Biomacromolecules 2005, 6, 1397-1404
13C
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Nuclear Magnetic Relaxation Study of Segmental Dynamics of Hyaluronan in Aqueous Solutions Photis Dais,*,† Emmanuel Tylianakis,† John Kanetakis,† and Francois R. Taravel‡
NMR Laboratory, Department of Chemistry, University of Crete, 71409 Heraklion, Crete, Greece, and Centre de Recherches sur les Macromolecules Vegetales (CERMAV), CNRS, BP 53, 38041 Grenoble Cedex 9, France Received October 29, 2004; Revised Manuscript Received January 17, 2005 13C
spin-lattice relaxation times (T1) and nuclear Overhauser enhancements (NOE) were measured as a function of temperature and magnetic field strength for the hetero-polysaccharide hyaluronan in water solutions. The relaxation data of the endocyclic ring carbons were successfully interpreted in terms of chain segmental motions by using the bimodal time-correlation function of Dejean de la Batie, Laupretre and Monnerie. On the basis of the calculated correlation times for segmental motion and amplitudes of librational motions of the C-H vectors at the various carbon sites of the HA repeating unit, we concluded that intramolecular hydrogen bonding of the secondary structure of HA plays a major role in the conformational flexibility of this carbohydrate molecule. The internal rotation of the free hydroxymethyl groups about the exocyclic C-5-C-6 bonds superimposed on segmental motion has been described as a diffusion process of restricted amplitude. The rate and amplitude of the internal rotation indicate that the hydroxymethyl groups are not involved in intramolecular hydrogen bonding. Finally, the motional parameters describing the local dynamics of the HA chain were correlated with the secondary structure of HA in aqueous solutions. Introduction Hyaluronan (HA) is a high molecular weight, linear polysaccharide with a repeating disaccharide unit poly [(1f3)-β-D-GlcNAc-(1f4)-β-D-GlcA] (Figure 1), found in the extracellular matrix of most animals.1,2 Its important medical applications and biological activities evoked intensive research work in the past decade.1,3 The consensus general chemical picture of HA is that this natural polymer adopts in aqueous solutions a tertiary structure (β sheets) consisted of 2-fold helices (secondary structure) stabilized by an intra and intermolecular hydrogen bonding network.2-7 The so formed β sheets degrade upon warming above ∼40 °C or upon alkalizing the solution to pH > 12.0.8 The secondary and tertiary structures of HA may explain the solution behavior of HA. Hydrodynamic measurements in aqueous solutions of HA are consistent with a stiffened wormlike coil, arising mainly from an extensive intramolecular hydrogen- bonding network stabilizing its secondary structure.2,8 Also, it has been suggested that intermolecular hydrogen bonds contribute to conformational ordering and promote a clustering of hydrophobic groups, which forms the basis for chain-chain intermolecular interactions in the tertiary structure.2,8,9 In the past, several experimental10-14 and theoretical studies15,16 attempted to correlate the properties of various polysaccharides with their chemical structures, conformations, and complete three-dimensional structures with re* To whom correspondence should be addressed. † University of Crete. ‡ CERMAV, CNRS; affiliated with the Joseph Fourier University of Grenoble.
Figure 1. Chemical structure of hyaluronan.
markable success. The structural and dynamic effects of intraand intermolecular interactions on local chain mobility were monitored experimentally by performing 13C NMR relaxation measurements. The relaxation parameters obtained from these experiments were interpreted by using second-rank theoretical time-correlation functions, which are projections of mechanisms and rates of motions occurring in the carbohydrate chain. The conformational freedom of hyaluronan was most studied by NMR spectroscopy by considering short oligosaccharide chains.17-20 In some instances, the experimental NMR relaxation data were compared with MD simulations19,21 and with theoretical values calculated using advanced second-rank theoretical time-correlation functions incorporating hydrodynamic terms in combination with MD simulations.16 These investigations demonstrated in a qualitative or semiquantitative manner the importance of the hydrogen-bonding network in local conformations and local sensitivity to conformational changes. Although theoretical and experimental relaxation studies on short HA chains are useful and give some preliminary information about local mobility, this dynamic picture may not be compatible while going to the polymeric material, where secondary and tertiary structures persist. In this case, different relaxation mechanisms with different relaxation
10.1021/bm040076d CCC: $30.25 © 2005 American Chemical Society Published on Web 02/26/2005
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Table 1. Experimental Carbon-13 Spin Lattice Relaxation Times (T1 in ms) and NOE Factors (in Parentheses) for the Protonated Carbons of Hyalorunan in D2O Solutions as a Function of Temperature and Magnetic Field Strength temp. °C
U1
U2
U3
U4
U5
A1
A2
A3
A4
A5
A6
391 (1.55) 367 (1.57) 379 (1.65) 388 (1.68) 407 (1.75) 425 (1.89) 469 (1.97)
383 (1.55) 372 (1.62) 384 (1.70) 393 (1.83) 414 (1.89) 429 (1.88) 469 (1.94)
430 (1.49) 421 (1.60)) 428 (1.70) 443 (1.71) 450 (1.74) 465 (1.93) 492 (1.99)
414 (1.51) 385 (1.59) 412 (1.70) 428 (1.79) 440 (1.80) 457 (1.85) 494 (1.95)
205 (1.60) 181 (1.59) 194 (1.70) 206 (1.79) 225 (1.80) 252 (1.85) 276 (1.95)
25 35 45 55 65 75 85
375 (1.51) 371 (1.53) 399 (1.70) 400 (1.80) 408 (1.74) 445 (1.80) 467 (2.03)
394 (1.42) 408 (1.55) 401 (1.62) 414 (1.67) 428 (1.78) 465 (1.85) 481 (1.90)
396 (1.50) 395 (1.53) 411 (1.56) 429 (1.65) 440 (1.71) 460 (1.80) 486 (2.00)
380 (1.50) 368 (1.55) 375 (1.60) 390 (1.65) 405 (1.75) 407 (1.81) 414 (1.98)
125.7 MHz 403 (1.67) 395 (1.52) 396 (1.72) 391 (1.55) 398 (1.76) 394 (1.65) 424 (1.78) 401 (1.79) 431 (1.78) 429 (1.77) 453 (1.84) 450 (1.82) 464 (2.00) 476 2.00)
25 35 45 55 65 75 85
321 (1.59) 297 (1.67) 334 (1.77) 354 (1.80) 373 (1.83) 385 (1.85) 408 (2.03)
356 (1.52) 326 (1.61) 312 (1.66) 359 (1.76) 371 (1.79) 388 (1.89) 432 (2.04)
305 (1.62) 291 (1.69) 342 (1.72) 364 (1.75) 391 (1.86) 405 (1.90) 429 (1.99)
307 (1.56) 294 (1.65) 306 (1.69) 322 (1.79) 330 (1.82) 351 (1.85) 367 (1.98)
100.5 MHz 355 (1.75) 311 (1.64) 340 (1.79) 330 (1.67) 333 (1.80) 340 (1.70) 347 (1.87) 362 (1.80) 360 (1.91) 370 (1.84) 385 (1.99) 396 (1.90) 411 (2.03) 425 (2.08)
336 (1.58) 324 (1.67) 320 (1.71) 337 (1.82) 350 (1.88) 378 (1.91) 393 (1.99)
319 (1.58) 285 (1.68) 310 (1.73) 336 (1.83) 361 (1.87) 370 (1.93) 403 (2.00
367 (1.58) 359 (1.64) 324 (1.73) 389 (1.79) 396 (1.83) 410 (1.97) 438 (2.07)
333 (1.56) 323 (1.74) 315 (1.80) 348 (1.87) 379 (1.92) 399 (1.99) 421 (2.08)
182 (1.50) 148 (1.61) 176 (1.74) 193 (1.95) 200 (2.01) 214 (2.06) 234 (2.26)
25 35 45 55 65 75 85
244 (1.71) 251 (1.78) 264 (1.82) 274 (1.89) 285 (1.95) 308 (2.00) 381 (2.10)
252 (1.66) 230 (1.75) 251 (1.87) 272 (1.92) 294 (2.01) 326 (2.03). 348 (2.07)
269 (1.68) 251 (1.75) 248 (1.78) 274 (1.82) 278 (1.95) 309 (2.06) 337 (2.12)
227 (1.66) 236 (1.73) 238 (1.84) 254 (1.85) 266 (1.94) 275 (2.00) 302 (2.08)
75.4 MHz 246 (1.75) 236 (1.68) 250 (1.85) 242 (1.75) 261 (1.89) 266 (1.86) 278 (1.97) 280 (1.94) 299 (2.02) 297 (2.02) 319 (2.10) 333 (2.10) 340 (2.23) 392 (2.14)
232 (1.68) 238 (1.88) 253 (1.93) 271 (1.96) 280 (2.05) 291 (2.08) 346 (2.12)
258 (1.69) 258 (1.79) 239 (1.81) 263 (1.93) 289 (1.99)) 308 (2.07) 343 (2.17)
250 (1.82) 240 (1.83) 269 (1.89) 297 (1.97) 322 (2.02) 335 (2.06) 347 (2.13)
258 (1.65) 250 (1.78) 263 (1.83) 288 (1.93) 312 (1.99) 360 (2.04) 374 (2.22)
124 (1.52) 122 (1.75) 136 (1.82) 154 (2.06) 167 (2.13) 179 (2.29) 194 (2.42)
rates are expected to describe the chain segmental dynamics and side-chain internal motions.10 Accordingly, we decided to perform variable temperature, multifield 13C NMR relaxation experiments of polymeric HA in water solutions at three magnetic fields to probe its dynamic features. We will show that the T1 and NOE data can be interpreted by the theoretical time-correlation function developed by Dejean-LaupretreMonerie (DLM) and provide a satisfactory quantitative picture of the local motions in HA. Experimental Section Materials. Deuterated water (D2O) solvent was purchased from Aldrich (Athens-Greece). The HA sample in its Na form was a gift from Professors M. Milas and M. Rinaudo and Dr Katia Haxaire at CERMAV. It was obtained by hydrolysis of hyaluronan purchased from ARD (Agroindustries R&D) (Pomacle-France) in 1 M HCl solution at 50 °C for 75 min and neutralized with NaOH. The HA polymer was recovered by precipitation with a mixture of water and ethanol, centrifuged, and washed with ethanol. The weightaverage molecular weight of HA was determined by steric exclusion chromatography (SEC), and it was found to be Mw ) 86 100. The polydispersity of the sample was Mw/Mn ) 1.3, and its intrinsic viscosity measured in 0.1 M NaCl solution was found to be 393 mL g-1. Experimental details for these measurements can be found in ref 22. NMR Relaxation Measurements. 13C NMR relaxation measurements were conducted at three 13C Larmor frequencies, 75.4, 100.5, and 125.7 MHz on Bruker AC300, AM400, and AMX500 spectrometers, respectively, under broadband proton decoupling. The temperature was controlled to within
(1° C by means of precalibrated thermocouples in the probe inserts. Spin-lattice relaxation times (T1) were measured by the standard IRFT method with a repetition time longer than 5 × T1. A total of 256-720 transients were accumulated for a set of 8-12 arrayed t values, depending on the type of spectrometer and temperature. The 180° pulse width was ranged from 27 to 29 µs in the three spectrometers. Values of T1 were determined by a three-parameter nonlinear procedure with a rms error of (5-8%. The reproducibility of each T1 value was (5% or better. NOE experiments were carried out by the inverse gated decoupling technique. At least three experiments have been performed at each temperature value. Delays of at least 10 times the longest T1 were used between 90° pulses. NOE values were estimated to be accurate to within (15%. Undegassed samples of HA in D2O solutions (5% w/v) were used for the 13C relaxation experiments. Measurements with degassed samples did not show any measurable difference in the 13C relaxation parameters relative to those of the undegassed samples in agreement with earlier reports11,13 in polysaccharide systems that show relaxation parameters in the milliseconds time-scale. Numerical Calculations. The relaxation data were analyzed by using the MOLDYN program23 modified by us to include the spectral density functions used in the present study. The parameters of a given model were optimized until the sum of the squares of deviations of the difference between theoretical and experimental relaxation data reached a minimum. Details of the program and calculation procedure by employing various models have been given elsewhere.10,23
Study of Segmental Dynamics of Hyaluronan
Biomacromolecules, Vol. 6, No. 3, 2005 1399
Figure 2. Temperature dependence of the experimental and calculated relaxation data for the GlcNAc ring carbons of hyaluronan in D2O at magnetic field strength 75.4 MHz (2), 100.5 MHz ([), and 125.7 MHz (b). For carbon A4 (a) NT1 and (b) NOE; for carbons A1, A2, A3 and A5 (c) NT1 and (d) NOE; for hydroxymethyl carbon A6. (e) NT1 and (f) NOE. Curves correspond to the DLM fitting of NT1 and NOE values.
Results and Discussion Frequency and Temperature Dependence of the 13C NMR Relaxation Data. The variable temperature, multifield relaxation 13C NT1 (N is the number of directly attached protons to carbons), and NOE factors of the individual protonated ring carbons and the exocyclic hydroxymethyl group of the β-D-GlcNAc ring in D2O solutions at each temperature and magnetic field strength are summarized in Table 1. The relaxation parameters of the ring carbons A1, A2, A3, and A5 and U1, U2, U3, and U5 (the usual notation A and U for the rings GlcNAc and GlcA, respectively, was adopted for each ring carbon atom in HA17) were similar within experimental error, and hence, the average values will be used to describe the dynamics of the present polysaccharide in water. However, the relaxation parameters for the A4 and U4 carbons of HA in water were different from the
corresponding values of the remaining ring carbons (Table 1). These data are also shown graphically in Figures 2a-d and 3a-d. Figures 2a,b and 3a,b present the temperaturedependence of the experimental NT1 and NOE values of the ring carbons A4 and U4, respectively, at three magnetic field strengths, whereas Figures 2c,d and 3c,d illustrate the average relaxation data of the remaining ring carbons. These results are different than those obtained from previous 13C relaxation studies for polymeric HA in aqueous solutions, which showed no significant differences in the relaxation parameters NT1 among the various protonated carbons in the β-DGlcNAc and β-D-GlcA rings.20,24 Nevertheless, these measurements were performed at one magnetic field strength and at low temperatures (22 and 35 °C), where viscous damping effects dominate the segmental motions of the polysaccharides.25 Moreover, it has been suggested by many authors10,26-28
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Figure 3. Temperature dependence of the experimental and calculated relaxation data for the GlcA ring carbons of hyaluronan in D2O at magnetic field strength 75.4 MHz (2), 100.5 MHz ([), and125.7 MHz (b). For carbon U4 (a) NT1 and (b) NOE; for carbons U1, U2, U3 and U5 (c) NT1 and (d) NOE. Curves correspond to the DLM fitting of NT1 and NOE values.
that nuclear magnetic relaxation measurements for polymeric materials should be performed at several magnetic field strengths to sample motions at a wider frequency range. Finally, the relaxation parameters of the hydroxymethyl carbon are shown graphically in Figure 2e,f. Inspection of these figures reveals a number of motional characteristics that are commonly observed in the 13C relaxation data for carbohydrate polymers:10-14 (1) as the temperature decreases, the NT1 values decrease monotonically, at all magnetic field strengths, reaching a minimum, which is followed by an increase in NT1 with further decrease in temperature; (2) the minimum is shifted to higher temperatures (shorter correlation times) as the magnetic field increases, the difference in NT1 values among the magnetic field strengths becoming more pronounced as the temperature decreases (slow motion regime); (3) at a given temperature, NT1 values increase, and the NOE factors decrease with increasing magnetic field strength; (4) at high temperatures, where motions become faster, NOE values are less than the theoretical asymptotic value of 2.988. These experimental observations are attributed to the local anisotropy of the relaxation process, and, thus preclude the possibility of describing the local dynamics of HA using a singleexponential time correlation function (TCF).10,26,27 The same trends are observed for the exocyclic hydroxymethyl carbon (Figure 2e,f), although the NT1 minimum in this curve is shifted to lower temperature relative to those of the ring carbon at the same magnetic field strength, indicating that this exocyclic carbon is more mobile than the ring carbons. This conclusion is further supported by the higher NOE
values of the hydroxymethyl carbon relative to those of the ring carbons (for instance compare parts b and f of Figure 2 and/or the corresponding data in Table 1). However, even for this mobile group, the NOE values do not reach their maximum values at high temperatures. Another interesting feature of the present data is that the ratios of the NT1 values of the A4 and U4 carbons to the NT1 values of the remaining ring carbons; that is, NT1 (A4)/ NT1 (A1, A2, A3, A5) and NT1 (U4)/NT1 (U1, U2, U3, U5) are fairly constant at 1.08 ( 0.04 and 0.91 ( 0.03, respectively, at all magnetic field strengths throughout the temperature range studied. These values differ from unity, which is expected from the number of directly bonded protons, and suggest different local motions for the C-H internuclear vectors associated with carbons A4 and U4 and the remaining ring carbons. Cowman et al.20 reported recently 13C NMR NT1 relaxation data for HA polymer and HA oligosaccharides in water and DMSO solutions at 22 °C and Larmor frequency of 75 MHz for the carbon nucleus. They concluded that the critical chain length of a HA oligomer in water for which the interior sugars have about the same characteristic NT1 average value (215 ms) as that of polymer (226 ms) in the same solvent is n ) 7, where n is the number of the disaccharides (GlcAGlcNAc) in the oligomer. Our relaxation data for the HA polymer in water at 75 MHz show that the minimum in the curve of NT1 vs temperature occurs at ∼35 °C corresponding to an NT1 average value of 243 ms. Slightly longer average relaxation time is observed at lower temperature (248 ms at 25 °C).
Biomacromolecules, Vol. 6, No. 3, 2005 1401
Study of Segmental Dynamics of Hyaluronan
Modeling the Dynamics of HA. When the dynamics of polysaccharides are modeled, two types of motions are considered:11-14 first the overall rotatory diffusion of the carbohydrate chain as a whole and second local chain motions. Local chain motions in a carbohydrate chain are considered to be (1) the oscillatory motions about the glycosidic bonds, which represent the so-called segmental motions; (2) internal motions of substituents attached to the carbohydrate chain via chemical bonds, such as the exocyclic hydroxymethyl group of HA. (3) A third type of very fast local motions (10-11-10-10 s), which have been found to occur in other polysaccharide systems,11-14 are the small amplitude librations of particular backbone C-H vectors within a potential well. Each of these motions is considered to be an independent source of motional modulation of the 13 C-1H dipole-dipole interactions for the protonated carbons of the polysaccharides. OVerall Motion. For sufficiently high molecular weight random coil polymers (above a critical value of 1000-10 000 depending on chemical structure), the overall motion is much slower than the chain local motions (10-7-10-5 s). Thus, it makes a negligible contribution to the NT1 values of the backbone and side-chain carbons.10,26 The molecular weight of the present polysaccharide molecule lies above this limit. Our neglect of the overall motion is further supported by estimation of the overall motion correlation time, τR of HA. Since, the correlation time of the overall motion cannot be determined from relaxation data alone (all carbons in the carbohydrate chain relax via both the overall and local motions), this parameter must be simulated by using either light scattering experiments or hydrodynamic measurements. Using the latter methodology, the correlation time τR of HA can be calculated from the following hydrodynamic equation:29 τR )
2MW[η]η0 3RT
(1)
Mw is the average molecular weight, [η] is the intrinsic viscosity of the polymer solution, and η0 is the solvent viscosity. By substituting in eq 1 the measured intrinsic viscosity of HA in 0.1 M NaCl solution [η] ) 393 mL‚g-1, its molecular weight, Mw ) 86 100 g mol-1, and the viscosity of water at 25 °C, 0.891 cP, we obtain the correlation time for the overall motion, τR ) 8.1 × 10-6 s. The calculated τR for HA should represent the polysaccharide behavior in the high molecular weight limit. Thus, the reported relaxation parameters should be dominated by local polymer dynamics. Backbone Motions. In polymers, the dominant relaxation process is the 13C-1H dipole-dipole interactions. For these systems, only interactions with directly bonded protons need be considered. Under conditions of complete proton decoupling, the 13C relaxation parameters, NT1 and NOE, can be written in terms of the spectral density function, Ji (ωi), as follows (in the SI system):30 Ω 1 ) [J0(ωH - ωC) + 3J1(ωC) + 6J2(ωH + ωC)] DD 10 T1
(2)
NOE ) 1 +
γH ΩTDD 1 [6J2(ωH + ωC) + J0(ωH - ωC)] γC 10
(3)
and Ω)
(
)
µ0γHγCh 2
8π rCH
3
2
where γΗ and γC are the gyromagnetic ratios of proton and carbon nuclei, respectively, ωΗ and ωC are their respective Larmor frequencies, µ0 is the vacuum magnetic permeability, h is the Planck’s constant, and rCH is the C-H internuclear distance. The spectral density function required for the calculation of the relaxation parameters by means of eqs 2 and 3 should be obtained upon Fourier transform of the appropriate timecorrelation function (TCF), Gm Jm(t) ) 2Re[
∫0∞ Gmeiωt dt]
(4)
Re indicates the real part of the complex Fourier transform. Several attempts10-14 have been made in the past to interpret the relaxation behavior of polysaccharides in solution by employing a variety of theoretical TCFs (models). The ability of the various models to describe the dynamics of the segmental motions of polysaccharides in solutions has been tested in previous publications on linear homo-, hetero-, and branched polysaccharides.10-14 Among these, the bimodal time-correlation function developed by Dejean, Laupreˆtre, and Monnerie31 (DLM) offered a much better description of the segmental dynamics of these biopolymers. Therefore, the DLM model will be used in the following analysis. The DLM time-correlation function describes the backbone reorientation in terms of two motional processes: (1) a diffusion process along the carbohydrate chain, which occurs via conformational transitions described by two correlation times τ0 and τ1, for isolated conformational transitions and for cooperative transitions, respectively, and (2) bond librations, i.e., wobbling in a cone motion of the backbone internuclear C-H vectors. The librational motion is associated with a correlation time τ2, whereas the cone-half-angle θ determines the extent of the libration about the rest position of the C-H bond that coincides with the axis of the cone. The DLM spectral density function is given explicitly by Dejean de la Batie et al.31 The best-fit NT1 and NOE data, as a function of temperature and magnetic field for the backbone ring carbons of the repetitive unit of HA by employing the DLM model is shown graphically in Figures 2 and 3. It is seen from these plots that good agreement between experimental and calculated values is obtained from this model throughout the entire temperature range studied. In all cases, the percent difference between the experimental and calculated values was within the experimental error ((5-8% for T1 and (15% for the NOE values) of the relaxation measurements. For this model, the values of the fitting parameters are summarized in Table 2. The simulated values for the angles θ of for both groups of ring carbons, i.e., A1, A2, A3, and A5 and U1, U2, U3, and U5, are similar. The average value of 33° indicates the
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Table 2. Correlation Times (10-10 s) for Segmental Motions (τ1 and τ2) and Hydroxymethyl Internal Motion (τi), Librational Amplitudes (θ, deg), Diffusional Angles (χ, deg), and Activation Energies (kJ mol-1) Obtained From the DLM and Restricted Diffusion TCFs for Hyaluronan in D2O Solutions temp. °C
τ1
τi
2χ
25 35 45 55 65 75 85
9.84 8.19 6.92 5.15 4.22 3.44 2.62
0.138 0.122 0.109 0.087 0.076 0.067 0.055
84 88 98 100 104 106 112
τ0/τ1 τ1/τ2 θ(A1,2,3,5) θ(U1,2,3,5) θ (A4) θ (U4) Ea r
6 450 33 33 35 31 19.6 0.99
13.5 0.99
same local dynamics at these carbon sites. On the other hand, different local dynamics of the C-H vectors is observed at the A4 and U4 carbons reflected on their calculated angles θ (Table 2), which are 35° and 31°, respectively. This trend in the values of angle θ reflects the magnitude of steric hindrance of neighboring substituents or other geometrical factors affecting the librational motion at the various carbon sites of HA (see below). The fit of the relaxation data of the two rings in water solvent using the DLM model was obtained by following the constraint that the ratios τ0/τ1 and τ1/τ2 are constant over the whole temperature range.10,14,26,31-33 This may indicate that the shape of the DLM correlation function does not change with temperature. We shall examine this point later with more details. Also, Table 2 contains the apparent activation energies, Ea, of the segmental dynamics of HA in water. This value was obtained from Arrhenius-type plots of the logarithms of the τ1 values vs 1/T (1/K). The plot was linear (r ) 0.99) over the whole temperature range studied, yielding an apparent activation energy of Ea ) 19.6 kJ mol-1 for the local segmental dynamics at various backbone carbon sites. Dynamic Modeling of the Hydroxymethyl Groups Internal Motions of HA. A number of models exist in the literature describing internal mobility as a free rotation, restricted rotation about a bond, a wobbling motion in which a vector diffuses within a cone, or jumps between equivalent, or nonequivalent states. An extensive discussion of these models can be found elsewhere.10,26 The internal motion of the hydroxymethyl group superimposed on segmental motion cannot be described by assuming free rotation of 360°. Indeed, composite TCFs26 based on the DLM model and the Woessner equations34 for stochastic diffusion and jump processes did not reproduce the experimental data for the hydroxymethyl carbon of HA. For this reason time-correlation functions describing restricted internal motions superimposed on segmental motion should be used in the present analysis. Such TCFs are the internal two-state jump TCF35 and the restricted-amplitude internal diffusion TCF.36 Both TCFs have been used previously to describe the hydroxymethyl internal motions of several linear and branched polysaccharides.11-14 Only the diffusion model was successful in reproducing the experimental NT1 and NOE data for the hydroxymethyl carbon of HA and resulted in physically realistic values of the correlation times, which follow an Arrhenius-type behavior. In this model, O-6 atom moves continuously between two limiting values of an angle χ (i.e.,
Figure 4. Frequency-temperature superposition of the average 13C NMR NT1 values for the endocyclic GlcA ring carbons (closed symbols) and the endocyclic GlcNAc ring carbons (open symbols) of hyaluronan in D2O at magnetic field strength 75.4 MHz ([,)), 100.5 MHz (9,0), 125.7 MHz and (b,O).
the amplitude of restricted motion is 2χ). Restricted diffusion about a single axis has been solved analytically,36 and the resulting TCF can be combined with the TCF of the DLM model to give a new composite TCF, which incorporates the correlation time τi (or the diffusion constant, Di) associated with internal motion. The composite TCFs and spectral density functions for both models can be found in reference cited.26 Table 2 summarizes the optimized parameters of the diffusion model. The correlation times, τi, for the hydroxymethyl internal rotation is about 2 orders of magnitude smaller than the correlation times, τ1, of the segmental motion. The Arrhenius plots of the correlation times, τi, gave an activation energy of 13.5 kJ mol-1 for the hydroxymethyl group in D2O solvent. Furthermore, internal rotation is restricted in nature characterized by amplitudes, 2χ, between 85°-110°. Temperature-Frequency Superposition. Guillermo et al.33 have proposed a model independent temperature-frequency method to test whether the distribution of relaxation times is temperature independent. This superposition method is successful only if all relaxation times in the vicinity of 1/ωC, where ωC is the Larmor frequency of the carbon nucleus, have the same temperature dependence. In particular, a plot of log[T1(T)/ωC] vs log[τ(T) ωC] should superimpose the relaxation data obtained at different magnetic field strengths in a given solvent provided that the shape of the TCF, which is a projection of mechanisms and rates of the segmental motions, is temperature independent, or in other words the same, all time constants that enter into explicit expression for the TCF have the same temperature dependence of a characteristic time constant τ(T). Such a superposition of our data for HA in D2O is presented in Figure 4. Constructing this plot, we have used the variable temperature relaxation data at the three magnetic fields in water (Table 1, and Figures 2 and 3) and the correlation time τ1 from Table 2. As can be seen from Figure 4, the relaxation data of the ring carbons superpose successfully over the whole temperature range of the present measurements. This indicates that the shape of the DLM time-correlation function is temperature independent. Interpretation of the Motional Parameters of HA. In a recent publication, Scott and Heatley8 reported the 13C
Study of Segmental Dynamics of Hyaluronan
chemical shifts of all ring carbon atoms of HA in aqueous solutions as a function of temperature. They observed shifts to higher frequencies, which were attributed to disruption of the tertiary structure of HA. This disaggregation effect, which can be also monitored by other means (alkalizing to pH > 12.0, digestion, and methylation of carboxylates), occurs at about 40 °C. Also, an inflection point was observed8 at the same temperature in the Arrhenius plot of log(line width) of acetamido CdO resonance vs 1/T, suggesting a change in the rotational state of the acetamido group upon disruption of the tertiary structure. No such inflection points were observed in the temperature dependence of the line widths of the other ring carbons of HA, although the corresponding signals sharpen somewhat with increasing temperature. On the basis of these findings, the authors concluded that above ∼40 °C the secondary structure of HA persists, stabilized by an intramolecular hydrogen-bonding network8 (Figure 1). Transition from the tertiary to secondary structure of HA in not reflected on the NT1 and NOE values of the protonated ring carbons of HA. In general, the NT1 values of carbons A4 and U4 diverge from the average NT1 values of the remaining ring carbons over the whole temperature range studied, indicating that the backbone local motions are affected solely by the geometry of the carbohydrate chain in the secondary structure. Also, neither the calculated correlation time τ1 of segmental motion (Table 2) nor the line widths (which are proportional to T/2) of the various signals of the protonated ring carbons in the spectra show any inflection point as a function of 1/T. Measurements of NT1, NT2, and NOE at low Larmor frequencies (
