Adaptation and survival of surface-deprived red blood cells
in mice
Ryan C.
Murdock,
Christopher
Reynolds,
Ingrid H.
Sarelius, and
Richard E.
Waugh
Department of Pharmacology and Physiology, University of
Rochester Medical Center, Rochester, New York 14642
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ABSTRACT |
The consequences of lost membrane area for long-term
erythrocyte survival in the circulation were investigated. Mouse red blood cells were treated with lysophosphatidylcholine to reduce membrane area, labeled fluorescently, reinfused into recipient mice,
and then sampled periodically for 35 days. The circulating fraction of
the modified cells decreased on an approximately exponential time
course, with time constants ranging from 2 to 14 days. The ratio of
volume to surface area of the surviving cells, measured using
micropipettes, decreased rapidly over the first 5 days after infusion
to within 5% of normal. This occurred by both preferential removal of
the most spherical cells and modification of others, possibly due to
membrane stress developed during transient trapping of cells in the
microvasculature. After 5 days, the cell area decreased with time in
the circulation, but the ratio of volume to surface area remained
essentially constant. These results demonstrate that the ratio of cell
volume to surface area is a major determinant of the ability of
erythrocytes to circulate properly.
circulation; spherocytosis; erythrocytes; senescence; deformability
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INTRODUCTION |
THE MECHANICAL
PROPERTIES of the red blood cell (RBC) have important effects on
blood perfusion and oxygen delivery. The shape and deformability of
RBCs have been shown to be significant factors in pathologies such as
sickle cell anemia (13, 14) and hereditary spherocytosis
(29), and, in many cases, the origin of RBC disorders has
been traced to specific molecular lesions in the structural proteins of
the RBC membrane (20). In the present study, we examine
the specific issue of how loss of cell surface area affects the ability
of the cell to circulate and what adaptations occur in vivo to improve
the cell's chances for survival.
The deformability of the RBC has been well studied (5,
30). The limited ability of the membrane area to change,
combined with constraints on cell volume resulting from the low
permeability of the membrane to cations, results in a strict limitation
on the ability of the RBC to deform and negotiate small vessels and constrictions within the microvasculature. Within this constraint, the
shear elasticity, viscosity, and the bending resistance of the membrane
determine the response of the cell to applied forces. However, the
forces required to deform the cell in shear or bending are very small
compared with the cell resistance to change in area and change in
volume. Thus the ratio of membrane surface area to cell volume is a
critical determinant of cellular deformability, and it is expected to
have a major influence on the ability of cells to circulate.
Over the past 50 years, there have been a number of studies examining
the relationship between RBC deformability and circulation. A number of
these studies provide evidence that, in many hemolytic disorders, the
membrane, or more specifically, the ratio of the surface area and
volume, is the significant factor that affects the ability of cells to
circulate. As early as the 1940s, investigators observed that highly
spherical RBCs that formed as a result of thermal injury disappeared
from the circulation of burn victims over a period of ~18 h
(9). In a more recent study (8), investigators made RBCs less deformable by using sulfhydryl reagents to
cross-link the membrane proteins and increase the shear rigidity of the
cells. Interestingly, they found no relationship between increased
shear rigidity and the removal of the cells from the circulation.
However, they did find that, when the cells were heated for 15 min at
50°C, a process that decreases the effective surface area of the cell
and thus increases the volume-to-surface area ratio, the cells were
rapidly removed from the circulation (half-time = 10-30 min).
In a recent study from our own laboratories, the effect of reduced
surface area on the short-term survival of RBCs was examined (32). Cell surface area was reduced by inducing
endocytosis of the membrane, and the cells were labeled with a
fluorescent marker to distinguish them from the rest of the cells in
the circulation after reinfusion into a mouse. As expected, a rapid
decrease in the circulating fraction of highly spherical cells was
observed over a period of ~30 min. Somewhat surprisingly, ~20% of
the modified cells remained in the system for up to 4 h, although
most of the highly spherical cells were rapidly removed from the
circulation. These surviving cells showed evidence of reductions in
cell volume, as if to compensate for the reduction in surface area and
maintain a more normal ratio of volume to surface area. In this present study, we extend this earlier study to examine long-term effects of
lost membrane area on cell circulation, focusing specifically on the
disappearance of spherical cells from the circulation and changes in
the dimensions (area and volume) of the surviving population.
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MATERIALS AND METHODS |
Cell preparation.
Donor mice (C57BLJ, 2-3 per experiment) were anesthetized
(pentobarbital sodium, 70 mg/kg ip), and cardiac puncture was performed with the use of a 1.0-ml syringe with a 25-gauge needle. The dead space
between the tip of the syringe and the needle was filled with heparin
before the blood was withdrawn. The blood was then placed in 1.5-ml
Eppendorf microcentrifuge tubes and spun for 4 min at 3,700 rpm
(Eppendorf model 54152). The plasma and buffy coat were aspirated, and
the cells were washed three times in 290 mosM PBS (160 mM NaCl,
25.0 mM Na2HPO4, and 6.2 mM
KH2PO4), pH 7.4. An 8.0 mM stock solution of
lysophosphatidylcholine (LPC; Avanti Polar Lipids, Alabaster, AL) in
1:1 chloroform/methanol was prepared. RBCs were suspended in ~100 ml
of 290 mosM PBS (1.0% vol/vol). LPC stock solution was added to 100 ml
of 290 mosM PBS to an LPC concentration of 0.23 µM and sonicated for
20 min at 40°C (Branson model 2210). The LPC-PBS solution was cooled
to room temperature, combined with an equal volume of the RBC-PBS solution, and then allowed to rotate for 10 min at 120 rpm. LPC-RBC-PBS solution was then divided equally, such that the solutions could be
placed into an even number of 50-ml centrifuge tubes, and centrifuged for 6 min at 2,000 rpm (IEC model HN-SIIC). After centrifugation, the
RBC pellets were collected and resuspended in a 50-ml centrifuge tube
and then washed in RBC storage solution [RBCSS (in g): 0.225 glucose,
2.330 KCl, 0.263 NaCl, 4.279 sucrose, and 1.247 HEPES hemisodium salt
dissolved in 250 ml of deionized H2O], pH 7.4, 340 mosM.
The suspension was then spun for 8 min at 2,000 rpm, and the
supernatant was removed. The pellet of RBCs was added to 35 ml of
HEPES-buffered salt solution, pH 7.4 (in mM: 22.8 sodium bicarbonate,
8.8 HEPES sodium salt, and 11.2 HEPES acid), 320 mosM, and centrifuged
for 8 min at 2,000 rpm. The supernatant was removed and discarded.
After incubation, the cells were labeled with substituted
tetramethylrhodamine isothiocyanate using previously published
protocols (23, 26). After cells were labeled, they were
stored overnight at 4°C in RBCSS.
Reinfusion and sampling of modified cells.
On the morning after cell incubation and labeling, the cells were
washed twice in the overnight storage solution, followed by two washes
in an excess of HEPES-buffered physiological salt solution containing
0.5% bovine serum albumin at pH 8.1 and then resuspended in storage
solution at pH 7.35. All wash solutions were at an osmolarity of 320 mosM. After the last wash, 0.15 ml of packed cells were drawn into a
0.5-ml syringe and injected and into the tail vein. To inject the bolus
of cells into the mouse, the animal was placed in a holding device that
allowed accessibility to the tail.
To collect blood samples for fraction analysis and area and volume
measurements, the mice were sedated with 0.15-0.17 ml of ketamine;
blood was collected from a small nick made in a toe pad. The blood
droplets were collected using a hematocrit capillary tube, suspended in
a solution of PBS + 2.0% fetal calf serum (FCS), and then diluted
to the desired concentration as determined by inspection. Samples,
which could be used for both the circulating fraction and the area and
volume measurements, were taken at day 0, day 1,
and day 5 and then approximately every 7 days thereafter until the circulating fraction fell below 0.1%.
The circulating fraction was determined using fluorescent light
microscopy and video image analysis software (1). The
number of cells counted did not exceed 10,000 and was such that the
coefficient of variation (CV) of the circulating fractions for all but
the last two samples for each mouse was <20% (24). For
the last two fractions, the CV was typically >25% because of the very
small number of labeled cells remaining in these samples.
Micropipette measurements.
Cell surface area and volume were measured using micropipettes
according to established procedures (29). Micropipettes
were prepared by fracturing off the tip of a glass capillary pulled to
a needle point. The pipettes had an inside diameter between 1.2 and 1.8 µm. Cells were suspended at low (<1.0%) hematocrit in PBS plus
2.0% (vol/vol) FCS adjusted to an osmolarity of 316-322 mosM, pH
7.35. Cells were placed in a U-shaped chamber on the stage of an
inverted microscope, and the micropipette was introduced via the open
side of the chamber. The aspiration pressure at the tip of the pipette
was controlled by adjusting the height of a water-filled reservoir
connected to the back of the pipette via water-filled tubing. The image
from the microscope was observed via a television camera and recorded
on videotape for subsequent analysis. To measure cell surface area and
volume, cells were aspirated at a pressure of ~1,200 Pa (12 cmH2O) to ensure that the membrane was fully extended into
the pipette and that there were no folds or creases in the membrane
projection (Fig. 1). The membrane area
(A) and the cell volume (V) were calculated from
measurements of the outer cell radius (Rc) and
the length of the projection in the pipette (Lp)
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(1)
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(2)
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where Rp is the inside radius of the
pipette. One measure of the volume-to-surface area ratio of the cell is
the sphericity (S). This is a dimensionless
quantity proportional to the ratio of the two-thirds power of the cell
volume to the membrane area
|
(3)
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The coefficient is constructed such that the maximum value of
the sphericity is 1.0 (a perfect sphere). The smaller the value of the
sphericity, the greater is the "excess" surface area of the cell,
that is, the area in excess of the area required to enclose the
spherical volume of the cell. The percentage of excess area can be
calculated as
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(4)
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Approximately 100 cells were measured for each population
that was sampled. Statistical significance of difference between samples was evaluated at the 95% confidence level.

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Fig. 1.
Video micrograph showing a mouse red blood cell aspirated into a
micropipette. The dimensions of the cell used to calculate surface area
(A), volume (V), and sphericity (S) are
indicated. For the cell depicted, A = 80 µm2, V = 44.4 µm3, S = 0.752, and percentage of excess A = 33.0%.
Rc, outer cell radius;
Lp, length of the projection in the pipette.
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RESULTS |
Nine different mice received modified cells and were sampled over
a minimum of 5 wk after reinfusion. For the presentation of the data,
day 0 denotes a sample taken at ~3 h after the infusion of
the modified cells into the mouse and day 1 denotes a sample taken at ~24 h after infusion. The remaining samples are labeled according to the number of days after the day 0 sample at
which they were retrieved. On day 0, the areas, volumes, and
sphericities of the modified cells were significantly different from
controls (Fig. 2), although the degree of
modification varied from one preparation to another. Generally, the
area of the modified cells was significantly reduced (Fig.
2A), and the volume of the cohorts was slightly elevated
(Fig. 2B), resulting in a substantial increase in the
sphericity of cells in the modified population (Fig. 2C).

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Fig. 2.
Effects of lysophosphatidylcholine treatment on cell
dimensions. A: distribution of cell surface areas shifts
toward lower values. B: distribution of cell volume changes
little, increasing very slightly. C: sphericity increases
substantially, with many cells becoming nearly perfect spheres.
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The percentage of modified cells remaining in the vasculature declined
with time (Fig. 3). The time course
appeared to be approximately that of a decaying exponential, but, for
at least one-half of the mice studied, the rate of disappearance was
more rapid during the first 5 days after reinfusion than during the subsequent time. This is illustrated in Table
1, in which the time constants are
tabulated for first-order exponential curves fit to the measured
circulating fractions for all days and for days
5-35. It is worthwhile to note that the uppermost curve
in Fig. 3, that is, the case in which the cells disappeared from circulation most gradually (experiment 5 in Table 1),
corresponds to the least modification in the sphericity of the modified
cells. In this case, an increase in sphericity of only 8% relative to control was achieved, whereas, in most other cases, increases of
12-20% were obtained. An inverse correlation was also observed between the mean sphericity of the modified cohort measured on day 5 and the time constant for cell disappearance
(R =
0.71). Thus smaller changes in sphericity
appeared to have a relatively smaller effect on the ability of cells to
circulate.

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Fig. 3.
Circulating fraction as a function of time after
reinfusion. Nine mice were studied, and each is represented by a
different symbol. Time course of disappearance appeared to be
approximately exponential, with time constants ranging from 2.2 to 13.7 days.
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Unlabeled cells from the host mouse were used as matched controls for
the labeled cohort in each sample. The absolute dimensions measured for
these controls varied systematically depending on the day on which the
measurements were made. That is, when two or more different mice were
measured on the same calendar day, the values tended to agree with each
other but were larger or smaller than controls measured for the same
mice on different days. We attribute this to either error in the
measurement of the pipette diameter, slight variations in the
concentration of the suspending buffer, or differences in light or
contrast levels in the recorded images on different days. To avoid
introducing errors in parameter values for the cohort populations
because of these systematic measurement fluctuations, data taken after the infusion of cells were normalized with respect to the mean value of
the corresponding parameter for the unmodified (control) sample for the
host mouse on that day.
The general trends for how the mean area, volume, and sphericity of the
labeled cohorts changed with time in the circulation are shown in Fig.
4. The normalized mean
values for all cohorts were averaged, and the averages were plotted as
a function of time after reinfusion. In general, the mean membrane area
increased during the first 5 days after reinfusion and then gradually
decreased thereafter. The normalized area for day 5 was
significantly larger (Student's t-test) than the normalized
area on both day 0 and day 33. The mean volume
decreased monotonically with time after reinfusion. The sphericity
decreased rapidly during the first 5 days and then remained relatively
constant for the duration of the study. The mean normalized sphericity
decreased by 7.8% during the first 5 days and then by less than 2%
during the next 7 days, and there was no significant change (Student's
t-test) from day 12 through day 33.

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Fig. 4.
Changes in the mean dimensions of the modified cell
populations as a function of time after reinfusion. All parameters are
expressed relative to the mean of the corresponding control parameter.
Points represent the average of 9 normalized population means, and
error bars indicate the standard deviation. A: mean surface
area of the surviving population generally increased in the first few
days after reinfusion and then declined gradually as the cells aged.
B: mean cell volume of the surviving population decreased
monotonically with time after reinfusion. C: mean sphericity
of the surviving cells decreased rapidly toward normal values in the
first week after reinfusion and then remained relatively constant
during the remainder of time in which cells were detectable in the
circulation.
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Single cell micropipette measurements enabled us to examine not only
changes in mean values for the circulating cohort but also changes in
the distribution of area, volume, and sphericity within the population.
In most of the mice studied (7 of 9), there was a shift in the areas of
the modified population toward control values during the first 5 days
after infusion (Fig. 5A). (In
the other 2 mice, the mean area of the cohort population did not change over the first 5 days.) This increase in mean cell area for the surviving population was accompanied by a slight decrease in the mean
cell volume (Fig. 5B) in five of the nine mice. In three of
the mice, the mean volume did not change, and, in one mouse, the mean
volume actually increased slightly. In all mice, there was a dramatic
shift in the mean cell sphericity for the surviving cells toward
control values (Fig. 5C).

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Fig. 5.
An example of the change in the distribution of cell
dimensions after reinfusion. Parameter values for each cell were
normalized with respect to the mean value of the corresponding
parameter for control population. A: distribution of cell
areas shifted toward higher values. Control means were 86.0, 86.6, and
82.5 µm2 for days 0, 1, and
5, respectively. B: distribution of cell volumes
changed little or decreased very slightly. Control means were 51.4, 52.9, and 45.7 µm3 for days 0, 1,
and 5, respectively. C: distribution of
sphericity decreased toward normal values. Control means were 0.776, 0.787, and 0.748 for days 0, 1, and 5,
respectively. Note that for these values of the control sphericity the
maximum normalized sphericity (i.e., the value for a perfectly
spherical cell) was 1.27-1.34.
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The change in the distribution of cell surface area and volume in the
surviving population appeared to be due to a combination of
preferential removal of spherical cells from the circulation and
changes in the dimensions of the remaining cells toward more normal
values. This conclusion was reached by comparing the distribution of
cell sphericity within the modified population on successive days with
each distribution multiplied by the corresponding circulating fraction
(Fig. 6). Between day 0 and
day 5, there is a decrease in the fraction of circulating
cells with sphericities greater than 20% above normal; however, there
is an increase in the fraction of circulating cells with sphericities
near normal. (Note that, in Fig. 6, the solid bars for day 5 are shorter than the day 0 bars at the right side of the
distribution but are taller than the day 0 bars at the left
side of the distribution.) The decrease in the fraction of circulating
cells with sphericities more than 20% above normal can be explained by
the selective removal of cells with high sphericity, but the increase
in the percentage of circulating cells with sphericities near normal
can only be explained by the modification or adaptation of some labeled
cells while they were in the circulation.

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Fig. 6.
Typical example of the distribution of sphericity
multiplied by the corresponding circulating fraction (circ frac) for
days 0-5. Note that the height of the bar in
each bin is proportional to the circulating fraction of cells within
that bin for the different days (bin width = 0.05). Note that the
number of cells with sphericities near normal increased with time after
reinfusion. Because there were no new cells introduced into the
circulation over this period, these results demonstrate that the
sphericity of individual cells was altered toward normal values after
the cells were reinfused into the animal. Control means for this mouse
were 0.736, 0.737, and 0.748 for days 0, 1, and
5, respectively. Note that the normalized value for a
perfectly spherical cell was ~1.35.
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Changes in the distribution of area, volume, and sphericity of the
labeled cohorts from day 5 onward were compared by first normalizing the cellular values by the mean of the matched control population, multiplying these values by the circulating fractions, and
then fitting the distribution with a Gaussian curve. The distributions for one of the mice used in the study are shown in Fig.
7. (Distributions for
the other mice in the study were similar.) Note that each successive
distribution falls within the boundary of the previous one. This result
is consistent with the possibility that the shifts in the distribution
could be occurring simply by the preferential removal of cells of a
certain size. However, these observations do not rule out the
possibility that there may be changes in the dimensions of individual
cells within the distribution.

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Fig. 7.
Changes in the number and distribution of cells with
different dimensions after 5 days in the circulation. Frequency
distributions were multiplied by the corresponding circulating
fractions so that the height of the fitted curves reflects the relative
number of cells having different dimension. Fitted curves, rather than
frequency histograms, are shown to avoid clutter. A: surface
area. B: volume. C: sphericity. Line styles
corresponding to different numbers of days after reinfusion are shown
in the insets.
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Model calculations.
Calculations were performed to estimate the magnitude of forces that
might be generated in the membranes of circulating cells as a basis for
evaluating possible mechanisms for cell removal or modification of cell
volume. The rationale for these calculations is that spherical cells
may not be able to negotiate the smallest capillaries in the
vasculature, particularly at sites of constriction as might occur where
nuclei of endothelial cells protrude into the vessel lumen. We were
particularly interested in estimating the size of vessels or vessel
constrictions that would trap cells of different dimensions and the
magnitude of the membrane stresses that might develop in cells trapped
in those constrictions. This analysis follows the work of Fischer
(7) but uses a slightly simpler geometric model of a
vascular constriction and extends the analysis to consider a wider
range of cell dimensions. We specifically address the
importance of volume-to-surface area ratio in determining cell
entrapment and the resulting mechanical forces in the membrane.
A simple geometry of a cell trapped in a tapered tube was chosen (see
Fig. 8). The RBC membrane was treated as
a thin-walled shell with isotropic properties in the plane of the
membrane (5). The exchange of water between the cell and
its environment due to osmotic and hydrostatic pressures was assumed to
be at steady state; thus the cell volume was taken to be constant. The
upstream (Ru) and downstream
(Rd) radii of the RBC are related to
the slope (M) of the tube taper and radius of the conical
tube at the middle of the conical portion of the cell [we will refer
to this as the midradius (Rm)]
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(5A)
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(5B)
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With the use of these relationships, the area and volume of the
shape were approximated as
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(6)
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(7)
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Force resultants in the membrane were determined by applying a
balance of forces at the upstream and downstream ends of the cell. The
force resultants in the membrane were assumed to be uniform, as was the
pressure inside the cell. The isotropic force resultant [or
"isotropic tension" in the membrane (T)] can then be written as
|
(8)
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where
P is the pressure difference between the upstream
and downstream ends of the cell.

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Fig. 8.
Schematic showing the dimensions and shape of the model of a cell
trapped in a vascular convergence. M, slope (taper) of the
convergence; Ru, upstream radius;
Rd, downstream radius;
Rm, midradius.
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Equations 5-7 completely describe the geometrical
aspects of the problem. By specifying the cell area, the midradius, and the tube taper, the length, volume, and sphericity of the cell can be
calculated, enabling us to evaluate how changes in cellular dimensions
affect the size of apertures in which the cell would become trapped.
For gradually tapering tubes ( |M| < 0.1), this part
of the problem becomes insensitive to the value of M,
and dependence of the trapping tube radius on cell area and sphericity can be explored using approximate relationships (see
APPENDIX). A particularly useful relationship is an
expression for the midradius as a function of the cell area and the
sphericity
|
(9)
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This expression is exact when M = 0, yielding the exact value of the minimum cylindrical tube
radius through which a cell of the given dimensions can pass.
Values for the area, the midradius, slope, and pressure were chosen to
approximate a range of physiological conditions. Five slopes for the
capillary taper were chosen to model possible changes in capillary
lumen diameter due to protrusions into the lumen. The largest slope
(
0.3) is close to the value used in a previous model of RBC flow in
capillaries with variable cross sections (25), and the
lowest value was chosen to model small changes in capillary geometry.
Estimates of the pressure drop across the capillaries of mice
(16) and rats (2) range from <1.0 mmHg (16) to >7.0 mmHg (2).
The calculations indicate that the trapping radius has a relatively
weak dependence on cell area but a stronger dependence on sphericity
(Fig. 9A). For example, at
sphericity = 0.85, a cell with an area of 65 µm2 has
midradius of 1.18 µm and a cell with the same sphericity but an area
of 105 µm2 has a midradius of 1.66 µm. Thus an ~60%
change in area results in an ~40% change in midradius. The same
change in midradius can be produced by just a 15% change in sphericity
(area held constant). For the results shown in Fig. 9A, the
chosen value of M was
0.1. The effect of changing the tube
taper on the relationship between the trapping radius and sphericity is
illustrated in Fig. 9B. Note that the relationship is
essentially independent of slope when |M| < 0.1.

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Fig. 9.
Calculations of the midradius at which a cell is trapped
as a function of sphericity. A: dependence for cells having
different areas in a tube with taper M = 0.1.
B: dependence for cells with a surface area of 85 µm2 in tubes with different tapers.
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The dependence of the cell membrane tension on these geometrical
parameters was also investigated. There is strong dependence of tension
on sphericity, but the dependence of tension on area is slight, as
evidenced by the overlap of the points for the different areas in Fig.
10A. (The tension scales
linearly with pressure; thus tensions at pressure differences other
than 10 mmHg can be determined readily from the values shown in Fig.
10.) There is also a strong dependence of the membrane tension
on the tube taper (Fig. 10B). As the taper becomes more
gradual, the membrane tensions can become very large. This is easily
explained by inspection of Eq. 8. As the upstream and
downstream radii approach a common value, the denominator in Eq. 8 approaches zero. Thus, for gradual tapers, large membrane
tensions result from moderate pressures for trapped cells of any size,
and, as cells become more spherical, tensions are large at all tapers
because the upstream and downstream regions are separated by shorter
distances and thus become similar in radius. It is important to note
that, for cells with elevated sphericities (S > 0.9) in
vessels with a slight taper (M =
0.01), tensions that
are large enough to lyse the cell can result, even for very small
pressure differences (1.0 mmHg).

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Fig. 10.
Dependence of membrane tension on cell and tube geometry
at a transcellular pressure of 10 mmHg. (Note that the tension scales
linearly with pressure so that tensions at other pressures can be
calculated by a simple proportionality.) A: for a tube taper
of slope = 0.1, tension becomes large for sphericity >0.9 for
cells of all surface areas. B: as taper decreases, tensions
at all values of sphericity increase significantly (cell area = 85 µm2).
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The calculations presented so far do not account for the ability of the
cell to increase its area or decrease its volume in response to applied
forces. When large but sublethal forces are applied to cells,
fractional area changes of 1-2% and changes in volume of similar
magnitude are possible. (This corresponds to changes in sphericity of
2-4%.) Such changes might enable the cells to escape local
constrictions in capillaries and continue to circulate. Therefore, it
is of interest to consider how much axial travel might occur past the
initial point of trapping if stress-induced changes in sphericity
occur. In Fig. 11, the displacement along the tube axis resulting from a decrease in sphericity of 3% is
plotted as a function of the taper for cells with different initial
sphericities. These results show that cells can move the farthest when
the taper is low and that the distances are significant. It is
interesting that, although small tapers are most "dangerous" for
cells because membrane tensions tend to be large, cells also have a
better chance to escape from local, slowly tapering constrictions by
small changes in area or volume.

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Fig. 11.
Effect of changing taper on the distance a cell would
travel down a tapering capillary as a result of a 3% decrease in
sphericity. Curves represent travel as a function of the tube taper for
5 different starting values for the sphericity. At small tapers, cells
can travel significant distances as a result of small changes in
sphericity (S), improving their chance to "escape" from
entrapment and continue in the circulation.
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DISCUSSION |
The importance of RBC deformability for RBC survival and for
proper cell flux and oxygen delivery has been widely accepted for many
years, but there has been little quantitative information published
about the precise consequences of alterations in cell deformability on
the ability of cells to circulate. The present study provides
quantitative information about how specific changes in RBC area and
volume affect long-term cell survival in the circulation. The results
point to the ratio of volume to surface area as a major determinant of
the ability of a cell to circulate properly. The tolerance of the
circulation for abnormalities in this parameter is extremely low.
Although cells having a wide range of different sizes circulate equally
well, the data indicate that a cell with abnormal volume-to-surface
area ratio is either removed from the circulation or its dimensions are
altered to bring the ratio of volume to surface area to within 5% of
the normal range.
Model calculations suggest that cell trapping is a likely mechanism
both for cell removal and for the modification of cell dimensions to
improve the chances of survival. For cells with average surface areas
and elevated sphericities, the calculations indicate that a cell will
become trapped in passages with diameters on the order of 2-3
µm. Average capillary dimensions in the mouse are ~5.0 µm
(18), but constrictions caused by endothelial nuclei and
other irregularities may reduce the local capillary diameter to <3.0
µm and in some cases to <1.0 µm (17, 21). Indeed, transient (~20 s) trapping of RBCs in such constrictions has been observed experimentally (21). Calculations show that cells
trapped in such constrictions may develop lytic or near-lytic membrane stresses when they become lodged in constrictions and subjected to
transcellular pressures of magnitudes found in capillary networks in
vivo (7). Past experiments have shown that membrane
tensions of 3-4 mN/m do not produce lysis, but membrane tensions
of 6 mN/m or greater result in lysis within ~10 s (6).
Thus cells may be lysed as a result of membrane stresses generated by
the pressure in the capillary and the geometry of the trap, or the
stresses induced in the membrane may cause changes in membrane
permeability, leading to a loss of intracellular cations and reductions
in cell volume.
The evidence that mechanical stress can cause changes in RBC membrane
cation permeability comes from experiments in which cation leak was
measured in cells subjected to fluid shear forces in a viscometer.
Under these conditions, cells become elongated and undergo a
tank-treading motion around the cell interior. Although there is
disagreement on the precise mechanism by which the increased permeability occurs, in several studies it has been shown that there is
significant loss of potassium in cells subjected to shear rates on the
order of 300 s
1 (10-12). Unfortunately,
the complexity of the cell motion and its interaction with the
suspending fluid make it difficult to determine the precise mechanical
forces generated in the membrane under these conditions. Approximate
analyses indicate that, when the fluid shear rate approaches this
magnitude, cells approach maximum deformation, and membrane force
resultants increase rapidly with further increases in shear rate. Thus,
at shear rates in excess of 300 s
1, at which significant
cation loss is known to occur, membrane force resultants are in excess
of 0.1 mN/m (27), well within the range that can be
generated in the membranes of trapped RBCs (7).
This mechanism could account for the increase in cell density that is
associated with RBC senescence (3). If a cell loses membrane area, either through a mechanical or chemical mechanism, then
it could become transiently trapped in a narrow passage in the
microvasculature. The resulting membrane stresses could lead to a
transient increase in cation permeability, loss of intracellular cations, and a decrease in cell volume. Studies of stress-induced cation loss show that these losses occur without loss of hemoglobin; therefore, as the cell volume decreases, the density of the cell would
increase, as the concentration of hemoglobin within the cell increases.
Such a scenario is consistent with findings from an earlier, short-term
study of surface-deprived RBCs in the circulation (32).
The volume of the modified cells decreased over a period of 4 h,
during which the reduced membrane area remained constant. The scenario
is also consistent with observations that senescent cells in humans are
not only more dense but are also smaller than younger populations of
cells (15, 19, 31). The present study is consistent with
these former studies in that the initial response of the cells was to
decrease volume (while the mean cell area of the population actually
increased), leading to a decrease in the mean sphericity of the
population. In the long term, after the volume-to-surface area ratios
of the cells in the population returned to nearly normal values, the
population of surviving cells decreased in size while maintaining a
requisite ratio of volume to surface area.
During this study we obtained some evidence that the ability of cells
to adapt and survive after surface loss may depend on the metabolic
state of the cell. In one strategy developed to create cells with
reduced membrane area, cells were incubated at 39°C in the absence of
glucose for 3-4 h in an attempt to facilitate echinocytosis and
shedding of membrane vesicles. On the three occasions in which this
strategy was employed, the modified cells all disappeared from the
circulation within 5 days, regardless of their volume-to-surface area
ratio (data not shown). Thus, although volume-to-surface area ratio is
an important determinant of cell survival, it is clear that other
factors can contribute to the removal of abnormal cells from the
circulation. Energy depletion can affect many cellular processes; thus
a number of mechanisms exist that might have contributed to the
disappearance of these cells. One possibility is that the cells lost
their ability to regulate their volume because of reduced activity of
the Na-K-ATPase or other transport proteins in the membrane. Another is
that cells may have lost their ability to maintain lipid asymmetry
because of reduced activity of the lipid translocase. The consequent
appearance of charged lipids in the outer leaflet of the membrane could
trigger removal of cells by the reticuloendothelial system.
The recognition that factors other than the ratio of volume to surface
area can affect cell survival does not take away from our conclusion
that this ratio is a critical determinant for circulation. There is
evidence from prior studies that the fluorescent label used in the
present study has no effect on the ability of cells to circulate
normally (22, 23). Furthermore, the present study demonstrates that cells that have undergone treatment to reduce area,
but which have reacquired a normal volume-to-surface area after 5 days,
will continue to circulate for up to 35-42 days, the full lifetime
of normal mouse erythrocytes (4, 28). Thus the present
procedures do not shorten cell lifetime as long as cells can achieve a
requisitely small ratio of volume to surface area.
In conclusion, the ratio of RBC volume to surface area (sphericity) is
a key factor in determining the ability of RBCs to circulate and
function in the living vasculature. Cells with sphericities more than
5% above the normal range were either removed from the circulation or
modified within a period of 5 days after infusion. Model calculations
support the hypothesis that both modification (probably by a reduction
in cell volume) and removal could result from mechanical trapping of
cells at constrictions within the microvasculature. Preliminary
evidence suggests that the modification of the cells may involve an
energy-dependent mechanism, inasmuch as cells incubated at body
temperature for 4 h in the absence of nutrients before reinfusion
did not survive past 5 days in the vasculature. The present results are
consistent with prior studies of RBC senescence in that, after the
5-day period of adjustment, cells became progressively smaller as they
aged but maintained a requisite ratio of volume to surface area.
 |
APPENDIX |
For cases in which the capillary taper M is small and
terms of order M2 are neglected, an approximate
expression for the cell surface area is obtained
|
(A1)
|
The corresponding approximate expression for volume is
|
(A2)
|
(These simplified forms are accurate for tapered tubes to order
M 2 because no terms of order
M appear in the expressions. For straight tubes, the
expressions are exact.) From the definition of the sphericity
(Eq. 3), the following expression for the volume is obtained
|
(A3)
|
Combining Eqs. A1
A3 to eliminate L and
V, a cubic equation in Rm is obtained
|
(A4)
|
There are three roots to this equation
|
(A5)
|
where
|
(A6)
|
and
|
(A7)
|
After substitution and simplification, the physically relevant
root takes the form
|
(A8)
|
 |
ACKNOWLEDGEMENTS |
We thank Pat Titus, Donna Brooks, and Richard Bauserman for
technical assistance.
 |
FOOTNOTES |
This work was supported by National Heart, Lung, and Blood Institute
Grant PO1-HL-18208.
C. Reynolds was a recipient of a Summer Undergraduate Research
Fellowship from the Strong Children's Fund at the University of Rochester.
Address for reprint requests and other correspondence: R. E. Waugh, Dept. of Pharmacology and Physiology, Univ. of Rochester Medical Center, 601 Elmwood Ave., Box 711, Rochester, NY 14642 (E-mail:
waugh{at}seas.rochester.edu).
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.
Received 4 February 2000; accepted in final form 12 April 2000.
 |
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