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

RISMiCal: A software package to perform fast RISM/3D-RISM calculations

Solvent plays an essential role in a variety of chemical, physical, and biological processes that occur in the solution phase. The reference interaction site model (RISM) and its three-dimensional extension (3D-RISM) serve as powerful computational tools for modeling solvation effects in chemical reactions, biological functions, and structure formations. We present the RISM integrated calculator (RISMiCal) program package, which is based on RISM and 3D-RISM theories with fast GPU code. RISMiCal has been developed as an integrated RISM/3D-RISM program that has interfaces with external programs such as Gaussian16, GAMESS, and Tinker. Fast 3D-RISM programs for single- and multi-GPU codes written in CUDA would enhance the availability of these hybrid methods because they require the performance of many computationally expensive 3D-RISM calculations. We expect that our package can be widely applied for chemical and biological processes in solvent. The RISMiCal package is available at https://rismical-dev.github.io.

Effect of Main and Side Chains on the Folding Mechanism of the Trp-Cage Miniprotein

Proteins that do not fold into their functional native state have been linked to diseases. In this study, the influence of the main and side chains of individual amino acids on the folding of the tryptophan cage (Trp-cage), a designed 20-residue miniprotein, was analyzed. For this purpose, we calculated the solvation free energy (SFE) contributions of individual atoms by using the 3D-reference interaction site model with the atomic decomposition method. The mechanism by which the Trp-cage is stabilized during the folding process was examined by calculating the total energy, which is the sum of the conformational energy and SFE. The folding process of the Trp-cage resulted in a stable native state, with a total energy that was 62.4 kcal/mol lower than that of the unfolded state. The solvation entropy, which is considered to be responsible for the hydrophobic effect, contributed 31.3 kcal/mol to structural stabilization. In other words, the contribution of the solvation entropy accounted for approximately half of the total contribution to Trp-cage folding. The hydrophobic core centered on Trp6 contributed 15.6 kcal/mol to the total energy, whereas the solvation entropy contribution was 6.3 kcal/mol. The salt bridge formed by the hydrophilic side chains of Asp9 and Arg16 contributed 10.9 and 5.0 kcal/mol, respectively. This indicates that not only the hydrophobic core but also the salt bridge of the hydrophilic side chains gain solvation entropy and contribute to stabilizing the native structure of the Trp-cage.

Structure-yeast α-glucosidase inhibitory activity relationship of 9-O-berberrubine carboxylates

Thirty-five 9-O-berberrubine carboxylate derivatives were synthesized and evaluated for yeast α-glucosidase inhibitory activity. All compounds demonstrated better inhibitory activities than the parent compounds berberine (BBR) and berberrubine (BBRB), and a positive control, acarbose. The structure-activity correlation study indicated that most of the substituents on the benzoate moiety such as methoxy, hydroxy, methylenedioxy, benzyloxy, halogen, trifluoromethyl, nitro and alkyl can contribute to the activities except multi-methoxy, fluoro and cyano. In addition, replacing benzoate with naphthoate, cinnamate, piperate or diphenylacetate also led to an increase in inhibitory activities except with phenyl acetate. 9, 26, 27, 28 and 33 exhibited the most potent α-glucosidase inhibitory activities with the IC50 values in the range of 1.61-2.67 μM. Kinetic study revealed that 9, 26, 28 and 33 interacted with the enzyme via competitive mode. These four compounds were also proved to be not cytotoxic at their IC50 values. The competitive inhibition mechanism of these four compounds against yeast α-glucosidase was investigated using molecular docking and molecular dynamics simulations. The binding free energy calculations suggest that 26 exhibited the strongest binding affinity, and its binding stability is supported by hydrophobic interactions with D68, F157, F158 and F177. Therefore, 9, 26, 28 and 33 would be promising candidates for further studies of antidiabetic activity.

Theoretical Analysis of the Role of Water in Ligand Binding to Cucurbit[n]uril of Different Sizes

The role of water in host-ligand binding was investigated using a combination of molecular dynamics simulation and three-dimensional reference interaction site model theory. Three different hosts were selected (CB6, CB7, and CB8). Six organic molecules were used as representative ligands: dimethyl sulfoxide (DMSO), N,N-dimethylformamide (DMF), acetone, 2,3-diazabicyclo[2.2.2]oct-2-ene (DBO), cyclopentanone (CPN), and pyrrole. From the binding free energy and its components, we divided the ligands into two groups: those with relatively small molecular size (DMSO, DMF, acetone, and pyrrole) and those with relatively large molecular size (DBO and CPN). We established that the solvent water in the CB6 cavity can be completely displaced by small ligands, resulting in a greater binding affinity compared with larger CBs, except in the case of the small pyrrole ligand, due to outstanding intrinsic properties such as the relatively high hydrophobicity and low dipole moment. In the case of the large ligands, the solvent water can be displaced by DBO and CPN in both CB6 and CB7; there were similar tendencies in their binding affinities, with the greatest affinity in the CB7 complexes. However, the tendencies of the binding affinity components are completely different due to the difference between the complex structure and the solvation structure when a ligand binds with a CB structure. The binding affinities suggest that the size fit between the ligand and CB cannot guarantee the greatest binding affinity gain because the binding structure and intrinsic properties of CB and ligand equally play a crucial role.

Reaction Entropies in Solution from Analytical Three-Dimensional Reference Interaction Site Model Derivatives with Application to Redox and Spin-Crossover Processes

An analytical approach to compute the excess entropy of solvation at constant pressure in three-dimensional reference interaction site model (3D-RISM) calculations is presented. It includes the changes in the macroscopic dielectric constant of the solvent upon variation of temperature and density. The approach is exact within the framework of force-field descriptions of the solute and gives reasonable results for self-consistently determined electrostatics as used in the 3D-RISM-self-consistent field approach, particularly for entropy differences. The new method is applied to simple examples of reaction entropies of iron complexes in aqueous solution, for which simple gas-phase calculations and many other approaches give unreliable estimates. For both redox half-reactions and spin-crossover processes, (semi)quantitative agreement with experimental reaction entropies can be achieved out of the box.

Computational Analysis of the SARS-CoV-2 RBD-ACE2-Binding Process Based on MD and the 3D-RISM Theory

The binding process of angiotensin-converting enzyme 2 (ACE2) to the receptor-binding domain (RBD) of the severe acute respiratory syndrome-like coronavirus 2 spike protein was investigated using molecular dynamics simulation and the three-dimensional reference interaction-site model theory. The results suggested that the protein-binding process consists of a protein-protein approaching step, followed by a local structural rearrangement step. In the approaching step, the interprotein interaction energy decreased as the proteins approached each other, whereas the solvation free energy increased. As the proteins approached, the glycan of ACE2 first established a hydrogen bond with the RBD. Thereafter, the number of interprotein hydrogen bonds increased rapidly. The solvation free energy increased because of the desolvation of the protein as it approached its partner. The spatial distribution function of the solvent revealed the presence of hydrogen bonds bridged by water molecules on the RBD-ACE2 interface. Finally, principal component analysis revealed that ACE2 showed a pronounced conformational change, whereas there was no significant change in RBD.

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.

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.

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.

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.

Analysis of molecular dynamics simulations of 10-residue peptide, chignolin, using statistical mechanics: Relaxation mode analysis and three-dimensional reference interaction site model theory

Molecular dynamics simulation is a fruitful tool for investigating the structural stability, dynamics, and functions of biopolymers at an atomic level. In recent years, simulations can be performed on time scales of the order of milliseconds using special purpose systems. Since the most stable structure, as well as meta-stable structures and intermediate structures, is included in trajectories in long simulations, it is necessary to develop analysis methods for extracting them from trajectories of simulations. For these structures, methods for evaluating the stabilities, including the solvent effect, are also needed. We have developed relaxation mode analysis to investigate dynamics and kinetics of simulations based on statistical mechanics. We have also applied the three-dimensional reference interaction site model theory to investigate stabilities with solvent effects. In this paper, we review the results for designing amino-acid substitution of the 10-residue peptide, chignolin, to stabilize the misfolded structure using these developed analysis methods.

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.

Performance of 3D-RISM-KH in Predicting Hydration Free Energy: Effect of Solute Parameters

The three-dimensional reference interaction site model molecular solvation theory with the Kovalenko-Hirata closure relation has been shown to produce excellent solvation characteristics for a large class of (bio)chemical systems in solution. Correct calculation of hydration free energy is central to successful application of any solvation model. In order to find out the best possible force-field parameters to be used for hydration free energy calculation with the aforementioned theory, we have developed an extended database containing a large number of experimental solvation free energies available in the current literature and used a plethora of theoretical models for assessment. The general Amber force field was found to perform satisfactorily, whereas special care should be taken in solute charge assignment with the universal force field.

Molecular Mechanism of Depolarization-Dependent Inactivation in W366F Mutant of Kv1.2

Voltage-gated potassium channels play crucial roles in regulating membrane potential. They are activated by membrane depolarization, allowing the selective permeation of K⁺ ions across the plasma membrane, and enter a nonconducting state after lasting depolarization, a process known as inactivation. Inactivation in voltage-activated potassium channels occurs through two distinct mechanisms, N-type and C-type inactivation. C-type inactivation is caused by conformational changes in the extracellular mouth of the channel, whereas N-type inactivation is elicited by changes in the cytoplasmic mouth of the protein. The W434F-mutated Shaker channel is known as a nonconducting mutant and is in a C-type inactivation state at a depolarizing membrane potential. To clarify the structural properties of C-type inactivated protein, we performed molecular dynamics simulations of the wild-type and W366F (corresponding to W434F in Shaker) mutant of the Kv1.2-2.1 chimera channel. The W366F mutant was in a nearly nonconducting state with a depolarizing voltage and recovered from inactivation with a reverse voltage. Our simulations and three-dimensional reference interaction site model analysis suggested that structural changes in the selectivity filter upon membrane depolarization trap K⁺ ions around the inner mouth of the selectivity filter and prevent ion permeation. This pore restriction is involved in the molecular mechanism of C-type inactivation.

An Atomistic Model of a Precursor State of Light-Induced Channel Opening of Channelrhodopsin

Channelrhodopsins (ChRs) are microbial light-gated ion channels with a retinal chromophore and are widely utilized in optogenetics to precisely control neuronal activity with light. Despite increasing understanding of their structures and photoactivation kinetics, the atomistic mechanism of light gating and ion conduction remains elusive. Here, we present an atomic structural model of a chimeric ChR in a precursor state of the channel opening determined by an accurate hybrid molecular simulation technique and a statistical theory of internal water distribution. The photoactivated structure features extensive tilt of the chromophore accompanied by redistribution of water molecules in its binding pocket, which is absent in previously known photoactivated structures of analogous photoreceptors, and widely agrees with structural and spectroscopic experimental evidence of ChRs. The atomistic model manifests a photoactivated ion-conduction pathway that is markedly different from a previously proposed one and successfully explains experimentally observed mutagenic effects on key channel properties.

Perspective: Structural fluctuation of protein and Anfinsen's thermodynamic hypothesis

The thermodynamics hypothesis, casually referred to as "Anfinsen's dogma," is described theoretically in terms of a concept of the structural fluctuation of protein or the first moment (average structure) and the second moment (variance and covariance) of the structural distribution. The new theoretical concept views the unfolding and refolding processes of protein as a shift of the structural distribution induced by a thermodynamic perturbation, with the variance-covariance matrix varying. Based on the theoretical concept, a method to characterize the mechanism of folding (or unfolding) is proposed. The transition state, if any, between two stable states is interpreted as a gap in the distribution, which is created due to an extensive reorganization of hydrogen bonds among back-bone atoms of protein and with water molecules in the course of conformational change. Further perspective to applying the theory to the computer-aided drug design, and to the material science, is briefly discussed.

Predicting Accurate Solvation Free Energy in n-Octanol Using 3D-RISM-KH Molecular Theory of Solvation: Making Right Choices

Molecular theory of solvation, a.k.a., three-dimensional reference interaction site model theory of solvation with Kovalenko-Hirata closure relation (3D-RISM-KH), is an accurate and fast theory predicting solvation free energy and structure. Here we report a benchmark study of n-octanol solvation free energy calculations using this theory. The choice of correct force field parameters is quintessential for the success of 3D-RISM theory, and we present a guideline to obtain them for n-octanol solvent. Our best prediction of the solvation free energy on a set of 205 small organic molecules supplemented with the so-called "universal correction" scheme yields relative mean unsigned error of 0.94 kcal/mol against the reported database. The best agreement is obtained with the united atom (UA) type force field parametrization of n-octanol with the van der Waals parameters of hydroxyl hydrogen reported by Kobryn et al. [ Kobryn , A. E. ; Kovalenko , A. J. Chem. Phys. 2008 , 129 , 134701 ].

A review of methods for the calculation of solution free energies and the modelling of systems in solution

Over the past decade, pharmaceutical companies have seen a decline in the number of drug candidates successfully passing through clinical trials, though billions are still spent on drug development. Poor aqueous solubility leads to low bio-availability, reducing pharmaceutical effectiveness. The human cost of inefficient drug candidate testing is of great medical concern, with fewer drugs making it to the production line, slowing the development of new treatments. In biochemistry and biophysics, water mediated reactions and interactions within active sites and protein pockets are an active area of research, in which methods for modelling solvated systems are continually pushed to their limits. Here, we discuss a multitude of methods aimed towards solvent modelling and solubility prediction, aiming to inform the reader of the options available, and outlining the various advantages and disadvantages of each approach.