Precipitation in Water-Miscible Organic Solvents

Addition of a water-miscible organic solvent tends to lower the dielectric constant e, which in turn enhances charge-dipole and dipole-dipole interactions, which again in turn reduces protein solubility and induces protein precipitation. The empirical correlation of Eq. (8.62) has been found very useful [S] is protein solubility, [S]0 is solubility at infinite e, and I( is a constant (K 0) at constant I and T but does depend on the charge and shape of the protein. 

2 Building Quantitative Models for the Hofmeister Series and Cohn-Edsall and Setschenow Equations 

While the Hofmeister series and the Cohn-Edsall and Setschenow equations are useful tools for the estimation of protein stability and precipitation behavior, their usefulness is limited because of the lack of a quantitative relationship to molecular or solution properties. The goal of past and current efforts is to quantify the Hofmeister series and to predict the constants Ks and /3 (or Ks and log [E]0) in the Cohn-Edsall or Setschenow equations, respectively. Some of the most relevant efforts focus on  

One approach (Melander, 1977) treats the protein as a dipole and applies the Kirkwood equation (Kirkwood, 1943), which attributes the influence of ionic strength to both electrostatic and hydrophobic forces [Eqs. (8.63) or (8.64)]. 

and D are constants, the electrostatic term is expressed by A = Dfi/RT in which fl is the dipole moment of the protein, and the hydrophobic term is expressed by Q, = [N E + 4.8N1 3V2/3(Ke -1)]/RT, where N is Avogadro s number, t is the non-polar surface area of the protein, V the molar volume of the solvent, and 7 is the surface tension increment, i.e., the difference between the surface tensions with and without salt x6 is a correction factor for the surface tension to take account of the curvature of the protein surface at molecular dimensions. 

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