Biology Reference
In-Depth Information
98
Figure 4-6. V plotted against V/[S] 0 .
One immediately realizes that not all the original three kinetic constants, k 1 ,
k -1 and k 2 can be determined in simple enzyme kinetics. If the initial enzyme
concentration, [E] 0 , is known, then V max can be used to determine k 2 , since:
However, K m is a combination of all three constants, and we cannot solve
for k 1 and k -1 separately. This is the consequence of the two simplifying
assumptions reducing the original four ordinary differential equations to
three algebraic equations. In order to understand the problems caused by
these assumptions, we need to examine the initial conditions carefully. At
time zero, [ES] = 0. However, in the “steady state” of simple enzyme
kinetics, [ES] has a non-zero value. Similarly, the enzyme concentration,
[E], is also discontinuous for t = 0- and t = 0+. As to the concentration of
the product, [P], at t = 0, its slope should be zero, not at a finite value, since
d[P]/dt = k 2 [ES] and [ES] = 0. These discontinuities of [S], [E], [ES] and
[P] are illustrated in Fig. 4-7.
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