IELECTRTC: I~ELAXATION SPECTRA OF
2987
WATER
axation Spectra of Water Adsorbed on Lysozyme
rtmouth College, Hanover, N e w Hampshire
03766
U . S'. .&mu Cold Regions Research and Engineering Laboratory, Hanooer, New Hampshire (Receioatl February 26, 197%) P u b F h t i o n costs assisted by the
03766
U.8. A r m 9 Cold Regions Research and Engineering Laboratory
The dielectric properties of water adsorbed on chicken egg white lysozyme have been investigated over the freyurricy range from lo7 to 2.5 X 1010 Hz, using time domain reflectometry (TDR) and standing wave measurements (SWM) in wave guides and coaxial lines. Measurements were made on packed powders with water contents ranging from 0.0 to 0.6 g of HzO/g of lysozyme. Two district dispersions are observed and are assigned to two layers of adsorbed water. The first layer is characterized by a single relaxation time near 10-9 sev. The relaxation process for this lager has a negative activation enthalpy and a negative activation entropy, indicating that the molecules in the first layer have a lesser degree of hydrogen bonding than in bulk water. A distribution of relaxation times (a = 0.3) about 2 X sec characterizes the second layer.
Introduction The earliest measurements of the electrical properties of protein solutions were made by Oncleya2" He ob-. served a dispersion near 2 iMHz which he attributed to the rotation of the protein molecule. Also working with solutioritx, HaggisjZbB ~ c h a n a nand , ~ their coworkers made measurenrents at frequencies above 3 GHz. Comparing their data with Oncley,2" they concluded that there Wac a dispersion between 20 MHz (the highest frequency uscd in Onciey's experiments) and 3 GI-Iz. They attri'buied t,his dispersion to the relaxation of a shell of bound water. Sehwan4 and Pennock and Schwan5 closed the gap in the earlier mork, measuring the dielectric constant of hemoglobin stilutions over the frequency range 1 MHz1.2 GHe. They explained their results in terms of three distinct dispersions. The rotation of the protein molecule was used to account for the first dispersion, below 30 MHz. The second dispersion, between 10 and 100 ,\!IHzwas , assigned- to the rotation of the polar side chains of tEe pwtein. The third dispersion, above 100 MHz, WLS assigned to a shell of water bound to the protein, Tli:c best agreement with experimental data was gotten 12-y assigning the bound water a static dielectric constant like that of ice and free water, in the range of 80 to 10i3. In addition, a characteristic frequency bctv,een 0 . 5 and I GRz was used for the bound water, and a wahe of 0.2 0.05 g of H,O/g of protein mas assurneci. (hi the basis of these assumptions and from the teznperatxe dependence of the characteristic frequency, E'mnock and Schwan5obtained an activation enthalpy of about 7 kcal/mol. Because of the characteristic frequency and the activation enthalpy, they concluded that tki~bound water was structurally between ice and frec water, but somewhat closer to the latter.
*
Unfortunately, there are difficulties in working with solutions. Because of the high dielectric constant of the bulk liquid, and because protein solutions cannot be made very concentrated, the effects of the bound water are not large. For instance, in the experiments of Pennock and S ~ h w a i ithe , ~ observed dielectric constant differs by only about 1%from the values predicted by a simple mixture equation for water and unhgdrated protein. The observation of the relaxation of the bound water and the determination of its characteristic parameters thus requires measurements of high precision. In addition, the interpretation of the experimental results requires a model with several assumptions. There are a large number of parameters to be chosen, including the shape of the protein molecule, the amount of bound water, the dielectric constant of the protein molecule, the dielectric constant of bound water, and the number of dispersions and the characteristic frequency of each dispersion. Because SO many parameters may be varied t o account for the small effects observed experimentally, the results cannot be considered definitive. To circumvent thcse difficulties, measurements have been made on hydrated protein powders.6- When (1) Address correspondence to Department of Ehgineering Biophysics, University of Alabama Medical Center, Birmingham, Ala. 35233. (2) (a) a. L. Oncley in "Proteins, Amino Acids, and Peptides as Ions and Dipolar Ions," E. J. Cohn and J. T. Edsall, Ed., Rheinhold, New Yorlc, N. Y., 1943, pp 546-567. (b) 6. €1. Haggis, T. J, Buchanan, and J. B. Hasted, Nature (London), 167, 607 (1951). (3) T. J. Buchanan, G. €I. Haggis, J. B. Hasted, and B. G. Robinson, Proc. Roy. SOC.,Ser. A , 213, 379 (1952). (4) H. P. Schwan, Ann. lV. Y . Acad. Sei., 125, ,744 (1965). (5) B. E. Pennocli and R. P. Schwan, J . Phys. Chem., 73, 2600 (1969). (6) S. T. Bayley, Trans. Faraday Soc., 47, 509 (1951). (7) D. Rosen, ibid., 5 9 , 2178 (1963). T h e Journal of Physical Chernistru, V o l . 7 6 , A'o. $1, 2972
s. c. HARVEY AND F.
2988
powders are used, the experimental problems described above are removed, at the cost of working with a system -cvhich i s more remote from thc true situation in v+w. The early work of Bayley6 on dry protein powders XT as followed by 1,hat of Rosen17who measured the dielectric constant and lobs of hydrated protein powders over the frequency range 50 kHz-20 MHz. Subsequently, Takashima and Sch.cvanacovered the frequency range 20 RZ-208 liliz, a i m working with crystalline powders. I n both sets of experiments, graphs of the dielectric constant as a function of water content fell into two sections, with the break occurring at a water content which Rosen7 called the critical hydration, h,. The critical hydratior1 n a s identified as that amount of water required to cover the protein molecule with a single layer of water. None of these investigations6--* covered the frequency which Pennock and Schwan5 identified with the dispersion of the bound water, so none of the parametms of the bound water dispersion were tlelermincd The purpose of the experiments described in this paper was to inves1,igate the properties of surfacebound water adsorbed on protein powders over the frequency range 10 R/IHz-25 GHz. While the environment of the surface water on powders is different from that of protein solutions, the correlation of the results of these experiments with the earlier work on solutions2-5 can yield useful inlormation.
The dielectric properties of a number of materials whose molecules have permanent dipole moments can be described by a modification of the Debye equationg due t o Cole and CoIelO e*(&) = e,
+ I +e, --
Em
-
(iw7)l-a
I n this equation, 8 i s the complex dielectric constant, E ’ ( w ) - ie”(w), (Gaussian units are used throughout this paper, so eo, the permittivity of free space, is one). The real part, e’, is the dielectric constant, and the imaginary part, e ” , is the dielectric loss. E , and es are the high- and lowfrequency limits of the dielectric constant, w is the angular frequency, and r is the relaxation time. a is a parameter indicating the width of the distribution of relaxsltion times around 7. For materials with a single relaxation time (such as water), CY = 0, and eq I rduces to the form given by Debyes E*(W)
I n this case, parts
E*
= E,
+ 1 +-i w r Es
E,
-__
can be separated into its real imaginary
(3) The Journal of Physical Chemistry, Vol. 76, N o . $ 1 , 1971
Cole and CoIelO have shown that a graphical representation of eq 1 gives the arc of a semicircle in the complex plane, with the diameter of the semicircle making an angle an/2 with the real axis. The Debye equation was also derived by ICauzmann,l1 who considered polarization to cess.12 In this treatment, the rotation of the dipole is equivalent to the passage over an energy barrier whose height i s equal to the molar free energy of activation AF’
=
AN‘
-- TA8’
(5)
where AH’ and A S ” are the molar activation enthalpy and entropy, and T is the absolute temperature. The relaxation time is
where h, IC, and R are Planck’s constant, the Boltzmann constant, and the gas constant, respectively. Equation 6 is particularly useful, since it allows the determination of the activation parameters (eq 5 ) from a plot of In r vs. 1/T,
Materials and Methods Measurements were made using crystalline lysozyme powder (Sigma Chemical Co.), three times recrystallized, dialyzed, and lyophilized. Lysozyme was chosen because it is fairly resistant to denaturation, and a simple assay procedure is available to determ:Inc enzyme activity, which is an indication of the extent to which the native structure is retained or lost. I n all of the samples used, enzyme activity was checked before and after measurements were made. All of the data reported here came from samples where 110 measureable loss of activity occurred during the experiments. The samples were hydrated in a closed humidifier by exposing the powder to water vapor a t a rclative humidity of about 90% for varying lengths of time. Hydration values were determined by weighing before and after drying at 110”. The complex dielectric constant was measured by two diff erent techniques. Standing wave nieasurementsl3 (SWlMJ were made over the frequency range from lo8 to 2.6 X 10*0Hz. At frequencies below 8 X (8) S. Takashima and EI. P. Schwan, J . Ph,ys. Chem,., 69, 4176
(1965). (9) P. Debye, “Polar Molecules,” Dover Publications, New York, IV. Y., 1929, Chapter V. (10) K. S. Cole and R. H . Cole, J . Chem. Phya., 9, 341 (1941). (11) W. Kauzmann, Rev. Mod. P h p . , 14, 12 (1942). (12) S. Glasstone, E;. J. Laidler, and H. Eyring, “The Theory of Rate Processes,” McGraw-Hill, New York, N. Y., 1941, pp 544551. (13) W. B. WestphaI in “DieIectric iMateriaIs and Applications,” A. R. Von HippeX, Ed., M I T Press, Cambridge, Mass., 1954, pp 63-122.
DIELECTRIC RELAXAWQNSPECTRAOF WATER
2989
1 0 9 Ea ( h $4 m),samples were placed in short-eir7t cuited coaxial P nes; for frequencies above 4 X lo9 Hz (X 30 em) is required to allow this change in the dependence of dielectric properties on steady state t o be attained before the incident pulse Tm7o explanations for this behavior water content. can be reflected off of the back face of the sample and First, since hydrogen bonding is might be invoked. detected. ‘I’he complex dielectric constant is then a
given by
(14) E. E’ellner-Feldegg, J . P h y s . Chem., 73? 616 (1969). (15) T. A. Whittingham, ibid., 74, 1824 (1970). (16) A. Suggett, P. A. Mackness, M. J. Tait, €1. W. Loeb, and G. 111. Young, Nature (London), 228, 456 (1970). T h e Journal of Physical Chemistry, Vol. 78,X o . 81, 1972
299
S. C. HARVEY AND P. NOBKSTRA
€'
"1
O
O Oo0
E'
r
t i
E' 0 1
3
FREQUENCY
E"
(HZ1
Figure 3. Dielectric constant ( e ' ) and loss ( e " ) as a function of frequency for packed lysozyme samples containing slightly more than one monolayer of water: h = 0.34 & 0.03 g of HsO/g of protein; T = 25".
2 1
0
0
0.1
0.2
0.3
0.4
0.5
I i Y DRATION
ym H20/grn protein
Figure 2. Dielectric constant (e') and loss (e") of packed lysozyme powder as a function of water content: f 25 GRz, T = 25'. =i(
known to be a cooperative phenomenon, l7 the increased water-water intet-actions a t higher hydrations could account for the observed behavior. I n this case, the dependence of dielectric constant on water content would be a smooth curve with a positive second derivative, as chosen by 'Takashima and Schwan.* Alternatively, there may be two distinct kinds of adsorbed v ater with diff elrcnt polarizabilities. Two straight line segments would then correctly represent the data. The physical properties of lysozyme powders depend on water content. At hydrations below about 0.3 g of & 0 / g of protein the powders cannot be distinguished from dry lysozyme. At greater hydrations the powders are sticky, and samples made with h, > 0.3 will mainhiin their shape and structural integrity on removal from the sample holder, whereas thc drier samples fall apart. In an oven, samples of low-water content ran be dried a t any temperature up to 150" with no visible effects except for some yellowing. Above h = 0.3 samples must be dried below 80" before raising the temperature, If not, they will scorch or dry into very hard granules. While these properties cannot be measured quantita1,ively the break in properties a t 0 3 g of &O/g of protcin is intcresting because it correlates with thrb observed break in dielectric properties a t h 0.3. Left for several days in the humidifier, lysozyme will come to equilibrium after adsorbing about 0.6 g of BzO/g of protein, Occasionally, after about 1 week, more water is adsorbed, and the crystalline powder changes to very hard transparent beads. This maI-.
TJie Journal of Phgsicai Chemistry, Vol. 7 6 , No. 11,1972
0
1
:
E"
FREQUENCY
(HZ)
Figure 4. Dielectric constant (e') and loss (e") as a function of frequency for powdered lysozyme samples containing nearly two monolayers of water: h = 0.54 I 0.04 g of RzO/g of protein; 2" = 25". The curves correspond t o the values given by the Debye equation for two dispersions with the parameters given in Table I, as described in Ihe text.
terial is difficult to handle, and attempts to measure its dielectric properties were unsuccessful. It appears that 0.3 g of HzO/g of protein corresponds to covering the surface of the lysozyme molecule with a single monolayer o,f water. The thickness of this layer would be about 2 A if uniform coverage is assumed and the macroscopic density of water is used in the calculation. This thickness is in reasonable agreement with the accepted dimensions of the water molecule. l8 Figures 3 and 4 show the dielectric behavior as a function of frequency over the entire range studied for samples with h = 0.34 i: 0.03 g of H,O/g of protein arid h = 0.54 i 0.04 g of H20/g of protein. The (17) H. S. Frank, Proc. Rog. ~Toc.,Ser. A , 247, 481 (1948), (18) D. Eisenberg and W. Kauzmann, "The Structure and Properties of Water." Oxford University Press, Kew Yorlr, K,Y., 1969.
DIELECTRIC RELAXA.TION SPECTRA OF WATER quoted moisture contents are average values for the several samples required to cover the entire frequency range; all samples fell within the ranges of hydration r frequency range, dry lysozyme valires given O ~ ethis had a dielectric cox~stmtof about 2 and a dielectric loss of. 0 f 0.2. The curves in Figure 4 represent the throretical valuts from the Debye equation wihh two dicpersfons, as disctnesed below. In Figure 3, which corresponds to slightly more than one monolayer of wafer covering the protein, a large, well-delined clispersion Is observed near 2 X 108 Hi, The smaller hit,;h-frccpiency dispersion is due to the prasence of S I ~ water C in the second layer. As the second monoiayer iii completed (Figure 4), the lowfrequency dispersion is nearly unchanged, so it must be due to the wafer in the first hydration shell. The growth of the ~ ~ ~ ~ f r dispersion e ~ ~ ~is proportional e n ~ y to thc amount in t h e second layer, as i s seen most clearly in F i g u ~ e2 . Ln particular, the dielectric loss is nearly aero 4 3 1 hydrations below 0.3 g of H20/g of protein, but grvws with increasing water content (Figures 2-4). Thcb second dispersion can thus be assigned to the second hydration shell. This two layer-two d.spersion model is supported by the breaks in physical ielectric properties as discussed above. It is also supported by t be abi;ence of Lhe high-frequency dispersion [or 2, c 0.3 g oE R20/g of protein and by the independence c f the h v - frequency dispersion on water contents beyond h == 0.3 g of N D / g of protein. Further, the dispersion cue to thc second monolayer disappears a t about - 25", while that due to the first monolayer pexsists to the lowest temperatures used here, .- 70". To assist in the analysis of the dispersions, ColeCole plots (Figures 5 arid 6) have been made using the data of Figure 4. Figure 5 shows only those points for frequencies below 4 5 GHz. The plot is semicircular, indicating De Dye behavior, and the diameter of the semicirc.le coincides vith the real axis, so the dispersion is characteriacd by :t single relaxation time ( a = 0). The dispc~sionciic to the first monolayer has a characteristic frequency of 2 5 X 108 Hz. The high-frequency tail ol this dispersion makes substantial contributions t o ;he observed dielectric constant and loss above 1 GEIz Thcw contributions can be determined from the Deb,ye equation and subtracted from the observed dielectric constant and loss; what remains will be due only l o the high-frequency dispersion. Figure 6 shows the Cole-Cole plot which results after these corrections. Aftbough there is considerable scatter in the data, %. scmicircular arc does give a reasonable fit, again indicating Debye behavior. A distribution of relaxation times :s indicated, with a = 0.3. While this is not a preciw value, clearly somp spread of relaxation timcs ( a >- 0) does exist. RQWwell does the proposed two dispersion model fit) the experimental data? The parameters of the Debye
6t
f"
1 *i
0
o
o
i 21-
20 00
6
0
pff
0
0 0
0
0
O
0
8
10
12
14
E'
Figure 5 . Cole-Cole plot of the low-frequency dispersion (f < 1.5 GBz) observed in Figure 4. From t>hisfigure, f~ = 0.26 GHZ, (Y = 0.
0
Figure 6. Cole-Cole plot of the high-frequency dispersion observed in Figure 4. The contributions made to E* by the low-frequency dispersion have been calculated using the Debye equation, with 1 0 = 0.25 GHz, (Y = 0. These contributions were then subtracted point by point from the da,ta of Figure 4, and the resulting values of e' and e" are plotted here
1
1.0
4
0.7
0.4
E-
o.2 ~ 2 i c
0.1 32
''0
-25"
I
c
. ) I + +
3.6
l/T
4.0 (X10-3
OK-')
Figure 7. Arrhenius plot for the dispersion due to molecules in the first monolayer when h = 0.34 i 0.03 g of HzO/g of protein. The activation parameters are given in Table I.
equation which result from the Cole- Cole plots have been used t o generate the solid curves in Figure 4. There is a reasonably good fit to the experimental data. The activation parameters can be obtained by plotting the logarithm of the relaxation time against the reciprocal temperature. The Arrhenius plots for the dispersion due to the first adsorbed monolayer (Figures The Journal of Physical Chemistry, Vol. 76, N o . ??I7 1978
s, c. HARVEY AND P.
2992 s
able I: Acti vation Parameters €or Surface-Adsorbed Water, Liquid Water, and Ice AH
Referencea
Present work, first layer; h = 0.34 g of &O/g of protein Present work, first layer; h = 0.54 g of BaO/g of protein Present work, second layer; h = 0. j 4 g of BzO/g of protein Nmr linc widths of surface water; frozen BSA solutionse (- 25') Dielectric relaxation of surface water m hemoglobin solutionsf Liquid 'iVatePv Iceg (0')
*,
AS
*,
kcal/mol
e11
AP
*,
koal/moi
9.5 x
10-10
--2.9
-27.3
5.2
6.5
x
10-10
-0.4
-18.1
5.0
16
x
b
b
b
3.5
x
10-8c
5.0
-4.0"
1 . 4 X 10-10
7.3
10.O d
8.4 X 10-l2
4.5 12.7
5.4 9 6
2
x
10-6
6 2
4.3d
2.4 10. I
a T -- 23' except where noted. Not determined because of scatter in data and spread of relaxation times a: = 0.3. Value revised since publicatioii of results (I. D. Kuntz, Jr., personal communication). Calculated from Pennock and Qchwan,6Figure 12. Reference 19. 1 Reference 5 . 0 Reference 18.
25"
1
0.1 ---3.2
c
0"c
-25" C
i
b.
;
3.6
I/ i iX10b3
4.0 OK-')
Figure 8. Arrhenius plot for the dispersion due to molecules in the first monolayer when k = 0.54 f 0.04 g of HZO/g of protein. The activation parameters are given in Table I.
'7 and 8) show a surprising result; the relaxation time increases ~1ith increasing temperature. From the slopes of the curves, the activation enthalpy is seen t o be negative The activation entropy, calculated from cq 6, is also negative. The free energy of activation is positive, as required by the theory of rate processes, because of the large negative entropy change. These results are summarized in Table I, which also gives the activation parametxm reported in earlier measurements on protein bound ~i.at,er.~ l9
Iliscussion The gcneral theory of dielectrics is not sufficiently developed to allow the determination of the properties of each of the components of a heterogeneous mixture from the observed macroscopic properties of the mixture.'O The problem has only been solved for a small number of casesUp1611 most of these a small amount of The Journal of PhzJsical Chemistry, Vol. 76, N o . ai, 1972
one material is dispersed throughout a continuum of another material, and the dispersed granu-les have a simple and well-defined shape. The hydrated protein samples have an unknown, and probably complex, microscopic geometry. Determination of the local fields and polarizations from the macroscopic properties is thus impossible, and the dielectric properties of the surface-bound water cannos be compared directly with those of the bulk liquid. It is, however, possible to assign a definite mechanism to the dispersion a t 0.25 GHz and say something about the local structure, based on the temperature dependence of 7. It is also possible to make some observations on the dispersion near 10 GHs, at least to the extent of assigning this dispersion to the second layer of water. To begin with, both dispersions are due to the polarization of the adsorbed water. First we consider the other possible mechanisms and show that contributions from each of them must be negligible a t these freyuencies. (1) Conduction Mechanisms. The contributions of low-frequency conductivity t o the loss is20 'E = v/o. Since the observed loss goes through peaks rather than falling off with increasing frequency, the low-frequency conduction contributions cannot be important at these frequencies. (2) Maxwell-Wagner Dispersion. WagneF developed a theory to explain the observed dispersion in mixtures of materials of different conductivities. Because of this difference, polarization is produced by the (59) I. D. Kuntz, Jr., and T. S. Brassfield, Arch. Biochem. B w p h y s . ,
142, 660 (1971). (20) C . P. Smyth, "Dielectric Behavior and Structure," McGrawHill, New York, N. Y., 1955, pp 52-74. (21) G. P. DeLoor, Ph.D. Thesis, Leiden, The Netherlands, 1956. (22) K. W.Wagner, Arch, EEektroteeh. (Berlin),2, 371 (1914).
IELEGTRIC
R,ET.AXBTIC)N SPECTRA OF WATER
accumulation of cha~geat the boundaries between the materials. Dispersions due to this effect ordinarily ~ ~ detailed occur at freqtiencics .ciell below I N I H Z , and caicdations2' sh 3 w that thry cannot be responsible for the results observed h e . (3) OtheT Dipolar elaxation Mechanisms. The dispersion due to rotation of the intact protein molecules in solution is ntm IO6 Zz,2aowing to the large size of the protein molecrrle. I n these samples, where the protein rnolecullr~is viot in solution, the rotation is more hindered and the diapersion would occur a t much lower frequencies. By the mme argument it is possible to eliminate the clispermn due to the rotation of the polar side chain >, idiich is observed near 3 X loy Hz in SOhltiOll.~
The ehninatron of these mechanisms, coupled with the observed dependence of the dielectric properties on water cmtent, leads to the conclusion that the tv7o dispersions are diie to the polarization of the adsorbed water 1 nolecmle$. 'Let us look first, a t the low-frequency dispersion. It is unusual in that it moves to lower frequencies as the texnperaturr 1s rarped ( T increases). This is because the activation canthalpy is negative. I n the activation process, hydrogen bonds are made, so heat is given off (AH' -< 0 ) dBakmg these bonds is equivalent to increasing the local structure, lowering the entropy (Ais* < 0) What is the physical basis for this process? In order f o rotate and make a contribution to the polarization. a naier molecule in the primary hydration layer must break its bond with the protein. With the removal o' this bond, it will be able to reduce the distortion in t w hydrogen bonds it made with neighboring water rxioleeules, or to make new bonds where none existed before. On balaiice, the molecule makes bonds going into this state, giving off heat, so the new state is enthalpitally Cavorable to the old. &4tthe same time, the mobride, by reducing the distortion in the bonds with its ncigbbors, fits better into the local hydrogen bonded net'> ork. The network becomes more ordered tha,n btforti so the entropy of the group of molecules in i,he netJmork is reduced. This group of molecuies, t h achrated complex, is thus in a state which is entropicall> less favorable than the old. I n summary the formation of the activated complex is enthalpicall y favorable, but entropically unfavorable. In that sense lil is reminiscent of the solution process of aliphatic hrd rncartronfi in water,24for the barrier to both procease,?1s entropic. The free-energy change on formation of he stcttvated complex is positive because of the magnitude of the entropy change., and the complex IS not stithle relative to the unactivated collection of molecules. Row rrlarly rnoiccules are in the complex? The activation procws ma~ybe looked a t as a local freezing, the activated complex corresponding to a microcrystal
2993
t
E"
8l L
4l 0
8
4
12
20
16 €'
Figure 9. Cole-Cole plots for low-frequency dispersion as measured by TDR, a t various temperatures. A detectable dispersion persists to -70°, the lowest temperatures used in these experiments.
of ice. Following I
