Lecture 9
Enzymes: Basic principles
SBS017
Basic Biochemistry
Dr. Jim Sullivan
j.a.sullivan@qmul.ac.uk
Learning Objectives Lecture 9
• You should be able to able to define the terms
Enzyme, Specificity and Co-factor
• You will understand the concept of Gibbs Free
Energy and its relation to reaction equilibrium
• You will be able to describe how enzymes effect the
rate of biological reactions and be able to define
the term Activation energy in the context of
Transition state theory
Enzymes
• Biological catalysts
• Almost all enzymes are proteins (but RNA can have
enzymic activity too, “ribozymes”)
• Function by stabilizing transition states in reactions
• Enzymes are highly specific
Enzymes accelerate biological
reactions
• e.g. Carbonic Anhydrase
• CO2 + H2O
H2CO3
• Each molecule of enzyme can hydrate 1,000,000
molecules of C02 per second, 10,000,000 times faster
than uncatalysed reaction
Catalase
• 2H2O2
2H2O + O2
Enzymes are highly specific
e.g Peptide bond hydrolysis (proteolysis)
A. Trypsin cleaves only after
arginine and lysine residues.
B. Thrombin cleaves between
arginine and glycine only in
particular sequences.
But Papain cleaves all peptide bonds
irrespective of sequence.
Specificity is important
e.g. DNA polymerase I
Adds nucleotides in sequence determined
by template strand.
Error rate of < 1 in 1,000,000
Due to precise 3D interaction of enzyme
with substrate
Many enzymes require cofactors
Cofactors are small molecules essential for
enzyme catalysis
Can be:
i.Coenzymes (small organic molecules)
ii. Metal ions
Holoenzymes
Enzyme without its cofactor “apoenzyme”
With its cofactor “holoenzyme”
Cofactors are essential for activity
e.g. many vitamins are cofactors, many
diseases associated with vitamin deficiency
due to lack of specific enzyme activity
Energy transformation
Many enzymes transform energy into different forms
Adenosine Triphosphate (ATP) is universal currency
Light
ATP
Photosynthesis
Food
ATP
Respiration
ATP
work
ATP is an energy carrier
e.g. ATP provides energy to pump Ca2+ across
membranes
Free energy
The free energy of a reaction is the difference
between its reactants and its products
This called the ΔG
If ΔG is negative, the reaction will occur
spontaneously “exergonic”
If ΔG is positive, energy input is required
“endogonic”:
Endogonic reactions
Energy
(G)
Products
ΔG
positive
Reactants
Reaction coordinates
Exergonic reactions
Energy
(G)
Reactants
ΔG
negative
Products
Reaction coordinates
Exergonic reactions
Energy
(G)
H2O2
ΔG
negative
2H2O + O2
Reaction coordinates
ΔG is independent of reaction
path
Energy
(G)
Reactants
ΔG
same
Products
Reaction coordinates
ΔG and reaction equilibria
• A negative ΔG indicates that a reaction can
occur spontaneously not that it will
• ΔG tells us nothing about the rate of
reaction only the energy of its end points
• The rate of reaction is defined by the
equilibrium constant
The equilibrium constant
Keq
A+B
C+D
[C][D]
Keq 
[A][B]
Calculating ΔG
The free energy of a reaction is given by:
[C][D]
G  G  RT ln 

[A][B] 
•
Where ΔG° is the standard free energy change (i.e. change at 1M
concentrations), R is the universal gas constant and T the absolute
temperature
Calculating ΔG at pH7 (ΔG’)
At equilibrium and standard pH7:
[C][D] 
0  G'RT ln 

[A][B] 

Calculating ΔG at pH7 (ΔG’)
Rearrange and substitute K’eq:
G' RT ln K'eq
At 25 °C, in log10, rearranged for K’eq:
K'eq  10
G' / 5.69
This means that a 10-fold change in Keq is equivalent to
5.69 kJ/mol difference in energy
Reaction equilibria
Keq
Energy
(G)
A
B
If [B] = 10
[A] = 1
Then ΔG = 5.69kJ/moll
A
[B]
Keq 
[A]

5.69
kJ/mol
B
Reaction coordinates
Reaction equilibria
Keq
Energy
(G)
A
B
If [B] = 100
[A] = 1
Then ΔG = 11.38 kJ/moll
A
11.38
kJ/mol
[B]
Keq 
[A]
B

Reaction coordinates
Catalysis
• Enzymes cannot change equilibrium of
reaction
• ΔG is independent of reaction pathway
• Enzymes accelerate rate of reaction
K+1
Keq
A
B
A
K-1
B
K 1
Keq 
K1
Catalysis
K+1
A
K-1
B
K 1 10 1000
Keq 
 
K1 1 100
No enzyme
Equilibrium is same but rate is 100x greater

+ enzyme
Enzymes accelerate reaction rates
Reaction reaches equilibrium much quicker with
enzyme catalysis
Why do exergonic reactions (those with –ΔG)
not take place spontaneously?
Activation energy
• Reactions go via a high energy intermediate
• This reduces the rate at which equilibrium is
reached
• The larger the activation energy the slower
the rate
Transition state theory
Transition state, S‡
Energy
(G)
ΔG‡
A
ΔG
B
Reaction coordinates
Transition state theory
• Enzymes reduces the activation barrier
• Transition state energy becomes smaller
Transition state theory
• The rate of reaction depends on ΔG‡
• Big ΔG‡ slow reaction
• Small ΔG‡ faster reaction
• Enzymes works by reducing ΔG‡
• Enzymes stabilise the transition state
Summary
• Enzymes are biological catalysts
• Enzymes are highly specific
• Enzymes increase reaction rates but do not
alter the equilibrium of reactions
• Enzymes stabilise transition states, reducing
activation energy and increasing the rate of
reaction
Learning Objectives Lecture 9
• You should be able to able to define the terms
Enzyme, Specificity and Co-factor
• You will understand the concept of Gibbs Free
Energy and its relation to reaction equilibrium
• You will be able to describe how enzymes effect the
rate of biological reactions and be able to define
the term Activation energy in the context of
Transition state theory
Lecture 10
Enzymes Kinetics
SBS017
Basic Biochemistry
Dr. Jim Sullivan
j.a.sullivan@qmul.ac.uk
Learning objectives Lecture 10
• You should be able to describe the evidence for
enzyme/substrate complexes
• You will be able to define the terms Active sites and
Active site residues
• You should be able to describe the Michaelis-Menten
model for enzyme kinetics and the significance of
KM and Vmax
Enzyme-Substrate (ES) complexes
• Most enzymes are highly selective in binding of
their substrates
• Substrates bind to specific region of enzyme called
Active Site
• Catalytic specificity depends on binding specificity
• Activity of many enzymes regulated at this stage
Evidence for ES complexes
i. Saturation effect:
At constant enzyme concentration
reaction rate increases with substrate
until Vmax is reached.
Vmax is rate (or velocity) at which all
enzyme active sites are filled.
Evidence for ES complexes
ii. Structural data:
Crystallography (3D
structures), shows substrates
bound to enzymes
Cytochrome P450 (green) bound to
its substrate camphor
Evidence for ES complexes
iii. Spectroscopic data:
Absorption and fluorescence of proteins
and cofactors change when mixed
together
Changes in fluorescence intensity in
the enzyme tryptophan synthetase
after addition of substrates
Active sites
• The active site of enzyme is region that binds the
substrate
• The catalytic groups are the amino acid side chains
in the active site associated with the making and/or
breaking of chemical bonds
Active sites
i. The active site is a 3D structure formed by
groups that can come from distant residues in the
enzyme (tertiary structure)
A. 3D structure of Lysozyme,
active site residues coloured
B. Linear schematic of Lysozyme
amino acid primary sequence,
active site residues coloured
Active sites
ii. The active site takes up only a small volume of the
enzyme
iii. Active sites are unique chemical
microenvironments, usually formed from cleft or
crevice in enzyme.
Active sites
Active sites often exclude water, and non-polar
nature of site can enhance binding of substrates
and allows polar catalytic groups to acquire special
properties required for catalysis
Active sites
iv. Active sites bind substrates with weak interactions
Bonds can be electrostatic, hydrogen bonds, Van
der Waals and hydrophobic interactions.
ES complexes have equilibrium constants (Keq) on
the 10-2 to 10-8 range, equivalent to -3 to -12
kcalmol-1
Active sites
v. The specificity of an enzyme for its substrate(s) is
critically dependent on the arrangement of amino
acid residues at the active site
Remember importance of tertiary structure
Lock and key model
• Proposed by Emil Fischer in 1890
Induced fit model
• Substrates and enzymes are not rigid but dynamic
and flexible
• Daniel Koshland in 1958 proposed the induced fit
model
• In induced fit model the enzyme changes shape in
order to optimise its fit to the substrate only after
the substrate has bound
Induced fit model
Reaction kinetics
First order reaction (uni-molecular):
A
K
P
Rate of reaction is:
V  k[A]
Units of k: s-1
Reaction kinetics
Second order reaction (bi-molecular):
A+B
K
P
Rate of reaction is:
V  k[A][B]
Units of k: M-1s-1
But if [A]>>[B] or [B]>>[A] reaction is Psuedo First Order
Michaelis-Menten Model
• In 1913 Leonor Michaelis and Maud Menten
proposed simple model to account for kinetic
characteristics of enzymes
• They observed that a maximal reaction velocity
with saturating substrate for a fixed amount of
enzyme implies a specific ES complex is a
necessary intermediate in enzyme catalysis
Michaelis-Menten Model
• Describes the kinetic property of enzymes
At a fixed concentration of enzyme increasing
[substrate] increases reaction rate
Initial velocity V0 for each
substrate concentration is
determined from the slope
of the curve at the beginning
of the reaction where any
reverse reaction is
insignificant
Michaelis-Menten Model
Rate of catalysis V0 varies with substrate concentration
Rate is initially proportional to
[S]
Reaches a saturation value
Vmax
Michaelis-Menten kinetics
E+S
k+1
k-1
ES
k+2
k-2
E+P
An enzyme E combines with S to from an ES complex with a rate constant
of K+1
In initial reaction where reverse reaction is minimal (we can effectively
ignore K-2)
ES complex has two possible fates:
i.Dissociate to E + S with rate constant of K-1
ii.Form P with rate constant of K+2
Michaelis-Menten equation
The Michaelis-Menten equation relates the rate of
catalysis to the concentration of substrate.
V0  Vmax
Where

[S]
[S]  K M
k1  k2
KM 
k1
For derivation see
Stryer Chapter 8
Michaelis constant
KM and Vmax are measurable constants for a particular
enzymic reaction
Michaelis-Menten kinetics
Plotting initial velocity V0 of a reaction against substrate concentration [S]
produces the Michaelis-Menten curve
Understanding KM
k+1
E+S
k-1
ES
k+2
At steady-state:
rate of formation of ES = rate of breakdown of ES
k1[E][S]  (k1  k 2 )[ES]
[E ][S] (k1  k 2 )

 KM
[ES]
k 1
E+P
Significance of KM
For many reactions [S] < KM
V  Vmax

[S]
X  KM
[S]
Vmax
V
[S]
KM
Significance of KM
At high [S], [S]>>KM, V is effectively independent of [S]
V  Vmax

[S]
X
X K
XM
[S]
V  Vmax
Significance of KM
• KM for any enzyme depends on pH, temp and ionic
strength
• KM is equal to the concentration of substrate
required for the reaction velocity to be half its
maximal value

when
[S] = KM
then
V = Vmax/2
Significance of KM
If k2 << k-1 then KM is equal to the dissociation
constant of the ES complex
E+S
k+1
k-1
ES
k+2
X
E+P
k1  kX2 [E][S]
KM 

 K ES
k1
[ES]
Large KM weak binding, small KM strong binding
Under these conditions KM tells us the enzyme-substrate
affinity
Vmax
• number of substrate molecules converted into
product by an enzyme molecule per unit time when
enzyme is fully saturated
i.e [ES] = [ET], ET is total enzyme concentration
Vmax  k2[ET ]
Catalytic power
• An enzyme’s turnover is its catalytic power
• The maximum number of substrate molecules
converted into product by an enzyme molecule in
unit time
• When E is fully saturated, it is equal to the kinetic
constant k2 – also known as kcat
We can calculate kcat from Vmax since Vmax= k2[ET]
Catalytic power
E+S
k+1
k-1
ES
k+2
V  Vmax
Vmax=k2[ET]
When [S] << KM

E+P
[S]
[S]  K M
k2
V  [ET ][S]
KM
i.e Rate will increase with [ET] and [S]
The max value of k2/KM is called the diffusion limit
The perfect enzyme
• The perfect enzyme is limited by diffusion
• Max possible value of k2/KM is limited by size of k+1
to between 106 and 109 M-1s-1
• In this case k+1 is effectively a measure of how
often the enzyme collides with its substrate
The perfect enzyme
• An enzyme with a k2/KM of between 108 and 109 M1s-1 is therefore only limited by the rate of collisions
and is called diffusion limited
• The catalytic processes of such enzymes are
considered kinetically perfect because they are not
slowing the enzyme's rate
• Any lower value of k2/KM suggests that the catalytic
processes are slowing the rate
Reactions with multiple substrates
• Most biological reactions start with 2 substrates
and yield 2 products
A +B
P+Q
• Multiple substrate reactions can be classified into
classes sequential reactions and double
displacement (ping-pong) reactions
Sequential Reactions
• All substrates bind to enzyme forming ternary
complex (can be ordered or random interaction)
A +B
P+Q
E + A
EA
EA + B
EAB
EAB
EPQ
EPQ
EP + Q
EP
E+P
Double Displacement Reactions
• Also called “ping-pong” reactions
• One or more products released before all substrates
bind to enzyme
A +B
E + A
EA
E’ + B
E’B
P+Q
EA
E’ + P
E’B
E+Q
Limitations of Michealis-Menten
• M-M kinetics is simple model of enzymology
• Many examples of enzymes that do not follow M-M
kinetics
e.g. Allosteric enzymes, which consist of multiple
subunits and multiple active sites, V0 shows a
sigmoidal dependence on [S]
Limitations of Michealis-Menten
Summary
• Enzymes form complexes with their substrates
• Substrates bind to the active sites of enzymes
• KM is the concentration of substrate required for
the reaction to be half the maximum value
• Vmax is the maximum rate of reaction when the
enzyme is fully saturated with substrate
Learning objectives Lecture 10
• You should be able to describe the evidence for
enzyme/substrate complexes
• You will be able to define the terms Active sites and
Active site residues
• You should be able to describe the Michaelis-Menten
model for enzyme kinetics and the significance of
KM and Vmax
Lecture 11
Enzyme Catalysis
SBS017
Basic Biochemistry
Dr. Jim Sullivan
j.a.sullivan@qmul.ac.uk
Learning objectives Lecture 11
• You should be able to use Lineweaver-Burk plots to
calculate KM and Vmax
• You will be able to describe competitive,
uncompetitive and non-competitive inhibitors and
how they alter enzyme kinetics
• You should understand the terms Allosteric and Cooperative regulation in relation to enzymes

Michaelis-Menten Reminder
V  Vmax
[S]
[S]  K M
V is the velocity (or rate) of reaction
[S] is the substrate concentration
Vmax is the maximal velocity of the reaction
KM is the Michaelis contstant ([S] at Vmax/2)
Michaelis-Menten Reminder
Michaelis-Menton Reminder
E+S
k+1
k-1
ES
k+2
E+P
At steady state:
rate of formation of ES = rate of breakdown
k1[E][S]  (k1  k 2 )[ES]
[E][S] k1  k2

 KM
[ES]
k 1
KM
• KM is equal to the concentration of substrate
required for the reaction velocity to be half the
maximal value
when [S] = KM then V = Vmax/2
When k2<<k-1 then KM is to the dissociation constant
of the ES complex
i.e.
k1  X
k2 [E][S]
KM 

 K ES
k1
[ES]
KM tells us about substrate affinity
Vmax
Is the number of substrate molecules converted per
unit time when enzyme is fully saturated
i.e [ES] = [ET]
Vmax=k2[ET]
Where [ET] is total enzyme concentration
Lineweaver-Burk plot
• Method of calculating KM and Vmax
• A plot of 1/V0 against 1/[S]
• Values of KM and Vmax can be obtained from
gradient of line and intercept on 1/[S] axis

Lineweaver-Burk plot
V  Vmax
[S]
[S]  K M
1
1
KM 1


V Vmax Vmax [S]
i.e. Y = c + mX
(formula for straight line graph)
Lineweaver-Burk plot
1/V
X
X
1/Vmax
X
slope = KM/Vmax
X
X
-1/KM
1/S
“Double reciprocal plot”
Enzyme Inhibition
• Inhibitors are molecules that prevent enzymes from
working
• Many enzymes are regulated through the action of
inhibitors
• Enzymes inhibitors can also act as medicinal drugs
or toxins
Enzyme Inhibition
• Two main types of enzyme inhibition:
Irreversible, the inhibitor is tightly bound to the
enzyme (sometimes covalently)
Reversible, inhibitor can bind and dissociate from the
enzyme
Enzyme Inhibitors
• Competitive inhibitors bind to active site of
enzyme
• Reduce the effective substrate concentration
Enzyme Inhibitors
• Non-competitive inhibitors stop enzyme from
working
• Reduce the effective enzyme concentration
Enzyme Inhibitors
• Uncompetitive inhibitors bind only to ES complex
• Cannot be overcome by adding more substrate
Enzyme Inhibitors
• Some enzyme inhibitors are very important
medicinal drugs
• Therefore understanding how inhibitors work is
very important
Enzyme inhibitors as drugs
• Methotrexate, structural analogue of substrate for
DHFR, prevents nucleotide synthesis, used to treat
cancer (reversible inhibitor)
• Penicillin, covalently modifies transpeptidase,
inhibiting bacterial cell wall synthesis and killing
bacteria (Irreversible inhibitor)
Methotrexate
• Substrate analog for Dihydroxyfolate reductase
(DHFR)
• DHFR plays important role in biosynthesis of
purines and pyrimidines.
Methotrexate binds to enzyme 1000 times
more effciently than dihyrdofolate
Significantly reduces effective substrate
concentration
Penicillin
• Inhibits glycopeptide transpeptidase which crosslinks bacterial cell walls
• Has similar structure to normal substrate, and
binds at active site
Glycopeptide transpeptidase
•
Enzyme essential for cell wall synthesis, without it
no cross-linking
Penicillin
• Irreversibly inhibits enzyme by reacting with serine
residue in active site
• “suicide”-substrate, reaction kills enzyme
Competitive Inhibition
[E ][I]
Ki 
[EI]
Competitive Inhibition
[E ][I]
Ki 
[EI]
Increasing inhibitor increases apparent KM
Vmax can still be reached by adding more substrate

50


[I]
app
K M  K M 1 
 K i 
Non-competitive Inhibition
Non-competitive Inhibition
Binding of molecule stops reaction, apparent
Vmax is reduced
app
max
V
Vmax

1 [I]/K i
No change in KM

Uncompetitive Inhibition
Uncompetitive Inhibition
Binding of molecule to ES stops reaction, apparent
Vmax and KM are reduced
Both Vmax and KM
lower
Lineweaver-Burk plot
1/V
X
X
1/Vmax
X
slope = KM/Vmax
X
X
-1/KM
1/S
“Double reciprocal plot”
Lineweaver-Burk plots and Inhibitors
• Double reciprocal plots can be used to see effects
of inhibitors
KM same, Vmax lower
Lineweaver-Burk plots and Inhibitors
• Double reciprocal plots can be used to see effects
of inhibitors
KM higher, Vmax same
Lineweaver-Burk plots and Inhibitors
• Double reciprocal plots can be used to see effects
of inhibitors
KM and Vmax lower
Transition state analogs
• In 1948 Linus Pauling proposed idea that
compounds which mimic the transition state of
enzymic reaction should be effective inhibitors
Energy
(G)
Transition state, S‡
ΔG‡
A
ΔG
B
Reaction coordinates
“Transition state
analogs”
Transition state analogs
• Enzyme work by stabilising transition state
• TS analogs bind tightly to active site
• Very good competitive inhibitors
Proline Biosynthesis
Conversion of L-Proline to D-Proline requires
proline racemase
Reaction proceeds via TS, Pyrrole 2carboxylic acid
resembles TS and is potent inhibitor
Catalytic antibodies
• Stabilising transition state should catalyse a
reaction
• Antibodies which recognise a transition state
should function as catalysts
Catalytic antibodies
• Insertion of Fe into porphyrin ring by ferrochelatase
proceeds via ‘bent’ porphyrin transition molecule.
Catalytic antibodies
• N-Methylmesoporphyrin, used to generate
antibodies
• Antibodies can catalyse ferrochelatase reaction
• Antibodies catalysed reaction at 2500 times rate of
uncatalysed reaction, only10-fold less efficient than
enzyme
Enzyme regulation
• Enzymes are often regulated
• Regulation can be allosteric and co-operative
• In co-operative regulation binding of substrate to
one binding site helps binding to other active sites
• Allosteric regulation involves product inhibition,
often used to control flux through metabolic
pathways
Allosteric regulation
A
a
B
b
C
c
D
d
regulates
Product X
Allosteric regulation
• Allosteric enzymes do not show Michaelis-Menton
kinetics
• Due to the presence of multiple subunits and
multiple active sites
• Multimeric enzymes often have sigmoidal kinetics
Allosteric kinetics
Hyperbolic
Sigmoidal
Summary
• Lineweaver-Burk plots can be used to calculate KM and
Vmax
• Inhibitors are substances that prevent enzymes from
working
• Inhibitors can be competitive, uncompetitive or noncompetitive
• Transition state analogues can be used as competitive
inhibitors of enzymes
• Enzymes needs to be regulated, regulation can be cooperative and allosteric
Enzyme summary
• Without enzymes biological reactions
would not take place
• Without inhibitors and regulation
biological reactions would happen that
we didn’t want
Learning objectives Lecture 11
• You should be able to use Lineweaver-Burk plots to
calculate KM and Vmax
• You will be able to describe Competitive,
Uncompetitive and Non-competitive inhibitors and
how they alter enzyme kinetics
• You should understand the terms Allosteric and Cooperative regulation in relation to enzymes