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R
...
Doolittle
...
The multiplicity of domains in proteins Annu
...
Biochem
...
(PubMed)
A
...
Holm
...
Rapid automatic detection and alignment of repeats in protein sequences Proteins 41: 224237
...
F
...
1992
...
1:
191-200
...
Zukerkandl and L
...
1965
...
Theor
...
8: 357-366
...
Krings, A
...
W
...
Krainitzki, M
...
Pääbo
...
Neandertal DNA sequences and
the origin of modern humans [see comments] Cell 90: 19-30
...
Krings, H
...
W
...
Krainitzki, and S
...
1999
...
Natl
...
Sci
...
S
...
96: 5581-5585
...
Gold, B
...
Uhlenbeck, and M
...
1995
...
Rev
...
64:
763-797
...
S
...
W
...
1999
...
Rev
...
68: 611-647
...
Hermann and D
...
Patel
...
Adaptive recognition by nucleic acid aptamers Science 287: 820-825
...
It currently contains
nearly 14,000 structures
...
rcsb
...
(http://www
...
nlm
...
gov/)
I
...
Enzymes: Basic Concepts and Kinetics
Enzymes, the catalysts of biological systems, are remarkable molecular devices that determine the patterns of chemical
transformations
...
The most striking
characteristics of enzymes are their catalytic power and specificity
...
Nearly all known enzymes are proteins
...
2
...

Proteins as a class of macromolecules are highly effective catalysts for an enormous diversity of chemical reactions
because of their capacity to specifically bind a very wide range of molecules
...
They catalyze reactions by stabilizing transition states, the highest-energy species in reaction pathways
...


I
...
Enzymes: Basic Concepts and Kinetics

The activity of an enzyme is responsible for the glow of the luminescent jellyfish at left
...
[(Left) Fred
Bavendam/Peter Arnold
...
The Molecular Design of Life

8
...
1
...
1)
...
Even a reaction as simple as the hydration of
carbon dioxide is catalyzed by an enzyme namely, carbonic anhydrase (Section 9
...
The transfer of CO2 from the
tissues into the blood and then to the alveolar air would be less complete in the absence of this enzyme
...
Each enzyme molecule can hydrate 106 molecules of CO2 per second
...
We will consider the mechanism of carbonic
anhydrase catalysis in Chapter 9
...
An enzyme usually catalyzes a single chemical reaction or a set of closely
related reactions
...


Let us consider proteolytic enzymes as an example
...


Most proteolytic enzymes also catalyze a different but related reaction in vitro namely, the hydrolysis of an ester bond
...
1
...


Proteolytic enzymes differ markedly in their degree of substrate specificity
...

Trypsin, a digestive enzyme, is quite specific and catalyzes the splitting of peptide bonds only on the carboxyl side of
lysine and arginine residues (Figure 8
...
Thrombin, an enzyme that participates in blood clotting, is even more
specific than trypsin
...
1B)
...
2), is another highly specific catalyst
...
DNA polymerase I is remarkably precise in carrying out the instructions given by the template
...

The specificity of an enzyme is due to the precise interaction of the substrate with the enzyme
...


8
...
1
...
Such an enzyme without its cofactor is referred to as an apoenzyme;
the complete, catalytically active enzyme is called a holoenzyme
...
2)
...
2
...
Glycogen phosphorylase (Section 21
...
5), which
mobilizes glycogen for energy, requires the small organic molecule pyridoxal phosphate (PLP)
...
Often derived from vitamins, coenzymes can be either
tightly or loosely bound to the enzyme
...
Loosely associated
coenzymes are more like cosubstrates because they bind to and are released from the enzyme just as substrates and
products are
...
Enzymes that use the same coenzyme are usually mechanistically similar
...
A more detailed discussion of coenzyme
vitamins can be found in Section 8
...


8
...
2
...
For
example, in photosynthesis, light energy is converted into chemical-bond energy through an ion gradient
...
Enzymes may then use the
chemical-bond energy of ATP in many ways
...
Pumps in the membranes of cells and organelles, which can be thought of as enzymes that
move substrates rather than chemically altering them, create chemical and electrical gradients by using the energy of
ATP to transport molecules and ions (Figure 8
...
The molecular mechanisms of these energy-transducing enzymes are
being unraveled
...


8
...
3
...
For example, a
proteolytic enzyme secreted by the pancreas is called trypsin
...
Thus, an ATPase is an enzyme that breaks down ATP,
whereas ATP synthase is an enzyme that synthesizes ATP
...
Reactions were divided into six major groups
numbered 1 through 6 (Table 8
...
These groups were subdivided and further subdivided, so that a four-digit number
preceded by the letters EC for Enzyme Commission could precisely identify all enzymes
...
4)
...

Consequently, it is a transferase, or member of group 2
...
Transferases that shift a phosphoryl group are designated 2
...
Various functional
groups can accept the phosphoryl group
...
7
...
The final
number designates the acceptor more precisely
...
7
...
4
...


I
...
Enzymes: Basic Concepts and Kinetics

8
...
Enzymes Are Powerful and Highly Specific Catalysts

Table 8
...
Rate enhancement by selected enzymes

Enzyme

Nonenzymatic half-life Uncatalyzed rate (k un, Catalyzed rate (k
-1
s -1)
cat, s )

OMP decarboxylase

78,000,000 years

2
...
4 × 1017

Staphylococcal nuclease

130,000 years

1
...
6 × 1014

AMP nucleosidase

69,000 years

1
...
0 × 1012

Carboxypeptidase A

7
...
0 × 10-9

578

1
...
7 × 10-7

66,000

3
...
9 days

4
...
0 × 109

Chorismate mutase

7
...
6 × 10-5

50

1
...
3 × 10-1

1 × 106

7
...

Source: After A
...
Wofenden
...


I
...
Enzymes: Basic Concepts and Kinetics

8
...
Enzymes Are Powerful and Highly Specific Catalysts

Figure 8
...
Enzyme Specificity
...


I
...
Enzymes: Basic Concepts and Kinetics

8
...
Enzymes Are Powerful and Highly Specific Catalysts

Table 8
...
Enzyme cofactors

Cofactor

Enzyme

Coenzyme
Thiamine pyrophosphate
Pyruvate dehydrogenase
Flavin adenine nucleotide
Monoamine oxidase
Nicotinamide adenine dinucleotide Lactate dehydrogenase
Pyridoxal phosphate
Glycogen phosphorylase
Coenzyme A (CoA)
Acetyl CoA carboxylase
Biotin
Pyruvate carboxylase
5 -Deoxyadenosyl cobalamin
Methylmalonyl mutase
Tetrahydrofolate
Metal

Thymidylate synthase

Zn2+

Carbonic anhydrase

Zn2+

Carboxypeptidase

Mg2+

EcoRV

Mg2+

Hexokinase

Ni2+
Mo
Se

Urease

Mn2+
K+

I
...
Enzymes: Basic Concepts and Kinetics

8
...
Enzymes Are Powerful and Highly Specific Catalysts

Nitrate reductase
Glutathione peroxidase
Superoxide dismutase
Propionyl CoA carboxylase

Figure 8
...
An Energy-Transforming Enzyme
...

I
...
Enzymes: Basic Concepts and Kinetics

8
...
Enzymes Are Powerful and Highly Specific Catalysts

Table 8
...
Six major classes of enzymes

Class

Type of reaction

1
...
Transferases
Group transfer
3
...
Lyases
5
...
Ligases

Example
Lactate dehydrogenase
Nucleoside monophosphate kinase (NMP
kinase)
Chymotrypsin

Hydrolysis reactions (transfer of functional
groups to water)
Addition or removal of groups to form
Fumarase
double bonds
Isomerization (intramolecular group
Triose phosphate isomerase
transfer)
Ligation of two substrates at the expense of Aminoacyl-tRNA synthetase
ATP hydrolysis

Chapter
16
9
9
18
16
29

I
...
Enzymes: Basic Concepts and Kinetics

8
...
Free Energy Is a Useful Thermodynamic Function for Understanding Enzymes
Some of the principles of thermodynamics were introduced in Chapter 1 notably the idea of free energy (G)
...
The former determines whether the reaction will be spontaneous, whereas the later determines the rate of the
reaction
...
First, we will consider the thermodynamics of reactions and then, in Section 8
...


8
...
1
...
3
...
A reaction can occur spontaneously only if Δ G is negative
...

2
...

3
...
An input of free energy is required to drive such a reaction
...

Two additional points need to be emphasized
...
The ΔG of a reaction is independent of the path (or
molecular mechanism) of the transformation
...
For example, the Δ G
for the oxidation of glucose to CO2 and H2O is the same whether it occurs by combustion in vitro or by a series of
enzyme-catalyzed steps in a cell
...
A negative Δ G indicates
that a reaction can occur spontaneously, but it does not signify whether it will proceed at a perceptible rate
...
3), the rate of a reaction depends on the free energy of activation (Δ G ), which is largely
unrelated to the Δ G of the reaction
...
2
...
The Standard Free-Energy Change of a Reaction Is Related to the Equilibrium
Constant
As for any reaction, we need to be able to determine Δ G for an enzymecatalyzed reaction in order to know whether the
reaction is spontaneous or an input of energy is required
...

Consider the reaction

The Δ G of this reaction is given by

in which Δ G° is the standard free-energy change, R is the gas constant, T is the absolute temperature, and [A], [B], [C],

and [D] are the molar concentrations (more precisely, the activities) of the reactants
...
0 M (for a gas, the standard state is usually chosen to be 1 atmosphere)
...


Units of energyA calorie (cal) is equivalent to the amount of heat required to raise
the temperature of 1 gram of water from 14
...
5°C
...

A joule (J) is the amount of energy needed to apply a 1-newton force
over a distance of 1 meter
...

1 kcal = 4
...
The standard state is
defined as having a pH of 7
...
The activity of water also is taken to be 1 in these equations
...
The kilocalorie (abbreviated kcal) and
the kilojoule (kJ) will be used as the units of energy
...
184 kilojoules
...
This
equation is important because it displays the energetic relation between products and reactants in terms of their
concentrations
...
Equation 1 then becomes

and so

The equilibrium constant under standard conditions, K eq, is defined as

Substituting equation 4 into equation 3 gives

which can be rearranged to give

Substituting R = 1
...
Thus, the
standard free energy and the equilibrium constant of a reaction are related by a simple expression
...
36 kcal mol-1 (-5
...
4)
...
36 kcal mol-1 (5
...

As an example, let us calculate Δ G° and Δ G for the isomerization of dihydroxyacetone phosphate (DHAP) to
glyceraldehyde 3-phosphate (GAP)
...
1
...
At equilibrium, the ratio of
GAP to DHAP is 0
...
Hence, K eq = 0
...
The standard free-energy change for this
reaction is then calculated from equation 6:

Under these conditions, the reaction is endergonic
...

Now let us calculate Δ G for this reaction when the initial concentration of DHAP is 2 × 10-4 M and the initial
concentration of GAP is 3 × 10-6 M
...
Note that Δ G for this reaction is
negative, although Δ G ° is positive
...
The criterion of spontaneity for a reaction is
Δ G, not Δ G °
...
This principle is the basis of the coupling of

reactions to form metabolic pathways (Chapter 14)
...
2
...
Enzymes Alter Only the Reaction Rate and Not the Reaction Equilibrium
Because enzymes are such superb catalysts, it is tempting to ascribe to them powers that they do not have
...
This
inability means that an enzyme accelerates the forward and reverse reactions by precisely the same factor
...
Suppose that, in the absence of enzyme, the forward rate constant (k F) is 10-4 s-1 and the
reverse rate constant (k R) is 10-6 s-1
...
However, it might take
considerable time to approach this equilibrium without enzyme, whereas equilibrium would be attained rapidly in the
presence of a suitable enzyme
...
The
equilibrium position is a function only of the free-energy difference between reactants and products
...
The Molecular Design of Life

8
...
2
...
4
...
82

28
...
46

22
...
09

17
...
73

11
...
36

5
...
36
-2
...
69
-11
...
09

-17
...
46

-22
...
82

-28
...
The Molecular Design of Life

8
...
3
...
How can we explain the rate enhancement in terms of
thermodynamics? To do so, we have to consider not the end points of the reaction but the chemical pathway between the
end points
...
The double dagger denotes a thermodynamic property of the transition state
...
The
difference in free energy between the transition state and the substrate is called the Gibbs free energy of activation or
simply the activation energy, symbolized by Δ G , as mentioned in Section 8
...
1 (Figure 8
...


Note that the energy of activation, or Δ G , does not enter into the final Δ G calculation for the reaction, because the
energy input required to reach the transition state is returned when the transition state forms the product
...

One approach to understanding how enzymes achieve this facilitation is to assume that the transition state (S ) and the
substrate (S) are in equilibrium
...

The rate of the reaction is proportional to the concentration of S :

because only S can be converted into product
...

Because the reaction rate is proportional to the concentration of S , and the concentration of S depends on Δ G , the
rate of reaction V depends on Δ G
...
The value of kT/h at 25°C is 6
...

Suppose that the free energy of activation is 6
...
53 kJ mol-1)
...
4)
...
2 × 107 s-1
...
36 kcal mol-1 (5
...
2 × 108 s-1
...
4
shows, a decrease of 1
...
A relatively small decrease in Δ G (20% in this
particular reaction) results in a much greater increase in V
...
The attraction of the enzyme molecule for
the activated complex would thus lead to a decrease in its energy and
hence to a decrease in the energy of activation of the reaction and to
an increase in the rate of reaction
...

The combination of substrate and enzyme creates a new reaction pathway whose transition-state energy is lower than
that of the reaction in the absence of enzyme (see Figure 8
...
The lower activation energy means that more molecules
have the required energy to reach the transition state
...
The essence of catalysis is specific binding of the
transition state
...
3
...
The Formation of an Enzyme-Substrate Complex Is the First Step in Enzymatic
Catalysis
Much of the catalytic power of enzymes comes from their bringing substrates together in favorable orientations to
promote the formation of the transition states in enzyme-substrate (ES) complexes
...
Most enzymes are highly selective in the substrates that they bind
...

What is the evidence for the existence of an enzyme-substrate complex?

1
...
4)
...
The fact that an enzyme-catalyzed reaction has a maximal velocity suggests the formation
of a discrete ES complex
...
Although indirect, this is the most general evidence for the existence of ES complexes
...
X-ray crystallography has provided high-resolution images of substrates and substrate analogs bound to the active

sites of many enzymes (Figure 8
...
In Chapter 9, we will take a close look at several of these complexes
...
A new technique, time-resolved crystallography, depends on cocrystallizing a photolabile
substrate analog with the enzyme
...

3
...
These

changes are particularly striking if the enzyme contains a colored prosthetic group
...
This enzyme catalyzes
the synthesis of l-tryptophan from l-serine and indole-derivative
...
6)
...
Thus, fluorescence spectroscopy
reveals the existence of an enzyme-serine complex and of an enzyme-serine-indole complex
...


8
...
2
...
It also contains the residues
that directly participate in the making and breaking of bonds
...
In essence,
the interaction of the enzyme and substrate at the active site promotes the formation of the transition state
...
Although enzymes differ widely in structure, specificity, and mode of catalysis, a
number of generalizations concerning their active sites can be stated:

1
...
In lysozyme, an enzyme that degrades the cell walls of some bacteria, the important groups in the active
site are contributed by residues numbered 35, 52, 62, 63, 101, and 108 in the sequence of the 129 amino acids (Figure
8
...

2
...
Most of the amino acid residues in an

enzyme are not in contact with the substrate, which raises the intriguing question of why enzymes are so big
...
The "extra" amino acids serve as a scaffold to create the three-dimensional active site from amino
acids that are far apart in the primary structure
...
In many proteins, the
remaining amino acids also constitute regulatory sites, sites of interaction with other proteins, or channels to bring the
substrates to the active sites
...
Active sites are clefts or crevices
...
Water is usually excluded unless it is a reactant
...
Nevertheless, the cleft may also contain polar residues
...
The internal positions of these polar residues are biologically crucial exceptions to the general rule
that polar residues are exposed to water
...
Substrates are bound to enzymes by multiple weak attractions
...
The noncovalent interactions in ES complexes are much weaker than covalent bonds, which have
energies between -50 and -110 kcal mol-1 (between -210 and -460 kJ mol-1)
...
3
...
Van der Waals forces become significant in binding only when numerous substrate atoms
simultaneously come close to many enzyme atoms
...
The directional character of hydrogen bonds between enzyme and substrate often enforces a high degree of
specificity, as seen in the RNA-degrading enzyme ribonuclease (Figure 8
...

5
...
Because the

enzyme and the substrate interact by means of short-range forces that require close contact, a substrate must have a
matching shape to fit into the site
...
9), expressed in 1890, has proved
to be highly stimulating and fruitful
...
Koshland, Jr
...
The
active sites of some enzymes assume a shape that is complementary to that of the transition state only after the substrate
is bound
...
10)
...
The Molecular Design of Life

8
...
3
...
3
...
Enzymes accelerate reactions by decreasing Δ G , the free
energy of activation
...
The Molecular Design of Life

8
...
3
...
4
...
An enzymecatalyzed reaction reaches a maximal velocity
...
The Molecular Design of Life

8
...
3
...
5
...
(Left) The enzyme cytochrome P-450 is illustrated bound to

its substrate camphor
...
Note
also the presence of a heme cofactor
...
The Molecular Design of Life

8
...
3
...
6
...

Fluorescence intensity of the pyridoxal phosphate group at the active site of tryptophan synthetase changes on addition
of serine and indole, the substrates
...
The Molecular Design of Life

8
...
3
...
7
...
(A) Ribbon diagram of the enzyme lysozyme with several
components of the active site shown in color
...


I
...
Enzymes: Basic Concepts and Kinetics

8
...
Enzymes Accelerate Reactions by Facilitating the Formation of the Transition State

Figure 8
...
Hydrogen Bonds between an Enzyme and Substrate
...
[After F
...
Richards, H
...
Wyckoff, and N
...
In The
Neurosciences: Second Study Program, F
...
Schmidt, Ed
...
970
...
The Molecular Design of Life

8
...
3
...
9
...
In this model, the active site of the unbound enzyme
is complementary in shape to the substrate
...
The Molecular Design of Life

8
...
3
...
10
...
In this model, the enzyme changes shape on substrate
binding
...


I
...
Enzymes: Basic Concepts and Kinetics

8
...
The Michaelis-Menten Model Accounts for the Kinetic Properties of Many
Enzymes
The primary function of enzymes is to enhance rates of reactions so that they are compatible with the needs of the
organism
...
For many enzymes, the
rate of catalysis V 0, which is defined as the number of moles of product formed per second, varies with the substrate
concentration [S] in a manner shown in Figure 8
...
The rate of catalysis rises linearly as substrate concentration
increases and then begins to level off and approach a maximum at higher substrate concentrations
...
Consider an enzyme that catalyzes the S to P
by the following pathway:

The extent of product formation is determined as a function of time for a series of substrate concentrations (Figure 8
...

As expected, in each case, the amount of product formed increases with time, although eventually a time is reached when
there is no net change in the concentration of S or P
...
Figure 8
...

Enzyme kinetics are more easily approached if we can ignore the back reaction
...
13B)
...
11, V 0 is determined for each substrate concentration by measuring the rate of product formation at early times
before P accumulates (see Figure 8
...

We begin our kinetic examination of enzyme activity with the graph shown in Figure 8
...
At a fixed concentration of
enzyme, V 0 is almost linearly proportional to [S] when [S] is small but is nearly independent of [S] when [S] is large
...
The
critical feature in their treatment is that a specific ES complex is a necessary intermediate in catalysis
...
The ES complex has two
possible fates
...
Again, we assume that almost none of the product reverts to the initial substrate, a condition that holds in
the initial stage of a reaction before the concentration of product is appreciable
...
Our starting point is that the catalytic rate is equal to the product of the concentration of the ES complex
and k 2
...
The rates of formation and breakdown of ES are given by:

To simplify matters, we will work under the steady-state assumption
...

This occurs when the rates of formation and breakdown of the ES complex are equal
...
K M is an important characteristic of enzyme-substrate interactions and is
independent of enzyme and substrate concentrations
...
The concentration of uncombined substrate [S] is very nearly equal to
the total substrate concentration, provided that the concentration of enzyme is much lower than that of substrate
...


Substituting this expression for [E] in equation 16 gives

Solving equation 18 for [ES] gives

or

By substituting this expression for [ES] into equation 10, we obtain

The maximal rate, V max, is attained when the catalytic sites on the enzyme are saturated with substrate
[ES] = [E]T
...
11
...
At high
substrate concentration, when [S] is much greater than K M, V 0 = V max; that is, the rate is maximal, independent of
substrate concentration
...
When [S] = K M, then V 0 = V max/2
...
K M is an important characteristic of an
enzyme-catalyzed reaction and is significant for its biological function
...
Such persons
exhibit facial flushing and rapid heart rate (tachycardia) after ingesting even small amounts of alcohol
...


Normally, the acetaldehyde, which is the cause of the symptoms when present at high concentrations, is processed to
acetate by acetaldehyde dehydrogenase
...
In susceptible persons, the mitochondrial enzyme is less active due to the substitution of a single amino acid, and
acetaldehyde is processed only by the cytosolic enzyme
...


8
...
1
...
Learn how the kinetic
parameters KMand Vmaxcan be determined experimentally using the enzyme
kinetics lab simulation in this media module
...
The
derivation of K M and V max is most commonly achieved with the use of curve-fitting programs on a computer (see the
appendix to this chapter for alternative means of determining K M and V max)
...
5)
...
The K M value for an enzyme depends on the
particular substrate and on environmental conditions such as pH, temperature, and ionic strength
...
First, K M is the concentration of substrate at which half the active sites are filled
...
In fact, for many
enzymes, experimental evidence suggests that K M provides an approximation of substrate concentration in vivo
...
In
equation 15, K M is defined as (k -1 + k 2)/k 1
...
Under such
circumstances, the ES complex dissociates to E and S much more rapidly than product is formed
...
When this
2

1

condition is met, K M is a measure of the strength of the ES complex: a high K M indicates weak binding; a low K M

indicates strong binding
...

The maximal rate, V max, reveals the turnover number of an enzyme, which is the number of substrate molecules
converted into product by an enzyme molecule in a unit time when the enzyme is fully saturated with substrate
...
The maximal rate, V max, reveals the turnover number of an enzyme
if the concentration of active sites [E]T is known, because

and thus

For example, a 10-6 M solution of carbonic anhydrase catalyzes the formation of 0
...
Hence, k 2 is 6 × 105 s-1
...
Each catalyzed
reaction takes place in a time equal to 1/k 2, which is 1
...
The turnover numbers of most
enzymes with their physiological substrates fall in the range from 1 to 104 per second (Table 8
...


8
...
2
...
4
...
However, most enzymes are not normally saturated with substrate
...
01 and 1
...
When [S] << K M, the enzymatic rate is much less than k
cat because most of the active sites are unoccupied
...
Under these conditions,
k cat/K M is the rate constant for the interaction of S and E and can be used as a measure of catalytic efficiency
...
Table 8
...
1
...
Chymotrypsin clearly has a preference
for cleaving next to bulky, hydrophobic side chains
...
Note that this ratio depends on k 1, k -1, and k cat, as can be shown by substituting for K M
...

The value of k cat/K M then approaches k 1
...
This rate cannot be faster than the diffusion-controlled encounter of an enzyme and its
substrate
...
Hence, the upper
limit on k cat/K M is between 108 and 109 s-1 M-1
...
Enzymes such as these that have k cat/K M ratios at the upper limits have attained kinetic
perfection
...
8)
...
Remember that the active site
is only a small part of the total enzyme structure
...
In these cases, there may be attractive electrostatic forces on the enzyme that entice
the substrate to the active site
...


Circe effectThe utilization of attractive forces to lure a substrate into a site in
which it undergoes a transformation of structure, as defined by
William P
...

A goddess of Greek mythology, Circe lured Odysseus's men to her
house and then transformed them into pigs
...
Indeed, some series of enzymes are associated into organized
assemblies (Section 17
...
9) so that the product of one enzyme is very rapidly found by the next enzyme
...


8
...
3
...
In oxidation-reduction reactions, electrons are transferred between substrates
...


Sequential Displacement
...
Consequently, in a
bisubstrate reaction, a ternary complex of the enzyme and both substrates forms
...

Many enzymes that have NAD+ or NADH as a substrate exhibit the sequential ordered mechanism
...
1
...
This enzyme reduces pyruvate to lactate
while oxidizing NADH to NAD+
...
This
sequence can be represented as follows in a notation developed by W
...

In the random sequential mechanism, the order of addition of substrates and release of products is random
...
1
...


Phosphocreatine is an important energy source in muscle
...


Although the order of certain events is random, the reaction still passes through the ternary complexes including, first,
substrates and, then, products
...


In double-displacement, or Ping-Pong, reactions, one or more products are released before all substrates bind the
enzyme
...
Reactions that shuttle amino groups between amino acids and α-keto acids
are classic examples of double-displacement mechanisms
...
3
...


The sequence of events can be portrayed as the following diagram
...
The first product, oxaloacetate, subsequently departs
...
In the
Cleland notation, the substrates appear to bounce on and off the enzyme analogously to a Ping-Pong ball bouncing on a
table
...
4
...
Allosteric Enzymes Do Not Obey Michaelis-Menten Kinetics
The Michaelis-Menten model has greatly assisted the development of enzyme chemistry
...
However, the Michaelis-Menten model cannot account for the kinetic properties of many enzymes
...
These
enzymes consist of multiple subunits and multiple active sites
...
14) of the reaction velocity V 0 versus substrate concentration
[S], rather than the hyperbolic plots predicted by the Michaelis-Menten equation (equation 23)
...
A
possible outcome of this interaction between subunits is that the binding of substrate becomes cooperative; that is, the
binding of substrate to one active site of the enzyme facilitates substrate binding to the other active sites
...
In addition, the activity of an
allosteric enzyme may be altered by regulatory molecules that are reversibly bound to specific sites other than the
catalytic sites
...
For this reason, allosteric enzymes are key regulators of metabolic pathways in the cell
...
The Molecular Design of Life

8
...
4
...
11
...
A plot of the reaction velocity (V 0) as a function of the substrate
concentration [S] for an enzyme that obeys Michaelis-Menten kinetics shows that the maximal velocity (V max) is
approached asymptotically
...

I
...
Enzymes: Basic Concepts and Kinetics

8
...
The Michaelis-Menten Model Accounts for the Kinetic Properties of Many Enzymes

Figure 8
...
Determining Initial Velocity
...
The initial velocity (V 0) for each substrate concentration is determined from the slope of
the curve at the beginning of a reaction, when the reverse reaction is insignificant
...
The Molecular Design of Life

8
...
4
...
13
...


Concentration changes under (A) steady-state conditions, and (B) the pre-steady-state conditions
...
The Molecular Design of Life

8
...
4
...
5
...
The Molecular Design of Life

8
...
4
300

8
...
The Michaelis-Menten Model Accounts for the Kinetic Properties of Many Enzymes

Table 8
...
Maximum turnover numbers of some enzymes

Enzyme
Carbonic anhydrase
3-Ketosteroid isomerase
Acetylcholinesterase
Penicillinase
Lactate dehydrogenase
Chymotrypsin
DNA polymerase I
Tryptophan synthetase
Lysozyme

Turnover number (per second)
600,000
280,000
25,000
2,000
1,000
100
15
2
0
...
The Molecular Design of Life

8
...
4
...
7
...
The Molecular Design of Life

8
...
4
...
8
...
6 × 108

Carbonic anhydrase

8
...
8 × 108

Fumarase

1
...
4 × 108

β-Lactamase
Superoxide dismutase

1 × 108
7 × 109

Source: After A
...
H
...
5
...
The Molecular Design of Life

8
...
4
...
14
...
Allosteric enzymes display a sigmoidal dependence of reaction
velocity on substrate concentration
...
The Molecular Design of Life

8
...
5
...
This means of
inhibiting enzyme activity serves as a major control mechanism in biological systems
...
In addition, many drugs and toxic agents act by inhibiting enzymes
...
The value of transition-state analogs as potent inhibitors will be discussed
shortly
...
An irreversible inhibitor dissociates very slowly from its
target enzyme because it has become tightly bound to the enzyme, either covalently or noncovalently
...
Penicillin acts by covalently modifying the enzyme transpeptidase, thereby preventing the
synthesis of bacterial cell walls and thus killing the bacteria (Section 8
...
5)
...

Reversible inhibition, in contrast with irreversible inhibition, is characterized by a rapid dissociation of the enzymeinhibitor complex
...
The competitive inhibitor resembles the substrate and binds to the active site of the enzyme (Figure 8
...

The substrate is thereby prevented from binding to the same active site
...
At any given inhibitor concentration,
competitive inhibition can be relieved by increasing the substrate concentration
...
Methotrexate is a structural analog of tetrahydrofolate, a coenzyme for the
enzyme dihydrofolate reductase, which plays a role in the biosynthesis of purines and pyrimidines (Figure 8
...
It binds
to dihydrofolate reductase 1000-fold more tightly than the natural substrate and inhibits nucleotide base synthesis
...

In noncompetitive inhibition, which also is reversible, the inhibitor and substrate can bind simultaneously to an enzyme
molecule at different binding sites (see Figure 8
...
A noncompetitive inhibitor acts by decreasing the turnover number
rather than by diminishing the proportion of enzyme molecules that are bound to substrate
...
A more complex
pattern, called mixed inhibition, is produced when a single inhibitor both hinders the binding of substrate and decreases
the turnover number of the enzyme
...
5
...
Competitive and Noncompetitive Inhibition Are Kinetically Distinguishable
How can we determine whether a reversible inhibitor acts by competitive or noncompetitive inhibition? Let us consider

only enzymes that exhibit Michaelis-Menten kinetics
...
In competitive inhibition, the inhibitor
competes with the substrate for the active site
...
17)
...
However, the apparent value of K M is altered; the effect of a competitive inhibitor is to
increase the apparent value of K M
...
As the
value of [I] increases, the value of K app M increases (see Figure 8
...
In the presence of a competitive inhibitor, an
enzyme will have the same V max as in the absence of an inhibitor
...
18), substrate can still bind to the enzyme-inhibitor complex
...
The value of V max is decreased to a new value
called V app max while the value of K M is unchanged
...
The remaining enzyme behaves like a more dilute
solution of enzyme; V max is lower, but K M is the same
...


8
...
2
...
The first step in obtaining the chemical
mechanism of an enzyme is to determine what functional groups are required for enzyme activity
...
5
...
Irreversible inhibitors that covalently bond to the enzyme provide an alternative and often complementary
means for elucidating functional groups at the enzyme active site because they modify the functional groups, which can
then be identified
...

Group-specific reagents react with specific R groups of amino acids
...
19) and iodoacetamide (Figure 8
...
DIPF modifies only 1 of the 28
serine residues in the proteolytic enzyme chymotrypsin, implying that this serine residue is especially reactive
...
DIPF also revealed a reactive serine
residue in acetylcholinesterase, an enzyme important in the transmission of nerve impulses (see Figure 8
...
Thus, DIPF
and similar compounds that bind and inactivate acetylcholinesterase are potent nerve gases
...
They are thus more specific for the enzyme active site than are group-specific reagents
...
21)
...
The compound 3-bromoacetol is an
affinity label for the enzyme triose phosphate isomerase (TIM)
...
22)
...
The inhibitor binds to the enzyme as a substrate and is initially processed by the normal catalytic
mechanism
...
The fact that the enzyme participates in its own irreversible inhibition strongly suggests
that the covalently modified group on the enzyme is catalytically vital
...
A flavin prosthetic group of monoamine oxidase (MAO) oxidizes the N,Ndimethylpropargylamine, which in turn inactivates the enzyme by covalently modifying the flavin prosthetic group by
alkylating N-5 (Figure 8
...
Monoamine oxidase deaminates neurotransmitters such as dopamine and serotonin,
lowering their levels in the brain
...
The drug (-)deprenyl, which is used to treat Parkinson disease and depression, is
a suicide inhibitor of monoamine oxidase
...
5
...
Transition-State Analogs Are Potent Inhibitors of Enzymes
We turn now to compounds that provide the most intimate views of the catalytic process itself
...
These mimics are called transition-state analogs
...

The racemization of proline proceeds through a transition state in which the tetrahedral α- carbon atom has become
trigonal by loss of a proton (Figure 8
...
In the trigonal form, all three bonds are in the same plane; C also carries a
α

net negative charge
...
This picture is supported by the finding that the inhibitor pyrrole 2-carboxylate binds to the
racemase 160 times as tightly as does proline
...
An analog that also carries a negative charge on C would be expected to bind even more tightly
...
The inhibitory power of transition-state analogs underscores the essence of
catalysis: selective binding of the transition state
...
5
...
Catalytic Antibodies Demonstrate the Importance of Selective Binding of the
Transition State to Enzymatic Activity
Antibodies that recognize transition states should function as catalysts, if our understanding of the importance of the
transition state to catalysis is correct
...
Ferrochelatase, the final enzyme in the biosynthetic pathway for
the production of heme, catalyzes the insertion of Fe2+ into protoporphyrin IX
...
The recently determined crystal structure of the ferrochelatase bound to a substrate analog confirms that
the enzyme does indeed bend one of the pyrole rings, distorting it 36 degrees to insert the iron
...
The solution came from the results of studies showing that an alkylated porphyrin,
N-methylprotoporphyrin, is a potent inhibitor of ferrochelatase
...
Moreover, it was known that N-alkylporphyrins chelate metal ions 104 times
as fast as their unalkylated counterparts do
...

An antibody catalyst was produced with the use of an N-alkylporphyrin as the immunogen
...
25) to facilitate the entry of a metal
...
Catalytic antibodies (abzymes) can indeed be produced by using transition-state analogs as
antigens
...
The results of studies with transition-state analogs
provide strong evidence that enzymes can function complementary in structure to the transition state
...


8
...
5
...
26A)
...
26B)
...
Indeed, this instability is closely tied to the antibiotic action of penicillin, as will be evident shortly
...
The organisms obtained in this way, called
protoplasts, are devoid of a cell wall and consequently lyse when transferred to a normal medium
...
The cell-wall macromolecule, called a peptidoglycan,
consists of linear polysaccharide chains that are cross-linked by short peptides (Figure 8
...
The enormous bag-shaped
peptidoglycan confers mechanical support and prevents bacteria from bursting in response to their high internal osmotic
pressure
...
In the formation of the cell wall of
Staphylococcus aureus, the amino group at one end of a pentaglycine chain attacks the peptide bond between two dalanine residues in another peptide unit (Figure 8
...
A peptide bond is formed between glycine and one of the d-alanine
residues; the other d-alanine residue is released
...

Bacterial cell walls are unique in containing d amino acids, which form cross-links by a mechanism different from that
used to synthesize proteins
...
The transpeptidase normally forms an
acyl intermediate with the penultimate d-alanine residue of the d-Ala-d-Ala peptide (Figure 8
...
This covalent acylenzyme intermediate then reacts with the amino group of the terminal glycine in another peptide to form the cross-link
...
30)
...
This penicilloyl-enzyme does not react further
...

Why is penicillin such an effective inhibitor of the transpeptidase? The highly strained, four-membered β-lactam ring of
penicillin makes it especially reactive
...
31)
...


I
...
Enzymes: Basic Concepts and Kinetics

8
...
Enzymes Can Be Inhibited by Specific Molecules

Figure 8
...
Distinction between a Competitive and a Noncompetitive Inhibitor
...

I
...
Enzymes: Basic Concepts and Kinetics

8
...
Enzymes Can Be Inhibited by Specific Molecules

Figure 8
...
Enzyme Inhibitors
...
Regions with
structural differences are shown in red
...
The Molecular Design of Life

8
...
5
...
17
...
As the concentration of a competitive inhibitor increases, higher
concentrations of substrate are required to attain a particular reaction velocity
...

I
...
Enzymes: Basic Concepts and Kinetics

8
...
Enzymes Can Be Inhibited by Specific Molecules

Figure 8
...
Kinetics of a Noncompetitive Inhibitor
...
Consequently, V max cannot be attained, even at high substrate concentrations
...
The Molecular Design of Life

8
...
5
...
19
...
DIPF can
inhibit an enzyme by covalently modifying a crucial serine residue (Section 9
...
1)
...
The Molecular Design of Life

8
...
5
...
20
...
Iodoacetamide can inactivate an
enzyme by reacting with a critical cysteine residue
...
The Molecular Design of Life

8
...
5
...
21
...
(A) Tosyl-l-phenylalanine chloromethyl ketone (TPCK) is a reactive analog of the
normal substrate for the enzyme chymotrypsin
...

I
...
Enzymes: Basic Concepts and Kinetics

8
...
Enzymes Can Be Inhibited by Specific Molecules

Figure 8
...
Bromoacetol Phosphate, an Affinity Label for Triose Phosphate Isomerase (TIM)
...

I
...
Enzymes: Basic Concepts and Kinetics

8
...
Enzymes Can Be Inhibited by Specific Molecules

Figure 8
...
Mechanism-Based (Suicide) Inhibition
...
N,N-Dimethylpropargylamine inhibits monoamine
oxidase by covalently modifying the flavin prosthetic group only after the inhibitor is first oxidized
...

I
...
Enzymes: Basic Concepts and Kinetics

8
...
Enzymes Can Be Inhibited by Specific Molecules

Figure 8
...
Inhibition by Transition State Analogs
...
(B) Pyrrole 2-carboxylate, a transition state analog because of its trigonal geometry, is a potent inhibitor of
proline racemase
...
The Molecular Design of Life

8
...
5
...
25
...
The insertion of a metal ion into a
porphyrin by ferrochelatase proceeds through a transition state in which the porphyrin is bent
...

I
...
Enzymes: Basic Concepts and Kinetics

8
...
Enzymes Can Be Inhibited by Specific Molecules

Figure 8
...
Structure of Penicillin
...
(A)
Structural formula of penicillin
...

I
...
Enzymes: Basic Concepts and Kinetics

8
...
Enzymes Can Be Inhibited by Specific Molecules

Figure 8
...
Schematic Representation of the Peptidoglycan in Staphylococcus aureus
...
The cell wall is a single, enormous, bag-shaped
macromolecule because of extensive cross-linking
...
The Molecular Design of Life

8
...
5
...
28
...
aureus Peptidoglycan
...

I
...
Enzymes: Basic Concepts and Kinetics

8
...
Enzymes Can Be Inhibited by Specific Molecules

Figure 8
...
Transpeptidation Reaction
...

I
...
Enzymes: Basic Concepts and Kinetics

8
...
Enzymes Can Be Inhibited by Specific Molecules

Figure 8
...
Conformations of Penicillin and a Normal Substrate
...
[After B
...
J
...
Biol
...
]

I
...
Enzymes: Basic Concepts and Kinetics

8
...
Enzymes Can Be Inhibited by Specific Molecules

Figure 8
...
Formation of a Penicilloyl-Enzyme Complex
...

I
...
Enzymes: Basic Concepts and Kinetics

8
...
Vitamins Are Often Precursors to Coenzymes
Earlier (Section 8
...
1), we considered the fact that many enzymes re- quire cofactors to be catalytically active
...
Vitamins themselves are organic molecules that are needed in small amounts in the diets of some higher
animals
...
For instance, whereas E
...
The biosynthetic pathways for vitamins can be complex; thus, it is
biologically more efficient to ingest vitamins than to synthesize the enzymes required to construct them from simple
molecules
...
Indeed,
vitamin deficiency can generate diseases in all organisms requiring these molecules (Tables 8
...
10)
...


8
...
1
...
9 lists the water-soluble vitamins ascorbic acid (vitamin C) and a series known as the vitamin B
complex (Figure 8
...
Ascorbate, the ionized form of ascorbic acid, serves as a reducing agent (an antioxidant),
as will be discussed shortly
...
Note that, in all cases except
vitamin C, the vitamin must be modified before it can serve its function
...
9)
...
For this reason and because vitamins are
required in relatively small amounts, pathological conditions resulting from vitamin deficiencies are often difficult to
diagnose
...
This water-soluble vitamin is not used
as a coenzyme but is still required for the continued activity of proyl hydroxylase
...
How is this unusual amino acid formed and what is its role? The results of radioactive-labeling studies
showed that proline residues on the amino side of glycine residues in nascent collagen chains become hydroxylated
...
The other oxygen atom of O2 is
taken up by α -ketoglutarate, which is converted into succinate (Figure 8
...
This complex reaction is catalyzed by
prolyl hydroxylase, a dioxygenase
...

The enzyme also converts α-ketoglutarate into succinate without hydroxylating proline
...
How is the active enzyme regenerated? Ascorbate
(vitamin C) comes to the rescue by reducing the ferric ion of the inactivated enzyme
...
34)
...

Primates are unable to synthesize ascorbic acid and hence must acquire it from their diets
...
Jacques Cartier in 1536 gave a vivid description of this dietary deficiency disease,
which afflicted his men as they were exploring the Saint Lawrence River:
Some did lose all their strength, and could not stand on their feet
...
Their mouths
became stinking, their gums so rotten, that all the flesh did fall off, even to the roots of the teeth, which did also almost
all fall out
...
Lind described a controlled study establishing that scurvy could be prevented by including
citrus fruits in the diet
...
" Lind's research was inspired by the plight of an expedition commanded by
Commodore George Anson
...
The remainder had died of
scurvy
...
Studies of the thermal stability of synthetic polypeptides have been
especially informative
...
The
abnormal fibers formed by insufficiently hydroxylated collagen contribute to the skin lesions and blood-vessel fragility
seen in scurvy
...
6
...
Fat-Soluble Vitamins Participate in Diverse Processes Such as Blood Clotting and
Vision
Not all vitamins function as coenzymes
...
35, Table 8
...
Vitamin K, which is required for normal blood
clotting (K from the German koagulation), participates in the carboxylation of glutamate residues to γ-carboxyglutamate,
which makes modified glutamic acid a much stronger chelator of Ca2+ (Section 10
...
7)
...
3
...
A deficiency of
this vitamin leads to night blindness
...
Retinoic acid, which
contains a terminal carboxylate in place of the alcohol terminus of retinol, serves as a signal molecule and activates the
transcription of specific genes that mediate growth and development (Section 31
...
A metabolite of vitamin D is a
hormone that regulates the metabolism of calcium and phosphorus
...
Infertility in rats is a consequence of vitamin E (α-tocopherol) deficiency
...


I
...
Enzymes: Basic Concepts and Kinetics

8
...
Vitamins Are Often Precursors to Coenzymes

Table 8
...
Water-Soluble Vitamins

Vitamin

Coenzyme

Typical reaction type

Consequences of deficiency

Thiamine (B1)

Thiamine pyrophosphate

Aldehyde transfer

Riboflavin (B2)

Flavin adenine dinucleotide
(FAD)

Oxidation-reduction

Pyridoxine (B6)

Pyridoxal phosphate

Group transfer to or from
amino acids
Oxidation-reduction

Beriberi (weight loss, heart
problems, neurological
dysfunction)
Cheliosis and angular
stomatitus (lesions of the
mouth), dermatitis
Depression, confusion,
convulsions
Pellagra (dermatitis,
depression, diarrhea)

Nicotinic acid (niacin) Nicotinamide adenine
dinucleotide (NAD+)
Pantothenic acid
Coenzyme A
Biotin
Biotin-lysine complexes
(biocytin)
Folic acid
Tetrahydrofolate

5 -Deoxyadenosyl cobalamin

B12
C (ascorbic acid)

I
...
Enzymes: Basic Concepts and Kinetics

Acyl-group transfer
ATP-dependent carboxylation
and carboxyl-group transfer
Transfer of one-carbon
components; thymine
synthesis
Transfer of methyl groups;
intramolecular rearrangements
Antioxidant

Hypertension
Rash about the eyebrows,
muscle pain, fatigue (rare)
Anemia, neural-tube defects in
development
Anemia, pernicious anemia,
methylmalonic acidosis
Scurvy (swollen and bleeding
gums, subdermal hemorrhages)

8
...
Vitamins Are Often Precursors to Coenzymes

Table 8
...
Fat-soluble vitamins

Vitamin Function
A
D
E
K

Roles in vision, growth, reproduction

Deficiency

Night blindness, cornea damage, damage to respiratory and
gastrointestinal tract
Regulation of calcium and phosphate metabolism Rickets (children): skeletal deformaties, impaired growth
Osteomalacia (adults): soft, bending bones
Antioxidant
Inhibition of sperm production; lesions in muscles and
nerves (rare)
Blood coagulation
Subdermal hemorrhaging

I
...
Enzymes: Basic Concepts and Kinetics

8
...
Vitamins Are Often Precursors to Coenzymes

Figure 8
...
Structures of Some Water-Soluble Vitamins
...
The Molecular Design of Life

8
...
6
...
33
...
Proline is hydroxylated at C-4 by the action of prolyl hydroxylase, an
enzyme that activates molecular oxygen
...
The Molecular Design of Life

8
...
6
...
34
...
Ascorbate is the ionized form of vitamin C, and dehydroascorbic
acid is the oxidized form of ascorbate
...
The Molecular Design of Life

8
...
6
...
35
...


I
...
Enzymes: Basic Concepts and Kinetics

Summary
Enzymes are Powerful and Highly Specific Catalysts
The catalysts in biological systems are enzymes, and nearly all enzymes are proteins
...
They can enhance reaction rates by factors of 106 or more
...
Such cofactors can be metal ions or small, vitamin-derived organic molecules called coenzymes
...
A reaction can occur spontaneously only if the change in free energy (Δ G) is
negative
...
Biochemists usually use Δ G° , the standard free-energy change at pH 7
...


Enzymes Accelerate Reactions by Facilitating the Formation of the Transition State
Enzymes serve as catalysts by decreasing the free energy of activation of chemical reactions
...

The first step in catalysis is the formation of an enzyme-substrate complex
...
The specificity of enzyme-substrate
interactions arises mainly from hydrogen bonding, which is directional, and the shape of the active site, which rejects
molecules that do not have a sufficiently complementary shape
...


The Michaelis-Menten Model Accounts for the Kinetic Properties of Many Enzymes
The Michaelis-Menten model accounts for the kinetic properties of some enzymes
...


The rate V 0 of formation of product is given by the Michaelis-Menten equation:

in which V max is the reaction rate when the enzyme is fully saturated with substrate and K M, the Michaelis constant, is
the substrate concentration at which the reaction rate is half maximal
...
The kinetic constant k cat, called the turnover number, is the number of
substrate molecules converted into product per unit time at a single catalytic site when the enzyme is fully saturated with
substrate
...
The ratio of k cat/K M provides a

penetrating probe into enzyme efficiency
...
These enzymes,
which do not conform to Michaelis-Menton kinetics, have multiple active sites
...


Enzymes Can Be Inhibited by Specific Molecules
Specific small molecules or ions can inhibit even nonallosteric enzymes
...
Covalent
inhibitors provide a means of mapping the enzyme's active site
...
A competitive inhibitor prevents the substrate from binding to the
active site
...
In noncompetitive inhibition, the inhibitor decreases the turnover number
...

The essence of catalysis is selective stabilization of the transition state
...
Transition-state analogs are stable compounds that mimic key features of this highest-energy
species
...
Proof that transition-state stabilization is a key aspect of
enzyme activity comes from the generation of catalytic antibodies
...


Vitamins Are Often Precursors to Coenzymes
Vitamins are small biomolecules that are needed in small amounts in the diets of higher animals
...
Ascorbate is
required for the hydroxylation of proline residues in collagen, a key protein of connective tissue
...


Key Terms
enzyme
substrate
cofactor
apoenzyme
holoenzyme
coenzyme
prosthetic group
free energy
transition state

free energy of activation
active site
induced fit
K M (the Michaelis constant)
V max
Michaelis-Menten equation
turnover number
k cat/K M
sequential displacement reaction
double-displacement (Ping-Pong) reaction
allosteric enzyme
competitive inhibition
noncompetitive inhibition
group-specific reagent
affinity label
mechanism-based (suicide) inhibition
transition-state analog
catalytic antibody (abzyme)
vitamin

I
...
Enzymes: Basic Concepts and Kinetics

Appendix: V max and K M Can Be Determined by Double-Reciprocal Plots
Before the availability of computers, the determination of K M and V max values required algebraic manipulation of the
basic Michaelis-Menten equation
...
11), it is impossible to
obtain a definitive value from a typical Michaelis-Menten plot
...
However, V max can be accurately determined if the
Michaelis-Menten equation is transformed into one that gives a straight-line plot
...
36)
...

Double-reciprocal plots are especially useful for distinguishing between competitive and noncompetitive inhibitors
...
37)
...
At a sufficiently high concentration, virtually all the active sites are filled by
substrate, and the enzyme is fully operative
...
In the presence of a competitive inhibitor, equation 31 is replaced by

in which [I] is the concentration of inhibitor and K i is the dissociation constant of the enzyme-inhibitor complex
...

Consider an enzyme with a K M of 10-4 M
...
In the presence
of 2 × 10-3 M competitive inhibitor that is bound to the enzyme with a K i of 10-3 M, the apparent K M (K app M ) will be
equal to K M × (1 + [I]/K i), or 3 × 10-4 M
...
The presence of the competitive inhibitor thus cuts the reaction rate in half at this substrate concentration
...
38), the inhibitor can combine with either the enzyme or the enzyme-substrate
complex
...
5
...
The value of V max is decreased to a new value
called V app max, and so the intercept on the vertical axis is increased
...
In contrast with V max, K M is not affected by pure noncompetitive inhibition
...
The Molecular Design of Life

8
...
36
...
A double-reciprocal plot of enzyme kinetics is generated
by plotting 1/V 0 as a function 1/[S]
...

I
...
Enzymes: Basic Concepts and Kinetics

Appendix: V max and K M Can Be Determined by Double-Reciprocal Plots

Figure 8
...
Competitive Inhibition Illustrated on a Double-Reciprocal Plot
...

I
...
Enzymes: Basic Concepts and Kinetics

Appendix: V max and K M Can Be Determined by Double-Reciprocal Plots

Figure 8
...
Noncompetitive Inhibition Illustrated on a Double-Reciprocal Plot
...


I
...
Enzymes: Basic Concepts and Kinetics

Problems
1
...
The hydrolysis of pyrophosphate to orthophosphate is important in driving forward

biosynthetic reactions such as the synthesis of DNA
...
For this enzyme, a unit of activity is
defined as the amount of enzyme that hydrolyzes 10 μmol of pyrophosphate in 15 minutes at 37°C under standard
assay conditions
...

(a) How many moles of substrate are hydrolyzed per second per milligram of enzyme when the substrate
concentration is much greater than K M?
(b) How many moles of active site are there in 1 mg of enzyme? Assume that each subunit has one active site
...

See answer
2
...
Penicillin is hydrolyzed and thereby rendered inactive by penicillinase (also known as

β-lactamase), an enzyme present in some resistant bacteria
...
6 kd
...
Assume that the concentration of
penicillin does not change appreciably during the assay
...
Does penicillinase appear to obey Michaelis-Menten
kinetics? If so, what is the value of K M?
(b) What is the value of V max?
(c) What is the turnover number of penicillinase under these experimental conditions? Assume one active site per
enzyme molecule
...
Counterpoint
...
Compare penicillinase with glycopeptide

transpeptidase
...
Mode of inhibition
...


(a) What are the values of V max and K M in the absence of inhibitor? In its presence?
(b) What type of inhibition is it?
(c) What is the binding constant of this inhibitor?
(d) If [S] = 10 μM and [I] = 2 mM, what fraction of the enzyme molecules have a bound substrate? A bound
inhibitor?
(e) If [S] = 30 μM, what fraction of the enzyme molecules have a bound substrate in the presence and in the absence
of 2 mM inhibitor? Compare this ratio with the ratio of the reaction velocities under the same conditions
...
A different mode
...
The concentration of this inhibitor is 100 μM
...

(b) What type of inhibition is it?
(c) What is the dissociation constant of this inhibitor?

(d) If [S] = 30 μM, what fraction of the enzyme molecules have a bound substrate in the presence and in the absence
of 100 μM inhibitor?

See answer
6
...
The plot of 1/V 0 versus 1/[S] is sometimes called a Lineweaver-Burk plot
...

(a) Rearrange the Michaelis-Menten equation to give V 0 as a function of V 0/[S]
...

See answer
7
...
The hormone progesterone contains two ketone groups
...
Competing substrates
...
Derive an expression relating

the ratio of the rates of utilization of A and B, V A/V B, to the concentrations of these substrates and their values of k
2 and K M
...
) Is specificity
determined by K M alone?
See answer
9
...
Suppose that a mutant enzyme binds a substrate 100-fold as tightly as does the native enzyme
...
Uncompetitive inhibition
...


(a) Draw a standard Michaelis-Menton curve in the absence and in the presence of increasing amounts of inhibitor
...

(b) Explain the results obtained in part a
...
More Michaelis-Menten
...
Varying the enzyme
...
Which of the following three families of curve would you expect to be
obtained? Explain
...
Too much of a good thing
...
The expected value of V max is shown on the y-axis
...

(b) Provide an explanation for the kinetic results
...
Rate-limiting step
...
If all of the substrates and products are present at a
concentration of 10-4 M, which step will be rate limiting and why?

See answer

Chapter Integration Problems

15
...
The effect of pH on the activity of an enzyme was examined
...
The
ionizable group has a pK a of 6
...
The substrate is positively charged throughout the pH range of the experiment
...

(b) Draw the V 0-versus-pH curve when the substrate concentration is much less than the enzyme K M
...
A question of stability
...
The

enzyme was purified from cells grown in PLP-deficient media as well as from cells grown in media that contained
pyridoxal phosphate
...
The following results were obtained
...


Not all data points are created equal
...
You argue for doing the
experiments at [S] = 1, 4, 16, and 100 μM
...
Who had the better idea, and why?

I
...
Enzymes: Basic Concepts and Kinetics

Selected Readings
Where to start
D
...
Koshland Jr
...
Evolution of catalytic function Cold Spring Harbor Symp
...
Biol
...
(PubMed)
W
...
Jencks
...
Economics of enzyme catalysis Cold Spring Harbor Symp
...
Biol
...
(PubMed)
R
...
Lerner and A
...
1988
...
Am
...
(PubMed)

Books
Fersht, A
...
Structure and Mechanism in Protein Science: A Guide to Enzyme Catalysis and Protein Folding
...
H
...

Walsh, C
...
Enzymatic Reaction Mechanisms
...
H
...

Page, M
...
, and Williams, A
...
), 1987
...
Royal Society of Chemistry
...
L
...
J
...
, 1984
...
WileyInterscience
...
N
...
I
...
), 1992
...
Academic Press
...
D
...
), 1970
...
Academic Press
...
(ed
...
Benchmark Papers in Biochemistry
...
1, Enzymes
...


Transition-state stabilization, analogs, and other enzyme inhibitors
V
...
Schramm
...
Enzymatic transition states and transition state analog design Annu
...
Biochem
...

(PubMed)
L
...
1948
...

G
...
Leinhard
...
Enzymatic catalysis and transition-state theory Science 180: 149-154
...
Kraut
...
How do enzymes work? Science 242: 533-540
...
J
...
L
...
1983
...
Rev
...
52: 825-869
...
P
...
1981
...
Am
...
(PubMed)
C
...
Walsh
...
Suicide substrates, mechanism-based enzyme inactivators: Recent developments Annu
...
Biochem
...
(PubMed)

Catalytic antibodies
D
...
2000
...
Rev
...
69: 751-794
...
Wade and T
...
Scanlan
...
The structural and functional basis of antibody catalysis Annu
...
Biophys
...

Struct
...
(PubMed)
R
...
Lerner, S
...
Benkovic, and P
...
Schultz
...
At the crossroads of chemistry and immunology: Catalytic

antibodies Science 252: 659-667
...
G
...
G
...
1990
...
(PubMed)

Enzyme kinetics and mechanisms
X
...
Xie and H
...
Lu
...
Single-molecule enzymology J
...
Chem
...
(PubMed)
E
...
Miles, S
...
R
...
1999
...
Biol
...
274: 1219312196
...
Warshel
...
Electrostatic origin of the catalytic power of en-zymes and the role of preorganized active sites J
...
Chem
...
(PubMed)
W
...
Cannon and S
...
Benkovic
...
Solvation, reorganization energy, and biological catalysis J
...
Chem
...
(PubMed)
W
...
Cleland, P
...
Frey, and J
...
Gerlt
...
The low barrier hydrogen bond in enzymatic catalysis J
...
Chem
...
(PubMed)
F
...
Romesberg, B
...
Santarsiero, B
...
Yin, D
...
G
...
C
...
1998
...
(PubMed)
H
...
Lu, L
...
S
...
1998
...
(PubMed)
A
...
Fersht, R
...
Leatherbarrow, and T
...
C
...
1986
...
Sci
...

W
...
Jencks
...
Binding energy, specificity, and enzymic catalysis: The Circe effect Adv
...
43: 219-410
...
R
...
J
...
1976
...
(PubMed)
I
...
Catalytic Strategies
What are the sources of the catalytic power and specificity of enzymes? This chapter presents the catalytic strategies
used by four classes of enzymes: the serine proteases, carbonic anhydrases, restriction endonucleases, and nucleoside
monophosphate (NMP) kinases
...
For the serine proteases, exemplified by chymotrypsin, the challenge is to promote a reaction that is almost
immeasurably slow at neutral pH in the absence of a catalyst
...
For restriction endonucleases
such as EcoRV, the challenge is to attain a very high level of specificity
...
The actions of these enzymes illustrate many
important principles of catalysis
...
These mechanisms include the use of binding energy and induced fit as well as several specific
catalytic strategies
...
Structural and mechanistic comparisons of enzyme action are thus sources of insight into the evolutionary
history of enzymes
...
In addition, our knowledge of catalytic strategies has been used to develop practical
applications, including drugs that are potent and specific enzyme inhibitors
...
4) explicitly in this chapter, the principles apply to these catalysts in addition to
protein catalysts

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