Approximation of the Planck-Benzinger thermal work function in protein refolding in ribonuclease systems

In reexamining the thermodynamic parameters of the protein refolding of ribonuclease systems over the temperature range of 220–360° K, based on the Nernst heat theorem, we found that at the temperature 〈Ts〉, the thermodynamic quantities ΔG0〈Ts〉 and ΔH0〈Ts〉 are of the same magnitude, while TΔS0〈Ts〉 approaches zero. Based on the Planck–Benzinger thermal work function, ΔW0(T) = ΔH0(T0) − ΔG0(T). Therefore, ΔH0(T0) = ΔW0〈Ts〉 + ΔG0〈Ts〉 at 〈Ts〉. Within the limits of statistical error, plotted values for ΔH0(T0) at 0° K and 〈Ts〉 are equivalent for each of the three ribonuclease systems we examined. Error-minimizing statistical simulation suggests that a reasonable a priori estimation of ΔH0(T0) can be made at 〈Ts〉, provided that the expansion coefficient of the Planck–Benzinger thermal work function is accurately determined. Values for ΔH0(T0) at 〈Ts〉 were determined to be 34.05 ± 1.30 and 19.49 ±0.42 kcal/mol in 20-S1 [I] and 14-S1 [II] systems, respectively. The value for ΔH0〈T0〉 at 〈Ts〉 in the ribonuclease A conformational transition as a function of pH was determined to be 59.0 kcal/mol. The magnitude of ΔH0(T0) values for 20-S1 [I] and 14-S1 [II] is an effective measure of the ease with which these molecules can be refolded to resemble the native protein structure, with greatest ease of folding at the lowest chemical bond energy. The Planck–Benzinger thermal work function, ΔW0(T), is an effective measure of the energy potentially available for any interaction to take place. ΔH0(T0), a temperature-invariant quantity, is a primary source of the chemical bond energy essential for any reaction to proceed in a biological system, and is indispensable in any consideration of macromolecular interaction. Certainly this function has yet to receive sufficient recognition in the field of thermodynamics. After applying it in studies of ribonuclease refolding and protein–protein interaction, we predict that this new state function will eventually supplant the Gibbs–Helmholtz expression in thermodynamic analysis.