18058
J. Phys. Chem. B 2006, 110, 18058-18063
Low-Frequency Cooperative Dynamics in L-, D-, and DL-Alanine Crystals: A Cross-Polarization Magic-Angle-Spinning NMR Study
13C
and
15N
Sabyasachi Sen,*,† Ping Yu,† Subhash H. Risbud,† Reay Dick,‡ and David Deamer‡ Department of Chemical Engineering and Materials Science, UniVersity of California at DaVis, DaVis, California 95616, and Department of Chemistry and Biochemistry and Department of Biomolecular Engineering, UniVersity of California at Santa Cruz, Santa Cruz, California 95060 ReceiVed: April 4, 2006; In Final Form: July 10, 2006
Knowledge of the dynamical changes in molecular configurations in various amino acid structures over a wide range of time scales is important since such changes may influence the structural transformations and the diverse biological functionalities of proteins. Using the temperature dependence of the rotating-frame NMR spin-lattice relaxation times T1F of protons as a probe, we have investigated the low-frequency (∼60100 kHz) dynamics in the crystal structures of L-, D-, and DL- alanine (C12H28O8N4) polymorphs. The proton relaxation times T1F were obtained from 13C r 1H and 15N r 1H cross-polarization magic-angle-spinning NMR experiments over a temperature range of 192-342 K. The data reveal that the time scales of these low-frequency dynamical processes are distinctly different from the localized, high-frequency rotational motion of methyl and amine groups. The strongly asymmetric T1F versus temperature curves and the subtle dynamical differences between the DL-alanine and the L- and D-enantiomorphs indicate that these low-frequency processes are cooperative in nature and are sensitive to molecular packing.
Introduction The structure and molecular dynamics of proteins control their specific biological function.1-3 However, proteins are difficult to study in vivo, so most research on their properties has been carried out using solutions or crystals. Because proteins are composed of the 20 naturally occurring amino acids, the atomic/ molecular structure and dynamic properties of amino acids play key roles in governing protein behavior. Previous studies have investigated the dynamics of the amine (R-NH3+) and methyl (R-CH3+) groups in a variety of crystalline amino acids using 2H nuclear magnetic resonance (NMR) line shape and 1H spinlattice relaxation techniques.4-7 These techniques have probed the relatively high-frequency (∼0.1-100 MHz) rotational dynamics of the amine and methyl groups. Typical activation energies for rotational jumps of the amine and methyl groups have been found to range from 20 to 60 kJ mol-1 and from 10 to 20 kJ mol-1, respectively.6 The higher activation energy of the amine group rotation compared to that of methyl groups corresponds to the extra energy required to break the hydrogen bond between the hydrogen atoms in the amine group and the oxygen atoms in the carboxyl group of the adjacent molecule. It may also be noted here that the formation of a protein backbone proceeds via condensation of the amine group of one amino acid with the carboxyl group of another to form amide linkages. Therefore, free rotation of amine groups in amino acids may not be directly relevant to the backbone dynamics of large proteins. However, charged amine and carboxyl groups are indeed present in the protein residues and play an important role in the folding and stabilization of the secondary structures of protein molecules such as R-helices or β-sheets.8 * Author to whom correspondence should be addressed. E-mail:
[email protected]. † University of California at Davis. ‡ University of California at Santa Cruz.
Another physical property that is fundamental to protein function is amino acid chirality. In their crystals, all amino acids except glycine occur as left- (L) and right-handed (D) enantiomorphs or as racemic (DL) mixtures.8 Subtle differences in the high-frequency dynamics of the amine and methyl groups between the L- and DL-polymorphs of the same amino acid have been reported in the literature.6,7,9 In particular, the rotation of amine groups was found to be slower in L-aspartic acid than in DL-aspartic acid crystals.6 However, the same dynamics of amine groups have been shown, in a recent study, to be slower in DLserine with a higher activation energy than in L-serine.7 This difference, in both studies, has been ascribed to the shorter, and therefore stronger N-H‚‚‚O, hydrogen bonds in the polymorph characterized by the slower dynamics.6,7 Proteins display a hierarchy of dynamic processes that are characterized by a wide range of time scales, typically ranging from seconds to picoseconds. Slow time scale motions in the nano- to millisecond range are of particular interest because biologically important processes such as enzyme catalysis, signal transduction, and ligand binding are expected to occur on this time scale.10,11 Low-frequency processes are also known to exist in structurally simpler amino acid crystals and are expected to be sensitive to the long-range intermolecular interaction. However, a systematic comparative study of these processes in D-, L-, and DL-amino acid crystals, including their dependence on temperature and molecular packing density, has not been attempted to date. Such studies would be a critical starting point for understanding similar phenomena in complex protein structures. NMR spin-lattice relaxation spectroscopy in the rotating frame is an ideal tool to investigate atomic dynamics in the frequency range of a few tens of kilohertz.12,13 The corresponding spin-lattice relaxation time T1F is proportional to the spectral density function at the spin-locking frequency ω1 ) γH1 where γ is the gyromagnetic ratio of the nuclide in question and H1 is the locking field. Because the frequency ω1
10.1021/jp0621023 CCC: $33.50 © 2006 American Chemical Society Published on Web 08/18/2006
CP-MAS NMR of Alanine Crystals
J. Phys. Chem. B, Vol. 110, No. 36, 2006 18059
is typically on the order of a few tens of kilohertz, measurement of T1F provides unique information regarding the time scale and activation energy of atomic motion in this frequency range. Hydrogen and π-bonding are primarily responsible for stabilizing the crystal structures of amino acids and secondary/ tertiary structures (e.g., R-helix or β-sheet) of proteins. Therefore, the dynamics of protons probably play the single most important role in controlling the dynamical stability of these structures and, particularly, the transformation between conformational substates in proteins. One way to obtain site-specific data for proton dynamics in the amino acid structure is to perform cross-polarization magic-angle-spinning (CP-MAS) NMR spectroscopy of various nuclides bonded to the protons in different functional groups at different crystallographic sites.14 13C r 1H and 15N r 1H CP-MAS NMR measurements can be used, for example, to obtain the T1F values for the protons in the methyl and amine groups of amino acids, respectively. We report here the results of a comprehensive 13C r 1H and 15N r 1H CP-MAS NMR study of the dynamics of protons in L-, D-, and DL-alanine (C12H28O8N4) crystals over a temperature range of 192-342 K. We have determined the nature of the correlation function and the activation energies of the dynamical processes responsible for the spin-lattice relaxation of the protons at low frequencies ω1, ranging between 59 and 96 kHz. We demonstrate, for the first time, the subtle dependence of the dynamics on the molecular packing and long-range intermolecular interactions in the crystal structures of alanine polymorphs. Experimental Section Sample Preparation. An initial set of NMR experiments was performed with samples of alanine enantiomers that were purchased as follows: D-alanine, ACROS Organics (99+%), L-alanine, Sigma (minimum 98% (TLC)), and DL-alanine, Sigma (minimum 99% (TLC)). Other than direct weighing, no other treatment was performed. A second set of NMR experiments was carried out with alanine samples that were recrystallized from saturated solutions of the appropriate enantiomer, and crystal powders were used in the experiments. Identical results were obtained from both sets of NMR experiments, and the results reported in this paper are from recrystallized powders of the crystals. CP-MAS NMR Spectroscopy. The NMR signal intensity for any nuclide X is enhanced in an X r 1H CP-MAS spectrum due to transfer of polarization from the protons to the X nuclides.14 The signal intensity I depends on the contact time tm between the X and 1H spin reservoirs, the inverse of the rate constant TXH of CP between X and neighboring 1H spins, and the T1F of the nearest-neighbor proton spins. For exponential relaxation and spin diffusion processes, I is given by14
I(t) ) I0 exp
( )[
( )]
-tm -tm 1 - λ exp T1F TXH
(1)
where I0 and λ are constants. In theory λ ) 1/(1 + n) where n is the number of nearest-neighbor protons around the X nuclides, and therefore its value is expected to be between 0 and 1. The experimental values of λ, obtained from 13C r 1H CP-MAS experiments in a wide range of materials, are indeed found to lie within this range, although often the above-mentioned functional dependence on n is not strictly obeyed. In fact, the experimental value of λ is found to be dependent on the mobility of the group containing the X and 1H nuclides.14
Typically, rapid spin diffusion between the 1H spins in a solid ensures a single T1F for all the protons in the system. However, when the X and H nuclides belong to the same functional group (e.g., CH3, NH3), then spin diffusion between these nuclides can be sufficiently rapid so that site-specific proton T1F can be measured by using X r 1H CP-MAS NMR and by fitting the I versus tm data with eq 1. However, in many cases the X nuclides of interest may not have any nearest-neighbor proton spins. One such example would be the carbon atoms in the carboxyl sites in alanine where the nearest protons are at the CH sites whereas the methyl and amine protons are situated further away in space. As a result, the spin diffusion between the protons is rapid enough compared to TXH such that the crosspolarization kinetics of the X atoms is controlled by an average T1F of the nearby protons, and no site-specific information can be obtained. In this scenario, I is given by14
(
I(t) ) I0 1 -
) [ ( ) ( )]
TXH T1F
-1
exp
-tm -tm - exp T1F TXH
(2)
All CP-MAS NMR experiments were performed using a Bruker Avance-500 spectrometer (operating at the resonance frequencies of 125.76 and 50.68 MHz for 13C and 15N, respectively) and Bruker CP-MAS probes. In the case of 13C r 1H CP-MAS NMR finely crushed samples were taken in 4 mm zirconia rotors and were spun at 8 kHz. The intensities I of the 13C CP-MAS NMR spectra were recorded as a function of cross-polarization contact time tm for the three C sites (R, methyl, and carboxyl) in the alanine molecules in L-, D-, and DL-alanine crystals at temperatures ranging between 192 and 342 K. The contact times at each temperature were varied from 0.04 to 10 ms. Each 13C r 1H CP-MAS spectrum was acquired with a 90° pulse length of 2.6 µs, a recycle delay of 30 s, and 1H spin-locking frequency of 96 kHz. An average of four transients were used to obtain each 13C spectrum with typical signal-to-noise ratios of 53:1. In the case of 15N r 1H CPMAS NMR, finely crushed samples were taken in 7 mm zirconia rotors and were spun at 5 kHz. The intensities I of the 15N CPMAS NMR spectra were recorded as a function of crosspolarization contact time tm in L-, D-, and DL-alanine crystals at temperatures ranging between 295 and 328 K. The contact times at each temperature were varied from 0.04 to 9 ms. Each 15N r 1H CP-MAS spectrum was acquired with a 90° pulse length of 4.2 µs, a recycle delay of 5 s, and 1H spin-locking frequency of 59 kHz. An average of 200 transients was used to obtain each 15N spectrum with typical signal-to-noise ratios of 9:1. The 15N CP-MAS NMR experiments could not be extended below 295 K as the 15N CP-MAS signal became extremely weak at these temperatures. The sample temperature in all experiments was controlled using hot or cold N2 gas. Pb(NO3)2 was used as an external standard to calibrate the sample temperature against the temperature of the exhaust N2 gas. The temperature calibration was performed using the well-known temperature dependence of the 207Pb chemical shift of Pb(NO3)2.15 Results 13C
CP-MAS NMR. The 13C CP kinetics (I versus tm) data for the CH and CH3 carbon atoms can be fitted well using eq 1, for all three polymorphs of alanine, over the entire temperature range of 192-342 K (Figure 1). These carbon atoms are expected to cross-polarize from their corresponding nearestneighbor protons. In contrast the carbon atom at the carboxyl (COO-) site is likely to cross-polarize predominantly from the nearest proton at the CH site and possibly, to a lesser extent,
18060 J. Phys. Chem. B, Vol. 110, No. 36, 2006
Sen et al.
Figure 1. 13C CP kinetics data for CH (squares), CH3 (diamonds), and COO- (circles) carbon sites in L-alanine at (a) 332 K and (b) 217 K. The curves through the data points are least-squares fits using eq 1 for the CH and CH3 sites and eq 2 for the COO- site.
Figure 3. Variation with inverse temperature of the logarithm of proton T1F values and the associated error bars, as obtained from fitting eqs 1 and 2 to the 13C CP kinetics data for (a) CH, (b) CH3, and (c) COO- carbon sites in L-alanine (open symbols) and DL-alanine (filled symbols). Error bars for the temperature values are within the size of the symbols.
Figure 2. Variation with inverse temperature of the logarithm of proton T1F values and the associated error bars, as obtained from fitting eqs 1 and 2 to the 13C CP kinetics data for CH (triangles), CH3 (circles), and COO- (squares) carbon sites in L-alanine (filled symbols) and D-alanine (open symbols). Error bars for the temperature values are within the size of the symbols.
from the methyl and amine protons. The corresponding CP kinetic data were described well by eq 2 (Figure 1). The temperature dependence of the logarithm of the resulting proton T1F values obtained from these fits is found to be very similar for all three carbon sites and is shown in Figure 2 for the L-alanine enantiomorph. This result indicates rapid spin diffusion
between the CH and CH3 protons that results in a single T1F. The corresponding proton T1F values for the D-alanine enantiomorph were the same within the limits of experimental uncertainty (Figure 2). However, the ln(T1F) versus temperature curve for the DL-alanine crystals paralleled those for the L- and D-enantiomorphs, but the former was shifted to higher temperatures (Figure 3). In the case of L- and D-alanine crystals the T1F minimum was located at 242 K while the position of this minimum, in the case of DL-alanine, was shifted to 254 K (Figure 3). In all cases, the slopes of the ln(T1F) versus temperature curves on the high-temperature side of the T1F minimum were steeper by a factor of ∼3.7 compared to those on the lowtemperature side (Figures 2 and 3). The activation energy of the dynamical process responsible for the spin-lattice relaxation of the corresponding protons at ω1 ) 96 kHz can be derived from the slope of the ln(T1F) versus temperature curve on the high-temperature side of the T1F minimum. This activation energy was found to be ∼22 ( 2 kJ mol-1. The kinetics of the 1H f 13C cross-polarization are
CP-MAS NMR of Alanine Crystals
Figure 4. Variation with inverse temperature of the logarithm of proton T1F values and the associated error bars, as obtained from fitting eq 1 to the 15N CP kinetics data, in L-alanine (open circles), D-alanine (open squares), and DL-alanine (filled circles).
clearly different for the three carbon sites in the alanine crystal structures (Figure 1). However, the fits of eq 1 to I versus tm data for these three carbon sites yielded the same proton T1F values at any particular temperature (Figure 2). However, the time scale TCH for polarization transfer between 13C and 1H nuclides was a temperature-independent constant that was significantly different for the three carbon sites. The TCH values for the carboxyl, R, and methyl carbons were 2.1, 0.42, and 0.36 ms, respectively. The relatively long TCH value for the carboxyl site results from the fact that the nearest protons for this site are located at significantly longer distances (∼2 Å or higher) compared to those in the case of CH and CH3 carbon sites (∼1 Å). Fitting eq 1 to I versus tm data also yielded values for the constant λ, 0.55 and 0.85, respectively, for the R and methyl carbon sites. The λ values were independent of temperature and in good agreement with the experimentally observed values for the CH and CH3 carbon sites in organics.13 15N CP-MAS NMR. The temporal evolution of the 15N CPMAS spectral intensity can be fitted well using eq 1, for all three polymorphs of alanine, over the temperature range of 295328 K. The TNH and λ values for such fits are found to be independent of temperature and to be equal to 0.4 ms and ∼0.9, respectively, for all the alanine polymorphs. The temperature dependence of the proton ln(T1F) values obtained from these fits is shown in Figure 4. It is clear from Figure 4 that the ln(T1F) versus temperature curves for the D- and L-alanine crystal structures are nearly identical, while that for the DL-alanine polymorph is shifted to higher temperatures by ∼11 K. Similar behavior was also observed in the case of the proton T1F values derived from the 13C CP-MAS data, which showed a shift of the T1F minimum by ∼12 K to a higher temperature for DLalanine compared to those of D- and L-alanine (Figure 3). The activation energy of the dynamical processes responsible for spin-lattice relaxation of the amine protons at ω1 ) 59 kHz, as derived from the slope of the ln(T1F) versus temperature curve was found to be ∼24 ( 2 kJ mol-1. A comparison between the temperature dependence of proton T1F values derived from the 13C and 15N CP-MAS experiments shows that the two sets of data are nearly indistinguishable, within experimental error (Figures 3 and 4). Such similarities between the proton T1F values and their activation energies are strongly indicative of rapid spin diffusion between all protons in these crystal structures, which ensures a single T1F for the entire proton spin system.
J. Phys. Chem. B, Vol. 110, No. 36, 2006 18061
Figure 5. Temperature dependence of the correlation time τ (open circle) for the low-frequency dynamical process responsible for spinlattice relaxation of protons associated with the CH/CH3 groups in Land D-alanines. The correlation time is obtained at the temperature where the proton T1F goes through a minimum in Figure 2, as the relationship ω1τ ) 1 (where ω1 ) 96 kHz) is satisfied at this temperature. The straight line through this data point corresponds to an activation energy of 22 kJ mol-1 (see text for details). The associated error bar for this data point is well within the size of the symbol. The data points represented by the filled circles correspond to the correlation times for the CH3 group rotation, as obtained in a previous study4 using 2H NMR line shape analyses.
Discussion Previous studies of the dynamics of alanine crystals primarily addressed the rotational jump processes in L-alanine and showed that the activation energies of these processes are ∼20 and 40 kJ mol-1 for rotational jumps of CH3 and NH3 groups, respectively.4,5 However, the results of the present study indicate that the dynamical processes in L-, D-, and DL-alanines, which are responsible for the spin-lattice relaxation of protons in the rotating frame at low frequencies (∼60-100 kHz), have activation energies of ∼22-24 kJ mol-1. These activation energies are found to be independent of the crystal structure and are similar to the activation energy for rotational jumps of the methyl groups, within experimental error. The smaller activation energy for these low-frequency dynamical processes compared to that for the rotational jumps of the NH3 groups in alanine indicates that the former do not involve breaking of the hydrogen bonds. The correlation time τc for the low-frequency dynamical process associated with the relaxation of protons in CH/CH3 groups can be easily obtained at the temperature where ln(T1F) goes through a minimum as the relationship ω1τc ) 1 is satisfied at this temperature. Since ω1 ) 96 kHz in the present experiments, the corresponding value of τc at the T1F minimum can be combined with the known activation energy to obtain the temperature dependence of the correlation time scale of this low-frequency dynamical process (Figure 5). A comparison of this τc with that of CH3 rotation clearly shows that despite the similarity in the activation energies the characteristic time scale of the low-frequency dynamical processes is nearly 3 orders of magnitude slower than that of the rotational jump of the methyl groups. In this respect it is particularly interesting to note that in all cases the slopes of the ln(T1F) versus temperature curves obtained from 13C CP-MAS NMR experiments are steeper on the high-temperature side of the T1F minimum than the the lowtemperature side (Figures 2 and 3). The spin-lattice relaxation
18062 J. Phys. Chem. B, Vol. 110, No. 36, 2006 of a nuclear spin such as 1H with I ) 1/2 is controlled by the fluctuation of the magnetic field at the site of the nucleus. Such fluctuations arise from the motion of the resonant nuclides under observation and/or the surrounding atoms. Thus, the frequency and temperature dependence of the spin-lattice relaxation time T1 (ω,T) can provide information regarding the correlation time scale and activation energy of the relevant microscopic dynamical processes. However, knowledge of the functional form of the orientational correlation function G(t) associated with spinlattice relaxation is crucial for understanding the nature of the dynamical processes related to the T1 (ω,T) data16-18. A simple exponential decay of the correlation function such that G (t) ) G(0) exp(-t/τ) forms the basis of the Bloembergen-PurcellPound (BPP) model. The BPP model predicts a symmetric V-shaped T1 versus 1/T curve whose slopes on the high- and low-temperature side of the T1 minimum are equal and yield the activation energy of the diffusive process responsible for spin-lattice relaxation. However, asymmetric ln(T1) versus 1/T curves such as those observed here imply a nonexponential decay of G (t). A nonexponential decay may represent an ensemble average of exponential decays corresponding to a distribution of jump processes, each with a characteristic barrier height and time constant. This is likely to be the case in proteins where the presence of conformational substates and the lack of translational invariance in the structure result in a distribution of relaxation times.19,20 However, in the case of crystalline amino acids this scenario of parallel processes may not be tenable. Alternatively, the temporal decay of G(t) may be inherently nonexponential. An empirical Kohlrausch-Williams-Watts (KWW) type stretched-exponential form of the decay function G(t) ≈ exp(-t/τ)β with 0 < β < 1 has been proposed in the literature to explain the experimentally observed temperature and frequency dependence of T1.18 The consequences of such a correlation function are: (i) an asymmetric T1 versus 1/T curve with β ) EL/EH where EL and EH are the activation energies derived from the low- and high-temperature slopes of the curve and (ii) a frequency dependence of the form T1 ≈ ω1+β for ωτ . 1. In this case EH provides the true activation energy of the dynamical process responsible for spin-lattice relaxation. The stretching of the relaxation kinetics of G (t) typically originates from hierarchical, serial relaxation processes that may be present in crystalline and disordered materials alike.21 Hence, the asymmetric ln(T1F) versus 1/T curves for spin-lattice relaxation of protons in alanine are consistent with the hypothesis that these low-frequency dynamical processes are cooperative and hierarchical in nature. The similarity in the activation energies of these low-frequency processes and of the high-frequency rotational jumps of CH3 groups may imply that the latter may be the rate-controlling, fundamental step for the former processes. In this scenario the fast, localized rotational jumps of the functional groups would be towards the bottom, and the slow, cooperative, dynamical processes associated with T1F would be at or near the top of the hierarchical, serial relaxation process.21 Moreover, the cooperative processes are expected to occur over relatively long length scales and to involve a larger number of atoms compared to the localized rotational jumps of the functional groups. This scenario of cooperative dynamics involving long length scales and a large number of atoms is also consistent with the subtle but consistent differences between L-/D- and DL-alanines in the observed temperature dependence of the proton T1F. This is because the X-ray and neutron refinements of the crystal structures of L- and DL-alanines show strong short-range
Sen et al. structural similarity including extremely similar intramolecular and hydrogen bond lengths.21-25 Therefore, the observation that the correlation time for these low-frequency processes at any temperature is consistently slower in DL-alanine compared to that in the case of L-/D-alanine cannot be ascribed to intramolecular structural differences. However, the densities and hence the molecular packing of these two crystal structures show significant difference. Although each of the unit cells of the L-/D- and DL-alanine crystal structures contains four alanine molecules; the unit cell volume for L-alanine is 430.6 Å3 while that for DL-alanine is 422.8 Å3, which results in their respective densities of 1.374 and 1.399 g cm-3. Therefore, the comparatively slower dynamical processes in DL-alanine compared to those in L-/D-alanine must be related to the differences in packing of the constituent molecules in these crystal structures. This result implies that the low-frequency dynamical processes in question must be sensitive to long-range structural effects involving cooperative motion of a large number of atoms. Summary A systematic investigation of the low-frequency (∼60-100 kHz) dynamics in L-, D-, and DL-alanine crystals was conducted over the temperature range of 192-342 K using proton spinlattice relaxation in the rotating frame as a probe. The temperature dependence of proton T1F values at frequencies ranging between 59 and 96 kHz yield activation energies of ∼22-24 kJ mol-1 for the dynamical processes responsible for relaxation of the protons. The unequal slopes of the ln(T)1F versus temperature curves on the high- and low-temperature sides of the T1F minimum indicate a stretched-exponential type temporal decay of the correlation function associated with the spin-lattice relaxation of the protons at low frequencies. The corresponding low-frequency dynamic processes in alanine polymorphs are cooperative and hierarchical in nature and involve a large number of atoms. The localized, high-frequency rotational jump dynamics of the functional groups serve as the fundamental, rate-limiting steps for these low-frequency, long-range dynamics. Further, the slower dynamics observed in DL-alanine compared to that in L- and D-alanine are attributable to the packing differences of the molecular units in these crystal structures. References and Notes (1) Parak, F. G. Rep. Prog. Phys. 2003, 66, 103. (2) Structure and Dynamics: Nucleic Acids and Proteins; Clementi, E., Sarma, R. H., Eds.; Adenine Press: New York, 1983. (3) Mechanisms of Protein Folding; Pain, R. H., Ed.; Oxford University Press: Oxford, 2000. (4) Beshah, K.; Olejniczak, E. T.; Griffin, R. G. J. Chem. Phys. 1987, 86, 4730. (5) Long, J. R.; Sun, B. Q.; Bowen, A.; Griffin, R. G. J. Am. Chem. Soc. 1994, 116, 11950. (6) Gu, Z.; Ebisawa, K.; McDermott, A. Solid State Nucl. Magn. Reson. 1996, 7, 161. (7) Kitchin, S. J.; Tutoveanu, G.; Steele, M.; Porter, E. L.; Harris, K. D. M. J. Phys. Chem. B 2005, 109, 22808. (8) Montgomery, R.; Conway, T. W.; Spector, A. A. Biochemistry: A Case Oriented Approach; C. V. Mosby Company: St. Louis, MO, 1990. (9) Keniry, M. A.; Rothgeb, M.; Smith, R. L.; Gutowsky, H. S.; Oldfield, E. Biochemistry 1983, 22, 1917. (10) Wolff, N.; Guenneugues, M.; Gilquin, B.; Drakopoulou, E.; Vita, C.; Menez, A.; Zinn-Justin, S. Eur. J. Biochem. 2000, 267, 6519. (11) Feher, V. A.; Cavanagh, J. Nature, 1999, 400, 289. (12) Harris, R. K. Nuclear Magnetic Resonance Spectroscopy: A Physico-Chemical View; Pitman: London, 1983. (13) Palmer, A. G.; Kroenke, C. D.; Loria, J. P. Methods Enzymol. 2001, 339, 204. (14) Kolodziejski, W.; Klinowski, J. Chem. ReV. 2002, 102, 613. (15) Takahashi, T.; Kawashima, H.; Sugisawa, H.; Baba, T. Solid State Nucl. Magn. Reson. 1999, 15, 119.
CP-MAS NMR of Alanine Crystals (16) Brinkmann, D. Prog. NMR Spectrosc.1992, 24, 527. (17) Martin, S. W. Mater. Chem. Phys. 1989, 23, 225. (18) Sen, S.; Mukerji, T. J. Non-Cryst. Solids 2001, 293-295, 268. (19) Frauenfelder, H.; Nienhaus, G. U.; Young, R. D. Relaxation and disorder in proteins. In Disorder Effects on Relaxational Processes: Glasses, Polymers, Proteins; Richert, R., Blumen, A., Eds.; Springer-Verlag: New York, 1994. (20) Settles, M.; Doster, W.; Kremer, F.; Post, F.; Schirmacher, W. Philos. Mag. B 1992, 65, 861.
J. Phys. Chem. B, Vol. 110, No. 36, 2006 18063 (21) Palmer, R. G.; Stein, D. L.; Abrahams, E.; Anderson, P. W. Phys. ReV. Lett. 1984, 53, 958. (22) Simpson, H. J.; Marsh, R. E. Acta Crystallogr. 1966, 20, 550. (23) Destro, R.; Marsh, R. E.; Bianchi, R. J. Phys. Chem. 1988, 92, 966. (24) Lehmann, M. S.; Koetzle, T. F.; Hamilton, W. C. J. Am. Chem. Soc. 1971, 94, 2657. (25) Subha Nandhini, M.; Krishnakumar, R. V.; Natarajan, S. Acta Crystallogr., Sect. C 2001, 57, 614.
