Viscometry and sedimentation equilibrium of partially hydrolyzed hyaluronate: Comparison with theoretical models of wormlike chains

Fractionated samples of sodium hyaluronate of low molecular weight were used to calibrate the carbazole method for glucuronyl analsis and to determine the density increment (based on dry weight) of 0.444 (±0.003) mL/g in water and 0.386 (±0.003) mL/g for samples dialyzed against 0.2M NaCl. Weight-average molecular weights obtained by high-speed sedimentation equilibrium were used to calibrate the limiting viscosity number [η] in 0.2M NaCl, which gave [η]/M_w = 0.0028 (±0.0002) mL/g, valid to M_w = 0.0028 (±0.0002) mL/g, valid to M_w = 10⁵. Experimental data from this work and the literature, including viscosity and light- and small-angle x-ray scattering measurements, were compared to theoretical chain models of the Kratky-Porod (KP) wormlike and the helical wormlike (HW) chain, as treated by Yamakawa and collaborators. Although either model could be fitted to experimental data about equally well with consistent parameters, provided those for the HW chain were of weakly helical nature, calculation of the unperturbed meansquare end-to-end distance as a function of chain length from a conformational model favored the KP chain alternative. The parameters that provide the best fit to experimental data for the KP wormlike model are a persistence length of 4.5–5 nm and a diameter of 1.1 nm. The latter is resonable for a hydrated hydrodynamic cylinder in view of the approximate unhydrated value of 0.7 nm estimated from the density increment.     

Semiflexibility of collagens in solution

The persistence length of lugworm cuticle collagen in 0.1M acetic acid was evaluated as 1600 ～ 1800 Å by Yamakawa-Fujii's model for a wormlike chain from the sedimentation constant and the intrinsic viscosity. The persistence length was further examined for a series of sample “collagen sonicates” produced by varying the duration of sonic irradiation. To estimate the salt effect on the persistence length, measurements were made over a range of NaCl concentrations from 0 to 0.1M. The results showed that the cuticle collagen and collagen sonicates had identical values of persistence length and that the neutral salt effect for the cuticle collagen was far smaller than that for DNA.     

Dilute solution of amylose in dimethylsuldoxide

Measurements of light scatting, sedimentation equilibrium, sedimentation velocity, and viscosity were carried out on fractions of native amylose in dimethylsulfoxide at 25°C. The data for statistical radius as a function of weight-average molecular weight M_w suggested a stiff nature of this biopolymer in the solvent studied when interpreted in terms of Kirste's recent calculations with a stiff chain model. The data for sedimentation coefficient were consistent with this suggestion, and when analyzed in terms of the theory Hearst and Stockmayer for wormlike chain, a value of 233 Ų was obtainedd for a/λ, where a is the length of a monomer unit projected on the chain axis and (2λ)^?1is the persistence length of the wormlike chain. The intrinsic viscosity data gave a high a value as 0.91 for the exoponent in the Houwink-Mark-Sakuarada equation, in Substantial agreement with Cowie's prenious work. We attempted to interpret these data by use of the Eizner-Ptitsyn equation for wormlike chains, with omission of the free-drainage term and introduction of the a/λ value obtained from sedimentation data. It was found that, except in the region of M_w above one million, the observed values were fitted well by the E-P theory with a = 1.4 Å and (2λ)^?1 = 87 Å. The disagreement in the high-molecular-weight region was tentatively attributed to excluded volume effect. The a value obtained suggests that the molecular conformation of amylose in dimethylsulfoxide is predominantly helical, in contrast to that of the same polymer in aqueous solutions of simple electrolyte. It was also found that a similar value of a was derived from our data for the second virial coefficient and partial specific volume if the molecule was assumed to be essentially rodlike.     

Light scattering from wormlike chains with excluded volume effects

This paper reports a calculation of the angular dependence of light scattering from wormlike chains with excluded volume effects. The Daniels distribution function, modified for excluded volume effects, is used to compute averages for scattering elements separated by contour lengths which are long with respect to the persistence length of the chain. An expansion in terms of exactly known moments of the distribution for the wormlike coil without excluded volume is used for short contour lengths. The results are applied to scattering from calf thymus (M = 18.1 × 10⁶) and T7 (M = 25.4 × 10⁶) DNA. It is demonstrated that the same values of excluded volume parameter (ε = 0.11) and statistical segment length (1/λ′ = 900 Å) which explain the sedimentation and viscosity behavior of DNA also account satisfactorily for the scattering behavior. Molecular weights and root-mean-square radii estimated by extrapolation from scattering data obtained in the angular region from 10° to 25° will be 5–10% too large for DNA of molecular weight 20 × 10⁶–30 × 10⁶.     

Characterization of rodlike RNA fragments.

Native calf thymus DNA was sheared by sonication in a viscous solvent to the molecular-weight range from 3 × 10⁴ to 3 × 10⁵ daltons, and fractionated by gel chromatography. Number and weight average molecular weights (M?_n and M?_w) were determined for individual fractions by electron microscopy; the ratio M?_w/M?_n for the peak fraction is approximately 1.1. Sedimentation coefficients (s⁰_20,w) of these fractionated samples show an approximately linear dependence on the logarithm of the molecular weight M?_w. This behavior is that expected for rodlike molecules, and is in quantitative agreement with the theory of Yamakawa and Fujii [(1973) Macromolecules 6 , 407–415] for the sedimentation coefficient of a wormlike chain with a persistence length of 625 Å, a diameter of 25 Å, and a mass per unit length of 195 daltons/Å. It appears that the wormlike coil model, without excluded volume, can represent the sedimentation behavior of DNA over the entire conformational range from rigid rod to flexible coil, using the above parameters. Equilibrium melting curves were determined for various fractions in aqueous 2.4 M tetraethylammonium bromide. A substantial broadening of the transition and decrease of the melting temperature were observed with decreasing molecular weight. Empirical expressions have been obtained relating both the transition temperature and breadth in this solvent to molecular weight.     

The LiCl effect on the conformation of lentinan in DMSO

Lentinan (β‐(1→3)‐D ‐glucan) was found to be successfully fractionated by the mixture of dimethyl sulfoxide (DMSO) and lithium chloride (LiCl) as a solvent and acetone as a precipitant. Light scattering and viscosity measurements were made on solutions of fractionated samples in pure DMSO and 0.2M LiCl/DMSO in the range of the molecular weight M_w from 21.7 × 10⁴ to 84.7 × 10⁴. The values of M_w in both solvents were almost the same, but the remarkable difference between the values of intrinsic viscosity [η] demonstrated that the LiCl/DMSO solvent greatly enhances the stiffness of the lentinan backbone. The observed intrinsic viscosity [η] was analyzed by the Yoshizaki‐Nitta‐Yamakawa theory of a worm‐like chain, and the persistence length q and molecular weight per unit contour length M_L were determined roughly as 6.0 nm and 890 g nm^?1 in 0.2M LiCl/DMSO, and 5.1 nm and 890 g nm^?1 in pure DMSO, respectively. This slightly larger persistent length in 0.2M LiCl/DMSO also confirmed the higher stiffness of lentinan enhanced by the LiCl/DMSO solvent. The enhancement of the chain stiffness was ascribed to the electrostatic repulsion because of the hydrogen bonding of the hydroxyl protons of lentinan with the chloride ion, which is in turn associated with the Li⁺(DMSO)_n macrocation complex. © 2012 Wiley Periodicals, Inc. Biopolymers 97: 840–845, 2012.     

Opticohydrodynamic properties of high-molecular-weight DNA. III. The effects of NaCl concentration

Excluded volume and persistence length of high-molecular-weight DNA from T2 bacteriophage have been evaluated over a range of NaCl concentrations from 0.005 to 2.0M using low-shear flow-birefringence and intrinsic-viscosity data. Uncertainty in persistence length due to ambiguity in the assignment of intrinsic birefringence has been avoided by calibrating the data at 0.2M NaCl using a recently reported persistence-length value based upon photon correlation spectroscopy [Jolly, D. & Eisenberg, H. (1976) Biopolymers 15 , 61]. Results at high salt concertrations are in satisfactory agreement with other estimates of excluded volume and chain flexibility in the literature, but at very low salt concentrations they reflect greater chain expansion than has heretofore been reported. The extinction-angle data imply a transition from a nondraining chain with excluded volume at 0.1M NaCl to an almost freely draining chain at 0.005M NaCl. Over this same salt range, the experimental persistencelength data agree very well with Flory's thermodynamic chain-expansion theory [Flory, P. J. (1953) J. Chem. Phys. 21 , 162], but are in generally poor agreement with other theoretical treatments. A detailed comparison of the results with other data in the literature suggests that the combined flow-birefringence-intrinsic-viscosity technique employed here may be more sensitive to the distribution of chain stiffness and excluded volume in polyelectroytechain expansion of DNA than are othe rhydrodynamic methods such as sedimentation or intrinsic viscosity alone.     

Double-stranded helix of xanthan: Rigidity in 0.01M aqueous sodium chloride containing 0.01 N hydrochloric acid

Six samples of Na xanthan in 0.01M aqueous NaCl containing 0.01 N HCl (pH = 2) were studied by light scattering and viscosity. This study was motivated by the finding that the intrinsic viscosity [η] fairly sharply decreased when the pH of the solvent was lowered from about 6 to 2 by adding HCl to 0.01M aqueous NaCl in which Na xanthan dissolves as rigid dimers having a double-helical structure. The data for weight-average molecular weight, radius of gyration, and [η] showed that Na xanthan at pH = 2 remains a dimer behaving as a semiflexible chain. Data analysis in terms of known theories for unperturbed wormlike chains yielded 0.47 ± 0.02, 2.0 ± 0.6, and 68 ± 7 nm for the contour length h per main-chain residue, diameter d, and persistence length q of the dimer, respectively. these h and d values agreed with the pitch per main-chain residue and the diameter of the double helix of Na xanthan in 0.01 or 0.1M aqueous NaCl. However, the q value, which was close to the intrinsic persistence length q₀ ( = q in the absence of electrostatic interaction) of Na xanthan at pH = 2, was much smaller than the q₀ (106 nm) of this helix. We concluded that the xanthan dimer at pH = 2 assumes a double-helical structure, which is geometrically the same as, but is more flexible than, that at neutral pH.     

Effects of sodium chloride,guanidine hydrochloride,and sucrose on the viscoelastic properties of sodium hyaluronate solutions

Effects of sodium chloride (NaCl), guanidine hydrochloride (GuHCl), or sucrose on the viscoelasticity of sodium hyaluronate (NaHA) solutions were studied. NaCl and GuHCl decreased both storage and loss moduli, while sucrose increased both moduli. The critical concentration C* was determined as an inflection point in the plot of zero shear specific viscosity vs concentration for NaHA solutions with and without NaCl, GuHCl, or sucrose. It is suggested that sodium ions or guanidinium ions shield the electrostatic repulsion of NaHA molecules, hence reduce the coil dimension, and C* shifted to higher concentrations. However, sucrose enhances the entanglement coupling between NaHA molecules and retards the disentanglement of molecular chains or promotes to create hydrogen bonds, and then C* for NaHA solutions with sucrose shifts to lower concentrations. This is in agreement with the results of light scattering measurements in the presence of 0.2M NaCl. Both the radius of gyration and hydrodynamic radius of NaHA were reduced in dilute solutions by the addition of sucrose, and added sucrose enhances the interaction between NaHA monomer units. In the case of concentrated NaHA solution, such interactions result to increase the storage and loss moduli because of the enhancement of temporary network formation. © 1999 John Wiley & Sons, Inc. Biopoly 50: 23–34, 1999     

Persistence length of DNA

In the wormlike chain (Kratky-Porod) model of DNA the stiffness of the chain is determined by the persistence length, a. The persistence length may be evaluated from light-scattering measurements of the molecular weight and the mean-square radius if the samples are not polydisperse or if the polydispersity can be quantitatively determined. The persistence length can also be evaluated with the aid of hydro dynamic theory from measurements of intrinsic viscosity and sedimentation coefficient. Data taken from the literature and from other studies by the authors are examined by these methods. The light-scattering method yields a value of a of 900 ± 200 Å the hydrodynamic data yield 600 ± 100 Å. These values are considerably larger than those obtained by most previous authors.     

The flexibility of low molecular weight double-stranded dna as a function of length: II. Light scattering measurements and the estimation of persistence lengths from light scattering,sedimentation and viscosity

In the preceding paper are described the isolation and physical characterization of seven narrowly disperse fractions of calf thymus DNA in the molecular weight range 0.3 to 1.3 × 10⁶ daltons. Herein, we have determined by light scattering the molecular weights and root mean square radii of these fractions in a solvent comprising 0.2 M NaCl, 2 mM EDTA, 2m MNa-PO₄, pH 7. Measurements were made in a modified Wippler—Scheibling photometer to a 20° lower limit of scattering angle on solutions rendered virtually dust-free by procedures described. The optical aniso tropics of the DNA fractions were measured permitting the experimental molecular weights and root mean square radii to be corrected to their true values. From these values, with appropriate polydispersity corrections, we calculate a Kratky—Porod persistence length, a, of 54.0 ± 5.6 nm which is invariant over the molecular weight range examined. From the sedimentation coefficients (preceding paper) and the theory of Yamakawa and Fujii, we calculate a to be 66 nm, a value found to apply equally well to several DNA samples of various origins whose sedimentation rates are known in the molecular weight range from about 4 × 10⁴ to 10⁸ daltons. Similarly, from the intrinsic viscosities and the theory of Yamakawa and Fujii, we calculate a to be 59 nm, which again adequately applies to a number of DNA samples whose viscosities have been measured by other workers in the molecular weight range 3 × 10⁵ to 10⁸ daltons. The Flory—Mandelkern parameter, β, was found to vary with molecular weight in the manner predicted by the theory of Yamakawa and Fujii. The average value of a from the three sets of measurements is 60 ± 6 nm, which we believe applies to double-stranded DNA molecules, independent of chain length, over the whole range of molecular weights for which reliable data exist.     

Asymmetrical-flow field-flow fractionation with on-line multiangle light scattering detection. 1. Application to wormlike chain analysis of weakly stiff polymer chains

Four samples of hyaluronan in the sodium form, ranging in weight-average molecular weight, M(w), from 6.67 x 10(5) to 4.23 x 10(6) were investigated by asymmetrical-flow field-flow fractionation coupled to multiangle light scattering (FlFFF-MALS) in 0.2 M aqueous NaCl at 25 degrees C. M(w) and z-average radii of gyration, R(G)(z)(), obtained via FlFFF-MALS showed a good agreement with the results obtained by conventional static light scattering. Furthermore, the molecular weight dependence of the radius of gyration for sodium hyaluronan obtained via FlFFF-MALS was analyzed on the basis of the Kratky-Porod model for unperturbed wormlike chains combined with the Yamakawa theory for radius expansion factor, and a sufficiently good agreement was observed between the theoretical prediction and experimental data. These results show the potential usage of FlFFF-MALS regarding size separation and molecular characterization even for weakly stiff chains.     

Potentiometric titration of poly-S-carboxymethyl-L-cysteine in aqueous NaCl solution

pH titration measurements of poly- S-carboxymethyl-L -cysteine were undertaken in the aqueous Nacl solution in relation to the β form–random coil transition. The titration curves show a marked molecular weight dependence because of the shortened chain length of materials. Comparison of the optical rotatory dispersion parameter a₀ with the titration curve reveals that the titration curve apparently reflects a β structure–random coil transition. The β form of this polymer is assumed to be an intramolecular β form, rather than a β structure stabilized by an intermolecular hydrogen bond, at least in the polymer concentration range considered here. The standard free energy change per amino acid residue for the transition from un-ionized random coil to un-ionized β form is estimated to be about ?750 cal/mole residue in the range of 0.005–0.2M NaCl concentration.     

Physicochemical studies on xylinan (acetan). I. Characterization by G permeation chromatography on sepharose Cl-2B coupled with static light scattering and viscometry

Laboratory-made samples of the polysaccharide xylinan (acetan) were fractionated on Sepharose Cl-2B using 0.1M NaCl as eluant. The weight average molar masses and intrinsic viscosities were estimated in the fractions by multiangle laser light scattering (off-line) and capillary viscometry, respectively. The Mark-Houwink-Sakurada plot was found to be indicative of semiflexible coils (a = 0.90). The angular dependence of scattered light was interpreted by fitting with theoretically calculated “Master Curves” in terms of a wormlike chain model. The ambiguity of the interpretation of scattering curves owing to the overlapping effects of chain stiffness and polydispersity is discussed in detail. The experimental data is found to be consistent with a persistence length of L_p = 100 nm. The main proportion consists of double-stranded chains (consistent with a robust double-helix), but single- and multistranded chains also are present. Our results suggest a fractionation according to the contour length rather than the molar mass. © 1996 John Wiley & Sons, Inc.     

Chain stiffness of heteropolysaccharide from Aeromonas gum in dilute solution by dynamic light scattering

Dynamic light scattering measurements have been made on 15 fractions of aeromonas (A) gum, an extracellular heteropolysaccharide produced by the strain Aeromonas nichidenii, with dimethylsulfoxide containing 0.2M lithium chloride as the solvent at 25 degrees C. Data for the translational diffusion coefficient D covering a molecular weight range from 4.5 x 10(5) to 2.1 x 10(6) and ratios of the z-average radius of gyration (z) (1/2) to the hydrodynamic radius R(H) (calculated with previous (z) data) suggest that the polymer behaves like a semiflexible chain in this solvent similar to the stiffness of cellulose derivatives. Thus the D data are analyzed on the basis of the Yamakawa-Fujii theory for the translational friction coefficient of a wormlike cylinder by coarse-graining the heteropolysaccharide molecule. Excluded-volume effects are taken into account in the quasi-two-parameter scheme, as was done previously for (z) and [eta] (the intrinsic viscosity) of A gum in the same solvent. The molecular weight dependence of R(H) is found to be explained by the perturbed wormlike chain with a persistence length of 10 nm, a linear mass density of 1350 nm(-1), an excluded-volume strength parameter of 1.3 nm, and a chain diameter of 2.8 nm. These parameters are in substantial agreement with those estimated previously from (z) and [eta] data, demonstrating that the solution properties (D, (z), and [eta]) of the heteropolysaccharide are almost quantitatively described by the current theories for wormlike chains in the molecular weight range studied.     

Properties of auricularia auricula-judae β-D-glucan in dilute solution

A Water-soluble glucan A was isolated from the fruit body of Auricularia auricula-judae. It is composed of a backbone chain of β-(1 → 3)-linked D -glucose residues, two out of three glucose residues being substituted at C-6 positions with a single glucose unit. The weight average molecular weight Mw, number average molecular weight Mn, and intrinsic viscosity [η] of the fractionated samples were studied at 25°C in water and in dimethylsulfoxide (DMSO). The Mark-Houwink equation was established as [η] = 6. 10 × 10^?4 Mw^1.14 for the glucan A having Mw ranging from 9 × 10⁵ to 1.6 × 10⁶ in water. The values of [η] in water are far higher than those in DMSO, but the values of Mn measured in water are the same as those in DMSO. Analysis of Mw and [η] in terms of the known theories for rods and wormlike chains yielded 1030 ± 100 nm^?1, 90 ± 20 nm, 1.3 ± 0.3 nm, and 0.26 ± 0.03 nm for molar mass per unit contour length M_L, persistence length q, diameter d, and contour length h per main-chain glucose residue, respectively. The present data suggest that glucan A dissolves in water as single-stranded helical chains and in DMSO as semiflexible chains. © 1995 John Wiley & Sons, Inc.     

Cholinergic ligand-induced affinity changes in Torpedo californica acetylcholine receptor

Measurement of small-angle X-ray scattering from a sample of hyaluronic acid of high molecular weight in 0.05 m HNO₃ gave persistence length plots which agreed in form with theory and led to apparent persistence lengths of from 4 to 6 nm. Similar measurements in 0.2 m NaCl gave plots which deviated somewhat in form from theoretical expectation, but which could be interpreted to give a persistence length of 4 nm in this solvent. Data for intrinsic viscosity [η] as a function of molecular weight were in reasonable agreement with the Yamakawa-Fujii treatment of [η] for the worm-like chain model for a persistence length of about 4 nm in both 0.5 m NaCl and 0.1 m HCl, perhaps slightly higher in the latter. The values of persistence length estimated from [η] depend somewhat on the choice of chain parameters and the method of correction of experimental data to unperturbed solvent conditions. Experimental data for the sedimentation coefficient, while less definitive, were consistent within experimental uncertainty with the same parameters of the worm-like chain model. These calculated results are in substantial agreement with the values derived from small-angle X-ray scattering. A fraction of hyaluronic acid of low molecular weight in 0.05 m HNO₃ gave an estimated molecular weight of 2.7 × 10⁴ and a radius of gyration of 8 nm, in reasonable agreement with expected values based on the worm-like chain model for a persistence length of about 4 nm.     

Light-scattering study on chick-embryo cartilage proteoglycan type H (PG-H)

Light-scattering measurements were carried out on chick-embryo cartilage proteoglycan type H (PG-H) in three different media. The number of uronates per PG-H was obtained as a measure of the molecular weight: 2.3 × 10³ in 4M GdnHCl, 7.1 × 10³ in 0.3M NaCl, and 5.7 × 10³ in 0.04 g/dL SDS + 0.1M NaCl (GdnHCl, guanidine hydrochloride; SDS, sodium dodecylsulfate). Self-association of PG-H occurred in 0.3M NaCl and 0.04 g/dL SDS + 0.1M NaCl.     

Dilute solution properties of proteoglycan fractions from bovine nasal cartilage

Fresh proteogycans (adult bovine nasal cartilage) isolated from the densest portion of a dissociative density gradient had a weight-average molecular weight of ca. 10⁶ in 4M guanidine hydrochloride (GdnHCI) by light scattering. Fractions of such material obtained by elution with 4M GdnHCI from 2% agarose gel, both normal and cross-linkd, has proteoglycan subunit molecular weights ranging from 0.8 to 2.6 × 10⁶ and root-mean-square radii ranging from 35 to 52 nm in the same solvent. The protein molecular weight per proteoglycan subunit was about 1.2 × 10⁵ and that of keratan sulfate about 1.8 × 10⁵, both independent of total molecular weight. A random-flight “graft copolymer” model having uniform side chains of chondroitin sulfate (40 disaccharides) and keratan sulfate (15 disaccharides) and a random-coil polypeptide back bone was used to estimate the unperturbed radius, whihc was about 19 nm for a mol wt of 1.5 × 10⁶. Experimental light-scattering data for fractions were fitted very well by theoretical curves for the particale scattering factor for both linear and appropriate branched polymers. Examination of coil expansion on the basis of perturbation calculations for branched polymer models suggested that expansion did not account for the experimentally observed radii in terms of unperturbed radii calculated from the model. A possible explanation is that substantial local stiffening of the polypeptide chain due to substitution of side-chain clusters increases the unperturbed radii. The intrinsic viscosity [η] is 4M GdnHCI ranged from 120 to 180 ml/g, and could be interpreted in terms of th eequivalent sphere model; the Flory number has approximately its normal value for flexible linear polymers. The treatment of the sedimentation coefficient by this is less successful, since the Man delkern-Flory parameter β apparently increases with increasing molecular weight; average value are similar to those for flexible polymers, but the variation in β makes this method useful only for rough estimation of molecular weight of proteoglycans. Molecular weights of purified proteoglycans are the same in 0.2M NaCI as in 4M GdnHCI, while crude preparations gave higher molecular weights in 0.2M NaCI, probably because of association due to incomplete removel of “linking” proteins.