Page 224 - Thermodynamics of Biochemical Reactions

224 Mathematica Solutions to rronlems

coA2 = calcdGmat[coA2sp];
Now the data entry for acetylcoA can be calculated from the apparent equilibrium constant (10.8) of this reaction at pH 7.12
and ionic strength 0.05 M.

acetylcoAsp2 = CalCGeflSp[
citrate+coA2+nadred-malate-x-nadox-h20== -8.314510.29815Log[10.8], 7.12, 0.05, 0,

{{-188.523, -, 0, 3))

acetylcoA2 = calcdGmat[acetylcoAsp2];
This calculation can be verified by using the data on coA and acetylcoA to calculate the apparent equilibrium constant for
this reaction at the experimental conditions.

calckprime[malate+acetylcoA2 +nadox+h2o+de == citrate+coA2 +nadred, 7.12, 0.051

10.8

m 9.7 Calculation of the thermodynamic properties of a biochemical reaction

It is convenient to be able to calculate the standard transformed reaction Gibbs energy, apparent equilibrium constant, and
change in binding of hydrogen ions in a biochemical reaction at a series of pHs and ionic strengths. The pH dependencies of
the standard transformed reaction Gibbs energies and IS can bt regarded as a consequence of the change in binding of
hydrogen ions.

calcNHrx[ee, pHlist-, islist-] := Module {energy),(*This program calculates the
change in the binding of hydrogen ions in a biochemical reaaction at specified ~HS and
ionic strengths.*)
energy = Solve[eq, del ;
D [energy [ [ 1,1,2 1 I , pH]/ (8.31451*0.29815*Log I101 ) / .
p~ -> pHlist /. is -> islist]

rxthermotab[ee, pHlist-, islist-] := Module[{energy, tg, tk, tn),
(*This program uses three other programs to make a thermodynamic table of
standard transformed reaction Gibbs energies, apparent equilibrium constants,
and changes in the number of hydrogen ions bound in a biochemical reaction.*)
tg = calctrGerx[eq, pHlist, islist]; tk= calckprirne[eq, pHlist, islist];
tn = calcNHrx[eq, pHlist, islist]; TableForm[Join[{tg, tk, tn)]]]

rxthermotab[pep + adp + de == pyruvate + atp, {5, 6, 7, 8, 9), {0, 0.1, 0.25}]

-33.4613 -32.7661 -30.6224 -25.1722 -19.2526
-34.1841 -33.1449 -29.2617 -23.6955 -17.993
-34.4724 -33.1063 -28.8451 -23.2908 -17.5968
728017. 549974. 231625. 25700.8 2359.9
914465. 640772. 133784. 14166.3 1419.79
6
1.09465 10 630867. 113085. 12032.5 1210.04

0.150557 0.151752 0.700597 1.06297 1.01353
0.0719355 0.38045 0.915575 0.99698 0.999809
0.0826948 0.480624 0.927296 0.993667 0.999384
The first row gives the standard transformed reaction Gibbs energies in kJ mol-l at zero ionic strength, the second row at
0.10 M ionic strength, and the third at 0.25 M ionic strength. The second part of the tsable is made up of apparent equilib-