Advanced Bioprocess Engineering
Enzymes & Enzymes Kinetics
Lecturer Dr. Kamal E. M. Elkahlout
Assistant Prof. of Biotechnology
ENZYMES
BASICS AND INTRODUCTION
ENZYMES
A protein with catalytic properties
due to its power of specific
activation
Chemical reactions
• Chemical reactions need an initial input of energy
= THE ACTIVATION ENERGY
• During this part of the reaction the molecules are
said to be in a transition state.
Reaction pathway
Making reactions go faster
• Increasing the temperature make molecules move
faster
• Biological systems are very sensitive to
temperature changes.
• Enzymes can increase the rate of reactions without
increasing the temperature.
• They do this by lowering the activation energy.
• They create a new reaction pathway “a short cut”
An enzyme controlled pathway
• Enzyme controlled reactions proceed 108 to 1011 times faster
than corresponding non-enzymic reactions.
Enzyme structure
• Enzymes are
proteins
• They have a
globular shape
• A complex 3-D
structure
Human pancreatic amylase
The active site
• One part of an enzyme,
the active site, is
particularly important
• The shape and the
chemical environment
inside the active site
permits a chemical
reaction to proceed
more easily
Cofactors
• An additional nonprotein molecule that is
needed by some enzymes
to help the reaction
• Tightly bound cofactors
are called prosthetic
groups
• Cofactors that are bound
and released easily are
called coenzymes
• Many vitamins are
coenzymes
Nitrogenase enzyme with Fe, Mo and ADP cofactors
)
The substrate
• The substrate of an enzyme are the
reactants that are activated by the enzyme
• Enzymes are specific to their substrates
• The specificity is determined by the active
site
The Lock and Key Hypothesis
• Fit between the substrate and the active site of the enzyme is
exact
• Like a key fits into a lock very precisely
• The key is analogous to the enzyme and the substrate
analogous to the lock.
• Temporary structure called the enzyme-substrate complex
formed
• Products have a different shape from the substrate
• Once formed, they are released from the active site
• Leaving it free to become attached to another substrate
The Lock and Key Hypothesis
S
E
E
E
Enzyme-substrate
complex
P
P
Reaction coordinate
Enzyme
may be
used
again
The Lock and Key Hypothesis
• This explains enzyme specificity
• This explains the loss of activity when
enzymes denature
The Induced Fit Hypothesis
• Some proteins can change their shape
(conformation)
• When a substrate combines with an enzyme, it
induces a change in the enzyme’s conformation
• The active site is then moulded into a precise
conformation
• Making the chemical environment suitable for the
reaction
• The bonds of the substrate are stretched to make
the reaction easier (lowers activation energy)
The Induced Fit Hypothesis
Hexokinase (a) without (b) with glucose
substrate
• This explains the enzymes that can react with a range
of substrates of similar types
http://www.biochem.arizona.edu/classes/bioc462/462a/NOTES/ENZYMES/enzyme_mechanism.html
Factors affecting Enzymes
•
•
•
•
substrate concentration
pH
temperature
inhibitors
Reaction velocity
Substrate concentration: Non-enzymic reactions
Substrate concentration
• The increase in velocity is proportional to the
substrate concentration
Reaction velocity
Substrate concentration: Enzymic reactions
Vmax
Substrate concentration
• Faster reaction but it reaches a saturation point when all the
enzyme molecules are occupied.
• If you alter the concentration of the enzyme then Vmax will
change too.
The effect of pH
Enzyme activity
Optimum pH values
Tryps
in
Pepsin
1
3
5
7
pH
9
11
The effect of pH
• Extreme pH levels will produce denaturation
• The structure of the enzyme is changed
• The active site is distorted and the substrate
molecules will no longer fit in it
• At pH values slightly different from the enzyme’s
optimum value, small changes in the charges of
the enzyme and it’s substrate molecules will occur
• This change in ionisation will affect the binding of
the substrate with the active site.
The effect of temperature
• Q10 (the temperature coefficient) = the increase
in reaction rate with a 10°C rise in temperature.
• For chemical reactions the Q10 = 2 to 3
(the rate of the reaction doubles or triples with
every 10°C rise in temperature)
• Enzyme-controlled reactions follow this rule as
they are chemical reactions
• BUT at high temperatures proteins denature
• The optimum temperature for an enzyme
controlled reaction will be a balance between the
Q10 and denaturation.
Enzyme activity
The effect of temperature
Denaturation
Q10
0
10
20
30
40
Temperature / °C
50
The effect of temperature
• For most enzymes the optimum temperature is
about 30°C
• Many are a lot lower,
cold water fish will die at 30°C because their
enzymes denature
• A few bacteria have enzymes that can withstand
very high temperatures up to 100°C
• Most enzymes however are fully denatured at
70°C
Inhibitors
• Inhibitors are chemicals that reduce the rate
of enzymic reactions.
• The are usually specific and they work at
low concentrations.
• They block the enzyme but they do not
usually destroy it.
• Many drugs and poisons are inhibitors of
enzymes in the nervous system.
The effect of enzyme inhibition
• Irreversible inhibitors: Combine with the
functional groups of the amino acids in the
active site, irreversibly.
Examples: nerve gases and pesticides,
containing organophosphorus, combine
with serine residues in the enzyme
acetylcholine esterase.
The effect of enzyme inhibition
• Reversible inhibitors: These can be
washed out of the solution of enzyme by
dialysis.
There are two categories.
The effect of enzyme inhibition
1. Competitive: These
compete with the
substrate molecules for
E+
the active site.
I
Reversi
The inhibitor’s action is
ble
proportional to its
reaction
concentration.
Resembles the substrate’s
structure closely.
EI
Enzyme
inhibitor
complex
The effect of enzyme inhibition
Succin
ate
Succinate
dehydrogenase
CH2CO
OH
COO
H
Fumarate +
2H++ 2eCHCO
OH
CH
CH2CO
OH
2
COO
H
Malonate
CHCO
OH
The effect of enzyme inhibition
2. Non-competitive: These are not influenced by the
concentration of the substrate. It inhibits by binding
irreversibly to the enzyme but not at the active site.
Examples
• Cyanide combines with the Iron in the enzymes
cytochrome oxidase.
• Heavy metals, Ag or Hg, combine with –SH groups.
These can be removed by using a chelating agent such as
EDTA.
Applications of inhibitors
• Negative feedback: end point or end product
inhibition
• Poisons snake bite, plant alkaloids and nerve
gases.
• Medicine antibiotics, sulphonamides,
sedatives and stimulants
ENZYMES
KINETICS OF ENZYME REACTIONS
INTRODUCTION
• The objectives of studying kinetics:
• 1) Gain an understanding of the mechanisms of
enzyme action;
• 2) Illuminate the physiological roles of enzymecatalyzed reactions
• 3) Manipulate enzyme properties for
biotechnological ends.
MICHAELIS–MENTEN KINETICS
• Michaelis–Menten equation expresses the initial rate
(v) of a reaction at a concentration (S) of the
substrate transformed in a reaction catalyzed by an
enzyme at total concentration E0:
Vmax [S ] k 2 [E 0 ][S ]
v

K m  [S ] K m  [S ]
• The parameters are k2, the catalytic constant, and
Km, the Michaelis constant.
Michaelis-Menten Kinetics
Enzyme Kinetics
Enzymatic reaction
E+S
k1
k-1
ES
k2
E+P
Rate expression for product formation
v = dP/dt = k2(ES)
d(ES)/dt = k1(E)(S)-k-1(ES)-k2(ES)
Conservation of enzyme
(E) = (E0) – (ES)
Two Methods to Proceed
• Rapid equilibrium assumption: define
equilibrium coefficient
K’m = k-1/k1 = [E][S]/[ES]
• Quasi-steady state assumption
[ES] = k1[E][S]/(k-1+k2)
• Both methods yield the same final equation
Michaelis- Menten Kinetics
Michaelis-Menten Kinetics
• When v= 1/2 Vmax, [S]= Km so Km is
sometimes called the half-saturation
constant and sometimes the Michaelis
constant
Vmax [S ] k 2 [E 0 ][S ]
v

K m  [S ] K m  [S ]
Michaelis-Menten Kinetics
Vmax [S ] k 2 [E 0 ][S ]
v

K m  [S ] K m  [S ]
• units on k2 are amount product per amount
of enzyme per unit time (also called the
“turnover number”). Units on E0 are
amount of enzyme (moles, grams, units,
etc.) per unit volume
• Km has the same units as [S] (mole/liter,
etc.)
Experimentally Determining Rate
Parameters for Michaelis-Menten
Kinetics
Lineweaver-Burk
Eadie-Hofstee
Hanes- Woolf
Batch Kinetics
Determining Parameters
• Rearrange the equation into a linear form.
• Plot the data.
• What kind of data would we have for an
experiment examining enzyme kinetics?
• Describe an experiment.
• The intercept and slope are related to the
parameter values.
Enzyme Kinetics Experiment
Place enzyme and substrate (reactants) in a
constant temperature, well stirred vessel.
Measure disappearance of reactant or
formation of product with time.
Why constant temperature?
Why well stirred?
What about the medium? Buffer?
Lineweaver-Burk
(double reciprocal plot)
– Rewrite Michaelis-Menten rate expression
1 Km 1
1


v Vmax [S ] Vmax
– Plot 1/v versus 1/[S]. Slope is Km/Vmax,
intercept is 1/Vmax
Graphical Solution
intercepts
1/ V
1 Km 1
1


v Vmax [S ] Vmax
-1/ Km
Slope = Km/ Vmax
1/ Vmax
1/ [S]
Example: Lineweaver-Burk
-5
[S] x 10 M
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
-5
V, M/min x 10
1.17
1.50
1.75
1.94
2.10
2.23
2.33
2.42
2.50
Resulting Plot
slope = Km/ Vmax= 0.5686
y intercept = 1/ Vmax= 2.8687
Michaelis-Menten Kinetics
Vmax [S ] k 2 [E 0 ][S ]
v

K m  [S ] K m  [S ]
Vmax = 1/2.8687 x 10-4 = 3.49 x 10-5 M/min
Km= 0.5686 x Vm = 1.98 x 10-5 M
Other Methods
• Eadie-Hofstee plot
v
v  Vmax  K m
[S ]
• Hanes- Woolf
[S ] K m


v
Vmax
1
[S ]
Vmax
Comparison of Methods
• Lineweaver-Burk: supposedly gives good
estimate for Vmax, error is not symmetric
about data points, low [S] values get more
weight
• Eadie-Hofstee: less bias at low [S]
• Hanes-Woolf: more accurate for Vmax.
• When trying to fit whole cell data – I don’t
have much luck with any of them!
Batch Kinetics
d[S ] Vmax [S ]
v

dt
K m  [S ]
integrate
[S 0 ]
Vmaxt  [S 0 ]  [S ]  K m ln
[S ]
rearrange
[S 0 ]  [S ]
K m [S 0 ]

ln
Vmax
t
t
[S ]
Inhibited Enzyme Kinetics
•
•
•
•
Competitive Inhibition
Noncompetitive Inhibition
Uncompetitive Inhibition
Substrate Inhibition
Effects of Temperature and pH
Experiments: Initial rate at
different substrate concentrations
E S1= 20
E
S2=10
E S3=6.7 E
S4=5
E
S5=4
Measure S for a short time period. Calculate v from:
v = [S(time 0) – S(time 1)]/delta time
Experiment
Using S1
Time (min)
0
0.5
S (g/L)
20
19.43
v= (20-19.3)g/L]/0.5 min = 1.14 g/L/min
Experiment
Using S2
Time (min)
0
0.5
S (g/L)
10
9.565
v= (10-9.565)g/L]/0.5 min = 0.87 g/L/min
Experimental Data
S (mmol/L)
20
10
6.7
5.0
4.0
v (mmol/L/min)
1.14
0.87
0.70
0.59
0.50
Problems with this method?
Rate is not measured at a constant substrate
concentration – substrate decreasing. Must have
sensitive assay for substrate to measure initial rates.
20
18
16
regression
S/v = 0.6S + 5.6
S/v (min)
14
12
10
8
experimental data
regression
6
4
2
0
0
5
10
15
S (g/L)
20
25
Allosteric Enzyme Kinetics
In an enzyme with more than one substrate
binding site, binding of one substrate
molecule affects the binding of another.
n
d[S ] V max[S]
v
 n
n
dt
K m  [S ]
n>1, cooperation; n<1, interference
Allosteric Enzymes
Shape of rate curve is sigmoidal
Michaelis-Menten
Allosteric
Inhibition of Enzymes
Can be irreversible (metals) or
reversible (product, substrate, salt,
etc.)
1. Competitive
2. Noncompetitive
3. Uncompetitive
Competitive Inhibition
Inhibitor is an analog of the substrate, and
binds to the active site of the enzyme.
E  S  ES  P

I
EI
[E ][S ]
K m 
[ES ]
[E ][I ]
KI 
[EI ]
[E 0 ]  [E ]  [ES ]  [EI ]
v  k 2 [ES]
What assumption have we make in defining the
parameters on the right?
Competitive Inhibition
Competitive Inhibition
Rate is given by:
Vmax [S ]
Vmax [S ]
v

 I 
K m,app
  [S ]
K m 1
 [S ]

 K I 

What is the magnitude of Km,app
relative to Km and what will be the
effect on v? How could you run a
process to minimize the effects of this
type of inhibition?
Competitive Inhibition
I>0
1/v
I=0
Vmax is unchanged
-1/Km
-1/Km,app
1/Vmax
1/[S]
Practice deriving kinetic
expressions
Derive competitive inhibition equation (3.22
in your text)? Write down all assumptions.
Noncompetitive Inhibition
Inhibitor binds to the enzyme, but not at the active
site. However, the enzyme affinity for substrate is
reduced.
E  S  ES  P


I
I
EI S  ESI
[E ][S ] [EI ][S ]
K m 

[ES ]
[ESI ]
[E ][I ] [ES ][I ]
KI 

[EI ]
[ESI ]
[E 0 ]  [E ]  [ES ]  [EI ]  [ESI ]
v  k 2 [ES]
Noncompetitive Inhibition
Cofactors and Coenzymes
Holoenzymes- three parts
• Apoenzyme- Protein portion
• Cofactor- inorganic ion (ex: metal ions),
improve the fit of enzyme with substrate
• Coenzyme- nonprotein organic molecule
(ex: NAD- nicotinamide adenine
dinucleotide), many synthesized from
vitamins (why vitamins are essential)
Noncompetitive Inhibition
Rate is given by:
Vmax
v

 [I ]  K m 
1
1

 [S ] 

 K I 

Vmax,app
 K m 
1

 [S ] 

Question: What is the magnitude of Vmax,app
relative to Vmax, and what will be the effect of
v? How can you moderate the effects of this
type of inhibition.
Noncompetitive Inhibition
I>0
1/v
I=0
1/Vmax,app
1/Vmax
-1/Km
Km is unchanged
1/[S]
Uncompetitive Inhibition
Inhibitor binds only to ES complex, and not
to E alone.
E  S  ES  P

I
ESI
[E ][S ]
K m 
[ES ]
[E ][I ]
KI 
[EI ]
[E 0 ]  [E ]  [ES ]  [ESI ]
v  k 2 [ES]
Uncompetitive Inhibition
Rate is given by:
Vmax
[S ]
 [I ] 
1 
Vmax,app [S ]
 K I 
v 

K m
 [S ] K m,app  [S ]
 [I ] 
1

 K I 

What is the magnitude of Vmax,app relative to Vmax?
What is the magnitude of Km,app relative to Km?
Uncompetitive Inhibition
1/v
I>0
I=0
1/Vmax,app
1/Vmax
-1/Km,app
-1/Km
1/[S]
Substrate Inhibition
No substrate inhibition
v
Substrate inhibition
Vmax [S ]
v 
[S]2
K m  [S ] 
KSi
[S ]max. rate  K mK Si
S
Enzyme Deactivation
• Enzymes are denatured by
– Temperature
– pH
– Radiation
– Irreversible binding by inhibitors
• Temperature can both increase
(thermal activation) and decrease
(thermal denaturation) rate
Temperature effects
At moderate temperatures, higher
temperatures give higher rates.
v  k 2 [E ], where k 2  Ae
E a
RT
At higher temperatures, rate starts to
decrease as enzyme denatures faster
E d
d[E ]
k d t
d
RT

 k d [E ], or [E]  [E 0 ]e , where kd  Ad e
dt
Temperature Effects
Effect on rate is a combination of the two effects
v  Ae
E a
RT
[E 0 ]e
k d t
Activation energy  10
kcal/mol
Deactivation energy  100
kcal/mol