12622
J. Phys. Chem. B 2001, 105, 12622-12627
Hydration Study of Globular Proteins by Microwave Dielectric Spectroscopy Keiichi Yokoyama, Takashi Kamei, Hiroshi Minami, and Makoto Suzuki* Department of Metallurgy, Graduate School of Engineering, Tohoku UniVersity, Aoba-yama 02, Sendai 980-8579, Japan ReceiVed: March 30, 2001; In Final Form: September 26, 2001
A microwave dielectric measurement was performed to study the hydration properties of proteins in solution with a precision network analyzer with high reproducibility within the errors of 0.02 in relative dielectric constant over 2 to 10 GHz. A measurement was carried out for catalase, chymotrypsinogen A, cytochrome C, hemoglobin, peroxidase, lysozyme, myoglobin, ovalbumin, and bovine serum albumin at 20.0 ( 0.01 °C. The hydration properties of protein molecules were evaluated based on the Wagner mixture theory combined with single Debye approximation to the complex dielectric constant of hydrated solutes in the above frequency range. This was used to evaluate the loosely bound water number Nw from the single Debye fitting, which gives the relaxation frequency (fc) of the hydration shell loosely bound and tightly bound water number Ns with lower relaxation frequencies than fc. Those hydration numbers were compared with the monolayer water numbers accessible to hydrophobic and hydrophilic exposed atoms, respectively, obtained from the calculation of accessible surface area of each protein structure based on the protein database. The result showed a good agreement both in the ratio and numbers.
1. Introduction Protein hydration is of fundamental interest in biology. One of the most intriguing issues is to understand the contribution of solvation energy to structure formation and stability.1,2 In a physiological condition, proteins play their roles mostly in water. The enzymatic activities related to their structure change according to the environmental chemical or physical stimulations. Generally, structural change of proteins in water relates to the change of the hydration states.3 Protein hydration has long been studied by various methods, such as calorimetry,4 infrared spectroscopy,5 osmotic pressure,6 NMR techniques7 by 17O relaxation measurement8 or 1H chemical shift analyses,9 and so on. Among these techniques, dielectric spectroscopy provides direct information of the orientational dynamics of molecular dipoles, such as whole-protein dipole, water molecule, polar side chains, or peptide bonds.10-13 In a dielectric spectrum of protein solution, a fairly large relaxation is observed in the range of approximately 0.1 to 1 MHz called β-dispersion corresponding to the orientational relaxation of protein dipoles.14 In the microwave frequency range, large relaxation with an absorption peak at 17 GHz at 20 °C is called γ-dispersion corresponding to the orientational relaxation of bulk water dipoles. Small relaxation in the intermediate frequency (subgiga- to gigahertz) range is called δ-dispersion.10 δ-Dispersion is considered to include the orientational relaxation of dipoles of water molecules in the hydration shell15 or flexible loops or side chains of protein. Although the δ-dispersion signal is relatively small, attractive information on protein hydration is included. The previous study16 described the property of hydration shell of hydrophobic side chains of amino acids, such as the number of water loosely bound on hydrophobic side chains of amino acids, as three water molecules per methylene group and the relaxation frequency of 5 GHz. Protein hydration was analyzed in the previous study17 in which the tightly bound water number Ns and the loosely bound water number Nw were separately evaluated based on the difference of those orientational relaxation frequencies. However, as the measured frequency range was from 2 to 8 * To whom correspondence should be addressed.
GHz, the hydration water with relaxation frequency higher than 8 GHz might be neglected. In this paper we show the result of the dielectric measurements carefully made in the frequency range from 0.2 to 20 GHz. We have adopted an improved method of measurement with a dielectric spectrometer with a temperature-stabilized oscillator. With a repetitive measurement procedure alternating a reference solution with a sample solution in a relatively short time, we obtained high reproducibility with the errors of 0.02 in relative dielectric constant over the frequency range 2 to 10 GHz and 0.05 for 0.2∼2 and 10∼20 GHz. In the previous report18 we proposed an estimation method of the hydration numbers of Ns and Nw from the accessible surface areas of exposed polar and hydrophobic atoms of a protein based on the crystal 3D structures. This method will be examined in this paper. 2. Method of Analysis This method is based on a two-component model, where spherical solutes (which are hydrated protein molecules) are dispersed in pure solvent. We assumed that (1) proteins in solution are spherical and have spherical hydration shells; (2) solvent outside of hydrated solutes has the same dielectric property as that of pure solvent; (3) the dielectric constant of solute (protein) is constant, here we used 2.5, based on the electronic polarization of atom groups; (4) the dielectric constant of hydration shell at the high-frequency limit is 5.6, the same as that of pure water;19 and (5) the dielectric relaxation of the hydration shell is approximated by using with a single Debye function in the gigahertz range. This assumption (5) is for the simplest case. Here we basically use SI units unless otherwise noted. The terms x* (x ) ap, a, q, etc.) represent the relative complex permittivity (complex dielectric constant). The apparent complex dielectric constant ap* of the protein solution is expressed with the dielectric constant of solvent a* and that of dispersed spheres q* as
ap* ) a*{2(1 - φ) a* + (1 + 2 φ) q*}/{(2 + φ) a* + (1 - φ) q*} (1) which is the Wagner equation20 for φ , 1, or
10.1021/jp011217y CCC: $20.00 © 2001 American Chemical Society Published on Web 11/27/2001
Hydration Study of Globular Proteins
{(ap* - q*)/(a* - q*)}(a*/ap*)1/3 ) 1 - φ
J. Phys. Chem. B, Vol. 105, No. 50, 2001 12623
(2)
which is the Hanai equation21 for 0 < φ < 1 where φ is the volume fraction of the solute (protein molecule covered with a hydration shell). Although the Hanai equation gives a good estimation for high-concentration emulsions, we used eq 1 for φ < 0.1 since the difference between the results by eqs 1 and 2 was negligibly small. With eq 1 we can calculate the complex dielectric constant of hydrated protein q* from the experimental values of ap* (solution) and a* (solvent) if the value φ is given. The values φ and q* must be determined consistently to satisfy the condition of high frequency limit by the following procedure. The high frequency limit condition is such that the dielectric constant of the hydrated solute at f f ∞, q∞, must be equal to the value by eq 3. When the solute is a shelled sphere (protein with a hydration shell) q* is expressed with the dielectric constant of the hydration shell h* and that of the core (protein) p* 22
q* ) h*{2(1 - φp) h* + (1 + 2φp) p*}/{(2 + φp) h* + (1 - φp) p*} (3) (for 0 < φp < 1) where φp ) V/φ (V is the volume fraction of protein in the solution calculated by V ) csv). Here c and sV are the concentration of protein in g/mL and the partial specific volume of protein in mL/g, respectively. The term sV is given by23
sV ) lim (1-V0)/c cf0 V0 (the apparent volume fraction of solvent in solution) ) (d c)/d0, where d and d0 are the density of the solution and solvent in g/mL, respectively. Equation 3 was used to obtain q∞, the high frequency limit (f f ∞) of q*, where h* ) h∞ ) 5.6 were used for f f ∞ by the assumptions (3) - (4), and p* ≡ p∞ ) 2.5.24 The procedure to obtain q* is as follows. First, assuming an initial value of φ, the dielectric spectrum of hydrated solute q* was calculated by using eq 1. Second, the obtained q* was fitted by a single Debye relaxation function in the frequency range of 2-10 GHz,
q* ≈ q∞ + (qs - q∞)/{1+ j(f/fc)}
(4)
Third, φ was adjusted in eq 1 and 3 until q∞ in eq 4 agreed with the value obtained by eq 3. Thus, we obtained φ, fc, qs, and q∞. In many globular proteins q∞ was around 3.5. Figure 1 shows the full spectra of ap* and a* in (a) and the difference spectra of ∆′ ) ap′ - a′, ∆′′ ) ap′′ - a′′ in (b). Figure 1c shows q* obtained by eq 1 from ap* and a*, and a single Debye fitting curve by eq 4. The single Debye function could approximate the experimental values. The numbers of bound water molecules per protein molecule Ntotal and Ns were then calculated as follows:
Ntotal ) {55.6(φ - V) Fhyd}/c
(5)
Ns ) {55.6(φ1 - V) Fhyd}/c
(6) Figure 1. (a) Full spectra of protein solution ap* and water a*. (b)
(7)
Difference spectra of 34.8 mg/mL peroxidase. ∆′ ) ap′ - a′, ∆′′ ) ap′′ - a′′. (c) q* obtained by eq 2 from ap* and a* and a single Debye fitting by eq 4. qm′′ ) q′′ - 8/f, where 8/f was assumed as the interfacial ionic conduction.
(8)
φ1 is the volume fraction of protein with a tightly bound hydration shell, which is given by Wei et al.’s method25 to
where
φ1 ) (a0 - ap0)(2a0 + a∞)/(2a0 + ap0) (a0 - a∞) Nw ) Ntotal - Ns ) {55.6(φ - φ1) Fhyd}/c
12624 J. Phys. Chem. B, Vol. 105, No. 50, 2001
Yokoyama et al. chamber and kept at 10-4-10-5 Torr by a turbo molecular pump and rotary pump. The dielectric spectra was obtained with a microwave network analyzer, Hewlett-Packard 8720C, and an open-end flat surface coaxial probe. To prevent the accumulation of microbubbles, the probe was fixed in an upward position in a glass cell controlled at 20.0 ( 0.01 °C by a Neslab thermobath. The solution temperature was monitored with a platinum-resistor thermosensor by the four-terminals method. The cell was filled with a sample solution degassed under reduced pressure. Microwaves in the frequency range 0.2-20 GHz were applied to the cell through the probe. The calibration was done by a procedure consisting of an open circuit in air and a short circuit with mercury and in pure water at 20.0 ( 0.01 °C. The reflected waves were sampled by the network analyzer and converted into a complex dielectric spectra with HP85070A software using the Nicolson-Ross method.27 For each sample, 15 dielectric spectra were sequentially obtained every 10 s at 20.0 ( 0.01 °C and then averaged.
Figure 2. Cole-Cole plots of horseradish peroxidase (HRP) solution (0) and water (9). The terms q*, fc, qs, q∞ are determined by Debye fitting eq 4. The symbol 2 represents fitting by ref 25.
distinguish from the loosely bound hydration shell having the relaxation frequency fc, which amount is given by eq 8. The terms a0 and ap0 are the static dielectric constants of solvent and solution, respectively. The term a∞ is the a′ at high frequency limit, we set a∞ ) 5.6. Figure 2 shows the typical Cole-Cole plots of ap* of a protein solution (peroxidase 35.8 mg/mL). Triangles are calculated by a single Debye fitting to the experimental points (rectangles) to obtain ap0 according to ref 25. The density of the hydration shell, Fhyd, was treated as equal to that of bulk water, which is 1 g/mL since the calculation of sv is based on the two component model consisting of solute and bulk water. Here, Fhyd does not mean the real density of the hydration shell. The real density of the tightly bound water shell is known to be larger than 1 g/mL, according to the crystallographic size of the proteins.26 Estimation of the Number of Water Molecules Accessible to Protein Surface. We first calculated the solvent-accessible surface area (ASA) for hydrophobic carbons (not bonded O, N, or S) on the surface of each protein. The division of the ASA by the occupied area of a water molecule (0.09 nm2 calculated from the radius of 0.14 nm and spacing) provides an estimation of the number of water molecules that are restrained around apolar moieties. We also counted the number of surfaceexposed charged or polar atoms with ASA > 0.08 nm2. We calculated the number of water molecules accessing to polar atoms as Nscal, which is the total accessible surface area of polar atoms divided by 0.28 nm2, considering the direction of hydrogen bond of the sp3 orbitals of oxygen and nitrogens.18 3. Experiments We examined catalase (Mw 240 000, bovine liver, Wako), chymotrypsinogen-A (Mw 25 000, bovin pancreas, Wako), cytochrome c (Mw 12 327, bovine heart, Sigma), hemoglobin (Mw 68 000, bovine, Sigma), horseradish peroxidase (Mw 44 000, horseradish, Wako), lysozyme (Mw 14 300, egg white, Wako), myoglobin (Mw 18 700, horse skeletal muscle, Sigma), ovalbumin (Mw 46 000, chicken egg, Sigma), albumin bovine serum (BSA, Mw 66 000, Wako). Proteins are dissolved in pure water and dialyzed for a day with pure water (by milli-Q, 18 MΩ). The protein concentration was measured using a dry-weight method, where the protein solutions were dried in a vacuum
4. Improvement of Signal-to-Noise Ratio The microwave network analyzer has specific drift properties. The baseline drifts at each frequency synchronized with each other. They changed gradually and suddenly at times. So we tried to reduce the noise of the instrument by using the following method. (1) Measurements were made in a thermoregulated room (20.0 ( 2 °C). (2) Equipment used included an airblower of 20.0 ( 2 °C to stabilize the inner temperature of the microwave generator at a temperature below 35 °C. (3) A thermostatic glass cell at 20.0 ( 0.01 °C was used. (4) The procedure of measurement was as follows: (i) standard deviations σ of the baseline drift at each frequency f were measured over 150 min before the protein measurement; (ii) for each protein, five solutions of different concentrations (c/cmax ) 0.2(S1), 0.4(S2), 0.6(S3), 0.8(S4), 1.0(S5)), were prepared. (iii) to reduce the slow baseline drift, the measurements were made with the sequence W1-S1a-S1b-W2-S2a-S2b-W3-S3aS3b-W4...W6 (where W is pure water); the difference spectrum for each concentration was obtained by S1a - W1, S1b - W2, S2a - W2, S2b - W3, ..., S5b - W6; (iv) the condition to exclude the effect of sudden drifts. In the test measurements we observed once or twice an instrumental sudden drift of the baseline over 150 min, which was typically required for one protein measurement. The magnitude of the sudden drifts is about five times larger than that of the ordinary drifts. Therefore, the reproducibility can be much improved after appropriate exclusion of sudden drifts. We adopted the following method. Between 2 and 10 GHz (18 frequency points), we obtained the mode spectrum (Xm) which is the most frequent spectrum among the 10 measured spectra for each protein. A few spectra, which were clearly apart from the others, were excluded in the calculation of the average Xm and the standard deviation σm. If one spectrum is deviated from Xm more than 3σm, we excluded the spectrum regarding it as affected by a sudden drift. 5. Result Figure 1a shows a dielectric spectrum of peroxidase 35.8 mg/ mL solution. The real part ap′ of ap* of the protein solution is slightly lower than a′. It is due to the low polarizability of hydrated protein compared to that of bulk water. Since the two curves are very close to each other, we present the difference spectra of protein solutions obtained by ∆ap′ ) ap′ - a′, ∆ap′′ ) ap′′ - a′′. Using ap* and a* in eq 1, we obtained q* as shown in Figure 1c. Here, q′ shows a simple relaxation of
Hydration Study of Globular Proteins
J. Phys. Chem. B, Vol. 105, No. 50, 2001 12625
Figure 3. Volume fraction of hydrated proteins in pure water. φ was obtained by eqs 1-4 and φ1 by the method of Wei et al., respectively. Here, V is the volume fraction of protein in solution according to the partial specific volume. Solid lines and dashed lines are drawn to show the proportionality with the concentration. Abbreviations are explained in Table 1.
Debye type, whereas q′′ showed deviation from the Debye relaxation below 1GHz. One can approximate the q* as in the following function, taking into account the 1/f effect for example by ionic conduction at the protein surface: q* ) qm* + jσ/ 2πf. Then the coefficient σ was simply assumed to make qm′′ to be zero at the low frequency limit as shown in Figure 1c. The fluctuations of q* or qm* seen in the frequency range from 2.5 to 8 GHz are due to the mismatch of cable connection and were exaggerated by arithmetic treatment such as multiplication and division between two fluctuating data. The actual fluctuation size is seen in Figure 1b, which was used in the present fitting treatment. In Figure 2 we show the Cole-Cole plots of ap* (protein (HRP) solution, open rectangles), a* (solvent: water,
filled rectangles), q* (solute: hydrated protein, filled circles) with the relaxation frequency fc, qs and q∞ for peroxidase (35.8 mg/mL). Triangles are calculated by using a single Debye fitting to the experimental points (rectangles) to obtain ap0. The results of catalase (CAT), chymotrypsinogen A(CA), cytochrome c (Cc), hemoglobin (Hb), peroxidase (HRP), lysozyme (Lyz), myoglobin (Mb), ovalbumin (Ov), and bovine serum albumin (BSA) are shown in Figure 3 where φ (volume fraction of protein with a full hydration shell), φ1 (volume fraction of protein with a tightly bound hydration shell), and V (volume fraction of bare protein) were proportional to the protein concentration. It indicates a monodispersion feature of proteins in water under the tested condition. In our analysis, the single
12626 J. Phys. Chem. B, Vol. 105, No. 50, 2001
Yokoyama et al.
TABLE 1: Results of Protein Hydration by Dielectric Measurement experimental data proteina Cc
CA Hb
HRP
Mb Lys
Ov
BSA CATg
conc (mg/mL)
Ntotal
6 12 18 22 29 8 32 38 8 16 24 38 14 21 28 35 6 12 25 7 13 28 34 8 15 21 29 36 32 13
259 213 208 243 207 655 643 657 2138 2258 1959 2145 657 653 657 796 397 402 364 474 460 429 426 846 902 1030 1051 1117 1422 5533
Ntotal - ave (1/protein)
calculation data
c
SD
221
18
651
7
2114
105
706
67
379
19
436
16
1033
86
Nsb 269 129 75 74 45 559 216 174 1682 1241 870 889 348 227 170 216 490 276 150 333 199 117 98 735 451 407 311 354 489 3031
SD1 (1/protein)
Ns - ave2*d
SD2*d
fc (GHz)
Ntotalcalf (1/protein)
Nscalf (1/protein)
86
57
72
27
5.1(0.4
345
110
229
110
193
21
5.8(0.9
577
214
1025
255
955
145
6.5(0.4
1375
437
224
55
224
55
4.5(0.1
731
255
233
117
191
59
4.6(0.1
458
159
140
67
122
36
7.2(0.4
333
155
394
107
367
48
5.7(0.4
891
285
1686 2361
544 874
Ns - ave1c
e
5.5 5.2
a
Cc, cytochrome c; CA, chymotrypsinogen-A; Hb, hemoglobin; HRP, horseradish peroxidase; Mb, myoglobin; Lyz, lysozyme; Ov, ovalbumin; BSA, albumin, bovine berum; CAT, catalase. b Ns, number of water molecule tightly bound per protein molecule. c Ns - ave1, SD1 are average and standard deviation of tightly bound water. d Ns - ave2*, SD2* are average and standard deviation of strongly bound water excluding data for low concentrations below 10 mg/mL. e fc, relaxation frequency of hydrated proteins (mean(SD); Ntotal, number of total bound water molecules per protein molecule. f Ntotalcal, Nscal are calculation numbers for Ntotal and Ns, respectively. g CAT was tetramer in experiment and dimer in calculation.
Debye fitting by eq 4 was made in the frequency range from 2 to 10 GHz to cover the minimum of ∆′ around 8 GHz. It has become possible to detect loosely bound water more precisely than in the previous work. Using eqs 5 and 6, we obtained Ntotal and Ns. Table 1 shows results obtained from the experiment: Ns, Ntotal, relaxation frequency fc, and Nscal, Ntotalcal from calculations based on threedimensional protein structures. The accessible surface areas (ASA) of polar atoms (N, O) and apolar atoms (-CHx-) exposed on a protein molecule were calculated with a water radius of 0.14 nm. Nscal was calculated by dividing (polar ASA) by 0.28 nm2. Nwcal was calculated by dividing (apolar ASA) by 0.09 nm2. Then Ntotalcal ) Nscal + Nwcal. The protein database files used are the following (in all cases water molecules were excluded). (i) 8CAT for catalase: Calculation was made on 8CAT (dimer), while tetramer was used in the experiment. (ii) 2CGA for chymotrypsinogen A: Calculation was made on monomer after dividing the dimer code into monomer. (iii) 1CCR for cytochrome c: 1CCR is from bovine heart, while horse heart protein was used in the experiment. (iv) 1HDA for hemoglobin: 1HDA from bovine blood. (v) 7ATJ for peroxidase: monomer. (vi) 132L for lysozyme: DML was excluded in the calculation. (vii) 1AZI for myoglobin: AZI and SO4 were excluded in the calculation. (viii) 1OVA for ovalbumin: Calculation was made on a monomer after division of 1OVA (tetramer) into monomer. (ix) 1AO6 for bovine serum albumin: only as a reference. (x) 1AO6 of human serum albumin (dimer) was used in the calculation since BSA was not available in the protein database. As shown in Table 1, SD of Ns is larger than SD of Ntotal. Ns is very sensitive to the drift, specially below a concentration of
10 mg/mL. One may find that values of SD2 are much smaller than SD1, as shown in Table 1. So, we had to measure the spectra above 10 mg/mL to investigate the features of protein hydration more precisely. The standard deviations of measured ∆′ above 10 GHz increased twice as much as compared to the range below it. As a result, the total bound water numbers Ntotal - ave were twice to three times that of the tightly bound water numbers Ns - ave2. These values were close to the estimated values from 3D structures with a monolayer hydration shell model. The relaxation frequencies fc of the loosely bound hydration shell of tested proteins were found in the range from 5 to 6 GHz. This frequency was close to that found in the hydrophobic hydration shell.16 The experimental values of Nw () Ntotal - ave - Ns - ave2) were close to Nwcal () Ntotalcal - Nscal). Therefore, the number of loosely bound water on a protein molecule was close to the number of water accessible to the hydrophobic surface of a protein molecule. The number of tightly bound water was close to the number of water accessible to polar atoms on the surface of protein. 6. Discussion The calculated numbers Nscal and Ntotalcal agreed with the experimental values fairly well. This suggests that the hydration shell of protein is mainly a monolayer of water molecules that is accessible to the protein surface. Generally speaking, water molecules surrounding polar moieties of protein molecule are restrained by the electrostatic field of polar atoms. Water molecules in the vicinity of apolar moieties become structurized28 and have lower mobility8 than those of bulk water having fc ) 17 GHz.
Hydration Study of Globular Proteins As those hydration water molecules have a different polarizability from bulk water, we could derive the hydration shell property from the dielectric spectra based on the mixture theory. It assumed that protein solution can be represented with a twocomponent model consisting of spherical solutes and pure solvent. When applying the Wagner equation for the estimate of hydration number, we adopted a Debye fitting on q* in the frequency range of 2-10 GHz. If the fitting range was shifted to 5-17 GHz, the estimated hydration number increased by 50%. If all of bulk water are restrained by solutes the hydration number should increase about 100 times, since the fc of bulk water is 17 GHz. Therefore, it indicates that the boundary between the hydration shell and bulk water is rather clear, in other words, the boundary layer thickness is smaller than one water layer. So the thickness of hydration shell is close to one layer and obviously less than two layers of water. In the present method, additional polarization, if any, such as by the polar side groups of amino acid residues located at the protein surface, could cause underestimation of the hydration number, because additional polarization should raise the dielectric constant ′ and decrease the amplitude of ∆′. At this moment we do not have sufficient information about this. It remains to future works. In this study we characterized the hydration layer based on the orientational mobility of water. A tightly bound water layer has the relaxation frequency fc lower than 0.1 GHz, and a loosely bound water layer has higher fc than 4 GHz but clearly separated from bulk water. The previous paper16 showed that hydrophobic chains such as methylene groups have hydration shells with fc of 4-5 GHz and the number of loosely bound water is about 3 per -CH2-. Therefore, the majority of loosely bound waters of protein are considered to be of hydrophobic hydration, and tightly bound water is on polar atoms. Recent study with the low-temperature X-ray crystallography by Nakasako29 showed the bound water structure of trypsin, where the hydration number of trypsin decreased with the packing density. It suggests that the additional bound water, obtained by lowering packing density, corresponds to loosely bound water on the protein. Considering his result, the rest of loosely bound water is probably located in the secondary hydration layer of polar atoms. Acknowledgment. One of the authors (M.S.) would like to thank Prof. Kodama, Prof. Yagihara, and Prof. Takashima for meaningful discussions. The authors thank Monbusho for the grant #11167203 and CIRTU for providing the research environment.
J. Phys. Chem. B, Vol. 105, No. 50, 2001 12627 References and Notes (1) Eisenberg, D.; McLachlan, A. D. Nature 1986, 319, 199-203. (2) Griko, Yu. V.; Privalov, P. L.; Venyaminov, S. Yu. J. Mol. Biol. 1988, 22, 127-138. (3) Gregory, R. B. Protein-SolVent Interactions; Marcel Dekker: New York, 1995. (4) Bull, H. B.; Breese, K. Arch. Biochem. Biophys. 1968, 128, 488. (5) Subramanian, S.; Fisher, H. F. Biopolymer 1972, 11, 1305. (6) Bull, H. B.; Breese, K. Arch. Biochem. Biophys. 1970, 137, 299. (7) Kubinek, M. G.; Wemmer, D. E. Curr. Opin. Struct. Biol. 1992, 2, 828. Pessen, H.; Kumosinski, T. F. Methods Enzymol. 1985, 117, 219. (8) Halle, B.; Anderson, T.; Forsen, S.; Lindman, B. J. Am. Chem. Soc. 1981, 103, 500. Ishimura, M.; Uedaira, H. Bull. Chem. Soc. Jpn. 1990, 63, 1. (9) Otting, G.; Wuthrich, K. J. Am. Chem. Soc. 1989, 111, 1871. Gerothanassis, I. P. Prog. Nucl. Magn. Reson. Spectrosc. 1994, 26, 171. Otting, G.; Liepinsh, E.; Wuthrich, K. Science 1991, 254, 974. (10) Takashima, S. Electrical properties of biopolymers and membranes; Adam Hilger: Philadelphia. 1989. (11) Grant, E. H.; Sheppard, R. J.; South, G. P. Dielectric behaVior of biological molecules in solution; Oxford University Press: New York, 1978. (12) Miura, N.; Asaka, N.; Shinyashiki, N. Biopolymers 1994, 34, 357364. (13) Mashimo, S.; Ota, T.; Shinyashiki, N.; Tanaka, S.; Yagihara, S. Macromolecules 1989, 22, 1285-1288. (14) Schlecht, P.; Mayer, A.; Hettner, B.; Vogel, H. Biopolymers 1969, 7, 963-974. (15) Pennock, B. E.; Schwan, H. P. J. Phys. Chem. 1969, 73, 26002610. (16) Suzuki, M.; Shigematsu, J.; Fukunishi, Y.; Kodama, T. J. Phys. Chem. B 1997, 101, 3839-3845. (17) Suzuki, M.; Shigematsu, J.; Kodama, T. J. Phys. Chem. 1996, 100, 7279-7282. (18) Suzuki, M.; Shigematsu, J.; Fukunishi, Y.; Harada, Y.; Yanagida, T.; Kodama, T. Biophys. J. 1997, 72, 18-23. (19) Kaatze, U. J. Chem. Eng. Data 1989, 34, 371. (20) Wagner, K. W. Arch. Electrotech. 1914, 2, 371. (21) Hanai, T. Kolloid-Z. 1960, 171, 23-31. (22) Zhang, H. Z.; Sekine, K.; Hanai, T.; Koizumi, N. Colloid Polymer Sci. 1983, 261, 381. (23) Gekko, K.; Noguchi, H. J. Phys. Chem. 1979, 83, 2706. (24) Pethig, R. Dielectric and Electronic Properties of Biological Materials; John Wiley & Sons: New York, 1979. (25) Wei, Y. Z.; Kumbharkhane, A. C.; Sadeghi, M.; Sage, J. T.; Tian, W. D.; Champion, P. M.; Sridhar, S.; McDonald, M. J. J. Phys. Chem. 1994, 98, 6644. (26) Millero, F. J.; Surdo, A. L.; Shin, C. J. Phys. Chem. 1978, 82, 784. (27) Misra, D. IEEE Trans. MTT, 1987, 35, 925. (28) Tanford, C. The hydrophobic effect; Wiley: New York. 1980; Chapter 13. (29) Nakasako, M. J. Mol. Biol. 1999, 289, 547-564.
