Page 21 - Thermodynamics of Biochemical Reactions

14 Introduction to Apparent Equilibrium Constants

change in the binding of magnesium ions in the hydrolysis of ATP at specified pH
is given by

( 1.5-2)
Since NH and NMg can be calculated for these reactants, Ar N, and ArNMg can be
calculated as a function of pH and pMg. However, when a computer is available
there is an easier way to do this by using equation 1.3-13 for the binding of
hydrogen ions and 1.3-14 for the binding of magnesium ions. For example,
equation 1.5-1 can be written

(1.5-3)

where of course T and P are also held constant. Note that this same result is
obtained by simply differentiating the expression for In K' (equation 1.4-8) with
respect to pH. Thus

(1.5-4)

The change in binding of Mg2+ ions can be calculated using

(1.5-5)

Since K' is a pretty complicated function of pH and pMg, it would be very
difficult to carry these calculations out by hand. However, with Mathernatica the
calculations can be done quickly. Figure 1.11 shows the change in the binding of
hydrogen ions in the hydrolysis of ATP as a function of pH and pMg. At high
pH the change in binding is -1 mole of H+ per mole of ATP hydrolyzed, as
expected from the reference reaction, which predominates at high pH. The
products bind fewer hydrogen ions, and so there is a net production of hydrogen
ions in the biochemical reaction. In the presence of magnesium ions there are
conditions where the change in binding is positive, which indicates that hydrogen
ions are consumed in the hydrolysis of ATP under these conditions.
Figure 1.12 shows the change in binding of magnesium ions as a function of
pH and pMg. Magnesium ions are always produced in the hydrolysis because

Figure 1.11 Change in the binding of hydrogen ions in the hydrolysis of ATP as a
function of pH and pMg at 298.1SK and 0.25 M ionic strength (see Problem 1.8).