Hydrophobic Effects on a Molecular Scale

A generic model for pH-sensitive collapse of hydrophobic polymers

The hydrophobic effect is an important contributor to the stability of proteins and may be influenced by many factors including the pH of the solution. To simplify the study of pH effects on proteins, we parameterize biologically motivated titratable monomers which we insert into the sequence of a hydrophobic polymer and study via constant pH molecular dynamics (MD) simulations. We calculate the potential of mean force of the polymer as a function of its radius of gyration at different pH values and observe that the collapsed state of the polymer is destabilized when the titratable monomer is more charged (high pH for an acid and low pH for a base). Further, the extent of the destabilization is influenced by the position of the titratable monomer along the polymer sequence. The pKa value of the titratable monomer is also observed to be sensitive to polymer conformation, in agreement with protein studies. We further study a zwitterionic polymer with an acidic and a basic monomer in the same sequence which presents a pH-dependent hairpin formation. Our model provides a simplified yet powerful framework to study pH effects on the hydrophobic effect, providing insights into mechanisms governing the behavior of intrinsically disordered proteins (IDPs) and pH-sensitive drug delivery, among other applications.

Unusual Hydrophobic Property of Blue Fluorescent Amino Acid 4-Cyanotryptophan

It is a common belief that the negative heat capacity change (ΔCp) associated with protein folding, which is a manifestation of the hydrophobic effect, results from a decrease in the solvent accessible hydrophobic surface area. Herein, we investigate the conformational energy landscape and dynamics of a tetrapeptide composed of two glycine and two 4-cyanotryptophan residues using time-resolved fluorescence spectroscopy, molecular dynamics simulations, and density functional theory calculations and find that, contrary to this expectation, the hydrophobic association of two 4-cyanotryptophan side chains leads to a positive ΔCp (approximately 543 J K-1 mol-1). Furthermore, we find that promoting one of the 4-cyanotryptophans to its excited electronic state strengthens this self-association. Taken together, our results provide not only insight into how modification of an aromatic amino acid can affect its hydrophobicity but also a potential strategy for designing protein sequences that can fold (unfold) at high (low) temperatures.

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.

Molecular-Scale Liquid Density Fluctuations and Cavity Thermodynamics

Equilibrium density fluctuations at the molecular level produce cavities in a liquid and can be analyzed to shed light on the statistics of the number of molecules occupying observation volumes of increasing radius. An information theory approach led to the conclusion that these probabilities should follow a Gaussian distribution. Computer simulations confirmed this prediction across various liquid models if the size of the observation volume is not large. The reversible work required to create a cavity and the chance of finding no molecules in a fixed observation volume are directly correlated. The Gaussian formula for the latter probability is scrutinized to derive the changes in enthalpy and entropy, which arise from the cavity creation. The reversible work of cavity creation has a purely entropic origin as a consequence of the solvent-excluded volume effect produced by the inaccessibility of a region of the configurational space. The consequent structural reorganization leads to a perfect compensation of enthalpy and entropy changes. Such results are coherent with those obtained from Lee in his direct statistical mechanical study.

Statistical Mechanical Design Principles for Coarse-Grained Interactions across Different Conformational Free Energy Surfaces

Systematic bottom-up coarse-graining (CG) of molecular systems provides a means to explore different coupled length and time scales while treating the molecular-scale physics at a reduced level. However, the configuration dependence of CG interactions often results in CG models with limited applicability for exploring the parametrized configurations. We propose a statistical mechanical theory to design CG interactions across different configurations and conditions. In order to span wide ranges of conformational space, distinct classical CG free energy surfaces for characteristic configurations are identified using molecular collective variables. The coupling interaction between different CG free energy surfaces can then be systematically determined by analogy to quantum mechanical approaches describing coupled states. The present theory can accurately capture the underlying many-body potentials of mean force in the CG variables for various order parameters applied to liquids, interfaces, and in principle proteins, uncovering the complex nature underlying the coupling interaction and imparting a new protocol for the design of predictive multiscale models.

Machine learning assisted coarse-grained molecular dynamics modeling of meso-scale interfacial fluids

A hallmark of meso-scale interfacial fluids is the multi-faceted, scale-dependent interfacial energy, which often manifests different characteristics across the molecular and continuum scale. The multi-scale nature imposes a challenge to construct reliable coarse-grained (CG) models, where the CG potential function needs to faithfully encode the many-body interactions arising from the unresolved atomistic interactions and account for the heterogeneous density distributions across the interface. We construct the CG models of both single- and two-component polymeric fluid systems based on the recently developed deep coarse-grained potential [Zhang et al., J. Chem. Phys. 149, 034101 (2018)] scheme, where each polymer molecule is modeled as a CG particle. By only using the training samples of the instantaneous force under the thermal equilibrium state, the constructed CG models can accurately reproduce both the probability density function of the void formation in bulk and the spectrum of the capillary wave across the fluid interface. More importantly, the CG models accurately predict the volume-to-area scaling transition for the apolar solvation energy, illustrating the effectiveness to probe the meso-scale collective behaviors encoded with molecular-level fidelity.

Defect-induced tuning of polarity-dependent adsorption in hydrophobic-hydrophilic UiO-66

Structural defects in metal-organic frameworks can be exploited to tune material properties. In the case of UiO-66 material, they may change its nature from hydrophobic to hydrophilic and therefore affect the mechanism of adsorption of polar and non-polar molecules. In this work, we focused on understanding this mechanism during adsorption of molecules with different dipole moments, using the standard volumetric adsorption measurements, IR spectroscopy, DFT + D calculations, and Monte Carlo calculations. Average occupation profiles showed that polar and nonpolar molecules change their preferences for adsorption sites. Hence, defects in the structure can be used to tune the adsorption properties of the MOF as well as to control the position of the adsorbates within the micropores of UiO-66.

Connecting Non-Gaussian Water Density Fluctuations to the Lengthscale Dependent Crossover in Hydrophobic Hydration

We connect density fluctuations in liquid water to lengthscale dependent crossover in hydrophobic hydration. Specifically, we employ indirect umbrella sampling (INDUS) simulations to characterize density fluctuations in observation volumes of various sizes and shapes in water and as a function of temperature and salt concentration. Consistent with previous observations, density fluctuations are Gaussian in small molecular scale volumes, but they display non-Gaussian "low-density fat tails" in larger volumes. These non-Gaussian tails are indicative of the proximity of water to its liquid to vapor phase transition and have implications on biomolecular interactions and function. We show that the onset of non-Gaussian fluctuations in large volumes is accompanied by the formation of a cavity in the observation volume. We develop a model that uses the physics of cavity-water interface formation as a key ingredient and show that it captures the nature of non-Gaussian density fluctuations over a broad region in water and in salt solutions. We discuss the limitations of this model in the very low density region of the distribution. Our calculations provide new insights into the origins of non-Gaussian density fluctuations in water and their connections to lengthscale dependent crossover in hydrophobic hydration.

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.

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.

Hydration of Linear Alkanes is Governed by the Small Length-Scale Hydrophobic Effect

Length-scale dependence of the hydrophobic effect is well understood for apolar spherical solutes: for small solutes (diameter, d ≲ 0.8 nm), the hydration free energy is entropically driven, while for larger solutes (d ≳ 2 nm), it is enthalpically driven. The nature of the hydrophobic effect in the case of anisotropic molecules such as linear alkanes is not understood yet. In this work, we have calculated the hydration free energy of linear alkanes going from methane to octadecane and of a spherical decane droplet of d ≈ 3 nm using molecular simulations. We show that the hydration free energies of alkanes, irrespective of their size, are governed by the small length-scale hydrophobic effect. That is, unlike the case of large spherical solutes, the hydration free energies of linear alkanes are entropically driven.

Small-to-large length scale transition of TMAO interaction with hydrophobic solutes

We report the effect of trimethylamine N-oxide (TMAO) on the solvation of nonpolar solutes in water studied with molecular dynamics (MD) simulations and free-energy calculations. The simulation data indicate the occurrence of a length scale crossover in the TMAO interaction with repulsive Weeks-Chandler-Andersen (WCA) solutes: while TMAO is depleted from the hydration shell of a small WCA solute (methane) and increases the free-energy cost of solute-cavity formation, it preferentially binds to a large WCA solute (α-helical polyalanine), reducing the free-energy cost of solute-cavity formation via a surfactant-like mechanism. Significantly, we show that this surfactant-like behaviour of TMAO reinforces the solvent-mediated attraction between large WCA solutes by means of an entropic force linked to the interfacial accumulation of TMAO. Specifically, this entropic force arises from the natural tendency of adsorbed TMAO molecules to mix back into the bulk. It therefore favours solute-solute contact states that minimise the surface area exposed to the solvent and have a small overall number of TMAO molecules adsorbed. In contrast to the well-known depletion force, its effect is compensated by enthalpic solute-solvent interactions. Correspondingly, the hydrophobic association free energy of the large α-helical solutes passes through a minimum at low TMAO concentration when cohesive solute-solvent van der Waals interactions are considered. The observations reported herein are reminiscent to cosolvent effects on hydrophobic polymer coil-globule collapse free energies (Bharadwaj et al., Commun. Chem. 2020, 3, 165) and may be of general significance in systems whose properties are determined by hydrophobic self-assembly.

Size-Dependent Order-Disorder Crossover in Hydrophobic Hydration: Comparison between Spherical Solutes and Linear Alcohols

Theory and computer simulation studies have predicted that water molecules around hydrophobic molecules should undergo an order-disorder transition with increasing solute size around a 1 nm length scale. Some theories predict the formation of a clathrate-like ordered structure around smaller hydrophobic solutes (<1 nm) and the formation of disordered vapor-liquid interfaces around larger solutes (>1 nm) and surfaces. Experimental validation of these predictions has often been elusive and contradictory. High-resolution Raman spectroscopy has detected that water around small hydrophobic solutes shows a signature similar to that of bulk water at lower temperature (increased ordering and a stronger hydrogen-bonded network). Similarly, water around larger solutes shows an increasing population of dangling OH bonds very similar to higher temperature bulk water. Thus, the solute size dependence of the structure and dynamics of water around hydrophobic molecules seems to have an analogy with the temperature dependence in bulk water. In this work, using atomistic classical molecular dynamics (MD) simulations, we have systematically investigated this aspect and characterized this interesting analogy. Structural order parameters including the tetrahedral order parameter (Q), hydrogen bond distribution, and vibrational power spectrum highlight this similarity. However, in contrast to the experimental observations, we do not observe any length-dependent crossover for linear hydrophobic alcohols (n-alkanols) using classical MD simulations. This is in agreement with earlier findings that linear alkane chains do not demonstrate the length-dependent order-disorder transition due to the presence of a sub-nanometer length scale along the cross section of the chain. Moreover, the collapsed state of linear hydrocarbon chains is not significantly populated for smaller chains (number of carbons below 20). In the context of our computational results, we raise several pertinent questions related to the sensitivity of various structural and dynamical parameters toward capturing these complex phenomena of hydrophobic hydration.

Reversal of the Temperature Dependence of Hydrophobic Hydration in Supercooled Water

Using simulations and theory, we examine the enthalpy and entropy of hydrophobic hydration which exhibit minima in supercooled water, contrasting with the monotonically increasing temperature dependence traditionally ascribed to these properties. The enthalpy/entropy minima are marked by a negative to positive sign change in the heat capacity at a size-dependent reversal temperature. A Gaussian fluctuation theory accurately captures the reversal temperature, tracing it to water's distinct thermal expansivity and compressibility influenced by its metastable liquid-liquid critical point.

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.

Bridging Gaussian Density Fluctuations from Microscopic to Macroscopic Volumes: Applications to Non-Polar Solute Hydration Thermodynamics

The hydration of hydrophobic solutes is intimately related to the spontaneous formation of cavities in water through ambient density fluctuations. Information theory-based modeling and simulations have shown that water density fluctuations in small volumes are approximately Gaussian. For limiting cases of microscopic and macroscopic volumes, water density fluctuations are known exactly and are rigorously related to the density and isothermal compressibility of water. Here, we develop a theory—interpolated gaussian fluctuation theory (IGFT)—that builds an analytical bridge to describe water density fluctuations from microscopic to molecular scales. This theory requires no detailed information about the water structure beyond the effective size of a water molecule and quantities that are readily obtained from water’s equation-of-state—namely, the density and compressibility. Using simulations, we show that IGFT provides a good description of density fluctuations near the mean, that is, it characterizes the variance of occupancy fluctuations over all solute sizes. Moreover, when combined with the information theory, IGFT reproduces the well-known signatures of hydrophobic hydration, such as entropy convergence and solubility minima, for atomic-scale solutes smaller than the crossover length scale beyond which the Gaussian assumption breaks down. We further show that near hydrophobic and hydrophilic self-assembled monolayer surfaces in contact with water, the normalized solvent density fluctuations within observation volumes depend similarly on size as observed in the bulk, suggesting the feasibility of a modified version of IGFT for interfacial systems. Our work highlights the utility of a density fluctuation-based approach toward understanding and quantifying the solvation of non-polar solutes in water and the forces that drive them toward surfaces with different hydrophobicities.

Comment on "The Gibbs free energy of cavity formation in a diverse set of solvents"[J. Chem. Phys. 153, 134501 (2020)]

It is pointed out that the unexpected result that the magnitude of the reversible work of cavity creation in ethylene glycol proves to be larger than that in water [I. Sedov and T. Magsumov, J. Chem. Phys. 153, 134501 (2020)] could be due to that (a) the density of the used computational model of this liquid is "significantly" larger than the experimental one and (b) the procedure adopted to perform the comparison among the different liquids is not "strictly" correct. It is also indicated that several lines of evidence suggest that the magnitude of the reversible work of cavity creation in water can be larger than that in ethylene glycol.

Non-extensitivity and criticality of atomic hydropathicity around a voltage-gated sodium channel's pore: a modeling study

Voltage-gated sodium channels (NavChs) are pore-forming membrane proteins that regulate the transport of sodium ions through the cell membrane. Understanding the structure and function of NavChs is of major biophysical, as well as clinical, importance given their key role in cellular pathophysiology. In this work, we provide a computational framework for modeling system-size-dependent, i.e., cumulative, atomic properties around a NavCh's pore. We illustrate our methodologies on the bacterial NavAb channel captured in a closed-pore state where we demonstrate that the atomic environment around its pore exhibits a bi-phasic spatial organization dictated by the structural separation of the pore domains (PDs) from the voltage-sensing domains (VSDs). Accordingly, a mathematical model describing packing of atoms around NavAb's pore is constructed that allows-under certain conservation conditions-for a power-law approximation of the cumulative hydropathic dipole field effect acting along NavAb's pore. This verified the non-extensitivity hypothesis for the closed-pore NavAb channel and revealed a long-range hydropathic interactions law regulating atom-packing around the NavAb's selectivity filter. Our model predicts a PDs-VSDs coupling energy of [Formula: see text] kcal/mol corresponding to a global maximum of the atom-packing energy profile. Crucially, we demonstrate for the first time how critical phenomena can emerge in a single-channel structure as a consequence of the non-extensive character of its atomic porous environment.

Rheological behavior of an artificial synovial fluid - influence of temperature, shear rate and pressure

Despite the excellent clinical performance of joint replacements, wear-induced aseptic loosening is a main cause of premature implant failure. Tribological testing is usually carried out using bovine serum as an artificial synovial fluid. In order to gain new insights into the suitability to simulate human synovial fluid and provide recommendations for the conditions of tribological testing, accurate rheological measurements on the influence of temperature, shear rate and pressure on density and viscosity were performed. Thus, a temperature dependence of density and viscosity could be verified, whereas both values decreased with higher temperatures. The temperature dependency of viscosity could be approximated by an Arrhenius model. Moreover, shear-thinning characteristics could be demonstrated and fitted to a Cross model, which agreed well with investigations on human synovial fluid reported in literature. Furthermore, an anomaly of pressure dependence of viscosity was found and correlated with the behavior of water as a main constituent. At room temperature, the viscosity initially decreased to a minimum and then increased again as a function of pressure. This was no longer distinct at human body temperatures. Consequently, the present study confirms the suitability of bovine serum as a substitute synovial fluid and emphasizes the importance of realistic testing conditions in order to ensure transferability and comparability.

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.

Thermoresponsive behavior of poly[trialkyl-(4-vinylbenzyl)ammonium] based polyelectrolytes in aqueous salt solutions

A systematic method to induce thermoresponsive behavior for polycations with salts from the reversed Hofmeister series is introduced.

Structure, dynamics and phase behavior of short rod inclusions dissolved in a colloidal membrane

Inclusions dissolved in an anisotropic quasi-2D membrane acquire new types of interactions that can drive assembly of complex structures and patterns. We study colloidal membranes composed of a binary mixture of long and short rods, such that the length ratio of the long to short rods is approximately two. At very low volume fractions, short rods dissolve in the membrane of long rods by strongly anchoring to the membrane polymer interface. At higher fractions, the dissolved short rods phase separate from the background membrane, creating a composite structure comprised of bilayer droplets enriched in short rods that coexist with the background monolayer membrane. These results demonstrate that colloidal membranes serve as a versatile platform for assembly of soft materials, while simultaneously providing new insight into universal membrane-mediated interactions.

Spontaneously Forming Dendritic Voids in Liquid Water Can Host Small Polymers

Some liquids are characterized by the presence of large voids with dendritic shapes and for this reason are dubbed transiently porous. By using a battery of data analysis tools, we demonstrate that liquid water and methane are both characterized by transient porosity. We show that the thermodynamics of porosity is distinct from that associated with cavitation á la classical nucleation theory. The shapes of dendritic voids in both liquids with very different chemistries resemble those of small polymers. We further show, using free energy calculations, that the cost of solvating small hydrophobic polymers in water is consistent with the work associated with creating dendritic voids. The entropic and enthalpic contributions associated with hosting these polymers can thus be rationalized by the thermodynamics of fluctuations in bulk water.

Contrasting the hydration thermodynamics of methane and methanol

The hydration thermodynamics of methane and methanol depend on the cavity creation work and energy of van der Waals and H-bonding attractions.

Mini-grand canonical ensemble: Chemical potential in the solvation shell

Quantifying the statistics of occupancy of solvent molecules in the vicinity of solutes is central to our understanding of solvation phenomena. Number fluctuations in small solvation shells around solutes cannot be described within the macroscopic grand canonical framework using a single chemical potential that represents the solvent bath. In this communication, we hypothesize that molecular-sized observation volumes such as solvation shells are best described by coupling the solvation shell with a mixture of particle baths each with its own chemical potential. We confirm our hypotheses by studying the enhanced fluctuations in the occupancy statistics of hard sphere solvent particles around a distinguished hard sphere solute particle. Connections with established theories of solvation are also discussed.

Single-Molecule Force Spectroscopy Reveals Self-Assembly Enhanced Surface Binding of Hydrophobins

Hydrophobins have raised lots of interest as powerful surface adhesives. However, it remains largely unexplored how their strong and versatile surface adhesion is linked to their unique amphiphilic structural features. Here, we develop an AFM-based single-molecule force spectroscopy assay to quantitatively measure the binding strength of hydrophobin to various types of surfaces both in isolation and in preformed protein films. We find that individual class II hydrophobins (HFBI) bind strongly to hydrophobic surfaces but weakly to hydrophilic ones. After self-assembly into protein films, they show much stronger binding strength to both surfaces due to the cooperativity of different interactions at nanoscale. Such self-assembly enhanced surface binding may serve as a general design principle for synthetic bioactive adhesives.

Transferable Coarse-Grained Models of Liquid-Liquid Equilibrium Using Local Density Potentials Optimized with the Relative Entropy

Bottom-up coarse-grained (CG) models are now regularly pursued to enable large length and time scale molecular simulations of complex, often macromolecular systems. However, predicting fluid phase equilibria using such models remains fundamentally challenging. A major problem stems from the typically low transferability of CG models beyond the densities and/or compositions at which they are parametrized, which is necessary if they are to describe distinct structural and thermodynamic properties unique to each phase. CG model transferability is compounded by the representation of the inherently multibody coarse interactions using pair potentials that neglect higher order effects. Here, we propose to construct transferable single site CG models of liquid mixtures by supplementing traditional CG pair interactions with local density potentials, which constitute a computationally inexpensive mean-field approach to describe many-body effects, in that site energies are modulated by the local solution environment. To illustrate the approach, we use intra- and interspecies local density potentials to develop CG models of benzene-water solutions that show impressive transferability in structural metrics (pair correlation functions, density profiles) throughout composition space, in contrast to pair-only CG representations. While further refinement may be necessary to represent more complex thermodynamic properties, like the liquid-liquid interfacial tension, the generality and improvement offered by the local density approach are highly encouraging for enabling complex phase equilibrium modeling using CG models.

Comment on “On the positional and orientational order of water and methanol around indole: a study on the microscopic origin of solubility” Phys. Chem. Chem. Phys., 2016, , 23006

Indole solubility is larger in methanol than in water due to lower magnitude of the cavity creation work.

Characterization of Water Solubility in n-Octacosane Using Raman Spectroscopy

In this study, we demonstrate the ability of polarization-difference Raman spectroscopy (PDRS) to detect dissolved free water molecules in a n-octacosane (n-C₂₈H₅₈) liquid-rich phase, and thus to determine its solubility, at temperatures and pressures relevant to the Fischer-Tropsch synthesis. Our results for the pure alkane reveal thermal decomposition above a temperature of 500 K as well as an increase of gauche conformers of the alkane chains with an increase in temperature. For binary homogeneous mixtures, raw spectra obtained from two different polarization scattering geometries did not show a relevant signal in the OH stretching frequency range. In contrast, isotropic spectra obtained from the PDRS technique reveal a narrow and tiny peak associated with the dangling OH bonds. Over the complete range of temperatures and pressures, no signature of hydrogen-bonded water molecules was observed in the isotropic Raman scattering intensities. A thorough investigation covering a large range of temperatures and pressures using PDRS signals showed that the higher the fraction of gauche conformers of hydrocarbon, the higher the solubility of water. The proportion of gauche and trans conformers was found to be water-concentration-independent, and the intensity of the OH-dangling peak increased linearly with increasing the vapor partial pressure of water. Therefore, we established a relation between a relevant intensity ratio and the concentration of water obtained from SAFT calculations. Contrary to the results from relevant literature, the calibration factor was found to be temperature-independent between 424 and 572 K. The isotropic Raman scattering intensities are corrected in order to provide a better representation of the vibrational density of states. The influence of correction of the isotropic scattering intensities on the solubility measurements as well as on the analysis of the molecular arrangement is discussed.

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.

Thermodynamics of mixtures of patchy and spherical colloids of different sizes: A multi-body association theory with complete reference fluid information

We present a theory to predict the structure and thermodynamics of mixtures of colloids of different diameters, building on our earlier work [A. Bansal et al., J. Chem. Phys. 145, 074904 (2016)] that considered mixtures with all particles constrained to have the same size. The patchy, solvent particles have short-range directional interactions, while the solute particles have short-range isotropic interactions. The hard-sphere mixture without any association site forms the reference fluid. An important ingredient within the multi-body association theory is the description of clustering of the reference solvent around the reference solute. Here we account for the physical, multi-body clusters of the reference solvent around the reference solute in terms of occupancy statistics in a defined observation volume. These occupancy probabilities are obtained from enhanced sampling simulations, but we also present statistical mechanical models to estimate these probabilities with limited simulation data. Relative to an approach that describes only up to three-body correlations in the reference, incorporating the complete reference information better predicts the bonding state and thermodynamics of the physical solute for a wide range of system conditions. Importantly, analysis of the residual chemical potential of the infinitely dilute solute from molecular simulation and theory shows that whereas the chemical potential is somewhat insensitive to the description of the structure of the reference fluid, the energetic and entropic contributions are not, with the results from the complete reference approach being in better agreement with particle simulations.

Simulated pressure denaturation thermodynamics of ubiquitin

Simulations of protein thermodynamics are generally difficult to perform and provide limited information. It is desirable to increase the degree of detail provided by simulation and thereby the potential insight into the thermodynamic properties of proteins. In this study, we outline how to analyze simulation trajectories to decompose conformation-specific, parameter free, thermodynamically defined protein volumes into residue-based contributions. The total volumes are obtained using established methods from Fluctuation Solution Theory, while the volume decomposition is new and is performed using a simple proximity method. Native and fully extended ubiquitin are used as the test conformations. Changes in the protein volumes are then followed as a function of pressure, allowing for conformation-specific protein compressibility values to also be obtained. Residue volume and compressibility values indicate significant contributions to protein denaturation thermodynamics from nonpolar and coil residues, together with a general negative compressibility exhibited by acidic residues.

Communication: Stiffening of dilute alcohol and alkane mixtures with water

We probe the anomalous compressibilities of dilute mixtures of alcohols and alkane gases in water using molecular simulations. The response to increasing solute concentration depends sensitively on temperature, with the compressibility decreasing upon solute addition at low temperatures and increasing at elevated temperatures. The thermodynamic origin of stiffening is directly tied to the solute's partial compressibility, which is negative at low temperatures and rises above water's compressibility with increasing temperature. Hydration shell waters concurrently tilt towards clathrate-like structures at low temperatures that fade with heating. Kirkwood-Buff theory traces the solute's partial compressibility to changes in the solute-water association volume upon heating and incongruous packing of waters at the boundary between the more structured hydration shell and bulk water.

A Quantitative Study of the Effects of Guest Flexibility on Binding Inside a Coordination Cage Host

We have performed a systematic investigation of the effects of guest flexibility on their ability to bind in the cavity of a coordination cage host in water, using two sets of isomeric aliphatic ketones that differ only in the branching patterns of their alkyl chains. Apart from the expected increase in binding strength for C9 over C7 ketones associated with their greater hydrophobic surface area, within each isomeric set there is a clear inverse correlation between binding free energy and guest flexibility, associated with loss of conformational entropy. This can be parameterized by the number of rotatable C-C bonds in the guest, with each additional rotatable bond resulting in a penalty of around 2 kJ mol-1 in the binding free energy, in good agreement with values obtained from protein/ligand binding studies. We used the binding data for the new flexible guests to improve the scoring function that we had previously developed that allowed us to predict binding constants of relatively rigid guests in the cage cavity using the molecular docking programme GOLD (Genetic Optimisation of Ligand Docking). This improved scoring function resulted in a significant improvement in the ability of GOLD to predict binding constants for flexible guests, without any detriment to its ability to predict binding for more rigid guests.