Enzyme kinetics- michaelis menten model, lineweaver burk plot

Mchaelis menten model, KM value, Lineweaver burk double reciprocal plot

1. MICROBIAL PHYSIOLOGY & BIOCHEMISTRY
SEMINAR ON : ENZYME KINETICS

➢MICHAELIS & MENTEN MODEL
➢Km VALUE
➢LINEWEAVER BURK DOUBLE
RECIPROCAL PLOT

SUMESH. M
21MBTB24
1st. M.Sc., MICROBIOLOGY
DEPARTMENT OF MICROBIAL BIOTECHNOLOGY
BHARATHIAR UNIVERSITY, COIMBATORE

2. CONTENTS
➢INTRODUCTION
➢MICHAELIS & MENTEN
➢KM VALUE.
➢LINEWEAVER BURK DOUBLE RECIPROCAL PLOT

3. INTRODUCTION
●Enzyme kinetics is the study of the rates of enzyme-catalysed chemical reactions. In
enzyme kinetics, the reaction rate is measured and the effects of varying the conditions
of the reaction are investigated. Studying an enzyme's kinetics in this way can reveal
the catalytic mechanism of this enzyme, its role in metabolism, how its activity is
controlled, and how a drug or a modifier (inhibitor or activator) might affect the rate.
●Enzymes are natural proteins which act as catalysts that speed up the rate of specific
chemical reactions. They either help create or break down molecules.
●An enzyme (E) is typically a protein molecule that promotes a reaction of another
molecule, its substrate (S).

4. ●This binds to the active site of the enzyme to produce an enzyme-substrate complex ES,
and is transformed into an enzyme-product complex EP and from there to product P, via
a transition state. The series of steps is known as the mechanism.
●There are many practical uses of enzyme kinetics. For example, the kinetic constants
can help explain how enzymes work and assist in the prediction of the behavior of
enzymes in living organisms.

5. MICHAELIS AND MENTEN
●In biochemistry, Michaelis–Menten kinetics is one of the best-known models of
enzyme kinetics. It is named after German biochemist Leonor Michaelis and Canadian
physician Maud Menten.
●The model takes the form of an equation describing the rate of enzymatic reactions, by
relating reaction rate V i.e., Enzyme velocity (rate of formation of product [P] to [S] )
and the concentration of a substrate S.

6. MICHAELIS
●Leonor Michaelis was a German biochemist, physical chemist, and physician, known
for his work with Maud Menten on enzyme kinetics in 1913, as well as for work on
enzyme inhibition, pH and quinones.
MENTEN
●Maud Leonora Menten was a Canadian bio-medical and medical researcher who made
significant contributions to enzyme kinetics and histochemistry. She is primarily known
for her work with Leonor Michaelis on enzyme kinetics in 1913.

7. ENZYME VELOCITY
➢Enzyme Velocity is the rate of an enzyme-catalyzed reaction is often called its velocity.
Enzyme velocities are normally reported as values at time zero (initial velocity, symbol
Vo; μmol min-1). This is because the rate is fastest at the point where no product is yet
present as the substrate concentration is greatest before any substrate has been
transformed to product.

SUBSTRATE CONCENTRATION
➢Substrate concentration is the amount of substrate present that can be turned into
product and is most commonly measured in molarity (moles per liter). The
concentration of substrates is used to measure enzyme activity

8. MICHAELIS MENTEN MODEL
●This model takes the form of an equation describing the rate of enzymatic reactions, by
relating reaction rate v (rate of formation of product [P]) to the concentration of a
substrate [S].
V0 = Vmax [S]
Km + [S]

●The Michaelis–Menten model uses the following concept of enzyme catalysis:

9. ●The enzyme (E), combines with its substrate (S) to form an enzyme–substrate complex
(ES). The ES complex can dissociate again to form E + S, or can proceed chemically to
form E and the product P.
●The rate constants k1, k2 and k3 describe the rates associated with each step of the
catalytic process.
●It is assumed that there is no significant rate for the backward reaction of enzyme and
product (E + P) being converted to ES complex. [ES] remains approximately constant
until nearly all the substrate is used, hence the rate of synthesis of ES equals its rate of
consumption over most of the course of the reaction; that is, [ES] maintains a steady
state.
●From this concept, the Michaelis–Menten equation was derived.

10. V0 = Vmax [S] = Michaelis menten equation
Km + [S]

●The normal pattern of dependence of enzyme rate on substrate concentration ([S]) is
that at low substrate concentrations a doubling of [S] will lead to a doubling of the
initial velocity (V0). However, at higher substrate concentrations the enzyme becomes
saturated and further increases in [S] lead to very small changes in V0.

●This occurs because at saturating substrate concentrations, all of the enzyme molecules
have bound substrates. The overall enzyme rate is now dependent on the rate at which
the product can dissociate from the enzyme, and adding further substrate will not affect
this. In situations where the substrate concentration is saturating, a doubling of the
enzyme concentration will lead to a doubling of V0.

11. MICHAELIS MENTEN MODEL

12. ●The following equation, known as the Equation of enzyme machanism, is used to
describe the kinetics of enzymes:

●Where E, S, ES, and P represent enzyme, substrate, enzyme–substrate complex, and
product, respectively.


●The Kf, Kr, & Kcat denote “the rate constants for the "forward" binding” and "reverse
unbinding of substrate”, and for the “catalytic conversion of substrate into product”,
respectively.
K1 = Kr, K2 = Kf,K3 = Kcat

13. ●According to Michaelis menten equation. The first linear part shown in the graph is
known as the 1st Order Kinetics. The linear increase in Velocity with increase in
Substrate concentration.
●The graph shows a plateau region where increase in substrate concentration no longer
increases with the velocity of the reaction. At this stage velocity has reached the
maximum velocity. Which is denoted as Vmax. This plateau region is called as 0th
order kinetics which means Velocity is independent of substrate concentration.
●The Michaelis Menten equation explains this curve (plateau) mathematically. The aim
of this equation is to find the mathematical relation between V0, Vmax, and Km. Such
that, both 0 Order and 1st Order kinetics can be explained.

14. ●According to Laws of mass action,
Kf [E][S] = Kr [ES]
●If we take the ratio of this equation we will get,
[E][S] = Kr = Kd
[ES]Kf
●This Kd is called the Dissociation constant. According to the Pseudo - steady - state
hypothesis, The state of ES in the first equation remains constant.
[ES] formation = [E][S] breakdown
So,
ES formation = Kf [E][S]
ES breakdown = Kr [ES] + Kcat[ES]

15. Ie we say that, Kf [E][S] = Kr [ES] + Kcat[ES]
Taking [ES] common gives, Kf [E][S] = [ES] (Kr+Kcat)
Taking the ratio, [E][S] = Kr+Kcat = Km (Michaelis menten constant)
[ES] Kf
According to our aim, our aim is to find the mathematical relation between V0, Vmax, and
Km. We have,
[E][S] = Km.
[ES]
Velocity is equal to rate of production per unit time. Ie, V0 = d[P]
dt
Velocity Vo depends on the breakdown of the ES complex. Ie,

V0 = Kcat [ES]

16. ●There are some molecules which are not bound with the substrate and other enzyme
molecules bound with the substrate, so that total enzyme concentration can be given as
E0 = E + ES

●When all enzyme molecules are bound with the substrate there is no free enzyme left,
hence, E0 = E+ES where E=0, E0=ES. As all enzymes are occupied by the substrates
the velocity reaches maximum velocity or Vmax.

●Therefore Vmax = Kcat[E0] were E0 = ES. Now let's rearrange the equation to get one
single equation.
E0 = E+ES
Taking E on the other side, (E0 - ES) = E or E = (E0 - ES)
This E can be replaced in the equation of Km.
Km = [E][S] = (E0 - ES)[S]
[ES] [ES]

17. Now let's multiply [S] with the term E = E0 - ES, So we get

Km = (E0 - ES)[S] = [E0][S] - [ES][S] = [E0][S] - [S]
[ES] [ES] [ES][ES] 1
Rearranging the equation,
Km = [E0][S] - [S]
[ES] 1
Now the term [E0] can be replaced by Vmax
Kcat
Km = Vmax[S] - [S]
Kcat [ES] 1
The product of Kcat [ES] = V0

Km = Vmax[S] - [S]
V0 1

18. If we take -[S] on the other side with Km, then we get,
Km + [S] = Vmax [S]
V0
Rearranging this equation finally we get,





This Equation is called the Michaelis menten equation. Which says when substrate
concentration is very large, The value of Km will be very less, as compared to the value of
S. Hence, Km can be ignored when compared to S.
Then equation becomes
V0 = Vmax [S]
[S]
[S] can be cancelled. Finally we will get

V0 = Vmax.

V0 = Vmax [S]
Km + [S]

19. The Michaelis Menten constant in turn is defined as follows:


●The Michaelis menten constant is equal to the substrate concentration at which the
enzyme converts substrates into products at half its maximal rate and hence is related to
the affinity of the substrate for the enzyme.
●The catalytic constant Kcat is the rate of product formation when the enzyme is
saturated with substrate and therefore reflects the enzyme's maximum rate. The rate of
product formation is dependent on both how well the enzyme binds substrate and how
fast the enzyme converts substrate into product once substrate is bound. For a
kinetically perfect enzyme, every encounter between enzyme and substrate leads to
product and hence the reaction velocity is only limited by the rate the enzyme
encounters substrate in solution. Hence the upper limit for Kcat/ Km is equal to the rate
of substrate diffusion.

20. Ie, Simply., V0 = Vmax
2
Applying in the main equation

V0 = Vmax = Vmax [S] = 1 = [S] _
2 Km + [S] 2 Km + [S]

Removing Vmax on both sides, and rearranging the equation

1 = 2 [S] _
Km + [S]

Km = 2 [S] - [S]

Km = [S] (definition of michaelis menten constant)

21. APPLICATIONS

➢The constant Km is a measure of how efficiently an enzyme
converts a substrate into a product.
➢The equation can also be used to describe the relationship
between ion channel conductivity and ligand concentration.

22. LINEWEAVER AND BURK - INTRODUCTION
●In biochemistry, the Lineweaver–Burk plot (or double reciprocal plot) is a graphical
representation of the Lineweaver–Burk equation of enzyme kinetics, described by Hans
Lineweaver and Dean Burk in 1934.
●The Lineweaver–Burk plot for inhibited enzymes can be compared to non inhibited
enzymes to determine how the inhibitor is competing with the enzyme.

23. LINEWEAVER & BURK

●Hans Lineweaver was an American physical chemist, who is credited (misleadingly)
with introducing the double-reciprocal plot or Lineweaver–Burk plot.
●The paper containing the equation was co-authored by Dr. Dean Burk,who was an
American biochemist, medical researcher, and a cancer researcher at the Kaiser
Wilhelm Institute and the National Cancer Institute, and was entitled "The
Determination of Enzyme Dissociation Constants (1934)".

24. LINEWEAVER-BURK DOUBLE RECIPROCAL PLOT
●Since, Vmax is achieved at infinite substrate concentration, it is impossible to estimate
Vmax and hence Km from a hyperbolic plot. Because of this difficulty, the
Michaelis–Menten equation was transformed into an equation for a straight line by
Lineweaver and Burk.
●The Lineweaver–Burk plot (or double reciprocal plot) is a graphical representation of
the Lineweaver–Burk equation of enzyme kinetics. This plot is a derivation of the
Michaelis–Menten equation and is represented as

Where,
●V is reaction velocity ( the reaction rate)
●Km is the Michaelis menten constant
●Vmax is the maximum reaction velocity, and
●S is the substrate concentration

25. LINEWEAVER BURK EQUATION
The plot provides a useful graphical method for analysis of the Michaelis–Menten
equation, as it is difficult to determine precisely the Vmax of an enzyme-catalysed reaction:

26. We have the Michaelis menten equation
V0 = Vmax[S] =
Km + [S]

Taking the reciprocal gives
_1 = Km + [S]
V0 Vmax[S]

_1 = Km + [S]__
V0 Vmax[S] Vmax[S]

_1 = Km + 1__
V0 Vmax[S] Vmax

27. _1 = Km + 1__
V0 Vmax[S] Vmax

If we compare this equation with equation of straight line Y = mx + c

Y = 1 _
V0

M = Km
Vmax

X = 1 _
[S]

C = 1 _
Vmax

28. ●Reversible enzyme inhibitors can be classified as either competitive or noncompetitive, and
can be distinguished via a Lineweaver–Burk plot. It is a useful way of determining how an
inhibitor binds to an enzyme.
●Competitive inhibition can be recognized by using a Lineweaver–Burk plot if V0 is
measured at different substrate concentrations in the presence of a fixed concentration of
inhibitor. A competitive inhibitor increases the slope of the line on the Lineweaver–Burk
plot, and alters the intercept on the x-axis (since Km is increased), but leaves the intercept on
the y- axis unchanged (since Vmax remains constant).
●Noncompetitive inhibition can also be recognized on a Lineweaver–Burk plot since it
increases the slope of the experimental line, and alters the intercept on the y-axis (since
Vmax is decreased), but leaves the intercept on the x-axis unchanged (since Km remains
constant).

29. APPLICATIONS
●It is used to determine important terms in enzyme kinetics, such as Km and Vmax,
before the wide availability of powerful computers and non-linear regression software.
●This plot gives a quick, visual impression of the different forms of enzyme inhibition.

30. CONCLUSION
The two main principles in Enzyme kinetics are Michaelis menten kinetics and Lineweaver burk
plot and we also discussed two constants in Enzyme kinetics ie: Km and Vmax. Michaelis–Menten
kinetics is one of the best-known models of enzyme kinetics. It is named after German biochemist
Leonor Michaelis and Canadian physician Maud Menten. The model takes the form of an equation
describing the rate of enzymatic reactions, by relating reaction rate V ( rate of formation of product
[P] to [S] ) and the concentration of a substrate S. According to the Lineweaver burk double
reciprocal plot, It is a graphical representation of the Lineweaver–Burk equation of enzyme kinetics,
described by Hans Lineweaver and Dean Burk in 1934. The Lineweaver–Burk plot for inhibited
enzymes can be compared to no inhibitor to determine how the inhibitor is competing with the
enzyme. In this plot Michaelis –Menten equation was transformed into an equation for a straight
line by Lineweaver and Burk.

31. REFERENCES
●David Hames and Nigel Hooper (2005). Biochemistry. Third ed. Taylor & Francis
Group: New York.
●Dean Burk/wikipedia
●Enzyme kinetics/Wikipedia
●Hans Lineweaver/wikipedia
●Leonor Michaelis/wikipedia
●Maud Leonora Menten/wikipedia
●Michaelis menten model/microbenotes
●Michaelis-Menten Model/wikipedia.
●Srinivasan, Bharath (2021-07-16). "A Guide to the Michaelis‐Menten equation: Steady
state and beyond"
●Stryer L, Berg JM, Tymoczko JL (2002). "Section 8.4: The Michaelis-Menten Model
Accounts for the Kinetic Properties of Many Enzymes". Biochemistry (5th ed.). San
Francisco: W.H. Freeman. ISBN 0-7167-4955-6.)

32. THANK YOU