Enzyme Kinetics
Enzyme Kinetics I
An enzyme-catalyzed reaction of substrate S to product P,
can be written
S
E
P
Actually, the enzyme and substrate must combine and E
recycled after the reaction is finished, just like any
catalyst.
Because the enzyme actually binds the substrate the
reaction can be written as:
k1
k2
E + S <->ES -> P + E
k- 1
The simplest reaction is a single substrate going to a single
product.
Rate or velocity of the reaction depends on the
formation of the ES
 The P -> ES is ignored
 The equilibrium constant Keq is based on the idea
that the reaction is limited to the formation of the ES
complex and that only K1 and K-1 are involved
because the thermodynamics of the reversal of K2
cause it to be minimal
k1
Keq =
K-1
How fast an enzyme catalyzes a reaction is it's rate. The rate of the
reaction is in the number of moles of product produced per
second
d[P]
rate (v) =
= k2 [ES]
dt
The relationship between the concentration of a substrate
and the rate of an enzymatic reaction is described by
looking at the concentration of S and v
 When the reaction is first order - the rate is dependent
on [S]
 When the reaction is zero order, there is no
relationship between v and S
 A second order is between 1st and 0 order, where the
relationship between V and [S] is not proportional to
[S]
Initial
Velocity
(Vi or V)
[ Substrate]
• To study enzymes, first order kinetics must be followed!
• Think of the graph of [S] vs. v in this way:
 The velocity increases as the substrate
concentration is increased up to a point where
the enzyme is "saturated" with substrate.
 At this point the rate of the reaction (v) reaches a
maximal value and is unaffected by further
increases in substrate because all of the enzyme
active site is bound to substrate
For the most part enzyme reactions are treated
as if there is only one substrate and one
product. If there are two substrates, one of
them is held at a high concentration (0 order)
and the other substrate is studied at a lower
concentration so that for that substrate, it is a
first order reaction. This leads us to the M and
M equation.
Conditions for Michaelis -Menten
Two assumptions must be met for the MichaelisMenten equation
 Equilibrium -the association and dissociation of
the substrate and enzyme is assumed to be a
rapid equilibrium and Ks is the
enzyme:substrate dissociation constant.
Conditions for Michaelis -Menten
Two assumptions must be met for the MichaelisMenten equation
• Steady state - the enzyme substrate complex ES is
at a constant value. That is the ES is formed as
fast as the enzyme releases the product. For this
to happen the concentration of substrate has to
be much higher than the enzyme concentration.
That is why we only study the initial velocity. Later
in the reaction the substrate concentration is
relatively lower and the rate of product starts to
be limited by diffusion and not the mechanism of
the enzyme.
Michaelis-Menten Enzyme kinetics
• Don't for get the two assumptions - They both lead
to the same equation, the michaelis-menten equation.
• What is this awe inspiring equation? The MichaelisMenten kinetic model explains several aspects of the
behavior of many enzymes. Each enzyme has a Km
value that is characteristic of that enzyme under
certain conditions.
Graphical model of the representation of the M&M eq.
– Reaction velocity (V) vs concentration of substrate
[S]
– - as [S] increases, velocity increases and
eventually levels off = V max
– 1st order vs zero order rates of reaction - back
to the two assumptions
– There are two important values for each enzyme
that are described by the M&M equation; V max
and Km (Michaelis-Menten constant)
• Graphically, these are shown as 1/2 V
not reach real V max so....
max
= Km can
 Mathematical model of the representation of the M&M eq. For the reaction:
k1
k2
E + S <-> ES -> P + E
k-1
1) The Michaelis constant Km is:
Km =
K-1 + K2
K1
Think of what this means in terms of the equilibrium.
Large vs. a small Km
2) When investigating the initial rate (Vo) the Michaelis-
Menten equation is:
Vo =
V max [S]
[S] + K m
Graphical representation is a hyperbola. Think of the
difference between O2 binding of myoglobin and
hemoglobin.
 When [S] << Km, the velocity is dependent on [S]
 When [S] >> Km, the initial velocity is independent of
[S]
 When [S] = Km, then Vo = 1/2 V max
Prove this mathematically and graphicaly.
• Km is a measure of the affinity of the enzyme
for it's substrate and also informs about the rate
of a reaction. The binding constant is
appoximated by Km
• Rules for using the M&M equation:
• The reaction must be first order and [S] >> E
(two assumptions)
Turnover Number - kcat - the direct measure of the
catalytic production of product. The larger the kcat is,
the more rapid the catalytic events at the enzyme's
active site must be. The number of times a binding and
reaction event "turns over"
- When the [S] << Km so that most of the enzyme is
in the free state [E]t = [E]free then V = kcat / Km
[E][S]
- This is a second order rate constant between the
substrate and the free enzyme. This is a good
measure of efficiency and specificity.
- When the kcat/Km is near very high, the fastest
the enzyme can catalyze a reaction is the diffusion
rate of a molecule!
108 - 109 / M . sec
Lineweaver-Burk (double reciprocal plot)
 Vmax and Km are not likely to be determined
by increasing [S]
 Instead the [S] vs. Vo data are transformed
to a plot of their reciprocal of each value.
 1/[S] vs. 1/Vo
Vo =
V max [S]
[S] + K
1
Vo
m
Km + [S]
=
V max [S]
And t his can be simplified t o:
1
Vo
=
Km
(V
max
) . [S]
1
+
1
V max
This is the equation for a straight line
Y = mX + b
Y = 1/Vo and X = 1 / [S]
So What?
 Km - relates to affinity ; Vmax relates to
efficiency
 Km tell how much substrate to use in an assay
 If more than one enzyme share the same
substrate, KM also will determine how to
decide which pathway the substrate will take
Vmax tells about pathways
 Rate limiting enzyme in pathway
 Km and Vmax can be used to determine
effectiveness of inhibitors and activators for
enzyme studies and clinical applications
Enzyme inhibitors
Competitive inhibition
Inhibitor is similar to substrate and
both bind to or near active site.
compete’ for binding
inhibitor is unreactive - EI state
Lineweaver Burke intersect at the
Y axis
Competitive Inhibition
Enzyme inhibitors
Noncompetitive inhibitor
inhibitor binds distal to active site
effects enzyme rate not affinity
binds E in E S or E
Reversible
Lineweaver Burke intersect at the
Y axis
Noncompetitive Inhibition
Mixed Inhibition
• Inhibitor binds to enzyme site that
involves both S binding and
catalysis
• binds E in E S or E
•
Forget the alpha business
Mixed Inhibition
Enzyme inhibitors
Uncompetitive inhibitor
binds covalently in the transition
state
suicide inhibitor
binds to the ES complex
lowers affinity and velocity
lineweaver Burke plots are
parallel
Uncompetitive Inhibition
Penicillin as a suicide substrate
• - suicide substrates are often un competitive
inhibitors that decrease the energy of the
transition state and allow the ES to have lower
energy that that of the EP.
• Bacterial cell wall - extensive cross linking of
sugars and peptides
• Penicillin (and ampicillin) have a highly reactive ß
lactam ring which makes a peptide bond very
reactive.
Penicillin as a suicide substrate
• Penicillin mimics the peptide alanine residues
and forms a low energy intermediate by
covalently reacting with a serine
• In molecular biology, we use this as a tool.
Ampicillin will stop E. coli growth. Bacteria that
have a gene (plasmid) inserted into the
bacteria have ß lactamase. An enzyme that
hydrolyses the reactive peptide bond found in
amicillin and penicillin
Competitive
Binds active site
inhibition reversed
by increasing [S]
Km app increases with
inhibitor (x axis
intercept changes)
Noncompetitive
binds to other than
binding site
not reversed by
increasing
no change in 1/Vm ax
no effect on S
binding (Km) only
slows down rate
(V)
Usually analogs of
substrate
decreased Vm axapp
(Y axis intercept)
inhibitor binds
both E free and ES
complex
Uncompetitive
Transition analog
binds covalently
ES not E free
changes both x and
y axis (Km and Vm ax)
Other Types of Inhibitors
Allosteric Regulation
• An organism must be able to regulate the catalytic
activities of its component enzymes
• coordinate many metabolic processes
• Respond to changes in the environment
• Growth and differentiation
• Both Inhibitors and affectors
Allosteric Regulation
• do not follow MichaelisMenten kinetics instead use a hill plot for
both + and – effects
• similar to O2 dissociation
of hemoglobin
Allosteric Regulation
• Two ways:
• Control enzyme availability
– Synthesis of enzyme
– Degeneration
• Control enzyme activity
– Alterations which affect
the substrate binding
affinity
– Turn over number
Allosteric Regulation
• Can cause large changes in enzymatic activity
• Regulated by covalent modifications
• Usually Phosphorylation and de-Phosphorylation of
specific Ser and Tyr residues.
Phosphorylation
• Phosphorylation is the addition of a phosphate (PO4) group to a
protein or other organic molecule.
• kinases (phosphorylation) and phosphatases (dephosphorylation)
are involved in this process. Many enzymes and receptors are
switched "on" or "off" by phosphorylation and dephosphorylation.
• Reversible phosphorylation results in a conformational change in
the structure in many enzymes and receptors, causing them to
become activated or deactivated. Phosphorylation usually occurs
on serine, threonine, and tyrosine residues in eukaryotic
proteins
Phosphorylation regulates phosphenolpyruvate (PEP) carboxylase
• CAM and C4 plants require a
separation of the initial carboxylation
from the following de-carboxylation
• Diuranal regulation is used
• IN CAM PLANTS:• Phosphorylation of the serine residue
of phosphenol-pyruvate (PEP)
carboxylase (Ser-OP) yields a form of
the enzyme which is active at night
– This is relatively insensitive to malic
acid
Photophorylation regulates phosphenolpyruvate (PEP)carboxylase
• During the day:
• De-Phosphorylation of the serine
(ser-OH) gives a form of the
enzyme which is inhibited by
malic acid
• THIS IS THE OPPOSITE WAY
AROUND FOR C4 PLANTS!
Phosphorylation
•
The addition of a phosphate (PO4) molecule to a polar R group of an
amino acid residue can turn a hydrophobic portion of a protein into a
polar and extremely hydrophilic portion of molecule.
•
In this way it can introduce a conformational change in the structure
of the protein via interaction with other hydrophobic and hydrophilic
residues in the protein
Examples:
•
•
Phosphorylation of the cytosolic components of NADPH oxidase, plays
an important role in the regulation of protein-protein interactions in
the enzyme
•
Phosphorylation of the enzyme GSK-3 by AKT (Protein kinase B) as
part of the insulin signaling pathway
Phosphorylation
• There are thousands of distinct phosphorylation sites
in a given cell since:
• There are thousands of different kinds of proteins in
any particular cell (such as a lymphocyte).
• It is estimated that 1/10th to 1/2 of proteins are
phosphorylated (in some cellular state).
• Phosphorylation often occurs on multiple distinct sites
on a given protein.
Oxidative Phosphorylation
Bisubstrate Reactions
• So far:
• Simple, single-substrate reactions that obey the
Michaelis-Menten model
• However, approx 60% of known biochemical reactions
involve two substrates and yield two products
• Either:
– transfer reactions – moving a functional group from
one substrate to the other
– Oxidation/reduction reaction between substrates
Bisubstrate Reactions
• Sequential reactions
• All substrates must combine with
the enzyme before the reaction
can occur and products are
released
• A - leading substrate
• B – following substrate
• P – 1st product leaving enzyme
• Q – 2nd product leaving enzyme
• ie NAD+ and NADH reactions
involving dehydrogenases
Bisubstrate Reactions
• Ping-pong reactions
• Group transfer reactions in which one
or more products are released before
all substrates have been added.
• Two stage reaction:
• A functional group from 1st sub (A) is
transferred to the 1st product (P)
forming a stable enzyme (F) –The Ping
• The functional group is displaced from
the enzyme by the 2nd substrate (B)
to yield 2nd product (Q), regenerating
the original form of the enzyme (E) –
The Pong
• ie many reactions involving Trypsin