The Hydration Response of Poly (L-Lysine) Dynamics Measured by 13C-NMR Spectroscopy SCOTT D. S W A N S O N ' , * and ROBERT C. BRYANT',' I k p i r t i n c ~ i i t so f 'Chemistry and 'Biophysics, University of Rochester Medical Center, Rochester, New York 14642
SYNOPSIS
'.'C-nmr measurements are reported for samples of poly (L-lysine) both static a n d spinning a t t h e magic angle in the @-sheetform as a function of water content. T h e addition of water decreases the side-chain line widths considerably. Measurements of the cross-polarization time constants indicate t h a t hydration by either H 2 0 or D 2 0 increases the time constant. Measurements of spin-lattice relaxation times in the laboratory frame and the rotating frame indicate t h a t hydration does not change the dynamics of the backbone carbon atoms in the P-sheet structure appreciably, but the side-chain atoms experience considerable increase in local mobility with increasing hydration. Deuteration of the exchangeable protons or the water has only small effects on the carbon relaxation times, indicating t h a t relaxation is driven by intramolecular dipole-dipole interactions.
INTRODUCTION The motions in a macromolecule may be crucial to its function, yet a considerable amount remains to be learned about the local and global dynamics in complicated polymeric structures such as proteins. The biochemically active polymers offer a n additional problem in that both the structure and the dynamics may be affected by the presence or absence of water. The interaction between water and macromolecules has been of intense interest for a long time. Applications of nmr methods to these problems have sometimes been controversial, but now the power of' higher field nmr spectrometers coupled with multinuclear observations in solids make this an increasingly powerful approach to the dynamical and structural questions about the macromolecule. The response of macromolecules to the addition of water is not uniform. The branched polysaccharide, glycogen, responds dynamically with increased motional amplitudes and frequencies a t even low water contents, * while catalytic proteins fold more tightly into a narrow distribution of structures with increasing h y d r a t i ~ n . ~Poly - ~ ( L-lysine ) has been
'
studied by ir spectroscopy,6 x-ray d i f f r a ~ t i o nand ,~ Raman spectroscopy,' as well as solid state nmr These studies have demonstrated that as poly ( L-lysine) hydrochloride is hydrated, the conformation changes from P-sheet to a-helix. The nmr studies have shown that the backbone carbonyl resonance and a-carbon resonances of polypeptides change on hydration and that the chemical shift values of these resonances may be used to determine the secondary structure of polypeptides. Solutionphase nmr studies on poly ( L-lysine ) have demonstrated a heterogeneity in the high-frequency motions that affect spin-lattice relaxation rates for the different side-chain positions of the carbon atoms. The backbone is most rigid and the side chain becomes more flexible as one moves toward the t carbon." Several models have been applied to the analysis of the side-chain motion in solution." We report here I3C-nmr studies of poly( L-lysine) in the @-sheet conformation that provide considerable information about the main- and side-chain motions a t different water contents.
EXPERIMENTAL Biopolyrners, Vol. 31, 967-973 (1991) (c'
magnetic resonance measurements were ccc o o o s - ~ s z s / ~ ~ / o s o ~ s ~ - o ~ ~ oNuclear ~.oo performed on a n nmr spectrometer constructed in * Present address: Department of Radiology, University of
1991 J o h n Wiley & Sons, Inc.
Michigan. Ann Arbor, MI.
this laboratory and described e l ~ e w h e r e . ' ~The ~'~ 967
968
SWANSON AND BRYANT
spinning probe employed a Doty Scientific stator and rotor assembly that was brought to resonance with high-power tuning elements remote from the resonance region. Poly (L-lysine) (Sigma Chemical Company) had a molecular weight range from 15,000 to 30,000 with a n average of 21,200. T h e dry poly( L-lysine) samples were prepared by dissolving about 200 mg of the cotton-like sample supplied in 3 mL of water, and the solution was placed in a 333 K oven overnight, which left a n hard transparent film on the bottom of the beaker. Further heating under vacuum did not change the weight of the sample. T h e deuterated dry samples were prepared by dissolving 170 mg of poly( I,-lysine) in 3 mL of 99.8% D 2 0 ( Aldrich Chemical Company), the vessel was closed, and the sample was allowed to equilibrate for two days. This solution was dried in a n oven overnight and a n additional 3 mL of 99.8% D 2 0 was added to redissolve the polymer. This solution was allowed t o equilibrate for another day; then the vial was opened and the sample was placed in a n oven a t 333 K for 24 h. If all -NH and -NH:3protons had free exchange with the deuterons of the solvent, which is a good assumption, 99% of the exchangeable sites should be deuterated by this procedure. Hydration of the poly ( L-lysine) was accomplished through the gas phase by equilibration of the polymer over a saturated salt solution chosen to provide the desired relative humidity as summarized in Table I. T h e deuterated dry sample was hydrated with D 2 0 using a saturated solution of NaNOz in D20. Hydrated samples were placed in the nmr magicangle rotor equipped with double O-ring seals in the end caps to ensure that all water remained in the rotor, which was confirmed gravimetrically a t t,he conclusion of the experiment. Water contents were determined gravimetrically by drying the samples a t 333 K for a minimum of 12 h to constant weight.
RESULTS T h e "(2-nmr spectrum for static and spinning poly( L-lysine) hydrochloride is shown in Figure 1. Table I
Poly(L-Lysine) Hydration
Saturated Salt
NaN02
NH&l
KCl
Relative humidity (%) % Hydration Water/monomer
66 16 1.8
79 28 2.5
86 49 4.6
b) static
I
a) spinning
200
I00
Figure 1. "'C-nmr spectra of dry poly ( I,-lysine) hydrochloride obtained a t 50.3 MHz and ambient temperature. The static spectrum ( t o p ) was obtained in 37,936 transients, 60-kHz proton decoupling field, 1-s repetition time, and 1-ms contact time for the polarization transfer. The spinning spectrum was obtained with the same parameters a t a spinning speed of 3.74 kHz and 28,600 transients.
In the spinning spectrum all carbon atoms are resolved and the assignments reported previously; '' however, the line widths are considerably wider than those found in crystalline lysine hydrochloride dihydrate.lS The chemical shifts were found to vary only a few tenths of a part per million up to a water content of 50% by weight, which is taken as evidence that the @sheet structure is maintained in the polymer over this water content range. line widths are summarized in Figure 2 The as a function of water content. T h e line widths in L-lysine hydrochloride dihydrate are shown for comparison. The main-chain resonances do not change significantly wit,h increased hydration, but the side-chain resonance line widths decrease dramatically yet do not achieve the breadth of the crystalline monomer. T h e time constant characterizing the growth of carbon magnetization during the Hartmann-Hahn match of the cross-polarization experiment is shown a s a function of carbon atom in Table 11. T h e cross-
969
HYDRATION RESPONSE OF POLY (L-LYSINE) DYNAMICS
80 . ln
I Y 0
I-
Weight % H20
u
-
Weight % D 0
0%
+ 16%
-t-
60
2
0% 18%
251 1 40
0
Carbonyl Alpha
20
Beta Gamma Delta Epsilon Carbon
Alpha
Figure 2. '"C-nmr line widths for poly(L-lysine) hydrochloride in the P-sheet form taken at 50.3 MHz using magic-angle spinningand the conditions of Figure 1. Data are shown as a function of water content for each carbon atom in the monomer unit. For L-lysine a and t resonances, t h e narrower line of the residual dipolar doublet is indicated.
Beta
Gamma Carbon
Delta
Figure 3. T h e time constant T I ,for cross-polarization of carbon spins from protons in poly ( L-lysine) hydrochloride samples as a function of carbon atom position. Data are shown for dry protonated and deuterated samples, a n d for these samples hydrated with H 2 0 and D 2 0 t o the level of 16% a n d 18%by weight, respectively. Data were taken a t 50.3 MHz a n d ambient temperature.
as a function of carbon atom position and water content in Table IV. The side-chain carbon resonances relax exponentially a t all levels of hydration, but the backbone carbon resonances are not exponential a t any level of hydration. A representative data set is shown in Figure 4 and the data summarized in Table IV. T h e relaxation times recorded in Table IV for the carbonyl and a-carbon atom are the time constants for the slowly decaying portion of the relaxation curve. Addition of either H 2 0 or D 2 0 decreases the relaxation times significantly. T h e relaxation times of the main-chain atoms are significantly longer than those of the side-chain
polarization time is a weak function of carbon atom posit ion in the dry samples, but the addition of either H,O or D 2 0causes a significant increase in the crosspolarization time that is greater the further the atom is from the main chain, as shown in Figure 3. 1i C spin-lattice relaxation times in the rotating frame, TI,,,are shown as a function of carbon atom in Table I11 for samples of different water content. For dry samples both protonated and deuterated, the dependence on carbon atom position is weak, but the addition of either D 2 0 or H 2 0 increases the time tor all side-chain carbon atoms. 1.1 (, spin-lattice relaxation times are summarized Y
Table I1 Proton-Carbon T I ,Values ( p s ) for Poly(Id-Lysine)as a Function of Weight Percent Hydration by D 2 0 and HzO Weight % D 2 0 Carbon
0%
(:arbonyl
460 (60) 38 (4) 32 (2) 37 (5) 49 (3) 45 ( 2 )
(I
i' 3 d c
18% 804 34 52 76 87 86
(82) (3) (2) (2) (4 ) (5)
Epsilon
Weight % H 2 0 0%
340 45 32 37 43 39
(17) (5) (2) (3) (3) (3)
16%
28%
50%
443 (35) 39 (3) 54 ( 3 ) 78 (5) 100 (6) 94 (6)
538 (61) 46 (5) 55 (3) 83 (5) 103 ( 4 ) 91 (6)
440 ( 8 0 ) 32 (4) 55 ( 4 ) 91 (4) 109 (6) 69 (5)
970
SWANSON AND BRYANT
Table I11 Carbon T I ,Values (ms) for Poly(L-Lysine) as a Function of Weight Percent Hydration by H 2 0 or DzO Weight % D 2 0 0%
Weight % H 2 0
18%
0%
16%
rf Power (kHz) Carbon
50
Carbonyl
117 24 6.6 4.3 4.3 4.1
N
B Y 6 c
50%
rf Power (kHz)
36
(8) (0.5) (0.3) (0.2) (0.1) (0.1)
28%
48
270 (90) 16 (0.8) 10 (0.5) 14 (0.6) 14 (0.8) 13 (0.7)
75 19 4.9 4.5 3.0 3.2
carbon atoms, and the side-chain atoms show a greater response to the addition of water than the main-chain atoms.
DISCUSSION The assignment of each resonance line in the magicangle spinning spectrum provides an interesting way to probe the dynamical response of different parts of the homopolymer in the 0-sheet structure to hydration. The constant values of the chemical shifts over the hydration range studied demonstrates that the polymer retains the P-sheet structure; thus, changes observed in other aspects of the spectrum may be attributed to specific effects of the hydration events, but not major structural rearrangements of the polymer. The considerable line broadening in the polymer over the crystalline monomer is commonly observed and generally attributed to the amorphous packing
(2.2) (0.3) (0.2) (0.2) (0.1) (0.1)
43
36
48 (2.3) 16 (0.6) 11 (0.4) 14 (0.7) 13 (0.6) 10 (0.2)
95 (13) 25 (0.9) 12 (0.5) 15 (1.0) 13 (0.6) 10 (0.4)
33 42.4 11.9 11.7 15.1 11.6 7.60
of the polymer creating a distribution of local environments and consequently a distribution of isotropic chemical shift values. T h e main-chain resonances are narrower than the side-chain resonances, which is consistent with the 0-sheet structure providing these atoms with a more homogeneous environment than the side-chain atoms. The addition of water to the sample causes a considerable decrease in the carbon line widths of the side-chain atoms, a decrease that is not a strong function of water content above 16% water by weight. Although the effects are small, it is interesting to note that the 49% sample provides somewhat broader lines in the magic-angle spinning experiment than the 28% sample. Also, the main-chain resonances for the 49% sample are broader than the dry sample, although the lower hydration level samples are narrower. We may speculate that this apparently peculiar observation may arise because a t the 49% hydration level the polymer is close to the water content that causes a transition to the a-helix
Table IV Carbon T I Values" ( s ) for Poly(L-Lysine) as a Function of Weight Percent Hydration by HzO or DzO Weight % D 2 0
Weight % H 2 0
Carbon
0%
18%
0%
16%
28%
50%
Carbonyl n
13.5 4.60 0.570 0.343 0.318 0.310
5.80 1.60 0.135 0.141 0.179 0.213
11.4 5.20 0.630 0.468 0.370 0.450
6.30 1.70 0.142 0.139 0.179 0.219
5.74 1.57 0.153 0.128 0.188 0.237
3.78 1.75 0.191 0.191 0.254 0.358
B Y d t
a
Errors less than 10% for all values.
(5.9) (0.6) (0.4) (0.7) (0.3) (0.2)
HYDRATION RESPONSE OF POLY (L-LYSINE) DYNAMICS
20,
I
I
I
c
1
i
15
2
v
10
a
I-
-
. --O-
-+-
5 -
----C
Beta Gamma Delta Epsilon
O
A Dry
16%
27.5%
50%
Weight%water Figure 4. '"C T,,measured as a function of water content for side-chain carbon atoms in poly (L-lysine) hydrochloride in the P-sheet form. The data are also shown in Table 111. The carbon resonance frequency was 50.3 MHz and the temperature was ambient.
form. If the P-sheet structure is becoming unstable a t the high water contents, the main-chain resonances would show the greatest change. The narrowing of the side-chain resonances with increased water content is consistent with a n increase in side-chain motion, the result of which is to average further the chemical shift tensor a t each carbon atom. T h e addition of water also may make the density of the sample more uniform, which will decrease the magnetic susceptibility fluctuations within the sample. The concept of increased molecular motion is also supported by the relaxation data discussed below. Nevertheless, the line widths of the hydrated polymer resonances remain about twice as broad as the crystalline monomer. The cross-polarization time constants summarized in Table I1 show that there is little difference between protonated and deuterated dry polymer, which indicates that the proton-carbon interactions that drive the magnetization transfer process do not depend on the distant ammonium protons. Further, hydration by either HzO or DzO increases the crosspolarization time. This result is shown graphically in Figure 3 , where it is clear that the further from the main chain, the larger the increase in relaxation time. It is interesting to note that the t-carbon atom is more efficiently polarized than the &carbon atom, even though each has two attached protons. This observation may reflect the hydrogen-bonding ca-
971
pability of the ammonium group which may slow the motion of the side-chain end. The carbon TI, is a sensitive but complicated measure of motion in the range of the radio frequency ( r f ) field strength used for the spin-locking portion of the experiment. A difficulty with the present data set is that the rf field is not a constant through the hydration range studied because the addition of water decreased the effective Q of the probe and dropped the rf level delivered by the amplifier. While the decline in rf level was less than 3596, from 48 kHz for the dry sample to 33 kHz for the 49% sample, this change is in a range that is particularly sensitive to the competition between carbon-proton dipolar contributions and carbonspin lattice contributions to the effective relaxation time. Thus, quantitative analysis of the data will not be attempted. Nevertheless, several qualitative observations are useful. The carbon T I , values for deuterated and protonated polymer samples are similar, except that the protonated samples relax slightly faster. This observation is consistent with elimination of the ammonium and amide protons from the proton pool that drives the carbon relaxation by a dipole-dipole mechanism. The main-chain resonance relaxation times change in a confusing way as a function of water content; however, the side-chain resonances behave consistently, as shown in Figure 5. The trend for all side-chain resonances is common in that add-
01
0.0
1
1.o
,
2.0
.
I
3.0
I
.
4.0
5.0
Delay time in pulse sequence (s)
Figure 5. 13C inversion recovery data for the C, and C, resonances of poly (L-lysine) as a function of time taken a t 50.3 MHz and ambient temperature. The solid lines are exponential fits to the longer time portions of the data.
972
SWANSON AND BRYANT
ing water increases the relaxation time until the 50% samples are reached, when it decreases again. This increased relaxation rate a t the 50% samples is very possibly due to the lower rf field used for the measurement and may not reflect a significant difference in the side-chain motion. However the spin-lattice relaxation data do not suffer from this difficulty. The carbon spin-lattice relaxation times summarized in Table IV are striking in that the mainchain carbon atom relaxation times are much longer than any of the side-chain relaxation times. The differences between the protonated and deuterated samples is small, indicating that the ammonium protons do not completely dominate the relaxation rate, nor do the water protons in the hydrated samples. Thus, the carbon relaxation rate is dominated by the bonded-proton-carbon dipole-dipole relaxation. T h e nonexponential relaxation observed for the carbon magnetization of the backbone resonances is consistent with a transient nuclear Overhauser effect ( NOE) . The pulse sequence used was designed to minimize and add out the effects of nonideal pulses; however, if there are protons coupled to the carbon atoms observed with z magnetization a t the beginning of the relaxation delay period, a transient NOE will develop and the magnetization then decays with the appropriate carbon T I .We therefore take the values entered in Table IV as good estimates of the carbon T I values. The long relaxation times for the backbone carbon atoms are consistent with their relatively rigid environment in the 0-sheet structure; 0.7
0.6
0.5
5
0.4
u)
v
0.3
0
e 9
0.2 0.1
\\
-
+ Beta
+ Gamma --c. Delta Epsilon
A
0.0
Dry
16%
2 8%
50%
Weight % water
Figure 6. 13C spin-lattice relaxation times for sidechain carbon atoms of poly( L-lysine) hydrochloride as a function of water content obtained a t 50.3 MHz and ambient temperature.
0.7
I
I
I
0.6
-
Weight % water
0.5
-
--b- 16% 27.5%
--t
0.4
-
0.3
-
0.2
-
0.1
r
0.0
I
I
50%
I Beta
Gamma
Delta
Epsilon
Carbon
Figure 7. "'(2 spin-lattice relaxation times as a function of carbon atom position for different water contents of poly ( I,-lysine ) hydrochloride samples recorded a t 50.3 MHz and ambient temperature.
however, even these relaxation times are not very long compared with other polymeric systems where T I values may exceed 50 s, indicating that there is still considerable motion a t the carbon Larmor frequency to relax the system. T h e striking feature of Table IV is the dramatic difference between the backbone carbon T I values and the side-chain values, which are shorter by about a n order of magnitude. This observation is consistent with there being very considerable motion present in the side chains that adds to the spectral densities a t the carbon resonance frequency. Such major differences are not observed in the lower frequency windows associated with the carbon T I ,for example. This dramatic difference in relaxation rate of the side-chain carbon resonances is preserved with increasing water concentrations, and is independent of whether the system is hydrated with H 2 0 or D20. Thus, the effect on the side chains is not caused by dipolar interactions between carbon atoms and the water protons, but is caused by the intramolecular CH couplings. As a consequence, the major difference between the a-carbon and the side-chain carbon atoms must be the frequency and amplitudes of polymer motions present. Figure 6 and Figure 7 present the spin-lattice relaxation times for the side-chain resonances in two instructive ways. Figure 6 shows that for each sidechain atom, the resonance passes through a minimum as a function of water content between the dry sample and the 50% sample. These observations are consistent with the addition of water carrying the
HYDRATION R E S P O N S E OF POLY (I.-I,YSINE:)
system from the low- to the high-temperature side of the relaxation time minimum; however, the value of the minimum is greater than expected based on the simplest relaxation equations. T h e data in Figure 7 demonstrate that for the dry system, the relaxation times pass through a minimum in going from the /l to the c resonance, which is consistent with increased motion a s one moves out on the side chain. T h e addition of water to the system appears to shift the minimum to the @-carbonor y-carbon atom, with the other resonances falling on the faster motion side. There are a number of ways to quantitatively discuss these relaxation data, but the data is not sufficient to support a unique interpretation. One simple and possibly useful description is to assume t h a t the side-chain carbon atoms execute a restricted diffusion in a cone of some half angle. Computing the value of the T , minimum as a function of the cone angle, we can compare the values observed with this model. In this case we find that the data for the dry side-chain carbon resonances suggest a half angle of 17", and t h a t when the system is hydrated this angle increases about a factor of 2. However, the assumptions of such a model are inadequate for describing this situation because it is clear that both the frequencies and amplitudes of the motions may change as a function of water content. T h e correlation time information could come from a study as a function of Larmor frequency, which we do not have available for carbon spectroscopy. Thus, further discussions of precise amplitudes appears more speculative than worthwhile. In summary, the 13C spectroscopy reported here provides a clear demonstration t h a t the backbone atoms o f the polymer in the 0-sheet structure are considerably more rigidly held in place than the sidechain atoms, as expected. Further, the side-chain resonances respond in a systematic way to hydration with increased motion both as a function of increasing water content and a s a function of distance from the main chain.
DYNAMICS
973
This work was supported by the National Institutes of Health, GM-34541, and the University of Rochester. The authors acknowledge with pleasure numerous helpful discussions with members of the magnetic resonance group including particularly Dr. Scott D. Kennedy. Stimulating discussions with Dr. P. Mark Henrichs and Dr. Nicholous Zumbulyadis are also gratefully acknowledged.
REFERENCES 1. Franks, F. & Mathias, S. F. (1982) Biophysics of Water, John Wiley & Sons, New York. 2. Jackson, C. L. & Bryant, R. G. (1989) Biochemistry 28, 5024-5028. 3. Kennedy, S. D. & Bryant, R. G. ( 1990) Biopolymers, in press. 4. Marchetti, P. S., Ellis, P. D. & Bryant, R. G. (1985) J. A m . Chem. Soc. 107,8191-8106. 5. Cole, H. B. R., Sparks, S. W. & Torchia, I). A. (1988) Proc Natl. Acad. Sci. 85, 6362-6365. 6. Blout, E. R. & Lenormant, H. (1957) hiature 179, 960-963. 7. Shmueli, U. & Traub, W. (1965) J . Mol. Biol. 12, 205-214. 8. Yu, T., Lippert, J. L. & Peticolas, W. L. (1973) Biopolymers 12, 2161-2176. 9. Saito, H., Tabeta, R., Shoji, A., Ozaki, T. & Ando, I. (1983) Macromolecules 16, 1050-1057. 10. Kricheldof, H. R. & Muller, D. ( 1983) Macromolecules 16, 615-623. 11. Wittebort, R. J., Szabo, A. & Curd, F. R. N. (1980) J . A m . Chem. SOC.102,5723-5728. 12. Wittebort, R. J. & Szabo, A. (1978) J . ('hem. Phys. 69, 1722-1736. 13. Kennedy, S. D. (1988) Ph.D. thesis, University of Rochester, Rochester, NY. 14. Swanson, S. D. (1989) Ph.D. thesis, University of Rochester, Rochester, NY. 15. Swanson, S. D. & Bryant, R. G. ( 1990) Magn. Reson. Chem., submitted.
Received January 3, I990 Accepted February 8, 1991
SYNOPSIS
'.'C-nmr measurements are reported for samples of poly (L-lysine) both static a n d spinning a t t h e magic angle in the @-sheetform as a function of water content. T h e addition of water decreases the side-chain line widths considerably. Measurements of the cross-polarization time constants indicate t h a t hydration by either H 2 0 or D 2 0 increases the time constant. Measurements of spin-lattice relaxation times in the laboratory frame and the rotating frame indicate t h a t hydration does not change the dynamics of the backbone carbon atoms in the P-sheet structure appreciably, but the side-chain atoms experience considerable increase in local mobility with increasing hydration. Deuteration of the exchangeable protons or the water has only small effects on the carbon relaxation times, indicating t h a t relaxation is driven by intramolecular dipole-dipole interactions.
INTRODUCTION The motions in a macromolecule may be crucial to its function, yet a considerable amount remains to be learned about the local and global dynamics in complicated polymeric structures such as proteins. The biochemically active polymers offer a n additional problem in that both the structure and the dynamics may be affected by the presence or absence of water. The interaction between water and macromolecules has been of intense interest for a long time. Applications of nmr methods to these problems have sometimes been controversial, but now the power of' higher field nmr spectrometers coupled with multinuclear observations in solids make this an increasingly powerful approach to the dynamical and structural questions about the macromolecule. The response of macromolecules to the addition of water is not uniform. The branched polysaccharide, glycogen, responds dynamically with increased motional amplitudes and frequencies a t even low water contents, * while catalytic proteins fold more tightly into a narrow distribution of structures with increasing h y d r a t i ~ n . ~Poly - ~ ( L-lysine ) has been
'
studied by ir spectroscopy,6 x-ray d i f f r a ~ t i o nand ,~ Raman spectroscopy,' as well as solid state nmr These studies have demonstrated that as poly ( L-lysine) hydrochloride is hydrated, the conformation changes from P-sheet to a-helix. The nmr studies have shown that the backbone carbonyl resonance and a-carbon resonances of polypeptides change on hydration and that the chemical shift values of these resonances may be used to determine the secondary structure of polypeptides. Solutionphase nmr studies on poly ( L-lysine ) have demonstrated a heterogeneity in the high-frequency motions that affect spin-lattice relaxation rates for the different side-chain positions of the carbon atoms. The backbone is most rigid and the side chain becomes more flexible as one moves toward the t carbon." Several models have been applied to the analysis of the side-chain motion in solution." We report here I3C-nmr studies of poly( L-lysine) in the @-sheet conformation that provide considerable information about the main- and side-chain motions a t different water contents.
EXPERIMENTAL Biopolyrners, Vol. 31, 967-973 (1991) (c'
magnetic resonance measurements were ccc o o o s - ~ s z s / ~ ~ / o s o ~ s ~ - o ~ ~ oNuclear ~.oo performed on a n nmr spectrometer constructed in * Present address: Department of Radiology, University of
1991 J o h n Wiley & Sons, Inc.
Michigan. Ann Arbor, MI.
this laboratory and described e l ~ e w h e r e . ' ~The ~'~ 967
968
SWANSON AND BRYANT
spinning probe employed a Doty Scientific stator and rotor assembly that was brought to resonance with high-power tuning elements remote from the resonance region. Poly (L-lysine) (Sigma Chemical Company) had a molecular weight range from 15,000 to 30,000 with a n average of 21,200. T h e dry poly( L-lysine) samples were prepared by dissolving about 200 mg of the cotton-like sample supplied in 3 mL of water, and the solution was placed in a 333 K oven overnight, which left a n hard transparent film on the bottom of the beaker. Further heating under vacuum did not change the weight of the sample. T h e deuterated dry samples were prepared by dissolving 170 mg of poly( I,-lysine) in 3 mL of 99.8% D 2 0 ( Aldrich Chemical Company), the vessel was closed, and the sample was allowed to equilibrate for two days. This solution was dried in a n oven overnight and a n additional 3 mL of 99.8% D 2 0 was added to redissolve the polymer. This solution was allowed t o equilibrate for another day; then the vial was opened and the sample was placed in a n oven a t 333 K for 24 h. If all -NH and -NH:3protons had free exchange with the deuterons of the solvent, which is a good assumption, 99% of the exchangeable sites should be deuterated by this procedure. Hydration of the poly ( L-lysine) was accomplished through the gas phase by equilibration of the polymer over a saturated salt solution chosen to provide the desired relative humidity as summarized in Table I. T h e deuterated dry sample was hydrated with D 2 0 using a saturated solution of NaNOz in D20. Hydrated samples were placed in the nmr magicangle rotor equipped with double O-ring seals in the end caps to ensure that all water remained in the rotor, which was confirmed gravimetrically a t t,he conclusion of the experiment. Water contents were determined gravimetrically by drying the samples a t 333 K for a minimum of 12 h to constant weight.
RESULTS T h e "(2-nmr spectrum for static and spinning poly( L-lysine) hydrochloride is shown in Figure 1. Table I
Poly(L-Lysine) Hydration
Saturated Salt
NaN02
NH&l
KCl
Relative humidity (%) % Hydration Water/monomer
66 16 1.8
79 28 2.5
86 49 4.6
b) static
I
a) spinning
200
I00
Figure 1. "'C-nmr spectra of dry poly ( I,-lysine) hydrochloride obtained a t 50.3 MHz and ambient temperature. The static spectrum ( t o p ) was obtained in 37,936 transients, 60-kHz proton decoupling field, 1-s repetition time, and 1-ms contact time for the polarization transfer. The spinning spectrum was obtained with the same parameters a t a spinning speed of 3.74 kHz and 28,600 transients.
In the spinning spectrum all carbon atoms are resolved and the assignments reported previously; '' however, the line widths are considerably wider than those found in crystalline lysine hydrochloride dihydrate.lS The chemical shifts were found to vary only a few tenths of a part per million up to a water content of 50% by weight, which is taken as evidence that the @sheet structure is maintained in the polymer over this water content range. line widths are summarized in Figure 2 The as a function of water content. T h e line widths in L-lysine hydrochloride dihydrate are shown for comparison. The main-chain resonances do not change significantly wit,h increased hydration, but the side-chain resonance line widths decrease dramatically yet do not achieve the breadth of the crystalline monomer. T h e time constant characterizing the growth of carbon magnetization during the Hartmann-Hahn match of the cross-polarization experiment is shown a s a function of carbon atom in Table 11. T h e cross-
969
HYDRATION RESPONSE OF POLY (L-LYSINE) DYNAMICS
80 . ln
I Y 0
I-
Weight % H20
u
-
Weight % D 0
0%
+ 16%
-t-
60
2
0% 18%
251 1 40
0
Carbonyl Alpha
20
Beta Gamma Delta Epsilon Carbon
Alpha
Figure 2. '"C-nmr line widths for poly(L-lysine) hydrochloride in the P-sheet form taken at 50.3 MHz using magic-angle spinningand the conditions of Figure 1. Data are shown as a function of water content for each carbon atom in the monomer unit. For L-lysine a and t resonances, t h e narrower line of the residual dipolar doublet is indicated.
Beta
Gamma Carbon
Delta
Figure 3. T h e time constant T I ,for cross-polarization of carbon spins from protons in poly ( L-lysine) hydrochloride samples as a function of carbon atom position. Data are shown for dry protonated and deuterated samples, a n d for these samples hydrated with H 2 0 and D 2 0 t o the level of 16% a n d 18%by weight, respectively. Data were taken a t 50.3 MHz a n d ambient temperature.
as a function of carbon atom position and water content in Table IV. The side-chain carbon resonances relax exponentially a t all levels of hydration, but the backbone carbon resonances are not exponential a t any level of hydration. A representative data set is shown in Figure 4 and the data summarized in Table IV. T h e relaxation times recorded in Table IV for the carbonyl and a-carbon atom are the time constants for the slowly decaying portion of the relaxation curve. Addition of either H 2 0 or D 2 0 decreases the relaxation times significantly. T h e relaxation times of the main-chain atoms are significantly longer than those of the side-chain
polarization time is a weak function of carbon atom posit ion in the dry samples, but the addition of either H,O or D 2 0causes a significant increase in the crosspolarization time that is greater the further the atom is from the main chain, as shown in Figure 3. 1i C spin-lattice relaxation times in the rotating frame, TI,,,are shown as a function of carbon atom in Table I11 for samples of different water content. For dry samples both protonated and deuterated, the dependence on carbon atom position is weak, but the addition of either D 2 0 or H 2 0 increases the time tor all side-chain carbon atoms. 1.1 (, spin-lattice relaxation times are summarized Y
Table I1 Proton-Carbon T I ,Values ( p s ) for Poly(Id-Lysine)as a Function of Weight Percent Hydration by D 2 0 and HzO Weight % D 2 0 Carbon
0%
(:arbonyl
460 (60) 38 (4) 32 (2) 37 (5) 49 (3) 45 ( 2 )
(I
i' 3 d c
18% 804 34 52 76 87 86
(82) (3) (2) (2) (4 ) (5)
Epsilon
Weight % H 2 0 0%
340 45 32 37 43 39
(17) (5) (2) (3) (3) (3)
16%
28%
50%
443 (35) 39 (3) 54 ( 3 ) 78 (5) 100 (6) 94 (6)
538 (61) 46 (5) 55 (3) 83 (5) 103 ( 4 ) 91 (6)
440 ( 8 0 ) 32 (4) 55 ( 4 ) 91 (4) 109 (6) 69 (5)
970
SWANSON AND BRYANT
Table I11 Carbon T I ,Values (ms) for Poly(L-Lysine) as a Function of Weight Percent Hydration by H 2 0 or DzO Weight % D 2 0 0%
Weight % H 2 0
18%
0%
16%
rf Power (kHz) Carbon
50
Carbonyl
117 24 6.6 4.3 4.3 4.1
N
B Y 6 c
50%
rf Power (kHz)
36
(8) (0.5) (0.3) (0.2) (0.1) (0.1)
28%
48
270 (90) 16 (0.8) 10 (0.5) 14 (0.6) 14 (0.8) 13 (0.7)
75 19 4.9 4.5 3.0 3.2
carbon atoms, and the side-chain atoms show a greater response to the addition of water than the main-chain atoms.
DISCUSSION The assignment of each resonance line in the magicangle spinning spectrum provides an interesting way to probe the dynamical response of different parts of the homopolymer in the 0-sheet structure to hydration. The constant values of the chemical shifts over the hydration range studied demonstrates that the polymer retains the P-sheet structure; thus, changes observed in other aspects of the spectrum may be attributed to specific effects of the hydration events, but not major structural rearrangements of the polymer. The considerable line broadening in the polymer over the crystalline monomer is commonly observed and generally attributed to the amorphous packing
(2.2) (0.3) (0.2) (0.2) (0.1) (0.1)
43
36
48 (2.3) 16 (0.6) 11 (0.4) 14 (0.7) 13 (0.6) 10 (0.2)
95 (13) 25 (0.9) 12 (0.5) 15 (1.0) 13 (0.6) 10 (0.4)
33 42.4 11.9 11.7 15.1 11.6 7.60
of the polymer creating a distribution of local environments and consequently a distribution of isotropic chemical shift values. T h e main-chain resonances are narrower than the side-chain resonances, which is consistent with the 0-sheet structure providing these atoms with a more homogeneous environment than the side-chain atoms. The addition of water to the sample causes a considerable decrease in the carbon line widths of the side-chain atoms, a decrease that is not a strong function of water content above 16% water by weight. Although the effects are small, it is interesting to note that the 49% sample provides somewhat broader lines in the magic-angle spinning experiment than the 28% sample. Also, the main-chain resonances for the 49% sample are broader than the dry sample, although the lower hydration level samples are narrower. We may speculate that this apparently peculiar observation may arise because a t the 49% hydration level the polymer is close to the water content that causes a transition to the a-helix
Table IV Carbon T I Values" ( s ) for Poly(L-Lysine) as a Function of Weight Percent Hydration by HzO or DzO Weight % D 2 0
Weight % H 2 0
Carbon
0%
18%
0%
16%
28%
50%
Carbonyl n
13.5 4.60 0.570 0.343 0.318 0.310
5.80 1.60 0.135 0.141 0.179 0.213
11.4 5.20 0.630 0.468 0.370 0.450
6.30 1.70 0.142 0.139 0.179 0.219
5.74 1.57 0.153 0.128 0.188 0.237
3.78 1.75 0.191 0.191 0.254 0.358
B Y d t
a
Errors less than 10% for all values.
(5.9) (0.6) (0.4) (0.7) (0.3) (0.2)
HYDRATION RESPONSE OF POLY (L-LYSINE) DYNAMICS
20,
I
I
I
c
1
i
15
2
v
10
a
I-
-
. --O-
-+-
5 -
----C
Beta Gamma Delta Epsilon
O
A Dry
16%
27.5%
50%
Weight%water Figure 4. '"C T,,measured as a function of water content for side-chain carbon atoms in poly (L-lysine) hydrochloride in the P-sheet form. The data are also shown in Table 111. The carbon resonance frequency was 50.3 MHz and the temperature was ambient.
form. If the P-sheet structure is becoming unstable a t the high water contents, the main-chain resonances would show the greatest change. The narrowing of the side-chain resonances with increased water content is consistent with a n increase in side-chain motion, the result of which is to average further the chemical shift tensor a t each carbon atom. T h e addition of water also may make the density of the sample more uniform, which will decrease the magnetic susceptibility fluctuations within the sample. The concept of increased molecular motion is also supported by the relaxation data discussed below. Nevertheless, the line widths of the hydrated polymer resonances remain about twice as broad as the crystalline monomer. The cross-polarization time constants summarized in Table I1 show that there is little difference between protonated and deuterated dry polymer, which indicates that the proton-carbon interactions that drive the magnetization transfer process do not depend on the distant ammonium protons. Further, hydration by either HzO or DzO increases the crosspolarization time. This result is shown graphically in Figure 3 , where it is clear that the further from the main chain, the larger the increase in relaxation time. It is interesting to note that the t-carbon atom is more efficiently polarized than the &carbon atom, even though each has two attached protons. This observation may reflect the hydrogen-bonding ca-
971
pability of the ammonium group which may slow the motion of the side-chain end. The carbon TI, is a sensitive but complicated measure of motion in the range of the radio frequency ( r f ) field strength used for the spin-locking portion of the experiment. A difficulty with the present data set is that the rf field is not a constant through the hydration range studied because the addition of water decreased the effective Q of the probe and dropped the rf level delivered by the amplifier. While the decline in rf level was less than 3596, from 48 kHz for the dry sample to 33 kHz for the 49% sample, this change is in a range that is particularly sensitive to the competition between carbon-proton dipolar contributions and carbonspin lattice contributions to the effective relaxation time. Thus, quantitative analysis of the data will not be attempted. Nevertheless, several qualitative observations are useful. The carbon T I , values for deuterated and protonated polymer samples are similar, except that the protonated samples relax slightly faster. This observation is consistent with elimination of the ammonium and amide protons from the proton pool that drives the carbon relaxation by a dipole-dipole mechanism. The main-chain resonance relaxation times change in a confusing way as a function of water content; however, the side-chain resonances behave consistently, as shown in Figure 5. The trend for all side-chain resonances is common in that add-
01
0.0
1
1.o
,
2.0
.
I
3.0
I
.
4.0
5.0
Delay time in pulse sequence (s)
Figure 5. 13C inversion recovery data for the C, and C, resonances of poly (L-lysine) as a function of time taken a t 50.3 MHz and ambient temperature. The solid lines are exponential fits to the longer time portions of the data.
972
SWANSON AND BRYANT
ing water increases the relaxation time until the 50% samples are reached, when it decreases again. This increased relaxation rate a t the 50% samples is very possibly due to the lower rf field used for the measurement and may not reflect a significant difference in the side-chain motion. However the spin-lattice relaxation data do not suffer from this difficulty. The carbon spin-lattice relaxation times summarized in Table IV are striking in that the mainchain carbon atom relaxation times are much longer than any of the side-chain relaxation times. The differences between the protonated and deuterated samples is small, indicating that the ammonium protons do not completely dominate the relaxation rate, nor do the water protons in the hydrated samples. Thus, the carbon relaxation rate is dominated by the bonded-proton-carbon dipole-dipole relaxation. T h e nonexponential relaxation observed for the carbon magnetization of the backbone resonances is consistent with a transient nuclear Overhauser effect ( NOE) . The pulse sequence used was designed to minimize and add out the effects of nonideal pulses; however, if there are protons coupled to the carbon atoms observed with z magnetization a t the beginning of the relaxation delay period, a transient NOE will develop and the magnetization then decays with the appropriate carbon T I .We therefore take the values entered in Table IV as good estimates of the carbon T I values. The long relaxation times for the backbone carbon atoms are consistent with their relatively rigid environment in the 0-sheet structure; 0.7
0.6
0.5
5
0.4
u)
v
0.3
0
e 9
0.2 0.1
\\
-
+ Beta
+ Gamma --c. Delta Epsilon
A
0.0
Dry
16%
2 8%
50%
Weight % water
Figure 6. 13C spin-lattice relaxation times for sidechain carbon atoms of poly( L-lysine) hydrochloride as a function of water content obtained a t 50.3 MHz and ambient temperature.
0.7
I
I
I
0.6
-
Weight % water
0.5
-
--b- 16% 27.5%
--t
0.4
-
0.3
-
0.2
-
0.1
r
0.0
I
I
50%
I Beta
Gamma
Delta
Epsilon
Carbon
Figure 7. "'(2 spin-lattice relaxation times as a function of carbon atom position for different water contents of poly ( I,-lysine ) hydrochloride samples recorded a t 50.3 MHz and ambient temperature.
however, even these relaxation times are not very long compared with other polymeric systems where T I values may exceed 50 s, indicating that there is still considerable motion a t the carbon Larmor frequency to relax the system. T h e striking feature of Table IV is the dramatic difference between the backbone carbon T I values and the side-chain values, which are shorter by about a n order of magnitude. This observation is consistent with there being very considerable motion present in the side chains that adds to the spectral densities a t the carbon resonance frequency. Such major differences are not observed in the lower frequency windows associated with the carbon T I ,for example. This dramatic difference in relaxation rate of the side-chain carbon resonances is preserved with increasing water concentrations, and is independent of whether the system is hydrated with H 2 0 or D20. Thus, the effect on the side chains is not caused by dipolar interactions between carbon atoms and the water protons, but is caused by the intramolecular CH couplings. As a consequence, the major difference between the a-carbon and the side-chain carbon atoms must be the frequency and amplitudes of polymer motions present. Figure 6 and Figure 7 present the spin-lattice relaxation times for the side-chain resonances in two instructive ways. Figure 6 shows that for each sidechain atom, the resonance passes through a minimum as a function of water content between the dry sample and the 50% sample. These observations are consistent with the addition of water carrying the
HYDRATION R E S P O N S E OF POLY (I.-I,YSINE:)
system from the low- to the high-temperature side of the relaxation time minimum; however, the value of the minimum is greater than expected based on the simplest relaxation equations. T h e data in Figure 7 demonstrate that for the dry system, the relaxation times pass through a minimum in going from the /l to the c resonance, which is consistent with increased motion a s one moves out on the side chain. T h e addition of water to the system appears to shift the minimum to the @-carbonor y-carbon atom, with the other resonances falling on the faster motion side. There are a number of ways to quantitatively discuss these relaxation data, but the data is not sufficient to support a unique interpretation. One simple and possibly useful description is to assume t h a t the side-chain carbon atoms execute a restricted diffusion in a cone of some half angle. Computing the value of the T , minimum as a function of the cone angle, we can compare the values observed with this model. In this case we find that the data for the dry side-chain carbon resonances suggest a half angle of 17", and t h a t when the system is hydrated this angle increases about a factor of 2. However, the assumptions of such a model are inadequate for describing this situation because it is clear that both the frequencies and amplitudes of the motions may change as a function of water content. T h e correlation time information could come from a study as a function of Larmor frequency, which we do not have available for carbon spectroscopy. Thus, further discussions of precise amplitudes appears more speculative than worthwhile. In summary, the 13C spectroscopy reported here provides a clear demonstration t h a t the backbone atoms o f the polymer in the 0-sheet structure are considerably more rigidly held in place than the sidechain atoms, as expected. Further, the side-chain resonances respond in a systematic way to hydration with increased motion both as a function of increasing water content and a s a function of distance from the main chain.
DYNAMICS
973
This work was supported by the National Institutes of Health, GM-34541, and the University of Rochester. The authors acknowledge with pleasure numerous helpful discussions with members of the magnetic resonance group including particularly Dr. Scott D. Kennedy. Stimulating discussions with Dr. P. Mark Henrichs and Dr. Nicholous Zumbulyadis are also gratefully acknowledged.
REFERENCES 1. Franks, F. & Mathias, S. F. (1982) Biophysics of Water, John Wiley & Sons, New York. 2. Jackson, C. L. & Bryant, R. G. (1989) Biochemistry 28, 5024-5028. 3. Kennedy, S. D. & Bryant, R. G. ( 1990) Biopolymers, in press. 4. Marchetti, P. S., Ellis, P. D. & Bryant, R. G. (1985) J. A m . Chem. Soc. 107,8191-8106. 5. Cole, H. B. R., Sparks, S. W. & Torchia, I). A. (1988) Proc Natl. Acad. Sci. 85, 6362-6365. 6. Blout, E. R. & Lenormant, H. (1957) hiature 179, 960-963. 7. Shmueli, U. & Traub, W. (1965) J . Mol. Biol. 12, 205-214. 8. Yu, T., Lippert, J. L. & Peticolas, W. L. (1973) Biopolymers 12, 2161-2176. 9. Saito, H., Tabeta, R., Shoji, A., Ozaki, T. & Ando, I. (1983) Macromolecules 16, 1050-1057. 10. Kricheldof, H. R. & Muller, D. ( 1983) Macromolecules 16, 615-623. 11. Wittebort, R. J., Szabo, A. & Curd, F. R. N. (1980) J . A m . Chem. SOC.102,5723-5728. 12. Wittebort, R. J. & Szabo, A. (1978) J . ('hem. Phys. 69, 1722-1736. 13. Kennedy, S. D. (1988) Ph.D. thesis, University of Rochester, Rochester, NY. 14. Swanson, S. D. (1989) Ph.D. thesis, University of Rochester, Rochester, NY. 15. Swanson, S. D. & Bryant, R. G. ( 1990) Magn. Reson. Chem., submitted.
Received January 3, I990 Accepted February 8, 1991
