Reginald H. Garrett
Charles M. Grisham
www.cengage.com/chemistry/garrett
Chapter 13
Enzyme Kinetics
Reginald Garrett & Charles Grisham • University of Virginia
Outline
• What characteristic features define enzymes?
• Can the rate of an enzyme-catalyzed reaction be defined
in a mathematical way?
• What equations define the kinetics of enzyme-catalyzed
reactions?
• What can be learned from the inhibition of enzyme
activity?
• What is the kinetic behavior of enzymes catalyzing
bimolecular reactions?
• How can enzymes be so specific?
• Are all enzymes proteins?
• Is it possible to design an enzyme to catalyze any desired
reaction?
Virtually All Reactions in Cells Are
Mediated by Enzymes
• Enzymes catalyze thermodynamically favorable
reactions, causing them to proceed at extraordinarily
rapid rates
• Enzymes provide cells with the ability to exert kinetic
control over thermodynamic potentiality
• Living systems use enzymes to accelerate and
control the rates of vitally important biochemical
reactions
• Enzymes are the agents of metabolic function
13.1 What Characteristic Features Define
Enzymes?
• Catalytic power is defined as the ratio of the enzymecatalyzed rate of a reaction to the uncatalyzed rate
• Specificity is the term used to define the selectivity of
enzymes for their substrates
• Regulation of enzyme activity ensures that the rate
of metabolic reactions is appropriate to cellular
requirements
• Enzyme nomenclature provides a systematic way of
naming metabolic reactions
• Coenzymes and cofactors are nonprotein
components essential to enzyme activity.
13.1 What Characteristic Features Define
Enzymes?
• Enzymes can accelerate reactions as much
as 1021 over uncatalyzed rates
• Urease is a good example:
• Catalyzed rate: 3x104/sec
• Uncatalyzed rate: 3x10 -10/sec
• Ratio (catalytic power) is 1x1014
Specificity
• Enzymes selectively recognize proper substrates
over other molecules
• Enzymes produce products in very high yields often much greater than 95%
• Specificity is controlled by structure - the unique
fit of substrate with enzyme controls the
selectivity for substrate and the product that’s
formed.
90% yield in each step; 35% over 10 steps
Enzyme Nomenclature Provides a Systematic
Way of Naming Metabolic Reactions
13.2 Can the Rate of an Enzyme-Catalyzed
Reaction Be Defined in a Mathematical Way?
• Kinetics is the branch of science concerned with the
rates of reactions
• Enzyme kinetics seeks to determine the maximum
reaction velocity that enzymes can attain and the
binding affinities for substrates and inhibitors
• Analysis of enzyme rates yields insights into enzyme
mechanisms and metabolic pathways
• This information can be exploited to control and
manipulate the course of metabolic events
Several Kinetics Terms to Understand
•
•
•
•
•
rate or velocity
rate constant
rate law
order of a reaction
molecularity of a reaction
Chemical Kinetics Provides a Foundation for
Exploring Enzyme Kinetics
• Consider a reaction of overall stoichiometry as
shown:
A® P
d[P] -d[ A]
v=
=
dt
dt
-[ A]
v=
= k[ A]
dt
• The rate is proportional to the concentration of A
Chemical Kinetics Provides a Foundation for
Exploring Enzyme Kinetics
• The simple elementary reaction of A→P is a firstorder reaction
• Figure 13.4 shows the course of a first-order reaction
as a function of time
• This is a unimolecular reaction
• For a bimolecular reaction, the rate law is:
v = k[A][B]
• Kinetics cannot prove a reaction mechanism
• Kinetics can only rule out various alternative
hypotheses because they don’t fit the data
The Time-Course of a First-Order Reaction
Figure 13.4 Plot of the course of a first-order reaction. The
half-time, t1/2 is the time for one-half of the starting amount of
A to disappear.
Catalysts Lower the Free Energy of Activation for
a Reaction
• A typical enzyme-catalyzed reaction must pass
through a transition state
• The transition state sits at the apex of the energy
profile in the energy diagram
• The reaction rate is proportional to the concentration
of reactant molecules with the transition-state energy
• This energy barrier is known as the free energy of
activation
• Decreasing ΔG‡ increases the reaction rate
• The activation energy is related to the rate constant
by:
- DG/ RT
k = Ae
Catalysts Lower the Free Energy of Activation for a
Reaction
Energy diagram for a chemical reaction (A→P) and the
effects of (a) raising the temperature from T1 to T2, or (b)
adding a catalyst.
The Transition State
Understand the difference between DG and DG‡
• The overall free energy change for a reaction,
DG, is related to the equilibrium constant
• The free energy of activation for a reaction, DG‡,
is related to the rate constant
• It is extremely important to appreciate this
distinction
13.3 What Equations Define the Kinetics of
Enzyme-Catalyzed Reactions?
• Simple first-order reactions display a plot of the
reaction rate as a function of reactant
concentration that is a straight line
• Enzyme-catalyzed reactions are more
complicated
• At low concentrations of the enzyme substrate,
the rate is proportional to S, as in a first-order
reaction
• At higher concentrations of substrate, the enzyme
reaction approaches zero-order kinetics
• This behavior is a saturation effect
As [S] increases, kinetic behavior changes from
1st order to zero-order kinetics
Figure 13.7 Substrate saturation
curve for an enzyme-catalyzed
reaction.
The Michaelis-Menten Equation is the
Fundamental Equation of Enzyme Kinetics
Louis Michaelis and Maud Menten's theory
• assumes the formation of an enzyme-substrate
complex
• assumes that the ES complex is in rapid
equilibrium with free enzyme
• assumes that the breakdown of ES to form
products is slower than
1) formation of ES and
2) breakdown of ES to re-form E and S
Michaelis-Menten Equation
• Derive Michaelis-Menten Equation
The Michaelis-Menten equation
Vmax [S]
v=
K m + [S]
where
and
Vmax = k2 [ET ]
Km
k-1 + k2 )
(
=
k1
Understanding Km
•
•
•
•
The "kinetic activator constant"
Km is a constant
Km is a constant derived from rate constants
Km is, under true Michaelis-Menten conditions,
an estimate of the dissociation constant of E
from S
Small Km means tight binding; high Km means
weak binding
Understanding Vmax
•
•
•
•
The theoretical maximal velocity
Vmax is a constant
Vmax is the theoretical maximal rate of the
reaction - but it is NEVER achieved in reality
To reach Vmax would require that ALL enzyme
molecules are tightly bound with substrate
Vmax is asymptotically approached as
substrate is increased
The dual nature of the Michaelis-Menten
equation
Combination of 0-order and 1st-order kinetics
• When S is low, the equation for rate is 1st order in S
• When S is high, the equation for rate is 0-order in S
• The Michaelis-Menten equation describes a
rectangular hyperbolic dependence of v on S
Table 13.3 gives the Km values for some enzymes
and their substrates
The Turnover Number Defines the Activity of
One Enzyme Molecule
A measure of catalytic activity
• kcat, the turnover number, is the number of substrate
molecules converted to product per enzyme
molecule per unit of time, when E is saturated with
substrate.
• If the M-M model fits, k2 = kcat = Vmax/Et
• Values of kcat range from less than 1/sec to many
millions per sec
The Turnover Number Defines the Activity of One
Enzyme Molecule
The Ratio kcat/Km Defines the Catalytic Efficiency
of an Enzyme
The catalytic efficiency: kcat/Km
An estimate of "how perfect" the enzyme is
• kcat/Km is an apparent second-order rate constant
• It measures how well the enzyme performs when
S is low
• The upper limit for kcat/Km is the diffusion limit the rate at which E and S diffuse together
The Ratio kcat/Km Defines the Catalytic Efficiency
of an Enzyme
Linear Plots Can Be Derived from the MichaelisMenten Equation
Be able to derive these equations
• Lineweaver-Burk:
• Begin with v = Vmax[S]/(Km + [S]) and take the
reciprocal of both sides
• Rearrange to obtain the Lineweaver-Burk equation:
1 æ Km ö æ 1 ö
1
=ç
+
÷
ç
÷
v è Vmax ø è [S] ø Vmax
• A plot of 1/v versus 1/[S] should yield a straight line
Linear Plots Can Be Derived from the MichaelisMenten Equation
Linear Plots Can Be Derived from the MichaelisMenten Equation
• Hanes-Woolf:
• Begin with Lineweaver-Burk and multiply both sides
by [S] to obtain:
Km
[S] æ 1 ö
=ç
[S]
+
÷
v è Vmax ø
Vmax
• Hanes-Woolf is best - why?
• Because Hanes-Woolf has smaller and more
consistent errors across the plot
Linear Plots Can Be Derived from the MichaelisMenten Equation
Enzymatic Activity is Strongly Influenced by pH
• Enzyme-substrate recognition and catalysis are
greatly dependent on pH
• Enzymes have a variety of ionizable side chains that
determine its secondary and tertiary structure and
also affect events in the active site
• The substrate may also have ionizable groups
• Enzymes are usually active only over a limited range
of pH
• The effects of pH may be due to effects on Km or
Vmax or both
Enzymatic Activity is Strongly Influenced by pH
The pH activity profiles of four different enzymes.
The Response of Enzymatic Activity to
Temperature is Complex
• Rates of enzyme-catalyzed reactions generally
increase with increasing temperature
• However, at temperatures above 50°to 60°C,
enzymes typically show a decline in activity
• Two effects here:
• Enzyme rate typically doubles in rate for ever 10º
C as long as the enzyme is stable and active
• At higher temperatures, the protein becomes
unstable and denaturation occurs
The Response of Enzymatic Activity to
Temperature is Complex
The effect of
temperature on enzyme
activity.
13.4 What Can Be Learned from the Inhibition of
Enzyme Activity?
• Enzymes may be inhibited reversibly or
irreversibly
• Reversible inhibitors may bind at the active site or
at some other site
• Enzymes may also be inhibited in an irreversible
manner
• Penicillin is an irreversible suicide inhibitor
Reversible Inhibitors May Bind at the Active Site
or at Some Other Site
Competitive Inhibitors Compete With Substrate for
the Same Site on the Enzyme
Lineweaver-Burk plot of competitive inhibition, showing lines
for no I, [I], and 2[I].
Pure Noncompetitive Inhibition – where S and I
bind to different sites on the enzyme
Lineweaver-Burk plot of pure noncompetitive inhibition. Note
that I does not alter Km but that it decreases Vmax.
Mixed Noncompetitive Inhibition: binding of I by E
influences binding of S by E
Lineweaver-Burk plot of mixed noncompetitive inhibition. Note
that both intercepts and the slope change in the presence of
I.
Uncompetitive Inhibition, where I combines only
with E, but not with ES
Lineweaver-Burk plot of
uncompetitive inhibition. Note that
both intercepts change but the slope
(Km/Vmax) remains constant in the
presence of I.
Enzymes Can Be Inhibited Irreversibly
Penicillin is an irreversible
inhibitor of the enzyme
glycoprotein peptidease,
which catalyzes an
essential step in bacterial
cell all synthesis.
13.5 - What Is the Kinetic Behavior of Enzymes
Catalyzing Bimolecular Reactions?
• Enzymes often catalyze reactions involving two
(or more) substrates
• Bisubstrate reactions may be sequential or
single-displacement reactions or doubledisplacement (ping-pong) reactions
• Single-displacement reactions can be of two
distinct classes:
1. Random, where either substrate may bind
first, followed by the other substrate
2. Ordered, where a leading substrate
binds first, followed by the other substrate
Conversion of AEB to PEQ is the Rate-Limiting
Step in Random, Single-Displacement Reactions
In this type of sequential reaction, all possible binary
enzyme-substrate and enzyme-product complexes are
formed rapidly and reversibly when enzyme is added to a
reaction mixture containing A, B, P, and Q.
In an Ordered, Single-Displacement Reaction,
the Leading Substrate Must Bind First
The leading substrate (A) binds first, followed by B.
Reaction between A and B occurs in the ternary complex
and is usually followed by an ordered release of the
products, P and Q.
An Alternative way of Portraying the Ordered,
Single-Displacement Reaction
13.5 - What Is the Kinetic Behavior of Enzymes
Catalyzing Bimolecular Reactions?
Single-deplacement bisubstrate mechanism.
The Double Displacement (Ping-Pong)
Reaction
Double-Displacement (Ping-Pong) reactions proceed via
formation of a covalently modified enzyme intermediate.
Reactions conforming to this kinetic pattern are characterized
by the fact that the product of the enzyme’s reaction with A
(called P in the above scheme) is released prior to reaction of
the enzyme with the second substrate, B.
An Alternative Presentation of the DoubleDisplacement (Ping-Pong) Reaction
The Double Displacement (Ping-Pong)
Reaction
Doubledisplacement
(ping-pong)
bisubstrate
mechanisms are
characterized by
parallel lines.
13.7 – How Can Enzymes Be So Specific?
• The “Lock and key” hypothesis was the first
explanation for specificity
• The “Induced fit” hypothesis provides a more
accurate description of specificity
• Induced fit favors formation of the transition state
• Specificity and reactivity are often linked. In the
hexokinase reaction, binding of glucose in the
active site induces a conformational change in
the enzyme that causes the two domains of
hexokinase to close around the substrate,
creating the catalytic site
13.7 – Are All Enzymes Proteins?
• Ribozymes - segments of RNA that display
enzyme activity in the absence of protein
• Examples: RNase P and peptidyl transferase
• Abzymes - antibodies raised to bind the transition
state of a reaction of interest
13.8 Is It Possible to Design An Enzyme to
Catalyze Any Desired Reaction?
• A known enzyme can be “engineered” by in vitro
mutagenesis, replacing active site residues with new
ones that might catalyze a desired reaction
• Another approach attempts to design a totally new
protein with the desired structure and activity
• This latter approach often begins with studies “in
silico” – i.e., computer modeling
• Protein folding and stability issues make this
approach more difficult
• Further, the cellular environment may provide
complications not apparent in the computer
modeling
13.8 Is It Possible to Design An Enzyme to
Catalyze Any Desired Reaction?
cis-1,2-Dichloroethylene (DCE) is an industrial solvent that
poses hazards to human health.
Site-directed mutations have enabled the conversion of a
bacterial epoxide hydrolase to catalyze the chlorinated
epoxide hydrolase reaction.