Page 323 - Thermodynamics of Biochemical Reactions

Matrices in Chcrnical and Biochemical Thermodynamics 323

Glutmate ATP Amm ADP Pi Glutmine
Glamate 1 0 0 0 0 1
ATP 0 1 0 0 0 1
Amm 0 0 1 0 0 1
ADP 0 0 0 1 0 -1
Pi 0 0 0 0 1 -1

Since this yeids the same row reduced conservation matrix as (a), the stoichiometric number matrix and the conservation
matrix are equivalent.

5.5 Carry out the matrix multiplications in equation 5.4-4 for the three chemical reactions involved in the hydration of
fumarate to malate in the pH range 5 to 9.

First we construct the stoichiometric number matrix (eqation 5.4-9) and the vector of chemical potentials.
Matrix 5.4-9 is given by

rx5 rx6 rx7
F2- -1 1 0
M2- 1 0 1
HF- 0 -1 0
HM- 0 0 -1
H+ 0 1 1

H20 -1 0 0
mu= { {muF,muM,muHF,muHM,muH,muIi20} 1 ;

Next we calclate the dot product of the chemical potential vector and the stoichiometric number matrix.

mu. nu

{{-muF - muH20 + muM, muF + muH - muHF, muH - muHM + muM})

The column matrix of extents of reaction is given by

TableForm [XI
xl
x2
x3

The last term in equation 5.4-4 is given by

mu. nu. x
{{(-muF - muH2O + muM) xl + (muF + muH - muHF) x2 + (muH - muHM + muM) x3}}

This corresponds with equation 5.4-10.