Mitsunori Ikeguchi

Direct numerical solution of the Ornstein–Zernike integral equation and spatial distribution of water around hydrophobic molecules

The Ornstein–Zernike integral equation (OZ equation) has been used to evaluate the distribution function of solvents around solutes, but its numerical solution is difficult for molecules with a complicated shape. This paper proposes a numerical method to directly solve the OZ equation by introducing the 3D lattice. The method employs no approximation the reference interaction site model (RISM) equation employed. The method enables one to obtain the spatial distribution of spherical solvents around solutes with an arbitrary shape. Numerical accuracy is sufficient when the grid‐spacing is less than 0.5 A for solvent water. The spatial water distribution around a propane molecule is demonstrated as an example of a nonspherical hydrophobic molecule using iso‐value surfaces. The water model proposed by Pratt and Chandler is used. The distribution agrees with the molecular dynamics simulation. The distribution increases offshore molecular concavities. The spatial distribution of water around 5α‐cholest‐2‐ene (C27H46) is visualized using computer graphics techniques and a similar trend is observed.

SIZE DEPENDENCE OF TRANSFER FREE ENERGIES : A HARD-SPHERE-CHAIN-BASED FORMALISM

The main purpose of this paper is to present a theoretical scheme which describes the solvation and transfer free energies of small molecules and relate them to solvent contributions in the biomolecular processes. Several proposals, based originally on Flory–Huggins theory, have been made recently that there is a non-negligible solute’s volume-proportional term in solvation free energy and the term should be subtracted to obtain solute/solvent contact free energy for biochemical applications. These proposals have resulted in the revision of the magnitude of the hydrophobic effect in biomolecules. The validity has been controversial, since the existence, physical origin, and magnitude of the volume-proportional term have been model dependent. In this paper, we cleared up this problem by using an accurate fused-hard sphere model and a perturbation scheme in which the compensation between the repulsive and attractive interactions has been clarified. The solvation free energy is shown to be dependent on the s...

EXTRACTING CONTACT FREE ENERGY FROM SOLUBILITY : EXCLUDED VOLUME EFFECTS OF POLYMERS IN CONTINUUM SPACE

Abstract We present a general thermodynamical theory that can be used to extract contact free energies from solubility data. The physical pictures of the long-disputed Flory-Huggins and Sharps theories of solvation were clarified by introducing a novel decomposition of the unitary process. It is shown that the Flory-Huggins theory takes insufficient account of excluded volume effects. We propose a theory of solvation using the fused hard-sphere theory, and the “packing entropy” introduced in this theory enables us to extend the accessible surface-area formalism to the case of chain solvents.

Parallel algorithm for efficient calculation of second derivatives of conformational energy function in internal coordinates

A parallel algorithm for efficient calculation of the second derivatives (Hessian) of the conformational energy in internal coordinates is proposed. This parallel algorithm is based on the master/slave model. A master processor distributes the calculations of components of the Hessian to one or more slave processors that, after finishing their calculations, send the results to the master processor that assembles all the components of the Hessian. Our previously developed molecular analysis system for conformational energy optimization, normal mode analysis, and Monte Carlo simulation for internal coordinates is extended to use this parallel algorithm for Hessian calculation on a massively parallel computer. The implementation of our algorithm uses the message passing interface and works effectively on both distributed‐memory parallel computers and shared‐memory parallel computers. We applied this system to the Newton–Raphson energy optimization of the structures of glutaminyl transfer RNA (Gln‐tRNA) with 74 nucleotides and glutaminyl‐tRNA synthetase (GlnRS) with 540 residues to analyze the performance of our system. The parallel speedups for the Hessian calculation were 6.8 for Gln‐tRNA with 24 processors and 11.2 for GlnRS with 54 processors. The parallel speedups for the Newton–Raphson optimization were 6.3 for Gln‐tRNA with 30 processors and 12.0 for GlnRS with 62 processors.u2003© 1998 John Wiley & Sons, Inc.u2003J Comput Chem 19: 1716–1723, 1998

An off-lattice theory of solvation: extension of the Flory χ parameter into continuum space

Abstract The off-lattice theory of solvation presented here is a generalization of the Flory–Huggins lattice theory of solvation using the fused hard-sphere system as a reference. The contact free energy, a generalization of the Flory χ , is formulated by a perturbation approach. The perturbation term contains the bulk-compression contribution in addition to the contact free energy, and the bulk-compression is shown to compensate with the hard-sphere pressure of the reference system. The contact free energy is shown to be a local thermodynamical quantity and is related to the solvent accessible surface area.

Calculation of temperature dependence of free energy caused by potential function changes

Abstract We propose a method to calculate the temperature dependence of free energy caused by potential function changes by combining λ dynamics with a method to obtain the potential of mean force (the weighted histogram analysis method) in which the free energy at any temperature can be evaluated from one or a few simulations. This method not only allows us to obtain the temperature dependence of free energy but it also has a built-in estimate for sampling errors. The temperature dependence of hydrophobic hydration at 20°C–80°C was successfully reproduced from two or four simulations.

Molecular volume, surface area, and curvature dependence of the configurational entropy change upon solvation: effects of molecular bonding

Abstract The dependence of configurational entropy change in the fused hard-sphere reference system upon solvation on the solutes volume, surface, and curvature is investigated by using the thermodynamical perturbation theory of the fused hard spheres based on a rigorous treatment of the PV term. It is shown that no volume-proportional terms exist in the solvation free energy for spherical solutes, except for the PV term which is usually negligible in liquids. The effect of solutes and solvents chain length on the configurational entropy is also presented.

Hydrophobic energy estimation for bio-molecules using liquid statistical mechanics theory

A method to estimate the hydrophobic tendency on the three dimensional lattice around a molecule which has a complex shape is proposed. The chemical potentials of non-polar amino acids are calculated with this method, and a clear correlation to the experimental data of the transfer energy of those molecules is found. This method seems to be of use to estimate the hydrophobic effect and to analyze the molecular hydrophobic affinity.