Scaled-particle theory, cavity free energy

A hybrid approach of the extended scaled particle theory (SPT) and the Poisson-Boltzmann (PB) equation for the solvation free energy of non-polar and polar solutes has been proposed by us. This new method is applied for the hydration free energy of the protein, avian pancreatic polypeptide (36 residues). The contributions form the cavity formation and the attractive interaction between the solute and the solvent to the solvation free energy compensate each other. The electrostatic conffibution is much larger than other terms in this hyelration free energy, because hydrophilic residues are ionized in water. This work is the first step toward further applications of our new method to free energy difference calculation appeared in the stability analysis of protein. 

The hard part. The first term in (7.249), AG H, corresponds to turning on the hard part of the protein-solvent interaction potential. This is the same as the free energy of creating a cavity of suitable size at some fixed position in the solvent. We assume that the globular protein is spherical with an effective diameter dp, so we can calculate AG H using the scaled particle theory (see section and Appendix N). If we choose dw = 2.8 A as the diameter of a water molecule, then the cavity suitable to accommodate the protein has a radius of... 

The free energy of the cavity formation, AG v, was calculated proceeding from the scaled particle theory (SPT) [52,53]. According to this theory, the free energy of formation of a spherical cavity is given by the following formula... 

As discussed above, solvation free energy is t3q)ically divided into two contributions polar and nonpolar components. In one popular description, polar portion refers to electrostatic contributions while the nonpolar component includes all other effects. Scaled particle theory (SPT) is often used to describe the hard-sphere interactions between the solute and the solvent by including the surface free energy and mechanical work of creating a cavity of the solute size in the solvent [148,149]. 

The expression for G av, that is the free energy required for the formation of a cavity (first step in Figure 12.2.7), at a temperature T and a pressure P, is taken from the Scaled Particle Theory (SPT) which has been successfully applied in the study of thermodynamic properties of aqueous and non-aqueous solutions ... 

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