Enzyme Kinetics and Metabolic Control Analysis
233
determination of the other elasticities since the first mass balance is now uncoupled from the other two
balances. This topic is taken up in Problem 6.3._________________________________________________
PROBLEM S
Problem 6.1 Simulation of an enzymatic reaction.
Consider the enzyme kinetics discussed in detail in Section 6.3, and specifically in Example 6.5. The rate
constants of r, and
r2 (k,
and
k2)
are respectively 0.5 and 1 g substrate
S
converted (L reactor h)'1.
is 1 g
L 1.
The
parameters
a
,
b
and
c
have
the
values
1,
0.5
and
0.5
at
=
1
g
L'1
.
A continuous, stirred tank reactor is fed with S' in a concentration sf .
p,
= 0. Make a simulation study in
which the productivity of P is determined for different values of dilution rate
D
and of sf
Problem 6.2 Analysis of an enzymatic two-step reaction sequence with a non-competitive inhibition
in the first step.
The two-step reaction sequence with a competitive inhibition of the first step has been exhaustively
analyzed in Section 6.3. Make the same analysis when the first step is non-competitively inhibited by the
intermediate S. Try as far as possible to work with dimensionless groups of parameters in order to make
the analysis of more general value. Give the dimensionless parameter groups specific numerical values in
order to make a simulation study of the results.
Problem 6.3 The Delgado and Liao method applied to deviation variables
a.
Prove that if e0| = 0 no information concerning en and e,2 can be obtained by measurement of
s(t)
in the experimental set-up described in eq (30) of example 6.5.
b.
For Ed # 0 derive formulas similar to eq (35) in Example 6.5 for determination of the elasticities
by measurement of the three deviation variables in a transient experiment - possibly at several
values of
D.
The analysis may be somewhat simplified if you work on the system matrix alone
without at first bothering to determine the actual solutions to the mass balances.
c.
Make an
in silico
experiment (as in Example 6.5) with random relative errors on the
concentration measurements to determine how robust the method is for determination of the flux
control coefficients
Problem 6.4 Flux control coefficients from
real
experiments.
Nielsen and Jorgensen (1995) and Delgado
et al.
(1993) are some recent references to studies of the flux
control in short pathways. There are other references that you might wish to retrieve by a literature
search. For the two references (and for other references that you might find) compare the experimental
results with calculations of the kind shown in this chapter. Is the quality of the experiments good enough
to merit a quantitative treatment of the results? Any other comments to the papers?