A thermodynamic analysis of solvation

Investigating the effects of solvent polarity and temperature on the molecular, photophysical, and thermodynamic properties of sinapic acid using DFT and TDDFT

Sinapic acid (SA) is widely used in cosmetics, foods, and pharmaceuticals due to its antioxidant, anti-inflammatory, neuroprotective, antimicrobial, antifungal, anticancer, and cardioprotective properties. However, environmental factors such as solvent polarity and temperature can influence its biological activity. This work determined how solvent polarity and temperature affected the molecular, photophysical, and thermodynamic properties of SA in gas and various solvents using semi-empirical (MP6), Hartree-Fock (HF) with the B3LYP method and a 6-311++G(d,p) basis set, and density functional theory (DFT) with various basis sets, such as 3TO-3G*, 3-21G+, 6-31G++G(d,p), 6-311++G(d,p), aug-CC-PVDZ, LanL2DZ, SDD, and DGD2VP. The results indicated that solvent polarity influences molecular and spectroscopic properties, such as bond angles, dihedral angles, bond lengths, FTIR spectra, solvation energy, dipole moments, HOMO-LUMO band gaps, chemical reactivity, and thermodynamic properties, resulting from interactions between the drug and solvent molecules. The findings suggested that increasing the temperature within the range of 100 to 1000 Kelvin leads to an increase in heat capacity, enthalpy, and entropy due to molecular vibrations, ultimately causing degradation and instability in SA. Furthermore, the results showed that SA underwent a redshift in the absorption peak (from 320.18 to 356.26 nm) and a shift in the fluorescence peak (from 381 to 429 nm) in the solvent phase compared to those in the gas phase. Overall, this study provides background knowledge on how solvent polarity and temperature affect the properties of SA molecules.

Structural Order in the Hydration Shell of Nonpolar Groups versus that in Bulk Water

The poor solubility of nonpolar compounds in water around room temperature is governed by a large and negative entropy change, whose molecular cause is still debated. Since the Frank and Evans original proposal in 1945, the large and negative entropy change is usually attributed to the formation of ordered structures in the hydration shell of nonpolar groups. However, the existence of such ordered structures has never been proven. The present study is aimed at providing available structural results and thermodynamic arguments disproving the existence of ordered structures in the hydration shell of nonpolar groups.

Why Solvent Response Contributions to Solvation Free Energies Are Compatible with Ben-Naim's Theorem

We resolve a seeming paradox arising from a common misinterpretation of Ben-Naim's theorem, which rests on the decomposition of the Hamiltonian of a molecular solute/solvent system into solute-solvent and solvent-solvent interactions. According to this theorem, the solvation entropy can also be decomposed into a solute-solvent term and a remaining solvent-solvent term that is commonly referred to as the solvent reorganization term. Crucially, the latter equals the average solvent-solvent interaction energy such that these two solvent-solvent terms cancel and thus do not change the total solvation free energy. This analytical result implies that changes in the solvent-solvent interactions cannot contribute to any thermodynamic driving force. The solvent reorganization term is often identified with the contribution of many-body solvent correlations to the solvation entropy, which seems to imply that these correlations, too, cannot contribute to solvation. However, recent calculations based on atomistic simulations of a solvated globular protein and spatially resolved mutual information expansions revealed substantial contributions of many-body solvent correlations to the solvation free energy, which are not canceled by the enthalpy change of the solvent. Here, we resolved this seeming contradiction and illustrate by two examples─a simple Ising model and a solvated Lennard-Jones particle─that the solvent reorganization entropy and the actual entropy contribution arising from many-body solvent correlations differ both conceptually and numerically. Whereas the solvent reorganization entropy in fact arises from both solvent-solvent as well as solute-solvent interactions and thus has no straightforward intuitive interpretation, the mutual information expansion permits an interpretation in terms of the entropy contribution of solvent-solvent correlations to the solvation free energy.

Solvation of Nanoions in Aqueous Solutions

In recent years it has been increasingly recognized that different classes of large ions with multiple valency have effects conceptually similar to weakly solvated ions in the Hofmeister series, also labeled by the term chaotropic. The term "superchaotropic effect" has been coined because these effects are much more strongly pronounced for nanometer-sized ions, whose adsorption properties often resemble typical surfactants. Despite this growing interest in these nanometer-sized ions, a simple conceptual extension of the Hofmeister series toward nanoions has not been achieved because an extrapolation of the one-dimensional surface charge density scale does not lead to the superchaotropic regime. In this work, we discuss a generic model that is broadly applicable to ions of nearly spherical shape and thus includes polyoxometalates and boron clusters. We present a qualitative classification scheme in which the ion size appears as a second dimension. Ions of different sizes but the same charge density differ in their bulk solvation free energy. As the ions grow bigger at constant surface charge density, they become more stable in solution, but the adsorption behavior is still governed by the surface charge density. A detailed molecular dynamics simulation study of large ions that is based on a shifted Lennard-Jones potential is presented that supports the presented classification scheme.

Structural Fluctuation, Relaxation, and Folding of Protein: An Approach Based on the Combined Generalized Langevin and RISM/3D-RISM Theories

In 2012, Kim and Hirata derived two generalized Langevin equations (GLEs) for a biomolecule in water, one for the structural fluctuation of the biomolecule and the other for the density fluctuation of water, by projecting all the mechanical variables in phase space onto the two dynamic variables: the structural fluctuation defined by the displacement of atoms from their equilibrium positions, and the solvent density fluctuation. The equation has an expression similar to the classical Langevin equation (CLE) for a harmonic oscillator, possessing terms corresponding to the restoring force proportional to the structural fluctuation, as well as the frictional and random forces. However, there is a distinct difference between the two expressions that touches on the essential physics of the structural fluctuation, that is, the force constant, or Hessian, in the restoring force. In the CLE, this is given by the second derivative of the potential energy among atoms in a protein. So, the quadratic nature or the harmonicity is only valid at the minimum of the potential surface. On the contrary, the linearity of the restoring force in the GLE originates from the projection of the water's degrees of freedom onto the protein's degrees of freedom. Taking this into consideration, Kim and Hirata proposed an ansatz for the Hessian matrix. The ansatz is used to equate the Hessian matrix with the second derivative of the free-energy surface or the potential of the mean force of a protein in water, defined by the sum of the potential energy among atoms in a protein and the solvation free energy. Since the free energy can be calculated from the molecular mechanics and the RISM/3D-RISM theory, one can perform an analysis similar to the normal mode analysis (NMA) just by diagonalizing the Hessian matrix of the free energy. This method is referred to as the Generalized Langevin Mode Analysis (GLMA). This theory may be realized to explore a variety of biophysical processes, including protein folding, spectroscopy, and chemical reactions. The present article is devoted to reviewing the development of this theory, and to providing perspective in exploring life phenomena.

Thermodynamic forces from protein and water govern condensate formation of an intrinsically disordered protein domain

Liquid-liquid phase separation (LLPS) can drive a multitude of cellular processes by compartmentalizing biological cells via the formation of dense liquid biomolecular condensates, which can function as membraneless organelles. Despite its importance, the molecular-level understanding of the underlying thermodynamics of this process remains incomplete. In this study, we use atomistic molecular dynamics simulations of the low complexity domain (LCD) of human fused in sarcoma (FUS) protein to investigate the contributions of water and protein molecules to the free energy changes that govern LLPS. Both protein and water components are found to have comparably sizeable thermodynamic contributions to the formation of FUS condensates. Moreover, we quantify the counteracting effects of water molecules that are released into the bulk upon condensate formation and the waters retained within the protein droplets. Among the various factors considered, solvation entropy and protein interaction enthalpy are identified as the most important contributions, while solvation enthalpy and protein entropy changes are smaller. These results provide detailed molecular insights on the intricate thermodynamic interplay between protein- and solvation-related forces underlying the formation of biomolecular condensates.

Molecular Dynamics Study of the Antifouling Mechanism of Hydrophilic Polymer Brushes

We perform all-atom molecular dynamics simulations of the adsorption of amino acid side-chain analogues on polymer brushes. The analogues examined are nonpolar isobutane, polar propionamide, negatively charged propionate ion, and positively charged butylammonium ion. The polymer brushes consist of a sheet of graphene and strongly hydrophilic poly(carboxybetaine methacrylate) (PCBMA) or weakly hydrophilic poly(2-hydroxyethyl methacrylate) (PHEMA). The effective interactions between isobutane and polymer chains are repulsive for PCBMA and attractive for PHEMA. Gibbs energy decomposition analysis shows that this is due to the abundance of water in the PCBMA brush, which increases the steric repulsion and decreases the Lennard-Jones attraction. The affinity of the hydrophilic analogues is low for both PCBMA and PHEMA chains, but the balance between the components of the Gibbs energy is different for the two polymers. The simulations are performed at several θ, where θ is the degree of overlap of polymer chains. The antifouling performance against the neutral analogues is better for PCBMA than for PHEMA in the low and high θ regimes. However, in the middle θ regime, the antifouling performance of PHEMA is close to or better than that of PCBMA. This is attributed to the formation of a dense layer of PHEMA on the graphene surface that inhibits direct adsorption of analogue molecules on graphene. The charged analogues do not bind to either the PHEMA or PCBMA brush irrespective of θ.

Ethylene glycol energetically disfavours oligomerization of pseudoisocyanine dyestuffs at crowded concentrations

The intriguing role of the intracellular crowded environment in regulating protein aggregation remains elusive. The convolution of several factors such as the protein sequence-dependence, crowder's shape and size and diverse intermolecular interactions makes it complex to identify systematic trends. One of the ways to simplify the problem is to study a synthetic model for self-assembling proteins. In this study, we examine the aggregation behaviour of the cationic pseudoisocyanine chloride (PIC) dyestuff which is known to self-assemble and form fibril-like J-aggregates in aqueous solutions, similar to those formed by amyloid-forming proteins. Prior experimental studies have shown that polyethylene glycol impedes and Ficoll-400 promotes the self-assembly of PIC dyes. To achieve molecular insights, we examine the effect of crowding by ethylene glycol on the solvation thermodynamics of oligomerization of dyes into H-type and J-type oligomers using extensive molecular dynamics simulations. The binding free energy calculations show that the formation of J-oligomers is more favourable than that of H-oligomers in water. The stability of H- and J- tetramers and pentamers decreases in crowded solutions. The formation of oligomers is supported by the favourable change in dye-solvent interaction energy in both pure water and aqueous ethylene glycol solution although it is opposed by the reduced dye-solvent entropy. Ethylene glycol, as a molecular crowder, disfavours the H- as well as J-oligomerization via preferential binding to the dye oligomers. An unfavourable change in dye-crowder and dye-dye interaction energy on dye association makes the H-oligomer formation less favourable in crowded solution than in pure water solution. In the case of J-oligomers, however, the unfavourable change in dye-crowder interaction energy primarily contributes to making total dye-solvent energy unfavourable. The results are supported by isothermal titration calorimetry measurements where the binding of ethylene glycol to PIC molecules is found to be endothermic. The results provide an emerging view that a crowded environment can disfavour self-assembly of PIC dyes by interactions with the oligomeric states. The findings have implications in understanding the role of a crowded environment in shaping the free energy landscapes of proteins.

Realization of the structural fluctuation of biomolecules in solution: Generalized Langevin mode analysis

A new theoretical method, referred to as Generalized Langevin Mode Analysis (GLMA), is proposed to analyze the mode of structural fluctuations of a biomolecule in solution. The method combines the two theories in the statistical mechanics, or the Generalized Langevin theory and the RISM/3D-RISM theory, to calculate the second derivative, or the Hessian matrix, of the free energy surface of a biomolecule in aqueous solution, which consists of the intramolecular interaction among atoms in the biomolecule and the solvation free energy. The method is applied to calculate the wave-number spectrum of an alanine dipeptide in water for which the optical heterodyne-detected Raman-induced spectroscopy (RIKES) spectrum is available to compare with. The theoretical analysis reproduced the main features of the experimental spectrum with respect to the peak positions of the four bands around ~90 cm^-1 , ~240 cm^-1 , ~370 cm^-1 , and 400 cm^-1 , observed in the experimental spectrum, in spite that the physics involved in the two spectrum was not exactly the same: the experimental spectrum includes the contributions from the dipeptide and the water molecules interacting with the solute, while the theoretical one is just concerned with the solute molecule, influenced by solvation. Two major discrepancies between the theoretical and experimental spectra, one in the band intensity around ~100 cm^-1 , and the other in the peak positions around ~370 cm^-1 , are discussed in terms of the fluctuation mode of water molecules interacting with the dipeptide, which is not taken explicitly into account in the theoretical analysis.

A theory of chemical reactions in biomolecules in solution: Generalized Langevin mode analysis (GLMA)

The generalized Langevin mode analysis (GLMA) is applied to chemical reactions in biomolecules in solution. The theory sees a chemical reaction in solution as a barrier-crossing process, similar to the Marcus theory. The barrier is defined as the crossing point of two free-energy surfaces that are attributed to the reactant and product of the reaction. It is assumed that both free-energy surfaces are quadratic or harmonic. The assumption is based on the Kim-Hirata theory of structural fluctuation of protein, which proves that the fluctuation around an equilibrium structure is quadratic with respect to the structure or atomic coordinates. The quadratic surface is a composite of many harmonic functions with different modes or frequencies. The height of the activation barrier will be dependent on the mode or frequency-the less the frequency, the lower the barrier. Hence, it is essential to decouple the fluctuational modes into a hierarchical order. GLMA is impeccable for this purpose. It is essential for a theoretical study of chemical reactions to choose a reaction coordinate along which the reaction proceeds. We suppose that the mode whose center of coordinate and/or the frequency changes most before and after the reaction is the one relevant to the chemical reaction and choose the coordinate as the reaction coordinate. The rate of reaction along the reaction coordinate is k_rate=ν⁡exp-ΔF^(†)/k_BT, which is similar to the Marcus expression for the electron transfer reaction. In the equation, ΔF^(†) is the activation barrier defined by ΔF^(†)≡F^(r)Q^†-F^(r)(Q_eq ^(r)), where F^(r)(Q_eq ^(r)) and F^(r)Q^† denote the free energies at equilibrium Q_eq ^(r) and the crossing point Q^†, respectively, both on the free energy surface of the reactant.

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.

Molecular dynamics study of the interactions between a hydrophilic polymer brush on graphene and amino acid side chain analogues in water

We perform all-atom molecular dynamics simulations of poly(2-hydroxyethyl methacrylate) (PHEMA) brushes in aqueous solutions of isobutane, propionamide, and sodium propionate. These solutes are side chain analogues to leucine, glutamine, and glutamic acid, respectively. We compute the Gibbs energy profile of the solute's adsorption to the polymer brush and decompose it into the contributions from the steric repulsion, van der Waals interaction, and Coulomb interaction to reveal the energetic origin of repulsion or attraction of the solute by the polymer brush. The Henry adsorption constant is the amount of adsorption normalized by the concentration in aqueous solution. We examine the dependence of this quantity on the grafting density and chain length. Our results suggest that the concurrent primary and ternary adsorption mechanism may be more important than previously expected when the solute is hydrophobic.

Some Clues about Enzymes from Psychrophilic Microorganisms

Enzymes purified from psychrophilic microorganisms prove to be efficient catalysts at low temperatures and possess a great potential for biotechnological applications. The low-temperature catalytic activity has to come from specific structural fluctuations involving the active site region, however, the relationship between protein conformational stability and enzymatic activity is subtle. We provide a survey of the thermodynamic stability of globular proteins and their rationalization grounded in a theoretical approach devised by one of us. Furthermore, we provide a link between marginal conformational stability and protein flexibility grounded in the harmonic approximation of the vibrational degrees of freedom, emphasizing the occurrence of long-wavelength and excited vibrations in all globular proteins. Finally, we offer a close view of three enzymes: chloride-dependent α-amylase, citrate synthase, and β-galactosidase.

Unraveling the acid-base characterization and solvent effects on the structural and electronic properties of a bis-bidentate bridging ligand

Understanding the interactions and the solvent effects on the distribution of several species in equilibrium and how it can influence the ¹H-NMR properties, spectroscopy (UV-vis absorption), and the acid-base equilibria can be especially challenging. This is the case of a bis-bidentate bridging ligand bis(2-pyridyl)-benzo-bis(imidazole), where the two pyridyl and four imidazolyl nitrogen atoms can be protonated in different ways, depending on the solvent, generating many isomeric/tautomeric species. Herein, we report a combined theoretical-experimental approach based on a sequential quantum mechanics/molecular mechanics procedure that was successfully applied to describe in detail the acid-base characterization and its effects on the electronic properties of such a molecule in solution. The calculated free-energies allowed the identification of the main species present in solution as a function of the solvent polarity, and its effects on the magnetic shielding of protons (¹H-NMR chemical shifts), the UV-vis absorption spectra, and the acid-base equilibrium constants (pK_as) in aqueous solution. Three acid-base equilibrium constants were experimentally/theoretically determined (pK_a1 = 1.3/1.2, pK_a2 = 2.1/2.2 and pK_a5 = 10.1/11.3) involving mono-deprotonated and mono-protonated cis and trans species. Interestingly, other processes with pK_a3 = 3.7 and pK_a4 = 6.0 were also experimentally determined and assigned to the protonation and deprotonation of dimeric species. The dimerization of the most stable neutral species was investigated by Monte Carlo simulations and its electronic effects were considered for the elucidation of the UV-vis absorption bands, revealing transitions mainly with the charge-transfer characteristic and involving both the monomeric species and the dimeric species. The good matching of the theoretical and experimental results provides an atomistic insight into the solvent effects on the electronic properties of this bis-bidentate bridging ligand.

Solubility of Hydrophobes into Macrocyclic Hosts

The intrinsic nature of macrocyclic molecules to preferentially absorb a specific solute has been opening up supramolecular chemistry. Nevertheless, the determinant factor with molecular perspectives in promoting host-guest complexations remains inconclusive, due to the lack of rigorous thermodynamic examination on the guest solubility inside the host. Here, we quantify the solute-solvent energetic and entropic contributions between the end states and on the docking route during inclusion of noble gases in cucurbit[5]uril, cucurbit[6]uril, and α-cyclodextrin, using molecular dynamics simulations in combination with the potential distribution theorem. Results show that in all of the pairs examined both the solute-solvent energy and entropy favor the inclusion, while the former is rather dominant. The frequency of interior drying, which pertains to the entropic contribution, differs between the hosts and is controlled by the existence of lid water at portal and the flexibility of host framework. Moreover, the hosts exhibit various types of absorption manners, involving non-, single-, and double-free-energy barriers.

A Rationalization of the Effect That TMAO, Glycine, and Betaine Exert on the Collapse of Elastin-like Polypeptides

Elastin-like polypeptides (ELPs) are soluble in water at low temperature, but, on increasing the temperature, they undergo a reversible and cooperative, coil-to-globule collapse transition. It has been shown that the addition to water of either trimethylamine N-oxide (TMAO), glycine, or betaine causes a significant decrease of T(collapse) in the case of a specific ELP. Traditional rationalizations of these phenomena do not work in the present case. We show that an alternative approach, grounded in the magnitude of the solvent-excluded volume effect and its temperature dependence (strictly linked to the translational entropy of solvent and co-solute molecules), is able to rationalize the occurrence of ELP collapse in water on raising the temperature, as well as the T(collapse) lowering caused by the addition to water of either TMAO, glycine, or betaine.

Water on hydroxylated silica surfaces: Work of adhesion, interfacial entropy, and droplet wetting

In the last few years, much attention has been devoted to the control of the wettability properties of surfaces modified with functional groups. Molecular dynamics (MD) simulation is one of the powerful tools for microscopic analysis providing visual images and mean geometrical shapes of the contact line, e.g., of nanoscale droplets on solid surfaces, while profound understanding of wetting demands quantitative evaluation of the solid-liquid (SL) interfacial tension. In the present work, we examined the wetting of water on neutral and regular hydroxylated silica surfaces with five different area densities of OH groups ρ_A ^OH, ranging from a non-hydroxylated surface to a fully hydroxylated one through two theoretical methods: thermodynamic integration (TI) and MD simulations of quasi-two-dimensional equilibrium droplets. For the former, the work of adhesion needed to quasi-statically strip the water film off the solid surface was computed by the phantom wall TI scheme to evaluate the SL interfacial free energy, whereas for the latter, the apparent contact angle θ_app was calculated from the droplet density distribution. The theoretical contact angle θ_YD and the apparent one θ_app, both indicating the enhancement of wettability by an increase in ρ_A ^OH, presented good quantitative agreement, especially for non-hydroxylated and highly hydroxylated surfaces. On partially hydroxylated surfaces, in which θ_YD and θ_app slightly deviated, the Brownian motion of the droplet was suppressed, possibly due to the pinning of the contact line around the hydroxyl groups. Relations between work of adhesion, interfacial energy, and entropy loss were also analyzed, and their influence on the wettability was discussed.

Spatially resolved free-energy contributions of native fold and molten-globule-like Crambin

The folding stability of a protein is governed by the free-energy difference between its folded and unfolded states, which results from a delicate balance of much larger but almost compensating enthalpic and entropic contributions. The balance can therefore easily be shifted by an external disturbance, such as a mutation of a single amino acid or a change of temperature, in which case the protein unfolds. Effects such as cold denaturation, in which a protein unfolds because of cooling, provide evidence that proteins are strongly stabilized by the solvent entropy contribution to the free-energy balance. However, the molecular mechanisms behind this solvent-driven stability, their quantitative contribution in relation to other free-energy contributions, and how the involved solvent thermodynamics is affected by individual amino acids are largely unclear. Therefore, we addressed these questions using atomistic molecular dynamics simulations of the small protein Crambin in its native fold and a molten-globule-like conformation, which here served as a model for the unfolded state. The free-energy difference between these conformations was decomposed into enthalpic and entropic contributions from the protein and spatially resolved solvent contributions using the nonparametric method Per|Mut. From the spatial resolution, we quantified the local effects on the solvent free-energy difference at each amino acid and identified dependencies of the local enthalpy and entropy on the protein curvature. We identified a strong stabilization of the native fold by almost 500 kJ mol-1 due to the solvent entropy, revealing it as an essential contribution to the total free-energy difference of (53 ± 84) kJ mol-1. Remarkably, more than half of the solvent entropy contribution arose from induced water correlations.

Crowding effects on water-mediated hydrophobic interactions

Understanding the fundamental forces such as hydrophobic interactions in a crowded intracellular environment is necessary to comprehensively decipher the mechanisms of protein folding and biomolecular self-assemblies. The widely accepted entropic depletion view of crowding effects primarily attributes biomolecular compaction to the solvent excluded volume effects exerted by the "inert" crowders, neglecting their soft interactions with the biomolecule. In this study, we examine the effects of chemical nature and soft attractive energy of crowders on the water-mediated hydrophobic interaction between two non-polar neopentane solutes using molecular dynamics simulations. The crowded environment is modeled using dipeptides composed of polar and non-polar amino acids of varying sizes. The results show that amongst the non-polar crowders, Leu₂ strengthens the hydrophobic interactions significantly, whereas the polar and small-sized non-polar crowders do not show significant strengthening. Distinct underlying thermodynamic driving forces are illustrated where the small-sized crowders drive hydrophobic interaction via a classic entropic depletion effect and the bulky crowders strengthen it by preferential interaction with the solute. A crossover from energy-stabilized solvent-separated pair to entropy-stabilized contact pair state is observed in the case of bulky non-polar (Leu₂) and polar (Lys₂) crowders. The influence of solute-crowder energy in affecting the dehydration energy penalty is found to be crucial for determining the neopentane association. The findings demonstrate that along with the entropic (size) effects, the energetic effects also play a crucial role in determining hydrophobic association. The results can be extended and have implications in understanding the impact of protein crowding with varying chemistry in modulating the protein free energy landscapes.

Length-Scale Effects in Hydrophobic Polymer Collapse Transitions

The study of molecular mechanisms for cosolvent-driven hydrophobic polymer collapse transitions in water is of pivotal importance in the field of smart responsive materials. Computational studies together with complementary experimental data have led to the discovery and understanding of new phenomena in recent years. However, elementary mechanisms, generally contributing to polymer coil-globule transitions in different classes of cosolvent-water systems, remain elusive due to compensating energy-entropy effects. Herein, I discuss the role of length scales in polymer solubility problems. New ideas on surfactant mechanisms are discussed based on examples in which these mechanisms drive polymer swelling or collapse.

Dissecting the Conformational Free Energy of a Small Peptide in Solution

The free energy surface of a small peptide was analyzed based on an unbiased microsecond molecular dynamics simulation. The peptide sampled disordered conformational ensembles of distinct compactness, and its free energy was decomposed into separate contributions from the intramolecular potential energy, conformational entropy, and solvation free energy. The latter was further broken down into enthalpic and entropic contributions due to peptide-water and water-water interactions. This decomposition was enabled by a generalized linear response relation between the peptide-water interaction energy and the solvation free energy, which was empirically parametrized by explicit solvation free energy calculations for representative peptide conformations. This full dissection of the peptide free energy identifies individual contributions that stabilize and destabilize compact and extended peptide conformational ensembles and reveals the origin of a free energy barrier associated with transitions between them.

Insignificant Effect of Temperature on the Structure and Angular Jumps of Water near a Hydrophobic Cation

The ambiguity in the behavior of water molecules around hydrophobic solutes is a matter of interest for many studies. Motivated by the earlier results on the dynamics of water molecules around tetramethylammonium (TMA) cation, we present the effect of temperature on the structure and angular jumps of water due to hydrophobicity using first principles molecular dynamics simulations. The average intermolecular distance between the central oxygen and four nearest neighbors is found to be the highest for water molecules in the solvation shell of TMA at 400 K, followed by the same at 330 K. The hydrogen bond (HB) donor-acceptor count, HB per water molecule, and tetrahedral order parameter suggests the loss of tetrahedrality in the solvation shell. Elevated temperature affects the tetrahedral parameter in local regions. The HB jump mechanism is studied for methyl hydrogen and water molecules in the solvation shell. Observations hint at the presence of dangling water molecules in the vicinity of the hydrophobic cation, and no evidence is found for the enhanced structural ordering of nearby water molecules.

Affinity of small-molecule solutes to hydrophobic, hydrophilic, and chemically patterned interfaces in aqueous solution

Performance of membranes for water purification is highly influenced by the interactions of solvated species with membrane surfaces, including surface adsorption of solutes upon fouling. Current efforts toward fouling-resistant membranes often pursue surface hydrophilization, frequently motivated by macroscopic measures of hydrophilicity, because hydrophobicity is thought to increase solute-surface affinity. While this heuristic has driven diverse membrane functionalization strategies, here we build on advances in the theory of hydrophobicity to critically examine the relevance of macroscopic characterizations of solute-surface affinity. Specifically, we use molecular simulations to quantify the affinities to model hydroxyl- and methyl-functionalized surfaces of small, chemically diverse, charge-neutral solutes represented in produced water. We show that surface affinities correlate poorly with two conventional measures of solute hydrophobicity, gas-phase water solubility and oil-water partitioning. Moreover, we find that all solutes show attraction to the hydrophobic surface and most to the hydrophilic one, in contrast to macroscopically based hydrophobicity heuristics. We explain these results by decomposing affinities into direct solute interaction energies (which dominate on hydroxyl surfaces) and water restructuring penalties (which dominate on methyl surfaces). Finally, we use an inverse design algorithm to show how heterogeneous surfaces, with multiple functional groups, can be patterned to manipulate solute affinity and selectivity. These findings, importantly based on a range of solute and surface chemistries, illustrate that conventional macroscopic hydrophobicity metrics can fail to predict solute-surface affinity, and that molecular-scale surface chemical patterning significantly influences affinity-suggesting design opportunities for water purification membranes and other engineered interfaces involving aqueous solute-surface interactions.

Ion Solvation Engineering: How to Manipulate the Multiplicity of the Coordination Environment of Multivalent Ions

Free energy analysis of solvation structures of free divalent cations, their ion pairs, and neutral aggregates in low dielectric solvents reveals the multiplicity of thermodynamically stable cation solvation configurations and identifies the micro- and macroscopic factors responsible for this phenomenon. Specifically, we show the role of ion-solvent interactions and solvent mixtures in determining the cation solvation free energy landscapes. We show that it is the entropic contribution of solvent degrees of freedom that is responsible for the solvation multiplicity, and the mutual balance between enthalpic and entropic forces or their concerted contributions is what ultimately defines the most stable ion solvation configuration and creates new ones. We show general consequences of ion solvation multiplicity on thermodynamics of complex electrolytes, specifically in the context of homogeneous or interfacial charge transfer. Identified factors and their interplay provide a pathway to formulation of solvation design rules that can be used to control bulk solvation, interfacial chemistry, and charge transfer. Our findings also suggest experimentally testable predictions.

Why small proteins tend to have high denaturation temperatures

Data indicate that small globular proteins (consisting of less than about 70 residues) tend to have high denaturation temperatures. This finding is analysed by comparing experimental denaturation enthalpy and entropy changes of a selected set of small proteins with values calculated on the basis of average and common properties of globular proteins. The conclusion is that the denaturation entropy change is smaller than expected, leading to an increase in denaturation temperature. The proposed molecular rationalization considers the existence of long-wavelength, low-frequency vibrational modes in the native state of small proteins due to their large surface-to-interior ratio. The effect of decreasing the conformational entropy gain associated with denaturation on thermal stability is directly verified by means of an already devised theoretical model [G. Graziano, Phys. Chem. Chem. Phys. 2010, 12, 14245-14252; 2014, 16, 21755-21767].

Binding Dynamics of siRNA with Selected Lipopeptides: A Computer-Aided Study of the Effect of Lipopeptides' Functional Groups and Stereoisomerism

The engineering issues pertaining to nanoparticle systems toward targeted gene therapies have not been fully probed. Recent experiments have identified specific structural characteristics of a novel class of lipopeptides (LP) that may lead to potent nanocarriers intended as RNAi therapeutics, albeit the molecular mechanism that underlies their performance remains unexplored. We conducted molecular dynamics simulations in atomistic detail coupled with free energy computations to study the dynamics and thermodynamics of an acrylate- and an epoxide-derived LP, members of the aforesaid class, upon their binding to siRNA in aqueous solution aiming at examining structure-potency relations. We found that the entropic part of the free energy of binding predominates; moreover, the first LP class tends to disrupt the Watson-Crick base pairing of siRNA, whereas the latter leaves the double helix intact. Moreover, the identified tug-of-war effect between LP-water and LP-siRNA hydrogen bonding in the supramolecular complex can underpin synthesis routes toward tuning the association dynamics. Our simulations on two diastereomers of the epoxide-derived LP showed significant structural and energetics differences upon binding, as a result of steric effects imposed by the different absolute configurations at their chiral centers. These findings may serve as crucial design parameters toward modulating the interplay between complex stability and ease of releasing the nucleic acid drug into the cell.

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.

Free Energies of Catalytic Species Adsorbed to Pt(111) Surfaces under Liquid Solvent Calculated Using Classical and Quantum Approaches

Solvent plays an important role in liquid phase heterogeneous catalysis; however, methods for calculating the free energies of catalytic phenomena at the solid-liquid interface are not well-established. For example, solvent molecules alter the energies of catalytic species and participate in catalytic reactions and can thus significantly influence catalytic performance. In this work, we begin to establish methods for calculating the free energies of such phenomena, specifically, by employing an explicit solvation method using a multiscale sampling (MSS) approach. This MSS approach combines classical molecular dynamics with density functional theory. We use it to calculate the free energies of solvation of catalytic species, specifically adsorbed NH*, NH₂*, CO*, COH*, CH₂OH*, and C₃H₇O₃* on Pt(111) surfaces under aqueous phase and under a mixed H₂O/CH₃OH solvent. We compare our calculated values with analogous values from implicit solvation for validation and to identify situations where implicit solvation is sufficient versus where explicit solvent is needed to compute adsorbate free energies. Our results indicate that explicit quantum-based methods are needed when adsorbates form chemical bonds and/or strong hydrogen bonds with H₂O solvent. Using MSS, we further separate the calculated free energies into energetic and entropic contributions in order to understand how each influences the free energy. We find that adsorbates that exhibit strong energies also exhibit strong and negative entropies, and we attribute this relationship to hydrogen bonding between the adsorbates and the solvent molecules, which provides a large energetic contribution but reduces the overall mobility of the solvent.

Theoretical analysis on thermodynamic stability of chignolin

Understanding the dominant factor in thermodynamic stability of proteins remains an open challenge. Kauzmann's hydrophobic interaction hypothesis, which considers hydrophobic interactions between nonpolar groups as the dominant factor, has been widely accepted for about sixty years and attracted many scientists. The hypothesis, however, has not been verified or disproved because it is difficult, both theoretically and experimentally, to quantify the solvent effects on the free energy change in protein folding. Here, we developed a computational method for extracting the dominant factor behind thermodynamic stability of proteins and applied it to a small, designed protein, chignolin. The resulting free energy profile quantitatively agreed with the molecular dynamics simulations. Decomposition of the free energy profile indicated that intramolecular interactions predominantly stabilized collapsed conformations, whereas solvent-induced interactions, including hydrophobic ones, destabilized them. These results obtained for chignolin were consistent with the site-directed mutagenesis and calorimetry experiments for globular proteins with hydrophobic interior cores.

Thermodynamics of Reactions Affected by Medium Reorganization

We present a thermodynamic analysis of the activation barrier for reactions which can be monitored through the difference in the energies of reactants and products defined as the reaction coordinate (electron and atom transfer, enzyme catalysis, etc.). The free-energy surfaces along the reaction coordinate are separated into the enthalpy and entropy surfaces. For the Gaussian statistics of the reaction coordinate, the free-energy surfaces are parabolas, and the entropy surface is an inverted parabola. Its maximum coincides with the transition state for reactions with zero value of the reaction free energy. Maximum entropic depression of the activation barrier, anticipated by the concept of transition-state ensembles, can be achieved for such reactions. From Onsager's reversibility, the entropy of equilibrium fluctuations encodes the entropic component of the activation barrier. The reorganization entropy thus becomes the critical parameter of the theory reducing the problem of activation entropy to the problem of reorganization entropy. Standard solvation theories do not allow reorganization entropy sufficient for the barrier depression. Complex media, characterized by many relaxation processes, need to be involved. Proteins provide several routes for achieving large entropic effects through incomplete (nonergodic) sampling of the complex energy landscape and by facilitating an active role of water in the reaction mechanism.

Counteraction of denaturant-induced protein unfolding is a general property of stabilizing agents

DSC measurements on RNase A at neutral pH show that five stabilizing agents, namely trimethylamine N-oxide, glucose, sucrose, betaine and sodium sulfate, can counteract the destabilizing action of urea, sodium perchlorate, guanidinium chloride and guanidinium thiocyanate. This is an important finding inferring that counteraction has a common physical origin, regardless of the chemical differences among the stabilizing agents and among the destabilizing ones. A rationalization is provided grounded on the following line of reasoning: (a) the decrease in solvent-excluded volume effect is the main stabilizing contribution of the native state; (b) its magnitude increases on increasing the density of the aqueous solution; (c) the density increases significantly in the ternary solutions containing water, a stabilizing agent and a destabilizing one, as indicated by the present experimental data.

Interfacial structural crossover and hydration thermodynamics of charged C60 in water

Classical molecular dynamics simulations of the hydration thermodynamics, structure, and dynamics of water in hydration shells of charged buckminsterfullerenes are presented in this study. Charging of fullerenes leads to a structural transition in the hydration shell, accompanied by creation of a significant population of dangling O-H bonds pointing toward the solute. In contrast to the well accepted structure-function paradigm, this interfacial structural transition causes nearly no effect on either the dynamics of hydration water or on the solvation thermodynamics. Linear response to the solute charge is maintained despite significant structural changes in the hydration shell, and solvation thermodynamic potentials are nearly insensitive to the altering structure. Only solvation heat capacities, which are higher thermodynamic derivatives of the solvation free energy, indicate some sensitivity to the local hydration structure. We have separated the solvation thermodynamic potentials into direct solute-solvent interactions and restructuring of the hydration shell and analyzed the relative contributions of electrostatic and nonpolar interactions to the solvation thermodynamics.

Hydration Free Energies in the FreeSolv Database Calculated with Polarized Iterative Hirshfeld Charges

Computer simulations of biomolecular systems often use force fields, which are combinations of simple empirical atom-based functions to describe the molecular interactions. Even though polarizable force fields give a more detailed description of intermolecular interactions, nonpolarizable force fields, developed several decades ago, are often still preferred because of their reduced computation cost. Electrostatic interactions play a major role in biomolecular systems and are therein described by atomic point charges. In this work, we address the performance of different atomic charges to reproduce experimental hydration free energies in the FreeSolv database in combination with the GAFF force field. Atomic charges were calculated by two atoms-in-molecules approaches, Hirshfeld-I and Minimal Basis Iterative Stockholder (MBIS). To account for polarization effects, the charges were derived from the solute's electron density computed with an implicit solvent model, and the energy required to polarize the solute was added to the free energy cycle. The calculated hydration free energies were analyzed with an error model, revealing systematic errors associated with specific functional groups or chemical elements. The best agreement with the experimental data is observed for the AM1-BCC and the MBIS atomic charge methods. The latter includes the solvent polarization and presents a root-mean-square error of 2.0 kcal mol-1 for the 613 organic molecules studied. The largest deviation was observed for phosphorus-containing molecules and the molecules with amide, ester and amine functional groups.