Page 21 - Academic Press Encyclopedia of Physical Science and Technology 3rd BioChemistry

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Encyclopedia of Physical Science and Technology EN005G-231 June 15, 2001 20:46

628 Enzyme Mechanisms

also be enzymes; this type of enzyme activity will not be version of a single substrate to product, the kinetic scheme
discussed in this article. For the purposes of this discus- is generally represented by
sion, we will explore how protein molecules, sometimes
k 1 k 2
in conjunction with cofactors, use chemistry to convert E + S ES E + P,
substrates to products. The availability within a protein, k −1 k −2
or through cofactors, of nucleophiles or electrophiles, acid where S and P are the substrate and the product, E is the
or base residues, redox centers, or other features associ- free enzyme, and ES is the associated enzyme · substrate
ated with chemical catalysts, when coupled to the selective complex, also called a Michaelis complex. The rate con-
pressure of evolution, has afforded selective and efficient stants k 1 , k −1 , k 2 , and k −2 describe the rates of each step
catalysts. The study of enzyme mechanisms aims to define in the reaction. Because the concentration of ES is not
as precisely as possible the nature of the chemical steps changing, and so is at the steady state, the kinetic scheme
that effect these conversions. can be solved by relating the initial velocity at a given sub-
A logical starting point is to consider the structures strate concentration to both the maximum velocity, V max ,
of four of the representative enzymes depicted in this and the substrate concentration at which the initial veloc-
article: chymotrypsin, dihydrofolate reductase, aspartate ity reaches one-half the maximum velocity, K M , through
aminotransferase, and cytochrome P450. In general, the equation
one observes a well-defined binding site for capturing
V = V max /(1 + K M /[S]).
the substrate and executing the chemical transformation
through various polar and nonpolar interactions between The term K M is the ratio (k −1 + k 2 )/k 1 and only approxi-
the substrate and the amino acids that line the active site. mates the binding of S to E. The turnover number, or k cat ,
8
Much of the rate acceleration (up to 10 -fold) for enzy- is simply V max /[E o ] where E o is the total enzyme concen-
matic catalysis can often be attributed to the juxtaposition tration. A description of the transformation of substrate
of substrates and catalytic residues within the active site to product generally shows V as a hyperbolic function of
cavity. There are currently available X-ray crystallo- S concentration with V increasing asymptotically toward
graphic structures of enzymes, many with active sites V max as the active site becomes saturated with S.
occupied with inhibitors and determined to a resolution of Even in this simple case, the extraction of the magni-
˚
less than 2.5 A, which permit inferences as to the mech- tude of the four specific rate constants requires numeri-
anism of the chemical transformation. Nuclear magnetic cal analysis, with additional complexity being introduced
resonance (NMR) and optical spectroscopic methods by the appearance of intermediates or the requirement
provide important, complementary data on solution for a second or third substrate. These complications lead
structure. Despite considerable differences in the primary to equations in which the additional rate constants can-
amino acid sequence, the overall protein fold with its α- not be calculated from steady-state data. However, the
helical and β-sheet secondary structural elements is often analogous terms for K M and k cat can be calculated and
retained for classes of transformations that are related hold similar meanings. Perhaps the most useful applica-
through a common mechanistic species and thus consti- tion of steady-state kinetics at this level is the recogni-
tute members of a protein superfamily. One implication tion of diagnostic patterns in the reciprocal replots of the
is that the entire tertiary structure, not merely the active initial velocity data as a function of substrate concentra-
site, is important in the efficiency and selectivity of the tion. Two-substrate reactions fall into two general classes
chemical transformation. The structures we have chosen represented by
will serve to illustrate how the convergence of the knowl-
k 1 k 2
edge of structure with the output from other experimental E + A EA EX + C
k −1 k −2
tools provides arguments for probable mechanisms of
catalysis. k 3 k 4
EX + B EXB E + D
k −3 k −4
and
II. ENZYME KINETICS
k 1 k 2 k 3 k 4
E + A EA + B EAB EDC ED
The study of the rates of enzyme-catalyzed transforma- k −1 k −2 k −3 k −4
tions provides invaluable information as to the number
of steps and their magnitude in the catalytic process. The + C k 5 E + D.
most common method is to use steady-state conditions in k −5
which the enzyme is at <10 −8 M concentration and the The difference is that in the former process a fragment X
substrate(s) µM or higher. In the simplest case of the con- of substrate A is transferred covalently to the enzyme and