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Sedimentation and Electrophoretic Mobility Behavior of Human Red Blood Cells in Various Dextran Solutions Bjo¨rn Neu* and Herbert J. Meiselman Department of Physiology and Biophysics, Keck School of Medicine, 1333 San Pablo Street, Los Angeles, California 90033 Received June 21, 2001. In Final Form: October 1, 2001 To obtain additional information relevant to polymer behavior near human red blood cells (RBC), sedimentation and electrophoretic mobility behavior of RBC in the same suspension were determined for cells in various isotonic solutions of 10.5, 74 and 519 kDa dextran. Regardless of medium viscosity or dextran molecular mass, RBC sedimentation rate could be predicted via the Stokes’ equation. Conversely, the effects of medium viscosity on RBC mobility were markedly overestimated by the HelmholtzSmoluchowski relation, with the error increasing with dextran molecular mass. These results confirm and extend prior electrophoretic mobility studies, agree with the concept of polymer depletion near the RBC surface, and lend strong support to a “depletion model” mechanism for dextran-mediated reversible RBC aggregation.
Introduction The interactions between neutral water-soluble polymers and human red blood cells (RBC) continue to be of current basic science and clinical interest.1-3 The effects of homopolymers have been extensively studied, with literature results indicating that, depending on molecular mass, the neutral polyglucose dextran can increase or decrease RBC aggregation,4,5 affect blood viscosity at low shear rates,5 and alter in vivo blood flow resistance and dynamics.6 Given this wide range of potentially beneficial effects, detailed knowledge regarding polymer adsorption and polymer concentration near the RBC surface is essential to understanding polymer-RBC interactions. Unfortunately, standard direct approaches to obtaining adsorption isotherms for polymer-RBC systems have been met with limited success owing to the nonspecific, relatively weak binding of the polymers and to artifacts associated with unbound polymer trapped in the fluid spaces between cells.4,7 One indirect approach that has been employed to examine polymer behavior near the RBC surface is microelectrophoresis, in which cells are suspended at a low volume fraction in various polymer solutions, subjected to a direct current electric field, and their electrophoretic mobility toward the anode determined via optical methods.8 Using cells suspended in isotonic dextran solutions, Brooks and co-workers9 indicate that if mobility results * To whom correspondence may be addressed. Phone: 323-4421268. Fax: 323-442-2283. E-mail:
[email protected]. (1) Lowe, G. D. O. Clinical blood rheology; CRC Press: Boca Raton, FL, 1988. (2) Ehrly, A. M. Therapeutic Hemorheology; Springer-Verlag: Berlin, 1991. (3) Bongrand, P. Physical basis of cell-cell adhesion. CRC Press: Boca Raton, FL, 1988. (4) Brooks, D. E.; Greig, R. G.; Janzen, J. In Erythrocyte Mechanics and Blood Flow; Cokelet, G. R., Meiselman, H. J., Brooks, D. E., Eds.; A. R. Liss: New York, 1980; pp 119-140. (5) Chien, S. In The Red Blood Cell; Surgenor, D. M., Ed.; Academic Press: New York, 1975; pp 1031-1133. (6) Cabel, M.; Meiselman, H. J.; Popel, A. S.; Johnson, P. C. Am. J. Physiol. 1997, 272, H1020-H1032. (7) Janzen, J. and Brooks, D. E. In Surfactant Science Series; Bender, M., Ed.; Marcel Dekker: New York, 1991; Vol. 39, pp 193-250. (8) Seaman, G. V. F. In The Red Blood Cell; Surgenor, D. M., Ed.; Academic Press: New York, 1975; pp 1135-1229. (9) Brooks, D. E. J. Colloid Interface Sci. 1973, 43, 700-713.
are “corrected” for the increased viscosity of the dextran solutions, RBC mobilities increase with increasing molecular mass and polymer concentration. Brooks thus developed a model based on the framework of Smoluchowski’s approach,8 in which an expansion of the electric double layer in the presence of adsorbed neutral polymer altered the classic relationship between fixed surface charge density and cell mobility.9 Snabre and Mills10 somewhat modified this approach and suggested that due to the action of weakly adsorbed polymer chains, the RBC glycocalyx is expanded and the frictional interaction of the surface coat with the flowing liquid is reduced. These authors thus suggest that this structural rearrangement of the outer membrane improves the penetration of the electro-osmotic flow within the glycocalyx and hence increases the effective cell mobility. Ba¨umler, Donath, and co-workers have provided an alternative explanation for the apparent increase of viscosity-corrected RBC mobility in dextran solutions. In a series of publications11-17 these authors have presented experimental and theoretical results favoring polymer depletion near cell and particle surfaces and indicate that the extent of this depletion increases with increasing polymer size (i.e., molecular mass). They thus suggest that, due to such depletion, the fluid viscosity is lower near the cell surface and that this lower viscosity rather than the higher bulk phase viscosity is the appropriate viscous term. That is, since electro-osmotic flow obeys potentiality outside of the diffuse part of the double layer, energy dissipation occurs only near the surface within the Debye-Hu¨ckel layer, and therefore only the lower viscosity within this layer affects cell mobility. Note that these authors do not reject the possibility of polymer (10) Snabre, P.; Mills, P. Colloid Polym. Sci. 1985, 263, 494-500. (11) Ba¨umler, H.; Donath, E.; Krabi, A.; Knippel, W.; Budde, A.; Kiesewetter, H. Biorheology 1996, 33, 333-351. (12) Ba¨umler, H.; Neu, B.; Donath, E.; Kiesewetter, H. Biorheology 1999, 36, 439-442. (13) Donath, E.; Kuzmin, P.; Krabi, A.; Voigt, A. Colloid Polymer Sci. 1993, 271, 930-939. (14) Ba¨umler, H.; Donath, E. Stud. Biophys. 1987, 120, 113-122. (15) Donath, E.; Walther, D.; Krabi, A.; Allan, G. C.; Vincent, B. Langmuir 1996, 12, 6263-6269. (16) Pratsch, L.; Donath, E. Stud. Biophys. 1988, 123, 101-108. (17) Donath, E.; Krabi, A.; Nirschl, M.; Shilov, V. M.; Zharkikh, M. I.; Vincent, B. J. Chem. Soc., Faraday Trans. 1997, 93, 115-119.
10.1021/la010945+ CCC: $20.00 © 2001 American Chemical Society Published on Web 11/16/2001
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Table 1. Physical Properties of Dextransa
DEX 10 DEX 70 DEX 500
molecular mass, kDa
Mw/Mn
intrinsic viscosity [η], dL/g
10.5 74.0 519
1.6 1.5 2.2
0.092 0.231 0.494
a Molecular mass data and weight-average (M ) to numberw average (Mn) molecular mass ratios (Mw/Mn) as supplied by the vendors. Intrinsic viscosity [η] was obtained by viscometry.19
absorption but rather propose that polymer concentration, and hence fluid viscosity, near the cell surface is markedly less than in the bulk phase. The current study was designed to provide additional insight into the behavior of the neutral polymer dextran at the RBC surface, with the experimental system designed such that both red cell electrophoretic mobility and unitgravity sedimentation rate could be determined using the same RBC suspension. Two hypotheses were tested: (1) The effects of suspending media viscosity on RBC sedimentation follows from Stokes’ law (i.e., exact inverse relation), whereas cell mobility may be less affected by suspending phase viscosity; (2) RBC viscosity-mobility relations are affected by polymer size (i.e., molecular mass), whereas RBC sedimentation depends only on suspending phase viscosity. Thus, the overall aim was to obtain concordant data for human RBC: separate studies have dealt with Stokes’ sedimentation and with polymer depletion, yet there appear to be no reports in which these phenomena have been studied simultaneously for red blood cells. Methods RBC electrophoretic mobilities and RBC unit-gravity sedimentation rates were both determined, at 25 °C, using an automated system (Electrophor model E4, HaSoTec GmbH, Rostock, Germany) that is especially designed for studies of biological particles.18 In brief, the system employs a special horizontal electrophoretic chamber that has a flat flow profile and a stationary layer at its center, thus ensuring stable measurements unaffected by out of focus particles. RBC motion is observed and quantified via a microscope-video-frame grabber-computer system, and RBC mobility for 200 or more cells can be obtained within 1-2 min with a coefficient of variation of less than 2%. Although the system is usually operated such that RBC horizontal speed toward the anode is determined, the computer software also allows determination of RBC vertical sedimentation rate in the absence of an applied electric field. For the data reported herein, a given RBC suspension was introduced into the Electrophor device and the mobility determined for at least 200 cells; the electric field was then turned off and red cell sedimentation rate at unit-gravity measured for cells in the same RBC suspension. Adult human blood was drawn into EDTA (1.5 mg/mL) by sterile venipuncture, the RBC washed twice in isotonic phosphate buffered saline (PBS, 10 mM phosphate, 285 ( 3 mOsm/kg, pH ) 7.4), following which the RBC were resuspended at ≈1% volume concentration in either PBS or in various PBS-dextran solutions. Physical properties of the dextrans used in the present study are shown in Table 1. DEX 10 and DEX 70 were obtained from Sigma Chemical Co., St. Louis, MO, and DEX 500 was obtained from Pharmacia Biotech AB, Uppsala Sweden. The viscosity and density of all solutions were measured, at 25 °C, via a capillary viscometer (Viscometer II, Coulter Electronics, Ltd. Luton, UK) and a density meter (DA-100M, Mettler-Toledo Co., Westerville, OH); solution osmolalities were measured using a vapor pressure osmometer (Wescor Co., Logan, UT). All RBC studies were completed within 4 h after venipuncture. Data are presented as mean ( standard deviation. (18) Gru¨mmer, G.; Knippel, E.; Budde, A.; Brockmann, H, Treichler, J. Instrum. Sci. Technol. 1996, 23, 265-276.
Results and Discussion The dextran concentrations employed (i.e., e6 g/dL for DEX 10 and DEX 70, e3 g/dL for DEX 500) resulted in marked increases of suspending phase viscosity and density (e.g., e2.5-fold for viscosity and e0.022 g/mL for density). Conversely, these dextran concentrations did not result in meaningful changes of solution osmolality from the dextran-free PBS buffer; PBS-dextran solution osmolality ranged from 285 to 303 mOsm/kg. Even at the highest osmolality, calculated mean RBC volume decreased by less than 3%,20 yielding a calculated increase of mean RBC density of less than 0.003 g/mL.21 Predicted RBC sedimentation rates in dextran-PBS solutions (Sdex) were obtained by applying the Stokes relation to red cell sedimentation results obtained in dextran-free PBS (Spbs)
Sdex (Frbc - Fdex)ηpbs ) Spbs (Frbc - Fpbs)ηdex
(1)
where F is the RBC or suspending medium density and η is the suspending phase viscosity. A constant value of 1.090 g/cm3 was used for RBC density.22 Predicted RBC mobilities in dextran-PBS solutions (bdex) were obtained by applying the Helmholtz-Smoluchowski relation to red blood cell mobility results obtained in dextran-free PBS (bpbs)
bdex ηpbs ) bpbs ηdex
(2)
where η is again the suspending phase viscosity. The mean mobility for RBC in dextran-free PBS was found to be 1.05 ( 0.04 µm s-1 V-1 cm (mean ( standard deviation) and thus in close agreement with published data.8 Mean RBC sedimentation rate in dextran-free PBS was (2.10 ( 0.18) × 10-3 cm/s, which is consistent with the value 1.92 × 10-3 cm/s for a 1.09 g/cm3, 6 µm diameter sphere. Note, however, that since the human RBC has an 8 µm diameter by 2 µm thick biconcave shape,22 such a spherical approximation for the red cell provides only an estimate for its sedimentation behavior; nevertheless, our mean experimental sedimentation value seems appropriate. RBC sedimentation and electrophoretic mobility results for cells in various viscosity solutions of DEX 10, DEX 70, or DEX 500 are shown in Figure 1; data are presented as values relative to control results obtained in dextran-free PBS. In each panel, the dashed line represents the predicted sedimentation-viscosity relation obtained using eq 1, and the solid line represents the predicted mobilityviscosity relation obtained using eq 2. Inspection of the results presented in Figure 1 leads to the following observations: (1) The effects of suspending phase viscosity on RBC sedimentation rate can be predicted via the Stokes relation and are independent of dextran molecular mass over the range employed herein (i.e., 10.5-519 kDa). For the data points shown, there were no significant correlations between the difference from predicted sedimentation rate and medium viscosity, nor did the average differences (19) Neu, B.; Armstrong, J. K.; Fisher, T. C.; Meiselman, H. J. Biorheology 2001, 38, 53-68. (20) Ponder, E. Hemolysis and related phenomena; Grune and Stratton: New York, 1948. (21) Schmalzer, E. A.; Manning, R. S.; Chien, S. J. Lab. Clin. Med. 1989, 113, 727-734. (22) Dittmer, D. S. Blood and other body fluids; Federation of American Societies for Experimental Biology: Washington, DC, 1961.
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Figure 1. Experimental and predicted values of red blood cell mobility and sedimentation rate versus suspending phase viscosity for red blood cells in various solutions of 10.5 kDa (DEX 10), 74 kDa (DEX 70), or 519 kDa (DEX 500) dextran. All mobility and sedimentation data are expressed relative to values obtained for cells in dextran-free buffer and thus have a value of unity at a suspending medium viscosity of 0.89 mPa s. Symbols are as follows: ∆, experimental mobility; Ο, experimental sedimentation; solid line, predicted mobility; dashed line, predicted sedimentation. Data are mean ( standard deviation.
for each dextran fraction differ significantly from unity; there was a slight but nonsignificant trend of average differences with molecular mass (experimental/predicted ratios of 0.93 for DEX 10, 0.99 for DEX 70, and 1.06 for DEX 500). (2) The effects of suspending phase viscosity on RBC electrophoretic mobility cannot be predicted based solely upon the Helmholtz-Smoluchowski relation, with the divergence from predicted behavior becoming greater with increasing molecular mass of the dissolved dextran. At a suspending phase viscosity of 1.5 mPa s, interpolated ratios of experimental/predicted mobility were 1.19 (DEX 10), 1.44 (DEX 70), and 1.60 (DEX 500); at a viscosity of 3 mPa s, interpolated values were 2.24 (DEX 70) and 2.90 (DEX 500). Thus at a suspending phase viscosity of 3.0 mPa s, there is about a 120% difference between experimental and predicted mobilities for DEX 70, while for DEX 500 the difference is nearly 200%.
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Our electrophoretic mobility results for cells in solutions of the neutral polymer dextran are consistent with the earlier studies by Ba¨umler and co-workers11-14,16 and are also consistent with electrorotation data for RBC in dextran solutions.19 Our mobility results thus add additional support to the concept of a depletion-related lower fluid viscosity near the RBC surface. Our results using DEX 10 have allowed us to more closely approach the polymer size at which depletion effects should vanish.11 That is, for DEX 10 the calculated Einstein hard sphere diameter is only 3 nm, whereas it is increased to 8 nm for DEX 70 and to 20 nm for DEX 500.19 Given a calculated depletion layer thickness of 3-4 nm for DEX 7011 and decreased depletion layer thickness with decreased polymer molecular mass, only very small depletion effects should be evident for 10.5 kDa dextran. Our experimental results should be of basic science and clinical interest, since they appear to be the first in which, for RBC in aqueous polymer solutions, both Stokes’ law is validated and the existence of a depletion layer is demonstrated for cells in the same suspension. In particular, they should be applicable to the phenomenon of dextran-induced reversible RBC aggregation: over a range of concentrations, dextran fractions of 60 kDa or larger cause RBC to form side-to-side structures of various lengths (i.e., rouleaux).4,5 One mechanism proposed for this process is the so-called “depletion model”: due to a polymer-poor region near the cell surface, osmotic forces favor fluid movement away from the intercellular gap between approaching cells and thus promote aggregation.3 This “depletion flocculation” mechanism for nonbiological particles has been accepted for decades,3 yet its application to normal and pathological RBC aggregation has been limited. Some investigators still favor a “bridging model”, in which polymers of sufficient size are proposed to span the intercellular gap and promote RBC aggregate formation.5 However, several recent reports favoring the depletion model now exist;11,12,24-29 by demonstrating the validity of the Stokes relation and the depletion zone for the same RBC population, our findings lend strength to the depletion model mechanism for dextran-induced RBC aggregation. Acknowledgment. Supported by Deutsche Forschungsgemeinschaft Grant NE 784/1-2 (B.N.) and NIH Research Grants HL15722 and HL48484 (H.J.M.). LA010945+ (23) Donath, E.; Budde, A.; Knippel, E.; Ba¨umler H. Langmuir 1996, 12, 4832-4839. (24) Armstrong, J. K.; Meiselman, H. J.; Wenby, R. B.; Fisher, T. C. Biorheology 2001, 38, 239-247. (25) Feigin, R. I.; Napper, D. H. J. Colloid Interface Sci. 1980, 75, 525-541. (26) Fleer, G. J.; Scheutjens, J. M. H. M.; Cohen Stuart, M. A. Colloids Surf. 1988, 31, 1-29. (27) Napper, D. H. Polymeric stabilization of colloidal dispersions; Academic Press: New York/London, 1983. (28) Armstrong, J. K.; Meiselman, H. J.; Fisher, T. C. Biorheology 1999, 36, 433-437. (29) Ba¨umler, H.; Neu, B.; Iovtchev, S.; Budde, A.; Kiesewetter, H.; Latza, R.; Donath, E. Colloids Surf., A 1999, 149, 389-396.
