Water-Protein Interactions - American Chemical Society

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8 Water-Protein Interactions Nuclear Magnetic Resonance Results on Hydrated Lysozyme R O B E R T G . B R Y A N T and W I L L I A M M . S H I R L E Y

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Department of Chemistry, University of Minnesota, Minneapolis, MN 5 5 4 5 5

Interest in water at protein surfaces and other surfaces arises from a desire to understand structural, functional, and dynamic factors as well as their interrelationships. Nuclear magnetic resonance (NMR) spectroscopy provides both structural and dynamic information. This presentation will focus on dynamical aspects of the water-protein interaction. In parti­ cular, the phenomenon of cross relaxation between the water and protein proton systems will be discussed and new evidence will be reported. Failure to recognize the importance of cross relaxation effects leads to incorrect conclusions about the dynamics of water at protein surfaces. Background The underlying strategy for extracting dynamical information from NMR relaxation data is based on the equations for either longitudinal (T1 ) or transverse (T2 ) relaxation rates. If relaxation is dominated by the magnetic dipole-dipole interaction between like-spin nuclei, then -1

-1

where γ is the nuclear magnetogyric ratio, I the nuclear spin, and J(ω) the spectral density at the resonance frequency, ω. Spectral densities are obtained from the Fourier transform of the autocorrelation function describing reorientation of the internuclear vector, r. The autocorrelation function is usually assumed to decay exponentially with a correlation time t . With the additional assumption of isotropic rotational motion, the relaxation equations become (]j c

Rowland; Water in Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

148

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1 _1 Τ 7 - 5

WATER IN POLYMERS

Y

γ

4>2 *

{

6

4 Λ Ι(Ι+Ί) * ^ 6

2 2

1 +

,

Γ {

ω

3

, T

C

+

T

c 5 τ

(3) 2

ε

ε . C 2 2 . . , 2 2 2 T

1

, .

+

C

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2

1 + Δ4ω τ

M }

'

(

4

)

C

In general, care must be taken to recognize both intra- and intermolecular contributions to relaxation; however, intermole­ cular relaxation is often neglected in discussions of liquids at surfaces. With this assumption there is direct access to characterization of liquid dynamics at a surface (2v3>£). A study of the relaxation rate at different temperatures or frequencies provides a measure of the correlation time for water at the surface of a protein i f the interproton distance, r, in the water molecule is known. The temperature dependence for longitudinal and transverse relaxation times predicted by equations 3 and 4 is shown schematically as the solid lines in Figure 1. At the position of the minimum in the longitudinal relaxation time, ωχ- is about 0.616 and T-|/T2 is about 1.6. Since ω is known, the correlation time is determined at the minimum in T]. The difficulty applying this simple approach in practice has been that the experimental results for a variety of systems do not f i t the theory {2 3 ^ 6). Though there are differences in detail, the basic features of the observations are summarized in Figure 1 as the dashed lines. The problems are clear: the T-j values usually obtained are much too long relative to the T2 values and the Ti minimum is much broader than is expected. One way to eliminate this apparent discrepancy is to assume that there is a distribution of correlation times experienced by the liquid molecules in the vicinity of the surface (Z.»8»DWith increasing width of the distribution of correlation times, the Ti calculated from an equation of the form 3 and Tg calcu­ lated from an equation of the form 4 does approach a fit to the data. One difficulty is that the distribution is often so broad that a rigid lattice correction must be made for very slow moving solvent molecules ( 8 ) . Extrapolation of protein results to solution situations appears to require a slow moving fraction of water at the surface, but irrotationally bound, slow moving water molecules in protein solutions are inconsistent with solution phase NMR results (!£,]]_). While i t appears to be of great value for some systems, this theoretical apparatus neglects an important feature of the water proton relaxation. Namely, that the longitudinal relaxation is generally not described by a single time constant. 9

9

9

Rowland; Water in Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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8. BRYANT AND SHIRLEY

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Nonexponential NMR relaxation was reported several years ago for water protons in protein crystals (1_2). This report has been largely ignored apparently because of a less than adequate explanation that leaned heavily on a chemical exchange model. There are two rather different hypotheses that may account for such behavior. Nonexponential relaxation may result i f there is a slow exchange of the observed species between two populations, water populations in this case, each characterized by substan­ tially different NMR relaxation rates (13j. Such a model is pulse width independent and also largely independent of the nucleus observed in the exchanging molecule. Comparison of the relaxation curves shown in Figure 2 indicate that the apparent shape is significantly pulse width dependent. Deuterium relax­ ation data also fail to show the rather striking nonexponential character indicated here ( ϋ ) . For these reasons a chemical exchange model must be dismissed as inadequate for the present situation and hence the difficulty of explaining the very long lifetimes implied by such a model is eliminated (12,15,16). Nonexponential NMR relaxation may also be caused by cross relaxation involving the exchange of spin magnetization between different spin systems through mutual proton spin-flips. Cross relaxation between the water phase and the protein phase has been studied in hydrated proteins (17,18) and protein solutions (19). The exchange of magnetization between the rotating methyl protons and the other protons of a macromolecule also involves a cross relaxation. Nonexponential behavior of proton relaxation has been demonstrated for proteins dissolved in D2O (20,2]J. However, there is a distinct difference between this cross relaxation involving only protein protons and the cross relaxation described by Edzes and Samulski for hydrated collagen (17). In the former case the sample is treated as a single system of coupled spins that behave according to a generalization of Solomon's treatment of a spin pair (22). In the hydrated protein case, however, the cross relaxation model assumes two separate thermodynamic systems, the water phase and the protein phase, each able to achieve a well defined temperature in a time short compared with the relaxation times measured. The time dependence of the magnetization for the proton systems in a hydrated protein may be described heuristically by two coupled equations containing three relaxation rates: R] , the longitudinal relaxation rate for the water in the absence of the protein proton interaction; R] , the longitudinal relaxation rate for protein protons in the absence of a relaxation path provided by water protons; and Rt, a rate of magnetization transfer between the two spin systems. The equations then become w

p

dM /dt=-(R w

dM /dt = - ( R p

l w +

lp

R )M t

w +

R M t

(5)

p

+ R /F)M + R M /F t

p

t

w

Rowland; Water in Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

(6)

WATER IN POLYMERS

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150

Figure 1. Schematic of the temperature dependence of the longitudinal and transverse relaxation times for water protons. Solid lines are predicted by Equations 3 and 4, while the dashed lines indicate the dependences often observed.

I/T

Figure 2. Water proton relaxation in hydrated lysozyme powder (0.17 g H 0/g lysozyme) at 57.5 MHz at 253 K. Amplitudes were measured after the second pulse of a 180°-r-90° sequence with the 180° pulse width either (φ) 8.6 μ*βο or (Ο) 55 yjsec. H

Rowland; Water in Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

8.

BRYANT AND SHIRLEY

Water-Protein

Interactions

151

where M and M are the water and protein normalized, reduced magnetizations, w

p

Μ^τ) = { S H - S(x)}/nS(«)

(7)

where S is the free induction decay amplitude after the second pulse of a 180°-τ-90° experiment (n = 2) or a 90°-t-90° experi­ ment (n = 1). F is the ratio of protein protons to water protons. The solution of these equations is a sum of exponentials cor­ responding to the fast, R-jf, and slow, R ] , components seen in Figure 2 (17,18). It is critical to note that while the appearance of the relaxation curve is significantly pulse width dependent, the limiting slopes for the fast and slow components are not. Due to the pulse width dependence and the rapid decay of the fast component, the double exponential nature of the curve is very easy to miss experimentally and there are reports that treat only the slow component. It is clear that any attempt to interpret the slow component as a simple relaxation time such as that described by equation 3 neglects a significant feature of the relaxation. The complete solutions of the coupled equations are given by Edzes and Samulski (Rj- becomes k and R^/F becomes k in their notation) (]_7). The water and protein proton relaxation curves are completely described by R^ , R-j , R , F, Μ^(0), and M (0). By observing both water and protein curves at different pulse lengths all the parameters may be obtained. However, R]n is generally expected to be too small to be obtained accurately from the relaxation curves so that the simpler procedure of finding R-| , R , M (0), and M (0) from a single water relaxation curve using estimates of R] and F seems to be reasonable. The aim of the present investigation is to study water dynamics in hydrated proteins while testing the cross relaxation model. According to equation 5, the temperature dependence of the observed water relaxation components could arise from changes in any of the three fundamental rate constants R] , R]p> and R^. Thus, extraction of R-] from the observed R and R] in order to find its temperature dependence is necessary before a detailed interpretation in terms of water motion is attempted.

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s

w

p

w

t

w

m

w

t

p

p

p

w

w

l f

s

Experimental Three times crystallized, dialyzed, and lyophilized hen egg white lysozyme powder from Sigma was used after a subsequent dialysis and lyophilization. Hydration of the dry powder was accomplished through the vapor phase by exposing the sample to a constant relative humidity for 5 days. In preparing the lysozyme-D 0 sample, the lysozyme was twice dissolved in D 0 and held at 40 deg C for 24 h both times before lyophilization. The D2O was treated with Chelex-100 before use; both were 2

Rowland; Water in Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

2

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152

WATER IN POLYMERS

obtained from Bio-Rad Laboratories. As in the hydration, D2O was deposited on the dry protein through the vapor phase. The water and deuterium oxide contents were determined by Karl Fischer titrations. The NMR measurements were made at 57.5 MHz on a pulsed NMR spectrometer that included a 12-inch Varian electromagnet and a Nicolet NMR-80 data system interfaced with a Biomation 805 wave form recorder. Unattenuated 90° pulse widths were 4 to 5 microsec using a 10 watt ENI power amplifier. At best, recovery time for the home built receiver was 10 microsec. Nitrogen gas boiled from a liquid nitrogen dewar was used to cool the sample. The temperature was measured to within 2 deg with a diode thermometer. Spin-lattice relaxation times for the protein protons were measured using the 90°-τ-90° pulse sequence. Free induction decay amplitude was measured 15-20 microsec after the end of the second pulse by averaging 30 repetitions. To obtain the obvious double exponential relaxation behavior from the water protons, the first pulse of a 180°-τ-90° sequence was attenuated so that the 180° pulse width was about 55 microsec while the second pulse remained near 4 microsec. Experimental considerations led us to believe the errors for the protein T i values and the slow component of the water T] curve are about 5% although linear least squares fits indicate better precision. A nonlinear least squares fit of the water relaxation data was used to find the four parameters R] , R^, M (0), and Mp(0) taking R-| from the lysozyme^O data and setting F = 3.5. The standard deviations from R^I and R£' are indicated in Figure 3 when they exceed 5%. According to these calculations, immediately following the 55 microsec pulse, the water magnet­ ization, M (0), was about 0.9 while the M (0) was near 0.5. The only exception is the 207 Κ measurement which shows M (0) = 0.51 and M (0) = 0.24. Standard deviations for the M (0) and M (0) were about 1% except at 207 Κ where i t was 5%. w

w

p

w

p

w

p

w

p

Results and Discussion The temperature dependence of the longitudinal relaxation of protein protons in a sample containing 0.07 g D2O/ g lysozyme is shown in Figure 3. Despite the presence of a small deuterium dipole-dipole contribution and a possibly changed protein in response to the substitution of deuterium oxide for water, these values are thought to be good estimates of R-| for the hydrated lysozyme. Previously published data for dry lysozyme shows a similar curve reaching a minimum near 180 Κ (23). Also shown in this figure is the temperature dependence of the proton T] for the protein in hydrated lysozyme (0.17 g HoO/g lysozyme). The presence of water on the protein is shown to cause a substantial increase in the relaxation rate. Thus, in the hydrated protein, p

Rowland; Water in Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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BRYANT AND SHIRLEY

Water-Protein

Interactions

0.06

o.o4

^

0.02H

0.01

4

5 Ι000/Τ

Figure 3. Temperature dependence of various proton relaxation times in lysozyme powder samples at 57.5 MHz. (U) indicates T for the lysozyme-D 0 sample; other symbols refer to the lysozyme-H O powder: (φ) protein R ~V (O) water R ; (A) water I W ; (φ) water Rf . 2

2

_ I

Jg

x

1

Rowland; Water in Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

J 8

154

WATER IN POLYMERS

the bulk of the protein relaxation occurs through the water phase and not through the rapidly rotating methyl groups that dominate relaxation in a dry protein system (23). No attempt was made to find the double exponential ..protein proton relaxation curve and only the slow component, R î | , was measured. Other data points in Figure 3 represent proton relaxation times of water on the hydrated lysozyme as calculated from relaxation curves with obvious double exponential character. Since the values of obtained from the water proton data agree with those obtained from the protein data, the present experiments strongly support the dominance of cross relaxation. As anticipated, R^ appears to be on the order of or slightly longer than T and thus indicates efficient spin transfer between water and protein protons. Although the slow component, R^, is a combination of more fundamental relaxation times and should not be treated using equation 3, a detailed interpretation of R^ is s t i l l not a straightforward problem. The values of R^ shown in Figure 3 suggest that the curve lies at the minimum or on the low temperature side of the minimum for the temperature range studied. The water content for this sample is approximately half the value usually associated with the "nonfreezing water" on lysozyme (24,25). Therefore, the motions in this system are expected to be slower than in a more water rich system. The increase in resonance frequency and the lower water content approximately account for the shift in the minimum from that previously reported for hydrated lysozyme (18). If the R]^ minimum lies near 273 Κ as seems possible, equation 3 suggests that the correlation time at the protein surface in this relatively dry sample is on the order of nsec at this temperature. While recognizing the uncertainty about the presence and position of the Rf^ minimum, the value of T-j estimated from equation 3 for intramolecular water proton relaxation indicates that Rïjj, is somewhat larger than predicted. Discrepancies could arise from several factors: 1) A distribution of correlation times may s t i l l have to be considered. 2) The temperature dependence of the water signal amplitude is difficult to monitor when transverse relaxation rates become large at low temperatures because the water signal is increasingly difficult to resolve from the solid protein proton signal. Freezing out of water at low temperature would distort the shape of the T-j plot by raising Ti of the apparent minimum and shifting it to higher temperatures. 3) Equation 3 neglects effects of anisotropic motion on both longitudinal and transverse relaxation rates (2). Recent experiments using deuterium NMR on samples similar to those studied here show significant nuclear electric quadrupole splittings that imply an anisotropic component in the water molecule motion (26). Such motional anisotropy will depress T and elevate T].

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2

1

w

2

Rowland; Water in Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 1980.

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Conclusion The present study has provided a critical test of the importance of cross relaxation involving both water and protein protons in hydrated protein systems. In addition it has successfully demonstrated that the temperature dependence of both the water and protein relaxation is dominated by motions in the water phase and not by motions in the solid phase such as methyl group rotations. While a detailed analysis has not yet been attempted, it appears that a picture of water in the interfacial regions around a protein that is consistent with the NMR relaxation data is one characterized by fast if slightly anisotropic motion. Structural models for water-protein inter­ actions must be consistent with this very fluid character of water in this interfacial region; however, it is also important to recognize that the time scale appropriate to the present experiments is s t i l l long when compared to the rotational correlation times or diffusion times usually associated with water in the pure liquid state. Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.

Abragam, Α., "Principles of Nuclear Magnetism", Clarendon Press, Oxford, 1961, Ch. 8. Pfeifer, H., NMR Basic Principles and Progress, 1972, 7, 53. Resing, Η. Α., Adv. Mol. Relax. Proc., 1972, 3, 199. Woessner, D. E . , Mol. Phys., 1977, 34, 899. Packer, K. J., Philos. Trans. Roy. Soc., London, Ser. B, 1977, 278, 59. Resing, Η. Α.; Wade, C. G., Eds, "Magnetic Resonance In Colloid and Interface Science", ACS Symposium Series No. 34, American Chemical Society, Washington, D.C., 1976. Odajima, Α., Prog. Theor. Phys., Suppl., 1959, 10, 142. Resing, Η. Α., J . Chem. Phys., 1965, 43, 669. Lynch, L. J.; Marsden, Κ. H.; George, E. P., J . Chem. Phys., 1969, 51, 5673. Koenig, S. H.; Hallenga, K.; Shporer, M., Proc. Natl. Acad. Sci. USA, 1975, 72, 2667. Bryant, R. G., Ann. Rev. Phys. Chem., 1978, 29, 167. Jentoft, J . E . ; Bryant, R. G., J . Amer. Chem. Soc., 1974, 96, 297. Zimmerman, J. R.; Brittin, W. E., J . Phys. Chem., 1957, 61, 1328. Hsi, E . ; Bryant, R. G., Arch. Biochem. Biophys., 1977, 183, 588. Hsi, E . ; Jentoft, J . E . ; Bryant, R. G., J . Phys. Chem., 1976, 80, 412. Hsi, E . ; Mason, R.; Bryant, R. G., J . Phys. Chem., 1976, 80, 2592.

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17. Edzes, H. T.; Samulski, E. T., J. Mag. Reson., 1978, 31, 207. 18. Hilton, B. D.; Hsi, E.; Bryant, R. G., J. Amer. Chem. Soc., 1977, 99, 8483. 19. Koenig, S. H.; Bryant, R. G.; Hallenga, K.; Jacob, G. S., Biochemistry, 1978,17,4348. 20. Kalk, Α.; Berendsen, H. J. C., J. Mag. Reson., 1976, 24, 343. 21. Sykes, B. D.; Hull, W. E.; Snyder, G. H., Biophys. J., 1978, 21., 137. 22. Solomon, I., Phys. Rev., 1955, 99, 559. 23. Andrew, E. R.; Green, T. J.; Hoch, M. J. R., J. Mag. Reson., 1978, 29, 331. 24. Kuntz, I. D.: Brassfield, T. S.; Law, G. D.; Purcell, G. V., Science, 1969, 163, 1329. 25. Hsi, E.; Bryant, R. G., J. Amer. Chem. Soc., 1975, 97, 3220. 26. Cygan, W.; Bryant, R. G., 1979, unpublished results. RECEIVED January 4, 1980.

Rowland; Water in Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 1980.