Voet D., Voet Ju.G. Biochemistry

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F. Structural Basis of BPG Binding

BPG decreases the oxygen-binding affinity of Hb by prefer-

entially binding to its deoxy state (Section 10-1D). The

binding of the physiologically quadruply charged BPG to

deoxyHb is weakened by high salt concentrations, which

suggests that this association is ionic in character. This ex-

planation is corroborated by the X-ray structure of a BPG–

deoxyHb complex, which indicates that BPG binds in the

central cavity of deoxyHb on its 2-fold axis (Fig. 10-21).The

anionic groups of BPG are within hydrogen bonding and

salt bridging distances of the cationic Lys EF6(82), His

H21(143), His NA2(2), and N-terminal amino groups of

both ␤ subunits (Fig. 10-21). The T S R transformation

brings the two ␤ H helices together, which narrows the cen-

tral cavity (compare Figs. 10-13a and 10-13b) and expels the

BPG. It also widens the distance between the ␤ N-terminal

amino groups from 16 to 20 Å, which prevents their simul-

taneous hydrogen bonding with BPG’s phosphate groups.

BPG therefore stabilizes the T conformation of Hb by cross-

linking its ␤ subunits. This shifts the T 34 R equilibrium to-

ward the T state, which lowers hemoglobin’s O

affinity.

The structure of the BPG–deoxyHb complex also indi-

cates why fetal hemoglobin (HbF) has a reduced affinity

for BPG relative to HbA (Section 10-1D).The cationic His

H21(143)␤ of HbA is changed to an uncharged Ser residue

in HbF’s ␤-like ␥ subunit, thereby eliminating a pair of

ionic interactions stabilizing the BPG–deoxyHb complex

(Fig. 10-21).

The excess positive charge lining Hb’s central cavity is

also partially responsible for the allosteric effect of Cl

⫺

ions in stabilizing the T state relative to the R state (the re-

mainder being due to the participation of Cl

⫺

in the T-state

salt bridge networks; Fig. 10-18a). The central cavity is

larger in the T state than in the R state (Fig. 10-13), so that

more Cl

⫺

ions occupy this channel in the T state than in the

R state. The additional Cl

⫺

ions, through electrostatic

shielding, reduce the mutual repulsions of the positive

charges, thereby stabilizing the T state.

G. Role of the Distal Histidine Residue

binding paradoxically protects the heme iron from au-

tooxidation: The rate of Mb oxidation decreases as the

partial pressure of O

increases. This is because heme iron

oxidation is catalyzed by protons that are reduced by the

heme iron and that in turn reduce O

in the solvent to su-

peroxide ion (O

). Bound O

evidently shields the Fe

from the attacking protons.

The mutagenic replacement of the distal His residue in

Mb by any other residue reduces Mb’s oxygen affinity and

increases its rate of autooxidation.Asp, a proton source, at

this position increases the rate of Mb autooxidation by 350-

fold, the largest increase of all residue replacements,

whereas Phe, Met, and Arg provide only 50-fold accelera-

tions, the smallest observed increases.The imidazole ring of

the distal His, which has a pK of 5.5 and is therefore neutral

at neutral pH and whose unprotonated N

atom faces the

heme pocket (Fig. 10-12), acts as a proton trap, thereby

ⴢ

⫺

protecting the Fe from protons. Thus, to quote Perutz,

“Evolution is a brilliant chemist.”

3 ABNORMAL HEMOGLOBINS

Mutant hemoglobins provided the original opportunity to

study structure–function relationships in proteins because

Hb is a readily isolated protein of known structure that has

a large number of well-characterized naturally occurring

variants. The examination of individuals with physiological

disabilities, together with the routine electrophoretic

screening of human blood samples, has led to the discovery

of over 1000 variant hemoglobins, ⬎90% of which result

from single amino acid substitutions in a globin polypeptide

Section 10-3. Abnormal Hemoglobins 341

Figure 10-21 Binding of BPG to deoxyHb. The view is down

the molecule’s exact twofold axis (the same view as in Fig. 10-13a).

BPG (red), with its five anionic groups, binds in the central cavity

of deoxyHb, where it is surrounded by a ring of eight cationic

side chains (blue) extending from the two ␤ subunits. In the R

state, the central cavity is too narrow to admit BPG (Fig. 10-13b).

The arrangement of salt bridges and hydrogen bonds between

the ␣

and ␤

subunits that partially stabilizes the T state (Fig.

10-18b) is indicated at the lower right. [Illustration, Irving Geis.

Image from the Irving Geis Collection, Howard Hughes Medical

Institute. Reprinted with permission.]

See Kinemage

Exercise 6-3

JWCL281_c10_323-358.qxd 8/10/10 9:41 AM Page 341

chain (a compendium of variant human hemoglobins is lo-

cated at http://globin.cse.psu.edu/). In this section, we con-

sider the nature of these hemoglobinopathies. Hemoglobin

diseases characterized by defective globin synthesis, the

thalassemias, are the subject of Section 34-2G. It should be

noted that ⬃300,000 individuals with serious hemoglobin

disorders are born every year and that ⬃5% of the world’s

population are carriers of an inherited variant hemoglobin.

A. Molecular Pathology of Hemoglobin

The physiological effect of an amino acid substitution on

Hb can, in most cases, be understood in terms of its molec-

ular location:

1. Changes in surface residues

Changes of surface residues are usually innocuous because

most of these residues have no specific functional role

[although sickle-cell Hb (HbS) is a glaring exception to this

generalization; Section 10-3Ba]. For example, HbE [Glu

B8(26)␤ S Lys], the most common human Hb mutant af-

ter HbS (possessed by up to 10% of the population in parts

of Southeast Asia), has no clinical manifestations in either

heterozygotes or homozygotes. About half of the known

Hb mutations are of this type and have been discovered

only accidentally or through surveys of large populations.

2. Changes in internally located residues

Changing an internal residue often destabilizes the Hb

molecule. The degradation products of these hemoglobins,

particularly those of heme, form granular precipitates

(known as Heinz bodies) that hydrophobically adhere to

the erythrocyte cell membrane. The membrane’s perme-

ability is thereby increased, causing premature cell lysis.

Carriers of unstable hemoglobins therefore suffer from

hemolytic anemia of varying degrees of severity.

The structure of Hb is so delicately balanced that small

structural changes may render it nonfunctional.This can oc-

cur through the weakening of the heme–globin association

or as a consequence of other conformational changes. For in-

stance, the heme group is easily dislodged from its closely fit-

ting hydrophobic binding pocket. This occurs in Hb Ham-

mersmith (Hb variants are often named after the locality of

their discovery), in which Phe CD1(42)␤, an invariant

residue that wedges the heme into its pocket (see Fig.10-12),

is replaced by Ser. The resulting gap permits water to enter

the heme pocket, which causes the hydrophobic heme to

drop out easily (Phe CD1 and the proximal His F8 are the

only invariant residues among all known hemoglobins).Sim-

ilarly, in Hb Bristol, the substitution of Asp for Val E11(67)␤,

which partially occludes the O

pocket, places a polar group

in contact with the heme. This weakens the binding of the

heme to the protein, probably by facilitating the access of

water to the subunit’s otherwise hydrophobic interior.

Hb may also be destabilized by the disruption of ele-

ments of its 2°, 3°, and/or 4° structures.The instability of Hb

Bibba results from the substitution of a helix-breaking Pro

for Leu H19(136)␣. Likewise, the instability of Hb Savan-

nah is caused by the substitution of Val for the highly con-

served Gly B6(24)␤, which is located on the B helix where

it crosses the E helix with insufficient clearance for side

chains larger than an H atom (Fig. 10-13). The ␣

–␤

con-

tact, which does not significantly dissociate under physio-

logical conditions, may do so on structural alteration. This

occurs in Hb Philly, in which Tyr C1(35)␤, which partici-

pates in the hydrogen bonded network that helps knit to-

gether the ␣

–␤

interface, is replaced by Phe.

3. Changes stabilizing methemoglobin

Changes at the O

-binding site that stabilize the heme in the

Fe(III) oxidation state eliminate the binding of O

to the de-

fective subunits. Such methemoglobins are designated

HbM and individuals carrying them are said to have

methemoglobinemia. These individuals usually have bluish

skin, a condition known as cyanosis, which results from the

presence of deoxyHb in their arterial blood.

All known methemoglobins arise from substitutions that

provide the Fe atom with an anionic oxygen atom ligand. In

Hb Boston, the substitution of Tyr for His E7(58)␣ (the dis-

tal His, which protects the heme from oxidation; Section 10-

2G) results in the formation of a 5-coordinate Fe(III) com-

plex, with the phenolate ion of the mutant Tyr E7 displacing

the imidazole ring of His F8(87) as the apical ligand (Fig.10-

22a). In Hb Milwaukee, the ␥-carboxyl group of the Glu

that replaces Val E11(67)␤ forms an ion pair with a 5-coor-

dinate Fe(III) complex (Fig. 10-22b). Both the phenolate

and glutamate ions in these methemoglobins so stabilize the

Fe(III) oxidation state that methemoglobin reductase is in-

effective in converting them to the Fe(II) form.

Individuals with HbM are alarmingly cyanotic and have

blood that is chocolate brown, even when their normal sub-

units are oxygenated. In northern Japan, this condition is

named “black mouth” and has been known for centuries;it is

caused by the presence of HbM Iwate [His F8(87)␣ S Tyr].

Methemoglobins have Hill constants of ⬃1.2.This indicates

a reduced cooperativity in comparison with HbA even

though HbM, which can bind only two oxygen molecules,

can have a maximum Hill constant of 2 (the unmutated ␣ or

␤ chains remain functional). Surprisingly, heterozygotes with

HbM, which have an average of one nonfunctional ␣ or ␤

subunit per Hb molecule, have no apparent physical disabil-

ities. Evidently, the amount of O

released in their capillaries

is within normal limits. Homozygotes of HbM, however, are

unknown; this condition is, no doubt, lethal.

4. Changes at the ␣

–␤

contact

Changes at the ␣

–␤

contact often interfere with hemoglo-

bin’s quaternary structural changes. Most such hemoglobins

have an increased O

affinity so that they release less than

normal amounts of O

in the tissues. Individuals with such

defects compensate for it by increasing their hematocrit

(concentration of erythrocytes in their blood). This condi-

tion, which is named polycythemia, often gives them a

ruddy complexion. Some amino acid substitutions at the

␣

–␤

interface instead result in a reduced O

affinity. Indi-

viduals carrying such hemoglobins are cyanotic.

Amino acid substitutions at the ␣

–␤

contact may change

the relative stabilities of hemoglobin’s R and T forms,

342 Chapter 10. Hemoglobin: Protein Function in Microcosm

JWCL281_c10_323-358.qxd 2/24/10 1:58 PM Page 342

thereby altering its O

affinity. For example, the replacement

of Asp G1(99)␤ by His in Hb Yakima eliminates the hydro-

gen bond at the ␣

–␤

contact that stabilizes the T form of Hb

(Fig. 10-17a). The interloping imidazole ring also acts as a

wedge that pushes the subunits apart and displaces them to-

ward the R state.This change shifts the T S R equilibrium al-

most entirely to the R state, which results in Hb Yakima hav-

ing an increased O

affinity (p

⫽ 12 torr under physiological

conditions vs 26 torr for HbA) and a total lack of cooperativ-

ity (Hill constant ⫽ 1.0). In contrast, the replacement of Asn

G4(102)␤ by Thr in Hb Kansas eliminates the hydrogen bond

in the ␣

–␤

contact that stabilizes the R state (Fig.10-17b),so

that this Hb variant remains in the T state on binding O

.Hb

Kansas therefore has a low O

affinity (p

⫽ 70 torr) and a

low cooperativity (Hill constant ⫽ 1.3).

B. Molecular Basis of Sickle-Cell Anemia

Most harmful Hb variants occur in only a few individuals,

in many of whom the mutation apparently originated.

However, ⬃10% of American blacks and as many as 25%

of African blacks are heterozygotes for sickle-cell hemo-

globin (HbS). HbS arises, as we have seen (Section 7-3Aa),

from the substitution of a hydrophobic Val residue for the

hydrophilic surface residue Glu A3(6)␤ (Fig. 10-13). The

prevalence of HbS results from the protection it affords

heterozygotes against malaria. However, homozygotes for

HbS, of which there are ⬃ 50,000 in the United States, are

severely afflicted by hemolytic anemia together with painful,

debilitating, and sometimes fatal blood flow blockages

caused by the irregularly shaped and inflexible erythro-

cytes characteristic of the disease (Fig. 7-19b).

a. HbS Fibers Are Stabilized by Intermolecular

Contacts Involving Val ␤6 and Other Residues

The sickling of HbS-containing erythrocytes results from

the aggregation (polymerization) of deoxyHbS into rigid

fibers that extend throughout the length of the cell (Fig. 10-23).

Section 10-3. Abnormal Hemoglobins 343

Figure 10-22 Mutations stabilizing the Fe(III) oxidation state

of heme. (a) Alterations in the heme pocket of the ␣ subunit on

changing from deoxyHbA to Hb Boston [His E7(58)␣ S Tyr].

The phenolate ion of the mutant Tyr becomes the fifth ligand of

the Fe atom, thereby displacing the proximal His [F8(87)a].

[After Pulsinelli, P.D., Perutz, M.F., and Nagel, R.L., Proc. Natl.

HbA

(a) (b)

Hb Boston

Heme

E Helix

His E7

Tyr E7

α Subunit

F Helix

β Subunit

His F8

G Helix G Helix

Glu E11

His E7

E Helix

Heme

Val E11

–

Milwaukee

Boston

Acad. Sci. 70, 3870 (1973).] (b) The structure of the heme pocket

of the ␤ subunit in Hb Milwaukee [Val E11(67)␤ S Glu]. Here

the mutant Glu residue’s carboxyl group forms an ion pair with

the heme iron atom so as to stabilize its Fe(III) state. [From

Perutz, M.F., Pulsinelli, P.D., and Ranney, H.M., Nature New Biol.

237, 259 (1972).]

Figure 10-23 Electron micrograph of deoxyHbS fibers spilling

out of a ruptured erythrocyte. [Courtesy of Robert Josephs,

University of Chicago.]

JWCL281_c10_323-358.qxd 2/24/10 1:58 PM Page 343

Electron microscopy indicates that these fibers are

⬃220-Å-diameter elliptical rods consisting of 14 hexago-

nally packed and helically twisting strands of deoxyHbS

molecules that associate in parallel pairs (Figs. 10-24 and

10-25a).

The structural relationship among the HbS molecules in

the pairs of parallel HbS strands has been established by

the X-ray structure analysis of deoxyHbS crystals. When

this crystal structure was first determined, it was unclear

whether the intermolecular contacts in the crystal resem-

bled those in the fiber. However, the subsequent observa-

tion that HbS fibers slowly convert to these crystals with

little change in their overall X-ray diffraction pattern indi-

cates that the fibers structurally resemble the crystals. The

crystal structure of deoxyHbS consists of double filaments

of HbS molecules whose several different intermolecular

contacts are diagrammed in Fig. 10-25b. Only one of the

two Val 6␤’s per Hb molecule contacts a neighboring mol-

ecule. In this contact, the mutant Val side chain occupies a

hydrophobic surface pocket on the ␤ subunit of an adja-

cent molecule whose Val 6␤ does not make an intermolec-

ular contact (Fig. 10-25c). This pocket is absent in oxyHb.

Other contacts involve residues that also occur in HbA, in-

cluding Asp 73␤ and Glu 23␣ (Fig. 10-25b). The observa-

tion that deoxyHbA does not aggregate into fibers, how-

ever, even at very high concentrations, indicates that the

contact involving Val 6b is essential for fiber formation.This

conclusion is corroborated by the observation that a genet-

ically engineed human Hb in which Glu 6␤ is replaced by

Ile (which differs from Val by an additional CH

group and

is therefore even more hydrophobic) has half the solubility

of HbS in 1.8M phosphate.

The importance of the other intermolecular contacts to

the structural integrity of HbS fibers has been demon-

strated by studying the effects of other mutant hemoglo-

bins on HbS gelation (polymerization). For example, the

doubly mutated Hb Harlem (Glu 6␤ S Val ⫹ Asp

73␤ S Asn) requires a higher concentration to gel than does

HbS (Glu 6␤ S Val); similarly, mixtures of HbS and Hb

Korle-Bu (Asp 73␤ S Asn) gel less readily than equivalent

344 Chapter 10. Hemoglobin: Protein Function in Microcosm

Figure 10-24 The 220-Å-diameter fibers of deoxyHbS. (a) An

electron micrograph of a negatively stained fiber.The

accompanying cutaway interpretive drawing indicates the

relationship between the inner and outer strands; each sphere

represents an individual HbS molecule. The fiber has a layer

repeat distance of 64 Å and a moderate twist such that it repeats

every 350 Å along the fiber axis. [Courtesy of Stuart Edelstein,

University of Geneva.] (b) A model, viewed in cross section, of

the HbS fiber based on the crystal structure of HbS and three-

dimensional reconstructions of electron micrographs of HbS

fibers.The residues in the 14 HbS molecules are represented by

spheres centered on their C

␣

positions.The residues making

inter-double strand, intra-double strand lateral, and intra-double

strand axial contacts are colored red, green, and blue, respectively,

with lighter and darker toned residues making intermolecular

contacts of ⬍8 Å and ⬍5 Å, respectively. The ␣ and ␤ chain

residues outside the contact regions are colored white. [Courtesy

of Stanley Watowich, Leon Gross, and Robert Josephs,

University of Chicago.]

(b)

JWCL281_c10_323-358.qxd 2/24/10 1:58 PM Page 344

mixtures of HbS and HbA.These observations suggest that

Asp 73␤ occupies an important intermolecular contact site

in HbS fibers (Fig. 10-25b). Likewise, the observation that

hybrid tetramers consisting of ␣ subunits from Hb Memphis

(Glu 23␣ S Gln) and ␤ subunits from HbS gel less readily

than does HbS indicates that Glu 23␣ also participates in

the polymerization of HbS fibers (Fig. 10-25b). The other

white-lettered residues in Fig. 10-25b have been similarly

implicated in sickling interactions.

b. The Initiation of HbS Gelation Is

a Complex Process

The gelation of HbS, both in solution and within the red

cell, follows an unusual time course.A solution of HbS can

be brought to conditions under which it will gel by lower-

ing the pO

, raising the HbS concentration, and/or raising

the temperature. On achieving gelation conditions, there is a

reproducible delay that varies according to conditions from

milliseconds to days: During this time, no HbS fibers can be

Section 10-3. Abnormal Hemoglobins 345

Figure 10-25 Structure of the deoxyHbS fiber. (a) The

arrangement of the deoxyHbS molecules in the fiber.The yellow

dots represent the side chains of Glu 6␤

. [Illustration, Irving

Geis/Geis Archives Trust. Copyright Howard Hughes Medical

Institute. Reproduced with permission.] (b) A schematic diagram

indicating the intermolecular contacts in the crystal structure of

deoxyHbS. The white-lettered residues are implicated in forming

these contacts. Note that the only intermolecular association in

which the mutant residue Val 6␤ participates involves subunit ␤

;

63 Å

His

116

Pro 114

( C=0)

Glu

121

Glu

121

Asp 73

Val 6

Thr 4

His

Gly

Glu

Phe

Leu

Val 6

Leu

Phe

(c)

(a)

(b)

Val 6 of subunit ␤

is free. [After Wishner, B.C.,Ward, K.B.,

Lattman, E.E., and Love,W.E., J. Mol. Biol. 98, 192 (1975).]

fits neatly into a hydrophobic pocket

formed mainly by Phe 85 and Leu 88 of an adjacent ␤

subunit.

This pocket, which is located between helices E and F at the

periphery of the heme pocket, is absent in oxyHb and is too

hydrophobic to contain the normally occurring Glu 6␤ side chain.

[Illustration, Irving Geis. Image from the Irving Geis Collection,

Howard Hughes Medical Institute. Reprinted with permission.]

JWCL281_c10_323-358.qxd 8/10/10 9:41 AM Page 345

detected. Only after the delay do fibers first appear, and

gelation is then completed in about half the delay time

(Fig. 10-26a).

William Eaton and James Hofrichter discovered that the

delay time, t

, has a concentration dependence described by

[10.13]

where c

is the total deoxyHbS concentration prior to gela-

tion, c

is the solubility of deoxyHbS measured after gela-

tion is complete, and k and n are constants. Graphical

analysis of the data indicates that k ⬇ 10

⫺7

⫺1

and that n is

between 30 and 50 (Fig. 10-26b). This is a remarkable re-

sult: No other known solution process even approaches a

30th power concentration dependence.

A two-stage process accounts for Eq. [10.13]:

1. At first, HbS molecules sequentially aggregate to

form a nucleus consisting of m HbS molecules (Fig. 10-27a):

Prenuclear aggregates are unstable and easily decompose,

but once a nucleus has formed it assumes a stable structure

that rapidly elongates to form an HbS fiber.

2. Once a fiber has formed, it can nucleate the growth

of other fibers (Fig. 10-27b). These newly formed fibers, in

turn, nucleate the growth of yet other fibers, etc., so that

this latter process is autocatalytic.

The initial homogeneous nucleation process (taking place

in solution) accounts for the very high concentration de-

pendence in Eq. [10.13], whereas the secondary heteroge-

neous nucleation process (taking place on a surface—that

of a fiber in this case) is responsible for the rapid onset of

gelation (Fig. 10-26a).

Δ (HbS)

Growth

HbS Δ (HbS)

Δ (HbS)

⫽ k a

The foregoing kinetic hypothesis suggests why sickle-

cell anemia is characterized by episodic “crises” caused by

blood flow blockages. HbS fibers dissolve essentially in-

stantaneously on oxygenation, so that none are present in

arterial blood. Erythrocytes take from 0.5 to 2 s to pass

through the capillaries, where deoxygenation renders HbS

insoluble. If the delay time, t

, for sickling is greater than

this transit time, no blood flow blockage occurs (although

sickling that occurs in the veins damages the erythrocyte

membrane). However, Eq. [10.13] indicates that small in-

creases in HbS concentration, c

, and/or small decreases in

HbS solubility, c

, caused by conditions known to trigger

sickle-cell crises, such as dehydration, O

deprivation, and

fever, result in significant decreases of t

. Once a blockage

occurs, the resulting lack of O

and slowdown of blood flow

in the area compound the situation.

The kinetic hypothesis of sickling has profound clinical

implications for the treatment of sickle-cell anemia. Het-

erozygotes of HbS, whose blood usually contains ⬃60%

HbA and 40% HbS, rarely show any symptoms of sickling.

The t

for the gelation of their Hb is ⬃10

-fold greater than

that of homozygotes.Accordingly, a treatment of sickle-cell

anemia that increases t

by this amount, which corresponds

to decreasing the ratio c

by a factor of ⬃1.6, would re-

lieve the symptoms of this disease.This has suggested three

different therapeutic strategies (besides gene therapy; Sec-

tion 5-5Hb) to increase t

, and thus inhibit HbS gelation:

1. The disruption of intermolecular interactions, thus in-

creasing c

. Of particular interest are compounds that have

been designed with the aid of the X-ray structure of HbS to

bind stereospecifically to its intermolecular contact regions.

However, a large amount of any such compound would be

necessary to bind to the ⬃400 g of hemoglobin in the human

body. Consequently, no antisickling drug yet tested has had a

sufficiently high ratio of efficacy to toxicity to merit clinical use.

346 Chapter 10. Hemoglobin: Protein Function in Microcosm

Figure 10-26 Time course of deoxyHbS gelation. (a) The

extent of gelation as monitored calorimetrically (yellow) and

optically (purple). Gelation of the 0.233 g ⴢ mL

⫺1

deoxyHbS

solution was initiated by rapidly increasing the temperature from

0ºC, where HbS is soluble, to 20ºC; t

is the delay time. (b) A

1.0

0.5

0 100 200 300

Time (min)

Fractional change

Calorimetric

Optical

(a)

1.30 1.35 1.40

0.001

0.01

0.1

1/t

(min

-1

)

log c

Slope≈30

(b)

log–log plot showing the concentration dependence of 1/t

for

the gelation of deoxyHbS at 30ºC.The slope of this line is ⬃30.

[After Hofrichter, J., Ross, P.D., and Eaton, W.A., Proc. Natl.

Acad. Sci. 71, 4865, 4867 (1974).]

JWCL281_c10_323-358.qxd 2/24/10 1:58 PM Page 346

2. The use of agents that increase hemoglobin’s O

affin-

ity, thus decreasing c

. For example, the administration of

cyanate carbamoylates the N-terminal amino groups of Hb

(Fig. 10-20). This treatment eliminates some of the salt

bridges that stabilize the T state (Section 10-2E) and thereby

increases the O

affinity of Hb.Although cyanate is an effec-

tive in vitro antisickling agent, its clinical use has been dis-

continued because of toxic side effects, cataract formation

and peripheral nervous system damage, that probably result

from the carbamoylation of proteins other than Hb.

3. Lowering the HbS concentration (c

) in erythrocytes.

Agents that alter erythrocyte membrane permeability so as

to permit the influx of water have promise in this regard.

The first, and as yet the only, effective treatment for

sickle-cell anemia is a variation of the latter strategy

through the administration of hydroxyurea.

Adults with sickle-cell anemia have two types of red blood

cells: S cells, which contain only HbS; and F cells, which

Hydroxyurea

CNHOH

contain ⬃20% HbF and the remainder HbS. In most

adults, the fraction of F cells is ⬃30%. However, in those

treated with hydroxyurea, this fraction increases to ⬃50%.

Although the mechanism by which hydroxyurea stimulates

the production of F cells is unknown, the mechanism by

which increased levels of F cells prevent sickling seems

clear. F cells contain three species of hemoglobin: HbS

(␣

␤

), HbF (␣

␥

), and their hybrid (␣

␤

␥), where ␤

sub-

units are the sickle-cell variants of the normal ␤ subunits.

Since neither HbF nor the ␣

␤

␥ hybrid Hb can form

sickle-cell fibers, they act to dilute the HbS in a cell.This, in

turn, increases the time it takes the F cells to sickle by a fac-

tor of ⬃1000, so that F cells do not significantly sickle in the

period (10–20 s) it takes them pass from the tissues to the

lungs, where they are oxygenated.Thus, the greater the pro-

portion of F cells in the blood,the smaller the proportion of

S cells that can sickle.

4 ALLOSTERIC REGULATION

One of the outstanding characteristics of life is the high de-

gree of control exercised in almost all of its processes.

Through a great variety of regulatory mechanisms, the

Section 10-4. Allosteric Regulation 347

(a) Homogeneous nucleation

(b) Heterogeneous nucleation

Growth of

thermodynamically

unstable aggregates

Critical

nucleus

Increasing

stability and

rapid growth

Figure 10-27 Double nucleation mechanism for deoxyHbS

gelation. (a) The initial aggregation of HbS molecules (spheres)

occurs very slowly because this process is thermodynamically

unfavorable and hence the intermediates tend to decompose

rather than grow. However, once an aggregate reaches a certain

size, the critical nucleus, its further growth becomes

thermodynamically favorable, leading to rapid fiber formation.

(b) Each fiber, in turn, can nucleate the growth of other fibers,

leading to the explosive appearance of polymer. [After Ferrone,

F.A., Hofrichter, J., and Eaton,W.A., J. Mol. Biol. 183, 614 (1985).]

JWCL281_c10_323-358.qxd 2/24/10 1:58 PM Page 347

exploration of which constitutes a significant portion of

this textbook, an organism is able to respond to changes in

its environment, maintain intra- and intercellular commu-

nications, and execute an orderly program of growth and

development. Regulation is exerted at every organiza-

tional level in living systems, from the control of rates of

reactions on the molecular level, through the control of ex-

pression of genetic information on the cellular level, to the

control of behavior on the organismal level. It is therefore

not surprising that many, if not most, diseases are caused by

aberrations in biological control processes.

Our exploration of the structure and function of hemo-

globin continues with a theoretical discussion of the regu-

lation of ligand binding to proteins through allosteric inter-

actions (Greek: allos, other ⫹ stereos, solid or space).These

cooperative interactions occur when the binding of one lig-

and at a specific site is influenced by the binding of another

ligand, known as an effector or modulator, at a different

(allosteric) site on the protein. If the ligands are identical,

this is known as a homotropic effect, whereas if they are

different, it is described as a heterotropic effect. These

effects are termed positive or negative depending on

whether the effector increases or decreases the protein’s

ligand-binding affinity.

Hemoglobin, as we have seen, exhibits both homotropic

and heterotropic effects. The binding of O

to Hb results in

a positive homotropic effect since it increases hemoglo-

bin’s O

affinity. In contrast, BPG, CO

⫹

, and Cl

⫺

are

negative heterotropic effectors of O

binding to Hb be-

cause they decrease its affinity for O

(negative) and are

chemically different from O

(heterotropic). The O

affin-

ity of Hb, as we have seen, depends on its quaternary struc-

ture. In general, allosteric effects result from interactions

among subunits of oligomeric proteins.

Even though hemoglobin catalyzes no chemical reac-

tion, it binds ligands in the same manner as do enzymes.

Since an enzyme cannot catalyze a reaction until after it

has bound its substrate(s) [the molecule(s) undergoing re-

action], the enzyme’s catalytic rate varies with its substrate-

binding affinity. Consequently, the cooperative binding of

to Hb is taken as a model for the allosteric regulation of

enzyme activity. Indeed, in this section, we shall consider

several models of allosteric regulation that, for the most

part, were formulated to explain the O

-binding properties

of Hb. Following this, we shall compare these models with

the realities of Hb behavior.

A. The Adair Equation

The derivation of the Hill equation (Section 10-1B) is pred-

icated on the assumption of all-or-none O

binding.The ob-

servation of partially oxygenated Hb molecules, however,

led Gilbert Adair, in 1924, to propose that the binding of

ligands to proteins occurs sequentially with dissociation

constants that are not necessarily equal.The expression for

the saturation function under this model is straightfor-

wardly derived.

For a protein such as Hb with four ligand-binding sites,

the reaction sequence is

where the K

are the macroscopic or apparent dissociation

constants for binding the ith ligand to the protein,

[10.14]

and the k

are the microscopic or intrinsic dissociation con-

stants, that is, the individual dissociation constants for the

ligand-binding sites.The intrinsic dissociation constants are

equal to the apparent dissociation constants multiplied by

statistical factors, 4, and that account for the number

of ligand-binding sites on the protein molecule. The statis-

tical factor 4 derives from the fact that a tetrameric protein

E bears four sites that can bind ligand to form ES (that is,

the concentration of ligand-binding sites is 4[E]) but only

one site from which ES can dissociate ligand to form E

(that is, the concentration of bound ligand is 1[E]); the sta-

tistical factor is a result of there being three remaining

sites on ES that can bind ligand to form ES

and two sites

from which ES

can dissociate ligand to form ES; etc. In

general, for a protein with n equivalent binding sites:

[10.15]

since (n ⫺ i ⫹ 1)[ES

i⫺1

] is the concentration of free ligand-

binding sites in ES

i⫺1

and i[ES

] is the concentration of

bound ligand on ES

.Therefore,solving sequentially for the

concentration of each protein–ligand species in a tetrameric

protein, we obtain:

The fractional saturation of ligand binding, the fraction of

occupied ligand-binding sites divided by the total concen-

tration of ligand-binding sites, is expressed

[10.16]

so that, substituting in the above relationships and cancel-

ing terms, we obtain

[10.17]

This is the Adair equation for four ligand-binding sites.

Equations describing ligand binding to proteins with dif-

ferent numbers of binding sites are similarly derived.

If the microscopic dissociation constants of the Adair

equation are not equal, the fractional saturation curve will

⫽

[S]

⫹

3[S]

⫹

3[S]

⫹

[S]

1 ⫹

4[S]

⫹

6[S]

⫹

4[S]

⫹

[S]

⫽

[ES] ⫹ 2[ES

] ⫹ 3[ES

] ⫹ 4[ES

]

4([E] ⫹ [ES] ⫹ [ES

] ⫹ [ES

])

[ES

] ⫽ [ES

][S]>K

⫽

[ES

][S]>k

⫽ [E] [S]

[ES

] ⫽ [ES

][S]>K

⫽

[ES

][S]>k

⫽ 4[E][S]

[ES

] ⫽ [ES][S]>K

⫽

[ES][S]>k

⫽ 6[E][S]

[ES] ⫽ [E][S]>K ⫽ 4[E][S]>k

⫽

(n ⫺ i ⫹ 1)[ES

i⫺1

][S]

i[ES

]

⫽ a

n ⫺ i ⫹ 1

⫽

[ES

i⫺1

][S]

[ES

]

⫹ S Δ ES

⫽

⫹ S Δ ES

⫽

ES ⫹ S Δ ES

⫽

E⫹ S Δ ES

⫽ 4K

348 Chapter 10. Hemoglobin: Protein Function in Microcosm

JWCL281_c10_323-358.qxd 2/24/10 1:58 PM Page 348

describe cooperative ligand binding. Decreasing and in-

creasing values of these constants lead to positive and neg-

ative cooperativity, respectively. Of course, the values of

the microscopic dissociation constants may also alternate

so that, for example, k

⬍ k

⬎ k

⬍ k

In our discussion of the O

-dissociation curve of Hb

(Section 10-1B), we have seen how its values of k

and k

may be obtained by extrapolating the lower and upper

asymptotes of the Hill plot to the log pO

axis. The remain-

ing microscopic dissociation constants can be evaluated by

fitting Eq. [10.17] to the Hill plot.The values of these Adair

constants for Hb are given in Table 10-2. Note that k

is rel-

atively insensitive to the presence of BPG. Hb therefore

binds and releases its last O

almost independently of the

BPG concentration.

Although the Adair equation is the most general rela-

tionship describing ligand binding to a protein and is

widely used to do so, it provides no physical insight as to

why the various microscopic dissociation constants differ

from each other.Yet, if the protein consists, as so many do,

of identical subunits that are symmetrically related, it is de-

sirable to understand how ligand binding at one site influ-

ences the ligand-binding affinity at a seemingly identical

site. This need led to the development of models for ligand

binding that rationalize how the binding sites of oligomeric

proteins can exhibit different affinities. Two of these mod-

els are described in the following sections.

B. The Symmetry Model

Perhaps the most elegant model for describing cooperative

ligand binding to a protein is the symmetry model of

allosterism, which was formulated in 1965 by Jacques

Monod, Jeffries Wyman, and Jean-Pierre Changeux. This

model, alternatively termed the MWC model, is defined by

the following rules:

1. An allosteric protein is an oligomer of protomers

that are symmetrically related (for hemoglobin, we shall

assume, for the sake of algebraic simplicity, that all four

subunits are functionally identical).

2. Each protomer can exist in (at least) two conforma-

tional states, designated T and R; these states are in equilib-

rium whether or not ligand is bound to the oligomer.

3. The ligand can bind to a protomer in either confor-

mation. Only the conformational change alters the affinity

of a protomer for the ligand.

4. The molecular symmetry of the protein is conserved

during conformational change. Protomers must therefore

change conformation in a concerted manner,which implies

that the conformation of each protomer is constrained by

its association with the other protomers; in other words,

there are no oligomers that simultaneously contain R-

and T-state protomers.

For a ligand S and an allosteric protein consisting of n

protomers, these rules imply the following equilibria for

conformational conversion and ligand-binding reactions

(for the sake of brevity, and ).

[10.18]

This is illustrated in Fig. 10-28 for a tetramer.

n⫺1

⫹ S Δ T

n⫺1

⫹ S Δ R

⫹ S Δ T

⫹ S Δ R

⫹ S Δ T

⫹ S Δ R

Δ R

⬅ RS

⬅ TS

Section 10-4. Allosteric Regulation 349

Figure 10-28 The species and reactions permitted under the

symmetry model of allosterism. Squares and circles represent

T- and R-state protomers, respectively.

Table 10-2 Adair Constants for Hemoglobin A at pH 7.40

Solution k

(torr) k

(torr)

Stripped 8.8 6.1 0.85 0.25

0.1M NaCl 41. 13. 12. 0.14

2 mM BPG 74. 112. 23. 0.24

0.1M NaCl ⫹ 2 mM BPG 97. 43. 119. 0.09

Source: Tyuma, I., Imai, K., and Shimizu, K., Biochemistry 12, 1493,

1495 (1973).

T-state

subunits

R-state

subunits

SSS

S S

JWCL281_c10_323-358.qxd 2/24/10 1:58 PM Page 349

The equilibrium constant L for the conformational in-

terconversion of the oligomeric protein in the absence of

ligand is expressed

[10.19]

The microscopic dissociation constant for the R state, k

which according to Rule 3 is independent of the number of

ligands bound to R, is expressed according to Eq. [10.15]:

[10.20]

The microscopic dissociation constant for ligand binding to

the T state, k

, is similarly expressed.The fractional satura-

tion, Y

, for ligand binding is

[10.21]

We shall make two definitions:

␣ may be considered a normalized ligand concentration. c is

the ratio of the ligand-binding dissociation constants; c in-

creases with the ligand-binding affinity of the T state rela-

tive to that of the R state. Then, combining the foregoing

relationships as is shown in Section A of the Appendix to

this chapter, we obtain the equation describing the symme-

try model of allosterism for homotropic interactions:

[10.22]

Note that this equation depends on three parameters, ␣, c,

and L, which are, respectively, the normalized ligand con-

centration, the relative affinities of the T and R states for

⫽

␣(1 ⫹␣)

n⫺1

⫹ Lc␣(1 ⫹ c␣)

n⫺1

(1 ⫹␣)

⫹ L(1 ⫹ c␣)

␣⫽[S]>k

c ⫽ k

([R

] ⫹ 2[R

] ⫹

⫹ n[R

]) ⫹ ([T

] ⫹ 2[T

] ⫹

⫹ n[T

])

n5([R

] ⫹ [R

] ⫹

⫹ [R

]) ⫹ ([T

] ⫹ [T

] ⫹

])6

⫽

⫽ a

n ⫺ i ⫹ 1

i⫺1

] [S]

]

(i ⫽ 1, 2, 3, p , n)

L ⫽

]

ligand, and the relative stabilities of the T and R states. In

contrast, the Hill equation (Section 10-1B) has but two pa-

rameters, K and n, whereas the number of parameters in

the Adair equation is equal to the number of ligand-

binding sites on the protein.

a. Homotropic Interactions

Let us examine the nature of the symmetry model by plot-

ting Eq. [10.22] for a tetramer (n ⫽ 4) as a function of ␣ for

different values of the parameters L and c (Fig. 10-29).Three

major points are evident from an inspection of these plots:

1. The degree of upward curvature exhibited by the ini-

tial sections of these sigmoid curves is indicative of their

level of cooperativity.

2. When only the R state binds ligand (c ⫽ 0), the ligand-

binding cooperativity increases as the oligomer’s conforma-

tional preference for the non–ligand-binding T state in-

creases (L increases; Fig. 10-29a). For high L values, if a

single ligand is to bind, it must “force” the protein into its less

preferred R state.The requirement that all protomers change

their conformational states in a concerted manner causes the

remaining three ligand-binding sites to become available.

The binding of the first ligand therefore promotes the bind-

ing of subsequent ligands, which is the essence of a positive

homotropic effect. Note that cooperativity and ligand-bind-

ing affinity are different quantities; in fact, for c ⫽ 0, curves

indicative of high ligand-binding affinity (those with low L)

exhibit low cooperativity and vice versa.

3. When the T state is highly preferred (L is large), lig-

and-binding cooperativity increases with the R state’s lig-

and-binding affinity relative to that of the T state (decreas-

ing c; Fig. 10-29b). At low ligand concentrations (low ␣)

the amount of ligand bound (Y

) increases with the lig-

and-binding affinity of the T state (increasing c) since the

protein is largely in the T state.As ␣ increases, however,the

amount of ligand bound to the intrinsically less stable R

state eventually surpasses that of the T state, thereby

resulting in a cooperative effect. This is because the free

350 Chapter 10. Hemoglobin: Protein Function in Microcosm

Figure 10-29 Symmetry model

saturation function curves for

tetramers according to Eq.

[10.22]. Here L ⫽ [T

]/[R

c ⫽ k

, and ␣⫽[S]/k

(a) Their variation with L when

c ⫽ 0. (b) Their variation with c

when L ⫽ 1000. [After Monod,

J., Wyman, J., and Changeux, J.P.,

J. Mol. Biol. 12, 92 (1965).]

0.5

0 2 5 0 2 5 10 2010 15

αα

(a) (b)

= 1

= 10

= 100

= 1000

= 10,000

= 0.00

= 0.10

= 0

= 4

= 1000

= 4

= 0.04

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