Hydration structure, thermodynamics, and functions of protein studied by the 3D-RISM theory

Modeling the interaction of SARS-CoV-2 binding to the ACE2 receptor via molecular theory of solvation

The angiotensin-converting enzyme 2 (ACE2) protein is a cell gate receptor for the SARS-CoV-2 virus, responsible for the development of symptoms associated with the Covid-19 disease.

Solvent Composition Effects on the Structural Properties of the Aβ42 Monomer from the 3D-RISM-KH Molecular Theory of Solvation

Structural characterization of amyloid (A)β peptides implicated in Alzheimer's disease is a challenging problem due to their intrinsically disordered nature and their high propensity for aggregation. Only limited information is currently available from experiments on conformational properties and aggregation pathways of the peptides in cellular environments. In silico modeling complements experimental information, providing atomistic insight into structure and dynamics of different Aβ species. All-atom explicit solvent molecular dynamics (MD) simulations with a properly selected force field can deliver reliable structural and dynamic information. In the case of intrinsically disordered Aβ peptides, enhanced sampling simulations beyond the nanosecond time scale are required to obtain statistically meaningful results even for simple solvent conditions. To overcome the challenges of conformational sampling in crowded cellular environments, alternative approaches have to be used, including postprocessing of MD data. In this study, we employ the statistical-mechanical, three-dimensional reference interaction site model with the Kovalenko-Hirata closure integral equation molecular theory of solvation to describe solvent composition effects on the conformational equilibrium in a structural ensemble of the Aβ42 (covering residues 1-42) monomer based on a statistical reweighting technique. The methodology enables a computationally efficient prediction on how different factors in the cellular environment, such as solvent composition, nonpolar solvation, and macromolecular crowding, affect the structural properties of the monomer. Similarities have been identified between changes in the structural ensemble caused by nonpolar solvation and crowded environments modeled by ionic solution with large negative ions. In particular, both solvent conditions reduce the random coil content and enhance the helical structure content of the monomer. In contrast to the previous studies, which reported increased α-helical content of peptides in crowded environments, this work attributes these structural features to the difference in solvent exposure of hydrophilic residues of the monomer for different secondary structure elements, rather than to (entropic) excluded volume effects.

A molecular density functional theory approach to electron transfer reactions

Beyond the dielectric continuum description initiated by Marcus theory, the standard theoretical approach to study electron transfer (ET) reactions in solution or at interfaces is to use classical force field or ab initio molecular dynamics simulations. We present here an alternative method based on liquid-state theory, namely molecular density functional theory, which is numerically much more efficient than simulations while still retaining the molecular nature of the solvent. We begin by reformulating molecular ET theory in a density functional language and show how to compute the various observables characterizing ET reactions from an ensemble of density functional minimizations. In particular, we define within that formulation the relevant order parameter of the reaction, the so-called vertical energy gap, and determine the Marcus free energy curves of both reactant and product states along that coordinate. Important thermodynamic quantities such as the reaction free energy and the reorganization free energies follow. We assess the validity of the method by studying the model Cl⁰ → Cl⁺ and Cl⁰ → Cl^- ET reactions in bulk water for which molecular dynamics results are available. The anionic case is found to violate the standard Marcus theory. Finally, we take advantage of the computational efficiency of the method to study the influence of a solid-solvent interface on the ET, by investigating the evolution of the reorganization free energy of the Cl⁰ → Cl⁺ reaction when the atom approaches an atomistically resolved wall.

Potential of Mean Force Calculations of Solute Permeation Across UT-B and AQP1: A Comparison between Molecular Dynamics and 3D-RISM

Membrane channels facilitate the efficient and selective flux of various solutes across biological membranes. A common approach to investigate the selectivity of a channel has been the calculation of potentials of mean force (PMFs) for solute permeation across the pore. PMFs have been frequently computed from molecular dynamics (MD) simulations, yet the three-dimensional reference interaction site model (3D-RISM) has been suggested as a computationally efficient alternative to MD. Whether the two methods yield comparable PMFs for solute permeation has remained unclear. In this study, we calculated potentials of mean force for water, ammonia, urea, molecular oxygen, and methanol across the urea transporter B (UT-B) and aquaporin-1 (AQP1), using 3D-RISM, as well as using MD simulations and umbrella sampling. To allow direct comparison between the PMFs from 3D-RISM and MD, we ensure that all PMFs refer to a well-defined reference area in the bulk or, equivalently, to a well-defined density of channels in the membrane. For PMFs of water permeation, we found reasonable agreement between the two methods, with differences of ≲3 kJ mol-1. In contrast, we found stark discrepancies for the PMFs for all other solutes. Additional calculations confirm that discrepancies between MD and 3D-RISM are not explained by the choice for the closure relation, the definition the reaction coordinate (center of mass-based versus atomic site-based), details of the molecule force field, or fluctuations of the protein. Comparison of the PMFs suggests that 3D-RISM may underestimate effects from hydrophobic solute-channel interactions, thereby, for instance, missing the urea binding sites in UT-B. Furthermore, we speculate that the orientational averages inherent to 3D-RISM might lead to discrepancies in the narrow channel lumen. These findings suggest that current 3D-RISM solvers provide reasonable estimates for the PMF for water permeation, but that they are not suitable to study the selectivity of membrane channels with respect to uncharged nonwater solutes.

SAMPL5: 3D-RISM partition coefficient calculations with partial molar volume corrections and solute conformational sampling

Implicit solvent methods for classical molecular modeling are frequently used to provide fast, physics-based hydration free energies of macromolecules. Less commonly considered is the transferability of these methods to other solvents. The Statistical Assessment of Modeling of Proteins and Ligands 5 (SAMPL5) distribution coefficient dataset and the accompanying explicit solvent partition coefficient reference calculations provide a direct test of solvent model transferability. Here we use the 3D reference interaction site model (3D-RISM) statistical-mechanical solvation theory, with a well tested water model and a new united atom cyclohexane model, to calculate partition coefficients for the SAMPL5 dataset. The cyclohexane model performed well in training and testing ([Formula: see text] for amino acid neutral side chain analogues) but only if a parameterized solvation free energy correction was used. In contrast, the same protocol, using single solute conformations, performed poorly on the SAMPL5 dataset, obtaining [Formula: see text] compared to the reference partition coefficients, likely due to the much larger solute sizes. Including solute conformational sampling through molecular dynamics coupled with 3D-RISM (MD/3D-RISM) improved agreement with the reference calculation to [Formula: see text]. Since our initial calculations only considered partition coefficients and not distribution coefficients, solute sampling provided little benefit comparing against experiment, where ionized and tautomer states are more important. Applying a simple [Formula: see text] correction improved agreement with experiment from [Formula: see text] to [Formula: see text], despite a small number of outliers. Better agreement is possible by accounting for tautomers and improving the ionization correction.

Characterization of selective binding of biologically relevant inorganic ions with the proline zwitterion by 3D-RISM theory

The features of selective binding of several biologically relevant mono- and divalent inorganic ions with the proline zwitterion were studied over a wide range of electrolyte concentrations.

Calculation of local water densities in biological systems: a comparison of molecular dynamics simulations and the 3D-RISM-KH molecular theory of solvation

Water plays a unique role in all living organisms. Not only is it nature's ubiquitous solvent, but it also actively takes part in many cellular processes. In particular, the structure and properties of interfacial water near biomolecules such as proteins are often related to the function of the respective molecule. It can therefore be highly instructive to study the local water density around solutes in cellular systems, particularly when solvent-mediated forces such as the hydrophobic effect are relevant. Computational methods such as molecular dynamics (MD) simulations seem well suited to study these systems at the atomic level. However, due to sampling requirements, it is not clear that MD simulations are, indeed, the method of choice to obtain converged densities at a given level of precision. We here compare the calculation of local water densities with two different methods: MD simulations and the three-dimensional reference interaction site model with the Kovalenko-Hirata closure (3D-RISM-KH). In particular, we investigate the convergence of the local water density to assess the required simulation times for different levels of resolution. Moreover, we provide a quantitative comparison of the densities calculated with MD and with 3D-RISM-KH and investigate the effect of the choice of the water model for both methods. Our results show that 3D-RISM-KH yields density distributions that are very similar to those from MD up to a 0.5 Å resolution, but for significantly reduced computational cost. The combined use of MD and 3D-RISM-KH emerges as an auspicious perspective for efficient solvent sampling in dynamical systems.

Association thermodynamics and conformational stability of beta-sheet amyloid beta(17-42) oligomers: effects of E22Q (Dutch) mutation and charge neutralization

Amyloid fibrils are associated with many neurodegenerative diseases. It was found that amyloidogenic oligomers, not mature fibrils, are neurotoxic agents related to these diseases. Molecular mechanisms of infectivity, pathways of aggregation, and molecular structure of these oligomers remain elusive. Here, we use all-atom molecular dynamics, molecular mechanics combined with solvation analysis by statistical-mechanical, three-dimensional molecular theory of solvation (also known as 3D-RISM-KH) in a new MM-3D-RISM-KH method to study conformational stability, and association thermodynamics of small wild-type Abeta(17-42) oligomers with different protonation states of Glu(22), as well the E22Q (Dutch) mutants. The association free energy of small beta-sheet oligomers shows near-linear trend with the dimers being thermodynamically more stable relative to the larger constructs. The linear (within statistical uncertainty) dependence of the association free energy on complex size is a consequence of the unilateral stacking of monomers in the beta-sheet oligomers. The charge reduction of the wild-type Abeta(17-42) oligomers upon protonation of the solvent-exposed Glu(22) at acidic conditions results in lowering the association free energy compared to the wild-type oligomers at neutral pH and the E22Q mutants. The neutralization of the peptides because of the E22Q mutation only marginally affects the association free energy, with the reduction of the direct electrostatic interactions mostly compensated by the unfavorable electrostatic solvation effects. For the wild-type oligomers at acidic conditions such compensation is not complete, and the electrostatic interactions, along with the gas-phase nonpolar energetic and the overall entropic effects, contribute to the lowering of the association free energy. The differences in the association thermodynamics between the wild-type Abeta(17-42) oligomers at neutral pH and the Dutch mutants, on the one hand, and the Abeta(17-42) oligomers with protonated Glu(22), on the other, may be explained by destabilization of the inter- and intrapeptide salt bridges between Asp(23) and Lys(28). Peculiarities in the conformational stability and the association thermodynamics for the different models of the Abeta(17-42) oligomers are rationalized based on the analysis of the local physical interactions and the microscopic solvation structure.

Computing accurate potentials of mean force in electrolyte solutions with the generalized gradient-augmented harmonic Fourier beads method

We establish the accuracy of the novel generalized gradient-augmented harmonic Fourier beads (ggaHFB) method in computing free-energy profiles or potentials of mean force (PMFs) through comparison with two independent conventional techniques. In particular, we employ umbrella sampling with one dimensional weighted histogram analysis method (WHAM) and free molecular dynamics simulation of radial distribution functions to compute the PMF for the Na(+)-Cl(-) ion-pair separation to 16 A in 1.0M NaCl solution in water. The corresponding ggaHFB free-energy profile in six dimensional Cartesian space is in excellent agreement with the conventional benchmarks. We then explore changes in the PMF in response to lowering the NaCl concentration to physiological 0.3 and 0.1M, and dilute 0.0M concentrations. Finally, to expand the scope of the ggaHFB method, we formally develop the free-energy gradient approximation in arbitrary nonlinear coordinates. This formal development underscores the importance of the logarithmic Jacobian correction to reconstruct true PMFs from umbrella sampling simulations with either WHAM or ggaHFB techniques when nonlinear coordinate restraints are used with Cartesian propagators. The ability to employ nonlinear coordinates and high accuracy of the computed free-energy profiles further advocate the use of the ggaHFB method in studies of rare events in complex systems.

Three-dimensional distribution function theory for the prediction of protein-ligand binding sites and affinities: application to the binding of noble gases to hen egg-white lysozyme in aqueous solution

The three-dimensional distribution function theory of molecular liquids is applied to lysozyme in mixtures of water and noble gases. The results indicate that the theory has the capability of predicting the protein-ligand binding sites and affinities. First, it is shown that the theory successfully reproduces the binding sites of xenon found by X-ray crystallography. Then, the ability of the theory to predict the size selectivity of noble gases is demonstrated. The effect of water on the selectivity is clarified by a theoretical analysis. Finally, it is demonstrated that the dose-response curve, which is employed in experiments for examining the binding affinity, is realized by the theory.

Theoretical analysis on changes in thermodynamic quantities upon protein folding: Essential role of hydration

The free energy change associated with the coil-to-native structural transition of protein G in aqueous solution is calculated by using the molecular theory of solvation, also known as the three-dimensional reference interaction site model theory, to uncover the molecular mechanism of protein folding. The free energy is decomposed into the protein intramolecular energy, the hydration energy, and the hydration entropy. The folding is accompanied with a large gain in the protein intramolecular energy. However, it is almost canceled by the correspondingly large loss in the hydration energy due to the dehydration, resulting in the total energy gain about an order of magnitude smaller than might occur in vacuum. The hydration entropy gain is found to be a substantial driving force in protein folding. It is comparable with or even larger than the total energy gain. The total energy gain coupled with the hydration entropy gain is capable of suppressing the conformational entropy loss in the folding. Based on careful analysis of the theoretical results, the authors present a challenging physical picture of protein folding where the overall folding process is driven by the water entropy effect.