Page 295 - Introduction to chemical reaction engineering and kinetics

276 Chapter 10: Biochemical Reactions: Enzyme Kinetics

where

V max,app = V,,,,,/U + cd&) < Vm,, (10.4-14)

Equations 10.4-13 and -14 illustrate that, relative to the uninhibited case, V,,, changes
(decreases), but K,,, remains the same.
If we do not make the assumption leading to K2 = K3, then the four-step mechanism
above also represents mixed (competitive and noncompetitive) inhibition, and both K,,,
and vmlu change. In this case, equation 10.4-12 may be written as

V man,appCS
rp = (10.4-15)
cs + Km,a*p

where

V max,app = V,,,/(l + cIIK3) (10.4-16)
K = K,(l + cIIK2)l(1 + cIIK3) (10.4-17)
maPP

Treatment of the full six-step kinetic scheme above with the SSH leads to very cum-
bersome expressions for cn, cm, etc., such that it would be better to use a numerical
solution. These can be simplified greatly to lead to a rate law in relatively simple form,
if we assume (1) the first four steps are at equilibrium, and (2) k,., = kr2:

V??UlXCS (10.4-18)
rp = cs + K,(l + c,lK,)l(l + cIIK3)

This represents competitive inhibition in the sense that V,,,,, is unchanged (relative to
the uninhibited reaction), but Km is changed.

10.5 PROBLEMS FOR CHAPTER 10

10-1 If the activation energy for the decomposition of Hz.02 in aqueous solution catalyzed by the
enzyme catalase is 50 kJ mol-‘, and that for the uncatalyzed reaction is 75 kJ mol-‘, calculate
the ratio of the rate of the catalyzed reaction to that of the uncatalyzed reaction at 300 K. What
assumptions have you made in your calculation?
equation, 10.2-9, is developed in Section 10.2.1 from the point of view
10-2
The Michaelis-Menten
v
of homogeneous catalysis and the formation of an intermediate complex. Use the Langmuir-
7O-v
0 10-3 Hinshelwood model of surface catalysis (Chapter 8), applied to the substrate in liquid solution
and the enzyme as a “colloidal particle” with active sites, to obtain the same form of rate law.
Ouellet et al. (1952) have reported a kinetics analysis of the enzymatic diphosphorylation of
adenosine triphosphate (ATP). Because of the suggestion that myosin might be the transducer
which, in muscles, converts the free energy of ATP into external mechanical work, the sys-
tem chosen for study was the hydrolysis of ATP (S) in the presence of myosin to give ADP
(adenosine diphosphate) and phosphate. Their initial-rate data obtained at 25°C are as follows