Page 185 - Thermodynamics of Biochemical Reactions

11.4 Semigrand Partition Function for a Biochemical Reaction System 185

glucose, G6P, F6P, and FBP) in the C, pseudoisomer group. Each term is
weighted by a factor that gives the dependence on the concentrations of coen-
zymes for the pseudoisomer group being discussed. For a mixture of reactants,
like C, and C,, r” is a product of two sums of exponentials, each raised to the
power of the number of molecules in each pseudoisomer group.
This chapter is important because it shows that the thermodynamic proper-
ties of a biochemical reactant at a specified pH can be discussed in terms of a
semigrand partition function in which terms for species are multiplied by
exp( ~ NH( j)pH), where NH( j) is the number of hydrogen atoms in thejth species.
This partition function contains all the thermodynamic information about the
reactant, and so it is of interest to note that the effect of the Legendre transform
to make the pH an independent variable is to put the pH and the number of
hydrogen atoms in a species into the exponent. Similarly the thermodynamic
properties of a sum of reactants at specified concentrations of coenzymes can be
discussed in terms of a semigrand partition function in which terms for reactants
are multiplied by exp( ~ NATP(i)A G’(ATP) + NADp(i)AA ,G’(ADP)), where N,,,
molecules “contained in” reactant i. This partition function contains all the
thermodynamic information about the sum of reactants, and so it is of interest to
note that the effect of making a Legendre transform to make [ATP] and [ADP]
independent variables is to put [ATP] and [ADP] into the exponent.