Page 294 - Introduction to chemical reaction engineering and kinetics

10.4 Inhibition and Activation in Enzyme Reactions 275

Competitive inhibition

Figure 10.4 Lineweaver-Burk plot illustrating
comparison of competitive inhibition with no in-
l&J hibition of enzyme activity

The same conclusions can be reached by means of the linearized Lineweaver-Burk form
of the rate law. From 10.4-8, for the initial rate,

(10.4-11)

In comparison with equation 10.3-2, the intercept, l/V,,,, remains the same, but the slope
is increased by the factor (1 + q/K,). This is illustrated schematically in Figure 10.4.

A case of noncompetitive inhibition is represented by steps (l), (2), (3), and (5) of
the general scheme above:

E + S&ES (1)
k-l
E + ICE1 (inactive) (2)
2
ES + ICEIS (inactive) (3)
3
E&E++ (5)

By applying the SSH to ES, EI, and EIS, we may obtain the rate law in the form

Vl?UXCS (10.4-12)
‘-’ = cs(l + cI/K3) + K,(l + q/K,)

where K, = k-,/k, (the dissociation constant for EI) and K3 = k-,/k3 (the dissociation
constant for EIS to ES and I). Equation 10.4-12 again shows that r, (inhibited) < rp
(uninhibited, cr = 0), and that the extent of inhibition depends on ci.
If we further assume that K2 = K3, that is, that the affinity for the inhibitor is the
same for both E and ES, equation 10.4-12 simplifies to

V masapp%
rp = (10.4-13)
cs + Km