Download Enzymes II: Regulation

CHAPTER
7
Enzymes II: Regulation
The metabolic rate of key substances, which can proceed
in multiple pathways, is regulated and integrated. A close
interrelationship exists among products formed by different metabolic pathways from a common metabolite. For
example, glucose can be consumed either by oxidation
to CO2 or by conversion to glycogen, lipid, nonessential
amino acids, or other sugar molecules. The glucose supply
of the body can be derived either from the diet or from the
breakdown of glycogen, a polymer of glucose (primarily
from the liver and the kidney), or it can be synthesized
from some amino acids or lactate (predominantly in the
liver). These processes of glucose utilization and synthesis are under tight regulation. In fact, the plasma glucose
level is maintained at the level at which tissues (e.g., brain,
erythrocytes, kidney medulla, and the lens and cornea of
the eye) that require glucose as a primary substrate are
not deprived of this essential fuel. Each of these metabolic
pathways is mediated by enzymes that are unique for a
given pathway and that are under control. Metabolic pathways do not usually compete with each other for utilization
of a substrate, and they operate only to serve a particular
physiological need or function.
7.1 Types of Regulation
A metabolic pathway involves many enzymes functioning
in a sequential manner or in some unique arrangement to
carry out a particular metabolic process. Control of a pathway is accomplished through modulation of the activity of
only one or a few key enzymes. These regulatory enzymes
usually catalyze the first or an early reaction in a metabolic
sequence. A regulatory enzyme catalyzes a rate-limiting
(or rate-determining) chemical reaction that controls the
overall pathway. It may also catalyze a chemical reaction unique to that pathway, which is known as a committed step. In the metabolic pathway for the formation of
E from A,
A -~ B -~-~ C -~ D -~ E
the conversion of A to B, catalyzed by the enzyme El, is
the rate-limiting step and also a committed step. The ratelimiting step need not be the same as the committed step.
In the branched metabolic pathway,
E1
A
E2
~B
E3
E4
~ C ------* D
E6
L
*E
E7
*M
~-N
if the conversion of A to B is the rate-limiting step, the
committed step in the pathway for the formation of N is
the conversion of B to L (B --+ L), catalyzed by the enzyme E5. Those enzymes which catalyze the rate-limiting
step or the committed step of a pathway are under regulation. When the end product exceeds the steady-state
level concentration, it inhibits the regulatory enzyme in an
109
110
attempt to normalize the overall process. This type of control, known as feedback inhibition (see below), ensures
a high degree of efficiency in the utilization of materials
and of energy in living systems.
Regulation may be achieved in other ways. The absolute
amount of a regulatory enzyme may be altered through
mechanisms that control gene expression (Chapter 26).
This regulation at the genetic level occurs during various
phases of reproduction, growth, and development, with
different metabolic pathways being turned on or off in
accordance with the special requirements of each phase.
In eukaryotic cells, regulation at the genetic level is relatively a long-term process. Several short-term regulatory mechanisms control metabolic activity rapidly (see
below). Both substrates and some hormones play significant roles in regulating the concentration of key enzymes
at this level. Many drugs or other chemicals can increase
levels of enzymes that affect their own metabolism. Thus,
phenobarbital and polycyclic hydrocarbons increase the
levels of microsomal enzyme systems involved in their
metabolism.
Regulation of metabolic processes can be accomplished
by other methods. One is the use of a multienzyme complex (e.g., pyruvate dehydrogenase complex or fatty acid
synthase complex) in which various enzymes are organized such that the product of one becomes the substrate
for an adjacent enzyme. A single polypeptide chain may
contain multiple catalytic centers that carry out a sequence
of transformations (e.g., the mammalian fatty acid synthase; see Chapter 18). Such multifunctional polypeptides
increase catalytic efficiency by abolishing the accumulation of free intermediates and by maintaining a stoichiometry of 1:1 between catalytic centers.
Another type of regulation is accomplished by a series
of proenzymes in which activation of the initial proenzyme by a biological signal activates the second proenzyme which, in turn, activates the third, and so on. Such
an enzyme cascade process provides great amplification
in terms of the amount of final product formed. Examples are blood coagulation, the dissolution of blood clots,
complement activation, and glycogen breakdown.
Regulation is also accomplished by compartmentalization of enzyme systems involved in anabolic and catabolic
pathways into different cell organelles. For example,
fatty acid synthesis occurs in the soluble fraction of the
cytoplasm, whereas fatty acid oxidation takes place in mitochondria. Heme synthesis begins and is completed in
mitochondria, but some of the intermediate reactions take
place in the cytosol. Heme catabolism is initiated in the
smooth endoplasmic reticulum. Transport of key metabolites across an organelle membrane system is also a form
of regulation.
CHAPTER7 Enzymes I1: Regulation
Many enzymes occur in several molecular forms called
isoenzymes (or isozymes), and those which are genetically
determined may be called primary isoenzymes. The different primary isoenzymes catalyze the same chemical reaction but may differ in their primary structure and kinetic
properties. The tissue distribution of isoenzymes imparts
distinctive properties and specific patterns of metabolism
to organs of the body. The presence of isoenzymes may reveal differences not only between organs but also between
cells that make up an organ or between organelles of a cell.
During different stages of differentiation and development
from embryonic life to adulthood, the isoenzyme distribution in an organ undergoes characteristic changes. When
an adult organ reverts to the embryonic or fetal state (e.g.,
in cancer), the isoenzyme distributions change to those
characteristic of that developmental state. The existence
of isoenzymes in human tissues has important implications
in the study of human disease.
Zymogen (e.g., trypsinogen and chymotrypsinogen)
synthesis, secretion, transport, and activation and the rate
of inactivation of the active enzyme by inhibitors may all
be considered means of enzyme regulation.
Enzyme activity can be regulated by covalent modification or by noncovalent (allosteric) modification. A few
enzymes can undergo both forms of modification (e.g.,
glycogen phosphorylase and glutamine synthetase). Some
covalent chemical modifications are phosphorylation and
dephosphorylation, acetylation and deacetylation, adenylylation and deadenylylation, uridylylation and deuridylylation, and methylation and demethylation. In mammalian
systems, phosphorylation and dephosphorylation are most
commonly used as means of metabolic control. Phosphorylation is catalyzed by protein kinases and occurs at
specific seryl (or threonyl) residues and occasionally at
tyrosyl residues; these amino acid residues are not usually
part of the catalytic site of the enzyme. Dephosphorylation
is accomplished by phosphoprotein phosphatases:
ATP
ADP
O
Mg2+
Enzyme-Ser-OH
~,.
f Phosphoprotein-"~
phosphatase
O
H20
II
Enzyme-Ser-O--P--O-
I
O-
II
HO--P--O-
I
O-
The overall process of phosphorylation and dephosphorylation is a cascade of reactions and consists of an extracellular signal, commonly referred to asfirst messenger (e.g.,
hormones, such as glucag0n); a specific receptor on the cell
membrane of the target cell; a transducer coupled to the
SECTION 7.2
AIIostericEnzymeRegulation
receptor that produces an intracellular signal (i.e., a second messenger); one or more modifying enzymes whose
activity is affected by the intracellular signal; a target enzyme, which is the substrate for the modifying enzyme
and subjected to covalent modification with consequent
metabolic alteration; and an enzyme that reverses the modification of the target enzyme. The transducer of the system is adenylate cyclase, and it catalyzes the cyclization
of ATP to cyclic AMP (cAMP), the second messenger.
The modifying enzyme is a protein kinase activated by
cAME Other protein kinases are activated by non-cAMPdependent or CaZ+-dependent systems (Chapter 30). Phosphorylation of a target enzyme may be either stimulatory or
inhibitory. For example, phosphorylation converts glycogen phosphorylase to an activated form and glycogen synthase to an inactivated form, thus preventing the simultaneous occurrence of glycogen breakdown and synthesis
(Chapter 15).
7.2 AIIosteric Enzyme Regulation
Those enzymes in metabolic pathways whose activities
can be regulated by noncovalent interactions of certain
compounds at sites other than the catalytic are known as
allosteric enzymes. They are usually rate-determining enzymes and play a critical role in the control and integration
of metabolic processes. The term "allosteric" is of Greek
origin, the root word "allos" meaning "other." Thus, an
allosteric site is a unique region of an enzyme other than
the substrate binding site that leads to catalysis. At the
allosteric site, the enzyme is regulated by noncovalent interaction with specific ligands known as effectors, modulators, or modifiers.
The properties of allosteric enzymes differ significantly
from those of nonregulatory enzymes. Ligands (in some
instances even the substrate) can bind at such sites by
a cooperative binding process. Cooperativity describes
the process by which binding of a ligand to a regulatory site affects binding of the same or of another ligand to the enzyme. Allosteric enzymes have a more complex structure than nonallosteric enzymes and do not
follow Michaelis-Menten kinetics. An allosteric site is
specific for its ligand, just as the active site is specific for
its substrate. Binding of an allosteric modulator causes a
change in the conformation of the enzyme (see below)
that leads to a change in the binding affinity of the enzyme for the substrate. The effect of a modulator may
be positive (activatory) or negative (inhibitory). The former leads to increased affinity of the enzyme for its substrate, whereas the reverse is true for the latter. Activatory
sites and inhibitory sites are separate and specific for their
111
respective modulators. Thus, if an end product of a
metabolic pathway accumulates in excess of its steadystate level, it can slow down or turn off the metabolic
pathway by binding to the inhibitory site of the regulatory
enzyme of the pathway. As the concentration of the end
product (inhibitor) decreases below the steady-state level,
the number of enzymes having bound inhibitor decreases
and they revert to their active form. In this instance, the
substrate and the negative modulator bear no structural resemblance. An allosteric enzyme may be positively modulated by the substrate itself or by a metabolite of another
pathway that depends on production of the end product
in question for its eventual utilization (e.g., pathways of
synthesis of purine and pyrimidine nucleotides in the formation of nucleic acids; see Chapter 27).
Most allosteric enzymes are oligomers (i.e., they consist of two or more polypeptide chains or subunits). The
subunits are known asprotomers. Two types of interaction
occur in allosteric enzymes: homotropic and heterotropic.
In a homotropic interaction, the same ligand influences
positively the cooperativity between different modulator
sites. An example is a regulatory enzyme modulated by
its own substrate. Thus, this class of enzyme has at least
two substrate binding sites which respond to situations that
lead to substrate excess by increasing its rate of removal.
Heterotropic interaction refers to the effect of one ligand
on the binding of a different ligand. For example, a regulatory enzyme modulated by a ligand other than its substrate
constitutes a heterotropic system, in which the cooperativity can be positive or negative. Some allosteric enzymes
exhibit mixed homotropic and heterotropic interactions.
Kinetics of Allosteric Proteins
The kinetic properties of allosteric enzymes vary significantly from those of nonallosteric enzymes, exhibiting
cooperative interactions between the substrate, the activator, and the inhibitor sites. These properties are responsible for deviations from the classic Michaelis-Menten
kinetics that apply to nonallosteric enzymes. Nonallosteric
enzymes yield a rectangular hyperbolic curve when the
initial velocity (v) is plotted against the substrate concentration [S]. For allosteric enzymes, a plot of v versus
[S] yields curves of different shapes, including sigmoidshaped curves in some cases. (A sigmoidal curve can result
from other mechanisms.)
The v versus [S] plot for a homotropic enzyme is shown
in Figure 7-1. The following features should be noted:
1. The substrate functions as a positive modulator; i.e.,
there is positive cooperativity between the substrate
binding sites so that binding of the substrate at one
112
CHAPTER7 Enzymes I1: Regulation
FIGURE 7-1
Relationship between the initial velocity (v) and the substrate
concentration [S] for an allosteric enzyme that shows a homotropic effect.
The substrate functions as a positive modulator. The profile is sigmoidal,
and during the steep part of the profile, small changes in [S] can cause
large changes in v. K0.5 representsthe substrate concentration
corresponding to half-maximalvelocity.
FIGURE 7-2
Relationship between the initial velocity (v) and the substrate
concentration [S] for an allosteric enzyme that shows a heterotropiceffect
with constant Vmaxbut with varying K0.5. Curve a is obtained in the
absence of any modulators,curve b in the presence of a positive modulator,
and curve c in the presence of a negativemodulator. Regulation is achieved
by modulation of K0.5 without change in Vmax.
binding site greatly enhances binding of the substrate
at the other sites. As the substrate concentration
increases, there is a large increase in the velocity of
the reaction.
2. Owing to the above effect, the shape of the curve is
sigmoidal.
3. The value of the substrate concentration
corresponding to half-maximal velocity is designated
as K0.5 and not Km since the allosteric kinetics do not
follow the hyperbolic M i c h a e l i s - M e n t e n relationship.
4. M a x i m u m velocity (Vmax) is attainable at a rather high
substrate concentration, implying saturation of the
catalytic site of the enzyme.
can be turned on or off with appropriate modulators.
Figure 7-3 shows v versus [S] plots for allosteric enzymes
modulated by changes in Vmax but retaining an essentially
constant K0.5. This type of modulation is less c o m m o n than
the two previous cases considered. The positive modulator
increases gmax(curve b), whereas the negative modulator
decreases Vmax (curve c).
We will consider two specific examples of allosteric
p r o t e i n s m o n e an e n z y m e and the other an oxygen
transport protein.
The v versus [S] plot for heterotropic enzymes is more
complex. The kinetic profiles can be divided into two
classes, depending upon whether the allosteric effector
alters K0.5 and maintains a constant Vmax or alters Vmax
and maintains a nearly constant K0.5. The v versus [S]
profile of an allosteric e n z y m e that follows the former
set of properties is shown in Figure 7-2. In the absence
of any modulators, the profile is sigmoidal (curve a). In
the presence of a positive modulator (curve b), the value
for K0.5 is decreased; i.e., a lower substrate concentration is required to attain half-maximal velocity. Curve
b is more hyperbolic than sigmoidal. Curve c obtained
with a negative modulator is more sigmoidal than curve
a, and the K0.5 value is increased, reflecting a decreased
affinity for the substrate, i.e., a higher substrate concentration is required to attain half-maximal velocity. Regulation of the e n z y m e is achieved through positive and negative modulators. Thus, at a given substrate concentration
(e.g., steady-state level), the activity of the e n z y m e
FIGURE 7-3
Relationship between the initial velocity (v) and the substrate
concentration [S] for an allosteric enzyme that shows a heterotropiceffect
with constant K0.5 but with varying Vmax.Curve a is obtained in the
absence of any modulator, curve b in the presence of a positive modulator,
and curve c in the presence of a negativemodulator. Regulationis achieved
by modulation of Vmaxwithout change in K0.5.
E x a m p l e s of A l l o s t e r i c P r o t e i n s
SECTION7.2 AIIosteric Enzyme Regulation
113
1. Aspartate transcarbamoylase (ATCase) is an
allosteric enzyme of the bacterium Escherichia coli,
which has been extensively studied. This enzyme
catalyzes the transfer of the carbamoyl group from
carbamoyl phosphate to the u-amino group of
aspartate:
CO2 +
Glutamine +
ATP
Carbamoyl phosphate
Aspartate---~l
N- Carbamoyl aspartate
O
O
II
II
H
+
I
3
I
E
m.
H2NmC--O--P~O- + H3N~C~COO-
I
O-
CH2
I
Uridine monophosphate (UMP)
[
O
,4
COO Carbamoyl phosphate
Aspartate
Uddine triphosphate (UTP)
o
--4
"o
O
II
HO~I~OOInorganic phosphate (P~
O
H
II
I
H2N--C--NmC--COO- + H +
H I
CH2
I
COO N-Carbamoyl aspartate
This committed reaction, catalyzed by a regulatory
enzyme, is the second step (Figure 7-4) in the
biosynthesis of pyrimidines. N-carbamoylaspartate
ultimately is converted to the pyrimidine nucleotide
cytidine triphosphate (CTP), which is the negative
modulator of the enzyme. That is, as the CTP
concentration increases, it inhibits the ATCase by
decreasing its affinity for substrates. The preceding is
an example of an allosteric feedback inhibition.
ATCase has a molecular weight of 310,000 and
consists of 12 polypeptide chains (subunits). The
catalytic and the regulatory sites reside on two
different sets of subunits: six larger subunits
(M.W. 33,000) have catalytic sites, and six smaller
subunits (M.W. 17,000) have regulatory sites. X-ray
crystallographic studies of ATCase by Lipscomb
showed that the molecule is roughly triangular. The
six catalytic subunits (C) are present as two trimers
(C3), one above the other (but not exactly parallel),
with the dimeric regulatory subunits (R2) forming an
equatorial belt around the edges of the trimers
(Figure 7-5). In the center of the molecule, an
aqueous cavity is accessible through several openings.
ATCase can be dissociated into two unequal clusters
with different subunit arrangements by treatment with
mercurials (e.g., p-hydroxymercuribenzoate). The
larger cluster containing three catalytic subunits (C3)
Cytidine triphosphate (CTP)
F I G U R E 7-4
Regulation of pyrimidine nucleotide biosynthesis in E. coli.
is catalytically active. The v versus [S] plot exhibits
a hyperbolic profile and is insensitive to CTE The
smaller cluster is a dimer of regulatory subunits (R2)
and, as expected, shows no catalytic activity but does
bind to CTE The native enzyme can be reconstituted
with return of the allosteric activity by removal of the
mercurial compound and mixing of both catalytic and
regulatory clusters:
2C3
-k3R2
--+ R6C6
Catalytic
Regulatory
Native
cluster
cluster
enzyme
Reconstitution also requires zinc ions (Zn2+), since
the native enzyme contains six atoms of Zn 2+. C3 and
R2 clusters can be dissociated further into their
respective, inactive monomeric subunits by strong
denaturing agents (Figure 7-5).
ATCase can assume different conformations
depending on whether it is active or inactive. In the
presence of the substrate or positive modulator, it is
in a catalytically more active conformation known as
the relaxed state or R-state. In the presence of the
negative modulator, the enzyme is in less active
conformation known as the taut state or T-state.
The allosteric kinetic effects of ATCase are
shown in Figure 7-6. The interaction of substrates
with the enzyme is cooperative (an example of
homotropic cooperativity), as indicated by the
sigmoidal shapes of the v versus [S] plots, CTP
being an inhibitor and ATP an activator. These
modulators compete for the same regulatory site
and modulate the affinity of the enzyme for its
114
CHAPTER7 Enzymes I1: Regulation
Hg 2+
(
+3
Native enzyme
Active catalytic subunit
Active regulatory su]~unit
I SDS
0
Inactive catalytic subunit
o
Inactive regulatory subunit
(a)
Substrates
~
'""J
~
CTP
R state
T state
(6)
F I ( ; U R E 7-5
Schematic representation of the subunit structure of aspartate transcarbamoylase and its dissociation into catalytic and
regulatory subunits by mercurials, which can be further converted to inactive monomeric subunits by strong denaturing
agents (e.g., sodium dodecyl sulfate). The native enzyme consists of two catalytic trimers placed one above the other,
along with three dimeric regulatory subunits surrounding the catalytic trimers in an equatorial plane (a). Substrate
maintains the enzyme in the catalytically more active relaxed (R) conformation, while cytidine triphosphate maintains it
in the catalytically less active taut (T) conformation (b). [Reproduced, with permission from E. L. Smith, R. L. Hill,
I. R. Lehman, et al: Principles of Biochemistry: General A.wects, 7th ed. McGraw-Hill, New York, 1983].
substrates, without altering Vmax. The biological
significance of the activation by the purine nucleotide
ATP can be appreciated, since both ATP and CTP
are eventually utilized in the biosynthesis of
double-helical DNA, which contains equal amounts
of purines and pyrimidines. Thus, modulation of
ATCase activity equalizes the rates of formation of
purine and pyrimidine nucleotides. Other regulatory
and metabolic aspects of purines and pyrimidines are
discussed in Chapter 27.
2. Hemoglobin binding of oxygen is a classic example
of the homotropic effect. Hemoglobin also shows
heterotropic effects with specific molecules in its
environment. These effects are intimately related to
the function of hemoglobin as a carrier not only of
oxygen but of H + and CO2 (Chapters 1 and 28). The
heterotropic modulators are H +, CO2, and
F I G U R E 7-6
Relationship between the initial velocity (v) of aspartate
transcarbamoylase and the substrate concentration. Note that ATP is a
positive allosteric modulator, which causes decreased K0.5, whereas
CTP is a negative allosteric modulator, which causes increased K0.5.
SECTION7.2 Allosteric Enzyme Regulation
FIGURE 7-7
Profiles of oxygenationof myoglobinand hemoglobinas a function of
partial pressure of oxygen.Myoglobinshows a typicalMichaelis-Menten
type of rectangularhyperbolicsaturationcurve, whereashemoglobin
shows a sigmoidalsaturationcurve, consistentwith its allostericproperties.
Myoglobinat any partial pressure of oxygenhas muchhigher affinityfor
oxygen than does hemoglobin. [Reproducedwith permissionfrom
A. Lehninger,Principles of Biochemistry. Worth,New York, 1982.]
2,3-bisphosphoglycerate (BPG or DPG). The
cooperativity of oxygen binding to hemoglobin and
the alterations of hemoglobin by various ligands
provide the most extensively investigated molecular
regulation of a biological process.
Hemoglobin carries oxygen from the lungs to
the tissues and carries CO2 and H + back from the
tissues to the lungs (Chapter 1), whereas myoglobin
functions as an oxygen store in muscle. Consistent
with its function, myoglobin has a higher affinity for
oxygen at any partial pressure of oxygen than does
hemoglobin (Figure 7-7). Thus, oxygen can be
transferred easily from hemoglobin to myoglobin.
Hemoglobin is a tetramer consisting of two different
subunit types (e.g., ot and/3 in hemoglobin A). Each
polypeptide contains one heme group (an
iron-porphyrin prosthetic group) that binds to one
oxygen molecule by a cooperative process.
Myoglobin, a monomeric protein with one heme
group, remains monomeric under a wide range of
concentrations and does not show cooperative binding
with oxygen. The polypeptides of myoglobin and
hemoglobin exhibit many differences with respect to
their primary structures. For example, the many
amino acid residues present on the surface of
115
myoglobin are polar, whereas many of those in the
individual hemoglobin polypeptide chains are capable
of participating in nonpolar interactions with other
subunits. Despite these differences, critical regions
are conserved in the polypeptide chains of myoglobin
and hemoglobin, namely, the proximal and distal
histidyl residues that interact with the heme iron, the
hydrophobic amino acid residues that surround the
heme group, and certain prolyl residues that interrupt
the helical regions to allow the chain to fold back
upon itself. The region of the polypeptide chain in
contact with the heme group is known as the heme
pocket. The amino acid residues in this pocket
maintain the heme iron in the divalent state, which is
the functional oxidation state of iron in both
myoglobin and hemoglobin. Thus, the single
polypeptide chain of myoglobin and the two different
chains of hemoglobin are remarkably similar in
secondary and tertiary structures (Figure 7-8). These
similarities support the hypothesis that myoglobin
and hemoglobin evolved by gene duplication and
subsequent mutation from a common ancestral
oxygen-binding heme protein.
The binding of oxygen to myoglobin is not cooperative,
but the binding of oxygen to hemoglobin is cooperative.
This difference can be accounted for kinetically by considering the equilibrium for dissociation of oxymyoglobin
(MbO2) to deoxymyoglobin (Mb) and oxygen (O2):
MbO2 ~- Mb + 02
(7.1)
The equilibrium constant,
Kd --
[Mb][O2]
[MbO2]
(7.2)
is expressed in moles per liter, and its value depends on
pH, ionic strength, and temperature. Since myoglobin has
a single oxygen binding site, a single equilibrium defines
the dissociation of oxymyoglobin.
So that we can deal with measurable parameters, Equation (7.2) needs to be modified by the introduction of
two terms, Y and Ps0. Y is defined as the fractional saturation of myoglobin, e.g., when Y = 0.3, 30% of the
available sites on the myoglobin are occupied by oxygen.
Thus,
Y
number of binding sites occupied by 02
total number of binding sites available for binding 02
or
Y=
[MbO2]
[Mb] + [MbO2]
(7.3)
116
CHAPTER7 Enzymes I1 Regulation
[F$
try{
NAI d
13-Chain of hemoglobin
Myoglobin
FIGURE 7-8
The remarkable similarity in the conformations of myoglobin and of the/3-chain of hemoglobin. [Reproduced with
permission from A. Fersht, Enzyme Structure and Mechanism. (W. H. Freeman, New York, 1977.]
Substituting Equation (7.2) into Equation (7.3), we obtain
[02]
Y =
(7.4)
Equation (7.8) is known as the Hill equation. A plot of
l o g ( Y / 1 - Y) versus log Po2 yields a straight line with a
slope of 1 (the Hill coefficient) (Figure 7-10). Thus, a value
[02] -']- Kd
Because 02 is a gas, it is convenient to express [02] in terms
of its partial pressure in units of Torr (or m m Hg; multiply by
0.133 to obtain kilopascals). Therefore,
y =
Po2
Po2 + Kd
(7.5)
Now we can substitute for Kd the term Ps0, which is defined as the partial pressure of oxygen at which 50% of the
sites are occupied (i.e., when Y -- 0.5), because this situation
is analogous to the M i c h a e l i s - M e n t e n treatment of e n z y m e
kinetics.
y =
Po2
(7.6)
Po: +/'50
A plot of Y versus Po2 yields an oxygen saturation profile
that is a rectangular hyperbola (Figure 7-9), indicating that
the binding of oxygen to myoglobin is noncooperative. Equation (7.6) can be rearranged to yield a linear plot as follows:
Y
1 -
=
Y
Po2
Ps0
(7.7)
Taking the logarithms of both sides of Equation (7.7) yields
log
1 -Y Y ) -- log Po2 - l o g / 5 0
(7.8)
FIGURE 7-9
Profiles of fractional saturation of myoglobin and of hemoglobin with
oxygen as a function of partial pressure of oxygen. Under physiological
conditions,/50 for myoglobin is only 1 or 2 torr, whereas for hemoglobin it
is 26 torr, indicating that oxygen is bound much more tightly to myoglobin
than to hemoglobin. The loading and unloading to oxygen are cooperative
in the case of hemoglobin but not cooperative in the case of myoglobin.
SECTION 7.2
AIIosteric EnzymeRegulation
117
Rearrangement of Equation (7.14) yields
Y
~.(eo2~ n
1 -Y
\-~5o/
The Hill equation is obtained by taking the logarithm of both
sides:
log
FIGURE 7-10
Hill plots for myoglobin and hemoglobin. A slope of 1.0 for myoglobin is
consistent with noncooperative oxygen binding, whereas a slope of 2.8 for
hemoglobin is indicative of cooperative oxygen binding.
of 1 for the Hill coefficient is indicative of noncooperativity;
as we will see with hemoglobin, values greater than 1 indicate positive cooperativity, and values less than 1 indicate
negative cooperativity.
A molecule of hemoglobin (Hb) can bind four molecules
of oxygen, and therefore four equilibrium expressions can
be written to describe the dissociations of HbO2, Hb(O2)2,
Hb(O2)3, and Hb(O2)4. For simplicity, we consider an equilibrium in which Hb(O2)4 dissociates into deoxyhemoglobin
and four molecules of oxygen:
Hb(O2)4 ~- Hb + 402
(7.9)
The equilibrium constant for Reaction (7.9) is"
K --
[Hb] [02] 4
[Hb (O2)4]
(7.10)
Based upon considerations similar to those for myoglobin
dissociation, the value for Y is
(Po2) 4
Y =
(7.11)
(P02)4 _Jr_(P50) 4
A plot of Y versus /~ yields a sigmoidal curve, indicating cooperative binding of oxygen to hemoglobin. A general
expression for the dissociation of oxyhemoglobin to deoxyhemoglobin and oxygen may be written as
Hb(O2)n ~-- Hb + nO2
(7.12)
where n is the number of molecules of oxygen. The equilibrium constant for reaction (7.12) is
K --
[Hb] [O21n
[Hb (O2)n]
(7.13)
and
Y =
(/'02)"
(P02) n --]--(P50) n
(7.14)
1-Y
--nlogPo2-nlogPs0
A plot of log ( Y / 1 - Y) versus log Po2 yields a straight
line with a slope of n, the Hill coefficient. For hemoglobin,
n = 2.8 (Figure 7-10), which signifies that the binding of
oxygen to hemoglobin exhibits positive cooperativity.
From a physiological point of view, the cooperative oxygen
binding characteristics of hemoglobin are eminently suited
for the transport of oxygen from the lungs to the tissues.
In the alveolar spaces of the lungs, the partial pressure of
oxygen is about 100 Torr, and about 97% of the hemoglobin is
combined with oxygen (i.e., 97% saturation with 02). As the
oxygenated blood passes through the tissue capillaries, where
the partial pressure of oxygen often falls below 40 Torr (in
actively exercising muscle, the Poe is about 20 Torr), about
30% of the oxygen is unloaded from oxyhemoglobin to tissue cells. This process is cooperative, so that as 02 is released from oxygen-saturated hemoglobin because of a drop
in Po2, the loss of a single 02 molecule causes rapid release
of the remaining ones. Similarly in the lungs, the affinity of
hemoglobin for binding the first 02 molecule is low; however, once this molecule is bound, the affinity increases. Myoglobin, in conformity with its storage function, has higher
affinity for oxygen than does hemoglobin at any partial pressure of oxygen (Figure 7-9).
X-ray studies have shown that oxyhemoglobin (R form)
and deoxyhemoglobin (T form) have different threedimensional conformations. However, no changes in the
tertiary structure of the individual subunits have been observed. The molecular mechanisms of cooperative binding of
oxygen are known, and the details of this process along with
other ligand interactions with hemoglobin are discussed in
Chapter 28.
Theoretical Models for Allosteric Effect
Two theoretical models for allosteric effects have been
proposed to explain the mechanism for ligand-protein cooperative interactions: the concerted (or symmetry) model of
Monod, Wyman, and Changeux and the sequentially inducedfit model of Koshland. The nomenclature associated with
allosterism and cooperativity originated from the concerted
model. Both models assume that
1. Each subunit of an oligomeric protein exists in two
forms, T and R, which bind the ligand with low and high
affinity, respectively; and
2. The T ~-- R transformations involve noncovalent bonds
and result in changes in the quaternary structure of the
enzyme.
118
CHAPTER 7
EnzymesI1 Regulation
Catalyticsiteswith low
affinityf.orsubstrate
Catalytic sites with low
affinity for substrate
AIIosteric
AIIosteric
site
site
eAiiosteric..___.~~
t is
~
"~
~,,_._.__ AIIosteric
site
TT state
TTstate
Positive
modulator (or substrate
in positive homotropic
cooperativity)preferentially
bindsto the R form and maintains
the allosteric protein in the
RR conformation.
Catalytic sites with high
affinity for substrate
modulator preferentially
binds to the T form and maintains
the allosteric protein in the TT
conformation,
Negative
Negative
modulator
Positive
modulator
Ne0atve
cooperativity
Postve
coope rativity
TR state
Negative
modulator
Positive
modulator
RR state
FIGURE 7-11
Schematic diagram of conformational changes of concerted model for a
dimeric allosteric enzyme. All subunits are either in the T-form with low
affinity for the substrate or in the R-form with high affinity for the substrate.
The concerted model has the following features. The allosteric protein exists only in two states: T or R. If, for example, an allosteric protein contains two subunits, the sole
permissible conformation states are TT and RR (RT is not
allowed because R and T cannot form a stable pair). Thus,
in this model (also called the "all or none" model), symmetry of the allosteric protein is preserved (Figure 7-11). It is
assumed that the T and R forms are in equilibrium, that significant binding of ligand occurs only to the R form, and that
this binding shifts the equilibrium strongly in favor of formation of the R form. Thus, a conformational change in one
subunit that occurs after it binds to a ligand causes a corresponding change in all of the subunits without formation of
hybrid species. The concerted model accounts for the kinetic
behavior of many allosteric proteins, but it cannot account
for negative cooperativity; i.e., the decrease in affinity for a
ligand by the allosteric protein as the sites become occupied.
The sequential model proposes that as the ligand binds
to a subunit a conformational change is induced that stabilizes the ligand-allosteric protein complex such that a second ligand molecule is bound more readily than the first
(Figure 7-12). This effect is of positive cooperativity. However, if the initial binding of the ligand results in a ligandprotein complex with decreased stability, the binding of additional ligand molecules, or ligand-induced substrate binding,
becomes increasingly difficult. This effect is negative cooperativity. In this model, the notion of symmetry is discarded,
since a conformational change induced by a ligand that binds
to a subunit also induces a conformational change in an adjacent subunit. Figure 7-13 shows sequential transmission of
conformational changes through contiguous subunits upon
RR state
FI(;URE 7-12
Schematic diagram of conformational changes of sequentially induced-fit
model for a dimeric allosteric enzyme. The TT conformation is
progressively converted to the RR conformation via the intermediateTR
conformation through cooperative interaction in the presence of the
positive modulator. In the presence of the negative modulator, the opposite
conformational changes occur. In this model, the notion of symmetryis
discarded and the concept of induced fit is emphasized.
ligand binding. The behavior of some allosteric proteins is
best explained by the concerted model, whereas for others the
sequential model is more appropriate. For many proteins, neither model is satisfactory and a more complex model may be
required.
T form
R form
m=m=FF 88---88
FIGURE 7-13
Sequential transmission of conformational changes through contiguous
subunits induced by a ligand (S). In idealized form, the conformational
changes proceed diagonally as the protein progressivelybinds ligand.
119
Supplemental Readings and References
Supplemental Readings and References
Enzyme Regulation (General)
Z. Dische: The discovery of feedback inhibition; Trends in Biochemical
Sciences 1, 269 (1976).
D. E. Koshland, G. Nemethy, and D. Filmer: Comparison of experimental binding data and theoretical models in proteins containing subunits;
Biochemistry 5, 365 (1966).
J. Monod, J.-E Changeux, and E Jacob: Allosteric proteins and cellular
control systems. Journal of Molecular Biology 6, 306 (1963).
J. Monod, J. Wyman, and J.-E Changeux: On the nature of allosteric transitions: A plausible model. Journal of Molecular Biology 12, 88 (1965).
H. L. Segal: Enzymatic interconversions of active and inactive forms of
enzymes. Science 180, 25 (1973).
G. Weber, (Ed): Advances in Enzyme Regulation, Vols. 1-6. Pergamon Press,
London, 1963-1979.
Allosteric Properties of Aspartate
Transcarbamoylase and Hemoglobin
Aspartate Transcarbamoylase
E Hensley and H. K. Schachman: Communication between dissimilar subunits in aspartate transcarbamoylase: Effect of inhibitor and
activator on the conformation of the catalytic polypeptide chains.
Proceedings of the National Academy of Sciences USA. 76, 3732
(1979).
E. V. Kantrowitz, S. C. Pastra-Landis, and W. N. Lipscomb: E. coli aspartate
transcarbamoylase. Part 2. Structure and allosteric interactions. Trends
in Biochemical Sciences 5, 150 (1980).
I. L. Monoco, J. L. Crawford, and W. N. Lipscomb: Three dimensional
structures of aspartate transcarbamoylase from Escherichia coli and its
complex with cytidine triphosphate. Proceedings of the National Academy
of Sciences USA. 75, 5276 (1978).
Hemoglobin
J. Baldwin and C. Chothia: Hemoglobin: The structural changes related to
ligand binding and its allosteric mechanism. Journal of Molecular Biology
129, 175 (1979).
M. F. Perutz: Stereochemistry of cooperative effects of hemoglobin. Nature
228, 726 (1970).
M. E Perutz: Hemoglobin structure and respiratory transport. Scientific
American 239(6), 92 (1978).
M. E Perutz: Regulation of oxygen affinity of hemoglobin: Influence of
structure of the globin on the heme iron. Annual Review of Biochemistry
48, 327 (1979).