ENZYME KINETICS
Medical Biochemistry, Lecture 24
Lecture 24, Outline
• Michaelis-Menten kinetics
• Interpretations and uses of the MichaelisMenten equation
• Enzyme inhibitors: types and kinetics
Enzyme Kinetics Equation
Michaelis-Menten Equation
Initial Velocity (vo) and [S]
• The concentration of substrate [S] present will
greatly influence the rate of product formation,
termed the velocity (v) of a reaction. Studying the
effects of [S] on the velocity of a reaction is
complicated by the reversibility of enzyme
reactions, e.g. conversion of product back to
substrate. To overcome this problem, the use of
initial velocity (vo) measurements are used. At the
start of a reaction, [S] is in large excess of [P], thus
the initial velocity of the reaction will be dependent
on substrate concentration
Michaelis-Menten Curve
Initial Velocity (vo) and [S]
(cont)
• When initial velocity is plotted against [S],
a hyperbolic curve results, where Vmax
represents the maximum reaction velocity.
At this point in the reaction, if [S] >> E, all
available enzyme is "saturated" with bound
substrate, meaning only the ES complex is
present.
Michaelis-Menten Curve
Substrate Saturation of an Enzyme
A. Low [S] B. 50% [S] or Km C. High, saturating [S]
Steady State Assumption
• The M-M equation was derived in part by making
several assumptions. An important one was: the
concentration of substrate must be much greater
than the enzyme concentration. In the situation
where [S] >> [E] and at initial velocity rates, it is
assumed that the changes in the concentration of the
intermediate ES complex are very small over time
(vo). This condition is termed a steady-state rate,
and is referred to as steady-state kinetics.
Therefore, it follows that the rate of ES
formation will be equal to the rate ES
breakdown.
Michaelis-Menten Equation
Derivation
• Rate of ES formation = k1([ET] - [ES])[S]
(where [ET] is total concentration of
enzyme E and k-2 is considered neglible)
• Rate of ES breakdown to product = k1[ES] + k2[ES]
Michaelis-Menten Equation
Derivation (cont)
• Thus for the steady state assumption:
• k1([ET] - [ES])[S] = k-1[ES] + k2[ES]
• This equation is the basis for the final MichaelisMenten following algebraic rearrangement and
substitution of Km and Vmax terms.
Meaning of Km
• An important relationship that can be derived from
the Michaelis-Menten equation is the following: If
vo is set equal to 1/2 Vmax, then the relation
Vmax /2 = Vmax[S]/Km + [S] can be simplied to Km
+ [S] = 2[S], or Km = [S]. This means that at
one half of the maximal velocity, the
substrate concentration at this velocity
will be equal to the Km. This relationship has
been shown experimentally to be valid for many
enzymes much more complex in regards to the
number of substrates and catalytic steps than the
simple single substrate model used to derive it.
Meaning of Km (cont)
• The significance of Km will change based on the
different rate constants and which step is the
slowest (also called the rate-limiting step). In
the simplest assumption, the rate of ES
breakdown to product (k2) is the ratedetermining step of the reaction, so k-1 >> k2
and Km = k-1/k1. This relation is also called a
dissociation constant for the ES complex and
can be used as a relative measure of the affinity
of a substrate for an enzyme (identical to Kd).
However if k2 >> k-1 or k2 and k-1 are similar,
then K remains more complex and cannot be
Uses of Km
• Experimentally, Km is a useful parameter for
characterizing the number and/or types of
substrates that a particular enzyme will utilize
(an example will be discussed). It is also useful
for comparing similar enzymes from different
tissues or different organisms. Also, it is the Km
of the rate-limiting enzyme in many of the
biochemical metabolic pathways that determines
the amount of product and overall regulation of a
given pathway. Clinically, Km comparisons are
useful for evaluating the effects mutations have
on protein function for some inherited genetic
Meaning of Vmax
• The values of Vmax will vary widely for different
enzymes and can be used as an indicator of an
enzymes catalytic efficiency. It does not find much
clinical use.
• There are some enzymes that have been shown to
have the following reaction sequence:
• In this situation, the formation of product is dependent
on the breakdown of an enzyme-product complex, and
Derivation of kcat
• A more general term has been defined, termed
kcat, to describe enzymes in which there are
multiple catalytic steps and possible multiple
rate-limiting steps. The Michaelis-Menten
equation can be substituted with kcat
Definition and Use of kcat
• The constant, kcat (units of sec-1), is also called
the turnover number because under saturating
substrate conditions, it represents the number
of substrate molecules converted to product in
a given unit of time on a single enzyme
molecule. In practice, kcat values (not Vmax) are
most often used for comparing the catalytic
efficiencies of related enzyme classes or
among different mutant forms of an enzyme.
Two Substrate Reactions
• Many enzyme reactions involve two or more
substrates. Though the Michaelis-Menten equation
was derived from a single substrate to product
reaction, it still can be used successfully for more
complex reactions (by using kcat).
Random
Ordered
Ping-pong
Two Substrate Reactions (cont)
• In random order reactions, the two
substrates do not bind to the enzyme in any
given order; it does not matter which binds first
or second.
• In ordered reactions, the substrates bind in a
defined sequence, S1 first and S2 second.
• These two reactions share a common feature
termed a ternary complex, formed between E,
ES1, ES2 and ES1S2. In this situation, no
product is formed before both substrates bind to
Two Substrate Reactions (cont)
• Another possibility is that no ternary
complex is formed and the first
substrate S1 is converted to product P1
before S2 binds. These types of
reactions are termed ping-pong or
double displacement reactions.
Km and kcat Example:
HSV-1 Thymidine Kinase
• A phosphorylation kinase reaction: T
(thymidine) + ATP is converted to TMP
(thymidine monophosphate) + ADP
• In herpesvirus infected cells, this viral encoded
TK phosphorylates the antiviral drug acyclovir;
this is the pharmacological basis of most
herpesvirus treatments
• In the last 10 years, this approach has been
applied to cancer gene therapies with HSV-TK
and ganciclovir
Thymidine Kinetic Constants for
HSV-1 Thymidine Kinase
(ONLY AN EXAMPLE!!)
HSV-1TK
-1
Km (M) kcat (s )
kcat / Km
Gln-125 WT
0.9
0.06
67000
Asn-125
20
0.13
6500
Glu-125
3
0.003
844
Ganciclovir Kinetic Constants for
HSV-1 Thymidine Kinase
(ONLY AN EXAMPLE!)
HSV-TK
Km (M)
kcat (s-1) kcat / Km
Gln-125 WT
69
0.47
6800
Asn-125
50
0.08
1700
Glu-125
473
0.04
82
Lineweaver-Burk (double
reciprocal plot)
• If the reciprocal (1/X) of the Michaelis-Menten
equation is done, after algebraic simplification
the following equation results:
• This relation is written in the format of the
equation for a straight line, y = mx + b, where
y = 1/vo, m (slope) = Km/Vmax, x = 1/[S] and the
y-intercept, b = 1/Vmax. When this relation is
plotted,the result is a straight line graph
Lineweaver-Burk (double
reciprocal plot) (cont)
Uses of double reciprocal plot
• The x intercept value is equal to -1/Km.
The biggest advantage to using the
double reciprocal plot is a more
accurate determination of Vmax, and
hence Km. It is also useful in
characterizing the effects of enzyme
inhibitors and distinguishing between
different enzyme mechanisms.
Enzyme Inhibitor Types
• Inhibitors of enzymes are generally molecules
which resemble or mimic a particular enzymes
substrate(s). Therefore, it is not surprising that
many therapeutic drugs are some type of
enzyme inhibitor. The modes and types of
inhibitors have been classified by their kinetic
activities and sites of actions. These include
Reversible Competitive Inhibitors, Reversible NonCompetitive Inhibitors, and Irreversible Inhibitors
Definition of Ki
• For reversible inhibitors, a term Ki can be
determined.
• For competitive inhibitors, the following relation
can be used: Km + I = Km (1 + [I] / Ki ) ;
(where Km + I is the determined Km in the
presence of [I]).
• Determining the Ki for other inhibitor types is
related but much more complex and not within
the scope of this lecture or course
Uses of Ki
• Ki values are used to characterize and
compare the effectiveness of inhibitors
relative to Km. This parameter is especially
useful and important in evaluating the
potential therapeutic value of inhibitors
(drugs) of a given enzyme reaction. For
example, Ki values are used for comparison
of the different types of HIV protease
inhibitors. In general, the lower the Ki
value, the tighter the binding, and hence
the more effective an inhibitor is.
Competitive Inhibition
Vmax - No change
Km INCREASES - indicates a direct interaction
of the inhibitor in the active site
Reversible Competitive
Inhibition
• Competitive inhibitors compete with the
substrate for binding at the active site (as E + I).
In the double reciprocal plot for a competitive
inhibitor acting at the substrate site for the
following reasons, notice with increasing
concentration of inhibitor, the Vmax does not
change; however, the Km of the substrate is
increased. This also reflects the reversible
nature of the inhibitor; there is always some
concentration of substrate which can displace
Non-Competitive Inhibition
Vmax DECREASES - inhibitor affects rate of reactio
by binding to site other than substrate active-site
Km - No change
Reversible Non-Competitive
Inhibition
• Non-competitive inhibitors combine with both the
enzyme (E + I) and the enzyme-substrate (EI + S)
complex. The inhibitor binds to a site other that the
substrate site, and is thus independent of the
presence or absence of substrate. This action results
in a conformational change in the protein that affects
a catalytic step and hence decreases or eliminates
enzyme activity (formation of P). Notice in the
reciprocal plot, a non-competitive inhibitor does not
affect the binding of the substrate (Km), but it does
result in a decrease in Vmax. This can be explained
by the fact that since inhibitor bound to an enzyme
inactivates it, the more EI formed will lower [ES] and
Irreversible Inhibitors
• Irreversible inhibitors generally result in the destruction
or modification of an essential amino acid required for
enzyme activity. Frequently, this is due to some type
of covalent link between enzyme and inhibitor. These
types of inhibitors range from fairly simple, broadly
reacting chemical modifying reagents (like
iodoacetamide that reacts with cysteines) to complex
inhibitors that interact specifically and irreversibly with
active site amino acids. (termed suicide inhibitors).
These inhibitors are designed to mimic the natural
substrate in recognition and binding to an enzyme
active site. Upon binding and some catalytic
modification, a highly reactive inhibitor product is
formed that binds irreversibly and inactivates the
Irreversible Inhibitor: Allopurinol
Irreversible Inhibitor: Penicillin (Ex)
Diisopropyl Phosphofluoridate:
Irreversible Acetylcholinesterase
Inhibitor (Example)
Inhibitor Summary
• REMEMBER - The types of enzyme inhibitors
described have been for relatively simple,
single substrate-product reactions that obey
Michaelis-Menten kinetics. However, not all
enzyme inhibitors will necessarily be one type
of inhibitor. Especially for some multisubstrate reactions, a particular inhibitor can
be competitive for one substrate and noncompetitive with a second or third substrate.
Also, suicide inhibitors by design are generally
competitive inhibitors of a substrate, and