Morphometric approach to thermodynamic quantities of solvation of complex molecules: Extension to multicomponent solvent

Abstract

The morphometric approach (MA) is a powerful tool for calculating a solvation free energy (SFE) and related quantities of solvation thermodynamics of complex molecules. Here, we extend it to a solvent consisting of m components. In the integral equation theories, the SFE is expressed as the sum of m terms each of which comprises solute-component j correlation functions (j = 1, . . . , m). The MA is applied to each term in a formally separate manner: The term is expressed as a linear combination of the four geometric measures, excluded volume, solvent-accessible surface area, and integrated mean and Gaussian curvatures of the accessible surface, which are calculated for component j. The total number of the geometric measures or the coefficients in the linear combinations is 4m. The coefficients are determined in simple geometries, i.e., for spherical solutes with various diameters in the same multicomponent solvent. The SFE of the spherical solutes are calculated using the radial-symmetric integral equation theory. The extended version of the MA is illustrated for a protein modeled as a set of fused hard spheres immersed in a binary mixture of hard spheres. Several mixtures of different molecular-diameter ratios and compositions and 30 structures of the protein with a variety of radii of gyration are considered for the illustration purpose. The SFE calculated by the MA is compared with that by the direct application of the three-dimensional integral equation theory (3D-IET) to the protein. The deviations of the MA values from the 3D-IET values are less than 1.5%. The computation time required is over four orders of magnitude shorter than that in the 3D-IET. The MA thus developed is expected to be best suited to analyses concerning the effects of cosolvents such as urea on the structural stability of a protein.

Structural stability of proteins in aqueous and nonpolar environments

“…The calculation of S is finished quite rapidly by combining the ADIET [17][18][19][20][21][22][23][24][25][26][27][28][29] or RSIET 30 with the morphometric approach (MA). [31][32][33] We refer to this combination as the hybrid method. The idea of the MA is to express a hydration quantity such as S by the linear combination of only four geometric measures of a solute molecule:…”

“…The most recent method of the least square fitting is described in one of our publications. 33 (3) The four geometric measures of a protein (V ex , A, X M , and Y M ) with a prescribed structure are calculated by means of an extension 32 of Connolly's algorithm. 37,38 The x-y-z coordinates of the protein atoms are used as part of the input data to account for the polyatomic structure at the atomic level.…”

“…S is the solvation entropy and is calculated using a hybrid of the angle-dependent [17][18][19][20][21][22][23][24][25][26][27][28][29] or radial-symmetric 30 integral equation theory and the morphometric approach. [31][32][33] A smaller value of the positive quantity, −S, represents higher efficiency of the backbone and side-chain packing promoted by the entropic effect arising from the translational displacement of solvent molecules. For a membrane protein, the entropic effect is attributable to the translational displacement of the CH 2 , CH 3 , and CH groups (the CH 2 groups form the major component) which constitute nonpolar chains of lipid molecules.…”

Physical origin of hydrophobicity studied in terms of cold denaturation of proteins: comparison between water and simple fluids

“…Considering a completely solvophobic model protein [18][19][20][21][22][23] immersed in water and three species of simple solvents for which the same solvent packing fraction is assumed, we analyze the temperature dependences of the changes in free energy, energy, and entropy of the solvent upon protein unfolding. The angle-dependent 6,[13][14][15][16] and radial-symmetric [24][25][26][27] integral equation theories and the morphometric approach [28][29][30] are employed in the analysis. The three species of simple solvents considered are (i) a solvent in which the particles interact through strongly attractive potential and the particle diameter is as small as that of water (simple solvent 1); (ii) a solvent in which the particles interact through strongly attractive potential but the particle diameter is about 1.9 times larger than that of water (simple solvent 2); and (iii) a hardsphere solvent whose particle diameter is the same as that of water.…”

A Theory to Tackle Supercooling

“…Our framework can be easily adapted to more complex liquids such as systems with soft repulsive interactions and polydisperse mixtures [65]. Integral geometry underlies the core equation (3), so this approach can extend to hard particles of more complex shapes where the interaction potential is still geometric in nature.…”