate the endpoints DFT charging integral when cavity particle simulation data is not available. We analyze a new approximation (two-points quadratic HNC) to the DFT charging integral which captures the correct behavior of the cavity distributions at both endpoints of the solute insertion. The behavior of the cavity particle in simple and complex liquids plays an important role in various theoretical treatments of the solute chemical potential. For pure Lennard-Jones fluids, the free energy to bring a cavity particle from the bulk to the center of a fluid particle is negative. However, for solutes of varying size, this is not generally true for Lennard-Jones fluids or the systems studied in this work. We carry out energetic and structural analyses of the cavity particle in aqueous solution with hydrophobic solutes of varying size and discuss the results in the context of the hydrophobic effect.

Colloidal stability of the living cell

Cellular function is generally depicted at the level of functional pathways and detailed structural mechanisms, based on the identification of specific protein–protein interactions. For an individual protein searching for its partner, however, the perspective is quite different: The functional task is challenged by a dense crowd of nonpartners obstructing the way. Adding to the challenge, there is little information about how to navigate the search, since the encountered surrounding is composed of protein surfaces that are predominantly “nonconserved” or, at least, highly variable across organisms. In this study, we demonstrate from a colloidal standpoint that such a blindfolded intracellular search is indeed favored and has more fundamental impact on the cellular organization than previously anticipated. Basically, the unique polyion composition of cellular systems renders the electrostatic interactions different from those in physiological buffer, leading to a situation where the protein net-charge density balances the attractive dispersion force and surface heterogeneity at close range. Inspection of naturally occurring proteomes and in-cell NMR data show further that the “nonconserved” protein surfaces are by no means passive but chemically biased to varying degree of net-negative repulsion across organisms. Finally, this electrostatic control explains how protein crowding is spontaneously maintained at a constant level through the intracellular osmotic pressure and leads to the prediction that the “extreme” in halophilic adaptation is not the ionic-liquid conditions per se but the evolutionary barrier of crossing its physicochemical boundaries.

Hydrophobic hydration and pairwise hydrophobic interaction of Lennard-Jones and Mie particles in different water models

The study provides a deep computational analysis of the thermodynamic and structural features associated with the hydration of xenon, Xe, and its pairwise hydrophobic interaction (i.e., the potential of mean force, PMF), over a large temperature range. Xe is described both as a Lennard-Jones particle, LJ-Xe, and as a Mie particle, Mie-Xe (pseudo hard sphere). Three different water models are used: TIP3P-Ew, SPCE and TIP4P-2005. Mie-Xe is more hydrophobic than LJ-Xe due to the lack of the attractive energetic interactions with water molecules; its hydration, around room temperature, is opposed by a large and negative entropy change and a positive enthalpy change. The PMF of Mie-Xe is characterized by a deep minimum at contact distance whose depth increases with temperature, and whose magnitude is significantly larger than that obtained for LJ-Xe. The contact minimum configuration of Mie-Xe is favoured by a large positive entropy change and contrasted by a positive enthalpy change. These results are qualitatively the same regardless of the water model used. There is no clear connection between the values determined for the thermodynamic functions and the structural features of the hydration shells surrounding the single Mie-Xe and the couple of Mie-Xe particles in the contact minimum configuration. This confirms that the structural reorganization of water associated with such processes is characterized by an almost complete enthalpy-entropy compensation.

Implicit Solvation Using the Superposition Approximation (IS-SPA): An Implicit Treatment of the Nonpolar Component to Solvation for Simulating Molecular Aggregation

Nonpolar solute-solvent interactions are the driving force for aggregation in important chemical and biological phenomena including protein folding, peptide self-assembly, and oil-water emulsion formation. Currently, the most accurate and computationally efficient description of these processes requires an explicit treatment of all solvent and solute atoms. Previous computationally feasible implicit solvent models, such as solute surface area approaches, are unsuccessful at capturing aggregation features including both structural and energetic trends while more theoretically rigorous approaches, such as Reference Interaction Site Model (RISM), are accurate but extremely computationally demanding. Our approach, denoted Implicit Solvation using the Superposition Approximation (IS-SPA), builds on previous theory utilizing the Kirkwood superposition approximation to approximate the mean force of the solvent from solute parameters. We introduce and verify a parabolic first solvation shell truncation of atomic solvation, fitting water distributions around a molecule, and a Monte Carlo integration of the mean solvent force. These extensions allow this method to be implemented as an efficient nonpolar implicit solvent model for molecular simulation. The approximations in IS-SPA are first explored and justified for the homodimerization of an array of different sized Lennard-Jones spheres. The accuracy and transferability of the approach are demonstrated by its ability to capture the position and relative energies of the desolvation barrier and free energy minimum of alkane homodimers. The model is then shown to reproduce the phase separation and solubility of cyclohexane and water. These promising results, coupled with 2 orders of magnitude speed-up for dilute systems as compared to explicit solvent simulations, demonstrate that IS-SPA is an appealing approach to boost the time- and length-scale of molecular aggregation simulations.

How Water's Properties Are Encoded in Its Molecular Structure and Energies

How are water's material properties encoded within the structure of the water molecule? This is pertinent to understanding Earth's living systems, its materials, its geochemistry and geophysics, and a broad spectrum of its industrial chemistry. Water has distinctive liquid and solid properties: It is highly cohesive. It has volumetric anomalies-water's solid (ice) floats on its liquid; pressure can melt the solid rather than freezing the liquid; heating can shrink the liquid. It has more solid phases than other materials. Its supercooled liquid has divergent thermodynamic response functions. Its glassy state is neither fragile nor strong. Its component ions-hydroxide and protons-diffuse much faster than other ions. Aqueous solvation of ions or oils entails large entropies and heat capacities. We review how these properties are encoded within water's molecular structure and energies, as understood from theories, simulations, and experiments. Like simpler liquids, water molecules are nearly spherical and interact with each other through van der Waals forces. Unlike simpler liquids, water's orientation-dependent hydrogen bonding leads to open tetrahedral cage-like structuring that contributes to its remarkable volumetric and thermal properties.

Polymer-Nucleic Acid Interactions

Gene therapy is an important therapeutic strategy in the treatment of a wide range of genetic disorders. Polymers forming stable complexes with nucleic acids (NAs) are non-viral gene carriers. The self-assembly of polymers and nucleic acids is typically a complex process that involves many types of interaction at different scales. Electrostatic interaction, hydrophobic interaction, and hydrogen bonds are three important and prevalent interactions in the polymer/nucleic acid system. Electrostatic interactions and hydrogen bonds are the main driving forces for the condensation of nucleic acids, while hydrophobic interactions play a significant role in the cellular uptake and endosomal escape of polymer-nucleic acid complexes. To design high-efficiency polymer candidates for the DNA and siRNA delivery, it is necessary to have a detailed understanding of the interactions between them in solution. In this chapter, we survey the roles of the three important interactions between polymers and nucleic acids during the formation of polyplexes and summarize recent understandings of the linear polyelectrolyte-NA interactions and dendrimer-NA interactions. We also review recent progress optimizing the gene delivery system by tuning these interactions.