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8/6/2019 Enzyme Kinetics Final
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Production Kinetics of Alkaline
Protease Production
Dr. Apurba Dey
Professor
Department of Biotechnology,
National Institute of Technology, Durgapur.
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ENZYMES
� Enzymes are Biocatalyst that increase the rates of chemical
reactions and they are protein in nature .
Properties of Enzymes
�Have enormous catalytic power �Highly specific
�Activities of some enzymes are regulated�Transform different kinds of energy
�Do not alter reaction equilibria
�Decrease the activation energy of reactions catalysed by them
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Class 1. OxidoreductasesOxidoreductases- catalyze redox
processes
Example: RCH2-OH p RCH=O
Class 2. TransferasesTransferases- transfer chemical groups
from one molecule to another or to another part
of the same molecule.
O O
Example: CH3-C-SCoA + XR p CH3-C-XR+ HSCoA
acetyl CoA acetyl group transferred
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Class 3. HydrolasesHydrolases- cleave a bond using water
to produce two molecules from one.
O H2O O
example: --CNH-R p --C-OH + H2N-R
cleavage of a peptide bond
Class 4. LyasesLyases- remove a group from or add a
group to double bonds.
H-X H X
---C=C--- p ---C--C---
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Class 5. IsomerasesIsomerases- interconvert isomeric
structures by molecular rearrangements.
CH3 CH3HC-OH HO-CH
COOH COOHClass 6. LigasesLigases -- join two separate molecules
by the formation of a new chemical bond usuallywith energy supplied by the cleavage of an ATP.
example:
O ATP ADP+Pi O-OOC-C-CH3 + CO2
-OOC-C-CH2-COO-
pyruvate oxaloacetate
enzyme = pyruvate carboxylase
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Enzymes from Microbial sources
Enzymes Sources Applications
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Enzymes from Animal and Plat sources
Enzymes Sources Applications
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Enzyme kinetics
Study of the rates of enzyme-catalyzed reactionsProvides information on enzyme specificities and
mechanisms
Why study enzyme kinetics?
a) the precise scheduling of reactions in a cell is
important to the cell and our understanding of its
workings
b) enzyme mechanisms, e.g., the number of kinetic
steps and the detailed chemistry can be learned(enzymology).
c) understanding enzyme function leads to better
drugs.
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E = free enzyme
S = substrateES = enzyme-substrate complex
P = product
12
1
k k
k
E S ES E P
��p ��p n��
Steps for a simple enzyme-catalyzed reaction
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LOCK and KEY MODEL
Active site of enzyme by itself is complementary in shape to that of the substrate.
INDUCED FIT MODEL
The enzyme changes shape upon binding substrate. The Active site has a
shape complementary to that of the substrate only after the substrate is bound.
MODELS FOR ENZ YME SUBSTRATE COMPLEX
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Enzyme-catalyzed reactions exhibit
saturation kinetics
At high [S], the
enzyme is said to
be saturated withrespect to
substrate
12
1
k k
k
E S ES E P
��p ��p n��
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Steady State
The more ES present, the faster ES will dissociate into E + P or E
+ S. Therefore, when the reaction is started by mixing enzymesand substrates, the [ES] builds up at first, but quickly reaches a
STEADY STATE, in which [ES] remains constant. This steady
state will persist until almost all of the substrate has been
consumed.
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MichaelisMichaelis- -MentenMenten EquationEquation
Vmax[S]
[S] + KmV =
Measuring Km and Vmax
Curve-fitting algorithms
can be used todetermine K m and V max
from v vs. [S] plots
Michaelis-Mentonequation can be
rearranged to the
"double reciprocal" plot
and K m and V max can
begraphically determined
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�Km is the [S] at 1/2 Vmax
�Km is a constant for a given enzyme�Km is an estimate of the equilibrium constant
for S binding to E
�Small Km means tight binding;
�High Km means weak binding
Km
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Vmax
Vmax is a constant for a given enzyme
Vmax is the theoretical maximal rate of the reaction- but it is NEVER achieved
To reach Vmax would require that ALL enzyme
molecules have tightly bound substrate
The theoretical maximal velocity
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Amount of reaction that a certain amount of enzyme
will produce in a specified period of time Activity
determined by measuring the amount of product
formed or substrate that disappeared
IU of enzyme activity is
The amount of enzyme necessary to produce 1 mole
of product (or the loss of 1 mol of substrate) per minute
under specified conditions of substrate concentration,
pH and Temperature
Enzyme Activity
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�The kcat is a direct measure of the catalytic
production of product under saturating substrate
conditions.
�kcat, the turnover number, is the maximum
number of substrate molecules converted to
product per enzyme molecule per unit of time.
�According to M-M model, kcat = Vmax/Et Values of
kcat range from less than 1/sec to many millions
per sec
A measure of catalytic activity
The Turnover Number
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Enzyme Inhibition
Many different kinds of molecules inhibit enzymeand act in a variety of ways.
One major distinction is whether the inhibition is
1. Competitive
Competitive
12
1
k k
k
I
E S ES E P
I
K
EI
��p ��p n��
c
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Non- Competitive
Non-competitive
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K inetic parameter
Antipain (Serine Protease
Competitive Inhibitor)
Aprotinine (Serine Protease
Competitive Inhibitor)
0.025mM 0.05mM 0.1mM 0.025mM 0.05mM 0.1mM
Maximum enzyme
activity (vm)
286.9 286.6 286.2 285.3 285.3 285.4
Saturation
constant (K Iamp)
0.006953 0.01348 0.02703 0.006073 0.01144 0.02288
Inhibition factor
(YI) 14.81 28.71 57.56 12.93 24.36 48.73
Effect of inhibitors on kinetic parameters for enzyme activity
NB. When no inhibitor then Vmax is 286.9 and Km is 0.0047mM
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Process Kinetics
Cell Growth Kinetics
Substrate Utilization Kinetics
Production Kinetics
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PROTEASES
Proteases are enzyme that hydrolytically cleave the peptide pond of proteins.
For enzyme digestive enzyme and Blood clotting enzymes.
Classification of proteases
�Serine proteases
�Cysteine proteases
�Aspartate proteases
�Metallo proteases
Application of Proteases
1.In beverage industry for stabilizing Beer
2.In cheese Industry for coagulation of casein and cheese ripening3.In leather Industry de hearing of hides and softening the lathers
4.In food industry as meat tenderizer
5.As ingredient in detergent industry for removing the stain
6.For cleaning contact lenses
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A. Monod Model
max
s
S
K S
Q Q !
0 10 20 30 40 500.00
0.02
0.04
0.06
0.08
Starch Concentration (gl-1
)
S p e c i f i c g r o w t
h r a t e ( h
- 1 )
Gabriel Monod (1844 - 1912)
dX X
dt Q! 0
( ) t X t X e
Q!
Cell Growth Kinetics
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Table 2. Substrate inhibition kinetic models used in this study.
Names of Model Substrate Inhibition model R 2 value
Andrew 0.9908
Aiba 0.9906
Competitive substrate
inhibition model0.9691
Non-competitive
substrate inhibition
model
0.9691
Edward 0.9177
max
2
s I
S
S S
Q Q !
max . i
S
s
S e
K S
Q Q
!
max
(1 ) s
i
S
S K S
K
Q Q !
max
(1 )(1 )S
i
S
K S
S K
Q Q !
max
2
( )(1 )S
i S
S
S S S K K K
Q Q !
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0 10 20 30 40 500.00
0.02
0.04
0.06
0.08
Starch Concentration (gl-1)
S p e c i f i c g r o w
t h r a t e ( h
- 1 )
Andrews Model
max
2
s I
S
K S K S
Q Q !
µmax = 0.109 h-1
KS = 11.1 gl-1
Ki =0.012 l/g
R2 =0.9908
Where KI is the inhibition constant in Andrews model
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Substrate Utilization Kinetics
1 1
X P S S
d S dX d P
m X dt Y dt Y dt
!
1
X S
d S d X m X
d t Y d t
!
Assumption: Amount of carbon substrate used for the
product formation is assumed to be negligible.
Where Y X/S
and Y P/S
are yields of cell mass and product with respect
to substrate and m is the maintenance coefficient for cells.
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Maintenance
CalculationAssumption: At the stationary
phase where dX/dt is zero and X is
Xm.
1
X S
d S d X m X
d t Y d t !
Therefore, m can be obtained
using the following equation:
[ ( )] st
m
d S dt
m X
!m= 0.0035 h-1
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YX/SCalculation
for Monod Model
Andrews Model
1
X S
d S d X m X
d t Y d t !
starch used for cell growth was
computed after deduction of
starch used for maintenance of
the cell from the experimental
residual starch.
YX/S = 1.003m= 0.0035 h-1/ X S
dX Y
d S !/
o X S
o
X X Y
S S
!
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Production kinetics
Alkaline protease production kinetics was done using Leudeking-Piret
model (Lu
edeking & Piret, 2000). According to th
is model, th
e produ
ctformation rate depends on both the instantaneous biomass
concentration, X and growth rate, in a linear manner.
d d X
X d t d t E F!
Where and are the product formation constants, which may vary with fermentation
conditions. Dividing both sides by X, we get the following equation
R E Q F!
Note: Regression analysis was used for best fit of straight line on
plot of and µ for finding out the parameters , .
1 1d d X
X d t X d t E F!
is specific production rate
µ is specific growth rate
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. .Fig. Plot of specific alkaline protease production rate
vs specific growth Rate using Leudeking-Piret model.
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References
A. Anwar, M. Saleemuddin, Alkaline protease from Spilosoma obliqua:
potential applications in bio-formulations,Biotechnol. Appl. Biochem, 31
(2000) 85-89.
J.F. Andrews, A mathematical model for the continuous culture of
microorganisms utilizing inhibitory substrates, Biotechnol Bioeng, 10
(1968) 702-723.
R. Luedeking, E.L. Piret, A kinetic study of the lactic acid fermentation. Batch
process at controlled pH, Biotechnol Bioeng, 67 (2000) 636-644.
M.L. Shuler, F. Kargi, Bioprocess Engineering: Basic Concepts, Practice Hall
of India Private Limited, New Delhi, 2008
S.D. Yuwono, T. Kokugan, Study of the effects of temperature and pH on lactic
acid production from fresh cassava roots in tofu liquid waste by
S treptococcus bovis, Biochem Eng J, 40 (2008) 175±183.M. Phisalaphong, N. Srirattana, W. Tanthapanichakoon, Mathematical
modeling to investigate temperature effect on kinetic parameters of ethanol
fermentation, Biochem Eng J, 28 (2006) 36±43.