A Site Density Functional Theory for Water: Application to Solvation of Amino Acid Side Chains

Predicting Solvation Free Energies from the Minnesota Solvation Database Using Classical Density Functional Theory Based on the PC-SAFT Equation of State

We critically assess the capabilities of classical density functional theory (DFT) based on the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state to predict the solvation free energies of small molecules in various hydrocarbon solvents. We compare DFT results with experimental data from the Minnesota solvation database and utilize statistical methods to analyze the accuracy of our approach, as well as its weaknesses. The mean absolute error of the solvation free energies is 3.7 kJ mol-1 for n-alkane solvents, ranging from pentane to hexadecane, with 473 solute-solvent systems. For solvents consisting of cyclic hydrocarbons (cyclohexane, benzene, toluene, and ethylbenzene) with 245 solute-solvent systems, we report a slightly larger mean absolute error of 4.2 kJ mol-1. We identify three possible sources of errors: (i) the neglect of solute-solvent and solvent-solvent Coulomb interactions, which limits the applicability of PC-SAFT DFT to nonpolar and weakly polar molecules; (ii) the solute's Lennard-Jones parameters supplied by the general AMBER force field, which are not parametrized toward solvation free energies; and (iii) the application of the Lorentz-Berthelot combining rules to the dispersive interactions between a segment of the PC-SAFT solvent and a Lennard-Jones interaction site of the solute. The approach is more accurate than standard implementations of phenomenological models in common chemistry software packages, which exhibit mean absolute errors larger than 9.12 kJ mol-1, even though newer phenomenological models achieve a mean absolute error of about 2 kJ mol-1. PC-SAFT DFT is more computationally efficient than state of the art explicit molecular simulations in combination with free energy perturbation methods. It is predictive with respect to solvation free energies, i.e., the input for the model is the (element-specific) molecular force field, the solute configuration from molecular dynamics simulations, and the (substance-specific) PC-SAFT parameters. The PC-SAFT parametrization uses pure-component data and does not require experimental solvation free energies. The PC-SAFT equation of state, without applying a DFT formalism, can also be used to calculate solvation free energies, provided that the PC-SAFT parameters for the solute are available. A large number of substances was recently parametrized by members of our group (Esper, T.; Bauer, G.; Rehner, P.; Gross, J. Ind. Eng. Chem. Res. 2023, 62), which enables a comparison to the DFT approach for 103 substances. Accurate results are obtained from the PC-SAFT equation of state with an MAE below 2.51 kJ mol-1. The DFT approach does not require PC-SAFT parameters for the solute and can be applied to all solutes that can be represented by the molecular force field.

Accelerating the 3D reference interaction site model theory of molecular solvation with treecode summation and cut-offs

The 3D reference interaction site model (3D-RISM) of molecular solvation is a powerful tool for computing the equilibrium thermodynamics and density distributions of solvents, such as water and co-ions, around solute molecules. However, 3D-RISM solutions can be expensive to calculate, especially for proteins and other large molecules where calculating the potential energy between solute and solvent requires more than half the computation time. To address this problem, we have developed and implemented treecode summation for long-range interactions and analytically corrected cut-offs for short-range interactions to accelerate the potential energy and long-range asymptotics calculations in non-periodic 3D-RISM in the AmberTools molecular modeling suite. For the largest single protein considered in this work, tubulin, the total computation time was reduced by a factor of 4. In addition, parallel calculations with these new methods scale almost linearly and the iterative solver remains the largest impediment to parallel scaling. To demonstrate the utility of our approach for large systems, we used 3D-RISM to calculate the solvation thermodynamics and density distribution of 7-ring microtubule, consisting of 910 tubulin dimers, over 1.2 million atoms.

Site Density Functional Theory and Structural Bioinformatics Analysis of the SARS-CoV Spike Protein and hACE2 Complex

The entry of the SARS-CoV-2, a causative agent of COVID-19, into human host cells is mediated by the SARS-CoV-2 spike (S) glycoprotein, which critically depends on the formation of complexes involving the spike protein receptor-binding domain (RBD) and the human cellular membrane receptor angiotensin-converting enzyme 2 (hACE2). Using classical site density functional theory (SDFT) and structural bioinformatics methods, we investigate binding and conformational properties of these complexes and study the overlooked role of water-mediated interactions. Analysis of the three-dimensional reference interaction site model (3DRISM) of SDFT indicates that water mediated interactions in the form of additional water bridges strongly increases the binding between SARS-CoV-2 spike protein and hACE2 compared to SARS-CoV-1-hACE2 complex. By analyzing structures of SARS-CoV-2 and SARS-CoV-1, we find that the homotrimer SARS-CoV-2 S receptor-binding domain (RBD) has expanded in size, indicating large conformational change relative to SARS-CoV-1 S protein. Protomer with the up-conformational form of RBD, which binds with hACE2, exhibits stronger intermolecular interactions at the RBD-ACE2 interface, with differential distributions and the inclusion of specific H-bonds in the CoV-2 complex. Further interface analysis has shown that interfacial water promotes and stabilizes the formation of CoV-2/hACE2 complex. This interaction causes a significant structural rigidification of the spike protein, favoring proteolytic processing of the S protein for the fusion of the viral and cellular membrane. Moreover, conformational dynamics simulations of RBD motions in SARS-CoV-2 and SARS-CoV-1 point to the role in modification of the RBD dynamics and their impact on infectivity.

Implicit Solvation Methods for Catalysis at Electrified Interfaces

Implicit solvation is an effective, highly coarse-grained approach in atomic-scale simulations to account for a surrounding liquid electrolyte on the level of a continuous polarizable medium. Originating in molecular chemistry with finite solutes, implicit solvation techniques are now increasingly used in the context of first-principles modeling of electrochemistry and electrocatalysis at extended (often metallic) electrodes. The prevalent ansatz to model the latter electrodes and the reactive surface chemistry at them through slabs in periodic boundary condition supercells brings its specific challenges. Foremost this concerns the difficulty of describing the entire double layer forming at the electrified solid–liquid interface (SLI) within supercell sizes tractable by commonly employed density functional theory (DFT). We review liquid solvation methodology from this specific application angle, highlighting in particular its use in the widespread ab initio thermodynamics approach to surface catalysis. Notably, implicit solvation can be employed to mimic a polarization of the electrode’s electronic density under the applied potential and the concomitant capacitive charging of the entire double layer beyond the limitations of the employed DFT supercell. Most critical for continuing advances of this effective methodology for the SLI context is the lack of pertinent (experimental or high-level theoretical) reference data needed for parametrization.

Solvation energetics of proteins and their aggregates analyzed by all-atom molecular dynamics simulations and the energy-representation theory of solvation

Solvation is a controlling factor for the structure and function of proteins. This article addresses the effects of solvation from an energetic perspective for the fluctuations and cosolvent-induced changes in protein structures and the equilibrium of aggregate formation for a peptide. A theoretical framework to analyze the solvation effects with an explicit solvent is introduced by adopting the energy-representation theory of solvation, and the connection of the solvation free energy to the protein structure and the aggregation tendency is quantitatively described in combination with all-atom molecular dynamics simulations. The interaction components that govern the solvation effects on the structural variations of proteins are further identified through correlation analysis, and a computational scheme to assess the shift of an aggregation equilibrium due to the addition of a cosolvent is provided.

Renormalized site density functional theory for models of ion hydration

The development of accurate statistical mechanics models of molecular liquid systems is a problem of great practical and fundamental importance. Site-density functional theory (SDFT) is one of the promising directions in this area, but its success hinges upon the ability to efficiently reconcile the co-existence of two distinct intra- and inter-molecular interaction regimes in a molecular liquid. The renormalized formulation of SDFT (RSDFT), which we have recently developed, resolves this problem by introducing an additional potential field variable that decouples two interaction scales and maps the molecular liquid problem onto the effective simple liquid mixture. This work provides a critical assessment of RSDFT for the hydrated ion system-a problem that historically has always been one of the most difficult cases for SDFT applications. Using a two-site model of water, we perform a comprehensive analysis of hydrated alkali metal and halogen ions, including both structural and free energy based characteristics. The results indicate that RSDFT provides a significant improvement over conventional three-dimensional reference interaction site model implementations and may prove useful in coarse grained simulations based on two-site solvent models.

Accurate prediction of hydration free energies and solvation structures using molecular density functional theory with a simple bridge functional

This paper assesses the ability of molecular density functional theory to predict efficiently and accurately the hydration free energies of molecular solutes and the surrounding microscopic water structure. A wide range of solutes were investigated, including hydrophobes, water as a solute, and the FreeSolv database containing 642 drug-like molecules having a variety of shapes and sizes. The usual second-order approximation of the theory is corrected by a third-order, angular-independent bridge functional. The overall functional is parameter-free in the sense that the only inputs are bulk water properties, independent of the solutes considered. These inputs are the direct correlation function, compressibility, liquid-gas surface tension, and excess chemical potential of the solvent. Compared to molecular simulations with the same force field and the same fixed solute geometries, the present theory is shown to describe accurately the solvation free energy and structure of both hydrophobic and hydrophilic solutes. Overall, the method yields a precision of order 0.5 k_BT for the hydration free energies of the FreeSolv database, with a computer speedup of 3 orders of magnitude. The theory remains to be improved for a better description of the H-bonding structure and the hydration free energy of charged solutes.

Predicting solvation free energies in non-polar solvents using classical density functional theory based on the PC-SAFT equation of state

We propose a predictive Density Functional Theory (DFT) for the calculation of solvation free energies. Our approach is based on a Helmholtz free-energy functional that is consistent with the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) equation of state. This allows for a coarse-grained description of the solvent based on an inhomogeneous density of PC-SAFT segments. The solute, on the other hand, is described in full detail by atomistic Lennard-Jones interaction sites. The approach is entirely predictive as it only takes the PC-SAFT parameters of the solvent and the force-field parameters of the solute as input. No adjustable parameters or empirical corrections are involved. The framework is applied to study self-solvation of n-alkanes and to the calculation of residual chemical potentials in binary solvent mixtures. Our DFT approach accurately predicts solvation free energies of small molecular solutes in three different non-polar solvents, namely n-hexane, cyclohexane, and benzene. Additionally, we show that the calculated solvation free energies agree well with those obtained by molecular dynamics simulations and with the residual chemical potential calculated by the bulk PC-SAFT equation of state. We observe higher deviations for the solvation free energy of systems with significant solute-solvent Coulomb interactions.

Chemical bond effects in classical site density functional theory of inhomogeneous molecular liquids

Intra-molecular interactions or chemical bonds represent one of the main distinguishing characteristics of molecular fluids. Development of accurate and practical methods to treat these effects is one of the long standing problems in classical site density functional theory (SDFT). One particular instance when these issues become particularly severe is the case of classical interaction potentials with auxiliary sites or dummy atoms. In this situation, current SDFT implementations, such as the three-dimensional reference interaction site model, lead to nonphysical results. We re-examine this issue in this work using our recent reformulation of SDFT (Valiev and Chuev, J. Stat. Mech.: Theory Exp. 2018, 093201). We put forward a simple practical solution to this problem and illustrate its utility for the case of spherical solutes in diatomic liquids.

Nanoporous carbon for electrochemical capacitive energy storage

This review summarizes the recent advances of nanoporous carbon materials in the application of EDLCs, including a better understanding of the charge storage mechanisms by combining the advanced techniques and simulations methods.

Dynamic Adsorption of Ions into Like-Charged Nanospace: A Dynamic Density Functional Theory Study

The adsorption processes of ions into charged nanospace are associated with many practical applications. Whereas a large number of microporous materials have been prepared toward efficient adsorption of ions from solutions, theoretical models that allow for capturing the characteristics of ion dynamic adsorption into like-charged nanopores are still few. The difficulty originates from the overlapping of electric potentials inside the pores. Herein, a theoretical model is proposed by incorporating dynamic density functional theory with modified Poisson equation for investigating the dynamic adsorption of ions into like-charged nanoslits. This model is rationalized by comparing the theoretical predictions with corresponding simulation results. Afterward, by analyzing the adsorption dynamics, we show that the overlapping effect is associated with the pore size, ion bulk concentration, and surface charge density, and it plays a dominant role in the coupling between the total adsorption amount of ions and total adsorption time. Specifically, with weak overlapping effect, the total adsorption amount is intuitively proportional to the total adsorption time; however, when the overlapping effect is strong, the total adsorption amount may be inversely proportional to the total adsorption time, indicating that both high adsorption amount and short adsorption time can be achieved simultaneously. This work provides a meaningful insight toward the rational design and optimization of microporous materials for efficient ion adsorption.

Energetics of cosolvent effect on peptide aggregation

The cosolvent effect on the equilibrium of peptide aggregation is reviewed from the energetic perspective. It is shown that the excess chemical potential is stationary against the variation of the distribution function for the configuration of a flexible solute species and that the derivative of the excess chemical potential with respect to the cosolvent concentration is determined by the corresponding derivative of the solvation free energy averaged over the solute configurations. The effect of a cosolvent at low concentrations on a chemical equilibrium can then be addressed in terms of the difference in the solvation free energy between pure-water solvent and the mixed solvent with the cosolvent, and illustrative analyses with all-atom model are presented for the aggregation of an 11-residue peptide by employing the energy-representation method to compute the solvation free energy. The solvation becomes more favorable with addition of the urea or DMSO cosolvent, and the extent of stabilization is smaller for larger aggregate. This implies that these cosolvents inhibit the formation of an aggregate, and the roles of such interaction components as the electrostatic, van der Waals, and excluded-volume are discussed.

A reaction density functional theory study of the solvent effect in prototype SN2 reactions in aqueous solution

Reaction density functional theory (RxDFT), combining quantum DFT with classical DFT, has been employed to investigate the solvent effect and free energy profiles of S_N2 reactions in aqueous solution.

Confinement Effect on Molecular Conformation of Alkanes in Water-Filled Cavitands: A Combined Quantum/Classical Density Functional Theory Study

The depletion force exerted on an alkane molecule from surrounding solvent may greatly alter its conformation. Such a behavior is closely related to the selective molecular recognition, molecular sensors, self-assembly, and so on. Herein, we report a multiscale theoretical study on the conformational change of a single alkane molecule confined in water-filled cavitands, in which the quantum and classical density functional theories (DFTs) are combined to determine the grand potential of alkane-water system. Specifically, the intrinsic free energy of the alkane molecule is tackled by quantum DFT, while the solvent effect arising from the solvent density inhomogeneity in confined space is addressed by classical DFT. By varying the alkane chain length, pore size, and wettability of inner pore surface, we find that pore confinement and hydrophilic inner surface facilitate the alkane conformational change from extended state to helical state, which becomes more significant as the alkane chain length increases. Our findings, which are in line with previous experimental observations, provide not only the microscopic mechanism but also theoretical guidance for elaborately manipulating molecular conformation at the nanoscale.

Efficient Molecular Approach to Quantifying Solvent-Mediated Interactions

The solvent-mediated interaction, or equivalently the depletion force, play a pivotal role in the processes, by which two objects in solution such as lock and key particles, antibody and antigen, macromolecule and substrate, are attracted to each other. The quantification of this interaction is important yet challenging since it depends on the microscopic solvent structure in the surrounding. Here, we report an efficient molecular approach for predicting the solvent-mediated interaction by combining the classical density functional theory with a reversible solvation thermodynamic circle. For demonstration, the solvent-mediated interactions between two nanoparticles and between a nanoparticle and a rough wall are examined, and good agreements compared with the simulation results are illustrated. This approach is thereafter employed to interpret the reported self-assembly phenomena of lock and key colloidal particles. We show that the binding probability between the lock and key colloids can be successfully characterized at different depletant concentrations and system temperatures. This approach provides a potential route for identifying the coarse-graining interaction between two objects in fluid systems.

Predicting hydration free energies of amphetamine-type stimulants with a customized molecular model

Amphetamine-type stimulants (ATS) are a group of incitation and psychedelic drugs affecting the central nervous system. Physicochemical data for these compounds are essential for understanding the stimulating mechanism, for assessing their environmental impacts, and for developing new drug detection methods. However, experimental data are scarce due to tight regulation of such illicit drugs, yet conventional methods to estimate their properties are often unreliable. Here we introduce a tailor-made multiscale procedure for predicting the hydration free energies and the solvation structures of ATS molecules by a combination of first principles calculations and the classical density functional theory. We demonstrate that the multiscale procedure performs well for a training set with similar molecular characteristics and yields good agreement with a testing set not used in the training. The theoretical predictions serve as a benchmark for the missing experimental data and, importantly, provide microscopic insights into manipulating the hydrophobicity of ATS compounds by chemical modifications.

Entropy prediction for H2 adsorption in metal-organic frameworks

Entropy is an important thermodynamic property and serves as a bridge connecting equilibrium and non-equilibrium systems, which provides a basic understanding of various practical phenomena. In this study, classical density functional theory was introduced to efficiently predict entropy. The theory was applied to a high-throughput prediction of entropy and excess entropy for H2 adsorption in metal-organic frameworks. It seems that the entropy screening and uptake screening are generally equivalent at high temperature. Based on the entropy screening, the best hydrogen storage materials have been identified. The correlations between entropy and thermodynamic properties, such as uptake, isosteric heat and adsorption degree, were examined and are explained. The results imply that among the tested thermodynamic properties, the correlation between entropy and isosteric heat is the strongest.

Molecular density functional theory of water including density-polarization coupling

We present a three-dimensional molecular density functional theory of water derived from first-principles that relies on the particle's density and multipolar polarization density and includes the density-polarization coupling. This brings two main benefits: (i) scalar density and vectorial multipolar polarization density fields are much more tractable and give more physical insight than the full position and orientation densities, and (ii) it includes the full density-polarization coupling of water, that is known to be non-vanishing but has never been taken into account. Furthermore, the theory requires only the partial charge distribution of a water molecule and three measurable bulk properties, namely the structure factor and the Fourier components of the longitudinal and transverse dielectric susceptibilities.

Parameterization of the Hamiltonian Dielectric Solvent (HADES) Reaction-Field Method for the Solvation Free Energies of Amino Acid Side-Chain Analogs

Optimization of the Hamiltonian dielectric solvent (HADES) method for biomolecular simulations in a dielectric continuum is presented with the goal of calculating accurate absolute solvation free energies while retaining the model's accuracy in predicting conformational free-energy differences. The solvation free energies of neutral and polar amino acid side-chain analogs calculated by using HADES, which may optionally include nonpolar contributions, were optimized against experimental data to reach a chemical accuracy of about 0.5 kcal mol(-1). The new parameters were evaluated for charged side-chain analogs. The HADES results were compared with explicit-solvent, generalized Born, Poisson-Boltzmann, and QM-based methods. The potentials of mean force (PMFs) between pairs of side-chain analogs obtained by using HADES and explicit-solvent simulations were used to evaluate the effects of the improved parameters optimized for solvation free energies on intermolecular potentials.

Fast Computation of Solvation Free Energies with Molecular Density Functional Theory: Thermodynamic-Ensemble Partial Molar Volume Corrections

Molecular density functional theory (MDFT) offers an efficient implicit-solvent method to estimate molecule solvation free-energies, whereas conserving a fully molecular representation of the solvent. Even within a second-order approximation for the free-energy functional, the so-called homogeneous reference fluid approximation, we show that the hydration free-energies computed for a data set of 500 organic compounds are of similar quality as those obtained from molecular dynamics free-energy perturbation simulations, with a computer cost reduced by 2-3 orders of magnitude. This requires to introduce the proper partial volume correction to transform the results from the grand canonical to the isobaric-isotherm ensemble that is pertinent to experiments. We show that this correction can be extended to 3D-RISM calculations, giving a sound theoretical justification to empirical partial molar volume corrections that have been proposed recently.

Massively parallel implementation of 3D-RISM calculation with volumetric 3D-FFT

A new three-dimensional reference interaction site model (3D-RISM) program for massively parallel machines combined with the volumetric 3D fast Fourier transform (3D-FFT) was developed, and tested on the RIKEN K supercomputer. The ordinary parallel 3D-RISM program has a limitation on the number of parallelizations because of the limitations of the slab-type 3D-FFT. The volumetric 3D-FFT relieves this limitation drastically. We tested the 3D-RISM calculation on the large and fine calculation cell (2048(3) grid points) on 16,384 nodes, each having eight CPU cores. The new 3D-RISM program achieved excellent scalability to the parallelization, running on the RIKEN K supercomputer. As a benchmark application, we employed the program, combined with molecular dynamics simulation, to analyze the oligomerization process of chymotrypsin Inhibitor 2 mutant. The results demonstrate that the massive parallel 3D-RISM program is effective to analyze the hydration properties of the large biomolecular systems.