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.

Solvation Behavior of Elastin-like Polypeptides in Divalent Metal Salt Solutions.

The effects of CaCl2 and MgCl2 on the cloud point temperature of two different elastin-like polypeptides (ELPs) were studied using a combination of cloud point measurements, molecular dynamics simulations, and infrared spectroscopy. Changes in the cloud point for the ELPs in aqueous divalent metal cation solutions were primarily governed by two competing interactions: the cation-amide oxygen electrostatic interaction and the hydration of the cation. In particular, Ca2+ cations can more readily shed their hydration shells and directly contact two amide oxygens by the formation of ion bridges. By contrast, Mg2+ cations were more strongly hydrated and preferred to partition toward the amide oxygens along with their hydration shells. In fact, although hydrophilic ELP V5A2G3 was salted-out at low concentrations of MgCl2, it was salted-in at higher salt concentrations. By contrast, CaCl2 salted the ELP sharply out of solution at higher salt concentrations because of the bridging effect.

Anions and Cations Affect Amino Acid Dissociation Equilibria via Distinct Mechanisms.

Salts reduce the pKa of weak acids by a mechanism sensitive to ion identity and concentration via charge screening of the deprotonated state. In this study, we utilize constant pH molecular dynamics simulations to understand the molecular mechanism behind the salt-dependent dissociation of aspartic acid (Asp). We calculate the pKa of Asp in the presence of a monovalent salt and investigate Hofmeister ion effects by systematically varying the ionic radii. We observe that increasing the anion size leads to a monotonic decrease in Asp pKa. Conversely, the cation size affects the pKa nonmonotonically, interpretable in the context of the law of matching water affinity. The net effect of salt on Asp acidity is governed by an interplay of solvation and competing ion interactions. The proposed mechanism is rather general and can be applicable to several problems in Hofmeister ion chemistry, such as pH effects on protein stability and soft matter interfaces.

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.

Bottom-Up Informed and Iteratively Optimized Coarse-Grained Non-Markovian Water Models with Accurate Dynamics.

Molecular dynamics (MD) simulations based on coarse-grained (CG) particle models of molecular liquids generally predict accelerated dynamics and misrepresent the time scales for molecular vibrations and diffusive motions. The parametrization of Generalized Langevin Equation (GLE) thermostats based on the microscopic dynamics of the fine-grained model provides a promising route to address this issue, in conjunction with the conservative interactions of the CG model obtained with standard coarse graining methods, such as iterative Boltzmann inversion, force matching, or relative entropy minimization. We report the application of a recently introduced bottom-up dynamic coarse graining method, based on the Mori-Zwanzig formalism, which provides accurate estimates of isotropic GLE memory kernels for several CG models of liquid water. We demonstrate that, with an additional iterative optimization of the memory kernels (IOMK) for the CG water models based on a practical iterative optimization technique, the velocity autocorrelation function of liquid water can be represented very accurately within a few iterations. By considering the distinct Van Hove function, we demonstrate that, with the presented methods, an accurate representation of structural relaxation can be achieved. We consider several distinct CG potentials to study how the choice of the CG potential affects the performance of bottom-up informed and iteratively optimized models.

Stability, Speed, and Constraints for Structural Coarse-Graining in VOTCA.

Structural coarse-graining involves the inverse problem of deriving pair potentials that reproduce target radial distribution functions. Despite its clear mathematical formulation, there are open questions about the existing methods concerning speed, stability, and physical representability of the resulting potentials. In this work, we make progress on several aspects of iterative methods used to solve the inverse problem. Based on integral equation theory, we derive fast Gauss-Newton schemes applicable to very general systems, including molecules with bonds and mixtures. Our methods are similar to inverse Monte Carlo in terms of convergence speed and have a similar cost per iteration as iterative Boltzmann inversion. We investigate stability problems in our schemes and in the inverse Monte Carlo method and propose modifications to fix them. Furthermore, we establish how the pair potential can be constrained at each iteration to reproduce the pressure, Kirkwood-Buff integral, or the enthalpy of vaporization. We demonstrate the potential of our approach in deriving coarse-grained force fields for nine different solvents and their mixtures. All methods described are implemented in the free and open VOTCA software framework for systematic coarse-graining.

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.

Influence of TMAO and Pressure on the Folding Equilibrium of TrpCage.

Trimethylamine-N-oxide (TMAO) is an osmolyte known for its ability to counteract the pressure denaturation of proteins. Computational studies addressing the molecular mechanisms of TMAO's osmolyte action have however focused exclusively on its protein-stabilizing properties at ambient pressure, neglecting the changes that may occur under high-pressure conditions where TMAO's hydration structure changes to that of increased water binding. Here, we present the first study on the combined effect of pressure and TMAO on a mini-protein, TrpCage. The results showed that at high pressures, nonpolar residues packed less tightly and the salt bridge of TrpCage was destabilized. This effect was mitigated by TMAO which was found to be strongly depleted from the protein/water interface at 1 kbar than at 1 bar ambient pressure, thus counterbalancing the thermodynamically unfavorable effect of elevated pressure in the free energy of folding. TMAO was depleted from charged groups, like the salt bridge-forming ones, and accumulated around hydrophobic groups. Still, it stabilized both kinds of interactions. Furthermore, enthalpically favorable TrpCage-water hydrogen bonds were reduced in the presence of TMAO, causing a stronger destabilization of the unfolded state than the folded state. This shifted the protein-folding equilibrium toward the folded state. Therefore, TMAO showed stabilizing effects on different kinds of groups, which were partially enhanced at high pressures.

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.

Cosolvent Exclusion Drives Protein Stability in Trimethylamine N-Oxide and Betaine Solutions.

Using a combination of molecular dynamics simulation, dialysis experiments, and electronic circular dichroism measurements, we studied the solvation thermodynamics of proteins in two osmolyte solutions, trimethylamine N-oxide (TMAO) and betaine. We showed that existing force fields are unable to capture the solvation properties of the proteins lysozyme and ribonuclease T1 and that the inaccurate parametrization of protein-osmolyte interactions in these force fields promoted an unphysical strong thermal denaturation of the trpcage protein. We developed a novel force field for betaine (the KBB force field) which reproduces the experimental solution Kirkwood-Buff integrals and density. We further introduced appropriate scaling to protein-osmolyte interactions in both the betaine and TMAO force fields which led to successful reproduction of experimental protein-osmolyte preferential binding coefficients for lysozyme and ribonuclease T1 and prevention of the unphysical denaturation of trpcage in osmolyte solutions. Correct parametrization of protein-TMAO interactions also led to the stabilization of the collapsed conformations of a disordered elastin-like peptide, while the uncorrected parameters destabilized the collapsed structures. Our results establish that the thermodynamic stability of proteins in both betaine and TMAO solutions is governed by osmolyte exclusion from proteins.

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.

Where Lennard-Jones Potentials Fail: Iterative Optimization of Ion-Water Pair Potentials Based on Ab Initio Molecular Dynamics Data.

The use of the Lennard-Jones (LJ) potential in computer simulations of aqueous electrolyte solutions is widespread. The standard approach is to parametrize LJ potential parameters against thermodynamic solution properties, but problems in representing the local structural and dynamic properties of ion hydration shells remain. The r-12-term in the LJ potential is responsible for this as it leads to overly repulsive ion-water interactions at short range. As a result, the LJ potential predicts blue-shifted vibrational peaks of the cations' rattling mode and too large negative ion hydration entropies. We demonstrate that cation-water effective pair potentials derived from ab initio MD data have softer short-range repulsions and represent hydration shell properties significantly better. Our findings indicate that replacing the LJ potential with these effective pair potentials offers a promising route to represent thermodynamic solution properties and local interactions of specific ions with nonpolarizable force field models.

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.

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.

Direct Calculation of Entropic Components in Cohesive Interaction Free Energies.

Cohesive interaction free energies entail an entropic component related to fluctuations of the energy associated with the attractive portion of the solute-solvent potential. The corresponding "fluctuation entropy" is fundamental in the solvation thermodynamics of macromolecular solutes and is linked to interfacial solvent density fluctuations and hydrophobic effects. Since the direct calculation of fluctuation entropy in molecular simulations is hampered by the poor sampling of high-energy tails in the solute-solvent energy distribution, indirect, and often approximate, routes for the calculation of fluctuation entropy are usually required, involving the modeling of geometrically frozen repulsive solute cavities in thermodynamic integration approaches. Herein, we propose a method to directly compute the fluctuation entropy by employing indirect umbrella sampling (INDUS). To validate the method, we consider model systems consisting of subnanometer oil droplets in water for which the fluctuation entropy can be computed exactly using indirect methods. The fluctuation entropy calculated with the newly proposed direct method agrees with the indirect reference calculations. We also observe that the solvation free energy and the contribution of the fluctuation entropy to it are of comparable magnitudes, particularly for larger oil droplets (∼1 nm). The proposed method can readily be employed for flexible macromolecular solutes and systems with extended hydrophobic surfaces or in the vicinity of a dewetting transition.

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.

Introducing Memory in Coarse-Grained Molecular Simulations.

Preserving the correct dynamics at the coarse-grained (CG) level is a pressing problem in the development of systematic CG models in soft matter simulation. Starting from the seminal idea of simple time-scale mapping, there have been many efforts over the years toward establishing a meticulous connection between the CG and fine-grained (FG) dynamics based on fundamental statistical mechanics approaches. One of the most successful attempts in this context has been the development of CG models based on the Mori-Zwanzig (MZ) theory, where the resulting equation of motion has the form of a generalized Langevin equation (GLE) and closely preserves the underlying FG dynamics. In this Review, we describe some of the recent studies in this regard. We focus on the construction and simulation of dynamically consistent systematic CG models based on the GLE, both in the simple Markovian limit and the non-Markovian case. Some recent studies of physical effects of memory are also discussed. The Review is aimed at summarizing recent developments in the field while highlighting the major challenges and possible future directions.

Length-Scale Effects in Hydrophobic Polymer Collapse Transitions.

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