Page 320 - Thermodynamics of Biochemical Reactions

320 Mathematica Solutions to Problems

{3, 8, 41

Note that Mathernatica makes no distinction between "row" and "column" vectors.

(d) Calculate the amounts of the components CO, H, , and CH4 for the system containing one mole of each of the five species.

ared.{l,l,l,l,l}

Note that the amount of a component can be negative.

5.2 (a) Construct the conservation matrix for the hydrolysis of ATP to ADP in terms of species. (b) Calculate a basis for
the stoichiometric matrix from the conservation matrix and show that it is consistent with equations 5.1-28 to 5.1-31.

(a) Construct the conservation matrix for the hydrolysis of ATP to ADP in terms of species.

a={{10,0,0,0,10,10,10,0}, {12,1,2,1,12,13,13,2}, {13,0,1,4,10,13,10,4}, {3,0,0,1,2,3,2,111
;
{
TableForm[a,TableHeadings-> { { "C" , "H" , "0" , "P" } , "ATPI-", "H+" , "H20", "HP042-", "mP3-
iiHATP3- WADP2- I*, "H2P04- 1 1, Tablespacing-> E 1,1.5 1 I
I#,
ATP4- H+ H20 HP042- ADP3- HATP3- HADP2- H2P04-
c 10 0 0 0 10 10 10 0
H 12 1 2 1 12 13 13 2
0 13 0 1 4 10 13 10 4

P 3 0 0 1 2 3 2 1
TableForm[RowFleduce [a] ,TableHeadings->{ { "ATP4-", "H+", 1'H20", 1'HP042-"}, ("ATP4-
'I, 'H+", "H20", 11HP042-11, "ADP3- 11, "HATP3- 'I, "KADPS- 'I, "H2PO4- } 1, Tablespacing-> { 1,l. 5 11

ATP4- H+ H20 HP042- ADP3- HATP3- HADP2- H2P04-
ATP4- 1 0 0 0 1 1 1 0
H+ 0 1 0 0 -1 1 0 1
H2 0 0 0 1 0 1 0 1 0

HP042- 0 0 0 1 -1 0 -1 1
(b) Calculate a basis for the stoichiometric matrix from the conservation matrix and show that it is consistent with equations
5.1-28 to 5.1-31.

1
TableForm[nu=~llSpace [a]
0 -10 - 1 0 0 0 1
-10 -11 0 0 1 0
-1-10 0 0 1 0 0
-11 -11 1 0 0 0

The transposed stoichiometric matrix for reactions 5.1-28 to 5.1-31 is

nutrexpected={E-l,l,-l,l,l,O,O,O},{l,l,O,O,O,-l,O,O},{O,l,O,O,l,O,-l,O},~O,l,O,l,O,O,O,
-111;