Page 77 - Thermodynamics of Biochemical Reactions

72 Chapter 4 Thermodynamics of Biochemical Reactions at Specified pH

calculated from the acid dissociation constants of the reactants using
N '
ArN, = 1 v;N,(i) (4.7-6)
i= 1
where mH(i) is the average number of hydrogen atoms bound by reactant i (see
equations 1.3-9 and 4.7-3).

H 4.8 CALCULATION OF THE CHANGE IN BINDING OF
MAGNESIUM IONS IN A BIOCHEMICAL
REACTION

The treatment (Alberty, 1998a) of the binding of Mg2+, or other metal ion that
is bound reversibly by a reactant, follows the same pattern as the treatment of
H'. A term n,(Mg)p(Mg) can be included in the Legendre transform with the
term for hydrogen as follows:

G' = G - n,(H)p(H+) - n,(Mg)p(Mg2+) (4.8-1)

where the amount of the magnesium component is given by

(4.8-2)

NMg(j) is the number of magnesium ions in speciesj. The inclusion of pMg as an
independent variable adds a term RT In( lO)n,(Mg)dpMg to the fundamental
equation for G' (see equation 4.3-l), where pMg = -log[Mg2+]. For a system
containing a single reactant, the fundamental equation for G' is

dG' = -S'dT+ VdP + p:dn: + RTln(lO)n,(H)dpH + RTln(lO)n,(Mg)dpMg
(4.8-3)
Thus, when pMg is specified. equations 4.4-9 and 4.4-1 1 become

AfGio = A,Gy - NH(j){AfGo(Hf) + RTln(lO-pH)j
- AJMg(j){Af Go(Mg2 +) + RTln( 1OPpMS)) (4.8-4)

A,Hio = A,HP - NH(j)A,Ho(H+) - NMg(j)AfHo(Mg2+) (4.8-5)
The equations for the average number of magnesium ions bound by a
reactant NMg and the change in binding of magnesium ions in a reaction ArNMg
follow the development of the preceding section:

(4.8-6)

(4.8-7)

The change in binding of magnesium ions in a biochemical reaction can also be
calculated from the acid dissociation and magnesium complex ion dissociation
constants using
"
A,NMg = 1 v;N~~(~) (4.8-8)
i=l
(See equation 1.5-5.)
The derivative of NMg (equation 4.8-6) with respect to pH at 7; P, and pMg,
and (' is equal to the derivative of N, (equation 4.7-3) with respect to pMg at 7: