Application of hierarchical thermodynamic interactions to the protonation equilibria of organic polyprotic acids

A general method for formulating complex thermodynamic systems in terms of hierarchical interactions has been developed, and has been applied in a pre vious analyses to the theoretical analysis of cooperativity in a dimeric pr otein, to the statistical analysis of hemoglobin oxygen binding data, and t o the protonation equilibria of inorganic polyprotic acids. Organic polypro tic acids have served as a demonstration system for the development of conc epts and methods for treating complex biochemical equilibria. Glutamic acid is the classic test case for understanding proton-proton interactions in o rganic polyprotic acids, and this system is analyzed using the concept of h ierarchical interactions. Second order interactions were apparent between a ll three possible proton interactions, as has been established previously. The third order interaction between the three protons was found to be insig nificant, indicating that protonation of one site on glutamate has no effec t on the interaction between the other two protonation sites. This further reinforces the premise that higher order terms, representing more complex i nteractions, are less likely to be significant than lower order terms. To a llow correlation of the interaction values from glutamate with other organi c acids, pairwise interaction values between protonation events were then c alculated from known pK(d) values for a number of diprotic acids and bases. For simple straight chain acids and bases a linear log-log relationship wa s apparent between the number of intervening atoms between the protons and the pK(d,hh) (pK(d) of interaction). This relationship extended from three atoms (carbonate) up to 11 atoms (azelaic acid) and applied to both dicarbo xylic acids and diamine bases. The pairwise interactions in glutamate also followed this simple relationship. (C) 2000 Elsevier Science B.V. All right s reserved.