Page 240 - Thermodynamics of Biochemical Reactions

240 Mathematica Solutions to Problems

1.7 Plot (a) the base 10 logarithm of the apparent equilibrium constant K' and (b) -RTlnK' in kJ mol-' for ATP + H20 = ADP
+ Piversus pH and pMg at 298.15 K and 0.25 M ionic strength.

klATP = 3.43 * 10 "-7;
k2ATP= .000140;
k3ATP= ,000123;
k4ATP= .0118;
kSATP= .0279;
klADP = 4.70 * 10 " -7;
k2ADP= .000161;
k3ADP = .00113;
k4ADP= .0431;
klP=2.24*10"-7;
k2P= -0266;
kref= .222;
pATP = 1 + (10 A -pH) / klATP + (10 A (-2 *pH) ) / (k1ATP * k2ATP) + (10 A -pMg) / k3ATP +
((lOA-pH) * (lO"-pMg)) / (klATP*k4ATP) + (10" (-2*pMg)) / (k3ATPek5ATP);
pADP= 1+ (10"-pH) /k1ADP+ (10" (-2*pH)) / (klADP*k2ADP) +
(lOA-pMg) /k3ADP+ ((lOA-pH) * (10"-pMg)) / (klADP*k4ADP);
pP= 1+ (10"-pH) /klP+ (lO"-pMg) /k2P;
kapp = kref * pADP * pP / ( (10 A -pH) * pATP) ;
Plot3D[Log[lO, kappl, {pH, 3, 9}, (pMg, 1, 6}, AxesLabel+ ("pH", "gMg", ''logK'"}];