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Investigation of Protein Hydration by Proton Spin Relaxation Time Measurements
BIOCHIMICA ET BIOPHYSICA ACTA
BBA
35583
INVESTIGATION OF PROTEIN HYDRATION BY PROTON SPIN RELAXATION TIME MEASUREMENTS
J. W. HENNELb, G. HELDc AND F. NOACKc Institute of Physics, jagiellonian University, Krakow (Poland), b Institute of Nuclear Physics, Krakow (Poland) and r I. Physikalisches Institut der Universitiit (TH) Stuttgart (Germany)
B. BLICHARSKAa, Z. FLORKOWSKib, a
(Received January 13th, 1970)
SUMMARY
Spin-lattice relaxation times T 1 in aqueous solutions of dialysed egg white were measured for concentrations between 4·5 and 9·3 wt. % in the magnetic field range corresponding to proton Larmor frequencies from o.or to r6o MHz. A strong dependence of T 1 on the magnetic field begins at approx. 0.5 MHz. It can be described by a log-Gauss distribution of rotational correlation times in the solvation layer with the maximum at r.sz · ro- 9 sec. The greater part of the distribution lies below the correlation time for the reorientation of the ovalbumin molecule itself. This means that the adsorbed water molecules have some freedom of motion with respect to the protein molecule. The width of the distribution is somewhat dependent on the concentration. This paper also contains the results of neutron activation, spectrochemical analysis and EPR measurements, which show that the amount of paramagnetic ions present in samples of protein solutions cannot be responsible for the decrease of T 1 with respect to pure water.
INTRODUCTION
Basic theory According to the theory of BLOEMBERGEN et al.l, the proton spin relaxation in liquid water is mainly caused by interaction with magnetic dipoles present in the liquid, i.e. with other protons or paramagnetic ions. The energy of such dipolar interactions depends on the vector r joining the two interacting dipoles and undergoes fast modulation as a result of the thermal motion of the molecules. This modulation can be roughly described by the mean time, the so-called "magnetic correlation time -,;", during which the magnetic interaction energy persists. If the modulation is caused only by rotation, as is the case when the two interacting dipoles are situated in the same rigid molecule, the relaxation is called "rotational". If there is also a change of 1 ; 1, the relaxation is called "translational". Often both types of relaxation contribute to the total relaxation rates rjT 1 (spinlattice) and r/T 2 (spin-spin). Biochim. Biophys. Acta, 207 (r97o) 38r-389
B. BLICHARSKA et al. The dependence of T 1 and T 2 on correlation time r: and Larmor frequency w = yH (y is magnetogyric ratio, H is, magnetic field) of the interacting spins has been calculated for rotational and translational motion within a "two-spin system" by SoLOMON 2 , ToRREY 3 and HEINZE AND PFEIFER4 • In the case of the rotational relaxation of spins with~quantum number 1 / 2 the result has the following form (I a)
(I b)
for like spins with magnetogyric ratio y, respectively,
-y; = I
I
~
2
2 2
YI Ys h
31:
7:
(
Y6
+ (WJ-Ws) 27: 2 +
I
I
+ WJ 27: 2 +
61:
I
+ (WI + Ws) 27: 2
)
2 ( )
for different spins with magnetogyric ratios y 1 and y 8 .1i is Planck's constant divided by 2n, r the distance between the magnetically coupled spins I and S, spin I being observed. Eqns. Ia and Ib give T 1 equal to T 2 in the limit w 2r: 2 «I, whereas T 1 > T 2 when w 2r: 2 > r. Therefore, from the inequality T 1 > T 2 one may conclude that the interaction responsible for the relaxation is modulated by a process which is slow with respect tow. The rotational correlation timer:, the mean time during which the orientation of the vector r persists with respect to the external magnetic field, may be related to the Debye dielectric relaxation time Tct as one-third of its value 1 . Regarding the dipole as a macroscopic sphere of radius a immersed in a medium of viscosity 'fJ one obtains 1 that r: is proportional to 'f}a (ref. 3). For small molecules like water this relation holds in a very rough approximation, but it may be more accurate for rigid macromolecules surrounded by much smaller molecules of a solvent such as globular protein in water solution. Previous results DASZKIEWICZ et al. 5 observed an inequality of the proton relaxation times in water solutions of proteins at a Larmor frequency w(2n = I4 MHz and showed that for concentrations c ~ o.I g of dry protein per g of solution the proton relaxation rates are linear functions of c: I
I
T1
T1w
-=--+kjC
j
=
I,2
(3)
k1 and k2 are constants specific for the given kind of protein, with k1 < k2 , and T 1 w, T 2 w are, respectively, spin-lattice and spin-spin relaxation times for pure water. The experimental evidence for the relation k1 < k 2 known at present is shown in Table I. The influence on T 1 and T 2 of protein dissolved in water cannot be accounted for simply by an increase of macroscopic viscosity. For egg white solutions this increase 6 amounts to 63% at c = o.I2 g/g and is too small to change the relation w 2 r:2 «I which holds for pure water and causes T 1 = T 2 • DASZKIEWICZ et aZ.S assumed that part of the adsorbed water is irrotationally bound, thus having the same correlation time as the macromolecules. For this kind of water molecules wr: R:O I and T 1 > T 2 • They also assumed that there is a fast exchange between the irrotationally Biochim. Biophys. Acta, 207 (I970) 381-389
PROTEIN HYDRATION TABLE I VALUES OF
k1
AND
k2
FOR DIFFERENT MACROMOLECULES
--------
1\!Iacromolecule
Frequency (MHz)
Temp. (0)
Ovalbumin Egg white Glycogen Glycogen Lysozyme Lysozyme
14 14 14 10 28 14
20 20 20 20 20 20
kl
(sec- 1 )
~
~~--~-
---
k.
Literature
6.8o 9.13 32.1
ref. ref. ref. ref. ref. ref.
( sec-1 )
-~------
3· 0 7 3.62 7·56 7-93 2.22 4.1 I
6.85
5 5 7 8 6 6
bound and free water molecules, so that the observed values of T 1 and T 2 can be calculated according to the formula of ZIMMERMAN AND BRITTIN 9 as an average value of the relaxation in the two phases with differing mobility. Using this theory, DAszKIEWICZ et al. 5 were able to calculate the correlation time for irrotationally bound water as 1.03 · ro- 8 sec in reasonably good agreement with the value known from dielectric measurements. Dielectric relaxation measurements at room temperature give correlation times on the order of ro- 12 sec for pure water and on the order of ro- 8 for aqueous solutions of globular proteins such as ovalbumin in agreement with the different values of radius a. This great change confirms that any kind of adsorption of water on dissolved macromolecules (hydration) should make at least some of the water molecules slower and thereby lengthen the rotational magnetic correlation time. Later investigations made by CAPUTA et al. 7 showed that the predicted dependence5 of k1- 1 on the Larmor frequency was too strong as compared with experiment. CAPUTA et al. 10 tried a refinement of the theory by assuming a distribution of correlation times within the solvation layer. As an approximation they attempted to distinguish between the irrotationally bound water and water which is only partially slowed down. Although the new model gave better agreement with experiment, a quantitative check was not possible without the capabilities of a frequency-variable NMR spectrometer. The purpose of this paper is to obtain further information concerning the nature of the interaction responsible for the relaxation process and the distribution of correlation times in aqueous protein solutions. This is done by measurements of proton relaxation time T 1 as a function of the concentration of deuterons 11 and the proton Larmor frequency 12 or the magnetic field strength. The NMR apparatus consists of a high-frequency12 and low-frequency13 spectrometer described elsewhere. Similar investigations on NMR dispersion in protein solutions in a more restricted frequency range have been published recently by KoENIG AND ScHILLINGER14 •15 ,*. Preparation of samples The solutions of egg white were prepared in the following manner. The egg white taken from five fresh hen's eggs were filtered through bolting cloth. Then approx. 7 g of EDTA (sodium salt) were added and the liquid was introduced into a * Note added after submission of the paper.
Biochim. Biophys. Acta, 207 (1970) 381-389
B. BLICHARSKA et al. cellophane dialysing bag. The bag was then kept 3 days in a glass container filled with approx. 20 1 of distilled water. About r ml of chloroform was added to the water in order to prevent the growth of bacteria. Then the bag was hung in air at room temperature to increase the concentration up to approx. rs%. Some precipitate which was found at the bottom of the bag was not taken for measurements. Changes of concentration were achieved by adding water. No salt for stabilization of pH was added. The value of pH was the same as for the distilled water being used for the dialyzation, i.e. about 6. The solutions of lysozyme and glycogen were prepared from dry substances obtained from Armour Corp., U.S.A., and F. Hoffman and Co., Ltd., Switzerland, respectively. INTERACTIONS RESPONSIBLE FOR RELAXATION IN THE SOLVATION LAYER Dipolar interactions of protons with deuterons are much weaker than with the protons because of the relatively small deuteron gyromagnetic ratio. For this reason H 2 0-D 20 mixtures have a longer proton relaxation time T 1 than that of pure water T 1 w, namely, according to the formula of ANDERSON AND ARNOLD 16 -
I
Tl
I
= - - [{J TlW
R
= -
r6 9
I
+ (r -{J)R]r)' " " - - fJ TlW
yd
2
-- =
Yv 2
o.o46
where {3 is the molar fraction of water, Yv and Yd are the proton and deuteron gyromagnetic ratios, respectively, and rj' is the ratio of the viscosity of the mixture to that of ordinary water. This formula cart be derived under two assumptions: (a) that the relaxation in ordinary undeuterated liquids is caused solely by proton-proton dipolar interactions, (b) that there exists a fast chemical exchange of hydrogen nuclei. The existence of such an exchange in water has been checked by MEIBOOM 17 . In solutions of protein in H 2 0-D 2 0 mixtures the deuterons penetrate the solvation layer as easily as the free water, and it is reasonable to assume that {3 has the same value in the adsorbed and the free water because of the chemical exchange. Thus, if the relaxation is caused by intramolecular dipolar interaction, we can apply Eqn. 4 for both kinds of water, free and adsorbed, obtaining the following result -
I
Tl
{J
= --
TlW
+ {Jkc + q
(s)
where q is a constant term due to possible paramagnetic impurities, mainly dissolved
02.
On the other hand, if the relaxation in adsorbed water is caused by intermolecular interactions, e.g. with paramagnetic ions or inexchangeable protons of the protein, then the relaxation time of adsorbed water should not be dependent on {3 and we get: -
I
Tl
{J = -TlW
+ kc + q
(6)
In order to decide which of the two formulae are in agreement with experiment, measurements of T1 of dialysed egg white and recrystallized lysozyme in H 20-D 20 Biochim. Biophys. Acta, 207 (1970) 381-389
PROTEIN HYDRATION
DIALVSED EGG WHITE 6,,
LVSOZ'IME 10'/,
--Fto
1'0
0.5
OS
I
0.5
-B
\0
DlALVSED EGG WHTE 13.8'/,
05
-B
0.5
-B
1.0
DlALVSED EGG WHTE 10'/,
1D
0.5 - B
1.0
Fig. r. Proton relaxation rate rjT 1 in protein solutions in H 2 0-D 2 0 mixtures as a function of molar fraction fJ of protons. a and b are the theoretical lines according to Eqns. 5 and 6.
mixtures were made at different {3's but constant c. All measurements were performed at least 24 h after the preparation of the solutions. No influence of lengthening this time on T 1 was observed. The results shown in Fig. r indicate that Eqn. 6 is valid and Eqn. 5 is not. The deviation of the experimental points from the theoretical Curve b is within the experimental error. Hence, we may conclude that the relaxation in the solvation layer is due to intermolecular interactions. ESTIMATION OF THE INFLUENCE OF PARAMAGNETIC IONS
It has been shown in the previous section that the relaxation of protons in the solvation layer is due to intermolecular interactions. There are two possibilities: interaction with paramagnetic ions adsorbed on the surface of the macromolecules or interaction with nuclei belonging to the macromolecules, e.g. nonexchangeable protons. Interaction with free radicals will not be taken into account as they do not occur in fresh non-denatured proteins. In order to decide what amount of paramagnetic ions is necessary to exert the same influence on T 1 as the 5% contents of pure protein, measurements were made in protein solutions containing different amounts of added Ni2+. Ni2+ were convenient for this purpose because they do not hydrolyse up to a pH of 8. It follows from the results shown in Fig. 2 that the necessary concentration is 5 · ro 17 Ni2+Jcm3. As the next step, the amounts of Fe, Cu and Mn present in the solution were estimated by means of different methods, in the belief that these transition elements are most likely to occur in a living tissue. Biochim. Biophys. Acta, 207 (1970) 381-389
B. BLICHARSKA et a/.
I
x H 0• 53'/, PROTEIN • Ni 2' o
:_____ L_.__~L-~ 0
2.0
2 H20 • Ni 2'
~
0
0
·~
. ~"-I
tO
I
10 17
·~.
1018
Fig. 2. Proton relaxation time T 1 in protein solution (dialysed egg white) as a function of concentration of Ni2+jcm 3 •
Neutron activation This method was applied for the investigation of dialysed egg white, crystallized bovine serum albumin and lysozyme. Also, control samples with the addition of Fe, Cu and Mn in amounts of ro 18 , ro 17 , ro 16 and ro15 atoms of each element per so mg dry dialysed egg white were prepared. The investigated substances were carefully dried, after which so mg of each were sealed in quartz vials of 2 cm3 volume and exposed to a thermal neutron flux of ro13 neutronsfcm 3 ·sec for 4 weeks. The vials were opened, baked in an oven at about 8ooo in order to burn the contents and treated with HCl. The investigated elements were then separated by means of an ion-exchange resin Dowex-r X8 as described by KRAUS AND MooRE18 . The activity of the fractions containing the 59 Fe, 56 Mn, and 64 Cu nuclei was measured by means of a Na(Tl) scintillation counter and a single-channel pulse analyser. The control samples containing 1016 and more added ions clearly showed increased activity due to each element investigated, but no increase in activity was observed in pure substances and in control samples containing ro15 added ions. Spectrochemical analysis Dry protein was mixed with powdered pure carbon and placed on carbon electrodes. Emission was induced by an a.c. arc and the ultraviolet spectrum was recorded by means of a medium dispersion quartz spectrograph. Dialysed egg white and crystallized bovine serum albumin did not show any traces of Mn, Cu and Fe, although the control sample of dialysed egg white, containing an addition of Cu and Mn (ro 15 atoms of each element per so mg dry proteins), gave deary visible lines of these elements. For Fe this method was rather insensitive, the lowest detectable amount of this element being ro 18 atoms per so mg of dry protein. EPR measurements A solution of 7-5% dialysed egg white was examined by means of a ro-GHz EPR spectrometer (AEG) at -60°. No lines were observed, although a control sample of the same solution containing FeH, CuH and MnH, 5.5 · ro 15 of each ion added per 3 I cm , showed EPR lines of Cu 2+ and MnH with a signal-to-noise ratio of about s. Biochim. Biophys. Acta, 207 (1970) 381-389
PROTEIN HYDRATION
J!.i_Q§_--'--=;i;::::;;::;;=<;=y;-fC~" - - - - 1 - - - + - -
• 9.3'1. ' 8.2"1• • 7.3'1.
4 5'1,
0
IO"'!\----.J.:-,---.,.S.--_!_----f.:IO,-------f.:I0:;2 ---:1:10:;-'------j -
iCMHzl
Fig. 3- Curves show values of k,- 1 computed from Eqns. 8 and g in arbitrary units as a function of wr0 for four values of a. Points show experimental values of k 1 - 1 in g · secfg as a function of the proton Larmor frequency v at 20° and different concentrations.
Because of the strong MnH lines, the lines of Fea+ could not be found with certainty. Samples of dry lysozyme and glycogen did not exhibit any EPR lines. N M R measurements
The results of all these analytical methods compared with Fig. 2 show that the amount of paramagnetic ions present in our samples cannot be responsible for the observed decrease of T 1 in protein solutions. This conclusion is also supported by the magnetic field dependence of k1-l, shown in Fig. 3, which corresponds to Eqn. ra rather than to Eqn. 2. According to Eqn. 2, the field dependence of rjT1 should exhibit two well-separated steps at ws = r- 1 and wr = r 1 , the first one decreasing r/T 1 by a factor of 3/IO. The experimental curve shown in Fig. 3 demonstrates only one step, reducing k1 much more strongly than by 3/ro. Also, 0 2 dissolved from air has a rather small influence on k1 . Dry crystalline lysozyme dissolved in vacuum in carefully degassed water gave k1 = 4.0 sec-1 at wj2n = I4 MHz, whereas k1 = 4-II sec-1 was observed in solutions exposed to air. DEPENDENCE OF T 1 ON LARMOR FREQUENCY OR MAGNETIC FIELD STRENGTH Proton spin relaxation time T 1 in dialysed egg white solutions of different concentrations was measured at 20° in magnetic fields H from 2.3 Oersted to 3.8 · ro 4 Oersted or, expressing the magnetic field strength in proton spin resonant frequency v = ypHj2n, from o.or MHz to r6o MHz. The measurements between 0.45 and r6o MHz were made by means of a variable frequency spin echo spectrometer described by HAUSSER AXD NoAcK 12 , while the measurements between o.or and r MHz were made using an apparatus constructed on the principle of free precession in the earth's magnetic field described by FLORKOWSKI et al.1 3 • The obtained results are shown in Fig. 3 in the form of k1- 1 = [(r/T1 - rjT1 w)/c]-1 , where r/T 1 w = 0-44 sec-1 Biochim. Biophys. Acta, 207 (rg7o) 38r-389
B. BLICHARSKA et al. was taken from the high-frequency asymptote of T 1 (v). This low value of T 1w compared with the well-known relaxation in pure water suggests that T 1 w still implies some influence of the proteins by sterical hindrance14 •15 . The field independence of T 1 in pure water has been demonstrated up to v = I6o MHz by HAUSSER19 . The main feature of the experimental results is that at higher fields k1 is dependent on the magnetic field but not on the concentration and at low fields it is dependent on the concentration but independent of the magnetic field. The independence of k1 on concentration at 14 MHz has already been demonstrated by DASZKIEWICZ et al. 5 • This experimentally found dependence of k1 on the magnetic field and concentration can be explained by means of Eqns. I and 3 under the assumption of logGauss distribution of correlation times within the hydration layer. This distribution can be considered to arise from the Gaussian distribution in the enthalpy of activation for the reorientation process 20 •21 . Let us first imagine the hydration layer as being composed of regions i containing fractions Pt of the whole amount of adsorbed water and characterized by correlation times Ti and relaxation times T 1(Ti)· For low protein concentrations c, the amount of adsorbed water cw (w being the amount of adsorbed water per g of protein), is much smaller than the amount of free water I - c- cw per g of solution, so that we may consider that each region i exchanges directly with the free water and neglect any exchange of water molecules inside the solvation layer. The fact that the observed spin-lattice relaxation in protein solutions is governed by a single exponential law allows us to assume that this exchange is fast in the sense used by ZIMMERMAN AND BRITTIN 9 . This means that the resultant relaxation rate (T1- 1)av is a weighted mean of particular relaxation rates I/T1 and I/T1 w, namely j
I
\
\--;;-:lav
Pw T1w
=
+
'""' p; Pa ~ T 1(r;)
(7)
where Pw = (I - cw - c)/(I - c) and Pa = cwj(I - c) are the fractions of water in the free and adsorbed state, respectively. The introduction of a continuous distribution of correlation times G(T) in the adsorbed water and~ neglect of c and cw compared with unity converts Eqn. 7 into the following form
J -G(r) -dr
00
-1 -1) -1 k 1 = ( (T1 >av-T1w c = w
T 1 (r)
(8)
Following the results of the previous sections, it will be assumed here that the relaxation of adsorbed water is due to proton-proton interaction modulated by rotation rather· than by changes in the distance r of the spins. Under this assumption T 1(T) is given by Eqn. Ia. Substitution of Eqn. Ia into Eqn. 8 and assumption of a log-Gauss distribution for G(T), namely:
.
G(r)
a
= ---
Vn
To
exp [ -a 2 (In rfr 0 ) 2 J
(9)
where a and To are parameters, converts the right side of Eqn. 8 into a function of multiplied by T 0 and a constant. Theoretical values of k1- 1 computed in this way for different values of a are shown in Fig. 3 in a double logarithmic scale. These curves nearly coincide for WTo ~ 6 · Io- 2. A diagram of experimental values of k1- 1 drawn in WT0 ,
Biochim. Biophys. Acta, 207 (1970) 381-389
PROTEIN HYDRATION the same scale as a function of wfzn was fitted to the theoretical curves by shifting in horizontal and vertical directions. This fit, shown in Fig. 3, gives To = 1.52 · ro- 9 sec with a = 0-46 for c = 0.045 and a = 0.34 for c = o.og3, respectively. The broader distribution ofT at higher concentrations can be understood as resulting from interactions between protein molecules. The distribution of correlation times of adsorbed water cannot, of course, extend above the correlation time Tp of the protein molecule itself. In this respect the Guassian distribution should be considered as an approximation. In the case discussed here, about go% of the area under the distribution curve G(T) lies below the correlation time Tp = r.6 · ro- 8 sec for the reorientation of the ovalbumin molecule itself round its longer axis. This value is calculated as I/3 of the Debye dielectric relaxation time from the data given by EDSALL 22 . Hence, a large number of the adsorbed water molecules have some freedom of motion with respect to the protein molecule and cannot be considered as irrotationally bound. Under these circumstances the relaxation time T 1 will be only weakly dependent on Tp and therefore only weakly dependent on the dimensions ofthe macromolecule-a fact observed with a number of proteins by GLASEL 23 . His likely, however, that the dependence of T 1 on Tp may differ for different macromolecules as a result of differences between T0 and Tp and a different value of a. ACKNOWLEDGEMENTS The authors wish to thank Dr. T. W. Szczepkowski for many helpful discussions during this work, Dr. I. Stronski and Dr. S. Kopta for making the measurements of neutron activation and Dr. ]. Dumanski for making the spectrochemical analysis.
REFERENCES r 2 3 4 5
N. BLOEMBERGEJ\', E. M. PuRCELL AND K V. Pomm, Phys. Rev., 73 (1948) 679. I. SoLOMON, Phys. Rev., 99 (1955) 559· H. C. ToRREY, Phys. Rev., 92 (1953) 962. H. E. HEINZE AND H. PFEIFER, Z. Physik, 192 (1966) 329. 0. K. DASZKIEWICZ, J. W. HEJ\'l\'EL, B. LUBAS AND T. \V. SzczEPKOWSKI, Nature, 200 (I963)
roo6. 6 K. CAPUTA, Thesis, Jagiellonian University, unpublished (r967). 7 K. CAPUTA, 0. K. DASZKIEWICZ, J. 'V.'. HENNEL, B. LUBAS AND T. W. SzCZEPKOWSKI, Proc. I]th Colloq. Ampere, North-Holland, Amsterdam, 1965, p. 326. 8 E. RAGOZZINO, Mol. Phys., IO (1965) 497· 9 J. R. ZIMMERMAN AND W. E. BRITTIN, j. Phys. Clzem., 6! (1957) 1328. IO K. CAPUTA, J. W. HENNEL AND T. W. SZCZEPKOWSKI, Proc. I4tlz Colloq. Ampere, NorthHolland, Amsterdam, 1967, p. r28. II D. MICHEL, Z. Naturjorsch., zra (r966) 366. rz R HAUSSER AND F. NoACK, Z. Physik, r82 (r964) 93. 13 Z. FLORKOWSK1, J. 'V.'. HENNEL Al\'D B. BLICHARSKA, Nukleonika, r6 (1969) 563. 14 S. H. KoEKIG AND W. E. ScH1LLil\'GER, ]. Biol. Chem., 244 (r969) 3283. 15 S. H. KoEKIG AND W. E. ScmLL1l\'GER, ]. Biol. Chem., 244 (1969) 6520. 16 W. A. ANDERSON AND J. T. ARNOLD, Phys. Rev., IOI (1956) 511. 17 S. MEIBOOM,]. Chem. Phys., 34 (1961) 375· rS K. A. KRAUS AND G. E. MooRE,]. Am. Chem., Soc., 75 (1955) q6o. 19 R. HAUSSER, Thesis, Technischc Hochschule, Stuttgart, 1964. 20 T. V.'. COJ\'l\'OR, Trans. Faraday Soc., 6o (1964) 1574. ZI H. A. RESING, .f. Chem. Phys., 43 (1965) 669. zz J. T. EDSALL, in H. NEURATH AND K. BAILEY, The Proteins, Academic Press, Kew York, I953. p. 702. 23 J. A. GLASEL, Nature, 220 (r968) 1124.
Biochim. Biophys. Acta, 207 (I970) 381-389
BBA
35583
INVESTIGATION OF PROTEIN HYDRATION BY PROTON SPIN RELAXATION TIME MEASUREMENTS
J. W. HENNELb, G. HELDc AND F. NOACKc Institute of Physics, jagiellonian University, Krakow (Poland), b Institute of Nuclear Physics, Krakow (Poland) and r I. Physikalisches Institut der Universitiit (TH) Stuttgart (Germany)
B. BLICHARSKAa, Z. FLORKOWSKib, a
(Received January 13th, 1970)
SUMMARY
Spin-lattice relaxation times T 1 in aqueous solutions of dialysed egg white were measured for concentrations between 4·5 and 9·3 wt. % in the magnetic field range corresponding to proton Larmor frequencies from o.or to r6o MHz. A strong dependence of T 1 on the magnetic field begins at approx. 0.5 MHz. It can be described by a log-Gauss distribution of rotational correlation times in the solvation layer with the maximum at r.sz · ro- 9 sec. The greater part of the distribution lies below the correlation time for the reorientation of the ovalbumin molecule itself. This means that the adsorbed water molecules have some freedom of motion with respect to the protein molecule. The width of the distribution is somewhat dependent on the concentration. This paper also contains the results of neutron activation, spectrochemical analysis and EPR measurements, which show that the amount of paramagnetic ions present in samples of protein solutions cannot be responsible for the decrease of T 1 with respect to pure water.
INTRODUCTION
Basic theory According to the theory of BLOEMBERGEN et al.l, the proton spin relaxation in liquid water is mainly caused by interaction with magnetic dipoles present in the liquid, i.e. with other protons or paramagnetic ions. The energy of such dipolar interactions depends on the vector r joining the two interacting dipoles and undergoes fast modulation as a result of the thermal motion of the molecules. This modulation can be roughly described by the mean time, the so-called "magnetic correlation time -,;", during which the magnetic interaction energy persists. If the modulation is caused only by rotation, as is the case when the two interacting dipoles are situated in the same rigid molecule, the relaxation is called "rotational". If there is also a change of 1 ; 1, the relaxation is called "translational". Often both types of relaxation contribute to the total relaxation rates rjT 1 (spinlattice) and r/T 2 (spin-spin). Biochim. Biophys. Acta, 207 (r97o) 38r-389
B. BLICHARSKA et al. The dependence of T 1 and T 2 on correlation time r: and Larmor frequency w = yH (y is magnetogyric ratio, H is, magnetic field) of the interacting spins has been calculated for rotational and translational motion within a "two-spin system" by SoLOMON 2 , ToRREY 3 and HEINZE AND PFEIFER4 • In the case of the rotational relaxation of spins with~quantum number 1 / 2 the result has the following form (I a)
(I b)
for like spins with magnetogyric ratio y, respectively,
-y; = I
I
~
2
2 2
YI Ys h
31:
7:
(
Y6
+ (WJ-Ws) 27: 2 +
I
I
+ WJ 27: 2 +
61:
I
+ (WI + Ws) 27: 2
)
2 ( )
for different spins with magnetogyric ratios y 1 and y 8 .1i is Planck's constant divided by 2n, r the distance between the magnetically coupled spins I and S, spin I being observed. Eqns. Ia and Ib give T 1 equal to T 2 in the limit w 2r: 2 «I, whereas T 1 > T 2 when w 2r: 2 > r. Therefore, from the inequality T 1 > T 2 one may conclude that the interaction responsible for the relaxation is modulated by a process which is slow with respect tow. The rotational correlation timer:, the mean time during which the orientation of the vector r persists with respect to the external magnetic field, may be related to the Debye dielectric relaxation time Tct as one-third of its value 1 . Regarding the dipole as a macroscopic sphere of radius a immersed in a medium of viscosity 'fJ one obtains 1 that r: is proportional to 'f}a (ref. 3). For small molecules like water this relation holds in a very rough approximation, but it may be more accurate for rigid macromolecules surrounded by much smaller molecules of a solvent such as globular protein in water solution. Previous results DASZKIEWICZ et al. 5 observed an inequality of the proton relaxation times in water solutions of proteins at a Larmor frequency w(2n = I4 MHz and showed that for concentrations c ~ o.I g of dry protein per g of solution the proton relaxation rates are linear functions of c: I
I
T1
T1w
-=--+kjC
j
=
I,2
(3)
k1 and k2 are constants specific for the given kind of protein, with k1 < k2 , and T 1 w, T 2 w are, respectively, spin-lattice and spin-spin relaxation times for pure water. The experimental evidence for the relation k1 < k 2 known at present is shown in Table I. The influence on T 1 and T 2 of protein dissolved in water cannot be accounted for simply by an increase of macroscopic viscosity. For egg white solutions this increase 6 amounts to 63% at c = o.I2 g/g and is too small to change the relation w 2 r:2 «I which holds for pure water and causes T 1 = T 2 • DASZKIEWICZ et aZ.S assumed that part of the adsorbed water is irrotationally bound, thus having the same correlation time as the macromolecules. For this kind of water molecules wr: R:O I and T 1 > T 2 • They also assumed that there is a fast exchange between the irrotationally Biochim. Biophys. Acta, 207 (I970) 381-389
PROTEIN HYDRATION TABLE I VALUES OF
k1
AND
k2
FOR DIFFERENT MACROMOLECULES
--------
1\!Iacromolecule
Frequency (MHz)
Temp. (0)
Ovalbumin Egg white Glycogen Glycogen Lysozyme Lysozyme
14 14 14 10 28 14
20 20 20 20 20 20
kl
(sec- 1 )
~
~~--~-
---
k.
Literature
6.8o 9.13 32.1
ref. ref. ref. ref. ref. ref.
( sec-1 )
-~------
3· 0 7 3.62 7·56 7-93 2.22 4.1 I
6.85
5 5 7 8 6 6
bound and free water molecules, so that the observed values of T 1 and T 2 can be calculated according to the formula of ZIMMERMAN AND BRITTIN 9 as an average value of the relaxation in the two phases with differing mobility. Using this theory, DAszKIEWICZ et al. 5 were able to calculate the correlation time for irrotationally bound water as 1.03 · ro- 8 sec in reasonably good agreement with the value known from dielectric measurements. Dielectric relaxation measurements at room temperature give correlation times on the order of ro- 12 sec for pure water and on the order of ro- 8 for aqueous solutions of globular proteins such as ovalbumin in agreement with the different values of radius a. This great change confirms that any kind of adsorption of water on dissolved macromolecules (hydration) should make at least some of the water molecules slower and thereby lengthen the rotational magnetic correlation time. Later investigations made by CAPUTA et al. 7 showed that the predicted dependence5 of k1- 1 on the Larmor frequency was too strong as compared with experiment. CAPUTA et al. 10 tried a refinement of the theory by assuming a distribution of correlation times within the solvation layer. As an approximation they attempted to distinguish between the irrotationally bound water and water which is only partially slowed down. Although the new model gave better agreement with experiment, a quantitative check was not possible without the capabilities of a frequency-variable NMR spectrometer. The purpose of this paper is to obtain further information concerning the nature of the interaction responsible for the relaxation process and the distribution of correlation times in aqueous protein solutions. This is done by measurements of proton relaxation time T 1 as a function of the concentration of deuterons 11 and the proton Larmor frequency 12 or the magnetic field strength. The NMR apparatus consists of a high-frequency12 and low-frequency13 spectrometer described elsewhere. Similar investigations on NMR dispersion in protein solutions in a more restricted frequency range have been published recently by KoENIG AND ScHILLINGER14 •15 ,*. Preparation of samples The solutions of egg white were prepared in the following manner. The egg white taken from five fresh hen's eggs were filtered through bolting cloth. Then approx. 7 g of EDTA (sodium salt) were added and the liquid was introduced into a * Note added after submission of the paper.
Biochim. Biophys. Acta, 207 (1970) 381-389
B. BLICHARSKA et al. cellophane dialysing bag. The bag was then kept 3 days in a glass container filled with approx. 20 1 of distilled water. About r ml of chloroform was added to the water in order to prevent the growth of bacteria. Then the bag was hung in air at room temperature to increase the concentration up to approx. rs%. Some precipitate which was found at the bottom of the bag was not taken for measurements. Changes of concentration were achieved by adding water. No salt for stabilization of pH was added. The value of pH was the same as for the distilled water being used for the dialyzation, i.e. about 6. The solutions of lysozyme and glycogen were prepared from dry substances obtained from Armour Corp., U.S.A., and F. Hoffman and Co., Ltd., Switzerland, respectively. INTERACTIONS RESPONSIBLE FOR RELAXATION IN THE SOLVATION LAYER Dipolar interactions of protons with deuterons are much weaker than with the protons because of the relatively small deuteron gyromagnetic ratio. For this reason H 2 0-D 20 mixtures have a longer proton relaxation time T 1 than that of pure water T 1 w, namely, according to the formula of ANDERSON AND ARNOLD 16 -
I
Tl
I
= - - [{J TlW
R
= -
r6 9
I
+ (r -{J)R]r)' " " - - fJ TlW
yd
2
-- =
Yv 2
o.o46
where {3 is the molar fraction of water, Yv and Yd are the proton and deuteron gyromagnetic ratios, respectively, and rj' is the ratio of the viscosity of the mixture to that of ordinary water. This formula cart be derived under two assumptions: (a) that the relaxation in ordinary undeuterated liquids is caused solely by proton-proton dipolar interactions, (b) that there exists a fast chemical exchange of hydrogen nuclei. The existence of such an exchange in water has been checked by MEIBOOM 17 . In solutions of protein in H 2 0-D 2 0 mixtures the deuterons penetrate the solvation layer as easily as the free water, and it is reasonable to assume that {3 has the same value in the adsorbed and the free water because of the chemical exchange. Thus, if the relaxation is caused by intramolecular dipolar interaction, we can apply Eqn. 4 for both kinds of water, free and adsorbed, obtaining the following result -
I
Tl
{J
= --
TlW
+ {Jkc + q
(s)
where q is a constant term due to possible paramagnetic impurities, mainly dissolved
02.
On the other hand, if the relaxation in adsorbed water is caused by intermolecular interactions, e.g. with paramagnetic ions or inexchangeable protons of the protein, then the relaxation time of adsorbed water should not be dependent on {3 and we get: -
I
Tl
{J = -TlW
+ kc + q
(6)
In order to decide which of the two formulae are in agreement with experiment, measurements of T1 of dialysed egg white and recrystallized lysozyme in H 20-D 20 Biochim. Biophys. Acta, 207 (1970) 381-389
PROTEIN HYDRATION
DIALVSED EGG WHITE 6,,
LVSOZ'IME 10'/,
--Fto
1'0
0.5
OS
I
0.5
-B
\0
DlALVSED EGG WHTE 13.8'/,
05
-B
0.5
-B
1.0
DlALVSED EGG WHTE 10'/,
1D
0.5 - B
1.0
Fig. r. Proton relaxation rate rjT 1 in protein solutions in H 2 0-D 2 0 mixtures as a function of molar fraction fJ of protons. a and b are the theoretical lines according to Eqns. 5 and 6.
mixtures were made at different {3's but constant c. All measurements were performed at least 24 h after the preparation of the solutions. No influence of lengthening this time on T 1 was observed. The results shown in Fig. r indicate that Eqn. 6 is valid and Eqn. 5 is not. The deviation of the experimental points from the theoretical Curve b is within the experimental error. Hence, we may conclude that the relaxation in the solvation layer is due to intermolecular interactions. ESTIMATION OF THE INFLUENCE OF PARAMAGNETIC IONS
It has been shown in the previous section that the relaxation of protons in the solvation layer is due to intermolecular interactions. There are two possibilities: interaction with paramagnetic ions adsorbed on the surface of the macromolecules or interaction with nuclei belonging to the macromolecules, e.g. nonexchangeable protons. Interaction with free radicals will not be taken into account as they do not occur in fresh non-denatured proteins. In order to decide what amount of paramagnetic ions is necessary to exert the same influence on T 1 as the 5% contents of pure protein, measurements were made in protein solutions containing different amounts of added Ni2+. Ni2+ were convenient for this purpose because they do not hydrolyse up to a pH of 8. It follows from the results shown in Fig. 2 that the necessary concentration is 5 · ro 17 Ni2+Jcm3. As the next step, the amounts of Fe, Cu and Mn present in the solution were estimated by means of different methods, in the belief that these transition elements are most likely to occur in a living tissue. Biochim. Biophys. Acta, 207 (1970) 381-389
B. BLICHARSKA et a/.
I
x H 0• 53'/, PROTEIN • Ni 2' o
:_____ L_.__~L-~ 0
2.0
2 H20 • Ni 2'
~
0
0
·~
. ~"-I
tO
I
10 17
·~.
1018
Fig. 2. Proton relaxation time T 1 in protein solution (dialysed egg white) as a function of concentration of Ni2+jcm 3 •
Neutron activation This method was applied for the investigation of dialysed egg white, crystallized bovine serum albumin and lysozyme. Also, control samples with the addition of Fe, Cu and Mn in amounts of ro 18 , ro 17 , ro 16 and ro15 atoms of each element per so mg dry dialysed egg white were prepared. The investigated substances were carefully dried, after which so mg of each were sealed in quartz vials of 2 cm3 volume and exposed to a thermal neutron flux of ro13 neutronsfcm 3 ·sec for 4 weeks. The vials were opened, baked in an oven at about 8ooo in order to burn the contents and treated with HCl. The investigated elements were then separated by means of an ion-exchange resin Dowex-r X8 as described by KRAUS AND MooRE18 . The activity of the fractions containing the 59 Fe, 56 Mn, and 64 Cu nuclei was measured by means of a Na(Tl) scintillation counter and a single-channel pulse analyser. The control samples containing 1016 and more added ions clearly showed increased activity due to each element investigated, but no increase in activity was observed in pure substances and in control samples containing ro15 added ions. Spectrochemical analysis Dry protein was mixed with powdered pure carbon and placed on carbon electrodes. Emission was induced by an a.c. arc and the ultraviolet spectrum was recorded by means of a medium dispersion quartz spectrograph. Dialysed egg white and crystallized bovine serum albumin did not show any traces of Mn, Cu and Fe, although the control sample of dialysed egg white, containing an addition of Cu and Mn (ro 15 atoms of each element per so mg dry proteins), gave deary visible lines of these elements. For Fe this method was rather insensitive, the lowest detectable amount of this element being ro 18 atoms per so mg of dry protein. EPR measurements A solution of 7-5% dialysed egg white was examined by means of a ro-GHz EPR spectrometer (AEG) at -60°. No lines were observed, although a control sample of the same solution containing FeH, CuH and MnH, 5.5 · ro 15 of each ion added per 3 I cm , showed EPR lines of Cu 2+ and MnH with a signal-to-noise ratio of about s. Biochim. Biophys. Acta, 207 (1970) 381-389
PROTEIN HYDRATION
J!.i_Q§_--'--=;i;::::;;::;;=<;=y;-fC~" - - - - 1 - - - + - -
• 9.3'1. ' 8.2"1• • 7.3'1.
4 5'1,
0
IO"'!\----.J.:-,---.,.S.--_!_----f.:IO,-------f.:I0:;2 ---:1:10:;-'------j -
iCMHzl
Fig. 3- Curves show values of k,- 1 computed from Eqns. 8 and g in arbitrary units as a function of wr0 for four values of a. Points show experimental values of k 1 - 1 in g · secfg as a function of the proton Larmor frequency v at 20° and different concentrations.
Because of the strong MnH lines, the lines of Fea+ could not be found with certainty. Samples of dry lysozyme and glycogen did not exhibit any EPR lines. N M R measurements
The results of all these analytical methods compared with Fig. 2 show that the amount of paramagnetic ions present in our samples cannot be responsible for the observed decrease of T 1 in protein solutions. This conclusion is also supported by the magnetic field dependence of k1-l, shown in Fig. 3, which corresponds to Eqn. ra rather than to Eqn. 2. According to Eqn. 2, the field dependence of rjT1 should exhibit two well-separated steps at ws = r- 1 and wr = r 1 , the first one decreasing r/T 1 by a factor of 3/IO. The experimental curve shown in Fig. 3 demonstrates only one step, reducing k1 much more strongly than by 3/ro. Also, 0 2 dissolved from air has a rather small influence on k1 . Dry crystalline lysozyme dissolved in vacuum in carefully degassed water gave k1 = 4.0 sec-1 at wj2n = I4 MHz, whereas k1 = 4-II sec-1 was observed in solutions exposed to air. DEPENDENCE OF T 1 ON LARMOR FREQUENCY OR MAGNETIC FIELD STRENGTH Proton spin relaxation time T 1 in dialysed egg white solutions of different concentrations was measured at 20° in magnetic fields H from 2.3 Oersted to 3.8 · ro 4 Oersted or, expressing the magnetic field strength in proton spin resonant frequency v = ypHj2n, from o.or MHz to r6o MHz. The measurements between 0.45 and r6o MHz were made by means of a variable frequency spin echo spectrometer described by HAUSSER AXD NoAcK 12 , while the measurements between o.or and r MHz were made using an apparatus constructed on the principle of free precession in the earth's magnetic field described by FLORKOWSKI et al.1 3 • The obtained results are shown in Fig. 3 in the form of k1- 1 = [(r/T1 - rjT1 w)/c]-1 , where r/T 1 w = 0-44 sec-1 Biochim. Biophys. Acta, 207 (rg7o) 38r-389
B. BLICHARSKA et al. was taken from the high-frequency asymptote of T 1 (v). This low value of T 1w compared with the well-known relaxation in pure water suggests that T 1 w still implies some influence of the proteins by sterical hindrance14 •15 . The field independence of T 1 in pure water has been demonstrated up to v = I6o MHz by HAUSSER19 . The main feature of the experimental results is that at higher fields k1 is dependent on the magnetic field but not on the concentration and at low fields it is dependent on the concentration but independent of the magnetic field. The independence of k1 on concentration at 14 MHz has already been demonstrated by DASZKIEWICZ et al. 5 • This experimentally found dependence of k1 on the magnetic field and concentration can be explained by means of Eqns. I and 3 under the assumption of logGauss distribution of correlation times within the hydration layer. This distribution can be considered to arise from the Gaussian distribution in the enthalpy of activation for the reorientation process 20 •21 . Let us first imagine the hydration layer as being composed of regions i containing fractions Pt of the whole amount of adsorbed water and characterized by correlation times Ti and relaxation times T 1(Ti)· For low protein concentrations c, the amount of adsorbed water cw (w being the amount of adsorbed water per g of protein), is much smaller than the amount of free water I - c- cw per g of solution, so that we may consider that each region i exchanges directly with the free water and neglect any exchange of water molecules inside the solvation layer. The fact that the observed spin-lattice relaxation in protein solutions is governed by a single exponential law allows us to assume that this exchange is fast in the sense used by ZIMMERMAN AND BRITTIN 9 . This means that the resultant relaxation rate (T1- 1)av is a weighted mean of particular relaxation rates I/T1 and I/T1 w, namely j
I
\
\--;;-:lav
Pw T1w
=
+
'""' p; Pa ~ T 1(r;)
(7)
where Pw = (I - cw - c)/(I - c) and Pa = cwj(I - c) are the fractions of water in the free and adsorbed state, respectively. The introduction of a continuous distribution of correlation times G(T) in the adsorbed water and~ neglect of c and cw compared with unity converts Eqn. 7 into the following form
J -G(r) -dr
00
-1 -1) -1 k 1 = ( (T1 >av-T1w c = w
T 1 (r)
(8)
Following the results of the previous sections, it will be assumed here that the relaxation of adsorbed water is due to proton-proton interaction modulated by rotation rather· than by changes in the distance r of the spins. Under this assumption T 1(T) is given by Eqn. Ia. Substitution of Eqn. Ia into Eqn. 8 and assumption of a log-Gauss distribution for G(T), namely:
.
G(r)
a
= ---
Vn
To
exp [ -a 2 (In rfr 0 ) 2 J
(9)
where a and To are parameters, converts the right side of Eqn. 8 into a function of multiplied by T 0 and a constant. Theoretical values of k1- 1 computed in this way for different values of a are shown in Fig. 3 in a double logarithmic scale. These curves nearly coincide for WTo ~ 6 · Io- 2. A diagram of experimental values of k1- 1 drawn in WT0 ,
Biochim. Biophys. Acta, 207 (1970) 381-389
PROTEIN HYDRATION the same scale as a function of wfzn was fitted to the theoretical curves by shifting in horizontal and vertical directions. This fit, shown in Fig. 3, gives To = 1.52 · ro- 9 sec with a = 0-46 for c = 0.045 and a = 0.34 for c = o.og3, respectively. The broader distribution ofT at higher concentrations can be understood as resulting from interactions between protein molecules. The distribution of correlation times of adsorbed water cannot, of course, extend above the correlation time Tp of the protein molecule itself. In this respect the Guassian distribution should be considered as an approximation. In the case discussed here, about go% of the area under the distribution curve G(T) lies below the correlation time Tp = r.6 · ro- 8 sec for the reorientation of the ovalbumin molecule itself round its longer axis. This value is calculated as I/3 of the Debye dielectric relaxation time from the data given by EDSALL 22 . Hence, a large number of the adsorbed water molecules have some freedom of motion with respect to the protein molecule and cannot be considered as irrotationally bound. Under these circumstances the relaxation time T 1 will be only weakly dependent on Tp and therefore only weakly dependent on the dimensions ofthe macromolecule-a fact observed with a number of proteins by GLASEL 23 . His likely, however, that the dependence of T 1 on Tp may differ for different macromolecules as a result of differences between T0 and Tp and a different value of a. ACKNOWLEDGEMENTS The authors wish to thank Dr. T. W. Szczepkowski for many helpful discussions during this work, Dr. I. Stronski and Dr. S. Kopta for making the measurements of neutron activation and Dr. ]. Dumanski for making the spectrochemical analysis.
REFERENCES r 2 3 4 5
N. BLOEMBERGEJ\', E. M. PuRCELL AND K V. Pomm, Phys. Rev., 73 (1948) 679. I. SoLOMON, Phys. Rev., 99 (1955) 559· H. C. ToRREY, Phys. Rev., 92 (1953) 962. H. E. HEINZE AND H. PFEIFER, Z. Physik, 192 (1966) 329. 0. K. DASZKIEWICZ, J. W. HEJ\'l\'EL, B. LUBAS AND T. \V. SzczEPKOWSKI, Nature, 200 (I963)
roo6. 6 K. CAPUTA, Thesis, Jagiellonian University, unpublished (r967). 7 K. CAPUTA, 0. K. DASZKIEWICZ, J. 'V.'. HENNEL, B. LUBAS AND T. W. SzCZEPKOWSKI, Proc. I]th Colloq. Ampere, North-Holland, Amsterdam, 1965, p. 326. 8 E. RAGOZZINO, Mol. Phys., IO (1965) 497· 9 J. R. ZIMMERMAN AND W. E. BRITTIN, j. Phys. Clzem., 6! (1957) 1328. IO K. CAPUTA, J. W. HENNEL AND T. W. SZCZEPKOWSKI, Proc. I4tlz Colloq. Ampere, NorthHolland, Amsterdam, 1967, p. r28. II D. MICHEL, Z. Naturjorsch., zra (r966) 366. rz R HAUSSER AND F. NoACK, Z. Physik, r82 (r964) 93. 13 Z. FLORKOWSK1, J. 'V.'. HENNEL Al\'D B. BLICHARSKA, Nukleonika, r6 (1969) 563. 14 S. H. KoEKIG AND W. E. ScH1LLil\'GER, ]. Biol. Chem., 244 (r969) 3283. 15 S. H. KoEKIG AND W. E. ScmLL1l\'GER, ]. Biol. Chem., 244 (1969) 6520. 16 W. A. ANDERSON AND J. T. ARNOLD, Phys. Rev., IOI (1956) 511. 17 S. MEIBOOM,]. Chem. Phys., 34 (1961) 375· rS K. A. KRAUS AND G. E. MooRE,]. Am. Chem., Soc., 75 (1955) q6o. 19 R. HAUSSER, Thesis, Technischc Hochschule, Stuttgart, 1964. 20 T. V.'. COJ\'l\'OR, Trans. Faraday Soc., 6o (1964) 1574. ZI H. A. RESING, .f. Chem. Phys., 43 (1965) 669. zz J. T. EDSALL, in H. NEURATH AND K. BAILEY, The Proteins, Academic Press, Kew York, I953. p. 702. 23 J. A. GLASEL, Nature, 220 (r968) 1124.
Biochim. Biophys. Acta, 207 (I970) 381-389