Cavity work scaled particle theory

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 essence of the scaled particle theory is that formation of a cavity in a fluid requires work. The theory for hard spheres has been well developed from statistical mechanics, and the work, W(R, p), can be calculated as follows ... 

Equation (7.126) is useful in actual estimation of the solvation Helmholtz energy. The cavity work is usually estimated by the scaled particle theory (Appendix N). If the soft part of the interaction is small, i.e., if fBB -C1, then we may estimate... 

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 scaled particle theory SPT) was developed mainly for the study of hard-sphere liquids. It is not an adequate theory for the study of aqueous solutions. Nevertheless, it has been extensively applied for aqueous solutions of simple solutes. The scaled particle theory (SPT) provides a prescription for calculating the work of creating a cavity in liquids. We will not describe the SPT in detail only the essential result relevant to our problem will be quoted. Let aw and as be the effective diameters of the solvent and the solute molecules, respectively. A suitable cavity for accommodating such a solute must have a radius of c ws = ((Tw + cTs) (Fig. 3.20b). The work required to create a cavity of radius a s at a fixed position in the liquid is the same as the pseudo-chemical potential of a hard sphere of radius as. The SPT provides the following approximation for the pseudochemical potential ... 

This chapter will not deal with theories of liquids per se. Instead we shall present only general relations between thermodynamic quantities and molecular distribution functions. The latter are fundamental concepts which play a central role in the modern theoretical treatment of liquids and solutions. Acquiring familiarity with these concepts should be useful in the study of more complex systems such as aqueous solutions, treated in Chapters 7 and 8. As an exception, a brief outline of the scaled particle theory is presented in section 5.11. This theory, although originally aimed at studying hard-sphere systems, has been used in systems as complex as aqueous protein solutions. The main result that will concern us is the work required to create a cavity in a fluid. This quantity is fundamental in the study of solvation phenomena of simple solutes, as well as very complex ones such as proteins or nucleic acids. 

In the preceding section we discussd the work required to create a cavity in the liquid. This concept is fundamental in the study of the solvation of solutes in any solvent. The simplest solute is a hard-sphere (HS) particle, and the simple solvent also consists of HS particles. We shall see in section 6.14 that the solvation of any solute in any solvent can always be decomposed into two parts, creating a suitable cavity and then turning on the other parts of the solute-solvent interaction. The scaled-particle theory (SPT) provides an approximate procedure to compute the work required to create a cavity. 

Each of the quantities on the rhs of (8.7.47) is the work required to create a cavity corresponding to one of the three solutes PL, P, or L. For spherical solutes, the best way to estimate these quantities is by the scaled-particle theory. For large and irregularly shaped solutes, say proteins, nucleic acids, etc., we can use the approximate expression for the cavity work (see section 5.10)... 

Brusatori and Van Tassel [20] presented a kinetic model of protein adsorption/surface-induced transition kinetics evaluated by the scale particle theory (SPT). Assuming that proteins (or, more generally, particles ) on the surface are at all times in an equilibrium distribution, they could express the probability functions that an incoming protein finds a space available for adsorption to the surface and an adsorbed protein has sufficient space to spread in terms of the reversible work required to create cavities in a binary system of reversibly and irreversibly adsorbed states. They foimd that the scale particle theory compared well with the computer simulation in the limit of a lower spreading rate (i.e., smaller surface-induced unfolding rate constant) and a relatively faster rate of surface filling. 

With the scaled particle theory, the work necessary to introduce a hard sphere solute into a liquid at a fixed position may be calculated. This is the same as the work needed to produce the cavity which is just large enough to accommodate such a hard sphere solute (Figure 1). The work is found by growing or scaling up a hard sphere particle, or equivalently the cavity, to the desired solute size. This is the origin of the name scaled particle theory. 

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