Page 297 - Introduction to chemical reaction engineering and kinetics

278 Chapter 10: Biochemical Reactions: Enzyme Kinetics

The reaction, S + 02 + L-DOPA, was conducted under a constant oxygen partial pressure,
such that the reaction was pseudo-zero order with respect to oxygen. Two possible kinetics
models were considered: (1) standard Michaelis-Menten kinetics, equation 10.2-9, and (2)
competitive production inhibition, in which the product L-DOPA (P) acts as inhibitor (I), and
P
= 3.9
the rate law is given by equation 10.4% Determine V,,, for each model given K,,,
“OP
and comment on the quality of the model predictions. Assume that ct
0 lo-11 The decomposition of 1-kestose is a key step in the production of fructo-oligosaccharides,
cs.
= csO -
mm01 L-l,
In model (2),
assume that the inhibition constant K2 is equal to 0.35 mm01 L-l.
which are found in many health foods because of their noncaloric and noncariogenic nature.
Duan et al. (1994) studied the decomposition of 1-kestose (S) using p-fructosfuranosidase
(E), both in the presence and absence of the competitive inhibitor glucose (G).
(a) The following initial rate data were obtained in the absence of glucose:
csJg L-l 66.7 100 150 200 250 325 500
(-rso)/g L-’ h-l 4.4 6.9 10.0 10.6 13.3 16.6 18.1
Determine the maximum reaction velocity (V,,,) and the Michaelis constant (Km) from
these data, using (i) Lineweaver-Burk analysis and (ii) nonlinear regression. Comment
on any differences between the parameter values obtained. The authors cite values of
30.7 g L-’ hhl and 349.5 g L-’ for V,,, and K,,,, respectively.
(b) The following initial rate data were obtained in the presence of 100 g L-’ glucose:

c&J g L-i 75.0 100 150 225 325 500
(-rso)l g L-l h-’ 1.5 2.3 3.0 4.0 6.2 8.6

Using the values of K,,, and V,,, estimated in part (a), estimate the value of the inhibition
constant, K2, in equation 10.4-8.
lo-12 As a model for enzyme activation (as opposed to inhibition), a six-step kinetics scheme
corresponding to that in Section 10.4.2 may be used, with activator A replacing inhibitor I.
A special case of this may involve different sites for the substrate S and A, and in which S
only binds to the EA complex. The simplified model is then
4
A+E-AB
k-l
AE++EAS
2
EA&AE+P

Derive the rate law for this model by applying the SSH to AB and AES. Show how the rate
law indicates activation (i.e., enhanced rate relative to the unactivated reaction).