ARTICLE pubs.acs.org/JPCB
Understanding the Molecular Dynamics Associated with Polymorphic Transitions of DL-Norvaline with Solid-State NMR Methods Pingping Ren,†,‡ Detlef Reichert,§ Qinghua He,† Limin Zhang,† and Huiru Tang†,* †
State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Wuhan 430071, P.R. China ‡ Graduate School of the Chinese Academy of Sciences, Beijing 100049, P. R. China § Physics Department, Halle University, Halle 06108, Germany
bS Supporting Information ABSTRACT: DL-Norvaline (NVA) is an important pharmaceutical intermediate and undergoes two polymorphic transitions between 140 and 300 K. To understand molecular dynamics of NVA accompanied with these transitions, we conducted a comprehensive study on its molecular motions at multiple time scales (10-9-1 s) with various solid-state NMR methods. 13C CPMAS NMR spectra revealed four sets of clearly resolved signals for NVA carbons corresponding to at least three crystal modifications with two polymorphic transitions. Proton and 13C relaxation results showed that, apart from the reorientations of methyl and amino groups, NVA had another relaxation process following the second transition with the activation energy of 16-21 kJ/mol corresponding to the side-chain motions. This was further confirmed with the data from dipolar and chemical shift experiments. No motions were detected at CODEX time scale (ms-s). These results provide essential information for understanding the mechanistic aspects of the polymorphic transitions in aliphatic R-amino acids with linear side-chains.
’ INTRODUCTION Polymorphism and polymorphic transitions are important topics for both fundamental and application research. For pharmaceutical applications, an appropriate polymorph is often essential to ensure expected physical, pharmacological, and stability properties. The polymorphism and their transitions of aliphatic R-amino acids with linear side-chains, such as R-aminon-butyric acid,1-3 R-amino-n-valeric acid (norvaline),3,4 and norleucine,5,6 have been under intensive research with a catalogue of methods including differential scanning calorimetry (DSC), X-ray crystallography, Raman spectroscopy, solid-state NMR, and theoretical calculations. This is because these molecules are pharmaceutical intermediates or excellent models for understanding the mechanistic aspects of polymorphic properties and structure-property relationships.7 Polymorphic exchanges or transitions are often accompanied with changes in the molecular dynamics. However, the relationships between the nature of motions and phase transitions remain to be fully understood. The measurements of proton relaxation times (T1H, T1FH), dipolar interactions and conformational exchanges in conjunction with high resolution solid state NMR spectroscopy are well established powerful tools for studying polymorphism and accompanied molecular dynamics. Such techniques have already been successfully applied to elucidate detailed molecular motions of plant polysaccharides8,9 and their structural units,10,11 amino acids12-14 and their derivatives,15-17 r 2011 American Chemical Society
proteins,18 and polyhydroxyalkanoates19 over a wide range of motional frequencies. These techniques ought to be useful for probing the molecular dynamics associated with polymorphic transitions in R-amino acids with linear side chains. DL-Norvaline (DL-R-aminovaleric acid, NVA) is an intermediate for antihypertensive drug, Perindopril, and a model for studying polymorphism and molecular dynamics of aliphatic R-amino acids with a linear side-chain (-CH2-CH2-CH3). NVA is a nonproteinogenic amino acid formed from pyruvate as a byproduct of the branched-chain amino acid biosynthetic pathway in Escherichia coli and other Gram-negative microorganisms.20 This amino acid has also been reported as a natural component of an antifungal peptide produced by Bacillus subtilis.21 Incorporating NVA into proteins affects the side-chain packing, stability, and activity of the proteins.22 Therefore, it is naturally important to understand the molecular dynamic and polymorphic properties of NVA in the solid state. NVA crystal has a space group of I2/a and is expected to have dimorphism under some conditions of crystallization.23 However, detailed crystal structural information has not been reported. An early solid-state NMR study24 revealed that three proton T1 minima (or R1 maxima) were present for NVA at 154, 198, and Received: October 26, 2010 Revised: February 11, 2011 Published: March 10, 2011 2814
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The Journal of Physical Chemistry B 352 K. The high temperature process was assigned to the 3-fold rotation of amino group whereas two other motions at 154 and 198 K were assigned to rotational motions of two methyl groups in nonequivalent environments. However, the 13C CPMAS NMR spectra in the same study showed only one methyl peak.24 It was therefore possible that these two lowtemperature processes coincided with two polymorphic transitions due to the magnetic field strength employed in previous study. Furthermore, the relaxation study also found a motional process assigned to reorientation of the whole molecule or of the side-chains from T1FH data,24 assuming T1FH was in the “weak-collision” limit (i.e., the strength of spin-lock field was far greater than that of the local dipolar field). However, such an assumption was not adequately satisfied for NVA since its local dipolar field strength was about 5-15 G and the spin-lock field in the study was 4 and 12 G.24 Since reorientation of the whole molecule is not expected even on the time scales of T1FH in the solid state without disrupting the crystal lattice, some conclusions from the early dynamic studies may require reconsideration. More recently, an elegant DSC and Raman study revealed two polymorphic transitions (at 156 and 197 K) for solid NVA and the transitions appeared to increase the disordering in the aliphatic side chain and decrease the hydrogen bonding strength.4 These changes were thought to be associated with the rearrangement of molecular layers due to changes of intermolecular interactions and conformational changes due to the rotation of carbon-carbon bonds in the alkyl chains.4 However, with limited Raman spectral changes, the study provided insufficient direct evidence for the detailed structural changes associated with the low temperature (156 K) transition.4 It was also not clear exactly how many polymorphic modifications or crystal sites were present for this amino acid. Consequently, a number of crucial questions remain to be answered for this amino acid, such as “how many structural polymorphs are present”, “what are the motions contributed to the proton relaxation minima observed previously”, “what motions are present on the time scales other than T1 and T1F”, and “are these motions associated with the polymorphic transitions”. The relaxation measurements, conformational exchange, and dipolar order analysis based on high resolution solid-state 13C NMR spectroscopy ought to provide this much needed information for the resolved specific carbons. As a continuous effort in understanding the molecular dynamics and interactions in metabolites, here we investigated the polymorphic transitions of NVA using variable temperature highresolution 13C CPMAS NMR. We also systematically studied the molecular dynamics of this amino acid by measuring the temperature dependence of spin relaxation times (T1H, T1FH, and T1C), order parameters with DIPSHIFT methods, and conformational exchanges with CODEX experiments. The data were interpreted to provide insights to polymorphic properties and molecular dynamics of this amino acid on multiple time scales.
’ EXPERIMENTAL SECTION 1. Materials. DL-Norvaline (NVA) was purchased from SigmaAldrich Co. with product No. N7502 and used without further purification. Its melting point is higher than 300 °C (573 K) according to Sigma data. We assigned the 1H and 13C NMR spectra (Figure S1, a-e, Supporting Information) recorded on a Bruker AVII 500 MHz spectrometer equipped with an inverse broad-band probe for this amino acid to confirm its identity since
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only a 13C spectrum was reported previously for this compound.24 The deuterated NVA was prepared by repeated freeze-drying from its D2O solution three times to ensure the complete exchange of exchangeable protons. The samples were dried over P2O5 under vacuum for at least 2 days before analysis. 2. Differential Scanning Calorimetry (DSC). DSC analysis was performed on a Perkin-Elmer Pyris 1 calorimeter with the NVA sample (8.64 mg) in a sealed aluminum pan. The sample was first cooled to 125 K from room temperature and subsequently heated to 305 K with a rate of 10 K/min, using boiled liquid nitrogen as the cooling gas and helium as the purge gas. The heat flow was recorded as a function of temperature with peak temperature noted. 3. Solid-State NMR Experiments. The proton spin-lattice relaxation time in the laboratory frame, T1H, was measured on a Bruker Mq-20 spectrometer (19.95 MHz) and a Varian Infinity Plus 300 spectrometer (299.78 MHz), respectively, using the classical inversion recovery sequence (recycle delay-180°-τ90°-acquisition). To make sure that the spread of τ values was sufficient to cover for possible existence of multiexponential relaxation, the relaxation delay τ was adjusted according to τ = A 10(m-1)/12, where A was a constant of 1-4 ms depending on the length of T1 and m is the number of data points.25 The τ values ranged from 40 μs to 8 s with 18-32 data points. The proton spin-lattice relaxation times in the rotating frame, T1FH, were determined by using the standard sequence (recycle delay-90°-spin lock-acquisition)26 on a Bruker Mq-20 spectrometer with a spin-lock time no larger than 100 ms when the spin-lock field strength was 51 kHz. Both relaxation times were measured over the temperature range 170-470 K, and values were extracted by fitting experimental data to an exponential decay function. The high-resolution solid-state NMR experiments were carried out on a Varian Infinity Plus 300 spectrometer, operating at 75.38 MHz for 13C, in the temperature range 137-403 K. Samples were spun at 4 kHz in a 4 mm ZrO2 rotor. 90° pulse lengths for 1H and 13C were 2.4 and 2.3 μs, respectively. The contact time during cross-polarization was adjusted to about 13 ms to obtain the best S/N ratio. A total of 32 scans were coadded with a delay of 2-5 s between scans in each cross-polarization magic-angle spinning (CPMAS) experiment. The acquisition time was limited to less than 60 ms with high power proton decoupling field strength of about 60 kHz to avoid stresses to the spectrometer. T1C was measured using the Torchia sequence27 over the temperature range 185-365 K. The strength of the 13C-1H dipolar couplings was measured using the constant time dipolar and chemical shift (DIPSHIFT) pulse sequence,28 where 1H-1H homonuclear decoupling was achieved using the phase modulated Lee-Goldburg (PMLG) sequence29,30 with the effective decoupling field strength of about 106 kHz. Signals were acquired over one rotor period in the indirect dimension since the dipolar-induced decay was periodic with the rotor period. Therefore, DIPSHIFT spectra were only Fourier transformed in the direct dimension and dipolar dephased signals were extracted for each resolved peak.31 The one-rotor-period time-domain data were fitted to yield the coupling strength of interests. The time evolution under the CH dipolar couplings in 2D DIPSHIFT experiments was simulated for one rotor period using a home-built Fortran program. Input parameters included the effective dipolar coupling constant, the LG scaling parameter, the number of t1 increments and the spinning rate. For all simulations, the T2 relaxation effects 2815
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Center-band only detection of exchange (CODEX)34 acquisitions was carried out with parameters similar to those in DIPSHIFT experiments except for a mixing time of 0.25 ms to 1 s. At each temperature, a reference experiment was also performed to cancel the influence of T1 relaxation.34,35 Proton-driven spin diffusion during the mixing time were also considered.36 All variable-temperature NMR experiments were started from the lowest temperature with an increment of 10 K except for experiments close to the polymorphic transition where a 4-6 K increment was used. A total of 20 min of waiting time was allowed after each temperature change to ensure temperature stabilization and equilibrium. The actual sample temperature on the high field spectrometer was calibrated with 207Pb chemical shifts of Pb(NO3)2 as reported before.37 Temperatures on Minispec Mq20 were calibrated by directly inserting a precalibrated thermal couple into a sample-filled tube in the probe head.
during the time evolution were taken into account by multiplying an exponential T2 decay as done previously.32 For measurements of the principal values of chemical shift anisotropy (CSA), the sample spinning rates were carefully adjusted to about 1 kHz and 300 Hz to enable spinning side bands (SSB) to be recorded for carbonyl and side-chain carbons, respectively. Such measurements were carried out from 298 to 358 K for carbonyl groups but only at room temperature for other carbons due to difficulties to maintain a stable spinning rate of 300 Hz at low temperatures. The principal values (δ11, δ22, δ33) were obtained from the SSB intensities with the previously reported method.33
’ RESULTS AND DISCUSSION
Figure 1. 75.38 MHz various temperatures.
Table 1.
13
13
C CPMAS NMR spectra of
DL-Norvaline
1. Differential Scanning Calorimetry (DSC). DSC curves of NVA (Figure S2, Supporting Information) showed two peaks during both cooling and heating processes. The peak temperatures for two endothermic peaks during heating process were 157 and 196 K with transition enthalpies of 0.34 and 1.96 kJ/mol, respectively. This is in good agreement with previously published results4 and implies that two reversible polymorphic transitions are present in this amino acid. 2. Variable Temperature 13C CPMAS NMR Spectra. Figure 1 shows the 13C CPMAS NMR spectra of NVA recorded in the temperature range 137-299 K with 13C signals readily assigned (Table 1). At ambient temperature, 13C chemical-shift differences for all five carbon resonances of NVA are present in the solid state and in aqueous solution (pH = 7.4, Figure S1e,
at
C Chemical Shifts (ppm) for the Four Crystal Sites of DL-Norvaline Chemical Shifts in the Solid State R-CH
β-CH2
CO
A
B
C
137
176.5
53.6
51.3
147
176.5
53.6
51.5
156
176.5
52.5
33.6
19.0
14.2
170 185
176.5 176.6
52.5 52.6
33.7 33.7
19.2 19.3
14.2 14.3
194
176.6
52.6
54.1
34.1
19.3
19.6
14.3
198
176.7
52.7
54.1
34.2
19.3
19.7
14.3
204
176.7
54.1
34.2
19.6
13.9
299
176.7
54.5
34.5
19.5
13.9
CO
A
B
C
52.3
34.1
33.3
52.5
34.1
33.3
D
A
B
C
33.6
20.7
17.7
33.6
20.7
17.8
R-CH3
temp(K)
transition
D
γ-CH2
33.7
A
B
C
18.8
14.9
13.4
14.2
19.1
14.9
13.4
Chemical Shift Changes (ppm) Accompanied with the Transitions R-CH β-CH2
D
γ-CH2
D
14.2
13.9 13.9
δ-CH3
AfC
0.0
1.2
0.5
1.6
0.7
BfC
0.0
1.0
0.3
1.3
0.8
CfD
0.1
1.4
0.4
0.3
0.4
Chemical Shifts in the Solution State temp (K) 298
CO
R-CH
β-CH2
γ-CH2
δ-CH3
176.0
55.5
33.3
18.7
13.7
2816
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Figure 2. Line width for carbonyl signal as a function of temperature obtained from 75.38 MHz 13C CPMAS NMR spectra.
Supporting Information) with the greatest difference (∼1.2 ppm) observed for β-CH2. This is not surprising since strong hydrogen-bonding interactions and crystal packing effect are often expected in the solid crystals. It is particularly interesting to note that the NVA 13C signals (Figure 1) had four different peaks for all the protonated carbons (R-CH, β-CH2, γ-CH2, and δ-CH3) over the temperature range 137-299 K. These four sets of NVA peaks are designated as A, B, C, and D here for the sake of clarity. Some obvious changes in the spectral patterns were observable for these peaks with the change of sample temperature. At 137 K, at least three sets of signals (A, B, and C) were observed for all protonated carbons (R-CH, β-CH2, γ-CH2, and δ-CH3). The signal intensities for peaks from C grew with the rise of temperature at the expense of signals from both A and B. When a temperature of about 156 K was reached, signals for A and B were almost completely transformed into one set of C-peaks. When the sample temperature reached about 194 K, another set of peaks (D) started to emerge and a clear transformation was observable from C to D with the further rise of temperature. When the temperature reached 204 K, the C-to-D transition appeared completed. For the transition from A and B to C, the transition temperature should be around the temperature where the sum of signal intensities from A and B peaks equals that of C peaks. The two transition temperatures observed here (about 147 and 198 K, Figure S3, Supporting Information) were broadly consistent with those detected in the DSC heating curve (157 and 196 K). Therefore, these two transitions detected in 13C CPMAS spectra corresponded to the two transitions observed in DSC. Both temperature gradients present in the NMR probe and the rate of temperature increment in DSC may contribute to the discrepancy in transition temperatures measured above. Although no apparent fine structure was observed for carbonyl signals at all temperatures, this signal showed clear narrowing around the transitions with two such transitions observed for its full-line-width at half-height (Figure 2). For instance, the line width of the carbonyl signal was about 87 Hz at 137 K and decreased to about 50 Hz at 156 K and further decreased to 25 Hz at 261 K. This might indicate that there were three overlapped peaks at 137 K and two overlapped peaks at 156-242 K. They finally transformed into a single peak above 261 K. Since the line width remained in the same order of magnitude around transition temperature for each set of carbon peaks (Table S1, Supporting Information), the transitions observed in this experiment were polymorphic transitions (from one crystal form to another). The line broadening for other carbons at the low
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temperature especially β-CH2 may result from the exchanges between AB and C forms. It is worth noting that the ratios between A and B for CR and Cδ peak areas were similar at 137 and 147 K (Figure 1). These two molecules might either be two different polymorphs that underwent simultaneous transitions to the C-form or two different sites in the unit cell of the same polymorph. Unfortunately, due to hardware restrictions to the temperature range on our spectrometer, we were unable to probe whether there were two stable polymorphic modifications (A and B) or only one modification with two distinct sites in the unite cell at temperature well below 137 K. Therefore, we considered them together as modification AB (or AB-form) in the following discussions. Nevertheless, the above results suggest that at least three crystal modifications (AB, C, and D) are present for NVA. A recent Raman study of NVA tentatively showed4 that three polymorphic phases were present for solid NVA. These were assigned to similar polymorphic forms found in DL-norleucine,5,6 on the basis of values of transition enthalpies and similar Raman spectral features for NVA (above 233 K) and DL-norleucine. In the present study, high-resolution 13C CPMAS NMR spectra unambiguously revealed the presence of at least three crystal modifications with four different crystal sites in solid NVA in the temperature range 137-299 K. Our results further showed that NVA underwent two polymorphic transitions from A and B to the C-form and further to the D-form from 137 to 299 K; such transitions were reversible as DSC results suggested. These three crystal modifications or four crystal sites had observable differences in 13C chemical shifts for all five carbons (Table 1) with smallest differences noted for the carbonyl signals (36 ms). The spin-lattice relaxation rates, R1H, as a function of temperature showed three maxima (Figure 3), indicating the presence of three motional processes. The high temperature maximum at 20 MHz (339 K) was readily assigned to the 3-fold reorientation of the amino group since this maximum disappeared upon deuteration of the exchangeable amino protons. This implies that NVA molecules exist as a zwitterion in the solid state with amino group being protonated as observed in other typical amino acids.12,14 Deuteration of NVA also led to an increase in the relaxation rate of the remaining two relaxation peaks (Figure 3) probably due to reduction in the relaxation loads for these two relaxation processes upon removal of amino protons.25 The maximum at 433 K observed on 300 MHz was also assigned to the 3-fold reorientation of the amino group, since this maximum has motional parameters similar to those of the maximum (339 K at 20 MHz) readily assigned to NH3þ reorientations (Table 2) which will be discussed later. The R1H maximum around 164 K (171 K for deuterated NVA) at 20 MHz, which was not reached, did not result from polymorphic transition (A and B to the C-form) since the relaxation maximum associated with such transition ought to occur at lower temperature than the transition temperature 157 K on the T1H time scale (10-9 s). However, no motion was found as low as to 77 K in studies reported previously.24
The maximum around 208 K (205 K for deuterated NVA) at 20 MHz (or 249 K at 300 MHz) was previously assigned to the rotations of another methyl group in a nonequivalent environment.24 However, our 13C CPMAS results (Figure 1) showed that at temperature above 204 K, there was only one set of carbon signals from D-form modifications. Thus the previous assignment of this motion requires reconsideration, which will also be dealt with in a later section. Additionally, the temperature for R1H maximum had a slight difference between NVA and deuterated NVA probably due to experimental errors. To evaluate the relaxation data quantitatively, the experimental R1H data were fitted to the well-known Kubo-Tomita expression38,39 (eq 1) assuming exponential correlation functions and no correlations between the motions: 1 τci 4τci ¼ Ci þ R1 ¼ ð1Þ T1 1 þ 4ω0 2 τci 2 1 þ 4ω0 2 τci 2 ig1
∑
where ω0 is the proton Larmor frequency and τci the rotational correlation time of the motion responsible for spin-lattice relaxation, which can be written as Eai τci ¼ τ0i exp ð2Þ RT where τ0i is the pre-exponential factor corresponding to the rotational correlation time at infinite temperature, Ea is the activation energy, and R is the gas constant. Ci is the relaxation constant given by eq 3 assuming that the motion occurring is fast on the NMR relaxation time scale: Ci ¼
9 ni γ4 p2 20 N r 6
ð3Þ
where γ is the proton magnetogyric ratio. N is the total number of protons in the molecule, ni is the number of protons contributing to the relaxation process, and r is the averaged interproton distance in motional groups without taking into consideration of contributions of other protons. Experimental data were fitted well into a model of threecomponents corresponding to three motions (as indicated by the solid lines in Figure 3) to obtain descriptive parameters (Ea, τ0, and C) for these motions (Table 2). To avoid fitting arbitrariness for a maximum that was not reached, parameters of τ0 and C from a previous study24 were used as constraints for fitting the relaxation maximum of both NVA and deuterated NVA at 20 MHz. The R1H maxima at low temperature (164 K on 20 MHz, 189 K on 300 MHz) are readily assignable to the 3-fold rotation of the methyl group in NVA with Ea of 8-12 kJ/mol and C value of
Figure 3. Temperature dependence of proton spin-lattice relaxation rates (R1H) for DL-Norvaline (NVA) at 300 and 20 MHz. The data points are experimental data and solid lines are fitted data.
Table 2. Proton Relaxation Parameters of DL-Norvaline Obtained from Spin-Lattice Relaxation Times in the Laboratory Frame groups 20M-T1
20M-T1 (ND3þ) 300M-T1
a
CH3
temp at
T1,min
time factor
activation energy
relaxation
T1,min (K)
(ms)
τ0(10-14 s)
Ea (kJ/mol)
constant C (108s-2)
164
43
52a
12.4 ( 0.1
proton
) distance r (Å
19.9a
side chain
208
39
0.9 ( 0.2
21 ( 2
17 ( 1
NH3þ
339
34
0.7 ( 0.1
39.0 ( 0.3
26.9 ( 0.3
CH3
171
30
28a
13.6 ( 0.1
26.9a
1.721 ( 0.003
side chain
205
32
3(1
21 ( 1
18.7 ( 0.6
CH3
189
512
131 ( 194
8(2
24 ( 1
1.754 ( 0.016
side chain NH3þ
249 433
501 403
23 ( 23 0.5 ( 0.2
16 ( 2 40 ( 1
16 ( 4 28.6 ( 0.7
1.704 ( 0.009
These data from ref 24 were used as constraints. 2818
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The Journal of Physical Chemistry B 19.9 108 s-2 to 24 108 s-2, being in good agreement with previously reported results for methyl rotations.13 The high temperature maxima (339 K at 20 MHz, 433 K at 300 MHz) are assigned to rotation of amino group with Ea value of about 39-40 kJ/mol and a C value of 26.9 108 s-2 to 28.6 108 s-2, which are also in accord with previously reported results for such groups.24 Other maxima (208 K on 20 MHz, 249 K on 300 MHz) are observable with Ea values of 16-21 kJ/mol and C values of about (17-18) 108 s-2, being agreeable with the previously reported results for this amino acid.24 However, this relaxation peak was not due to rotation of another nonequivalent methyl group as previously assigned since no 13C signal for such methyl group was observable above 204 K in 13C CPMAS NMR spectra (Figure 1). Since results from previous Raman study and the 13C CPMAS NMR results from this study showed the polymorphic transitions involved changes of the side-chain packings, we think that this relaxation peak is associated with the motions of the alkyl chain, which probably is restricted into the hydrophobic array formed by the side chain. The activation energy of this process (16 kJ/mol) obtained from data on 300 MHz is also in excellent agreement with the trans-gauche reorientation of ethyl groups observed in a liquid crystal.40 Furthermore, motions of the whole molecule cannot be responsible for this process since fast reorientations of whole molecule are only expected to occur at temperature closer to its melting point (about 573 K). No interproton distances for methyl and amino groups in NVA have been reported for the time being and the data can be extracted tentatively from C values of the related motional groups. Assuming that protons in the methyl and amino groups were equilateral and they were the major contributors to C values, the averaged interproton distance, rH-H, was calculated to be 1.754 Å for methyl groups and 1.704-1.721 Å for amino groups (according to eq 3) using the C values obtained from the relaxation measurements. Such values are slightly smaller than the values reported for common amino acids, such as norleucine, where the reported r values for methyl protons were 1.776 and 1.793 Å, respectively, whereas the r values for amino protons were 1.713 and 1.716 Å, respectively.14 It is well-known that the interproton distances for such groups are underestimated to some extent by the proton relaxation measurements if the contributions of the dipolar interactions of nonmethyl protons to constant C are not taken into consideration.12 Of course, only the results from neutron diffraction were considered as more reliable for interproton distances. Although our results here are fairly similar to those for the proton separations in the methyl and amino groups in alanine (1.755 and 1.686 Å, respectively),41 the accurate interproton distances for NVA remain to be obtained. To obtain information of molecular dynamics on time scale of 10-5-10-6 s, T1FH was measured on a 20 MHz spectrometer over the same temperature range as for T1H measurements. Single-exponential processes (Figure S5, Supporting Information) were found for T1FH with values of about 2-120 ms, though experimental error would be large when the values were greater than 20 ms. This suggests that spin diffusion is also efficient on the T1FH time scale for NVA molecules, which is broadly agreeable with the T1H results from 20 MHz obtained above. With five carbons in an NVA molecule, we can speculate that NVA molecules are packed in the side-by-side fashions in the unit cell. Therefore, hydrophobic arrays are preferred for side chains with hydrogen-bonding systems
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Figure 4. Temperature dependence of R1FH for with a spin-lock field of 51 kHz.
DL-Norvaline
(NVA)
involving NH3þ and COO- groups as proposed in a previous study.4 The relaxation rates, R1FH, as a function of temperature (Figure 4) showed an obvious peak at 243 K. Deuteration eliminated this peak, suggesting that the 3-fold reorientation of amino groups was responsible for this relaxation processes instead of the motion of whole molecule. Figure 4 also showed an implied trend at the low-temperature side which was due to the side-chain motion in NVA according to T1H analysis, although such peak was not completely acquired due to the limited temperature range. The motions of whole molecule cannot be responsible for this process since such motions ought to be present closer to the melting point of NVA, which is well above this temperature. 4. 13C Spin-Lattice Relaxation Measurements. At room temperature, measured T1C values were about 0.37, 0.46, and 1.32 s for β-CH2, γ-CH2, and δ-CH3, respectively. The values for R-CH and CO signals were estimated to be larger than 4 and 20 s, respectively. It is clear that T1C is much longer for R-CH (>4 s) and CO (>20 s) than that for β-CH2, γ-CH2, and δ-CH3 moieties probably due to different motional properties of these moieties. It is also noted that T1C is much shorter for β-CH2 and γ-CH2 than expected,24 and even shorter than that of CH3 indicating the presence of some motions for these moieties. T1C of β-CH2 was an order of magnitude shorter in the D-form (175 ms) than that in the C-form (2.5 s) around the transition temperature (198 K) whereas, in contrast, T1C values for γCH2 were fairly similar in the C-form (180 ms) and D-form (194 ms); T1C of δ-CH3 had a small difference between the C-form (115 ms) and D-form (120 ms). Therefore, motions of β-CH2 appeared to be accompanied by the transition from the C- to D-form. T1C values for R-CH and CO moieties remain unchanged at all temperatures and were estimated to be larger than 4 and 20 s, indicating no thermally activated fast motions for these two moieties. For proton bearing carbons, T1C in the solid state is normally dominated by 1H-13C dipolar interactions and its changes normally imply motional average of such dipolar interactions. Therefore, long and unchanged T1C for R-CH and CO moieties indicates lack of effective fast motional processes for these carbons. 2819
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Table 3.
13
C T1 Relaxation Parameters for DL-Norvaline
groups
temp at T1,min (K)
T1,min (ms)
time factor τ0 (10-14 s)
activation
relaxation
energy Ea (kJ/mol)
constant k (109 rad s-2)
β-CH2
221
118
14 ( 3
17.2 ( 0.4
2.1 ( 0.1
γ-CH2
221
131
11 ( 2
17.6 ( 0.3
1.9 ( 0.1
δ-CH3
145
36
10 ( 2
11.7 ( 0.3
7.0a
T1C Values (ms) 198 K, C 198 K, D
groups
185 K, C
213 K, D
223 K, D
β-CH2
2500
2500
175
128
118
γ-CH2
280
180
194
140
132
δ-CH3
77
115
120
217
263
a
Relaxation constant for the methyl group was constrained to be 7.0 109 rad s-2.
Figure 5. Temperature dependence of R1C at 75.38 MHz. Open symbols represent values for C-form while solid symbols for D-form DL-Norvaline. Solid lines were fitted data for D-form values. The k value for CH3 group was constrained to be 7.0 109 rad s-2 according to eq 6 and taking a C-H bond length of 1.1 Å.
To further evaluate the T1C processes, we fitted our experimental data for D-form to the well-known expression25 R1 ¼
1 T1 "
τc 3τc 6τc ¼k þ þ 1 þ ðωp - ωc Þ2 τc 2 1 þ ωc 2 τc 2 1 þ ðωp þ ωc Þ2 τc 2
#
ð4Þ where ωp and ωc are the Larmor frequency for H and C, respectively. τc is the same as in eq 2. k is the relaxation constant and can be written as 3 μ0 2 2 2 2 -6 k¼ γp γc p rpc ð5Þ 10 4π 1
13
where rpc is the mean C-H distances and γp and γc are the magnetogyric ratios for 1H and 13C, respectively. However, a constrained fitting was considered more reasonable for δ-CH3 since R1C maxima (or T1C minima) were not reached in the temperature range studied. Since k values were dependent on the proton-carbon distances and dominated by the directly attached protons (i.e., C-H bond lengths), we estimated k values for δ-CH3 to be 7.0 109 rad s-2 assuming the C-H bond length of 1.1 Å.41 The fitted results for both CH2 groups and CH3 group (with constrained k) showed that the experimental data were fitted satisfactorily with assumption of one-component (i.e., one motion) for each group (Figure 5 and Table 3). For two CH2 moieties, the activation energy together with the k and τ0 values was the same within the margin of error, suggesting similar relaxation processes experienced by these two groups. The Ea values for these two CH2 groups obtained here (17.2-17.6 kJ/ mol) are agreeable with the values obtained from R1H results, especially with the value (16 ( 2 kJ/mol) obtained from spinning samples on 300 MHz (on the same spectrometer). Therefore, the unambiguous observation of these R1C relaxation processes for the side-chain carbons confirms our assignments from R1H analysis. On the other hand, the δ-CH3 group only exhibited a
decreasing trend for R1C values with the rise of temperatures and the obtained Ea value (11.7 kJ/mol) was consistent with the 3-fold reorientations of methyl group. No information for the side-chain motions was extracted for the methyl group probably due to overwhelming relaxation contribution of the methyl rotation and limited data points. Nevertheless, our results here suggest that the overall molecular motions are absent since such motions are not observed for CH and carbonyl moieties and are only expected to be observed at a temperature closer to the melting point of NVA, which is well above the temperature range investigated in this study. 5. Dipolar Couplings and Chemical Shift Correlation (DIPSHIFT). Molecular motions in the fast exchange limit (τc < 10-6 s) often partially average out the dipolar couplings, and thus the averaged couplings carry important information about the amplitude of the motions. We measured these dipolar couplings for each resolved 13C signal in 2D DIPSHIFT spectra. The amount of dephasing is a characteristic of dipolar coupling with a more dephased signal corresponding to a stronger dipolar coupling.28 The dipolar coupling strength depends on the number of protons bound to a 13C nucleus. For an isolated 13C-1H bond, the theoretical rigid limit value is about 22.8 kHz assuming the bond length of 1.1 Å.41 In practice, the measured dipolar coupling value from DIPSHIFT spectra is normally reduced by a scaling factor due to the attenuation by homonuclear decoupling applied in the sequence. The scaling factors have already been reported to differ significantly from experimental conditions.42 To overcome such problems, the rigid-limit values obtained from a similar crystalline compound were normally used as a reference for the full dipolar coupling.32 In this study, we used two typical amino acids, alanine and glycine, as such references for relevant moieties in NVA. Therefore, in our measurements, the DIPSHIFT experiments were first carried out on dry alanine and glycine samples and full coupling strengths were found to be 5.8, 17.5, and 21.0 kHz for CH3, CH2, and CH groups, respectively. The couplings for CH3 groups were substantially weaker than for CH2 and CH groups due to the 3-fold reorientations of methyl group.43 Figure 6 showed the DIPSHIFT dephased signal intensities recorded over one rotor period in the temperature range 137403 K covering both polymorphic transitions. The dipolar coupling values were extracted by simulating the dipolar dephased signals numerically with typical simulation curves for CH2 and CH3 groups shown as solid lines. The data were well 2820
dx.doi.org/10.1021/jp110224b |J. Phys. Chem. B 2011, 115, 2814–2823
The Journal of Physical Chemistry B
ARTICLE
Figure 6. Normalized dephasing intensity (I/I0) over one rotor period τr from DIPSHIFT spectra of DL-Norvaline and simulated values of order parameters (S) as a function of temperature for β-CH2 (a, d), γ-CH2 (b, e), and δ-CH3 (c, f). Solid lines are simulated data.
simulated except for those at 137 K, which was probably due to signal overlapping and low signal-to-noise ratios resulting from full dephasing as rotor period came to τr/5 to 4τr/5. Figure 6 also shows the temperature dependence of the molecular order parameters of the C-H bonds, indicating the geometry or amplitudes of motions. The order parameters (S) were calculated as the ratio for the dipolar coupling values of the concerned groups against the values of these groups in alanine or glycine (as the rigid limit values). If the S value is close to 1, no motional average occurs for the dipolar coupling whereas dipolar couplings are completely averaged by motions if the S value is close to 0. At 137 K, the order parameters were above 0.86 for βCH2, γ-CH2, and δ-CH3 groups in the A- and B-sites, indicating these groups were largely rigid in the fast limit (
