Dr. Farooq Ahmed
Biochemical Engineering
Chapter Two: Enzymes
Enzymes are biological catalysts, protein molecules in nature, produced by living
cells (animals, plants, and microorganisms) and are absolute essentials as catalysts
in biochemical reactions. The catalytic ability of enzymes depends on their particular
protein structure and a specific chemical reaction and is catalyzed at a small portion
of the enzyme surface which is known as the active site.
Substrate, in the biological reaction, is equivalent to the term reactant in the chemical
reaction.
Differences between chemical reaction and enzyme reaction
1. An enzyme catalyst is highly specific and catalyst only one or a small number
of chemical reactions.
2. The rate of an enzyme-catalyzed reaction is usually much faster than that of
the same reaction when directed by the non-biological catalyst.
3. Only a small amount of enzymes is required to produce the desired effect.
4. The reaction conditions for the enzyme reaction are very mild: the pressure
and temperature are at 1 atm and 25-40oC.
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Dr. Farooq Ahmed
Biochemical Engineering
5. Enzymes are comparatively sensitive or unstable molecules and require care
in their use.
6. The enzymatic reaction does not form a by-product which reduces the
production costs.
Classification of enzymes
The enzymes can be classified into three major categories:
1. Industrial enzymes
2. Analytical enzymes
3. Medical enzymes
Factors influencing the rate of reaction
The important factors influencing the rate of reaction are:
1. Concentration of the substrate (Cs)
2. Temperature (T)
3. Pressure (P)
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Biochemical Engineering
The theories
1. Collision theory
The reactants form products only if they are in collision with each other and the
conditions (C, T, P) influence the collision of molecules. It should also be noted that
all collisions do not effectively lead to a reaction that:
a. Not all colliding molecules possess sufficient energy between them to
undergo a reaction.
b. Not all collisions bring the right molecules in contact with each other.
2. Transition state theory
According to the transition state theory, chemical reactions proceed via the
formation of an unstable intermediate between reactants and products, this
unstable intermediate disintegrates to a more stable one.
Activation energy
Colliding molecules must possess a certain amount of energy to cross a potential
barrier for the reaction to take place. The activation energy of the reaction can be
calculated by the Arrhenius equation as follows:
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Biochemical Engineering
k = k o exp (
−E
)
RT
where k is the rate constant, ko is the Arrhenius constant, E is the activation of the
bio-energy, R is the gas constant, and T is the absolute temperature.
The role of catalysts (enzyme)
Catalysts enhance the rate of reaction and reduce the activation energy of the
reaction. The catalyst binds to the reactant and forms a different transition state
complex from the uncatalyzed reaction, which is more stable and therefore requires
less activation energy to cross the potential barrier for the reaction to proceed the fig
below show the rok of catalyst
Biochemical reactors are generally multiphase systems handing air (in the aerobic
process) liquid and immobilized microorganism biochemical reactors are made of
1. A simple geometric-shape Stainless steel has.
2. A minimum number of flanges and welds.
3. Measuring and sampling nozzles.
4. No dead zones and minimum surfaces roughness.
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Dr. Farooq Ahmed
Biochemical Engineering
Enzymes Kinetics
Simple enzyme kinetics is as follows:
E
S→P
The substrate (S) is converted to product (P) with the existence of the enzyme (E) in
a biochemical reactor. The product concentration will increase and reach a maximum
value, where case the substrate concentration will decrease as shown in the figure
below.
Figure 1: Rates of the substrate and product concerning the time.
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Dr. Farooq Ahmed
Biochemical Engineering
Model of Enzyme kinetics
Michaelis - Menten Equation is used for a single substrate reaction catalyzed by an
enzyme, there are several steps involved as follows:
a. Substrate binds to the enzyme at the active site to form an enzyme – Substrate
complex.
b. Formation of a transition state.
c. Enzyme – product complex.
d. Separation of products from the enzyme and freeing the active enzyme site.
The active enzyme site is once again available for the reaction. These steps can be
mathematically represented as below:
E + S ⇌ ES
ES ⇌ EP
EP ⇌ E + P
The second equation is ignored.
K1
E+S
ES
(1)
K2
ES ⟶ P + E
(2)
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Dr. Farooq Ahmed
Biochemical Engineering
The Michaelis’s and Menten assumption
Equation 2 is much slower than Equation 1 and the slow step determines the rate
while the other is at equilibrium. This is an assumption that is often employed in
heterogeneous catalytic reactions in chemical kinetics.
−
dCs
dt
dCP
dt
= K1 CS CE− K 2 CES
= K 3 CES
(3)
(4)
at steady–state,
dcs
dt
=0
∴ Equation 3 becomes K1 CS CE = K 2 CES
∴
CES =
(5)
K1
C C
K2 S E
The material balance for the total amount of enzyme.
CE° = CE + CES → CE = CE° − CES
(6)
Sub Equation 6 into Equation 5,
CES =
K1
C (C − CES )
K 2 S E°
CES =
K1
K1
CS CE° −
C C
K2
K 2 S ES
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CES +
Biochemical Engineering
K1
K1
CS CES =
C C
K2
K 2 S E°
K1
C C
K1
K1
K 2 S E°
CES (1 +
C )=
C C → CES =
K
K2 S
K 2 S E°
1 + 1 CS
K2
CES =
CES =
K1 CS CES
K2
K2 +K1 CS
K2
→ CES =
K1 CS CE°
K2 +K1 CS
→ CES =
CS CE°
K2
+CS
K1
K1 CS CE°
K
K1 ( 2 +CS )
K1
(7)
From a slow step in Equation 4
rP = K 3 CES
Sub. Equation 7 into Equation 4 and
rp
CS CE
= k3 K
2
K1
°
+ CS
K2
= K m = Michaelis′s constant
K1
K 3 = K r = For the slow step of production.
∴ rp =
Kr .Cs .CEo
Km +Cs
M. M. E.
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Dr. Farooq Ahmed
Biochemical Engineering
The initial rate is given by the following:
rp° =
K r C s° C E °
it is proportional to cs°
Km +Cs°
1. For low values of cs° (cs° <<< k m )
∴ rP° =
K r Cso CEo
Km
2. The maximum initial rate is obtained for
CS° >>> K m
rP° max =
K m is a very low value.
K r Cso CEo
Cs o
∴ rP° max = K r . CE° = Vmax
Vmax is the maximum rate.
Sub in the M. M. E.
∴ rP =
Vmax . Cs
K m + CS
The final form of Michaelis - Menten Equation
3. Cs° = K m
rP° =
Vmax . CS°
Vmax . CS°
1
→
→ ∴ rP° = Vmax
CS ° + CS °
2CS°
2
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Biochemical Engineering
Evaluation of kinetic parameters (k m and Vmax )
The Michaelis – Menten equation can be rearranged to be expressed in the linear
form in three ways:
1. Langmuir plot
Vmax . CS
K m + CS
rP =
1
K m + CS
=
rP
Vmax . CS
1
Km
CS
=
+
rP
Vmax . cs Vmax . CS
1
Km 1
1
. +
[ =
]C
rP
Vmax cs Vmax s
CS
Km
CS
=
+
rP
Vmax Vmax
CS
rP
=
Plot
Km
Vmax
+
1
Vmax
CS
This is Langmuir plot
CS
vs. CS
rP
Slope =
1
Vmax
and Intercept =
Km
Vmax
2. Lineweaver – Burk plot
𝑟𝑝 =
𝑉𝑚𝑎𝑥 . 𝐶𝑆
𝐾𝑚 + 𝐶𝑆
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Biochemical Engineering
1
𝐾𝑚 + 𝐶𝑆
=
𝑟𝑃
𝑉𝑚𝑎𝑥 . 𝐶𝑆
1
𝐾𝑚
1
𝐶𝑆
=
.
+
𝑟𝑃
𝑉𝑚𝑎𝑥 𝐶𝑆
𝑉𝑚𝑎𝑥 . 𝐶𝑆
1
𝑟𝑃
𝐾𝑚
=
Plot
1
rP
𝑉𝑚𝑎𝑥
vs.
Slope =
1
.
𝐶S
+
1
Vmax
This is line weaver – Burk from
1
CS
Km
Vmax
and Intercept =
1
Vmax
3. Eadie- Hofstee plot
rP =
Vmax . CS
K m + CS
[ rP (K m + CS ) = Vmax . CS ] ÷ CS
rP (Km + CS )
CS
=
Vmax . CS
CS
rP K m rP . CS
rP . K m
+
= Vmax →
+ rP = Vmax
CS
CS
CS
rP =
Vmax − K m
Plot rP vs.
rP
rP
CS
This is Eadie – Hofstee from
CS
Slope = −K m
and Intercept = Vmax
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Dr. Farooq Ahmed
Biochemical Engineering
Example 1
From a series of batch runs with a constant enzyme concentration, the following
initial rate data were obtained as a function of initial substrate concentration.
Substrate Concentration,
mmol/L
1
2
3
4
5
7
15
10
20
Initial Reaction Rate,
mmol/L.min
0.20
0.22
0.30
0.40
0.45
0.41
0.50
0.40
0.33
Evaluate the Michaelis-Menten kinetic parameters by employing the Langmuir plot,
the Lineweaver-Burk plot, and the Eadie-Hofstee plot.
Solution:
For the Langmuir plot,
Substrate Concentration,
mmol/L
Initial Reaction Rate,
mmol/L.min
CS
rP
1
2
3
4
5
7
15
10
20
0.20
0.22
0.30
0.40
0.45
0.41
0.50
0.40
0.33
5
9.090909
10
10
11.11111
17.07317
30
25
60.60606
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Dr. Farooq Ahmed
Biochemical Engineering
Langmaiur Plot
70
60
y = 2.5926x + 0.4639
R² = 0.923
Cs/rP
50
40
30
20
10
0
0
5
10
15
20
25
Cs
Slope =
1
Vmax
Intercept =
= 2.59 → Vmax = 0.38
Km
= 0.46 → K m = 0.17
Vmax
For the Lineweaver-Burk plot,
Substrate Concentration,
mmol/L
Initial Reaction Rate,
mmol/L.min
1
CS
1
rP
1
2
3
4
5
7
15
10
20
0.20
0.22
0.30
0.40
0.45
0.41
0.50
0.40
0.33
1
0.5
0.333333
0.25
0.2
0.142857
0.066667
0.1
0.05
5
4.545455
3.333333
2.5
2.222222
2.439024
2
2.5
3.030303
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Dr. Farooq Ahmed
Biochemical Engineering
Lineweaver-Burk plot
6
y = 3.0908x + 2.1557
R² = 0.7795
5
1/rp
4
3
2
1
0
0
0.2
0.4
0.6
0.8
1
1.2
1/Cs
Intercept =
Slope =
1
Vmax
= 0.46
Km
= 3.09 → Km = 1.43
Vmax
For the Eadie-Hofstee plot,
Substrate Concentration,
mmol/L
1
2
3
4
5
7
15
10
20
Initial Reaction Rate,
mmol/L.min
0.20
0.22
0.30
0.40
0.45
0.41
0.50
0.40
0.33
𝑟𝑝
Cs
0.2
0.11
0.1
0.1
0.09
0.058571
0.033333
0.04
0.0165
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Dr. Farooq Ahmed
Biochemical Engineering
Eadie-Hofstee plot
0.6
0.5
rp
0.4
0.3
0.2
y = -1.2348x + 0.4594
R² = 0.4479
0.1
0
0
0.05
0.1
0.15
0.2
0.25
rp/Cs
Slope = −K m = 1.23 → K m = 1.23
Intercept = Vmax = 0.45
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