Urry D.W. (Ed.) What Sustains Life? : Consilient Mechanisms for Protein-Based Machines and Materials
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7.2 The Movable Cusp of Insolubility
255
O
Positive Cooperativity
H
04-
-1
i:
n=
1.47 (GVGVP GVGVP GEGVP GVGVP GVGVP GVGVP)
3^
ii:
n=1.6 (GVGVP GVGFP GEGFP GVGVP GVGVP
GVGVP)
^^
hi:
n=1.9 (GVGVP GVGVP GEGVP GVGVP GVGFP GFGFP)
3^
iv:
n=2.6 (GVGVP GVGFP GEGFP GVGVP GVGFP GVGFP) ,5
v:
n=8.0 (GVGVP GVGFP GEGFP GVGVP GVGFP GFGFP),.
P :
n=l-
9'
1 if \W \W IV.
^F^^^^^^^^^^^^^^^—•^•¥i-^F"
^^^^^^—^"i|F-^^—^^^^^^^^^^^^
B
PH
Myoglobin
n=1.0
Hemoglobin
n = 2.8
log (pO,)
FIGURE
7.7. Hill plots to obtain Hill coefficients
using log[a/(l - a)] versus activity of reactant. (A)
For the acid-base titration curves of the Model Pro-
teins i through v of Table 5.5, showing a supralinear
increase in Hill coefficient from n =
1.5,1.6,1.9,
2.7
to 8.0 as the hydrophobicity increases linearly. (B)
For the oxygenation of myoglobin (n = 1) and for the
oxygenation of hemoglobin (n = 2.8). A more
dramatic increase in positive cooperativity can be
observed with the designed model proteins.
256
7.
Biology Thrives Near a Movable Cusp of Insolubility
In these elastic model proteins development of
such dramatic positive cooperativity occurs
without significant conformational strain^ but
rather simply results from competition for
hydration between hydrophobic and charged
residues. Obviously, this positive cooperativity
occurs without an electrostatic component to
the conformational energy, such as repulsion
between charges. The charge-charge repulsion
of poly(methacrylic acid) (PMA) results in a
negative cooperativity, which, when repre-
sented by a Hill coefficient, gives an n of 0.5
with 1/2 the slope of myoglobin in Figure 7.7B.
Recall the data for the elastic model proteins
discussed in Chapter 5, section 5.7. Increased
positive cooperativity results from competition
for hydration between the polar carboxylate
and the hydrated hydrophobic domains. Com-
petition for hydration with hydrophobic groups
increases the Gibbs free energy of the car-
boxylate. Not only can the elastic model pro-
teins be designed to exhibit the magnitude of
positive cooperativity exhibited by Hb, they can
also be designed with positive cooperativity
that substantially surpasses the vaunted hemo-
globin example.
7.2.4.3.2 Analogy to Hemoglobin
Binding of Oxygen
In the case of hemoglobin, an analogy exists
between the higher pH, that is, the higher
hydroxyl ion concentration, required to form
carboxylate and the higher oxygen concentra-
tion, the higher pOi values, required for the first
oxygen molecule to bind one of the four hemes
in hemoglobin. Hill plots of the carboxyl-
containing elastic protein-based polymers in
Figure 7.7 A can be compared with those of myo-
globin and hemoglobin in Figure 7.7B. A struc-
tural analysis of oxygen binding will be required
to consider whether the oxygen acts as a polar
species to destroy hydrophobic hydration and
enable ion pairs of hydrophobic domains to sep-
arate or in some other manner to cause the asso-
ciated hydrophobic domains to separate.
The cases are quite analogous; both exhibit
delayed formation of the more polar species.
For the tetrameric hemoglobin, binding of the
more polar oxygen molecule requires a higher
p02,
a higher chemical potential of oxygen.
than for the related monomeric myoglobin. For
the model proteins with increased hydropho-
bicity, deprotonation of carboxyl to form the
more polar carboxylate requires a higher chem-
ical potential of hydroxyl ion. Thus, ionization
is delayed on raising the pH as the hydropho-
bicity of the model protein increases. The ion-
ization is delayed because the carboxylate must
do the work of destructuring hydrophobic
hydration in order to form. Once one carboxy-
late forms, having destructured substantial
hydrophobic hydration, subsequent carboxy-
lates form more easily because they have less
hydrophobic hydration to destructure. The
magnitude of the Hill coefficient (/i), that
is,
the
positive cooperativity, increases with each
replacement of a Val (V) residue by a more
hydrophobic Phe (F) residue, because the task
of the initial charge formation in obtaining ade-
quate hydration increases as the elastic model
protein becomes more hydrophobic.
7.2.4.3.3 Dissociation of the ai^i Tetramer
on Oxygenation at Low Concentrations
(<3|xMHeme)
At concentrations of less than
3
jiM heme, the
deoxygenated state occurs as the a2p2 tetramer,
and oxygen binding exhibits positive coopera-
tivity. On oxygenation the tetramer splits into
a^p^ and a^P^ dimers. As discussed below, sepa-
ration at low concentration of the tetramer into
dimers on oxygen binding results from the sep-
aration of ion pairs that had been brought into
salt-bridge formation due to the dominance of
hydrophobic domains. In other words, the asso-
ciation between the a^P^ and a^p^ dimers is
dominantly hydrophobic.
7.2.4.3.4 Is the Consilient Mechanism
Relevant to Oxygen Binding by Hemoglobin?
Should the structural data show the a^P^-a^p^
interface to be one of hydrophobic association
that is disrupted on oxygenation, then in our
view the answer is clearly yes, the cooperative
binding of oxygen to hemoglobin results
from the consilient mechanism. In our view the
presence of hydrophobic association at the
a^P^-a^P^ interface would indicate that positive
cooperativity, essential to hemoglobin function
in oxygen transport, arises due to the consilient
7.2 The Movable Cusp of Insolubility
257
mechanism with the underlying physical
process being an apolar-polar repulsive free
energy of hydration. Once the first oxygen mol-
ecule in the process of binding effects some
hydrophobic dissociation of the a^p^ and a^P^
dimers, by destructuring hydrophobic hydra-
tion that would occur on partial dissociation at
the interface between the two dimers, the
second oxygen can bind more readily to the
second subunit because its intersubunit
hydrophobic hydration has already been par-
tially destructured. Thus, there would result a
sigmoid binding curve, quantified in terms of a
Hill coefficient of greater than 1.
Yet much more phenomenological data,
showing the coherence of phenomena between
hemoglobin function and the consilient
mechanism of the inverse temperature transi-
tion for hydrophobic association, continues
below, before direct examination of the molec-
ular structures, as generally presented. Subse-
quently, in section 7.3, the molecular structures
are examined to look for the specific
interactions most significant to the consilient
mechanism.
7.2.4.4
Existence of Two Conformational
States, T and R, of Hemoglobin
7.2.4.4.1 Definition of the T State: The Tense
or Taut Form Exhibited by Deoxyhemoglobin
The T state is like a rigor or contracted state
and is analogous to dephosphorylated, low pH
(protonated), and ion-paired states apparent in
the contracted state of elastic model proteins
and of muscle. In our perspective, the T state is
the state with more hydrophobic association
between subunits. Within the associated
hydrophobic domains of the T state can be
anticipated ion pairs and hydrogen bonds
within and between the a^P^ and a^p^ dimers
that would facilitate shifting the cusp of insolu-
bility. The cluster of ion pairs and hydrogen
bonds that change at the a^P^-a^P^ interface on
oxygenation are shown in Figure 7.8. What is
not apparent in Figure 7.8 is that these interac-
tions form because these polar groups are
under the influence of hydrophobic domains.
The spatially localized hydrophobic contacts
between subunits represent movable regions
that begin on the insolubility side of the cusp of
B
FIGURE 7.8. Networks of ion pairs and hydrogen
bonds of the "switch region" (A) and the "joint-
associated region" (B) at the interface between the
a^p^ and the a^P^ dimers that comprise the hemo-
globin tetramer. These polar interactions result from
the hydrophobic association between the dimers that
is
maximal in deoxyhemoglobin and partially relaxed
on oxygenation. The key ion pairs that orient the a^P^
and the
a^P^
dimers are indicated by the circled
1
and
2 and are identified as such on the interface in Figure
7.18. See text for discussion. (Adapted with permis-
sion from Voet and Voet.^°^)
insolubility, but binding of the polar oxygen
molecule moves the cusp of insolubility to
higher temperature such that now the system
shifts toward the more soluble side of the cusp
of insolubility. The T state with no bound
oxygen contains hydrophobic domains thermo-
dynamically poised on the insolubility side of
the cusp of insolubility.
258
7.
Biology Thrives Near
a
Movable Cusp
of
Insolubility
7.2.4.4.2 Definition
of the R
State:
The
Relaxed Form Exhibited
by
Oxyhemoglobin
The
R
state
is the
more polar, more hydrated,
relaxed state
of
hemoglobin. With respect
to the
separable paired hydrophobic domains, that
is,
the separated
a^p^ and a^P^
dimers seen
at low
concentration,
the R
state resides
on the
solu-
bility side
of the
movable cusp
of
insolubility.
It
is the
hydrophobically dissociated state
resulting from introduction
of a
polar species,
namely, oxygen.
By the
consilient mechanism,
the spatially localized hydrophobic domains
poised
on the
insolubility side
of the
Tfdivide
in
the T
state become disrupted
on
introduction
of
a
polar species
and are now
found
on the
sol-
ubility side
of the
Tt-divide. This disrupts
the
intersubunit hydrophobic associations between
the
a^P^ and a^P^
dimers that
had
been made
possible
by the now
disrupted
ion
pairs
and
hydrogen bonds.
In
other words,
in the
case
of
hemoglobin,
as the
result
of
oxygen binding,
the
cusp
of
insolubility moves
to a
higher temper-
ature along
the
temperature axis,
as
repre-
sented
by the
rightmost cuspid
in
Figure
7.1.
Again, with regard
to the
dissociable pairs
of
hydrophobic domains,
the R
state
of
hemoglo-
bin
at
physiological concentrations with four
bound oxygen molecules
has
shifted toward
the
solubility side
of the
cusp
of
insolubility.
7.2.4.5
The T ^ R
State Transition
Involves Uptake
of
Water Despite
a
Decrease
in
Volume of Aqueous Channel
of Oxyhemoglobin
7.2.4.5.1 General Considerations
of
Transient
Openings
of
Hydrophobically Associated
Domains
of the T
State
Recall from Figure
5.27 and
associated discus-
sion that,
as the
amount
of
hydrophobic hydra-
tion increases,
the
value
of Tj
decreases.
The
cusp
of
insolubility moves
to
lower tempera-
tures,
from above
to
below physiological tem-
perature. Accordingly, hydrophobic association
between
two
surfaces occurs because
the
sur-
faces
are
sufficiently hydrophobic that during
a
transient opening
so
much hydrophobic hydra-
tion forms that
the
Tt-divide
is
below
the
oper-
ating temperature. This causes
the
transiently
opened paired hydrophobic domains
to
reasso-
ciate.
If a
sufficiently polar species should
be
introduced into
the
protein during
a
transient
opening, then,
due to
competition
for
hydra-
tion,
the
polar species results
in a
decrease
in
the amount
of
hydrophobic hydration.
As a
result,
the
thermodynamic driving force
for
association
can be
lost, that is,
the
Tt-divide
can
be raised above
the
operating temperature.
Direct competition
for
hydration between
the
added polar species
and the
hydrophobic
groups
of the
hydrophobic domain
may be the
most obvious
way to
achieve
the
loss
of
hydrophobic hydration,
but it
should
not be
considered
the
only
way to do
so.
Any
interac-
tion that causes
the
associated hydrophobic
domains
to be
less hydrophobic, that
is,
to
have
less hydrophobic hydration
on
separation,
constitutes
the
central feature
of the
consilient
mechanism.
7.2.4.5.2
The
Uptake
of
Water
on
Transition
from
the T to the R
State
Bulone
et
al.^^'^^ report
the
average number
of
water molecules that attends
the T to R
state
transition
in
hemoglobin
is 75.
Colombo
and
coworkers^^ independently report
the
uptake
of
a similar number
of
water molecules,
60, on
conversion from
the
hydrophobically associ-
ated
to the
partially dissociated
state.
At
normal
concentrations, this addition
of
water
can be
identified with
the
partial hydrophobic dissoci-
ation
at the
interfaces between
the
paired
ap
dimers
(a^P^ and
a^p^).
As
noted above,
at low
concentrations (less than
3|iM
heme),
the
dissociation
of the
functional units,
the
paired
ap dimers
(a^p^ and
a^p^),
is
complete
on the
binding
of
oxygen.^^
7.2.4.6
Hydrophobic Interfaces Between
Subunits Identified
by
Mean Residue
Hydrophobicity Plots
7.2.4.6.1 Mean Residue Hydrophobicity Plots
for
the
Hemoglobin
a- And
p-Chains
and
for Myoglobin
Figure
7.9
provides
a
comparison
of the Tt-
based mean residue hydrophobicity plots
of the
a- and
p-chains
and
myoglobin
as a
function
of
7.2 The Movable Cusp of Insolubility
259
FIGURE 7.9. Mean residue hydropho-
bicity plots of the a-chain (A) and the
P-chain (B) of hemoglobin and of myo-
globin (C). The strong hydrophobicity
peaks just above 100 residues are
responsible for stable formation of the
a^P^ dimer. The strong hydrophobicity
peaks near 40 residues may be con-
sidered part of the "switch region."
These hydrophobic residues provide an
arc for hydrophobic association at the
a^P^-a^P^ interface. By the consilient
mechanism, decreased heme hydropho-
bicity on oxygen binding relaxes this
inter-dimer hydrophobic association
and allows the T
—>
R transition, as
shown in Figure 7.10, to occur. This is
further visualized in Figure 7.18 as dis-
cussed in the text. See text for further
discussion.
Hemoglobin a-chain
1—\—I—I—I—I—r
80 90 100110120130140150
Hemoglobin ^-chain
100
T
r I I I I I I I I I I I r
0 10 20 30 40 50 60 70 80 90 100110
120
130140 150
Myoglobin chain
-i—I—I—i—n—I—I—I—I—I—I—I—I—r
10 20 30 40 50 60 70 80 90 100110120 130140150
Residue number
sequence. A sliding window of the average
value for 11 residues is used with the data point
given for the central residue. Upward deflect-
ing peaks from the 37° C baseline identify the
more hydrophobic
sequences.
The plot for myo-
globin exhibits only minor upward deflections
that are recognized as contributing to the
intramolecular (tertiary) hydrophobic folding
(see Figure 7.9C).
The prominent peaks of the mean residue
hydrophobicity plots for the a- and p-chains in
Figure 7.9A,B, immediately upon inspection,
260
7.
Biology Thrives Near a Movable Cusp of Insolubility
provide interesting insight into the hydropho-
bic quaternary structural interactions that hold
the subunits together. The effect of the changes
in amino acid residues from myoglobin to the
a- and p-chains of hemoglobin is to create
hydrophobic domains. These hydrophobic
domains become the basis for the hydrophobic
association betw^een subunits to form the stable
a-p functional dimeric unit and the hydropho-
bic association at the interface between the a^p^
and a^p^ functional units.
7.2.4.6.2 Hydrophobic Association Holds
Together the Fundamental Functional Unit,
the ap Dimer
The mean residue hydrophobicity plots for the
a- and P-chains of hemoglobin exhibit two
prominent upward deflections. These promi-
nent hydrophobic sequences, not present in
myoglobin, are responsible for the hydrophobic
associations between chains. Those residues
responsible for two of the four peaks in the
mean hydrophobicity plots of the a-chain
and P-chains in Figure 7.9A,B, specifically
due to residues 100 to 110 of the a-chain
(LLSHCLLVTLA) and 105 to 115 of the
p-chain (LLGNVLVCVLA), form the primary
hydrophobic association that holds together the
basic structural unit, the aP dimers (a^P^ and
a^P^). Except for the hydrophobic histidine
residue, H^^^, these sequences contain no ioniz-
able functions. Because of this they form the
nondissociating aP functional unit. Hydropho-
bic association within each basic aP dimer is
represented in Figure 7.10 as the association
of G-helices. This hydrophobic association
remains unchanged on oxygenation.
(a) DeoxyHb
C3{38)ai
C6(41)ai
FG4{97)P2
CD2(44)a
C3(38)a2
06(41)02
FG4(97)pi
CD2(44)a2
C3(38)ai
FG4(97)P2
C6{41)ai
CD2(44)ai
(h) OxyHb
C3(38)a2
' FG4(97)Pi
' C6(41)a2
' CD2(44)a2
FIGURE
7.10.
Perspective of hemoglobin to
demonstrate the change on oxygenation
to be the rotation of the a^P^ dimer with
respect to the a^P^ dimer. The fulcrum of
the rotation is the "joint-associated"
region, and the shift at the "switch region"
is noted. Also shown are the contacts
between the a- and p-chains of the a^p^
dimer. See text for discussion here and
Figure 7.18 and associated text there for
insight into the rotation that occurs at the
a^-p^ and a^-P^ interface. (A Reproduced
with permission from The Irving Geis
Archives. Rights owned by Howard
Hughes Medical Institute, reproduced
from D. Voet and J. Voet, Biochemistry,
Second Edition, John Wiley & Sons, Inc.
New York, 1995.)
7.2 The Movable Cusp of Insolubility
261
7.2.4.6.3 Positive Cooperativity Due to
Changeable Hydrophobic Interface Between
a|3 Dimers
The additional identified hydrophobic se-
quences of Figures 7.9A,B undergo changes on
oxygenation. Residues 36 to 49 of the a-chain,
FPTTKTYFPHFDLS, contribute to the so-
called switch region, whereas the more
hydrophobic residues 31 to 41 of the (J-chain,
LLVVYPWTQRF, contribute to the so-called
joint region (Figure 7.10A). Also shown in
Figure 7.9B, the P2 carboxyl-terminal sequence
LAHKYH provides another prominent hydro-
phobic sequence that contributes to the switch
region.
In particular as shown in Figure 7.8a, the
Y145 and the terminal H146 contribute to two
ion pairs and a hydrogen bond as key polar
interactions of the hydrophobic switch region
while being quite hydrophobic in their own
right. In an analogous way, as shown in Figure
7.8b, the ai-carboxyl-terminal Y140 and R141
with the aid of a chloride ion (CI") stitch
together three ion pairs and two hydrogen
bonds while in association and influenced by
the hydrophobicity of the joint region. In our
view, the neutralization of these polar groups by
ion pairing and hydrogen bonding lowers the
cusp of insolubility for an enlarged hydropho-
bic domain at the interface between aP dimers
that includes residues 31 through 41 of the
p-chain, identified in the corresponding
hydrophobic peak in Figure 7.9B. The shift
between ion pair enhanced and enlarged
hydrophobic association of the T state to the
more limited hydrophobic association on disso-
ciation of the ion pairs of the R state provides
for the pivotal 15° motion of the joint region at
the interface between the pairs of ap dimers, as
depicted in Figure 7.10.
7.2.4.6.4 Changes in Tertiary Structure on
Oxygen Binding Disrupt Geometry Required
for Ion-pair Formation
Drawing on the consilient mechanism for a
working hypothesis, changes in tertiary struc-
ture on oxygen binding alter the positioning
of the polar species in Figure 7.8, particularly
of the charged species, such that they can no
longer be sufficiently proximal to function as
ion pairs. The separated ion pairs now function
more as individual charged species and derive
more hydration from their vicinity. Accord-
ingly, fluctuations that separate the proximal
hydrophobic domains allow the newly emerged
charged species to destructure nascent
hydrophobic hydration and thereby decrease
the driving force for the associations of these
hydrophobic domains. The result would be that
hydrophobic associations of the T state open
up with an uptake of water to give the R state.
The fundamental question becomes, what is the
principal reason for the disruption of the ion-
pair and hydrogen-bonding interactions. This
will be discussed further below in relation to
the Perutz and consilient mechanisms.
7.2.4.6.5 More Detailed Identification of
the Paired Hydrophobic Domains That
Alter Association During the T to R
State Transition
The principal sites considered responsible for
the change in hydration, noted above, involve
networks of ion pairs and hydrogen bonds
(see Figure 7.8) between paired hydrophobic
domains that are disrupted during oxygen
binding. They occur at the ai-P2 interface and
are referred to as the switch region. Changes
occur at another site of hydrophobic associa-
tion, the interface between the ai and a2 chains,
but this joint region only partially disassociates
for increased exposure to water. These features
are visited further in section 7.3 with additional
representations of the crystal structures that
focus on these domains.
7.2.4.7
Role of Ion-pair Formation in
Hydrophobic Association of Elastic-
contractile Model Proteins
7.2.4.7.1 Moving the Spatially Localized
Hydrophobic Associations of Hemoglobin
Back and Forth Across the Tt-divide
(Moving the Cusp of Insolubility)
7.2.4.7.1.1
Polar Species Act Cooperatively.
When separated, negatively and positively
charged species individually act in a coopera-
tive manner to destructure hydrophobic hydra-
262
7.
Biology Thrives Near a Movable Cusp of Insolubility
tion. When ion paired, this capacity of the sep-
arated ions to destroy hydrophobic hydration
becomes muted. In the case of hemoglobin,
the negative species would be carboxylates,
carbamates, biphosphoglycerates, and the elec-
tronegative oxygen molecule
itself,
and positive
species, though inherently less effective than
negative species, w^ould be positively charged
amino, guanidinium, and imidazolium groups.
Such polar species when part of, or sufficiently
proximal to, a pair of hydrophobic domains,
shift the system to the solubility side of the
divide, which is the R state. Charged species,
whether positive or negative, shift the cusp of
insolubility toward higher temperatures than
the operating temperature, that is, toward
solubihty.
7.2.4.7.1.2
Ion-pair Formation Decreases the
Effect of Charge. Because polar species co-
operate to shift a pair of hydrophobic domains
toward solubility (hydrophobic dissociation),
ion pairing and to a lesser extent hydrogen
bonding simultaneously neutralize pairs of
polar species and markedly shift the system
toward insolubiUty (hydrophobic association).
It is important in understanding the state of
hemoglobin to recognize that ion pairing dra-
matically decreases the effect of charge to disrupt
hydrophobic association. Ion-pair formation is
about half as effective as protonation of a car-
boxylate in shifting a spatially localized site
toward the insolubility side of the divide as
demonstrated in Figure 5.34 with the model
proteins in Table 5.5.
7.2.4.7.2 Ion Pairing Between Chains of
Model Proteins
The striking effectiveness of ion-pair formation
in lowering the free energy of hydrophobic
association,
AGHA,
between moderately hydro-
phobic chains of elastic model proteins is
demonstrated in Figure 6.3. The elastic
Model Protein x' in Table 5.5, but with an
n of 36 instead of 22, that is, (GVGVP
GVGVP GKGVP GVGVP GVGVP
GVGVP)36(GVGVP), does not begin
hydrophobic association at pH 7.5 in water
until 70° C (158°F) and the Glu (E)-containing
elastic model protein. Model Protein v,
(GVGVP GVGFP GEGFP GVGVP GVGFP
GFGFP)42(GVGVP), even with 5 Phe (F)
residues per 30 mer and under the same solvent
conditions, does not begin hydrophobic associ-
ation until 55° C (131°F). Remarkably, when
these model protein chains are combined in
the same solution, aggregation begins at 5°C
(41°F).
Even when the paired model proteins have
no Phe (F) residues, the effects of hydrophobic
association are notable. In solution alone,
the K-containing chain exhibits a Tt of 70° C
(158°F), as above, and separately in solution
the E-containing chain, (GVGVP GVGVP
GEGVP GVGVP GVGVP GVGVP)36
(GVGVP), exhibits a Tt-value that extrapolates
to over 100° C (212°F). On combining in a 1:1
ratio,
the Tt-value is 35° C (95°F).The formation
of ion pairs between these chains lowers the
free energy for hydrophobic association on a
per GEGVP and GKGVP (ion pair) basis by
some 3.5kcal/mole-pentamer. This exemplifies
the importance of ion-pair formation, even
between modestly hydrophobic chains, in
promoting hydrophobic association. As more
hydrophobic residues—such as He (I), Leu (L),
Phe (F), Tyr (Y), and Trp (W)—participate in
the hydrophobic domain, the free energy for
hydrophobic association becomes even more
favorable.
Specific effects described below are known
for shifting the equilibrium in the direction of
either the T or the R state. These effects are
explicable in terms of the ATt-mechanism for
moving the Tt-divide and the approximately
equivalent Gibbs free energy of hydrophobic
association,
AGHA,
and its component the
apolar-polar repulsive free energy of hydra-
tion, AGap. In all cases ion-pair formation
associated with hydrophobic domains drives
hydrophobic association.
7.2.4.8
Further Correlation of Phenomena
7.2.4.8.1 The Bohr Effect
7.2.4.8.1.1
The Bohr Effect is the Release of W
on Binding of
O2.
Hemoglobin releases about
0.6 protons for each O2 bound. These protons
derive from partial proton release from the
QL2-
chain Val^(a-NH3^) and the p2-chain H146(imi-
dazolium). These charged species are part of
the ion-paired clusters shown in Figure 7.8. On
7.3 Hemoglobin Structures Demonstrate the Consilient Mechanism
263
oxygenation the polarity sufficiently in-
creases to relieve the hydrophobic hydration
driving force for maintaining these ion-paired
networks. ^^'^°
7.2.4.8.1.2
Reversible Combining of CO2 to
the N-terminal Amino Groups. Associated with
the Bohr effect is the reversible combining of
CO2 to the N-terminal amino groups such as the
Vl(a-NH3^) to result in carbamates. The reac-
tion for carbamate formation is written, R-NH2
+ CO2 = R-NH-COO" + W. This -COO"
provides a more effective negative charge to
replace the CI" (shown in Figure 7.8B) that
bridged between the Vl(a-NH3^) and the
R141(guanidinium) in the ion-pairing network
of the T state that is deoxyhemoglobin.
7.2.4.8.1.3
Analogy of Cl~ in the Associated
Region of Deoxyhemoglobin and the Effect of
NaCl on Lys-containing Elastic Model Proteins.
For the Lys-containing elastic model protein
poly[0.76(GVGVP),0.24(GKGVP)] in water,
the Tt-value is greater than
100°
C.
On addition
of 0.05 N NaCl, the value of T^ occurs at 70° C,
and at 0.25 N NaCl the value of Tt occurs at
35°
C.
On a per mole NaCl basis, this would
be a ATt of -175°
C.
The value of ASt for
poly(GK^GVP), when ionized, is 3.9 cal/
mole-pentamer °K. Using these values in
Equation (5.9) of Chapter 5,
AGHA(%)
=
ATt(x)ASt(ref), gives a AGHA(Cr ion pairing) of
-0.68 cal/mole-pentamer.
This estimate of a favorable change in Gibbs
free energy for CI" ion pairing with positively
charged Lys(K^) would be greater for more
hydrophobic domains, as appears to be the case
for the relevant paired hydrophobic domain of
deoxyhemoglobin. When the model protein
is the more hydrophobic (GVGIP GVGIP
GK^GIP GVGIP GVGIP GVGIP)42, the
favorable decrease in AGHA(Cr ion pairing)
becomes -1,480 cal/mole-pentamer. Even the
more modest ion pairing of CI' with Lys(K^)
contributes significantly to enhance hydropho-
bic association.
7.2.4.8.2 2,3-Biphosphoglycerate Binding:
[CH2(POr)-CH(P04=)-COO-]
The interaction of 2,3-biphosphoglycerate
(BPG) represents the most dramatic use of ion
pairing in the oxygen transport process of
hemoglobin. A single molecule of BPG inter-
acts with a total of eight positive charges.
Four positive charges derive from the first two
residues of the two p-chains, Vla-NHa^ and
the His^ imidazolium and an additional four
positive charges come from two K82 e-amino
groups of the p-chains and two additional H143
imidazolium residues of the p-chains. By the
consilient mechanism, such dramatic ion-pair
formation and its proximity to the switch region
decreases polarity and shifts the equilibrium
from the R state toward the T state, that is, it
induces dissociation of oxygen. In terms of the
ATt-mechanism, BPG binding lowers the T^-
divide. The cusp of insolubility moves to lower
temperatures and shifts the interface between
the aP dimers toward the greater hydrophobic
association of deoxyhemoglobin.
7.2.4.8.3
Fetal Hemoglobin. The subunit com-
position of fetal hemoglobin is a2Y2 instead of
the a2p2 of adult hemoglobin A. The y-chain
differs from the P-chain by replacement of the
positively charged side chain of the P-chain
H143 with an uncharged Ser residue. The two
H143 residues, one on each of the two adult P-
chains, are part of the BPG binding site of the
maternal hemoglobin. Replacement of the two
P-chain H143 residues by Ser residues in fetal
hemoglobin reduces the number of charges
from eight to six and reduces BPG affinity to
fetal hemoglobin. The result is retention of a
higher affinity for oxygen due to a decrease in
the shift to the deoxygenated T state. This facil-
itates transfer of oxygen from maternal to fetal
hemoglobin in utero.
13 Hemoglobin Structures
Demonstrate the Consilient
Mechanism
7.3.1 Extending the Structural
Insights
In the foregoing phenomenological considera-
tions of muscle and hemoglobin function, a
clear pattern emerged. It was one of a correla-
tion of phenomena exhibited by muscle and
hemoglobin on the one hand and elastic-
264
7.
Biology Thrives Near a Movable Cusp of Insolubility
contractile protein-based polymers on the
other. At the core of elastic protein-based
polymer function resides the phenomenon of
an inverse temperature transition of hydropho-
bic association. Control of hydrophobic associ-
ation became the basis for the de novo design
of a family of efficient protein-based machines
capable of performing the energy conversions
extant in biology.
As developed in Chapter 5, control of
hydrophobic association derived from control
of hydrophobic hydration, and the physical
basis for controlling hydrophobic hydration to
achieve the diverse functions became described
as an apolar-polar repulsive free energy of
hydration, AGap. More directly stated, AGap
derives from a competition for hydration
betv^een apolar (hydrophobic) and polar (e.g.,
charged) groups constrained by structure to
coexist in a limited, shared space. As charged
species gain dominance in the competition, they
reduce the amount of hydrophobic hydra-
tion and effect hydrophobic dissociation. As
hydrophobic residues gain dominance in the
competition, they gather so much hydrophobic
hydration that they become insoluble. Yes, too
much hydrophobic hydration for a given tem-
perature results in an inverse temperature tran-
sition to hydrophobic association with loss of
water. Butler's 1937 report^^ contains within it
this insight into the thermodynamics of the
thermodynamics of solubility of hydrophobic
groups.
We grew to understand this reality while
designing diverse protein-based machines. The
demonstrably empowering mechanism was
given the name of the consilient mechanism,
because it provides a "common groundwork of
explanation," as noted initially in Chapter 1.
Despite the above noted correlation of phe-
nomena, current descriptions of molecular
structure and resulting function of hemoglobin
and myoglobin (as well as of muscle contrac-
tion to be addressed at the molecular level in
Chapter 8) proceed without consideration of
the consilient mechanism. With the consilient
mechanism in mind, however, a distinctive way
of looking at protein structure and function
materializes. The availability of so many protein
crystal structures from The Protein Data Bank^^
and, as employed in our case, the capacity to
examine them by the software FrontDoor to
Protein Explorer^^ and to illustrate them by
Adobe® Photoshop® 5.5 provides the oppor-
tunity to consider the function of biology's
proteins specifically in terms of the consilient
mechanism. Immediately below, we begin with
the hemoglobin molecule, the first of several
proteins thus considered in this volume.
7.3.2 Resulting Functional Insights
Positive cooperativity (demonstrated by the
sigmoid oxygen binding curve of hemoglobin)
simply results when the binding of oxygen at
one heme increases the affinity for oxygen
binding at a second heme. An earlier proposal
of direct heme-heme interaction in hemoglobin
due to a theoretically calculated dramatic
change in heme polarizability on oxygen
binding was shown to be incorrect based on
analysis of spectroscopic data of model
heme-heme interacting systems.^"^ Further con-
sideration of the direct interaction between
heme groups in hemoglobin has generally been
discounted because the heme centers of the
a^-P^-subunits are separated by
40
A and the
heme centers of the p^-a^-subunits are sepa-
rated by
24
A.
Nonetheless, as discussed below, detailed
comparisons of the crystal structures of T state
deoxyhemoglobin,^^ deoxyHb, and T state oxy-
hemoglobin,^^'^^ oxyHb(T), demonstrate
signif-
icant changes due to oxygen binding that occur
in a crevasse separating the hemes of the p^-
and a^-subunits and the equivalent crevasse
between the hemes of the p^- and a^-subunits.
It is our view, drawn from the developments in
Chapter 5, that those changes reflect a decrease
in the apolar-polar repulsive free energy of
hydration, AGap, emanating from the heme as
the result of oxygen binding. AGap acts through
water and propagates as a function of distance
as charged groups, associated with the crevasse,
change their state.
In particular, the decrease in heme
hydrophobicity on oxygen binding eases the
competition for hydration with proximal
charged groups. The charged groups, once held
due to lack of hydration as ion pairs or with
their charge turned away (repulsed) from the