Enzyme kinetics

2/13/2013 By Mohd Anzar Sakharkar 1

Enzymes
Enzymes are proteins
which acts as
biocatalyst. It alters the
rate of reaction in
biological process.
2/13/2013 By Mohd Anzar Sakharkar
2

Enzyme action
Like all catalysts, enzymes accelerate the rates of
reactions while experiencing no permanent
chemical modification as a result of their
participation.
Enzymes can accelerate, often by several orders of
magnitude, reactions that under the mild
conditions of cellular
concentrations, temperature, p H, and pressure
would proceed imperceptibly in the absence of the
enzyme.

Enzyme Kinetics
Enzyme kinetics is the study of the chemical
reactions that are catalysed by enzymes.
In enzyme kinetics, the reaction rate is measured
and the effects of varying the conditions of the
reaction is investigated.
Studying an enzyme's kinetics in this way can
reveal the catalytic mechanism of this enzyme


• Enzymes are usually protein molecules that
manipulate other molecules the enzymes'
substrates.
• These target molecules bind to an enzyme's active
site and are transformed into products through a
series of steps known as the enzymatic
mechanism.
• These mechanisms can be divided into single-
substrate and multiple-substrate mechanisms.
• Kinetic studies on enzymes that only bind one
substrate, such as triosephosphate isomerase, aim
to measure the affinity with which the enzyme
binds this substrateMohd Anzar Sakharkar
2/13/2013 By and the turnover rate. 5

Michealis-Menten
Analysis
• Michaelis–Menten kinetics is one of the simplest
and best-known models of enzyme kinetics.
• The model serves to explain how an enzyme can
cause kinetic rate enhancement of a reaction and
why the rate of a reaction depends on the
concentration of enzyme present.


• To begin our discussion of enzyme
kinetics, let's define the number of moles of
product (P) formed per time as V.
• The variable, V, is also referred to as the rate
of catalysis of an enzyme.
• For different enzymes, V varies with the
concentration of the substrate, S.
• At low S, V is linearly proportional to S, but
when S is high relative to the amount of total
enzyme, V is independent of S.

• To understand Michaelis-Menten
Kinetics, we will use the general enzyme
reaction scheme shown below, which
includes the back reactions in addition the
forward reactions:

• The table below defines each of the rate
constants in the above scheme.


The table below defines each of the rate constants in the
above scheme.
Rate
Reaction
Constant

The binding of the enzyme to the substrate forming
k1 the enzyme substrate complex.

The dissociation of the enzyme-substrate complex to
k2 free enzyme and substrate .

Catalytic rate; the catalysis reaction producing the
k3 final reaction product and regenerating the free
enzyme. This is the rate limiting step.

k4 The reverse reaction of catalysis.

Substrate Complex

The ES complex is formed by combining enzyme E with
substrate S at rate constant k1. The ES complex can
either dissociate to form EF (free enzyme) and S, or
form product P at rate constant k2 and k3, respectively.

The velocity equation can be
derived following method:
• The rates of formation and breakdown of
the E - S complex are given in terms of
known quantities:
o The rate of formation of E-S =
(with the assumption that [P] =0)
o The rate of breakdown of E-S =
=

• At steady state,

=

Therefore, rate of formation of E-S = rate of breakdown of E-S

So,

Dividing through by k1: [E] [S] = [E-S]

Substituting with kM:

kM =

implies that half of the active sites on the
enzymes are filled. Different enzymes have
different values. They typically range
from 10-1 to 10-7 M. The factors that
affect are:
• pH
• temperature
• ionic strengths
• the nature of the substrate

• Substituting [EF] with [ET]-[ES]:
ET = [ES] + [EF]

([ET] - [ES]) [S] = kM [ES]
[ET] [S] -[ES][S] = kM [ES]
[ET] [S] = [ES] [S] + kM [ES]
[ET] [S] = [ES] ([S] + kM)

• Solving for [ES]: [ES] =


• The rate equation from the rate limiting step is:

Vo = = k2[ES]
Multiplying both sides of the equation by k2:
k2 [ES] =

Vo =

When S>>KM, vo is approximately equal to k2[ET]. When
the [S] great, most of the enzyme is found in the bound
state ([ES]) and Vo = Vmax

We can then substitue k2[ET] with Vmax to get the Michaelis
Menten Kinetic Equation:
2/13/2013 vo = By Mohd Anzar Sakharkar 15

Lineweaver-Burk Plot
• The Lineweaver–Burk plot is a graphical
representation of the Lineweaver–Burk equation
of enzyme kinetics, described by Hans
Lineweaver and Dean Burk in 1934.


Derivation
• The plot provides a useful graphical method for
analysis of the Michaelis-Menten equation:

• Taking the reciprocal gives

Km is the Michaelis–Menten constant
[S] is the
substrate concentration
V is the reaction velocity (the reaction
rate)
2/13/2013 By Mohd Anzar Sakharkar the maximum reaction velocity
Vmax is 17

Apply this to equation for a straight line and we have:

When we plot versus , we obtain a straight
line.


• The Lineweaver–Burk plot was widely 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. The y-intercept of such a
graph is equivalent to the inverse of Vmax; the x-
intercept of the graph represents −1/Km. It also
gives a quick, visual impression of the different
forms of enzyme inhibition.
• The double reciprocal plot distorts the error
structure of the data, and it is therefore unreliable
for the determination of enzyme kinetic
parameters.


Eadie–Hofstee diagram
• Eadie–Hofstee diagram is a graphical
representation of enzyme kinetics in
which reaction velocity is plotted as
a function of the velocity
vs. substrate concentration ratio:

V =reaction velocity

Km = Michaelis–Menten constant
[S] = substrate concentration
Vmax = maximum reaction velocity.

• It can be derived from the Michaelis–
Menten equation as follows:

• invert and multiply with :

• Rearrange:

• Isolate v:

• A plot of v vs v/[S] will yield Vmax as the y-
intercept, Vmax/Km as the x-intercept, and Km as the
negative slope.
• Like other techniques that linearize the Michaelis–
Menten equation, the Eadie-Hofstee plot was used
historically for rapid identification of important kinetic
terms like Km and Vmax, but has been superseded
by nonlinear regression methods that are significantly
more accurate and no longer computationally
inaccessible.
• It is also more robust against error-prone data than
the Lineweaver–Burk plot, particularly because it
gives equal weight to data points in any range of
substrate concentration or reaction velocity.
• Both plots remain useful as a means to present data
graphically.

BIBILIOGRAPHY
• Atkins, Peter and de Paula, Julio. Physical
Chemistry for the Life Sciences. New
York, NY: W. H. Freeman and
Company, 2006. Page 309-313.
• Stryer, Lubert. Biochemistry (Third Edition).
New York, NY: W.H. Freeman and
Company, 1988. Page 187-191.
• Chang, Raymond. Physical Chemistry for the
Biosciences. Sansalito, CA: University
Science, 2005. Page 363-371.


Enzyme kinetics

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