Polymer Structure and Solubility of Deoxyhemoglobin S in the
Presence of High Concentrations of Volume-excluding 70-kDa
Dextran
EFFECTS OF NON-S HEMOGLOBINS AND INHIBITORS*
Robert M.
Bookchin
and
Tania
Balazs
From the Department of Medicine, Albert Einstein College of
Medicine, Bronx, New York 10461
Zhiping
Wang, and
Robert
Josephs
From the Department of Molecular Genetics and Cell Biology,
University of Chicago, Chicago, Illinois 60637
Virgilio L.
Lew
From the Physiological Laboratory, University of Cambridge,
Cambridge CB2 3EG, United Kingdom
 |
ABSTRACT |
Earlier observations indicated that volume exclusion
by admixed non-hemoglobin macromolecules lowered the polymer solubility ("Csat") of deoxyhemoglobin (Hb) S,
presumably by increasing its activity. In view of the potential
usefulness of these observations for in vitro studies of
sickling-related polymerization, we examined the ultrastructure,
solubility behavior, and phase distributions of deoxygenated mixtures
of Hb S with 70-kDa dextran, a relatively inert, low ionic strength
space-filling macromolecule. Increasing admixture of dextran
progressively lowered the Csat of deoxyHb S. With 12 g/dl dextran, a 5-fold decrease in apparent
Csat
("dextran-Csat") was obtained together with
acceptable sensitivity and proportionality with the standard
Csat when assessing the effects of non-S Hb admixtures (A, C, and F) or polymerization inhibitors (alkylureas or
phenylalanine). The volume fraction of dextran excluding Hb was
70-75% of total deoxyHb-dextran (12 g/dl) volumes. Electron microscopy showed polymer fibers and fiber-to-crystal transitions indistinguishable from those formed without dextran. Thus when Hb
quantities are limited, as with genetically engineered recombinant Hbs
or transgenic sickle mice, the dextran-Csat
provides convenient and reliable screening of effects of Hb S
modifications on polymerization under near-physiological conditions,
avoiding problems of high ionic strength.
 |
INTRODUCTION |
The solubility of deoxyHb1 S
polymers at equilibrium with the tetrameric "monomers" is a basic
thermodynamic property of the polymerization process that underlies red
cell sickling. Measurement of the polymer solubility,
"Csat"(1) (also termed Cs (2) or Csol (3)), of Hb S in conditions similar
to those within the cells has served as a critical estimate of the
relative polymerization tendency when comparing the native or modified Hb S, alone or in mixtures with non-S Hbs or inhibitors of
polymerization. A concentrated solution of Hb S is fully deoxygenated
to form a gel, and after high speed centrifugation to sediment the
polymerized solid phase, the concentration of soluble Hb in the
supernatant is the measured Csat.
It is well documented that volume exclusion by macromolecules admixed
with proteins results in their increased activity and corresponding
interactions (4). Thus, when protein macromolecules capable of
interacting, such as deoxyHb S, occupy a substantial fraction of the
total volume of their medium, the addition of a second species of
noninteracting macromolecules crowds the protein molecules closer
together, increasing their interactions. More specifically, addition of
macromolecules that do not copolymerize with deoxyHb S reduces its
polymer solubility by this mechanism (5, 6). However, for the use of
such observations in further investigations on the properties of
deoxyHb S polymers, it is first necessary to characterize the
morphology and properties of the polymer fibers generated in
volume-excluded domains by comparison with those previously
characterized for standard conditions.
In the course of our recent experiments designed to measure the Hb
concentration in the deoxyHb S polymers, CP, we sought a macromolecular extrapolymer marker that would be excluded from
the polymer water compartment and also would have minimal interaction
with the polymer (7), and we found that dextran (70 kDa) appeared to
behave as such an inert extrapolymer space filler.
In the present work, we demonstrate that volume exclusion by admixture
of relatively high concentrations of 70-kDa dextran with Hb S, at close
to physiological ionic strength, markedly reduces the solubility
(Csat) of the deoxyHb while maintaining both its
overall polymer architecture and general proportionality with the
standard Csat in binary mixtures of Hb S with
Hbs A, F, or C or in the presence of noncovalent inhibitors of polymerization.
 |
EXPERIMENTAL PROCEDURES |
Preparation of Hemoglobin--
Heparinized venous blood was
obtained, with informed consent, from SS patients, and hemolysates were
prepared by the method of Drabkin (8). For experiments using highly
purified Hb S, it was separated from the minor components Hb
A2 and Hb F by chromatography on columns of microgranular
diethylaminoethyl cellulose (DE52, Whatman) and developed with 0.05 mol/liter Tris-HCl, pH 8.3. The Hb S solutions were dialyzed overnight
at 4 °C against 0.05 M potassium phosphate buffer, pH
7.50, concentrated by vacuum ultrafiltration to 30-35 g/dl (with
continued simultaneous dialysis), and the concentrated Hb S either used
at once or stored as frozen pellets in liquid nitrogen until use.
Standard Csat Assay--
This assay was performed as
described previously (7), in the presence of 50 mM sodium
dithionite, at 37 °C. When sufficient data were available from
recent measurements in our laboratory using this method, they were used
for comparison with the dextran-Csat, without
repetition. Following addition of the dithionite, the pH of the Hb
solution was 7.10 ± 0.05.
Dextran-Csat Assay--
A stock solution of dextran
(average mass 70-kDa, Sigma), 32 g/dl, was prepared in 0.05 M potassium phosphate buffer, pH 7.50. Mixtures of dextran
and Hb, either Hb S alone or in equimolar mixtures with non-S Hbs
("Hb S-X"), were initially prepared in 1.5-ml microcentrifuge
tubes, to give final concentrations of 6-12 g Hb·dl
1
and 10-21 g dextran·dl
1 in 0.05 M
potassium phosphate, pH 7.50. The solutions were overlaid with paraffin
oil, chilled on ice, and deoxygenated by adding and stirring in the
deoxy solution of sodium dithionite with a gas-tight syringe to give a
final concentration of 0.05 M, and total volume of 500
700
µl. After incubation for 30 min at room temperature (22 °C) or in
a 37 °C water bath, the resulting gel under the oil layer was
carefully but vigorously disrupted with a narrow plunger or wire
loop,2 and the tubes were spun at
room temperature in an Eppendorf model 5415 centrifuge at 14,000 rpm
(16,000 × g) for 20 min. The gel disruption was
repeated twice, followed by a final 30-min spin. Pilot experiments
indicated that no further decrease in supernatant Hb concentration
occurred with additional or longer incubation or centrifugation. After
determining the presence or absence of a pelleted solid Hb phase by
viewing the tube before a bright light, the oil was aspirated, and
replicate 10- or 20-µl samples of the supernatant were mixed with
Drabkin's solution to measure the supernatant Hb concentration that
represented the
dextran-Csat.3
For the reasons noted below, the final total dextran concentrations
chosen for the assay were 10 or 12 g/dl. It was found possible to scale
down the total volume of the mixtures to 100 µl, reducing the total
Hb needed per measurement to about 5-10 mg per tube, and still
maintain good reproducibility of results. In order to have a sufficient
volume of the soluble phase after centrifugation to permit replicate
measurements of the Hb concentrations, it was important to limit the
volume fraction of the polymer; this was found to be satisfactory when
the initial total Hb concentrations were about 1-2 g/dl higher than
the dextran-Csat, whereby the polymer pellet did
not comprise most of the Hb. As with the standard Csat measurements, achieving this balance
between soluble and pellet volume sometimes required trial and error,
i.e. one or more pilot experiments to determine the
appropriate total Hb concentrations with Hb mixtures or with inhibitors
of polymerization.
Electron Microscopy of DeoxyHb S Fibers--
These studies
employed a Philips CM120 electron microscope operating at 120 kV.
Micrographs were recorded at a magnification of 45,000. Hb S fibers
were prepared as described previously (9, 10) except that in the
present studies, Hb S fibers were obtained in the presence of a variety
of dextran concentrations up to 20 g/dl, and with Hb S concentrations
of 7 g/dl. Higher concentrations of dextran were not used because the
high viscosity of the solutions resulted in poor staining. It was
necessary to ensure that nearly all of the dextran was removed during
the negative staining, since residual dextran prevented penetration of
the stain into the particles. Even with this precaution, individual
fibers produced very weak diffraction patterns; bundles of fibers,
however, which have a higher signal-to-noise ratio, did produce optical
diffraction patterns whose spacings and intensity distributions were
clearly visible.
 |
RESULTS |
Effects of Varying Concentrations of Dextran--
We first
explored the effect of dextran concentrations on the
Csat of deoxyHb S. Fig.
1 shows that the
dextran-Csat fell progressively with increasing
concentrations of dextran. Increasing the initial Hb concentrations at
constant dextran had a much smaller effect on the
dextran-Csat, as shown in Figs. 1 and
2. As analyzed below, these results are
consistent with the increased activity (or "effective" concentration) of the Hb with increasing volume exclusion by
dextran, whereas most of an increase in the initial Hb concentration is incorporated into a larger polymer fraction, resulting in small or no
changes in the Csat (Fig. 2).

View larger version (16K):
[in this window]
[in a new window]
|
Fig. 1.
Effect of increasing concentration of 70-kDa
dextran on the Csat of deoxyHb S. Each point represents the mean of at least two replicate measurements,
none of which differed by more than 0.3 g/dl. Samples were incubated at
room temperature (21 °C) (circles, with initial Hb
concentration 4 g/dl, , or 5 g/dl, ; or 37 °C, inverted
triangles, with initial Hb concentration 4 g/dl, , or 5 g/dl,
, prior to centrifugation (see "Experimental Procedures").
|
|

View larger version (13K):
[in this window]
[in a new window]
|
Fig. 2.
Effect of varying initial total Hb
concentrations on the dextran (12 g/dl)-
Csat of deoxyHb S alone ( ) and of
deoxygenated equimolar mixtures of Hbs S + A ( ), S + C ( ), or S + F ( ).
|
|
Although the dextran-Csat could be reduced to
1 g of Hb/dl or less with dextran concentrations over 20 g/dl, the
sensitivity of the assay for detecting polymer solubility differences
induced by inhibitors or admixtures of non-S Hbs was correspondingly
reduced in these conditions by larger proportionate errors (not shown). We therefore sought one or more dextran concentrations that would provide a satisfactory balance of a relatively low
dextran-Csat together with reasonably good
sensitivity in detecting inhibition of polymerization. As seen in Fig.
2, with 12 g/dl dextran, the dextran-Csat values
were fairly stable over a range of initial Hb concentrations, and the
expected directional increases in dextran-Csat occurred upon equimolar admixture of Hb S with the non-S Hbs A and F. The dextran-Csat values with mixtures of Hbs S
and C were close to, but consistently slightly lower than, those of
Hb S + A mixtures4 with both
dextran concentrations, 10 or 12 g/dl (Tables
I and II).
View this table:
[in this window]
[in a new window]
|
Table I
Comparison of standard and dextran (12 g/dl)-Csat;
effects of admixture of non-S Hbs and of non-covalent inhibitors of
polymerization
All Csat measurements were performed at 37 °C.
Values for Standard Csat (in the absence of dextran)
were taken from previous studies in this laboratory for Hb S alone and
Hb mixtures; new measurements were made for Hb S mixed with the
non-covalent inhibitors, where each value represents the mean of at
least two replicate measurements; the two or more replicates were
always within 2% of one another.
|
|
View this table:
[in this window]
[in a new window]
|
Table II
Comparison of standard and dextran (10 g/dl)-Csat;
effects of admixture of non-S Hbs and of non-covalent inhibitors of
polymerization
All Csat measurements were performed at 37 °C.
Values for Standard Csat (in the absence of dextran)
were taken from previous studies in this laboratory for Hb S alone and
Hb mixtures; new measurements were made for Hb S mixed with the
non-covalent inhibitors, where each value represents the mean of at
least two replicate measurements; the two or more replicates were
always within 2% of one another.
|
|
Comparison of Standard and Dextran-Csat, Effects of Hb
Mixtures and Inhibitors of Polymerization--
Tables I and II compare
the standard Csat and
dextran-Csat values (in the presence and absence
of 10 and 12 g/dl dextran, respectively) of Hb S alone, the above Hb
mixtures, and of Hb S in the presence of some noncovalent inhibitors of
deoxyHb S polymerization, phenylalanine, ethylurea, and butylurea. For
each test condition, the directional increases of the
dextran-Csat paralleled those of the standard
Csat. But the ratio of
dextran-Csat/Csat was not
constant; it was lowest with Hb S alone, and generally tended to
increase with increasing Csat (see explanation
derived under "Appendix" and summarized under "Discussion").
Nevertheless, there was good overall proportionality between the
relative increases in Csat and
dextran-Csat, in that the relative order of
differences was maintained.
Ultrastructure of DeoxyHb S Polymers Formed in the Presence of
Dextran--
We wished to determine if dextran caused changes in the
structure of deoxyHb S fibers, which could affect their appearance or
their interactions. We examined electron micrographs to determine if
the presence of dextran had an effect on the fiber appearance or the
interactions associated with the fiber-to-crystal transition.
An electron micrograph of negatively stained deoxyHb S fibers formed in
the presence of dextran, shown in Fig. 3,
reveals that the overall appearance and dimensions of the fibers were the same as those observed previously in the absence of dextran (9,
10). With dextran, optical diffraction patterns from individual fibers
were very faint, barely showing the 32-Å layer line, and the 64-Å and
near equatorial diffraction were also not evident. We attribute this to
incomplete removal of the dextran, which tends to adhere to the fibers.
Such binding occurs with a variety of specimens suspended in viscous
solutions. With fiber bundles, however, each of those characteristic
features of the optical diffraction patterns were seen (Fig.
4).

View larger version (110K):
[in this window]
[in a new window]
|
Fig. 3.
An electron micrograph of deoxyHb S fibers
formed in the presence of dextran (12 g/dl). The fiber diameter is
about 220 Å. Optical diffraction from individual fibers was very weak,
probably because some dextran remained associated with the fiber and
inhibited the penetration of the negative stain. However, the 32- and
64-Å layer lines and near equatorial diffraction previously observed
in fibers formed in dilute phosphate were evident in micrographs of
fiber bundles (see Fig. 4).
|
|

View larger version (60K):
[in this window]
[in a new window]
|
Fig. 4.
a, an electron micrograph of a bundle of
deoxyHb S fibers formed in the presence of dextran. b, an
optical diffraction pattern of the bundle. The diffracted intensity was
stronger than in individual fibers, since many fibers contribute to the
pattern, increasing the signal-to-noise ratio. The pattern shows the
32- and 64-Å layer lines and the near equatorial region and is typical
of those previously observed for fiber bundles formed in 0.05 M phosphate buffer (9).
|
|
It was previously shown that deoxyHb S fibers undergo a series of
transitions over several hours, ultimately forming crystals (9, 10).
There are two crystallization pathways. At pH levels above 6.5, fibers
form bundles which then crystallize (10). Fig. 4a shows a
micrograph of a bundle of fibers formed in dextran. Optical diffraction
patterns from such bundles display the 32- and 64-Å layer lines seen
with fibers formed in dilute phosphate buffers. In addition, there is
diffracted intensity near the equator arising from the helical twist of
the fibers. The 32-Å meridional reflection coupled with the 64-Å
layer line confirm that the Hb molecules are arranged in the same
half-staggered disposition as with fibers formed under physiological
conditions. Since bundles contain many fibers, they generate a higher
signal-to-noise ratio and reveal the diffraction pattern more clearly
than do single fibers.
Below pH 6.5, fibers form macrofibers (10) in which the arrangement of
the hemoglobin molecules is similar to that in crystals, except that
they form a helical array, whereas in crystals the molecules are
arranged in a linear array. Fig.
5a presents an electron micrograph
of a macrofiber formed from fibers grown in the presence of dextran.
Its appearance and the spacings in its optical diffraction pattern are
indistinguishable from macrofibers obtained in the absence of
dextran.

View larger version (64K):
[in this window]
[in a new window]
|
Fig. 5.
a, an electron micrograph of a deoxyHb S
macrofiber formed in the presence of dextran. The diameter of the
macrofiber varies from a maximum of 620 Å to a minimum of 520 Å, as
observed previously for macrofibers formed in 0.05 M
phosphate buffer (31). b, an optical transform of the
macrofiber, displaying the 32- and 64-Å layer lines and near
equatorial intensity.
|
|
Both macrofibers and bundles form crystals. An example of a typical
crystal formed from fibers grown in dextran is shown in Fig.
6a along with its optical
diffraction pattern (Fig. 6b). The crystal spacings of
53 × 64 Å are the same as those of crystals grown without
dextran. This view corresponds to a b axis projection of the
crystal. Vassar et al. (12) found that deoxyHb S polymer fibers and crystals formed in polyethylene glycol (PEG) exhibit the
same structure as those formed in dilute phosphate. Crystallization was
preceded by the formation of short precursors, similar to those seen in
Fig. 6, suggesting that dextran and PEG may have similar effects in
promoting polymerization.

View larger version (103K):
[in this window]
[in a new window]
|
Fig. 6.
a, an electron micrograph of a crystal
of deoxyHb S formed in the presence of dextran. The unit cell
dimensions are 53 × 64 Å, which corresponds to a b
axis projection of the crystal. The background also shows
short crystallization precursors (see arrow) similar to
those seen when crystals form in the presence of PEG (see text).
b, the optical diffraction displays unit cell dimensions of
64 Å in the axial direction and spacings of 53 Å in the radial
direction. These are the same as the unit cell dimensions of the
Wishner-Love crystal of deoxyHb S (32).
|
|
 |
DISCUSSION |
The present results demonstrate that admixture with 70-kDa dextran
markedly reduced the polymer solubility of deoxyHb-S, as reflected in
the dextran-Csat, while maintaining general
proportionality with the standard Csat when
assessing the effects of non-S Hb admixtures and polymerization
inhibitors. Furthermore, the polymer architecture, viewed by electron
microscopy, appeared unchanged by the presence of dextran. The general
appearance and the spacings in optical diffraction patterns of deoxyHb
S fibers formed in the presence of dextran were indistinguishable from
those of fibers formed without dextran. In addition, the
fiber-to-crystal transitions exhibited by deoxyHb S, which must depend
on the basic fiber structure, were also unaltered by the presence of dextran.
These findings suggest that the effects of 70-kDa dextran in this
system can be attributed essentially to its excluded volume and are
consistent with our previous studies using
[14C]dextran (70 kDa) as a marker of the extrapolymer
phase (7), which indicated that it showed no measurable interaction
with Hb and might serve as an inert space-filling macromolecule. This behavior stands in contrast to that of some other non-polymerizing macromolecules such as albumin, which contribute volume to the system
and lower the polymer solubility (6) but do not behave consistently as
an inert macromolecule, probably because its extensive surface charges
result in ionic interactions with Hb (7).
A quantitative characterization of the various phases or compartments
generated by deoxygenation of dextran-Hb mixtures, as derived and
analyzed under "Appendix," is presented in Table
III. We consider first the condition with
deoxyHb S alone, without admixture of other Hbs. The coefficients of
variation (CV) for the different parameters show that
P and fP, which are largely determined by
the total Hb concentration (CT) used in each assay,
show large variations, whereas the other parameters, which reflect
intrinsic physical properties of the system and would thus be expected
to vary little with the different experimental conditions, are
relatively constant. The volume fraction of dextran that excludes Hb
(fDex) constitutes about 75% of the
total volume of the dextran-Hb system, and the remaining volume is
distributed between that occupied by deoxyHb S polymer
(fP, about 8%) and a soluble phase containing the
soluble deoxyHb S molecules at equilibrium with polymer
(fs, about 17%). The ratio between the volume of
dextran that excludes soluble Hb S to that which excludes water (rex) is about 9.4, indicating that the
molecular frame of the 70-kDa dextran molecules is nearly 10-fold less
accessible to macromolecules than to water.
View this table:
[in this window]
[in a new window]
|
Table III
Statistical parameters of the dextran-deoxy-Hb system for SS, SA, SC,
and SF mixtures, as described in the Appendix
The table presents the mean ± S.E. of the mean, standard
deviation, and coefficient of variation for the dextran
12-Csat (Csatdex) for the
fraction of Hb which is polymerized (P), the volume
fractions of polymer (fp), of dextran which excludes
soluble macromolecules (fDex), of solution
available for soluble deoxy-Hb molecules (fS), and
for the ratios of polymer volume which excludes macromolecules to that
which excludes water (rex), and for
fS/(1 fP), which is
equivalent to dextran-Csat/standard
Csat reported in Table I, according to Equation 22.
See "Appendix" for the derivation of each parameter.
|
|
Similar results were obtained with the different binary Hb mixtures
(S-X) investigated. However, some characteristic differences were
apparent. The volume fraction of dextran
(fDex) was somewhat reduced, to about
70% of the total volume, and this was matched by a proportional
reduction in dextran's macromolecule/water exclusion ratio
(rex). In this system, the Hb S-X mixtures
differed from Hb S alone primarily in their forming a proportionally
larger residual (non-dextran) volume (fs + fP, about 30% compared with 25% for Hb S alone)
which was partitioned between smaller polymer phases
(fP, 3.5-5.5% relative to 8% for Hb S alone) and
larger soluble Hb phases (fs, 23-30% relative to
17% for Hb S alone). Similar changes of a smaller degree were seen
when the noncovalent polymerization inhibitors were added to Hb S. Possible explanations for these differences from Hb S alone are
currently under investigation.
These relative changes in the total fP and
fs and their partitioning are reflected in the
observed variations in the ratio of
dextran-Csat/standard
Csat shown in Tables I and II. The net effect is
a rise in this ratio with a rise in the
dextran-Csat, which serves to magnify the
effects of polymer inhibition on the
dextran-Csat.
Refinements in our knowledge of the mechanisms of polymerization of
deoxyHb S and the effects of molecular and cellular alterations that
might prove useful in treating sickle cell disease have become possible
with the advent of techniques such as site-directed mutagenesis for
preparing selected mutant Hbs (13, 14), recombinant Hbs having both the
Val-
6 (sickle) substitution and another chosen substitution (double
mutants) (15), as well as the development of varieties of sickling
transgenic mice (16, 17). In each case, it is important to assess
accurately the polymerization and sickling tendency obtained with the
new Hb or mixture, yet these Hbs are generally available in very
limited amounts.
The standard Csat assay requires relatively
large quantities of Hb (usually over 100-150 mg) at high
concentrations (usually more than 25 g/dl). Two alternative assays that
require smaller amounts of Hb than the standard
Csat have been used to try to circumvent this
problem. One assay, devised by Benesch et al. (18), is
based on the sharp decrease in Hb O2 affinity associated with Hb S polymerization and gelation. In experienced hands, this can
be a fairly accurate scanning assay of the minimum Hb concentration for
gelation, albeit with some limitations (19, 20); but each measurement
requires multiple determinations of Hb O2 affinity (p50)
and for micro-scale determinations requires equipment (such as the
Hem-O-Scan from Aminco, no longer manufactured) that is not readily available.
Another method commonly employed to assay deoxyHb S solubility with
small amounts of Hb is based on its marked decrease in solubility in
concentrated phosphate buffers (21), originally described by Itano (22)
as a "salting out" of the protein in 2.24 M phosphate.
This method was modified by Adachi and Asakura (23, 24) into a kinetic
assay which measures the delay time of deoxyHb aggregation, generally
in 1.8 M phosphate buffers. Adachi and co-workers (23, 24)
have found many similarities in the high phosphate solubility behavior
of some structurally modified Hb S or Hb S in mixtures with other Hbs,
as compared with the more physiological Csat
assay. However, the solubility behavior of modified deoxyHb S or Hb
mixtures in high ionic strength media does not consistently reflect its
properties in more physiological conditions (25, 26), in part because
of the shielding of electrostatic (ionic) intermolecular interactions
that appear to be involved in deoxyHb S polymerization (27, 28).
A new kinetic micromethod that determines the solubility of deoxyHb S
in a gel by measuring the recombination rate of tracer amounts of CO
after laser photolysis was recently described by Ferrone and co-workers
(20). This elegant method requires only a few microliters of
concentrated Hb and can estimate the temperature dependence of the
solubility. The sophisticated equipment required for the method (29),
however, limits its general application as a screening procedure on
small samples.
Recent application of our dextran-Csat method to
studies of a recombinant sickle Hb triple mutant showed similar
inhibitory effects on polymerization when compared with the method
based on the shift in oxygen affinity (18, 30). That study employed 10 g/dl 70-kDa dextran in mixtures with Hb S and the variants. Our present
work indicates that a satisfactory balance between reduction in the
Csat values and adequate sensitivity for
screening polymer solubility can be obtained with 12 g/dl dextran in
the mixtures with Hb, which reduces further the quantities of Hb needed for assay.
Furthermore, the increase in the ratio of dextran
Csat/standard Csat
observed in conditions that increase polymer solubility (Tables I and
II) magnifies the effects of polymer inhibition on the
dextran-Csat. This effect should help
counterbalance the lesser sensitivity that accompanies the much smaller
absolute values obtained with this method.
 |
FOOTNOTES |
*
This work was supported by Grants HL28018, HL58512, and
HL22654 from the National Institutes of Health and the Wellcome Trust (UK).The costs of publication of this
article were defrayed in part by the
payment of page charges. The article
must therefore be hereby marked
"advertisement" in
accordance with 18 U.S.C. Section
1734 solely to indicate this fact.
To whom correspondence should be addressed: Albert Einstein
College of Medicine, 1300 Morris Park Ave., Bronx, NY 10461. Tel.: 718-430-2123; Fax: 718-904-1164; E-mail: bookchin{at}aecom.yu.edu.
2
In the presence of high concentrations of
dextran, centrifugation of the gels without prior disruption, either in
the Eppendorf 5415 centrifuge at 14,000 rpm or, as with the standard
Csat determination (7), in a Sorvall RC-80
ultracentrifuge with a TST 60.4 rotor at 45,000 rpm, did not sediment
the polymer phase. After mechanical disruption of the gel, however, the
solid phase was readily sedimented by centrifugation in the microcentrifuge.
3
In many instances, after centrifugation, a light
yellow firm pellet layer was observed between the supernatant and the
oil. It varied considerably in thickness, even between replicate tubes, and was presumed to be a dextran gel. Since the
dextran-Csat values measured in such replicates
were consistently in good agreement despite grossly different sized
dextran pellets, we concluded that the concentration of dextran in the
gel must have been about equal to that in the soluble phase and that
its formation and size did not affect the results.
4
We found somewhat larger differences (with
Csat of S+ C < S+ A) in measurements
closer to physiological ionic strength (11). For the purposes of the
present studies, however, delineation of those modest differences was
considered secondary to the need to maintain full deoxygenation with 50 mM sodium dithionite, which raised the ionic strength above
normal levels.
 |
ABBREVIATIONS |
The abbreviations used are:
Hb, hemoglobin;
Csat, polymer solubility of deoxyhemoglobin S;
CP, concentration of Hb in the polymer;
PEG, polyethylene glycol; see "Appendix" for definitions used in
equations.
 |
APPENDIX |
The experimental protocol described under "Experimental
Procedures" provides the quantities from which we can compute the relevant parameters of the dextran-Hb system, which are listed in
Tables II and III and discussed above. We consider a solution containing dextran (70 kDa) and Hb; we measure the density of dextran
(
D), the total concentrations of dextran
(CDT) and of hemoglobin
(CT), and the concentration of soluble deoxyHb S in
the supernatant after sedimenting the gel
(Csat). By using the equations derived below
with these measured quantities, we can compute the concentration of
dextran in its water-exclusion volume (CD), the
fraction of polymerized deoxyHb S (P), the ratio between
dextran volume which excludes Hb molecules relative to that which
excludes water molecules (fex), the volume
fractions of Hb excluding dextran
(fDex), of Hb polymer
(fP), and of extra polymer solution containing
soluble Hb (fs). We can also analyze observed differences in the empirically determined ratios between the standard Csat values, measured in the absence of dextran,
and the dextran-Csat, in pure Hb S solutions in
the presence and absence of polymerization inhibitors and in mixtures
of Hb S with non-S Hbs.
Definitions, Conventions and Glossary--
Units are given only
when relevant. Since most equations use and derive relative quantities,
those measurements used for ratios must be expressed in identical units
for comparability. The definitions used are as follows:
CDT, total dextran concentration
(in g/dl); CD, concentration of dextran
in its water-exclusion volume (inverse of the specific volume of
dextran, in g/dl); CH, concentration of soluble Hb
in its water-exclusion volume (inverse of the specific volume of Hb, in
g/dl); CP, concentration of deoxyHb S within the
polymer, either in g/dl or mM, defined by
CP = PQ/VP. For the purpose of
this analysis, we assume that CP is constant under
all the experimental conditions, but this has not been established.
Csatdex, measured concentration of soluble
deoxyHb in the supernatant (in g/dl) after centrifugation of the gel of
deoxygenated Hb S (or Hbs S + Hb X, a non-S Hb) and dextran mixtures,
identical to the "dextran Csat" in the text
above; Csat, identical to
Csat in the text above; concentration (in g/dl)
of soluble deoxyHb S (or Hbs S + X) in the aqueous phase external to Hb
S polymers and to dextran, when present, and at equilibrium with
polymer. The standard Csat was measured in the
absence of dextran and is assumed to remain unchanged in its presence.
The value obtained before and used here was 16 g/dl.
CT measured total concentration of Hb in tube (in
g/dl). fDex, volume fraction of dextran
that excludes Hb molecules; fDwex,
volume fraction of dextran that excludes water; fP, volume fraction of polymerized Hb (S or S + X); fs,
volume fraction of extra-polymer solution (sol) containing soluble Hb;
D and
x, densities of dextran solution and water,
respectively (in g/dl); P, fraction of total Hb in polymer; Q, total amount of Hb in tube (in g);
rex, ratio of dextran volume that excludes Hb
molecules to that which excludes water molecules; rexH, ratio of deoxyHb polymer volume
that excludes Hb or dextran molecules to that which excludes water
molecules; VS, volume of solution available for
soluble macromolecules. Vws,
volume of water in extrapolymer solution (in dl). The volume of
small osmoticants (salts) is neglected.
VD volume of dextran inaccessible to
water. VP volume of polymer, comprising the volume
occupied by Hb tetramers in the polymer and by the polymer water
compartment; it can also be defined by exclusion, as the volume
of polymer which excludes dextran and soluble Hb.
VT, total volume of Hb solution in tube. This volume
has been shown to remain constant during polymerization (28).
VDex, volume of dextran that excludes
soluble macromolecules (Hb). wD, weight of dextran
used to prepare solution of concentration CDT. ww,
weight of water used to prepare dextran solution of concentration
CDT.
Computation of CD, the Inverse of the Molar Volume of
Dextran--
We weigh an amount wD of dextran and
add a sufficient volume of water, Vw, to dissolve it
in a total measured volume VT. By definition (see
Equations 1-4),
|
(Eq. 1)
|
|
(Eq. 2)
|
|
(Eq. 3)
|
and
|
(Eq. 4)
|
CD is estimated from the measured density and
total dextran concentration, by combining Equations 1, 3, and 4 and using
w = ww/Vw = 100 g/dl, as a units conversion factor. We obtain Equation 5.
|
(Eq. 5)
|
Definition of Csatdex and
Computation of P, the Polymer Fraction Formed on Deoxygenation of a
Solution of Hb + Dextran with Known Total Hb Concentration
(CT)--
We measure
Csatdex in the supernatant after
centrifugation (see Equations 6-8). By definition,
|
(Eq. 6)
|
|
(Eq. 7)
|
and
|
(Eq. 8)
|
Solving for P, we obtain Equation 9.
|
(Eq. 9)
|
Computation of the Different Volume Fractions Present in Solutions
of Hb S and Dextran after Deoxygenation and Polymerization of DeoxyHb
S, at Equilibrium--
The total volume (VT)
includes the polymer volume (VP), the volume of
dextran which excludes macromolecules (VDex), and the volume of solution
available for soluble deoxyHb molecules (VS)
(Equation 10). Thus
|
(Eq. 10)
|
Dividing by VT we rewrite Equation 1 using
volume fractions (Equation 11).
|
(Eq. 11)
|
We can compute each of these volume fractions in different ways,
depending of the choice of measured variables and parameters we wish
displayed in the equations. We will compute fP, fS, and fDex
independently from definitions of CP and
Csat.
By definition (Equation 12),
|
(Eq. 12)
|
Rearranging and solving for fP = VP/VT we obtain (Equation 13).
|
(Eq. 13)
|
Assuming that dextran behaves as an inert space filler that does
not disturb the equilibrium between polymer and soluble deoxyHb S, the
equilibrium concentration of soluble deoxyHb S in the aqueous phase,
external to both the insoluble polymer and soluble dextran molecules,
is Csat. Thus, by definition (Equation 14),
|
(Eq. 14)
|
from which we obtain Equation 15
|
(Eq. 15)
|
To derive fDex we re-write Equation 14 as Equation 16
|
(Eq. 16)
|
Combining Equations 6 and 16 and solving for
fDex we obtain Equation 17:
|
(Eq. 17)
|
By using Equations 1-3 we can also define the volume fraction of
dextran which excludes water (fDwex) at
each dextran concentration. By definition,
|
(Eq. 18)
|
From Equations 1-3, VD/VT
in Equation 18 may be replaced by measured
CDT and CD;
thus Equation 19
|
(Eq. 19)
|
We can now estimate the ratio rex between
the volume of dextran that excludes soluble Hb,
VDex, to that which excludes water,
VD. From Equations 18 and 19 we obtain Equation 20
|
(Eq. 20)
|
For reference, it is useful to compute the equivalent
rex parameter for deoxyHb polymers,
rexH. By definition,
rexH is the ratio of polymer volume that
excludes macromolecules to that which excludes water. This is given by
Equation 21:
|
(Eq. 21)
|
With CH and CP values of 136 and 55 g/dl, respectively {7}, rexH
is about 2.5.
Comparison between CsatValues Obtained in the Presence
and Absence of Dextran--
The ratio
Csatdex/Csat
which may be obtained by dividing Equation 6 by Equation 14. This
renders Equation 22
|
(Eq. 22)
|
which expresses the comparison in terms of the volume fractions of
polymer and extrapolymer solution.
 |
REFERENCES |
-
Magdoff-Fairchild, B.,
Poillon, W. N.,
Li, T.,
and Bertles, J. F.
(1976)
Proc. Natl. Acad. Sci. U. S. A.
73,
990-994[Abstract]
-
Hofrichter, J.,
Ross, P. D.,
and Eaton, W. A.
(1976)
Proc. Natl. Acad. Sci. U. S. A.
73,
3035-3039[Abstract]
-
Goldberg, M. A.,
Husson, M. A.,
and Bunn, H. F.
(1977)
J. Biol. Chem.
252,
3414-3421[Medline]
[Order article via Infotrieve]
-
Zimmerman, S. B.,
and Minton, A. P.
(1993)
Annu. Rev. Biophys. Biomol. Struct.
22,
27-65[CrossRef][Medline]
[Order article via Infotrieve]
-
Ross, P. D.,
and Minton, A. P.
(1979)
Biochem. Biophys. Res. Commun.
88,
1308-1314[Medline]
[Order article via Infotrieve]
-
Behe, M. J.,
and Englander, S. W.
(1978)
Biophys. J.
23,
129-145[Abstract]
-
Bookchin, R. M.,
Balazs, T.,
and Lew, V. L.
(1994)
J. Mol. Biol.
244,
100-109[CrossRef][Medline]
[Order article via Infotrieve]
-
Drabkin, D. L.
(1946)
J. Biol. Chem.
164,
703-723[Free Full Text]
-
Wellems, T. E.,
and Josephs, R.
(1979)
J. Mol. Biol.
135,
651-674[Medline]
[Order article via Infotrieve]
-
Wellems, T. E.,
Vassar, R. J.,
and Josephs, R.
(1981)
J. Mol. Biol.
153,
1011-1026[Medline]
[Order article via Infotrieve]
-
Bookchin, R. M.,
and Balazs, T.
(1986)
Blood
67,
887-892[Abstract]
-
Vassar, R. J.,
Potel, M. J.,
and Josephs, R.
(1982)
J. Mol. Biol.
157,
395-412[Medline]
[Order article via Infotrieve]
-
Nagai, K.,
Perutz, M. F.,
and Poyart, C.
(1985)
Proc. Natl. Acad. Sci. U. S. A.
82,
7252-7255[Abstract]
-
De Llano, J. J. M.,
Schneewind, O.,
Stetler, G.,
and Manning, J. M.
(1993)
Proc. Natl. Acad. Sci. U. S. A.
90,
918-922[Abstract]
-
De Llano, J. J. M.,
and Manning, J. M.
(1994)
Protein Sci.
3,
1206-1212[Abstract/Free Full Text]
-
Greaves, D. R.,
Fraser, P.,
Vidal, M. A.,
Hedges, M. J.,
Ropers, D.,
Luzzatto, L.,
and Grosveld, F.
(1990)
Nature
343,
183-185[CrossRef][Medline]
[Order article via Infotrieve]
-
Ryan, T. M.,
Townes, T. M.,
Reilly, M. P.,
Asakura, T.,
Palmiter, R. D.,
Brinster, R. L.,
and Behringer, R. R.
(1990)
Science
247,
566-568[Medline]
[Order article via Infotrieve]
-
Benesch, R. E.,
Edalji, R.,
Kwong, S.,
and Benesch, R.
(1978)
Anal. Biochem.
89,
162-173[Medline]
[Order article via Infotrieve]
-
Sunshine, H. R.,
Ferrone, F. A.,
Hofrichter, J.,
and Eaton, W. A.
(1979)
in
Development of Therapeutic Agents for Sickle Cell Disease (Rosa, J., Beuzard, Y., and Hercules, J., eds), pp. 31-46, New York
-
Liao, D.,
De Llano, J. J. M.,
Himanen, J. P.,
Manning, J. M.,
and Ferrone, F. A.
(1996)
Biophys. J.
70,
2442-2447[Abstract]
-
Perutz, M. F.,
and Mitchison, J. M.
(1950)
Nature
166,
677-679[Medline]
[Order article via Infotrieve]
-
Itano, H. A.
(1953)
Arch. Biochem. Biophys.
47,
148-159
-
Adachi, K.,
and Asakura, T.
(1979)
J. Biol. Chem.
254,
4079-4084[Abstract]
-
Adachi, K.,
and Asakura, T.
(1979)
J. Biol. Chem.
254,
7765-7771[Medline]
[Order article via Infotrieve]
-
Roth, E. F., Jr.,
Bookchin, R. M.,
and Nagel, R. L.
(1979)
J. Lab. Clin. Med.
93,
867-871[Medline]
[Order article via Infotrieve]
-
Vedvick, T. S.,
Koenig, H. M.,
and Itano, H. A.
(1998)
Clin. Biochem.
8,
288-290
-
Bookchin, R. M.,
and Nagel, R. L.
(1973)
in
Symposium on Sickle Cell Disease (Abramson, H., Bertles, J., and Wethers, D., eds), pp. 140-154, C. V. Mosby, St. Louis
-
Eaton, W. A.,
and Hofrichter, J.
(1990)
Adv. Protein Chem.
40,
63-279[Medline]
[Order article via Infotrieve]
-
Ferrone, F. A. (1998) in Hemoglobins: Biophysical
Methods (Everse, J., Vandegriff, K. D., and
Winslow, R. M., eds), Part C, pp. 292-321, Academic Press, New
York
-
Himanen, J.,
Mirza, U. A.,
Chait, B. T.,
Bookchin, R. M.,
and Manning, J. M.
(1996)
J. Biol. Chem.
271,
25152-25156[Abstract/Free Full Text]
-
Potel, M. J.,
Wellems, T. E.,
Vassar, R. J.,
Deer, B.,
and Josephs, R.
(1984)
J. Mol. Biol.
177,
819-839[Medline]
[Order article via Infotrieve]
-
Wishner, B. C.,
Ward, K. B.,
Lattman, E. E.,
and Love, W. E.
(1975)
J. Mol. Biol.
98,
179-194[Medline]
[Order article via Infotrieve]
Copyright © 1999 by The American Society for Biochemistry and Molecular Biology, Inc.