Download Red blood cell deformability and protein adsorption on

Red blood cell deformability and protein
adsorption on red blood cell surface
YUJI KIKUCHI
AND TOMIYASU
KOYAMA
Division of Physiology, Research Institute of Applied Ekctricity,
Sapporo 060, Japan
KIKUCHI,
YUJI, AND TOMIYASU
KOYAMA.
Red blood cell
deformability
and protein adsorption
on red blood cell surface.
Am. J. Physiol.
247 (Heart Circ. Physiol.
16): H739-H747,
1984.-Effects
of protein and NaCl concentrations
in plasma
on red blood cell (RBC) deformability
were studied using fresh
human blood and a 5pm Nuclepore filtration
test. The protein
and salt concentrations
were varied by diluting the plasma with
saline and adding crystalline
NaCl to the fluids, respectively.
The mean pore passage time of the RBCs, which was measured
as an index of the deformability,
increased with increasing
plasma protein and NaCl concentrations.
A marked interdependence was observed; the relation of RBC deformability
with
plasma protein was accentuated by an increase in plasma NaCl,
whereas the effect of increasing
plasma NaCl was diminished
by a decrease in plasma protein. It is suggested that the RBCprotein interaction
which is modified by the fluid ionic strength
plays a dominant
role in producing
these characteristic
changes
in RBC deformability
with protein
and salt contents in the
plasma. An analysis is made of the cell-protein
interaction;
the
electric repulsive and van der Waals attractive
forces are calculated with a result that the protein
adsorption
on a RBC
increases with increasing
fluid ionic strength above normal.
This analysis, furthermore,
provides information
on the surface
charge distribution
on a RBC.
filterability;
surface charge;
albumin
WHEN
A RED BLOOD CELL (RBC) is suspended in blood
plasma, adsorption of plasma albumin on its surface
occurs to such an extent that the RBC becomes covered
with a more or less continuous protein layer (20, 24).
This protein layer plays an important role in maintaining
the functions of RBCs. For example, it protects the cell
membrane from osmotic and mechanical destructive
forces (10, 24) and stabilizes the biconcave disk shape of
the RBCs against fluctuations in intra- and extracellular
factors (20). RBCs are always subjected to mechanical
stresses when suspended in flowing blood and undergo
large deformations whenever they pass through the capillary circulation. The stiffness of the red cell membrane
and its high cellular deformability,
which is closely related to cell shape (5), are therefore essential factors in
the function and survival of RBCs in the blood circulation.
In preceding studies (14,16) the Nuclepore filterability
of fresh human RBCs was measured under varying concentrations of plasma proteins and NaCl in the sus-
0363-6135/&I
$1.50 Copyright
0 1984 the American
Physiological
Society
Hokkaido
University,
pending fluid. It was suggested that !;he protein layer on
the RBC surface would restrict the flexibility of the cell
membrane with a consequent reduction in RBC deformability with increasing protein concentration
in the
plasma. Furthermore,
the hyperosmotic
reduction in
RBC deformability
was interpreted as being caused by
an increased adsorption of albumin on the RBC surface
due to the elevated ionic strength of the medium. The
mechanical properties of the cell membrane were considered to be more important than the internal viscosity in
producing alterations in RBC deformability
in a hyperosmotic plasma. This viewpoint is based on the assumption that interactions between the red cell membrane,
plasma proteins, and electrolytes were unsaturated at
physiological concentrations of both plasma proteins and
electrolytes. However, several investigations have shown
that the effects of albumin on RBCs and their dependence on the ionic strength of the medium become saturated at much lower concentrations,
e.g., 1 g/d1 for albumin (9, 24) and 50 mM/l for NaCl (8). The particular
results obtained might depend on the methods utilized
and the particular properties of the RBCs studied. In
view of the known importance of proteins and electrolytes being at physiological concentrations in the plasma,
further study using different methods is required on the
interactions between RBCs and the components of normal plasma. Such studies would appear to be especially
important, as small changes in concentrations of plasma
proteins and electrolytes are known to be associated with
pathological anomalies of both hematological
and hemorheological properties.
The present study provides data on the relationships
between RBC filterability and RBC-albumin interaction,
which has been analyzed by taking into account an
electric repulsive force and van der Waals attractive
force. It has been found that the interaction
and its
dependence on the ionic strength of the medium depend
markedly on the surface structure of the red cell membrane, in fact the distribution
of surface charge. The
RBC surface charge is associated with the glycocalix and
therefore distributes apart from the cell surface by a
certain distance. Such distribution of the charge is shown
to cause the RBC-albumin
interaction and hence RBC
deformability
to be modified strongly by the protein
concentration
and ionic strength varying around their
physiological levels.
I3739
Y. KIKUCHI
H740
MATERIALS
AND
METHODS
Red Cell Filterability
with Varied Protein
in Normosmotic
Concentration
Plasma
AND T. KOYAMA
atocrit changes in blood samples with no alterations
red cell number).
Red Cell Filterability
in
with Increasing
Osmolarity in Plasma with Normal (7 g/dl) and
Venous blood (20 ml) from each of five healthy volReduced (1 g/dl) Protein Contents
unteers was withdrawn into disposable syringes containing 1 ml heparin sodium solution (1,000 IU). The blood
RBC suspensions in plasma [total protein (TP) 7 g/
samples were centrifuged at 3,000 g for 5 min, then
dl] and a plasma-saline mixture (TP 1 g/dl) with hemaplasma and RBCs with poor buffy coat were carefully
tocrits nearly 10% were prepared using fresh blood samtaken. Suspensions of the RBCs with a hematocrit of ples. Each suspension was divided into four portions, to
nearly 10% were prepared using the plasma and plasmawhich appropriate amounts of crystalline NaCl were
saline mixtures (volume ratios of 2:1, l:l, 1:2, and 1:4) added so that the fluid osmolarity was increased up to
and saline as the suspending fluid. The suspensions were 550 mosmol. The RBC filterability, final fluid osmolarity,
gently agitated in a water bath at 37°C for 30 min and ’ and final hematocrit were determined for each sample
then applied to the Nuclepore filtration
measurement
after 30-min incubation at 37OC.
system. The time taken for a 0.5.ml sample to pass
through a Nuclepore filter with pores of 5-pm diameter
Protein Adsorption on Red Cell Surface
was determined in duplicate under a pressure difference
of 10 cmHaO at 37OC. A fresh filter was used for each
Amount of plasma proteins adsorbed on RBCs susdetermination;
pore density was calibrated by measuring
pended in normal plasma. RBCs were washed with saline
the passage time of 0.5 ml saline before each sample was three times, and different amounts of the RBCs (1-7 x
tested. The filter was repeatedly flushed with saline prior
10’ RBCs) were suspended in the native plasma (1 ml,
to every measurement to remove air bubbles trapped in TP 7 g/dl on average). After incubation at 37°C for 30
the filter pores; complete removal of air bubbles from the min the suspensions were again centrifuged. The protein
filter was found to be essential for reproducible measureconcentration
in the separated plasma was compared
ments (12). Small portions of the samples were used for with the value obtained before the addition of washed
measurement of hematocrit (microhematocrit
11,000 g RBCs. The reduction in the plasma protein concentrafor 5 min in duplicate). The refractive index of the fluid
tion was considered to give the amount of plasma proportions separated in the hematocrit tubes was measured
teins adsorbed on the RBCs. It was difficult to add
(an Abbe-type refractometer,
Atago, Tokyo, Japan) and washed RBCs to plasma without contamination
by a
then converted to the protein concentration
[with use of small amount of saline. Reduction in the protein concenthe equation of Yoshikawa (25) proposed as a slight
tration due to this unavoidable plasma dilution was
modification
of the equation of Reiss (22)]. The mean
corrected by estimating the saline contents in the RBC
pore passage time of single RBCs was calculated as an samples, which were suspended in the definite volume of
index of RBC filterability
from the suspension passage plasma, from their volume and hematocrit and the retime, hematocrit,
and mean corpuscular volume (as- sultant hematocrit of the suspensions.
sumed to be 100 pm3) using a previously derived equation
Amount of plasma proteins additionally
adsorbed on
(13). This equation and a brief description of its derivaRBCs suspended in hyperosmotic plasma. Crystalline
tion are given in APPENDIX
I. The present method and
NaCl was added to RBC-plasma (TP 7 g/dl) suspensions
apparatus for RBC filterability
measurement have been with hematocrit values of 10, 20, and 30% to increase
described in detail elsewhere (11).
the plasma osmolarity to about 400 mosmol. Each suspension was centrifuged after 30-min incubation at 37°C.
The refractive index of the separated plasma and its final
Red Cell Filterability in Hyperosmotic Plasma
osmolarity were measured to calculate the protein conwith Varied Protein Concentration
centration. The protein concentration in the plasma was
Crystalline
NaCl was added to freshly separated
reduced by this treatment of increasing the osmolarity
plasma to increase the osmolarity to about 400 mosmol.
because of both the water shift from the RBCs to the
RBC suspensions were prepared using this hyperosmotic
plasma and the additional adsorption of plasma proteins
plasma and its mixtures with a 4000mosmol NaCl soluon the RBCs. The amount of water shifted was calculated
tion. The filtration measurement was carried out on the from the reduction in the sample hematocrit value. The
suspensions after incubation at 37°C for 30 min. A small
amount of plasma proteins additionally adsorbed on the
portion of each sample was centrifuged, and the osmoRBCs was estimated by subtracting the decrease due to
larity (depression in the freezing point, Knauer Halbthe plasma dilution from the observed total decrease in
mikro-osmometer,
FRG) and the protein concentration
the plasma protein concentration.
of the separated fluid were measured. The refractive
index obtained was corrected for the elevated electrolyte
RESULTS
concentration
in the fluid before the conversion to proThe effect of plasma proteins in the suspending fluid
tein concentration
was made. Decreases in the mean
on the RBC passage time through a 5-pm pore filter is
volume of RBCs due to the increased plasma osmolarity
shown in Fig. 1. The RBC passage time and protein
were determined from changes in hematocrit of blood
concentration obtained for samples from different donors
samples to which crystalline NaCl was added (i.e., hem-
RED CELL
DEFORMABILITY
AND PROTEIN
I
1
I
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0
1
2
3
4
5
6
T, P, ( g/dL
H741
ADSORPTION
I
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8
)
1. Changes in pore passage time of single RBCs with total
protein concentration (TP) in the suspending fluid with normal osmolarity (290 mosmol). Means and SD are given for samples from 4
different subjects.
FIG.
400
MosmL/L
I
1
I
300
400
SO0
OsunARITY
hosPloL/L
1
Changes in pore passage time of single RBCs with increasing
osmolarity of suspending fluids with protein contents of 7 and 1 g/dl.
Osmolarity was increased by adding NaCl.
FIG.
290
OL
tumux/L
I
1
I
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I
I
I
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0
1
2
3
4
5
6
7
8
T.P.
(6/OL)
2. Changes in pore passage time of single RBCs with total
protein concentration (TP) in the suspending fluid with ionic osmolarity of 400 mosmol. Curve given in Fig. 1 is also shown for comparison.
FIG.
3.
time at 400 mosmol is already shown in Fig. 2. These
observations indicate that the reduction in RBC filterability in a hyperosmotic plasma may not be a direct result
of osmotic effects such as dehydration of RBCs but may
be associated with some RBC-protein
interaction modified by the ionic strength of the plasma.
The protein concentration in plasma (initially 6.8~7.2
g/dl) decreased slightly when washed RBCs were suspended in it. The reduction in the protein concentration
is plotted in Fig. 4A against the amount of added RBCs
(i.e., resultant hematocrit). This reduction in the fluid
protein is obviously attributable
to the adsorption of
protein on the RBCs.
The protein concentration in plasma (initially 6.8~7.2
g/dl) decreased by an extent greater than expected from
the water shift when ‘crystalline NaCl was added to RBCplasma suspensions. The decrease in the plasma protein
obtained by subtracting the decrease due to the plasma
dilution from the observed decrease was again nearly
proportional to the amount of RBCs suspended in it (Fig.
4B). This excess reduction in the plasma protein content
is attributable to the protein adsorption induced by the
increased plasma osmolarity on the RBCs that had already adsorbed a considerable amount of protein at normal osmolarity. The number of protein molecules adsorbed on a RBC appears to be doubled when the plasma
osmolarity is increased from 290 to 400 mosmol.
are summarized as mean values t SD. The pore passage
time’of RBCs became shorter as the fluid protein was
reduced. Minimum values of the pore passage time were
obtained for RBCs suspended in saline. RBC deformability appears to be improved with a decrease in the fluid
protein concentration. The relation of RBC pore passage
time to fluid protein which was obtained for suspensions
with ionic osmolarity of 400 mosmol is shown in Fig. 2.
An . increment in the pore passage time with a rise in the
was much greater at 400 mosmol . than that
flu1 .d protein
resulting from a corresponding change obtained at 290
mosmol. In other words, the effect of protein in the
solution on RBC filterability
was more accentuated in
the hyperosmotic fluid. Figure 3 shows changes in the
pore passage time with fluid osmolarity in plasma with
normal (7 g/dl) and reduced (1 g/dl) protein contents.
DISCUSSION
The pore passage time increased with increasing osmolarity in the normal plasma while it remained un .altered
The change in RBC pore passage time with varying
up to 450 mosmol in the plasma- saline mixtu .re, In the protein content in the suspending fluid (Fig. 1) and the
latter case a steep increase in the pore passage time was enhanced change with protein observed in the hyperosobserved when the osmolarity was increased to above
motic fluid (Fig. 2) give clear evidence of the effects of
450 mosmol. The difference in the RBC pore passage plasma proteins on RBC deformability. The plasma pro-
H742
Y. KIKUCHI
AND T. KOYAMA
0
0
0
20
30
50
HEMATOCRIT(8)
0
FIG. 4. A: decreases in total protein
concentration (TP) in plasma (initial TP
7 g/dl on average) due to addition of
different amounts of washed RBCs. B:
decreases in plasma TP in RBC-plasma
(initial TP 7 g/d1 on average) suspensions due to an increase in plasma osmolarity from 290 to 400 mosmol. Crystalline NaCl was added to suspensions
to increase osmolarity. Decreases in
plasma TP due to plasma dilution caused
by water shift from RBCs to plasma were
estimated from changes in the sample
hematocrit and subtracted from observed decreases in TP; (ATP)d and
(ATP)a indicate observed changes in TP
and estimated decreases in TP due to
the plasma dilution, respectively. Differences obtained are plotted against the
initial hematocrit values of the suspensions.
0
0
0
0
10
20
30
40
HEMATOCRIT (%I
tein most strongly influencing the RBC mechanics appears to be albumin since its adsorption on a RBC is
known to occur to such an extent that the RBC becomes
covered with the protein layer and consequently shows a
reduced fragility to destructive forces. The average number of albumin molecules adsorbed on a RBC suspended
in normal plasma has been reported to be 6.5 x lO’/RBC
by Ponder (20) and 2.7 x lO’/RBC by Williams (24).
The reduction obtained in the protein concentration
in
plasma due to the addition of washed RBCs (Fig. 4A)
gives a value of 4.2 X 106/RBC, which is similar to the
estimate of Ponder, if the adsorbed protein is assumed
to be mainly albumin (mol wt 66,000) and the mean
volume of a RBC is taken to be 100 pm3. Errors of about
5% or more are inevitable in the determination
of hematocrit and volume; further correction in the hematocrit
values for trapped saline and/or plasma was not made in
the present estimation. There remains, therefore, a possibility that the present value might still be an overestimate for the amount of adsorbed protein. The surface
area of a RBC has been given as 152 pm2 by Ponder (20)
and 135 pm2 by Evans and Fung (3). The number of
albumin molecules that can be packed in a single layer
of this area can be estimated as 5.4 x lo6 and 4.8 X 106,
respectively, by approximating
an tlbumin
molecule
as a sphere having a radius of 30 A. It is therefore
suggested that a RBC suspended in plasma is covered
with a single layer or multilayer of albumin. The forma-
RED CELL
DEFORMABILITY
AND PROTEIN
tion of such a protein layer with a thickness of about
60 A or more on the red cell membrane having thickness
of about 100 A or so may well affect the stiffness of the
membrane and at the same time restrict its flexibility
with a consequent reduction in the cellular deformability.
The accentuated effects of protein in the hyperosmotic
fluid (Fig. 2) suggest that the adsorption of albumin on
RBCs may proceed with increasing ionic strength of the
fluid. It has been well known that an electric repulsive
force between colloidal particles decreases with an increase in the ionic strength of the suspending medium
and that coagulation of the particles occurs above a
certain critical concentration
of electrolytes. The theory
on the interactions between colloidal particles in electrolyte solutions has been established [Derjaguin-LandauVerwey-Overbeck theory (23)]. The assumption that the
protein adsorption on RBCs increases in a hyperosmotic
fluid is supported by such general features of the interactions in colloid suspensions. However, it is uncertain
whether or not an elevation in the electrolyte concentration from its physiological level may actually induce an
increment in the adsorption of albumin on RBCs because
the physiological concentration
of electrolytes may be so
high that the effects of increasing medium ionic strength
on the RBC-protein
interaction
level off. The above
assumption should be examined from a numerical point
of view. For this purpose, the potential curve of the
interaction between an albumin molecule and the red
cell surface was calculated, taking into account the electric repulsive force between negative charges existing on
both surfaces and the van der Waals attractive force.
Some examples of the calculated potential curve are
shown in Fig. 5. The detailed procedure and physical
x 10.*l
H743
ADSORPTION
constants used for this calculation are given in APPENDIX
II. The electric repulsive force exceeds the van der Waals
attractive force at electrolyte concentrations lower than
50 mM. The electric repulsive force decreases as the
electrolyte concentration
increases. The electric repulsive force can be smaller than the van der Waals attractive force, so that the whole interaction becomes attractive at sufficiently high electrolyte concentrations.
The calculations also show that the electrolyte dependence of the interaction almost levels off above 100
mM. This numerical analysis makes it seem unlikely
that an elevation in the electro lyte concentration around
150mM induces an inc :rement in the protein adsorption
on RBCs. However, an increased protein adsorption has
been experimentally shown for RBC-plasma suspensions
whose osmolarities were elevated to 400 mosmol (Fig.
4B). This contradiction suggests that the physical process of the protein adsorption on RBCs is inadequately
represented by the model used in the calculation. As
shown in Fig. 8 in APPENDIX
II, the interaction
between
the red cell surface and an albumin molecule was treated
as the interaction between a semi-infinite
plate and a
sphere. The negative charges on the red cell surface were
taken into account as charges existing on the surface of
the plate. That is, it is assumed in this model that the
electric charges are embedded just in the surface of the
semi-infinite
plate. In other words, the surface for the
charge distribution
was assumed to coincide with the
surface given from the mass distribution.
Studies on the
microstructure of the red cell membrane have shown that
the negative charges are mainly associated with mucopolysaccharides extending outward from the red cell
surface (4, 15). The surface of the charge distribution
J
5
-5
FIG.
5. Potential
0
curves for RBC-albumin
50
interaction
100
150
calculated for different concentrations of a univalent
200
A
electrolyte in the medium.
Y. KIKUCHI
H744
AND T. KOYAMA
J
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c
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I,/
250
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DISTRNCE
surface is moved toward outside by 15 A from
FIG. 6. Potential
curves for RBC-albumin interaction calculated for
different concentrations of a univalent electrolyte in the medium. RBC
surface charge is assumed to distribute on the plane shown by d&shed
line (charge distribution
cell surface)
ought, therefore, to be displaced by some distance outward from the mass surface. Calculations were made
taking into account this possible displacement of the
charge surface. Figure 6 shows examples of the potential
curve calculated for a case in which the charge surface
was moved 15 A outward from the mass surface. The
whole interaction is considerably altered with this small
modification
in the charge distribution
surface. Especially marked effects appear in the range of electrolyte
concentration
around 150 mM. A potential valley is
formed above 100 mM whose depth increases with an
elevation in the electrolyte concentration.
This result
supports the present assumption that the protein adsorption on RBCs increased with increasing fluid osmolarity
above normal.
It thus seems possible to remove the contradiction
between the experimental
evidence and the numerical
analysis by taking into account the surface structure of
the red cell membrane. The value 15 A was taken so that
calculated potential curves appeared to be most likely to
explain the observed increase in the protein adsorption
on RBCs in the hyperosmotic
plasma. The distribution
-of the surface charge thus determined depends on the
model and values used for the physicochemical variables
involved in the interaction.
Despite few data available
for those variables in the RBC-albumin
interaction, the
obtained value of 15 A appears to coincide well with the
distance estimated from the actual length of the polysaccharide chains. The length of the chains, which are
considered to consist of five or six hexose rings (l5), is
given to be 22.5 or 27 A. The distance of the sialic acid
from the peptide chain in a glycoprotein molecule can be
estimated as 16 or 19 A by considering the three-dimensional structure of the saccharide chain.
Such a displacement of the charge distribution
surface
may also be caused by the protein adsorption itself. If a
RBC is covered with a single protein layer in normal
plasma and a further adsorption of albumin takes place
on this layer in a hyperosmotic plasma, the conditions
for the second-layer adsorption, i.e., the adsorption induced by an elevated osmolarity, will be different from
those for the first-layer adsorption,
i.e., for albumin
molecules to be adsorbed directly on the red cell surface.
The first protein layer will probably be formed in such a
manner that negative charges of the albumin molecules
distribute far apart from the ceil surface. The plane
connecting the charge-dense region will be displaced by
a certain distance outward from the plane connecting the
center of mass of the molecules. Therefore, an analysis
similar to the one above will also be required for the case
of multilayer protein adsorption. It is suggested that the
further protein adsorption on the preformed protein layer
may be more dependent on the difference of the electrolyte concentration from normal.
The dehydration of RBCs proceeds in a hyperosmotic
fluid, causing an increment in the intracellular hemoglobin concentration.
The cytoplasm viscosity, which increases with the hemoglobin content, has been discussed
as one of the factors determining
RBC deformability
(17). The increment in this internal viscosity might be
RED CELL
DEFORMABILITY
AND PROTEIN
suspected as a cause of the reduction in RBC filtrability
in hyperosmotic plasma. However, changes in the pore
passage time were not observed for the RBCs suspended
in the plasma with reduced protein in the osmolarity
range from 280 to 450 mosmol (Fig. 3). This result
indicates more clearly that the reduction in RBC filtrability in the plasma with normal protein with increasing
osmolarity in the same range was not produced by the
dehydration effect but caused by the strengthened RBCalbumin interaction in the hyperosmotic plasma (Fig. 6).
The viscosity of the intracellular
hemoglobin solution,
although increased considerably
by dehydration
(1))
would be still too low to restrict the pore passage of
RBCs.
Recent studies by Markle et al. (18) on the shape
recovery time course of stretched RBCs have shown that
the membrane viscosity increases with increasing albumin concentration in the suspending fluid. Furthermore,
the importance of the membrane-protein
interaction has
been also demonstrated
by Nash and Meiselman (19)
with respect to the internal factor. They have shown
that the intracellular
hemoglobin concentration
is involved in RBC deformability
not simply as the viscosity
factor but through the concentration-dependent
membrane-hemoglobin
interaction. The steep increase in the
RBC pore passage time in the low protein plasma observed above 450 mosmol (Fig. 3) might be related to an
increase in this interaction at the inner surface of the
cell membranes and/or the crenation of the RBCs that
was observed to proceed above 450 mosmol.
Thus the present observations can be reasonably explained with the following assumptions: 1) RBC filtrability is affected by adsorbed protein molecules, 2) more
protein molecules are adsorbed on the erythrocyte membrane surface as the ionic strength of the surrounding
fluid increases, 3) the charge distribution
surface on the
erythrocyte is lo-20 A apart from the membrane surface.
APPENDIX
H745
ADSORPTION
PUMA
CELL PASSAGE
FIG. 7. Schematic representation
pm-diam pore. See text for details.
PASSAGE
of passage of RBC through
a 5-
apparent that this derivation is based on the assumption that only one
RBC is in a pore at a given time. This is valid for low hematocrit values
and will hold up to a hematocrit value of a/(a + I) (at this hematocrit
b becomes equal to 1) on the average. This limiting value is 33% for
human RBCs, since a is about Z/2. A linear relationship between T and
h, which follows the above equation, has been observed in human blood
below hematocrit about 30% (11,13).
APPENDIX
II
The interaction between the red cell surface and an albumin molecule may be treated as one between a semi-infinite plate and a sphere
(Fig. 8). The interaction energy is obtained by summing the potential
of electric repulsive force and the potential of van der Waals attractive
force
v = v, + v,
Each potential
UA)
energy is given as
wu
I
Blood flow through the Nuclepore filter is composed of flow through
many parallel pores in which the RBCs and plasma are passing successively. A schematic time course of the passage of a RBC through a pore
in the filter is shown in Fig. 7. On average, the length of RBC as a
column in a pore (a) relative to that of successive columns of plasma
in the same pore (b) should be related to the hematocrit value (h,
expressed as a fraction): h = ~/(a + b) on average. RBCs take various
times to pass through individual pores; the mean pore passage time
(T,) is defined as the average time taken for single RBCs to pass
through the pores. The plasma can flow at its own speed (V’) for a
time interval of (b - 1)/V, (I, length of a pore) until the next RBC
blocks the pore opening. Therefore, a blood volume of (a + b)S (S,
cross-sectional area of a pore) flows through a pore for an interval of
TEp + (b - 2)/V,. When (a + b)S is multiplied by the total number of
pores Ad (A, total area through which blood flows; d, pore density), a
value is obtained for the total blood volume which flows through the
whole filter during the same interval. Thus the flow rate through the
filter is given by the following relationship
T = (T, + (b - l)/V,)/(Ad(a
+ b)S)
where T is the time for unit volume of blood to flow through the filter.
When the relation h = a/(a + b) is inserted into the above equation it
can be transformed into
T = (l/V,
+ (T, - (a + O/V,b/MAW
This eauation exnresses the linear relationshin
between T and h. It is
and
(3A)
where p is the charge density at a point in the albumin molecule, If, is
the electric diffuse double-layer potential due to the negative charges
on the red cell surface, V1 is integral region for the albumin sphere, Vz
is the integral region for the plate, A is Hamaker constant, y is distance
between a point in the sphere and a point in the plate as shown in Fig.
8.
Electric Diffuse Double-Layer
Potential Around a RBC
Ions with positive charge ze and with negative charge -ze distribute
in a field of electric potential Q,according to the Boltzmann distribution
Nk = Noexp(+ze@/kT)
= N*xp(~&
(4A)
where No is the number of each ionic species in a unit volume in the
region of Q, = 0. 4 is defined by
The charge distribution
4 = ze@/kT
q in the field is given by
Q = ze(N+
-
NJ
(5A)
64)
Y. KIKUCHI
H746
Cpand Q must satisfy the Poisson equation
-q/tree
A<p =
(7A)
where cois the permitivity of vacuum and er is the relative permitivity
of the solution. Putting Eqs.4A-6A into Eq. 7A, the Poisson-Boltzmann
equation
is obtained.
K
@A)
A4 = K*sinh#
is called the Debye-Huckel constant, which is defined by
K2
= 2NG*e*/c,tokT
Equation 8A can be approximated
(94
by the Debye-Hiickel
A# =
I
K(x)
=
a,+(~
s
+ r cos B)2w
sin Brdtl
r and 6 are taken as shown in Fig. 8. The following
obtained
47ra
K(x) = -
result is easily
ff,*sinh(Ka)exp(-Kx)
U4A)
K
K*$
(104
d+/h I n + + o = -a,/wo
(114
where x is the direction normal to the surface with the positive direction
taken outward from the surface and uc is the surface charge density of
a RBC. The potential decreases within the length of the order of K-~
from the surface; the potential decreasing region is called the electric
diffuse double layer.
The red cell surface can be regarded as a semi-infinite plate since
the radius of curvature of the surface is much greater than the thickness
of the electric diffuse double layer; the one-dimensional Poisson-Boltzmann equation can be used to calculate the electric potential due to
the surface charges. The integration of Eq. 8A of one dimensional form
gives
-2~
acid are negatively ionized. Therefore, the total net charge of an
albumin molecule at pH 7.4 is -14 e. It is possible to integrate Eq. 2A
analytically if the approximate solution of Eq. 13A is used and the
negative charges of an albumin molecule are assumed to distribute on
its surface at a constant density of grn
equation
when 4 << 1. The electric potential due to the charges on the surface
of a RBC can be calculated from Eq. 8A or approximately from the Eq.
IOA using the boundary condition of
dcj&lx =
AND T. KOYAMA
sinh( @/2)
(124
Numerically calculated potential curves showed only slight differences
from the ones given by Eq. 14A. The following values were used for er
(21)
NaCl (M)
tr (35°C)
0
0.05
74.8
74.2
73.7
73.1
72.5
72.0
0.1
0.15
0.2
0.25
Van der
Walls
Interaction
The integration
shown in Fig. 8
of Eq. 3A can be made as follows, using coordinates
The further integration of this equation must be done numerically.
When the Debye-Huckel approximation is acceptable, the above equation gives a simple exponential solution of
<p =
+,eXp(
(13A)
-KX)
where +m is the surface potential of a RBC.
The one-dimensional structure (amino acid arrangement) of a human serum albumin molecule has been determined (2); the number of
each amino acid is as follows: Ala 62, Arg 24, Asn 17, Asp 36, Cys 35,
Gln 21, Glu 61, Gly 12, His 16, Ile 8, Leu 61, Lys 59, Met 6, Phe 31,
Pro 24, Ser 24, Thr 28, Trpl, Tur 18, Val 141. At normal blood pH 7.4
arginine and lysine are positively ionized and aspartic acid and glutamic
r
R
The Hamaker constant A for the lipid-water system has been reported to be 10e20 - lO-*l J (7).
The potential curves shown in Figs. 5 and 6 were calculated using
A = 5 x lo-*l J and reported value for the surface charge of human
RBCs [1.2 - 2.4 x 10’ e/cell (4, 6); mean 1.8 X 10’ e/cell was used]
for 6#.
PROTEIN
RED BLOODCELL
FIG. 8. Model used for calculating
albumin molecule and RBC surface.
interaction
energy between an
The authors express their thanks to Professor H. Wayland, California Institute of Technology, and Professor G. M. Hughes, Bristol
University, for their very helpful comments on the manuscript.
Present address of Y. Kikuchi: Division of Biomedical Engineering,
Institute of Basic Medical Sciences, University of Tsukuba, Ibaraki
305, Japan.
Received 28 July 1983; accepted in final form 19 June 1984.
RED CELL
DEFORMABILITY
AND PROTEIN
ADSORPTION
H747
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