title: Application of hierarchical thermodynamic interactions to the protonation equilibria of organic polyprotic acids.
abstract: A general method for formulating complex thermodynamic systems in terms of hierarchical interactions has been developed, and has been applied in a previous analyses to the theoretical analysis of cooperativity in a dimeric protein, to the statistical analysis of hemoglobin oxygen binding data, and to the protonation equilibria of inorganic polyprotic acids. Organic polyprotic acids have served as a demonstration system for the development of concepts and methods for treating complex biochemical equilibria. Glutamic acid is the classic test case for understanding proton-proton interactions in organic polyprotic acids, and this system is analyzed using the concept of hierarchical interactions. Second order interactions were apparent between all three possible proton interactions, as has been established previously. The third order interaction between the three protons was found to be insignificant, indicating that protonation of one site on glutamate has no effect on the interaction between the other two protonation sites. This further reinforces the premise that higher order terms, representing more complex interactions, are less likely to be significant than lower order terms. To allow correlation of the interaction values from glutamate with other organic acids, pairwise interaction values between protonation events were then calculated from known pKd values for a number of diprotic acids and bases. For simple straight chain acids and bases a linear log-log relationship was apparent between the number of intervening atoms between the protons and the pK(d,hh) (pKd of interaction). This relationship extended from three atoms (carbonate) up to 11 atoms (azelaic acid) and applied to both dicarboxylic acids and diamine bases. The pairwise interactions in glutamate also followed this simple relationship.
authors.affiliation: Division of Pharmaceutical Sciences, School of Pharmacy, University of Missouri-Kansas City, 64110, USA. gutheilw@umkc.edu
authors.forename: W G
authors.initials: WG
authors.lastname: Gutheil
mesh_terms: D000143:Acids / Q000737:chemistry*; D018698:Glutamic Acid / Q000737:chemistry*; D006863:Hydrogen-Ion Concentration; D007700:Kinetics; D011522:Protons; D013816:Thermodynamics
chemical_list: D000143:Acids; D011522:Protons; D018698:Glutamic Acid