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Flow conductivity of solutions of hyaluronic acid : effects of concentration and molecular weight Lam, Luk Sang 1988

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FLOW CONDUCTIVITY OF SOLUTIONS OF HYALURONIC ACID: EFFECTS OF CONCENTRATION AND M O L E C U L A R WEIGHT by LUK SANG L A M B.S., The University of Oregon, 1984 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF CHEMICAL ENGINEERING We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A September 1988 © L U K S A N G L A M , 1988 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Ghemlcal Engineering The University of British Columbia Vancouver, Canada Date September 30, 1988  DE-6 (2/88) A B S T R A C T Hyaluronic acid plays an important role in regulating the transport of fluid and solutes in the interstitium. The concentration and molecular weight of hyaluronic acid in different connective tissues are different. These factors influence the hydraulic flow conductivity, K', of connective tissues. A n experimental study of the effect of concentration and molecular weight of hyaluronic acid on the hydraulic flow conductivity is the subject of this work. Hyaluronic acid of different molecular weights were obtained by fractionating commercially available hyaluronic acid using ion-exchange column chromatography. The results were not reproducible, partly because of the elution process was not continuous. Nevertheless, three molecular weight fractions (6.99 5 to 11.1X10 ) were obtained. 5 Hyaluronic acid of lower molecular weights (0.454 to 1.65X10 ) were obtained by acid hydrolysing some of the chromatographed fractions for 15 min. , 1 hour and 2 hours. A more homogeneous hyaluronic acid fraction 5 ( M . W . = 1.96 X10 ) was obtained by fractionating hyaluronic acid materials acid hydrolysed for 15 min. The hydraulic flow conductivity of solutions of hyaluronic acid can be calculated from the sedimentation coefficient of the solutions at 20 ° C , ^20' measured by ultracentrifugation. Centrifugation experiments determining the S of the molecular weight fractions of hyaluronic acid at various concentrations were n therefore undertaken. The results showed that S0 decreased with increased concentration of hyaluronic acid. Also, the curves of as a function of hyaluronic acid concentration, c, converged at high concentration, indicating that a three dimensional molecular network is formed at high concentration and the extent of entanglement between molecules is the same for the high and low M . W . fractions. A t lower concentrations, for the acid hydrolysed fractions, S^Q increased with M . W . , which is in agreement with past sedimentation data. For the non-acid hydrolysed fractions, the difference in SgQ between two higher M . W . fractions is small, and the lowest M . W . fraction has consistently higher S^Q than the higher M . W . fractions. This finding does not agree with past literature results, and the difference in results is most probably due to experimental errors. However, when the fractionated non-acid hydrolysed fractions are taken as a high 5 M . W . group (M.W. = 6.99 to 11 .1X10 ) and the acid hydrolysed fractions as a 5 low M . W . group ( M . W . = 0.454 to 1 .96X10 ), the curves of S 2 Q as a function of c of the low M . W . group fall below those of the high M . W . group, which is in agreement with past sedimentation data. The hydraulic conductivities (K'), calculated from S^Q data, for all the H A fractions varied inversely with concentration. T h e log-log plots of K' versus c compared well with the results of Ethier (1986). The K' versus c relationships for all the fractions converged at high concentrations. A t low concentrations, the H A molecules of the high M . W . group has a higher K' than those of the low M . W . group. i n T A B L E OF CONTENTS A B S T R A C T ii T A B L E O F C O N T E N T S iv L I S T O F T A B L E S vi L I S T O F F I G U R E S vii A C K N O W L E D G E M E N T S ix Chapter 1. I N T R O D U C T I O N 1 1.1. Hyaluronic A c i d 1 1.1.1. Conformation 3 1.1.2. Viscosity 6 1.1.3. Colloid Osmotic Pressure 9 1.1.4. Mass Transport through Hyaluronic Acid Solutions . . . 11 1.2. The Components of the Interstitium 13 1.2.1. Proteoglycan 13 1.2.2. Collagen 17 1.2.3. The Hydraul ic Resistance of Flow in the Interstitium 18 1.3. Objective of the Thesis 19 Chapter 2. T H E O R E T I C A L B A C K G R O U N D 21 2.1. Introduction 21 2.2. Enzyme Degradation Method 22 2.3. Filtration-Chamber Method 24 2.4. Sedimentation Method 26 2.5. Sedimentation Theory 32 2.5.1. T h e Analyt ical Ultracentrifuge 32 2.5.2. Transport in the Ultracentrifugal Cell 35 2.5.3. Measuring the Sedimentation Coefficient 42 2.6. Ion-Exchange Chromatography Theory 46 Chapter 3. E X P E R I M E N T A L P R O C E D U R E 52 3.1. Introduction 52 3.2. Hyaluronic A c i d Concentration Determination 52 3.3. Fractionation of Hyaluronic Acid 54 3.3.1. Desalting Hyaluronic A c i d 54 3.3.2. Preparation of DEAE-cel lu lose 55 3.3.2.1. Precycling 55 3.3.2.2. Fines Removal 56 3.3.2.3. Equilibration 57 3.3.3. Prel iminary Fractionation 58 3.3.4. Fractionation 65 3.3.5. Purification and Isolation of H A 66 3.4. Acid Hydrolysis of H A 67 i v 3.5. Fractionation of Acid Hydrolysed H A 69 3.5.1. Acid Hydrolysis 69 3.5.2. Fractionation 69 3.6. Dialysis 70 3.6.1. Preparation of Dialysis Tubings 71 3.6.2. Dialysis 72 3.7. Viscosity 74 3.8. Sedimentation Velocity 77 3.8.1. Preparation of Sample Cell 78 3.8.2. M a k i n g a Sedimentation Velocity Run 83 3.8.3. Taking Photographs 87 3.8.4. Ending a Sedimentation Velocity Run 88 Chapter 4. R E S U L T S A N D D I S C U S S I O N 90 4.1. Hyaluronic Acid Concentration Determination 90 4.2. Fractionation of Hyaluronic , acid 92 4.3. Acid Hydrolysis of Hyaluronic Acid 98 4.4. Fractionation of Acid Hydrolysed H A 98 4.5. Sedimentation Coefficient 102 4.6. Hydraulic Conductivity 117 Chapter 5. C O N C L U S I O N S A N D R E C O M M E N D A T I O N S 123 R E F E R E N C E S 127 A P P E N D I C E S 134 A . Sample Calculations 134 B. Experimental D a t a 146 v List of Tables 2.1 Buffer used by different workers 25 3.1 Results of preliminary fractionation I 59 3.2 Results of preliminary fractionation II 61 3.3 Results of prel iminary fractionation III 62 4.1 Results of the uronic acid carbazole test 90 4.2 Results of the large scale fractionation experiment 93 4.3 Intrinsic viscosity and molecular weight of 1 5 m i n A H , l h r A H and 2 h r A H Fractions 98 4.4 Results of the fractionation of acid hydrolysed H A 100 4.5 Sedimentation coefficient and hydraulic conductivity for all H A Fractions .. 103 4.6 Values of A and B in E q n [4.4] for all H A Fractions 117 A . l Viscosity data for 0.325M-9 Fraction 136 A . 2 Results for sedimentation Run C l 139 A . 3 c and K' data for 0.325M-9 Fraction 142 VI List of Figures 1.1 Chemical structures of the dominant disaccharide units of various glycosaminoglycans 2 1.2 Schematic demonstration of the volume occupied by a hyaluronic acid molecule 4 1.3 Diagramatic representation of a synovial joint 9 1.4 Osmotic pressure of hyaluronic acid versus concentration 10 1.5 Illustration of the steric exclusion mechanism 14 1.6 Structure of cartilage proteoglycan manomer 15 1.7 Schematic model of the structure of cartilage proteoglycan aggregates 16 2.1 A system of macromolecules sedimenting in an ultracentrifuge 27 2.2 Sector-shaped cell used in all analytical ultracentrifuge 30 2.3 (a) The concentration profile of a sedimentation run. (b) A Schlieren trace of the cell along the radial direction. The Schlieren peak represents the boundary position 31 2.4 Schematic diagram of an analytical ultracentrifuge 32 2.5 The analytical ultracentrifuge cell 33 2.6 Geometry of a sector-shaped cell 35 2.7 Solute concentration profile during ultracentrifugation of a typical solution of a homogeneous macromolecule, D = 0 38 2.8 Demonstration of radial dilution 39 2.9 Concentration profile of the sedimentation of a real solution 43 2.10 Structures of the D E A E and C M cellulosic ion-exchangers 48 3.1 The set up for the equilibration of the ion-exchanger 57 3.2 Intrinsic viscosity plot of the 0 . 3 M and 0 . 4 M Fractions 64 3.3 The set up for performing dialysis 73 3.4 The Ubbelohde type semi-micro dilution viscometer 75 3.5 Position of the torque wrench and the cell housing 80 vii 3.6 Installing the rotor 82 4.1 Relationship between the absorbance and the concentration of glucuronolactone. 91 4.2 Intrinsic viscosity plot for the H A Fractions 96 4.3 Intrinsic viscosity plot for the acid hydrolysed Fractions 99 4.4 Intrinsic viscosity plot of the 1 5 m A H - 0 . 3 2 5 M Fraction and unfractionated H A 101 4.5 Sedimentation coefficient as a function of concentration for 0 .25M, 0 .325M and 0.325M-9 Fractions 105 4.6 Sedimentation coefficient as a function of concentration for 1 5 m i n A H , l h r A H , 2 h r A H and 1 5 m A H - 0 . 3 2 5 M Fractions 106 4.7 Sedimentation coefficient as a function of concentration for all Fractions. . 107 4.8 Sedimentation data of Laurent et al. (1960). •.: 108 4.9 Sedimentation patterns of the 0 .25M, 0 .325M and 0.325M-9 Fractions 110 4.10 Sedimentation patterns of the acid hydrolysed H A Fractions I l l 4.11 Sedimentation patterns of the 1 5 m A H - 0 . 2 5 M and 1 5 m A H - 0 . 3 2 5 M Fractions. 112 4.12 Sedimentation pattern and concentration profile of acid hydrolysed H A Fractions 115 4.13 Hydraul ic conductivity data for 0 .25M, 0 .325M and 0.325M-9 Fractions. 118 4.14 Hydraul ic conductivity data for all acid hydrolysed Fractions 119 4.15 Hydraul ic conductivity data for all H A Fractions 120 A . l Sedimentation photograph of R u n C l 138 A.2 The sedimentation plot for R u n C l 140 viii ACKNOWLEDGEMENTS I wish to thank my supervisor, D r . Joel Bert, for his patience, understanding and supervision throughout the project. Thanks are also due to D r . Bob Cushley of S . F . U . who has given the permission to use the Model E analytical ultracentrifuge, and to the faculty, staff and personnel of the Department of Chemical Engineering who have in one way or the other contributed to the completion of the program. Finally, financial assistance in the form of a Research Assistanceship from the Natura l Sciences and Engineering Research Council of Canada is gratefully acknowledged. IX CHAPTER 1. INTRODUCTION 1.1. HYALURONIC ACID Hyaluronic acid (synonym: hyaluronate) is a high molecular weight polysaccharide which is found in most if not all connective tissue. Its chemical structure consists of repeating disaccharide units of N-acetyl-D-glucosamine and D-glucuronic acid linked by a /3(l->3) glycosidic bond. These disaccharide units are linked together to form a long linear, unbranched polymer chain by /3(l->4) glycosidic bonds. Under physiological conditions, the carboxylate group is fully ionized. Therefore, the charge distribution is one negative charge per disaccharide unit. Hyaluronic acid is a member of a group of similar polysaccharides known as glycosaminoglycans (GAGs) which all contain hexosamines (amino sugars). The other polysaccharides are chondroitin 4-sulphate, chondroitin 6-sulphate, dermatan sulphate, keratan sulphate, heparan sulphate and heparin (see Figure 1.1). The concentration and size (chain length) of hyaluronic acid vary widely from tissue to tissue (Laurent, 1970; Laurent & Tengblad, 1980). For example, rooster comb contains 7.5 mg hyaluronic acid/g fresh wt (Laurant, 1970), while synovial fluid contains 1-3 m g / m L (Sunblad, 1965). H u m a n plasma has a very low content of = 0.3 Mg/mL (Laurent & Tengblad, 1980). Recent research has revealed that hyaluronic acid is synthesized in the cell membrane (Prehm, 1983, 1984). It is then polymerized at the membrane and the chain moves through a hole in the membrane into the extracellular space. Interestingly, hyaluronic acid is a valuable surgical aid in ophthalmic surgery (Miller et al. , 1977; Pape & Balazs, 1980). High molecular weight, sterile pyrogen-free solutions of sodium hyaluronic acid 1 Figure 1.1 Chemical structures of the dominant disaccharide units of various glycosaminoglycans. (Modified from Comper & Laurent , 1978) I N T R O D U C T I O N / 3 have been used as a vitreous substitute (Denlinger & Balazs, 1980). It also has a therapeutic effect in certain joint diseases (Asheim & Lindblad, 1976). The physicochemical properties of hyaluronic acid are summarized below. The reader is referred to some recent reviews (Laurent, 1987; Bert & Pearce, 1984; Comper and Laurent , 1978) for more details. 1.1.1. Conformation Detailed physicochemical studies on dilute hyaluronic acid solutions have shown that the molecule forms an extended random coil (Laurent & Gergely, 1955; Laurent et al. , 1960; Cleland & Wang, 1970; Cleland, 1977). However, some degree of local conformation ordering could exist. One of the hydroxyl groups of the glucuronic acid residue is involved in a H-bond to the oxygen atom of the N-acetyl group of the next following hexosamine residue (Cleland, 1979). The presence of inter-residue H-bonding provides an extra degree of stiffness in the conformation — the stiffened random-coil configuration (Morris et al. , 1980). Recently, Cleland (1984) has revealed that hyaluronic acid molecules in solution can take the form of a hydrodynamic worm-like chain. The conformation of hyaluronic acid in the solid state has been studied extensively by X - r a y crystallography (for review, see Hadler & Napier, 1977). The packing of hyaluronic acid into films and fibres is influenced by the nature of the counterion, p H and degree of hydration. In all the oriented films and fibres, the configuration of hyaluronic acid is a stable left-handed helix. Most commonly, the helix is found to be threefold, i.e. three disaccharide units per complete helical turn. I N T R O D U C T I O N / 4 The molecule also occupies a very large hydrodynamic volume (Figure 1.2). 5 In the case of the hyaluronic acid of synovial fluid (M.W. = 8 X 1 0 , where M . W . , as throughout this work unless otherwise stated, is the weight average molecular weight) the hydrodynamic volume it occupies is 1,000 times larger than the space occupied by the unhydrated polysaccharide chain (Ogston & Stanier, 1951). In such a hyaluronic acid domain, solvent water is the principal component. Water is held to the hyaluronic acid by H-bonds and by polar bonds to the O H groups and charged carbonyl groups on the polysaccharide chains. T h e anionic charges on the backbone of the polysaccharide repel one another to expand the coil. O n the other hand, the retention of water by hyaluronic acid is found to Figure 1.2 Schematic demonstration of the volume occupied by a hyaluronic acid molecule. For comparison, some other macromolecules are shown. (Modified from Comper & Laurent , 1978) I N T R O D U C T I O N / 5 have increased the stability of a system of hyaluronic acid in a collagen gel (Fessler, 1957, 1960a). The retention of water provides resistance both to compression and to the bulk flow of water through the hyaluronic acid solution. Hyaluronic acid behaves as a typical polyelectrolyte in that its conformation changes with the changes both in the ionic concentration of its environment and the type of counterion. A s the ionic strength of the hyaluronic acid solution is lowered, less counterions are available to screen the negative charges on the polysaccharide backbone from each other. Therefore, the negative charges on the hyaluronic acid chain have a greater tendency to repel one another. The polyion then forms an extended random coil. The process is fully reversible. The changes in conformation can be monitored by observing the changes in the intrinsic viscosity of, for example, solutions of sodium hyaluronic acid (Cleland & Wang , 1970; Cleland, 1984). It is believed that the phenomenon has some biological implications (Katchalsky, 1954; Comper & Laurent, 1978). Changes in the ionic environment of the hyaluronic acid molecules can be converted to mechanical energy on expansion or contraction of the polyion — a chemical-mechanical transduction. Also, one can expect that changes in p H will have a large effect on the rheological properties of hyaluronic acid solutions. Changes in p H alter the ionization of the glucuronate residue. When hyaluronic acid solution is treated with an alkali, the viscosity (Swann, 1970) and radius of gyration are lowered, but the molecular weight is not (Mathews & Decker, 1977). This finding demonstrates that hyaluronic acid has a higher flexibility in alkaline p H (less extended form) than in neutral p H (more extended form). The decrease in viscosity is a result of the ionization of hydroxyl groups involved in I N T R O D U C T I O N / 6 H-bonding (Morris et al., 1980). A t low concentrations and acidic p H , the viscosity is reduced, which is attributed to the molecular coil contraction resulting from the suppression of intramolecular electrostatic repulsion (Morris et al. , 1980). 1.1.2. Viscosi ty Hyaluronic acid solutions are very viscous even at low concentrations. This can be explained by the fact that hyaluronic acid has a large solution domain. A s mentioned above, the hydrodynamic volume of hyaluronic acid can be 1,000 times larger than the volume of unhydrated molecule. A t concentration in the order of 1 m g / m L , the molecules will start to entangle (Comper & Laurent, 1978). A t higher concentration, a continuous polymer network is expected to form. In fact, a solution of undegraded umbilical cord hyaluronic acid in isotonic saline can gel at a concentration of 2-5 m g / m L (Bert & Pearce, 1984). The evidence supporting the entanglement of hyaluronic acid molecules in solutions come from the viscosity and sedimentation studies on hyaluronic acid solutions (Comper & Laurent, 1978). A t concentrations below those at which a gel is formed, the non-Newtonian viscosity of hyaluronic acid is strongly concentration dependent ~ the viscosity increases sharply with concentration (Ogston & Stanier, 1953). A n explanation for the observation is that the hyaluronic acid molecules with very large hydrodynamic volumes entangle with each other. Sedimentation studies on hyaluronic acid solutions have shown that at low concentrations, hyaluronic acid molecules of different molecular weights sediment at different rates. However, at higher concentrations, (above 2 mg/mL), the hyaluronic acid molecules sediment at about the same slow rate (Laurent et al. , 1960). These I N T R O D U C T I O N / 7 findings indicate that at high concentration, the hyaluronic acid molecules form a continuous polysaccharide network and sediment as a porous plug through the ultracentrifuge cell, rather than as individual molecules. The viscosity of solutions of hyaluronic acid is dependent not only on the solution environment of the hyaluronic acid molecules, but also on their molecular weights. For hyaluronic acid in 0 . 2 M N a C l , the intrinsic viscosity [77] in m L / g hyaluronic acid is fitted to the Mark-Houwink equation: [77] = 0.0228M^'^''"^ where M is the molecular weight (Cleland & Wang, 1970). B y definition, the intrinsic viscosity [77] = j l ^ Q ( T } ~ v 0 ) / v 0 • c, where 77 and 770 are the viscosities of the polymer solution and the solvent, respectively, and c is the polymer concentration. In addition, hyaluronic acid solutions are viscoelastic (Myers et al . , 1966; Welsh et al . , 1980) which is attributed to molecular entanglement. A t low strain frequency, it shows elastic behavior, and the elasticity is directly proportional to concentration. Since the concentration of hyaluronic acid in synovial fluid is high (1-3 mg/mL) , it is believed that these rheological properties of hyaluronic acid m a y have an important role in the mechanical functioning of joints (Balazs, 1974). In fact, in joint diseases, the concentration and the molecular weight of hyaluronic acid in the synovial fluid are decreased, and the rheological properties are deteriorated (Schurz & Ribitch, 1987). Moreover, a viscometric study of high molecular weight hyaluronic acid has shown that the high molecular weight hyaluronic acid in the pericardial fluid could provide the heart tissue with resiliency and compliance when the tissue is subjected to stretching or compressive forces (Honda et al . , 1986). I N T R O D U C T I O N / 8 The surface rheological study of hyaluronic acid solutions has revealed that hyaluronic acid is a surface active polyanionic molecule that exists in solution as a random coil and concentrates at the interface or surface (Kerr & Warburton, 1980). The rheological property of hyaluronic acid in the bulk phase is very different from that in the surface phase. The viscosity of a very thin film of hyaluronic acid at the surface is very much higher than the bulk viscosity (Kerr & Warburton, 1985). This surface rheological property of hyaluronic acid is important in the functioning of joints. In normal joints, certain proteins are excluded from the synovial cavity, but in rheumatoid arthritis, they are found in the synovial fluid (Levick, 1983). Hyaluronic acid in the synovial fluid has been postulated to form a barrier to exclude these proteins. Levick reports that to function in this manner, it is necessary to have a hyaluronic acid concentration of 13 mg/raL, which is not present in the joint. However, the results of K e r r & Warburton's (1985) study show that high enough concentrations (as obvious from the high surface viscosity) could be present at the articular cartilage/synovial fluid and synovium/synovial fluid interfaces (see Figure 1.3) to exclude the proteins. Temperature also has an effect on the viscosity of hyaluronic acid solutions. The study by Cleland (1979) shows that in non-alkaline solution, the intrinsic viscosity [77] decreases with increasing temperature. However, in very alkaline solution, [77] increases with increasing temperature. The author interprets that the hyaluronic acid solution can be considered to be an equilibrium mixture of a high [77] form existing both in acidic and in neutral solutions and a low [77] form existing in very alkaline solution. The shift from the low [77] form to the high [77] form is endothermic. Therefore, when the temperature is increased, I N T R O D U C T I O N / 9 synovial fluid j articular cartilage . synoviunr bone bone! Figure 1.3 Diagramatic representation of a synovial joint. the low [77] form is shifted to the high [77] form, and the [77] of the solution is increased. 1.1.3. Co l lo id Osmotic Pressure The osmotic behavior of solutions of hyaluronic acid is very non-ideal — the osmotic pressure rises rapidly with the concentration of the polysaccharide. A s shown in Figure 1.4, the osmotic pressure of hyaluronic acid solutions is considerably higher than that of serum albumin (M.W. 67,500) with a molecular weight 50-100 times lower than that of hyaluronic acid. The osmotic pressure 7T of a non-ideal polymer is described by the virial expansion it/RT = c/M^ + A2c2 + A 3 c 3 + [Ll] I N T R O D U C T I O N / 10 Figure 1.4 Osmotic pressure of hyaluronic acid versus concentration. For comparison, the osmotic pressure curve for albumin is shown. (Modified from Comper & Laurent, 1978) where R is the universal gas constant, T is the absolute temperature, c is the concentration of the polymer in g /mL, its number average molecular weight, and A 2 , A3 are the virial coefficients. Since is generally large, at physiological concentration, the term c / M n has a relatively small value. Therefore the dominating term is A 2 c 2 . Over the years, a large amount of work has been done to determine the second virial coefficient of hyaluronic acid in various conditions (e.g. Cleland, 1984; Wik, 1979; Cleland & Wang, 1970; Laurent & Ogston, 1963). Since the osmotic behavior of hyaluronic acid is extremely non-ideal, some workers believe this special property of hyaluronic acid, along I N T R O D U C T I O N / 11 with other G A G s , can contribute to the homeostasis in vivo (Landis & Pappenheimer, 1963, Comper & Laurent, 1978). In some conditions when there is a fluid loss from the GAG-containing tissue, a large osmotic restoring force is then developed in the tissue, due to the non-ideal behavior of the polysaccharide. O n the other hand, a dilution in the tissue will cause a relatively small decrease in the osmotic pressure. 1.1.4. Mass Transport through Hyaluronic Acid Solutions Since hyaluronic acid is a major constituent of the intercellular matrix of connective tissues, a lot of studies have been performed to determine its role in regulating transport in tissue. The effects of a hyaluronic acid matrix on the transport of water and globular particles are discussed below. In the case of water transport, D a y (1950, 1952) has measured the permeability of mouse fascia before and after the addition of hyaluronidase, an enzyme which degrades hyaluronic acid. The permeability increases 10 to 20 times after the enzyme is added. Us ing the same enzymatic degradation method, Hedbys (1963) obtains a similar finding for corneal stroma. These experiments show that hyaluronic acid in tissue resists the flow of water and immobilizes it. Also, from a sedimentation study (Laurent et al . , 1960), which is discussed earlier, hyaluronic acid molecules at high concentration form a polymer network and resist the flow of solvent through it. Therefore, the sedimentation rate of hyaluronic acid (or the rate of upward movement of solvent) is slower than that of other macromolecules of the same concentration. I N T R O D U C T I O N / 12 The effect of hyaluronic acid on the transport of globular particles can be estimated by the sedimentation method. Johnston (1955) has shown that hyaluronic acid decreases the sedimentation rate of albumin. Laurent and co-workers (Laurent et al. , 1963; Laurent and Persson, 1964; Laurent & Pietruskiewicz, 1961) have done a series of sedimentation studies of proteins and colloidal particles through hyaluronic acid solutions. T h e y have found that the presence of hyaluronic acid decreases the sedimentation rate of the solute particles. In addition, the rate of transport of particles decreases with increases in the concentration of hyaluronic acid and increases in the sizes of the particles. Their data are shown to follow the empirical relationship: i s/s0 = Ae'Bc [1.2] where s and s 0 are the sedimentation coefficients of the macromolecular solute in hyaluronic acid of concentration c and in water or buffer solution, respectively. A is a constant exceeding 1 and usually less than 2, depending on the solute, and B is a constant proportional to the hydrodynamic radius of the solute particle. Laurent et al. (1963) describe the slowing down of particle movement in hyaluronic acid as a molecular sieving mechanism. The sieving process is like a filtration of particles by the macromolecular meshwork formed by hyaluronic acid. The sedimentation behavior of lysozyme in sodium hyaluronic acid has been studied by Wedlock et al . (1981). The authors describe the sedimentation behavior of lysozyme in hyaluronic acid as independent sedimentation of a slightly associated protein through a three-dimensional network acting partially as a macromolecular sieve. The sieving effect is evident from the decrease of sedimentation rate with the increase in hyaluronic acid concentration. The retarding effect of hyaluronic acid on the particles can also be explained by the I N T R O D U C T I O N / 13 steric exclusion mechanism (Comper & Laurent , 1978). Steric exclusion refers to the fact that two or more particles cannot occupy the same space at the same time. Figure 1.5 is an illustration of the phenomenon. A s depicted in C of Figure 1.5, the available space for a spherical particle to move in a random network of fibres is greatly reduced. One can then postulate that hyaluronic acid may have a role in regulating the distribution of plasma proteins in the tissue space. 1.2. THE COMPONENTS OF THE INTERSTITIUM In order to understand the flow of water in the interstitium, which is the connective tissue space outside the vascular and lymphatic systems and the cells, the major components in the interstitium and their properties are studied first. The three major structural components are hyaluronic acid, proteoglycan and collagen. F o r recent reviews of the structure and transport of the interstitium, see Laurent (1987) and Bert & Pearce (1984). Hyaluronic acid has been discussed in the previous section. In this section, the structure and properties of proteoglycans and collagen fibres are mentioned briefly. Then the contribution of the three major components to the hydraulic flow resistance in the interstitium is discussed. 1.2.1. P r o t e o g l y c a n Like hyaluronic acid, proteoglycans are found throughout the tissues of the body. The size and composition of the proteoglycans vary widely from tissue to I N T R O D U C T I O N / 14 Figure 1.5 Illustration of the steric exclusion mechanism. A: steric exclusion of sphere b from the domain of sphere a. Centre of b cannot come closer to centre of a than 2r and therefore is excluded from a volume (dotted) that is 8 times larger than the volume of each sphere. B: steric exclusion of a sphere with radius rr from the domain of a rod with the radius rr and length /. Excluded volume is equal to a cylinder with the radius rs + rr and the length I. E n d effects have been disregarded. C: available space for a sphere in a random network of rods is equal to the volume (dotted) in which the centre of the sphere can move freely. (Modified from Comper & Laurent , 1978) I N T R O D U C T I O N / 15 tissue. Usual ly , they are distinguished by the number, type and chain length of their component glycosaminoglycans, and the length of the protein core. Due to the diversity of the group of proteoglycans, the reader is referred to some reviews on the chemical properties and structure of the macromolecules (Poole, 1986; Heinegard & Paulsson, 1984). Only some of their typical structure and properties are discussed below. Light scattering and viscosity studies on bovine nasal cartilage proteoglycan have shown that the molecule takes the conformation of a bottle brush (Figure 1.6). The molecule has a protein core to which a large number of chondroitin sulfate chains (GAGs) are attached. M a n y proteoglycans keratin sulphate rich binding region globular protein and protein core Figure 1.6 Structure of cartilage proteoglycan monomer. I N T R O D U C T I O N / 16 form large aggregates with hyaluronic acid (e.g. Hardingham & Muir , 1972; Hascal l & Heinegard, 1974a, 1974b). Figure 1.7 is an illustration of such an aggregate. There is a binding site for hyaluronic acid on the globular protein on the proteoglycan. The aggregates may contain over 100 proteoglycan monomers, 5 each with M . W . 2 .5X10 . Studies of the 1:1 complexes formed by small hyaluronic acid oligosaccharides with proteoglycan monomers have revealed that the shortest hyaluronic acid chain which forms a strong complex is the decasaccharide H A , 0 , where the subscript 10 refers to 10 monosaccharides (Cleland, 1979; Nieduszynski et al. , 1980). A recent viscometric study by Cleland (1983) has shown that the minimum chain length of hyaluronic acid for the Figure 1.7 Schematic model of the structure of cartilage proteoglycan aggregates. I N T R O D U C T I O N / 17 , formation of proteoglycan-hyaluronic acid (2:1) dimer is H A 2 0 . Proteoglycans occupy a large hydrodynamic volume in solution. For example, the proteoglycan of bovine nasal cartilage has a mean hydrodynamic volume of 140 m L / g (Bert & Pearce, 1984). The hydrodynamic volume it occupies is much less than that of hyaluronic acid of equivalent molecular weight (Figure 1.2). The reason is that the attachment of a large number of G A G chains to the core protein limits the volume occupied by a given weight of the molecule. In the native tissue, the large proteoglycan aggregates influence the transport of molecules passing through the extracellular matrix either by ion-exchange or by steric exclusion properties. Their branched structures are capable of localizing a large amount of charges. Comper & Laurent (1978) describes that the branched structure of charge-packing of proteoglycans is analogous to the branched structures of energy-storage of glycogen and starch. 1.2.2. C o l l a g e n The third major component of the interstitium is collagen. The basic structural unit of a collagen fibre is the collagen molecule, which is also known as tropocollagen. A collagen molecule is a protein of molecular weight 285,000. It is composed of three peptidic a-chains coiled together to form a triple helix -giving a ropelike configuration. The cylindrical structure of the collagen molecule is stabilized by cross-linking of the three a-chains (Light & Bailey, 1980). The collagen molecules are packed together, molecules parallel to each other, to form the collagen fibre. The side-to-side interaction of the collagen molecules is believed to be stabilized by electrostatic and hydrophobic bonds between amino acids on I N T R O D U C T I O N / 18 the outside of the molecules (Bert & Pearce, 1984). The collagen fibres are then cross-linked together to give a higher structure. The diameter of the collagen fibre may be from one to several hundred microns (Schubert & Hamerman, 1968). It is found that the organization of the fibres is loose enough to permit the passage of molecules as large as plasma proteins between the individual fibrils (Meyer et al . , 1977). The main function of collagen fibres are that they resist changes in tissue configuration and volume, exclude proteins and immoblize the G A G s (Aukland & Nicolaysen, 1981). 1.2.3. The Hydraulic Resistance of Flow in the Interstitium The connective tissues in the interstitium consist of interpenetrating networks of polysaccharides and collagen fibres. The collagen fibres are relatively stiff and give a solid structure to the compartments. The interfibrillar space is filled with solvent trapped inside the hyaluronic acid and proteoglycan complexes. In such a structure with interpenetrating molecules, a large amount of work has been done to determine which component(s) contribute to the hydrodynamic flow resistance. It is often suggested that G A G chains are responsible for the high hydraulic resistance in the interstitium (e.g. Aukland & Nicolayen, 1981). However, recent reviews by Ja in (1987) and Levick (1987) have shown that in a general tissue, all three main components of the interstitium are responsible for the high hydraulic resistance. A s mentioned above, hyaluronic acid has the potential to offer a high resistance to water flow by forming a molecular network, by immobilizing the water, and by its steric exclusion properties. The contribution of collagen to hydraulic resistance is mainly from its steric exclusion I N T R O D U C T I O N / 19 properties. Because of the presence of collagen fibres, the space available for the movement of hyaluronic acid is reduced. Therefore the concentration of hyaluronic acid in the interfibrillar space is increased. Then the flow conductivity is further reduced. In the case of proteoglycans, their contribution to the flow resistance is from the retention of water and their steric exclusion properties. 1.3. OBJECTIVE OF THE THESIS Over the years, there has been great interest in the transport and distribution of water, ions, p lasma proteins, etc. in the interstitium. Since hyaluronic acid is a major component in the interstitial space, it is believed that hyaluronic acid plays an important role in the regulation of transport of solvent and solute (e.g. Levick, 1987). Also, the non-ideal osmotic behavior of hyaluronic acid may contribute to the homeostasis in animals (Comper & Laurent, 1978). O n the other hand, the concentration and distribution of the polysaccharide within connective tissues are not constant. In bovine vitreous, hyaluronic acid has its highest concentration in the cortical tissue layer of the vitreous, and concentration gradually decreases toward the center (Balazs, 1965). Also, the content of glycosaminoglycans in the intervertebral disk is increasing toward the center of the disk (Szirmai, 1970). In addition, hyaluronic acid is not fixed in tissue (Aukland & Nicolaysen, 1981). Over a few days, a large amount of hyaluronic acid will diffuse out of umbilical cord slices incubated in saline (Meyer & Silberberg, 1974). Since hyaluronic acid is mobile in tissue, compaction is very likely to occur in membrane transport processes. O n the other hand, the molecular weight of hyaluronic acid is different in different tissues (Section 1.1). I N T R O D U C T I O N / 20 Therefore a study of the relationship between hydraulic flow conductivity and concentration of hyaluronic acid, with different molecular weights, will give a better picture on the role of hyaluronic acid in the real tissue. In Chapter 2 of the present work, the different methods of estimating hydraulic flow conductivity of hyaluronic acid are discussed. The sedimentation theory of particles sedimenting in the ultracentrifuge is then presented. The chapter is then concluded with a brief review of the ion-exchange theory in ion-exchange chromatography. Chapter 3 discusses in detail the experimental procedures and the techniques used in obtaining the data. The results are then discussed in Chapter 4. The summary and conclusions are presented in Chapter 5. CHAPTER 2. THEORETICAL BACKGROUND 2.1. INTRODUCTION A s discussed in Chapter 1, hyaluronic acid plays an important role in the mass exchange in the interstitium. Therefore, many studies have been performed to estimate the contribution of hyaluronic acid to the- hydrodynamic resistance in the tissue (e.g. Jackson & James, 1982; Ethier , 1986). The hydrodynamic resistance has been estimated by three methods: enzyme degradation, filtration-chamber and sedimentation. A l l three methods are in vitro studies. This is because of the fact that hyaluronic acid is not the only component in the extracellular matrix. It is mixed or entangled with other components. In vivo studies of the hydraulic resistance of the whole tissue can be made. However, it will be extremely difficult to estimate the contribution of hyaluronic acid alone to the hydrodynamic resistance by in vivo experiments because hyaluronic acid cannot be singled out. The three methods, as well as their problems, are discussed in this chapter. The best method amongst the three, which is the sedimentation velocity method, is taken as the approach in the present study. A discussion of the theory of macromolecular particles sedimenting in the ultracentrifuge will then follow. In this study, hyaluronic acid samples of different molecular weights are investigated. The hyaluronic acid is fractionated by the ion-exchange chromatography. The theory of this chromatographic technique is also briefly discussed. 21 T H E O R E T I C A L B A C K G R O U N D / 22 2.2. ENZYME DEGRADATION METHOD This method makes use of the fact that hyaluronic acid is degradable by the enzyme hyaluronidase. The permeability of some selected tissues is measured before and after the administration of the enzyme. The selected tissue membrane is fixed at one end of a glass tube. The glass tube is then filled with saline, and the flow rate of saline through the membrane is measured. The membrane is then perfused with hyaluronidase solution. Then the flow rate of saline through the membrane is again measured. When the two flow rates are compared and if there are no other changes in the tissue, the contribution of hyaluronic acid to the resistance to flow can then be quantified. D a y (1950, 1952) measured the flow under a pressure head of saline (0.85%(w/v) NaCl) across a membrane of mouse fascia. He observed that the rate of flow of saline through the membrane increased ten to twenty times after the addition of testicular hyaluronidase. Hedbys and Mish ima (1962, 1963) have done a similar study on the flow of water through corneal stroma. They also observed an increase of up to 16 times in the permeability after the addition of the hyaluronic acid-degrading enzyme. These two experiments show that hyaluronic acid plays an important role in regulating the flow of liquid through the tissue. If the concentration of hyaluronic acid in the selected tissue is known, and there is no changes in the tissues, the resistance of flow of hyaluronic acid at the particular concentration in the tissue can be quantified by this method. However, there are several potential drawbacks in this approach. A s T H E O R E T I C A L B A C K G R O U N D / 23 described in Chapter 1, many proteoglycans bind to hyaluronic acid and form a superstructure in the tissue. Jackson and James (1982) have pointed out that the addition of hyaluronidase will not only hydrolyze the hyaluronic acid, but will also break down the glycosaminoglycan superstructure, and therefore the protein network. Also, Knepper et al. (1984) have shown that despite the low concentration used and the purification steps performed, hyaluronidase enzyme preparations still have detectable protease activity. In addition, as mentioned in Chapter 1, not all hyaluronic acid is fixed in tissue. Since hyaluronic acid diffuses out of the umbilical cord slices incubated in saline (Meyer & Siberberg, 1974), it is possible that some tissue hyaluronic acid is washed-out into the solution during the conductivity test. O n the other hand, the hydraulic conductivity (K') is dependent on the water content (Z). A power law equation between K' and Z has been developed by Bert and Fat t (1970): K' = aZb [2.1] where a and 6 are constants. In view of this, Ja in (1987) explains that during in vitro conductivity experiments, the water content may v a r y as a result of the applied pressure, and therefore may lead to erroneous conductivity measurements. In fact, conductivity has been shown to be dependent on the applied pressure for many tissues (Levick, 1987). Moreover, as pointed out by Levick (1987), the interpretation of tissue conductivity is complicated by the fact that connective tissues commonly have a gradient of fibre concentration (Comper & Laurent, 1978; U r b a n & Maroudas, 1980). Since the relation between hydraulic conductivity and fibre concentration is not linear (Levick 1987), the measured value in conductivity across the tissue is just a weighted average of the whole tissue (Mow et al . , 1984). Due to the number of possible problems in the T H E O R E T I C A L B A C K G R O U N D / 24 enzyme degradation method, it is therefore very difficult to make accurate estimates of the contribution of hyaluronic acid resistance in the whole tissue using this method. 2.3. FILTRATION-CHAMBER METHOD In this approach, pure hyaluronic acid solutions, instead of the whole tissue, are used. The hyaluronic acid solution is held in place between two backing filters in a chamber. The solvent is forced through the hyaluronic acid solution by a pressure head, and the pressure applied and the flow rate are measured. In conjunction with known hyaluronic acid concentration in tissue, this method presumably will permit the calculation of the resistance contributed by hyaluronic acid in the tissue. Some workers (Ogston & Sherman, 1961; C a r r & Hadler, 1980; Adamson & C u r r y , 1982; Jackson & James, 1982) have studied the hydraulic conductivity of hyaluronic acid with this method. However, their results differ considerably, partly because the flow of buffer is time-dependent (Levick, 1987). This is evidence from the work of Adamson & C u r r y (1982), who have reported that at constant pressure, the flow falls continuously with time. Another reason for the variability of the results is that the buffers the workers used are different. The buffers used by the workers are shown in Table 2.1. A s mentioned in Chapter 1, the p H of the solution and the ionic environment of the hyaluronic acid have a large effect on the shape and the hydrodynamic volume of the hyaluronic acid molecules. Therefore, the results in the perfusion experiments are affected by the T H E O R E T I C A L B A C K G R O U N D / 25 buffer used. There are other potential problems with the filtration-chamber method. Thi s method over-estimates the conductivity initially because of the buffer and hyaluronic acid matrix moving together, upstream from the restraining filter membrane (Levick, 1987). In addition, Parker & Winlove (1984) have shown that concentration polarization (or compaction) can develop upstream from the filter in the solution chamber. In their experiment, the concentration of hyaluronic acid was uniform along most of the tubular chamber, but rose very steeply at the region close to the restraining filter. Us ing a computational method, Ethier (1986) showed that the pressure drop across the hyaluronic acid solution with concentration polarization was greater than that without concentration polarization; and therefore, filtration-chamber experiments would tend to underestimate the flow conductivity. Also, compaction reduces the effective porosity in the hyaluronic acid matrix, and therefore the amount of hydration. Since conductivity is very sensitive to hydration (Bert, 1969) and is directly related to a power function of T a b l e 2.1 Buffer used bj' different workers Buffer (M) workers p H N a C l N a 2 H P O , K H 2 P O « 1. Ogston & Sherman (1961) 0.2 0.0077 0.0023 7.3 2. C a r r & Hadler (1980) 0.1 not shown 7.0 3. Adamson & C u r r y (1982) 0.2 not shown 7.25 4. Jackson & James (1982) 0. 0.0077 0.0023 7.25 T H E O R E T I C A L B A C K G R O U N D / 26 water content (Bert & Fatt, 1970), its measurement is affected by the presence of compaction. Another disadvantage of the filtration-chamber method, as pointed out by Ethier (1986), is that in the perfusion experiments, the buffer is forced through the hyaluronic acid solution matrix, and the total pressure drop across the whole matrix is measured. Because of the presence of flow compaction, the pressure gradient along' the direction of flow is non-uniform; and therefore the conductivity data produced by the total pressure drop is just an average measurement for the whole solution matrix. F inal ly , the flow of buffer is affected by the interaction of the hyaluronic acid with the filter (Parker & Winlove, 1984). The extent and method of interaction are hard to determine. 2.4. SEDIMENTATION METHOD In this method, hyaluronic acid solution is contained in an ultracentrifuge cell. The cell is then centrifuged at very high speed (> 50,000 rpm) and the sedimentation coefficient of hyaluronic acid is determined. The hydraulic conductivity is then calculated from the sedimentation coefficient. A s mentioned in Chapter 1, Laurent et al. (1960) concluded from their sedimentation velocity studies of hyaluronic acid that at high concentration, the hyaluronic acid molecules formed a 3-dimensional polysaccharide network, and the whole network, rather than the individual molecules, sedimented in the ultracentrifuge cell. Fessler & Ogston (1951) pointed out that a system of particles sedimenting together through a stationary buffer was analogous to the passage of the buffer through a porous plug. F r o m this point of view, Ethier (1983) has reasoned that the effective centrifugal driving force on the particles per unit volume is equivalent to T H E O R E T I C A L B A C K G R O U N D / 27 the pressure gradient created by the flow of solvent through the particles (Figure 2.1). Consider the sedimentation of a single kind of suspended particles in a uniform solvent. The mass m7 of each hydrodynamic particle is n mh = (1 + 6, ) M / J V A [2.2] where M is the molecular weight of unsolvated macromolecules, N is the Avogadro's number and 5 ^ is the solvation factor, which is the number of grams of solvent associated with 1 gram of the unsolvated macromolecule. The factor 6 \ in the equation accounts for the fact that solvent is bound to macromolecules like hyaluronic acid. In general, 5 : is unknown or very difficult to determine. However, we will see later that in the derivation of the net centrifugal force on the particle, 8y is cancelled out. The total volume of the solvated particle is solvent sedimenting macromolecules Figure 2.1 A system of macromolecules sedimenting in an ultracentrifuge. T H E O R E T I C A L B A C K G R O U N D / 28 vh = (v2 + 6 , u 1 ) M / i V A [2.3] where u 2 is the partial specific volume of the polymer, and v ^ is the specific volume of the solvent. In the ultracentrifuge, the centrifugal force per particle is m^oi2r, where a) and r are the angular velocity and the radial position, respectively. Opposing this force is a buoyant force pxVjG)2r exerted by the solvent with density p , on the particle. The net force per particle is then F = (mh - p y v h ) u 2 r [2.4] Substituting Equation [2.2] and [2.3] into [2.4], F = (M/NA)a>2r(l + 5, - p , u 2 - p ^ u , ) [2.5] F o r dilute solution, the solvent density, p y, is the reciprocal of the solvent specific volume, u , . Therefore Equation [2.5] becomes F = (M/NA)o2r( 1 - D 2 P 1 ) [2.6] The effective centrifugal force per unit volume is F = F X no. of particles per volume = (M/N )cj2r( 1 - v 2 p , ) XJV / v o l . A p = c 2 c j 2 r ( 1 - D 2 p , ) [2.7] because the product of M/N^ and the number of particles per volume is just the polymer concentration c 2 . B y definition, the sedimentation coefficient, s, is s = v2/a)2r [2.8] where v 2 is the sedimentation velocity of the polymer. Then , the centrifugal force per unit volume can be written as c2v2{\ - v 2 P \ ) / s • The pressure gradient, from Darcy's law, can be expressed as: dP/dy = -r\vjK [2.9] T H E O R E T I C A L B A C K G R O U N D / 29 where 77 is the solvent viscosity, v , is the velocity of the solvent relative to the sedimenting polymer, and K is the specific hydraulic conductivity. Making the dilute solution approximation v 2 = v , , K' = K/rj = S / C 2 ( 1 - D 2 p , ) [2.10] where K' is the hydraulic conductivity (Preston et al., 1965; Mijnlieff & Jaspers, 1971; Ethier, 1983). Therefore, if the sedimentation coefficient of a hyaluronic acid solution is measured, then, along with other known physical parameters, the hydraulic conductivity can be obtained. Recently, an in-depth discussion of the sedimentation method has been given by Ethier (1986). He has pointed out that there is an advantage of the sedimentation method which is not present in the filtration-chamber studies. A s long as the solvent/solution boundary is not near the centrifuge cell bottom, the sedimentation velocity, and therefore the conductivity, depends only on the local hyaluronic acid concentration at the boundary. Therefore, the conductivity obtained by the sedimentation method is related to the polysaccharide concentration at the boundary. This is different from the filtration-chamber method in which the conductivity measured is an average value for the entire layer of solution. However, as mentioned by Ethier (1986), there are potential problems in the sedimentation method. The wall frictional effects on the sedimenting hyaluronic acid m a y lower the sedimentation velocity, and the tendency of the hyaluronic acid at the boundary to swell may lead to erroneous results. Ethier shows that the frictional force on the hyaluronic acid due to the presence of the wall is insignificant. In fact, in the ultracentrifuge cell, the acceleration force is T H E O R E T I C A L B A C K G R O U N D / 30 radial, and therefore sedimenting molecules will move along radii. Therefore, the sector-shape design of the ultracentrifuge cell (Figure 2.2) will reduce the frictional wall effect to a min imum. Also, the solvent/solution boundary is visualized by the Schlieren optical system as a Schlieren peak (Figure 2.3). The swelling of the hyaluronic acid at the boundary will result in a broadening of the Schlieren peak. This swelling problem can be minimized by establishing a "sharp peak" criterion (Ethier, 1986). In calculating the conductivity, only the sedimentation data which show a sharp Schlieren peak are used. Therefore, the error in the conductivity is kept to a min imum. In fact, the study by Ethier shows that conductivity data calculated, following this criterion, from the past sedimentation experiments show little scatter — implying that the data are true conductivities of the hyaluronic acid matrix. Base on the above discussion, it is clear that sedimentation method is the best among the three. Therefore, in the present investigation, it is adopted as the approach in studying the conductivity of hyaluronic acid solutions. Figure 2.2 Sector-shaped cell used in all analytical ultracentrifuge. T H E O R E T I C A L B A C K G R O U N D / 31 Figure 2.3 (a) The concentration profile of a sedimentation run. (b) A Schlieren trace of the cell along the radial direction. The Schlieren peak represents the boundary position. (Modified from M c C a l l & Potter, 1973) T H E O R E T I C A L B A C K G R O U N D / 32 2.5. SEDIMENTATION THEORY 2.5.1. The Analytical Ultracentrifuge The analytical ultracentrifuge is a device capable of spinning a sample of solution at up to 70,000 rpm. Figure 2.4 is a schematic diagram of the instrument. The sample solution is contained in an ultracentrifuge cell as shown in Figure 2.5. The cell is then put in an a luminum or titanium rotor driven by an electric motor. The ultracentrifugal force generated causes the macromolecules in the solution to sediment outward, i.e. towards the bottom of the cell. A t C a m e r a F i l m holder M o t o r lens I Rotor lens Armored chamber C o o l i n e Temperature control V a c u u m pump Light source Figure 2.4 Schematic diagram of an analytical ultracentrifuge. (Modified from Cantor & Schimmel, 1980) T H E O R E T I C A L B A C K G R O U N D / 33 Cell Screw ring (^^^) Screw-ring gasket K^Cj5 |^ Upper window holder (^^^) Window gasket Window liner e Window (^^^) Centerpiece gasket Aluminum centcrpeice Centerpiece gasket ^ ^ ^ ^ Window Window line Window gasket Lower window holder Cell housing Housing-plug gasket Housing plug Centerpiece Single-sector centerpiece Double-sector centerpiece Figure 2.5 The analytical ultracentrifuge cell. (Modified from the Instruction M a n u a l , Model E Analyt ical Ultracentrifuge, Beckman) T H E O R E T I C A L B A C K G R O U N D / 34 typical rotor speeds, the friction between the rotor and air will generate an enormous amount of heat. Therefore, the rotor chamber is brought to a high vacuum before spinning is started. The temperature of the sample is regulated precisely by an automatic temperature control unit to avoid convective mixing. The analytical ultracentrifuge has an optical system which sends. U V light through the sample parallel to the axis of rotation. The three commonly used optical systems are absorbance, Raleigh interference and Schlieren. In a typical high speed sedimentation run of a single macrospecies, the concentration distribution along the radial direction is shown in Figure 2.3(a). The Schlieren optical system, for example, detects the variation of the refractive index gradient {dn/dr) with radial distance r. The variation is then recorded as a Schlieren peak (Figure 2.3(b)) on a photographic film. The design of the sample cell for the analytical ultracentrifuge is very critical. The cell has to be sector-shaped when viewed parallel to the axis of rotation (Figure 2.2). During a centrifugal run , the molecules will sediment along the radii because the acceleration force generated is in the radial direction. Only the use of the sector-shaped cell will not result in the stirring of the sample. The mathematical development of the ultracentrifugal theory has been presented in standard texts (e.g. Wil l iams, 1963; Fujita, 1975; Cantor & Schimmel, 1980). Therefore, only a simplified development of the theory, based on the texts, is given below. T H E O R E T I C A L B A C K G R O U N D / 35 2.5.2. Transport in the Ultracentrifugal Cell Figure 2.6 is an expanded view of a sector-shaped ultracentrifuge cell and its position relative to the axis of rotation in the ultracentrifuge. The coordinate r defines the radial distance from the axis of rotation. Before the rate of change of concentration of a macromolecular species in the volume bounded by surfaces at radii r and r+dr is determined, the rate of solute mass transport across the surface at radius r is first studied. Consider a simple system with two components, solvent denoted by subscript (1) and solute by (2). The flux, J 2 , which is defined as the rate of solute mass transport across a surface of unit area, can be written as J2 = c 2 ( v 2 ) [2.11] r b Figure 2.6 Geometry of a sector-shaped cell. The radial distance is r, the position of the meniscus is r m ; the bottom of the cell is r^. The axis of rotation is at r = 0 . T H E O R E T I C A L B A C K G R O U N D / 36 where c 2 is the mass concentration of molecules at the surface, and v2 is the average velocity of the molecules. In the ultracentrifuge, the applied force causing flow at radial distance r is u 2 r per unit mass of molecules. It is then obvious that the flow velocity, like the sedimenting force, is dependent on the rotor speed and on the distance of the molecules from the centre of rotation. The sedimentation coefficient, s, is therefore defined as: s = v2/cj2r = (dr/dt)/u2r [2.8] If the concentration of solute molecules at r is c 2 , and if the solute molecules are all moving at velocity v2 = o 2 r s due to the applied centrifugal force, then the flux caused by the angular acceleration is described by: J2 = u>2rsc2 [2.12] If there is a concentration gradient at r, a driving force caused by diffusion will develop at r. The flux due to diffusion is given by Fick's law: J2 = -D(dc2/dr) [2.13] where D is the diffusion constant of the molecules. Combining Equations [2.12] and [2.13] gives an equation for the rate of mass transport of the molecules across a surface at radius r in the ultracentrifuge: J2 = io2rsc2 - D(dc2/dr) [2.14] Since J2 is the flux per unit area, the total rate of mass transport at the surface r is J2A, where A is the surface area. T h e n the total rate of change of solute mass in the volume between surfaces at radii r and r+dr is given by dm2/dt = J2A{r) - J2A(r+dr) [2.15] The volume between the two surfaces is the area of the sector times the height of the sector, which is (f>rdrXa. The rate of change of concentration, which is the rate of change of mass divided by the volume between the two surfaces, is T H E O R E T I C A L B A C K G R O U N D / 37 dc2/bt = [J2A(r) - J2A(r+dr) ]/(<j>radr) = ( - l / 0 r o ) (dJ2A/dr) • = - ( l / r ) [ 3 ( r « / 2 ) / 3 r ] [2.16] Substituting Equation [2.14] into [2.16] gives: dc2/dt = (]/r)-^[rD(dc2/dr) - cj2r2sc2] [2.17] Equation [2.17] is called the L a m m equation for the ultracentrifuge. The equation gives a general description of the solute mass transport of a two component system in the ultracentrifuge. In general s and D are functions of solute concentration, c 2 (Fujita, 1975). Most of the observed s versus c 2 relationships for dilute macromolecular solutions can be represented empirically by either s = S 0 / ( 1 + K,c2) [2.18] or s = s 0 ( 1 - K2c2 ) [2.19] where s 0 is the value of s at infinite dilution, and and K2 are empirically derived positive constants. O n the other hand, for dilute solutions of macromolecules, the dependence of D on c 2 can be represented by an empirical relation: D = D 0 ( \ + & D c 2 ) [2.20] where D0 is the value of D at infinite dilution, and is an empirically derived constant. Because of the dependence of s and D on c 2 , Equation [2.17] is non-linear in c 2 , and the mathematical treatment of Equation [2.17] becomes very difficult. In fact, the L a m m equation has been solved analytically or numerically in certain limiting cases only (Cantor & Schimmel, 1980). T H E O R E T I C A L B A C K G R O U N D / 38 For the case of s=constant=s 0 and D=0, the solutions of Equation [2.17] from Fujita (1975) is c 2 (r,t) = 0 if r <r<r^ c2(r,t) = c 0 e 2 ( J S Q t if r,<r<r2 where = r e " 2 s ° r [2.22] and c 0 is the solute concentration at zero time throughout the chamber. In Equation [2.21], the compaction of solute at the bottom of the cell is ignored. Figure 2.7 is a schematic diagram of the results. A s shown in the diagram, the boundary is an infinitely sharp line because there is no diffusion. The position of the solvent-solution boundary, r*, is represented by Equation [2.22]. There is a plateau region in which the solute concentration is independent of r at any particular time. The second equation of [2.21] shows that the solute concentration in the plateau region decreases exponentially with time. The reason that the Figure 2.7 Solute concentration profile during ultracentrifugation of a typical solution of a homogeneous macromolecule, D = 0. (Modified from Cantor & Schimmel, 1980) T H E O R E T I C A L B A C K G R O U N D / 39 solute concentration in the plateau region can be maintained r-independent while it decreases exponentially with time is because both the cross-sectional area of the cell and the centrifugal acceleration increase with the radial distance. Consider a very thin layer of solution at r , >r^ at time ty (Figure 2.8). The molecules there are sedimenting at a velocity v (r, ) =co2 s r , . F o r another layer of solution at r 2 > r 1 , the molecules are sedimenting with velocity v ( r 2 ) =co 2 sr 2 > v ( r , ) . The two layers define a volume V , as shown in Figure 2.8. A t a latter time t2, the molecules originally at r 2 have sedimented farther than those molecules originally at r , , because they have been subjected to a stronger centrifugal acceleration at all times. O n the other hand, the volume between the two layers also increases because of the sector shape. Since the number of solute molecules in the volume is fixed, as a result, the concentration decreases with time. This phenomenon is called radial dilution. B y combining Equation [2.22] with the second equation of [2.21], an equation describing the radial dilution is obtained (Tanford, 1961): Figure 2.8 Demonstration of radial dilution. Solute in two equal volumes are followed from an early to a late time during sedimentation. C 2 A 0 [2.23] time t time t2 T H E O R E T I C A L B A C K G R O U N D / 40 Therefore, the solute concentration at the plateau region is inversely proportional to the square of the distance from the solvent-solution boundary to the axis of rotation; or the product of c 2 and r%2 remains constant during the course of the sedimentation experiment. A s mentioned above, the solute concentration at the plateau region at a particular time is independent of r. This can be shown by demonstrating that all volumes in the cell are subject to the same degree of radial dilution (Cantor & Schimmel, 1980). Suppose there is a volume V 2 = V 1 as shown in Figure 2.8. A t t,, the solute concentrations in the two volumes are the same, and V, = ( 0 / 2 T T ) [ 7 T r 2 2 - 7 T r , 2 ] a = U a / 2 ) [ r 2 2 - r , 2 ] [2.24] The velocity of the molecules at the surface of volume V , is j>(r , ) = drx/dt = u>2srr [2.25] The location of the surface, originally (at time t,) located at ^ ( f , ) , at time t2 is obtained by integrating Equation [2.25] to give r , ( * 2 ) = r , ( t , ) e ° } 2 s ° { t 2 ~ t ' ) [2.26] Similarly, for a surface originally located at r 2 ( t } ) , r 2 ( t 2 ) = r 2 U , ) e ° } 2 s Q { t 2 ~ t ' ) [2.27] Then, from Equation [2.24], the ratio of volume V , at time t2 to the volume at time tx is Vy(t2)/VyUi) = i r 2 ( t 2 ) 2 - r , ( t 2 ) 2 ] / [ r 2 ( t , ) 2 - r , ( t , ) 2 ] = e 2 " 2 s o U 2 - < i ) [ 2 2 8 ] This volume ratio is independent of the radial distance, r. Since T H E O R E T I C A L B A C K G R O U N D / 41 V 2 (t : ) = Vf (t! ), therefore, the volume ratio V 2 (1 2 ) / V 2 (ty ) is also 2 C J 2 S (t -t ) e 0 2 1 , or V 2 ( t 2 ) = V , (f 2 ). Because the number of solute molecules in each volume remains the same, and the ratio of volume increase is the same, the concentrations in all the volumes at a particular time are all equal. Therefore, a plateau region is maintained. In fact, if we let t i = 0 , and c 0 be the original solute concentration, then the concentration at a later time tz will 2CJ 2 s t be c 0 e 0 2 , which is identical to Equation [2.21]. Also, if ^ = 0 , Equation [2.26] is identical to Equation [2.22], and r , is the boundary position. The other limiting cases of the L a m m equation which have been solved deal with more realistic situations in which D is a positive constant and s varies with concentration. The derivations and the solutions obtained are very complex (Cantor & Schimmel, 1980). Thus , they are briefly mentioned below. H . F a x e n (in 1929) solved the equation by considering an infinite sector in which r =0, r^ = <», instead of the sector-shaped cell. The solutions he obtained can be used to predict the experimental results in the limiting case of early time (2scj 2 r<<1 ) and weak diffusion (2D/so) 2 r<< 1 ) . W . J . Archibald (in 1938) found an exact analytical solution for the L a m m equation with constant s and D. However, his solution, written in the form of an infinite series, is too complex to be used in evaluating sedimentation results. Fujita (in 1956) extended Faxen ' s solution to the case where D is constant, and s varies with concentration in accordance with Equation [2.19], i.e. s=s0 ( 1 ~K2c). Dishon et al. (in 1966-67) numerically solved the L a m m equation subjected to initial and boundary conditions for some actual experiments. In their computations, D is constant and s varies with concentration according to Equation [2.18] or [2.19]. T H E O R E T I C A L B A C K G R O U N D / 42 The results from the studies of the more realistic cases discussed above show that, as long as the sedimentation forces are strong (high centrifuge speed) compared to the driving force caused by diffusion, there is a boundary and a plateau region. Since there is a concentration gradient at the boundary, D is not 0, and the boundary is not infinitely sharp. The width of the boundary is dependent on D. Also, the solute concentration at the plateau region decreases with time. A s already mentioned, the solutions obtained for the L a m m equation by treating some limiting cases are very complex. The solutions are of limited value in determining the sedimentation coefficient from actual experiments. A more satisfactory treatment of the problem of measuring s is given by Goldberg (1953). This treatment does not require a general solution of the L a m m equation. The treatment is discussed in the next section. 2.5.3. Measuring the Sedimentation Coefficient The treatment of Goldberg is valid for any sedimentation experiment in which there is a plateau region. When the sedimentation forces are strong compared to the driving force of diffusion, there is a plateau region. In the plateau region, is independent of r. Thus , dc/dr and 3 2 c / 3 r 2 in the L a m m equation are zero. Then Equation [2.14] and [2.17] become J = oi2rs c [2.29] P P P dc /dt = -2c s C J 2 [2.30] P P P Now consider a fixed cross-sectional plane at r (Figure 2.9). The area of the plane is a<j>r^. Then the total number of moles of solute crossing the plane per unit time is a<f>r J . This amount of solute transport across the plane must T H E O R E T I C A L B A C K G R O U N D / 43 m Figure 2.9 Concentration profile of the sedimentation of a real solution. equal the decrease in the total amount of solute between the meniscus and the plane at r . Therefore, P ad>r J = — 5 7 ( J* ^ad>rcdr) p p at J [2.31] If is the position of the infinitely sharp boundary, as in the case of no diffusion, then at any time t, the total amount of solute between r* and r P with no diffusion (in which c along the radial distance = c ) is equal to the total amount of solute between r and r with the presence of diffusion: m P r r J* ^a<j>rc dr = j ^cuprcdr r* P r * m [2.32] T H E O R E T I C A L B A C K G R O U N D / 44 The left hand side of Equation [2.32] is simply r S Pa<t>rc dr = ia<p(r 2 - r*2)c [2.33] r* P P . P Substituting this value into Equation [2.31] a<t>r J = --L[la4>(r 2 - r „ 2 ) c ] [2.34] P P °t P P Since r is a fixed coordinate, it is independent of time. Therefore, Equation [2.34] becomes rJ = ~ i ( r 2 - r2)(dc/dt) + c rAdrJdt) [2.35] P P P P P Substituting Equations [2.29] and [2.30] for Jp and dc^/dt into Equation [2.35], we get sp = {dr^/dt) /u2r% [2.36] If an experimental plot of c versus r is available, the right hand side of Equation [2.32] is determined. Then can be obtained from Equation [2.32] and Equation [2.33]. However, in the ultracentrifuge, c cannot be measured directly by the optical system. Instead, K {dc/dr), where K is an optical constant, is o o obtained, for example, from the Schlieren system measuring dn/dr. Therefore, has to be expressed in terms of 3 e / 3 r in Equation [2.32]. This can be achieved by integrating the right hand side of Equation [2.32] by parts: r r a 0 f Prcdr = £ a 0 ( c r 2 - c r 2) - i a t f f Pr2 {dc/dr) dr [2.37] p p m m t r r m m where c is the solute concentration at the meniscus. After a finite time in the m ultracentrifuge, the sedimentation boundary is completely separated from the meniscus, so c m = 0 - T h e n , combining Equation [2.32] and [2.37] and solving for T H E O R E T I C A L B A C K G R O U N D / 45 r r * 2 = ( 1 / c ) / Pr2(dc/dr)dr [2.38] p t r r m r Also, can be replaced by / P(dc/dr)dr. Therefore, r m r r r * 2 = / Pr2(dc/dr)tdr/S P ( 9 c / 3 r ) ^ r [2.39] r r Equation [2.39] can be used to determine for each individual photograph of the sedimentation experiment. Since Equation [2.36] can be rewritten as s = [rf ( ln r*)/dt]/a>2 [2.40] P therefore, the sedimentation coefficient can be obtained by plotting In ( ) versus time. The advantage of this method of determining s is that it is based on the principle of conservation of mass. This method, therefore, is independent of the shape of the boundary. However, this method is very time-consuming. A more practical method can be used to obtain s if the Schlieren peak, r , of the sedimentation boundary is symmetrical. When the boundary is symmetrical at its peak, the values of dc/dr at r=r -dr and r=r +dr are identical. Then the difference between and is small enough so that the sedimentation coefficient can be calculated from s = (dr /dt)/(J2r [2.41] If the Schlieren peaks for sedimentation boundaries are markedly skewed, the use of Equation [2.41] will result in a large error. Therefore, Equation [2.40] still has to be used. T H E O R E T I C A L B A C K G R O U N D / 46 2.6. ION-EXCHANGE CHROMATOGRAPHY THEORY Several methods of fractionation of hyaluronate according to molecular weight are reported in the literature. In one method (Laurent et al . , 1960), cetylpyridinium salt of hyaluronic acid is fractionated on the basis of its solubility in aqueous sodium sulfate. Hyaluronate forms a cetylpyridinium salt with cetylpyridinium chloride. When hyaluronate of different molecular weights are mixed with cetylpyridinium chloride, cetylpyridinium salts of different molecular weights are formed. However, the salts formed have different solubilities in aqueous sodium sulfate. The higher the molecular weight of the cetylpyridinium salt, the higher the concentration of the aqueous sodium sulfate is needed to dissolve the salt. Therefore, upon dilution of a solution containing hyaluronate (of different molecular weights), cetylpyridinium chloride and sodium sulfate, a fraction of the highest molecular weight hyaluronate is obtained as precipitates of the cetylpyridinium salt. Fractions of decreasing molecular weights are then obtained in sucessive dilutions. A more rapid and more efficient method is the chromatographic fractionation of hyaluronate according to molecular weight on DEAE-cel lulose (Cleland et al . , 1968). A salt free solution of hyaluronate and a slurry of DEAE-cel lulose are mixed together and charged to a column. Hyaluronate fractions of increasing molecular weights are obtained as the column is eluted with N a C l solutions of increasing concentration, with use of stepwise elution method. In the present study, the above chromatographic technique is used to fractionate hyaluronate. T H E O R E T I C A L B A C K G R O U N D / 47 The theory of ion-exchange chromatography is summarized below. The reader is referred to some standard texts (e.g. Peterson, 1970; Morris & Morris , 1976) for more details of the technique. Ion-exchange chromatography distinguishes one component in a mixture from another component on the basis of net charge. Poly-electrolyte molecules of different net charges are adsorbed on the ion-exchanger (adsorbent) with different affinities. They are then separated when a buffer gradient of increasing ionic strength is used as the eluant. The molecular size and the distribution of charges of the molecules are important factors that have to be considered. The association forces between the ion-exchanger and the poly-electrolyte molecules are usually secondary forces, i.e. ionic, hydrophobic and hydrogen bonding. A n ion-exchanger commonly used to separate biological molecules is cellulosic materials. O n the cellulosic ion-exchangers, the functional groups are attached to matrices consisting of modified celluloses. The ion exchangers which bear positively charged functional groups are called anion exchangers because they interact with anions on the molecules, and the exchangers which bear negatively charged functional groups are called cation exchangers because they interact with cations on the molecules. The most commonly used cellulosic ion-exchangers are D E A E - ( o r diethylaminoethyl-)cellulose, which is an anion exchanger, and CM-(or carboxylmethyl-)cellulose, which is a cation exchanger. Their structures are shown in Figure 2.10. The cellulosic ion-exchangers are widely used because they have a low level of functional group substitution, which results in a low density of charges. The low charge density allows the elution of large poly-electrolyte molecules under relatively mild buffer conditions. Also, they have an open T H E O R E T I C A L B A C K G R O U N D / 48 O _ W + O CzK<* rr j C 2 H l 4 + \ U + H + I / \ / X C 2 H 5 C 2 H 5 C 2 H S C 2 H 5 charged uncharged Figure 2.10 Structures of the D E A E and C M cellulosic ion-exchangers. T H E O R E T I C A L B A C K G R O U N D / 49 microstructure which provides easy accessibility of the ionized sites to the molecules. During adsorption, electrostatic bonds are formed between opposite charges on the cellulosic ion-exchanger and the poly-electrolyte molecules. A s more bonds are formed, there is a greater affinity between the exchanger and the molecules. In some conditions, the number of bonds formed between the exchanger and the molecules becomes large enough so that the simultaneous dissociation of all the bonds is rare to occur. The molecules will remain adsorbed on the exchanger so long as the ionic environment remains the same. This situation is termed 'tight adsorption'. It has to be noted that in 'tight adsorption', the ion-exchanger is in dynamic equilibrium with the charged polyelectrolyte molecules and the ions in the buffer solution. Individual electrostatic bonds are constantly dissociating and reforming, but the probability of all the bonds to dissociate simultaneously is very low. Changing the composition of any part of the system will disrupt the equilibrium, and will change the binding of the molecules to the ion-exchanger. Usual ly , the equilibrium is disrupted by the changes in the buffer concentration. If there is an increase in the buffer concentration, the effectiveness of the buffer ions to compete for bonding partners is increased. When the increase in buffer concentration is high enough, the probability of all the electrostatic bonds to dissociate simultaneously is raised. The adsorbed molecules will then move down the column. The adsorbed molecules are said to be in 'finite adsorption equilibrium' with the exchanger. A s long as the probability of simultaneous dissociation is less than unity, the migration rate of the molecules will always be slower than that of the buffer that carries the molecules. T H E O R E T I C A L B A C K G R O U N D / 50 Therefore, when performing the ion-exchange chromatography, a general approach is to apply the mixture of poly-electrolyte molecules to the column under conditions that favor the 'tight adsorption' of the molecules. For example, consider negatively charged molecules such as hyaluronic acid adsorbed on a positively charged ion-exchanger (anion exchanger), originally at the 'tight adsorption' state. If the eluant buffer concentration is gradually increased, the negative ions of the buffer will shield the positive charges of the exchanger, and the positive ions of the buffer will shield the negative ions of the molecules. The attractive forces between the exchanger and the molecules become progressively weaker. Some molecules will be at the 'finite adsorption equilibrium' state. The molecules will then move down the column and will be collected. A s the buffer concentration is further increased, more molecules will reach the 'finite adsorption equilibrium' state and will be eluted. The sample molecules can be eluted by either gradient or stepwise elution. In the gradient elution method, the eluant buffer concentration is gradually increased. A s the buffer concentration increases, the ion-exchanger becomes less effective in immobilizing the molecules. The molecules lightly bound will move slowly as a band down the column in 'finite adsorption equilibrium'. However, the adsorbed molecules move more slowly than the buffer. Therefore, they are overtaken by the buffer gradient. The eluting power of the medium surrounding the molecules is constantly increasing and the molecules move faster and faster, until they move at the same rate as the eluant buffer. Since the eluting power at the rear of the band is always higher than that at the front, the molecules at the rear of the band will move faster. T h a t will result in a sharper band, or T H E O R E T I C A L B A C K G R O U N D / 51 higher resolution is obtained. However, the gradient elution method has its disadvantages. The method requires more equipment, which include a gradient maker and a fraction collector, and more time. Also, since the volume of eluant buffer is large, the molecule concentration in the eluate is lower. In the stepwise elution method, a series of buffer solutions, each stronger in elution power than the previous one, is applied. Each increase in the eluting power of the eluant will bring successively the lightliest bound molecules into the unadsorbed state. Some other molecules of different net charges in the 'finite adsorption equilibrium' state will move at different rates. The rest of the molecules remains tightly bound (adsorbed) to the column until a subsequent eluant of suitable eluting power is used. Therefore, the advantages of the stepwise elution method are that the method is faster, the molecules are collected in a higher concentration because a smaller volume of buffer is used, and only simple equipment are needed. The primary disadvantage is lower resolution is obtained. CHAPTER 3. EXPERIMENTAL PROCEDURE 3.1. INTRODUCTION The objective of this work was to investigate experimentally the effect of concentration and molecular weight on the flow conductivity of solutions of hyaluronate. Different molecular weight fractions of hyaluronate were obtained by fractionation with diethylaminoethyl-(or D E A E - ) cellulose, and the flow conductivity was obtained by measuring the sedimentation velocity of solution of hyaluronate as a function of concentration. In this chapter, a chemical method for determining the unknown concentration of hyaluronate in solutions is first described. Then, the procedure for fractionating hyaluronate according to molecular weight is discussed in detail. This is then followed by the description of the method of dialysis, and the procedure for taking viscosity measurements. F ina l ly , the method of taking sedimentation velocity measurements in the analytical ultracentrifuge is discussed. The results obtained are presented in Chapter 4. 3.2. HYALURONIC ACID CONCENTRATION DETERMINATION The method used in this study for the determination of unknown concentration of hyaluronate was a modification of the carbazole method (Dische, 1947) described by Bitter & M u i r (1962) - the modified uronic acid carbazole method. Known concentrations of the standard (glucuronolactone) were used for the preparation of a calibration line. The reagent solutions made up for the modified uronic acid carbazole method were: 52 E X P E R I M E N T A L P R O C E D U R E / 53 1. 0 .025M di-sodium tetraborate* 1 OH 2 0 (AnalaR, B D H ) in sulfuric acid, sp. gr. 1.84 (AnalaR or analytical reagent, B D H ) . 2. 0.125% carbazole ( K O D A K ) in absolute ethanol (Stanchem). 3. glucuronolactone standards of 9.85, 19.70, 29.55, 39.40 and 49.25 ag/mL prepared by dilution with distilled water saturated with benzoic acid (99%, Aldrich) from a stock standard solution, 985 jug/mL, of D-glucurono-6,3-lactone (99 + %, Aldrich). The procedure for the uronic acid carbazole reaction is described as follows. F ive m L of sulfuric acid reagent were pipetted into glass test tubes and cooled in an ice bath to about 4 ° C . One m L of the standard or sample (hyaluronic acid solution) was carefully layered by means of a pipette onto the acid, avoiding splashing of the acid. The tubes were stoppered and swirled with continual cooling. Swirling was stopped when the content in the tubes appeared to be homogeneous. The tubes were then heated for 10 min. in a vigourously boiling water bath and cooled to about room temperature. T h e n 0.2 m L of carbazole reagent was added to the tubes. T h e tubes were swirled again until the content appeared to be homogenous. The tubes were then heated in the boiling water bath for 15 min. and then cooled to room temperature. The absorbance of the solutions (purple in color) was then read on a V a r i a n Model 2390 spectrophotometer at 525 nm. Pathlength of the cells was 1 cm. F o r each standard or sample, the carbazole reaction test was done in triplicates. The absorbance for each test was recorded, and the average of the three absorbances was taken as the true absorbance. E X P E R I M E N T A L P R O C E D U R E / 54 3.3. FRACTIONATION OF HYALURONIC ACID 3.3.1. D e s a l t i n g H y a l u r o n i c A c i d Fibrous human umbilical cord hyaluronic acid (Sigma, Grade 1, Lot numbers 124F-0329 and 75F-0519) had a salt content ( N a + + K + ) of 3 to 7 % (w/w). Since the hyaluronic acid used for fractionation had to be salt free, the commercially obtained hyaluronic acid was desalted by precipitation in ethanol. To a 1000 m L Erlenmeyer flask, 2.0779 g of hyaluronic acid were added. Then, 60 m L of distilled water were added to the flask to dissolve the H A . Since H A dissolves slowly in water, the flask was left overnight in a refrigerator. To precipitate the H A , about 600 m L of absolute ethanol (Stanchem) were added to the flask containing the gel-like H A solution. The flask was occasionally swirled for 5 hours. The white fibrous precipitates which formed were then collected by centrifuging at about 1300 X g for 5 min. in a centrifuge (International Centrifuge, Universa l Model U V ) . The H A collected was redissolved in about 60 m L of water and then reprecipitated with about 540 m L of ethanol. The H A collected was further reprecipitated with 300 m L of ethanol (90% v/v). The resulting H A , which was essentially free of salt, was dissolved in 70 m L of distilled water in a 100 m L R B flask. The flask was then connected to a rotary evaporator (Rotavapor R E 120, Buchi) to remove solvent (ethanol 4- water). After all the solvent had been removed, 70 m L of distilled water were added to dissolve the residue remaining E X P E R I M E N T A L P R O C E D U R E / 55 in the flask. The H A solution was freeze-dried in a Unitrap II freeze-dryer (Virtis) for 3 days to yield 1.61 g of white fibrous H A . The H A was then stored desiccated in the freezer. 3.3.2. Preparation of DEAE-cellulose The DEAE-cel lulose used for the fractionation of H A was a fibrous, fine reduced cellulose (DE23 , Whatman , Maidstone, England), stated capacity of 1.0 m E q / g . The cellulose was supplied in a dried form. Before use it was fully hydrated so that its charged sites became fully accessible to charged H A molecules. In the dried state, many of the O H groups of the cellulose formed hydrogen bonds within the cellulose which caused some ion-exchange sites to become inaccessible to the large H A molecules. Therefore, the cellulose was precycled (treatment with concentrated acid and then alkali for the DEAE-cel lulose) to expose these ion-exchange sites. 3.3.2.1. Precycling The procedure used follows the method described in the Information Leaflet for W h a t m a n Advanced Ion Exchange Cellulose (Whatman, Clifton, New Jersey). DEAE-cel lulose (DE23 , 28.5 g) was precycled in 2 portions (11.0 g and 17.5 g). E a c h portion of cellulose was added to a 500 m L plastic Erlenmeyer flask. HC1 solution (0.5N, diluted from concentrated volumetric solution, B D H ) was then added to the flask (15 m L of liquor/g dry weight of ion exchanger). T h e E X P E R I M E N T A L P R O C E D U R E / 56 content was occasionally stirred for 1 hour. The supernatent liquor was filtered and the wet cellulose washed in a funnel until the filtrate was at about p H 4 (judged by p H paper, Fisher). The wet cellulose was transferred to the 500 m L Erlenmeyer flask. N a O H solution (0.5N, from reagent grade pellets, B D H ) was added to the flask (15 m L liquor/g dry weight of ion exchanger). The content was then occasionally stirred for 30 min. The supernatent was filtered and the alkali treatment was repeated. The wet cellulose was then washed in a funnel until the filtrate was near neutral. 3.3.2.2. Fines Removal Smal l fragments ("fines") within the cellulose could clog the bed support (the filter disc at the bottom of the column). In addition, they could interfere with the performance of the column because of a tendency to accentuate non-uniformity of column packing. It was necessary, therefore, to remove the fines. The procedure for fine removal of the ion exchanger is described below. The wet precycled DEAE-cel lulose was dispersed in 2 m M N a 2 H P 0 4 , p H adjusted to 7.30 by 0 . 5 M N a H 2 P O „ (15 m L liquor/g dry weight of cellulose). The slurry was allowed to settle for 30 min. The cloudy supernatent was then removed by suction through an aspirator. The above procedure was repeated 5 times to remove most of the fines. E X P E R I M E N T A L P R O C E D U R E / 57 3.3.2.3. Equilibration The exchanger had to be equilibrated to bring the weakly ionizing exchanger into equilibrium with the dilute buffer. T h e 'fines reduced' DEAE-cel lulose was redispersed in 15 volumes of 2 m M phosphate buffer. The p H of the solution, measured by a Digital Ionalyzer/501 (Orion Research), was about 10.0. It was then adjusted to 7.30 by 0 . 5 M N a H 2 P O f l . The s lurry was filtered in a funnel and then equilibrated with 2 m M phosphate buffer (see Figure 3.1). The p H of the first filtrate was about 6.90. Phosphate buffer was added to the funnel until the filtrate was at p H 7.30. 2 m M phosphate buffer i - precycled DEAE-cel lu lose filter paper Figure 3.1 The set up for the equilibration of the ion-exchanger. E X P E R I M E N T A L P R O C E D U R E / 58 3.3.3. P re l imina ry Fractionation Prel iminary fractionation experiments were done according to the method described by Cleland et al. (1968) and Cleland (1984). In their method, the DEAE-cel lu lose was prepared according to Sections 3.3.2.1 and 3.3.2.2. Water was used in the fines reduction step and there was no equilibration step. A salt free solution of hyaluronic acid dissolved in distilled water (about 35 mg H A / m L water) was mixed with a slurry of about six fold excess of DEAE-cellulose (about 75 m g D E 2 3 / m L water). The mixture was then charged to a column. The column was eluted by stepwise elution method with successively increasing concentration of N a C l , and hyaluronic acid fractions of increasing molecular weights were obtained. In preliminary fractionation I, a hyaluronic acid solution of 72.5 mg in 7.2 m L H 2 0 was mixed with a s lurry of 0.6. g D E 2 3 in 7.0 m L H 2 0 . The mixture was then charged to a 2 cm i.d. column; packing occurred by gravity flow to give a bed about 3.8 cm long. The column was then washed by 22 m L of distilled water. However, the flow rate was very slow — after 15 min. , no flow was noticed. The reason for the slow flow rate was probably because the fine pores in the filter disc at the bottom of the column were clogged with the hyaluronic acid solution. The content in the column was then decanted into a 5.1 cm i.d. Kontex glass column with a coarse glass filter disc as the bed support. Stepwise elution was then carried out at room temperature with successively increasing concentration of N a C l . The flow rate was controlled to about 0.5 L / h r by a stop-cock. The eluate of each salt concentration was collected in 1 fraction. E X P E R I M E N T A L P R O C E D U R E / 59 The concentration of hyaluronate in each fraction was then determinated by the modified uronic acid carbazole method as described in Section 3.2. The results of the fractionation are tabulated in Table 3.1. The sample calculations leading to the evaluation of the glucuronolactone concentration and amount of hyaluronate collected are presented in Appendix A . A s is obvious from Table 3.1, a large amount of H A was not bound to the cellulose adsorbent and was washed out by the water. This suggests that at the beginning of the fractionation, the H A molecules were not at 'tight adsorption equilibrium' with the adsorbent. Therefore, the H A molecules were washed out by water. Before the cellulose s lurry and the H A solution were mixed together, the p H of the cellulose slurry was about 7. The p H of the H A solution, which was just H A dissolved in distilled water, could be assumed to be close to 7. When the two were mixed together, and if there was no change in the p H , the cellulose (pKa 9.5) would be positively charged, and the H A (negatively charged at p H 7.30) negatively charged. Therefore, the H A molecules should adsorb tightly on the cellulose molecules. However, they were not. A change in the p H when the H A solution was mixed T a b l e 3.1 Results of preliminary fractionation I Eluant [NaCl], Eluate volume, Glucuronolactone H A recovery, M m L concentration, / ig /mL m g 0 50 39.63 25.5 0.1 420 5.51 5.3 0.2 381 4.78 4.2 0.3 446 6.45 6.6 0.4 449 3.61 2.7 0.5 440 1.80 1.8 46.1 E X P E R I M E N T A L P R O C E D U R E / 60 with the cellulose s lurry was hence suspected. In fact, as mentioned in Section 3.3.2.3 (Equilibration), the p H of the unequilibrated cellulose slurry changed from about 7 to about 10 when a weak phosphate buffer (pH 7.30) was added. If the p H was changed and one of the two species (cellulose & H A ) became uncharged, then the H A was not adsorbed and was washed out. Therefore, in the next fractionation experiment, the p H was controlled by adding a weak phosphate buffer ( 2 m M , p H 7.30), and the cellulose was equilibrated with the buffer (Section 3.3.2.3). The recovery of H A in preliminary fractionation I was just 64%. The amount lost was probably due to the transfer of the HA-cellulose mixture from the small column to the large column. In preliminary fractionation II, 61.4 mg of H A were dissolved in about 3 m L of I m M phosphate buffer, p H 7.30. A s lurry of about 1.4 g D E 2 3 (equilibrated, processed according to Section 3.3.2) in 15 m L 2 m M phosphate buffer, p H 7.30 was mixed with the H A solution. A large excess of cellulose was used to ensure that enough adsorbent was available for the H A molecules. The mixture was poured into the 5.1 cm i.d. column to give a bed about 0.7 cm long. The column was then eluted by stepwise elution method with successively increasing concentration of N a C l . The p H of the salt solutions was kept at 7.30 by adding 2 m M phosphate buffer. Flow rate was about 0.5 L /hr . The eluate at each salt concentration was collected in one fraction. The results are presented in Table 3.2. The recovery of H A was 72%. Probably, some H A was tightly bound to the cellulose and could not be eluted. Since H A was very hygroscopic, some moisture was absorbed to the H A during handling. Therefore, the true weight of the H A charged to the column might be less than 61.4 mg. E X P E R I M E N T A L P R O C E D U R E / 61 F r o m Table 3.2, molecular weight fractionation was apparently obtained. Most of the H A was adsorbed to the cellulose. There was little low molecular weight H A in the original sample because the H A recovery for the low [NaCl] eluant was small. In this fractionation experiment, the eluate for each concentration of salt was collected in one fraction. In the next fractionation experiment, the eluate was collected in subfractions in order to study the change of H A concentration with elution volume. The intrinsic viscosities of the fractions were also determined. In preliminary fractionation III, a solution of 100.4 mg H A dissolved in 4.0 m L 2 m M phosphate buffer, p H 7.30 was mixed with about 2.0 g D E 2 3 in 20 m L 2 m M phosphate buffer, p H 7.30. The mixture was charged to the column. The column was then eluted with successively increasing concentration of N a C l . Flow rate was about 0.5 L / h r . The results are presented in Table 3.3. The recovery of H A was at least 63%. Again , the low yield was probably because some H A was tightly adsorbed to the cellulose and couldn't be eluted, T a b l e 3.2 Results of preliminary fractionation II Eluant [NaCl], M Eluate volume, m L Glucuronolactone concentration, ng/mL H A recovery, mg 0 15.5 0.015 0.2 0.1 378 0.014 0.6 0.2 373 0.033 1.6 0.3 407 0.204 11.3 0.4 373 0.372 19.3 0.5 413 0.203 11.4 44.4 E X P E R I M E N T A L P R O C E D U R E / 62 Table 3.3 Results of preliminary fractionation III Eluant [NaCl], Subfraction Glucuronolactone H A recovery, M volume, m L concentration, Mg/mL mg 23.6 = 0 = 0 1. 100 = 0 = 0 2. 100 = 0 = 0 3. 100 4. 100 1. 100 11.09 2.5 2. 100 2.76 0.6 3. 100 4. 100 5. 33.6 1. 100 117.7 26.8 2. 100 33.28 8.0 3. 100 4. 100 5. 100 1. 100 74.10 16.9 2. 100 24.30 5.5 3. 100 4. 100 5. 69.6 1. 100 11.57 2.6 2. 100 2.22 0.5 3. 100 4. 100 5. 70.4 63.4 E X P E R I M E N T A L P R O C E D U R E / 63 and there was moisture absorbed by the original H A sample. For each eluate, there was a large decrease in H A concentration from subfraction 1 to subfraction 2. The two subfractions of 0 . 3 M N a C l fraction and 0 . 4 M N a C l fraction were combined and the H A in each fraction was precipitated according to Section 3.3.5. The H A of each fraction was dissolved in 0 . 2 M N a C l , and the viscosity of each solution was measured according to Section 3.5. The intrinsic viscosity plot for the two fractions is presented in Figure 3.2. The intrinsic viscosities for the 0 . 3 M and 0 .4M fractions were 934 m L / g and 958 m L / g , respectively, and the molecular weights were determined from the Mark-Houwink equation (Cleland & Wang, 1970): [T?] = 0 . 0 2 2 8 M ° " 8 1 6 to be 4 . 4 9 X 1 0 5 and 4 . 6 3 X 1 0 5 , respectively. For the same polymeric material , the intrinsic viscosity plot for the higher molecular weight sample is steeper than that of the lower molecular weight sample (Tanford, 1961). This behavior is shown in Figure 3.2. The difference in the molecular weight is not large. However, the H A solutions were not dialysed. The solutions were H A precipitates dissolved in 0 . 2 M N a C l . Nevertheless, molecular weight fractionation was still obtained because the H A recovered for each eluant salt concentration decreased with eluant volume and then increased when the next higher eluant salt concentration was added. A large scale molecular weight fractionation experiment of H A was then performed in the next section. In the fractionation experiment, H A solutions were dialysed before physical measurements were made. More reliable results were then obtained. E X P E R I M E N T A L P R O C E D U R E / E X P E R I M E N T A L P R O C E D U R E / 65 3.3.4. Fractionation A slurry of 360 m L containing approximately 28.0 g of processed D E 2 3 cellulose in 2 m M phosphate buffer was mixed with a solution of 40 m L containing 1.39 g of hyaluronic acid in 2 m M phosphate buffer in a 500 m L plastic Erlenmeyer flask. Results from preliminary experiments showed that after about 10 min. , most of the hyaluronic acid would bind to the cellulose. The mixture was then packed in a 5.1 cm i.d. glass column giving a bed 14.0 cm long. The column was washed with about 600 m L of 2 m M phosphate buffer. Stepwise elution was then carried out with aqueous N a C l at 0 . 1 0 M to 0 . 4 0 M with increments of 0 .075M at each step. Then a final step of elution was carried out at 0 .5M. The p H of the eluant salt solutions was adjusted to p H 7.30 by adding 2 m M phosphate buffer. For each salt concentration, at least 8 subfractions of about 500 m L each were collected, except the last concentration (0 .5M NaCl ) in which 5 subfractions were collected. Elution at a particular salt concentration was terminated when the eluate H A concentration had dropped to about 10-20 ng/mh. The H A concentration was determined by collecting 2 to 3 m L of eluate and then conducting the modified uronic acid carbazole test (Section 3.2). The eluant flow rate was kept at about 1.0 L/hour. For the elution by 0 .325M N a C l solution, fractionation was stopped after subfraction 8. Although the H A concentration found for the eluate was above 20 / ig /mL, it was thought that degradation of H A in the column was slow and the column was left overnight. Elution was resumed with 0 .325M N a C l solution. However, at the beginning, the flow rate of E X P E R I M E N T A L P R O C E D U R E / 66 eluate was very slow. Later on, the flow rate was back to the regular level and was controlled at l L / h r . For subfraction 9 (500 m L ) , the collection time was 85 min. Elution was continued until subfraction 14 was collected, in which the concentration of H A was less than 10 Mg/mL. Also, when the elution for one salt concentration was terminated, the eluant above the bed was pipetted out before fresh salt solution of the next higher concentration step was added. This procedure ensured a discrete rise in the eluant salt concentration. E a c h subfraction was then analyzed for H A concentration with the uronic acid carbazole test. 3.3.5. Purification and Isolation of HA The eluate fractions collected as described in Section 3.3.4 were in different salt concentrations, and the H A concentrations were very low, thus rendering the fractions unsuitable for further physical measurements (viscosity and sedimentation velocity). To prepare materials for later work, the first few subfractions of each salt concentration, which contained 85% or more of the eventually eluted hyaluronate for that salt concentration, were combined and evaporated on a R E 120 rotary evaporator to a concentrated solution or to dryness. A n exception was that for the 0 .325M N a C l eluate, subfractions 1 to 4 and 6 were evaporated to a concentrated solution, and subfraction 9 was evaporated to another concentrated solution. Since the volumes of the combined eluate sub-fractions were large, evaporation was done, portion by portion, in a I L round bottomed flask. E X P E R I M E N T A L P R O C E D U R E / 67 H A was then precipitated out from the concentrated solutions. Since a lot of N a C l was present in the solutions, and in fact the solutions were nearly saturated with salt, a few reprecipitation steps were required to remove most of the salt. Prel iminary precipitation experiment had shown that after about 4 reprecipitation steps, the amount of H A precipitated was very small. In other words, a large amount of H A was in the solution phase and could not be precipitated. In some cases, especially for the fractions with lower H A content, H A might fail to precipitate out after 3 reprecipitation steps. Therefore, the concentrated solutions were first precipitated twice with four volumes of ethanol. The supernatant was then decanted and the precipitate washed two to three times with four volumes of 75% ethanol (v/v). In the latter step, salt went into solution, and the H A remained as precipitate. The supernatant was decanted and the precipitate redissolved in water in a round bottomed flask. The solution, which was H A and a little bit of salt in water and ethanol, was evaporated to dryness on the rotary evaporator. To remove traces of ethanol remained in the H A residue, the flask containing the residue was connected to a Cenco-Hyvac Pump (Central Scientific) at -28 to -30 in. H g for 30 min. or more. The H A fractions obtained for the 0 .25M, 0.325M, 0 .325M subfraction 9, 0 . 4 M and 0 .5M N a C l eluate were named 0 .25M, 0.325M, 0.325M-9, 0 .4M and 0 .5M Fractions, respectively. 3.4. ACID HYDROLYSIS OF HA The H A fractions obtained in the fractionation experiment (Section 3.3) 5 was found to be in a narrow M . W . range (6.99 to 1 1 . 1 X 1 0 ). Smaller M . W . E X P E R I M E N T A L P R O C E D U R E / 68 fractions were obtained by degrading H A with hydrochloric acid. The acid hydrolysis method used for the degradation of H A followed the one described by Cleland (1984). About 44 ml of H A solution (4.57 mg 0 .325M Fraction per m L 0 . 2 M N a C l in concentration) were added to a 250 m L beaker. The H A solution was then diluted withj water to about 150 m L . About 17 m L of concentrated HC1 ( B D H , analytical reagent grade) were added to the H A solution. Distilled water was then added to the solution until the meniscus reached the 200 m L mark on the beaker, giving a solution of H A of about 1 m g H A / m L concentration and 1 M in HC1. The H A solution was stirred and heated on a hot plate-stirrer (Corning, PC351) at 5 0 ± 2 ° C for 1 hour. T h e n about one half of the H A solution was decanted into a beaker. The H A solution was neutralized with solid N a O H ( B D H , reagent grade pellets) and back titrated to p H about 7.0 with cone. HC1. The remaining one half of the H A solution in the 250 m L beaker was heated on the hot plate-stirrer at 5 0 + 2 ° C for another 1 hour. Then the H A solution was neutralized to about p H 7.0 as described above. The two neutralized H A solutions, one acid hydrolysed for 1 hour and the other for 2 hours, were purified as described in Section 3.3.5. The H A fractions obtained were named l h r A H Fraction and 2 h r A H Fraction. In addition, a solution of H A prepared by dissolving about 120 mg of 0.325M-9 Fraction in 100 m L of distilled water was acid hydrolysed as described above for 15 min. The H A solution was then neutralized and purified as described above. The H A fraction obtained was named 1 5 m i n A H Fraction. E X P E R I M E N T A L P R O C E D U R E / 69 3.5. FRACTIONATION OF ACID HYDROLYSED HA In each of the H A fractions obtained in the previous Section by acid hydrolysing H A , the range of M . W . of H A is broad. A n attempt to obtain low M . W . H A with a small range of M . W . was done by acid hydrolysing H A and then fractionating the resulting sample. This is described below. 3.5.1. Acid Hydrolysis The procedure for the acid hydrolysis of H A was described in Section 3.4. About 400 mg of H A (50 mg 0 . 2 5 M Fraction, 230 mg 0 .325M Fraction and 120 mg 0.325M-9 Fraction) were dissolved in 320 m L of water in a 400 m L beaker. T h e n 30 m L of concentrated HC1 were added to the beaker to give an H A solution approximately 1 M concentration in HC1. The H A solution was heated and stirred on a hot plate-stirrer at 50 to 5 2 . 5 ° C for 15 min. The solution was then neutralized with N a O H pellets and back titrated to p H about 7.0. The H A in the solution was precipitated and freeze-dried as described in Section 3.3.1. 3.5.2. Fractionation The procedure for fractionation followed the one described in Section 3.3.4. A n H A solution of 324.4 mg acid hydrolysed H A dissolved in 10 m L of 2 m M phosphate buffer was mixed with a 80 m L slurry of DEAE-cel lulose prepared from 6.5 g of D E 2 3 as described in Section 3.3.2. The mixture was then charged to a 5.2 cm i.d. column. T h e mixture was packed from 4.1 cm to a E X P E R I M E N T A L P R O C E D U R E / 70 constant bed height of 2.6 cm by applying air pressure at the top of the column. T h e column was washed with about 50 m L of 2 m M phosphate buffer. Stepwise elution was then carried out with 0 . 1 M , 0 .175M, 0 .25M, 0 .325M, 0 . 4 M and 0 . 5 M N a C l solutions. A t each salt concentration, eluate subfractions of 250 m L each were collected until the H A concentration in the eluate was less than 10-20 Mg/mL. The H A concentration was determined by the carbazole method (Section 3.2). The H A in the 0 .25M eluate (subfraction 1) and 0 .325M eluate (subfractions 1 to 5) were precipitated out as described in Section 3.3.5. The 0 . 2 5 M and 0 .325M H A fractions were named 1 5 m A H - 0 . 2 5 M Fraction and 1 5 m A H - 0 . 3 2 5 M Fraction, respectively. 3.6. DIALYSIS M a n y physical properties available in the literature for hyaluronic acid (e.g. viscosity and sedimentation velocity) have been measured in 0 . 2 M N a C l . In order to compare properties including estimates of the molecular weight with the literature results, the H A solutions as prepared and used in this study must be in 0 . 2 M N a C l . E a c h of the H A fractions purified in the previous Sections (3.3.5, 3.4, 3.5) was dissolved in 30 m L of 0 . 2 M N a C l to give a H A solution of 2-3 m g / m L concentration. Since there was salt in the purified H A fractions, the H A solutions were to be dialysed in 0 . 2 M N a C l to make sure that the H A solutions were in that buffer concentration. E X P E R I M E N T A L P R O C E D U R E / 71 3.6.1. P r e p a r a t i o n of D i a l y s i s T u b i n g s The dialysis tubing used was Spectrapor membrane tubing (Spectrum) made of cellulose, 25mm flat width and molecular weight cut off at 12,000-14,000 Daltons. The dialysis tubing contained glycerin as a plasticizer, traces of sulphurous compounds and heavy metal ions, and therefore was treated before being used. Tube of this material 20 and 30 cm in length were cut out and washed in running water for 15 to 20 min. to remove most of the glycerin. Some vigorous procedures listed below were then employed to remove the other contaminants from the tubings. The cut and washed lengths of dialysis tubing were treated as follows: Procedure I 1. S immer for 1 hour in 2 L . of 50% ethanol (v/v). 2. Repeat step 1. 3. Soak in l O m M sodium carbonate, I m M E D T A for 1 hour. 4. Repeat step 3. 5. W a s h in distilled water. E X P E R I M E N T A L P R O C E D U R E / 72 Procedure II 1. Soak for 1 hour in 1% acetic acid (v/v). 2. Stir gently in distilled water for 15 min. 3. Soak in 1% sodium carbonate, I m M E D T A for 15 min. with gentle stirring. 4. Heat to 75 ° C with N a 2 C 0 3 - E D T A . 5. Repeat step 4 with fresh N a 2 C O 3 - E D T A . 6. Soak in distilled water and heat to 75 ° C 7. Repeat step 6 with fresh water. 8. Rinse in distilled water for 15 min. Procedure I is for the removal of the glycerin and some heavy metal ions, and Procedure II is for the removal of sulphurous compounds and the remaining heavy metal ions. Unused dialysis tubing was suspended and stored in water in a wide mouth plastic bottle. A few drops of dichloromethane were added to restrict bacterial growth. The bottle containing the tubing and water solution was then stored in the freezer. 3.6.2. Dialysis One end of the cleaned dialysis tubing was sealed by tieing two knots at one end so that a dialysis bag was formed. The dialysis bag was first filled with distilled water to check for leaks. The distilled water was then poured out and H A solution was pipetted into the dialysis bag. The tubing was then sealed at the top by tieing two knots, leaving a small dead space above the H A E X P E R I M E N T A L P R O C E D U R E / 73 solution surface to allow for the flow of solvent into the bag during the course of dialysis. The bag was then suspended in a flask of dialysate (0 .2M N a C l , 100 fold volume excess). The dialysate was stirred by a magnetic stirring bar, and the bag was spinned in the vortex of the dialysate. The mouth of the Erlenmeyer flask was covered with a piece of parafilm (see Figure 3.3). The dialysis was carried out in a cold room controlled at 4 - 7 ° C for at least 2 days. Dialysate was changed after about 24 hours. When the dialysis was finished, the content of the bag was removed by holding the bag with one hand while holding a Pasteur pipet with rubber bulb squeezed in the other hand. Figure 3.3 The set up for performing dialysis. E X P E R I M E N T A L P R O C E D U R E / 74 The tip of the Pasteur pipet was quickly stabbed through the air bubble and plunged into the H A solution. The H A solution was pipetted out and stored in a centrifuge tube. 3.7. VISCOSITY Solution viscosities were measured in a Cannon-Ubbelohde semi-micro dilution viscometer (Cannon Instrument Co.). A diagram of the viscometer is shown in Figure 3.4. One special feature of this viscometer is that dilution can be made in the viscometer. The viscosities of hyaluronic acid solutions of various molecular weights at different concentrations are to be measured in order to determine the intrinsic viscosities. The use of the Cannon-Ubbelohde viscometer will save the time used in cleaning and rinsing between successive runs. Solutions of hyaluronic acid were dialysed against 0 . 2 M N a C l for at least 2 days (Section 3.6) prior to use in viscosity determination. Dialysate was changed after about 24 hours. The final dialysate was used as a diluent. Before addition to the viscometer, the dialysed H A solutions and the dialysates were cleaned by centrifuging at about 2 0 0 0 X g for 10 min. , as recommended by Cleland (1984). Viscosity measurement was started . with a concentrated solution of hyaluronic acid. Then the solution of hyaluronic acid was diluted a few times in the viscometer and the viscosity of each diluted solution was measured. The starting concentration of the H A solution was chosen such that the viscosities E X P E R I M E N T A L P R O C E D U R E / 75 Figure 3.4 The Ubbelohde type semi-micro dilution viscometer. E X P E R I M E N T A L P R O C E D U R E / 76 measured for the starting solution and the diluted solutions fell in the recommended viscosity range of the viscometer, which was 0.8 to 4 centistokes. Preliminary experiments have shown that for H A solutions with the same M . W . but of different concentrations, the viscosity would be higher for the solution with higher concentration; and for H A solutions with the same concentration and of different M . W . , the viscosity would be higher for the solution with higher M . W . Therefore, in general, a lower starting concentration was chosen for solutions of H A with higher M . W . (precipitates of H A eluted with higher salt concentrations), and a higher concentration was chosen for the solutions of H A with lower M . W . (precipitates of H A eluted with lower salt concentrations). Also, the choice of starting concentration was complicated by the fact that as the starting H A solution was diluted a few times to measure the viscosities at different concentrations, the error in the term ( T } - 7 7 0 ) / T } 0 »c (for determining the intrinsic viscosity) became larger as solution viscosity T J became closer to solvent viscosity 7 j 0 - For each H A solution, 4 viscosity measurements were made. If the standard deviation of the term {T)-T]0)/ri0 « c of the last diluted H A solution was more than 5%, another starting concentration was chosen. The procedure for taking viscosity measurements is described as follows: Before use, the viscometer was thoroughly cleaned with chromic acid. The viscometer was filled with chromic acid, and it was then left for about an hour. Then the chromic acid was decanted. The viscometer was rinsed thoroughly with distilled water, and then with acetone. The viscometer was dried in an oven or by sucking air through the viscometer. E X P E R I M E N T A L P R O C E D U R E / 77 H A solution (1 mL) was charged directly from a pipette through tube G into the lower reservoir J of the viscometer. The viscometer was then placed into a holder and then inserted into a water bath kept at 25.00 ± .05 ° C by a Thermomix 1420 heater (B. Braun). Approximately 20 minutes were allowed for the solution to come to the bath temperature. A finger was placed over tube B and suction was applied to tube A until the liquid reached the centre of bulb C . Suction and finger were then removed. The efflux time for the meniscus to move from etch mark D to reach etch mark F was measured. Five to six dilutions were made by pipetting measured amounts of dialysate into the reservoir J . The concentration of the final solution examined was 1/10 of the concentration of the initial solution examined. For each diluted H A solution, 20 minutes were allowed for temperature equilibration with the water bath before measurements were taken. Quadruple measurements of efflux time were made for each concentration. The average value of the 4 measurements of efflux time was multiplied with the viscosity constant (determined by the manufacturer) to give the kinematic viscosity. 3.8. SEDIMENTATION VELOCITY The hydraulic flow conductivity of a polymer solution can be related to its sedimentation coefficient by the equation: K' = K/ri = s/c2{\ - U 2 p , ) [2.10] The sedimentation coefficient of H A was measured in a Beckman Model E analytical ultracentrifuge (Spinco Division, Beckman). The procedure for measuring the sedimentation velocity using this device, as described in the Instruction E X P E R I M E N T A L P R O C E D U R E / 78 Manual supplied by Beckman, can be divided into 4 parts: preparation of sample cell, making a sedimentation velocity run, taking photographs and ending a sedimentation velocity run. The following description of the procedure is a simplified version of the one described in the Instruction Manua l . 3.8.1. Preparation of Sample Cell A diagram of the cell assembly is shown in Figure 2.5. The procedure for the preparation of the sample cell is described as follows: 1. Check that all parts are clean. 2. Place a white window gasket, window liner and window in each window holder. Place the window liner around the window, making sure that the ends of the liner face away from the keyway of the holder once the window is in place. The "key" is the ridge down one side of the cell housing. There is a black arrow on the edge of the window. Al ign the arrow on the window with the keyway of the holder and with the arrow pointing down, push the window into the holder. 3. Slide the bottom window holder, window facing up, into the bottom of the cell housing. Keep the keyway aligned with the key (also in steps 4 and 5). 4. Place two red centerpiece gaskets in the aluminum centerpiece, one at the top and the other one at the bottom. 5. Add top window holder, with the window facing down. 6. After the cell components are properly seated in the housing, apply a thin film of Spinkote (vacuum sealant) to the brown screw ring gasket. Place E X P E R I M E N T A L P R O C E D U R E / 79 the gasket in the cell housing on the upper window holder. Then apply a thin film of Spinkote to the threads of the screw ring. The letter B for "Buttress Threads" is stamped on the top on the screw ring. Screw the ring into the housing, with the "B" side up, just enough so that the screw ring is f irmly in place. Tighten the cell with a torque wrench which is shown in Figure 3.5. To use the torque wrench, raise the verticle rod and slide the assembled cell, screw ring up, inside the aligning pins. The filling hole of the cell assembly should be either facing or' directly opposite the experimenter. M a k e sure that the key at the base fits into the cell housing slots at the bottom. Then lower the verticle rod and align its key with the slots in the screw ring. F i t the wrench driver into the socket on top of the rod. Before turning the torque wrench, rotate the dial until the needle reads 0. Then press down on the driver with one hand while turning the wrench clockwise. T u r n the wrench in a series of about 5 fluid turns to 120 inch-pounds. F i l l centerpiece with sample. Hold the cell in a horizontal position, with the filling hole facing up. Us ing a 1 m L syringe, fill the centerpiece with about 0.75 m L of H A solution. If the sample overflows, immediately wipe it away from the filling hole to prevent corrosion. Then place a red housing plug gasket in the filling hole and screw the housing plug into the filling hole. Screw the plug in, with two fingers, just enough to provide a good seal. If the plug is tightened too much, it will distort the cell housing. Weigh filled cell and counterbalance. E X P E R I M E N T A L P R O C E D U R E / Figure 3.5 Position of the torque wrench and the cell housing. (Modified from the Instruction M a u n a l , Model E Analyt ical Ultracentrifuge, Beckman) E X P E R I M E N T A L P R O C E D U R E / 81 Note: the analytical rotor used is of A n - H type with a m a x i m u m speed rating of 67,700 rpm. There are two holes on two sides of the rotor (see Figure 3.6), one for the sample cell and the other one for the counterbalance. The acceptable tolerance limits between the weights of the sample cell and the counterbalance are +0.5 g. a. Remove counterbalance from Side 2 of rotor. b. Balance with the filled sample cell. The counterbalance and cell must be of equal weight: tolerance - the counterbalance m a y be from 0 to 0.5 g lighter. In no case m a y the counterbalance be heavier than the cell. c. If the cell and counterbalance exceed the acceptable tolerance limits, replace the original plug in the counterbalance with a brass or aluminum plug that will make the weight of the counterbalance equal to that of the cell. d. Clean the rotor holes with Kimwipes and apply a very thin film of Spinkote on the counterbalance. Slide the counterbalance, screw side up, into Side 2. Hold rotor up and using the cell aligning tool, align the counterbalance by matching the scribe lines on the bottom of the counterbalance with the corresponding lines on the bottom of the rotor hole. Note: For all the sedimentation velocity experiments, the samples are H A solutions which have a very close if not identical density. Therefore, steps a to d are done once only. e. Place the sample cell in Side 1 of rotor. The sample chamber in the centerpiece is sector-shaped so as to E X P E R I M E N T A L P R O C E D U R E / 82 Figure 3.6 Installing the rotor. (Modified from the Instruction Manual , Model E Analyt ical Ultracentrifuge, Beckman) E X P E R I M E N T A L P R O C E D U R E / 83 minimize wall effect. It is important that the cell be aligned precisely in the rotor. Otherwise, the benefit of the sector-shape centerpiece may be lost and may possibly produce convection in the cell. Apply a thin film of Spinkote on the cell housing. Slide the cell, screw ring end up, into the rotor hole (Side 1) with the housing plug or narrow part of the sector facing in toward the centre of the rotor. Hold rotor up and using the cell aligning tool, align the cell by matching the scribe lines on the bottom of the cell with the corresponding lines on the bottom of the rotor hole. 3.8.2. Making a Sedimentation Velocity Run The following procedure has been applied uniformly when making a sedimentation run. A diagram of the face panel of the analytical ultracentrifuge along with a description of the controls is contained in the Instructional Manua l . 1. T u r n main power on and the M A I N P O W E R pilot light (C-20) will come on. 2. Open the vacuum chamber by turning the vacuum chamber switch (B-4) to O P E N . 3. Attach the rotor to the drive shaft. Place the rotor in the chamber, with the rotor support ring resting on the support fork (see Figure 3.6). A l ign the threads of the coupling nut with the threads of the rotor coupling stem. Then lower the coupling nut clockwise (as viewed from above) until it engages the threads in the coupling stem and lifts the rotor off the support fork. T u r n the coupling E X P E R I M E N T A L P R O C E D U R E / 84 nut so that its flat sides are parallel to the side of the support fork. Slide the coupling wrench, jaws down and open end first, over the coupling nut and support fork. After the coupling wrench is in place, turn the rotor counterclockwise (as viewed from above) until it is tightened. Then remove the coupling wrench. 4. Close the vacuum chamber (B-4). After the chamber is closed, turn the vacuum chamber switch to S A F E T Y . 5. Close the V A C U U M P U M P A I R V A L V E by turning B-5 closewise until tight. Then turn on the vacuum pump ( B - l l ) . 6. T u r n on the refrigeration (B-3) 7. T u r n on the R T I C automatic temperature control unit. T u r n the R T I C function selector switch ( C - l l ) to Z E R O A D J U S T , the R T I C pilot light (C-12) will come on. Al low the unit to warm up for 5 minutes. Then using the Z E R O A D J U S T knob (C-10), zero the black needle on the R T I C meter (C-9). Activate the R T I C unit by turning the function selector switch to I N D I C A T E . Then turn the switch to R E G U L A T E . The R T I C unit will then control the relay circuit for the heater. The refrigeration unit is on at all time. If the temperature drops below the designated temperature, the heater is then turned on. After the temperature is attained, the heater is shutted off. 8. The temperature calibration with the R T I C unit has previously been performed. Sedimentation experiments are performed at 20 ° C , which corresponds to a B A L A N C E dial (C-14) reading of 5.619. 9. Make sure the V O L T A G E C O N T R O L knob (A-12) is counterclockwise to zero. Otherwise, the diffusion pump cannot be turned on. E X P E R I M E N T A L P R O C E D U R E / 85 10. When the pressure gauge (C- l ) is = 50-100 micron, open the water inlet to the diffusion pump by turning D I F F U S I O N P U M P W A T E R V A L V E (B-6) counterclockwise until tight and aligning the slot in the water valve with the D I F F U S I O N P U M P switch (B-10). Then turn on the diffusion pump. The D I F F U S I O N P U M P pilot light (C-19) will come on. Wait 15 min. for the pressure to drop to =1 micron. 11. Load the photographic plate holder in the camera. The film used is K O D A L I T H O R T H O film, type 2556, size 2in. x 8in. The film is loaded into the photographic plate holder. Before placing the loaded plate holder into the camera, turn the P L A T E H O L D E R D R I V E switch (C-22) to O U T and press the P L A T E H O L D E R D R I V E button (C-23) until the plate position dial (C-5) stops revolving. The plate position dial should read between 0 and 5. T u r n the P L A T E H O L D E R D R I V E switch to I N and pull down the cover for the plate holder slot. Push the plate holder all the way into the slot with the cover of the plate holder facing the rotor chamber. To ensure that the teeth on the plate holder engage the clutch in the plateshift drive mechanism, hold the plate holder in place and press the P L A T E H O L D E R D R I V E button. After the edge of the plate holder is in past the slot, release the P L A T E H O L D E R D R I V E button and close the plate holder slot. The plate position dial should then be at zero. 12. The E X P O S U R E T I M E dial (A-14) is set at 10 sec , which is determined by previous exposure testings. The E X P O S U R E I N T E R V A L switch is turned to 8 min. or 16 min. , depending on the concentration and molecular weight of the H A solution being tested. 13. The operating speed is set at 52,640 rpm using the speed selector knob E X P E R I M E N T A L P R O C E D U R E / 86 (A-11). Brake (B-8) is set at S L O W . 14. Set timer (A-15) for 4 hours. The timer will be activated when the V O L T A G E C O N T R O L knob(A-12) is turned clockwise (i.e. when voltage is greater than 0 volt). 15. When the vacuum gauge is = 1 micron, set drive current to =5 amps (A- l ) by turning the V O L T A G E C O N T R O L knob clockwise. The timer is turned on and the E X P O S U R E T I M E dial (A-14) will start revolving counterclockwise. After the needle in the ammeter (A-l) stablizes, increase the voltage by turning the voltage control knob clockwise to 12-13 amps. Mainta in the drive current between 12 and 13 amps with the voltage control knob until 90% speed (=47,000 rpm in A-3) is attained. Then reduce the current to 5 amps. The automatic speed control system will take over. 16. W h e n the rotor speed is at =20,000 rpm, open the water inlet to the light source by turning the L I G H T S O U R C E W A T E R V A L V E (B-7) counterclockwise (until tight). Make sure that the C A M E R A selector switch (C-26) is at Schlieren camera. Al ign the slot in the W A T E R V A L V E with the L I G H T S O U R C E switch (B-9). Then turn the light source intensity switch (B-13) to H I and turn the L I G H T S O U R C E switch on. T h e L I G H T S O U R C E pilot light (C-18) will come on. After the light comes on for about 10 sec , turn light intensity switch to L O (start on HI , run on L O to ensure long lamp life). 3.8.3. Taking Photographs E X P E R I M E N T A L P R O C E D U R E / 87 1. As the rotor speed approaches the 2/3 value (=35,000 rpm), turn the P L A T E H O L D E R D R I V E switch (C-22) to the O U T position. T u r n the A U T O M A T I C P H O T O switch (C-21) to O N . T h e n turn the E X P O S U R E T I M E dial (A-14) counterclockwise until the shutter clicks open; back off until the shutter clicks shut and hold the E X P O S U R E T I M E dial steady at this position. Then turn off the A U T O M A T I C P H O T O switch and turn the P L A T E H O L D E R D R I V E switch to I N . While holding the E X P O S U R E T I M E dial steady, push the P L A T E H O L D E R D R I V E button (C-23) to move the plate holder to the No. 1 position on the plate position dial (C-5). A t zero time (when the rotor speed is at =35,000 rpm), turn on the A U T O M A T I C P H O T O switch and release the E X P O S U R E T I M E dial. The shutter will click open, indicating that the first photograph has been taken. The next photograph will be taken after the interval specified by the E X P O S U R E I N T E R V A L setting (8 min. or 16 min.) 2. A max imum of 5 photographs can be taken on the photographic plate. F o r each sedimentation velocity experiment, 10 to 15 photographs are taken. To change the photographic plate holder, turn off the A U T O M A T I C P H O T O switch. T u r n the P L A T E H O L D E R D R I V E switch to O U T . Push the P L A T E H O L D E R D R I V E button until the plate holder butts against the plate holder slot cover. Pull down the cover for the slot and push the P L A T E H O L D E R D R I V E button until the plate holder stops moving out. Take the plate holder out and E X P E R I M E N T A L P R O C E D U R E / 88 place another one in the slot. Then repeat step 11 in Section 3.6.2. T u r n on the A U T O M A T I C P H O T O switch and turn the P L A T E H O L D E R D R I V E switch to IN . 3. A procedure for calculating sedimentation coefficient from the photographic plate is shown in Appendix A . 3.8.4. Ending a Sedimentation Velocity Run 1. Set brake (B-8) at R A P I D . Terminate a run by turning T I M E R dial (A-15) to O F F . T h e diffusion pump is automatically shut off. 2. T u r n off light source (B-9) and shut the water inlet to the light source by turning the L I G H T S O U R C E W A T E R V A L V E clockwise (until tight). 3. T u r n off the R E F R I G E R A T I O N switch (B-3) and the R T I C system ( C - l l ) . 4. T u r n off the A U T O M A T I C P H O T O switch (C-21) and take out the plate holder. When the rotor comes to complete stop, go to step 5. 5. Set braking rate at S L O W . 6. T u r n off the V A C U U M P U M P ( B - l l ) and open the air valve by turning B-5 counterclockwise. Before opening the vacuum chamber, allow 2 min. for the vacuum to be released completely. 7. T u r n off the D I F F U S I O N P U M P (B-10) and close the water valve by turning B-6 clockwise. 8. T u r n V O L T A G E C O N T R O L knob (A-12) counterclockwise to zero. 9. Open the rotor chamber (B-4) and remove the rotor. E X P E R I M E N T A L P R O C E D U R E / 89 10. Close the rotor chamber and turn main power off. 11. The sample cell is pushed out of Side 1 of the rotor by means of a plastic rod. The screw ring is unscrewed by the torque wrench. The cell is then taken apart. The different parts are rinsed with distilled water and then dried with acetone. C H A P T E R 4. R E S U L T S A N D D I S C U S S I O N The experimental results obtained for the various experiments performed are presented and discussed in this chapter. The sample calculations leading to the evaluation of the results are presented in Appendix A . Detailed experimental data are listed in Appendix B . 4.1. HYALURONIC ACID CONCENTRATION DETERMINATION The uronic acid carbazole method (Bitter & M u i r , 1962) was used to determine the concentration of H A . Absorbance data for 5 concentrations of glucuronolactone standards are presented in Table 4.1 and Figure 4.1. The indicated error in absorbance represents 2 standard deviations. The absorbance data are fitted by the least-squares method to give the calibration line ABS = -0 .03554 + (0.01651 ± 0.00087) X c [4.1] T a b l e 4.1 Results of the uronic acid carbazole test Concentration of glucuronolactone, f ig/mL * Absorbance 0. 0.0186* 9.85 0 . 1 2 6 5 ± 0 . 0 0 9 0 19.70 0.2984 + 0.0050 29.55 0.4423 + 0.0052 39.40 0.6116 + 0.0016 49.25 0.7831 + 0.0098 * average of 3 measurements at 525 nm *read against cone. H 2 S O ( , 90 R E S U L T S A N D D I S C U S S I O N / 91 O .0 Concentration of Glucuronolactone, /xg/mL Figure 4.1 Relationship between the absorbance and the concentration of glucuronolactone. R E S U L T S A N D D I S C U S S I O N / 92 where ABS is the absorbance at 525 nm and c is the concentration of glucuronolactone in Mg/mL; the indicated error, as throughout this work unless otherwise stated, represents the 95% confidence interval (see Sample Calculations, Appendix A) . The structure of hyaluronic acid consists of repeating disaccharide units of D-glucuronic acid residue and N-acetylglucosamine residue. When hyaluronic acid is treated with concentrated boric acid (sodium borate in cone. H 2 S O a ) , the glucosidic bonds linking the residues are broken and the D-glucuronic acid residues form complexes with boric acid (Hough & Richardson, 1965). T h e complexes then react with carbazole to give a purple color. The formula weight of the sodium salt of the repeating disaccharide unit is 401.3. Glucuronolactone, which is the anhydride of D-glucuronic acid, has the same formula weight (176.1) as the glucuronic acid residue in the polymer. Therefore, the weight fraction of the disaccharide repeating unit in hyaluronic acid to glucuronolactone is 401.3/176.1 = 2.279. When the concentration of hyaluronic acid solution is determined by the uronic acid carbazole method, the concentration obtained from the calibration line (Eqn [4.1]) is in terms of glucuronolactone concentration. T h e glucuronolactone concentration is then multiplied by the factor 2.279 to give the concentration of the hyaluronic acid solution. 4.2. FRACTIONATION OF HYALURONIC ACID The results of the fractionation experiment (Section 3.3.4) are presented in Table 4.2. The intrinsic viscosities [77] of the hyaluronic acid fractions, which R E S U L T S A N D D I S C U S S I O N / 93 T a b l e 4.2 Results of the large scale fractionation experiment Eluant subfraction H A recovery, [77J [NaCl], M volume, m L mg m L / g M . W . X 1 0 5 0. 0.10 0.175 0.25 612 = 0 1. 505 2. 502 = 0 3. 500 4. 502 5. 500 6.. 501 7. 501 8. 500 1. 500 4.027 2. 500 3.896 3. 500 4. 500 5. 500 6. 500 7. 500 8. 500 1. 500 42.67 2. 500 33.60 3. 500 18.95 4. 500 15.20 5. 500 12.48 6. 500 7. 500 8. 500 9. 500 10. 500 1340 6.99 R E S U L T S A N D D I S C U S S I O N / 94 0.325 0.40 0.50 1. 500 300.35 2. 500 128.44 3. 500 74.73 4. 500 54.10 5. 500 46.61 6. 500 41.09 7. 500 31.97 8. 500 28.59 9. 500 315.53 10. 500 22.48 11. 500 7.947 12. 500 5.235 13. 500 14. 500 1. 500 60.27 2. 500 11.40 3. 500 11.59 4. 500 9.396 5. 500 6. 500 7. 500 8. 500 1. 500 46.63 2. 500 3.93 3. 500 4. 500 = 0 5. 500 •1530 8.44 unfractionated 1331.1 H A 1830 11.1 1500 8.19 1880 11.6 2260 15.5 R E S U L T S A N D D I S C U S S I O N / 95 were obtained by extrapolating (17—TJ 0 ) /r\0 • c to c=0, are shown in Figure 4.2. F o r comparison, the intrinsic viscosity of the unfractionated hyaluronic acid was also determined and shown in Figure 4.2. According to Cleland & W a n g (1970), for [57] values above 1400 raL/g, correction to zero shear rate was necessary and was done by the following equation derived by the authors: [ T J ] Z S / [ T J ] = 1 + ([7?] - 1 4 0 0 ) / 6 2 5 0 [4.2] where l^ lgg m m ^ S is the corrected intrinsic viscosity at zero shear rate. The molecular weights M of hyaluronic acid in 0 . 2 M N a C l were evaluated by the Mark-Houwink equation (Cleland & Wang , 1970): [ T ] ] z s = 0.228 M 0 - 8 1 6 [4.3] F r o m Table 4.2, since no H A was washed out by the weak buffer (0 .M N a C l , 2 m M phosphate buffer, p H 7.30), the H A was tightly bound to the cellulose ion-exchanger before elution was carried out. The amount of low M . W . fractions was very little, as obvious from the small amount of H A collected from the 0 .175M N a C l eluate. The carbazole test (done in triplicate) was performed only on the 0 . 1 M eluate, subfraction 2 because the amount of H A collected in the 0 .175M eluate was very small. The p H of the eluate gradually decreased from about 8.0 at the beginning of the elution to about 7.3 for the 0 .175M eluate. The p H then stayed at about 7.3 in the remaining elution period. Since the p K a of the D E 2 3 cellulose is 9.5 and that of H A is below 7.30, therefore, throughout the elution period, the cellulose was positively charged and the H A was negatively charged. The [77] of each of the H A fractions collected was lower than that of the unfractionated material. In fact, the weight average [77] for the major fractions collected was 1625 m L / g , which was substantially lower than the R E S U L T S A N D D I S C U S S I O N / CO CO 1 1 ' 1 ' 1 1 1 1 1 0.0 0.3 0.6 0.9 1.2 1.5 Concentration of HA, mg/mL Figure 4.2 Intrinsic viscosity plot for the H A Fractions R E S U L T S A N D D I S C U S S I O N / 97 [77] value of 2260 m L / g for the unfractionated hyaluronic acid. Obviously, degradation of H A occurred during the fractionation process. In general, for each eluant salt concentration, the concentration of hyaluronic acid in the eluate decreased with the increase in the volume of eluate. Elution with 0 .325M N a C l was stopped after eluate subfraction 8 was collected and the column was left overnight. The amount of hyaluronic acid collected in subfraction 9 was very large compared to other subfractions. The reason was probably because degradation of H A occurred in the column. Some of the H A originally adsorbed m a y have been degraded by bacteria into smaller molecular weight fractions which then became unadsorbed. Also, the column was not tightly packed. The height of the column decreased from about 14.0 cm at the beginning of the fractionation to about 9.5 cm after the elution with 0 .325M N a C l eluant was completed. A t the beginning of the elution, since the column was not tightly packed, some regions in the column bed might not be reached by the buffer. Convective flow of the eluate might be present in the column and the H A in the regions unreached by the buffer were not eluted. A s elution continued, the bed was packed to a fixed volume. The H A in regions previously unreached by the buffer were then eluted. The reason why the [77] for the 0 . 4 M N a C l fraction is lower than that of the 0 .325M subfraction 9 is not fully known but m a y be attributed to the degradation of H A and the convective flow of eluate. The overall recovery of H A was at least 95.7% (i.e. 1.33 g/1.39 g). R E S U L T S A N D D I S C U S S I O N / 98 4.3. ACID HYDROLYSIS OF HYALURONIC ACID Three H A fractions were obtained by hydrolysing H A with hydrochloric acid for 15 min., 1 hour and 2 hours. The intrinsic viscosity plot for the three fractions are shown in Figure 4.3. The intrinsic viscosities and the molecular weights of the three acid hydrolysed H A Fractions are tabulated in Table 4.3. A s expected, the molecular weight of the Fractions decreases with the duration of acid hydrolysis. 4.4. FRACTIONATION OF ACID HYDROLYSED HA The results of the fractionation of hyaluronic acid hydrolysed for 15 min. are tabulated in Table 4.4. The intrinsic viscosity plot for the 1 5 m A H - 0 . 3 2 5 M Fraction and unfractionated acid hydrolysed H A is shown in Figure 4.4. F r o m Table 4.4, when the H A solution was mixed with the cellulose, the H A were tightly bound and were not eluted by the 2 m M phosphate buffer. Since the 5 M . W . of the unfractionated acid hydrolysed H A ( M . W . = 2 . 0 2 X 1 0 ) was Table 4.3 Intrinsic viscosity and molecular weight of 1 5 m i n A H , l h r A H and 2 h r A H Fractions Fraction Intrinsic viscosity, M . W . m L / g X 1 0 15 min A H 413 1.65 l h r A H 233 0.819 2hrAh 144 0.454 R E S U L T S A N D D I S C U S S I O N / 99 C O O to d o O d o , o -x—x-HA Fraction A = 15minAH x = lhrAH • = 2hrAH o d 0.0 0.7 1.4 2.1 2.8 Concentration of HA, mg/mL 3.5 Figure 4.3 Intrinsic viscosity plot for the acid hydrolysed Fractions. R E S U L T S A N D D I S C U S S I O N / 100 Table 4.4 Results of the fractionation of acid hydrolysed H A Eluant subfraction H A recovery, [77] M . W . [NaCl], M volume, m L m g m L / g X 1 0 5 120 = 0 0.1 1. 250 = 0 2. 250 3. 250 4. 235 = 0 0.175 1. 250 1.84 2. 250 1.46 3. 250 4. 238 0.25 1. 250 9.93 2. 250 4.59 3. 250 3.36 4. 250 2.52 0.325 1. 250 203.06 2. 250 27.58 3. 250 11.98 4. 227 7.46 5. 250 11.17 6. 250 1.71 7. 250 1.71 8. 244 = 0 0.4 1. 250 4.96 2. 250 1.49 3. 250 1.39 4. 250 = 0 0.5 1, 250 ==0 2- 250 = 0 3. 250 = 0 296.2 unfractionated H A V 475 1.96 J 486 2.02 R E S U L T S A N D D I S C U S S I O N / 101 O 1 ' i ' i 1 i • i 1 r 0.0 1.2 2.4 3.6 4.8 6.0 Concentration of HA, mg/mL Figure 4.4 Intrinsic viscosity plot of the 1 5 m A H - 0 . 3 2 5 M Fraction and unfractionated H A . R E S U L T S A N D D I S C U S S I O N / 102 substantially lower than that of the unfractionated H A in the large scale 5 fractionation ( M . W . = 15 .5X10 , Section 3.3.4), it was expected that a large fraction of H A would be eluted by the low [NaCl] eluants. However, the amount of H A eluted by the 0 . 1 M and 0 .175M N a C l eluants was very small, and the amount of H A eluted by 0 .25M and 0 . 4 M eluants was small compared to that by the 0 .325M eluant. It therefore appeared that the H A molecules were tightly adsorbed to the cellulose at the beginning of the experiment and were desorbed when the ionic environment was above 0 . 3 M [NaCl]. The recovery of H A was about 91.3%. The [TJ] of the major fraction collected (15mAH-0.325M) is slightly lower than that of the unfractionated H A material. Therefore, the degradation of H A during elution was not extensive. Unfortunately, the samples of the 1 5 m A H - 0 . 2 5 M Fraction were carelessly discarded after the sedimentation velocity experiment. A s a result, the [77] for the 1 5 m A H - 0 . 2 5 M Fraction was not determined. 4.5. SEDIMENTATION COEFFICIENT After dialysis with 0 . 2 M N a C l solutions for at least 2 days, the hyaluronic acid solutions made up from all the H A Fractions were diluted to different concentrations with the 0 . 2 M N a C l dialysate. T h e sedimentation velocity of each of the H A solutions was then measured. The sedimentation coefficient for each H A solution was calculated from E q n [2.41]. The results are tabulated in Table 4.5 and plotted in Figures 4.5 to 4.7. The plot of sedimentation velocity as a function of concentration from Laurent et al. (1960) is shown in Figure 4.8. In Table 4.5, S 0 „ is the sedimentation coefficient of the solution at 2 0 ° C . R E S U L T S A N D D I S C U S S I O N / 103 T a b l e 4.5 Sedimentation coefficient and hydraulic conductivity of all H A Fractions Run Fraction M . W . Concentration, 1 0 ± J X S 2 ( ) , lOLyjXK', XIO'^ m g / m L s c m V d y n - s A l 0 .25M 6.99 0.3542 4 . 1 8 ± 0 . 1 6 36.311.4 A 2 0.7084 3 . 1 5 ± 0 . 0 7 13.7 + 0.3 A 3 1.0626 2 . 6 7 ± 0 . 0 6 7.7310.17 A 4 1.4168 2 . 2 8 ± 0 . 0 2 4.9510.05 A 5 1.7710 2 . 1 0 ± 0 . 0 5 3.6410.09 B l 0 .325M 8.44 0.4601 3 . 6 5 ± 0 . 1 1 24.410.7 B2 0.9202 2 . 4 7 ± 0 . 0 4 8.2510.12 B3 1.3803 2 . 0 5 ± 0 . 0 3 4.57 + 0. OS B4 1.8404 1.9010.06 3.1710.10 B5 2.3005 1 . 5 5 ± 0 . 0 2 2.0610.03 B6 2.7606 1 . 5 0 ± 0 . 0 4 1.6710.05 C I 0.325M-9 11.1 0.4840 3.2210.13 20.510.8 C2 0.9680 2.4710.04 7.8510.12 C3 1.4520 1.8810.06 3.9810.13 C4 1.9360 1.7010.02 2.6910.04 C5 2.4200 1.6010.03 2.0410.04 D l 15minAH 1.65 0.5916 2.51 + 0.11 13.010.6 D2 1.1832 2.1210.06 5.5110.15 D3 1.7748 1.8610.03 3.2210.04 D4 2.3664 1.5210.08 1.9710.10 D5 2.9580 1.4210.04 1.47+0.04 R E S U L T S A N D D I S C U S S I O N / 104 E l lh t -AH 0.819 0.6167 1.6410.56 8.1912.78 E 2 1.2333 1.9910.06 4.9510.16 E 3 1.8500 1.7410.10 2.8910.17 E 4 2.4666 1.4410.06 1.7910.07 E 5 3.0833 1.4510.06 1.4510.06 F l 2 h r A H 0.454 0.6109 1.9910.79 10.013.95 F 2 1.2218 1.65+0.12 4.1410.30 F 3 1.8326 1.5210.06 • 2.55+0.09 F 4 2.4435 1.3810.09 1.7310.11 F 5 3.0544 1.2210.11 1.2310.11 G l 1 5 m A H - 0 . 3 2 5 M 1.96 1.0954 2 . 2 6 ± 0 . 3 0 6 .3510.85 G2 1.6431 1.7010.05 3 .1910 .09 G3 2.1908 1.5610.05 2 .1910 .07 G 4 2.7385 1.44±0.03 1.6110.03 G5 3.2862 1.3010.07 1.2110.07 R E S U L T S A N D D I S C U S S I O N / 105 Figure 4.5 Sedimentation coefficient as a function of concentration for 0 .25M, 0 .325M and 0.325M-9 Fractions. R E S U L T S A N D D I S C U S S I O N / 106 O o TT1 »0 O <D O o • f H •a CO CO CM HA Fraction o = 15minAH • = lhrAH x = 2hrAH o = 15mAH-0.325M 0.0 0.7 1.4 2.1 2.8 Concentration of HA, mg/mL 3.5 Figure 4.6 Sedimentation coefficient as a function of concentration for l o m i n A H , l h r A H , 2 h r A H and 1 5 m A H - 0 . 3 2 5 M Fractions. R E S U L T S A N D D I S C U S S I O N / 107 O q T T 1 l O Ifl ~ O (L> • P H O o O •s CO CO o • — • = A = O = HA Fraction 0.25M 0.325M 0.325M-9 15minAH lhrAH 2hrAH 15mAH-0.325M 0.0 0.7 1.4 2.1 2.8 Concentration of HA, mg/mL 3.5 Figure 4.7 Sedimentation coefficient as a function of concentration for all Fractions. R E S U L T S A N D D I S C U S S I O N / 108 CO H I O q Figure 4.8 Sedimentation data of Laurent et al. (1960). R E S U L T S A N D D I S C U S S I O N / 109 Since the uncertainty in S^Q for Runs E l , F l and G l was high, the data points for the three runs were not included in the figures. The sedimentation patterns of the Fractions are shown in Figures 4.9 to 4.11, in which the sedimentation direction is from left to right. A s shown in Figure 4.7, the sedimentation coefficient decreases with concentration, which is in agreement with Laurent et al. (1960) and Preston et al. (1965). A s the H A concentration increases, the entanglement between individual molecules becomes greater. Therefore, the resistance to the flow of solvent through the H A network becomes higher and the sedimentation rate is lower. In view of the results of Laurent et al. (1960), it was expected that at high H A concentrations (above 2 mg/mL) , the different Fractions of H A would sediment at the same slow rate, and at low H A concentrations, the higher M . W . Fraction would sediment faster than the lower M . W . Fraction. A t low concentrations, the H A molecules sediment independently and therefore the higher M . W . molecules sediment faster than the lower M . W . molecules. O n the other hand, at high concentrations, since the H A molecules (low or high M . W . ) entangle with each other and form a three dimensional network, the H A molecules will sediment at the same slow rate. F r o m Figure 4.7, at high H A concentrations (> 2.1 mg/mL) , the sedimentation coefficient curves for all H A Fractions are converging. A t lower concentrations, two different trends in sedimentation coefficient were found — for the fractionated, non-acid hydrolysed Fractions (0.25M, 0 .325M and 0.325M-9), the lower M . W . Fraction sediments faster than the higher M . W . H A Fraction; and for the acid hydrolysed Fractions (15minAH, l h r A H and 2 h r A H ) , the higher M . W . Fraction sediments faster than R E S U L T S A N D D I S C U S S I O N / 110 Fraction: 0 .25M c = 0.7084 m g / m L t= 64 min 0 .325M 0.9202 m g / m L 64 min 0 .325M 0.9202 m g / m L 112 min 0.325M-9 0.4840 m g / m L 64 min Fraction: 0 .25M c = 1.4168 m g / m L r= 64 min 0 . 3 2 5 M 1.3803 m g / m L 64 min 0 .325M 1.3803 m g / m L 112 min 0.325M-9 1.4520 m g / m L 64 min Figure 4.9 Sedimentation patterns of the 0 .25M, 0 .325M and 0.325M-9 Fractions. R E S U L T S A N D D I S C U S S I O N / 111 Fraction: 1 5 m i n A H c = 1.1832 m g / m L t= 64 min l h r A H 1.2333 mg/mL 64 min 2 h r A H 1.2218 m g / m L 56 min Figure 4.10 Sedimentation patterns of the acid hydrolysed H A Fractions. R E S U L T S A N D D I S C U S S I O N / 112 Fraction: 1 5 m A H - 0 . 2 5 M c = 1 unit c t— 64 min 1 5 m A H - 0 . 3 2 5 M 1.0954 m g / m L 64 min 1 5 m A H - 0 . 3 2 5 M 1.6431 m g / m L 64 min 1 5 m A H - 0 . 3 2 5 M 2.7385 m g / m L 64 min Fraction: 1 5 m A H - 0 . 2 5 M c = 1 unit c t= 32 min 1 5 m A H - 0 . 3 2 5 M 1.0954 m g / m L 32 min 1 5 m A H - 0 . 3 2 5 M 1.6431 m g / m L 144 min 1 5 m A H - 0 . 3 2 5 M 2.7385 m g / m L 128 min Figure 4.11 Sedimentation patterns of the 1 5 m A H - 0 . 2 5 M and 1 5 m A H - 0 . 3 2 5 M Fractions. R E S U L T S A N D D I S C U S S I O N / 113 the .lower M . W . Fraction. The former trend in sedimentation coefficient is opposite to the trend found by Laurent et al. (Figure 4.8) and other workers (Preston et al. , 1965; Silpananta et al. , 1968). The difference between the 0 .325M curve and the 0.325M-9 curve is small (about 7 % at c=1.4 mg/mL) . However, the difference between the 0 .25M curve and the 0.325M-9 curve is large (about 18% at 1.4 mg/mL) . Since the Fractions were in isotonic saline solutions (0.2M NaCl) , the molecules of the Fractions were expected to form random coils and have similar shape. The reason for the difference in the results for the fractionated, non-acid hydrolysed fractions and that of Laurent et al. (1960) is not known, but may be attributed to systematic errors in the dilution of samples and in measuring the concentration of samples, etc. Nevertheless, when the sedimentation coefficient curves of all Fractions are looked at, the H A molecules of the high 5 M . W . Fractions (6.99 to 11 .1X10 ) sediment faster than those of the low M . W . 5 Fractions (0.454 to 1 .96X10 ), which is in agreement with Laurent et al. (1960). F r o m Figures 4.9 to 4.11, it can be seen that the sharpness of the Schlieren peak, and therefore the sharpness of the solvent/solution boundary, varies directly with concentration and molecular weight. F o r the fractionated, non-acid hydrolysed H A Fractions (Figure 4.9), the Schlieren peaks were sharp and symmetrical , so the use of E q n [2.41] to evaluate the sedimentation coefficient was justified. However, for the acid hydrolysed H A Fractions (Figure 4.10), the Schlieren peaks broadened out very quickly, especially in the low concentration samples, which explains why the uncertainty in the sedimentation coefficients for the low concentration samples (Runs D l , E l and F l in Table R E S U L T S A N D D I S C U S S I O N / 114 4.5) is very high. The broad Schlieren peaks also imply that the range of molecular weight in the samples is large. In all the sedimentation runs for the acid hydrolysed Fractions, except Runs D4 and D5 in Table 4.5, the Schlieren peaks are skewed to the right. In fact, the degree of skewness appears to v a r y directly with the duration of acid hydrolysis and indirectly with concentration. A s the duration of acid hydrolysis increases, the average M . W . decreases, and the range of M . W . of the H A molecules increases. Therefore, the Schlieren peaks broadened out quickly, and the degree of skewness increased with the duration of acid hydrolysis. Figure 4.12 depicts the sedimentation pattern and the concentration profile of the acid hydrolysed H A Fractions. Since the Schlieren peak is skewed to the right, and higher M . W . H A molecules sediment faster than lower M . W . H A molecules, the lower M . W . H A molecules trail behind the higher M . W . ones and form a tail on the left of the concentration profile. Also, the position of the Schlieren peak, r , is farther away from the axis of rotation than the position of the theoretical infinitely sharp boundary, rt, as defined in Section 2.5.2. T h e position of r # is where the shaded areas on the two sides of r # in (a) and (b) of Figure 4.12 are equal. The distance between r and increases with time, as shown in Figure 4.12. Therefore, the sedimentation coefficients calculated from E q n [2.41] for Runs D l to F 5 in Table 4.5 are higher than the true sedimentation coefficients which, theoretically, can be calculated from E q n [2.40]. In other words, the higher M . W . molecules in the acid hydrolysed Fractions are overemphasized. Also, when the degree of skewness in the Schlieren peak is higher, the difference between r and is larger. Thus , the difference between R E S U L T S A N D D I S C U S S I O N / 115 Figure 4.12 Sedimentation pattern and concentration profile of acid hydrolysed H A Fractions, (a) time tu and (b) time t2, where t2>t-i. R E S U L T S A N D D I S C U S S I O N / 116 the measured S^Q and the true S^Q is larger for Schlieren peaks with higher degree of skewness. Since the degree of skewness of the Schlieren peaks increases with the duration of acid hydrolysis, or decreases with molecular weight, the trend found in the sedimentation coefficient for the acid hydrolysed Fractions, i.e. the higher M . W . Fraction has a higher sedimentation coefficient than the lower M . W . Fraction, is expected to be correct although the sedimentation coefficients for Runs D l to F 5 , listed in Table 4.5, are higher than the true values. A s for the fractionated acid hydrolysed Fractions ( 1 5 m A H - 0 . 2 5 M and 15mAH-0 .325M) , the Schlieren peaks of the 1 5 m A H - 0 . 2 5 M Fraction were markedly skewed, and the peaks flattened out very quickly with time (Figure 4.11). Therefore, the sedimentation coefficient of this Fraction was not measured. O n the other hand, the Schlieren peaks of the 1 5 m A H - 0 . 3 2 5 M Fraction were symmetrical and sharp, except for the lower concentration samples (Runs G l and G 2 in Table 4.5) in which the peaks were slightly skewed to the right. Nevertheless, the sedimentation coefficients measured for the 1 5 m A H - 0 . 3 2 5 M Fraction were expected to be very close to the true values, for reasons discussed in Section 2.5.3. For Run G l , because the sedimentation photographs were not clear, the error interval in S^Q was high. In general, at each H A concentration, the 1 5 m A H - 0 . 3 2 5 M Fraction (M.W. = 1.96X 10 5 ) has a lower S 2 Q than the 5 1 5 m i n A H Fraction (M.W. = 1 .65X10 ), as shown in Figures 4.6 and 4.7. This finding is in agreement with the discussion above that for the 1 5 m i n A H Fraction, because the Schlieren peaks are skewed to the right, the true S^Q for the 1 5 m i n A H Fraction are lower than the measured values. R E S U L T S A N D D I S C U S S I O N / 117 4.6. HYDRAULIC CONDUCTIVITY The hydraulic conductivity, K', for each H A solution was calculated from E q n [2.10] and is listed in Table 4.5. T h e conductivity data is fitted by least squares method to give straight lines represented by K' = Ac'B [4.4] where K' is in c m 4 /dyn • s and c is in m g / m L . The conductivity data for Runs E l , F l and G l were not used for line fitting because the error intervals were very high. The values of A and B in E q n [4.4] for the H A Fractions are shown in Table 4.6. The conductivity data as a function of concentration are plotted in Figures 4.13 to 4.15. Ethier (1986), using E q n [2.10], computed the specific hydraulic conductivity, K, of H A ( M . W . = 1 to 13X10 ) from past sedimentation data (Preston et al. , 1965; Fessler, 1960b; Laurent & Pietruszkiewicz, 1961; Laurent et al. , 1960). The results were fitted by the equation K = 2.92 X 1 0 " 1 6 c " 1 ' 4 7 [4.5] T a b l e 4.6 Values of A and B in E q n [4.4] for all H A Fractions Fraction M . W . X 1 0 5 1 0 1 0 X A B 0 . 2 5 M 6.99 8.28 1 . 4 3 ± 0 . 0 4 0 .325M 8.44 7.50 1 . 5 0 ± 0 . 0 7 0.325M-9 11.1 7.17 1 .4610.10 1 5 m i n A H 1.65 6.62 1.3610.14 l h r A H 0.819 6.59 1.3810.33 2 h r A H 0.454 5.50 1.3210.22 1 5 m A H - 0 . 3 2 5 M 1.96 6.44 1.3910.17 R E S U L T S A N D D I S C U S S I O N / 118 Figure 4.13 Hydraul ic conductivity data for 0 .25M, 0 .325M and 0.325M-9 Fractions. For comparison, the results of Ethier (1986) is included. R E S U L T S A N D D I S C U S S I O N / 1 CO to a HA Fraction x = 15minAH o = lhrAH v = 2hrAH a = 15mAH-0.325M • = Ethier (1986) J i i i i i i J I I L 10 10 101 Concentration of HA, mg/mL Figure 4.14 Hydraulic conductivity data for all acid hydrolysed Fractions. R E S U L T S A N D D I S C U S S I O N / 120 oo o a HA Fraction o = 0:25M A = 0.325M + = 0.325M-9 x = 15minAH o = lhrAH v = 2hrAH a = 15mAH-0.325M • = Ethier (1986) J i i i i i I j i ' • ' • 10"1 io° i d Concentration of HA, mg/mL Figure 4.15 Hydraul ic conductivity data for all H A Fractions. R E S U L T S A N D D I S C U S S I O N / 1 2 1 where K is in c m 2 and c is in g /mL. Since K'=K/i\, where rj is the solvent viscosity, E q n [ 4 . 5 ] can be converted to the form K' = 7 . 5 1 X 1 0 " 1 0 c'1A1 [4.6] where K' is in c m V d y n ' S and c is in mg /mL. For comparison, E q n [4 .6] is also plotted in Figures 4 . 1 3 to 4 . 1 5 . F r o m Figures 4 . 1 3 to 4 . 1 5 , the conductivity lines for the Fractions have similar slopes with the line represented by E q n [4 .6]. The hydraulic conductivity decreases with concentration, because as concentration increases, the entanglement between the H A molecules becomes larger, and the resistance to the flow of solvent is higher. Also, the lines are converging at high concentrations (> 2 mg/mL) , which is as expected because the higher and lower M . W . H A molecules have more or less the same entanglement with each other at high concentrations, i.e. the H A molecules entangled with each other to form a three-dimensional molecular network. 5 A t lower concentrations, the higher M . W . group ( 6 . 9 9 to 1 1 . 1 X 1 0 ) has a 5 higher hydraulic conductivity than the low M . W . group ( 0 . 4 5 4 to 1 . 9 6 X 1 0 ). This finding is consistent with the trend in S^Q obtained by Laurent et al. ( 1 9 6 0 ) from which K' can be determined as shown in E q n [ 2 . 1 0 ] , One explanation for this result is that the high M . W . molecules are more compact than the low M . W . molecules, and therefore they may have less resistance to the flow of solvent, i.e. they may behave in a more discrete manner. Another interpretation is that at the same low concentration, since there are more low M . W . molecules than high M . W . molecules, the degree of entanglement between molecules is higher for the low M . W . molecules. Wi th more entanglement between molecules, the resistance to the flow of solvent is therefore higher. R E S U L T S A N D D I S C U S S I O N / 122 In addition, since the sedimentation coefficients measured for the acid hydrolysed H A Fractions are higher than the true values because of skewed Schlieren peaks, the hydraulic conductivities, evaluated from E q n [2.10], for the acid hydrolysed H A Fractions are therefore higher than the true conductivity values. It is therefore expected that the true positions of the conductivity lines for the acid hydrolysed Fractions be lower in Figure 4.15, and the difference between the lines of the lower M . W . group (and Ethier's line) is even larger. CHAPTER 5. CONCLUSIONS AND RECOMMENDATIONS In this study, hyaluronic acid has been fractionated by ion-exchange chromatography with DEAE-cel lulose . The hyaluronic acid adsorbed was eluted with N a C l solutions by stepwise elution method. Prel iminary experiments had revealed that molecular fractionation was attained when the p H of the eluant and the column was controlled by 2 m M phosphate buffer to within 7 to 8. A t each N a C l concentration, the amount of hyaluronic acid eluted decreased with the eluate volume. In a formal fractionation experiment, molecular weight fractionation was partially successful. The results obtained in the preliminary fractionation experiment could not be reproduced, partly because the elution process was not continuous. Because of the long time taken for the elution, degradation of hyaluronic acid occurred, which was evident from the large drop in the weight average [TJ] after the fractionation experiment. In general, the amount of hyaluronic acid eluted at each N a C l concentration decreased with the eluate volume, and the M . W . of the H A fraction increases with the N a C l concentration 5 of the eluant. Three distinct molecular weight fractions, M . W . = 6.99 to 11 .1X10 , determined from [77] data, were obtained from the fractionation. Three hyaluronic acid fractions of lower molecular weight were obtained by acid hydrolysing the previous fractions for 15 min. , 1 hour and 2 hours. The 5 molecular weight of the fractions (0.454 to 1 .65X10 ) decreased with the duration of acid hydrolysis. Also, from sedimentation experiments, the range of 123 C O N C L U S I O N S A N D R E C O M M E N D A T I O N S / 124 M . W . in the acid hydrolysed fractions increased with the duration of acid hydrolysis. Another fractionation experiment was performed on hyaluronic acid hydrolysed for 15 min. The hyaluronic acid was found to be eluted in one major fraction. This finding showed that the results of the fractionation by ion-exchange chromatography was not consistent. Hyaluronic acid was tightly adsorbed to the cellulose until the ionic environment in the column was above 0 . 3 M [NaCl]. F r o m 5 sedimentation experiments, the major fraction obtained ( M . W . = 1.96X 10 ) has a narrow range of molecular weight. Sedimentation experiments performed on all the H A fractions have revealed that sedimentation coefficient, varies indirectly with concentration. This observation is in accordance with expectation because the entanglement between molecules, and therefore the hydraulic resistance to solvent flow, increases with concentration. Also, the S^Q curves of all the fractions converged at high concentration, because at high concentration, a three-dimensional molecular network was formed and the entanglement between molecules was the same for the high and the low M . W . fractions. However, at lower concentrations, two trends in S^Q were found — for the fractionated, non-acid hydrolysed H A fractions, S^Q decreased with M . W . and for the acid hydrolysed fractions, increased with M . W . The former trend in S does not agree with past sedimentation data. The A u reason is unknown and may be attributed to experimental errors. If the fractionated non-acid hydrolysed fractions are treated as a high M . W . group ( M . W . = 6.99 to 1 1 . 1 X 1 0 5 ) and the acid hydrolysed fractions as a low M . W . C O N C L U S I O N S A N D R E C O M M E N D A T I O N S / 125 5 group ( M . W . = 0.454 to 1.96X10 ), the S 2 Q curves of the low M . W . group fall below those of the high M . W . group, which is in agreement with past sedimentation data. In fact, since the Schlieren peaks of the acid hydrolysed fractions were skewed to the right, the S^Q calculated for the acid hydrolysed fractions were higher than the true values. Therefore, the actual difference between the curves of the high M . W . group and those of the low M . W . group will be even higher. The hydraulic conductivities, K', of all the hyaluronic acid fractions have been calculated from the S^Q data. The results revealed that the K' for all the H A fractions varied indirectly with concentration. The reason for this finding is that as concentration increases, molecular entanglement between molecules increases and the resistance to the flow of solvent therefore increases. The conductivity lines for all the fractions converged at high concentration because a three-dimensional molecular network is formed. A t lower concentrations, the H A molecules of the high M . W . group has a higher K' than those of the low M . W . group. The reasons for this may be that the high M . W . molecules are more compact and there is less entanglement between the high M . W . molecules than the low M . W . molecules. Consequently, the resistance to the flow of solvent is lower for the high M . W . molecules. Due to the skewness of the Schlieren peaks, the sedimentation coefficients, determined from the optical measurements, are overestimates. A s such the K' relationships for the acid hydrolysed fractions which exhibited this skewness should fall below the relationships shown in Figures 4.14 and 4.15. Nevertheless, C O N C L U S I O N S A N D R E C O M M E N D A T I O N S / 126 the K' calculated are believed to be close to the actual values. F r o m the results obtained in this study, the hydraulic conductivity of hyaluronic acid appears to be a function of both concentration and molecular weight. 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J . Mol . Biol. 138:383-400. Mow, V . C , Holmes, M . H . & L a i , W . M . (1984) Fluid transport and mechanical properties of articular cartilage: a review. J . Biomech. 5:377-394. Myers , R. R., Negami, S. & White, R. K . (1966) Dynamic mechanical properties of synovial fluid. Biorheology 3:197-209. Nieduszynski, I. A . , Sheehan, J . K . , Phelps, C . F . , Hardingham, T . E . & M u i r , H . (1980) Equilibrium-binding studies of pig laryngeal cartilage proteoglycans with hyaluronate oligosaccharide fraction. Biochem. J . 185:107-114. Ogston, A . G . & Sherman, T . F . (1961) Effects of hyaluronic acid upon diffusion of solutes and flow of solvent. J . Physiol . 156:67-74. Ogston, A . G . & Stanier, J . E . (1951) T h e dimensions of the particle of hyaluronic acid complex in synovial fluid. Biochem. J . 49:585-599. / 132 Ogston, A . G . & Stanier, J . E . (1953) The physiological function of hyaluronic acid in synovial fluid: viscous, elastic and lubricant properties. J . Physiol . , London 119:244-252. Pape, L . G . & Balazs, E . A . (1980) The use of sodium hyaluronate ( H e a l o n ® ) in human anterior segment surgery. Ophthalmology 87:699-705. Parker, K . H . & Winlove, C . P. (1984) The macromolecular basis of the hydraulic conductivity of the arterial wall. Biorheology 21:181-196. Peterson, E . A . (1970) Cellulosic ion exchangers. In: Laboratory Techniques in Biochemistry and Molecular Biology, ed. Work, T . S. & Work, E . , vol. 2, part II, pp. 223-396. Amsterdam: North Holland. Poole, A . (1986) Proteoglycans in health and disease: structures and functions. Biochem. J . 236:1-14. Prehm, P. (1983) Synthesis of hyaluronate in differentiated teratocarcinoma cells. Characterization of the synthetase. Mechanism of chain growth. Biochem. J . 211:181-198. Prehm, P. (1984) Hyaluronate is synthesized at plasma membranes. Biochem. J . 220:597-600. Preston, B . N . , Davies, M . & Ogston, A . G . (1965) The composition and physicochemical properties of hyaluronic acids prepared from ox synovial fluid and from a case of mesothelioma. Biochem. J . 96:449-471. Schubert, M . & H a m e r m a n , D . (1968) A Primer on Conncetive Tissue Biochemistry, pp. 317. Philadelphia, P A : L e a & Febiger. Schurz, J . & Ribitsch, V . (1987) Rheology of synovial fluid. Biorheology 24:385-399. Si lpananta, P. , Dunstone, J . R. & Ogston, A . G . (1968) Fractionation of a hyaluronic acid preparation in a density gradient. Biochem. J . 109:43-50. Sunblad, L . (1965) Glycosaminoglycans and glycoproteins in synovial fluid. In: The Amino Sugars, ed. Balazs, E . A . & Jeanloz, R. W . , pp. 230-250. New York: Academic. Swann, D . A . (1970) O n the state of hyaluronic acid in a connective tissue matrix. In: Chemistry and Molecular Biology of the Intercellular Matr ix , ed. Balazs, E . A . , vol. 2, pp. 743-748. New York: Academic. Sz irmai , J . A . (1970) Structure of the intervertebral disc. In: Chemistry and Molecular Biology of the Intercellular Matrix , ed. Balazs, E . A . , pp. 1279-1308. New York: Academic. Tanford, C . (1961) Physical Chemistry of Macromolecules. New York: Wiley. / 133 Urban , J . P. G . & Maroudas, A . (1980) The chemistry of the intervertebral disc in relation to its physiological function and requirements. Cl in . Rheum. Dis. 6:51-76. Wedlock, D . J . , Phillips, G . O . & Balazs, E . A . (1981) Sedimentation velocity of sodium hyaluronate-lysozyme mixtures. Int. J . Biol. Macromol. 3:384-388. Welsh, E . J . , Rees, D . A . , Morris , E . R. & Madden, J . K . (1980) Competitive inhibition evidence for specific intermolecular interactions in hyaluronate solutions. J . Mol . Biol. 138:375-382. Wik, K . O. (1979) Physicochemical studies on hyaluronate. Uppsala , Sweden: Univ . Upsaliensis. Dissertation. Williams, J . W . (1963) Ultracentrifugal Analysis in Theory and Experiment. New York: Academic. APPENDICES A. SAMPLE CALCULATIONS A . l . Calibration Line for the Glucuronolactone Concentration The results obtained from the uronic acid carbazole method (Section 3.2) was tabulated in Table 4.1. The absorbance data for 5 concentrations of glucuronolactone were fitted by the least squares method. If the least squares fitted straight line is represented by y = A + Bx [ A . l ] where y is the absorbance, A is the y-intercept, B is the slope of the line and x is the concentration of glucuronolactone, from Mendenhall (1987), B = SS / S S [A. 2] xy x and A = y - B x [A.3] where SS = .2 x.y. - ( 2 z . ) ( .2 y . ) / n xy 1 = 1 I ' I 1 = 1 l i = [A.4] S S = .2 x. 2 - ( .2 x. ) 2 / n [A.5] x i = 1 1 1=1 l and n is the number of data points. Then, for the calibration line, n = 5 y = 0.45238 x = 29.55 SS = 970.225 x S S = 16.02004 xy and substituting these values into Eqns [A.2] and [A.3], B = 16.02004/970.225 = 0.01651(17) 134 / 135 A = 0.45238 - 0.01651(17) X 29.55 = -0 .03554 Therefore, the least squares calibration line for the glucuronolactone concentration is ABS = -0 .03554 + 0.01651 X c [4.1] where ABS is the absorbance at 525 nm and c is the concentration of glucuronolactone. A.2. Amount of Hyaluronic Acid in an Eluate Fraction To determine the amount of H A in an eluate fraction, the glucuronolactone concentration in the fraction was first evaluated from the absorbance by E q n [4.1]. The concentration of H A was obtained by multiplying the concentration of glucuronolactone with the factor 2.279 (Section 4.1). Consider the 0 .325M N a C l eluate, subfraction 6 in the fractionation experiment (Table 4.2). The volume of the subfraction was 500 ml. The average absorbance (of 3 measurements) of the subfraction after the carbazole test was 0.5598. The concentration of glucuronolactone in the subfraction was c = (0.5598 + 0.03554 ) / 0 . 0 1 6 5 1 = 36.06 Mg/mL The concentration of H A in the sufbraction was C H A = 3 6 - 0 6 X 2 - 2 7 9 = 8 2 - 1 8 M g / m L The amount of H A in the subfraction is therefore = 82.18 Mg/mL X 500 m L = 41.09 m g / 136 A . 3 . In tr ins i c V i s c o s i t y , [77] The intrinsic viscosity was obtained by extrapolating (77-770)/VQ * c to c=0, where 7j 0 and 17 are the viscosities of solvent and H A solution, respectively. Consider, for example, the 0.325M-9 Fraction of H A . The efflux time of H A solution measured by the viscometer at each concentration of the H A Fraction, from Appendix B-Experimental Data , is shown in Table A . l . The viscometer constant of the Cannon-Ubbelohde viscometer as determined by the manufacturer was 0.004176 c m 2 / s 2 . The viscosity 77 was calculated by multiplying the efflux time with the viscometer constant. A t concentration = 0.8067 m g / m L , the efflux time is 746.96 s. The viscosity, 77, is 746.96 X 0.004176 = 3.1193 c m 2 / s The efflux time for the solvent (0 .2M NaCl ) is 220.26. The solvent viscosity, J?o> is 220.26 X 0.004176 = 0.9198 c m 2 / s T a b l e A . 1 Viscosity data for 0.325M-9 Fraction Concentration, Efflux time, V, (•n-"Qo)/vo *c> m g / m L s c m 2 / s m L / m g 0.8067 746.96 3.1193 2.9643 0.4034 424.81 1.7740 2.3021 0.2689 347.56 1.4514 2.1493 0.2017 311.81 1.3021 2.0607 0.1613 291.97 1.2193 2.0187 0.08067 254.31 1.0620 1.9164 / 137 Therefore, (77 -770 ) / T ? 0 * C = (3.1193 - 0 . 9 1 9 8 ) / 0 . 9 1 9 8 • 0.8067 = 2.9643 m L / m g The data for ( 7 7 - 7 7 0 ) / T 7 0 - C versus c were plotted as shown in Figure 4.2. The intrinsic viscosity obtained by extrapolating (77 -770 ) / r j 0 -c to c = 0 was 1.830 m L / m g or 1830 m L / g . A.4. Molecular Weight The molecular weight of H A was evaluated using E q n [4.3]. Consider again the 0.325M-9 Fraction. Since [77] was above 1400 m L / g , the intrinsic viscosity at zero shear, [*?]__, was first calculated using E q n [4.2]. [ T } ] Z S = [ 77 ] < 1 + ( [ 7 7 ] - 1 4 0 0 ) / 6 2 5 0 ) = 1830( 1 + (1830 - 1 4 0 0 ) / 6 2 5 0 ) = 1956 m L / g Substituting this value into E q n [4.3], where M is the molecular weight of H A , 1956 = 0.0228 M ° ' 8 1 6 log M = [ log (1956 /0 .0228) ] / 0 .816 then M = 1.11 X 1 0 6 A.5. Sedimentation Coefficient The sedimentation coefficient, S , was calculated using Eqn [2.41]. A sedimentation photograph of R u n C l is shown in Figure A . 1. Because of magnification in the optical system, the distance measured on the photograph was not the actual distance. The actual distance between the inner reference edge / 138 H E R E : Figure A . l Sedimentation photograph of R u n C l . CiRE in Figure A . l ) and the outer reference edge (Oj^g)» as given by the manufacturer, was 1.60 cm. The distance between the two reference edges was measured by a travelling microscope (Micro-Master M-150, V . W . & R . ) to be 3.248 cm. Therefore, the magnification factor M F = 3 .248/1 .60 = 2.03 The distance from 1 ^ to the centre of the rotor was 5.70 cm (given by the manufacturer). The distance, r , between the Schlieren peak and on the mS Kill photograph was measured by the travelling microscope. T h e n the actual distance, r , between the Schlieren peak and the centre of the rotor was r = 5.70 + r / 2 .03 S mS [A. 7] E q n [2.41] can be rewritten as S 2 Q = [d(\n rs)/dt]/a>2 2.303[d{ log r )/dt]/a>2 [A. 8] S2Q can then be evaluated from the slope of the plot of log versus time. In / 139 all the sedimentation runs, co= 52640 r p m , or u = 52640 r p m X 2 i r r a d / s X 1 m i n / 6 0 s = 5512.4 r a d / s E q n [A. 8] then reduces to S 2 Q = 2 .303[d( log rs)/dt]/( 5512.4) 2 = 7.579 X 10" 8 [c i( log r^/dt] s 2 [A.9] The distances were determined for R u n C l . The results from Appendix B along with the r , calculated from E q n [A. 7], and the log r , are tabulated in Table A . 2 . The plot of log r versus time is shown in Figure A . 2 . The slope of the least squares straight line was calculated using E q n [A.2] to [A.5]: SS = 5.28 X 1 0 3 x SS = 1.3465 xy and slope B = 1.3465/5.28 X 1 0 3 = 2.55 X 10" 4 m i n " 1 T a b l e A . 2 Results of sedimentation Run C l . Time, min rmc:> c m rc> c m L o g r< 0 0.427 5.9103 0.7716 8 0.485 5.9389 0.7737 16 0.538 5.9650 0.7756 24 0.588 5.9897 0.7774 32 0.646 6.0182 0.7795 40 0.729 6.0591 0.7824 48 0.754 6.0714 0.7833 56 0.822 6.1049 0.7857 64 0.885 6.1360 0.7879 72 0.949 6.1675 0.7901 / 140 Si ° f 1 1 1 1 1 1 1 1 > 1 0.0 15.0 30.0 45.0 60.0 75.0 Time, min Figure A . 2 The sedimentation plot for Run C l . / 141 Then, the sedimentation coefficient at 2 0 ° C , using E q n [A.9] is: S 2 Q = (7.579 X 10" 8 ) (2 .55 X 1 0 " 4 ) / 6 0 s = 3.22 X 1 0 " 1 3 s A.6. Hydraulic Conductivity F r o m Section 2.4, K' = S 2 0 / C 2 ( 1 - D 2 p , ) [2.10] A t 2 0 ° C , p , = 1.0068 g / m L v2 = 0.67 m L / g (from Preston et al., 1965) E q n [2.10] then reduces to K' = S 2 Q / 0 . 3 2 5 4 c 2 [A. 10] For sedimentation R u n C I , S = 3.22 X 1 0 " 1 3 s c 2 = 0.484 m g / m L Therefore, K' = 3.22 X 1 0 " 1 3 / ( 0 . 3 2 5 4 ) (0.484) = 2.05 X 1 0 " 1 2 s « m L / m g = 2.05 X 10" 9 c m ' / d y n . s A.7. Equation for K' as a function of c Consider R u n C I to C5 for the 0.325M-9 Fraction. The concentration and the hydraulic conductivity, along with the values of their logarithm, are listed in Table A . 3. The log K' versus log c data were fitted by the least squares method. The slope and the y-intercept for the least squares straight line were / 142 obtained from E q n [A.2] to [A.5]: y = -9 .2908 Then Therefore x -SS = SS xy B = A = log K' K' 0.100676 0.3047 -0 .443751 -0 .443751 /0 .3047 = -1 .456 -12 .2906 - ( -1 .456 ) (0.100676) -9 .1442 -9 .1442 - 1.456 X log c , . -9 .1442 v -1.456 ll) x c 7.17 X 1 0 - 1 0 c - L 4 5 6 A . 8 . E r r o r s i n Son a n d K' There are many potential errors in measuring SgQ, such as errors due to temperature control of the ultracentrifuge. However, the primary source of error T a b l e A . 3 c and K' data for 0.325M-9 Fraction c, m g / m L L o g c 1010XK', c m " / d y n « s L o g K' 0.484 -0.3152 20.5 -8.6882 0.968 -0.01412 7.85 -9.1051 1.452 0.1620 3.98 -9.4001 1.936 0.2869 2.69 -9.5702 2.420 0.3838 2.04 -9.6904 / 143 is thought to be from measuring the distance of the Schlieren peak from the centre of the rotor, r . The error in r is manifested in the error of the slope S S of the plot of log r versus time, which is used for the evaluation of Thus , the task here is to determine the error interval of the slope of the plot of log versus time. In determining the error interval of the slope, it is assumed that the errors in r and therefore in log r are approximately normally distributed. Also, the error interval calculated is the 95% confidence interval based on the Student's t-distribution. F o r the least squares straight line y = A + Bx derived from n data points, the 95% confidence interval for B is (from Mendenhall, 1987) B ± ( t O , 0 .025) X cr^ / / S S [A. 11] n-A JJ x where ( t n 2>0.025) is the t-distribution test statistic with n-2 degrees of freedom for a 95% probability that the true slope will be within the interval shown, a „ a is the standard deviation of the slope given by the expression: a 2 = ( S S - B X SS ) / ( n - 2 ) [A.12] B y xy in which SS =.S y . 2 - (.2 x.)2/n y 1=1/1 1=1 l [A. 13] and S S and SS are as defined in Eqns [A.4] and [A.5], respectively. The xy x error interval for the slope B can therefore be calculated from the above equations and the t-distribution test statistic obtained from a t-table (Mendenhall, 1987). Consider, for example, Run C l : / 144 n = 10 SS = 3.443 X 10" y s s = 5.28 X 1 0 3 X s s = 1.3465 xy B = 2.55 X io - 4 a B = [ ( 3 . 4 4 3 X 10" 4 - 2.55 X 10" 4 X 1 . 3 4 6 5 ) / 8 ] 0 , 5 = 3.43 X 10" 4 F r o m t-table (Mendenhall, 1987), (t 9 , 0 . 0 2 5 ) = 2.306, and therefore, from E q n [A. 11], the 95% confidence interval for the slope is B ± 2.306 X 3.43 X 1 0 " 4 / ( 5 . 2 8 X 1 0 3 ) ° " 5 = 2.55 ± 0.109 X 1 0 ' 4 To calculate the error interval for SNN, first the % error in the slope, % E 0 , is obtained: % E „ = 1.09 X 10" 5 / 2.55 X 10" 4 X 100% = 4.27% F r o m E q n [A.9], S 2 Q = 7.579 X 10" 8 X B / 6 0 Therefore, the error interval in S^Q is S 2 Q ± 4.27% = 3.22 ± 0.14 X 1 0 " 1 3 s1" Similarly, for K', since K' = S 2 Q / 0 . 3 2 5 4 c 2 [A. 10] and it is assumed that c 2 is accurate, the error interval in K' is K' + 4.27% = 2.05 ± 0.09 X 10" 9 c m V d y n - s 1 " The error intervals in the slopes for the plot of absorbance versus concentration / 145 (carbazole reaction test) and for the plot of log K' versus log c were obtained in a similar manner. 'The values of the error interval for S^Q and K' calculated here are slightly different from the values listed in Table 4.5. It is because in Table 4.5, the error intervals were evaluated from values of SS , SS , etc, which were x y calculated by computer and were not rounded off, whereas in here, those values were rounded off. B. E X P E R I M E N T A L D A T A / 146 B . l . V i s c o s i t y D a t a Fraction: preliminary Concentration, mg/mL 0.2M NaCl 0.7347 0.4898 0.3674 0.2939 0.1837 0.07347 fractionation III, Efflux time, 220.26 403.69 339.20 304.39 286.16 259.95 235.69 0.3M V. cm 2fs 0.9198 1.6858 1.4165 1.2711 1.1950 1.0856 0.9842 (Tlo )/lo mL/mg 1.1335 1.1025 1.0396 1.0180 0.9813 0.9530 Fraction: preliminary fractionation III, 0.4M 1.330 0.8867 0.665 0.532 0.4433 0.3325 0.266 0.133 Efflux time 646.52 473.28 397.40 355.82 330.17 299.35 282.32 249.54 V 2.6999 1.9764 1.6595 1.4859 1.3788 1.2501 1.1790 1.0421 ('T'Jo )/Vo ' C 1.4551 1.2955 1.2093 1.1569 1.1257 1.0800 1.0594 0.9997 Fraction: 0.25M 1.4168 0.7084 0.4723 0.3542 0.2834 0.1417 Efflux time 1007.47 503.07 389.01 340.21 313.56 264.09 V 4.2072 2.1008 1.6245 1.4207 1.3094 1.1028 (')-i)o)/'7o-c 2.5226 1.8125 1.6222 1.5375 1.4946 1.4041 Fraction: 0.325M 0.9202 0.4601 0.3067 0.2301 0.1840 0.09202 Efflux time 739.50 420.59 342.95 308.42 288.70 252.89 n 3.0882 1.7564 1.4321 1.2880 1.2056 1.0561 2.5619 1.9768 1.8160 1.7397 1.6887 1.6103 Fraction: 0.325M-9 0.8067 0.4034 0.2689 0.2017 0.1613 0.08607 Efflux time 746.96 424.81 347.56 311.81 291.97 254.31 V 3.1193 1.7740 1.4514 1.3021 1.2193 1.0620 2.9643 2.3021 2.1493 2.0607 2.0187 1.9164 Fraction: 0.4M 0.6315 0.3158 0.2105 0.1579 0.1263 0.06315 Efflux time 504.68 338.21 294.83 274.97 263.79 241.53 V 2.1075 1.4124 1.2312 1.1483 1.1016 1.0086 ( VVo )/i)0 'C 2.0447 1.6959 1.6083 1.5733 1.5649 1.5288 Fraction: 0.5M 0.8432 0.4216 0.2811 0.2108 0.1686 0.08432 Efflux time 833.90 444.29 355.63 317.26 295.82 256.36 1 3.4824 1.8554 1.4851 1.3249 1.2353 1.0706 ( t r i o ' / l o 3.3041 2.4127 2.1864 2.0893 2.0345 1.9444 Fraction: unfractionated HA 0.5594 0.2797 0.1865 0.1399 0.1119 0.05594 Efflux time 646.23 393.42 323.74 294.67 278.29 248.58 V 2.6987 1.6429 1.3519 1.2305 1.1621 1.0381 ( J ? - 7 j 0 ) /T ) 0 3.4573 2.8107 2.5193 2.4154 2.3545 2.2992 Fraction: 15minAH 2.958 1.972 1.479 0.986 0.7395 0.5916 0.2958 Efflux time 597.25 455.75 392.11 324.49 295.80 279.33 248.52 V 2.4941 1.9032 1.6375 1.3551 1.2353 1.1665 1.0378 0.5786 0.5422 0.5276 0.4800 0.4638 0.4534 0.4337 Fraction: lhrAH 3.0833 2.0555 1.5417 1.0278 0.7708 0.6167 0.30833 Efflux time 413.66 343.71 310.37 277.35 262.09 253.37 236.37 n 1.7275 1.4353 1.2961 1.1582 1.0945 1.0581 0.9871 (v-no )/lo 0.2848 0.2727 0.2654 0.2522 0.2464 0.2438 0.2373 Fraction: 2hrAH 3.0544 2.0363 1.5272 1.0181 0.7636 0.6109 0.3054 Efflux time 330.58 293.18 274.33 254.80 245.65 240.37 230.13 n 1.3805 1.2243 1.1456 1.0640 1.0258 1.0038 0.9610 0.1640 0.1626 0.1607 0.1540 0.1509 0.1495 0.1467 Fraction: 15mAH-0.325M 5.4770 2.7385 1.8257 1.3693 1.0954 0.5477 Efflux time 1480.82 651.83 472.38 395.56 355.31 282.25 n 6.1839 2.7220 1.9727 1.6519 1.4838 1.1787 1.0449 0.7155 0.6270 0.5813 0.5598 0.5139 Fraction: unfractionated acid hydrolysed HA c Efflux time n 4.770 1238.22 5.1708 2.385 582.33 2.4318 1.590 432.52 1.8062 1.1925 370.48 1.5471 0.9540 336.83 1.4066 0.4770 274.58 1.1466 0.9689 0.6892 0.6061 0.5719 0.5548 0.5169 B.2. Sedimentation Data / 148 Samp Is: 0.2SM Fraction HA Concentrations 0.3542 mg/mL From sedimentation velocity experiment: Time (min) Distance from peak to Actual dist. (Y) of peak LOG V left ref. edge (cm) from centre of rotor (cm) 0.0 0.469 5.9310 0.7731 8.0 0.542 5.9670 0.7758 16.0 0.614 6.0025 0.7783 24.0 0.684 6.0369 0.7808 32.0 0.768 6.0783 0.7838 40.0 0.831 6.1094 0.7860 48.0 0.923 6.1547 0.7892 From the graph of LOG Y vs Time : SL0P£= 0.33107E-03/min Y-INTERCEPT; 0.77306 CORRELATION COEFFICIENTS 0.99944 SSXs 0.17920E*04 SSYs 0.19663E-03 SSXYs 0.59328£«00 SSE= 0.21908E-06 SIGMAs 0.20932E-03 95% confidence interval for SL0PE= 0.12713E-04 Sedimentation coefficient at 20.0 deg.= 0.41819E-12 s. K/AETA= 0.3628E-11 s'mL/mg Permeability. K=0.36278E-10 cm"2 Sample: 0.25M Fraction HA Concentrations 0.7084 mg/mL From sedimentation velocity experiment: Time (min) 0.0 B.O 16.0 24.0 32.0 40.0 48.0 56.0 64.0 Distance from peak to left ref. edge (cm) 0.380 0.441 0.500 0.557 0.611 0.659 0.721 0.777 0.830 Actual dist. (Y) of peak LOG Y from centre of rotor (cm) 5.8872 5.9172 5.9463 5.9744 6.0010 6.0246 6.0552 6.0828 6.1089 0.7699 0.7721 0.7742 0.7763 0.7782 0.7799 0.7821 0.7841 0.7860 From the graph of LOG Y vs Time : SL0PE= 0.24906E-03/min Y-INTERCEPT= 0.77013 CORRELATION COEFFICIENTS 0.99967 SSX= 0.384006-04 SSYs 0.23836E-03 SSXY= 0.9S640E*00 SSEs 0.15664E-06 SIGMAs 0.14959E-03 95% confidence interval for SL0PE= 0.57091E-05 Sedimentation coefficient at 20.0 deg.= 0.31460E-12 s. K/AETA= 0.1365E-11 s-mL/mg Permeability. K=0. 13646E-10 cm"2 Sample: 0.25M Fraction HA Concentrations 1.0626 mg/mL From sedimentation velocity experiment: Time (min) Distance from peak to Actual dist. (Y) of peak LOG Y left ref. edge (era) from centre of rotor (cm) 0 .0 0 .487 5.9399 0 .7738 8 .0 0 .544 5.9680 0. 7758 16 .0 0 .590 5.9906 0. 7775 24 .0 0. 632 6.0113 0 .7790 32 .0 0. 688 6.0389 0. 7810 40 .0 0 . 727 6.0581 0. 7823 48 .0 0 .770 6.0793 0 .7839 56 .0 0 .820 6.1039 0 .7856 64 .0 0 .865 6.1261 0 .7872 72 .0 0. 918 6.1522 0. 7890 80 .0 0. 976 6.1808 0 .7910 88 .0 1. 028 6.2064 0. 7926 From the graph of LOG Y vs Time : SL0PE= 0.21157E-03/min Y-INTERCEPT= 0.77393 CORRELATION COEFFICIENTS 0.99944 SSX = 0.91520E*04 SSYs 0.41011E-03 SSXYs 0.19363E«01 SSE= 0.46188E-06 SIGMA= 0.21491E-03 95% confidence interval for SLOPEs 0.50052E-05 Sedimentation coefficient at 20.0 deg.s 0.26724E-12 s. K/AETAs 0.7728E-12 s'mL/mg Permeability. KsO. 77278E-11 cm"2 Sample: 0.25M Fraction HA Concentrations 1.4168 mg/mL From sedimentation velocity experiment / 149 Distance from peak to Actual dist. (Y) of peak LOG Y left ref. edge (cm) from centre of rotor (cm) 0.0 0.414 5.9039 0.7711 16.0 0.495 5.9436 0.7741 32.0 0.578 5.9847 0.7770 48 .0 0.661 6.0256 0.7600 64 .0 0. 734 6.0616 0.7826 60.0 0.819 6.1034 0.7656 96 .0 0.909 6. 1478 0.7887 112.0 0.987 6.1862 0.7914 126.0 1 .067 6.2256 0.7942 144 .0 1. 157 6.2700 0.7973 the graph of LOG Y vs Time : SLOPEs 0.l8066E-03/min Y-INTERCEPTS 0.77119 CORRELATION COEFFICIENTS 0.99992 SSXs 0.21120E»05 SSY= 0.68944E-03 SSXYs 0.38156E«O1 SSEs 0.11489E-06 SIGMAs 0.11984E-03 95% confidence interval for SLOPE- 0.19016E-05 Sedimentation coefficient at 20.0 deg.= 0.22820E-12 s. K/AETAs 0.4949E-12 s-mL/mg Permeability. K=0.49492E-11 cm,-2 Sample: 0.25M Fraction HA Concentration^  1.7710 mg/mL From sedimentation velocity experiment: 0.0 16.0 32.0 48.0 64.0 60.0 96.0 112.0 128.0 144.0 Distance from peak to left ref. edge (cm) Actual dist. (Y) of peak LOG Y from centre of rotor (cm) 4 38 519 595 675 753 831 887 967 1.045 1. 128 5.9158 5.9557 5.9931 6.0325 6.0709 6.1094 6.1369 6.1764 6.2148 6.2557 .7720 .7749 .7777 . 7805 .7833 .7860 . 7880 0.7907 0.7934 0.7963 From the graph of LOG Y vs Time : SLOPEs 0.16604E-03/min Y-INTERCEPT= 0.77232 CORRELATION COEFFICIENTS 0.99953 SSX = 0.21120E»05 SSYs 0.58278E-03 SSXYs 0.35067E-»01 SSEs 0.54321E-06 SIGMAs 0.26058E-03 95% confidence interval for SLOPEs 0.41348E-0S Sedimentation coefficient at 20.0 deg.= 0.20973E-12 s. K/AETA= 0.3639E-12 s"mL/mg Permeability. K=0.36388E-11 cm,-2 Sample: 0.325M Fraction HA Concentrations 0.4601 mg/mL From sedimentation velocity experiment: Time (min) Distance from peak to 0.0 8.0 16.0 24.0 32.0 40.0 48.0 left ref. edge (cm) Actual.dist. (Y) of peak from centre of rotor (cm) 510 582 649 .714 .776 .840 .905 5.9512 5.9867 6.0197 6.0517 6.0833 6.1136 6.14 58 0.7746 0.7772 0.7796 0.7619 0.7841 0.7863 0.7886 From the graph of LOG Y vs Time : SL0PE= 0.28895E-03/min Y-INTERCEPTS 0.77482 CORRELATION COEFFICIENTS 0.99966 SSXs o .17920E»04 SSYs 0.14972E-03 SSXYs 0.51780E«00 SSEs 0.10291E-06 SIGMAs 0.14346E-03 95% confidence interval for SLOPEs 0.87131E-0S Sedimentation coefficient at 20.0 deg.s 0.36498E-12 s. K/AETAs 0.2438E-11 9-mL/mg Permeability. KsO . 24375E- 10 cm"2 Sample: 0.325M Fraction HA Concentrations 0.9202 mg/mL From sedimentation velocity experiment: 0.0 6.0 16 .0 24.0 32.0 40.0 46.0 56.0 64 .0 72.0 60.0 ea.o 96.0 104 .0 112.0 Distance from peak to Actual dist. (Y) of peak LOG Y left ref. edge (cm) from centre of rotor (cm) 0 378 5.8862 0. 7698 0 .432 5.9126 0. 7718 0 .474 5.9335 0. 7733 0 .518 5.9552 0. 7749 0 .563 5.9773 0. 7765 0 .608 5.9995 0. 7781 0 .644 6.0172 0. 7794 0 .666 6.0379 0. 7809 0 . 735 6.0621 0 .7 826 0 . 777 6.0828 0 .784 1 0 .823 6.1054 0. 7857 0 .863 6.1251 0. 7871 0 .907 6.1468 0. 7886 0 .966 6.1759 0 . 7907 1 .009 6.1970 0. 7922 / 150 From the graph of LOG Y vs Time : SL0PE= 0.19565£-03/min Y- INTERCEPTS 0.77010 CORRELATION COEFFICIENTS 0.99971 SSXs 0.17920E>05 SSYs 0.68635E-03 SSXYs 0.35060E»01 SSEs 0.39360E-06 SIGMAs 0.17400E-03 95X confidence interval for SLOPEs 0.28076E-OS Sedimentation coefficient at 20.0 deg.s 0.24713E-12 s. K/AETAs 0.8252E-12 s'mL/mg Permeability. KsO.82523E-11 cm-,2 Sample: 0.325M Fraction HA Concentrations 1.3803 mg/mL From sedimentation velocity experiment: Time (min) Distance from peak to Actual dist. (Y) of peak LOG Y left ref. edge (cm) from centre of rotor (cm) 0 .0 0. 533 5 .9626 0 .7754 16 .0 0. 602 5. 9966 0. 7779 32 .0 0. 681 6. 0355 0. 7807 48 0 0 .745 6 .0670 0 .7830 64 .0 0. 818 6. 1030 0. 7855 80 .0 0. 897 6. 1419 0 .7883 96 .0 0 960 6. 1729 0. 7905 112 .0 1. 055 6 .2197 0 .7938 128 .0 1. 124 6. 2537 0. 7961 144. 0 1. 163 6. 2828 0. 7982 160. 0 1. 268 6. 3246 0. 8010 176 .0 1. 346 6. 3631 0. 8037 192. 0 1. 434 6. 4064 0. 8066 208. 0 1. 526 6. 4517 0. 809 7 From the graph of LOG Y vs Time : SLOPEs 0.16262E-03/min Y-INTERCEPTS 0.77526 CORRELATION COEFFICIENTS 0.99964 SSX= 0.58240E*05 SSY= 0.15412E-02 SSXYs 0.94709E'0I SSE= 0.1I055E-05 SIGMAs 0.30352E-03 95X confidence Interval for SLOPEs 0.27405E-05 Sedimentation coefficient at 20.0 deg.s 0.20541E-12 s. K/AETAs 0.4573E-12 S-mL/mg Permeability. KsO.45727E-11 cm"2 Sample: 0.325M Fraction HA Concentrations 1.8404 mg/mL From sedimentation velocity experiment: Time (min) Distance from peak to Actual dist. (Y) of peak LOG Y left ref. edge (cm) from centre of rotor (cm) 0.0 16.0 32.0 48 .0 64.0 80.0 96.0 112. 1 2 e 144 160 176. 192 0.390 0.447 0.498 0.582 0.640 0. 737 0.804 0.874 0.925 1.005 1 .066 1 . 129 1 . 188 5.8921 5.9202 5.9453 5.9867 6.0153 6.0631 6.0961 6.1306 6.1557 6.1951 6.2251 6.2562 6.2852 0.7703 0.7723 0.7742 0.7772 0.7793 0.7827 0.7850 0.7875 0.7893 0.7920 0.7941 0.7963 0.7983 From the graph of LOG Y vs Time : SLOPEs 0.IS023E-03/min Y- INTERCEPT^  0.77008 CORRELATION COEFFICIENTS 0.99891 SSX = 0.46592E-05 SSYs o.10538E-02 SSXYs 0.69995E-01 SSE= 0.22950E-05 SIGMAs o.45677E-03 95t confiaence interval for SLOPEs 0.46575E-05 Sedimentation coefficient at 20.0 deg.s 0.18976E-12 s K/AETA= 0.3168E-12 s*mL/mg Permeability. KsO. 3168 3E- 11 cm"2 Sample: 0.325U Fraction HA Concentrations 2.3005 mg/mL From sedimentation velocity experiment: distance from peak to Actual dist. (Y) of peak loft ref. edge (cm) from centre of rotor 0 .0 0. 543 5. 9675 16 .0 0 .604 5. 9975 32 .0 0 .650 6. 0202 ta. .0 0 . 708 6. 0488 64 .0 0 .752 6. 0704 80 .0 0 .820 6 . 1039 96 .0 0 .666 6. 1266 112 .0 0 .932 6. 159 1 128 .0 0 .983 6. 1842 144 .0 1 .040 6 .2123 160 .0 1 . 105 6 .2443 176 .0 1 . 153 6 .2660 192 .0 1 .210 6 .2961 208 .0 1 .270 6 .3256 224 .0 1 .341 6 .3606 0.7758 0.7 7 80 0.7796 0.7817 0.7632 0.7856 0.7872 0.7895 0.7913 0.7933 0.7955 0.7971 0.7991 0 .8011 0.8035 / 151 From the graph of LOG Y vs Time : SL0PE= o.l2232E-03/min Y-INTERCEPTS 0.77573 CORRELATION COEFFICIENTS 0.99976 SSXs 0.71680E«05 SSY= 0.1073OE-02 SSXYs 0.87681E«01 SSEs 0.51736E-06 SIGMAs o.19949E-03 95% confidence interval for SLOPEs 0. Sedimentation coefficient at 20.0 deg.s 0.15451E-K/AETAs 0.2064E-12 s-«sL/mg Permeability, IO0.20638E-11 cm"2 Sample: 0.325M Fraction HA Concentrations 2.7606 mg/mL From sedimentation velocity experiment: Time (min) Distance from peak to Actual dist. (Y) of peak LOG Y left ref. edge (cm) from centre of rotor (cm) 0 .0 0. 395 5.8946 0. 7705 16 .0 0. 461 5.9271 0. 7728 32 .0 0. 510 5.9512 0 .7746 48 .0 0. 565 5.9783 0 .7766 64 .0 0. 601 5.9961 0. 7779 60 .0 0. 685 6.0374 0. 7809 96 .0 0. 719 6.0542 0. 7821 112 .0 0. 767 6.0778 0. 7837 128 .0 0. 821 6.1044 0. 7856 144 .0 0. 869 6.1281 0. 7873 160 .0 0. 939 6.1626 0. 7898 176 .0 0. 998 6.1916 0. 7918 192 .0 1. 053 6.2167 0 .7937 From the graph of LOG Y vs Time : SL0PE= 0.11868E-03/«in Y-INTERCEPTS 0.77070 CORRELATION COEFFICIENTS 0.99907 SSXs 0.46S92E.05 SSYs 0.6S752E-03 SSXY= 0.55298E»01 SSEs 0.12193E-05 SIGMAs 0.33294E-03 95% confidence interval for SLOPEs 0.33949E-05 Sedimentation coefficient at 20.0 deg.s 0.14992E-12 s. K/AETAs 0.1669E-12 s'mL/mg Permeability. K=0.16687E-11 cm,-2 Sample: 0.325M-9 Fraction HA Concentrations 0.4840 mg/mL From sedimentation velocity experiment: Time (min) Distance from peak to left ref. edge (cm) 0.0 6.0 16 .0 24.0 32.0 40.0 48.0 56.0 64.0 72.0 0.427 0.485 0.538 0.588 0.646 0. 729 0.754 0.822 0.885 0.949 Actual dist. (Y) of peak LOG Y from centre of rotor (cm) 5.9103 0.7716 5.9389 0.7737 5.9650 0.7756 5.9897 0.7774 6.0162 0.7795 6.0591 0.7824 6.0714 0.7833 6.1049 0.7857 6.1360 0.7879 6.1675 0.7901 From the graph of LOG Y vs Time : SLOPEs 0.25503E-03/min Y-INTERCEPTS 0.77154 CORRELATION COEFFICIENTS 0.99870 SSXs 0.52800E'04 SSYs 0.34430E-03 SSXYs 0.13465E-01 SSEs 0.89197E-06 SIGMAs 0.33391E-03 95% confidence interval for SLOPEs 0.10597E-O4 Sedimentation coefficient at 20.0 deg.s 0.32214E-12 s. K/AETAs 0.2045E-1 I s'mL/mg Permeability. KsO.2045 IE - 10 cm*"2 Sample: 0.325M-9 Fraction HA Concentrat1on= 0.9680 mg/mL From sedimentation velocity experiment: Time (min) Olstance from peak to Actual dist. (Y) of peak LOG Y left ref. edge (cm) from centre of rotor (era) 0 0 0. 408 5.9010 0. 7709 e. 0 0. 454 5.9236 0. 7726 16 .0 0. 495 5.9438 0. 774 1 24 .0 0. 551 5.9714 0. 7 761 32 .0 0. 586 5.9867 0. 7773 40 .0 0. 633 6.0118 0. 7790 46. 0 0. 67 1 6.0305 0. 7804 56 .0 0. 717 6.0532 0. 7820 64 .0 0 . 760 6.0744 0. 7835 .72 .0 0. 799 6.0936 0. 7849 80 .0 0 .860 6.1236 0 .7870 88 .0 0 .897 6. 1419 0 .7883 96 .0 0 .938 6.1621 0 .7897 104 .0 0 .987 6.1662 0 .7914 / 152 From the graph of LOG Y vs Time : SLOPEs 0. 19S73E-03/«l1n Y- INTERCEPTS 0.77105 CORRELATION COEFFICIENTS 0.99969 SSXs 0.14560E.05 SSYs 0.55816E-03 SSXYs 0.28499E«01 SSEs 0.34661E-06 SIGMAs 0.16995E-03 95% confidence Interval for SLOPEs 0.30691E-05 Sedimentation coefficient at 20.0 deg.= 0.24724E-12 s. K/AETAs 0.7848E-12 s"mL/mg Permeability. KsO. 78481E-11 cra"2 Sample: 0.325M-9 Fraction HA Concentrations 1.4520 mg/mL From sedimentation velocity experiment: me (min) Oistance from peak to left ref. edge (cm) 0.0 0.352 8.0 0.394 16.0 0.429 24.0 0.462 32.0 0.480 40.0 0.534 48.0 0.555 56.0 0.588 64.0 0.627 72.0 0.650 80.0 0.690 88.0 0.731 96.0 0.753 Actual dist. (Y) of peak LOG Y from centre of rotor (cm) 5.8734 5.894 1 5.9113 5.9276 5.9365 5.9631 5.9734 5.9697 6.0089 6.0202 6.0399 6.0601 6.0709 0.7689 0.7704 0.7717 0.7729 0.7735 0.7755 0.7762 0.7774 0.7 788 0.7796 0.7810 0.7825 0.7833 From the graph of LOG Y vs Time : SLOPEs 0.14873E-03/min Y-INTERCEPTS 0.76914 CORRELATION COEFFICIENTS 0.99888 SSX= 0.11648E«05 SSYs 0.25825E-03 SSXY= 0.17324E.01 SSE= 0.58062E-06 SIGMAs 0.22975E-03 95% confidence interval for SL0PE= 0.46854E-05 Sedimentation coefficient at 20.0 deg.s 0.18787E-12 s K/AETA= 0.3976E-12 s"mL/mg Permeability. K=0.39757E-11 cm,-2 Sample: 0.325M-9 Fraction HA Concentrations 1.9360 mg/mL From sedimentation velocity experiment: Time (min) 0.0 16.0 32.0 48.0 64.0 80.0 96.0 112.0 128.0 144.0 Oistance from peak to left ref. edge (cm) Actual dist. (Y) of peak LOG Y from centre of rotor (cm) 380 442 502 559 626 686 744 798 864 928 5.8872 5.9177 5.9473 5.9754 6.0084 6.0379 6.0665 6.0931 6.1256 6.1571 0.7699 0.7722 0.7743 0.7764 0.7768 0.7809 0.7829 0.7848 0.7871 0.7894 From the graph of LOG Y vs Time : SLOPEs 0.13434E-03/min Y-INTERCEPls 0.77000 CORRELATION COEFFICIENTS 0.99986 SSXs 0.21120E'05 SSY= 0.38125E-03 SSXY= 0.26372E»01 SSEs 0.10908E-06 SIGMAs 0.11677E-03 95% confidence Interval for SLOPEs 0.18529E-05 Sedimentation coefficient at 20.0 deg.s 0.16969E-12 s. K/AETAs 0.2693E-12 s"mL/mg Per«eat> i 1 i ty. KsO . 26932E-11 cm"? Sample: 0.325M-9 Fraction HA Concentration= 2.4200 mg/mL From sedimentation velocity experiment: Time (min) Distance from peak to Actual dist. (Y) of peak LOG Y left ref. edge (cm) from centre of rotor (cm) 0 .0 0 .398 5 .8961 0 .7706 16 .0 0. 457 5 .9251 0. 7727 32 .0 0. 508 5 .9502 0. 7745 48 .0 0. 571 5 .9813 0. 7768 64 .0 0. 624 6 .0074 0. 7787 80 .0 0. 686 6 .0379 0. 7809 96 .0 0. 738 6 .0635 0. 7827 112 .0 0. 796 6 .0921 0. 7848 From the graph of LOG Y vs Time : SL0PE= 0.12689E-03/min Y-INTERCEPTS 0.77060 CORRELATION COEFFICIENTS 0.99983 SSXs 0.10752E»05 SSYs 0.17318E-03 SSXYs 0.13643E*01 SSEs O.S7283E-07 SIGMAs 0.97709E-04 95% confidence interval for SLOPEs 0.23058E-05 Sedimentation coefficient at 20.0 deg.s 0.16028E-12 s. K/AETAs 0.2035E-12 s-mL/mg Permeability. KsO.20352E-11 cm"2 Sample: 15minAH Fraction HA Concentrations 0.5916 mg/nL From sedimentation velocity experiment: Time (min) Oistance from peak to left ref. edge (cm) 0.0 8.0 16.0 24.0 32.0 Actual dist. (Y) of peak from centre of rotor (cm) 0.437 0.484 0.526 0.568 0.616 9153 9384 9591 9798 0.7720 0.7737 0.7752 0.7767 0.7784 From the graph of LOG Y vs Time : SLOPEs 0.19835E-03/min Y-INTERCEPTs 0.77201 CORRELATION COEFFICIENTS 0.99969 SSXs 0.64000E+03 SSY= 0.25195E-04 SSXYs 0.12694E.O0 SSEs 0.15660E-07 SIGMAs 0.72249E-04 95% confidence interval for SLOPEs 0.90874E-05 Sedimentation coefficient at 20.0 deg.s 0.25054E-12 s. K/AETA= 0.1301E-11 S-mL/mg Permeability. KsO.13013E-10 cm,-2 Sample: ISminAH Fraction HA Concentrations 1.1832 mg/mL From sedimentation velocity experiment: Time (min) 0.0 8.0 16.0 24.0 32.0 40.0 48.0 56.0 64.0 72.0 Oistance from peak to left ref. edge (cm) 0.443 0.491 0.516 0.558 0.590 0.633 0.668 0.706 0. 749 0.786 Actual dist. (YI of peak LOG Y from centre of rotor (cm) 5.9182 0.7722 5.9419 0.7739 5.9542 0.7748 5.9749 0.7763 5.9906 0.7775 6.0118 0.7790 6.0291 0.7802 6.0478 0.7816 6.0690 0.7831 6.0872 0.7844 From the graph of LOG Y vs Time : SLOPEs 0.!6783E-03/min Y * INTERCEPTS 0.77227 CORRELATION COEFFICIENTS 0.99941 SSXs 0.52800E.04 SSYs 0.14889E-03 SSXYs 0.86613E*00 SSEs 0.17548E-06 SIGMAs 0.14810E-03 95% confidence interval for SLOPEs 0.47001E-05 Sedimentation coefficient at 20.0 deg.= 0.21199E-12 s. K/AETA= 0.5505E-12 S-mL/mg Permeability. K=0. 55053E-11 ctiT'2 Sample: 15minAH Fraction HA Concentrations 1.7748 mg/mL From sedimentation velocity experiment: Time (min) 0.0 16.0 32.0 46.0 64.0 80.0 96.0 112.0 128.0 144.0 Oistance from peak to left ref. edge (cm) 0.436 0.502 0.573 0.629 0.700 0.771 0.629 0.699 0.971 1.040 Actual dist. (¥) of peak LOG Y from centre of rotor (cm) 5.9148 0.7719 5.9473 0.7743 5.9823 0.7769 - 6.0099 0.7789 6.0448 0.7814 6.0798 0.7839 6.1084 0.7859 6.1429 0.7884 6.1783 0.7909 6.2123 0.7933 / 154 From the graph of LOG Y vs Time : SL0PE= 0.14731E-03/min Y-INTERCEPTS 0.77196 CORRELATION COEFFICIENTS 0.99985 SSX= 0.2U20E*05 SSY= 0.45647E-03 SSXY= 0.311!3E*01 SSEs 0.13448E-06 SIGMAs 0.12965E-03 95% confidence Interval for SLOPEs 0.20573E-05 Sedimentation coefficient at 20.0 deg.s 0.18608E-12 s. K/AETA= 0.3222E-12 S-mL/mg Permeability. K=0.32216E-11 c<n"2 Sample: 15minAH Fraction HA Concentrations 2.3664 mg/mL From sedimentation velocity experiment: Time (min) Oistance from peak to Actual dist. (Y) of peak LOG Y left ref. edge (cm) from centre of rotor (cm) 0.0 8.0 16.0 24.0 32.0 40.0 48.0 56.0 64.0 72.0 0.506 0.528 0.573 0.589 0.614 0.647 0.667 0.696 0.719 0.755 5.9493 5.9601 5.9823 5.9901 6.0025 6.0187 6.0286 6.0429 6.0542 6.0719 0.7745 0.7753 0.7769 0.7774 0.7783 0.7795 0.7802 0.7812 0.7821 0.7833 From the graph of LOG Y vs Time : SLOPEs 0.12028E-03/min Y-INTERCEPTS 0.77454 CORRELATION COEFFICIENTS 0.99794 SSX= 0.52800E*04 SSYs 0.76706E-04 SSXYs 0.63509E*00 SSEs 0.31578E-06 SIGMAs 0.19868E-03 95% confidence interval for SLOPEs O.63050E-05 Sedimentation coefficient at 20.0 deg.s 0.16193E-12 s. K/AETAs 0.1973E-12 s-mL/mg Permeability. K=0. 19728E-1 1 cm"2 Sample: 15minAH Fraction HA Concentrations 2.9580 mg/mL From sedimentation velocity experiment: Distance from peak to left ref. edge (cm) Actual dist. (Y) of peak from centre of rotor (cm) 0.0 16.0 32.0 48.0 64.0 96.0 112.0 128 .0 144.0 160.0 0.506 0.560 0.608 0.666 0.715 0.803 0.872 0.921 0.965 1.016 5.9493 5.9759 5.9995 6.0291 6.0522 6.0956 6.1296 6.1537 6.1754 6.2005 0.7745 0.7764 .7781 .7802 .7819 .7850 .7874 . 7891 . 7907 .7924 From the graph of LOG Y vs Time : SLOPEs 0.11215E-03/min Y-INTERCEPT= 0.77461 CORRELATION COEFFICIENTS 0.99949 SSX= 0.28160E*05 SSY= 0.35455E-03 SSXYs 0.31581E»01 SSEs 0.36333E-06 SIGMAs 0.21311E-03 95% confidence interval for SLOPEs 0.29285E-05 Sedimentation coefficient at 20.0 deg.s 0.14166E-12 s. K/AETAs 0.1472E-12 s'mL/mg Permeability. KsO . 1 4 7 16E - 1 1 cm"2 Sample: lhrAH Fraction HA Concentrations 0.6167 mg/mL From sedimentation velocity experiment: Time (min) 0.0 8.0 16.0 24.0 32.0 Distance from peak to left ref. edge (cm) 0.386 0.393 0.439 0.461 0.496 Actual dist. (V) of peak LOG Y from centre of rotor (cm) 5.8901 5.8936 5.9163 5.9271 5.9443 / 155 0.7701 0.7704 0.7720 0.7728 0.7741 From the graph of LOG Y vs Time : SLOPEs 0.13019E-03/min Y-INTERCEPTS 0.76982 CORRELATION COEFFICIENTS 0.98336 SSX= 0.64000E»03 SSY= 0.11219E-04 SSXY= 0.83325E-01 SSEs 0.37022E-06 SIGMAs 0.35129E-03 95% confidence interval for SLOPEs 0.44165E-04 Sedimentation coefficient at 20.0 deg.s 0.16446E-13 s. K/AETAs 0.8194E-12 s-mL/mg Permeability. Ks0.81940E-11 cm,-2 Sample: lhrAH Fraction HA Concentrations 1.2333 mg/mL From sedimentation velocity experiment: Time (mini 8.0 16.0 24.0 32.0 40.0 48.0 56.0 64.0 72.0 Distance from peak to left ref. edge (cm) Actual dist. (Y) of peak LOG Y from centre of rotor (cm) 421 455 490 ' 528 568 602 634 666 699 5.9074 5.9241 5.9414 5.9601 5.9798 5.9966 6.0123 6.0281 6.0443 0.7714 0.7726 0.7739 0.7753 0.7767 0.7779 0.7790 0.7802 0.7813 From the graph of LOG Y vs Time : SLOPEs 0.15715E-03/min Y-INTERCEPTS 0.77019 CORRELATION COEFFICIENTS 0.99937 SSXs 0.38400E-04 SSYs 0.94949E-04 SSXYs 0.60344E»00 SSEs o.12013E-06 SIGMAs 0.13100E-03 95% confidence interval for SL0PE= 0.49996E-05 Sedimentation coefficient at 20.0 deg.s 0.19850E-12 s. K/AETAs 0.4946E-12 s'mL/mg Permeability. K=0.49455E-11 cm,-2 Sample: lhrAH Fraction HA Concentrations 1.8500 mg/mL From sedimentation velocity experiment: Time (min) 8.0 16.0 24.0 32.0 40.0 46.0 56 .0 64.0 72.0 Distance from peak to left ref. edge (cm) 0.467 0.506 0.525 0.563 0.584 0.619 0.644 0.687 0.720 Actual dist. (Y) of peak LOG Y from centre of rotor (cm) 5.9 300 5.9493 5.9566 5.9773 5.9877 6.0049 6.0172 6.0384 6.0547 0.7731 0.7745 0.7751 0.7765 0.7773 0.7785 0.7794 0.7809 0.7821 From the graph of LOG Y vs Time : SLOPEs 0.13753E-03/min Y-INTERCEPTs 0.77198 CORRELATION COEFFICIENTS 0.99785 SSXs 0.38400E-04 SSY= 0.72950E-04 SSXYs 0.52813E'00 SSE= 0.31400E-06 SIGMAs 0.21180E-03 95% confidence interval for SLOPEs 0.80832E-05 Sedimentation coefficient at 20.0 deg.s 0.17373E-12 s. K/AETA= 0.2885E-12 6-mL/mg Permeability. K=0. 28855E-11 cm"2 Sample: lhrAH Fraction HA Concentrations 2.4666 mg/mL From sedimentation velocity experiment: j Time (min) Oistance from peak to Actual dist. (Y) of peak LOG Y left ref. edge (cm) from centre of rotor (cm) 0.514 0.547 .567 .538 .622 .641 .670 .695 .724 5.9532 5.9695 5.9793 5.9946 6.0064 6.0158 6.0300 6.0424 6.0567 7748 7759 7767 7778 7786 7793 7803 7812 7822 From the graph of LOG Y vs Time : SL0PE= 0.11378E-03/min Y-INTERCEPTS 0.77398 CORRELATION COEFFICIENTS 0.99902 SSXs 0.38400E*04 SSYs 0.49811E-04 SSXYs 0.43692E*00 SSE= 0.97357E-07 SIGMAs 0.11793E-O3 95% confidence Interval for SLpPE= 0.45009E-05 Sedimentation coefficient at 20.0 deg.s 0.14372E-12 s. K/AETAs 0.1790E-12 s-mL/mg Permeability. KsO.17904E-11 cm-,2 Sample: lhrAH Fraction HA Concentrations 3.0833 mg/mL From sedimentation velocity experiment: Time (min) Distance from peak to Actual dist. (Y) of peak LOG Y left ref. edge (cm) from centre of rotor (cm) 8.0 16.0 24.0 32.0 40.0 48.0 56.0 64.0 72.0 80.0 88.0 96.0 523 545 578 599 617 647 673 694 715 757 786 809 5.9576 5.9685 5.9847 5.9951 6.0039 6.0187 6.0315 6.0419 6.0522 6.0729 6.0872 6.0985 0.775! 0.7759 0.7770 0.7778 0.7784 0.7795 0.7804 0.7812 0.7819 0.7834 0.7844 0.7852 From the graph of LOG Y vs Time : SLOPEs O.11486E-03/min Y-INTERCEPTS 0.77405 CORRELATION COEFFICIENTS,0.99813 SSX= O.91520E*O4 SSYs 0.12123E-03 SSXYs 0.10513E*01 SSEs 0.45388E-06 SIGMAs 0.21305E-03 95X confidence interval for SLOPEs 0.49617E-05 Sedimentation coefficient at 20.0 deg.s 0.14510E-12 s. K/AETAs 0.1446E-12 S-mL/mg Permeability. K=0. 1446IE-11 cm"2 Sample: 2hrAH Fraction HA Concentrations 0.6109 mg/mL From sedimentation velocity experiment: Time (min) Oistance from peak to Actual dist. (Y) of peak LOG Y left ref. edge (cm) from centre of rotor (cm) 8.0 0.452 5.9227 0.7725 16.0 0.500 5.9463 0.7742 24.0 0.529 5.9606 0.7753 32.0 0.559 5.9754 0.7764 From the graph of LOG Y vs Time : SLOPEs 0.15732E-03/min Y-INTERCEPTs 0.77146 CORRELATION COEFFICIENTS 0.99169 SSXs 0.32000E*03 SSY= 0.80536E-05 SSXYs 0.S0344E-01 SSEs 0.13328E-06 SIGMAs 0.25815E-03 951 confidence interval for SL0PE= 0.62096E-04 Sedimentation coefficient at 20.0 deg.s 0.19872E-12 s. K/AETAs 0.9995E-12 s'mL/mg Permeability. KsO.99955E-11 c«r-2 Sample: 2hrAH Fraction HA Concentrations 1.2218 mg/mL From sedimentation velocity experiment: Time (min) 8.0 16.0 24.0 32.0 48.0 56.0 Distance from peak to left ref. edge (cm) Actual dist. (V) of peak LOG Y from centre of rotor (cm) / 157 398 429 456 485 537 577 From the graph of LOG Y vs Time : SL0PE= 0.13041E-03/min Y-INTERCEPTS 0.76953 CORRELATION COEFFICIENTS 0.99861 5.8961 5.9113 5.9246 5.9389 5.9645 5.9842 7706 7717 7727 7737 7756 7770 SSXs 0.17173E*04 SSY= 0.29289E-O4 SSXYs 0.22396E*00 SSE= 0.81156E-07 SIGMAs 0.14244E-03 95% confidence interval for SLOPEs 0.95416E-05 Sedimentation coefficient at 20.0 deg.s 0.16473E-12 s. K/AETAs 0.4143E-12 s-raL/mg Permeability. K=0.41428E-11 cm"2 Sample: 2hrAH Fraction HA Concentrations 1.8326 mg/mL From sedimentation velocity experiment: Tim  ( 1) 8.0 16.0 24.0 32.0 40.0 48.0 56.0 64.0 72.0 Oistance from peak to left ref. edge (c ) 0.418 0.443 0.468 0.495 0.528 0.546 0.573 0.607 0.632 Actual dist. (Y) of peak LOG Y from centre of rotor (cm) 5.9059 0.7713 5.9182 0.7722 5.9305 0.7731 5.9438 0.7741 5.9601 0.7753 5.9690 0.7759 5.9823 0.7769 5.9990 0.77B1 6.0113 0.7790 From the graph of LOG Y vs Time : SLOPEs 0.12036E-03/min Y-INTERCEPTs 0.77026 CORRELATION COEFFICIENTS 0.99916 SSXs 0.38400E*04 SSYs 0.55725E-04 SSXYs 0.46219E.00 SSEs 0.93754E-07 SIGMAs 0.11573E-03 95% confidence interval for SLOPEs 0.44168E-05 Sedimentation coefficient at K/AETA= 0.2549E-12 s'mL/mg Permeability. Ks0.25492E-11 i 20.0 deg.= 0.15204E-12 s. Sample: 2hrAH Fraction HA Concentrations 2.4435 mg/mL From sedimentation velocity experiment: Time (min) 16.0 24.0 32.0 40.0 48.0 56.0 64.0 72.0 Distance from peak to left ref. edge (cm) Actual dist. (Y) of peak from centre of rotor (cm) 424 444 475 488 520 547 570 590 From the graph of LOG Y vs Time : SLOPEs 0.10915E-03/min Y-INTERCEPTS 0.76970 CORRELATION COEFFICIENTS 0.99803 SSXs 0.26860E*04 SSY= 0.321S3E-04 SSXY= 0.29341E*00 SSE= 0.12673E-06 SIGMAs 0.I4533E-03 95% confidence interval for SLOPEs 0.68593E-05 9089 9187 9340 9404 9562 9695 9808 9906 0.7715 0.7722 0.7733 0.7738 0.7750 0.7759 0.7768 0.7775 Sedimentation coefficient at 20.0 deg. K/AETAs 0.17346-12 s'mL/mg Permeability. KsO.17338E-11 cm-"2 0. I3788E-12 s. Sample: 2hrAH Fraction HA C o n c e n t r a t i o n s 3.0544 mg/mL From sedimentation velocity experiment: Time (min) Distance from peak to left ref. edge (cm) 16.0 24.0 32.0 40.0 48.0 56.0 64.0 72.0 Actual dist. (Y) of peak from centre of rotor (cm) .421 .443 .461 .489 .503 .533 0.557 0.564 9074 9182 927 1 9409 9478 9626 9744 / 158 0.7714 0.7722 0.7728 0.7739 0.7744 0.7754 0.7763 0.7765 From the graph of LOG Y vs Time : SL0PE= 0.96461E-04/min Y-INTERCEPTs 0.76987 CORRELATION COEFFICIENTS 0.99580 SSXs 0.26880E»04 SSYs 0.25223E-04 SSXYs 0.25929E'00 SSEs 0.21163E-06 SIGMAs 0.18781E-03 95X confidence interval for SL0PE= 0.88640E-05 Sedimentation coefficient at 20 K/AETA= 0.1226E-12 S-mL/mg Permeability. K=0 . 12258E-11 cm"2 0 deg.s 0.12184E-12 s. Sample: 15mAH-0.325M Fraction HA Concentrations 1.0954 mg/mL From sedimentation velocity experiment: Time (min) Distance from peak to left ref. edge (cm) 16.0 24.0 32.0 48.0 56.0 64.0 72.0 80.0 0.545 0.603 0.621 0.739 0.762 0.819 0.832 0.861 Actual dist. (Y) of peak LOG Y from centre of rotor (cm) 5.9685 0.7759 5.9970 0.7779 6.0059 0.7786 6.0640 0.7828 6.0754 0.7836 6.1034 0.7856 6.1099 0.7860 6.1241 0.7870 From the graph of LOG Y vs Time : SL0PE= 0.17920E-03/min Y- INTERCEPTS 0.77339 CORRELATION COEFFICIENTS 0.99113 SSXs 0.37680E*04 SSY= 0.12317E-03 SSXY= 0.67522E+00 SSEs 0.21744E-05 SIGMAs 0.60200E-03 95X confidence interval for SLOPEs 0.23998E-04 Sedimentation coefficient K/AETAs 0.6349E-12 s'mL/mg Permeability. Ks0.63495E-11 cm" 20.0 deg.s 0.22635E-12 s. Sample: 15mAH-0.325M Fraction HA Concentrations 1.6431 mg/mL From sedimentation velocity experiment: Time (min) Distance from peak to Actual dist. (Y) of peak LOG Y left ref. edge (cm) from centre of rotor (cm) 8 .0 0. 507 5.9498 0. 7745 16 .0 0. 538 5.9650 0. 7756 24 .0 0. 56 3 5.9773 0. 7765 32 .0 0. 595 5.9931 0. 7777 40 .0 0. 620 6.0054 0. 7785 48 .0 0. 653 6.0217 0. 7797 56. 0 0. 679 6.0345 0. 7806 64, .0 0. 714 6.0517 0. 7819 72 .0 0. 742 6.0655 0. 7829 60. 0 0. 789 6.0887 0. 7845 86. 0 0. 808 6.0960 0. 7852 96 .0 0 .835 6.1113 0. 7861 104 .0 0 .872 6.1296 0. 7874 From the grapn of LOG Y vs Time : SLOPEs 0.13485E-03/min Y-INTERCEPT= 0.77331 CORRELATION COEFFICIENTS 0.99919 SSX= 0.11648E*05 SSYs 0.21217E-03 SSXYs 0.15708E»01 SSEs 0.34474E-06 SIGMAs 0.17703E-03 95X confidence interval for SLOPEs 0.36103E-05 Sedimentation coefficient at 20.0 deg.s O.17034E-12 s. K/AETA= 0.3185E-12 s'mL/mg Permeability. KsO . 3 1855E - 11 cm"2 Sample: 15mAH-0.325M Fraction HA Concentration= 2.1908 mg/mL From sedimentation velocity experiment: Time (mini Oistance from peak to left ref. edge ten) 16. 0 0. 511 24 0 0. 524 32 .0 0. 553 40. 0 0. 580 48 .0 0. 620 56 .0 0. ,645 64 .0 0. 660 72 .0 0 .684 80 .0 0 .732 88 .0 0 .749 96 .0 0 .773 104 .0 0 .789 112 .0 0. 832 120 .0 0 .880 128 .0 0 .892 136 .0 0 .929 144 .0 0 .949 Actual dist. (Y) of peak from centre of rotor (cm) 5.9517 5.9581 5.9724 5.9857 6.0054 6.0177 6.0251 6.0369 6.0606 6.0690 6.0808 6.0887 6.1099 6.1335 6.1394 6.1576 6.1675 7746 7751 7761 777 1 7785 7794 7600 7808 0.7825 0.7831 0.7840 0.7845 0.7860 0.7877 0.7881 0.7894 0.7901 / 159 From the graph of LOG Y vs Time : SL0PE= 0.12383E-03/min Y-INTERCEPTS 0.77229 CORRELATION COEFFICIENTS 0.99811 SSXs 0.26112E«05 SSY= 0.40191E-03 SSXYs 0.32334E*01 SSEs O.15202E-05 SIGMAs 0.31835E-03 95% confidence Interval for SL0PE= 0.41983E-05 Sedimentation coefficient at 20.0 deg.s 0.15641E-12 s. K/AETAs 0.2194E-12 s*«L/mg Permeability, K=di21938E-11 cm"2 Sample: 15mAH-0.325M Fraction.HA Concentrations 2.7385 mg/mL From sedimentation velocity experiment: Time (min) Distance from peak to Actual dist. (Y) of peak LOG Y left ref. edge (cm) from centre of rotor (cm) 16.0 32.0 48.0 64 .0 80.0 96.0 112.0 128.0 144.0 160.0 176.0 0.530 0.576 0.621 0.673 0.728 0.783 0.831 0.889 0.943 0.990 1 .038 From the graph of LOG Y vs Time : SLOPEs 0.11360E-03/min Y*INTERCEPTS 0.77331 CORRELATION COEFFICIENTS 0.99973 5.9611 5.9837 6.0059 6.0315 6.0586 6.0857 6.1094 6.1379 6.1645 6.1877 6.2113 0.7753 0.7770 0.7786 7804 7824 7843 7860 7880 7899 7915 7932 SSXs 0.28160E-05 SSY= 0.36490E-03 SSXY= 0.32047E»01 SSEs O.20O45E-06 SIGMAs 0.14924E-03 95% confidence Interval for SLOPEs 0.20117E-05 Sedimentation coefficient at 20.0 deg.s 0.14375E-12 s K/AETA= 0.1613E-12 s-mL/mg Permeability. KsO.16129E-11 cm-,2 Sample: 15mAH-0.325M Fraction HA Concentrations 3.2862 mg/mL From sedimentation velocity experiment: Time (min) Oistance from peak to Actual dist. (Y) of peak LOG Y left ref. edge (cm) from centre of rotor (cm) 16 .0 0. 530 5 .961 1 0. 7753 32 .0 0. 592 5 .9916 0. 7775 48 .0 0. 618 6 .0044 0. 7785 64 .0 0. 649 6 .0197 0. 7796 80 .0 0. 710 6 .0498 0. 7817 96 .0 0. 757 6 .0729 0. 7834 112 .0 0. 804 6. 0961 0. 7850 128 .0 0. 852 6 .1197 0. 7867 144 .0 0. 895 6. 1409 0. 7882 160 .0 0. 960 6 .1729 0. 7905 From the graph of LOG Y vs Time : SLOPEs 0.10252E-O3/min Y-INTERCEPTS 0.77363 CORRELATION COEFFICIENTS 0.99766 SSX= 0.21120E»05 SSY= 0.22303E-03 SSXYs 0.21653E>01 SSEs 0.10442E-05 SIGMAs 0.36129E-03 95% c o n f i d e n c e i n t e r v a l for SLOPEs 0.57328E-O5 S e d i m e n t a t i o n c o e f f i c i e n t at 2 0 . 0 d e g . s 0.12950E-12 s . K/AETAs 0.1211E-12 s'mL/mg P e r m e a b i l i t y . KsO.12109E-11 c n T ' 2 B.3. Log K' Vs Log c Plots / 160 F r a c t i o n : 0.2511 Froe th« p l o t of LOG K v« LOG C : Slopes -1.432614 Y - I n t e r c e p t at LOG C=0. U -9.0810 C o r r e l a t i o n c o e f f i c i e n t * -.99969 SSXs 0.304700 SSYs 0.625503 SSXYs -0.436518 SSEs «.00014156 SIGMAs 0.00686933 95X confidence I n t e r v a l for S l o p e s 0.039S9842 F r a c t i o n : 0.325M From the p l o t of LOG K vs LOG C : S l o p e s -1.498351 Y - I n t e r c e p t at LOG CsO. It -9.1247 C o r r e l a t i o n c o e f f i c i e n t s . .99935 SSXs 0.414094 SSYs 0.930866 SSXY«s -0.620458 SSEs 0.00120232 SIGUAs 0.01733721 95% confidence I n t e r v a l for S l o p e s 0.07479099 F r a c t i o n : 0.32SU-S F r o a the p l o t o f LOG K vs LOG C : Slopes -1.456352 Y - l n t e r c e p t et LOG CsO. Is -S.1442 C o r r e l a t i o n c o e f f i c i e n t s -.99924 SSXs 0.304700 SSYs 0.647242 SSXYs -0.4437S1 SSEs 0.00098411 SIGMAs 0.01811182 95% confidence I n t e r v a l for S l o p e s 0.10440607 F r a c t i o n : 15«1nAH From the p l o t of LOG K ve LOG C : Slopes -1.361907 Y - 1 n i e r c e p t at LOG CsO. Is -9.1792 C o r r e l a t i o n c o e f f i c i e n t s -.99839 SSXs 0.304700 SSYs 0.566974 SSXYs -0.414973 SSEs 0.00181898 SIGMAs 0.02462372 95% confidence I n t e r v a l for S l o p e s 0.14194410 F r a c t i o n : lhrAH From the p l o t of LOG K vs LOG C : Slopes -1.376716 Y - l n t e r c e p t at LOG CsO. Is -9.1810 C o r r e l a t i o n c o e f f i c i e n t s ..99694 SSXs 0.088552 SSYs 0.168869 SSXYs -0.121911 SSEs 0.00103258 SIGMAs 0.02272203 95% confidence I n t e r v a l for S l o p e s 0.32856356 F r a c t i o n : 2hrAH Fro» the p l o t of LOG K vs LOG C : Slopes -1.317213 Y - l n t e r c e p t at LOG CsO. Is -9.2594 C o r r e l a t i o n c o e f f i c i e n t s -.99853 SSXs 0.088544 SSYs 0.154081 SSXYs -0.116632 SSEs 0.00045181 SIGMAs 0.01503010 95% confidence I n t e r v a l for S l o p e s 0.21734643 F r a c t i o n : 15»AH-0.325U F r o - the p l o t of LOG K vs LOG C : Slopes -1.391124 Y - l n t e r c e p t at LOG CsO. is -9.1912 C o r r e l a t i o n c o e f f i c i e n t s -.99923 SSXs 0.050529 SSYs 0.097936 SSXYs -0.070292 SSE= 0.00015142 SIGMAs 0.00870122 95% confidence I n t e r v a l for S l o p e s 0.16656450 

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