Molecular Dynamics in Solid Riboflavin as Studied by 1H NMR

Solid State Nuclear Magnetic Resonance 18, 89–96 (2000) doi:10.1006/snmr.2000.0013, available online at http://www.idealibrary.com on

Molecular Dynamics in Solid Riboflavin as Studied by 1 H NMR E. R. Andrew and S. Glowinkowski∗ Department of Physics and Department of Radiology, University of Florida, P.O. Box 118440, Gainesville, Florida 32611; and ∗ Institute of Physics, A. Mickiewicz University, Ul. Umultowska 85, 61-627 Poznan, Poland Received August 29, 2000 Spin–lattice relaxation times T1 and T1d as well as NMR second moment were employed to study the molecular dynamics of riboflavin (vitamin B2 ) in the temperature range 55–350 K. The broad and flat T1 minimum observed at low temperatures is attributed to the motion of two nonequivalent methyl groups. The motion of the methyl groups is interpreted in terms of Haupt’s theory, which takes into account the tunneling assisted relaxation. An additional mechanism of relaxation in the high temperature region is provided by the motion of a proton in one of the hydroxyl groups. The Davidson–Cole distribution of correlation times for this motion is assumed. © 2000 Academic Press Key Words: riboflavin; vitamin B2 ; NMR; solid state; methyl relaxation; tunneling assisted relaxation.

1. INTRODUCTION Riboflavin, with chemical name 7,8-dimethyl-10-d-ribitylisoalloxazine, C17 H20 O6 N4 , is known as vitamin B2 [1, 2]. In its free form riboflavin occurs in the retina of the eye, whey, and urine. Its function in metabolism is concerned with the oxidation of carbohydrates of amino acids in the body. It is widely used in the pharmaceutical, food-enrichment, and feed supplement industries. It is found, to some degree, in virtually all naturally occurring food. Clinical signs and symptoms specific to mucous membranes and skin characterize its deficiency. Riboflavin forms fine yellow to orange–yellow needless. It melts with decomposition at 551–552 K. A schematic diagram of riboflavin is shown in Fig. 1. Due to the importance of riboflavin, many studies have been performed on this compound, but mainly on the form in which it appears in food and tissues. The main goal of the present studies was to examine molecular dynamics in solid riboflavin. 2. EXPERIMENTAL Polycrystalline riboflavin was kindly provided by Sigma. Without additional purification, the sample was sealed off in a glass tube under a vacuum. The NMR measurements were carried out on a homemade spectrometer operating at 14 and 25 MHz. Spin–lattice relaxation time T1 was determined using a saturation sequence 89 0926-2040/00 $35.00

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FIG. 1.

Molecular structure of riboflavin.

of 32π/2 pulses followed by a variable time interval τ and an inspecting π/2 pulse. The recovery of magnetization was found to be exponential within the experimental error, which was less than 10%, in the temperature range studied. In order to check the exponentiality of the magnetization recovery, the π/2–τ–π/2 sequence was also applied in some cases. The dipolar spin–lattice relaxation time T1d was measured by the method proposed by Jeener and Broekaert [3]. The second moment was found from fitting the magic-echo signal obtained by the simplified magic-echo sequence developed by Bowman and Rhim [4]. The temperature of the sample was controlled by means of a stationary variable-temperature controlled cryostat and monitored to an accuracy better than 1 K. 3. RESULTS The temperature dependences of proton spin–lattice relaxation time T1 at 14 and 25 MHz as well as T1d are shown in Fig. 2. Two minima of T1 at each frequency are observed. The low-temperature minimum is very broad and flat and has values of 65 and 94 ms for 14 and 25 MHz, respectively. The shape of the minimum is asymmetrical with a smaller slope on the low-temperature side of the minimum. The high-temperature minimum is less pronounced and amounts to 1.55 and 2.5 s for 14 and 25 MHz, respectively. The dipolar relaxation time increases as the temperature rises and goes through a shallow minimum at about 185 K. Figure 3 shows the temperature dependence of the second moment, M2 . It is characteristic that within the experimental error M2 almost does not change in the temperature range studied. 4. DISCUSSION The fact that the measured second moment is temperature independent may be interpreted in two ways. First, one can assume that no motion takes place in the temperature range studied. The other possibility involves an assumption that the

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FIG. 2. Proton spin–lattice relaxation times T1 and T1d in riboflavin versus reciprocal temperature: (◦) T1 , 25 MHz; (•) T1 , 14 MHz; (∇) T1d . Solid line represents the theoretical fit, while the dashed (1, 2) and dotted lines represent contributions at 25 MHz due to methyl and hydroxyl group motions, respectively.

observed second moment represents the plateau resulting from the motion, which started well below the temperatures available in the experiment. The existence of the low-temperature minimum of T1 supports the second possibility. Taking into account the chemical structure of riboflavin, it is reasonable to assume the occurrence of rotation of the methyl groups.

FIG. 3.

Proton second moment in riboflavin versus temperature.

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Since the proton relaxation processes are entirely governed by the dipolar interaction, the observed spin–lattice relaxation data can be approximated by the general expression [5, 6] 2
1 = γ2 M2i [J(ω) + 4J(2ω)] T1 3 i

(1)

where M2i is a part of the second moment averaged by the considered motion, Js are the spectral densities of the motion correlation functions, and ω is the Larmor frequency. The form of J depends on the details of a model used to explain the molecular dynamics. For methyl group rotation, very often a single correlation time is sufficient to describe its dynamical behavior and the spectral density is given by the relation [7] J(ω τ) =

τ  1 + ω2 τ 2

(2)

where τ is a correlation time for the motion whose temperature dependence is usually described by the Arrhenius relation. The motionally averaged part of the second moment depends on the molecular arrangement and the type of motion considered. The experimental data of Fig. 2 were fitted simultaneously to Eqs. (1) and (2) using the Marquardt technique [8]. Since the minimum of T1 is broad, flat, and asymmetrical, it was assumed that the methyl groups are inequivalent and their motional parameters are different. The reasonable fit was obtained with the motionally averaged part of the second moment equal to 0.035 mT2 . According to Van Vleck’s theory [9] of dipolar interaction, the second moment for a polycrystalline rigid sample is given by the relation M2 =

N 3γ 2
I(I + 1)
−6 rjk  5N j k

(3)

where rjk is the distance between nuclei j and k and N is a number of nuclei over which the sum is taken. Usually, the calculation of the second moment is separated into two terms known as intra- and intermolecular contributions. The intra contribution arises from the interaction between nuclei within the same molecule and is dependent on molecular structure, whereas the inter contribution results from the interaction between nuclei of neighboring molecules. The calculation of M2 can be performed only if the data on molecular structure and mutual arrangement of neighboring molecules are available. Due to lack of crystallographic data on riboflavin, the precise calculation of the second moment is not possible, but the measured value is similar to that in other compounds in which methyl groups are rotating [6, 10–13]. In the case of rotation of the methyl group, the motionally averaged part of the second moment results mainly from the reduction of the intra methyl groups contribution. The calculation [14] of this part of M2 was based on the positions

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of protons obtained by minimizing the potential energy of the molecule using the HyperChem program. The calculation performed assuming typical proton distances in methyl and methylene groups of 0.180 nm yielded the rigid lattice intramolecular contribution to the second moment in riboflavin of 0.129 mT2 . In the case of a rapid reorienting pair of nuclei, the motionally averaged part of the second moment amounts to M2i = M2 (1 − ρ)

(4)

where M2 is a second moment for rigid lattice and ρ is the reduction factor [15], ρ=

(3 cos2 θjk − 1)2  4

(5)

where θjk is the angle between the internuclear vector and the rotation axis. For the assumed molecule structure, the motionally averaged part of the second moment resulting from the methyl group rotation [14] is 0.052 mT2 , which is much greater than the value derived from fitting. This indicates that the description of methyl group rotation in terms of the single correlation time does not hold in the case of riboflavin. Much better, but still not satisfactory agreement was obtained with the assumption that the distribution of correlation times given by the Davidson–Cole asymmetrical distribution function [16] takes place. For such a distribution the spectral density J has the form [17]. J(ω β) =

sin[βarctan(ωτ)]  ω(1 + ω2 τ2 )β/2

(6)

where β is width of the distribution. The derived second moment reduction, which then equals 0.044 mT2 , with β = 065, is still too large to account for the experimental value of 0.035 mT2 . Taking into account the small slope of ln(T1 ) = f (1/T ) dependence, especially on the low-temperature side of the T1 minimum (about 4 kJ/mol), one can assume the existence of tunneling assisted relaxation [18–24], i.e., the methyl group moving either by thermally activated jumps over the barrier or by tunneling through it. In the model proposed by Haupt [19] and extended by others [20, 24] in the high-temperature region, the motion involves jumps over the barrier and its activation energy is determined by the height of a potential barrier, while at the lowtemperature region the relaxation is mainly due to the tunneling process and its apparent activation energy is identified with the energy difference between the torsional ground state and the first excited state. In such a case the relaxation of the methyl group is given by the Haupt equation [19, 20], +2 +2

1 n 2 τc n2 τ c = CAE + C  EE 2 2 2 2 2 T1 n=−2 1 + (ωt + nω0 ) τc n=1 1 + n ω0 τc

(7)

where ωt is the tunneling frequency while CAE and CEE represent relaxation constants [20, 23], related to M2 , used in Eq. (1), which account for dipole–dipole relaxation connected with the change of symmetry of CH3 rotor from A to E and

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from Ea to Eb , respectively. The last term is allowed only when the methyl group interacts with other protons [19, 21]. The temperature behavior of spin–lattice relaxation described by Eq. (7) depends on the height of the hindering barrier and on the relation between tunneling and Larmor frequencies. The temperature dependence of correlation time τc [20] and the tunneling frequency ωτ [23] is usually approximated by −1

τc−1 = (τ0 )

exp(−Ea /RT ) + (τ0 )−1 exp(−Ea /RT )

(8)

and ωt = ω0t /(1 + αT 6 )

(9)

The high-temperature limit of Ea may be identified with the classical activation energy Ea , while Ea approaches E01 , the energy separation between the torsional ground and the first excited states if the potential barrier is low. The coefficient α is characteristic of the material studied and amounts to the order of magnitude 10−10 – 10−11 K−6 [25]. Due to a lack of experimental data concerning tunneling frequency ω0t , its value was estimated from the correlation between the experimental tunnel splitting and classical activation energy [26]. The high-temperature minimum of T1 and the minimum of T1d are probably connected with some kind of motion of the ribityl side chain, i.e., rotation of the hydroxyl groups or the CH2 OH group. This motion can be fitted well assuming asymmetrical distribution of the correlation times given by the Davidson–Cole function. The derived fitting parameters obtained simultaneously with Eqs. (7)–(9) for the motion of methyl groups and Eqs. (1) and (6) for the motion of a ribityl group are summarized in Tables 1 and 2 and the best fit is shown by the solid line in Fig. 2. The fast spin-diffusion process between mobile and rigid protons was taken into account. It has been found that the methyl groups in riboflavin molecule are not dynamically equivalent. Their contributions to T1 at 25 MHz are represented by the dashed lines. The parameters found for methyl groups compare well with those observed in other ring-substituted compounds, where two methyl groups are also bonded to the adjacent carbons of the ring [20, 25], especially with the data for o-xylene, where a similar shape of T1 minimum in the same temperature region was TABLE 1 Motional Parameters of Methyl Groups as Derived from the Fitting Procedurea Methyl τ0 τ0 Ea Ea CAE CEE group (10−13 s) (10−10 s) (kJ/mol) (kJ/mol) (109 s−2 ) (109 s−2 ) (1) (2)

10 50

015 004

71 82

42 60

19 20

19 20

a 0 ωt = 56 × 107 s−1 for methyl (1) and 40 × 107 s−1 for methyl (2) [20]; α = 5 × 10−11 K−6 .

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MOLECULAR DYNAMICS IN SOLID RIBOFLAVIN TABLE 2 Motional Parameters for the High-Temperature Minimum as Derived from the Fitting Procedure Type of motion Hydroxyl proton motion

τ0 (10−11 s)

Ea (kJ/mol)

M2 (mT2 × 102 )

β

24

125

009

055

observed [25]. This may indicate that the arrangement of methyl groups is decisive for their motional behavior. The high-temperature minimum was fitted with M2 equal to 0.0009 MT2 , which agrees well with 0.001 mT2 calculated theoretically when a motion of one hydroxyl group is assumed. Its contribution to T1 at 25 MHz is represented by the dotted line. Other possible kinds of motion such as rearrangement of CH2 OH group will lead to a much higher reduction of the second moment than that observed. A similar weak relaxation arising from the dynamics of the OH groups was observed in polycrystalline saccharides [27]. 5. CONCLUSIONS Proton NMR techniques have been used to study molecular dynamics in riboflavin. The low- and high-temperature relaxation minima observed were ascribed to the motion of methyl and hydroxyl groups, respectively. The shape of the low-temperature minimum of T1 indicates motional nonequivalency of methyl groups in riboflavin. The motions have been consistently described taking into account the tunneling assisted relaxation process described by Haupt’s theory. The high-temperature minimum of T1 is consistent with the motion of the proton in one of the hydroxyl groups described by the asymmetrical distribution of correlation times. REFERENCES 1. R. S. Rivlin, “Riboflavin,” Plenum Press, New York (1975). 2. “Encyclopedia of Food, Science and Technology,” Vol. 4, p. 2745, Wiley–Interscience, New York, 1981. 3. J. Jeneer and P. Broekaert, Phys. Rev. 157, 232 (1967). 4. R. C. Bowman and W. K. Rhim, J. Magn. Reson. 49, 93 (1982). 5. E. O’Reilly and T. Tsang, J. Chem. Phys. 46, 129 (1967). 6. E. R. Andrew, J. Radomski, Solid State Magn. Reson. 2, 57 (1993). 7. N. Bloembergen, E. M. Purcell and R. V. Pound, Phys. Rev. 73, 679 (1948). 8. P. R. Bevington, “Data Reduction and Error Analysis for the Physical Sciences,” p. 237, McGraw– Hill, New York (1969). 9. J. H. Van Vleck, Phys. Rev. 74, 1168 (1948). 10. E. R. Andrew and B. Peplinska, Mol. Phys. 70, 505 (1990). 11. E. R. Andrew and M. Kempka, Solid State Nucl. Magn. Reson. 2, 261 (1993).

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12. E. R. Andrew and M. Kempka and A. Szyczewski, Mol. Phys. 88, 605 (1996). 13. E. R. Andrew, S. Glowinkowski, J. Radomski, and E. Szczesniak, Solid State Nucl. Magn. Reson. 15, 227 (2000). 14. R. Goc, Z. Naturforsch. 52a, 477 (1997). 15. E. R. Andrew, “Nuclear Magnetic Resonance,” p. 165, Cambridge Univ. Press, Cambridge, UK, (1969). 16. D. W. Davidson and R. H. Cole, J. Chem. Phys. 19, 1484 (1951). 17. A. P. Beckman, Phys. Rep. 171, 85 (1988). 18. J. Haupt and W. M¨ uller-Warmuth, Z. Naturforsch. 24a, 1066 (1969). 19. J. Haupt, Z. Naturforsch. 26a, 1578 (1971). 20. W. Muller-Warmuth, R. Sch¨ uler, M. Prager, and A. Kollmar, J. Chem. Phys. 69, 2382 (1978). 21. W. M¨ uller-Warmuth, R. Sch¨ uler, M. Prager, and A. Kollmar, J. Magn. Reson. 34, 83 (1979). 22. P. S. Allen and S. Clough, Phys. Rev. Lett. 22, 1351 (1969). 23. H. Langen, A.-S. Montjoie, W. M¨ uller-Warmuth, and H. Stiller, Z. Naturforsch. 42a, 1266 (1987). 24. S. Clough, J. Phys. C Solid State Phys. 9, 1553 (1976). 25. M. Prager, R. Hempelmann, H. Langen, and W. M¨ uller-Warmuth, J. Phys. Condens. Matter, 2, 8625 (1990). 26. A.-S. Montjoie and W. M¨ uller-Warmuth, Z. Naturforsch. 40a, 596 (1985). 27. L. Latanowicz, E. C. Reynhardt, R. Utrecht, and W. Medycki, Ber. Bunsenges. Phys. Chem. 99, 152 (1995).