The influence of the Debye-Hückel factor in estimating the distance between interacting monomers in self-assembling...

In the study of protein self-assembly, knowledge of the extent of electrical and hydrophobic interactions is important. In previous work our group deduced an expression for the hydrophobic energy between the monomers of an assembly. This energy decays exponentially with a characteristic distance r_H. The object of this work is to obtain a more precise physical interpretation of r_H. In very simple systems, according to our model, r_H turns out to be the distance between the hydrophobic dipole moment vectors H. As systems become more complex and the action of the electrostatic dipole moment vectors D appear, discrepancies begin to be seen between the values obtained for r_H and the distances between vectors. It is observed that the simple application of Coulomb's law is not sufficient to explain these discrepancies. We introduce the (D-H) factor into the electrostatic interaction, since proteins interact within an ionic medium. This formulation implies the appearance of an exponential decay factor r_D, which is the thickness of the ionic atmosphere surrounding protein molecules. The distance adopted by two interacting monomers in a protein assembly is affected by both types of interaction and therefore is a function of both r_H and r_D. In a number of cases, the electrostatic interaction between D vectors is repulsive, generating a potential barrier that monomers are able to cross thanks to an overwhelmingly attractive hydrophobic potential well. In other cases both interactions are attractive and the distance between monomers appears as a compromise of both r_H and r_D.