Page 227 - Thermodynamics of Biochemical Reactions

Basii3iochemData2 227

Plot [calcappredpot [nadox+de==nadred,2,pH, .251, {pH,5,9),AxesLabe1->{"pH1',"E' /V"l] ;

E' /V
-0.2
-0.2

PH
-0.3
-0.3
-0.3

9.10 Calculation of equilibrium compositions of a single biochemical reaction or a system of
biochemical reactions at specified pH

Equilibrium compositions of systems of biochemical reactions can be calculated using the following two programs. The first
was written by Fred Krambeck (Mobil Research and Development) and the second was written by Krambeck and Alberty.
The Newton-Raphson method is used to iterate to the composition with the lowest possible Gibbs energy or transformed
Gibbs energy.
equcalcc[as_,lnk_,no_I:=Module[Cl,x,b,ac,m,n,e,k},
(* as=conservation matrix
Ink=-(l/RT)(Gibbs energy of formation vector at T)
no=initial composition vector *)
( *Setup*)
{m,n)=Dimensions[asl;
b=as .no;
ac=as;
(*Initialize*)
l=LinearSolve[ as.Transpose[asl,-as.(lnk+Log[nl) 1;
(*Solve*)
Do[ e=b-ac.(x=E"(lnk+l.as) );
If[(lO*-lO)>Max[ AbsIel 1, Break11 I;
l=l+LinearSolve[ac.Transpose[as*Table~x,~mlll,el,
{k, 100) 1 ;
If [ k=lOO,Return[i*Algorithm Failed"1 1 ;
Return [XI
1
equcalcrx[nt-,lnkr-,no-]:=Module[{as,lnk},
(*nt=transposed stoichiometric number matrix
lnkr=ln of equilibrium constants of rxs (vector)
no=initial composition vector*)
( *Setup*)
lnk=~inearSolve~nt,lnkrl;
as="ullSpace [nt ;
1
equcalcc[as,lnk,nol
1
The reaction considered here is the hydrolysis of glucose 6-phosphate to glucose and inorganic hosphate at 298.15 K, pH 7,
and 0.25 M ionic strength. The objective is to calculate the equilibrium concentrations when the enzyme is added to a 0.10
M solution of glucose 6-phosphate.
G6P + H2 0 = Glu + Pi
This is a single reaction, and so the equilibrium comosition can be readily calculated without a computer program. However,