Potentials of mean force of simple ions in ambient aqueous solution. I. Three-dimensional reference interaction site model approach

Effect of caffeine on the aggregation of amyloid-β-A 3D RISM study

Alzheimer's disease is a detrimental neurological disorder caused by the formation of amyloid fibrils due to the aggregation of amyloid-β peptide. The primary therapeutic approaches for treating Alzheimer's disease are targeted to prevent this amyloid fibril formation using potential inhibitor molecules. The discovery of such inhibitor molecules poses a formidable challenge to the design of anti-amyloid drugs. This study investigates the effect of caffeine on dimer formation of the full-length amyloid-β using a combined approach of all-atom, explicit water molecular dynamics simulations and the three-dimensional reference interaction site model theory. The change in the hydration free energy of amyloid-β dimer, with and without the inhibitor molecules, is calculated with respect to the monomeric amyloid-β, where the hydration free energy is decomposed into energetic and entropic components, respectively. Dimerization is accompanied by a positive change in the partial molar volume. Dimer formation is spontaneous, which implies a decrease in the hydration free energy. However, a reverse trend is observed for the dimer with inhibitor molecules. It is observed that the negatively charged residues primarily contribute for the formation of the amyloid-β dimer. A residue-wise decomposition reveals that hydration/dehydration of the side-chain atoms of the charged amino acid residues primarily contribute to dimerization.

The Three-Dimensional Reference Interaction Site Model Approach as a Promising Tool for Studying Hydrated Viruses and Their Complexes with Ligands

Viruses are the most numerous biological form living in any ecosystem. Viral diseases affect not only people but also representatives of fauna and flora. The latest pandemic has shown how important it is for the scientific community to respond quickly to the challenge, including critically assessing the viral threat and developing appropriate measures to counter this threat. Scientists around the world are making enormous efforts to solve these problems. In silico methods, which allow quite rapid obtention of, in many cases, accurate information in this field, are effective tools for the description of various aspects of virus activity, including virus-host cell interactions, and, thus, can provide a molecular insight into the mechanism of virus functioning. The three-dimensional reference interaction site model (3D-RISM) seems to be one of the most effective and inexpensive methods to compute hydrated viruses, since the method allows us to provide efficient calculations of hydrated viruses, remaining all molecular details of the liquid environment and virus structure. The pandemic challenge has resulted in a fast increase in the number of 3D-RISM calculations devoted to hydrated viruses. To provide readers with a summary of this literature, we present a systematic overview of the 3D-RISM calculations, covering the period since 2010. We discuss various biophysical aspects of the 3D-RISM results and demonstrate capabilities, limitations, achievements, and prospects of the method using examples of viruses such as influenza, hepatitis, and SARS-CoV-2 viruses.

Elucidation of a Thermodynamical Feature Attributed to Substrate Binding to the Prokaryotic H+/Oligopeptide Cotransporter YdgR with Calorimetric Analysis: The Substrate Binding Driven by the Change in Entropy Implies the Release of Bound Water Molecules from the Binding Pocket

Here, we have elucidated the substrate recognition mechanism by a prokaryotic H⁺/oligopeptide cotransporter, YdgR, using isothermal titration calorimetry. Under acidic conditions (pH 6.0), the binding of a dipeptide, Val-Ala, to YdgR elicited endothermic enthalpy, which compensated for the increase in entropy due to dipeptide binding. A series of dipeptides were used in the binding titration. The dipeptides represent Val-X and X-Val, where X is Ala, Ser, Val, Tyr, or Phe. Most dipeptides revealed endothermic enthalpy, which was completely compensated by the increase in entropy due to dipeptide binding. The change in enthalpy due to binding correlated well with the change in entropy, whereas the Gibbs free energy involved in the binding of the dipeptide to YdgR remained unchanged irrespective of dipeptide sequences, implying that the binding reaction was driven by entropy, that is, the release of bound water molecules in the binding pocket. It is also important to clarify that, based on the prediction of water molecules in the ligand-binding pocket of YdgR, the release of three bound water molecules in the putative substrate binding pocket occurred through binding to YdgR. In the comparison of Val-X and X-Val dipeptides, the N-terminal region of the binding pocket might contain more bound water molecules than the C-terminal region. In light of these findings, we suggest that bound water molecules might play an important role in substrate recognition and binding by YdgR.

Aggregation propensities of proteins with varying degrees of disorder

The hydration thermodynamics of a globular protein (AcP), three intrinsically disordered protein regions (1CD3, 1MVF, 1F0R) and a fully disordered protein (α-synuclein) is studied by an approach that combines an all-atom explicit water molecular dynamics simulations and three-dimensional reference interaction site model (3D-RISM) theory. The variation in hydration free energy with percentage disorder of the selected proteins is investigated through its nonelectrostatic and electrostatic components. A decrease in hydration free energy is observed with an increase in percentage disorder, indicating favorable interactions of the disordered proteins with the solvent. This confirms the role of percentage disorder in determining the aggregation propensity of proteins which is measured in terms of the hydration free energy in addition to their respective mean net charge and mean hydrophobicity. The hydration free energy is decoupled into energetic and entropic terms. A residue-wise decomposition analysis of the hydration free energy for the selected proteins is evaluated. The decomposition shows that the disordered regions contribute more than the ordered ones for the intrinsically disordered protein regions. The dominant role of electrostatic interactions is confirmed from the residue-wise decomposition of the hydration free energy. The results depict that the negatively charged residues contribute more to the total hydration free energy for the proteins with negative mean net charge, while the positively charged residues contribute more for proteins with positive mean net charge.

Protein 3D Hydration: A Case of Bovine Pancreatic Trypsin Inhibitor

Characterization of the hydrated state of a protein is crucial for understanding its structural stability and function. In the present study, we have investigated the 3D hydration structure of the protein BPTI (bovine pancreatic trypsin inhibitor) by molecular dynamics (MD) and the integral equation method in the three-dimensional reference interaction site model (3D-RISM) approach. Both methods have found a well-defined hydration layer around the protein and revealed the localization of BPTI buried water molecules corresponding to the X-ray crystallography data. Moreover, under 3D-RISM calculations, the obtained positions of waters bound firmly to the BPTI sites are in reasonable agreement with the experimental results mentioned above for the BPTI crystal form. The analysis of the 3D hydration structure (thickness of hydration shell and hydration numbers) was performed for the entire protein and its polar and non-polar parts using various cut-off distances taken from the literature as well as by a straightforward procedure proposed here for determining the thickness of the hydration layer. Using the thickness of the hydration shell from this procedure allows for calculating the total hydration number of biomolecules properly under both methods. Following this approach, we have obtained the thickness of the BPTI hydration layer of 3.6 Å with 369 water molecules in the case of MD simulation and 3.9 Å with 333 water molecules in the case of the 3D-RISM approach. The above procedure was also applied for a more detailed description of the BPTI hydration structure near the polar charged and uncharged radicals as well as non-polar radicals. The results presented for the BPTI as an example bring new knowledge to the understanding of protein hydration.

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.

Developing end-point methods for absolute binding free energy calculation using the Boltzmann-quasiharmonic model

Understanding the physical forces underlying receptor-ligand binding requires robust methods for analyzing the binding thermodynamics. In end-point binding free energy methods the binding free energy is naturally decomposable into physically intuitive contributions such as the solvation free energy and configurational entropy that can provide insights. Here we present a new end-point method called EE-BQH (Effective Energy-Boltzmann-Quasiharmonic) which combines the Boltzmann-Quasiharmonic model for configurational entropy with different solvation free energy methods, such as the continuum solvent PBSA model and the integral equation-based 3D-RISM, to estimate the absolute binding free energy. We compare EE-BQH with other treatments of configurational entropy such as Quasiharmonic models in internal coordinates (QHIC) and in Cartesian coordinates (QHCC), and Normal Mode analysis (NMA), by testing them on the octa acids host-guest complexes from the SAMPL8 blind challenge. The accuracies in the calculated absolute binding free energies strongly depend on the configurational entropy and solvation free energy methods used. QHIC and BQH yield the best agreements with the established potential of mean force (PMF) estimates, with R² of ∼0.7 and mean unsigned error of ∼1.7 kcal mol^-1. These results from the end-point calculations are also in similar agreement with experiments. While 3D-RISM in combination with QHIC or BQH lead to reasonable correlations with the PMF results and experiments, the calculated absolute binding free energies are underestimated by ∼5 kcal mol^-1. While the binding is accompanied by a significant reduction in the ligand translational/rotational entropy, the change in the torsional entropy in these host-guest systems is slightly positive. Compared with BQH, QHIC underestimates the reduction of configurational entropy because of the non-Gaussian probability distributions in the ligand rotation and a small number of torsions. The study highlights the crucial role of configurational entropy in determining binding and demonstrates the potential of using the new end-point method to provide insights in more complex protein-ligand systems.

Integral equation models for solvent in macromolecular crystals

The solvent can occupy up to ∼70% of macromolecular crystals, and hence, having models that predict solvent distributions in periodic systems could improve the interpretation of crystallographic data. Yet, there are few implicit solvent models applicable to periodic solutes, and crystallographic structures are commonly solved assuming a flat solvent model. Here, we present a newly developed periodic version of the 3D-reference interaction site model (RISM) integral equation method that is able to solve efficiently and describe accurately water and ion distributions in periodic systems; the code can compute accurate gradients that can be used in minimizations or molecular dynamics simulations. The new method includes an extension of the Ornstein–Zernike equation needed to yield charge neutrality for charged solutes, which requires an additional contribution to the excess chemical potential that has not been previously identified; this is an important consideration for nucleic acids or any other charged system where most or all the counter- and co-ions are part of the “disordered” solvent. We present several calculations of proteins, RNAs, and small molecule crystals to show that x-ray scattering intensities and the solvent structure predicted by the periodic 3D-RISM solvent model are in closer agreement with the experiment than are intensities computed using the default flat solvent model in the refmac5 or phenix refinement programs, with the greatest improvement in the 2 to 4 Å range. Prospects for incorporating integral equation models into crystallographic refinement are discussed.

Ion Pairing of the Neurotransmitters Acetylcholine and Glutamate in Aqueous Solutions

Neurotransmitters (NTs) play an important role in neural communication, regulating a variety of functions such as motivation, learning, memory, and muscle contraction. Their intermolecular interactions in biological media are an important factor affecting their biological activity. However, the available information on the features of these interactions is scarce and contradictory, especially, in an estimation of possible ion binding. In this paper, we present the results of a study for two well-known NTs, acetylcholine (ACh) and glutamate (Glu), with relation to the NT-inorganic ion and the NT-NT binding in a water environment. The features of NT pairing are investigated in aqueous AChCl and NaGlu solutions over a wide concentration range using the integral equation method in 1D- and 3D- reference interaction site model (RISM) approaches. The data for ACh are given for its two bioactive TG (trans, gauche) and TT (trans, trans) conformers. As was found, for both NTs, the results indicate the NT-inorganic counterion contact pair to be the predominant associate type in the concentrated solutions. In this case, the counterions occupy the vacated "water" space in the hydration shell of the onium moiety (ACh) or carboxylate groups (Glu). For ACh, the "unfolded" TT conformer demonstrates a slightly greater possibility for counterion pairing in comparison with the "folded" TG conformer. For Glu, the probability of its binding with a counterion is slightly stronger for the "side-chain" carboxylate group than for the "backbone" group. The obtained results also revealed an insignificant probability of Glu^--Glu^- pairing. Namely, the RISM data indicate Glu^--Glu^- binding by NH₃⁺-COO^- interactions. A link between the ion binding of NTs and their biological activity is discussed. This contribution adds new knowledge to our understanding of the interactions between the NTs and their molecular environment, providing further insights into the behavior of these compounds in biological media.

A Joint Venture of Ab Initio Molecular Dynamics, Coupled Cluster Electronic Structure Methods, and Liquid-State Theory to Compute Accurate Isotropic Hyperfine Constants of Nitroxide Probes in Water

The isotropic hyperfine coupling constant (HFCC, Aiso) of a pH-sensitive spin probe in a solution, HMI (2,2,3,4,5,5-hexamethylimidazolidin-1-oxyl, C9H19N2O) in water, is computed using an ensemble of state-of-the-art computational techniques and is gauged against X-band continuous wave electron paramagnetic resonance (EPR) measurement spectra at room temperature. Fundamentally, the investigation aims to delineate the cutting edge of current first-principles-based calculations of EPR parameters in aqueous solutions based on using rigorous statistical mechanics combined with correlated electronic structure techniques. In particular, the impact of solvation is described by exploiting fully atomistic, RISM integral equation, and implicit solvation approaches as offered by ab initio molecular dynamics (AIMD) of the periodic bulk solution (using the spin-polarized revPBE0-D3 hybrid functional), embedded cluster reference interaction site model integral equation theory (EC-RISM), and polarizable continuum embedding (using CPCM) of microsolvated complexes, respectively. HFCCs are obtained from efficient coupled cluster calculations (using open-shell DLPNO-CCSD theory) as well as from hybrid density functional theory (using revPBE0-D3). Re-solvation of "vertically desolvated" spin probe configuration snapshots by EC-RISM embedding is shown to provide significantly improved results compared to CPCM since only the former captures the inherent structural heterogeneity of the solvent close to the spin probe. The average values of the Aiso parameter obtained based on configurational statistics using explicit water within AIMD and from EC-RISM solvation are found to be satisfactorily close. Using either such explicit or RISM solvation in conjunction with DLPNO-CCSD calculations of the HFCCs provides an average Aiso parameter for HMI in aqueous solution at 300 K and 1 bar that is in good agreement with the experimentally determined one. The developed computational strategy is general in the sense that it can be readily applied to other spin probes of similar molecular complexity, to aqueous solutions beyond ambient conditions, as well as to other solvents in the longer run.

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.

Biomolecular Simulations with the Three-Dimensional Reference Interaction Site Model with the Kovalenko-Hirata Closure Molecular Solvation Theory

The statistical mechanics-based 3-dimensional reference interaction site model with the Kovalenko-Hirata closure (3D-RISM-KH) molecular solvation theory has proven to be an essential part of a multiscale modeling framework, covering a vast region of molecular simulation techniques. The successful application ranges from the small molecule solvation energy to the bulk phase behavior of polymers, macromolecules, etc. The 3D-RISM-KH successfully predicts and explains the molecular mechanisms of self-assembly and aggregation of proteins and peptides related to neurodegeneration, protein-ligand binding, and structure-function related solvation properties. Upon coupling the 3D-RISM-KH theory with a novel multiple time-step molecular dynamic (MD) of the solute biomolecule stabilized by the optimized isokinetic Nosé-Hoover chain thermostat driven by effective solvation forces obtained from 3D-RISM-KH and extrapolated forward by generalized solvation force extrapolation (GSFE), gigantic outer time-steps up to picoseconds to accurately calculate equilibrium properties were obtained in this new quasidynamics protocol. The multiscale OIN/GSFE/3D-RISM-KH algorithm was implemented in the Amber package and well documented for fully flexible model of alanine dipeptide, miniprotein 1L2Y, and protein G in aqueous solution, with a solvent sampling rate ~150 times faster than a standard MD simulation in explicit water. Further acceleration in computation can be achieved by modifying the extent of solvation layers considered in the calculation, as well as by modifying existing closure relations. This enhanced simulation technique has proven applications in protein-ligand binding energy calculations, ligand/solvent binding site prediction, molecular solvation energy calculations, etc. Applications of the RISM-KH theory in molecular simulation are discussed in this work.

Progress toward B-Cell Lymphoma 6 BTB Domain Inhibitors for the Treatment of Diffuse Large B-Cell Lymphoma and Beyond

B-cell lymphoma 6 (BCL6) is a master regulator of germinal center formation that produce antibody-secreting plasma cells and memory B-cells for sustained immune responses. The BTB domain of BCL6 (BCL6^BTB) forms a homodimer that mediates transcriptional repression by recruiting its corepressor proteins to form a biologically functional transcriptional complex. The protein-protein interaction (PPI) between the BCL6^BTB and its corepressors has emerged as a therapeutic target for the treatment of DLBCL and a number of other human cancers. This Perspective provides an overview of recent advances in the development of BCL6^BTB inhibitors from reversible inhibitors, irreversible inhibitors, to BCL6 degraders. Inhibitor design and medicinal chemistry strategies for the development of novel compounds will be provided. The binding mode of new inhibitors to BCL6^BTB are highlighted. Also, the in vitro and in vivo assays used for the evaluation of new compounds will be discussed.

Hydration Thermodynamics of Familial Parkinson's Disease-Linked Mutants of α-Synuclein

The hydration thermodynamics of different mutants of α-synuclein (α-syn) related to familial Parkinson's disease (PD) is explored using a computational approach that combines both molecular dynamics simulations in water and integral equation theory of molecular liquids. This analysis focuses on the change in conformational entropy, hydration free energy (HFE), and partial molar volume of α-syn upon mutation. The results show that A53T, A30P, E46K, and H50Q mutants aggregate more readily and display increased HFE and less negative interaction volume than the wild-type α-syn. In contrast, an opposite trend is observed for the G51D mutant with a lower experimental aggregation rate. The residuewise decomposition analysis of the HFE highlights that the dehydration/hydration of the hydrophilic residue-rich N- and C-termini of α-syn majorly contributes to the change upon mutation. The hydration shell contributions of different residues to the interaction volume are consistent with its increase/decrease upon mutation. This work shows that both HFE and interaction volume determine the aggregation kinetics of α-syn upon mutation and may serve as an appropriate benchmark for the treatment of PD.

Hydration Thermodynamics of the N-Terminal FAD Mutants of Amyloid-β

The hydration thermodynamics of amyloid-β (Aβ) and its pathogenic familial Alzheimer's disease (FAD) mutants such as A2V, Taiwan (D7H), Tottori (D7N), and English (H6R) and the protective A2T mutant is investigated by a combination of all-atom, explicit water molecular dynamics (MD) simulations and the three-dimensional reference interaction site model (3D-RISM) theory. The change in the hydration free energy on mutation is decomposed into the energetic and entropic components, which comprise electrostatic and nonelectrostatic contributions. An increase in the hydration free energy is observed for A2V, D7H, D7N, and H6R mutations that increase the aggregation propensity of Aβ and lead to an early onset of Alzheimer's disease, while a reverse trend is noted for the protective A2T mutation. An antiphase correlation is found between the change in the hydration energy and the internal energy of Aβ upon mutation. A residue-wise decomposition analysis shows that the change in the hydration free energy of Aβ on mutation is primarily due to the hydration/dehydration of the side-chain atoms of the negatively charged residues. The decrease in the hydration of the negatively charged residues on mutation may decrease the solubility of the mutant, which increases the observed aggregation propensity of the FAD mutants. Results obtained from the theory show an excellent match with the experimentally reported data.

A computational method to simulate global conformational changes of proteins induced by cosolvent

A computational method to investigate the global conformational change of a protein is proposed by combining the linear response path following (LRPF) method and three-dimensional reference interaction site model (3D-RISM) theory, which is referred to as the LRPF/3D-RISM method. The proposed method makes it possible to efficiently simulate protein conformational changes caused by either solutions of varying concentrations or the presence of cosolvent species by taking advantage of the LRPF and 3D-RISM. The proposed method is applied to the urea-induced denaturation of ubiquitin. The LRPF/3D-RISM trajectories successfully simulate the early stage of the denaturation process within the simulation time of 300 ns, whereas no significant structural change is observed even in the 1 μs standard MD simulation. The obtained LRPF/3D-RISM trajectories reproduce the mechanism of the urea denaturation of ubiquitin reported in previous studies, and demonstrate the high efficiency of the method.

Failure of molecular dynamics to provide appropriate structures for quantum mechanical description of the aqueous chloride ion charge-transfer-to-solvent ultraviolet spectrum

The lowest band in the charge-transfer-to-solvent ultraviolet absorption spectrum of aqueous chloride ion is studied by experiment and computation. Interestingly, the experiments indicate that at concentrations up to at least 0.25 M, where calculations indicate ion pairing to be significant, there is no notable effect of ionic strength on the spectrum. The experimental spectra are fitted to aid comparison with computations. Classical molecular dynamic simulations are carried out on dilute aqueous Cl-, Na+, and NaCl, producing radial distribution functions in reasonable agreement with experiment and, for NaCl, clear evidence of ion pairing. Clusters are extracted from the simulations for quantum mechanical excited state calculations. Accurate ab initio coupled-cluster benchmark calculations on a small number of representative clusters are carried out and used to identify and validate an efficient protocol based on time-dependent density functional theory. The latter is used to carry out quantum mechanical calculations on thousands of clusters. The resulting computed spectrum is in excellent agreement with experiment for the peak position, with little influence from ion pairing, but is in qualitative disagreement on the width, being only about half as wide. It is concluded that simulation by classical molecular dynamics fails to provide an adequate variety of structures to explain the experimental CTTS spectrum of aqueous Cl-.

Dynamics of Ionic Interactions at Protein-Nucleic Acid Interfaces

Molecular association of proteins with nucleic acids is required for many biological processes essential to life. Electrostatic interactions via ion pairs (salt bridges) of nucleic acid phosphates and protein side chains are crucial for proteins to bind to DNA or RNA. Counterions around the macromolecules are also key constituents for the thermodynamics of protein–nucleic acid association. Until recently, there had been only a limited amount of experiment-based information about how ions and ionic moieties behave in biological macromolecular processes. In the past decade, there has been significant progress in quantitative experimental research on ionic interactions with nucleic acids and their complexes with proteins. The highly negatively charged surfaces of DNA and RNA electrostatically attract and condense cations, creating a zone called the ion atmosphere. Recent experimental studies were able to examine and validate theoretical models on ions and their mobility and interactions with macromolecules. The ionic interactions are highly dynamic. The counterions rapidly diffuse within the ion atmosphere. Some of the ions are released from the ion atmosphere when proteins bind to nucleic acids, balancing the charge via intermolecular ion pairs of positively charged side chains and negatively charged backbone phosphates. Previously, the release of counterions had been implicated indirectly by the salt-concentration dependence of the association constant.

Recently, direct detection of counterion release by NMR spectroscopy has become possible and enabled more accurate and quantitative analysis of the counterion release and its entropic impact on the thermodynamics of protein–nucleic acid association. Recent studies also revealed the dynamic nature of ion pairs of protein side chains and nucleic acid phosphates. These ion pairs undergo transitions between two major states. In one of the major states, the cation and the anion are in direct contact and form hydrogen bonds. In the other major state, the cation and the anion are separated by water. Transitions between these states rapidly occur on a picosecond to nanosecond time scale. When proteins interact with nucleic acids, interfacial arginine (Arg) and lysine (Lys) side chains exhibit considerably different behaviors. Arg side chains show a higher propensity to form rigid contacts with nucleotide bases, whereas Lys side chains tend to be more mobile at the molecular interfaces. The dynamic ionic interactions may facilitate adaptive molecular recognition and play both thermodynamic and kinetic roles in protein–nucleic acid interactions.

Evaluation of an Efficient 3D-RISM-SCF Implementation as a Tool for Computational Spectroscopy in Solution

The 3D-RISM-SCF solvent-model implementation of Gusarov et al. [ J. Phys. Chem. A 2006, 110, 6083-6090] in the Amsterdam density functional program has been improved and extended. In particular, an accurate yet efficient representation of the solute electrostatic potential is provided. The Coulomb-potential fitting of many DFT codes can be used advantageously in this context. The extra effort compared to a point-charge representation is small for a given SCF cycle and compensated by faster SCF convergence. This allows applications to large solutes, as demonstrated by evaluation of the solvatochromism of Reichardt's dye. In general, TDDFT applications to excitation energies in solution stand out and are highlighted. Applications to the ¹⁷O NMR chemical shifts of N-methylformamide in different solvents also demonstrate the distinct advantages of 3D-RISM over continuum solvents. Limitations are observed in this case for water solvent, where the solvent shielding is overestimated. This shortcoming applies also to the ¹⁷O gas-to-liquid shift of water, where we used localized molecular orbital analyses for a deeper understanding. For such cases of extremely strong solute-solvent interactions, couplings between solute and solvent orbitals induced by the magnetic perturbation are relevant. These clearly require a quantum-mechanical treatment of the most closely bound solvent molecules. Except for such extreme cases, 3D-RISM-SCF is very well suited to treat solvent effects on NMR parameters. More serious limitations pertain to the treatment of vibrational spectra, where the absence of the coupling between solute and solvent vibrational modes limits the accuracy of applications of 3D-RISM-SCF. The reported extended, efficient, and numerically accurate 3D-RISM-SCF implementation should provide a useful tool to study chemical and spectroscopic properties of molecules of appreciable size in a realistic solvent environment.

Adsorption of CO2 and CH4 in MIL-47 investigated by the 3D-RISM molecular theory of solvation

Metal-organic frameworks (MOFs) comprise a class of highly porous nanomaterials formed by the assembly of organic molecular templates connected by metal ions. These materials exhibit a large diversity of pore size and geometry, topology, surface area, and chemical functionality. MOFs are particularly promising materials for developing new technologies for capture and storage of greenhouse gases such as methane and carbon dioxide. Here we apply the three dimensional reference interaction site model (3D-RISM) molecular theory of solvation to study the interactions of CO₂ and CH₄ with the metal-organic material MIL-47. The 3D-RISM integral equations were solved to determine the three dimensional density correlation functions of the gas (solvent) relative to the atomic positions of the MIL-47 framework, treated as static solute sites. The computed solvent spatial distributions inside MIL-47 pores were used to identify whether or not there exist preferable binding sites and the binding free energy landscape for the gas of interest at low computational costs compared with other molecular modeling techniques, such as grand canonical Monte Carlo and molecular dynamics simulations. The 3D-RISM formalism was applied to pure CO₂, pure CH₄, and binary mixtures of these gases of various compositions under different pressure conditions. The results indicate that both gases bind very weakly to MIL-47 and that this material exhibits nearly vanishing CO₂/CH₄ selectivity. The 3D-RISM computations presented here can be extended to investigate the physical adsorption of gases on other MOFs and nanoporous materials, providing an alternative low-cost computational approach to study gas capture and storage in nanoporous materials in general and, in particular, to determine the binding free-energy landscape in these systems.

Systematic microsolvation approach with a cluster-continuum scheme and conformational sampling

Solvation is a notoriously difficult and nagging problem for the rigorous theoretical description of chemistry in the liquid phase. Successes and failures of various approaches ranging from implicit solvation modeling through dielectric continuum embedding and microsolvated quantum chemical modeling to explicit molecular dynamics highlight this situation. Here, we focus on quantum chemical microsolvation and discuss an explicit conformational sampling ansatz to make this approach systematic. For this purpose, we introduce an algorithm for rolling and automated microsolvation of solutes. Our protocol takes conformational sampling and rearrangements in the solvent shell into account. Its reliability is assessed by monitoring the evolution of the spread and average of the observables of interest.

Mutation-induced change in chignolin stability from π-turn to α-turn

A mutation from threonine to proline at the eighth residue in chignolin changes π-turn to α-turn.

Enhanced solvation force extrapolation for speeding up molecular dynamics simulations of complex biochemical liquids

We propose an enhanced approach to the extrapolation of mean potential forces acting on atoms of solute macromolecules due to their interactions with solvent atoms in complex biochemical liquids. It improves and extends our previous extrapolation schemes by additionally including new techniques such as an exponential scaling transformation of coordinate space with weights complemented by an automatically adjusted balancing between the least square minimization of force deviations and the norm of expansion coefficients in the approximation. The expensive mean potential forces are treated in terms of the three-dimensional reference interaction site model with Kovalenko-Hirata closure molecular theory of solvation. During the dynamics, they are calculated only after every long (outer) time interval, i.e., quite rarely to reduce the computational costs. At much shorter (inner) time steps, these forces are extrapolated on the basis of their outer values. The equations of motion are then solved using a multiple time step integration within an optimized isokinetic Nosé-Hoover chain thermostat. The new approach is applied to molecular dynamics simulations of various systems consisting of solvated organic and biomolecules of different complexity. For example, we consider hydrated alanine dipeptide, asphaltene in toluene solvent, miniprotein 1L2Y, and protein G in aqueous solution. It is shown that in all these cases, the enhanced extrapolation provides much better accuracy of the solvation force approximation than the existing approaches. As a result, it can be used with much larger outer time steps, leading to a significant speedup of the simulations.

Distinct ionic adsorption sites in defective Prussian blue: a 3D-RISM study

Ferric hexacyanoferrate (FeHCF) or Prussian blue (PB) exhibits selective alkali ion adsorption and has great potential for use in various applications. In the present work, alkali ion (Li⁺, Na⁺, K⁺, and Cs⁺) and water configurations in defective PB (d-PB) were studied by using the statistical mechanics of molecular liquids. The three-dimensional (3D) distribution functions of the ions and water were determined by solving the 3D-reference interaction site model (RISM) equation of systems of a unit lattice of d-PB in electrolyte solutions, i.e., LiCl, NaCl, KCl, and CsCl. The results show the difference in the ion-water configurations and distributions between small (Li⁺ and Na⁺) and large ions (K⁺ and Cs⁺). The adsorption sites of Li⁺ and Na⁺ are located off-center and lie on the diagonal axis. By contrast, the larger ions, K⁺ and Cs⁺, are adsorbed at the center of the unit cell. The degree of dehydration due to the adsorption of alkali ions indicates that there was no water exchange during Li⁺ and Na⁺ adsorption, whereas two and three water molecules were removed after adsorption of K⁺ or Cs⁺ in the unit cell.

A molecular reconstruction approach to site-based 3D-RISM and comparison to GIST hydration thermodynamic maps in an enzyme active site

Computed, high-resolution, spatial distributions of solvation energy and entropy can provide detailed information about the role of water in molecular recognition. While grid inhomogeneous solvation theory (GIST) provides rigorous, detailed thermodynamic information from explicit solvent molecular dynamics simulations, recent developments in the 3D reference interaction site model (3D-RISM) theory allow many of the same quantities to be calculated in a fraction of the time. However, 3D-RISM produces atomic-site, rather than molecular, density distributions, which are difficult to extract physical meaning from. To overcome this difficulty, we introduce a method to reconstruct molecular density distributions from atomic-site density distributions. Furthermore, we assess the quality of the resulting solvation thermodynamics density distributions by analyzing the binding site of coagulation Factor Xa with both GIST and 3D-RISM. We find good qualitative agreement between the methods for oxygen and hydrogen densities as well as direct solute-solvent energetic interactions. However, 3D-RISM predicts lower energetic and entropic penalties for moving water from the bulk to the binding site.

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.

Predicting Site-Binding Modes of Ions and Water to Nucleic Acids Using Molecular Solvation Theory

Site binding of ions and water shapes nucleic acids folding, dynamics, and biological function, complementing the more diffuse, nonspecific "territorial" ion binding. Unlike territorial binding, prediction of site-specific binding to nucleic acids remains an unsolved challenge in computational biophysics. This work presents a new toolset based on the 3D-RISM molecular solvation theory and topological analysis that predicts cation and water site binding to nucleic acids. 3D-RISM is shown to accurately capture alkali cations and water binding to the central channel, transversal loops, and grooves of the Oxytricha nova's telomeres' G-quadruplex ( Oxy-GQ), in agreement with high-resolution crystallographic data. To improve the computed cation occupancy along the Oxy-GQ central channel, it was necessary to refine and validate new cation-oxygen parameters using structural and thermodynamic data available for crown ethers and ion channels. This single set of parameters that describes both localized and delocalized binding to various biological systems is used to gain insight into cation occupancy along the Oxy-GQ channel under various salt conditions. The paper concludes with prospects for extending the method to predict divalent cation binding to nucleic acids. This work advances the forefront of theoretical methods able to provide predictive insight into ion atmosphere effects on nucleic acids function.

3D matters! 3D-RISM and 3D convolutional neural network for accurate bioaccumulation prediction

In this work, we present a new method for predicting complex physical-chemical properties of organic molecules. The approach utilizes 3D convolutional neural network (ActivNet4) that uses solvent spatial distributions around solutes as input. These spatial distributions are obtained by a molecular theory called three-dimensional reference interaction site model. We have shown that the method allows one to achieve a good accuracy of prediction of bioconcentration factor which is difficult to predict by direct application of methods of molecular theory or simulations. Our research demonstrates that combination of molecular theories with modern machine learning approaches can be effectively used for predicting properties that are otherwise inaccessible to purely theory-based models.

Characterizing hydration sites in protein-ligand complexes towards the design of novel ligands

Water is an essential part of protein binding sites and mediates interactions to ligands. Its displacement by ligand parts affects the free binding energy of resulting protein-ligand complexes. Therefore the characterization of solvation properties is important for design. Of particular interest is the propensity of localized water to be favorably displaced by a ligand. This review discusses two popular computational approaches addressing these questions, namely WaterMap based on statistical mechanics analysis of MD simulations and 3D RISM based on integral equation theory of liquids. The theoretical background and recent applications in structure-based design will be presented.

Structure and permeability of ionomers studied by atomistic molecular simulation combined with the theory of solutions in the energy representation

Ionomers play a key role in forming the catalyst layer of polymer electrolyte fuel cells. In the present work, we performed atomistic molecular dynamics simulations and free-energy calculations with the energy-representation method for sulfonated polyethersulfone (SPES) and its derivatives toward the rational design of ionomers for carbon alloy catalysts. It was observed that H₂O aggregates strongly in the branched SPES systems with fluorocarbons and is located homogeneously in the systems without fluorocarbons. The O₂ permeability was then examined within the framework of the solubility-diffusion mechanism. The permeability was seen to be large for the branched SPES with fluorocarbons, indicating that the performance of ionomers as a permeation medium for O₂ may be tuned by the flexibility and branching of the polymer chain.

Influence of Solvent Representation on Nuclear Shielding Calculations of Protonation States of Small Biological Molecules

In this study, we assess the influence of solvation on the accuracy and reliability of isotropic nuclear magnetic shielding calculations for amino acids in comparison to experimental data. We focus particularly on the performance of solvation methods for different protonation states, as biological molecules occur almost exclusively in aqueous solution and are subject to protonation with pH. We identify significant shortcomings of current implicit solvent models and present a hybrid solvation approach that improves agreement with experimental data by taking into account the presence of direct interactions between amino acid protonation state and water molecules.

Architecture and hydration of the arginine-binding site of neuropilin-1

Neuropilin‐1 (NRP1) is a transmembrane co‐receptor involved in binding interactions with variety of ligands and receptors, including receptor tyrosine kinases. Expression of NRP1 in several cancers correlates with cancer stages and poor prognosis. Thus, NRP1 has been considered a therapeutic target and is the focus of multiple drug discovery initiatives. Vascular endothelial growth factor (VEGF) binds to the b1 domain of NRP1 through interactions between the C‐terminal arginine of VEGF and residues in the NRP1‐binding site including Tyr297, Tyr353, Asp320, Ser346 and Thr349. We obtained several complexes of the synthetic ligands and the NRP1‐b1 domain and used X‐ray crystallography and computational methods to analyse atomic details and hydration profile of this binding site. We observed side chain flexibility for Tyr297 and Asp320 in the six new high‐resolution crystal structures of arginine analogues bound to NRP1. In addition, we identified conserved water molecules in binding site regions which can be targeted for drug design. The computational prediction of the VEGF ligand‐binding site hydration map of NRP1 was in agreement with the experimentally derived, conserved hydration structure. Displacement of certain conserved water molecules by a ligand's functional groups may contribute to binding affinity, whilst other water molecules perform as protein–ligand bridges. Our report provides a comprehensive description of the binding site for the peptidic ligands’ C‐terminal arginines in the b1 domain of NRP1, highlights the importance of conserved structural waters in drug design and validates the utility of the computational hydration map prediction method in the context of neuropilin.

Database

The structures were deposited to the PDB with accession numbers PDB ID: 5IJR, 5IYY, 5JHK, 5J1X, 5JGQ, 5JGI.

Multiscale methods framework: self-consistent coupling of molecular theory of solvation with quantum chemistry, molecular simulations, and dissipative particle dynamics

In this work, we will address different aspects of self-consistent field coupling of computational chemistry methods at different time and length scales in modern materials and biomolecular science.

Discovery of Pyrazolo[1,5-a]pyrimidine B-Cell Lymphoma 6 (BCL6) Binders and Optimization to High Affinity Macrocyclic Inhibitors

Inhibition of the protein-protein interaction between B-cell lymphoma 6 (BCL6) and corepressors has been implicated as a therapeutic target in diffuse large B-cell lymphoma (DLBCL) cancers and profiling of potent and selective BCL6 inhibitors are critical to test this hypothesis. We identified a pyrazolo[1,5-a]pyrimidine series of BCL6 binders from a fragment screen in parallel with a virtual screen. Using structure-based drug design, binding affinity was increased 100000-fold. This involved displacing crystallographic water, forming new ligand-protein interactions and a macrocyclization to favor the bioactive conformation of the ligands. Optimization for slow off-rate constant kinetics was conducted as well as improving selectivity against an off-target kinase, CK2. Potency in a cellular BCL6 assay was further optimized to afford highly selective probe molecules. Only weak antiproliferative effects were observed across a number of DLBCL lines and a multiple myeloma cell line without a clear relationship to BCL6 potency. As a result, we conclude that the BCL6 hypothesis in DLBCL cancer remains unproven.

Simple Physics-Based Analytical Formulas for the Potentials of Mean Force of the Interaction of Amino Acid Side Chains in Water. VII. Charged-Hydrophobic/Polar and Polar-Hydrophobic/Polar Side Chains

The physics-based potentials of side-chain-side-chain interactions corresponding to pairs composed of charged and polar, polar and polar, charged and hydrophobic, and hydrophobic and hydrophobic side chains have been determined. A total of 144 four-dimensional potentials of mean force (PMFs) of all possible pairs of molecules modeling these pairs were determined by umbrella-sampling molecular dynamics simulations in explicit water as functions of distance and orientation, and the analytical expressions were then fitted to the PMFs. Depending on the type of interacting sites, the analytical approximation to the PMF is a sum of terms corresponding to van der Waals interactions and cavity-creation involving the nonpolar sections of the side chains and van der Waals, cavity-creation, and electrostatic (charge-dipole or dipole-dipole) interaction energies and polarization energies involving the charged or polar sections of the side chains. The model used in this work reproduces all features of the interacting pairs. The UNited RESidue force field with the new side-chain-side-chain interaction potentials was preliminarily tested with the N-terminal part of the B-domain of staphylococcal protein A (PDBL 1BDD ; a three-α-helix bundle) and UPF0291 protein YnzC from Bacillus subtilis (PDB: 2HEP ; an α-helical hairpin).