3D-RISM Theory Research Articles

A new method for finding the minimum free energy pathway of ions and small molecule transportation through protein based on 3D-RISM theory and the string method

A new method for finding the minimum free energy pathway (MFEP) of ions and small molecule transportation through a protein based on the three-dimensional reference interaction site model (3D-RISM) theory combined with the string method has been proposed. The 3D-RISM theory produces the distribution function, or the potential of mean force (PMF), for transporting substances around the given protein structures. By applying the string method to the PMF surface, one can readily determine the MFEP on the PMF surface. The method has been applied to consider the Na+ conduction pathway of channelrhodopsin as an example.

Solvation Structure of LiClO4/Ethylene Carbonate Solution near a Graphite Electrode in Lithium-ion Batteries: 3D-RISM Study

Solvation structure of an electrolyte solution near graphite electrode was elucidated by means of three-dimensional reference interaction site model (3D-RISM) theory, a statistical mechanical theory for molecular liquids. The electrolyte solution we used was 1.0 M LiClO4/ethylene carbonate (EC) solution, a typical solution of lithium-ion batteries. We discussed the effect of the geometry and charge distribution of graphite on the solvation structure.

Theoretical analysis of the domain-swapped dimerization of cytochrome c: An MD and 3D-RISM approach.

The structural stability of a cytochrome c domain-swapped dimer compared with that of the monomer was investigated by molecular dynamics (MD) simulations and by three-dimensional reference interaction site model (3D-RISM) theory. The structural fluctuation and structural energy of cytochrome c were treated by MD simulations, and the solvation thermodynamics was treated by 3D-RISM theory. The domain-swapped dimer state is slightly less stable than the monomer state, which is consistent with experimental observations; the total free energy difference is calculated as 25 kcal mol-1. The conformational change and translational/rotational entropy change contribute to the destabilization of the dimer, whereas the hydration and vibrational entropy contribute to the stabilization. Further analyses on the residues located at the hinge loop for swapping were conducted, and the results reveal details at the molecular level of the structural and interaction changes upon dimerization.

3DRISM-HI-D2MSA: an improved analytic theory to compute solvent structure around hydrophobic solutes with proper treatment of solute–solvent electrostatic interactions

ABSTRACTThe 3D reference interaction site model (3DRISM) is a powerful tool to study the thermodynamic and structural properties of liquids. However, for hydrophobic solutes, the inhomogeneity of the solvent density around them poses a great challenge to the 3DRISM theory. To address this issue, we have previously introduced the hydrophobic-induced density inhomogeneity theory (HI) for purely hydrophobic solutes. To further consider the complex hydrophobic solutes containing partial charges, here we propose the D2MSA closure to incorporate the short-range and long-range interactions with the D2 closure and the mean spherical approximation, respectively. We demonstrate that our new theory can compute the solvent distributions around real hydrophobic solutes in water and complex organic solvents that agree well with the explicit solvent molecular dynamics simulations.

Role of Solvation in Drug Design as Revealed by the Statistical Mechanics Integral Equation Theory of Liquids.

Recent developments and applications in theoretical methods focusing on drug design and particularly on the solvent effect in molecular recognition based on the three-dimensional reference interaction site model (3D-RISM) theory are reviewed. Molecular recognition, a fundamental molecular process in living systems, is known to be the functional mechanism of most drugs. Solvents play an essential role in molecular recognition processes as well as in ligand-protein interactions. The 3D-RISM theory is derived from the fundamental statistical mechanics theory, which reproduces all solvation thermodynamics naturally and has some advantages over conventional solvation methods, such as molecular simulation and the continuum model. Here, we review the basics of the 3D-RISM theory and methods of molecular recognition in its applications toward drug design.

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 ].

Comparative study of 3D-RISM theory and molecular dynamics calculations for the free-energy landscape of a hydrated dipeptide

In the present study, the free-energy landscape of a hydrated alanine dipeptide has been studied by the 3D-RISM theory. We calculate the hydration free energy as a function of dihedral angles and using both the 3D-RISM theory and the umbrella sampling method. The 3D-RISM results are found to be in good agreement with those by the umbrella sampling calculations, demonstrating the reliability of the integral equation theory applied to bimolecular systems.

Multi-scale molecular modeling of fluorescent rosette nanotubes

Event Abstract Back to Event Multi-scale molecular modeling of fluorescent rosette nanotubes Arthur Gonzales1, Takeshi Yamazaki2, Belete Legesse1 and Hicham Fenniri1 1 Northeastern University, Chemical Engineering, United States 2 National Institute for Nanotechnology, Canada Rosette nanotubes (RNTs) are soft organic nanomaterials self-assembled under aqueous conditions from Watson-Crick inspired guanine-cytosine (G∧C) hybrid building blocks with complementary hydrogen bonding sites[1]. These materials have substantial design flexibility and a range of applications, which is partly attributed to their diverse surface functionalization and a chemically/physically tunable channel for guest molecule loading. Several studies have established their biocompatibility and applications in nanomedicine such as in coatings for medical devices, materials for tissue engineering and for drug display and delivery. With novel applications in mind and in an effort to streamline its synthesis, a new tricyclic G∧C motif was designed to self assemble into fluorescent RNT in various solvents. Its self-assembly and fluorescence properties were verified by scanning electron microscopy (SEM), atomic force microscopy (AFM), transmission electron microscopy (TEM), and UV-visible spectroscopic studies. Temperature, pH and other solvent properties affect the self-assembly process and structure of the RNTs. To aid in the characterization of this new RNT, multi-scale molecular modeling techniques were applied to predict its structure in various solvent conditions. Molecular dynamics (MD), molecular mechanics (MM), and the statistical mechanical theory of solvation, also known as the 3 dimensional reference interaction site model (3D-RISM) theory were applied to predict the conformation of RNTs. MM was used to determine the possible conformations of the individual motifs. From these, RNT models were built and MD simulations were run in different solvent properties to determine the stability and probable structure of the nanotubes. The results suggest that this tricyclic G∧C motif can either form ring stacks (RSs) or helical coils (HCs) depending on the solvent used. 3D-RISM integral equations were then solved for the system to determine the solvation structure, energetics, and to propose a self-assembly pathway for the RNTs.

Encapsulation of ferrocene by self-assembled rosette nanotubes: An investigation using statistical mechanical theory of molecular liquids

Encapsulation thermodynamics of a guest molecule by self-assembled rosette nanotubes (RNTs) was investigated using the statistical mechanical theory of molecular liquids also known as 3D-RISM theory. Ferrocene was chosen as a guest molecule because it is a good mimic for a small drug molecule in terms of logP value. The present computational study predicts that ferrocene can penetrate the channel of all three RNTs examined, however, the potential of mean force profile along the RNT channel suggested that RNT that has the smallest channel diameter has relatively high potential barrier for uptake and release of ferrocene, and therefore it was suggested that this could be a suitable mechanism to trap (during self-assembly) and release (during disassembly) a drug candidate. This work suggests also that tuning the RNT channel dimensions and chemistry should allow us to develop a palette of RNT delivery systems for a variety of drugs.

A highly efficient hybrid method for calculating the hydration free energy of a protein.

We develop a new method for calculating the hydration free energy (HFE) of a protein with any net charge. The polar part of the energetic component in the HFE is expressed as a linear combination of four geometric measures (GMs) of the protein structure and the generalized Born (GB) energy plus a constant. The other constituents in the HFE are expressed as linear combinations of the four GMs. The coefficients (including the constant) in the linear combinations are determined using the three-dimensional reference interaction site model (3D-RISM) theory applied to sufficiently many protein structures. Once the coefficients are determined, the HFE and its constituents of any other protein structure are obtained simply by calculating the four GMs and GB energy. Our method and the 3D-RISM theory give perfectly correlated results. Nevertheless, the computation time required in our method is over four orders of magnitude shorter.

Multi-scale dynamics simulation of protein based on the generalized Langevin equation combined with 3D-RISM theory

A theory to realize a multiscale dynamics of protein is proposed based on the generalized Langevin equation combined with the 3D-RISM theory. The idea of normal mode analysis (NMA) is adopted to decouple the dynamics into different modes having respective time scales. In order to decouple the modes, the variance–covariance matrix concerning the structural fluctuation of protein in solution is diagonalized, instead of the Hessian matrix of a harmonic oscillator in vacuum. An algorithm to estimate the friction coefficient exerted on each atom of protein due to solvent is also proposed.

A solvation-free-energy functional: a reference-modified density functional formulation.

The three-dimensional reference interaction site model (3D-RISM) theory, which is one of the most applicable integral equation theories for molecular liquids, overestimates the absolute values of solvation-free-energy (SFE) for large solute molecules in water. To improve the free-energy density functional for the SFE of solute molecules, we propose a reference-modified density functional theory (RMDFT) that is a general theoretical approach to construct the free-energy density functional systematically. In the RMDFT formulation, hard-sphere (HS) fluids are introduced as the reference system instead of an ideal polyatomic molecular gas, which has been regarded as the appropriate reference system of the interaction-site-model density functional theory for polyatomic molecular fluids. We show that using RMDFT with a reference HS system can significantly improve the absolute values of the SFE for a set of neutral amino acid side-chain analogues as well as for 504 small organic molecules.

Communication: Accurate hydration free energies at a wide range of temperatures from 3D-RISM.

We present a new model for computing hydration free energies by 3D reference interaction site model (3D-RISM) that uses an appropriate initial state of the system (as suggested by Sergiievskyi et al.). The new adjustment to 3D-RISM theory significantly improves hydration free energy predictions for various classes of organic molecules at both ambient and non-ambient temperatures. An extensive benchmarking against experimental data shows that the accuracy of the model is comparable to (much more computationally expensive) molecular dynamics simulations. The calculations can be readily performed with a standard 3D-RISM algorithm. In our work, we used an open source package AmberTools; a script to automate the whole procedure is available on the web (https://github.com/MTS-Strathclyde/ISc).

Structural fluctuation of proteins induced by thermodynamic perturbation.

A theory to describe structural fluctuations of protein induced by thermodynamic perturbations, pressure, temperature, and denaturant, is proposed. The theory is formulated based on the three methods in the statistical mechanics: the generalized Langevin theory, the linear response theory, and the three dimensional interaction site model (3D-RISM) theory. The theory clarifies how the change in thermodynamic conditions, or a macroscopic perturbation, induces the conformational fluctuation, which is a microscopic property. The theoretical results are applied, on the conceptual basis, to explain the experimental finding by Akasaka et al., concerning the NMR experiment which states that the conformational change induced by pressure corresponds to structural fluctuations occurring in the ambient condition. A method to evaluate the structural fluctuation induced by pressure is also suggested by means of the 3D-RISM and the site-site Kirkwood-Buff theories.

Determination of the formylglycinamide ribonucleotide amidotransferase ammonia pathway by combining 3D-RISM theory with experiment.

Molecular tunnels in enzyme systems possess variable architecture and are therefore difficult to predict. In this work, we design and apply an algorithm to resolve the pathway followed by ammonia using the bifunctional enzyme formylglycinamide ribonucleotide amidotransferase (FGAR-AT) as a model system. Though its crystal structure has been determined, an ammonia pathway connecting the glutaminase domain to the 30 Å distal FGAR/ATP binding site remains elusive. Crystallography suggested two purported paths: an N-terminal-adjacent path (path 1) and an auxiliary ADP-adjacent path (path 2). The algorithm presented here, RismPath, which enables fast and accurate determination of solvent distribution inside a protein channel, predicted path 2 as the preferred mode of ammonia transfer. Supporting experimental studies validate the identity of the path, and results lead to the conclusion that the residues in the middle of the channel do not partake in catalytic coupling and serve only as channel walls facilitating ammonia transfer.

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.

A 3D-RISM integral equation study of a hydrated dipeptide

In this study, thermodynamic and molecular properties of a hydrated alanine dipeptide have been studied by the three-dimensional reference interaction site method (3D-RISM) theory. The excess chemical potential regarding hydration is calculated as a function of the dihedral angles and . The calculated results are found to be in reasonable agreement with extended ensemble simulation results. Partial molar volume is also calculated for each major structural state of the dipeptide. Overall trend is well described by the 3D-RISM calculations in comparison with molecular simulation and other integral equation results.

Distinct configurations of cations and water in the selectivity filter of the KcsA potassium channel probed by 3D-RISM theory

The potassium channel is highly selective for K+ over other monovalent cations, and the narrow pore structure with 3Å in diameter named the selectivity filter (SF) is responsible for the selective permeation. Here we applied the statistical mechanics of liquids called three-dimensional reference interaction site model (3D-RISM) theory, and the binding configurations of the monovalent cations, Li+, Na+ and K+, with special attention on the contribution of water in the KcsA potassium channel were examined. All the three types of cations are bound in the open SF with high affinity, but with different binding coordinations: the in-cage configuration by eight carbonyl oxygens for K+, and the in-plane configuration by four carbonyl oxygens for Li+, whereas both configurations are allowed for Na+. In each case, water contributes an integral part of the ion coordination. In the case of Li+, a linear water-Li+-water complex is settled into two adjacent cages with the Li+ centered at the in-plane site. Positions of water around Na+ are more flexible, which may allow a transition between in-plane and in-cage configurations. K+ stably occupied in-cage configuration, and water occupies adjacent cages. The results provide the distinct configuration of ion and water in the SF, and serves clues for elementary process of selectivity.

Probing “ambivalent” snug-fit sites in the KcsA potassium channel using three-dimensional reference interaction site model (3D-RISM) theory

Abstract The potassium channel is highly selective for K+ over Na+, and the mechanism underlying this selectivity remains unclear. We show the three-dimensional distribution functions (3D-DFs) of small cations (Li+, Na+, and K+) and the free energy profile of ions inside the open selectivity filter (SF) of the KcsA channel. Our previous results [S. Phongphanphanee, N. Yoshida, S. Oiki, F. Hirata. Abstract Book of 5th International Symposium on Molecular Science of Fluctuations toward Biological Functions, P062 (2012)] indicate that the 3D-DF for K+ exhibits distinct peaks at the sites formed by the eight carbonyl oxygen atoms belonging to the surrounding peptide-backbone and residues (the cage site). Li+ has sharp distributions in the 3D-DF at the center of a quadruplex composed of four carbonyl oxygen atoms (the plane site). Na+ has a rather diffuse distribution throughout the SF region with peaks both in the plane and in cage sites. The results provide microscopic evidence of the phenomenological findings that Li+ and Na+ are not excluded from the SF region and that the binding affinity alone does not cause the ion selectivity of KcsA. In the present study, with an ion placed explicitly along the pore axis, the free energy profiles of the ions inside the SF were calculated; from these profiles we suggest a new mechanism for selective K+ permeation. According to the model, a K+ ion must overcome a free energy barrier that is approximately half that of Na+ to exit from either of the SF mouths due to the existence of an intermediate local minimum along the route for climbing the barriers.

Statistical Thermodynamics for Binding of an RNA Aptamer and a Partial Peptide of a Prion Protein

It has been reported that a novel RNA aptamer with 12 residues (R12) binds to a partial peptide of a prion protein (P16) [1]. This binding is expected to prevent prion diseases, but its driving force remains rather unclear. Here we calculate the free-energy change upon the binding of R12 and P16 using molecular mechanics, the three-dimensional (3D) reference interaction site model (RISM) theory [2], and the hybrid method in which the angle-dependent integral equation theory [3] applied to a multipolar water model [4] is combined with the morphometric approach [5]. The 3D-RISM theory and the hybrid method are employed for calculating the hydration energy and the hydration entropy, respectively. We show that the large decrease in the intermolecular energy upon the binding is almost cancelled out by a correspondingly large increase in the hydration energy. The binding is driven by a large gain in the translational, configurational entropy of water originating primarily from the reduction in water crowding in the system. Our physical picture of the binding can be described as follows: The binding, which is driven by the water-entropy effect, accompanies a loss of R12-water and P16-water electrostatic attractive and van der Waals interactions. But the loss is compensated by a gain in R12-P16 electrostatic attractive and van der Waals interactions.[1] T. Mashima, et al., Nucleic Acids Res. 41, 1355 (2013).[2] T. Imai, et al., J. Chem. Phys. 126, 225102 (2007).[3] M. Kinoshita, J. Chem. Phys. 128, 0245071 (2008).[4] P. G. Kusalik and G. N. Patey, Mol. Phys. 65, 1105 (1988).[5] R. Roth, Y. Harano, and M. Kinoshita, Phys. Rev. Lett. 97, 078101 (2006).