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A nuclear magnetic resonance study of molecular motion in solid l -glutamic acid
JOURNAL
OF
MAGNETIC
RESONANCE
40, 1-7 (1980)
A Nuclear Magnetic ResonanceStudy of Molecular Motion in Solid L-Glutamic Acid S. GANAPATHY,
C. A. MCDOWELL AND P. RAGHUNATHAN"
Department of Chemistry, The University of British Columbia, Vancouver, British Columbia V6T 1 W5, Canada Received August 23, 1979 Proton magnetic resonance absorption and spin-lattice relaxation time measurements have been carried out on solid L-glutamic acid, NHs’CH(CHz)zCOOHCOO-, in the temperature range 77 to 400K. The absorption line measurements show that the structure is rigid on the NMR time scale at the lowest temperatures studied, while at higher temperatures the amino group executes hindered rotation about the N-C bond. The proton spin-lattice relaxation measurements in both the Zeeman and rotating frames of reference (TI and T,,) reveal a single minimum in each case due to the dominant amino group motion. Analysis of the relaxation data yields an activational energy barrier of 31.1 f 0.3 kJ mol-’ to the amino group motion. An additional motional process involving the rotational oscillation of the methylene side chain has been invoked to explain the slight discrepancy in the second moment and the rotatingframe relaxation data. Both the absorption and the relaxation data are in accord with the fact that this amino acid exists as a zwitterion, wherein the u-amino group is protonated.
INTRODUCTION
Hindered rotations of small molecular groups, such as amino and/or methyl groups have been investigated in organic solids by a variety of methods, each providing its own or complementary information. Nuclear magnetic resonance has been used by us extensively to study the dynamics of molecular motion in a variety of such structures (1-3). Since glutamic acid is one of the 20 important amino acids encountered in protein structures which has been little investigated by NMR previously, we have undertaken a study of the proton dynamics in solid L-glutamic acid by continuous-wave and pulsed NMR methods. EXPERIMENTAL
L-Glutamic acid, obtained from Eastman Kodak Company, was recrystallized before use by slow evaporation of an aqueous solution at room temperature, powdered, and sealed in glass sample tubes under vacuum. Broadline PMR spectra in the temperature range 77 to 400 K were recorded at 16.0 MHz using a Varian 4200 variable-frequency spectrometer and a Princeton * Present address: Department of Chemistry, Indian Institute of Technology, Kanpur 208 016, India. OOZZ-2364/80/100001-07%02.00/0 1
Copyright 0 1980 by Academc Press. Inc. All rights of reproduction in any form reserved. Printed in Great Britain
2
CANAPATHY,
MC
DOWELL,
AND
RAGHUNATHAN
Applied Research Model 121 lock-in amplifier. After phase-sensitive detection, the signals were time-averaged on a Varian C-1024 computer for maximal signal-tonoise ratio. Second moments were computed numerically from derivative tracings and were corrected for modulation broadening (4). Spin-lattice relaxation times in the laboratory (Tr) and rotating (Tr,) frames were measured at 29.2 MHz using a Bruker B-KR 321s variable frequency pulsed spectrometer. A r-t-r/2 pulse sequence was employed for the Tl measurements, and the recovery of nuclear magnetization was found to be exponential within experimental error. T,, was measured by “spin-locking” the magnetization in the rotating HI field. The HI field used was 11.5 G. The temperature of the sample, both for cw and pulse experiments, was controlled by regulation of cold nitrogen gas flow using a Bruker B-ST 100/700 temperature controller. Temperature measurements are believed to be accurate to within *l K. Receiver dead-time problems did not allow reliable relaxation data to be recorded at temperatures below 200 K, while degradation of the sample precluded any measurements being made above 430 K. RESULTS
AND
DISCUSSION
Broadline Measurements
The observed temperature dependence of second moments and linewidths of the proton magnetic resonance absorption for L-glutamic acid is shown in Fig. 1. The second moment decreases from a low-temperature plateau value of 25.3 G2 to a high-temperature plateau value of 14.4 G2, the transition taking place in the temperature range 220 to 320 K. Theoretical second moments in the absence of any motional process (i.e., a rigid lattice) and in the presence of reorientations of NH,+ group about the C, symmetry axis were calculated using the hydrogen atom positions (corrected for thermal motion) given in a recent neutron diffraction study (5). The evaluation was done using Van Vleck’s formula (6), applied to polycrystalline samples, for all interproton and proton-nitrogen distances 5 10 A. Fifty eight neighboring molecules, generated
FIG. resonance
1. Temperature absorption
dependence for L-glutamic
of the acid.
linewidths
and second
moments
of the proton
magnetic
SOLID
GLUTAMIC
ACID
3
TABLE 1 SECONDMOMENT(G')DATAFORL-GLUTAMICACID Calculated second moment for Contribution Intragroup:
NHs+ CH2
Intergroup:
NHs+-CHz CHI-CH2
Other H-H N-H Intramolecular total Intermolecular total Total second moment (theoretical) Mean experimental plateau valueb
Rigid structure
NHs+ group reorientation about its Cs axis
10.73 4.74 1.31 1.20 1.59 0.61 20.18 5.22 25.40
2.68 4.74” 0.83 1.20 1.24 0.06 10.75 4.40 15.15
25.3(0.3)
14.4(0.3)
’ For a motional process where the CHz-CH2 side chain executes rotational oscillation, the reduction factor to the intra-CHz contribution, defined by Eq. [l], has been calculated to be 0.84, which corresponds to a rotational oscillation amplitude of approximately 19”. b Values in parentheses denote experimental standard deviations.
using the space group symmetry, P212121,were included in the calculation. Second moments computed using the above-mentioned procedures are set out in Table 1. Upon comparing the observed “plateau” values of the second moment with those calculated for the assumed models (Table l), it is seen clearly that any molecular motion on the NMR timescale, viz., at frequencies greater than the rigid lattice linewidth (-53 kHz), is absent at temperatures below -220 K, while the observed motional narrowing corresponding to the heavy second moment reduction is mainly accounted for by the reorientation of the amino group. The agreement between the experimental and theoretical second moments is very good and shows that the zwitterion description NH,+CHRCOO-, where R is the side group, holds well for this amino acid in the solid state.’ Since the amino group is involved in hydrogen bonding with nearest-neighbor molecules, the second moment transition occurs at temperatures close to room temperature. This behavior is also consistent with that noticed for other similar hydrogen-bonded solids (8). The small difference between calculated and experimental second moments in the high-temperature plateau region, 15.15 and 14.4 G2, respectively, can be accounted for by invoking low-frequency rotational oscillations of the CHP-CH* side chain, which is invariably present in structures of this type (9, 10). For such a motional model, reduction factor p, to be applied to the second moment contribution of the ’ A cw PMR study of glutamic acid was reported recently (7). The results of this study point to the existence of the molecule as NH2CHRCOOH, and the authors interpret the second moment variations as arising due to motion of the NH2 group. In Fig. 2 is also shown the relaxation behavior expected of an NH2 group. Clearly our data points fall far apart from this curve and only fit a zwitterion description NHs+CHRCOO-. We feel that the compound studied earlier perhaps belongs to a different crystalline modification.
4
GANAPATHY,
pair interaction (11)
in methylene groups, can be calculated by the well-known
MC DOWELL,
AND
RAGHUNATHAN
sin2 2 y + (1 -Ji(2a))
P = l- (3/4)[(1 -J&4)
sin4 ~1,
relation
Cl1
where the symbols have their usual meanings. The observed reduction in second moment is consistent with methylene group rotational oscillation with an amplitude of approximately 19” about an axis perpendicular to the interproton line. Relaxation
Measurements
The experimental results for Tl and TIP are shown in Fig. 2. The main feature of the temperature dependence for both Tl and TIP is the distinct minimum in each case. In Fig. 2, Tl is seen to exhibit a relaxation minimum at 103/T = 2.60 (384 K) due to molecular motion; TIP exhibits a minimum at 103/T = 3.88 (258 K). The two minima are associated with the same motion, which we identify as the hindered rotation of the NH3+ group. The transition in M2 below 320 K in Fig. 1 is also associated with this motion. The assumptions that (i) the dominant spin-lattice relaxation is provided by the reorienting NH3+ group with correlation time T, and (ii) the rest of the amino acid chain comes to a common “spin temperature” with the lattice by spin diffusion allow Tl to be written as (12, 13)
PI
l/T* = C[{~,/(1+&:)}+{4~,/(1+4&:)}].
Similarly the expression for TIP in the “weak collision” limit, i.e., for Hi >>Hioca, (which is appropriate for our measurements), can be written as (14) l/Ti,
= C[{3~,/2(1+4~:~~)}+{5~,/2(1+w~~~)}+{~,/(1+4w~~,2)}].
131
In the above equations, o. = yJJo expresses the angular frequency of the nuclei at resonance and w1 = rH1 denotes the angular frequency corresponding to the intensity of the rf field in which spin-locking is accomplished. Further, the tempera-
d
IV20
I 30
I 40
I 50
lOOO/T(K-‘) FIG. 2. Temperature dependence of the proton Tl and Ti, of L-glutamic acid. Dashed line: theoretical behavior expected for L-glutamic acid with the description NH&H(CH&COOHCOOH.
SOLID
GLUTAMIC
ACID
5
ture dependence of rc is assumed to obey a simple activation law ~~= 7. exp(E/RT), [41 where E is the activation energy. Initial estimates of the values for the parameters C, ro, and E were made from the experimental value of TImin, the temperature at Timin, and the data points which gave a limiting slope at the low-temperature side of the Timin. Taking C of Eq. [2] and TO and E of Eq. [4] as adjustable parameters, the experimental data of Fig. 2 were satisfactorily fitted to Eq. [2] by application of a nonlinear least-squares procedure. The resulting best-fit values of the parameters are given in Table 2. In a similar manner, the TIP data were fitted to Eq. [3] and the best-fit values are also included in Table 2. The theoretical curves, drawn with the best-fit values given in Table 2, are also shown in Fig. 2. In the light of recent work on amino acids by neutron diffraction (15) and NMR (2,3), a comparison of our values with those reported is in order. From our T1 analysis, the product nC, where n is the total number of protons in the molecule, comes out to 26.5 x lo9 set-* and falls within the range of 25 to 32 x lo9 set-* found by Andrew et al. (2) for NH3+ relaxation in other amino acids. With the assumption that the reorienting amino group has only its own protons to relax, the value of C expected for an isolated NH3+ group is calculated to be 8.8 x 10’ set-*. For protons equidistant from each other and arranged at the basal apices of a trigonal pyramid, the relaxation constant C is related to the interproton separation r by (16) C NH3=(9/20)[Y4h2/&
[51
Insertion of 8.83 x lo8 set-* for C in Eq. [5] yields an interproton distance of 1.752 A within the NH3+ group, corresponding to an N-H bond length of 1.073 A in a pyramidal configuration of the protonated amino group. This is consistent with the neutron diffraction work on amino acids (15) where the N-H bond length is found to vary between 1.007 and 1.083 A. Andrew et al. (Z), in a study of 18 amino acids in the solid state by spin-lattice relaxation measurements, discuss the relative values of G-~and E. The correlation TABLE RELAXATIONPARAMETERSFOR
THEMOLECULAR
2 MOTION OFNH~+GROUPINL-GLUTAMIC
ACID Value” Parameter Relaxation constant: C(lOs set-*) Time factor: ro(10-*4 set) Activation energy: E (kJ mol-‘) Relaxation time minimum: expt (msec) Relaxation time minimum: theory (msec) Temperature at relaxation minimum: expt (K) Temperature at relaxation minimum: theory (K) a Values in parentheses denote computed standard deviations.
From Tr
From Lrr,
29.5(0.3) 17.8(1.7) 31.1(0.3) 35.7 43.6 384 360
12.4(0.8) 25.9(10.0) 28.4(0.9) 0.62 0.66 258 256
6
GANAPATHY,
MC DOWELL,
AND
RAGHUNATHAN
time factor 7. is of the same order of magnitude as found for other amino acids. The activation energy of 3 1.1 kJ mall’ obtained in the present study is characteristic of a hydrogen bonded NH3’ group, and falls in the range of 28 to 52 kJ mall’ reported for other amino acids. Such a wide variation in the barriers to reorientation of NH3+ groups from one solid amino acid to another has been attributed to changes in crystal packing and hydrogen bond environment (2). From neutron diffraction study (5) one gets the averagevaluesN-H s-.0 = 2.890 A andN-$I.-.0 = 169.6”for glutamic acid. Upon comparing these values with those found for other amino acids, the inference could be made that the hydrogen bond in glutamic acid is less strong and less bent. This would account for the lower value of the activation energy observed in our study. The results obtained from the analysis of Ti, data, presented in Table 2, compare well with those obtained from Ti analysis. The activation energy of 28.4 kJ mall’ is again characteristic of an amino group whose motion is hindered by hydrogen bonding. The value of r. is of the same order of magnitude as that obtained from T1 data. The relaxation constant C obtained from our T,, experiments is, however, significantly smaller than that obtained from T1 analysis. This discrepancy could be explained by invoking the same low-frequency oscillations of the CH2-CH2 side chain that was earlier sought to explain the difference between calculated and observed second moments. While the twofold reorientation of the side chain is arrested by the constraints imposed on the p and y carbon atoms which constitute the side chain, the low-frequency oscillation mentioned above causes these protons to relax via the amino protons. The correlation time due to this low-frequency motion is too long compared to the Larmor period to contribute effectively to T1, but the strength of this low-frequency relaxation interaction in the rotating frame will increase (10,14). This will in turn decrease the measured value of rotating-frame relaxation constant C, which is indeed observed. Furthermore, any distribution of correlation time T=would reduce the measured value of C, since Eq. [3] holds only for a single correlation time. It ought to be noted, however, that the values of Tlpmin and temperature at Tlpmin, calculated from Eq. [3] (Table 2) are in very good agreement with the experimental values. For the same motion, the T1, minimum and the middle of the line narrowing are expected to occur at motional correlation frequencies which are of the same order of magnitude. We expect the dipolar averaging due to molecular reorientation to narrow the spectrum when rc is of the same order as (2&v)-‘, where SV is the linewidth in frequency units (17). The linewidth was found to be 12.4 G, and using Eq. [4] for ~~with r. and E from Table 2 the temperature at which the spectra may be expected to narrow was calculated to be 224 K, in excellent agreement with observation (Fig. 1). In conclusion, both absorption and relaxation data are in accord with the fact that L-glutamic acid exists as a zwitterion, wherein the a-amino group is protonated.
ACKNOWLEDGMENT We are indebted to the National Research Council of Canada for a Grant-In-Aid
of this research.
SOLID
GLUTAMIC
ACID
REFERENCES 1. C. A. MCDOWELL, P. RAGHUNATHAN, AND D. S. WILLIAMS, J. Mugn. Reson. 24, 113 (1976). 2. E. R. ANDREW, W. S. HINSHAW, M. G. HUTCHINS, AND R. 0. I. SJOBLOM, Mol. Phys. 34,1695 (1977). 3. E. R. ANDREW, T. J. GREEN, AND M. J. R. HOCH, J. Magn. Reson. 29,331 (1978). 4. E. R. ANDREW, Phys. Rev. 91,425 (1953). 5. M. S. LEHMANN, T. F. KOETZLE, AND W. C. HAMILTON, J. Cryst. Mol. Struct. 2,225 (1972). 6. J. H. VAN VLECK, Phys. Rev. 74,116s (1948). 7. S. C. MISHRA AND R. C. GUPTA, Indian J. Pure. Appl. Phys. 15,773 (1977). 8. R. SJOBLOM, Doctoral thesis, University of Uppsala, Uppsala, Sweden, 1975. 9. J. C. ROWELL, W. D. PHILLIPS, L. R. MELBY, AND M. PANAR, .J. Chem. Phys. 43,3442 (1965). 10. R.T.THOMPSONAND M. M.PINTAR,J. Chem.Phys.65,1787(1976). 11. E. R. ANDREW, J. Chem. Phys. 18,607 (1950). 12. N. BLOEMBERGEN, E. M. PURCELL, AND R. V. POUND, Phys. Rev. 73,679 (1948). 13. M. B. DUNN AND C. A. MCDOWELL, Mol. Phys. 24,969 (1972). 14. D. C. AILION, Adv. Magn. Reson. 5, 177 (1971). 15. T. F. KOETZLE AND M. S. LEHMANN, “The Hydrogen Bond-Recent Developments in Theory and Experiments” (P. Schuster et al., Eds.), p. 459, North-Holiand, Amsterdam, 1976. 16. A. ABRAGAM, “The Principles of Nuclear Magnetism,” p. 457, Oxford Univ. Press, London, 1961. 17. H. S. GUTOWSKY AND G. E. PAKE, J. Chem. Phys. 18, 162 (1950).
7
OF
MAGNETIC
RESONANCE
40, 1-7 (1980)
A Nuclear Magnetic ResonanceStudy of Molecular Motion in Solid L-Glutamic Acid S. GANAPATHY,
C. A. MCDOWELL AND P. RAGHUNATHAN"
Department of Chemistry, The University of British Columbia, Vancouver, British Columbia V6T 1 W5, Canada Received August 23, 1979 Proton magnetic resonance absorption and spin-lattice relaxation time measurements have been carried out on solid L-glutamic acid, NHs’CH(CHz)zCOOHCOO-, in the temperature range 77 to 400K. The absorption line measurements show that the structure is rigid on the NMR time scale at the lowest temperatures studied, while at higher temperatures the amino group executes hindered rotation about the N-C bond. The proton spin-lattice relaxation measurements in both the Zeeman and rotating frames of reference (TI and T,,) reveal a single minimum in each case due to the dominant amino group motion. Analysis of the relaxation data yields an activational energy barrier of 31.1 f 0.3 kJ mol-’ to the amino group motion. An additional motional process involving the rotational oscillation of the methylene side chain has been invoked to explain the slight discrepancy in the second moment and the rotatingframe relaxation data. Both the absorption and the relaxation data are in accord with the fact that this amino acid exists as a zwitterion, wherein the u-amino group is protonated.
INTRODUCTION
Hindered rotations of small molecular groups, such as amino and/or methyl groups have been investigated in organic solids by a variety of methods, each providing its own or complementary information. Nuclear magnetic resonance has been used by us extensively to study the dynamics of molecular motion in a variety of such structures (1-3). Since glutamic acid is one of the 20 important amino acids encountered in protein structures which has been little investigated by NMR previously, we have undertaken a study of the proton dynamics in solid L-glutamic acid by continuous-wave and pulsed NMR methods. EXPERIMENTAL
L-Glutamic acid, obtained from Eastman Kodak Company, was recrystallized before use by slow evaporation of an aqueous solution at room temperature, powdered, and sealed in glass sample tubes under vacuum. Broadline PMR spectra in the temperature range 77 to 400 K were recorded at 16.0 MHz using a Varian 4200 variable-frequency spectrometer and a Princeton * Present address: Department of Chemistry, Indian Institute of Technology, Kanpur 208 016, India. OOZZ-2364/80/100001-07%02.00/0 1
Copyright 0 1980 by Academc Press. Inc. All rights of reproduction in any form reserved. Printed in Great Britain
2
CANAPATHY,
MC
DOWELL,
AND
RAGHUNATHAN
Applied Research Model 121 lock-in amplifier. After phase-sensitive detection, the signals were time-averaged on a Varian C-1024 computer for maximal signal-tonoise ratio. Second moments were computed numerically from derivative tracings and were corrected for modulation broadening (4). Spin-lattice relaxation times in the laboratory (Tr) and rotating (Tr,) frames were measured at 29.2 MHz using a Bruker B-KR 321s variable frequency pulsed spectrometer. A r-t-r/2 pulse sequence was employed for the Tl measurements, and the recovery of nuclear magnetization was found to be exponential within experimental error. T,, was measured by “spin-locking” the magnetization in the rotating HI field. The HI field used was 11.5 G. The temperature of the sample, both for cw and pulse experiments, was controlled by regulation of cold nitrogen gas flow using a Bruker B-ST 100/700 temperature controller. Temperature measurements are believed to be accurate to within *l K. Receiver dead-time problems did not allow reliable relaxation data to be recorded at temperatures below 200 K, while degradation of the sample precluded any measurements being made above 430 K. RESULTS
AND
DISCUSSION
Broadline Measurements
The observed temperature dependence of second moments and linewidths of the proton magnetic resonance absorption for L-glutamic acid is shown in Fig. 1. The second moment decreases from a low-temperature plateau value of 25.3 G2 to a high-temperature plateau value of 14.4 G2, the transition taking place in the temperature range 220 to 320 K. Theoretical second moments in the absence of any motional process (i.e., a rigid lattice) and in the presence of reorientations of NH,+ group about the C, symmetry axis were calculated using the hydrogen atom positions (corrected for thermal motion) given in a recent neutron diffraction study (5). The evaluation was done using Van Vleck’s formula (6), applied to polycrystalline samples, for all interproton and proton-nitrogen distances 5 10 A. Fifty eight neighboring molecules, generated
FIG. resonance
1. Temperature absorption
dependence for L-glutamic
of the acid.
linewidths
and second
moments
of the proton
magnetic
SOLID
GLUTAMIC
ACID
3
TABLE 1 SECONDMOMENT(G')DATAFORL-GLUTAMICACID Calculated second moment for Contribution Intragroup:
NHs+ CH2
Intergroup:
NHs+-CHz CHI-CH2
Other H-H N-H Intramolecular total Intermolecular total Total second moment (theoretical) Mean experimental plateau valueb
Rigid structure
NHs+ group reorientation about its Cs axis
10.73 4.74 1.31 1.20 1.59 0.61 20.18 5.22 25.40
2.68 4.74” 0.83 1.20 1.24 0.06 10.75 4.40 15.15
25.3(0.3)
14.4(0.3)
’ For a motional process where the CHz-CH2 side chain executes rotational oscillation, the reduction factor to the intra-CHz contribution, defined by Eq. [l], has been calculated to be 0.84, which corresponds to a rotational oscillation amplitude of approximately 19”. b Values in parentheses denote experimental standard deviations.
using the space group symmetry, P212121,were included in the calculation. Second moments computed using the above-mentioned procedures are set out in Table 1. Upon comparing the observed “plateau” values of the second moment with those calculated for the assumed models (Table l), it is seen clearly that any molecular motion on the NMR timescale, viz., at frequencies greater than the rigid lattice linewidth (-53 kHz), is absent at temperatures below -220 K, while the observed motional narrowing corresponding to the heavy second moment reduction is mainly accounted for by the reorientation of the amino group. The agreement between the experimental and theoretical second moments is very good and shows that the zwitterion description NH,+CHRCOO-, where R is the side group, holds well for this amino acid in the solid state.’ Since the amino group is involved in hydrogen bonding with nearest-neighbor molecules, the second moment transition occurs at temperatures close to room temperature. This behavior is also consistent with that noticed for other similar hydrogen-bonded solids (8). The small difference between calculated and experimental second moments in the high-temperature plateau region, 15.15 and 14.4 G2, respectively, can be accounted for by invoking low-frequency rotational oscillations of the CHP-CH* side chain, which is invariably present in structures of this type (9, 10). For such a motional model, reduction factor p, to be applied to the second moment contribution of the ’ A cw PMR study of glutamic acid was reported recently (7). The results of this study point to the existence of the molecule as NH2CHRCOOH, and the authors interpret the second moment variations as arising due to motion of the NH2 group. In Fig. 2 is also shown the relaxation behavior expected of an NH2 group. Clearly our data points fall far apart from this curve and only fit a zwitterion description NHs+CHRCOO-. We feel that the compound studied earlier perhaps belongs to a different crystalline modification.
4
GANAPATHY,
pair interaction (11)
in methylene groups, can be calculated by the well-known
MC DOWELL,
AND
RAGHUNATHAN
sin2 2 y + (1 -Ji(2a))
P = l- (3/4)[(1 -J&4)
sin4 ~1,
relation
Cl1
where the symbols have their usual meanings. The observed reduction in second moment is consistent with methylene group rotational oscillation with an amplitude of approximately 19” about an axis perpendicular to the interproton line. Relaxation
Measurements
The experimental results for Tl and TIP are shown in Fig. 2. The main feature of the temperature dependence for both Tl and TIP is the distinct minimum in each case. In Fig. 2, Tl is seen to exhibit a relaxation minimum at 103/T = 2.60 (384 K) due to molecular motion; TIP exhibits a minimum at 103/T = 3.88 (258 K). The two minima are associated with the same motion, which we identify as the hindered rotation of the NH3+ group. The transition in M2 below 320 K in Fig. 1 is also associated with this motion. The assumptions that (i) the dominant spin-lattice relaxation is provided by the reorienting NH3+ group with correlation time T, and (ii) the rest of the amino acid chain comes to a common “spin temperature” with the lattice by spin diffusion allow Tl to be written as (12, 13)
PI
l/T* = C[{~,/(1+&:)}+{4~,/(1+4&:)}].
Similarly the expression for TIP in the “weak collision” limit, i.e., for Hi >>Hioca, (which is appropriate for our measurements), can be written as (14) l/Ti,
= C[{3~,/2(1+4~:~~)}+{5~,/2(1+w~~~)}+{~,/(1+4w~~,2)}].
131
In the above equations, o. = yJJo expresses the angular frequency of the nuclei at resonance and w1 = rH1 denotes the angular frequency corresponding to the intensity of the rf field in which spin-locking is accomplished. Further, the tempera-
d
IV20
I 30
I 40
I 50
lOOO/T(K-‘) FIG. 2. Temperature dependence of the proton Tl and Ti, of L-glutamic acid. Dashed line: theoretical behavior expected for L-glutamic acid with the description NH&H(CH&COOHCOOH.
SOLID
GLUTAMIC
ACID
5
ture dependence of rc is assumed to obey a simple activation law ~~= 7. exp(E/RT), [41 where E is the activation energy. Initial estimates of the values for the parameters C, ro, and E were made from the experimental value of TImin, the temperature at Timin, and the data points which gave a limiting slope at the low-temperature side of the Timin. Taking C of Eq. [2] and TO and E of Eq. [4] as adjustable parameters, the experimental data of Fig. 2 were satisfactorily fitted to Eq. [2] by application of a nonlinear least-squares procedure. The resulting best-fit values of the parameters are given in Table 2. In a similar manner, the TIP data were fitted to Eq. [3] and the best-fit values are also included in Table 2. The theoretical curves, drawn with the best-fit values given in Table 2, are also shown in Fig. 2. In the light of recent work on amino acids by neutron diffraction (15) and NMR (2,3), a comparison of our values with those reported is in order. From our T1 analysis, the product nC, where n is the total number of protons in the molecule, comes out to 26.5 x lo9 set-* and falls within the range of 25 to 32 x lo9 set-* found by Andrew et al. (2) for NH3+ relaxation in other amino acids. With the assumption that the reorienting amino group has only its own protons to relax, the value of C expected for an isolated NH3+ group is calculated to be 8.8 x 10’ set-*. For protons equidistant from each other and arranged at the basal apices of a trigonal pyramid, the relaxation constant C is related to the interproton separation r by (16) C NH3=(9/20)[Y4h2/&
[51
Insertion of 8.83 x lo8 set-* for C in Eq. [5] yields an interproton distance of 1.752 A within the NH3+ group, corresponding to an N-H bond length of 1.073 A in a pyramidal configuration of the protonated amino group. This is consistent with the neutron diffraction work on amino acids (15) where the N-H bond length is found to vary between 1.007 and 1.083 A. Andrew et al. (Z), in a study of 18 amino acids in the solid state by spin-lattice relaxation measurements, discuss the relative values of G-~and E. The correlation TABLE RELAXATIONPARAMETERSFOR
THEMOLECULAR
2 MOTION OFNH~+GROUPINL-GLUTAMIC
ACID Value” Parameter Relaxation constant: C(lOs set-*) Time factor: ro(10-*4 set) Activation energy: E (kJ mol-‘) Relaxation time minimum: expt (msec) Relaxation time minimum: theory (msec) Temperature at relaxation minimum: expt (K) Temperature at relaxation minimum: theory (K) a Values in parentheses denote computed standard deviations.
From Tr
From Lrr,
29.5(0.3) 17.8(1.7) 31.1(0.3) 35.7 43.6 384 360
12.4(0.8) 25.9(10.0) 28.4(0.9) 0.62 0.66 258 256
6
GANAPATHY,
MC DOWELL,
AND
RAGHUNATHAN
time factor 7. is of the same order of magnitude as found for other amino acids. The activation energy of 3 1.1 kJ mall’ obtained in the present study is characteristic of a hydrogen bonded NH3’ group, and falls in the range of 28 to 52 kJ mall’ reported for other amino acids. Such a wide variation in the barriers to reorientation of NH3+ groups from one solid amino acid to another has been attributed to changes in crystal packing and hydrogen bond environment (2). From neutron diffraction study (5) one gets the averagevaluesN-H s-.0 = 2.890 A andN-$I.-.0 = 169.6”for glutamic acid. Upon comparing these values with those found for other amino acids, the inference could be made that the hydrogen bond in glutamic acid is less strong and less bent. This would account for the lower value of the activation energy observed in our study. The results obtained from the analysis of Ti, data, presented in Table 2, compare well with those obtained from Ti analysis. The activation energy of 28.4 kJ mall’ is again characteristic of an amino group whose motion is hindered by hydrogen bonding. The value of r. is of the same order of magnitude as that obtained from T1 data. The relaxation constant C obtained from our T,, experiments is, however, significantly smaller than that obtained from T1 analysis. This discrepancy could be explained by invoking the same low-frequency oscillations of the CH2-CH2 side chain that was earlier sought to explain the difference between calculated and observed second moments. While the twofold reorientation of the side chain is arrested by the constraints imposed on the p and y carbon atoms which constitute the side chain, the low-frequency oscillation mentioned above causes these protons to relax via the amino protons. The correlation time due to this low-frequency motion is too long compared to the Larmor period to contribute effectively to T1, but the strength of this low-frequency relaxation interaction in the rotating frame will increase (10,14). This will in turn decrease the measured value of rotating-frame relaxation constant C, which is indeed observed. Furthermore, any distribution of correlation time T=would reduce the measured value of C, since Eq. [3] holds only for a single correlation time. It ought to be noted, however, that the values of Tlpmin and temperature at Tlpmin, calculated from Eq. [3] (Table 2) are in very good agreement with the experimental values. For the same motion, the T1, minimum and the middle of the line narrowing are expected to occur at motional correlation frequencies which are of the same order of magnitude. We expect the dipolar averaging due to molecular reorientation to narrow the spectrum when rc is of the same order as (2&v)-‘, where SV is the linewidth in frequency units (17). The linewidth was found to be 12.4 G, and using Eq. [4] for ~~with r. and E from Table 2 the temperature at which the spectra may be expected to narrow was calculated to be 224 K, in excellent agreement with observation (Fig. 1). In conclusion, both absorption and relaxation data are in accord with the fact that L-glutamic acid exists as a zwitterion, wherein the a-amino group is protonated.
ACKNOWLEDGMENT We are indebted to the National Research Council of Canada for a Grant-In-Aid
of this research.
SOLID
GLUTAMIC
ACID
REFERENCES 1. C. A. MCDOWELL, P. RAGHUNATHAN, AND D. S. WILLIAMS, J. Mugn. Reson. 24, 113 (1976). 2. E. R. ANDREW, W. S. HINSHAW, M. G. HUTCHINS, AND R. 0. I. SJOBLOM, Mol. Phys. 34,1695 (1977). 3. E. R. ANDREW, T. J. GREEN, AND M. J. R. HOCH, J. Magn. Reson. 29,331 (1978). 4. E. R. ANDREW, Phys. Rev. 91,425 (1953). 5. M. S. LEHMANN, T. F. KOETZLE, AND W. C. HAMILTON, J. Cryst. Mol. Struct. 2,225 (1972). 6. J. H. VAN VLECK, Phys. Rev. 74,116s (1948). 7. S. C. MISHRA AND R. C. GUPTA, Indian J. Pure. Appl. Phys. 15,773 (1977). 8. R. SJOBLOM, Doctoral thesis, University of Uppsala, Uppsala, Sweden, 1975. 9. J. C. ROWELL, W. D. PHILLIPS, L. R. MELBY, AND M. PANAR, .J. Chem. Phys. 43,3442 (1965). 10. R.T.THOMPSONAND M. M.PINTAR,J. Chem.Phys.65,1787(1976). 11. E. R. ANDREW, J. Chem. Phys. 18,607 (1950). 12. N. BLOEMBERGEN, E. M. PURCELL, AND R. V. POUND, Phys. Rev. 73,679 (1948). 13. M. B. DUNN AND C. A. MCDOWELL, Mol. Phys. 24,969 (1972). 14. D. C. AILION, Adv. Magn. Reson. 5, 177 (1971). 15. T. F. KOETZLE AND M. S. LEHMANN, “The Hydrogen Bond-Recent Developments in Theory and Experiments” (P. Schuster et al., Eds.), p. 459, North-Holiand, Amsterdam, 1976. 16. A. ABRAGAM, “The Principles of Nuclear Magnetism,” p. 457, Oxford Univ. Press, London, 1961. 17. H. S. GUTOWSKY AND G. E. PAKE, J. Chem. Phys. 18, 162 (1950).
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