From the Department of Physiology, State University of New York Health Science Center, Syracuse, New York 13210
Current-voltage curves for DIDS-insensitive Cl conductance have been determined in human red
blood cells from five donors. Currents were estimated from the rate of cell shrinkage using flow cytometry and differential laser light scattering. Membrane potentials were estimated from the extracellular pH of unbuffered suspensions using the proton ionophore FCCP. The width of the Gaussian distribution of cell volumes remained invariant during cell shrinkage, indicating a homogeneous Cl
conductance among the cells. After pretreatment for
30 min with DIDS, net effluxes of K+ and Cl
were induced by valinomycin and were measured in the continued presence of DIDS; inhibition was maximal at ~65% above 1 µM DIDS at both 25°C and 37°C. The nonlinear current-voltage curves for DIDS-insensitive net Cl
effluxes, induced by valinomycin or gramicidin at varied [K+]o,
were compared with predictions based on (1) the theory of electrodiffusion, (2) a single barrier model, (3) single
occupancy, multiple barrier models, and (4) a voltage-gated mechanism. Electrodiffusion precisely describes the
relationship between the measured transmembrane voltage and [K+]o. Under our experimental conditions (pH
7.5, 23°C, 1-3 µM valinomycin or 60 ng/ml gramicidin, 1.2% hematocrit), the constant field permeability ratio
PK/PCl is 74 ± 9 with 10 µM DIDS, corresponding to 73% inhibition of PCl. Fitting the constant field current-voltage equation to the measured Cl
currents yields PCl = 0.13 h
1 with DIDS, compared to 0.49 h
1 without DIDS,
in good agreement with most previous studies. The inward rectifying DIDS-insensitive Cl
current, however, is inconsistent with electrodiffusion and with certain single-occupancy multiple barrier models. The data are well described either by a single barrier located near the center of the transmembrane electric field, or, alternatively, by a
voltage-gated channel mechanism according to which the maximal conductance is 0.055 ± 0.005 S/g Hb, half the
channels are open at
27 ± 2 mV, and the equivalent gating charge is
1.2 ± 0.3.
The transport of carbon dioxide from the tissues to the
lungs is facilitated by the formation of bicarbonate by
red blood cells in a cyclic reaction scheme known as
the Jacobs-Stewart cycle (Jacobs and Stewart, 1942; for
review, see Klocke, 1988
). The hydration of carbon dioxide to carbonic acid, catalyzed by red cell carbonic
anhydrase, and then its dissociation into bicarbonate, is
followed by rapid electroneutral exchange of bicarbonate for Cl
across the red cell membrane. These reactions increase the carbon dioxide carrying capacity of
the blood, while minimizing acidification of venous
blood. Red cell Cl
/HCO3
exchange, known as the
"Hamburger shift" or "chloride shift", is mediated by
the membrane domain of capnophorin, a protein also denoted as anion exchanger AE1. This integral glycoprotein (mol wt 101,700) comprises 25% of the mass of
membrane protein in red blood cells and is the predominant protein located in band 3 of SDS polyacrylamide gels (for reviews see Knauf, 1979
; Passow, 1986
;
Jennings, 1989
, 1992
; Reithmeier, 1993
).
In addition to electroneutral anion exchange, capnophorin is also thought to mediate a small conductive
net anion flux, which could be important as the rate
limiting step for electrolyte and water movements during patho-physiological dehydration of the red cell
(Freedman et al., 1988). Previous studies of conductive anion fluxes mediated by red cells treated with the irreversible covalent inhibitor DIDS revealed DIDS-sensitive and DIDS-insensitive components of the net Cl
fluxes (Knauf et al., 1977
; Kaplan et al., 1983
). DIDS is
the most potent of a series of stilbene derivatives originally found by Cabantchik and Rothstein (1972)
specifically to inhibit red cell anion transport. In our studies
of anion conductance with human red blood cells, we
found that the DIDS-insensitive component of net anion efflux increases with increasing extents of membrane hyperpolarization (Freedman and Novak, 1987
;
Freedman et al., 1988
, 1994).
Models for the mechanism of conductive ion transport can be tested and are constrained by the characteristic current-voltage and conductance-voltage relationships (e.g., Hodgkin and Huxley, 1952; Läuger,
1973
). In the equivalent circuit shown in Fig. 1, the K+,
Na+, and Cl
concentration gradients across the red
cell membrane are represented as batteries (EK, ENa,
and ECl) in parallel with the membrane capacitance Cm.
Each battery is in series with its respective ionic conductance (gK, gNa, and gCl). The electrical potential inside
the cell is Em, while that outside is at ground. Because it
has not proven possible to use microelectrodes to drive
currents or to clamp the voltage across the human red
cell membrane (Lassen, 1972
), ionophores have been
used instead to increase the permeability to cations,
thus permitting ionic currents to flow under the influence of diffusion potentials, which can then be measured indirectly. Treatment of red cells with valinomycin, or with gramicidin in sodium-free medium, increases gK above the normally low value of gCl and
allows the flow of the ionic currents, iK and iCl (Fig. 1,
arrows); the net efflux of K+ and Cl
discharges the potassium battery while charging the chloride battery.
The K+ and Cl
currents are opposite in sign and approximately equal in magnitude; a small disparity
(within 10%) at hyperpolarizing voltages is accounted
for by proton fluxes (Freedman et al., 1994
). Whereas the total net current across the membrane is zero in
the absence of an external circuit, the individual ionic
currents induced by the addition of ionophores can be
measured directly, or, as in the present study, inferred
from the rate of cell shrinkage. Fluorescent potentiometric indicators that monitor the voltages continuously show that the voltage is indeed clamped at a
steady value after the addition of valinomycin or gramicidin; steady levels of dye fluorescence are seen with
the oxacarbocyanine dye, diO-C6(3) (Hoffman and
Laris, 1974
), or with the thiadicarbocyanine, diS-C3(5),
or indodicarbocyanine, diI-C3(5), dyes (Freedman and Hoffman, 1979; Freedman and Novak, 1989
). In the
present study, the change in voltage has been estimated
from the change in the extracellular pH of unbuffered
DIDS-treated red cell suspensions (Macey et al., 1978
)
using the proton ionophore FCCP; we previously used
this method to calibrate fluorescent potentiometric indicators (Freedman and Novak, 1983
, 1989
; Bifano et
al., 1984
). In this report, which has been briefly summarized (Freedman and Novak, 1996
), we show that
the inward rectifying current-voltage curve describing
DIDS-insensitive Cl
conductance is inconsistent with
an electrodiffusion mechanism and with certain single-occupancy multiple barrier models, but instead is consistent either with a single barrier located near the center of the transmembrane electric field, or with a voltage-gated mechanism with an equivalent gating charge
of
1.2 ± 0.3 under our experimental conditions.
Blood from healthy human donors was drawn by venipuncture into heparinized tubes and immediately centrifuged at 13,800 g for 3 min at 4°C. The plasma and buffy coat were aspirated and discarded, and the packed cells were then washed three times by centrifugation, each time resuspending in about 5 vol of chilled medium containing 1 mM KCl and 149 mM NaCl for experiments with valinomycin, or 1 mM KCl and 149 mM choline chloride for experiments with gramicidin. The cells were then adjusted to 50% hematocrit (HCT) in the cold wash solution and kept on ice for use on the same day.
To determine cell potassium, [K+]c, the cells were diluted with
the washing medium to 1.2% hematocrit, and were packed by
centrifugation in 0.4 ml microcentrifuge tubes attached to syringe tubes as previously described (Freedman and Hoffman,
1979a; Freedman et al., 1994
). Triplicate samples of packed cells
with weight (w) (40-80 mg) were hemolyzed in 10 ml deionized
water. Portions of the hemolysates were then diluted in half with
30 mM LiNO3, followed by flame photometric analysis for the
concentration of potassium in the hemolysate, [K+]h. [K+]c was
calculated from [K+]c = [K+]h·2·10/fw, where f (g H2O/g
packed cells) is the packed cell water determined gravimetrically,
in triplicate, as previously described (Freedman et al., 1994
). The
cellular potassium concentration, [K+]c
, corrected for trapped
medium,
, (0.026 ml/g packed cells, as determined previously
with [14C]inulin) is given by [K+]c
= (f [K+]c
[K+]o)/(f
).
The corrected cell water content, f
(g cell water/g cells) is obtained from f
= (f
)/(1
). Other portions of the same
hemolysates were diluted with Drabkin's reagent, and were analyzed spectrophotometrically for hemoglobin, Hb (g/ml packed
cell water), using cyanmethemoglobin standards; the corrected hemoglobin concentrations, Hb
(g/ml cell water) are obtained from Hb
= fHb/(f
). The initial membrane potential, Em, was estimated from the chloride equilibrium potential, ECl = 58.7 log
rCl, where the Donnan ratio, rCl, was determined in triplicate after
equilibration of 1.2 percent hematocrit suspensions for 15 min
with 36Cl at pH 7.5 and 23°C, as previously described (Freedman
et al., 1994
). The Donnan ratio, r
, corrected for trapped medium is obtained from r
= (fr
)/(f
). These measurements permitted calculation of initial values of the membrane
potential, Em = (RT/
)ln r
Cl, and of the equilibrium potentials,
EK and ECl.
Current-voltage curves for DIDS-insensitive net effluxes of Cl
and K+ from human red blood cells treated with valinomycin or
gramicidin at varied concentrations of extracellular K+, or [K+]o,
were determined as previously described (Freedman et al., 1994
).
The cells were diluted to 1.2% hematocrit and were pretreated with 10 µM DIDS for 30 min at 23°C. The net effluxes of K+ and
Cl
were estimated at 23°C in the continued presence of DIDS in
duplicate flasks from the rate of cell shrinkage, as measured by
flow cytometry and differential laser light scattering in the Technicon H-1 Hematology Analyzer (Technicon Instruments Corporation, Tarrytown, NY). For each sample the mean cell volume,
MCV, and the relative distribution width, RDW, or coefficient of
variation of the Gaussian distribution of cell volumes in the cell
suspension, was noted. For the experiments in Fig. 3, net effluxes
of K+ and Cl
were determined directly by the cold-quench
method, which involves stopping the efflux at desired times by inserting a cold-finger condenser into a sample of the cell suspension, separating the cells from the medium by centrifugation,
and then measuring the cellular contents of K+ by flame photometry, and of Cl
with a chloridometer (Freedman et al., 1994
).
Fluxes estimated from cell volume changes are more convenient
and have better time resolution, and were previously found to
agree with those determined directly by the cold-quench method.
For the five current-voltage experiments shown in Fig. 5, net
effluxes of chloride induced by valinomycin or gramicidin were estimated from the rate of decrease of the mean cell volume.
Changes in the membrane potential were estimated in parallel in
unbuffered DIDS-treated suspensions from the change in the external pH, or pHo, from an initial pHo of 7.5 at 23°C before
DIDS, to the final steady value attained after adding 1 µM of the
proton ionophore FCCP, also as described previously (Freedman
et al., 1994). Controls showed that, after the initial K+/H+ exchange, 1 µM FCCP had no effect on the rate of cell shrinkage induced by 3 µM valinomycin in suspensions treated at 23°C with 10 µM DIDS between 1 and 150 mM [K+]o. In three other control experiments, doubling the concentration of FCCP from 1 µM to 2 µM increased the extent of hyperpolarization induced
by 1 µM valinomycin at 1 mM [K+]o by 7 ± 3 mV. The effect of
FCCP in increasing the extent of hyperpolarization without significantly affecting the net efflux is consistent with a stimulation
of PK, as described by Bennekou (1984
, 1988
) for the related protonophore CCCP.
A curve-fitting program (Sigmaplot 4.1, Jandel Scientific, Corte Madera, CA) that uses the Marquardt-Levenberg algorithm to minimize the weighted variance of a nonlinear least squares regression on the data was used to obtain the best-fit estimates of model parameters.
Homogeneity of Chloride Efflux in the Cell Population
For human red blood cell suspensions treated with 10 µM DIDS at 1 mM [K+]o, the decrease in mean cell volume, MCV, relative to the initial mean cell volume,
MCVo, is linear for up to 15 min after addition of 1 µM
valinomycin (Fig. 2 A) or 60 ng/ml gramicidin (Fig. 2
B). The initial mean cell volume, MCVo, averaged 93.2 fl for the two experiments with valinomycin shown in
Fig. 2 A, and 90.0 fl for the two experiments with gramicidin shown in Fig. 2 B. The linearity of the time
course of the decrease of cell volume in the presence of
DIDS is consistent with that previously seen in the presence or absence of DIDS (Fig. 4 in Freedman et al.,
1994), and is shown here along with the relative distribution width (RDW)1 at each time point. The results
show that RDW remains relatively constant, changing
by <1% in 15 min (Fig. 2, C and D). For all of the time
points in two experiments with valinomycin, RDW was 13.2 ± 0.6 (SD, n = 12) (Fig. 2 C, square), and in two
experiments with gramicidin RDW was 14.4 ± 0.3 (SD,
n = 12) (Fig. 2 D, square). In the absence of DIDS,
RDW also remained constant after addition of valinomycin or gramicidin at 1 mM [K+]o: in one experiment
with six identical suspensions (Fig. 4 A of Freedman et
al., 1994
) RDW was 13.4 ± 0.3 (SD, n = 6) initially, and
was 13.7 ± 0.3 (SD, n = 6) 16 min after addition of 3 µM valinomycin; in a similar experiment (Fig. 4 B of
Freedman et al., 1994
) RDW was 14.2 ± 0.3 (SD, n = 6)
initially, and was 14.2 ± 0.5 (SD, n = 6) 10 min after
addition of 60 ng/ml gramicidin. The invariance of the
width of the Gaussian distributions of cell volume in
red cell suspensions during cell shrinkage induced by
valinomycin or gramicidin in the presence or absence
of DIDS implies that the rate limiting permeability to
Cl
is uniform among the cells in the population. If
some of the cells had a higher permeability to Cl
than
other cells, and consequently shrunk faster, then the
Gaussian distribution of cell volumes would have
broadened, and the value of RDW would have increased after the addition of ionophores, in contrast to
the invariance of RDW that was observed. A similar conclusion concerning the homogeneity of PCl in the cell
population was reached recently by Raftos et al. (1996)
,
who estimated the distribution of Cl
permeabilities indirectly by measuring the slope of the osmotic fragility
curve of red cells taken at different times after the addition of valinomycin.
Effect of Varied [DIDS] on Net K+ and Cl Efflux
at 23°C and 37°C
With the membrane potential measured by using the
proton ionophore CCCP, Bennekou and Stampe
(1988) reported at least 95% inhibition of Cl
conductance by DIDS at 37°C. They attributed the disparity between this rather complete inhibition, and the 62-72%
partial inhibition of PCl repeatedly seen by others
(Knauf et al., 1977
, 1983
; Kaplan et al., 1983
), to the
use in prior studies of the constant field theory, and
they questioned the existence of a DIDS-insensitive component of anion fluxes across human red blood
cell membranes. For cells pretreated with varied
[DIDS], we previously reported that the degree of inhibition by DIDS of the efflux of K+ induced by 1 µM valinomycin at 1 mM [K+]o reaches a maximum of 65% at
23°C (Freedman and Novak, 1987
; Fig. 7 in Freedman
et al., 1994
), in agreement with the partial inhibition
reported by others (Knauf et al., 1977
, 1983
; Kaplan et
al., 1983
). The experiments whose results are shown in
Figs. 3-4 test whether or not the differing experimental
conditions might influence the existence of the DIDS-insensitive fluxes. The results in Fig. 3 show the effluxes
of K+ (circles) and of Cl
(squares) induced by 3 µM valinomycin at varied [DIDS] at both 23°C, the temperature we used previously (Freedman et al., 1988
, 1994),
and at 37°C, the temperature used by Bennekou and
Stampe (1988)
. The results show that the inhibition of
the fluxes is maximal above about 1 µM DIDS, but remains partial at around 65% at both temperatures. The
percent inhibition of the fluxes themselves at a particular [K+]o is less than the inhibition of Cl
conductance
because the membrane potential hyperpolarizes, and the driving force increases, with increasing [DIDS].
Thus, an inhibited flux divided by an increased driving
force yields a conductance which has a greater percent
inhibition than that of the flux itself. The partial inhibition persists, however, when either PCl or the Cl
conductance are estimated from measured net effluxes of
Cl
and from measured membrane potentials (Freedman and Novak, 1987
; Freedman et al., 1994
; and Fig. 5
A as discussed below).
Table I.
Initial Cell Potassium and Hemoglobin Concentrations, Water Content,
Donnan Ratio and Membrane Potential, and Constant Field K+
and Cl |
Effect of Varied Duration of Pretreatment with DIDS
In the experiments of Bennekou and Stampe (1988),
the fluxes were reportedly determined during the first
90 s after adding cells to medium containing DIDS at
37°C, with the flux initiated by addition of valinomycin.
Longer times were used to determine the slower fluxes
(Stampe, P., personal communication). Conceivably, the cells might have had a mixture of reversibly and irreversibly bound DIDS, depending on the time of exposure to DIDS. DIDS is known to react with capnophorin in at least two steps: a reversible binding leading
to complex I, followed by a slower irreversible covalent
reaction leading to complex II as follows:
![]() |
![]() |
If band 3 had different chloride conductances with reversibly and irreversibly bound DIDS, with complex I showing greater inhibition than complex II, the partial inhibition by DIDS could be a consequence of the irreversible reaction of the inhibitor with the transport protein. From the activation energy for irreversible binding determined by Janas et al. (1984), the halftime of the covalent reaction is 3.6 min at 23°C and 0.46 min at 37°C; thus, the preincubation of 30 min with DIDS that we used would be sufficient to ensure complete irreversible binding. To determine whether or not the duration of exposure to DIDS influences the existence of the DIDS-insensitive efflux, valinomycin was added 1 min (Fig. 4, circles) or 30 min (Fig. 4, squares) after DIDS, and the fluxes were determined in duplicate (filled and hollow symbols) in the continued presence of DIDS, either at 23°C (Fig. 4 A) or at 37°C (Fig. 4 B). The average fluxes in the duplicate suspensions for 1 min exposure to DIDS were within 20% of those determined for 30 min exposure to DIDS, and thus the DIDS-insensitive flux persists with a brief exposure as well as for complete irreversible binding.
Current-Voltage and Conductance-Voltage Curves
Current-voltage curves for DIDS-insensitive chloride
conductance were determined in five experiments, for
which the mean initial cell K+ and hemoglobin concentrations, cell water content, Donnan ratio and membrane potential are given in Table I. The current-voltage curves from two experiments, which were shown
previously (Fig. 8 in Freedman et al., 1994), and from
three additional experiments, are all shown together in
Fig. 5 A, and also in Fig. 5 C. The data points from experiments with valinomycin at 1 µM (filled circles and
squares) or at 3 µM (filled triangles), or with gramicidin at 60 ng/ml (hollow circles and squares) all fall closely
about the same curve. The solid lines are the best-fit
predictions of the voltage-gated mechanism of transport (Fig. 5 A) or the single barrier model (Fig. 5 B), as
discussed below. The slopes between adjacent points
represent the chloride slope conductance, gCl, in accordance with the relation gCl = di Cl/d(Em
E Cl). The measured slope conductances from each of the five experiments are shown in the conductance-voltage plots in
Fig. 5, B and D, in which it is seen that the slope conductance increases from a value of 0.015 ± 0.005 S/g
Hb (SD, n = 5) near the reversal potential where Em = ECl, to a maximal value of 0.055 ± 0.005 (SD, n = 5) at
hyperpolarizing voltages, representing a fourfold increase
(P < 0.001, paired Student's t test). The significant fourfold increase in slope conductance at hyperpolarizing
voltages (Fig. 5 B) implies that the current-voltage plot
in Fig. 5 A is superlinear; if the current-voltage plot (Fig.
5 A) were linear, then the slope conductances in Fig. 5
B would have been constant at varied voltage, in contrast to the results. The solid line in Fig. 5 D represents
the best fit to a single barrier model, as discussed below, and the solid line in Fig. 5 B represents the best fit
to a Boltzmann distribution of gating charge, according to which half the channels are open at
27 ± 2 mV, with an equivalent gating charge of
1.2 ± 0.3, also as discussed below.
Comparison of Data with Electrodiffusion, Barrier, and Voltage-gated Mechanisms
We next show that in human red blood cells treated
with valinomycin or gramicidin, the inward rectifying
DIDS-insensitive Cl conductance (Fig. 5 A) is inconsistent with electrodiffusion through pores that are always
open (Fig. 7, lower left quadrant). Moreover, the magnitude of the increase in conductance at hyperpolarizing voltages is quantitatively inconsistent with single-occupancy multiple barrier models (Läuger, 1973
) that
have described nonlinear ion currents through gramicidin channels. In contrast, the data are well described
either by a single barrier model (Fig. 5, C and D, solid
lines) or by a voltage-gated mechanism (Fig. 5, A and B,
solid lines).
Because the
theory of electrodiffusion (Goldman, 1943; Hodgkin
and Katz, 1949
; for discussion see Silver, 1985
) predicts
rectifying nonlinear current-voltage curves when the
concentrations of internal and external permeant ions
are unequal, we evaluated whether or not the experimentally determined inward rectifying DIDS-insensitive current-voltage curve for Cl
(Fig. 5 A) is compatible
with an electrodiffusion mechanism. To understand
the current-voltage curves predicted according to the
theory of electrodiffusion, as applied to the present experimental conditions, it is helpful to examine each of
the following measured parameters at varied [K+]o: (1)
the membrane potential Em (Fig. 6 C, middle line); (2) the equilibrium potentials EK =
(RT/
)ln[K+]c/
[K+]o and ECl = (RT/
)ln[Cl
]c/[Cl
]o (Fig. 6 C, lower
and upper lines, respectively); (3) the driving forces, Em
ECl and Em
EK (Fig. 6 B); and (4) the ionic currents, iK and iCl (Fig. 6 A).
With an electrodiffusion mechanism, the membrane potential Em for human red blood cells treated with the K+ ionophore valinomycin, or with gramicidin in sodium-free choline medium, is given by the Goldman-Hodgkin-Katz equation as follows:
![]() |
(1) |
where PK and PCl are the constant field permeabilities
(s1) and RT/
is 25.5 mV at 23°C. Alternatively, with
iK = gK(Em - EK), and iCl = gCl(Em
ECl), then for iK =
iCl, it follows that Em (Fig. 6 C, filled circles and middle
line) is the conductance-weighted average of EK (Fig. 6
C, bottom line) and ECl (Fig. 6 C, top line):
![]() |
(2) |
The data points in Fig. 6 C represent the average values
of Em at each value of [K+]o from the same five experiments (i.e., the values from the absissa of Fig. 5 but
without subtracting ECl); the solid line through the data
is the best fit of Eq. 1, according to which the ratio = PK/PCl = 74 ± 9.
Defining the inhibition I by DIDS of PCl as I = (PClo PCl)/PClo, where PClo is the uninhibited constant field
permeability to Cl
, it follows that I = 1
(
o/
).
From the fluorescence of diO-C6(3), as reported by
Hoffman and Laris (1974)
, we previously estimated the
uninhibited ratio
o = PK/PClo in valinomycin-treated
red cells to be 20 ± 5 at pH 7.4 and 23°C (Freedman
and Hoffman, 1979b
), in agreement with the value of 17 at pH 7.3 and 20°C determined from the partitioning
of diS-C3(5) (Hladky and Rink, 1976
), and also in
agreement with the value of 18 at pH 7.4 and 37°C determined from constant field analysis of 42K fluxes
(Hunter, 1977
). Thus, I = 1
(20/74) = 0.73, or 73% inhibition of PCl by 10 µM DIDS at 23°C, in good agreement with the value of 72 ± 8 (n = 2) percent inhibition of PCl with 10 µM DIDS at pH 7.04 and 37°C determined by Knauf et al. (1983)
by a different method.
The driving forces Em ECl (Fig. 6 B, circles) and Em
EK (Fig. 6 B, squares) were also calculated from the measured values of Em (Fig. 6 C, circles), and from the measured values of EK and ECl (see MATERIALS AND METHODS).
The solid lines in Fig. 6 B were calculated versus [K+]o
using Eq. 1 with the value of PK/PCl = 74, and are seen
to fit the measured driving forces. Thus, the theory of
electrodiffusion describes adequately the measured
membrane potentials (Fig. 6 C) and the driving forces
(Fig. 6 B).
The measured currents iK and iCl (mA/g Hb) from the five experiments are shown plus and minus their standard deviations in Fig. 6 A; the solid lines were computed from the theory of electrodiffusion as follows:
![]() |
(3) |
![]() |
(4) |
where = 96,490 coul/eq,
is the reduced potential
Em/RT, and the factor
= 2.11 (10
3) liter H20/g Hb = (0.717 liter H20/liter cells)/(340 g Hb/liter cells) converts the units of current from mA/liter H2O to mA/g Hb. The best fit of Eq. 4 to the DIDS-insensitive Cl
current, using the measured values of Em, is obtained
with a value of PCl = 3.7 ± 0.4 (10
5) s
1, or 0.13 h
1
(Table I). The upper solid line in Fig. 6 A was computed using this value of PCl and the ratio
= 74, corresponding to PK = 2.7 (10
3) s
1, or 9.9 h
1. The uninhibited constant field Cl
permeability may be obtained from PClo = PCl/(1-I) = 1.4 (10
4) s
1, or 0.49 h
1 (Table I). Hunter (1971
, 1977
) reported a constant
field PCl of 0.036 min
1 (n = 7, pH 7.4, 37°C), corresponding to 2.2 h
1, with a Q10 of about three and an
activation energy between 14°C and 37°C of 16.4 kcal/
mol, from which we estimate his PCl at 23°C to be 0.63 h
1, in close agreement with what we find. A comparable value of 0.033 min
1, or 2.0 h
1 (n = 7, pH 7.1, 37°C) was reported by Knauf et al. (1977)
. A value of
0.06 min
1, or 3.6 h
1 (pH 7.8, 25°C), some sevenfold
higher than what we find, was estimated by Fröhlich et
al. (1983)
, and values of 0.055 and 0.061 min
1 (pHc
7.2, 37°C), or 3.3 and 3.7 h
1, were reported by Bennekou and Stampe (1988)
.
Whereas the theory of electrodiffusion adequately
describes the voltages (Fig. 6 C) and the driving forces
(Fig. 6 B), the predicted currents (Fig. 6 A, solid lines)
lie outside of the standard deviations of the data. As
[K+]o is decreased, the slope between the measured
currents is either constant or increases monotonically
(Fig. 6 A, data), whereas the predicted slopes of the
best fit lines decrease monotonically (Fig. 6 A, solid
lines). The disparity between the theory of electrodiffusion and the currents is even more apparent when the
currents are plotted against the driving forces in the
current-voltage curve, as seen by comparing the data in
Fig. 5 A with the predictions in Fig. 7. The predicted
current-voltage curves in Fig. 7 were calculated for values of = PK/PCl of 20, 40, and 200, corresponding to 0, 50, and 90 percent inhibition of PCl, respectively. Examination of Fig. 7 reveals that the theory of electrodiffusion predicts linear2
current-voltage curves for Cl
between 0 and 90% inhibition of PCl (lower left quadrant), but sublinear current-voltage curves for K+ (upper
right quadrant). Clearly, the finding of an inward rectifying current-voltage curve for Cl
(Fig. 5 A) is inconsistent with the predictions of electrodiffusion (Fig. 7). If
Eq. 4 is used to calculate PCl from the measured currents and voltages at each [K+]o, then the data are described if PCl (hr
1) is assumed to increase linearly with
hyperpolarizing voltages, between 0 and
100 mV, according to PCl =
0.0010Em + 0.05. The voltage dependence of DIDS-insensitive Cl
permeability could be
due either to an effect of voltage on ion permeation
over a barrier, or alternatively, to an effect of voltage on
channel gates, as evaluated below.
The explanation for the prediction of electrodiffusion theory that the current-voltage curves are nearly
linear for Cl but sublinear for K+ (Fig. 7) is found by
examining the membrane potential, the driving forces,
and the currents (Fig. 6). As [K+]o is decreased at constant [Cl]o and constant ECl, the membrane potential
increasingly hyperpolarizes upon addition of K+ ionophores (Fig. 6 C), thus increasing the outward driving
force, Em
ECl, for Cl
(Fig. 6 B, lower line). The inside
negative voltage thus drives an outward Cl
efflux, or
inward current iCl (Fig. 6 A, lower line), which parallels the increased negative driving force (Fig. 6 B, lower
line). Thus, chloride conductance gCl is nearly constant,
and the predicted current-voltage curves for Cl
are
nearly linear (Fig. 7, lower left quadrant). Considering potassium, the effect of decreased [K+]o is greater on
EK than on Em as both become more negative (Fig. 6 C,
lower two lines), resulting in an increased positive driving force Em
EK (Fig. 6 B, upper line), which drives the
efflux of K+. Decreasing [K+]o, however, increases the
outward concentration gradient for efflux of K+, but simultaneously creates a negative electrical potential
which impedes the efflux. Thus, the predicted potassium current, iK, tends to plateau (Fig. 6 A, upper line)
while the driving force, Em
EK, continues to increase
(Fig. 6 B, upper line), resulting in a predicted voltage-
dependent potassium conductance gK and sublinear
current-voltage curves for K+ (Fig. 7, upper right quadrant). The data for K+, however, were restricted to only
a 25-mV range of Em
EK (Fig. 6 B), and the corresponding measured current-voltage curves (not shown)
were thereby unsuitable for comparison with the predictions of the complex mechanisms of ion permeation
described for the ionophore valinomycin (Läuger and
Stark, 1970
; Stark and Benz, 1971
), or for the channel-forming antibiotic gramicidin (Läuger, 1973
; Andersen,
1983a
, b
).
For a single barrier
located at a fractional distance l from the intracellular
side of a membrane of thickness l (0
1), separating an intracellular solution of concentration c1 from an extracellular solution of concentration c2, the theory of absolute reaction rates predicts the following
current-voltage relationship (Jack et al., 1983
):
![]() |
(5) |
where K = zA exp(
Go/RT), z is the ionic valence,
Go is the free energy height of the barrier in the absence of a voltage, and
is the reduced potential
Em/
RT. For a centrally located barrier (
= 1/2) with symmetric solutions (c1 = c2), the current-voltage relationship simplifies to
![]() |
(6) |
where K = cK.
From Eq. 5, the slope conductance g, relative to that at zero voltage g0, is given by
![]() |
(7) |
Fitting Eq. 7 to the conductance-voltage data in Fig. 5 D
yields a best-fit value of of 0.43 ± 0.02. Using this
value for
, a value of K = 0.0033 ± 0.0001 is obtained
from a fit of Eq. 5 to the data in Fig. 5 C. Thus, we conclude that a single barrier located near the center of
the transmembrane electric field is consistent with the
nonlinear conductance-voltage and current-voltage curves
for DIDS-insensitive Cl
conductance. Moreover, in the
context of the generalized Nernst-Planck electrodiffusion theory (Neumke and Läuger, 1969
), which is an alternative to absolute reaction rate theory but which
also takes into account the existence of a membrane
barrier, the shape of the barrier, as well as its location,
can also influence the degree of rectification (Hall et
al., 1973
).
Applying the theory of absolute reaction rates to ion transport through
pores with multiple barriers, Läuger (1973) calculated the slope conductance g as a function of voltage V, relative to the limiting conductance at zero voltage g0, for
single-occupancy channels for the specialized case in
which the multiple internal barriers have equal heights.
At low salt concentrations (c 0),
![]() |
(8) |
and at high salt concentrations3 (c
),
![]() |
(9) |
where q = e z/(n+1),
is the reduced potential (
V/
RT), z is the ionic valence, n is the number of barriers,
and ki and kpa are the rate constants for an ion jumping
over the internal and surface barriers, respectively. For
the case of n = 9, with the ratio of ki/kpa ranging from
zero to infinity, Läuger (1973)
(his Fig. 3) showed that
at low ion concentrations (c
0) sublinear current-voltage curves are predicted when the surface barriers
are rate-limiting, with superlinear current-voltage curves
predicted when the internal barriers are rate-limiting.
At high ion concentrations (c
), the predicted current-voltage curves are nearly linear if the internal barriers are rate-limiting, and slightly superlinear when
the surface barriers are rate-limiting. For the conditions in which superlinear current-voltage curves are
predicted by single-occupancy multiple barrier models,
the extent of the predicted increase in conductance at
100 mV is only 10-20% greater than at 0 mV, far less
than the fourfold increase seen for DIDS-insensitive Cl
conductance over the same range of voltage (Fig.
5). An extension of these model calculations, based on
Eqs. 8 and 9, showing the relative conductance at
100
mV, relative to that at 0 mV, for n ranging from 2 to 10 is shown in Fig. 8. The calculations show that at high
salt concentration, g/g0 is always within 20% of unity
(Fig. 8 B), and at low salt concentration g/g0 is within a
factor of 2 of unity (Fig. 8 A). Thus, single-occupancy
multiple barriers have insufficient rectification to explain the fourfold increase of conductance seen for
DIDS-insensitive Cl
conductance.
A multiple occupancy channel could have a steeper voltage dependence of conductance if a second ion blocked the transport of the first ion, and if the second ion exhibited voltage-dependent binding. Fluctuating barrier models could also give rise to a steep voltage dependency if an electrically charged part of the transport protein crossed the transmembrane electric field during channel gating. Both of these types of barrier models could be viewed as examples of voltage-gated mechanisms, the gating being effected either by an ion or by part of the protein.
Predictions of a Voltage-gated Mechanism.We next tested
the consistency of the data with a voltage-gated mechanism (Hodgkin and Huxley, 1952; for discussion see
Hille, 1992
). For a population of channels whose open
(O) and closed (C) states are controlled by gates with
charge z, if the charged gates distribute across the
transmembrane electric field in accordance with a Boltzmann distribution, then
![]() |
(10) |
where kT/e = 24, Em is the transmembrane electrical potential, and Eo is the voltage at which half the channels are open.
The open state probability, Po, is given by
![]() |
(11) |
For simplicity, this treatment assumes a single closed
state rather than multiple states (see Bezanilla, 1994,
for review). Note that the limit of (dlnPo/dE) as Em approaches minus infinity is ze/kT, or z/24, so that z is 24 divided by the change in voltage for an e-fold increase
in F (Hille, 1992
). Since the conductance, g, is proportional to the open state probability, or Po = g/gmax, then
![]() |
(12) |
A satisfactory fit of Eq. 12 to the measured Cl conductances as a function of varied Em is shown in Fig. 5 B
(solid line), with the best-fit parameters given in the RESULTS. To derive an expression for the current-voltage
curve itself, the conductance-voltage expression, g(E) = di(E)/dE, was integrated as follows:
![]() |
(13) |
Integration results in the following expression for the current-voltage curve:
![]() |
(14) |
The solid line in Fig. 5 A is the best-fit of Eq. 14 to the
experimental data with the parameters given in RESULTS. Clearly, the voltage-gated mechanism with a
Boltzmann distribution of gating charge is also consistent with the inward rectifying conductance-voltage and current-voltage curves characterizing DIDS-insensitive Cl transport; the percentage deviation between
the predicted and observed Cl
currents is threefold
less with the voltage-gated mechanism than for the theory of electrodiffusion. The derived value for the gating
charge of
1.2 ± 0.3 represents an equivalent value
and a lower limit since more charges could distribute
across a smaller portion of the transmembrane electric
field.
The most significant conclusion from this analysis of
our data on DIDS-insensitive Cl conductance is that
an electrodiffusion mechanism, and single occupancy
multiple barrier models, are quantitatively inconsistent with the inward rectifying current-voltage curve for Cl
,
whereas either a single barrier or, alternatively, a voltage-gated mechanism involving a Boltzmann distribution of negative gating charge across the transmembrane electric field are consistent with the experimental results. An important aspect of the gating charge
mechanism is that the negative gating charge is mobile. A gating mechanism could involve a gating charge on
the channel itself, or alternatively, a voltage-dependent
block by some ionic gating particle (see chapter 18 in
Hille, 1992
).
The theory of electrodiffusion assumes that the ionic
currents are independent, that the membrane is symmetrical, that the transmembrane electric field is constant, and that ions first partition into the membrane
and then diffuse across, driven by concentration and
electrical gradients (Goldman, 1943; Hodgkin and
Katz, 1949
). This theory specifically predicts the dependence on ion concentrations of the transmembrane
electrical potential (Eq. 1 and Fig. 6 C, middle solid line)
and the ionic currents (Eqs. 3-4 and Fig. 6 A, solid
lines), and also predicts the relationship of current to
voltage (Eqs. 3-4, with Em taken from Eq. 1, and Fig. 7).
Interestingly, and in contrast, barrier models and the
voltage-gated mechanism predict the dependence on
voltage of conductance (Eqs. 7-9 and 12, and Figs. 5, B
and D, solid lines), and of current (Eqs. 5 and 14, and
Fig. 5, A and C, solid lines), independently of the relationship between voltage and ion concentration. With a
voltage-gated mechanism, the maximal conductance,
gmax, would itself depend on ion concentrations in accordance with the specific heights of electrical barriers
and the depths of wells, and their locations within the
membrane. Remarkably, the postulation of a voltage-gated process per se permits the prediction of an inward rectifying current-voltage curve (Eq. 14, and Fig. 5
A, solid line) without knowledge of the mechanism of
ion permeation when the gate is open. The finding of
an inward rectifying DIDS-insensitive Cl
current (Fig.
5 A) with moderate voltage-dependency thus excludes nongated electrodiffusion (Fig. 7) and single occupancy multiple barrier models, but does not rule out
the possibilities that Cl
crosses the membrane by hopping over a single barrier or via electrodiffusion when
voltage-gated channels are open.
Prior estimates of the conductive Cl permeability of
human red blood cells (Hunter, 1977
; Knauf et al.,
1977
, Kaplan et al., 1983
; Fröhlich et al., 1983
) relied
on the applicability of the constant field theory (Goldman, 1943
; Hodgkin and Katz, 1949
). Hunter (1977)
originally considered his estimate of PCl to be "order of
magnitude" because of the assumptions inherent in deriving the necessary equations relating voltage to ion
concentrations (Eq. 1) and to ion fluxes (Eqs. 3-4). Instead of calculating membrane potentials theoretically,
Bennekou and Christophersen (1986)
estimated red
cell membrane potentials from changes in the external
pH of unbuffered suspensions in the presence of the
proton ionophore CCCP, and inferred that the flux ratio for K+ mediated by valinomycin is less than unity. If
correct, this apparent contradiction with the assumption of independence would invalidate the use of the
constant field theory for red cells treated with valinomycin, thus calling into question the validity and meaning of prior estimates of PCl. We also have evaluated the
applicability of the constant field theory to red cells
treated with valinomycin, first by calibrating optical potentiometric indicators to measure voltages (Freedman
and Hoffman, 1979b
; Freedman and Novak, 1983
,
1984
, 1987
, 1989
; Bifano et al., 1984
; Freedman et al.,
1988
), and then by focusing on DIDS-insensitive Cl
net fluxes with membrane potentials measured by
means of FCCP (Freedman and Novak, 1987
; Freedman et al., 1994
). Our results for DIDS-treated cells
show that the constant field theory (Eq. 1) precisely describes the relationship between membrane potential and [K+]o (Fig. 6 C); the constant field theory also gives
a reasonable numerical approximation to the K+ and
Cl
currents (Fig. 6 A). From the change in the value of
the ratio PK/PCl with DIDS (from 20 to 74), we inferred
the degree of inhibition of PCl by DIDS (73%). By fitting the measured Cl
currents versus [K+]o (Fig. 6 A),
using the measured membrane potentials (Fig. 6 C), we
estimated a value for the inhibited PCl (0.13 h
1), which
together with the degree of inhibition, yields a value for the uninhibited PCl (0.49 h
1). Despite the reported
deviation of the flux ratio from unity (Bennekou and
Christophersen, 1986
), our derived value for PCl, based
on measured net fluxes and voltages, agrees remarkably well with previous estimates (Hunter, 1977
; Knauf
et al., 1977
, 1983
). Our analysis shows that Hunter's
(1977) original estimate of PCl was considerably more
accurate than realized at the time. The inward rectifying current-voltage curve for the DIDS-insensitive fraction of Cl
net transport (Fig. 5), however, deviates
markedly from the nearly linear curve predicted by the
constant field theory (Fig. 7). A single barrier model
(Eq. 5 and Fig. 5 C; Eq. 7 and Fig. 5 D) and a voltage-gated mechanism (Eq. 14 and Fig. 5 A; Eq. 12 and Fig. 5 B) are both consistent with the available experimental data. Examination of the predicted conductance-voltage plots (Figs. 5, B and D) suggests that extension
of the voltage range in further experiments could allow
discrimination between the two-state voltage-gating mechanism and rectification produced by a single barrier.
Two-dimensional arrays of the membrane domain of
capnophorin have been reconstituted with lipids and
crystallized (Wang et al., 1993, 1994
; Reithmeier,
1993
). Reconstructed images of the protein topography at 20 Å resolution indicate a dimeric structure with
a cavity between the two monomers. 35Cl nuclear magnetic resonance studies suggest that intracellular and
extracellular hemichannels lead to the transport site of
capnophorin (Falke and Chan, 1986b
), and indicate
that DIDS lies between the transport site and the extracellular medium, partially blocking the outward-facing
transport site (Falke and Chan, 1986a
). Earlier structure activity studies with a series of benzene sulfonic
acid and stilbene disulfonates led to a proposed model
of the DIDS-binding site that included juxtaposed positively charged groups providing electrostatic stabilization of the sulfonates on DIDS with adjacent hydrophobic and electron-donor centers (Barzilay et al., 1979
). Fluorescence resonance energy transfer experiments
indicate that the stilbene disulfonate-binding site is located only 34-42 Å from sulfhydryl reagents bound to
cysteine residues on the 40,000-D amino-terminal cytoplasmic domain of capnophorin, consistent with DIDS
residing in a cleft in the outer hemichannel (Rao et al., 1979
). Moreover, substrate anions traverse only 10-
15% of the transmembrane potential between the extracellular medium and the outward-facing transport
site (Jennings et al., 1990
), indicative of a low resistance
for the outer hemichannel. With DIDS bound covalently in such a cavity, the possibility that the negatively charged sulfonic acid groups on the inhibitor
could themselves traverse the transmembrane electric
field and constitute the presumptive gating charge
seems improbable, but cannot strictly be ruled out; further experiments with neutral inhibitors would be
needed to resolve this question.
Further experiments should also be directed at resolving the question of whether covalently-bound DIDS
partially blocks anion conductance mediated by capnophorin, or, alternatively, whether some other transport
protein is responsible for DIDS-insensitive Cl conductance. DIDS-insensitive net efflux of Cl
persists in the
presence of 1 mM PCMBS (p - chloromercuribenzene-sulfonate) (Knauf et al., 1983
), a sulfhydryl reagent
that inhibits the red cell monocarboxylate transport
system (Deuticke et al., 1982
). Moreover, lactate efflux
is unaffected by extracellular Cl
or sulfate (Deuticke
et al., 1982
). Both of these observations are inconsistent with the lactate transporter mediating net Cl
efflux. Chloride conductances that activate at hyperpolarizing voltages have been described in Aplysia neurons (Chesnoy-Marchais, 1983
), in cultured mouse
astrocytes (Nowak et al., 1987
), and in rabbit urinary
bladder (Hanrahan et al., 1985
) and cortical collecting
duct basolateral membranes (Sansom et al., 1990
). A background chloride channel (denoted ClC-2), said to
be "ubiquitously expressed" in epithelial and nonepithelial cells, is in the same gene family as Cl
channels
from Torpedo electroplax (ClC-0) and skeletal muscle (ClC-1). ClC-2 has a 3-5 pS single channel conductance and opens at negative voltages (Thiemann et al.,
1992
; Pusch and Jentsch, 1994
); the voltage-gating is
thus similar to DIDS-insensitive Cl
conductance in human red blood cells (Fig. 5). Moreover, the inactivation
gate of the double-barelled Cl
channel from Torpedo
californica (Miller and White, 1984
) opens at hyperpolarizing voltages with an equivalent gating charge of
2.2 ± 0.1 (White and Miller, 1979
), also similar to
what we find in red cells.
As the concentration of DIDS is increased, the degree of inhibition of net Cl efflux is maximal at
around 65% at 1 mM [K+]o when the cells are pretreated
with the inhibitor, and the valinomycin-induced fluxes
are then measured in the continued presence of the inhibitor either at 23°C (Fig. 7 in Freedman et al., 1994
)
or at 37°C (Fig. 3). Assuming 0.34 g Hb/1010 cells, with
each cell having a surface area of 133 µ2, our value for
the maximal DIDS-insensitive chloride conductance of
0.055 S/g Hb at 23°C corresponds to 1.4 µS/cm2, in
reasonable agreement with the value of 2.8 µS/cm2 at
the higher temperature of 37°C estimated from the
data of Bennekou and Stampe (1988
, their Fig. 4 and
their Table II). The DIDS-insensitive conductive efflux
of chloride characterized in the present study at hyperpolarizing voltages contrasts with the 99.999% inhibition by DIDS of the unidirectional efflux of Cl in the
absence of ionophores at the normal resting potential
of
9 mV (Gasbjerg et al., 1993
); we previously reported that the degree of inhibition increases as the
membrane potential becomes less negative (Freedman
et al., 1994
).
The results in Fig. 4 indicate that DIDS-insensitive
conductance is largely unaffected (20%) by whether
DIDS is bound reversibly (1 min preincubation) or irreversibly (30 min preincubation). Circular dichroism
spectra (Batenjany et al., 1993
) and proteolytic digestion experiments (Kang et al., 1992
) indicate that irreversible binding of DIDS changes the conformation of
capnophorin to a more compact structure, possibly reflecting a conformational change that occurs during
transport (Reithmeier, 1993
).
After the cloning and sequencing of the murine
cDNA coding for band 3 protein (AE1) by Kopito and
Lodish (1985), the cDNA for the human red cell chloride transporter was also cloned and sequenced (Tanner et al., 1988
; Lux et al., 1989
; see Alper, 1991, for review). Band 3 protein has also been functionally expressed in Xenopus laevis toad oocytes microinjected
with mRNA prepared from the cDNA clone from humans (Garcia and Lodish, 1989
) and from mice (Bartel
et al., 1989
). Site-directed mutagenesis experiments with the mouse protein indicate that one of the isothiocyanate (NCS) groups on DIDS binds irreversibly to
Lys-558 on the extracellular side of the 65-kD chymotryptic NH2-terminal fragment with a stoichiometry of
one inhibitor molecule per capnophorin monomer
(Bartel et al., 1989
; for review, see Passow et al., 1992
).
The lock-carrier model for red cell anion transport
proposed by Gunn (1978) included a titratable, positively charged transport site and a gating mechanism.
The dependence on pH of Cl
self-exchange in resealed ghosts (Funder and Wieth, 1976
; Wieth and
Bjerrum, 1982
), and of sulfate fluxes in ghosts and intact cells (Schnell et al., 1977
; Milanick and Gunn,
1984
), indicated that the "carrier" could be singly or
doubly protonated, and chemical labeling experiments
with phenylglyoxal have implicated arginine residues in
the mechanism of red cell anion transport (Wieth et al., 1982
). Sulfate-chloride exchange normally includes
a proton flux and is thereby electroneutral (Jennings,
1976
), consistent with at least two positive charges and
one negative charge at the transport site. When intact
red cells are treated with Woodward's reagent K and
borohydride (BH4
), glutamate 681 on human capnophorin is converted into an alcohol (Jennings and
Smith, 1992
), thus neutralizing its negative charge. Under these conditons sulfate-chloride exchange becomes
electrogenic, and a positive charge on the protein now
accompanies Cl
transport. Jennings (1995)
reasoned
that in unmodified cells, during normal Cl
translocation the mobile positive charge is neutralized by the negative charge on glutamate 681 which must itself
traverse most of the transmembrane electric field. The
negative gating charge that is consistent with DIDS-
insensitive Cl
conductance is not necessarily glutamate
681, although this amino acid would be a possible candidate if the fluxes turn out to be mediated by capnophorin by a voltage-gated mechanism.
Since capnophorin (AE1) functions mainly as an
electroneutral exchanger with "ping-pong" kinetics
(Gunn and Fröhlich, 1979; Jennings, 1982
), it would be
of considerable interest to find indications of gating
properties from analysis of current-voltage curves. The
red cell membrane resistance has been estimated at around 106
·cm2, corresponding to a total membrane
conductance of around 25 pS/cell (Hoffman et al.,
1980
). Capnophorin (AE1) is the most prevalent integral glycoprotein in the red cell membrane. If this conductance were uniformly distributed among the 1.2(106)
band 3 monomers per cell, the "single channel conductance" would be of the order of 10
5 pS, making it unlikely ever to be able to observe such channel gating directly. Alternatively, one or a few DIDS-insensitive background chloride channels per cell could account for
the Cl
currents observed in this study. Preliminary observations of anion selective channels in human red
blood cells have been recorded with the patch clamp
technique (Schwarz et al., 1989
), and also after fusing
vesicles from red cell suspensions into planar lipid bilayers (Freedman and Miller, 1984
). Additional biophysical studies of chloride conductance, together with
structural and molecular biological studies, should potentially aid in relating the mechanisms of conductance
and exchange, and in revealing the detailed mechanism of chloride transport across red cell membranes.
Original version received 27 November 1995 and accepted version received 1 November 1996.
Address correspondence to J.C. Freedman, Department of Physiology, SUNY Health Science Center, 766 Irving Avenue, Syracuse, NY 13210. Fax: 315-464-7712; E-mail: FREEDMAJ{at}VAX.CS.HSCSYR.EDU
2 Due to the inward ClWe thank Drs. P. Stampe, E. Moczydlowski, P. Pratap, and P. Dunham for valuable discussions, and for reading and commenting on a draft of the manuscript. We thank DeForest Brooker, Hematology Supervisor, Division of Clinical Pathology, SUNY Health Science Center at Syracuse, for use of the Technicon H-1 Hematology Analyzer and for phlebotomy services. We also thank Christopher J. Perigard, Clinical Pathology Supervisor, Bristol-Myers Squibb Company, Pharmaceutical Research Institute (Syracuse, NY) for use of the Technicon H-1 Hematology Analyzer.
We gratefully acknowledge the initial support of National Institutes of Health grant GM28839, continued support from the Department of Physiology and the Hendrick's Fund for Medical Research of SUNY Health Science Center at Syracuse, and a grant from the National Kidney Foundation of Central New York, Inc.
RDW, relative distribution width.