enzyme kinetics final

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.



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



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



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---



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



Enzymes from Microbial sources

Enzymes Sources Applications



Enzymes from Animal and Plat sources

Enzymes Sources Applications



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.



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



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



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��



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.



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



�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



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



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



�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



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



Non- Competitive

Non-competitive



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



Process Kinetics

Cell Growth Kinetics

Substrate Utilization Kinetics

Production Kinetics



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



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



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 !



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



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.



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



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

!



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



. .Fig. Plot of specific alkaline protease production rate

vs specific growth Rate using Leudeking-Piret model.



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.



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enzyme kinetics final

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