Protein-binding model, Franke

Figure 12 Comparison of the parabolic Hansch model (left curve) and Franke s protein binding model (right curve). Log P, is the lipophilicity limit, where steric hindrance or other unfavorable interactions cause a change of the linear lipophilicity-activity relationship to a parabola (reproduced from Figure 9 of ref. [175] with permission from Birkhauser Verlag AG, Basel, Switzerland).

The protein-binding model of Franke yields a complex function between the logarithm of the biological activity and some suitable hydrophobic parameter consisting of a linear part that passes into a parabola if steric hindrance occurs (Franke and Schmidt, 1973). 

The second hypothesis claims that the denaturants preferentially bind to the snr-face of the proteins (Timasheff 2002a) the larger the snrface area, the more denatur-ant molecules are bound to each protein the denatured state therefore becomes more stable than the native state. Both of these proposals have been founded upon primitive and antiquated models of solutions the lattice theory of solution is the foundation of the water structure breaker hypothesis (Frank and Franks 1968), whereas the stoichiometric binding model of solvation is the basis of the preferential binding hypothesis (Scheltman 1987 Timasheff 2002a). Consequently, the weak theoretical foundation had prompted much debate, not only over the validity of these hypotheses, but also over the true meaning of these hypotheses at a molecular level. 

Franke developed another empirical model to bridge the gap between so many linear relationships and a nonlinear model (Figure 12). He considered binding of ligands at a hydrophobic protein surface of limited size as being responsible for nonlinear lipophilicity-activity relationships and formulated two equations, one for the linear left side (eq. 82) and the other one for the right side, the nonlinear part (eq. 83 log P = critical log P value, where the linear relationship changes to a nonlinear one) [435]. 

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