A Molecular Thermodynamic Model of Coacervation in Solutions of Polycations and Oppositely Charged Micelles.

To guide the rational design of personal care formulations, we formulate a molecular thermodynamic model that predicts coacervation from cationic polymers and mixed micelles containing neutral and anionic surfactants and added salt. These coacervates, which form as a result of dilution of conditioning shampoos during use, deposit conditioning agents and other actives to the scalp or skin and also provide lubrication benefits. Our model accounts for mixing entropy, hydrophobic interactions of polycation with water, free energies of bindings of oppositely charged groups to micelles and polycations, and electrostatic interactions that capture connectivity of charged groups on the polycation chain and the micelle. The model outputs are the compositions of surfactants, polycation, salt, and water in the coacervate and in its coexisting dilute phase, along with the binding fractions and coacervate volume fraction. We study the effects of overall composition (of surfactant, polycation, and added salt), charge fractions on micelles and polycations, and binding free energies on the phase diagram of coacervates. Then, we perform coacervation experiments for three systems: sodium dodecyl sulfate (SDS)-JR30M, sodium methyl cocoyl taurate (Taurate)-JR30M, and sodium lauryl alaninate (Alaninate)-JR30M, where JR30M is a cationic derivative of hydroxyethylcellulose (cat-HEC), and rationalize their coacervation data using our model. For comparison with experiment, we also develop a parametrization scheme to obtain the requisite binding energies and Flory-Huggins χ parameter. We find that our model predictions agree reasonably well with the experimental data, and that the sulfate-free surfactants of Taurate and Alaninate display much larger 2-phase regions compared to SDS with JR30M.

Salt- and pH-Dependent Viscosity of SDS/LAPB Solutions: Experiments and a Semiempirical Thermodynamic Model.

We present novel data on the composition-, pH-, and salt-dependent zero shear viscosity of the commercially important mixture of anionic sodium dodecyl sulfate (SDS) and zwitterionic lauramidopropyl betaine (LAPB). We show via proton NMR experiments that the notionally zwitterionic LAPB exhibits a large pKa shift in the presence of SDS and can become partially cationic at formulation-relevant pH ranges of 4.5-6.0-that is, the binary system is effectively a ternary system. This has a pronounced effect on the viscosity of the system at low pH, especially if the fraction of LAPB is high. We use theoretical arguments to motivate a semiempirical but practical approach to model the viscosity of the mixtures using thermodynamic parameters such as the excess chemical potentials or activity coefficients of the surfactants. We demonstrate this using an augmented regular solution theory-based mixed micelle thermodynamic model and develop robust regression models using Bayesian approaches. We also show how the pKa shift from NMR experiments can be used to parameterize the thermodynamic model. This framework should be extensible to other arbitrary surfactant mixtures in the future and hence will be of broad interest for the development of surfactant formulations for household, personal care, and other applications.

A new equation of state for homo-polymers in dissipative particle dynamics.

A chain-revised Groot-Warren equation of state (crGW-EOS) was developed and tested to describe systems of homo-oligomeric chains in the framework of dissipative particle dynamics (DPD). First, thermodynamic perturbation theory is applied to introduce correction terms that account for the reduction in pressure with an increasing number of bonds at constant bead number density. Then, this EOS is modified by introducing a set of switching functions that yields an accurate second virial coefficient in the low-density limit. The crGW-EOS offers several improvements over the revised Groot-Warren equation of state and Groot-Warren equation of state for chain molecules. We tested the crGW-EOS by using it to predict the pressure of oligomeric systems and the B2 virial coefficient of chain DPD particles for a range of bond lengths. Additionally, a method is developed for determining the strength of cross-interaction parameters between chains of different compositions and sizes and for thermal and athermal mixtures. We explored how different levels of coarse-graining affect the upper-critical solution temperature.

Probing Additive Loading in the Lamellar Phase of a Nonionic Surfactant: Gibbs Ensemble Monte Carlo Simulations Using the SDK Force Field.

Understanding solute uptake into soft microstructured materials, such as bilayers and worm-like and spherical micelles, is of interest in the pharmaceutical, agricultural, and personal care industries. To obtain molecular-level insight on the effects of solutes loading into a lamellar phase, we utilize the Shinoda-Devane-Klein (SDK) coarse-grained force field in conjunction with configurational-bias Monte Carlo simulations in the osmotic Gibbs ensemble. The lamellar phase is comprised of a bilayer formed by triethylene glycol mono- n-decyl ether (C10E3) surfactants surrounded by water with a 50:50 surfactant/water weight ratio. We study both the unary adsorption isotherm and the effects on bilayer structure and stability caused by n-nonane, 1-hexanol, and ethyl butyrate at several different reduced reservoir pressures. The nonpolar n-nonane molecules load near the center of the bilayer. In contrast, the polar 1-hexanol and ethyl butyrate molecules both load with their polar bead close to the surfactant head groups. Near the center of the bilayer, none of the solute molecules exhibits a significant orientational preference. Solute molecules adsorbed near the polar groups of the surfactant chains show a preference for orientations perpendicular to the interface, and this alignment with the long axis of the surfactant molecules is most pronounced for 1-hexanol. Loading of n-nonane leads to an increase of the bilayer thickness, but does not affect the surface area per surfactant. Loading of polar additives leads to both lateral and transverse swelling. The reduced Henry's law constants of adsorption (expressed as a molar ratio of additive to surfactant per reduced pressure) are 0.23, 1.4, and 14 for n-nonane, 1-hexanol, and ethyl butyrate, respectively, and it appears that the SDK force field significantly overestimates the ethyl butyrate-surfactant interactions.

Liquid-liquid equilibria for soft-repulsive particles: improved equation of state and methodology for representing molecules of different sizes and chemistry in dissipative particle dynamics.

Three developments are presented that significantly expand the applicability of dissipative particle dynamics (DPD) simulations for symmetric and non-symmetric mixtures, where the former contain particles with equal repulsive parameter for self-interactions but a different repulsive parameter for cross-interactions, and the latter contain particles with different repulsive parameters also for the self-interactions. Monte Carlo and molecular dynamics simulations for unary phases covering a wide range of repulsive parameters and of densities for single-bead DPD particles point to deficiencies of the Groot and Warren equation of state (GW-EOS) [J. Chem. Phys. 107, 4423 (1997)]. A revised version, called rGW-EOS, is proposed here that is significantly more accurate over a wider range of parameters/densities. The second development is the generalization of the relationship between the Flory-Huggins χ parameter and the repulsive cross-interaction parameter when the two particles involved have different molecular volumes. The third aspect is an investigation of Gibbs ensemble Monte Carlo simulation protocols, which demonstrates the importance of volume fluctuations and excess volumes of mixing even for equimolar symmetric mixtures of DPD particles. As an illustrative example, the novel DPD methodology is applied to the prediction of the liquid-liquid equilibria for acetic anhydride/(n-hexane or n-octane) binary mixtures.

Sitting at the edge: how biomolecules use hydrophobicity to tune their interactions and function.

Water near extended hydrophobic surfaces is like that at a liquid-vapor interface, where fluctuations in water density are substantially enhanced compared to those in bulk water. Here we use molecular simulations with specialized sampling techniques to show that water density fluctuations are similarly enhanced, even near hydrophobic surfaces of complex biomolecules, situating them at the edge of a dewetting transition. Consequently, water near these surfaces is sensitive to subtle changes in surface conformation, topology, and chemistry, any of which can tip the balance toward or away from the wet state and thus significantly alter biomolecular interactions and function. Our work also resolves the long-standing puzzle of why some biological surfaces dewet and other seemingly similar surfaces do not.

Extended surfaces modulate hydrophobic interactions of neighboring solutes.

Interfaces are a most common motif in complex systems. To understand how the presence of interfaces affects hydrophobic phenomena, we use molecular simulations and theory to study hydration of solutes at interfaces. The solutes range in size from subnanometer to a few nanometers. The interfaces are self-assembled monolayers with a range of chemistries, from hydrophilic to hydrophobic. We show that the driving force for assembly in the vicinity of a hydrophobic surface is weaker than that in bulk water and decreases with increasing temperature, in contrast to that in the bulk. We explain these distinct features in terms of an interplay between interfacial fluctuations and excluded volume effects--the physics encoded in Lum-Chandler-Weeks theory [Lum K, Chandler D, Weeks JD (1999) J Phys Chem B 103:4570-4577]. Our results suggest a catalytic role for hydrophobic interfaces in the unfolding of proteins, for example, in the interior of chaperonins and in amyloid formation.

Hydrophobicity of proteins and interfaces: insights from density fluctuations.

Macroscopic characterizations of hydrophobicity (e.g., contact angle measurements) do not extend to the surfaces of proteins and nanoparticles. Molecular measures of hydrophobicity of such surfaces need to account for the behavior of hydration water. Theory and state-of-the-art simulations suggest that water density fluctuations provide such a measure; fluctuations are enhanced near hydrophobic surfaces and quenched with increasing surface hydrophilicity. Fluctuations affect conformational equilibria and dynamics of molecules at interfaces. Enhanced fluctuations are reflected in enhanced cavity formation, more favorable binding of hydrophobic solutes, increased compressibility of hydration water, and enhanced water-water correlations at hydrophobic surfaces. These density fluctuation-based measures can be used to develop practical methods to map the hydrophobicity/philicity of heterogeneous surfaces including those of proteins. They highlight that the hydrophobicity of a group is context dependent and is significantly affected by its environment (e.g., chemistry and topography) and especially by confinement. The ability to include information about hydration water in mapping hydrophobicity is expected to significantly impact our understanding of protein-protein interactions as well as improve drug design and discovery methods and bioseparation processes.

Mapping hydrophobicity at the nanoscale: applications to heterogeneous surfaces and proteins.

Approaches to quantify wetting at the macroscale do not translate to the nanoscale, highlighting the need for new methods for characterizing hydrophobicity at the small scale. We use extensive molecular simulations to study the hydration of homo and heterogeneous self-assembled monolayers (SAMs) and of protein surfaces. For homogeneous SAMs, new pressure-dependent analysis shows that water displays higher compressibility and enhanced density fluctuations near hydrophobic surfaces, which are gradually quenched with increasing hydrophilicity, consistent with our previous studies. Heterogeneous surfaces show an interesting context dependence--adding a single -OH group in a CH3 terminated SAM has a more dramatic effect on water in the vicinity compared to that of a single CH3 group in an -OH background. For mixed -CH3/-OH SAMs, this asymmetry leads to a non-linear dependence of hydrophobicity on the surface concentration. We also present preliminary results to map hydrophobicity of protein surfaces by monitoring local density fluctuations and binding of probe hydrophobic solutes. These molecular measures account for the behavior of protein's hydration water, and present a more refined picture of its hydrophobicity map. At least for one protein, hydrophobin-II, we show that the hydrophobicity map is different from that suggested by a commonly used hydropathy scale.

Designing heteropolymers to fold into unique structures via water-mediated interactions.

Hydrophobic homopolymers collapse into globular structures in water driven by hydrophobic interactions. Here we employ extensive molecular dynamics simulations to study the collapse of heteropolymers containing one or two pairs of oppositely charged monomers. We show that charging a pair of monomers can dramatically alter the most stable conformations from compact globular to more open hairpin-like. We systematically explore a subset of the sequence space of one- and two-charge-pair polymers, focusing on the locations of the charge pairs. Conformational stability is governed by a balance of hydrophobic interactions, hydration and interactions of charge groups, water-mediated charged-hydrophobic monomer repulsions, and other factors. As a result, placing charge pairs in the middle, away from the hairpin ends, leads to stable hairpin-like structures. Turning off the monomer-water attractions enhances hydrophobic interactions significantly leading to a collapse into compact globular structures even for two-charge-pair heteropolymers. In contrast, the addition of salt leads to open and extended structures, suggesting that solvation of charged monomer sites by salt ions dominates the salt-induced enhancement of hydrophobic interactions. We also test the ability of a predictive scheme based on the additivity of free energy of contact formation. The success of the scheme for symmetric two-charge-pair sequences and the failure for their flipped versions highlight the complexity of the heteropolymer conformation space and of the design problem. Collectively, our results underscore the ability of tuning water-mediated interactions to design stable nonglobular structures in water and present model heteropolymers for further studies in the extended thermodynamic space and in inhomogeneous environments.

Self-assembly of TMAO at hydrophobic interfaces and its effect on protein adsorption: insights from experiments and simulations.

We offer a novel process to render hydrophobic surfaces resistant to relatively small proteins during adsorption. This was accomplished by self-assembly of a well-known natural osmolyte, trimethylamine oxide (TMAO), a small amphiphilic molecule, on a hydrophobic alkanethiol surface. Measurements of lysozyme (LYS) adsorption on several homogeneous substrates formed from functionalized alkanethiol self-assembled monolayers (SAMs) in the presence and absence of TMAO, and direct interaction energy between the protein and functionalized surfaces, demonstrate the protein-resistant properties of a noncovalently adsorbed self-assembled TMAO layer. Molecular dynamics simulations clearly show that TMAO molecules concentrate near the CH(3)-SAM surface and are preferentially excluded from LYS. Interestingly, TMAO molecules adsorb strongly on a hydrophobic CH(3)-SAM surface, but a trade-off between hydrogen bonding with water, and hydrophobic interactions with the underlying substrate results in a nonintuitive orientation of TMAO molecules at the interface. Additionally, hydrophobic interactions, usually responsible for nonspecific adsorption of proteins, are weakly affected by TMAO. In addition to TMAO, other osmolytes (sucrose, taurine, and betaine) and a larger homologue of TMAO (N,N-dimethylheptylamine-N-oxide) were tested for protein resistance and only N,N-dimethylheptylamine-N-oxide exhibited resistance similar to TMAO. The principle of osmolyte exclusion from the protein backbone is responsible for the protein-resistant property of the surface. We speculate that this novel process of surface modification may have wide applications due to its simplicity, low cost, regenerability, and flexibility.

Unfolding of hydrophobic polymers in guanidinium chloride solutions.

Guanidinium chloride (GdmCl) is a widely used chemical denaturant that unfolds proteins. Its effects on hydrophobic interactions are, however, not fully understood. We quantify the effects of GdmCl on various manifestations of hydrophobicity--from solvation and interactions of small solutes to folding-unfolding of hydrophobic polymers--in water and in concentrated GdmCl solutions. For comparison, we also perform similar calculations in solutions of NaCl and CsCl in water. Like NaCl and CsCl, GdmCl increases the surface tension of water, decreases the solubility of small hydrophobic solutes, and enhances the strength of hydrophobic interactions at the pair level. However, unlike NaCl and CsCl, GdmCl destabilizes folded states of hydrophobic polymers. We show that Gdm(+) ions preferentially coat the hydrophobic polymer, and it is the direct van der Waals interaction between Gdm(+) ions and the polymer that contributes to the destabilization of folded states. Interestingly, the temperature dependence of the free energy of unfolding of the hydrophobic polymer in water is protein-like, with signatures of both heat and cold denaturation. Addition of GdmCl shifts the cold denaturation temperature higher, into the experimentally accessible region. Finally, translational as well as conformational dynamics of the polymer are slower in GdmCl and correlate with dynamics of water molecules in solution.

How hydrophobic hydration responds to solute size and attractions: Theory and simulations.

We focus on the hydration of a methane and spherical single and multisite C60 and C180 solutes over a range of solute-water attractions to quantify the vicinal water structure and their hydration thermodynamics using extensive molecular dynamics simulations and theory. We show that water structure near larger solutes is more sensitive to solute-water attractions compared to that near smaller ones. To understand the sensitivity, we separate the solute-water potential of mean force into a direct solute-water interaction and an indirect or solvent contribution [omega(r)]. In the absence of omega(r), water density in the solute vicinity would increase exponentially with solute-water interactions. Instead, omega(r) becomes increasingly repulsive with strengthening of solute-water attractions thereby opposing those direct interactions. We term this phenomenon "competitive expulsion," which characterizes the repulsion of a test water molecule by the hydration shell solvent waters. We develop a physically motivated theoretical approach to predict changes in omega(r) with attractions. We call this approach the modified-EXP (M-EXP) approximation owing to the similarity of ideas and especially our final expression with that of the EXP approximation of Chandler and Andersen [J. Chem. Phys. 57, 1930 (1972)]. Solute-water radial distribution functions and chemical potentials calculated using the M-EXP approach are in good agreement with simulation data. These calculations highlight the sensitivity of hydration structure and thermodynamics of bucky ball like solutes to solute-water interactions. We find that excess chemical potentials of bucky balls with standard alkane-like carbon-water interactions parameters are negative, suggesting the need for a careful calibration of those parameters for predictions of solubility, wetting, and water-mediated interactions using molecular simulations.

Characterizing hydrophobicity of interfaces by using cavity formation, solute binding, and water correlations.

Hydrophobicity is often characterized macroscopically by the droplet contact angle. Molecular signatures of hydrophobicity have, however, remained elusive. Successful theories predict a drying transition leading to a vapor-like region near large hard-sphere solutes and interfaces. Adding attractions wets the interface with local density increasing with attractions. Here we present extensive molecular simulation studies of hydration of realistic surfaces with a wide range of chemistries from hydrophobic (-CF(3), -CH(3)) to hydrophilic (-OH, -CONH(2)). We show that the water density near weakly attractive hydrophobic surfaces (e.g., -CF(3)) can be bulk-like or larger, and provides a poor quantification of surface hydrophobicity. In contrast, the probability of cavity formation or the free energy of binding of hydrophobic solutes to interfaces correlates quantitatively with the macroscopic wetting properties and serves as an excellent signature of hydrophobicity. Specifically, the probability of cavity formation is enhanced in the vicinity of hydrophobic surfaces, and water-water correlations correspondingly display characteristics similar to those near a vapor-liquid interface. Hydrophilic surfaces suppress cavity formation and reduce the water-water correlation length. Our results suggest a potentially robust approach for characterizing hydrophobicity of more complex and heterogeneous surfaces of proteins and biomolecules, and other nanoscopic objects.

How surface wettability affects the binding, folding, and dynamics of hydrophobic polymers at interfaces.

We present an extensive molecular simulation study of the behavior of a flexible hydrophobic 25-mer polymer at interfaces presenting a range of chemistries from hydrophobic (-CH(3)) to hydrophilic (-CONH(2)). We quantify the free energy of adsorption, conformational equilibria, and translational and conformational dynamics of the polymer at these diverse interfaces. Water-mediated interactions drive the polymer to adsorb strongly at a hydrophobic interface and repel it from hydrophilic ones. At hydrophilic surfaces, van der Waals interactions between the polymer and the surface mitigate this water-mediated repulsion, leading to weak adsorption of the polymer. Although the polymer is strongly adsorbed to hydrophobic surfaces, it is also most dynamic there. Translational diffusion and conformational dynamics are faster at hydrophobic surfaces compared to those at hydrophilic ones. In bulk water, the polymer collapses into compact globular shapes, whereas the thermodynamic stability of folded polymers is significantly lowered at hydrophobic surfaces. The polymer spreads into pancake-like 2D conformations at hydrophobic surfaces and gradually beads up into globular shapes as the surface is made more hydrophilic. Interestingly, the binding thermodynamics and dynamics correlate with macroscopic droplet contact angles that characterize the wetting properties of the different interfaces.

How interfaces affect hydrophobically driven polymer folding.

Studies of folding-unfolding of hydrophobic polymers in water provide an excellent starting point to probe manybody hydrophobic interactions in the context of realistic self-assembly processes. Such studies in bulk water have highlighted the similarities between thermodynamics of polymer collapse and of protein folding, and emphasized the role of hydration-water structure, density, and fluctuations-in the folding kinetics. Hydrophobic polymers are interfacially active-that is, they prefer locations at aqueous interfaces relative to bulk water-consistent with their low solubility. How does the presence of a hydrophobic solid surface or an essentially hydrophobic vapor-water interface affect the structural, thermodynamic, and kinetic aspects of polymer folding? Using extensive molecular dynamics simulations, we show that the large hydrophobic driving force for polymer collapse in bulk water is reduced at a solid alkane-water interface and further reduced at a vapor-water interface. As a result, at the solid-water interface, folded structures are marginally stable, whereas the vapor-liquid interface unfolds polymers completely. Structural sampling is also significantly affected by the interface. For example, at the solid-water interface, polymer conformations are quasi-2- dimensional, with folded states being pancake-like structures. At the vapor-water interface, the hydrophobic polymer is significantly excluded from the water phase and freely samples a broad range of compact to extended structures. Interestingly, although the driving force for folding is considerably lower, kinetics of folding are faster at both interfaces, highlighting the role of enhanced water fluctuations and dynamics at a hydrophobic interface.