Food Biochemistry and Food Processing

186 Part II: Water, Enzymology, Biotechnology, and Protein Cross-linking

for understanding in vivo function and metabolism
and for the development and clinical use of drugs
aimed at selectively altering rate constants and inter-
fering with the progress of disease states (Bauer et
al. 2001). The central scope of any study of enzyme
kinetics is knowledge of the way in which reaction
velocity is altered by changes in the concentration of
the enzyme’s substrate and of the simple mathemat-
ics underlying this (Wharton 1983, Moss 1988, Wat-
son and Dive 1994). As already discussed above, the
enzymatic reactions proceed through an intermedi-
ate enzyme-substrate complex (ES) in which each
molecule of enzyme is combined, at any given in-
stant during the reaction, with one substrate mole-
cule. The reaction between enzyme and substrate to
form the enzyme-substrate complex is reversible.
Therefore, the overall enzymatic reaction can be
shown as:

E + S ES E + P

k

k

+1 k

-1

←⎯⎯⎯→⎯ ⎯→⎯+2

where k 1 , k-1and k 2 are the respective rate con-

stants. The reverse reaction concerning the conver-

sion of product to substrate is not included in this

scheme. This is allowed at the beginning of the reac-

tion when there is no, or little, product present. In

1913, biochemists Michaelisand Mentensuggest-

ed that, if the reverse reaction between E and S is

sufficiently rapid, in comparison with the break-

down of ES complex to form product, the latter reac-

tion will have a negligible effect on the concentra-

tion of the ES complex. Consequently, E, S, and ES

will be in equilibrium, and the rates of formation

and breakdown of ES will be equal. Based on these

assumptions Michaelis and Menten produced the

following equation:

This equation is a quantitative description of the

relationship between the rate of an enzyme-

catalyzed reaction (v) and the concentration of sub-

strate [S]. The parameters Vmaxand Kmare con-

stants at a given temperature and a given enzyme

concentration. The Kmor Michaelis constant is the

substrate concentration at which vVmax/2,and its

usual unit is M. The Kmprovides information about

the substrate binding affinityof the enzyme. A high

Kmindicates a low affinity, and vice versa (Moss

1988, Price and Stevens 1999).

The Vmaxis the maximum rate of the enzyme-

catalyzed reaction, and it is observed at very high

substrate concentrations where all the enzyme mole-

cules are saturated with substrate, in the form of ES

complex. Therefore:

Vmaxkcat[Et]

where [Et] is the total enzyme concentration and kcat

is the rate of breakdown of the ES complex (k 2 ) in

scheme 8.4, which is known as the turnover num-

ber. The kcatrepresents the maximum number of

substrate molecules that the enzyme can convert to

product in a set time. The Kmdepends on the partic-

ular enzyme and substrate being used and on the

temperature, pH, ionic strength, and so on. Note,

however, that Kmis independent of the enzyme con-

centration, whereas Vmaxis proportional to enzyme

concentration. A plot of the initial rate (v)against

initial substrate concentration ([S]) for a reaction

obeying Michaelis-Menten kinetics has the form of

v

VS

KSm

=

⋅

+

max []

[]

Figure 8.8.A schematic representation of the induced-
fit hypothesis.