Voet D., Voet Ju.G. Biochemistry

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energy of ligand binding stabilizes the R state with respect to

the T state.

b. Heterotropic Interactions

The symmetry model of allosterism is also capable of

accounting for heterotropic effects. This comes about by

assuming that each protomer has specific and independent

binding sites for the three types of ligands: a substrate, S,

that for simplicity let us assume binds only to the R state

(c ⫽ 0); an activator, A, that also binds only to the R state;

and an inhibitor, I, that binds only to the T state (Fig. 10-30).

Then, through the derivation in Section B of the Appendix

to this chapter, we obtain a more general equation for the

symmetry model that describes heterotropic interactions

as well as homotropic interactions:

[10.23]

where ␣⫽[S]/k

as before and, analogously, ␤⫽[I]/k

and ␥⫽[A]/k

Note that this equation differs from Eq. [10.22] for c ⫽ 0

only in that the second term in the denominator is modu-

lated by terms related to the amounts of activator and in-

hibitor bound to the oligomer.

Figure 10-31 indicates the consequences of effector

binding to a tetramer that follows this model:

1. Activator binding (␥⬎0) increases the concentra-

tion of the substrate-binding R state (the second term in

the denominator of Eq. [10.23] decreases) because it is the

only state capable of binding activator. The presence of ac-

tivator therefore increases the protein’s substrate-binding

affinity (a positive heterotropic effect), although it de-

creases the protein’s degree of substrate-binding coopera-

tivity (compare Curves 1 and 2 in Fig. 10-31). (Note: There

is nothing in the derivation of Eq. [10.23] that differentiates

the roles of substrate and activator; consequently, the sub-

strate and the activator each bind to the protein with a

positive homotropic effect as well as being positive het-

erotropic effectors of each other.)

2. The presence of inhibitor (␤ ⬎ 0), which only binds to

the T state, reduces the binding affinity for substrate (a neg-

ative heterotropic effect) by increasing the concentration

of the T state (the second term in the denominator of Eq.

[10.23] increases). Therefore, since substrate must “work

harder” to convert the oligomer to the substrate-binding R

state, inhibitor increases the cooperativity of substrate

binding (compare Curves 2 and 3 of Fig. 10-31), as well as

that for activator binding.

The model derived here is a rather simple one.In a more

realistic but algebraically much more complicated symme-

try model, all types of ligands would bind to both confor-

mational states of the oligomer. Nevertheless, this model

demonstrates that both homotropic and heterotropic effects

can be explained solely by the requirement that the molecu-

lar symmetry of the oligomer be conserved rather than by

the existence of any direct interactions between ligands. In

Section 10-4D, we compare the theoretical predictions of

⫽

␣(1 ⫹␣)

n⫺1

(1 ⫹␣)

⫹

L(1 ⫹␤)

(1 ⫹␥)

the symmetry model with our experimentally based model

of hemoglobin oxygen binding.

C. The Sequential Model

The symmetry model provides a reasonable rationalization

for the ligand-binding properties of many proteins. There

are, however, several valid objections to it. Foremost of

these is that it is difficult to believe that oligomeric symmetry

is invariably preserved in all proteins so that there are never

any hybrid conformations such as R

n⫺2

. Furthermore,

Section 10-4. Allosteric Regulation 351

Figure 10-30 Heterotropic interactions in the symmetry model

of allosterism. Heterotropic effects arise when substrates and

activators bind exclusively (or at least preferentially) to the R

state (right), and inhibitors bind exclusively (or at least

preferentially) to the T state (left).The binding of substrate

and/or activator to the oligomer therefore facilitates the further

binding of substrate and activator. Conversely, the binding of

inhibitor prevents (or at least inhibits) the oligomer from binding

substrate or activator.

1.0

0.5

0 1.0 2.0

= 100

= 0

= 2.5

= 1000

= 4

Figure 10-31 The effects of allosteric activator (␥ ⫽ [A]/k

)

and inhibitor (␤ ⫽ [I]/k

) on the shape of the fractional

saturation curve for substrate (␣ ⫽ [S]/k

) according to Eq.

[10.23] for tetramers. [After Monod, J., Wyman, J., and

Changeux, J.-P., J. Mol. Biol. 12, 94 (1965).]

JWCL281_c10_323-358.qxd 2/24/10 1:58 PM Page 351

there are well-established instances of negative homotropic

effects (e.g., in the GroEL–GroES complex, the binding of

ATP to the cis ring of GroEL prevents ATP from binding

to the trans ring; Section 9-2Cd), although the symmetry

model, which permits only positive homotropic effects, is

unable to account for them.

The symmetry model implicitly assumes Emil Fischer’s

“lock-and-key” model of ligand binding in which ligand-

binding sites of proteins are rigid and complementary in

shape to their ligand (Fig. 10-32, left).A more sophisticated

extension of the lock-and-key model, known as the

induced-fit hypothesis, postulates that a flexible interaction

between ligand and protein induces a conformational

change in the protein, which results in its increased ligand-

binding affinity (Fig. 10-32, right).The observation, through

X-ray crystal structure analysis, that such conformational

changes occur in numerous proteins has established the va-

lidity of the induced-fit hypothesis.

Daniel Koshland, George Némethy, and David Filmer

adapted the induced-fit hypothesis to explain allosteric ef-

fects. In the resulting sequential model (alternatively, the

induced-fit or KNF model), ligand binding induces a confor-

mational change in a subunit; cooperative interactions arise

through the influence that these conformational changes

have on neighboring subunits (Fig. 10-33). If, for example,

they increase the neighbor’s ligand-binding affinity, then

ligand binding is positively cooperative. The strengths of these

interactions depend on the degree of mechanical coupling

between subunits. In the limit of very strong coupling, con-

formational changes become concerted, so that the

oligomer maintains its symmetry (the symmetry model).

With looser coupling, however, conformational changes

occur sequentially as more and more ligand is bound

(Fig. 10-34). Thus, the essence of the sequential model is that

a protein’s ligand-binding affinity varies with its number of

bound ligands, whereas in the symmetry model this affinity

depends only on the protein’s quaternary state.

The degree of coupling between oligomer subunits de-

pends on how these subunits are arranged, that is, on the

protein’s symmetry. Consequently, in the sequential model,

the fractional saturation has a different algebraic form for

each oligomeric symmetry.The form of the Adair equation

(Eq. [10.17] for a tetramer) similarly depends on the num-

ber of subunits in the protein. In fact, the sequential model

of allosterism may be considered an extension of the Adair

model that provides a physical rationalization for the val-

ues of its microscopic dissociation constants, k

D. Hemoglobin Cooperativity

Hemoglobin’s fractional saturation curve is closely approx-

imated by both the symmetry model and the sequential

model (Fig. 10-35). Clearly such curves cannot by them-

selves be used to differentiate between these two models,

if, in fact, either is correct. It is of interest, however, to com-

pare these models with the mechanistic model of Hb we

developed in Section 10-2C.

Hb, of course,is not composed of identical subunits, as the

symmetry model demands. At least to a first approximation,

however, the functional differences of Hb’s closely related ␣

and ␤ subunits may be ignored (although their structural dif-

ferences are essential to the molecular mechanism of Hb co-

operativity). To this approximation, Hb largely follows the

symmetry model, although it also exhibits some features of

the sequential model. The quaternary T S R conformation

change is concerted as the symmetry model requires.Yet lig-

and binding to the T state does cause small tertiary struc-

tural changes as the sequential model predicts.This phenom-

enon is evident in the X-ray structure of crystals of human

Hb whose ␣ subunits are fully oxygenated and whose ␤ sub-

units are unliganded. This particular crystal form constrains

352 Chapter 10. Hemoglobin: Protein Function in Microcosm

Figure 10-32 Models of ligand binding. In the lock-and-key

mechanism of ligand binding (left), proteins are postulated to

have preformed ligand-binding sites that are complementary in

shape to their ligand. Under the induced-fit mechanism, a protein

does not have this complementary binding site in the absence of

ligand (right). Rather, the ligand induces a conformational

change at the binding site that results in the complementary

interaction.

Figure 10-33 The sequential model of allosterism. Substrate

binding to the low-affinity T state induces conformational

changes in unliganded subunits that give them ligand-binding

affinities between those of the low-affinity T state and the

high-affinity R state.

Lock and key Induced fit

Ligand

Protein

Protein–Ligand

complex

Substrate

JWCL281_c10_323-358.qxd 2/24/10 1:58 PM Page 352

the partially liganded Hb to remain in the T state. Neverthe-

less, its ␣ subunit Fe’s are 0.15 Å closer to the still domed

porphyrins than they are in deoxyHb (25% of the total dis-

tance moved in the T S R transition). Such tertiary struc-

tural changes are undoubtedly responsible for the buildup of

strain that eventually triggers the T S R transition.

A more telling but more difficult question to answer is

does ligand-binding cooperativity in Hb arise solely from

the T S R transition, in agreement with the symmetry

model, or do the T and R states themselves exhibit at least

some degree of cooperativity, in accord with the sequential

model? Put another way, does the ligand-binding affinity of

Hb subunits depend only on Hb’s quaternary state (symme-

try model) or does this affinity vary with the number of lig-

ands bound to Hb (sequential model)? Although this matter

has been under experimental scrutiny and a subject of spir-

ited debate for over four decades, it is still not fully resolved.

For example, the determination, by Andrea Mozzarelli and

Eaton, of the Hill plot of the above-described single crystals

of T-state Hb via sophisticated optical spectroscopic tech-

niques is indicative of noncooperative ligand binding, in ac-

cord with the symmetry model. Likewise, time-resolved

spectroscopic measurements covering the picosecond to

microsecond time scales after ligand binding was initiated

indicate that the conformational changes that Hb initially

undergoes on binding ligand are consistent with the symme-

try model. However, detailed thermodynamic analysis, by

Gary Ackers, of the interactions associated with the formation

of each of Hb’s 10 different ligation microstates (Fig. 10-36)

indicates that the Hb tetramer undergoes a T S R transition

Section 10-4. Allosteric Regulation 353

Figure 10-34 Sequential binding of ligand in the sequential

model of allosterism. Ligand binding progressively induces

conformational changes in the subunits, with the greatest changes

occurring in those subunits that have bound ligand.The coupling

Figure 10-35 The sequential and the symmetry models of

allosterism can provide equally good fits to the measured

-dissociation curve of Hb. [After Koshland, D.E., Jr., Némethy,

G., and Filmer, D., Biochemistry 5, 382 (1966).]

Figure 10-36 Free energy penalties for binding O

to various

ligation states of Hb tetramers relative to O

-binding to

noncooperative Hb ␣␤ dimers. Only the ten unique liganding

states are diagrammed (an additional six states are related to

those shown by Hb’s 2-fold symmetry). Penalties (in kJ ⴢ mol

⫺1

)

for individual binding steps are shown beside the arrows.

Cumulative free energy penalties are shown to the left of each

Hb tetramer state. Ligation states that predominantly assume the

T state are blue and those that predominantly assume the R state

are red.The preferred pathways, those in which the free energy

penalty of ligand binding progressively decreases with each

successively bound ligand (those with all solid arrows), pass

through the T state in which O

is bound to both sites on one ␣␤

dimer before its conversion to the R state. Note that the T S R

transition predominantly occurs via pathways in which at least

one subunit in each ␣␤ protomer is liganded. [Based on data

from Ackers, G.K., Adv. Prot. Chem. 51, 193 (1998).]

S S S S

S SS SS

between subunits is not necessarily of sufficient strength to

maintain the symmetry of the oligomer as it is in the symmetry

model.

1.00

0.75

0.50

0.25

–1 0 1 2 3 4

Symmetry

model

Sequential

(induced-fit)

model

log pO

11.7 11.7

–2.5–2.5

26.4

11.7 11.7

28.9

27.6

28.0

20.9

9.2

16.7 15.9

16.3

9.216.3

8.0

0.4 1.3

0.9

0.9 8.0

28.5

JWCL281_c10_323-358.qxd 2/24/10 1:58 PM Page 353

A. Homotropic Interactions—Equation [10.22]

The fractional saturation Y

for ligand binding is

expressed:

⫽

[10.21]

Defining ␣⫽[S]/k

and c ⫽ k

, and using Eq. [10.20] to

substitute [R

n⫺1

] for [R

], [R

n⫺2

] for [R

n⫺1

] etc., the terms

enclosed by the first set of parentheses in the numerator of

Eq. [10.21] are reduced to

and similarly, the terms in the first set of parentheses of the

denominator of Eq. [10.21] become

Likewise, the terms in the second set of parentheses of the

numerator and the denominator of Eq. [10.21] assume the

respective forms

and

Accordingly,

which, on cancellation of terms, yields the equation

describing the symmetry model for homotropic interactions:

[10.22]Y

⫽

␣(1 ⫹␣)

n⫺1

⫹ Lc␣(1 ⫹ c␣)

n⫺1

(1 ⫹␣)

⫹ L(1 ⫹ c␣)

⫽

]␣n(1 ⫹␣)

n⫺1

⫹ L[R

]c␣n(1 ⫹ c␣)

n⫺1

n5[R

](1 ⫹␣)

⫹ L[R

](1 ⫹ c␣)

](1 ⫹ [S]>k

)

⫽ L[R

](1 ⫹ c␣)

]([S]>k

)n(1 ⫹ [S]>k

)

n⫺1

⫽ L[R

]c␣n(1 ⫹ c␣)

n⫺1

] e1 ⫹ n␣⫹

⫹

n!␣

f⫽ [R

](1 ⫹␣)

⫽ [R

]␣n(1 ⫹␣)

n⫺1

⫽ [R

]␣n e1 ⫹

2(n ⫺ 1)␣

⫹

n(n ⫺ 1)!␣

n⫺1

n(n ⫺ 1)!

] en␣⫹

2n(n ⫺ 1)␣

⫹

n n!␣

([R

] ⫹ 2[R

] ⫹

⫹ n[R

]) ⫹ ([T

] ⫹ 2[T

] ⫹

⫹ n[T

])

n5([R

] ⫹ [R

] ⫹

⫹ [R

]) ⫹ ([T

] ⫹ [T

] ⫹

⫹ [T

])6

B. Heterotropic Interactions—Equation [10.23]

For an oligomer that binds activator A and substrate S to

only its R state, and inhibitor I to only its T state, the frac-

tional saturation for substrate, Y

, the fraction of substrate-

binding sites occupied by substrate, is expressed:

Here the subscripts i, j, and k indicate the respective

numbers of S, A, and I molecules that are bound to one

oligomer; that is, R

i, j

⬅ RS

and T

⬅ TI

.Then defining

␣⫽[S]/k

and following the foregoing derivation of

Eq. [10.22]:

where

In analogy with the definition of ␣, we define ␤⫽[I]/k

and

␥⫽[A]/k

, and again follow the derivation of Eq. [10.22]

to obtain

and

so that

The symmetry model equation extended to include het-

erotropic effects is therefore expressed

[10.23]Y

⫽

␣(1 ⫹␣)

n⫺1

(1 ⫹␣)

⫹

L(1 ⫹␤)

(1 ⫹␥)

L¿ ⫽

L(1 ⫹␤)

(1 ⫹␥)

j⫽0

0, j

] ⫽ [R

0, 0

](1 ⫹␥)

k⫽0

] ⫽ [T

](1 ⫹␤)

L¿ ⫽

k⫽0

j⫽0

0, j

]

⫽

j⫽0

0, j

]b ␣n(1 ⫹␣)

n⫺1

n ea

j⫽0

0, j

]b(1 ⫹␣)

⫹

k⫽0

⫽

␣(1 ⫹␣)

n⫺1

(1 ⫹␣)

⫹ L¿

⫽

i⫽1

j⫽0

i[R

i, j

]

n a

i⫽0

j⫽0

i, j

] ⫹

k⫽0

] b

APPENDIX Derivations of Symmetry Model Equations

only when at least one liganding site on each of its ␣␤ pro-

tomers is occupied.This heretofore unrecognized symmetry is

inconsistent with the symmetry model. Moreover, as Takashi

Yonetani has shown, heterotropic effectors such as BPG can

decrease Hb’s oxygen affinity without changing its quaternary

state. Evidently,cooperativity arises both from concerted qua-

ternary switching (as called for by the symmetry model) and

from sequential modulation of ligand binding within each

quaternary state through ligand-induced alterations in terti-

ary structure (in accord with the sequential model).

354 Chapter 10. Hemoglobin: Protein Function in Microcosm

JWCL281_c10_323-358.qxd 2/24/10 1:58 PM Page 354

References 355

1 Hemoglobin Function The heme group in myoglobin

and in each subunit of hemoglobin reversibly binds O

. In de-

oxyHb, the Fe(II) is five-coordinated to the four pyrrole nitro-

gen atoms of the protoporphyrin IX and to the protein’s prox-

imal His. On oxygenation, O

becomes the sixth ligand of

Fe(II). Mb has a hyperbolic fractional saturation curve (Hill

constant, n ⫽ 1). However, that of Hb is sigmoidal (n ⬇ 2.8) as

a consequence of its cooperative O

binding: Hb binds its

fourth O

with 100-fold greater affinity than its first O

.The

variation of O

affinity with pH, the Bohr effect, causes Hb to

release O

in the tissues in response to the binding of protons

liberated by the hydration of CO

to . Hb facilitates the

transport of CO

, both directly, by binding CO

as N-terminal

carbamate, and indirectly, by increasing the concentration of

through the Bohr effect. The presence of BPG in ery-

throcytes, which only binds to deoxyHb, further modulates the

affinity of Hb. Short-term high-altitude adaptation results

from an increase of BPG concentration in the erythrocytes,

which increases the amount of O

delivered to the tissues by

decreasing hemoglobin’s O

affinity.

2 Structure and Mechanism The ␣ and ␤ subunits of Hb

consist mostly of seven or eight consecutive helices arranged to

form a hydrophobic pocket that almost completely envelops

the heme. Oxygen binding moves the Fe(II) from a position

⬃0.6 Å out of the heme plane on the side of the proximal His

to the center of the heme, thereby relieving the steric interfer-

ence that would otherwise occur between the bound O

and

the porphyrin.The Fe(II) pulls the attached proximal His after

it in a motion that can only occur if its imidazole ring reorients

so as to avoid collision with the heme. In the T S R conforma-

tional transition, the symmetry equivalent ␣

C–␤

FG and

␣

C–␤

FG contacts simultaneously shift between two stable

positions. Intermediate positions are sterically prevented, so

that these contacts act as a two-position conformational switch.

The Perutz mechanism of O

binding proposes that the low

affinity of the T state arises from strain that prevents the

Fe(II) from moving into the heme plane to form a strong

Fe¬O

bond. This strain is relieved by the concerted 4º shift

of the Hb molecule to the high O

affinity R state. The quater-

nary shift is opposed by a network of salt bridges in the T state

that involve the C-terminal carboxyl groups and that are rup-

tured in the R state.The stability of the R state relative to the T

state increases with the degree of oxygenation as a result of the

strain of binding O

in the T state. The existence of this strain

has been demonstrated through the breakage of the

Fe(II)–proximal His bond on hemoglobin’s simultaneous bind-

ing of IHP, a tight-binding BPG analog that forces Hb into the

T state, and NO, a strong ligand that forces Hb into the R state.

Conversely, mutagenically detaching the proximal His from

the protein eliminates most of hemoglobin’s cooperativity.

HCO

⫺

HCO

⫺

The Bohr effect results from increases in the pK’s of the ␣

N-terminal amino group and His 146␤ on forming the T-state

salt bridges.Surface-exposed His residues also participate in the

Bohr effect. BPG binding occurs in the central cavity of T-state

Hb through several salt bridges.The distal His residue protects

deoxyHb from autooxidation by taking up the protons that

would otherwise catalyze the oxidation of the heme Fe.

3 Abnormal Hemoglobins Over 1000 mutant varieties of

Hb are known.About half of them are innocuous because they

result in surface residue changes. However, alterations of inter-

nal residues often disrupt the structure of Hb, which causes he-

molytic anemia.Changes at the O

-binding site that stabilize the

Fe(III) state eliminate O

binding to these subunits, which re-

sults in cyanosis. Mutations affecting subunit interfaces may sta-

bilize either the R state or the T state, which, respectively, in-

crease and decrease hemoglobin’s O

affinity. Sickle-cell

anemia is caused by the homozygous Hb mutant Glu 6␤ S Val,

which promotes the gelation of the resulting deoxyHbS to form

rigid 14-strand fibers that deform erythrocytes. Under gelation

conditions,fiber growth occurs via a two-stage nucleation mech-

anism, resulting in a delay time that varies with the 30th to 50th

power of the initial HbS concentration. Agents that increase

this delay time to longer than the transit times of erythrocytes

through the capillaries should therefore prevent sickle-cell

crises and thus relieve the symptoms of sickle-cell anemia.

4 Allosteric Regulation The Adair equation rationalizes

the O

-binding cooperativity of Hb by assigning a separate

dissociation constant to each O

bound. Positive cooperativity

results if these constants decrease sequentially. However, the

Adair equation offers no physical insight as to why this occurs.

The symmetry model proposes that symmetrical oligomers

can exist in one of two conformational states, R and T, that dif-

fer in ligand-binding affinity. Ligand binding to the high-

affinity state forces the oligomer to assume this conformation,

which facilitates the binding of additional ligand. This ho-

motropic model is extended to heterotropic effects by postu-

lating that activator and substrate can bind only to the R state

and inhibitor can bind only to the T state. The binding of acti-

vator forces the oligomer into the R state, which facilitates the

binding of substrate and additional activator. The binding of

inhibitor, however, forces the oligomer into the T state, which

prevents substrate and activator binding. The sequential

model postulates that an induced fit between ligand and sub-

strate confers conformational strain on the protein that alters

its affinity for binding other ligands without requiring the

oligomer to maintain its symmetry. The Perutz mechanism for

binding to Hb is structurally largely consistent with the

symmetry model but exhibits some elements of the sequential

model. However, Hb’s ligand-binding cooperativity is in full

accord with the symmetry model.

CHAPTER SUMMARY

General

Bunn, F.H. and Forget, B.G., Hemoglobin: Molecular, Genetic and

Clinical Aspects, Saunders (1986). [A valuable compendium on

normal and abnormal hemoglobins.]

Dickerson, R.E. and Geis, I., Hemoglobin, Benjamin/Cummings

(1983). [A beautifully written and lavishly illustrated treatise

on the structure, function, and evolution of hemoglobin.]

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Ferry, G., Max Perutz and the Secret of Life, Cold Spring Harbor

Laboratory Press (2007). [A definitive biography.]

Hendgen-Cotta, U.B., et al., Nitrite reductase activity of myoglo-

bin regulates respiration and cellular viability in myocardial

ischemia–reperfusion injury, Proc. Natl. Acad. Sci. 105,

10256–10261 (2008).

Judson, H.F., The Eighth Day of Creation (expanded edition),

Chapters 9 and 10, Cold Spring Harbor Laboratory Press

(1996). [Includes a fascinating historical account of how our

present perception of hemoglobin structure and function came

about.]

Lukin, J.A. and Ho, C.,The structure–function relationship of he-

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Royer, W.E., Jr., Zhu, H., Gorr, T.A., Flores, J.F., and Knapp, J.E.,

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Vinogradov, S.N. and Moens, L., Diversity of globin function: enzy-

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Brunori, M., Nitric oxide moves myoglobin to center stage,Trends

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o-pivalamidophenyl)porphinato iron(II)-ethanol and its dioxy-

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picket-fence complex.]

Liddington, R., Derewenda, Z., Dodson, G., and Harris, D., Struc-

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Mechanism of Hemoglobin Oxygen Binding

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and deoxyHb.]

Barrick, D., Ho, N.T., Simplaceanu,V., Dahlquist, F.W., and Ho, C.,

A test of the role of the proximal histidines in the Perutz

model for cooperativity in haemoglobin, Nature Struct. Biol. 4,

78–83 (1997). [Describes the experiments in which the proxi-

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Gelin, B.R., Lee, A.W.-N., and Karplus, M., Haemoglobin tertiary

structural change on ligand binding, J. Mol. Biol. 171, 489–559

(1983).[A theoretical study of the dynamics of O

binding to Hb.]

Perutz, M.F., Stereochemistry of cooperative effects in haemoglo-

bin, Nature 228, 726–734 (1970). [The landmark paper in which

the Perutz mechanism was first proposed. Although many of

its details have since been modified, the basic model remains

intact.]

Perutz, M.F., Regulation of oxygen affinity of hemoglobin, Annu.

Rev. Biochem. 48, 327–386 (1979). [An examination of the

Perutz mechanism in light of structural and spectroscopic data.]

Perutz, M.F., Mechanisms of cooperativity and allosteric regula-

tion in proteins, Q. Rev. Biophys. 22, 139–236 (1989). [Contains

a detailed structural description of allosterism in hemoglobin.]

Perutz, M.F., Wilkinson, A.J., Paoli, M., and Dodson, G.G., The

stereochemical mechanism of the cooperative effects in hemo-

globin revisited, Annu. Rev. Biophys. Biomol. Struct. 27, 1–34

(1998).

Bohr Effect and BPG Binding

Arnone, A., X-ray studies of the interaction of CO

with human

deoxyhaemoglobin, Nature 247, 143–145 (1974).

Benesch, R.E. and Benesch, R., The mechanism of interaction of

red cell organic phosphates with hemoglobin, Adv. Prot. Chem.

28, 211–237 (1974).

Kilmartin, J.V. and Rossi-Bernardi, L.,Interactions of hemoglobin

with hydrogen ion, carbon dioxide and organic phosphates,

Physiol. Rev. 53, 836–890 (1973).

Lenfant, C., Torrance, J., English, E., Finch, C.A., Reynafarje, C.,

Ramos, J., and Faura, J., Effect of altitude on oxygen binding by

hemoglobin and on organic phosphate levels, J. Clin. Invest. 47,

2652–2656 (1968).

Perutz, M.F., Kilmartin, J.V., Nishikura, K., Fogg, J.H., and Butler,

P.J.G., Identification of residues contributing to the Bohr effect

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Richard, V., Dodson, G.G., and Mauguen, Y., Human deoxy-

haemoglobin-2,3-diphosphoglycerate complex low-salt struc-

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histidyl residues in the ␣-chain of the Bohr effect of human

normal adult hemoglobin: Roles of global electrostatic effects,

Biochemistry 36, 6663–6673 (1997).

Abnormal Hemoglobins

Baudin-Chich, V., Pagnier, J., Marden, M., Bohn, B., Lacaze, N.,

Kister, J., Schaad, O., Edelstein, S.J., and Poyart, C., Enhanced

polymerization of recombinant human deoxyhemoglobin ␤6

Glu S Ile, Proc. Natl. Acad. Sci. 87, 1845–1849 (1990).

Bunn, F.H., Pathogenesis and treatment of sickle cell disease, New

Engl. J. Med. 337, 762–769 (1997).

Bunn, F.H., Human hemoglobins: sickle hemoglobin and other

mutants, in Stamatoyannopoulos, G., Majerus, P.W., Perlmut-

ter, R.M., and Varmus, H. (Eds.), The Molecular Basis of Blood

Diseases (3rd ed.), Chapter 7, Elsevier (2001).

Eaton,W.A. and Hofrichter,J., Sickle cell hemoglobin polymeriza-

tion, Adv. Prot. Chem. 40, 63–279 (1990). [An exhaustive re-

view of HbS polymerization.]

Eaton, W.A. and Hofrichter, J., The biophysics of sickle cell hy-

droxyurea therapy, Science 268, 1142–1143 (1995).

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tion crystal structure of deoxyhemoglobin S, J. Mol. Biol. 272,

398–407 (1997).

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Perutz, M., Protein Structure. New Approaches to Disease and

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haemoglobin, Nature 219, 902–909 (1968). [A ground-breaking

study correlating the clinical symptoms and inferred structural

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1488–1490 (1999). [A short history of Pauling’s characteriza-

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(1989).

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moglobinopathies, in Valle, D. (Ed.), The Online Metabolic &

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detailed review of abnormal hemoglobins.]

Allosteric Regulation

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metric tetramer: human hemoglobin, J. Biol. Chem. 281,

11441–11443 (2006); and Ackers, G.A., Deciphering the molec-

ular code of hemoglobin allostery, Adv. Prot. Chem. 51,

185–253 (1998).

Eaton, W.A., Henry, E.R., Hofrichter, J., Bettati, S., Viappiani, C.,

and Mozzarelli, A., Evolution of allosteric models for hemo-

globin, IUBMB Life 59, 586–589 (2007). [A critical review.]

Fersht, A., Structure and Mechanism in Protein Science, Chapter

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Koshland, D.E., Jr., Némethy, G., and Filmer, D., Comparison of

experimental binding data and theoretical models in proteins

containing subunits, Biochemistry 5, 365–385 (1966). [The

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losteric transitions: A plausible model, J. Mol. Biol. 12, 88–118

(1965). [The exposition of the symmetry model of allosteric

regulation.]

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losteric behaviours of hemoglobin, Biochim. Biophys. Acta

1784, 1146–1158 (2008).

1. The urge to breathe in humans results from a high blood

content; there are no direct physiological sensors of blood

. Skindivers often hyperventilate (breathe rapidly and deeply

for several minutes) just before making a protracted dive in the be-

lief that they will thereby increase the O

content of their blood.

This belief results from the fact that hyperventilation represses the

breathing urge by expelling significant quantities of CO

from the

blood. In light of what you know about the properties of hemoglo-

bin, is hyperventilation a useful procedure? Is it safe? Explain.

2. Explain why the Hill constant, n, can never be larger than

the number of ligand-binding sites on the protein.

*3. In the Bohr effect, protonation of the N-terminal amino

groups of hemoglobin’s ␣ chains is responsible for ⬃30% of the

0.6 mol of H

⫹

that combine with Hb on the release of 1 mol of O

at pH 7.4. Assuming that this group has pK ⫽ 7.0 in oxyHb, what

is its pK in deoxyHb?

4. As one of the favorites to win the La Paz, Bolivia,marathon,

you have trained there for the several weeks it requires to become

adapted to its 3700-m altitude. A manufacturer of running equip-

ment who sponsors an opponent has invited you for the weekend

to a prerace party at a beach house near Lima, Peru, with the as-

surance that you will be flown back to La Paz at least a day before

the race. Is this a token of his respect for you or an underhanded

attempt to handicap you in the race? Explain (see Fig. 10-9).

5. In active muscles, the pO

may be 10 torr at the cell surface

and 1 torr at the mitochondia (the organelles where oxidative me-

tabolism occurs). How might myoglobin (p

⫽ 2.8 torr) facilitate

the diffusion of O

through these cells? Active muscles consume

much faster than do other tissues. Could myoglobin also be an

effective O

-transport protein in other tissues? Explain.

6. Erythrocytes that have been stored for over a week in stan-

dard acid–citrate–dextrose medium become depleted in BPG.

Discuss the merits of using fresh versus week-old blood in blood

transfusions.

7. The following fractional saturation data have been meas-

ured for a certain blood sample:

PROBLEMS

20 0.14 60 0.59

30 0.26 70 0.66

40 0.39 80 0.72

50 0.50 90 0.76

What are the Hill constant and the p

of this blood sample? Are

they normal?

8. An anemic individual, whose blood has only half the normal

Hb content, may appear to be in good health.Yet a normal individ-

ual is incapacitated by exposure to sufficient carbon monoxide to

occupy half of his/her heme sites ( pCO of 1 torr for ⬃1 h; CO

binds to Hb with 200-fold greater affinity than does O

). Explain.

*9. The X-ray structure of Hb Rainier (Tyr 145␤ S Cys) indi-

cates that the mutant Cys residue forms a disulfide bond with Cys

93␤ of the same subunit. This holds the ␤ subunit’s C-terminal

residue in a quite different orientation than it assumes in HbA.

How would the following quantities for Hb Rainier compare with

those of HbA? Explain. (a) The oxygen affinity, (b) the Bohr ef-

fect, (c) the Hill constant, and (d) the BPG affinity.

10. The crocodile, which can remain under water without

breathing for up to 1 h, drowns its air-breathing prey and then

dines at its leisure. An adaptation that aids the crocodile in doing

so is that it can utilize virtually 100% of the O

in its blood,

whereas humans, for example, can extract only ⬃65% of the O

their blood. Crocodile Hb does not bind BPG. However, crocodile

deoxyHb preferentially binds . How does this help the

crocodile obtain its dinner?

11. The gelation time of an equimolar mixture of HbA and HbS

is less than that of a solution of only HbS in the same concentration

HCO

⫺

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358 Chapter 10. Hemoglobin: Protein Function in Microcosm

15. Derive the equilibrium constant for the reaction R

34 T

for a symmetry model n-mer in terms of the parameters L, c,

and ␣.

*16. Derive the equation for the fraction of protein molecules

in the R state, , for the homotropic symmetry model in terms of

the parameters n, L, c, and ␣. Plot this function versus ␣ for n ⫽ 4,

L ⫽ 1000, and c ⫽ 0 and discuss its physical significance.

17. In the symmetry model of allosterism, why must an in-

hibitor (which causes a negative heterotropic effect with the sub-

strate) undergo a positive homotropic effect?

18. At low concentrations, the hemoglobin tetramer re-

versibly dissociates into two ␣

␤

dimers.What is the Hill constant

for O

binding to these dimers? Explain.

19. Describe the nature of the allosteric changes (homotropic

or heterotropic, positive or negative) that take place in the

GroEL/ES system during the various stages of its catalytic cycle

(Fig. 9-25).

that it has in the mixture. What does this observation imply about

the participation of HbA in the gelation of HbS?

12. The severely anemic condition of homozygotes for HbS

results in an elevated BPG content in their erythrocytes. Discuss

whether or not this is a beneficial effect.

13. As organizer of an expedition that plans to climb several

very high mountains, it is your responsibility to choose its mem-

bers. Each of the applicants for one of the positions on the team is

a heterozygote for one of the following variant hemoglobins:

(1) HbS, (2) Hb Hyde Park [His F8(92)␤ S Tyr], (3) Hb

Riverdale–Bronx [Gly B6(24)␤ S Arg], (4) Hb Memphis [Glu

B4(23)␣ S Gln], and (5) Hb Cowtown [His HC3(146)␤ S Leu].

Assuming that all of these candidates are equal in ability at low al-

titudes, which one would you choose for the position? Explain

your reasoning.

14. Show that the Adair equation for a tetramer reduces to

the Hill equation for k

⬇ k

W k

and to a hyperbolic rela-

tionship for k

⫽ k

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359

CHAPTER 11

Sugars and

Polysaccharides

1 Monosaccharides

A. Classification

B. Configurations and Conformations

C. Sugar Derivatives

2 Polysaccharides

A. Carbohydrate Analysis

B. Disaccharides

C. Structural Polysaccharides: Cellulose and Chitin

D. Storage Polysaccharides: Starch and Glycogen

E. Glycosaminoglycans

3 Glycoproteins

A. Proteoglycans

B. Bacterial Cell Walls

C. Glycoprotein Structure and Function

D. Glycomics

weight. Polysaccharides such as starch in plants and glyco-

gen in animals serve as important nutritional reservoirs.

The elucidation of the structures and functions of carbo-

hydrates has lagged well behind those of proteins and nu-

cleic acids. This can be attributed to several factors. Carbo-

hydrate compounds are often heterogeneous, both in size

and in composition, which greatly complicates their physi-

cal and chemical characterization. They are not subject to

the types of genetic analysis that have been invaluable in

the study of proteins and nucleic acids because saccharide

sequences are not genetically specified but are built up

through the sequential actions of specific enzymes (Section

23-3B). Furthermore, it has been difficult to establish as-

says for the biological activities of polysaccharides because

of their largely passive roles. Nevertheless, it is abundantly

clear that carbohydrates are essential elements in many, if

not most, biological processes.

In this chapter, we explore the structures, chemistry,

and, to a limited extent, the functions of carbohydrates,

alone and in association with proteins. Glycolipid struc-

tures are considered in Section 12-1D. The biosynthesis of

complex carbohydrates is discussed in Section 23-3.

1 MONOSACCHARIDES

Monosaccharides or simple sugars are aldehyde or ketone

derivatives of straight-chain polyhydroxy alcohols contain-

ing at least three carbon atoms. Such substances, for exam-

ple,

D-glucose and D-ribulose, cannot be hydrolyzed to

form simpler saccharides.

In this section, the structures of the monosaccharides and

some of their biologically important derivatives are dis-

cussed.

HO HC

HCOH

D-Glucose

HCOH

D-Ribulose

Carbohydrates or saccharides (Greek: sakcharon, sugar)

are essential components of all living organisms and are, in

fact, the most abundant class of biological molecules. The

name carbohydrate, which literally means “carbon hy-

drate,” stems from their chemical composition, which is

roughly (C ⴢ H

, where n ⱖ 3. The basic units of carbo-

hydrates are known as monosaccharides. Many of these

compounds are synthesized from simpler substances in a

process named gluconeogenesis (Section 23-1). Others

(and ultimately nearly all biological molecules) are the

products of photosynthesis (Section 24-3), the light-powered

combination of CO

and H

O through which plants and

certain bacteria form “carbon hydrates.” The metabolic

breakdown of monosaccharides (Chapters 17 and 21)

provides much of the energy used to power biological

processes. Monosaccharides are also principal components

of nucleic acids (Section 5-1A), as well as important ele-

ments of complex lipids (Section 12-1D).

Oligosaccharides consist of a few covalently linked

monosaccharide units. They are often associated with pro-

teins (glycoproteins) and lipids (glycolipids) in which they

have both structural and regulatory functions (glycopro-

teins and glycolipids are collectively called glycoconju-

gates). Polysaccharides consist of many covalently linked

monosaccharide units and have molecular masses ranging

well into the millions of daltons. They have indispensable

structural functions in all types of organisms but are most

conspicuous in plants because cellulose, their principal

structural material, comprises up to 80% of their dry

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360 Chapter 11. Sugars and Polysaccharides

A. Classification

Monosaccharides are classified according to the chemical

nature of their carbonyl group and the number of their C

atoms. If the carbonyl group is an aldehyde, as in glucose,

the sugar is an aldose. If the carbonyl group is a ketone, as

in ribulose, the sugar is a ketose. The smallest monosaccha-

rides, those with three carbon atoms, are trioses. Those

with four, five, six, seven, etc., C atoms are, respectively, tet-

roses, pentoses, hexoses, heptoses, etc. These terms may be

combined so that, for example, glucose is an aldohexose,

whereas ribulose is a ketopentose.

Examination of

D-glucose’s molecular formula indicates

that all but two of its six C atoms¬C1 and C6¬are chiral

centers, so that

D-glucose is one of 2

⫽ 16 stereoisomers

that comprise all possible aldohexoses. In general, n-carbon

aldoses have 2

n⫺2

stereoisomers. The stereochemistry and

names of the

D-aldoses are presented in Fig. 11-1. Emil

Fischer elucidated these configurations for the aldohexoses in

1896.According to the Fischer convention (Section 4-2B),

sugars have the same absolute configuration at the asymmet-

ric center farthest removed from their carbonyl group as does

D-glyceraldehyde. The L sugars, in accordance with this con-

vention, are mirror images of their

D counterparts, as is

shown below in Fischer projection for glucose.

HO HC

HCOH

HOHC

HO C H

HO C

D-Glucose

L-Glucose

Figure 11-1 The stereochemical relationships, shown in

Fischer projection, among the

D-aldoses with three to six carbon

atoms. The arrows indicate stereochemical relationships (not

biosynthetic reactions).The configuration about C2 (red)

CHO

HCOH

D-Glyceraldehyde

HCOH

HOCH

HCOH

D-Allose

HCOH

HOCH

D-Altrose

HCOH

HOCH

D-Glucose

(Glc)

HCOH

CHO

HOCH

D-Talose

HCOH

CHO

HOCH

D-Mannose

(Man)

HOCH

HCOH

HOCH

D-Gulose

HCOH

HOCH

D-Idose

HOCH

HCOH

HOCH

D-Galactose

(Gal)

HOCH

D-Lyxose (Lyx)D-Ribose (Rib)

D-Arabinose (Ara)

D-Xylose (Xyl)

HCOH

HOCH

HCOH

HOCH

HCOH

HOCH

HCOH

D-ThreoseD-Erythrose

Aldotriose

Aldotetroses

Aldopentoses

Aldohexoses

distinguishes the members of each pair.The L- counterparts of

these 15 sugars are their mirror images.The biologically most

common aldoses are boxed.

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