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
245
heating, the system passes from soluble to insol-
uble.
On heating, the protein of muscle forms
the contracted, the rigid, the stiff state as the
result of hydrophobic association.
More than a century ago Roy attached a 50-
gram weight to a 1cm wide strip of human
aorta^^ and heated the strip repeatedly back
and forth from room temperature to physio-
logical temperature. The aortic vascular tissue
primarily composed of smooth muscle and
elastic fibers reversibly contracted on heating
and relaxed on cooling, thereby performing the
mechanical work of raising and lowering the
weight. Approximately half of the force devel-
oped on heating results from smooth muscle
contraction and the other half from the inverse
temperature transition of the elastic fibers.
7,2.2.4
Rigor Mortis, "The Stiffening of
a Dead Body, Accompanying the
Depletion of Adenosine Triphosphate
in the Muscle Fibers''
Death is the ultimate manifestation of excur-
sion excess into the realm of insolubility. ATP
Adenosine Triphosphate (ATP), the universal
biological energy currency, is the ultimate solu-
bilizer of protein. In our view, the negative
hypercharged phosphate functions as a super-
carboxylate to destroy hydrophobic hydration
in the process of satisfying its own thirst for
hydration.
Thus,
as paired associated hydropho-
bic surfaces undergo an opening fluctuation,
hydrophobic hydration that would form is
immediately recruited for hydration of added
phosphate. As substantial hydrophobic hydra-
tion is required for the positive (-TAS) to dom-
inate and to result in insolubility, the result of
phosphorylation is solubility. In this way bound
phosphate provides for protein solubilization
by separation of hydrophobically associated
domains.
Organic phosphates, for example, phospho-
rylated protein and the phosphates of adeno-
sine,
are generally unstable and break down
over time to water-soluble inorganic phosphate.
Accordingly, ATP must be continually re-
supplied by the metabolism of a living organ-
ism. At death, respiration stops; oxidative
phosphorylation stops; the re-supply of ATP
terminates; and the pool of ATP decreases with
time.
As is well known, the development of
rigor mortis provides a measure of the time of
death. In our view and by the consiUent mech-
anism, based on the inverse temperature tran-
sition of hydrophobic association, depletion of
ATP in muscle necessarily results in the
hydrophobic association of muscle protein, that
is,
in the formation of the
stiff,
rigid, contracted
state of muscle.
Interestingly, death is not a case of the disor-
dering, dissolving, or melting away of structure
maintained by the energy conversions of the
living organism. Quite the contrary, death
results in the rigidification of structures ordered
by hydrophobic association. The ultimate
disintegration of a dead body is due to active
processes such as degradation by proteolytic
enzymes (primarily of other organisms), toxic
chemicals, excess heat, and so forth.
These examples of rigor at the gross anatom-
ical level in muscle are manifestations of
hydrophobic association at the molecular level;
they reflect the fundamental role of hydropho-
bic association/dissociation in the function of
muscle. These occurrences of rigor in muscle
do not support the view of electrostatic inter-
actions, of direct charge-charge interactions
independent of hydrophobic domains, being
predominant in muscle function. These anatom-
ical manifestations that correlate muscle con-
traction with hydrophobic association continue
below the physiological level.
7.2.3 Hydrophobic Association
in Muscle Contraction and in
Contractile Model Proteins:
Phenomenological Correlations
The phenomena that drive muscle contrac-
tion—thermal activation, pH activation, calcium
ion activation, stretch activation in insect flight
muscle, and dephosphorylation itself—have all
been shown to drive contraction by hydropho-
bic association in the elastic-contractile model
proteins discussed in Chapter 5. As concerns a
pair of hydrophobic domains, all of these
processes surmount the Tt-divide (the cusp of
insolubility in Figure 7.1) to go from a soluble
state to an insoluble state either by raising the
246
7.
Biology Thrives Near a Movable Cusp of Insolubility
temperature from below to above the Tfdivide
or by lowering the temperature of the Tt-divide
(moving the cusp of insolubility) from above to
below physiological temperature.
Thus,
as is discussed below in terms of
phenomenological correlations, we recognize
hydrophobic association as the fundamental
molecular process of muscle contraction. In
general, the perspective is one of controlling
the association/dissociation of localized
hydrophobic domains in the process of con-
traction/relaxation. In Chapter 8, molecular
details of muscle contraction are examined in
this context. Here at the physiological level,
phenomenological correlations are considered
in terms of solubility/insolubility of hydropho-
bic domains, or, as included in the title of this
chapter, in terms of the relationship of the
operating temperature to the location along
the temperature axis of the cusp of insolubiUty,
the temperature at which occurs the inverse
temperature transition of hydrophobic
association.
7.2.3.1
Thermal Activation of
Muscle Contraction
7.2.3.1.1 The Inverse Temperature Transition
and Thermal Activation in Muscle
The phenomenon of hydrophobic association
on raising the temperature, as noted above and
treated in detail in Chapter 5, derives from the
thermodynamics of structured water surround-
ing hydrophobic moieties. Hydrophobic hydra-
tion disappears, due to an unfavorable Gibbs
free energy for solubility, as the temperature is
raised from below to above the transition tem-
perature that reaches the cusp of insolubility
represented in Figure 7.1. This causes the
hydrophobic domains to separate from water
by means of intra- and intermolecular
hydrophobic association.
Under the conditions at which the coexis-
tence line in the phase diagram in Figure 5.3
occurs, associated and dissociated states of a
pair of hydrophobic domains coexist, and the
change in the Gibbs free energy is zero, that is,
AGt = AHt - TtASt = 0. This means for the tran-
sition that Tt - AHt/ASt. The temperature, Tt, at
which the hydrophobic association transition
occurs, depends on the quantity of hydrophobic
hydration. When there is more water of
hydrophobic hydration, the transition tempera-
ture is lower, that is, the value of Tt is lower
because AHt/ASt is a smaller quantity. When
there is less water of hydrophobic hydration,
the value of Tt is higher because AHt/ASt is a
larger quantity.
7.2.3.1.2 Muscle and the Mammalian Elastic
Fiber Are Exothermic on Stretching
Stretching of the mammalian elastic fiber in
water (as well as that of cross-linked
poly[GVGVP], the most prominent repeating
sequence of bovine and pig elastic fibers)^^ is an
exothermic process^^ due to the hydration of
hydrophobic groups that become exposed to
water as extension forces disassociation of
hydrophobic groups.
^^
Stretching of muscle also
gives off heat, as would occur on forced sepa-
ration of hydrophobically associated domains
of protein within muscle.^'* For the mammalian
elastic fiber, the exothermic heat of hydration
on extension is several times (about four times)
greater than the elastic energy stored in the
entropic elastic fiber on extension.^^
7.2.3.1.3 Muscle and Cross-linked Elastic
Protein-based Polymer, (GVGVP)n, Contract
on Raising the Temperature over the Same
Temperature Range
Just as stretching releases heat, heating causes
contraction. For cross-linked poly(GVGVP)
under isometric conditions, as shown in Figure
5.7B, raising the temperature from near 0° C to
25° C results in a small linear increase in force,
but raising the temperature from 25° C to 40° C
results in a supralinear development of tension
under isometric conditions or in the lifting of a
weight under isotonic conditions. The marked
force development above 25° C is clearly the
result of the inverse temperature transition of
hydrophobic association.
In 1970, Hill described the same properties
for intact frog sartorius muscle. ^^ Hill reported
a linear increase in isometric tension on raising
the temperature from 0° to 23° C, but on raising
the temperature higher there occurred a more
7.2 The Movable Cusp of Insolubility
247
pronounced increase in tension, which Hill
ascribed to an "active" process. Given the above
considerations and those of isometric force
development represented in Figures 5.7 and 5.8
and associated discussion in section 5.2.4, it is
reasonable to view the "active" process in terms
of a thermally driven inverse temperature tran-
sition of hydrophobic association.
More recently, Ranatunga described analo-
gous properties'^ for chemically skinned, glyc-
erinated, rabbit psoas muscle fibers immersed
in relaxing solution (pH ~ 7.2, pCa ~ 8, ionic
strength 200 mM) where membrane active
processes would be less likely. It is not unrea-
sonable, therefore, to suggest that a hydropho-
bic association transition is the source of the
pronounced thermally induced tension devel-
opment in mammahan skeletal muscle, not
unlike that of our elastic protein-based polymer
model system.
Mammalian muscle acts as though it
is
poised
for hydrophobic association at room tempera-
ture much as is the (GVGVP)^ elastic-contrac-
tile protein-based polymer on which are based
the visually demonstrated contractions reviewed
in Chapter 5.
7.2.3,2
pH Activation of
Muscle Contraction
As discussed in Chapter 5, a single Glu (E) in
a sequence of 30 residues, or 1 Asp (D) per 30
mer, exhibits very large, very nonlinear pKa
shifts,
as Val residues are stepwise replaced by
more hydrophobic Phe residues.'^ This demon-
strates, in yet another way, hydrophobic-
induced pKa shifts resulting from the
competition for hydration between hydropho-
bic and charged residues. For our particular
purposes here, it demonstrates that the pKa of
a carboxyl group can be hydrophobically
shifted over the range from 4 to 10.'^ Further-
more, the data demonstrate a nonlinear
increase in positive cooperativity (quantified by
the Hill coefficient)'^ that parallels the nonlin-
ear shift in pKa. This means that a carboxylate
moiety can readily have a pKa just below phys-
iological pH and that a small change in pH can
result in the complete protonation of the
hydrophobically perturbed carboxylate.
As noted in Chapter 5, as listed in Table 5.5
and as given in Figure 5.34, the pKa of Model
Protein ii, (GVGVP GVGFP GEGFP GVGVP
GVGVP GVGVP)4o(GVGVP), is 4.8 (Hill
coefficient of 1.6), whereas the pKa for Model
Protein I, (GVGIP GFG£P G^GFP GVGVP
GFGFP GFGIP)26(GVGVP), is 5.9 (Hill
coef-
ficient of 2.7) and that of Model Protein v,
(GVGVP GVGFP GEGFP GVGVP GVGFP
GFGFP)42(GVGVP), is 6.6 with a Hill coeffi-
cient of 8. Because in ischemia the pH can
drop to 6.5 or lower,^^ a carboxylate such as
in Model Protein v could be protonated in
ischemia to drive muscle contraction. In partic-
ular, pH-induced contraction has been reported
in the aorta of rats, and increasing blood pres-
sure enhances such pH-induced contraction.^^
The latter effect would, with an elevation in
blood pressure, be aided by a stretch-induced
increase in pKa (see below and Figure 5.23)
and would make the effect of ischemia more
profound.
7.2.3.3
Calcium Ion Activation of
Muscle Contraction
Data regarding the dependence of Tt and
NHH
on calcium ion concentration for Model Pro-
teins I and ii in Figure 5.27, and the above
self-
consistent analysis of muscle contraction being
one of controlling the hydrophobic association
of an inverse temperature transition, combine
to support the hypothesis that calcium ion
binding at carboxylates increases the water of
hydrophobic hydration. This would, in our
view of competition for hydration between
hydrophobic domains and phosphate, increase
the free energy of bound phosphate leading to
an increase in the rate of phosphate
release.
The
loss of the very polar phosphate, whether as a
covalently bound phosphate, as a free phos-
phate, or as bound nucleotide phosphate, favors
the hydrophobic association of contraction that
was deduced above to occur as part of muscle
contraction. This point of view is considered in
more detail in Chapter 8, after discussion has
progressed from the anatomical and physiolog-
ical levels considered in this chapter to the
molecular level for the myosin II motor to be
considered in that chapter.
248
7.
Biology Thrives Near
a
Movable Cusp
of
Insolubility
7.2.3.4
Stretch Activation
of
Muscle Contraction
With
the
elastic model system, y-irradiation
cross-linked poly[0.82(GVGIP),0.18(GEGIP)],
extension increases
the pKa in a
supralinear
fashion,
as
previously emphasized
in
Figure
5.23
of Chapter
5.^^
This demonstrates what could
be
called
a
stretch activation
of the
carboxylate
moiety;
the
free energy
of the
carboxylate
increases nonlinearly
as the
extension increases.
As stretching exposes hydrophobic groups
of
the hydrophobically associated matrix,
the
increased waters
of
hydrophobic hydration
resulting from stretch exposure
of the
hydro-
phobic moieties must necessarily
be
considered
as unsuited
for
hydration
of the
carboxylate
moiety;
the
result
is the
observed increase
in
free energy
of the
carboxylate.
As noted
in
Chapter
5,
phosphate
is a
super-
carboxylate, being equivalent
to
several
car-
boxylates
in its
capacity
to
shift
the
value
of Tt,
that is,
in its
capacity
to
destructure hydropho-
bic hydration. Thus,
we
anticipate that stretch-
ing
of a
muscle fiber with exposure
of
hydrophobic moieties would,
in an
entirely
analogous manner, increase
the
free energy
of
a phosphate. Such
an
increase
in the
free energy
of
a
phosphate would increase
the
rate
of
phos-
phate release. This would naturally
be
inter-
preted
by the
biochemist
as an
increase
in
ATPase activity.
Stretch activation
of
muscle
is a
well-
described phenomenon;
it was the
subject
of
The Croonian Lecture (1977) given
by
Pringle,^^
and it has
been extensively
researched
and
reported
in the
literature over
the ensuing decades.
For
example,
the
basic
description becomes "When active insect flight
muscle
is
stretched,
its
ATPase rate increases.
..
."^^
This
we
take
as yet
another demonstra-
tion
of a
fundamental process whereby
a
phos-
phate present
in a
protein
can be
activated,
"energized,"
as the
result
of an
increase
in
hydrophobicity.
It is an
example
of the
compe-
tition
for
hydration between apolar
and
polar
species, that
is, an
example
of the
apolar-polar
repulsive free energy
of
hydration active
in
muscle contraction.
7.2.3.5
Dephosphorylation Initiates
Hydrophobic Associations
of
Muscle Contraction
Phosphate attached
to a
model protein
is
three
to four times more effective
on a
mole fraction
basis than carboxylate
in
raising
the
Tf-divide
for hydrophobic association, which
we
have
shown
is due to a
decrease
in
hydrophobic
hydration
(see
Figures
5.25 and
5.27). Dephos-
phorylation, therefore, would re-establish
hydrophobic hydration
and
dramatically lower
the Tt-divide, which
is to
lower
the
temperature
range
of the
cusp
of
insolubility
to
below phys-
iological temperature.
The
result would
be an
insolubilization
of
hydrophobic domains
(a
hydrophobic association) that
we
consider
to be
the power stroke
of
muscle contraction.
A consistent feature
of the
myosin
II
motor
in
its
many facets
is
that binding
ATP
causes
dissociation. Again,
a
spatially localized pair
of
associated hydrophobic domains remains
as
such
as
long
as
during
an
opening fluctuation
there develops
too
much hydrophobic hydra-
tion,
and
they reassociate.
The
binding
of a
water-thirsty
ATP
molecule
in the
proximity
of
an opening fluctuation would recruit
the
nascent hydrophobic hydration
for its own
hydration
and
leave
the
pair
of
hydrophobic
domains dissociated,
as
depicted
in
Figure
2.16.
Thus,
the
most natural feature of ATP binding
as seen
by the
consilient mechanism would
be
dissociation
of
hydrophobic domains
The relationship between
the
states
of the
myosin
II
motor domain, subfragment
1 (SI),
and waters
of
hydrophobic hydration
has
been
directly observed
by the
same microwave
dielectric relaxation measurements
as
used
with
the
data
in
Figures
5.24 and 5.25.
Suzuki
and coworkers^"^ have observed
the ADP-
bound state
of SI to
have more water
of
hydrophobic hydration than
the
ADP*Pi state,
that
is,
than
the
most polar state. Thus,
the
effects
of the
additional negative charges
are to
destroy water
of
hydrophobic hydration
and to
raise
the
value
of Tt
above physiological tem-
peratures.
The
removal
of the
phosphate would
result
in an
increase
in
Nhh
and a
lowering
of Tt
below
the
physiological temperature with
the
consequence
of the
association
of
paired
7.2
The
Movable Cusp
of
Insolubility
249
hydrophobic domains
in the
process
of
muscle
contraction.
7.2.3.6
Scenario
of
Muscle Contraction
by
the Inverse Temperature Transition
of
Hydrophobic Association
Whether concern
is for an
explanation
of the
cause
of
rigor
at the
gross anatomical level
or
whether
it is a
more detailed consideration
of
the physiology
of
muscle contraction, there
occurs
a
correlation
of
phenomena whereby
contraction
is
well described
by the
hydropho-
bic association
of an
inverse temperature
transition.
In
Chapter
8,
detailed molecular
interactions attending
the
contraction/relax-
ation cycle
of the
myosin
II
motor
are
consid-
ered
in
terms
of the
consilient mechanism
of
the control
of
association/dissociation
of
hydrophobic domains.
In
particular, detailed
comparisons
of the
crystal structures
of
scallop
muscle cross-bridge
in the
near rigor,
and
bound
ATP
analogue states demonstrate
a
dra-
matic hydrophobic dissociation between
the
head
of the
lever
arm and the
N-terminal
domain
for the ATP
analogue state that
becomes
a
hydrophobic association
for the
near
rigor state. The latter markedly changes
the
ori-
entation
of the
lever
arm.
7.2.4 Hemoglobin Transport
of
Oxygen
by
Positioning
the
"Cusp
of
Insolubility" Through Control
of
Intersubunit Hydrophobic
Association/Dissociation
The globin protein provides
an
example
of
particular interest
to the
present discussion.
As
stated
by
Perutz,^^ "Ionized residues
are
excluded from
the
interior
of
globin chains,
which
is
filled largely
by
hydrocarbon side
chains,
but
some serines
and
threonines also
occur there." This perspective immediately
emerged from
the
first
few
protein structures
determined
by
X-ray diffraction methods.
As
many more protein structures have been
so
determined,
the
only essential modification
of
this quotation
is
that whenever charge
is
found
buried within
the
hydrophobic associations,
it is
always found
ion
paired (also referred
to as a
salt bridge). This
is,
of
course,
as
required
by the
consilient mechanism
of
protein structure
and
function. Reemergence
of the
separated
charges contributes
to the
destruction
of
hydro-
phobic hydration
on
dissociation
and
makes
facile
the
modulation
of
hydrophobic associa-
tion/dissociation when assisted
by
introduction
of
a
proximal modest charge
or
other polarity.
Armed only with
the
information that
two
states exist, determination
of the
involvement
of
the
consilient mechanism
of an
inverse tem-
perature transition becomes straightforward.
Raising
the
temperature
and
decreasing
net
charge under conditions that change
the
state
both bring about formation
of the
hydrophobi-
cally associated state. Hydrophobic association
occurs with loss
of
water,
and
hydrophobic
dissociation occurs with
an
uptake
of
water.
This
too can be
diagnostic. Application
of
these
simple tests
to the
diverse data
on
hemoglobin
below makes
it
quite clear that
the two
states,
deoxygenated
and
oxygenated,
are
related
by
an inverse temperature transition, with
the
deoxygenated state being
the
hydrophobically
associated state. This
is
discussed below. What
is less clear from analysis
of
structural data
in
the literature
is
exactly
how the
binding
of the
polar group
of
oxygen, O2, triggers
the
conver-
sion from hydrophobically associated
to
hydrophobically dissociated.
Can it be a
direct
effect
of the
introduction
of the
polar oxygen
molecule?
Or
does
the
binding
of
oxygen cause
conformational changes such that
a
mismatch
of salt bridges
and
hydrogen bonds develops
within and/or between
the
hydrophobically
associated domains?
The
latter could expose
these polar species
and
thereby disrupt
a
par-
ticular hydrophobic association
of a
pair
of
hydrophobic domains.
7.2.4.1
Hemoglobin: Hydrophobic
Association
of
Four Myoglobin-Like
Proteins
7.2.4.1.1
The
Relationship Between
the
Oxygen Binding Proteins
of
Hemoglobin
and Myoglobin
Hemoglobin
is a
tetramer composed
of two a-
chains
and two
P-chains, with paired
ap
dimers
delineated
as a^p^ and a^P^. (In the
nomencla-
ture used here,
the
superscript identifies
the
250
7.
Biology Thrives Near a Movable Cusp of Insolubility
subunit and the subscript indicates the number
of such subunits.) Myoglobin and the a-chain of
hemoglobin arose evolutionarily from the same
primordial globin gene, and the p-chain of
hemoglobin evolved from the a-chain. Each
chain binds a heme group, which is the site of
oxygen binding.
The sequences of the a- and P-chains of adult
hemoglobin A (HbA) and of myoglobin are rep-
resented in Figure 7.2 in terms of single residue
hydrophobicity plots. This is based on the Tt-
based hydrophobicity scale reported in Chapter
5,
section 5.3.2. The Tt-values for each amino
acid residue are given in Table 5.1 and were
derived from the data in Figure 5.9. As shown
in Table 5.1, the most vinegar-like residue is
glutamic acid (Glu, E); it is the most effective
residue for disrupting or preventing hydro-
phobic association. The Glu (E) residue is the
most polar residue, as represented in Figure 7.2,
with the largest downward deflection. The car-
boxylate, -COO", of the Glu (E) residue is the
most effective amino acid side chain in destruc-
turing hydrophobic hydration. Because of the
special thermodynamic properties of hydro-
phobic hydration discussed in Chapter 5, an
increase in the potential for hydrophobic hydra-
tion leads to hydrophobic association, whereas
a decrease in the potential for hydrophobic
hydration disrupts hydrophobic association.
7.2.4.1.2 Distribution of Charged and
Oil-like Residues in the Globin Chain
In general, from the perspective of the con-
silient mechanism, the distribution of charged
or polar residues (shown by the downward
deflections from the 37° C line in Figure 7.2)
and the oil-like or hydrophobic residues
(shown by the upward deflection from the 37°
C line in Figure 7.2), constitutes the primary
contribution to the common tertiary structure
for myoglobin in Figure 7.3 and to that of the
a- and p-chains of hemoglobin in Figure 7.4.
7.2.4.1.3 Insights into Association of Chains
from the Single Residue Tt-based
Hydrophobicity Plots
From the viewpoint of hydrophobic association
between chains, therefore, the primary differ-
ence in amino acid sequence between myoglo-
bin and the a- and P-chains of hemoglobin
resides in the number and distribution of glu-
tamic acid (Glu, E) residues. As shown in
Figure 7.2, myoglobin contains 14 Glu (E)
residues, whereas the a-chain contains only 4
and the p-chain only 8. Of all the amino acid
residues, the presence of Glu (E) residues is the
most effective means of disrupting subunit
interaction by hydrophobic association. Pri-
marily because of this, myoglobin exists as a
monomer and exhibits little or no tendency
for intermolecular hydrophobic association,
whereas the propensity for the a- and P-chains
to associate hydrophobically is much greater,
resulting in the a2P2 tetramer under physiolog-
ical conditions.
7.2.4.1.4 The Relative Oxygen
Binding Properties of Myoglobin
and Hemoglobin
Myoglobin exhibits a hyperbolic curve for the
binding of oxygen as the result of a simple
binding process wherein a linear increase in
bound oxygen results from a linear increase in
the partial pressure of oxygen, pOz, until satu-
ration is approached. On the other hand, hemo-
globin exhibits a sigmoidal oxygen-binding
curve, in which hemoglobin initially exhibits a
lower affinity for oxygen (Figure 7.5). When
hemoglobin completes its binding of oxygen at
a higher chemical potential, that is, at a higher
partial pressure of oxygen, it has done so with
a sigmoid binding curve in which the binding of
the fourth oxygen molecule to the tetramer
occurs with a 200-fold greater affinity, that is,
oxygen binding occurs with positive coopera-
tivity (Figure 7.6). The initial bound oxygen
faciUtates binding of the second oxygen. This
means that hemoglobin can change its degree
of saturation markedly with a small change in
partial pressures of oxygen with near saturation
in the lungs and near complete release on going
to the tissues. Myoglobin, on the other hand,
shows little change in degree of saturation for
the same change in partial pressure of oxygen.
For hemoglobin, this, of course, is the required
property for transport of oxygen from the lungs
to the tissues.
7.2 The Movable Cusp of Insolubility
251
Hemoglobin a-chain
Hemoglobin P-chain
Myoglobin
Residue
FIGURE
7.2. Single residue hydrophobicity plots for
the a- and P-chains of hemoglobin and for myoglo-
bin. Note the marked decrease in polar residues (the
negative deflections) in the plots for the a- and p-
chains of hemoglobin compared with the plot for
myoglobin; this is responsible for hydrophobic asso-
ciation between a- and P-chains in the formation of
the tetramer of chains that is hemoglobin.
FIGURE
7.3. Structure of myoglobin
(Kendrew sausage representation),
showing location of the oxygen binding
heme group and indicating its coordina-
tion to the imidazole of His^°. (Repro-
duced with permission. Illustration, Irving
Geis.
Rights owned by Howard Hughes
Medical Institute.)
B
FIGURE 7.4. Structure of hemoglobin
(Perutz sausage model representation). A
Deoxyhemoglobin. B oxyhemoglobin.
Dyad axis view showing four subunits,
constituted by two a-chains and two p-
chains with the same folding of individual
chains as in myoglobin. (Reproduced with
permission. Illustration, Irving Geis.
Rights owned by Howard Hughes
Medical Institute.)
7.2 The Movable Cusp of Insolubility
253
Arterial pressure!
J l_
40 60 80
p02 (torr)
100 120
FIGURE 7.5. Plots of the oxygen binding curves for
myoglobin and hemoglobin in whole blood, with a
dashed curve for the binding that hemoglobin would
exhibit with the same average binding affinity but
without positive cooperativity.
Y02
is the fraction of
sites occupied by oxygen (i.e., the fraction of satura-
tion),
and PO2 is the partial pressure of oxygen. The
arterial p02 reflects the pressure of oxygen in the
lungs.
7.2.4.1.5 Positive Cooperativity Arises from
the Subunit Interactions
The isolated heme bound a-chain and the
tetramer of p-chains, like myoglobin, bind
oxygen with a simple hyperbolic curve; they do
not exhibit positive cooperativity. Furthermore,
a wide change in neither pH nor CO2 signifi-
cantly affects the binding of oxygen by
myoglobin, whereas these have significant and
physiologically relevant effects on the oxygen
transport binding properties of hemoglobin.
Therefore, the interactions between subunits
must contain the source of the positive cooper-
ativity that provides for effective transport
function of hemoglobin.
7.2.4.1.6 A Small Difference in the Geometry
of the Heme Binding Site in the Oxygenated
and Deoxygenated States of Myoglobin
and Hemoglobin
In deoxymyoglobin and in deoxyhemoglobin,
the heme iron is out of the heme (porphyrin)
plane by 0.55 and 0.60 A, respectively, whereas
in oxymyoglobin and in oxyhemoglobin the
heme iron is out of the porphyrin plane by 0.22
and 0.00 A, respectively. In all cases of dis-
placement, the heme iron is displaced toward
the coordinated imidazole side chain of a
histidine residue in formation of a tetragonal
pyramid bond structure, and oxygen binds to
the opposite side of the heme, restoring or
partially returning the heme iron to the plane
defined by the heme.
This difference in heme iron displacement
from the porphyrin plane has been proposed by
Perutz^^ to be the basis for the positive cooper-
ativity, that is, for the sigmoid oxygen binding
curve essential for the function of hemoglobin
in its oxygen transport role. Our purpose here
is to bring function into focus in terms of the
consilient mechanism of inverse temperature
transitions of hydrophobic association/dissocia-
tion of defined pairs of hydrophobic domains
within the hemoglobin tetramer. More to the
point is the question, could the consilient
mechanism involving changes in the Gibbs free
FIGURE 7.6. Hill plots, log[Yo2/(l - YoJ],
to obtain the coefficients that show oxygen
binding affinity to hemoglobin from the
start to the finish of the titration. As mea-
sured from the intercepts with the 0.0 line,
the binding affinity to hemoglobin increases
100-fold from binding of the first oxygen to
the fourth oxygen; this is positive coopera-
tivity. In contrast, the oxygen binding to
myoglobin shows a slope of one, that is, no
cooperativity. (Adapted with permission
from Voet and Voet.^°^)
^02
i-Ya
100
10
1.0
0.1
-
T^
' ' 1 > 1 y -1
PSo'of // /
the last
^/ 1 X
oxygen ^/ / X J
bound ^5/ // -|
^/ Ir Hemoglobin
<>V jf
slope
=3.0
X y 1
X / /I 1
/^
1
/ i 1
Myoglobin ^^ // Rsoof
slope
= 1
\ y^ //' the first
^/js'
f oxygen J
X^ / bound
Z-j Z_i LJ 1 1
H 0.99
H 0.9
0.01 0.1
0.5 Yo-
H 0.1
1 10 100 1000
PO2
254
7.
Biology Thrives Near
a
Movable Cusp
of
Insolubility
energy
of
hydrophobic association contribute
to
the
sigmoid oxygen binding property
and
thereby contribute
to
hemoglobin function?
7.2,4,2
Occurrence
of a
Temperature
Effect Diagnostic
of the
Consilient
Mechanism Despite Absence
of an
Essential Functional Role
The consilient mechanism
is
most fundamen-
tally identified
by an
inverse temperature tran-
sition that results
in
hydrophobic association
on
increasing
the
temperature through
the
transi-
tion zone, that
is,
through
the
responsive
temperature interval.
The
observation
of a
temperature-driven release
of
oxygen from
tetrameric hemoglobin
has no
recognized phys-
iological role, because there
is no
significant
increase
in
temperature
on
going from
the
lungs
to the
tissues.
Also,
it is
important
to
note that thermally
driven release
of
oxygen from tetrameric
hemoglobin
is
greater than
the
temperature-
effected release from
the
related monomer
myoglobin.
The
state obtained
on
raising
the
temperature
for a
molecular system functioning
by
the
consilient mechanism
of an
inverse
temperature transition
of
hydrophobic associa-
tion would necessarily
be a
state
of
greater
hydrophobic association.
By the
consilient
mechanism, therefore, thermally driven oxygen
dissociation that
is
greater
for
hemoglobin than
for myoglobin defines deoxyhemoglobin
as the
more hydrophobically associated state
of
hemoglobin.
A modest increase
in
temperature moves
the
hemoglobin tetramer across
the
Tfdivide,
surmounting
the
cusp
of
insolubility,
to
arrive
at
the
more insoluble side wherein pairs
of
hydrophobic domains have moved from having
greater exposure
to
water
to
exhibiting more
hydrophobic association. This prediction
of the
consilient mechanism
is
borne
out by the
crystal
structures
of the
oxygenated
and
deoxygenated
states
of
hemoglobin. Associated pairs
of
hydrophobic domains characterize deoxyhe-
moglobin
in the
crystal structure,
and
certain
components
of
these domains become exposed
to water
in
oxyhemoglobin.
7.2.4.3
Positive Cooperativity
on O2
Binding Analogous
to
Formation
of
Carboxylates Within Increasingly
Hydrophobic Domains
7.2.4.3.1 Positive Cooperativity
of
Carboxyl
Ionization
in
Elastic Model Proteins Increases
with Increasing Hydrophobicity
The above prediction
of the
consilient mecha-
nism that deoxyhemoglobin
is the
state
of
greater hydrophobic association would allow
that binding
of an
initial polar oxygen molecule
could
be
analogous
to the
formation
of an
initial carboxylate group,
as
occurs
in our
step-
wise increasingly hydrophobic model elastic
protein-based polymeric machines described
in
Chapter
5.
Specifically,
as
shown
in
Figure
5.34,
ionization
of the
initial carboxyl
to
form
the
polar carboxylate group
is
increasingly delayed,
that
is,
occurs
at
increasingly higher
pH
values,
as
the
hydrophobicity
of the
model protein
increases. Associated with
the
supralinear
increase
in pKa
shifts with
a
linear increase
in
hydrophobicity, there occur corresponding
supralinear increases
in
positive cooperativity.
The Hill coefficients,^^
(n),
increase from
1.5 to
8.0 as the
result
of
stepwise increases
in
hydrophobicity. Figure
7.7A
contains plots
of
the Hill coefficients.
The set of
model proteins
from Table
5.5 and
their Hill coefficients
follow:
Model Protein
i:
(GVGVP GVGVP GEGVP GVGVP GVGVP GVGVP)36(GVGVP), E/OF
=^
1.5
Model Protein
ii:
(GVGVP GVGFP GEGFP GVGVP GVGVP GVGVP)4o(GVGVP),
E/2F
=>
1.6
Model Protein
iii:
(GVGVP GVGVP GEGVP GVGVP GVGFP GFGFP)39(GVGVP),
E/3F
=>
1.9
Model Protein
iv:
(GVGVP GVGFP GEGFP GVGVP GVGFP GVGFP) 15(GVGVP),
E/4F
=>
2.7
Model Protein
v:
(GVGVP GVGFP GEGFP GVGVP GVGFP GFGFP)42(GVGVP),
E/5F ^ 8.0