J. Phys. Chem. 1996, 100, 7279-7282
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Hydration Study of Proteins in Solution by Microwave Dielectric Analysis Makoto Suzuki,*,† Junji Shigematsu,‡ and Takao Kodama‡ National Institute for AdVanced Interdisciplinary Research/Mechanical Engineering Laboratory, AIST, 1-1-4 Higashi, Tsukuba City, Ibaraki 305, Japan, and Kyushu Institute of Technology at Iizuka, Fukuoka 820, Japan ReceiVed: NoVember 10, 1995; In Final Form: February 5, 1996X
We propose a method for evaluating protein hydration which enables one to evaluate the amount of restrained water and distinguish between “weakly” and “strongly” restrained water on proteins in an aqueous solution using microwave dielectric measurement. Measurements were taken with a precision microwave network analyzer and a thermostated glass cell at 20.0 ( 0.01 °C with an open-end flat-surface coaxial probe. Examined proteins were cytochrome c, myoglobin, ovalbumin, bovine serum albumin, and hemoglobin. The present method is based on the Wagner equation and the Hanai equation for emulsion analysis and assumes that there is “weakly” restrained water on proteins which has a simple Debye-type relaxation in the gigahertz region and that the dielectric constants of hydrated solutes at high-frequency limits are given by the electron polarizations of atom groups. This analysis enabled us to characterize more precisely the hydration state of proteins in water.
1. Introduction Protein hydration has long been studied by various methods such as calorimetry,1 infrared spectroscopy,2 osmotic pressure analysis,3 dielectric spectroscopy,4 and NMR techniques5 by 17O relaxation measurement6 or chemical shift analysis.7 Among these methods, dielectric spectroscopy offers a unique advantage in analyzing protein aqueous solutions since it is able to analyze dynamic behavior of molecular dipole orientation in a solution. General overviews can be seen in some books.8 Although hydration measurements by dielectric analysis have been rather model-dependent in many cases, Wei et al.9 have shown a unique, reliable method of hydration measurement based on the Wagner equation10 and density measurement. Assuming only a spherical shape for hydrated proteins and a single Debye relaxation of the dielectric spectrum of a sample solution, they evaluated the dielectric excluded volume of hydrated proteins in the solution. On the other hand, there are several reports on hydration of some hydrophobic amino acids, which showed high frequency relaxation at several gigahertz. This may be attributed to the restrained water on hydrophobic groups, although it is not clear.11 When adopting the dielectric excluded volume given by Wei et al.’s method, the dielectric constants of the hydrated solutes at the high-frequency limit often become negative according to the Wagner equation. This means that the method might neglect “weakly” restrained water which has a relaxation frequency higher than sub-gigahertz. For the sake of argument, let us refer to “strongly” restrained water as having relaxation frequencies lower than 107 Hz and “weakly” restrained water as having frequencies that are higher than that. This frequency was derived as a boundary by referring to previous works on dielectric measurement4 and NMR.5 We have tried to develop a method to analyze the hydration states of protein, which takes into account most types of restrained water and distinguishes between “strongly” and “weakly” restrained water on protein. 2. Method of Analysis We assumed that (1) proteins in solution are spherical and have spherical hydration shells, (2) solvents other than hydrated * To whom correspondence should be addressed. † National Institute for Advanced Interdisciplinary Research. ‡ Kyushu Institute of Technology at Iizuka. X Abstract published in AdVance ACS Abstracts, April 1, 1996.
0022-3654/96/20100-7279$12.00/0
solutes have the same dielectric properties as those of pure solvents, (3) the dielectric constant of solute (protein) is constant, here we used 2.5 based on the electronic polarization of atom groups8), (4) the dielectric constant of the hydration shell at the high-frequency limit is 5.6, the same as that of pure water,12 and (5) “weakly” restrained hydration shells have a dielectric relaxation of a single Debye-type in the gigahertz region. The last assumption, 5, is for the simplest case in which there is “weakly” restrained water on proteins. The apparent complex dielectric constant ap* of the emulsion is expressed with the dielectric constant of solvent a* and that of dispersed spheres q* as
2(1 - φ)a* + (1 + 2φ)q*
ap* ) a*
(2 + φ)a* + (1 - φ)q*
( )
ap* - q* a* a* - q* ap*
1/3
(Wagner equation10 for φ , 1) (1) )1-φ (Hanai equation13 for 0 < φ < 1) (2)
where φ is the volume fraction of the solute. The Hanai equation gives precise results for high-concentration emulsions, although it is more time-consuming for the analysis than the Wagner equation, which was used here for φ < 0.1. When the solute is a shelled sphere q*, it is again expressed with the dielectric constant of the hydration shell h* and that of the core(protein) p*.14
2(1 - φp)h* + (1 + 2φp)p*
q* ) h*
(2 + φp)h* + (1 - φp)p*
(for 0 < φp < 1) (3)
where φp ) V/φ. V is the volume fraction of protein in solution calculated by cMwsv/1000. c, Mw, and sv are the concentrations of protein in moles/liter, the molecular weight in grams, and the partial specific volume of protein in liters/kilogram, respectively. sv’s were given in a previous work.17 This equation is used to obtain q∞, the high-frequency limit (f f ∞) of q*, where h* ) h∞ ) 5.6 and p* ) p∞ ) 2.5 were used for f f ∞ by the assumptions 3 and 4. We set q∞ ) 3.5. © 1996 American Chemical Society
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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 eq 1 or 2. Secondly, the obtained q* was fitted by a single Debye relaxation function in the high frequency range of 2-8 GHz,
q* ≈ q∞ +
qs - q∞ 1 + j(f/fc)
(4)
Thirdly, φ was iteratively adjusted in eqs 1-3 until q∞ in eq 4 agreed with the value obtained by eq 3. Thus, we obtained φ, fc, and qs. The number of restrained water molecules per protein molecule Ntotal was then calculated as follows.
Ntotal )
55.6(φ - V)Fhyd c
Fhyd ≡ {(φ - φ1)Fhw + (φ1 - V)Fhs}/(φ - V) Nw )
55.6(φ - φ1)Fhw c
Ns ) Ntotal - Nw )
55.6(φ1 - V)Fhs c
(5) (6) (7)
(8)
where φ1 is the volume fraction of protein with the “strongly” restrained water shell, which is Wei et al.’s dielectric excluded volume fraction, Fhs is the density of the “strongly” restrained hydration shell, and Fhw is the density of hydration shells “weakly” restrained. Fhs is 1 g/cm3 whenever we use sv’s to calculate V by its definition. Wei et al. suggested that the real density of the “strongly” restrained water shell is larger than 1 g/cm3 according to their discussions based on the crystallographic size of the proteins. Similarly Fhw is 1 g/cm3. φ1 was obtained from the low-frequency limit of the fitting curve of a single Debye relaxation function to ap*. It is worth noting that the first four assumptions are essentially the same as those of Wei et al.’s method. The main difference is the frequency adopted in the fourth assumption. Wei et al. adopted it at a frequency lower than 107 Hz, while we did it at a frequency higher than 10 GHz. 3. Sample Preparation We examined cytochrome c(Cc, Mw 12 500, horse heart), myoglobin (Mb, Mw 17 800, whale), ovalbumin (Ov, Mw 45 000), bovine serum albumin (BSA, Mw 66 000), and hemoglobin (Hb, Mw 65 000, bovine). These proteins were purchased from Wako Pure Chemical Ind., Ltd., and dialyzed for a day against pure water (by milli-Q, 18 MΩ) or against a buffer solution A containing 20 mM KCl and 10 mM MOPS (pH ) 7.0). Buffer A was used to obtain physiological pH. The concentrations of these protein solutions were determined with absorbance coefficients15 1mg/mL280nm ) 0.63 for BSA, 1mg/mL280nm ) 1.93 for Mb, and 1mg/mL526.5nm ) 0.88 cm-1 for Cc16 and by the Biuret method for Ov calibrated by the intensity ratio of 115% relative to BSA and for Hb calibrated by protein weight dried at 105 °C for 5 h after being sufficiently dialyzed in pure water, respectively. 4. Experiment The dielectric spectra were obtained with a microwave network analyzer, Hewlett Packard 8720C, and an open-end flatsurface coaxial probe. To avoid accumulation of microbubbles, the probe was fixed upward in a glass cell controlled at 20.0 ( 0.01 °C by a Neslab thermobath. The cell was a cylinder with
Figure 1. Dielectric spectra of BSA solution at 20.0 ( 0.01 °C. dw, Buffer, and the numbers after BSA indicate distilled water, buffer A, and BSA concentrations in mg/mL in buffer A, respectively.
a conical top for a stirrer space, with dimensions of 33 mm in inner diameter, 30 mm in maximum height, and 20 mL in volume. The solution temperature was monitored with a platinum-resistor thermosensor by the four-terminal method. The cell was filled with a sample solution degassed under reduced pressure. Microwaves in the frequency range from 0.2 to 20 GHz were introduced to the cell through the probe. The calibration was done by a procedure that was open termination in air and short termination with mercury and soaking in pure water at 20.0 ( 0.01 °C. The reflected waves were sampled by a network analyzer and converted to complex dielectric spectra with HP85070A software using the Nicolson-Ross method.18 Since the oscillator of the network analyzer quickly loses its stability at high temperature (>53 °C), we kept the inside of the network analyzer below 50 °C by increasing air flow and suppressed the total drift of dielectric constant within 0.025 for 1-10 GHz and 0.015 for 2.5-8 GHz, which is 1 order of magnitude smaller than the usual case. Therefore, we used the dielectric spectra of frequency points from 2.5 to 8 GHz for the q* analysis. For each sample, 20 dielectric spectra of 51 frequency points were sequentially obtained every 10 s at 20.0 ( 0.01 °C and averaged. 5. Results We first examined the effect of buffer composition on the protein hydration for BSA solution. q* is independent of a* unless the solute molecule reacts on some of the buffer components. The BSA solution dialyzed against pure water was initially prepared at the concentration of 68 mg/mL (pH ) 5.0) and diluted with pure water sequentially to obtain 51, 34, and 17 mg/mL concentrations. BSA solutions dialyzed against buffer A were prepared at 43mg/ml and diluted with buffer A
Hydration Study of Proteins in Solution
J. Phys. Chem., Vol. 100, No. 17, 1996 7281
Figure 2. Cole-Cole plots of BSA solution. q* is the dielectric spectrum of the hydrated BSA obtained by eq 2. fc is the relaxation frequency of q*. q∞ and qs are obtained by Debye fitting (solid curve) using eq 4. Filled symbols show the points used for Debye fitting.
In the same way, solutions of Cc, Mb, Ov and Hb were then examined. Using eqs 5 and 8, we obtained Ns and Ntotal. Table 1 shows the results of Ntotal, Ns, relaxation frequency fc, and δ ) (qs - q∞) of hydrated protein. The relaxation frequency of the restrained water found in this study was in the range of 3-4 GHz. A large value of δ corresponds to a large amount of weakly restrained water according to eq 3. These values differed by proteins and indicate their hydration features. 6. Error Analysis
Figure 3. Volume fractions of hydrated BSA in different solutions. φ, φ1 were obtained by eqs 1-4 and by Wei et al.’s method,9 respectively. V is the volume fraction of protein in solution according to the partial specific volume.17 dw, A, and M indicate distilled water, buffer A, and buffer A with 5 mM MgCl2. Solid lines are the fitted ones for the dw case.
to obtain 34, 22, and 11 mg/mL concentrations. In the analysis, a*’s were independently obtained for pure water and buffer A. Figure 1 shows the dielectric spectra for different BSA concentrations. Figure 2 shows the typical Cole-Cole plot of the complex dielectric constant q* of hydrated BSA in buffer A fitted with the Hanai equation. In our analysis, Debye fittings were made in the frequency range 2.5-8 GHz since there were considerable effects of ionic conduction and unassigned relaxation at low frequencies below 1 GHz and because of the high S/N values. Figure 3 shows the volume fractions of φ, φ1, and V against the BSA concentration. Obviously, the volume fraction φ’s obtained by the present method were larger than the φ1’s given by Wei et al.’s method. We found that there is no significant difference between pure water and buffer A in the total hydration measured by the present method. Solid lines show the fitted lines to the cases of dw (distilled water). In addition, we examined another buffer, M, which contains 5 mM MgCl2 in buffer A. The effect of Mg2+ was not negligible, and it increased the total dielectric excluded volume of BSA by 3-5% compared to the cases of dw or buffer A.
The absolute error of the measured value Ntotal possibly resulted from the stability of the network analyzer, the accuracy of protein concentration, the accuracies of partial specific volume of protein molecules and q∞, the shape of the protein, and/or the plausibility of single Debye relaxation for “weakly” restrained water. The error of concentration is not negligible. Depending on the method of determining concentration, such as the dry weight method or UV absorbance method, the values deviated by 2-4%. Considering that the average amount of hydration was about 0.4 g/g protein, this discrepancy generates 7% ()(φ - 0.96V)/(φ - V) - 1) of the error of the volume of the hydration shell, Vhs. The values of partial specific volume reported in the literature16 were obtained in different solution compositions from ours. We estimate the error was below 3% from density measurements on BSA in buffer A with a density meter, Anton-Paar DMA-58 provided courtesy of Nihon SiberHegner Corp. It causes a 5.5% error of Vhs. q∞ has a maximum possible error of 0.5, which causes 4.5% error in Vhs according to the Wagner equation, which is independent of protein concentration. The single Debye fitting on q* may cause underestimation of Vhs because any relaxations higher than 10 GHz, if there were indeed any, were neglected. Therefore, we should say that in this study the measured amount of “weakly” restrained water corresponds to that of a hydration shell having a relaxation frequency of less than 10 GHz. The standard deviation of measured dielectric constants by the network analyzer was 0.025 from 1 to 10 GHz and 0.015 from 2.5 to 8 GHz. The error of average value for the 20 sequentially measured dielectric constants in this frequency range reduced to 0.0056. Applying this error to the Wagner equation, the error of the volume of hydration shell becomes 1.0% for 30 mg/mL protein solution and is inversely proportional to the protein concentration. However, the long time drift of the network
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TABLE 1: Results of Protein Hydration Measured by the Present Methoda protein
concentration range (mg/mL)
Ntotal (1/protein)
Ns (1/protein)
Wtotal (g/g protein)
Ws (g/g protein)
htotal (Å)
hs (Å)
fc (GHz)
δ
Cc(A) Mb(A) Ov(dw) Ov(A) Ov(M) BSA(dw) BSA(A) BSA(M) Hb(A)
15-65 14-56 12-49 14-60 15-58 17-68 11-43 14-61 17-66
290 ( 30 350 ( 40 870 ( 100 860 ( 95 840 ( 95 1300 ( 140 1260 ( 150 1410 ( 160 1260 ( 140
150 ( 60 150 ( 100 460 ( 190 360 ( 230 400 ( 200 630 ( 290 740 ( 260 900 ( 250 930 ( 190
0.42 ( 0.04 0.36 ( 0.04 0.35 ( 0.04 0.34 ( 0.04 0.34 ( 0.04 0.34 ( 0.04 0.34 ( 0.04 0.38 ( 0.04 0.35 ( 0.04
0.22 ( 0.09 0.21 ( 0.10 0.18 ( 0.08 0.14 ( 0.09 0.16 ( 0.08 0.17 ( 0.08 0.20 ( 0.07 0.24 ( 0.07 0.26 ( 0.05
2.5 2.4 3.2 3.2 3.1 3.8 3.7 4.0 3.6
1.4 1.1 1.8 1.4 1.6 1.9 2.3 2.7 2.8
4.3 ( 1 4.0 ( 0.5 3.0 ( 0.9 3.0 ( 0.5 4.0 ( 0.4 3.1 ( 0.4 3.0 ( 0.4 2.9 ( 0.4 4.0 ( 0.4
18 ( 1 18.3 ( 0.6 19.5 ( 1.1 19.5 ( 0.5 18.6 ( 0.6 16.8 ( 1.0 16.5 ( 0.7 16.5 ( 0.7 12.1 ( 0.4
a dw, distilled water; A, buffer A, which contains 20 mM KCl and 10 mM MOPS (pH ) 7.0). M, buffer M, which contains 20 mM KCl, 5 mM MgCl2, and 10 mM MOPS (pH ) 7.0). Cc, cytochrome c; Mb, myoglobin; Ov, ovalbumin; BSA, bovine serum albumin; Hb, hemoglobin; fc, relaxation frequency of hydrated protein; δ ) qs - q∞ in eq 4. Ntotal, number of total restrained water molecules per protein molecule by the present method; Ns, number of water restrained on a protein molecule obtained by Wei et al.’s method; Wtotal, the weight of total restrained water per protein weight calculated from Ntotal; Ws, the weight of restrained water per protein weight calculated from Ns; htotal and hs, the thickness of the hydration shells corresponding to Ntotal and Ns, respectively, assuming a spherical smooth surface for each protein. Here we must note that the solvent-accessible surface area of each protein is 2-3 times larger than the surface area of each smooth sphere model.
analyzer was 0.06 per hour in the average value. Since it took 30 min to exchange sample solutions, we should take into account the long time drift, which causes 10% error of Vhs. This is actually most dominant for the total absolute error of Vhs. Taken together, the total absolute error of Ntotal, Ert in %, becomes Ert ) (72 + 5.52 + 4.52 + 102)0.5 ) 14. Hence, Ntotal has 14% of the absolute error for a 30 mg/mL protein solution. For Ns, we estimated the error similarly to the above. The error of Ns becomes enlarged by the value Ntotal/Ns. It should be noted that when looking at the relative variation or the dynamic change of total hydration within 5 min, the error of Ntotal becomes 2.5% (simply by 10% × 0.015/0.06) only from the error of the network analyzer. 7. Conclusion We studied protein hydration by microwave dielectric measurement. By assuming a single Debye relaxation for the “weakly” restrained water on proteins and taking into account the high-frequency limit of the dielectric constant of the solute, we obtained the number of “weakly” restrained water molecules having a relaxation frequency of 3-4 GHz to distinguish them from a more strongly restrained one on a protein molecule in solution. Ns, Ntotal, the measured relaxation frequency, and δ reflect the features of protein hydration. Acknowledgment. The authors thank Prof. A. Minakata and Prof. K. Asami for their helpful discussions. They also thank Dr. T. Tateishi, the project director, for his support. This work was supported by AIST and STA.
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