Page 338 - Thermodynamics of Biochemical Reactions

338 Mathernatica Solutions to Problems

7.1 Use the equilibrium constants in equations 7.1-3 to 7.1-6 to calculate the further transformed Gibbs energies of formation
of the forms of the tetramer of hemoglobin and of the pseudoisomer group at Oz] = 5 x~O-~, and 2 xlO-'M. (a)
Make a table with the last three columns like Table 7.1. (b) Calculate the equilibrium mole fractions of forms of the tetramer
at 21.4 OC, 1 bar, pH 7.4, Cl-] = 0.2 M, and 0.2 M ionic strength and make a table like Table 7.2.

(a) Calculate further transformed Gibbs energies of forms of the tretramer and the pseudoisomer group Ttot.

calctgfT[ke~,conco2~]:=Module[{b,m,tgf,ge~nO2,gtrans,g~so,out~ut~,~*This program
returns the standard further transformed Gibbs energies of formation of the forms of
the tetramer of hemoglobin and the standard further transformed Gibbs energy of the
pseudoisomer group at a specified molar concentration of molecular oxygen and
specified equilibrium constants. keg_ is a vector of equilibrium constants. conco2
is the molar concentration of molecular oxygen.*)
b=-1*(8.31451*10A-3)*294.65*Log[ke~li16.1;
m=~~1.0,0,03,~-1.1,0,0~,~0,-1,1,0~,~0,0,-1,1~~;
ge=LinearSolve[m,bl;
tgf={Flatten[{O,ge}I};
n02=C{Oll,2,3,4~1;
gtrans=Transpose[tgf]-Transpose[nO2l*(16.l+(8.3l45l*lOA-3)*294.65*Log~conco2l~;
giso=-l*(8.31451*10A-3)*294.65*Log[Aggly[Plus,Exp[-gtrans/((8.31451*10A-3)*294.65~lll;
output={gtrans,giso};
Return[output] I

keq={43970.,12210.,404900.,664400.};

coll=Flatten[calctgfT[keq,5*10A-611;

co12=Flatten[calctgfT[keq,10A-511;

co13=Flatten[calctgfT[keq,2*10A-511;
TableForm[Transpose[{coll,col2,col3~l,TableHead~ngs-
> { { T n, "T ( 02 ) I', " T ( 02 ) 2 " , "T ( 02 ) 3 'I, 'IT ( 02 ) 4 'I, 'IAf G ' I o ( TO tT ) " } , " 5x1 0 A - 6 M" , " 10 A - 5
{
M","2x10A-5 M")}l
5~10"-6 M 10A-5 M 2~10"-5 M
T 0 0 0
"(02) 3.71109 2.01297 0.314846

T(02)2 10.5611 7.16484 3.76859
T(02)3 8.83313 3.73877 -1.3556
T(02)4 5.89189 -0.900589 -7.69307
AfG' 'O(T0tT) -0.736508 -2.8149 -8.06907

(b) Calculate the equilibrium mole fractions of the various foms of the tetramer.

TableForm[Transpose[{colll,coll2,coll3~~,TableHead~ngs-
{
)
)
> { { "T" , "T (02 'I, "T (02 2 'I, "T (02 3 'I, 'IT (02 4" } , "5x1 0 - 6 M" , " 10 A - 5 M" , "2x1 0 A - 5 M" 1 1 1
)
)
A