Ordered Conformation of Succinoglycan in Aqueous Sodium

Tereza Cristina Luque Castellane , Manoel Victor Franco Lemos , Eliana Gertrudes de Macedo Lemos. Carbohydrate Polymers 2014 111, 191-197 ...
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Biomacromolecules 2001, 2, 952-957

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Ordered Conformation of Succinoglycan in Aqueous Sodium Chloride Sumihito Kido, Tomoko Nakanishi, and Takashi Norisuye* Department of Macromolecular Science, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan

Isamu Kaneda and Toshio Yanaki Shiseido Basic Center, 2-2-1 Hayabuchi, Tsuzuki-ku, Yokohama, 224-8558, Japan Received March 26, 2001; Revised Manuscript Received May 28, 2001

Succinoglycan samples ranging in weight-average molecular weight from 1.0 × 105 to 8.7 × 106 (in 0.1 M aqueous NaCl at 25 °C), prepared by ultrasonication of a native sample (Rheozan), followed by fractionation, were investigated by static light scattering, sedimentation equilibrium, and viscometry in 0.1 M aqueous NaCl at 25 °C where the polysaccharide assumes a certain ordered (helical) conformation. The measured radii of gyration and intrinsic viscosities showed the polysaccharide to behave like a semirigid chain in the aqueous salt. Their analysis based on the unperturbed wormlike chain yielded about 1500 nm-1 and 50 nm for the linear mass density and the persistence length, respectively. The former value was almost twice that expected for the single succinoglycan molecule, and thus it was concluded that the predominant molecular species of succinoglycan present in the aqueous salt is a double helix or an aggregate composed of paired single helices. Introduction Succinoglycan is a charged polysaccharide produced by such bacterial species as Pseudomonas, Rhizobium, Agrobacterium, and Alcaligenes.1 It consists of the repeating units shown in Figure 1, but in actuality, the content of the succinate monoester linked to either one or both of the two side chain glucoses varies depending on bacterial source or cultivation condition, and in some cases, an acetyl group may be contained in the backbone.1-3 As was shown by previous workers4-10 with a variety of experimental techniques, succinoglycan in aqueous solution with or without added salt undergoes an order-disorder conformation change with raising temperature. Although its ordered conformation at low temperatures has been explored by a few groups6,7,9 in relation to this conformation change, the conclusions derived are at variance as mentioned below. Dentini et al.6 concluded from static light scattering, polarimetry, and calorimetry for a native sample in 0.1 M aqueous NaCl at 25 °C that the predominant molecular species of succinoglycan present in the ordered state is laterally aggregated rigid single helices with a mean aggregation number of 1.3. A single helix was also proposed by Gravanis et al.,7 who showed on the basis of Manning’s polyelectrolyte theory11 that their conductivity data for a native sample in 0.01 M aqueous NaCl at 25 °C is consistent with the linear charge density expected for a single chain. On the other hand, analysis of heat capacity curves by Burova et al.9 led to the proposal that, except for cases of low ionic strength at low polymer concentrations, the thermally induced conformation change is the dissociation of a double helix followed by the melting of the dissociated single helices.

Figure 1. Repeating unit of succinoglycan. The succinate is linked to either one or both of the two side chain glucoses.

These different proposals or findings may arise partly from approximations or assumptions underlying the theories used. At present the most reliable approach to the experimental determination of the global conformation of a semiflexible polymer may be to analyze the molecular weight dependence of such properties as the intrinsic viscosity [η] and the meansquare radius of gyration 〈S2〉 under a fixed solvent condition on the basis of available theories12 for the wormlike chain13

10.1021/bm010064h CCC: $20.00 © 2001 American Chemical Society Published on Web 07/26/2001

Ordered Conformation of Succinoglycan

(or more generally the helical wormlike chain12). The accuracy of those theories have been checked by extensive experiments12,14,15 with a variety of polymers, either helical or nonhelical. In the study of the ordered succinoglycan conformation, it is also desirable to use samples purified by fractionation. As far as we know, no previous worker attempted such purification. In the present work, we made static light scattering and viscosity measurements on fractionated succinoglycan samples of different molecular weights with 0.1 M aqueous NaCl at 25 °C as the solvent, hoping to deduce the ordered conformation of the polysaccharide. Additionally, we determined [η] for those fractions in 0.01 aqueous NaCl at 25 °C to confirm the earlier finding6 that [η] for ordered succinoglycan is insensitive to NaCl concentration. The data obtained for 〈S2〉z (the z-average 〈S2〉) and [η] in 0.1 M aqueous NaCl as functions of weight-average molecular weight Mw are analyzed below on the basis of the wormlike chain model. Experimental Section Samples. Aqueous sodium acetate solutions (0.1 M) of a succinoglycan sample (Rhone-Poulenc Rheozan from Agrobacterium tumefaciens) with a D-glucose:D-galactose:pyruvate:succinate ratio of 7:1:1:0.8 were exposed to 20 kHz sonic irradiation (Nissei US-150T) for 1-100 h at 0 °C to fragment the polysaccharide to lower molecular weights. The polymer concentration was adjusted to 0.1-1%. Each of the sonicated solutions was treated with activated charcoal and filtered through a filter paper (No. 101, Toyo-Roshi, Tokyo) and a membrane filter (0.45-1.0 µm, Millipore). In this way, six sonicated samples covering a wide range of [η] (in 0.1 M aqueous NaCl at 25 °C) from 1.2 to 34 cm3 g-1 (without shear rate correction) were prepared. Four sonicated samples of lower molecular weight were each divided into 2-4 parts at a fixed temperature of 25 °C by fractional precipitation with 0.5 M aqueous sodium acetate as the solvent and methanol as the precipitant. The composition of added methanol ranged from 0.48 to 0.75 depending on sample’s molecular weight. The turbid solution was separated into two phases with the aid of a centrifuge operated at 25 °C and 10000 rpm for 20-30 min, since no complete phase separation was attained. After the products had been reprecipitated and dried as described below, the same fractionation procedure was repeated 2-5 times. From 36 fractions thus obtained, five appropriate middle ones designated below as S-4, S-5, ..., and S-8 in order of decreasing molecular weight were chosen for the present work; S-6 was used only for differential refractometry and densitometry. Two sonicated samples of higher molecular weight and the original Rheozan sample were each divided into six to eight parts in a similar manner but by repeated fractional solution with either the same solvent + precipitant system as above or the 0.1 M aqueous NaCl + acetone system, and three middle fractions, S-1 (from the original Rheozan sample) and S-2 and S-3 (from the sonicated samples), were added to the above five fractions as the final products. All these fractions were reprecipitated from 0.5 M aqueous sodium acetate or 0.1 M aqueous NaCl solutions

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into methanol or 95% aqueous acetone, washed with the precipitant two to three times and pure acetone, and vacuumdried. Each fraction was dissolved in deionized water and passed through a mixed-bed ion exchanger (Amberlite IR-120 + IR-400). The solution (pH ∼ 2.8) was neutralized with 0.05 N aqueous NaOH (Beckman φ 70 PH meter) at a temperature lower than 25 °C and lyophilized over more than 4 days. After being further dried in a vacuum at room temperature for 1 day, a given sample was mixed with aqueous NaCl of a desired salt concentration. The polymer mass concentration c was calculated from the gravimetrically determined weight fraction with the solvent density. Light Scattering. Scattering intensities were measured for succinoglycan samples in 0.1 M aqueous NaCl at 25 °C on a Fica-50 light-scattering photometer in an angular range from 30 to 150°, using vertically polarized incident light of a wavelength λ0 of 436 or 546 nm. Pure benzene at 25 °C was used to calibrate the apparatus. Its Rayleigh ratio for unpolarized light was taken as 46.5 × 10-6 cm-1 at 436 nm and 16.1 × 10-6 cm-1 at 546 nm,16 and its depolarization ratio was determined to be 0.411 at 436 nm and 0.406 at 546 nm by the method of Rubingh and Yu.17 The concentration dependence of scattering intensity at fixed scattering angles θ was analyzed by the square-root plot, and the angular dependence at fixed c, by the linear plot. Test solutions and the solvent were made optically clean by filtration through Millipore filters (0.3-3 µm), followed by 4-h centrifugation at about 2.5 × 104g in a Sorvall RC 5C centrifuge, and were transferred into light scattering cells using pipets. The cells and pipets had been rinsed with acetone vapor for 6 h. Excess refractive indices of dialyzed 0.1 M aqueous NaCl solutions of succinoglycan were measured at 25 °C for λ0 ) 436 and 546 nm using a modified Schulz-Cantow type differential refractometer. Dialysis was effected by the apparatus described elsewhere.18 The specific refractive index increments (∂n/∂c)µ at 436 and 546 nm were 0.143 and 0.140 cm3 g-1, respectively. Here, the subscript µ attached to ∂n/ ∂c signifies that the chemical potentials µ of all diffusible components are held constant. Sedimentation Equilibrium. Sedimentation measurements were made on two low molecular weight samples S-7 and S-8 in 0.1 M aqueous NaCl at 25 °C in a Beckman model E ultracentrifuge with a 12 mm Kel-F double-sector cell. The liquid column was adjusted to 1.5-1.8 mm, and the rotor speed was chosen so that the ratio of the equilibrium polymer mass concentration at the cell bottom to that at the meniscus became about 3. The equilibrium sedimentation patterns obtained were analyzed by the method described elsewhere19 to determine Mz/Mw (the z-average to weightaverage molecular weight ratio) as well as Mw. Densities F of dialyzed 0.1 M aqueous NaCl solutions of succinoglycan at 25 °C were determined with a bicapillary pycnometer of 30 cm3 capacity. The density increment (∂F/ ∂c)µ at fixed µ was 0.382. Polarimetry. To ascertain that our succinoglycan in aqueous NaCl at room temperature is in the ordered state, specific rotations [R]300 at λ0 ) 300 nm were measured at

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Figure 2. Thermal changes in [R]300 (solid curves) observed by successively raising T for an unfractionated succinoglycan sample in aqueous NaCl of the indicated salt concentrations. Dashed line: cooling curve for pure water solutions.

different temperatures T for an unfractionated, sonicated sample S-US-A (with a viscosity-average molecular weight Mv of 5.6 × 105 in 0.1 M aqueous NaCl at 25 °C) on a Jasco J-725 CD spectropolarimeter equipped with an ORD detector. A cylindrical quartz cell of 10 cm path length was used, and the polymer concentration was adjusted to about 3 × 10-3 g cm-3. The solid curves in Figure 2 show the temperature dependence of [R]300 determined by successively raising T at the indicated NaCl concentrations Cs. The dashed line represents the data in pure water that were obtained by lowering T after the measurement at 60 °C. Theses curves confirm earlier findings:6,7 (1) Succinoglycan in aqueous NaCl undergoes a thermally induced change from a certain helical to disordered conformation in a relatively narrow T range, (2) the ordered conformation is maintained up to about 40 °C in pure water and stable up to a higher T in aqueous NaCl of a higher Cs, and (3) the conformation change is not always reversible; cooling curves for 0.01, 0.05, and 0.1 M NaCl (not shown here) also exhibited thermal hysteresis, but the hysteresis became less pronounced with increasing ionic strength. Viscometry. Zero-shear rate intrinsic viscosities for succinoglycan samples in 0.01 and 0.1 M aqueous NaCl at 25 °C were determined using a conventional capillary or lowshear four-bulb viscometer of the Ubbelohde type. The apparent shear rate was about 800 s-1 for the former viscometer and 13-91 s-1 for the latter. In relation to the thermal hysteresis observed for [R]300, the reversibility of the relative viscosity ηr at a fixed polymer weight fraction was examined for the original Rheozan sample and sample S-US-A. When T was successively raised to 75-80 °C, (ln ηr)/c for both samples sharply decreased around 55 (in 0.01 M aqueous NaCl) and 70 °C (in 0.1 M aqueous NaCl), showing that the conformation change accompanies a large decrease in molecular size. Upon cooling of the heated solutions, (ln ηr)/c increased but stayed at values far below those for the corresponding nonheated solutions at 25 °C. Furthermore, when a 0.01 M aqueous NaCl solution of sample S-US-A was heated to different temperatures above 40 °C and cooled to 25 °C, (ln ηr)/c did not recover the original value at 25 °C. These observations also confirm what was observed for native succinoglycan samples by others.4,6,8 All the findings from polarimetry and viscometry suggest

Kido et al.

Figure 3. Concentration dependence of (Kc/R0)1/2 for succinoglycan samples in 0.1 M aqueous NaCl at 25 °C.

Figure 4. Angular dependence of P(θ)-1 for succinoglycan samples in 0.1 M aqueous NaCl at 25 °C. The dashed lines indicate the initial slopes of the plots.

that the thermally induced conformation change of succinoglycan is not an event occurring in a single molecule. Results Figures 3 and 4 show the concentration dependence of (Kc/R0)1/2 and the angular dependence of P(θ)-1, respectively, for succinoglycan samples in 0.1 M aqueous NaCl at 25 °C. Here, K is the optical constant, R0 is the excess reduced scattering intensity at zero angle, P(θ) is the particle scattering function, and k is the magnitude of the scattering vector defined by k ) (4πn0/λ0) sin (θ/2), with n0 being the refractive index of the solvent. The straight lines for the three highest molecular weight samples in Figure 3 are essentially horizontal, indicating that the second virial coefficients A2 for them are almost zero. Dentini et al. also obtained a similar A2 value for a native succinoglycan sample in the same solvent. The values of Mw and 〈S2〉z1/2 evaluated are summarized in Table 1, along with those of Mw and Mz/Mw from sedimentation equilibrium. The Mz/Mw values indicate that samples S-7 and S-8 are relatively narrow in molecular weight distribution. However, their considerable deviations from unity imply that our fractionation was not very effective.

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Ordered Conformation of Succinoglycan Table 1. Results from Light Scattering and Viscosity Measurements on Succinoglycan Samples in 0.1 M Aqueous NaCl at 25 °C sample

Mw × 10-6

S-1 S-2 S-3 S-4 S-5 S-7 S-8

8.7 4.88 1.85 0.756 0.476 0.174 (( 0.013)a 0.104b

b

〈S2〉z1/2, nm Mz/Mw [η] × 10-2, cm3 g-1 290 230 155 92 66 34

1.25b 1.3b

98.0 54.9 24.3 10.9 6.37 1.96 1.04

102c 59.0c 24.5c 11.0c 6.65c 1.99c 1.11c

a Mean of the values from light scattering and sedimentation equilibrium. From sedimentation equilibrium. c In 0.01 M aqueous NaCl at 25 °C.

Figure 6. Molecular weight dependence of [η] for succinoglycan in 0.1 M aqueous NaCl at 25 °C. The curve represents the theoretical values calculated from the Yamakawa-Fujii-Yoshizaki theory25,26 with q ) 52 nm, ML ) 1460 nm-1, and d ) 2.5 nm.

Discussion

Figure 5. Molecular weight dependence of 〈S2〉z for succinoglycan in 0.1 M aqueous NaCl at 25 °C. The curve represents the theoretical values calculated from eqs 1 and 2 with q ) 46 nm and ML ) 1520 nm-1.

Figure 5 shows that the double-logarithmic plot of 〈S2〉z against Mw is roughly linear for Mw < 106 with a slope of about 1.3 and bends down for Mw > 106. This molecular weight dependence resembles that observed for typical semirigid polymers,12,14,15 though the downward bending at high Mw is rather remarkable. The significance of the indicated curve is interpreted in the next section. The intrinsic viscosity data for succinoglycan samples in 0.01 and 0.1 M aqueous NaCl at 25 °C are presented in the fifth and sixth columns of Table 1. It can be seen that the values of [η] in the two aqueous salts do not significantly differ for any samples. This is consistent with the finding by Dentini et al.,6 who showed [η] for a native succinoglycan sample (Mw ) 3.3 × 106) in aqueous NaCl at 25 °C to be almost independent of Cs over the range from 0.01 to 1 M. These findings imply that the backbone stiffness of ordered succinoglycan is high enough to be unaffected by electrostatic repulsions between charged groups in the region of Cs higher than 0.01 M. We found, however, that, as may be expected for a semiflexible polyelectrolyte,20-22 [η] for sample S-US-A and a fractionated sample (Mw ) 3.5 × 105) slightly increased (by 4-8%) when Cs was lowered to 0.005 M. Our [η] data in 0.1 M aqueous NaCl are plotted doublelogarithmically against Mw in Figure 6. The viscosity exponent decreases gradually from 1.3 to 1.0 with increasing Mw, confirming the above finding from 〈S2〉z that ordered succinoglycan in the aqueous salt (in 0.01 M aqueous NaCl as well) is semirigid. The indicated curve is explained in the next section.

Data Analysis. We model the ordered succinoglycan chain in 0.1 M aqueous NaCl by the unperturbed wormlike chain, whose 〈S2〉 is determined by two parameters, the contour length L and the persistence length q.23 The former is related to the molecular weight M by L ) M/ML, with ML being the molar mass per unit contour length. In analyzing the present 〈S2〉z data, we take into account the polydispersity of our samples using the Schulz-Zimm distribution function f(M) ) βh+1MhM0-(h+1)[Γ(h + 1)]-1 exp (-βM/M0), where β and h are parameters related to Mn (the number-average molecular weight), Mw, Mz, ... by βMw ) M0(h + 1), Mw/Mn ) (h + 1)/h, Mz/Mw ) (h + 2)/(h + 1), ..., M0 is the monomer molecular weight, and Γ denotes the gamma function. We take h to be 3 so that Mz/Mw comes close to the experimentally determined values 1.25 and 1.3 (see Table 1). For this h, 〈S2〉z is given by24 〈S2〉z/q2 ) (5/12)x - 1 + (2/x) - [8/(3x2)]{1 - [1 + (x/4)]-3} (h ) 3) (1) where x ) Mw/(qML)

(2)

We searched for a set of q and ML leading to the closest agreement between the 〈S2〉z data in Figure 5 and the theoretical values computed from eq 1 with eq 2. The values of q and ML thus estimated were 46 ( 5 nm and 1520 ( 80 nm-1, respectively. The solid curve in Figure 5 represents the best-fit theoretical values calculated (for h ) 3) with q ) 46 nm and ML ) 1520 nm-1. The agreement between theory and experiment is not bad. The theory of Yamakawa, Fujii, and Yoshizaki25,26 for [η] of a wormlike cylinder contains three parameters, q, ML, and d (the cylinder diameter). These three unknowns cannot uniquely be determined from our [η] data. Since the theoretical [η] is relatively insensitive to d, we estimated q and ML by curve-fitting for an assumed d value within the range between 1.5 and 3.5 nm. The q and ML values obtained in this way varied from 48 to 56 nm and from 1590 to 1330 nm-1, respectively, depending on the input d value. Since the diameters examined seem to cover the range reasonable for ordered succinoglycan, we may determine q and ML from [η] to be 52 ( 4 nm and 1460 ( 130 nm-1, respectively.

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These values are close to those estimated above from 〈S2〉z. The curve in Figure 6 represents the theoretical values calculated from the Yamakawa-Fujii-Yoshizaki theory with q ) 52 nm, ML ) 1460 nm-1, and d ) 2.5 nm. The present estimate of ML (about 1500 nm-1 from both 2 〈S 〉z and [η]) is much larger than the value of 1000 nm-1 determined by Dentini et al.6 from asymptotic kRθ/πKc data for a native sample in 0.1 M aqueous NaCl at 25 °C. On the other hand, our q of about 50 nm is roughly one-third of that (144 nm) reported by these workers, who utilized the kRθ/πKc data (see ref 27 for the procedure), assuming the Schulz-Zimm distribution with Mw/Mn ) 2 for the native sample. The large discrepancy in the wormlike-chain parameter set is beyond the possible uncertainties arising from light scattering measurements and approximations involved in the theories and thus remains to be seen by further experiment. Ordered Conformation. The molecular weight of the succinoglycan repeat unit shown in Figure 1 is equal to 1512 in the Na salt form, but for the average succinate content 0.8 (see the Experimental Section), it is 1491. If the ordered succinoglycan conformation in 0.1 M aqueous NaCl is assumed to be a single helix with a contour length of 1.92 nm per repeating unit,7 the M0 of 1491 yields a value of 777 nm-1 for ML. This linear mass density is approximately half those obtained from the above analyses of the 〈S2〉z and [η] data. Hence, we may conclude that, in contrast to the earlier proposals by Dentini et al.6 and Gravanis et al.7 mentioned in the Introduction, the predominant molecular species of the polysaccharide present in 0.1 M aqueous NaCl 25 °C, i.e., in the ordered state, is a double helix or an aggregate of paired single helices. This does not seem to contradict the observed irreversibility of the thermally induced conformation change. To reconcile the single helix model with the observed irreversibe viscosity change for a native sample, Gravanis et al.4,7,8 hypothesized the following: the main chain of succinoglycan in the native form contains some breaks that are masked by main chain-side chain interactions at low temperatures but revealed by heating to produce shorter chains; and cooling of the heat-treated solution no longer restores the original masked state. However, this hypothesis does not apply to sonicated samples exhibiting similar irreversible changes, because sonication should readily break such masked portions in the main chain. In any event, our ML from light scattering and viscometry is inconsistent with Gravanis et al.’s estimate of the linear charge density based on the Manning theory11 for the transport coefficient appearing in the conductivity. On the other hand, the aggregated single-helix model by Dentini et al.6 came from the ML value of 1000 nm-1, which is intermediate between those expected for single and double chains. This model differs from ours only in the number of single helices pertaining to aggregates provided that we choose the aggregate of paired single helices for the ordered conformation. Hence, the difference directly reflects that in the estimated ML. The light scattering data of Dentini et al. were self-consistent, in that the estimated wormlike-chain parameters (ML ) 1000 nm-1 and q ) 144 nm) gave 〈S2〉z a

Kido et al.

value of 2.21 × 105 nm2 very close to the measured one (2.17 × 105 nm2). However, as anticipated from these parameters, this experimental 〈S2〉z is much larger than ours when compared at the same Mw (see Figure 5), even though our samples are considerably sharper in molecular weight distribution. Thus, the contradictory molecular pictures come from a quantitative difference in light scattering data between Dentini et al. and us. We have shown that our 〈S2〉z data are consistent with the [η] data in Figure 6. In this connection, we note that Dentini et al.’s [η] for the native sample in 0.1 M aqueous NaCl seems too small compared to what is expected from their wormlike-chain parameters or 〈S2〉z. Concluding Remarks The molecular weight dependence of 〈S2〉z and [η] for succinoglycan in 0.1 M aqueous NaCl at 25 °C is explained by an unperturbed wormlike chain with a persistence length of about 50 nm and a linear mass density of about 1500 nm-1. The latter value is almost twice that expected for a single chain, so that the ordered conformation of the polysaccharide is a double-stranded helix or an aggregate composed of paired single helices. Both models require Mw to decrease to one-half when the polymer is brought to the completely disordered state at elevated temperature. Experimental evidence for this is available,28 but an important problem still remains as to which of the models is the case with the ordered structure of succinoglycan. No crystalline structure is yet known probably because of the low crystallinity of the polysaccharide. In this situation, a detailed analysis of thermally induced changes in both chirooptical and conformation-dependent properties including the molecular weight, i.e., changes in both local and global conformations, for a given sample seems mandatory to settle the problem. Such work will give a clear-cut answer to the ordered structure and also to a clear molecular picture for its thermal-breaking process. Acknowledgment. This work was commenced according to the suggestion by Professor M. Rinaudo, to whom one of the authors (T. Norisuye) is very grateful. References and Notes (1) Harada, T.; Harada, A. In Polysaccharides in Medical Applications; Dumitriu, S., Ed.; Marcel Dekker: New York, 1996; p 21. (2) Harada, T.; Amemura, A.; Jansson, P. E.; Lindberg, B. Carbohydr. Res. 1979, 77, 285. (3) Matulova, M.; Toffanin, R.; Navarini, L.; Gilli, R.; Paoletti, S.; Cesaro, A. Carbohydr. Res. 1994, 265, 167. (4) Gravanis, G.; Milas, M.; Rinaudo, M.; Tinland, B. Carbohydr. Res. 1987, 160, 259. (5) Fidanza, M.; Dentini, M.; Crescenzi, V.; Del Vecchio, P. Int. J. Biol. Macromol. 1989, 11, 372. (6) Dentini, M.; Crescenzi, V.; Fidanza, M.; Coviello, T. Macromolecules 1989, 22, 954. (7) Gravanis, G.; Milas, M.; Rinaudo, M.; Clarke-Sturman, A. J. Int. J. Biol. Macromol. 1990, 12, 195. (8) Gravanis, G.; Milas, M.; Rinaudo, M.; Clarke-Sturman, A. J. Int. J. Biol. Macromol. 1990, 12, 201. (9) Burova, T. V.; Golubeva, I. A.; Grinberg, N. V.; Mashkevich, A. Ya.; Grinberg, V. Ya.; Usov, A. I.; Navarini, L.; Cesaro, A. Biopolymers 1996, 39, 517. (10) Boutebba, A.; Milas, M.; Rinaudo, M. Biopolymers 1997, 42, 811. (11) Manning, G. S. Biopolymers 1970, 9, 1543.

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Ordered Conformation of Succinoglycan (12) Yamakawa, H. Helical Wormlike Chains in Polymer Solutions; Springer: Berlin, 1997. (13) Kratky, O.; Porod, G. Recl. TraV. Chim. Pays-Bas 1949, 68, 1106. (14) Fujita, H. Polymer Solutions; Elsevier: Amsterdam, 1990. (15) Norisuye, T. Prog. Polym. Sci. 1993, 18, 543. (16) Dezˇelic´, Gj.; Vavra, J. Croat. Chem. Acta 1966, 38, 35. (17) Rubingh, D. N.; Yu, H. Macromolecules, 1976, 9, 681. (18) Sato, T.; Norisuye, T.; Fujita, H. Macromolecules, 1983, 16, 185. (19) Norisuye, T.; Yanaki, T.; Fujita, H. J. Polym. Sci., Polym. Phys. Ed. 1980, 18, 547. (20) Odijk, T. J. Polym. Sci: Polym. Phys. Ed. 1977, 15, 477. (21) Skolnick, J.; Fixman, M. Macromolecules 1977, 10, 944.

(22) (23) (24) (25) (26) (27)

Le Bret, M. J. Chem. Phys. 1982, 76, 6243. Benoit, H.; Doty, P. J. Phys. Chem. 1953, 57, 958. Schmidt, M. Macromolecules, 1984, 17, 553. Yamakawa, H.; Fujii, M. Macromolecules 1974, 7, 128. Yamakawa, H.; Yoshizaki, T. Macromolecules 1980, 13, 633. Schmidt, M.; Paradossi, G.; Burchard, W. Makromol. Chem., Rapid Commun. 1985, 6, 767. (28) Kaneda, I.; Kobayashi, A.; Miyazawa, K.; Yoshida, M.; Ohno, K.; Yanaki, T. Manuscript in preparation.

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