Disagreement between calorimetric and van't Hoff enthalpies of assembly of protein supramolecular structures

The effect of temperature on the extent of association of self-assembling protein polymers is expressed mathematically in terms of the van't Hoff enthalpy of polymerization, deltaHV.H. This quantity has been experimentally defined in two ways--from the respective temperature derivatives of the critical polymerization concentration and of the fractional conversion of protein into polymer. These two definitions are shown not to be identical, except in certain limits. In terms of both definitions, it is shown that deltaHV.H. depends not only upon the enthalpy changes but also upon the corresponding equilibrium constants for the various equilibria involved in polymer formation. This has two consequences: (i) large deltaHV.H. values may result from reactions having small calorimetric enthalpy changes; and (ii) deltaHV.H. can depend strongly on temperature. These considerations are applied to two systems for which there exist considerable experimental data--namely, hemoglobin S and tubulin. The large discrepancy between the calorimetric and van't Hoff enthalpies for the polymerization of tubulin is shown to be explicable in terms of these considerations.