Anion Competition at Positively Charged Surfactant Monolayers.

Interactions of anions with hydrophobic surfaces of proteins and water-soluble polymers depend on the ability of the ions to shed their hydration shells. At positively charged surfactant monolayers, the interactions of anions are less well understood. Due to the interplay of electrostatic surface forces, hydration effects, and ion-ion interactions in the electrostatic double layer, a comprehensive microscopic picture remains elusive. Herein, we study the interactions of chloride, bromide, and a mixture of these two anions at the aqueous interface of dihexadecyldimethylammonium (DHDA+) and dioctadecyldimethylammonium (DODA+) cationic monolayers. Using molecular dynamics simulations and three surface-sensitive X-ray scattering techniques, we demonstrate that bromide interacts preferentially over chloride with both monolayers. The structure of the two monolayers and their interfacial electron density profiles obtained from the simulations quantitatively reproduce the experimental data. We observe that chloride and bromide form contact ion pairs with the quaternary ammonium groups on both monolayers. However, ion pairing with bromide leads to a greater reduction in the number of water molecules hydrating the anion, resulting in more energetically stable ion pairs. This leads to long-range (>3 nm) lateral correlations between bromide ions on the structured DODA+ monolayer. These observations indicate that ion hydration is the dominant factor determining the interfacial electrolyte structure.

Interactions of adsorbing cosolutes with hydrophobic hydration shells.

The analysis of water density fluctuations in the hydration shell of nonpolar solutes provides insights into water-mediated interactions, especially hydrophobic interactions. These fluctuations are sensitive to small perturbations due to changes in thermodynamic conditions, such as temperature and pressure, but also to the presence of cosolutes, such as salts or small organic molecules. Herein, we investigate the effect of two classes of adsorbing cosolutes, using urea and methanol as representatives, on the fluctuations in energy and solvent density within the solvation shell of a model extended hydrophobic solute. We focus on the interactions of the cosolutes with the hydrophobic hydration shell, rather than with the solute itself, which though important remain largely unexplored. We calculate and analyze the interfacial partial molar energy of the cosolute, using a methodology based on the small system method. This approach provides correlated solvent density and energy fluctuations and allows us to decompose them into contributions due to interactions between the different components present in the solvation shell of the solute. The results show that adsorbed urea molecules interact more favorably with water than nonadsorbed urea molecules, which leads to the attenuation of interfacial density fluctuations and thus to the stabilization of the solvation shell. By contrast, the adsorbed methanol molecules interact preferably with other methanol molecules in the solvation shell, leading to a nano-phase segregated structure, which enhances interfacial fluctuations.

A Gauss-Newton method for iterative optimization of memory kernels for generalized Langevin thermostats in coarse-grained molecular dynamics simulations.

In molecular dynamics simulations, dynamically consistent coarse-grained (CG) models commonly use stochastic thermostats to model friction and fluctuations that are lost in a CG description. While Markovian, i.e., time-local, formulations of such thermostats allow for an accurate representation of diffusivities/long-time dynamics, a correct description of the dynamics on all time scales generally requires non-Markovian, i.e., non-time-local, thermostats. These thermostats typically take the form of a Generalized Langevin Equation (GLE) determined by a memory kernel. In this work, we use a Markovian embedded formulation of a position-independent GLE thermostat acting independently on each CG degree of freedom. Extracting the memory kernel of this CG model from atomistic reference data requires several approximations. Therefore, this task is best understood as an inverse problem. While our recently proposed approximate Newton scheme allows for the iterative optimization of memory kernels (IOMK), Markovian embedding remained potentially error-prone and computationally expensive. In this work, we present an IOMK-Gauss-Newton scheme (IOMK-GN) based on IOMK that allows for the direct parameterization of a Markovian embedded model.

Transferable local density-dependent friction in tert-butanol/water mixtures.

Coarse-grained (CG) models informed from molecular dynamics simulations provide a way to represent the structure of an underlying all-atom (AA) model by deriving an effective interaction potential. However, this leads to a speed-up in dynamics due to the lost friction, which is especially pronounced in CG implicit solvent models. Applying a thermostat based on the Langevin equation (LE) provides a way to represent the long-time dynamics of CG particles by reintroducing friction to the system. To improve the representability CG models of heterogeneous molecular mixtures and their transferability over the mixture compositions, we parameterize an LE thermostat in which the friction coefficient depends on the local particle density (LD). The thermostat friction was iteratively optimized with a Markovian variant of the recently introduced Iterative Optimization of Memory Kernels (IOMK) method. We simulated tert-butanol/water mixtures over a range of compositions, which show a distinct clustering behavior. Our model with LD-dependent friction reproduces the AA diffusion coefficients well over the full range of mixtures and is, therefore, transferable with respect to dynamics.

Dynamical coarse-grained models of molecular liquids and their ideal and non-ideal mixtures.

Coarse-grained (CG) simulation models of condensed-phase systems can be derived with well-established methods that perform coarse-graining in space and provide an effective Hamiltonian with which some of the structural and thermodynamic properties of the underlying fine-grained (FG) reference system can be represented. Coarse-graining in time potentially provides CG models that furthermore represent dynamic properties. However, systematic efforts in this direction have so far been limited, especially for moderately coarse-grained, chemistry-specific systems with complicated conservative interactions. With the aim of representing structural, thermodynamic, and dynamic properties in CG simulations of multi-component molecular systems, we investigated a recently introduced method in which the force on a CG particle originates from conservative interactions with surrounding particles and non-Markovian dissipative interactions, the latter introduced by means of a colored-noise thermostat. We examined two different methods to derive isotropic memory kernels required for integrating the corresponding generalized Langevin equation (GLE) of motion, based on the orthogonal dynamics of the FG forces and on an iterative optimization scheme. As a proof of concept, we coarse-grain single-component molecular liquids (cyclohexane, tetrachloromethane) and ideal and non-ideal binary mixtures of cyclohexane/tetrachloromethane and ethanol/tetrachloromethane, respectively. We find that for all systems, the FG single particle velocity auto-correlation functions and, consequently, both the short time and long time diffusion coefficients can be quantitatively reproduced with the CG-GLE models. We furthermore demonstrate that the present GLE-approach leads to an improved description of the rate with which the spatial correlations decay, which is artificially accelerated in the absence of dissipation.

Cononsolvency of thermoresponsive polymers: where we are now and where we are going.

Cononsolvency is an intriguing phenomenon where a polymer collapses in a mixture of good solvents. This cosolvent-induced modulation of the polymer solubility has been observed in solutions of several polymers and biomacromolecules, and finds application in areas such as hydrogel actuators, drug delivery, compound detection and catalysis. In the past decade, there has been a renewed interest in understanding the molecular mechanisms which drive cononsolvency with a predominant emphasis on its connection to the preferential adsorption of the cosolvent. Significant efforts have also been made to understand cononsolvency in complex systems such as micelles, block copolymers and thin films. In this review, we will discuss some of the recent developments from the experimental, simulation and theoretical fronts, and provide an outlook on the problems and challenges which are yet to be addressed.

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.

Nonadditive ion effects on the coil-globule equilibrium of PNIPAM: a computer simulation study.

The combined effect of a weakly hydrated and a strongly hydrated anion on the lower critical solution temperature (LCST) of poly(N-isopropylacrylamide)(PNIPAM) is nonadditive (Bruce et al., J. Am. Chem. Soc., 2019, 141, 6609). Herein, we revisit the molecular origin of this effect by performing atomistic molecular dynamics simulations of a 40mer PNIPAM chain in solutions with a fixed concentration of Na2SO4 and an increasing concentration of NaI. Our results show that the nonadditive ion effects on the coil-to-globule transitions of PNIPAM arise due to the interplay between the depletion of the strongly hydrated sulfate ions and the preferential accumulation of the iodide ions on the polymer surface leading to favourable PNIPAM-I- interactions. The depletion of the sulfate ions and the binding of the iodide ions are coupled through the role of the cation leading to a mutual enhancement of both effects. This mutual enhancement effect correlates with the partitioning of the Na+ cations from the counterion cloud of the weakly hydrated iodide ions to the counterion cloud of the strongly hydrated sulfate ions and the corresponding changes in water affinity of the ions.

Cross-correlation corrected friction in generalized Langevin models: Application to the continuous Asakura-Oosawa model.

The development of dynamically consistent coarse-grained models for molecular simulations is often based on generalized Langevin equations, motivated by the application of the projection operator formalism (Mori-Zwanzig theory). While Mori's projection operator yields linear generalized Langevin equations that can be computationally efficiently implemented in numerical simulations, the downside is that Mori's generalized Langevin equation does not encompass the multi-body potential of mean force required to correctly encode structural and thermodynamic properties in coarse-grained many-body systems. Zwanzig's projection operator yields nonlinear generalized Langevin equations including the multi-body potential of mean force, while the remaining force contributions are not as cheap to implement in molecular simulation without making it formally hard to justify approximations. For many-particle coarse-grained models, due to computational and conceptual simplicity, an often used approach is to combine nonlinear conservative interactions with linear expressions to model dissipation. In a previous study [V. Klippenstein and N. F. A. van der Vegt, J. Chem. Phys. 154, 191102 (2021)], we proposed a method to parameterize such models to achieve dynamic consistency in coarse-grained models, allowing us to reconcile Mori's and Zwanzig's approach for practical purposes. In the current study, by applying the same strategy, we develop coarse-grained implicit solvent models for the continuous Asakura-Oosawa model, which under certain conditions allows us to develop very accurate coarse-grained potentials. By developing coarse-grained models for different reference systems with varying parameters, we test the broader applicability of the proposed procedure and demonstrate the relevance of accurate coarse-grained potentials in bottom-up derived dissipative models. We study how different system parameters affect the dynamic representability of the coarse-grained models. In particular, we find that the quality of the coarse-grained potential is crucial to correctly model the backscattering effect due to collisions on the coarse-grained scale. As hydrodynamic interactions are not explicitly modeled in the presented coarse-graining approach, deviations are observed in the long-time dynamics. The Asakura-Oosawa model allows for the tuning of system parameters to gain an improved understanding of this limitation. We also propose three new iterative optimization schemes to fine-tune the generalized Langevin thermostat to exactly match the reference velocity-autocorrelation function.

A unique piezolyte mechanism of TMAO: Hydrophobic interactions under extreme pressure conditions.

We report a computer simulation study of the effect of trimethylamine N-oxide (TMAO) on the pressure stability of the hydrophobic contact interaction of two nonpolar α-helices. We found that TMAO counterbalanced the disruptive effect of pressure destabilization on account of an earlier reported electronic polarization effect that led to an increased TMAO dipole moment under compression of the solvent. This direct stabilization mechanism became ineffective when the dipole polarization of TMAO was not considered and was linked to nonspecific van der Waals interactions of TMAO with the nonpolar surfaces of the two helices, which became weaker as TMAO became stronger polarized at high pressure. The corresponding thermodynamic driving forces are discussed and should be generic for hydrophobic interactions under high pressure. The proposed mechanism suggests that TMAO stands out as a piezolyte among stabilizing osmolytes, potentially protecting biological assemblies formed by hydrophobic interactions under extreme pressure conditions.

Temperature induced change of TMAO effects on hydrophobic hydration.

The effect of trimethylamine-N-oxide (TMAO) on hydrophobic solvation and hydrophobic interactions of methane has been studied with Molecular Dynamics simulations in the temperature range between 280 and 370 K at 1 bar ambient pressure. We observe a temperature transition in the effect of TMAO on the aqueous solubility of methane. At low temperature (280 K), methane is preferentially hydrated, causing TMAO to reduce its solubility in water, while above 320 K, methane preferentially interacts with TMAO, causing TMAO to promote its solubility in water. Based on a statistical-mechanical analysis of the excess chemical potential of methane, we find that the reversible work of creating a repulsive methane cavity opposes the solubility of methane in TMAO/water solution more than in pure water. Below 320 K, this solvent-excluded volume effect overcompensates the contribution of methane-TMAO van der Waals interactions, which promote the solvation of methane and are observed at all temperatures. These van der Waals interactions with the methyl groups of TMAO tip the balance above 320 K where the effect of TMAO on solvent-excluded volume is smaller. We furthermore find that the effective attraction between dissolved methane solutes increases with the increasing TMAO concentration. This observation correlates with a reduction in the methane solubility below 320 K but with an increase in methane solubility at higher temperatures.

Solvation shell thermodynamics of extended hydrophobic solutes in mixed solvents.

The ability of various cosolutes and cosolvents to enhance or quench solvent density fluctuations at solute-water interfaces has crucial implications on the conformational equilibrium of macromolecules such as polymers and proteins. Herein, we use an extended hydrophobic solute as a model system to study the effect of urea and methanol on the density fluctuations in the solute's solvation shell and the resulting thermodynamics. On strengthening the solute-water/cosolute repulsive interaction, we observe distinct trends in the mutual affinities between various species in, and the thermodynamic properties of, the solvation shell. These trends strongly follow the respective trends in the preferential adsorption of urea and methanol: solute-water/cosolute repulsion strengthens, urea accumulation decreases, and methanol accumulation increases. Preferential accumulation of urea is found to quench the density fluctuations around the extended solute, leading to a decrease in the compressibility of the solvation shell. In contrast, methanol accumulation enhances the density fluctuations, leading to an increase in the compressibility. The mode of action of urea and methanol seems to be strongly coupled to their hydration behavior. The observations from this simple model is discussed in relation to urea driven swelling and methanol induced collapse of some well-known thermo-responsive polymers.

Cross-correlation corrected friction in (generalized) Langevin models.

We propose a route for parameterizing isotropic (generalized) Langevin [(G)LE] thermostats with the aim to correct the dynamics of coarse-grained (CG) models with pairwise conservative interactions. The approach is based on the Mori-Zwanzig formalism and derives the memory kernels from Q-projected time correlation functions. Bottom-up informed (GLE and LE) thermostats for a CG star-polymer melt are investigated, and it is demonstrated that the inclusion of memory in the CG simulation leads to predictions of polymer diffusion in quantitative agreement with fine-grained simulations. Interestingly, memory effects are observed in the diffusive regime. We demonstrate that previously neglected cross-correlations between the "irrelevant" and the CG degree of freedom are important and lie at the origin of shortcomings in previous CG simulations.

An interplay of excluded-volume and polymer-(co)solvent attractive interactions regulates polymer collapse in mixed solvents.

Cosolvent effects on the coil-globule transitions in aqueous polymer solutions are not well understood, especially in the case of amphiphilic cosolvents that preferentially adsorb on the polymer and lead to both polymer swelling and collapse. Although a predominant focus in the literature has been placed on the role of polymer-cosolvent attractive interactions, our recent work has shown that excluded-volume interactions (repulsive interactions) can drive both preferential adsorption of the cosolvent and polymer collapse via a surfactant-like mechanism. Here, we further study the role of polymer-(co)solvent attractive interactions in two kinds of polymer solutions, namely, good solvent (water)-good cosolvent (alcohol) (GSGC) and poor solvent-good cosolvent (PSGC) solutions, both of which exhibit preferential adsorption of the cosolvent and a non-monotonic change in the polymer radius of gyration with the addition of the cosolvent. Interestingly, at low concentrations, the polymer-(co)solvent energetic interactions oppose polymer collapse in the GSGC solutions and contrarily support polymer collapse in the PSGC solutions, indicating the importance of the underlying polymer chemistry. Even though the alcohol molecules are preferentially adsorbed on the polymer, the trends of the energetic interactions at low cosolvent concentrations are dominated by the polymer-water energetic interactions in both the cases. Therefore, polymer-(co)solvent energetic interactions can either reinforce or compensate the surfactant-like mechanism, and it is this interplay that drives coil-to-globule transitions in polymer solutions. These results have implications for rationalizing the cononsolvency transitions in real systems such as polyacrylamides in aqueous alcohol solutions where the understanding of microscopic driving forces is still debatable.

Iterative integral equation methods for structural coarse-graining.

In this paper, new Newton and Gauss-Newton methods for iterative coarse-graining based on integral equation theory are evaluated and extended. In these methods, the potential update is calculated from the current and target radial distribution function, similar to iterative Boltzmann inversion, but gives a potential update of quality comparable with inverse Monte Carlo. This works well for the coarse-graining of molecules to single beads, which we demonstrate for water. We also extend the methods to systems that include coarse-grained bonded interactions and examine their convergence behavior. Finally, using the Gauss-Newton method with constraints, we derive a model for single bead methanol in implicit water, which matches the osmotic pressure of the atomistic reference. An implementation of all new methods is provided for the open-source VOTCA package.

Molecular Mechanism for the Interactions of Hofmeister Cations with Macromolecules in Aqueous Solution.

Ion identity and concentration influence the solubility of macromolecules. To date, substantial effort has been focused on obtaining a molecular level understanding of specific effects for anions. By contrast, the role of cations has received significantly less attention and the underlying mechanisms by which cations interact with macromolecules remain more elusive. To address this issue, the solubility of poly(N-isopropylacrylamide), a thermoresponsive polymer with an amide moiety on its side chain, was studied in aqueous solutions with a series of nine different cation chloride salts as a function of salt concentration. Phase transition temperature measurements were correlated to molecular dynamics simulations. The results showed that although all cations were on average depleted from the macromolecule/water interface, more strongly hydrated cations were able to locally accumulate around the amide oxygen. These weakly favorable interactions helped to partially offset the salting-out effect. Moreover, the cations approached the interface together with chloride counterions in solvent-shared ion pairs. Because ion pairing was concentration-dependent, the mitigation of the dominant salting-out effect became greater as the salt concentration was increased. Weakly hydrated cations showed less propensity for ion pairing and weaker affinity for the amide oxygen. As such, there was substantially less mitigation of the net salting-out effect for these ions, even at high salt concentrations.

Molecular Scale Solvation in Complex Solutions.

Complex solution environments are ubiquitous in nature. Most life science systems contain hydrated macromolecules whose solubility, function and stability are modulated by several small organic molecules or salts (cosolutes) present simultaneously. This Perspective discusses solvation of mixed cosolutes in water. Recent computer simulations and experiments have shown that nonadditive cosolute effects on the water solubility of thermoresponsive polymers and on protein stability have a common physical origin, rooted in solvent-excluded volume effects determined by mutually enhanced cosolute hydration in bulk. We discuss mixtures of weakly and strongly hydrated salts in the anionic Hofmeister series and mixtures of urea and trimethylamine N-oxide. Nonadditive phenomena in these mixtures lead to intriguing effects including consecutive polymer collapse and swelling transitions and counteraction of denaturant-induced protein unfolding. The combination of today's advanced simulation methods and spectroscopy techniques should be used to improve further the understanding of these complex aqueous solubility problems.

Nonadditive Ion Effects Drive Both Collapse and Swelling of Thermoresponsive Polymers in Water.

When a mixture of two salts in an aqueous solution contains a weakly and a strongly hydrated anion, their combined effect is nonadditive. Herein, we report such nonadditive effects on the lower critical solution temperature (LCST) of poly( N-isopropylacrylamide) (PNiPAM) for a fixed concentration of Na2SO4 and an increasing concentration of NaI. Using molecular dynamics simulations and vibrational sum frequency spectroscopy, we demonstrate that at low concentrations of the weakly hydrated anion (I-), the cations (Na+) preferentially partition to the counterion cloud around the strongly hydrated anion (SO42-), leaving I- more hydrated. However, upon further increase in the NaI concentration, this weakly hydrated anion is forced out of solution to the polymer/water interface by sulfate. Thus, the LCST behavior of PNiPAM involves competing roles for ion hydration and polymer-iodide interactions. This concept can be generally applied to mixtures containing both a strongly and a weakly hydrated anion from the Hofmeister series.

Trimethylamine N-oxide Counteracts Urea Denaturation by Inhibiting Protein-Urea Preferential Interaction.

Osmolytes are small organic molecules that can modulate the stability and function of cellular proteins by altering the chemical environment of the cell. Some of these osmolytes work in conjunction, via mechanisms that are poorly understood. An example is the naturally occurring protein-protective osmolyte trimethylamine N-oxide (TMAO) that stabilizes cellular proteins in marine organisms against the detrimental denaturing effects of another naturally occurring osmolyte, urea. From a computational standpoint, our understanding of this counteraction mechanism is hampered by the fact that existing force fields fail to capture the correct balance of TMAO and urea interactions in ternary solutions. Using molecular dynamics simulations and Kirkwood-Buff theory of solutions, we have developed an optimized force field that reproduces experimental Kirkwood-Buff integrals. We show through the study of two model systems, a 15-residue polyalanine chain and the R2-fragment (273GKVQIINKKLDL284) of the Tau protein, that TMAO can counteract the denaturing effects of urea by inhibiting protein-urea preferential interaction. The extent to which counteraction can occur is seen to depend heavily on the amino acid composition of the peptide.

Water-Mediated Ion Pairing: Occurrence and Relevance.

We present an overview of the studies of ion pairing in aqueous media of the past decade. In these studies, interactions between ions, and between ions and water, are investigated with relatively novel approaches, including dielectric relaxation spectroscopy, far-infrared (terahertz) absorption spectroscopy, femtosecond mid-infrared spectroscopy, and X-ray spectroscopy and scattering, as well as molecular dynamics simulation methods. With these methods, it is found that ion pairing is not a rare phenomenon only occurring for very particular, strongly interacting cations and anions. Instead, for many salt solutions and their interfaces, the measured and calculated structure and dynamics reveal the presence of a distinct concentration of contact ion pairs (CIPs), solvent shared ion pairs (SIPs), and solvent-separated ion pairs (2SIPs). We discuss the importance of specific ion-pairing interactions between cations like Li(+) and Na(+) and anionic carboxylate and phosphate groups for the structure and functioning of large (bio)molecular systems.