Biomedical Engineering Reference
In-Depth Information
The overall rate of the enzyme catalyzed reaction with a single substrate is a function of
the amount of enzyme and substrate and is given as
¼
K
2
Enzyme
Substrate
Reaction Rate
ð
8
:
32
Þ
K
M
þ
Substrate
where
K
M
is called the Michaelis constant). We will
derive and discuss this equation in more detail later in this section.
In an enzyme catalyzed reaction with much more substrate than enzyme, the reaction
rate depends linearly on enzyme concentration according to Eq. (8.32), since the substrate
concentration is essentially a constant. When there is much more enzyme than substrate,
only a small portion of the enzyme is combined with the substrate, and the reaction rate
is determined by both the enzyme and substrate levels. The typical enzyme catalyzed reac-
tion consists of a series of reactions, each step with its own reaction rate. As we will see, the
overall reaction rate is determined by the slowest reaction in the chain of reactions. The
slowest reaction is called the capacity-limited reaction.
Enzyme catalyzed reactions serve a regulatory role, as well as accelerating biochemical
reactions. Consider the relationship between adenosine diphosphate (ADP) and ATP inside
the cell. ATP is created in the mitochondria where oxidation of nutrients (carbohydrates,
proteins, and fats) produces carbon dioxide, water, and energy. The energy from the oxida-
tion of nutrients converts ADP into ATP. ATP is used as fuel for almost all activities of the
body, such as the
K
2
and
K
M
are reaction rate constants (
pump, action potentials, synthesis of molecules, creation of hor-
mones, and contractions of muscles. At steady state, the concentration of ADP is very low
in the cell, and thus the creation of ATP in the mitochondria is at a low rate. During periods
of high cell activity, ATP is consumed, releasing energy through the loss of one phosphate
radical, leaving ADP. The increased concentration of ADP causes an increase in the oxida-
tion of nutrients in the mitochondria, producing more ATP. Thus, the ADP-ATP cycle is
balanced and based on the needs of the cell. The reactions necessary to synthesize ATP
are described in Section 8.5.
Enzyme reactions do not appear to follow the law of mass action; that is, as the substrate
increases, the reaction rate does not increase without bound but reaches a saturation level
(that is, it is capacity-limited). Capacity-limited reactions are quite prevalent and describe
most metabolic reactions and functions of the body, such as the movement of molecules
across the cell membrane and how substrates are removed from the body through the
kidneys.
Na
K
8.2.1 Michaelis-Menten Kinetics and the Quasi-Steady-State Approximation
In 1903, Victor Henri first described the relationship between a substrate and an enzyme,
followed by Michaelis and Menten in 1913, and Briggs and Haldane in 1925, with a capac-
ity-limited elimination rate for the chemical reaction. The first assumption is that the
enzyme and substrate quickly reach steady state in the formation of the complex, and then
the complex more slowly dissociates into the product and enzyme. We also assume that the
amount of enzyme is much smaller than the substrate. We refer to the combined work here
