Unit 11 Enzyme Kinetics and Regulation

UNIT 11
ENZYME KINETICS AND
REGULATION

Structure
11.1 Introduction 11.3 Regulation of Enzymes

Objectives 11.4 Summary

11.2 Enzyme Kinetics 11.5 Terminal Questions

Michaelis-Menten Equation 11.6 Answers

Lineweaver-Burk Plot

Significance of Km and Vmax

Kcat and Turnover Number

11.1 INTRODUCTION
Kinetics is the study of reaction rates, their quantitative measurement and a
systematic study of the factors influencing the activity of enzymes. In this unit,
you will gain an insight of the enzymatic mechanisms as well as role played by
enzyme activity in regulating metabolic pathways. Enzymes convert substrates
to products through a series of steps (enzymatic mechanism). Therefore the
effect of substrate concentration on enzyme activity is one of key concepts in
enzyme kinetics. Several models have been proposed to explain the kinetics
of enzyme catalyzed reactions. Classical experimental work for single enzyme
catalyzed reactions is Henri-Michaelis-Menten plot, Briggs Haldane equation,
Lineweaver-Burk plot, etc.

The catalytic efficiency of enzymes needs to be effectively controlled to ensure

proper homeostasis. Several different mechanisms are prevalent in the cell to
regulate the activity of enzymes. The effector molecules regulating the activity
of enzymes act as vital elements in the integration of metabolic pathways. The
necessity for regulation of enzyme arises from the fact that the complex
system of biological transformations has to be regulated so that concentrations
of key metabolites are controlled both in terms of space and time to direct
metabolism in a desired direction and not allow drifting. Any abnormalities in
the metabolic pools of enzymes or their regulation will lead to severe disorders
or diseases such as cancer, diabetes or neurodegeneration. 69
Block 3 Essential Molecules of Biochemistry

Objectives
After studying this unit, you should be able to:

derive Michaelis-Menten equation,

explain the mechanisms of enzyme catalysis,

draw Lineweaver-Burk plot,

describe Km and Vmax, and

determine different regulatory mechanisms for directionality of

metabolic pathways.

11.2 ENZYME KINETICS

Kinetic analysis helps to disclose the number and order of the individual steps
involved in the transformation of substrates to products. In the past, data
generated from the experiments of enzyme catalyzed reactions was collected
and analyzed to determine the rate of a reaction. It was found out that at low
concentrations of substrate, the reaction was of first-order with respect to the
substrate. However, at the higher concentrations of substrate, the reaction
became zero-order. Please recall from your chemistry books regarding the
zero order or first order enzyme catalyzed reactions. Generally all single
substrate enzyme catalyzed reactions and even multi-substrate reactions
where concentrations of all but one were kept constant follows the same order.
At constant enzyme concentration, graph of initial velocity [vo] (on y-axis)
against substrate [S] concentration (on x-axis) was found to exhibit a
hyperbolic curve (Fig. 11.1).

Fig. 11.1: Graph of initial velocity against substrate concentration for a single
substrate enzyme catalyzed reaction.

The general equation from the graph is

V max [ So ]
vo =
70 [ So ] + b
Unit 11 Enzyme Kinetics and Regulation
Vmax = Maximum velocity = maximum value of vo

b = constant = value of [ So ] where vo = ½ Vmax

In general terms, in a mono substrate enzyme catalyzed reaction and

considering just one substrate binding site per enzyme molecule, substrate [S]
comes in physical contact with enzyme [E] to form an enzyme substrate
complex [ES] complex which eventually undergoes a further reaction and
leads to the formation of product [P]. It can be represented as:

rate constant k1 rate constant k2

E+S ES E+P

rate constant k-1

k1 = rate constant for the association of substrate and enzyme

k2 = rate constant for the breakdown of enzyme and product

k-1 = rate constant for the dissociation of [ES] complex to form free enzyme
and substrate

The overall rate of reaction is limited by two factors:

1) The amount of concentration of enzyme

2) The breakdown of enzyme-substrate complex

At low substrate concentrations, the overall rate of reaction will be limited by

the rate at which enzyme and substrate molecules react to form enzyme-
substrate complex. At constant enzyme concentration, the rate of reaction will
be proportional to the substrate concentration (first-order reaction). However,
at high substrate concentration enzyme will be saturated with the substrate
and therefore no free enzyme will be available. So the overall rate of reaction
will be independent of the substrate concentration. The maximum initial
velocity possible will be

Vmax = k2 [Eo]

SAQ 1
How does substrate concentration affect the rate of enzymatic reactions?

11.2.1 Michaelis-Menten Equation

Kinetic models used to explain above mentioned findings were proposed by
Michaelis and Menten (1913). The Michaelis-Menten equation demonstrates
the relationship between initial reaction velocity and substrate concentration.
Derivation of this equation begins with the generalized scheme of events
considering a single substrate enzyme catalyzed reaction as stated earlier;
Substrate [S] interacts with enzyme [E] to form an enzyme substrate complex
[ES] complex which eventually breaks down to free enzyme [E] and the
formation of product [P]. The Michaelis and Menten set out the following
scheme: 71
Block 3 Essential Molecules of Biochemistry
k1 k2

E + S ⇌ ES ----- E + P

k-1

The term k1 denotes the rate constant for the formation of ES complex. ES
complex has two fates, it can dissociate back to enzyme and substrate with
rate constant k-1, or proceed to form product and release the free enzyme with
a rate constant k2. In any enzyme catalyzed reaction, the concentration of
substrate should be five or six orders higher than that of enzyme. The above
model also assumes that k2 << k1. There is every possibility that reaction can
go backward but if we consider only the initial rate of a reaction, we can ignore
the backward reaction.

The overall rate of reaction is termed as initial velocity (vo) and it will depend
on two factors – the rate of formation of product (k2) and the concentration of
enzyme bound with the substrate i.e [ES]

So vo = k 2[ ES ] …………….equation 1

Michaelis and Menten made two assumptions in their model. First, the
availability of excess substrate [S] >> [E]. Secondly a rapid equilibrium is
established between the reactants ([E] + [S]) and [ES] complex. Moreover, the
breakdown of enzyme-substrate complex is too slow to cause any change in
equilibrium. Hence Michaelis and Menten model is also known as “Rapid
equilibrium model”. Thus at the equilibrium state:

k 1[ E ][ S ] = k − 1[ ES ] …………….equation 2

[ E ][S ] k − 1
= = Ks …………….equation 3
[ ES ] k1

Ks is the dissociation constant. If Eo is the total enzyme concentration, it is

equal to the sum of free enzyme [E] and enzyme bound to the substrate [ES]
as represented in the following equation:

Eo = [ E ] + [ ES ] …………….equation 4

E = [ Eo ] − [ ES ]

Substituting the value of E in equation 3

([ Eo] − [ ES ])[S ]
= Ks
[ ES ]

([ Eo ] − [ ES ])[S ] = Ks[ ES ]

[ Eo][ S ] − [ ES ][ S ] = Ks[ ES ]

[ Eo ][ S ] = Ks[ ES ] + [ ES ][ S ]

[ Eo ][ S ] = [ ES ]( Ks + [ S ])

[ Eo][S ]
[ ES ] =
72 ( Ks + [ S ])
Unit 11 Enzyme Kinetics and Regulation

Substituting the value of [ES] in equation 1 we get

[ Eo ][ S ]
So vo = k 2 ……………..equation 5
( K s + [ S ])

Maximum rate of enzyme reaction will be achieved when all the enzyme
molecules are bound to the substrate molecules.

So V max = k 2 [ Eo ] …………….equation 6

Substituting this value in equation 5 we get

V max [ S ]
vo =
( K s + [ S ])

Michaelis and Menten also made the supposition that initial substrate
concentration [So] is much higher than the initial enzyme concentration [Eo], in
such a scenario the formation of enzyme-substrate complex will have no such
big change in free substrate concentration. The expression for vo will be:

V max [ So ]
vo = …………….equation 7
( K s + [ So])

The above equation equation 7 is well known as Michaelis-Menten equation

Briggs Haldane modified Michaelis-Menten Plot:

The Michaelis-Menten model is dependent on the assumption of rapid

equilibrium approach in any enzyme catalyzed reaction. It limits the
applicability of the equation to only rapid kinetic reactions which might not be
the case with many of the other enzyme reactions. Most of enzyme catalyzed
reactions assume a constant concentration of enzyme-substrate complex [ES].

Generally if an enzyme is mixed with high concentration of a substrate there is

an initial period expressed as pre-steady state (lasts in micro seconds) where
concentration of [ES] slowly builds up. Eventually the concentration of [ES]
builds up and attains a steady state, remains constant over time. The steady-
state concept was introduced by Briggs and Haldane in 1925, a modified
Michaelis-Menten method. This concept was considered more valid
assumption than the earlier ones. The Michaelis-Menten model gave
importance to the formation of [ES] while Briggs-Haldane method focuses on
the consistency of [ES] complex, its maintenance at constant concentration
and breakdown to products.

Considering the single substrate enzyme catalyzed reaction one more time. In
this reaction at steady state, rate of formation of [ES] will be equal to the rate
of its decomposition to products. Therefore

k 1[ E ][ S ] = k − 1[ ES ] + k 2[ ES ] -------------------- equation 8 73
Block 3 Essential Molecules of Biochemistry
Separating the constant from variables:

[ E ][S ] k − 1 + k 2[ ES ]
= = Km -------------------- equation 9
[ ES ] k1

Where K m = Michaelis constant

Substituting Ks with Km in the above equations (4-7)

E = [ Eo ] − [ ES ]

Substituting the value of E in equation 9

([ Eo ] − [ ES ])[S ]
= Km
[ ES ]

([Eo] − [ ES ])[S ] = K m [ ES ]

[ Eo][S ] − [ ES ][ S ] = K m [ ES ]

[ Eo][S ] = K m [ ES ] + [ ES ][S ]

[ Eo][S ] = [ ES ]( K m + [ S ])

[ Eo][S ]
[ ES ] =
( K m + [ S ])

Substituting the value of [ES] in equation 1 we get

[ Eo ][ S ]
So vo = k 2
( K m + [ S ])

Since V max = k 2 [ Eo ]

Substituting this value in above equation

V max [ S ]
vo =
( K m + [ S ])

Since substrate concentration is much higher than the enzyme concentration

[S]~ [ So ] so

V max [ So ]
vo = ……………..equation 10
( K m + [ S o ])

The above equation equation 10 is similar to well known Michaelis-Menten

equation. The only change is the Km instead of Ks in the denominator. So the
equation retains its previous name of Michaelis-Menten equation and constant
Km is known as Michaelis-Menten constant.

A graph of vo at y-axis vs substrate concentration [S] at x-axis will be in the

74 form of a hyperbolic curve (Fig. 11.2).
Unit 11 Enzyme Kinetics and Regulation

Fig. 11.2: Michaelis-Menten plot of a single substrate catalyzed enzyme reaction.

SAQ 2
Explain how the rate of an enzyme-catalyzed reaction reaches a maximum
value at high substrate in a Michaelis-Menten equation?

11.2.2 Lineweaver Burke Plot

If you look at the Michaelis-Menten plot, you will observe that vo approaches
Vmax in a tangential manner at higher substrate concentrations. So if you want
to determine Vmax and Km from the plot, it will be difficult and unsatisfactory. A
hyperbolic curve nature of the graph makes it difficult to determine the
accurate value of Vmax and Km. Therefore, to overcome this difficulty,
Lineweaver and Burk (1934) suggested a straight line graph for enzyme
catalyzed reactions obeying Michaelis-Menten equation. They did not made
any new assumptions and derive the Lineweaver-Burk plot, which is also
known as double reciprocal plot. Lineweaver and Burk took the Michaelis-
Menten equation and inverted it.

V max [ So ]
vo =
( K m + [ So ])

1 ( K m + [ So ])
=
vo V max [ So ]

1 [ So ] Km
= +
vo V max [ So ] V max [ So ]

1 1 Km
= +
vo V max V max [ So ]

This equation is known as Lineweaver-Burk equation. It is in the form of y =

mx+c …………….equation 11 75
Block 3 Essential Molecules of Biochemistry
which is the equation of a straight line graph. Plot of 1/v against 1/So is linear
and obeys Michaelis-Menten equation (Figure 11.3). This is known as
Lineweaver-Burk plot or double reciprocal plot.

Fig. 11.3: Double reciprocal plot of the Michaelis-Menten equation.

11.2.3 Significance of Km and Vmax

Km or Michaelis constant is defined as the substrate concentration which
allows the enzyme to achieve half of Vmax (maximal velocity) [refer Figure 11.2
and 11.3]. Moreover, Km has the units of concentration but it is independent of
the enzyme and substrate concentration. Km measures inverse of affinity. The
substrate concentration (Km) needed to transfer half of the enzyme molecules
into ES complex denotes the affinity of the enzyme for the substrate. Low
values of Km denote high affinity of enzyme for the substrate. On the other
hand, high values of Km suggest that enzyme needs relatively high levels of
substrate concentration for its saturation thereby implying poor affinity of the
enzyme for substrate.

Both Km and Vmax are kinetic parameters. The rate of reaction becomes
maximum when the enzyme is fully saturated with substrate molecules and is
denoted as Vmax.

SAQ 3
Tick [√] mark the correct option:

a) Michaelis-Menten equation relates the rate of an enzyme-catalyzed

reaction to substrate concentration/product concentration (pick one).

b) A hyperbolic curve gives an accurate value of Vmax and Kmax

(True/False).

c) Lineweaver-Burk plot is linear/hyperbolic (Choose one option).

d) Km is equal/more to the substrate concentration at ½ Vmax (Choose one

option).
76
Unit 11 Enzyme Kinetics and Regulation
11.2.4 kcat and Turnover Number
To determine the enzyme efficiency in enzyme kinetics, we are interested to
know how many maximum molecules of substrate can be converted into
product per catalytic site of a given concentration of enzyme per unit time.

kcat = Vmax/Et

where

kcat = Turnover number,

Vmax = Maximum rate of reaction when enzyme catalytic site is saturated with
substrate Et =Total enzyme concentration or concentration of total enzyme
catalytic sites.

The kcat is a direct measure of catalytic production of product under optimal

conditions. The units of Turn over number (kcat) = (moles of product/sec)/
(moles of enzyme) or sec-1.

Enzyme carbonic anhydrase catalyzes conversion of carbon dioxide to

carbonic acid and bicarbonate ions. Its turnover number of 400,000 to 600,000
s−1 suggests that each enzyme molecule can produce up to 600,000
molecules of product (bicarbonate ions) per second.

11.3 REGULATION OF ENZYME ACTIVITY

Have you thought of ways by which enzyme activity can be regulated? There
are various mechanisms of enzyme regulation as listed below:

1. Enzyme Quantity

2. Inhibition

a) Reversible Inhibition

b) Irreversible Inhibition

3. Allosteric Regulation

4. Feedback Regulation or Inhibition

5. Co-valent Modification

6. Proteolytic degradation

1. Enzyme Quantity

The quantity of enzymes or turnover number is determined by the overall rate

of synthesis and rate of degradation of the enzyme. Any change in its quantity
can be affected by a change in rate constant for the overall synthesis and
degradation processes or both. The concentration of proteins or enzymes
remained essentially constant in a state of ‘dynamic equilibrium’. It gets
influenced by a wide range of physiologic, hormonal or dietary factors. The
turnover number of the enzymes can vary from minutes to hours to days for
different enzymes. 77
Block 3 Essential Molecules of Biochemistry
1.1 Genetic Control: Enzyme synthesis at the gene level

Genes involved in the synthesis of enzymes can be induced or repressed.

Induction of enzymes can be done at the gene expression, RNA translation or
at the level of post-translational modifications. Hormones or growth factors
signal cascade may lead to an increase in the expression or translation of
enzyme not present before the signal. Inducers induce the synthesis of
enzymes while repressors decrease the production of enzyme. Inducers are
generally substrates or structurally similar molecules that initiate the synthesis
of enzymes. Inducible enzymes in humans include tryptophan pyrrolase,
threonine dehydratase, HMG-CoA reductase and cytochrome P-450. On the
other hand, a metabolite or repressor when produced in excess inhibits the
synthesis of enzymes involved in its formation. These regulatory molecules
block the transcription of mRNA by binding to a part of DNA termed as
operator. Repressors are allosteric proteins to which specific molecules can
bind to alter their shape and ability to bind DNA. Inducer molecules bind to the
repressor molecule and prevent its binding to the operator region of DNA. It
allows the transcription of the coding sequences for the enzymes. For
example, lac operon in E.coli, lactose acts an inducer to transcribe the
synthesis of three enzymes (β-galactosidase, permease and transacetylase)
involved in its degradation if it is present in the surrounding environment.

2. Inhibition

Molecules that bind to the enzymes and cause a decrease in their activity are
called enzyme inhibitors. These molecules either bind at the active site of
enzyme thereby preventing the substrate molecule to bind to the enzyme or
they may inhibit the catalytic activity of enzyme. You should know that many of
these molecules perform several regulatory roles in the metabolism. Some of
them are used as herbicides or pesticides. Most of the drug molecules also
act as enzyme inhibitors. Natural enzymes inhibitors e.g. poison are a part of
the defense mechanisms in wild life animals.

Enzyme inhibitions are mainly classified into two types:

a) Reversible Inhibition

b) Irreversible Inhibition

a) Reversible Enzyme inhibition: In reversible enzyme inhibition, loss of

the enzyme activity due to inhibitory molecule is reversible. Enzyme
activity gets restored on the removal of inhibitor. These inhibitors bind
non-covalently and give rise to different kinds of inhibition. Multiple weak
bonds between the inhibitor and the enzyme combine to give strong
binding which prevents the formation of product. They can be easily
removed by dilution or dialysis to restore full enzyme activity. Reversible
inhibitors tend to form equilibrium with an enzyme leading to certain level
of inhibition.

b) Irreversible Enzyme Inhibition: Irreversible inhibition is different from

temporary enzyme inactivation by the reversible inhibitor. The enzyme
activity is lost on the binding of inhibitor molecule to enzyme and its
78 activity cannot be recovered afterwards. These inhibitory molecules are
Unit 11 Enzyme Kinetics and Regulation
highly specific and can modify enzyme 3D structure. The enzyme gets
inactive or there is time dependent loss of enzyme concentration.
Inhibition cannot be removed by dilution or dialysis without losing
enzyme activity. They generally form or break covalent bonds with the
amino acid residues essential for substrate binding, catalysis or
maintenance of enzyme conformation.

Examples: Heavy metal ions such as mercury, lead, aldehydes and

haloalkanes. Alkylating agents such as iodoacetate and iodoacetamide forms
covalent linkages with –SH groups of the enzyme.

E-SH + ICH2.CO-2 ---- -------- E-S-CH2.CO-2 + HI

Several important drugs are well known examples of irreversible inhibitors.

Widely used drugs such as penicillin act by covalently inhibiting the enzyme
transpeptidase, thereby preventing the synthesis of bacterial cell walls and
thus killing the bacteria. You must have heard of tablet aspirin. The drug
aspirin inhibits the enzyme cyclooxygenase thereby reducing the synthesis of
inflammatory signals. Enzyme monoamine oxidase deaminates
neurotransmitters such as dopamine and serotonin, and lowers the levels of
these hormones in the brain. A neurodegenerative disease such as
Parkinson’s disease is linked with low levels of dopamine, while depression is
related with low levels of serotonin. Suicide inhibitor such as drug (-) deprenyl,
is widely used to treat Parkinson disease and depression.

3. Allosteric Regulation

Allosteric means ‘other structure or different site’. Allosteric enzymes are the
enzymes whose catalytic activity can be modulated by the effector molecules.
These molecules do not participate in catalysis directly. They bind at a site
other than the active site on the enzyme and can cause activation or inhibition
of the enzyme. The binding is reversible, non-covalent and brings about the
conformational change in the active site. These conformational changes occur
at the tertiary and quaternary levels of protein organization. Allosteric
enzymes are generally bigger and composed of multiple subunits having
distinct active site and allosteric site. Several studies on X-ray crystallography
and site directed mutagenesis have confirmed the existence of two separate
sites on variety of enzymes.

Allosteric enzymes exhibit a characteristic sigmoidal saturation curve rather

than hyperbolic curve [Michaelis-Menten curve] when vo is plotted versus [S]
on account of cooperativity of structural changes between enzyme subunits
(Fig. 11.4). Allosteric enzymes behave in a cooperative system manner with
both the substrate as well as modulator. A small change in substrate, inhibitor
or activator concentrations brings about a huge change in the rate of reaction.
The effectors that increase the catalytic activity are called positive effectors
and those that reduce or inhibit the catalytic activity are called negative
effectors.

For example, Phosphofructokinase (PFK) is regulated by

a) Negative effectors: High levels of ATP and citrate

b) Positive effectors: High levels of ADP and AMP 79

Block 3 Essential Molecules of Biochemistry

Fig. 11.4: Sigmoidal kinetics of allosteric enzymes.

4. Feedback Regulation or Inhibition

Another interesting aspect of enzyme regulation is the feedback regulation;

inhibition of an enzyme in the biosynthetic pathway by the end product of the
pathway. This type of inhibition is also termed as feedback inhibition and it
develops when metabolic demand for the end product of the pathway gets
declined. The end product binds to the regulatory site of the enzyme at the
start of metabolic pathway and suppresses its activity. Feedback inhibitors do
not bear any structural similarity to the substrates of the enzymes. For
example, consider the following reaction:

Enz 1 Enz 2 Enz 3

A----------- B--------- C --------- D

High concentrations of end product D will act as feedback inhibitor of enzyme

Enz 1. Small molecules such as amino acids or nucleotides act as feedback
inhibitors in several biosynthetic pathways. In the bacterial enzyme system, L-
threonine is converted to L-isoleucine in a sequence of five steps metabolic
pathway. Isoleucine binds to the first enzyme in the pathway threonine
dehydratase in a non-covalent manner and inhibits its own production.

SAQ 4
Do as directed:

a) The concentration of proteins or enzymes remained essentially constant

in a state of ‘_______________equilibrium’ (Fill in the Blank).

b) Repressors are _______________ proteins to which specific molecules

can bind to alter their shape and ability to bind DNA (Fill in the Blank).

c) Feedback inhibitors do not bear any structural similarity to the substrates

of the enzymes (True/False).

d) High/Low concentrations of end product will act as feedback inhibitor

(Pick one option).
80
Unit 11 Enzyme Kinetics and Regulation
5. Covalent Modification

Covalent modification is also a means of regulating enzyme activity. The

reversible covalent modification process of enzyme regulation involves many
target proteins and membrane channels. Modified groups are attached to the
enzyme by covalent bond. The covalent modification activates some enzymes
as well as inactivates others. Most modifications are reversible.
Phosphorylation and dephosphorylation are the most common but not the only
means of covalent modification. Enzyme regulation by phosphorylation-
dephosphorylation plays a key role in cell signaling. It allows the cell to
respond to a signal at its surface and transmits its effect to intracellular
enzymes. Phosphorylation cascade is highly selective. Seryl, Threonyl or
Tyrosyl residues on the regulatory enzymes are phosphorylated by specific
protein kinases. The very nature of protein folding determines whether protein
kinase has access to the substrate undergoing phosphorylation. The removal
of phosphoryl groups is catalyzed by protein phosphatases. Mammalian cell
possesses contain many phosphorylated proteins, several protein kinases and
phosphatases that catalyses their interconversion for regulatory control.
Phosphorylation influences the functional properties of affected enzyme by
altering its three-dimensional structure. Phosphorylation of one enzyme can
lead to phosphorylation of a different enzyme which in turn acts on another
enzyme, and so on.

Other covalent modifications such as glycosylation, hydroxylation, fatty acid

acylation, palmitoylation and prenylation are unique changes that shape
structure and localization of enzyme for its lifetime. Hydrophobic acylations
can cause the target protein to be associated with a membrane rather than the
cytosol.

6. Proteolytic enzymes

Certain enzymes are secreted as precursors in an inactive form and are

known as proenzymes or zymogens. Proenzymes help the proteins to be
transported or stored in inactive forms that can be converted in active forms at
the particular site. Precursor of pepsin is pepsinogen, trypsin is synthesized as
trypsinogen and procarboxypeptidase is zymogen of carboxypeptidase.
Several other examples include blood clotting enzymes, procollagen and
proinsulin. Zymogens underlie the mechanism whereby the levels of enzymes
can be readily increased at the post translational level by proteolytic cleavage,
an irreversible modification. Generally, cellular and bacterial proteolytic
enzymes are synthesized as inactive precursor (zymogen) to prevent
undesired protein degradation. Conversion of zymogens to active form either
requires accessory molecules or the autocatalytic processes in response to
drop in pH.

Some examples of enzymes and their zymogens are as given below:

Enzyme Precursor Function

Trypsin Trypsinogen pancreatic secretion

Chymotrypsin Chymotrypsinogen pancreatic secretion

Carboxypeptidase procarboxypeptidase pancreatic secretion

81
Block 3 Essential Molecules of Biochemistry
Elastase proelastase pancreatic secretion

Phosphalipase A2 prophospholipase A2 pancreatic secretion

Pepsin Pepsinogen Secreted in gastric juice

(Most active in pH
range 1-5)

11.4 SUMMARY
• Enzyme kinetics is the basis for enzyme catalyzed biochemical
reactions. Therefore, understanding of enzyme kinetics is important to
understand these biological processes.

• Kinetics provides a rationale for the complex behavior of enzymes. The

rational is based on simple chemical principles.
• For single substrate reactions, at constant E, increasing S results in
increased product formation to a point where product formation no
longer increases. This saturation is presumed to reflect the fact that all E
is now in the form of ES.

• Kinetic model proposed by Michaelis-Menten used equilibrium

assumption for deriving Michaelis-Menten equation.

• The equilibrium assumption was later modified to introduce a more valid

steady state assumption. The equation remains the same except the
definition of Michaelis constant (Km). The substrate concentration at
which velocity is half of Vmax (maximal velocity) is known as Michaelis
constant (Km). This constant gives an idea about the affinity of the
enzyme for its substrate.
• The hyperbolic graph of v versus S obtained by Michaelis-Menten
equation proved inadequate for determining the accurate value of Vmax
and Km. Lineweaver and Burk gave the solution by inverting the
Michaelis-Menten equation to give double reciprocal plot.

• Tight integration of metabolic pathways is possible using regulatory

enzymes. Regulatory enzymes generally catalyzed the slowest step in
the metabolic pathway. These enzymes tend to maintain the
homeostasis in spite of numerous changes in the external environment
of the cell.

• Enzyme can be regulated by the end product of a biosynthetic pathway.

The final end product inhibits the first enzyme of that pathway by binding
to an allosteric site which is distinct from the active site. The inhibition
results from a conformational change in the oligomeric structure of the
first enzyme.

• In another type of regulation, amino acid chains of the enzyme are

reversibly modified, mainly by phosphorylation and dephosphorylation.
This produces an active or inactive enzyme.

• Regulation of enzyme activity by inhibitors, allosteric and covalent

modifiers has wide range of applications in the fields of medicine and
82 agriculture.
Unit 11 Enzyme Kinetics and Regulation

11.5 TERMINAL QUESTIONS

1. Why is the rate of an enzyme-catalyzed reaction proportional to the
amount of ES complex?

2. Explain the maximal velocity Vmax in the vo vs S graph?

3. Derive double-reciprocal equation from Michaelis-Menten equation and

give its importance.

4. How a value for Km can be obtained from the vo vs S graph when vo =

1/2 Vmax?

5. Describe allosteric regulation of the enzyme activity?

6. What are proteolytic enzymes? Give examples.

11.6 ANSWERS
Self Assessment Questions
1. At low substrate concentrations, the overall rate of reaction will be limited
by the rate at which enzyme and substrate molecules react to form
enzyme-substrate complex. At constant enzyme concentration the rate
of reaction will be proportional to the substrate concentration (first-order
reaction). However, at high substrate concentration enzyme will be
saturated with the substrate and therefore no free enzyme will be
available. So the overall rate of reaction will be independent of the
substrate concentration.

2. At high substrate concentration So, Km <<<< So (numerically), so the

term Km + So in the Michaelis-Menten equation becomes equal to So. vo
= (Vmax So)/So, and So cancels. Therefore, at high So, vo = Vmax.

3. a) Substrate concentration, b) False, c) Linear, d) Equal

4. a) dynamic, d) allosteric, c) True, d) High

Terminal Questions
1. The product formation takes place after ES complex formation in an
enzyme catalyzed reaction. Enzyme E must bind to the substrate S
before the product is formed. Therefore, the rate of an enzyme-catalyzed
reaction is proportional to the amount of ES.

2. At high substrate concentrations, enzyme E will be bound to substrate S.

So the maximum amount of E.S is formed under these conditions. Since
the rate is proportional to the amount of ES, the rate is at a maximum
value under these conditions.

3. Refer to section 11.2.1 and 11.2.2

4. When vo = Vmax/2, then Vmax/2 = Vmax.S/Km + S

cancelling Vmax, 83
Block 3 Essential Molecules of Biochemistry
1/2 = S/(Km + S)

Km + S = 2S

or Km= S at vo = Vmax/2

5. Allosteric control is one of the important mechanisms of enzyme

regulation. In an allosteric enzyme, activity of the enzyme is controlled
by the binding of molecule at a site other than the active site. This other
site is known as allosteric site. The binding of an allosteric modulator
induces conformational changes which results in the alterations in the
catalytic activity of the enzymes. There are two types of allosteric
modulation-positive allosteric modulation when binding of modulator to
enzyme increases the rate of reaction. On the other hand negative
allosteric modulator decreases the activity of enzyme (for details refer to
section 11.3, subsection-3).

6. Refer to section 11.3, subsection-6.

FURTHER READINGS
1. David L. Nelson and Michael M. Cox: Lehninger Principles of
Biochemistry6th Ed., W.H. Freeman.

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