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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 I I I I 0 1 2 3 4 5 6 T, P, ( g/dL H741 ADSORPTION I I 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 I I I I I I 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 I I I I I I I I I I I I I I I c I I I I I I I I I,/ 250 I I I I I I 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. 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