Solvation Thermodynamics and Its Applications.

In this article, we start by describing a few "definitions" of the solvation processes, which were used in the literature until about 1980. Then, we choose one of these definitions and show that it has a simple molecular interpretation. This fact led to a new definition of the solvation process and the corresponding thermodynamic quantities. The new measure of the solvation Gibbs energy has a simple interpretation. In addition, the thermodynamic quantities associated with the new solvation process have several other advantages over the older measures. These will be discussed briefly in the third section. In the fourth section, we discuss a few applications of the new solvation process.

Solvation free energy arithmetic for small organic molecules.

Solvent-mediated interactions contribute to ligand binding affinities in computational drug design and provide a challenge for theoretical predictions. In this study, we analyze the solvation free energy of benzene derivatives in water to guide the development of predictive models for solvation free energies and solvent-mediated interactions. We use a spatially resolved analysis of local solvation free energy contributions and define solvation free energy arithmetic, which enable us to construct additive models to describe the solvation of complex compounds. The substituents analyzed in this study are carboxyl and nitro-groups due to their similar sterical requirements but distinct interactions with water. We find that nonadditive solvation free energy contributions are primarily attributed to electrostatics, which are qualitatively reproduced with computationally efficient continuum models. This suggests a promising route for the development of efficient and accurate models for the solvation of complex molecules with varying substitution patterns using solvation arithmetic.

Is Time's Asymmetry Related to Irreversible Processes and the Second Law?

In this article, we start by describing one of the most characteristic properties of time: "time can never decrease". From this property, numerous authors have concluded that irreversible processes, that always proceed in one direction, must be related to time's arrow. It is shown that while time's decrease can never occur, irreversible processes can be reversed, although with extremely low probability. Similarly, it is argued that both entropy and the Second Law are timeless, i.e., have nothing to do with either time or with time's arrow.

Information, Entropy, Life, and the Universe.

In (2015), I wrote a book with the same title as this article. The book's subtitle is: "What we know and what we do not know." On the book's dedication page, I wrote [1]: "This book is dedicated to readers of popular science books who are baffled, perplexed, puzzled, astonished, confused, and discombobulated by reading about Information, Entropy, Life and the Universe." In the first part of this article, I will present the definitions of two central concepts: the "Shannon measure of information" (SMI), in Information Theory, and "Entropy", in Thermodynamics. Following these definitions, I will discuss the framework of their applicability. In the second part of the article, I will examine the question of whether living systems and the entire universe are, or are not within the framework of applicability of the concepts of SMI and Entropy. I will show that much of the confusion that exists in the literature arises because of people's ignorance about the framework of applicability of these concepts.

Entropy and Time.

The idea that entropy is associated with the "arrow of time" has its roots in Clausius's statement on the Second Law: "Entropy of the Universe always increases." However, the explicit association of the entropy with time's arrow arises from Eddington. In this article, we start with a brief review of the idea that the "increase in entropy" is somehow associated with the direction in which time increases. Then, we examine three different, but equivalent definitions of entropy. We find that none of these definitions indicate any hint of a relationship between entropy and time. We can, therefore, conclude that entropy is a timeless quantity. We also discuss the reasons as to why some scientists went astray in associating entropy with time's arrow. Finally, we shall discuss Boltzmann's H-Theorem, which is viewed by many as a proof of the Second Law of Thermodynamics.

An Informational Theoretical Approach to the Entropy of Liquids and Solutions.

It is well known that the statistical mechanical theory of liquids has been lagging far behind the theory of either gases or solids, See for examples: Ben-Naim (2006), Fisher (1964), Guggenheim (1952) Hansen and McDonald (1976), Hill (1956), Temperley, Rowlinson and Rushbrooke (1968), O'Connell (1971). Information theory was recently used to derive and interpret the entropy of an ideal gas of simple particles (i.e., non-interacting and structure-less particles). Starting with Shannon's measure of information (SMI), one can derive the entropy function of an ideal gas, the same function as derived by Sackur (1911) and Tetrode (1912). The new deviation of the same entropy function, based on SMI, has several advantages, as listed in Ben-Naim (2008, 2017). Here we mention two: First, it provides a simple interpretation of the various terms in this entropy function. Second, and more important for our purpose, this derivation may be extended to any system of interacting particles including liquids and solutions. The main idea is that once one adds intermolecular interactions between the particles, one also adds correlations between the particles. These correlations may be cast in terms of mutual information (MI). Hence, we can start with the informational theoretical interpretation of the entropy of an ideal gas. Then, we add correction due to correlations in the form of MI between the locations of the particles. This process preserves the interpretation of the entropy of liquids and solutions in terms of a measure of information (or as an average uncertainty about the locations of the particles). It is well known that the entropy of liquids, any liquids for that matter, is lower than the entropy of a gas. Traditionally, this fact is interpreted in terms of order-disorder. The lower entropy of the liquid is interpreted in terms of higher degree of order compared with that of the gas. However, unlike the transition from a solid to either a liquid, or to a gaseous phase where the order-disorder interpretation works well, the same interpretation would not work for the liquid-gas transition. It is hard, if not impossible, to argue that the liquid phase is more "ordered" than the gaseous phase. In this article, we interpret the lower entropy of liquids in terms of SMI. One outstanding liquid known to be a structured liquid, is water, according to Ben-Naim (2009, 2011). In addition, heavy water, as well as aqueous solutions of simple solutes such as argon or methane, will be discussed in this article.

Hydrophobic-hydrophilic forces in protein folding.

The process of protein folding is obviously driven by forces exerted on the atoms of the amino-acid chain. These forces arise from interactions with other parts of the protein itself (direct forces), as well as from interactions with the solvent (solvent-induced forces). We present a statistical-mechanical formalism that describes both these direct and indirect, solvent-induced thermodynamic forces on groups of the protein. We focus on 2 kinds of protein groups, commonly referred to as hydrophobic and hydrophilic. Analysis of this result leads to the conclusion that the forces on hydrophilic groups are in general stronger than on hydrophobic groups. This is then tested and verified by a series of molecular dynamics simulations, examining both hydrophobic alkanes of different sizes and hydrophilic moieties represented by polar-neutral hydroxyl groups. The magnitude of the force on assemblies of hydrophilic groups is dependent on their relative orientation: with 2 to 4 times larger forces on groups that are able to form one or more direct hydrogen bonds.

Theoretical aspects of self-assembly of proteins: a Kirkwood-Buff-theory approach.

A new approach to the problem of self-assembly of proteins induced by temperature, pressure, or changes in solute concentration is presented. The problem is formulated in terms of Le Chatelier principle, and a solution is sought in terms of the Kirkwood-Buff theory of solutions. In this article we focus on the pressure and solute effects on the association-dissociation equilibrium. We examine the role of both hydrophobic and hydrophilic effects. We argue that the latter are more important than the former. The solute effect, on the other hand, depends on the preferential solvation of the monomer and the aggregate with respect to solvent and co-solvent molecules. An experimental approach based on model compounds to study these effects is suggested.

Myths and verities in protein folding theories: from Frank and Evans iceberg-conjecture to explanation of the hydrophobic effect.

Starting from the seminal article by Frank and Evans where the "iceberg formation" idea was first expressed, we follow the evolution of this idea to the explanation of the hydrophobic effect. We show that the idea of iceberg formation can provide an explanation to the entropy, and enthalpy of solvation of non-polar solutes in water, provided one first explains why a simple non-polar solute would form icebergs in the first place. Having done that, the questions regarding the outstanding large hydrophobic solvation Gibbs energy remains unexplained. This conclusion follows from the exact entropy-enthalpy-compensation pertaining to any structural changes induced in the solvent. We also comment on some misinterpretation of the partial molar heat capacity of non-polar solutes in water.

Theoretical aspects of pressure and solute denaturation of proteins: A Kirkwood-buff-theory approach.

A new approach to the problem of pressure-denaturation (PD) and solute-denaturation (SD) of proteins is presented. The problem is formulated in terms of Le Chatelier principle, and a solution is sought in terms of the Kirkwood-Buff theory of solutions. It is found that both problems have one factor in common; the excluded volumes of the folded and the unfolded forms with respect to the solvent molecules. It is shown that solvent-induced effects operating on hydrophilic groups along the protein are probably the main reason for PD. On the other hand, the SD depends on the preferential solvation of the folded and the unfolded forms with respect to solvent and co-solvent molecules.

Some aspects of the protein folding problem examined in one-dimensional systems.

Some concepts, such as energy landscape, Gibbs energy landscape, and cooperativity, frequently used in the theory of protein folding, are examined exactly in one-dimensional systems. It is shown that much of the confusion that exists regarding these, and other concepts arise from the misinterpretation of Anfinsen's thermodynamic hypothesis.

Temperature Dependence of Hydrophobic and Hydrophilic Forces and Interactions.

Molecular dynamics simulations are used to compare the forces and Gibbs free energies associated with bringing small hydrophobic and hydrophilic solutes together in an aqueous solution at different temperatures between 280 and 360 °K. For the hydrophilic solutes, different relative orientations are used to distinguish between direct, intersolute hydrogen bonds (Hbond) and solutes simultaneously hydrogen bonding to a solvent water bridge. Interestingly, the temperature dependence of the hydrophobic and directly hydrogen bonding solutes turns out to be opposite to that of the bridged hydrophilic solutes, with the ΔG becoming more negative for the former and less negative for the latter with increasing temperature. Dissection of the free energy curves into enthalpy and entropy contributions, and further separation of the enthalpy term into solute-solute, solute-solvent, and solvent-solvent components provides insight into the physical molecular causes for the distinctive thermodynamic results. Finally, it is reasoned how the opposite temperature dependencies of the two types of hydrophilic interactions provide a rationale for the cold denaturation of proteins.

One dimensional model for water and aqueous solutions. Part V. Monte Carlo simulation of dilute solutions of hard rod in waterlike particles.

We have carried out Monte Carlo simulation on the primitive one dimensional model for water described earlier [A. Ben-Naim, J. Chem. Phys. 128, 024506 (2008)]. We show that by taking into account second nearest neighbor interactions, one can obtain the characteristic anomalous solvation thermodynamic quantities of inert solutes in water. This model clearly demonstrates the molecular origin of the large negative entropy of solvation of an inert solute in water.

Local and global properties of mixtures in one-dimensional systems. II. Exact results for the Kirkwood-Buff integrals.

The Kirkwood-Buff integrals for two-component mixtures in one-dimensional systems are calculated directly. The results are applied to square-well particles and found to agree with those obtained by the inversion of the Kirkwood-Buff theory of solutions.

The Kirkwood-Buff integrals for one-component liquids.

The Kirkwood-Buff integrals (KBIs) for one-component systems are calculated from either the pair correlation functions or from experimental macroscopic quantities. As in the case of mixtures, the KBIs provide important information on the local densities around a molecule. In the low density limit (rho-->0) one can extract from the KBI some information on the strength of the intermolecular forces. No such information may be extracted from the KBIs at higher densities. We used experimental data on densities and isothermal compressibilities to calculate the KBIs for various liquids ranging from inert molecules, to hydrocarbons, alcohols, and liquid water.

One-dimensional model for water and aqueous solutions. IV. A study of "hydrophobic interactions".

The solute-solute pair correlation function and the potential of mean force (PMF) between two hard-rod solutes in two solvents are studied in one-dimensional systems. One solvent consists of particles interacting via square well (SW) potential. The second consists of particles interacting via "hydrogen-bond-like" (HB) pair potential. It was found that the first minimum of the solute-solute PMF at infinite dilution in the two solvents grows deeper as we increase the strength of the solvent-solvent interaction. In the SW (but not in the HB) solvent, we found that the range of solute-solute pair correlation is larger at lower temperatures (or at larger epsilon(BB)/k(B)T). The relevance of this finding to the problem of hydrophobic interactions is discussed.

Pair correlation functions of simple solutes in a Lennard-Jones solvent.

We have calculated the pair correlation functions for several binary mixtures composed of simple solutes in a Lennard-Jones solvent. In particular, we have studied the solute-solute pair correlation functions and their dependence on the total density, the solvent Lennard-Jones parameters, and on the solute-solute energy parameter. All the results were obtained from solving the Percus-Yevick equations, as well as from Monte Carlo simulations. The relevance of these results to the problem of hydrophobic interactions is also discussed.

Pair correlation functions in mixtures of Lennard-Jones particles.

The pair correlation functions for a mixture of two Lennard-Jones particles were computed by both the Percus-Yevick equations and by molecular dynamics. The changes in the pair correlation function resulting from changes in the composition of the mixtures are quite unexpected. Essentially, identical changes are obtained from the Percus-Yevick equations and from molecular dynamics simulations. The molecular reason for this unexpected behavior is discussed.

Hydrophobic hydrophilic phenomena in biochemical processes.

The evolution of concepts developed in the study of the hydrophobic affect is surveyed, within the more general context of solvent-induced effects. A systematic analysis of the solvent-induced contribution to the driving force for the process of protein folding has led to two important modifications in our understanding of these effects. First, the conventional concepts of hydrophobic solvation and hydrophobic interactions had to be replaced by their respective conditional effects. Second, each of the hydrophobic effects has also a corresponding hydrophilic counterpart. Some of the latter effects could contribute significantly to the total driving force for the process of protein folding, and perhaps even dominate the driving force for biochemical processes.