RBC aggregation is known to be a consequence of the presence of high-molecular weight proteins in the plasma, primarily fibrinogen (340,000) and immunoglobulins IgM (950,000) and IgG (150,000). These proteins are present at baseline levels in health, and thus some degree of RBC aggregation is an invariable finding in blood from normal donors, the rate and extent of which varies from individual to individual. In disease, a high ESR is usually associated with an elevated plasma fibrinogen concentration (Hardwicke and Squire, 1952; Lowe, 1988), but occasionally occurs due to increased IgM levels (Waldenstrom's macroglobulinemia) or very high concentrations of IgG or IgA, such as may occur in myeloma (MacKenzie and Babcock, 1975; Preston et al., 1978; Imaizumi and Shiga, 1983). Several other large plasma proteins, such as ceruloplasmin (135,000), haptoglobin (multiple isoforms from 100,000-900,000) and α-2 macroglobulin (725,000) have also been shown to aggregate RBCs or to enhance fibrinogen-mediated aggregation in vitro (Ruhenstroth-Bauer et al., 1962; Schmid-Schönbein et al., 1973; Weng et al., 1996). Small proteins such as hemoglobin and albumin (65,000 and 66,000) do not induce RBC aggregation in their native state (Rampling and Martin, 1992), but albumin oligomers (Forsdyke et al., 1982) and polymerized hemoglobin (average molecular weight >200,000) (Tsai and Wong, 1996; Sakai et al., 2000) are strongly pro-aggregant. These observations suggest that the effects of any protein on RBC aggregation may depend mostly upon its size, rather than any particular functional or structural property.

Nonionic polymers such as polysaccharides and synthetic polymers also promote RBC aggregation when infused in vivo or added to suspensions of RBCs in buffer or plasma in vitro. Examples of polymers that induce human RBC aggregation are dextrans of molecular weights 60,000–500,000, polyvinylpyrrolidone of 360,000, and polyoxyethylene (POE) of 20,000 and above (Hardwicke and Squire, 1952; Hint, 1971; Sewchand and Canham, 1979; Sewchand and Bruckschwaiger, 1980; Geller et al., 1981; Nash and Meiselman, 1983; Donner et al., 1993; Armstrong et al., 2002). In general, for each of these polymers, the aggregating potential tends to increase with degree of polymerization (dP) and hence the molecular weight, but the precise relationship is polymer-specific, and varies over an order of magnitude for different polymer types.

A less widely recognized property of these same nonionic polymers is that fractions with a lower dP (or molecular weight) can inhibit RBC aggregation. Studies in the 1950s and 1960s with dextran fractions showed a strong dose-dependent and molecular weight-dependent reduction of aggregation when added to blood in vitro, with a detectable effect on ESR at ~10,000 and a maximum inhibitory effect at 30,000 (Ruhenstroth-Bauer et al., 1962; Hint, 1964; Richter, 1966; Hint, 1971). In vivo, solutions of 40,000 dextran reduced RBC aggregation and low-shear viscosity after infusion into experimental animals or hospitalized patients (Thorsén and Hint, 1950; Bergan et al., 1965; Hint, 1969). This observation led to the realization that administration of a 40,000 dextran (e.g., “RheoMacrodex,” Pharmacia, Sweden) was advantageous when an improvement in blood flow was specifically required, whereas a higher molecular weight dextran (e.g., 70,000 “Macrodex”) was preferable when plasma volume expansion was the primary goal (Arturson et al., 1964; Hint, 1969), because it has a longer circulation time. More recently, Geller et al. (1981) showed that 4000–6000 POE strongly inhibits RBC aggregation in whole blood. This observation is consistent with the known rheologic effects of poloxamer 188, an 8400 triblock copolymer composed of 80% POE and 20% polyoxypropylene, which reduces RBC aggregation in blood in vitro and in vivo (Toth et al., 1997, 2000), and has shown some benefit as an infusible agent to improve blood rheology in sickle cell disease (Orringer et al., 2001).

The key finding of this study was that the different polymers showed very similar effects on RBC aggregation when compared on the basis of their hydrodynamic radius, a measurement that reflects the contribution of all the above-mentioned physicochemical properties. Specifically, samples of all three polymers with R_h <4 nm inhibited aggregation, whereas those with R_h >4 nm promoted RBC aggregation. The ability of the smaller polymers to inhibit aggregation increased with R_h, with a maximum effect between 2 and 3 nm. Whether there is a significant difference in the inhibitory “potency” of the different polymers at their optimum R_h is unclear from this study, since they could not be directly compared at the same molar concentration, and also because the dextran and PVP samples (especially the latter) were more polydisperse than the POE samples, and thus contained a broader mixture of molecules of different sizes.

For all polymers, the inhibitory effect became less evident above 3 nm until there was no effect on aggregation at 4 nm. Above 4 nm, the aggregating increased with R_h, reaching a maximum somewhere between 6 and 12 nm, despite the decrease in molar concentration for the CC experiments and mass concentration for the CSV experiments. For polymers with R_h >12 nm, both the Myrenne and viscometric measures of aggregation were lower than the maximum value, but it is not obvious that this reflects a true decrease in the aggregating “potential” of the suspending phase. Microscopically, aggregation was clearly evident, and the aggregates tended to form rounded and compressed clumps rather than elongated rouleaux. Such differences in aggregate morphology have been noted previously, e.g., with RBCs exposed to α-2 macroglobulin (Schmid-Schönbein et al., 1973), or suspended in solutions of hemoglobin polymers or conjugates (Sakai et al., 2000), and suggest that the net aggregating “force” may in fact be greater with these very large macromolecules. Although very high molecular weight polymers have a large effect on solution viscosity, the difference between the samples studied at CC and CSV clearly shows that the apparent decrease in aggregation is not simply an artifact of the suspending phase viscosity. However, other possible measurement artifacts may affect the Myrenne data for large polymers, such as incomplete disruption of strongly interacting RBCs at high shear rates, a nonuniform cell concentration gradient, or an anomaly due to non-Newtonian behavior of the suspending phase, and cannot be ruled out.

At present, there are two coexisting yet mutually exclusive “models” for red blood cell aggregation—the so-called “bridging” and “depletion” models. The bridging model proposes that RBC aggregation occurs when the attractive bridging force arising from the nonspecific adsorption of macromolecules onto adjacent cell surfaces exceeds the disaggregating forces due to electrostatic repulsion, membrane strain, and mechanical shearing (Brooks, 1973; Chien and Lang, 1987; Brooks, 1988). Chien has formalized this model using a force balance equation (Chien, 1975), and data for RBC surface adsorption of dextrans (Chien et al., 1977) and RBC intracellular separation as a function of dextran molecular weight (Chien and Jan, 1973) have been published. In contrast, depletion-mediated RBC aggregation is driven by a relatively lower concentration of protein or polymer in the fluid near the cell surface (termed the “depletion layer”) compared to the bulk-phase suspending medium. Aggregation occurs if the energy available from merging the depletion layers of adjacent cells is sufficient to overcome the steric and electrostatic repulsive forces arising from the RBC glycocalyx. The role of depletion-mediated particle aggregation in colloidal systems is well known (Asakura and Oosawa, 1954, 1958; Vrij, 1976; de Gennes, 1989; van Oss, 1994), and the theory has been extended to red blood cell aggregation (van Oss et al., 1990; Bäumler et al., 1999). It is important to note that the depletion model does not preclude some degree of polymer adsorption onto the RBCs; it is only necessary that the concentration of the polymer in the depletion layer must be less than the bulk solution (de Gennes, 1989; Bäumler et al., 2001).

Either model provides a possible mechanism for RBC aggregation, but neither has been explicitly verified by experiment. Although it may appear intuitive and simpler in concept, some features of RBC aggregation are difficult to reconcile in terms of the bridging model. One problem is simply the requirement for relatively strong nonspecific adsorption of the macromolecule (the origin or nature of which is unclear), which seems at odds with the observation that so many different types of polymer and large plasma proteins induce RBC aggregation. Another is the observation that aggregating RBCs slip quickly into a face-to-face rouleaux configuration after initial contact (McMillan et al., 1989). This phenomenon is not easily explained with a bridging mechanism, since it would call for a very rapid turnover of multiple attachment points, otherwise unstructured agglutinates would be observed rather than rouleaux. In contrast, with a depletion-mediated aggregation mechanism, the type of macromolecule in solution is essentially irrelevant: it is only necessary that a sufficiently large depletion layer be developed relative to the bulk-phase concentration. Also, since the attractive forces do not involve direct contact between the cell surfaces and the macromolecules, the RBCs can slide freely into a reduced energy configuration as seen in rouleaux. Several other lines of evidence favoring the depletion over bridging for polymer- or protein-mediated RBC aggregation have been discussed in detail in recent articles (Bäumler et al., 1996, 2001; Armstrong et al., 1999; Neu and Meiselman, 2001, 2002) but debate still continues as to the relative merits of each model.

Both the bridging and depletion models require the macromolecules to exceed a critical size in order to induce aggregation: For bridging, a macromolecule would clearly have to be large enough to span the gap between adjacent RBCs at their closest point of approach. Similarly, depletion-mediated aggregation would occur only if the depletion layer exceeds a certain minimum thickness, which is also a function of the size of the depleted macromolecules (Bäumler et al., 2001; Neu and Meiselman, 2001). Thus, superficially, the results of this present study appear to be consistent with either model. However, it is important to recognize that the hydrodynamic radius—the radius of a hypothetical hard sphere that would increase fluid viscosity the same amount (or diffuse at the same rate) as the molecule under examination—is merely an abstraction. In practice, most macromolecules in solution are not spherical and are in continuous motion, including rotation: the calculated R_h thus represents an average “dynamic” size of these hydrated, tumbling, asymmetric molecules. Since the depletion layer results from the dynamic behavior of the macromolecules in solution, the depletion model of aggregation would predict that polymers with similar hydrodynamic radii should also have similar effects on aggregation. The same is not true for the bridging model, which assumes that the macromolecules are static, bound simultaneously to the surfaces of two adjacent cells. Different polymers or proteins, even if they have similar hydrodynamic radii in solution, may not exhibit the same relative dimensions when immobilized on a RBC surface, due to loss of entropy, stabilization of orientation (if asymmetrical), and differences in the length of polymer chain required to attach to the putative binding sites. Thus, for the bridging model, the effective “span” of the bridge would be expected to vary not only with R_h but also with the polymer type. The close relationship between hydrodynamic radius and RBC aggregation observed in this study for all types of macromolecule therefore appears to support the depletion model more strongly than the bridging model.

With regard to the mechanism of the anti-aggregating effect of low-molecular weight polymers, the possible interpretations are again model-specific. The bridging model explanation is that macromolecules too small to form an intercellular bridge will reduce aggregation by competing for binding sites, interfering with the attachment of larger, bridging macromolecules. This explanation appears to be reasonable if the inhibiting and aggregating molecules are similar (e.g., low-molecular weight and high-molecular weight fractions of the same polymer), but it is much less plausible for polymers of different types. For example, it would follow that any small macromolecules that can reduce RBC aggregation in plasma, such as low-molecular weight dextran and POE, must somehow interfere with the nonspecific adsorption of fibrinogen and immunoglobulins despite the fact that they only bind weakly and nonspecifically themselves.

The depletion model allows for a generally neater and more convincing explanation for the inhibitory effect of smaller polymers, although the precise details still need to be worked out. RBCs are covered with a glycocalyx, which extends out several nanometers from the RBC membrane into the suspending phase, and contains large numbers of sialic acid residues providing a strong net negative charge. We hypothesize that small polymers (R_h <4nm) can permeate the RBC glycocalyx. If true, then the depletion layer for these smaller molecules may not extend beyond the limits of the glycocalyx, thus adjacent RBCs would remain separated due to the mutual repulsion and aggregation would not occur. In a mixture containing both large (proaggregating) and small polymer molecules, the small molecules will tend to inhibit aggregation, since although the depletion layer of the larger polymer would still be present, the smaller polymer is not excluded from this region and will decrease the osmotic potential, reducing the attractive force between the cells (Neu et al., 2001).

Proteins are also polymers, but they are composed of amino acids with different side chains with different chemical properties, and are structurally much more complex than the simple nonionic polymers used in the experimental part of this study. The plasma proteins that were compared all have smaller R_h values for their molecular weight than any of the nonionic polymers, indicating a much more compact structure. The 12 proteins also differ substantially from each other in terms of primary sequence, molecular weight, numbers of subunits, secondary structure (folding), and intramolecular and intersubunit cross-links, and contain different numbers of ionizable, hydrophobic or hydrophilic groups that might potentially influence their interaction with the RBC surface. Thus, it was remarkable that these proteins showed not only the same general relationship between R_h and RBC aggregation, but also that the critical R_h for aggregation was precisely the same as for the three nonionic polymers. Taken together, these results indicate that the hydrodynamic radius is by far the most important determinant of RBC aggregation, at least for nonionic polymers and most plasma proteins, and it seems reasonable to predict that this simple relationship between R_h and aggregation will also be found for numerous other types of polysaccharides, proteins, and synthetic polymers.

An appreciation of the relationship between the effective size of a protein and RBC aggregation allows some earlier studies to be reinterpreted and better understood. For example, many investigators have noted the correlation between the increase in concentration of several plasma proteins seen after inflammation or trauma (the so-called acute-phase reactants) and an elevation of the ESR (Scherer et al., 1975; Kollmeier et al., 1972; Talstad et al., 1997). Some of the acute-phase proteins, such as fibrinogen and haptoglobin, are known to directly aggregate RBCs. Others, such as ceruloplasmin and C-reactive protein have been shown to enhance RBC aggregation when added to blood in vitro, but some acute-phase proteins, such as α-1 acid glycoprotein and α-1 antitrypsin, show no effect on aggregation in vitro (Weng et al., 1996) despite a strong correlation between their in vivo concentration and the ESR. These observations are fully consistent with the findings of this study: the hydrodynamic radii of the aggregating proteins, fibrinogen, haptoglobin, and ceruloplasmin (11.0, >25.0, and 4.6 nm, respectively) all exceed 4 nm, whereas the radii of α-1 acid glycoprotein (3.6 nm) and α-1 antitrypsin (3.8 nm) do not reach the 4-nm threshold for aggregation. It appears, therefore, that changes in the concentration of these small glycoproteins during the acute-phase response have no direct effect on the ESR, but rather reflect a parallel change in the concentration of fibrinogen or other large proteins.

The existence of a minimum R_h for RBC aggregation also neatly explains the results of some other RBC aggregation studies, such as in vitro investigations into the effect of enzymatically cleaved fibrinogen. Incubation of fibrinogen with plasmin initially yields two fragments designated as X and Y (Marder et al., 1969) which are then further cleaved by plasmin to produce the end-stage products D and E. Studies of the effects of these fragments on the ESR (Hormann, 1975; Marsh, 1979), showed that fragment X retained a strong aggregating effect, though less than the native fibrinogen, fragment Y had a reduced effect, and fragments D and E had no demonstrable aggregating effect. These findings were later confirmed by direct observation with a rheoscope by Maeda et al. (1987), who suggested that the cleavage of fragments X and Y into D and E disrupts the binding site required for the interaction of fibrinogen with the RBC surface. The R_h values for each fragment (from Marder et al., 1969, Table 4) suggest an explanation that is much simpler: the radii of fragments X and Y are relatively large, with X > Y, which is consistent with their effects on aggregation, but the radii of fragments D and E are both <4 nm, and thus they would not be expected to cause aggregation.

Similarly, IgG molecules can be cleaved with pepsin or papain into Fc, Fab, or F(ab′)₂ fragments. Unmodified IgG and the F(ab′)₂ fragment accelerated RBC aggregation in 60% diluted plasma (Imaizumi and Shiga, 1983) but the Fc and Fab fragments had no accelerating effect, and, in another study (Izumida, 1991), were shown to inhibit aggregation. Table 5 contains representative R_h values for these fragments, calculated from sedimentation coefficients from various sources (Fang and Mukkur, 1976; Jossang et al., 1988; Morgan et al., 1992; Carrasco et al., 2001). The F(ab′)₂ fragment (R_h = 4.48 nm) is large enough to promote RBC aggregation, but the Fc (R_h = 3.19 nm) and Fab (R_h = 2.91 nm) fragments are too small. Interestingly, the radii of the Fc and Fab fragments are in the appropriate size range for inhibition of aggregation (R_h ≈ 3 nm), consistent with their reported inhibitory effects.

Blood from different animal species shows a great variability in the tendency of RBCs to aggregate. For example, horse blood shows a remarkably fast aggregation and a very high ESR (Popel et al., 1994) whereas bovine RBCs can only be induced to aggregate by adding supranormal concentrations of fibrinogen or by enzyme pretreatment (Kaibara, 1983). When suspended in the same aggregating medium (e.g., 3% dextran, 70,000), different human donors may show up to a twofold variation in their “intrinsic aggregation,” and even within the same subject, older RBCs show enhanced aggregability relative to younger RBCs (Meiselman, 1993; Rampling et al., 2003). These differences among individuals and species have long intrigued hemorheologists, since they should provide insight into the mechanisms and possible physiological role of RBC aggregation, but few hard facts have yet emerged. The methodologies presented herein may provide a useful additional tool for comparative studies of this type. If we are correct in our assumption that the ability of a polymer to promote or inhibit RBC aggregation depends primarily upon whether it is excluded from the glycocalyx, then the use of a series of well-characterized, near-monodisperse, polymer probes of increasing molecular mass to identify the R_h threshold for aggregation will indicate the size exclusion limit for the glycocalyx (which may or may not relate to the glycocalyx thickness). An advantage of this technique is that it looks only for the critical R_h at which aggregation occurs, not the magnitude of aggregation, and thus should be relatively independent of the precise methodology used to study aggregation.