Page 74 - Thermodynamics of Biochemical Reactions

4.5 Thermodynamics of Pseudoisomer Groups at Specified pH 69

written in the form

A~G;' = -RTln
RT RT
(4.5-5)

This is equivalent to
AfGio = AfG;' - RTlnP (4.5-6)
where the binding polynomial is given by

(4.5-7)

and ArGi0 is the standard transformed Gibbs energy of formation of the species
with the smallest number of dissociable hydrogen atoms. The K,, K,, . . . are the
successive acid dissociation constants at the specified pH and ionic strength,
starting with the highest pK. This equation is also useful for calculating AfG?
from the experimental value of AfG:'. The value of A,Gi' at a desired pH and
ionic strength can be calculated using equation 4.4-10.
When transformed Gibbs energies of formation are used rather than chemical
potentials, equation 4.3-4 can be written

A,Gi = AfGlo + RTln[Bi] (4.5-8)
From now on we will assume that Af GI' and A, Hio of biochemical reactants made
up of single species have been calculated using equations 4.4-10 and 4.4-12 and
that AfG;' and AfHIo of biochemical reactants with more than one species have
been calculated using equations 4.5-1 and 4.5-3.
The discussion above has emphasized A,G" and A,Ho for biochemical
reactions, but it is also useful to consider ArG' and A,H'. These quantities
correspond with changes from reactants at arbitrary concentrations to products
at arbitrary concentrations, rather than standard states (i.e., 1 M). Substituting
equation 4.5-8 in equation 4.4-1 yields
" "
ArG' = 1 v~A,G~' + RTln n [Bi]": (4.5-9)
i= 1 i= 1
which can be written
A,G' = A,G" + RTln Q' (4.5- 10)
The apparent reaction quotient Q' is given by

"
Q' = JJ [Bi]"' (4.5-1 1)
i= 1
where the concentrations of reactants can be chosen arbitrarily.
Applying equation 4.2-12 to 4.5-10 yields

ArS = A,S' - RlnQ' (4.5- 12)
where
"
A,S" = 1 vlAfSi0 (4.5-13)
i=l
Application of the Gibbs-Helmholtz equation derived from equation 4.2-16 to
equation 4.5-10 yields
ArHt = A,Ho (4.5-14)

Note A,H" does not depend on Q'.