Page 339 - Thermodynamics of Biochemical Reactions

Thermodynamics of Binding of Ligands by Proteins 339

5~10"-6 M 10A-5 M 2x10A-5 M
T 0.740351 0.316953 0.0371174
T(02) 0.162766 0.139364 0.032641
T(02)2 0.00993687 0.0170164 0.00797093
T(02)3 0.0201172 0.0688993 0.0645486
T(02)4 0.0668293 0.457767 0.857722

7.2 Use the equilibrium constants in equations 7.3-2 and 7.3-3 to calculate the further transformed Gibbs energies of forma-
tion of the forms of the dimer of hemoglobin and of the pseudoisomer group at O,] = 5 x~O-~, and 2 xlO-'M.
Make a table with the last three columns and first four rows of Table 7.3.

calctgfD[ke~,conco2~]:=Module[{b,bl,b2,m,tgf,ge,nO2,gtrans,giso,out~ut},(*This
program returns the standard frurther transformed Gibbs energies of formation of the
forms of the dimer 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.*)
b1=-1*(8.31451*10A-3)*294.65*Log[keq[[ll~l+l6.l+3O.O832;
b2~-1*(8.31451*10"-3)*294.65*L0~~k~~[[2]11+16.1;
b={bl,b2);
m={{1,0), {-1,1}3;
ge=LinearSolve [m, bl ;
tgf={Flatten[{30.0832,ge)l);
n02={{0,1,2});
gtrans=Transpose[tgf]-Transpose[nO2]*(16.l+(8.3l45l*lOA-3)*294.65*Log[conco2]);
giso=-1*(8.31451*1OA-3~*294.65*Log[A~~ly[P~us,E~[-gtrans/( (8.31451*10A-3)*294.65)lll;
output={gtrans,giso);
R€~tUrn[OUtpUtl]

keq={3.253*1OA6,8.155*lOA5);

co121=Flatten[calctgfD[keq,5*10A-611;
co122=Flatten[calctgfD[keq,10A-511;

co123=Flatten[calctgfD[keq,2*10A-511;

Table 7.3 Standard further transformed Gibbs energies of formation of dimer at 21.5 C, pH 7.4, C1-] = 0.2 M and 0.2 M
ionic strength

Tab~eForm[Transpose[{col2l,co~~~,co~~~~],TableHeadings-
)
{
> { { "D" , "D (02 ) " , "D (02 2 " , "A f G ' ' 0 (Tot D) " } , " 5x10 - 6 M" , " 10 A - 5 M" , "2x10 A - 5 M" 1 1 1
A
5x10A-6 M 10"-5 M 2x10A-5 M
D 30.0832 30.0832 30.0832
D(02) 23.2505 21.5524 19.8542
D(02)2 19.8072 16.411 13.0147
AfG' 'o(TotD) 19.2404 16.1194 12.8668
7.3 Calculate the fractional saturation YT of the tetramer of human hemoglobin with molecular oxygen using the equilibrium
constants determined by Mills, Johnson, and Akers (1976) at 21.5 OC, 1 bar, pH 7.4, [Cl-] = 0.2 M and 0.2 M ionic strength.
Make the calculation with the Adair equation and also by using the binding polymomial Y, .

kT1=4.397*10*4;