Page 330 - Thermodynamics of Biochemical Reactions

330 Mathematica Solutions to Problems

6.4 The following reaction is carried out enzymatically at 298.15 K, pH 7, and 0.25 M ionic strength.
ATP + glucose = glucose6phos + ADP
The initial concentrations of ATP and glucose are 0.001 M. What is the equilibrium composition? Solve this problem using
Mathematica in two ways.

(BasicBiochemData2 has to be loaded)

Use equcalcrx: First calculate the apparent equilibrium constant.

18973.7

equcalcrx [nt-, lnkr-,no-l :=Module [ {as, Ink},
(*nt=transposed stoichiometric number matrix
lnkr=ln of equilibrium constants of rxs (vector)
no=initial canposition vector*)
( *Setup*
lnk=LinearSolve Int , lnkrl ;
I
as-Nullspace [nt ;
equcalcc [as,lnk,nol
I

-6 -6
{7.20251 10 , 7.20251 10 , 0.000992797, 0.000992797)
These are the equilibrium concentrations of ATP, glucose, glucose6phos, and ATP.
This problem can also be solved using NSolve. Since there are four unknown concentrations, there have to be four indepen-
dent relations between these four unknowns. There is one equilibrium constant expression and three conservations equations,
which we take here to be the conservation of adenosine, glucose entity, and phosphorus.

NSolve[{cglucose6phos*cad~/(catp*cglucose)==l.9O*lOA4,catp+cad~==O.OOl,cg~ucose+cg~ucos
e6phos==.001,cat~+cglucose6~hos==.OOl},{catp,cglucose,cglucose6phos,cadp~l
-6 -6
{{cglucose -> -7.30778 10 , catp -> -7.30778 10 , cadp -> 0.00100731,
-6 -6
cglucose6phos -> 0.00100731}, {cglucose -> 7.20251 10 , catp --> 7.20251 10
cadp -> 0.000992797, cglucose6phos -> 0.000992797)}

The first solution is impossible because concentratins have to be positive. The second solution agrees with that obtained
using equcalcrx.

6.5 Calculate the apparent equilibrium constant for the net reaction for the first five reactions of glycolyis that is, reactions
6.6-1 to 6.6-5) using equation 6.1-6. Check this by simply using the net reaction.

(BasicBiochemData has to be loaded)

The stoichiometric number matrix is

TalsleForm[nu,TableHeadings-
1,
"f
>{ {llglcll, lmatp", "g6p1*, i*adpil, 6p1*, "f 16bip", 'Idihydroxyacetonephos", llglyceraldehydephos''
Automatic} I