2009_Book_FoodChemistry

118 2 Enzymes
termediary enzyme-substrate complex, EA. The
complex then forms the product P and releases
the free enzyme:
(2.30)
In order to determine the catalytic activity of the
enzyme, the decrease in substrate concentration
or the increase in product concentration as a function
of time can be measured. The activity curve
obtained (Fig. 2.21) has the following regions:
a) The maximum activity which occurs for
a few msec until an equilibrium is reached
between the rate of enzyme-substrate
formation and rate of breakdown of this
complex.
Measurements in this pre-steady state region
which provide an insight into the reaction
steps and mechanism of catalysis are difficult
and time consuming. Hence, further analysis
fo the pre-steady state will be ignored.
b) The usual procedure is to measure the enzyme
activity when a steady state has been
reached. In the steady state the intermediary
complex concentration remains constant
while the concentration of the substrate and
end product are changing. For this state, the
following is valid:
dEA
dt
= − dEA
dt
(2.31)
c) The reaction rate continuously decreases in
this region in spite of an excess of substrate.
The decrease in the reaction rate can be consideredtobearesultof:
Enzyme denaturation which can readily occur,
continuously decreasing the enzyme concentration
in the reaction system, or the product
formed increasingly inhibits enzyme activity
or, after the concentration of the product
increases, the reverse reaction takes place,
converting the product back into the initial reactant.
Since such unpredictable effects should be
avoided during analysis of enzyme activities, as
a rule the initial reaction rate, v 0 , is measured as
soon as possible after the start of the reaction.
The basics of the kinetic properties of enzymes
in the steady state were given by Briggs and
Fig. 2.21. Progress of an enzyme-catalyzed reaction
Haldane (1925) and are supported by earlier
mathematical models proposed by Michaelis and
Menten (1913).
The following definitions and assumptions should
be introduced in relation to the reaction in Equation
2.30:
[E 0 ] = total enzyme concentration available at
the start of the catalysis.
[E]
= concentration of free enzyme not bound
to the enzyme-substrate complex, EA,
i. e. [E] = [E 0 ]−[EA].
[A 0 ] = total substrate concentration available at
the start of the reaction. Under these conditions,
[A 0 ] ≫ [E 0 ]. Since in catalysis
only a small portion of A 0 reacts, the
substrate concentration at any time, [A],
is approximately equal to [A 0 ].
When the initial reaction rate, v 0 , is considered,
the concentration of the product, [P], is 0. Thus,
the reaction in Equation 2.30 takes the form:
dP
dt = υ 0 = k 2 (EA) (2.32)
The concentration of enzyme-substrate complex,
[EA], is unknown and can not be determined experimentally
for Equation 2.32. Hence, it is calculated
as follows: The rate of formation of EA,
according to Equation 2.30, is:
dEA
= k 1 (E)(A 0 ) (2.33)
dt
and the rate of EA breakdown is:
− dEA = k −1 (EA) ∗ k 2 (EA) (2.34)
dt