enzyme kinetics

12/13/2013 By Mohd Anzar Sakharkar

EnzymesEnzymes are proteins

which acts as

biocatalyst. It alters the

rate of reaction in

biological process.2/13/2013 2

By Mohd Anzar Sakharkar

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.2/13/2013 3By Mohd Anzar Sakharkar

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

2/13/2013 4By Mohd Anzar Sakharkar

• 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 substrate and the turnover rate.2/13/2013 5By Mohd Anzar Sakharkar

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

ConstantReaction

k1

The binding of the enzyme to the substrate forming

the enzyme substrate complex.

k2

The dissociation of the enzyme-substrate complex to

free enzyme and substrate .

k3

Catalytic rate; the catalysis reaction producing the

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.2/13/2013 10By Mohd Anzar Sakharkar

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 =2/13/2013 12By Mohd Anzar Sakharkar

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:

vo =2/13/2013 15By Mohd Anzar Sakharkar

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

V is the reaction velocity (the reaction

rate)

Km is the Michaelis–Menten constant

Vmax is the maximum reaction velocity

[S] is the

substrate concentration


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 todetermine important terms in enzymekinetics, such as Km and Vmax, before the wideavailability of powerful computers and non-linearregression software. The y-intercept of such agraph is equivalent to the inverse of Vmax; the x-intercept of the graph represents −1/Km. It alsogives a quick, visual impression of the differentforms of enzyme inhibition.

• The double reciprocal plot distorts the errorstructure of the data, and it is therefore unreliablefor the determination of enzyme kineticparameters.


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.


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