Molecular dynamics simulations of theoretical cellulose nanotube models.

Nanotubes are remarkable nanoscale architectures for a wide range of potential applications. In the present paper, we report a molecular dynamics (MD) study of the theoretical cellulose nanotube (CelNT) models to evaluate their dynamic behavior in solution (either chloroform or benzene). Based on the one-quarter chain staggering relationship, we constructed six CelNT models by combining the two chain polarities (parallel (P) and antiparallel (AP)) and three symmetry operations (helical right (HR), helical left (HL), and rotation (R)) to generate a circular arrangement of molecular chains. Among the four models that retained the tubular form (P-HR, P-HL, P-R, and AP-R), the P-R and AP-R models have the lowest steric energies in benzene and chloroform, respectively. The structural features of the CelNT models were characterized in terms of the hydroxymethyl group conformation and intermolecular hydrogen bonds. Solvent structuring more clearly occurred with benzene than chloroform, suggesting that the CelNT models may disperse in benzene.

Free energy calculation using molecular dynamics simulation combined with the three-dimensional reference interaction site model theory. II. Thermodynamic integration along a spatial reaction coordinate.

We propose the thermodynamic integration along a spatial reaction coordinate using the molecular dynamics simulation combined with the three-dimensional reference interaction site model theory. This method provides a free energy calculation in solution along the reaction coordinate defined by the Cartesian coordinates of the solute atoms. The proposed method is based on the blue moon algorithm which can, in principle, handle any reaction coordinate as far as it is defined by the solute atom positions. In this article, we apply the present method to the complex formation process of the crown ether 18-Crown-6 (18C6) with the potassium ion in an aqueous solution. The separation between the geometric centers of these two molecules is taken to be the reaction coordinate for this system. The potential of mean force (PMF) becomes the maximum at the separation between the molecular centers being ∼4 Å, which can be identified as the free energy barrier in the process of the molecular recognition. In a separation further than the free energy barrier, the PMF is slightly reduced to exhibit a plateau. In the region closer than the free energy barrier, approach of the potassium ion to the center of 18C6 also decreases the PMF. When the potassium ion is accommodated at the center of 18C6, the free energy is lower by -5.7 ± 0.7 kcal/mol than that at the above mentioned plateau or converged state. By comparing the results with those from the free energy calculation along the coupling parameters obtained in our previous paper [T. Miyata, Y. Ikuta, and F. Hirata, J. Chem. Phys. 133, 044114 (2010)], it is found that the effective interaction in water between 18C6 and the potassium ion vanishes beyond the molecular-center-separation of 10 Å. Furthermore, the conformation of 18C6 is found to be significantly changed depending upon the 18C6-K(+) distance. A proper conformational sampling and an accurate solvent treatment are crucial for realizing the accurate PMF, and we believe that the proposed method is useful to evaluate the PMF in a solution. A discussion upon the PMF in terms of the three-dimensional distribution function for the solvent is also presented.

Molecular approach to understand the tacticity effects on the hydrophilicity of poly(N-isopropylacrylamide): solubility of dimer model compounds in water.

Although it has been suggested that the tacticity affects the hydrophilicity of poly(N-isopropylacrylamide) (PNiPA), little is known about the physical background of this phenomenon. In this study, we investigated the solubility of the dimer model compounds (DNiPA). The partition coefficient of DNiPA in the two phases of a water/chloroform mixture has indicated that DNiPA with the racemo configuration (r-DNiPA) is more soluble in water than DNiPA with the meso configuration (m-DNiPA). The difference of the hydration free energy between m- and r-DNiPA is estimated to be 1.2 kJ mol(-1). The molecular mechanics (MM) calculations with the GB/SA model have revealed that r-DNiPA in water is more stable by ca. 1 kJ mol(-1) than m-DNiPA, which is in excellent agreement with the experimental result. The MM calculations have also indicated that the intramolecular interaction of m-DNiPA is stronger than that of r-DNiPA, while r-DNiPA is advantageous in terms of the hydration free energy and conformational entropy.

Free energy calculation using molecular dynamics simulation combined with the three dimensional reference interaction site model theory. I. Free energy perturbation and thermodynamic integration along a coupling parameter.

This article proposes a free energy calculation method based on the molecular dynamics simulation combined with the three dimensional reference interaction site model theory. This study employs the free energy perturbation (FEP) and the thermodynamic integration (TDI) along the coupling parameters to control the interaction potential. To illustrate the method, we applied it to a complex formation process in aqueous solutions between a crown ether molecule 18-Crown-6 (18C6) and a potassium ion as one of the simplest model systems. Two coupling parameters were introduced to switch the Lennard-Jones potential and the Coulomb potential separately. We tested two coupling procedures: one is a "sequential-coupling" to couple the Lennard-Jones interaction followed by the Coulomb coupling, and the other is a "mixed-coupling" to couple both the Lennard-Jones and the Coulomb interactions together as much as possible. The sequential-coupling both for FEP and TDI turned out to be accurate and easily handled since it was numerically well-behaved. Furthermore, it was found that the sequential-coupling had relatively small statistical errors. TDI along the mixed-coupling integral path was to be carried out carefully, paying attention to a numerical behavior of the integrand. The present model system exhibited a nonmonotonic behavior in the integrands for TDI along the mixed-coupling integral path and also showed a relatively large statistical error. A coincidence within a statistical error was obtained among the results of the free energy differences evaluated by FEP, TDI with the sequential-coupling, and TDI with the mixed-coupling. The last one is most attractive in terms of the computer power and is accurate enough if one uses a proper set of windows, taking the numerical behavior of the integrands into account. TDI along the sequential-coupling integral path would be the most convenient among the methods we tested, since it seemed to be well-balanced between the computational load and the accuracy. The numerical results reported in this article qualitatively agree with the experimental data for the potassium ion recognition by the 18C6 in aqueous solution.

Systematic docking study of the carbohydrate binding module protein of Cel7A with the cellulose Ialpha crystal model.

A computer docking study has been carried out on the crystal surfaces of cellulose Ialpha crystal models for the carbohydrate binding module (CBM) protein of the cellobiohydrolase Cel7A produced by Trichoderma reesei. Binding free energy maps between the CBM and the crystal surface were obtained by calculating the noncovalent interactions and the solvation free energy at grid points covering the area of the unit cell dimensions at the crystal surface. The potential maps obtained from grid searches of the hydrophobic (110) crystal surface exhibited two distinct potential wells. These reflected the 2-fold helical symmetry of the cellulose chain and had lower binding energies at the minimum positions than those for the hydrophilic (100) and (010) crystal surfaces. The CBM-cellulose crystal complex models derived from the minimum positions were then subjected to molecular dynamics (MD) simulation under an explicit solvent system. The (110) complex models exhibited larger affinities at the interface than the (100) and (010) ones. The CBM was more stably bound to the (110) surface when it was placed in an antiparallel orientation with respect to the cellulose fiber axis. In the solvated dynamics state, the curved (110) surface resulting from the fiber twist somewhat assisted a complementary fit with the CBM at the interface. In addition to the conventional Generalized Born (GB) method, the three-dimensional reference interaction site model (3D-RISM) theory was adopted to assess a solvent effect for the solvated MD trajectories. Large exothermic values for the noncovalent interactions appeared correlated to and were mostly compensated by endothermic values for the solvation free energy. These gave total binding free energies of -13 to -28 kcal/mol. Results also suggested that the hydrogen bonding scheme was not essential for substrate specificity.

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.

Evaluation of pore size distribution in boundary region of micropore and mesopore using gas adsorption method.

This paper discusses an accurate method of pore size distribution evaluation in boundary regions of micropores and mesopores using the gas adsorption process on the basis of the capillary condensation theory, which is liable to be underestimated with the existing BJH and DH methods. A typical nitrogen adsorption isotherm for highly ordered mesoporous silica, which has cylindrical pores with diameter smaller than 4 nm, is considered to be type IV and it is well known for the steep increase of the amount adsorbed through capillary condensation in the region of the relative pressure P/P0 smaller than 0.4. In calculating the distribution of the pore size from the change of the amount adsorbed due to capillary condensation, it is important to accurately predict both the multilayer thickness t of the adsorbed nitrogen molecules and the critical radius rc where capillary condensation occurs. It is necessary to consider the curvature of the adsorption layer-gas phase interface when predicting the multilayer thickness t of nitrogen adsorbed within the pore of highly ordered mesoporous silica. Revision of the Kelvin equation is also required when rc is to be predicted. While the predicted value of t based on the Broekhoff and de Boer theory is matched well with the value of t which is actually measured using highly ordered mesoporous silica, and the predicted value of rc based on the GTKB-Kelvin-cylindrical equation that has been revised considering the effect of the interfacial curvature on the interfacial tension of the adsorption layer-gas phase interface is matched with the value of rc which is actually measured using highly ordered mesoporous silica. A combination method of the Broekhoff and de Boer equation and the GTKB-Kelvin-cylindrical equation is proposed as a means of accurately evaluating, from the nitrogen adsorption isotherm, the pore size distribution in the highly ordered mesoporous silica in boundary region of micropore and mesopore. The proposed new method of pore size evaluation features high accuracy and offers the convenience of obtaining the pore size distribution without repeated calculations by employing the same algorithm as DH method. The pore size predicted by the Halsey equation and the Kelvin equation of the conventional DH method is about 20% smaller than the pore size predicted by the newly proposed evaluation method.

TiO2-montmorillonite composites via supercritical intercalation.

The successful preparation of TiO2-montmorillonite mesoporous composites using intercalation of titanium isopropoxide dissolved in supercritical carbon dioxide involved ion exchange of interlayer cations by hydrophobic cations.