Biochemistry - Chemical Reactions in Living Cells, Volume 1 - D. Metzler 1980

Bioenergetics of Biochemical Reactions
Thermodynamics
Activity Coefficients and Apparent Equilibrium Constant

Strictly speaking, equation (3-30) applies only to thermodynamic equilibrium constants, i.e., constants calculated using activities rather than concentrations. To determine such constants experimentally, one must measure the apparent equilibrium constants K' across a range of concentrations and then extrapolate the resulting relationship to infinite dilution.

Extrapolating K' to infinite dilution is usually straightforward, because the activity coefficients for many ionic compounds are simply related to Ionic strength and, in very dilute solutions (at an ionic strength <0.01), obey the Debye—Hückel equation:

The integers Z₁ and Z₂ represent the number of charges (valencies) of the cation and anion that make up the salt molecule. The ionic strength μ is given by

Here C_i is the molar concentration of the respective ion, and the summation is carried out over all ions. The activity coefficient [equation (3-32)] is the mean activity coefficient of the cation and anion.

As can be seen from equation (3-32), to extrapolate K' to infinite dilution, it is convenient to plot lg K' versus . Such a plot [10] is shown in Fig. 3-1, illustrating The change in pK'a for the dissociation of H₂PO^-₄, AMP^-, ADP^2-, and ATP^3-. At low concentrations, the dependence of pK'a on is determined using the Debye—Hückel equation [equation (3-32)]:

Graphically, this relationship is represented by a straight line with a slope equal to

The observed (negative) slope of the curves (Fig. 3-1) is –1.5 for H2PO^-₄ and AMP^-, ∼2.5 for ADP^2-, and ∼3.5 for ATP^3-. Over the entire range of ionic strength, such curves are described by empirical relationships of the form

where a and b are determined empirically. For example, for H₂PO^-₄, a = 1.52, b = 1.96. The resulting pKa value is 7.18, which is 0.22 higher than at μ = 0.2—the ionic strength most frequently used in laboratory practice—and is close to the corresponding value in Tissues. Note that for ATP^3-, the difference between the extrapolated pKa value of 7.68 and the value of ∼7.04 at μ = 0.2 is even larger. Using extrapolated values of K in calculations applied to solutions of high ionic strength can lead to serious errors. Furthermore, the higher the ionic charge (ATP^3-, ATP^4-), the greater the error.

Another difficulty in determining the equilibrium constants of reactions that consume or release hydrogen ions is the lack of an exact relationship between pH and a_H⁺ or [H⁺]. Indeed, from a thermodynamic standpoint, METABOLISM/2.html">THE CONCEPT OF a single-ion activity is virtually meaningless. Nevertheless, within the pH range of interest to biochemists—assuming that a pH meter measures hydrogen ion activity—the results obtained are very close to those yielded by more rigorous Methods. In biochemical practice, it is almost universally assumed that pH meter readings obtained with a Glass electrode yield values of — lg uH⁺, and instead of the resulting value a_H+, [H⁺] is always substituted, thereby defining the apparent equilibrium constants.

FIG. 3-1. Plot of versus apparent pK values for the secondary ionization of AMP (I), ADP (II), H₃PO₄ (III), and ATP (IV). Data obtained at 25 °C. (Phillips et al., Biochemistry, 2, 503, 1963.)

Often, data obtained for The equilibrium state cannot be extrapolated to μ = 0, in which case K' values are used to determine the apparent change in Free energy ∆G'.