An asymptotic comparative analysis of the thermodynamics of non-covalent association

There is an ambiguity in the theoretical models for computing association constants, the key observable in a laboratory, of non-covalent associations. We show that three different models give unique result asymptotically in the limit of strong associate. For weak associations, the disagreement reflects the nature of ill-defined "associated complex'' which can be defined, among various ways, either geometrically or thermodynamically depending on measurement techniques. Furthermore, even when the free energy of association is unique, the corresponding entropy and enthalpy can still be different from different types of measurements--a surprising source of entropy-enthalpy compensation. This work provides a mathematical basis for modeling non-covalent association processes in biology.