MAXWELL RELATIONS FOR THERMODYNAMIC QUANTITIES OF BIOCHEMICAL REACTIONS

Since equilibrium calculations for biochemical reactions such as reaction 1, ATP1 + H2O = ADP + Pi, are generally carried out with expressions of the type Kobsd = (ADP)(Pi)(ATP), where the concentrations include all species, the various thermodynamic quantities are all functions of pH and concentrations of any cations present which form complexes with reactants or products as well as temperature, pressure, and electrolyte medium. In this paper the only complexing cation considered to be present is Mg2+, so that the thermodynamic quantities are considered to be functions of only temperature, pH, and pMg2 at constant ionic strength and 1 atm. The Maxwell relations give relations between rates of change of thermodynamic quantities with respect to different independent variables. For example, it is shown that the rate of change of the heat of reaction with pH is proportional to the rate of change of the production, nH, of H+ with temperature. The rate of change of the heat of reaction with pMg is proportional to the rate of change of the production, of Mg2+ with temperature. Equations are also derived for dε∆S°obSd/εpH, ε∆S°obSd/εpMg, ε∆C°obSd/εpH, and ε∆C°obSd/εpMg in terms of NH, nMg, εnH/εr, εnmgεεT, ε2nH/εT2 and ε2nmgεT2. Contour plots are given for ε∆G°obad/ε>pH, ε∆G°obsd/pMg, ε∆H°obsd/ε)pH, ε>∆H°obsd/ εpMg, Tε∆S°obsd/ε)pH), and T(ε∆5°obsd/ε)pMg) for reaction 1 which present the dependence on pH and pMg at 25° and 0.2 ionic strength in the range pH 4-10 and pMg 1-7. The equation is derived for the change in heat capacity, ∆C°obsd, for reaction 1 and estimates of this quantity are also presented for the range pH 4-10 and pMg 1-7. In order to estimate ∆C°obsd it has been necessary to assume values of ∆C°p for the dissociations of ATP and ADP on the basis of analogy with structurally related compounds. © 1969, American Chemical Society. All rights reserved.