(Received for publication, June 19, 1995)
From the
We have previously proposed a role of hydration in the allosteric control of hemoglobin based on the effect of varying concentrations of polyols and polyethers on the human hemoglobin oxygen affinity and on the solution water activity (Colombo, M. F., Rau, D. C., and Parsegian, V. A.(1992) Science 256, 655-659). Here, the original analyses are extended to test the possibility of concomitant solute and water allosteric binding and by introducing the bulk dielectric constant as a variable in our experiments.
We present data which indicate that glycine and glucose influence HbA oxygen affinity to the same extent, despite the fact that glycine increases and glucose decreases the bulk dielectric constant of the solution. Furthermore, we derive an equation linking changes in oxygen affinity to changes in differential solute and water binding to test critically the possibility of neutral solute heterotropic binding. Applied to the data, these analyses support our original interpretation that neutral solutes act indirectly on the regulation of allosteric behavior of hemoglobin by varying the chemical potential of water in solution. This leads to a displacement of the equilibrium between Hb conformational states in proportion to their differential hydration.
It is well established that differential water binding occurs
between distinct conformations of a protein. Hence, whether or not
differential water binding contributes to the energetic of protein
reactions, as some ions and metabolites do, is a key question to fully
comprehend the mechanism of biological control. The role of water on
allosteric regulation had been previously investigated, using Hb
oxygenation as a model, by the so-called osmotic stress
method(1, 2) . The concept of this method is to use
solutes, which are potentially excluded from the protein surface, to
set the bulk water activity a(3) . Haire
and Hedlund(4) , using ethylene glycol, observed that at a low
concentration range ethylene glycol decreases Hb oxygen affinity while
at a higher concentration causes the opposite effect. They interpreted
these results as reflecting preferential binding of ethylene glycol to
Hb at the low solute concentration range, whereas, at high ethylene
glycol concentration range, the increased O
binding
affinity of Hb was attributed to an effect of water activity on the R
to T allosteric equilibrium(4) . In our former studies of the
effect of water activity on Hb O
binding properties, we
have used chemically different solutes like sucrose, stachyose, and
polyethylene glycols to distinguish solute from water binding to
Hb(1) . Besides finding evidences for an indirect effect of
solutes through water on the deoxy- to oxy-Hb conformational
equilibrium, we have also determined quantitatively this solvation
effect on Hb allosteric transition in terms of the differential number
of water molecules bound between the two extreme conformations of Hb.
By using two different model approaches, the Wyman linkage equation or
the Gibbs Duhem equation, we found that 65-72 (
)water
molecules are linked to the binding of four oxygen molecules to human
Hb under the experimental conditions used. Furthermore, this hydration
change was found to be in agreement with the difference between the
solvent-accessible surface areas of deoxy- and oxy-Hb computed from
x-ray structures by Clothia et al.(5, 6) .
The experimental approach and analyses originally used by us to
assess and quantify the role of water on the allosteric control of Hb
have been tested in several other biochemical
systems(7, 8, 9, 10, 11, 12, 13, 14) .
A standard linear dependence of equilibrium and kinetic free energy
parameters on water activity rather than solute activity has been
lately reported. It has been also found that this phenomenon is
independent of the nature of the solute used to set the chemical
potential of water. However, it can be dependent on solute size for
certain processes used to set the chemical potential of water,
µ(11, 12, 13, 14) .
In parallel with our work, these solute effects have been interpreted
as a solvation effect and have been used by several authors to measure
the apparent number of water molecules involved in biochemical
reactions.
However, the proposed role for water in allosteric control has been recently challenged with results which indicate that sucrose has no effect on the energy of trout Hb-I oxygen binding(15) . In addition, it was shown that 1.45 M sucrose causes increased dissociation of human Hb-CO into dimers, as measured by flash photolysis. In contrast to our proposition, these results were interpreted by the same authors in terms of solute-specific differential binding to Hb, i.e. that sucrose acts as a weak allosteric effector or, alternatively, that the change in the oxygen affinity of Hb is due to the decreased dielectric constant of the water/sucrose solution as compared to pure water.
In this report, we consider these two proposed hypothesis. Initially, to assess a possible role of bulk dielectric constant on the allosteric control of Hb, we present oxygen binding experiments with human Hb in the presence of either glycine or glucose. These solutes cause opposite changes in the bulk dielectric constant of the solution. To evaluate the hypothesis of direct allosteric solute binding, we treat our data with an extended linkage equation that accounts for the global effect of changes in the differential binding of solute and of water molecules to Hb on oxygen binding. This equation, which is developed here in detail, has recently been applied to re-analyze the effect of chloride ions in human Hb(16) , where it proved to be appropriate to quantify coupled anion and water heterotropic binding to Hb. Similar equations, as the one proposed by Tanford (17) to account hydration effects on ligand binding, have been applied to analyze the effect of water differential binding on the free energy of binding of lac-rep to DNA (18) and charged peptides to synthetic polynucleotides studied at varying salt concentrations(19) .
Oxygen binding experiments were performed with
60 µM (heme) hemoglobin solutions in 50 mM bis-Tris acetate buffer, pH 7.0, at room temperature by the
tonometric method(21, 22) . The functional parameters P (O
partial pressure at half
saturation) and cooperativity (n
) were calculated
from the Hill Plot by linear regression around half saturation.
P
represents P
obtained
in the absence of neutral solutes. Hemoglobin and methemoglobin
(Hb
) concentrations were estimated using the
extinction coefficients of Benesch et al.(23) . At the
end of the experiments, Hb
concentration was below 5%.
The solution osmolalities (Osm) of Hb samples were determined from
freezing point depression measurements using a Osmette A model 5002
osmometer (Precision Systems, Inc.) after O-binding
experiments. The logarithm of water activity was then obtained through
the following relation:
where is the freezing point depression, K
= 1.86 K Kg mol
is the cryoscopic
constant, and M
is the molarity of pure water (24) .
from the sensitivity of P, the oxygen
pressure at Hb half saturation, on a
, the activity
of X. Therefore, the slope of ln P
versus ln a
gives the difference in
the number of X bound to oxy and deoxy structures of Hb,
n
. This analysis is strictly correct when
only the activity of a single heterotropic ligand varies, i.e. the activity of any other heterotropic ligand than X present in the solution, a
, is maintained
constant. In our previous analysis of the effect of neutral solutes on
Hb binding characteristics using , we considered two
extreme cases: (i) direct solute binding only or (ii) considering only
the indirect effect of solute on water activity(1) . We made
the distinction between these two cases using different solutes and
found a common dependence of ln P
on ln a
, with a
adjusted using
sucrose, stachyose, or polyethylene glycols. This independence on the
different chemical natures of the solutes supported the assumption of
the exclusion of these solutes from protein hydration water and from
any specific interaction with deoxy or oxy Hb structure.
even in a presence of tens of micromolar of protein. Another
Gibbs-Duhem relationship, the one including protein, can be also used
to correctly describe changes in the chemical potential of a protein
due to ligand binding(17, 27) . Specifically, at
constant temperature and hydrostatic pressure, the effect of
O, water, and solute binding on Hb chemical potential,
dµ
, is given by the following:
where: n accounts for the number of each of
these ligands bound to Hb and dµ
for the change in
their chemical potentials(1, 16) . Combining and , we obtain the following:
enabling us to write the following Maxwell relation:
which correlates the measured change in O saturation
due to changes in a
at fixed oxygen partial
pressure with changes in solute and water saturation due to changes in pO
at constant a
. If Hb
oxygen affinity depends solely on either n
or n
, it is possible to integrate this equation over
the saturation isotherm to determine the differential binding of either n
or n
(1) .
However, to quantify the concomitant binding of solute and water, has to be rearranged. We start re-writing
Since n
Inserting and into produces the following:
Integrating from fully deoxygenated to fully
oxygenated state of Hb, following Wyman and his definition of the
median ligand activity, P(25, 26) , we find the
relationship we have used to analyze concomitant changes in solute and
water binding upon allosteric regulation, as shown in the following
example:
Thus, the slope of a plot lnP (or to a good
approximation lnP
, the logarithm of the oxygen
pressure at half saturation) versus ln a
,
reflects the apparent difference in the number of solute and water
molecules (
n
and
n
,
respectively) bound to the fully oxygenated and fully deoxygenated
hemoglobin molecules. These same results can be obtained from the plot
of ln P
versus ln a
, as a consequence of the interdependence of
dlna
and dlna
expressed by . In such a case, becomes the following:
Tanford (17) has originally derived an equation similar to this starting from the definition of the equilibrium constants for ligand and water binding to a macromolecule.
The effect of glucose and glycine on Hb oxygen affinity in 50
mM bis-Tris/acetate, pH 7.0, expressed as
ln(P/P
), is presented in Fig. 1Fig. 2Fig. 3representing three distinct
linkage plots.
Figure 1:
Relative shift in P,
ln(P
/P
) as a dependent
on solution water activity (a
) at different
conditions (glycine (A), glucose (B), and glucose in
the presence of 0.1 M sodium chloride (C)). The straight lines are a linear fit of the data using the
integrated form of Wyman linkage equation (). We subtracted
buffer contribution from the measured osmolality. Experimental
conditions: 50 mM bis-Tris acetate buffer, room
temperature.
Figure 2:
Relative shift in P with increasing solute osmolality for glycine (A),
glucose (B), and glucose in the presence of 0.1 M NaCl (C). The solid lines are a nonlinear fit of
the data using the integrated form of the extended linkage equation (). Experimental conditions: 50 mM bis-Tris
acetate buffer, room temperature.
Figure 3:
The dependence of
ln(P/P
) on the
dielectric constant of a solution imposed by glucose (empty
circles) and glycine (filled circles). The dielectric
constants were evaluated with the following equations:
= 78.54 - 4.46 M(21) and
= 78.54 +
22.58 M(22) . M is the molar solute
concentration. The dashed lines were drawn by
hand.
First, we considered a linkage between O and heterotropic water binding by plotting
ln(P
/P
) versus ln(a
), the logarithm of water activity
varying glucose (Fig. 1A) and glycine (Fig. 1B), both in a Cl
-free buffer
solution. Measurements carried out with Hb in the presence of 0.1 M NaCl and glucose are shown in Fig. 1C. We also
measured the effect of glycine with Hb in a buffer containing 0.1 M NaCl (data not shown). The observed effect on
ln(P
/P
) was in this case much
smaller than that shown in Fig. 1B, measured also with
glycine but in the absence of Cl
. This effect is
probably caused by a decrease on the activity coefficient of ion
chloride with added glycine(27) .
The plots in Fig. 1, A-C, show that
ln(P/P
) varies linearly
with changes in the chemical potential of water, in agreement with our
previous report on the effect of sucrose, polyethylene glycols, and
stachyose on Hb O
affinity(1) . Following the Wyman
linkage equation (), the rate of change of
ln(P
/P
) on
ln(a
) gives the apparent number of water molecules
(
n
) involved with the allosteric transition
from the fully deoxygenated to fully oxygenated state of Hb. The
measured hydration change for each set of data is shown in the third
column of Table 1and appears to be constant within the
experimental error and independent of the chemical differences between
glycine and glucose.
Fig. 2illustrates the same data shown
in Fig. 1, A-C, plotted as a function of the
logarithm of solution osmolality, a quantity which is directly
proportional to the solute activity. In such a case, the analyses of
these plots based only on the Wyman linkage equation ()
could be interpreted as reporting a weak allosteric solute binding
since we assume no energetic contribution from water differential
binding promoted by the indirect effect of solutes on the chemical
potential of water. However, these data can be better analyzed by the
extended linkage , which avoids any assumption about
binding identity (water, solute, or both). This allows us to quantify
the separated contribution of solute and water binding to the
regulation of O binding to Hb. The continuous lines drawn
in Fig. 2, A-C, represent the best fit of the
data to . The adjusted parameters
n
and
n
, the heterotropic contribution of
solute and water binding to the control of Hb oxygenation,
respectively, are also shown in Table 1.
We have further
analyzed the correlation between changes in O affinity and
changes in dielectric constants. In Fig. 3, we plotted the free
energy change of oxygenation (expressed as ln P
)
as a function of the solution bulk dielectric constant with increasing
glycine (27) and glucose (28) concentrations. As seen
in Fig. 3, the Hb-O
affinity cannot be attributed to
electrostatic differences between R and T Hb conformations, since the
changes in ln P
are in opposite directions for
changes in dielectric constant below and above its value in pure water.
Clearly, the dielectric hypothesis can be ruled out on the basis of
these experiments.
The data shown in Fig. 1Fig. 2Fig. 3clearly resolve part of the
controversy raised by Bellelli et al.(15) , who have
challenged our interpretation of the effect of neutral solutes on Hb
oxygenation via protein solvation. These authors suggested that the
lowering of the solvent dielectric constant produced by sucrose
promotes increased stability of the deoxy T form of Hb. The decreased
oxygen affinity of Hb in neutral solutes ( Fig. 1and Fig. 2) is independent of the changes in the dielectric constant
of the solution produced by glycine (27) and glucose (28) as indicated in Fig. 3. In agreement with this
finding, results reported by Ackermann et al.(29) have shown that the rate constants for the reaction
of carbon monoxide with HbO are also insensitive of changes
of bulk dielectric constant produced by addition of glycine, glycerol,
and sucrose. The lack of a dielectric effect on Hb binding
characteristics appears to be widespread among macromolecular
reactions. Other studies of the effect of cosolvents on protein-DNA (9) and drug-DNA (30) interactions have also shown no
correlation between solution dielectric constant and the energy of
binding.
Furthermore, the lack of sensitivity of Hb cooperative oxygen binding toward bulk dielectric constant provides extra evidence for the exclusion of polyols, polyethers, and glycine from the protein surface, in agreement with the experimentally measured enhancement of preferential hydration of proteins in cosolutions of these neutral solutes(31) . From the experimental point of view, this is an important observation since the osmotic stress method, as a tool to measure the water effect on biochemical reactions, relies on our ability to separate direct from indirect effects of solutes. The more effective the solute exclusion from protein the simpler the analyses of its effect.
Hb oxygen uptake depends on solvent and solute
allosteric binding. A common allosteric mechanism controlling oxygen
binding to Hb by glucose and glycine is suggested by the close
superposition of the experimental points shown in Fig. 1, A-C (and Fig. 2, A-C), a
characteristic already observed in our previous report on the effect of
sucrose, polyethylene 200 and 400, and stachyose Hb
affinity(1) . These plots analyzed with the traditional Wyman
linkage equation () offer two distinct interpretations of
the effect of solutes on O uptake: (a) Fig. 1indicates the role of water, linking a fixed differential
change in hydration between the structures of the fully oxygenated and
fully deoxygenated state of Hb with oxygen affinity; (b) Fig. 2indicates an identical heterotropic binding of glucose and
glycine, despite their different chemical structures.
We have
previously indicated that the discrimination between these two
hypotheses, in favor of the water effect, is possible by using
different solutes to set water chemical potential. All the solutes we
tested, although chemically distinct, belong to the class of cosolvents
that are excluded by protein and macromolecular surfaces. This
phenomenon is supported by different experimental approaches, like
hydration forces (3) and density measurements(31) , as
well as by equilibrium dialyses of sucrose and proteins(32) .
However, solute exclusion does not imply the non-existence of solute
specific binding. For instance, we have shown that when titrating Hb
with NaCl to measure the heterotropic chloride effect on this protein,
both Cl-specific heterotropic binding and water
differential binding are operative in the control of the energy of
O
saturation(16) . Similarly, water-cation combined
effects have been considered in the interpretation of the non-linear
dependence of
G of protein (18) and peptides (19) on salt activity. Thus, the functional profile of the
linkage plots, illustrated in Fig. 1and Fig. 2, carries
considerable information about the mechanism of heterotropic action of
ligand- and non-ligand-soluble species.
The curved dependence of ln P on ln (m
) seen in Fig. 2is appropriately analyzed with the extended linkage (). As described under ``Materials and
Methods,'' this equation contains both the energetic contribution
of water and solute binding to Hb oxygen affinity. The differential
numbers of water (
n
) and solute molecules
(
n
) linked with full oxygenation found by the
fitting procedure are shown in the second and third columns of Table 1, respectively. They show, in average, that
n
= -0.08 ± 0.06 glucose
or glycine and
n
= 66.8 ± 2.8
water molecules per Hb are involved in the equilibrium between deoxy
and oxy Hb. While this number of water molecules agrees with that
previously reported by us(1) , the number of glycine and
glucose molecules coupled with the allosteric equilibrium remains near
zero, independent of the chemical nature, size, and charge of these
``inert'' solutes. Table 1also shows a slight increase
in
n
measured with glucose in a
Cl
-free medium compared to
n
measured in the presence of the anion. It is not clear, however,
if this change in
n
reports some
conformational change of the deoxy T structure produced by the
neutralization of positive charges in the central cavity by diffusive,
unbound chloride ions, as recently proposed by Perutz et
al.(33) . If our analysis of the data by does not allow a molecular interpretation of small changes
in
n
, it permits, however, to state that the
magnitude of
n
found through this equation
indicates a rather negligible specific solute binding, if it exists at
all. Therefore, we found extra evidence favoring our original
interpretation that the effect of the neutral solutes on Hb binding
energy is indirect, i.e. through changes in the chemical
potential of water and not through ``weak'' allosteric
binding as proposed by Bellelli et al. (15).
The effects of ligands acting as allosteric regulators of biochemical reactions have its importance long recognized. Without this knowledge, it is inconceivable to fully understand the mechanisms of protein regulatory interactions. While one can strip almost any ligand off macromolecules, we cannot strip solvent. Often it is difficult to maintain the activity of the solvent constant, especially when studying processes involving binding of weak ligands. The work presented here, along with others(1, 7, 8, 9, 10, 11, 12, 13, 14, 17, 18, 19, 27) , shows some strategies, by choosing appropriated inert solutes and thermodynamic models, that can be useful to reveal and quantify the role of solvation on biochemical regulation.