4782
J. Phys. Chem. B 2000, 104, 4782-4790
Molecular Dynamics and Kinetics of Monosaccharides in Solution. A Broadband Ultrasonic Relaxation Study J. Stenger,| M. Cowman,† F. Eggers,‡ E. M. Eyring,§ U. Kaatze,*,| and S. Petrucci⊥ Drittes Physikalisches Institut, Georg-August-UniVersita¨ t, Bu¨ rgerstrasse 42-44, D-37073 Go¨ ttingen, Germany, Department of Chemical Engineering, Chemistry, and Material Science, Polytechnic UniVersity, Brooklyn, New York 11201, Max-Planck-Institut fu¨ r Biophysikalische Chemie, Am Fassberg, D-37077 Go¨ ttingen, Germany, Department of Chemistry, UniVersity of Utah, Salt Lake City, Utah 84112, and Chemistry Department, Polytechnic UniVersity, Route 110, Farmingdale, New York 11735 ReceiVed: NoVember 12, 1999; In Final Form: February 18, 2000
Between 100 kHz and 2 GHz ultrasonic absorption spectra have been measured for aqueous solutions of D-galactose, D-mannose, D-glucose, D-arabinose, D-ribose, D-lyxose, and D-xylose, as well as of the methylated derivatives methyl-β-D-xylopyranoside, methyl-β-D-glucopyranoside, and methyl-β-D-arabinopyranoside at 25 °C. A 1 molar solution of the latter carbohydrate did not show absorption in excess of the asymptotic high frequency contribution. The other solutions revealed relaxation characteristics which are described by up to three Debye spectral terms per spectrum. The relaxation times τR...τ of these terms indicate the existence of five relaxation regions for the carbohydrate solutions under investigation (500 e τR e 1500 ns; 40 e τβ e 150 ns; 3 e τγ e 12 ns; 0.5 e τδ e 2.1 ns; 0.1 e τ e 0.8 ns; 0.5 e c e 3.2 mol/L; 25 °C). These regions have been attributed to ring isomerization processes such as chair conformational changes and pseudorotations, to rotational isomerization of exocyclic groups, and to a carbohydrate association mechanism. Additional broadband dielectric relaxation measurements of some solutions showed that the reorientational motions of the hydration water molecules are much faster (relaxation time e 0.03 ns) than the aforementioned molecular processes.
1 Introduction Constituting one of the four major classes of biomolecules, carbohydrates play multiple roles in living nature. They serve as the main resource of energy in biological cells and form significant components of nucleic acids; they are linked to many proteins and lipids and contribute essentially to the structure and function of cell walls of bacteria and plants. Monosaccharides, though following the simple empirical formula (CH2O)n, display a great variety of structures and a fascinating conformational flexibility. The properties of monosaccharides in aqueous solutions are, therefore, of considerable significance not only in biochemistry. The interactions of these outstanding molecules with the unique hydrogen bond network of water are also a topic of current wide interest in liquid-state physics. Aiming at an experimental characterization of the molecular dynamics of monosaccharides in water we performed a systematic comparative study of their acoustical relaxation spectra. For this purpose, ultrasonic absorption measurements have been performed in the frequency range from 100 kHz to 2 GHz, corresponding with a relaxation time domain from about 1 µs to 100 ps. Previous ultrasonic studies of aqueous solutions of D-glucose and of some other carbohydrates1-4 have indicated that interesting processes such as ring conformational interconversions or exocyclic group rotations can be investigated using * Corresponding author. † Polytechnic University, Brooklyn. ‡ Max-Planck-Institut. § University of Utah. ⊥ Polytechnic University, Farmingdale. | Drittes Physikalisches Institut.
ultrasonic spectrometry at those frequencies. These processes are hardly accessible by other methods. 2 Experimental Section A. Carbohydrate Solutions. A survey of the monosaccharides considered in this paper is given in Figure 1. To accentuate the chemical differences between the compounds, only the dominating conformation of each carbohydrate in aqueous solution is shown. For simplicity and clearness chemical equilibria between the displayed structure and other molecular forms and confirmations are first neglected here. D(+)Glucose is included for reasons of comparison though, the spectra for solutions of this saccharide are taken from a previous paper.4 D(+)glucose and methyl β-D-glucopyranoside had been purchased from Fluka (Neu-Ulm, Germany), the other compounds from Sigma (Steinheim, Germany). With the exception of methyl-β-D-arabinopyranoside (>97%), D(+)mannose (> 98%), and D(+)galactose (>98%), the purity of the chemicals was higher than 99%. After being dried for at least 12 h at 60 °C under reduced pressure, the monosaccharides have been used as delivered by the manufacturer. Solutions have been prepared in volumetric flasks by weighing the carbohydrate and adding doubly distilled and deionized water up to the fiduciary mark. The water had been also sterilized by UV irradiation. To allow the anomer equilibrium to be established the first measurements have been started not earlier than 15 h after sample preparation, respectively. Between measurements the solutions were stored at 4 °C. Nevertheless, no solution was used longer than 10 days after the time of preparation. A survey of the solutions is given in Table 1 where some parameters of the liquids are also presented. The density F of the samples has been measured using
10.1021/jp9940194 CCC: $19.00 © 2000 American Chemical Society Published on Web 04/21/2000
Ultrasonic Spectrometry of Monosaccharide Solutions
J. Phys. Chem. B, Vol. 104, No. 19, 2000 4783
Figure 1. Structures of monosaccharides used in this study. Where more than one conformation exists in water, only the most frequent one is shown here.
TABLE 1: Mass Fraction Y, Molality m, Molar Concentration c of Solute, Density G, Viscosity ηs, and Sound Velocity cs of the Liquid for Aqueous Solutions of Monosaccharides at 25 °C solute D-glucose D-mannose D-galactose D-arabinose D-ribose D-lyxose D-xylose methyl-β-D-xylopyranosid
methyl-β-D-arabinopyranosid methyl-β-D-glucopyranosid
Y ((0.1%)
m, mol/kg ((0.1%)
c, mol/L ((0.2%)
F, g/cm3 ((0.2%)
103ηs, Pa‚s ((2%)
cs, m/s ((0.1%)
0.1691 0.1690 0.1690 0.1525 0.1525 0.1525 0.1525 0.0897 0.1759 0.2281 0.3904 0.4608 0.1759 0.0922
1.130 1.129 1.129 1.199 1.199 1.199 1.199 0.600 1.300 1.800 3.900 5.205 1.300 0.500
1.000 1.003 1.003 1.078 1.073 1.081 1.072 0.558 1.126 1.482 2.687 3.205 ∼1.1 0.465
1.065 1.069 1.069 1.061 1.056 1.064 1.055 1.021 1.051 1.067 1.130 1.142
1.47 1.54 1.57 1.37 1.41 1.53 1.41 1.17 1.60 2.01
1.025
1.20
1563 1562.5 1570 1566.5 1553 1560 1555 1537 1571 1600 1678 1713 1578 1532
a pycnometer that had been calibrated against distilled and degassed water. The (static) shear viscosity ηs of the solutions has been determined with the aid of a falling ball viscometer (type B/BH, Haake, Berlin, Germany). The sound velocity cs has been measured at around 300 kHz from the distances of a series Vrn, n ) 1, 2, ... of resonance frequencies of a cavity resonator cell used in the measurement of the absorption coefficient. Suitable theoretical expressions have been applied to properly account for the non-equidistancy of the Vn data.5 B. Ultrasonic Absorption Meausrements. Measurements of the sound absorption coefficient R of the sample liquids as a function of frequency V between 100 kHz and 2 GHz have been performed at the Drittes Physikalisches Institut. Two different spot frequency methods and altogether 8 specimen cells, each matched to a particular frequency range, have been used. At low frequencies (V < 15 MHz) we used a resonator method that was especially designed for small sample loss. Two planoconcave circular cylindrical cells,5 operated at frequencies between 0.1 and 2.7 MHz and between 0.5 and 2 MHz, respectively, mainly differed from one another by their cell length, l, which was 19 mm for the first cell and 9 mm for the second. The active transducer area (radius rT ) 35 mm), fundamental frequency VT (≈ 1 MHz) of transducer thickness vibrations, and the radius of curvature RT () 2 m) of the concavely shaped transducer were nearly the same for both cells. A biplanar6 circular cell (l ) 6 mm, rT ) 8.4 mm, VT ) 4 MHz) was applied in measurements between 0.8 and 15 MHz. A computer-controlled network analyzer has been utilized to record the complex transfer function of the resonator in a frequency
range around each resonance frequency of interest. The resonance frequency and quality factor have been obtained by fitting the transfer function data to analytical expressions, including higher order spurious modes. Corrections for the intrinsic instrumental cell loss have been made on grounds of calibration measurements in which the sample liquid had been replaced by a reference of well-known attenuation coefficient and with sound velocity and density as close as possible to the sample data. At frequencies above 3 MHz absolute measurements of R have been performed by transmitting a pulse-modulated traveling wave of frequency V through a cell of variable sample length. We used four different cells which mainly differ from one another by their dimensions and by the type of piezoelectric transducers used as transmitter and receiver. At low frequencies (3 e V e 60 MHz) X-cut quartz disks (VT ) 1 MHz, rT ) 20 mm) were operated at (2n + 1)VT, n ) 0, 1, ...7 Also operated at the transducer fundamental frequency VT and its odd overtones have been two other cells of which one was provided with 35° rotated Y-cut lithium niobate disks (VT ) 10.8 MHz, rT ) 6 mm, 30-500 MHz) sticking to acoustical delay lines made of quartz.8 The piezoelectric devices of the other cell (V > 0.8 GHz) consisted of thin ZnO films (VT ) 1.3 GHz, rT ) 1 mm, dT ) 1 µm) sputtered onto delay rods made of sapphire.9 At V > 0.5 GHz we also used a cell in which small lithium niobate rods (rT ) 1.5 mm) were driven as nonresonant broad-band transducers9 according to the method by Bo¨mmel and Dransfeld.10 To avoid errors arising from nonlinear characteristics of the electronic apparatus, calibration procedures were routinely run in which we replaced the specimen cells by specially
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Figure 2. Ultrasonic excess absorption spectra for 1 mol/L aqueous solutions of D-glucose (b) and D-galactose (]) at 25 °C. Dotted curves show the subdivision of the former spectrum into two Debye relaxation terms, dashed curves indicate the subdivision of the latter spectrum into three Debye terms. Full curves represent the complete excess absorption with the parameter values given in Table 2.
constructed high-precision below-cutoff piston attenuators.7,11 Because we got rather unexpected results for the methyl-β-Darabinoside sample, another solution of this carbohydrate has been additionally measured. In those measurements a further plano-concave resonator cell (rT ) 27.5 mm; VT ) 1.09 GHz; l ) 9.25 mm; RT ) 2 m; 500 kHz < V < 6 MHz) has been utilized. C. Sound Velocity Measurements. At V < 15 MHz the sound velocity cs of the samples has been determined from the frequencies of successive principal resonance peaks of the resonator cells, taking into account the non-equidistant distribution of the resonance frequencies.12 At high frequencies cs values have been derived from the waviness of the transfer function T(x), resulting from multiple reflections within the transmission cells at small transducer spacing x. D. Experimental Errors. The temperature T of the sample cells was controlled to within (0.03 K and it was measured with an accuracy of (0.02 K. Temperature gradients and differences in the temperature of different cells did not exceed 0.05 K, corresponding to the small estimated error of less than 0.1% in the R data of the liquids. During the period of measurement, fluctuations in the frequency of the sonic signals were smaller than 0.01% and can thus be completely neglected here. With the resonator measurements, the main sources of possible errors are small disturbances in the cell geometry and cell adjustment that might result from the cleaning and refilling procedure when the sample liquid is exchanged for the reference. The R values obtained from the pulse-modulated travelling wave transmission measurements may be affected by an imperfect parallelism of the transmitter and receiver transducer unit and by insufficient corrections for diffraction losses. Though strictly depending on the R values themselves the following errors may be taken to characterize the experimental accuracy of the absorption coefficient data: ∆R/R ) 0.1, 0.1-3 MHz; ∆R/R
) 0.05, 0.3-3 MHz; ∆R/R ) 0.015, 3-25 MHz; ∆R/R ) 0.01, 25-70 MHz; ∆R/R ) 0.008, 70-300 MHz; ∆R/R ) 0.03, 300-1000 MHz; ∆R/R ) 0.01, 1000-2000 MHz. Due to the overlaps in the frequency range of different apparatus and cells, systematic errors exceeding these values are most unlikely to remain unnoticed. The error in the sound velocity is ∆cs/cs ) 0.005, 0.1-500 MHz; ∆cs/cs ) 0.01, 500-2000 MHz. 3 Results and Analytical Description of Spectra In Figure 2 the ultrasonic excess absorption per wavelength, (∆λ)exc is displayed as a function of frequency V for 1 molar aqueous solutions of the hexoses D-glucose and D-galactose. The excess absorption, defined by
(Rλ)exc ) Rλ - BV
(1)
is shown here as the asymptotic high frequency contribution
(Rλ)asy ) BV
(2)
to the total absorption per wavelength; Rλ, is of minor interest here. In these relations
λ ) cs/V
(3)
is the sonic wavelength. Obviously quite different sonic spectra result for the solutions though the monosaccharides differ by the structural arrangement of only one OH group. Sonic excess absorption spectra for 1 molar aqueous solutions of two pentoses, D-ribose and D-xylose, are presented in Figure 3. Again, distinct differences in the ultrasonic properties of the solutions emerge, due to just small changes in the structure of the saccharide molecules. To gain more information on the nature of the observed relaxation processes, three methylated
Ultrasonic Spectrometry of Monosaccharide Solutions
J. Phys. Chem. B, Vol. 104, No. 19, 2000 4785
Figure 3. Ultrasonic excess absorption per wavelength, (Rλ)exc, displayed versus frequency V for 1 mol/L aqueous solutions of D-xylose (0) and D-ribose (b) at 25 °C. Full curves are the graph of the relaxation spectral function defined by eq 4 with the parameter values given in Table 2. Dashed curves indicate the Debye type relaxation contributions to the xylose spectrum.
derivatives have been included in this study. Figure 4 shows the (Rλ)exc spectra for five methyl-β-D-xylopyranoside solutions at different concentrations. These spectra exhibit a relaxation term at around 3 MHz, the relaxation frequency of which appears to be independent of the solute concentration c, whereas the relaxation frequency of relaxation contributions in the 200 MHz to 2 GHz region seems to depend on c. Methyl-β-Dglucopyranoside reveals relaxation characteristics similar to those of glucose (Figure 2). No ultrasonic excess absorption has been detected with the 1 M methyl-β-D-arabinopyranoside solution at 25 °C. It was found that the frequency dependent excess absorption per wavelength of the studied solutions can be adequately represented by a sum of up to three Debye-type relaxation terms. Hence, the total absorption per wavelength spectra have been analytically described by the relaxation function
R(V) )
N
Anωτn
n)1
1 + ω2τ2n
∑
+ BV
(4)
with N ) 1, 2, or 3. An and τn, n ) 1-3 are the relaxation amplitudes and relaxation times, respectively, and ω ) 2πV. The relaxation function has been fitted to the measured spectra using a nonlinear least-squares regression analysis13 that causes the reduced variance
χ2 )
1
I
∑
I - J - 1 i)1
(
)
(Rλ)i - R(Vi, Pj) ∆(Rλ)i
2
(5)
to adopt its minimum. Here (Rλ)i and ∆(Rλ)i, i ) 1, ..., I, are the data measured at frequencies Vi and the corresponding experimental errors, respectively. The Pj, j ) 1, ..., J, are the adjustable parameters of the model function, I is the number of frequencies of measurement, and J () 2N + 1) is the number of free parameters of the R(V) function (eq 4). The values obtained for the parameters Pj, along with their uncertainties as resulting from the fitting procedure, are given in Table 2. Since an inspection of the measured spectra (Figures 2-4) indicates five different relaxation regions, the data in Table 2, to facilitate their discussion in the light of molecular processes, have been ordered in terms of these relaxation regions. Between the following ranges of relaxation frequencies (2πτn)-1 is to be discriminated: R, 0.1-0.4 MHz; β, 1-4 MHz; γ, 10-40 MHz; δ, 70-300 MHz; , 200-2000 MHz. 4 Discussion A. Chair-Chair Conformational Transformation: The r Process. The sonic excess absorption spectra of 1 molar aqueous solutions of the three pentoses D-arabinose, D-lyxose, and D-ribose, at variance with D-xylose, clearly exhibit relaxation characteristics at frequencies around some one-hundred kHz (Figure 3). As the relaxation frequency of this process corresponds with the low frequency limit of our measuring range,
4786 J. Phys. Chem. B, Vol. 104, No. 19, 2000
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Figure 4. Ultrasonic excess absorption spectra for methyl-β-D-xylopyranoside solutions of different concentration (25 °C): (O), 0.5 mol/L; 9, 1 mol/L; ], 1.5 mol/L; 2, 2.7 mol/L; 3, 3.2 mol/L. The graphs represent the model relaxation spectral function eq 4 with the parameter values given in Table 2.
TABLE 2: Parameters of the Relaxation Spectral Function as Defined by Equation 4 for Monosaccharide Solutions at 25 °C A R, c, mol/L τR, ns 10-3 τβ, ns ((0.2%) ((8%) ((7%) ((8%) D-galactose
1.003 1.003 D-glucose 1.000 D-arabinose 1.078 512 D-ribose 1.073 1480 D-lyxose 1.081 1303 D-xylose 1.072 methyl-β-D-xylopyranosid 0.558 1.126 1.482 2.687 3.205 methyl-β-D-glucopyranosid 0.465 methyl-β-δD-arabinopyranosid ∼1.1
152 69
D-mannose
0.20 0.92 0.88 40 69.6 51.0 56.6 57.8 61.6
Aβ,
10-3
τγ, ns
Aγ, 10-3 ((14%)
τδ, ns
Aδ, 10-3
τ, ns
A, 10-3
0.042 ( 0.003 5.5 ( 0.7 0.154 0.57 ( 0.06 1.08 ( 0.09 0.026 ( 0.011 12 ( 3 0.120 1.68 ( 0.06 1.17 ( 0.02 1.94 ( 0.07 2.01 ( 0.08 0.12 ( 0.09 3 ( 4 9.9 ( 1.2 0.067 0.38 ( 0.06 0.54 ( 0.11 3.3 ( 0.3 0.128 0.17 ( 0.07 0.8 ( 0.5 7.2 ( 0.9 0.118 0.6 ( 0.3 0.19 ( 0.08 0.041 ( 0.003 0.78 ( 0.06 0.43 ( 0.02 0.103 ( 0.003 0.69 ( 0.05 0.54 ( 0.03 0.271 ( 0.003 1.2 ( 0.4 0.28 ( 0.19 0.36 ( 0.01 1.23 ( 0.12 0.359 ( 0.004 1.3 ( 0.3 0.50 ( 0.23 0.35 ( 0.08 1.80 ( 0.17 0.963 ( 0.013 1.0 ( 0.1 2.3 ( 0.3 0.10 ( 0.03 17 ( 8 1.208 ( 0.014 1.1 ( 0.1 2.9 ( 0.3 0.16 ( 0.02 19 ( 3 1.65 ( 0.03 1.51 ( 0.02
the parameters of the relaxation term are only incompletely characterized by our measurements. Work is on progress at the University of Go¨ttingen to extend the measuring range down to significantly lower frequencies. Despite the considerable error in the present AR, τR data, it is possible to assign the R relaxation to the underlying molecular mechanism. Studying ultrasonic absorption spectra for solutions of methyl cyclohexane in xylene at different temperatures around 80 °C, Piercy has proposed a chair-chair 1C4 H 4C1 conformational equilibrium to be the cause of the acoustical relaxation.14 Extrapolating his results down to 25 °C leads to an estimated relaxation frequency of about 500 kHz. As compared
B, ps ((4%) 40.48 40.6 40.2 37.35 37.06 38.24 38.0 34.59 38.73 56.6 59.6 78.8 35.36 39.0
to the inert methyl cyclohexane/xylene mixtures, a stabilization of pentose structures in aqueous solution, due to solute/solvent interactions, accompanied by a downshift of the relaxation frequency, seems to be likely. We thus tentatively relate the R-relaxation to the 1C4 H 4C1 conformational equilibrium of the pentoses. The above suggestion is in conformity with the calculated interaction energies of pyranoses with water as shown in Table 3. In general, axial OH groups tend to destabilize the carbohydrate ring structure in water, particularly if the electric dipole moments of several hydroxy groups are aligned15 in parallel. Consequently, for pyranose with equal numbers of axial and
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TABLE 3: Chain Conformations and Conformational Free Energies for Aldopyranoses in Aqueos Equilibrium Solution39 conformation aldose R-D-glucose β-D-glucose R-D-mannose β-D-mannose R-D-galactose β-D-galactose R-D-arabinose β-D-arabinose R-D-lyxose β-D-lyxose R-D-ribose β-D-ribose R-D-xylose β-D-xylose
exp,NMR 4C
4C
1
4
1
4
4
4
4C
1
4C
1
4C
1
C1 C1 4C 1 4C 1 4C 1 1 C4
C1
4C
1 1 C4 4C ,1C 1 4 4C ,1C 1 4 4C 1 4C ,1C 1 4 4C ,1C 1 4 4C 1 4C 1
4
C1,1C4
4C
free energy calc., kJ/mol
calc.
1
4
C1,1C4 4C ,1C 1 4 4 C1 4C 1
C1
1C
10.08 8.61 10.5 12.37 11.97 10.5 13.44 12.18 8.61 10.5 14.49 10.5 8.19 6.72
27.51 33.6 23.31 32.13 36.46 32.55 8.61 10.08 10.92 14.91 14.91 13.02 15.12 16.38
4
TABLE 4: Percentage of the Pyranose and Furanose Forms in Aqueous Equilibrium Solution of Some Aldopyranoses39 pyranose
furanose
aldose
R
β
glucose mannose galactose arabinose lyxose ribose xylose
36 67 27 61 71 21.5 35
64 33 73 35 29 58.5 65
R
β
R+β
