Hydrodynamics of concentrated proteoglycan solutions.

The dynamics of water transport in proteoglycan compartments has been studied in relation to osmotic flow (proteoglycan diffusion) and hydraulic permeability (proteoglycan sedimentation) in concentrated solutions of proteoglycan subunit and native proteoglycan aggregate isolated from Swarm rat chondrosarcoma. A central parameter that describes the kinetics of both types of water movement is the hydrodynamic frictional coefficient of water with proteoglycan. The frictional coefficient is markedly concentration dependent, increasing with increasing concentration, and highlights important structural features and types of organization of the proteoglycans in concentrated solutions. These include the requirements that proteoglycans in the extracellular matrix not to be immobilized but to have translational diffusive mobility and concentration gradients to be osmotically active, that chondroitin sulfate segmental mobility describing translational motion largely determines osmotic flow and hydraulic permeability of the proteoglycans, and that the proteoglycans exhibit an enhanced ability to resist flow as compared to other macromolecules. Additional dynamic studies suggest the formation of transient super-aggregate structures may occur at high concentrations which endows the proteoglycan subunit hydrodynamic properties similar to proteoglycan aggregate.

components have been generally considered to exist in a simple biphasic arrangement (2, 3) consisting of a porous network of insoluble collagen fibers filled with a soluble phase of water and proteoglycans up to 50-80 mg ml" in concentration (4). The major proteoglycan population has a hierarchical branching organization that enables efficient packing and concentration of the anionic charges, provided by fully ionized sulfate and carboxyl groups on the repeat disaccharide units of the constituent polysaccharide chains. The proteoglycan subunit (5) exists as a large molecule in which many pendant polyanionic polysaccharide chains are covalently bound to a * This work has been supported by the Australian Research Grants Scheme and a Monash University Special Research Grant. The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "aduertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
4 To whom correspondence should be addressed.

Q Supported by the Commonwealth Graduate Scholarship Scheme.
This work represents partial fulfilment of the Ph.D. degree. protein core (6). Proteoglycans are normally present in the matrix as aggregates in which 20-50 PGS' molecules are bound through noncovalent interactions to an hyaluronate core (7); the interactions being stabilized by link proteins (8). The significance of aggregate formation is not clearly understood although it is commonly thought that aggregates by virtue of their large size, are retained within the pores of the cross-linked collagen network by a physical entrapment mechanism. Weak electrostatic and hydrogen-bonding interactions between proteoglycans and collagen, which may be facilitated by the relatively lower NaCl concentration in proteoglycan compartments (lo), may augment the retention of the proteoglycans in this structure. There is a paucity of information, however, as to the microstructural organization of macromolecules in the matrix, i.e. the nature of macromolecular concentration gradients (with attendant micro-ion concentration gradients) and other regional variations, of the network structure, and of proteoglycan interactions with other matrix macromolecules and structures.
In relation to the mechanical properties of cartilage its most important component is water. The load-bearing properties of cartilage result largely from its ability to retain water (an essentially incompressible fluid) under the application of load. On a molecular level, this has to be interpreted in relation to the hydrodynamic properties of the proteoglycan-containing collagen network. A correlation has been established between the proteoglycan content of the matrix and factors which reflect retained water in the matrix namely high swelling pressure and low hydraulic permeability (4, 9). A polemic exists as to the relative importance of these factors; Mow et al. (3) concluded that the frictional drag of the relative motion between water and the matrix components is the most important factor governing the tissues response to compression, whereas Maroudas et al. (4,11) have emphasized that maintenance of tissue hydration under load can be described in terms of proteoglycan osmotic pressure. Other less substantiated claims have been made in relation to the fact that the proteoglycan itself has rigidity or acts as a mechanical "spring" within the cartilage. The investigations reported in this study set out to examine the relative influence of osmotic pressure and hydrodynamic friction in governing the movement of water in proteoglycan solutions. The results are discussed in terms of the specific features of proteoglycan structure.

Isolation and Purification of Proteoglycan Subunit, Proteoglycan
Aggregate, and Chondroitin Sulfate Proteoglycan aggregate (PGA) was purified from Swarm rat chondrosarcoma tumors that were grown in female Wistar rats following the methods of Faltz et al. (12) and Kimata et al. (13). Minced tumors were extracted with 1 g of extractant solution per g of tissue where the extractant was 0.4 M GdnHCl, 50 mM sodium acetate, pH 5.8, which contained the protease inhibitor mixture 0.025 M EDTA, 10 mM N-ethylmaleimide, 0.1 mM phenylmethylsulfonyl fluoride, 1 mM benzamidine hydrochloride, 0.1 mM c-aminocaproic acid, and 2 mM iodoacetic acid. The PGA was purified as an d l 2 fraction by equilibrium CsCl gradient centrifugation and then further purified from proteoglycan monomers on cesium sulfate rate-zonal density gradient.
PGS was prepared by extracting the tumors with 4 M GdnHC1,50 mM sodium acetate, pH 5.8, containing the inhibitor mixture described above. The proteoglycan material was then purified as a Dl2 fraction as previously described (5).
[35S]PGS was prepared from the tumors by a modification of the method described by Kimura et al. (14). Sterile minced tumors were washed with PBS (0.14 M NaC1, 2.6 mM KCl, 1.5 mM KH2P04, 8.1 mM Na2HP04; pH 7.5) and then centrifuged. The cell pellet was incubated with trypsin at 37°C for 30 min then collagenase for 30 min. The cells were pelleted and resuspended in Dulbecco's modified Eagle's medium and pH indicator at a concentration of 0.5 X lo6 cells/ml. Carrier-free Na;'S04 in isotonic saline (1 mCi) was incubated for 24 h with 5 X lo6 cells in culture medium. Extraction of [%]PGS for 24 h at 4 "C used an equal volume of 8 M GdnHC1,lOO mM acetate buffer plus inhibitor mixture (double strength). The [35S]PGS was then purified by equilibrium gradient centrifugation as a D l fraction with a specific activity 1200 dpm pg-'.
The commercially supplied preparation of chondroitin sulfate was further purified to remove protein by &elimination, proteolytic digestion, and trichloroacetic acid precipitation. The chondroitin sulfate was precipitated with ethanol and then dried.
All polysaccharides were dialyzed extensively against 1 M NaCl to yield the Na+ form and then dialyzed against PBS. The preparations were stored frozen in PBS.

Ultracentrifuge Experiments
Diffusion-Mutual diffusion coefficients were measured by free diffusion in a Beckman Model E analytical ultracentrifuge using the where t is the time. Values of D. , were calculated from the slope of the plots of ( WXh)' against t from eight pictures taken at regular time intervals. We assume that D,, closely approximates the differential * The abbreviations for identifying proteoglycan fractions follow the nomenclature of Heinegird (20). mutual diffusion coefficient (D) at the corresponding mean concentration [c = (C, + Cb)/2]. This is probably an acceptable approximation considering the small step concentration gradients involved.
All "b" solutions were dialyzed against PBS prior to their use, whereas "t" solutions were obtained by dilution of the b solution with the dialysate. This procedure was employed to minimize the initial activity gradients of salt in the diffusion experiments. Diffusion boundaries formed from solutions prepared in this way have previously been demonstrated to give rise to normal diffusional transport (15,16). Sedimentation-Subsequent to the diffusion experiment described above, the speed of the rotor was increased to 44,000 rpm to sediment the material. For very slow sedimenting material maximal speeds of 60,000 rpm were used. The displacement of the sedimentation boundary with time was recorded photographically at regular intervals. Generally, at high macromolecule concentrations, which were of experimental interest, the sedimentation coefficient was very low in magnitude. In some concentrated solutions, no sedimentation was observed over an 8-h period. Errors associated with radial dilution effects were assumed to be negligible. Furthermore, substantially similar results were obtained by performing the sedimentation experiment either as described above or by sedimenting the material away from the meniscus. This demonstrates that errors associated with hydrostatic pressure effects exerted by the column of solvent above the solvent-solution boundary were also negligible in relation to the magnitude of the sedimentation coefficient.
HTO Transport in Proteoglycan Solutions-A transport apparatus of similar design to that described by Linder et al. (17) and developed by Sundelof (18) was used to measure HTO transport. The analysis was similar to previous studies of HTO transport in dextran polysaccharide solutions (19).
Membrane Transport-Transport of [35S]PGS through Nuclepore capillary pore membranes was performed with the membrane fixed between two identical cylindrical chambers (15 mm diameter and 7 mm deep) of a perspex cell. The solutions in the chambers were not stirred. The concentration of PGS on both sides of the membrane was equal with one side initially containing trace quantities of [35S] PGS; the transport of [%3]PGS to the other chamber was measured over a period of 72 h.
Each transport measurement was made in quadruplicate. The [35S]PGS was fractionated on Sephacryl S-500 prior to use in this experiment; a similar profile to that shown in Fig.  1B was obtained and fractions 44-65 were pooled for subsequent transport measurements.
Preparation of Solutions-The preparation of concentrated polysaccharide or proteoglycan solutions was done by ultrafiltration using an Amicon ultrafilter and PM-10 membrane. The highest concentrations we were able to prepare for PGA and PGS were -38 mg ml" and -60 mg ml-', respectively; these solutions were extremely viscous and difficult to transfer. After ultrafiltration, the polysaccharide solution was dialyzed against PBS to ensure thermodynamic equilibrium of simple electrolyte. All dilutions of the proteoglycan solutions warranted gentle mixing at 4 "C for at least 24 h prior to use.
Analytical Procedures-Uronic acid was determined by an automated carbazole method (20). Radioactivity was determined using described by Fox (211, and recorded on an LKB Wallac 1214 Rack 1.0-ml aqueous samples with 8.0 ml of a scintillant mixture as Beta scintillation counter. Dry weights of proteoglycan preparations that were extensively dialyzed against water were measured by heating samples over P20~ at 60 "C and 133-Pa pressure (under vacuum) until constant weight was obtained. Solution densities were measured on a DMA 55 density meter (Anton Paar, Austria) equipped with Haake F4-K Cryostat (Haake, Federal Republic of Germany) that controlled the temperature to 20.0 2 0.02 "C. Refractive index measurements were performed on a Brice-Phoenix differential refractometer at a wavelength of 546 nm (Phoenix Precision Instrument Co., Philadelphia) using NaCl solutions as standards. The physical constants and concentration conversion factors associated with the various polysaccharide fractions are described in Table I.
Integrity of Proteoglycan Preparations-The chromatographic profiles of the various proteoglycan fractions are shown in Fig. 1. The distribution of material in the PGA preparation (curue I , Fig. la) was clearly confined to material eluting at or near the void volume (unmeasured) of Sephacryl S-1000 column and was easily distinguished from PGS that was well included into the column (curue 3, Fig. la). The aggregate appeared relatively stable as indicated by its behavior in the ultracentrifuge even when it was stored frozen and subsequently used. Only in the most prolonged processing involving a concentration to -25 mg/ml", by ultrafiltration, followed by anal-  (graph I ) and

Hydrodynamics of Proteoglycan Solutions
[%]PGS (----) (graph 3 ) on Sephacryl S-1000 (column dimensions, 50 X 1 cm) in 0.5 M sodium acetate, 0.05 M sodium sulfate, and 0.01% CHAPS, pH 7.0. PGA fractions were monitored for uronic acid and [35S]PGS fractions were monitored for radioactivity. Graph 2 represents the PGA sample that was concentrated to -25 mg rnl-', used in centrifuge for diffusion analysis at that concentration, recovered, diluted, and then re-applied to the column. Each fraction was 0.72 g. b, profile of PGS on Sephacryl-500 (column dimensions, 67.5 X 5 cm) in PBS. The PGS fractions were monitored for uronic acid. Each fraction was 12.3 g. ysis in the centrifuge, dilution, and re-analysis on the column, did we notice a 20% disaggregation (curue 2, Fig. la). The aggregate preparations were always checked on the column prior to use. PGS fractions eluted at much later volumes on Sephacryl S-1000 and showed no sign of high molecular weight aggregates in either the [35S]PGS preparation or in the unlabeled PGS preparation on the preparative Sephacryl S-500 column (Fig. l b ) .

A Summary of Equations Describing Molecular Transport
Diffusional Transport-We will be developing arguments in this study which suggest that the diffusive mobility of the proteoglycan is critical for the manifestation of its properties. We start by describing the usual diffusion equation of Fick's Law, i.e.
where J , is the flux of component 1 (which is proteoglycan), Dl the mutual diffusion coefficient, T the temperature, P the pressure, and acl/ax the concentration (mol ~m -~) gradient. We can rewrite Equation l in another form which now includes the osmotic pressure gradient @"/ax) and the effective diffusion coefficient (Defr), (22).
where and T~l z and where b1 is the volume fraction of 1, flz is the hydrodynamic frictional coefficient between the proteoglycan and solvent (component 2), C1 the concentration in g.ml", and pz in the chemical potential of solvent.
The nature of flz in relation to the structure of the proteoglycan is little understood. We do know that in dilute solution we have the Stokes-Einstein equation which relates f12 to the hydrodynamic radius of the diffusing solute Rh where u1 is the partial specific volume of 1, 6, and M1 the volume fraction and molecular weight, respectively, of 1, K a geometric factor associated with the membrane and A n is the overall gradient in osmotic pressure. In summary, the important factors associated with the osmotic flow caused by proteoglycan are the osmotic pressure gradient, the geometric nature of the membrane, and the diffusional mobility of the proteoglycan as embodied in the f12 term. The f1z factor is a new consideration in the manifestation of osmotic flow. The interpretation of this equation may be made in the following way. If an inert semipermeable membrane is interposed at the interface between the proteoglycan solution and solvent (or by analogy a collagen matrix retaining the proteoglycan) then osmotic flow will be governed by two processes in series namely: 1) the diffusive volumeexchange process associated concentration gradients of proteoglycan on the solution side of the membrane and 2) the hydraulic flow of water through the membrane (independent of proteoglycan concentration).
Hydraulic Permeability-D'Arcy (24) introduced the coefficient k, the hydraulic permeability coefficient, to describe the relationship between flow in response to a mechanical pressure gradient (aP) across a membrane of thickness (Ax) as the following.

Balance of Osmotic and Mechanical Pressures
The balance of osmotic and mechanical pressures on proteoglycan retaining systems, such as cartilage, can be described in terms of an equation analogous to that describing sedimentation-equilibrium in the ultracentrifuge such that J, = I,iL,'(hp -A n )

(9)
where the Lp coefficients describe (i) the geometric (pore size) factor of the system ( L i ) and (ii) concentration-dependent diffusive mobility of the osmotically active solute (L,'aM1/fl2). Fig. 2. At low concentrations, the relative differences in the diffusion coefficients are marked with CS having a diffusion coefficient 2 orders of magnitude greater than the PGA sample. The diffusion coefficient of PGA is, as expected, very low (-lo-' cm2 s-') in dilute solution. As the concentration is increased the diffusion coefficient for all samples increases markedly and converges to molecular weight independence up to concentrations of 40 mg ml". This approach to molecular weight independence at high concentrations has also been observed with different molecular weight fractions for the uncharged polysaccharide dextran (22). At -25 mg ml" polysaccharide concentration the relative difference in the diffusion coefficient between CS and PGA is negligible; t,he PGA is now moving with a diffusion coefficient of -10 x cm2 s-'. The relatively rapid movement of PGA was probably not due to any significant degradation as shown by 1) diluting the 25 mg ml-* PGA sample to 0.33 mg ml" and observing a single peak during sedimentation which had a sedimentation coefficient of 43.75 S and 2) re-analyzing the same sample on Sephacryl S-1000 (Fig. 1) after the diffusion run; approximately 80% of this sample was still aggregate (according to its column profile) and 20% as PGS. At high concentrations (greater than 45 mg ml-l) the PGS coefficients may diverge from those measured for CS.

Mutual Diffusion-The concentration dependence of the mutual diffusion coefficient of the various polysaccharide preparations is shown in
Sedimentation Velocity-The concentration dependence of the sedimentation coefficient is shown in Fig. 3. At low concentrations the S1 values are markedly different for each of the preparations; the extrapolated S1 to infinite dilution for PGA was in the range of 60-100 S which is in accord with reported SI of other aggregate preparations (26). As the concentration is increased, SI decreases markedly and not only approaches molecular weight independence but approaches The calculated values of hydraulic permeability, k, from Equations 7 and 8 using S1 from Fig. 3 and shown in Fig. 4 demonstrate that on a volume fraction basis, PGS (and PGA although not shown) is most efficient in retarding water flow as compared to other macromolecules, namely globular albumin, uncharged dextran, and polyanionic dextran sulfate at salt concentrations similar to the PBS. Values of k for dextran sulfate is demonstrated to decrease with decreasing ionic strength which reflects the influence of the "primary charge effect" on f l z and hydraulic permeability (29). However, dextran sulfate behavior at 0.01 M NaCl is still not significantly different from PGS. In fact the extraordinary effectiveness of proteoglycans in restricting fluid flow clearly demonstrates that apart from established shape/charge effects (29), there are other structural features of the proteoglycans associated with their resistance to flow. These features are similar to those found for chondroitin sulfate solutions. The results may suggest that the chemical and structural features of the CS chains may be important in giving rise to higher resistance to hydraulic flow of water. Effective Diffusion Coefficient-The effective diffusion coefficient defined in Equation 2a may be evaluated from the sedimentation coefficient data using Equation 7, and its concentration dependence for both PGS and PGA is shown in Fig. 5a. The very low effective diffusion coefficient, which decreases with concentration, is matched by the corresponding apparent Stokes radius shown in Fig. 5b which shows a very large increase with increasing concentration. While (De& or (RJappis markedly concentration dependent we note that (Rh)app for PGS at high concentration (>lo mg ml-') approaches (Rh)app for PGA in dilute solution. On this basis, concentrated PGS could be viewed as hydrodynamically equivalent to the dilute hydrodynamic volume of PGA. Preliminary experiments do suggest that the marked concentration dependence of (Deff), is reflected in [35S]PGS transport across capillary pore (400-nm diameter) membranes over a PGS concentration range of 0.4-12 mg m1-l.
The results shown in Table I1 demonstrate that for systems with equal concentrations of PGS on both sides of the membrane the quantitative transport of [35S]PGS is decreased markedly on increasing the PGS concentration. Note that it has been previously demonstrated (15,22) that the diffusional ex-   "Errors are given as f standard deviation. Measurements were made in quadruplicate. Note that maximum transfer can only be 50% as the two compartments were of equal volume. change in this type of experiment is quantitatively similar to (Deff)l. While the membrane results are consistent, in part, with the decrease in (Deff), with concentration they also highlight that, in a dynamic sense, the PGS molecule at high concentrations appears larger to the pores of the membrane.
HTO Transport-Analysis of HTO transport in a PGS solution of 41 mg ml" gave a diffusion coefficient of HTO of 182 X cm2 s" which was 96% of its value in the absence of PGS. The small reduction is similar to that obtained in other polymer solutions (19) and can be accounted for by steric hindrance effects and not by any marked alteration in water structure in the vicinity of the proteoglycan.

DISCUSSION
The magnitude and the rate of increase with concentration of the mutual diffusion coefficient of CS, PGS, and PGA is considerably larger than that observed for its uncharged counterpart, dextran (22). This may be understood in terms of the parameters described in Equation 2b. The osmotic term for these polyelectrolytes is essentially determined by the influence of the polyion on the micron-ion distribution in its vicinity (the Donnan effect (10, 27, 28)) and thus we would expect molecular weight-independent behavior. This has been shown by Urban et al. (28) who demonstrated that the magnitude and concentration dependence of osmotic pressures of bovine nasal cartilage CS, PGS, PGA (measured by an equilibrium dialysis technique) were essentially identical over a wide range of concentration when compared on the basis of anionic charge concentration. We would expect similar behavior in this study except that our comparisons of diffusion data are made on the basis of total mass concentrations. A small difference in osmotic behavior between CS and the proteoglycans would then be anticipated as the concentration of anionic charge/molecular mass is about 10-15% higher for the CS as compared to PGS and PGA. This is mainly due to the presence of protein and Nand 0-linked oligosaccharides in the chondrosarcoma proteoglycan structures (30). While the nature of the frictional coefficient in Equation 2b is not well understood (in contrast to osmotic pressure) it is evident from the sedimentation studies that the Ml/flo will be essentially molecular weight independent in semidilute solutions. This has also been shown for dextran sedimentation (22). All these considerations are then consistent with the observed molecular weight independence of Dl for CS, PGS, and PGA at high concentrations. The actual increase in Dl with concentration is due to the predominance of the (an/dC,) term in Equation 2b over the frictional term, f12.
The approach of the Ml/fi2 term to molecular weight independence does suggest that the flexibility and diffusive mobility of segments of the CS chains and its associated counterions are critical in determining f12 for both PGA and PGS.
It is emphasized that the segmental mobility referred to here represents translational motion, and is subject to marked concentration dependence. It is of interest to note that in another related study, Torchia et al. (31) established from 13C nmr studies that chondroitin sulfate motion in cartilage is relatively free, i.e. independent of aggregation and placement of the proteoglycans within the collagen network of cartilage. While there is no direct relationship between translational motion studied here and that segment motion measured by 13C nmr (interpretated on the basis of rotational diffusion (31)) it is clear that both show molecular weight independence.
In discussing the factors associated with volume flow in cartilage described in Equation 9, a number of interesting features emerge. First, the role of osmotic flow in cartilage is envisaged to be important in two situations namely (i) to oppose the tendency of water being pushed out of cartilage under compressive load and (ii) as the only mechanism by which water is reimbibed into the tissue once the mechanical load is removed (i.e. hp = 0 in Equation 9). For osmotic flow to occur, there must be osmotic or concentration gradients of osmotically active material (namely proteoglycan) which drive the diffusional exchange with water. If the osmotically active material is immobilized (i.e. Dl = 0) then no osmotic flow will occur. We also note that osmotic flow should be faster for low molecular weight material as compared to high molecular weight material (23). To a certain extent, these considerations seem paradoxical to the presence of PGA in cartilage rather than PGS. However, we have demonstrated in this study that all the parameters governing osmotic flow due to the proteoglycan as embodied in Equation 4 are molecular weight independent.
A further feature of proteoglycan solutions examined in this study is their high resistance to hydraulic flow of water (i.e. with hp >> AT in Equation 9) as demonstrated in the sedimentation experiments. These studies highlighted the relative influence of hydraulic permeability as compared to osmotic pressure in resisting water flow. For example, bovine nasal cartilage proteoglycan solution of 50 mg ml" has an osmotic pressure of -4.7 x lo5 dyne cm-' (28). During the course of the sedimentation experiment the proteoglycan will experience a centripetal force (32) of (1pul)C,w2?/2, where w is the rotor speed in radians s" and r the radius to the compartment containing the proteoglycan solution; this force is calculated to be -1 X lo7 dyne cm-'. The resistance to flow, subject to this relatively large hp value, therefore, clearly lies with molecular parameters contributing to the frictional coefficient flz rather than osmotic pressure. Actual values for hydraulic permeability of cartilage are reported to be in the range of 1-6 X cm3 s g" (Ref. 4 and earlier references). When these values are multiplied by the viscosity of water, namely 0.01 poise, then they can be compared directly with those in Fig. 4. For example, a PGS concentration of 50 mg ml" gives a k of cm', whereas that of cartilage containing -50 mg ml" of proteoglycan is -3 X cm3 s g" or 3 x cm2. These values seem to be in the right order and differences may be accommodated by the influence of the collagen network as embodied in the term L, ' in Equation 9 and the specific concentration distribution of proteoglycans in cartilage.
The significance of the concentration dependence of Ml/f12 or k can also be appreciated in the following model of cartilage. A simplified cartilage structure could be viewed as an array of porous spaces, each "space" surrounded by a network of collagen which retains but does not immobilize the proteoglycan within the space. When these units are subject to mechanical compression, water will be ultrafiltered out of the space in a particular direction (of least resistance) which will   Calculated by assuming length of so00 nm and radius of 100 nm.
simultaneously give rise to a build up of proteoglycan concentration on the face of the porous wall. The permeability of the proteoglycan compartment will decrease dramatically for a very small change in proteoglycan concentration in accord with the variation of k in Fig. 4. The application of mechanical load will result in a pattern of concentration gradients in the tissue corresponding to the array of porous cells. When the load is released, the proteoglycan concentration gradients relax by diffusion (therefore the requirement for proteoglycan diffusive mobility) and in so doing osmotically reimbibes water into the porous network and tissue as a whole. In summary, the results of hydraulic permeability, at least when AI' >> AT, would be in agreement with the conclusions of Up to this stage we have considered the hydrodynamics of proteoglycan solutions in terms of molecular weight-independent quantities, such as osmotic pressure and translational segmental mobility. Another important aspect that will influence proteoglycan hydrodynamics, especially in relation to proteoglycan retention and organization in extracellular matrices, is the effective size of the molecule and the magnitude of the fi2 term. It is appreciated that in constructing proteoglycan solutions above their critical concentrations (Table   111) it is necessary, purely through space filling requirements, that the proteoglycan must occupy a reduced volume (see also Ref. 33) as compared to its hydrodynamic volume at infinite dilution. The conformational changes involved are not clear, however. We envisage two factors of importance namely ( a ) the flexibility of the protein core for PGS or the hyaluronate core for PGA and ( b ) the balance between the internal and external osmotic pressures in relation to the domains of the molecule (note that the HTO transport studies described earlier demonstrated that water in the hydrodynamic volume of the proteoglycan is unstructured and will therefore be subject to osmotic forces). The osmotic pressure of the internal hydrodynamic domain of the proteoglycan will be directly related to the concentration of CS chains within the domain. We know from the structure of chondrosarcoma PGS (30) that the mean concentration of CS in its hydrodynamic volume is -1.2 mg m1-I. A fully extended molecule has a cylindrical structure, with a reduced volume (Table IV) and an average cylindrical domain concentration of CS of -11 mg m1-l. The variation in the mean radial concentration of CS extending from the protein core is not known. It is likely that with increasing concentration of PGS the proteoglycan will initially prefer to take on a more restrictive extended conformation without changing the average cylindrical domain concentration of CS. Conformational changes resulting in increasing the cylindrical domain CS concentration through chain folding or the intermeshing of CS chains from different molecules are more likely to occur at higher concentrations. The extended conformation with restricted translational and global rotational mobility due to the presence of other molecules is consistent with the behavior of flz from sedimentation analysis which suggested a molecule undergoing substantial intermolecular contacts. We speculate that the proteoglycans may create transient aggregate or multipolyion structures. This interpretation would also be consistent with the apparent increase in the dynamic size of the proteoglycan in relation to pores in a membrane. We would also predict similar changes in the proteoglycan aggregate (Table IV). There is a growing body of work that suggests that concentration-dependent aggregation, in the form of loose aggregates (35) or liquid-crystal-type structures (36), through the sharing of counterions or counterion clouds, is a general property of polyelectrolytes.