Hydration Effects on Dynamics of Polyglycine and Sodium Poly( 1-Glutamate) SCOTT D. KENNEDY' and ROBERT G. BRYANT','

'

Departments of Biophysics and 'Chemistry, University of Rochester Medical Center, Rochester, New York 14642

SYNOPSIS

Solid state nmr methods were applied to the study of the motions and structural heterogeneity in polyglycine, sodium poly (L-glutamate), and poly (L-alanine) . The response of both the main-chain and side-chain resonances to the addition of water was studied using static and magic-angle sample-spinningline shapes as well as the carbon spin-lattice relaxation times, the proton spin-lattice relaxation time in the rotating frame, and the protoncarbon cross-polarizationtime. The polyglycine motions are not drastically affected by the addition of water when the polymer is in the 31-helixor the P-sheet structure. The sodium poly (L-glutamate), however, responds to increased hydration with little motion in the main-chain carbon atoms, but considerableflexibility of the side-chain atoms. The greatest motions are reported for the C, carbon with rotational amplitudes about the C,-C, bond of about of 50". In addition, motions somewhat less than half this size are required closer to the main chain.

I N T R O DUCT10N Protein response to environmental stress is fundamental to understanding survival as well as functional control. One simple and common stress is a change in the water content or activity in the vicinity of a protein. Although a number of studies have been reported on protein-water interactions, the large number of resonances makes it difficult to isolate and characterize signals from a particular side chain of interest. Fundamentally useful information may be obtained, however, by studying homopolymers that may be made to adopt a particular configuration by control of the preparation conditions. We report here solid state nmr studies on polyglycine, poly ( Lalanine) , and sodium poly (L-glutamate) that address the dynamical response of these polypeptides to the addition of water.

EXPERIMENTAL Polyglycine (DP N 175), poly (L-alanine) (DP = 3 5 2 ) , and sodium poly(L-glutamate) ( D P N 93) 0 1990 John Wiley & Sons, Inc. CCC 0006-3525/90/7-80691-11 $04.00 Biopolymers, Vol. 30,691-701 (1990)

were obtained from Sigma Chemical Company. Each of these polypeptides may form an alpha a-helix or a @-sheetstructure. Polyglycine was prepared in the @-sheetform by slow evaporation of dichloroacetic acid (DCA) from a solution of 0.35 g of polyglycine in 20 mL of DCA',' a t 318 K until the majority of the solvent was gone followed by air drying for two weeks, oven drying at 31 1 K for four days, and finally drying by mechanical vacuum for 24 h. The 31-helix was prepared by precipitation of polyglycine from a n aqueous lithium bromide solution by quickly diluting the concentrated salt solution containing the polymer with a 10 fold excess of water.' The polymer was collected by centrifugation and the excess lithium bromide extracted three times with water. The a-helix of poly (L-alanine) was produced by dissolving 300 mg of polymer in 1-2 mL of DCA and the solvent extracted with three or four washings of methanol employing 12-24 h soaking time for each.3r4The @-sheetform may be produced from the a-helix form by ~ t r e t c h i n g . ~ - ~ The @-sheet forms of poly (L-glutamic acid) ( P G A ) and the sodium salt ( NaPG) were obtained by evaporating water from a sodium free suspension below p H 4 or from a n aqueous solution a t neutral pH, respectively. At relative humidities greater than 70% the a-helix is more stable and generally 69 1

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KENNEDYANDBRYANT

forrned.’~~T h e dry sodium salt was obtained by evaporating a n aqueous solution to dryness in a n oven a t 338 K and stored at this temperature for 24 h after all the liquid was gone. Further drying under vacuum did not decrease the weight. A deuteronexchanged sample was made by dissolving 0.2 g of dry NaPG in 4.0 mL of deuterium oxide and redrying. This procedure results in exchange of greater than 99% of the amide protons because the amide exchange is rapid.’ Hydration of all PGA and NaPG samples was performed in a sealed crystallization dish containing a saturated sodium nitrite solution a t a temperature that produced the desired relative humidity. Hydration of polyglycine and poly (L-alanine ) was performed over water a t 308 K for 1-4 weeks until no further weight change was observed. All samples were analyzed gravimetrically for water content a t the conclusion of the nmr experiment by drying under a mechanical vacuum a t 338 K. Nuclear magnetic resonance measurements were conducted on a nmr instrument assembled in this laboratory operating with a 4.7 T Oxford magnet, a Nicolet-GE 1280 data system, and ENI, Henry Radio, and Amplifier Research rf power amplifiers. The probe included a Doty Scientific stator that employed sapphire rotors sealed with macor caps employing a double O-ring seal. These caps prevented water from leaving the sample and permitted rotor speeds from 2-3.5 kHz. Integrity of the samples was checked by weighing the rotor before and after the experiment. All spectra are referenced in parts per million ( ppm ) relative to tetramethylsilane.

RESULTS AND DISCUSSION Polyglycine 13C cross-polarization magic-angle spinning nmr spectra are shown in Figure 1 for the dry 31-helix and P-sheet forms of polyglycine. There is little chemical shift difference between the C, resonances; however, the carbonyl resonance of the 31-helix is approximately 4 ppm downfield relative to the resonance for the P-sheet form. The observed chemical shifts are in agreement with earlier assignments that identify them with the helix and 0-sheet structures of the polymer.’0*” Compared with glycylglycine (Figure 1E) or polycrystalline glycine spectra, the resonances of polyglycine are considerably broadened. The origin of this broadening may be examined with a spinecho train experiment, which consists of the equiv-

alent of a Carr-Purcell spin-echo train, the entirety of which is digitized and Fourier transformed to yield a spectrum displaying a comb of lines. The width of each component of the comb is a good approximation to the transverse relaxation rate and the envelop of the lines map the original line shape.12-14In a spinning sample, care must be taken to match the refocusing time of the spin echo with a n integral multiple of the sample rotation period. Figure 2 shows the spin-echo spectrum obtained on dry polyglycine in the 31-helix form in a magic-angle rotor spinning a t 4.24 kHz. T h e originally broad magic-angle spinning lines are broken into a comb of lines that individually nearly reach the baseline. This result demonstrates that the dominant line broadening observed in the magic-angle spinning (MAS) experiment is inhomogeneous. The origin of the inhomogeneous broadening is unclear. T h e breadth of the MAS line may result from a distribution of isotropic chemical shifts that may result from a distribution of local polymer conformations, a common occurrence in noncrystalline compounds. However, in this case all the carbon atoms in the sample may experience a n incompletely averaged carbon-nitrogen dipole-dipole coupling that may contribute to a n inhomogeneous line Polycrystalline glycylglycine represents a sample in which the distribution of local conformations, and therefore chemical shifts, is minimal but exhibits inhomogeneous line broadening from the 13C- 14N dipole-dipole coupling. The spectrum shown in E of Figure 1 indicates that a t 4.7 T glycylglycine lines are sharp while those of the polymer ( A and C of Figure 1) are significantly broader. Comparison of these line widths indicates that a 3.84.3 ppm contribution from a chemical shift dispersion must be present in the polymer spectra. The spectra obtained at 1.32 T show a similar contribution, but in this case the nitrogen effects are very much larger and clearly dominate the line widths of all the spectra. T h e proton-decoupled 13C cross-polarization ( C P ) MAS spectra for polyglycine in both forms are shown for different levels of hydration in Figure 3. There is no detectable chemical shift change on hydration, suggesting that the polymer conformation does not change. The hydration of polyglycine t o 30% produces no detectable change in the static 13Cnmr line shape of which demonstrates that hydration does not induce large amplitude motions with correlation times less than 0.1 ms that would average the chemical shift tensor (data not shown) .17 Slower motions with correlation times of a few tenths of a millisecond to tens of milliseconds can

HYDRATION EFFECTS ON POLYGLYCINE AND NA POLY ( L-GLUTAMATE)

4.n \

/

693

1.321

c=o A

,

200

100

0

,

,

200

,

q

,

,

I

100

1

l

l

0

PPM

Figure 1. Proton-decoupled 13C CP / MAS spectra of polyglycine and glycylglycine at 4.7 T ( A , C, E ) and 1.32 T (B, D, F ) . (A, B ) The 3,-helix form of dry polyglycine. (C, D ) The P-sheet form of dry polyglycine. (E, F ) The polycrystalline glycylglycine.

be detected by the use of a spin-echo spectrum, as shown in Figure 4, where the echo-refocusing time defines the relevant time period for the motion. The distinct changes in the spectra upon hydration demonstrate t h a t there are changes in the sample t h a t defeat the refocusing of the spin echos. Interpretation of the data in Figure 4 is not transparent because, in addition to molecular motion, relaxation of directly bonded 14N nuclei can modulate the carbon Larmor frequency and increase the spin-echo decay rate. Using glycylglycine as a model for the orientation of the carbon-nitrogen bond relative t o the principal axes of the carbon chemical shift tensors, spectral simulation suggests that the nitrogen T I would have t o be shifted t o on the order of 3 ms by the hydration to produce the effects shown in Figure 4 while values of 6-12 ms approximate the echo-train spectra of the dry p ~ l y r n e r . ’In ~ an effort to determine whether these are reasonable I4N re-

laxation times, the echo-train spectra of static dry and hydrated poly (L-alanine) were acquired and are shown in Figure 5. T h e C3 resonance of poly( L-alanine) has a chemical shift anisotropy similar t o t h a t of the C , resonance but does not experience a significant carbon-nitrogen dipolar coupling. Furthermore, any reorientation of the C2 and C3 shift tensors should be approximately the same except for the rapid methyl rotation. Thus, slow motions but not nitrogen relaxation should dominate the echo-train spectrum of the C3 resonance, and differences between the C2 and C3 resonances may be attributed t o the effects of 14Nrelaxation on the C, resonance. Unlike polyglycine, there is very little difference in the spin-echo spectra of the dry and hydrated forms of poly( L-alanine), indicating t h a t for poly( L-alanine) the effects of water on the local motions must be minimal. However, the spin-echo spectra show that the C z resonances are broader than

694

KENNEDY AND BRYANT

r-200

r-7----r-v 150

50

100

PPM

Figure 2. Proton-decoupled 13C CP/MAS echo-train spectrum a t 4.7 T of the 31-helix form of polyglycine. The spinning speed is 4.25 kHz and the spacing between 7r pulse centers is 9.4 ms, i.e., the 7r pulses are synchronized to integral numbers of the rotor period. Number of transients = 200, contact time = 1.5 ms, 5 Hz of Lorentzian line broadening.

I

-

200

100

PPM

200

C

100

PPM

Figure 3. Proton-decoupled 13C CP/MAS spectra at 4.7 T and room temperature of polyglycine ( A ) dry 3,-helix, ( B ) hydrated 31-helix, ( C ) dry 8-sheet, and ( D ) hydrated psheet. Hydration in an environment of 100% humidity a t 35°C resulted in 0.3 g HZO/g polyglycine ( u 1 : 1 H,O/monomer). Spinning speed Y 4 kHz except in B where it was N 2 kHz (note large side band). Number of transients = 100-500, contact time = 1 ms, recycle time = 2 s, and 20 Hz Lorentzian line broadening was appIied.

HYDRATION EFFECTS ON POLYGLYCINE AND NA POLY ( L-GLUTAMATE)

695

induce large changes in the carbon relaxation times by direct water-proton-carbon-dipole-dipole effects, a situation that was observed for poly (vinyl acetate) .la The magnitude of the change in the carbon TI on hydration provides a good estimate of the changes expected in the nitrogen relaxation parameters. The nitrogen Larmor frequency is lower than that for carbon by a factor of 3.48 or 0.5 on a logarithmic scale. Thus, if we assume that the spectral density profile in the polymer system is fairly flat over this range, the change in the relaxation rates for nitrogen should scale approximately with those for carbon. That is, we may expect a factor of 3 or less change in the nitrogen relaxation parameters. Simulations show that a factor of 3 change may be sufficient to produce the effects seen in Figure 4, and therefore,

Figure 4. Proton-decoupled 13C CP echo train spectra of @-sheetform of polyglycine at 4.7 T and 295 K. (A, D ) Dry, (B, E ) hydrated to 5 1H20/monomer, (C, F) excess water. The A pulse spacing (TCP)= 3.0 ms (A, B, C ) or 5.0 ms (D, E, F). Number of transients = 4000, 1 ms contact time, 2 s recycle time.

the C3 resonances, which is more clearly seen by comparison of the ratios of peak intensities to intensities between peaks, indicating that '*N relaxation times must be on the order of a few milliseconds and make a significant contribution to the width of the C2 resonance even in the dry polymer. Thus, it is not unreasonable that 14N T1 be on the order of a few milliseconds in polyglycine as well and the hydration dependence of the polyglycine echo-train spectra may be explained if 14Nrelaxation rates change by a factor of 2-4 upon hydration. Measurements of the 13C relaxation times for polyglycine samples are summarized in Table I. The carbon T1values are long for both the 31-helix and P-sheet, indicating a lack of much motion at the carbon Larmor frequency. The addition of water decreases these times for both forms of the polymer by only a factor between 2 and 3. It is also significant that the addition of water to the system does not

c3

I

I 200

I

I

I

I 0

I

PPM

Figure 5. Proton-decoupled 13C CP echo train spectra with 3 ms A pulse spacing of dry (bottom) and hydrated (top) poly(L-alanine) at 4.7 T and 293 K. Hydration at 100%humidity a t 308 K for three weeks gave 0.29 g HzO/ g poly(L-alanine); drying was at 348 K for 2-3 days. Number of transients cz 9000, 1 ms contact time.

696

KENNEDY AND BRYANT

-

Table I I3CarbonTI, Proton TI,, and Tls Obtained for Dry and Hydrated (30%H 2 0 by Weight 1 H20/Monomer) Polyglycine at 295 K" Dry

Hydrated

Very Wet

173 f 14 223 k 15 40 f 12 234 f 11 13.2 f 0.7 11.4 f 0.5

66.6 k 4 82 f 5 42 t 10 214 f 6 13.0 f 0.5 13.9 f 0.6

60 f 5 75 f 4 46 t 19 253 t 12 11.8 f 0.7 11.5 ? 0.8

103 f 5 132 f 6 24.2 f 3 360 t 34 12.2 f 0.9 13.3 t 1.5

55.7 2 4 69 f 5 29.4 f 2 315 f 15 10.1 t 0.3 10.1 f 0.2

P-Sheet

Ti ( s ) Tis ( P )

C,

c=o C, c=o

T1,AH) (ms) C, 31-Helix TI ( s ) TlS

(m)

T d H ) (ms)

c=o

C,

c=o C,

c=o C, c=o

The "very wet" sample was suspended in H 2 0 and then pelleted by low-speed centrifugation.

that motions on the millisecond time scale may be absent or small in hydrated polyglycine. The cross-polarization measurements made as a function of contact time permit estimation of the cross-relaxation rate and the proton spin-lattice relaxation time in the rotating frame, both of which are summarized in Table I. Both of these relaxation times are insensitive to the hydration of the sample, again indicating that hydration does not cause significant motional changes in the time range of tenths of milliseconds. In summary, the hydration effects on the dynamics of the S1-helix and @-sheetstructures of polyglycine are very small.

Polyglutamate and Polyglutamic Acid

C P / M A S spectra of dry and hydrated PGA and the NaPG are shown in Figure 6 for dry and hydrated @-sheet.Earlier work has shown that the carbon chemical shifts of C, , C2,and C3resonances in polypeptides behave similarly in all polypeptides when the secondary structure changes from a-helix to @sheet. 10.11.19-23 T he resonances of the two backbone carbons are shifted about 3-7 ppm upfield when the structure changes from helix to sheet, while the C, resonance shifts downfield. The C, and C, resonances of dry PGA appear a t 172.6 and 53.5 ppm, and of dry NaPG a t 172.6 ppm and 51.9 ppm, respectively, indicating that both polymers are in the P-sheet form." The downfield shift of the C5 resonance is always observed on ionization of the acid

function (cf. Figure 6 ( a and b ) ) .24 The C, and C4 resonances are not resolved a t 4.7 T. The hydration of PGA to the level of 0.12 g water/ g polymer does not cause a shift in the backbone resonances, indicating that the P-sheet is still the dominant form. Spectrum E was recorded for a sample that was prepared by lyophilization from a solution a t p H 3. The spectrum shows new peaks for the C p , C3, and C4 resonances that are in the positions of the a-helix resonances. Apparently the lyophilization process has trapped or induced a-helix formation that is avoided using more gentle drying procedures. Rehydration of a lyophilized sample reproduces the @-sheets p e ~ t r u m . ' ~ T h e hydration of NaPG t o 1.8 water/monomer yields spectrum B, which exhibits significantly narrowed lines. T h e C3 and C4 resonances are resolved, while the chemical shifts of the Cl and C z resonances demonstrate that the @-sheet structure is maintained. Further, the C1 resonance remains broader than the C5 resonance, which is a cause for its decreased amplitude; a second cause is a significantly larger chemical shift anisotropy for the backbone resonance, which is demonstrated by slow spinning measurements to be discussed shortly. Echo-train spectroscopy indicates the MAS spectra of the dry polymer are inhomogeneously broadened and the MAS spectra of the wet polymer are dominated by homogenous b r ~ a d e n i n g . ' ~ T h e 13C relaxation times for dry and hydrated NaPG are shown in Table 11. Also included are measurements on the sodium form when the amide protons are exchanged for deuterons and the polymer

HYDRATION EFFECTS ON POLYGLYCINE AND NA POLY ( L-GLUTAMATE)

I

1111

200

697

NaPG

A

100

II I I

PPM

200

100

PPM

Figure 6. Proton-decoupled 13C CP/MAS spectra at 4.7 T and room temperature of NaPG and PGA. ( A ) The @-sheetform of dry NaPG; ( B ) @-sheetform of dry PGA; ( C ) @-sheetform of hydrated NaPG (0.22 g H,O/g NaPG or 1.8 H20/monomer); ( D ) @-sheet form of hydrated PGA (0.12 g H,O/g PGA or 0.86 H20/monomer); ( E ) PGA lyophilized from solution at pH 3. For all spectra, 1 ms contact time and 10 Hz Lorentzian line broadening was employed.

is hydrated with D 2 0 instead of H20. The effects of hydration on T I are large. The dominant contribution to the carbon spin relaxation derives from the proton-carbon dipole-dipole coupling. For the two-spin heteronuclear case, excluding cross-relaxation effects, the carbon relaxation rate is given by25

where J ( w) is the spectral density characterizing the frequency dependence of the coupling, and OH and w ( ~are the proton and carbon Larmor frequencies, respectively. In the case of random isotropic reorientation,

and

More appropriate models have been developed for the case of solids where anisotropic jump or diffusional motion is l i k e l ~ . ' ~ - The ~ ' result is that Eqs. ( 1) - ( 3 ) may provide an estimate of the maximum rate expected for a particular correlation time. For instance, TI of the C3 and C, nuclei when NaPG is hydrated to 2.5 DzO molecules per monomer is 121 ms. TI for a methylene carbon undergoing isotropic reorientation in a 4.7 T field is less than 121 ms for correlation times ranging from 0.25 to 15 ns. Thus, the motions driving relaxation of C3 and C , in NaPG hydrated to 2.5 DzO molecules per monomer cannot have correlation times outside this range.

698

KENNEDY AND BRYANT

Table I1 TIand TIs for Dry NaPG (Dry), NaPG Hydrated with H20 to 1.8 H20/Monomer [Wet (1.8)], Perdeuterated Dry NaPG (d-Dry), Perdeuterated NaPG Hydrated with D 2 0 to 1.9 D20/Monomer [d-Wet (1.9)], and Perdeuterated NaPG Hydrated with D 2 0 to 2.5 DzO/Monomer [d-Wet (2.5)]"

C4

C3

C2

Cl

C5

32.7 f 2.3

58.3 k 4.7

36.3 k 2.0

1.8 (0.55) 12 (0.45) 55.6 f 3.1

14.2 f 0.5

2.3 (0.76) 17.3 (0.24) 74.2 +- 5.6

Ti (s) Dry Wet (1.8) d-Dry d-Wet (1.9) d-Wet (2.5) Tis (PSI Dry Wet (1.8) d-Dry d-Wet (1.9) d-Wet (2.5) a

2.5 (0.55) 38.2 (0.45) 0.148 -t 0.007 0.152 f 0.005 2.8 (0.53) 61.4 (0.47) 0.162 f 0.01 0.159 f 0.01 0.121 f 0.005

0.121 f 0.005

31.1 k 1.5 46.0 f 3.1

50.0 f 2.9 28.1 f 2.1 42.8 f 2.9 79 f 7

94.3 k 6.8

1.6 (0.64) 9.7 (0.36) 1.2 f 0.1

10.0 f 0.6 2.0 f 0.5

1.8 (0.75) 15.2 (0.25) 0.64 k 0.1

37.9 k 2.5 33.8 f 2.2 34.9 k 2.5 34.8 k 2.3 39.8 f 3.6

283 +- 31 240 k 24 410 +- 25 393 f 28 461 f 58

418 f 40 586 f 40 455 f 34 557 -t 30 1180 k 88

Where two T, values are given, the numbers in parentheses are the amplitudes of two components of a biexponential decay.

A consequence of the anisotropic nature of the motion is that the relaxation will depend on orientation of the CH vectors. However, the nonexponential character is largely eliminated by rapid sample rotation that averages the orientation of the CH pairs in a time that is short compared with the relaxation times measured and long compared to the motions causing relaxation. T h e decay of the C3and C, resonances is not exponential in the dry case, however. The nonexponential decay is not a result of the superposition of two resonances with different relaxation rates because, although the shape of the C3,4resonance indicates that two unresolved components are present, the shape does not change shape as the intensity decays. Thus, it appears most likely that this behavior results from dynamical heterogeneity in the sample. The replacement of the amide proton by a deuteron in the dry material leads t o the interesting result that all of the carbon resonances except the rapid component of the C3,, resonance show a n increased relaxation time. Nevertheless, hydration of the deuterated sample with deuterium oxide yields relaxation times that are essentially the same as those for the protonated sample hydrated with HzO. This result indicates that it is not water molecule motion that drives carbon relaxation in this case but motion of the polymer. The Czand C5resonance decays become biexponential with the more rapidly relaxing component dropping by over an order of magnitude on hydration to 1.8 water molecules per

monomer. T h e nonexponential character of these resonances is removed with the addition of D 2 0 to a level of 2.5 water molecules per monomer. This response suggests that the origin of the nonexponential decays in the less hydrated samples is local heterogeneity of the hydration. T h e cross-polarization rates of the carbon resonance with attached protons respond to the hydration with large effects in all three side-chain resonances, but very small changes in the C, and Cz resonances. This result is consistent with large amplitude side-chain motion causing the proton-carbon dipole-dipole coupling in the hydrated samples t o average. At the same time, the amplitudes of the backbone motions are little affected by hydration. T h e effects of hydration on the static spectrum of PGA or NaPG are difficult to detect because the chemical shift anisotropies are large and lines overlap. However, this problem may be overcome with a slow spinning experiment that permits resolution of the central resonances while the side-band intensity pattern permits evaluation of the effective principal values of the chemical shift t e n ~ o r . ~ T~h, e~ ' carbonyl region of a representative slow spinning experiment is shown in Figure 7 for NaPG both dry and hydrated to 2.5 DzO molecules per monomer. I t is clear that the line widths of the two components in the spinning experiment are very different, and that the amplitudes of the resonances change significantly on hydration. The narrowness of the spinning side bands of the C5 carbon resonances

HYDRATION EFFECTS ON POLYGLYCINE AND NA POLY ( L-GLUTAMATE)

699

B

demonstrates that there are no motions that interfere with the formation of the rotary echos. The rotor frequency is only about a factor of 6 less than the width of the powder pattern. Thus, significant motions on the order of the reciprocal of the powder pattern width should also affect the side-band linewidths. T h a t this is not the case demonstrates that the motions that average the C5 chemical shift tensor are in the fast motion limit, i.e., fast compared to both the rotor period and the reciprocal of the pattern width. The analysis of Herzfeld and Berger31was applied to the side band intensities of the C5 resonance and the results are summarized in Table 111. The accuracy of this procedure is lower for the hydrated case because of the range of values that will approximately yield the observed spectrum. However, the width of the powder pattern, oZz- uxxis well determined. Comparison of the dry and hydrated values of the chemical shift tensor deduced demonstrates

that the motions induced by hydration are of suficient amplitude to alter significantly the chemical shift tensor. T h e uzzand ,a elements are affected more by the hydration than the B, value. Further, the values of uzzand a,,, become more nearly equal with increasing hydration, which indicates that the Table I11 Principal Values in ppm of Chemical Shift Tensor of Cs Carbon of NaPG Obtained from Herzfeld and Berger Analysis Applied to Spectra in Figure 7"

Dry Wet

2385 2.5 2255 4

194 f 4 167 f 6

112 f 2 150 f 3.5

127 5 2 74 f 4

* A spectrum of wet NaPG taken at a spinning speed of 0.86 kHz was also analyzed and averaged with the results of analysis of Figure 7b. The uncertainties given are obtained by sampling a range of p and p values as suggested by the uncertainty in the point of intertion of the contours. uls0 = 181.5 ppm.

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KENNEDY AND BRYANT

motion present averages the y and z directions of the chemical shift tensor more than the x direction. These data provide a means for estimating the amplitude of motion that produces the averaged tensor provided a n assumption is made about the orientation of the chemical shift tensor for the C5 carbon atom. We take the orientation for the shift tensor from model compounds that have been analyzed in detail demonstrating that the most shielded component, uZz,is normal t o the plane of the carboxylic acid, u,,, the least shielded component, is almost parallel to the C4-C5bond. T h e ,a is normal to both and thus lies in the plane of the oxygen With the assumption that these orientations are maintained in the side chain of NaPG, rotations about the C4-C5bond produce rotations about the x axis of the chemical shift tensor, while rotations about the bonds closer to the main chain produce rotational components about the y and z axes of the shift tensor. Using the fast motion model, that is, that the motions averaging the chemical shift tensor are fast compared to the reciprocal of the breadth of the powder pattern, we may estimate the amplitudes of the motion by averaging the chemical shift tensor over a distribution of orientations. If we let 0 be the Euler angles describing the rotation of the shift tensor away from a n arbitrary initial orientation a n d p ( Q ) be the probability of the tensor being a t orientation Q, then a motionally averaged shift tensor can be calculated from the weighted sum of rotational transformations of the principal-axis system chemical shift tensor:

T h e rzmare elements of the principal axes representation of the chemical shift in spherical irreducible tensor form and DL,,( Q ) are elements of the Wigner rotation matrix for tensors of rank We assume principal values of the shift tensor implied by the side-band pattern of the dry sample and assume Gaussian reorientational distributions of the tensor in the hydrated sample with rms deviations of (Ox), ( O , ) , and (0,) about the principal x , y , and z axes, respectively. The observed changes in the shift tensor are consistent with (8,) = 15"-ZOO,(0,) = 45"-50", and (0,) anywhere between 1" and 20". It is possible to simulate the collapse approximately with (0,) = lo-5" with (0,) = 50"-55" and (8,) = 35"-40°,but it seems unlikely that motions about the y and z axes are so dramatically different when the flexibility about x is so great. Thus, the most

reasonable picture of the motion is one where there is considerable rotational freedom about the C4-C5 bond and sufficient flexibility closer to the main chain to produce about 15" excursions about the other axes.

CONCLUSION In summary, these solid state nmr measurements demonstrate that in the folded structures examined here, the dynamical changes induced by hydration in the backbone regions of the polymer are small, which is consistent with the nature of the compact structures examined. By contrast, the changes in NaPG side-chain dynamics are major with the addition of water and may be characterized by very rapid motions about the C4-C5 bond of amplitude 40"-50" while those about the other directions are less than half this size, with correlation times between 0.25 and 15 nanoseconds. This work was supported by the National Institutes of Health, GM-34541, and the University of Rochester. We gratefully acknowledge helpful discussions with Dr. Scott Swanson and Dr. P. Mark Henrichs.

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HYDRATION EFFECTS ON POLYGLYCINE AND NA POLY (L-GLUTAMATE)

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