Page 78 - Thermodynamics of Biochemical Reactions

4.9 Effect of Temperature on Transformed Thermodynamic Properties 73

P, pH, and (', and so

(4.8-9)

(4.8 - 1 0)

Thus the effect of pH on the binding of magnesium ions by a reactant is equal to
the effect of pMg on the binding of hydrogen ions. The effect of pH on the change
in binding of magnesium ions in a biochemical reaction is equal to the effect of
pH on the binding of magnesium ions. Thus the binding of H+ and Mg2+ are
linked.

H 4.9 EFFECT OF TEMPERATURE ON TRANSFORMED
THERMODYNAMIC PROPERTIES

The effect of temperature on standard transformed thermodynamic properties of
species has been discussed in the preceding chapter on the assumption that
A,HO(Z = 0) for species are independent of temperature, or in other words,
0
C,, = 0. In order to make calculations at finite ionic strengths, it is necessary to
adjust the Debye-Huckel coefficient CI and the coefficients of the ionic strength
terms in the equations for adjusting A,Go and A,Ho for the effect of pH and ionic
strength. As discussed in Section 3.7, Clarke and Glew (1980) gave values of the
various coefficients at a series of temperatures. But in order to make calculations
at arbitrary temperatures, it is necessary to fit SI to an empirical equation, such as
3.7-3. The effects of temperature on A,G" and A,H" for biochemical reactants at
specified pH and ionic strength can be calculated by calculating these effects for
the species involved by use of equation 3.7-2. Alberty (2001d) calculated standard
A,GO and A,HO values for 22 species of biochemical interest at 283.15 and
313.15K and went on to calculate A,G" and A,H" at pH 7 and ionic strength
0.25 M for the corresponding reactants. This made it possible to calculate
apparent equilibrium constants for six biochemical reactions at 283.15 and
313.15 K. Mathenzatica programs (calcdGTsp and calcdHTsp) were written to
calculate A,G" and A,H" of species at arbitrary temperatures, pHs, and ionic
strengths. In the second program, the standard transformed enthalpies of species
are calculated using the Gibbs-Helmholtz equation. A biochemical reactant that
consists of two or more species, A,G" and A,H" can be calculated for the
pseudoisomer group in the usual way, but one must be careful to change the RT
factor in the program for A,G"(iso). When standard enthalpies of all of the
species involved in a reaction are available, K' can be calculated at desired
temperatures not too far from 298.15 K. The effect of temperature on the standard
transformed Gibbs energy of hydrolysis of ATP is shown in Table 4.1 (see
Problem 4.6).
This discussion has not included the more accurate calculations that can be
made when C: values of species are known (see equation 3.5-18). These values are
not known for many species of biochemical interest. The effects of heat capacity
terms are discussed in Chapter 10 because the existing information on Arc;'
comes primarily from calorimetric data. In principle, Ar Cp can be calculated from
measurements of apparent equilibrium constants over a range of temperatures.
Over short ranges of temperature, K' can be represented by

Ar H'O
RlnK'=A,S''-- (4.9- 1)
T
But over wider ranges of temperature, ArS0 and A,Ho are functions of tempera-
ture. Clarke and Glew (1966) have used Taylor series expansions of the enthalpy