Statistical mechanics in homopolypeptides. I. Theoretical approach for titration process in α helix

Abstract

We can view the titration processes in α helix conformation as a one-dimensional lattice where any site can be either charged (occupied) or uncharged (empty) as a lattice gas. Using this representation, we assume that the characteristic repulsive nature of the Coulombian interaction between charged groups is taken into account for a repulsive pair potential of Kac type: φ(x)=ν exp(−γx) where ν>0. Furthermore, the long range character of the Coulombian interaction will be saved by obtaining the grand partition function in the limit γ→0. Through this analysis we can obtain an analytical expression for the dissociation constant pK, degree of ionization α, and ionization rate dα/dpH. On the other hand, we find good agreement between the theoretical and experimental curve when we plot α vs pH. It is important to remark that the model does not have fitting parameters. Finally, we compare this result with those obtained in other models and then we mention the possibility of applying this analysis to the study of the transition region in denaturation processes induced by pH change.