Biology Reference
In-Depth Information
103
At t = 0, [P] = 0 and d[P]/dt = 0. After some time, d[P]/dt will reach the
“steady state” of simple enzyme kinetics. A critical time, t
c
, can be defined
by extrapolating the linear portion of the [P] curve to intersect the time or
horizontal axis (Dixon and Webb, 1964). From the equation of [P] just
derived, we have
Note that this critical time depends on the three kinetic constants and also
the initial substrate concentration. Together with V
max
and K
m
, t
c
provides
the third equation to determine the three kinetic constants. Therefore,
finally we have:
and
For most enzymatic reactions, t
c
is usually very small and can only be
measured by special devices.
LOW SUBSTRATE CONCENTRATION
In the original paper of Michaelis and Menten (1913), the concentration of
the product was measured at various times for different concentrations of the
substrate at the beginning of the enzymatic reaction. An example of one of
their measurements is illustrated here (Figs. 4-9 to 4-16). For higher initial
substrate concentrations, the initial rate of product formation had a constant
region followed by another slower constant region. However, for lower
initial substrate concentrations, this rate was constant for a very short
duration of probably just a few minutes. The reason for this non-linearity
was most likely due to the depletion of substrate as time went on. Without
this simplifying assumption, the rate equations mentioned above are thus
non-linear, and can only be solved numerically.
