Reference Interaction Site Model Theory Research Articles

Ligand Mapping on Protein Surfaces by the 3D-RISM Theory: Toward Computational Fragment-Based Drug Design

In line with the recent development of fragment-based drug design, a new computational method for mapping of small ligand molecules on protein surfaces is proposed. The method uses three-dimensional (3D) spatial distribution functions of the atomic sites of the ligand calculated using the molecular theory of solvation, known as the 3D reference interaction site model (3D-RISM) theory, to identify the most probable binding modes of ligand molecules. The 3D-RISM-based method is applied to the binding of several small organic molecules to thermolysin, in order to show its efficiency and accuracy in detecting binding sites. The results demonstrate that our method can reproduce the major binding modes found by X-ray crystallographic studies with sufficient precision. Moreover, the method can successfully identify some binding modes associated with a known inhibitor, which could not be detected by X-ray analysis. The dependence of ligand-binding modes on the ligand concentration, which essentially cannot be treated with other existing computational methods, is also investigated. The results indicate that some binding modes are readily affected by the ligand concentration, whereas others are not significantly altered. In the former case, it is the subtle balance in the binding affinity between the ligand and water that determines the dominant ligand-binding mode.

Theoretical study of solvent effects on the coil-globule transition

The coil-globule transition of a polymer in a solvent has been studied using Monte Carlo simulations of a single chain subject to intramolecular interactions as well as a solvent-mediated effective potential. This solvation potential was calculated using several different theoretical approaches for two simple polymer/solvent models, each employing hard-sphere chains and hard-sphere solvent particles as well as attractive square-well potentials between some interaction sites. For each model, collapse is driven by variation in a parameter which changes the energy mismatch between monomers and solvent particles. The solvation potentials were calculated using two fundamentally different methodologies, each designed to predict the conformational behavior of polymers in solution: (1) the polymer reference interaction site model (PRISM) theory and (2) a many-body solvation potential (MBSP) based on scaled particle theory introduced by Grayce [J. Chem. Phys. 106, 5171 (1997)]. For the PRISM calculations, two well-studied solvation monomer-monomer pair potentials were employed, each distinguished by the closure relation used in its derivation: (i) a hypernetted-chain (HNC)-type potential and (ii) a Percus-Yevick (PY)-type potential. The theoretical predictions were each compared to results obtained from explicit-solvent discontinuous molecular dynamics simulations on the same polymer/solvent model systems [J. Chem. Phys. 125, 194904 (2006)]. In each case, the variation in the coil-globule transition properties with solvent density is mostly qualitatively correct, though the quantitative agreement between the theory and prediction is typically poor. The HNC-type potential yields results that are more qualitatively consistent with simulation. The conformational behavior of the polymer upon collapse predicted by the MBSP approach is quantitatively correct for low and moderate solvent densities but is increasingly less accurate for higher densities. At high solvent densities, the PRISM-HNC and MBSP approaches tend to overestimate, while the PRISM-PY approach underestimates the tendency of the solvent to drive polymer collapse.

Reference interaction site model investigation of homonuclear hard dumbbells under simple fluid theory closures: Comparison with Monte Carlo simulations

We revisit the thermodynamic and structural properties of fluids of homonuclear hard dumbbells in the framework provided by the reference interaction site model (RISM) theory of molecular fluids. Besides the previously investigated Percus-Yevick (PY) approximation, we test the accuracy of other closures to the RISM equations, imported from the theory of simple fluids; specifically, we study the hypernetted chain (HNC), the modified HNC (MHNC) and, less extensively, the Verlet approximations. We implement our approach for models characterized by several different elongations, up to the case of tangent diatomics, and investigate the whole fluid density range. The theoretical predictions are assessed against Monte Carlo simulations, either available from literature or newly generated by us. The HNC and PY equations of state, calculated via different routes, share on the whole the same level of accuracy. The MHNC is applied by enforcing an internal thermodynamic consistency constraint, leading to good predictions for the equation of state as the elongation of the dumbbell increases. As for the radial distribution function, the MHNC appears superior to other theories, especially for tangent diatomics in the high density limit; the PY approximation is better than the HNC and Verlet closures in the high density or elongation regime. Our structural analysis is supplemented by an accurate inversion procedure to reconstruct from Monte Carlo data and RISM the "exact" direct correlation function. In agreement with such calculations and consistent with the forecast of rigorous diagrammatic analysis, all theories predict the occurrence in the direct correlation function of a first cusp inside the dumbbell core and (with the obvious exception of the PY) of a second cusp outside; the cusps' heights are also qualitatively well reproduced by the theories, except at high densities.

Description of the Structure of Polystyrene with Six-Site Semiflexible Model

In this work, a six-site semiflexible chain model for the polymer reference interaction site model (PRISM) theory was proposed and applied to describe the structure and properties of atactic polystyrene (aPS) melt. In the model, the local monomer structure is composed of six independent sites corresponding to A and B in the backbone and C, D, E, and F in the side phenyl ring group. The intramolecular correlation functions were obtained analytically with the Koyama distribution function and the generator matrix method. To improve the calculation of the intermolecular correlation functions, the potential of mean force was introduced. The calculated X-ray scattering intensity and total radial distribution function were compared with both simulation and experiment data. The results indicate that the model is an effective way to investigate the microscopic structure of styrene polymers.

Solvation Dynamics in Polar Solvents Studied by Means of RISM/Mode-Coupling Theory

The extended reference interaction site model (RISM) theory coupled with the generalized Langevin/mode-coupling theory (MCT) is applied to the investigation of solvation dynamics in polar solvents. The RISM/ MCT framework used in this paper significantly upgrades the previous report by Nishiyama and co-workers [Nishiyama, K.; et al. J. Chem. Phys. 2003, 118, 2279.] for the calculation of the solvation response function, Ss(t). This function is experimentally observable from dynamic Stokes shift measurements, for example. Ss(t) obtained by RISM/MCT relaxes with an initial Gaussian decay followed by damped oscillation, which is in accordance with experimental results or molecular dynamics simulations published elsewhere. Ss(t) is then decoupled into the acoustic and optical modes of solvent, which indicate the translational and rotational motions of solvent, respectively. The majority (> 90%) of Ss(t) is explained by the optical mode, whereas the slower acoustic mode also plays an important role. Resultingly, RISM/MCT is shown to be an appropriate theoretical methodology to capture a molecular view of solvation dynamics, without assuming any empirical parameters.

Thermodynamically consistent reference interaction site model theory of the tangent diatomic fluid

Thermodynamic and structural properties of the tangent diatomic fluid are studied in the framework provided by the reference interaction site model (RISM) theory, coupled with a modified hypernetted chain closure. The enforcement of the internal thermodynamic consistency of the theory is described in detail. The results we obtain almost quantitatively agree with available or newly generated simulation data. We envisage the possibility to characterize real colloidal particles of dumbbell shape, and to extend the consistent RISM formalism to generic molecular fluids.

Roles of water in protein structure and function studied by molecular liquid theory

The roles of water in the structure and function of proteins have not been completely elucidated. Although molecular simulation has been widely used for the investigation of protein structure and function, it is not always useful for elucidating the roles of water because the effect of water ranges from atomic to thermodynamic level. The three-dimensional reference interaction site model (3D-RISM) theory, which is a statistical-mechanical theory of molecular liquids, can yield the solvation structure at the atomic level and calculate the thermodynamic quantities from the intermolecular potentials. In the last few years, the author and coworkers have succeeded in applying the 3D-RISM theory to protein aqueous solution systems and demonstrated that the theory is useful for investigating the roles of water. This article reviews some of the recent applications and findings, which are concerned with molecular recognition by protein, protein folding, and the partial molar volume of protein which is related to the pressure effect on protein.

Packing of poly(tetrafluoroethylene) in the liquid state: Molecular dynamics simulation and theory

Molecular dynamics simulations and polymer reference interaction site model theory calculations were carried out on the C(48)F(98) oligomer of poly(tetrafluoroethylene) (PTFE) at 500 and 600 K. The exp-6 force field of Borodin, Smith, and Bedrov, was used in both the simulation and theory. The agreement between theory and simulation was equivalent to earlier studies on polyolefin melts. The intermolecular pair correlation functions of PTFE were shifted to larger distances relative to polyethylene (PE) due to the difference in the van der Waals radii of F and H atoms. A similar shift to lower wave vectors was found in the structure factor of PTFE relative to PE.

Effective Interactions, Structure, and Phase Behavior of Lightly Tethered Nanoparticles in Polymer Melts

We have generalized the microscopic polymer reference interaction site model (PRISM) theory to study the structure and phase behavior of polymer-tethered spherical nanoparticles in a dense homopolymer melt. In the absence of a polymer matrix, fluids of such hybrid nanoparticles show strong concentration fluctuations indicative of aggregate formation and/or a tendency for microphase separation as the total packing fraction and/or nanoparticle attraction strength increase. In the presence of a polymer matrix, there is a competition between tether-mediated microphase separation and matrix-induced macrophase separation. For a single tether of eight segments on a nanoparticle twice the diameter of a segment, the apparent microphase spinodal curve exhibits both dilution-like and depletion-like features and a nonmonotonic dependence of the spinodal temperature on matrix chain length. As the particle size and tether length are both increased, such that the total space filling volume of the tether continues to equ...

Characterization of nanofibers formed by self-assembly of β-peptide oligomers using small angle x-ray scattering

Helical oligomers of beta-peptides represent a particularly promising type of building block for directed assembly of organic nanostructures because the helical secondary structure can be designed to be very stable and because control of the beta-amino acid sequence can lead to precise patterning of chemical functional groups over the helix surfaces. In this paper, we report the use of small angle x-ray scattering measurements (SAXS) to characterize nanostructures formed by the directed assembly of beta-peptide A with sequence H(2)N-beta(3)hTyr-beta(3)hLys-beta(3)hPhe-ACHC-beta(3)hPhe-ACHC-beta(3)hPhe-beta(3)hLys-ACHC-ACHC-beta(3)hPhe-beta(3)hLys-CONH(2). Whereas prior cryo-TEM studies have revealed the presence of nanofibers in aqueous solutions of beta-peptide A, SAXS measurements from the nanofibers were not well-fit by a form factor model describing solid nanofibers. An improved fit to the scattering data at high q was obtained by using a form factor model describing a cylinder with a hollow center and radial polydispersity. When combined with a structure factor calculated from the polymer reference interaction site model (PRISM) theory, the scattered intensity of x-rays measured over the entire q range was well described by the model. Analysis of our SAXS data suggests a model in which individual beta-peptides assemble to form long cylindrical nanofibers with a hollow core radius of 15 A (polydispersity of 21%) and a shell thickness of 20 A. This model is supported by negative stain transmission electron microscopy.

Effect of the Number and Placement of Polymer Tethers on the Structure of Concentrated Solutions and Melts of Hybrid Nanoparticles

We have generalized and applied the microscopic polymer reference interaction site model theory to study intermolecular pair correlation functions and collective structure factors of concentrated solutions and melts of spherical nanoparticles carrying one, two, or four tethered polymer chains. A complex interplay of entropy (translational, conformational, and packing) and enthalpy (particle-particle attraction) leads to different structural arrangements with distinctive small- and wide-angle scattering signatures. Strong concentration fluctuations indicative of aggregate formation and/or a tendency for microphase separation occur as the total packing fraction and/or particle-particle attraction strength increase. In analogy with block copolymers, the microphase spinodal curve is estimated by extrapolation of the inverse of the amplitude of the small-angle scattering peak. As the number of tethered chains on nanoparticles increases, the microphase separation boundary spinodal occurs at higher particle-particle attraction strength or lower temperature. For nanoparticles with two tethers, increasing the angle between the attached chains shifts the microphase spinodal to lower temperatures. For nanoparticles with four tethers, the structural correlations are insensitive to various symmetric placements. The tendency for microphase transition is enhanced upon asymmetrically placing all four tethers on one side of the particle due to the high anisotropy of steric hindrance.

The potential of mean force of water and ions in aquaporin channels investigated by the 3D-RISM method

The three dimensional (3D) distributions of sodium, chloride, and hydronium ions along with water, in two aquaporin channels, AQP1 and GlpF, were calculated using the three dimensional reference interaction site model (3D-RISM) theory. It was found from the potential of mean force (PMF) obtained from the 3D-distribution that water inside the both channels is slightly more stable than bulk, and that PMF does not have high barriers for a water molecule to cross. The results are completely in harmony with the experimental observations, while they are in accord with none of the molecular simulation studies. All the ions studied are hard to permeate through either of the channels. However, the reasons why the permeability is so low are different depending on the channels and the ions. In the AQP1 channel, the cations, or Na + and H 3O +, are largely excluded from the channel essentially by the electrostatic repulsion due to the positively charged residues, while the Cl − ion is blocked by a high steric barrier at the selective filter (SF) region. In the GlpF, the PMFs of Na + and H 3O + inside the channel are mostly positive, and they have three large barriers to cross, which may be preventing the ions from permeation. On the other hand, the PMF of Cl − is largely negative, but it has wide and deep well which likely prevents the ion from permeating through the channel by “trapping” mechanism.

Comparison of DNA hydration patterns obtained using two distinct computational methods, molecular dynamics simulation and three-dimensional reference interaction site model theory

Because proteins and DNA interact with each other and with various small molecules in the presence of water molecules, we cannot ignore their hydration when discussing their structural and energetic properties. Although high-resolution crystal structure analyses have given us a view of tightly bound water molecules on their surface, the structural data are still insufficient to capture the detailed configurations of water molecules around the surface of these biomolecules. Thanks to the invention of various computational algorithms, computer simulations can now provide an atomic view of hydration. Here, we describe the apparent patterns of DNA hydration calculated by using two different computational methods: Molecular dynamics (MD) simulation and three-dimensional reference interaction site model (3D-RISM) theory. Both methods are promising for obtaining hydration properties, but until now there have been no thorough comparisons of the calculated three-dimensional distributions of hydrating water. This rigorous comparison showed that MD and 3D-RISM provide essentially similar hydration patterns when there is sufficient sampling time for MD and a sufficient number of conformations to describe molecular flexibility for 3D-RISM. This suggests that these two computational methods can be used to complement one another when evaluating the reliability of the calculated hydration patterns.

Structure and assembly of dense solutions and melts of single tethered nanoparticles

The microscopic polymer reference interaction site model theory is generalized and applied to study intermolecular pair correlation functions and collective structure factors of dense solutions and melts of spherical nanoparticles carrying a single tethered chain. The complex interplay of entropy (translational, conformational, and packing) and enthalpy (particle-particle attraction) leads to different structural arrangements with distinctive small and wide angle scattering signatures. Strong concentration fluctuations, indicative of aggregate formation and/or a tendency for microphase separation, occur as the total packing fraction and/or particle-particle attraction strength increase. In analogy with block copolymers, the microphase spinodal curve is estimated by extrapolation of the inverse of the amplitude of the small angle scattering peak. For nanoparticles that are twice the diameter of monomers, the microphase separation boundary spinodal occurs at higher particle-particle attraction strength (or lower temperature) as compared to the macrophase demixing curve for nanoparticles with no tethers when the packing fraction is below 0.45, while the opposite trend is observed above 0.45. Increasing nanoparticle diameter results in a reduction in the microphase spinodal temperature and a qualitative change in its packing fraction dependence.

A Singlet Reference Interation Site Model Theory for Solid/Liquid Interfaces Part II: Electrical Double Layers

The previously established singlet reference interaction site model (SRISM) theory for the calculation of the fluid structure in the vicinity of a plane impenetrable interface is renormalized for the application to electrical double layers. In combination with the HNC and KH closures, the equations are solved numerically for a 1 M electrolyte solution adjacent to a charged wall with varying surface charge densities. The wall-solvent and wall-ion density distributions as well as the profiles of the electrical field and the electrical potential are compared to computer simulation results. Reasonable agreement is obtained.

An integral equation theory for inhomogeneous molecular fluids: The reference interaction site model approach

An integral equation theory which is applicable to inhomogeneous molecular liquids is proposed. The "inhomogeneous reference interaction site model (RISM)" equation derived here is a natural extension of the RISM equation to inhomogeneous systems. This theory makes it possible to calculate the pair correlation function between two molecules which are located at different density regions. We also propose approximations concerning the closure relation and the intramolecular susceptibility of inhomogeneous molecular liquids. As a preliminary application of the theory, the hydration structure around an ion is investigated. Lithium, sodium, and potassium cations are chosen as the solute. Using the Percus trick, the local density of solvent around an ion is expressed in terms of the solute-solvent pair correlation function calculated from the RISM theory. We then analyze the hydration structure around an ion through the triplet correlation function which is defined with the inhomogeneous pair correlation function and the local density of the solvent. The results of the triplet correlation functions for cations indicate that the thermal fluctuation of the hydration shell is closely related to the size of the solute ion. The triplet correlation function from the present theory is also compared with that from the Kirkwood superposition approximation, which substitutes the inhomogeneous pair correlation by the homogeneous one. For the lithium ion, the behavior of the triplet correlation functions from the present theory shows marked differences from the one calculated within the Kirkwood approximation.

Reference interaction site model and molecular dynamics study of structure and thermodynamics of methanol

Thermodynamic and structural properties of various models of liquid methanol are investigated in the framework provided by the reference interaction site model (RISM) theory of molecular fluids. The theoretical predictions are systematically compared with molecular dynamics simulations both at ambient conditions and along a few supercritical isotherms. RISM results for the liquid-vapor phase separation are also obtained and assessed against available Gibbs ensemble Monte Carlo data. At ambient conditions, the theoretical correlations weakly depend on the specific details of the molecular models and reproduce the simulation results with different degrees of accuracy, depending on the pair of interaction sites considered. The position and the strength of the hydrogen bond are quite satisfactorily predicted. RISM results for the internal energy are almost quantitative whereas the pressure is generally overestimated. As for the liquid-vapor phase coexistence, RISM predictions for the vapor branch and for the critical temperature are quite accurate; on the other side, the liquid branch densities, and consequently the critical density, are underestimated. We discuss our results in terms of intrinsic limitations, and suitable improvements, of the RISM approach in describing the physical properties of polar fluids, and in the perspective of a more general investigation of mixtures of methanol with nonpolar fluids of specific interest in the physics of associating fluids.

Combination of generalized-ensemble algorithms and one-dimensional reference interaction site model theory

The article reports an attempt to study the protein folding problem by generalized-ensemble Monte Carlo simulations with reference interaction site model theory. Generalized-ensemble algorithms greatly enhance the configurational space sampling in computer simulations. The reference interaction site model theory treats solvent effects with solvent molecular shape and estimate solvation free energy around proteins. We have developed simulation algorithms which combine generalized-ensemble algorithms and one-dimensional reference interaction site model theory. This treatment can also use a simulation with three-dimensional reference interaction site model theory. In this review, we describe the methods and present the results of these simulations for a peptide.

Combination of molecular dynamics method and 3D‐RISM theory for conformational sampling of large flexible molecules in solution

We have developed an algorithm for sampling the conformational space of large flexible molecules in solution, which combines the molecular dynamics (MD) method and the three-dimensional reference interaction site model (3D-RISM) theory. The solvent-induced force acting on solute atoms was evaluated as the gradient of the solvation free energy with respect to the solute-atom coordinates. To enhance the computation speed, we have applied a multiple timestep algorithm based on the RESPA (Reversible System Propagator Algorithm) to the combined MD/3D-RISM method. By virtue of the algorithm, one can choose a longer timestep for renewing the solvent-induced force compared with that of the conformational update. To illustrate the present MD/3D-RISM simulation, we applied the method to a model of acetylacetone in aqueous solution. The multiple timestep algorithm succeeded in enhancing the computation speed by 3.4 times for this model case. Acetylacetone possesses an intramolecular hydrogen-bonding capability between the hydroxyl group and the carbonyl oxygen atom, and the molecule is significantly stabilized due to this hydrogen bond, especially in gas phase. The intramolecular hydrogen bond was kept intact during almost entire course of the MD simulation in gas phase, while in the aqueous solutions the bond is disrupted in a significant number of conformations. This result qualitatively agrees with the behavior on a free energy barrier lying upon the process for rotating a torsional degree of freedom of the hydroxyl group, where it is significantly reduced in aqueous solution by a cancellation between the electrostatic interaction and the solvation free energy.

Integral equation theory study on the phase separation in star polymer nanocomposite melts

The polymer reference interaction site model theory is used to investigate phase separation in star polymer nanocomposite melts. Two kinds of spinodal curves were obtained: classic fluid phase boundary for relatively low nanoparticle-monomer attraction strength and network phase boundary for relatively high nanoparticle-monomer attraction strength. The network phase boundaries are much more sensitive with nanoparticle-monomer attraction strength than the fluid phase boundaries. The interference among the arm number, arm length, and nanoparticle-monomer attraction strength was systematically investigated. When the arm lengths are short, the network phase boundary shows a marked shift toward less miscibility with increasing arm number. When the arm lengths are long enough, the network phase boundaries show opposite trends. There exists a crossover arm number value for star polymer nanocomposite melts, below which the network phase separation is consistent with that of chain polymer nanocomposite melts. However, the network phase separation shows qualitatively different behaviors when the arm number is larger than this value.