Energy of cavity formation

The nonelectrostatic components of the free energy such as the energy of cavity formation AGcav or components that take into account atomistic details of the medium (interactions between atoms inside the cavity and those in the medium) are calculated using empirical approximations (see Reference 164 for review or 165 for recent developments). These terms are do not affect the SCF procedure since their dependence on electron density p is usually neglected. 

Qausius-Mosotti ftmction for species i, Eq. (42) free energy of cavity formation, Eqs. (20). (22)... 

In the case of the hydrophobic component of the interaction, the energy of cavity formation in the mobile phase is related to the surface tension y and surface area of the molecule Atota , according to... 

Kocher JP, Prevost M, Wodak S, Lee B (1996) Properties of the protein matrix revealed by the free energy of cavity formation. Structure 4 1517-1529... 

A quite reliable estimate of the solvent effect results from theories that combine micro- and macro-scopic parameters of solute and solvent. For example, in the solvophobic theory, the energy of a solute molecule in solvent, Ejoin, is given as the sum of isolated molecule energy, Ej, and the solvation term, Ejo,v. The latter term encompasses the energy of cavity formation in the solvent to accommodate the solute, E, v, and the energy of subsequent solvent-solute interactions, Ej ,. The interaction part is composed of the energy of dispersion, Edi.p> and electrostatic, interactions. The final expression for E i can be written as... 

According to SPT, the Gibbs energy of cavity formation is calculated by (see appendix N). 

For an atom in the enzyme or the substrate to interact with the solvent it must be able to form Van der Waals contact with water molecules. The accessible surface area of an atom is defined as the area on the surface of a sphere, radius R on each point of which the centre of a solvent molecule can be placed in contact with the atom without penetrating any other atoms of the molecule (Fig. 12). R is the sum of the Van der Waals radii of the atom and solvent molecule [27]. There is a linear relationship between the solubility of hydrocarbons and the surface area of the cavity they form in water [28]. It has been estimated that the hydrophobicity of residues in proteins is 100 J/mole/A of accessible surface area [29]. The surface tension of water is 72 dynes/cm so to form a free surface area of water of 1 A costs 435 J/mole/A. The implication is that the free energy of cavity formation in water to receive the hydrophobic group is offset by favourable interactions (dispersion forces) between the solute and water. 

Another theoretical approach for the calculation of the free energy of cavity formation proceeds from the theory of microscopic curved surfaces. According to this theory, ... 

The free energy of cavity formation has been also estimated from the data on isothermal compressibility, Pr, as follows ... 

Table 4.14 contains AG values calculated in two ways, together with the experimental standard AG values for dissolution of sodium chloride, determined in various solvents. As regards the calculated values, the first (I) was obtained from the above equation, whereas in the calculation of the second (II) the term proportional to the standard free energy of vaporization, describing the energy of cavity formation in the solvent, was replaced with a constant C. 

The simplest approach is based on the concept of microscopic surface tension on the boundary between the solute cavity and the solvent. Within this approach, the fi ee energy of cavity formation is assumed simply proportional to the surface of the solute cavity, Sm ... 

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