Page 283 - Introduction to chemical reaction engineering and kinetics

264 Chapter 10: Biochemical Reactions: Enzyme Kinetics

are constant, and that shear effects are negligible, and focus on the effects of concen-
tration (of substrate and enzyme) in a rate law. These are usually studied by means of
a batch reactor, using either the initial-rate method or the integrated-form-of-rate-law
method (Section 3.4.1.1). The initial-rate method is often used because the enzyme con-
centration is known best at t = 0, and the initial enzyme activity and concentration are
reproducible.

10.2 MODELS OF ENZYME KINETICS

10.2.1 Michaelis-Menten Model

The kinetics of the general enzyme-catalyzed reaction (equation 10.1-1) may be
simple or complex, depending upon the enzyme and substrate concentrations, the
presence/absence of inhibitors and/or cofactors, and upon temperature, shear, ionic
strength, and pH. The simplest form of the rate law for enzyme reactions was proposed
by Henri (1902) and a mechanism was proposed by Michaelis and Menten (1913)
which was later extended by Briggs and Haldane (1925). The mechanism is usually
referred to as the Michaelis-Menten mechanism or model. It is a two-step mechanism,
the first step being a rapid, reversible formation of an enzyme-substrate complex,
ES, followed by a slow, rate-determining decomposition step to form the product and
reproduce the enzyme:

S + E$ES (fast) (1)
1
E&P+E (slow) (2)

Henri and Michaelis and Menten assumed that the first step is a fast reaction virtually
at equilibrium, such that the concentration of the complex, ES, may be represented by:

klcSCE
cES = k-,
ens and cn are related by a material balance on the total amount of enzyme:

cE + cES = cEo (10.2-2)
Thus, combining 10.2-1 and 10.2-2, we obtain the following expression for ens:

CSCEO
klCSCEo =- (10.2-3)
cEs = klcs + k-,

The ratio k-,/k, is effectively the dissociation equilibrium constant3 for ES in step (1)
and is usually designated by K,,, (Michaelis constant, with units of concentration). The
rate of formation of the product, P, is determined from step (2):4

V = ?-, = krCES (10.2-4)

31n the biochemical literature, equilibrium constants are expressed as dissociation constants (for complexes),
rather than as association constants.
41n the biochemical literature, the rate of reaction (e.g., rp) is expressed as a reaction “velocity” (v). In this
chapter, we continue to use r to represent reaction rate.