BERNARD E. PENNOCK AND HERMAN P. SCHWAN
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Further Observations on the Electrical Properties of Hemoglobin-Bound Water by Bernard E. Pennockl and Herman P. Schwan Electromedical Division, The Moore School of Electrical Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 1010.4 (Received November 21, 1968)
Solutions of horse hemoglobin of varying concentrations (7.5-26.6 g of Hb/100 cc) were prepared from crystallized Hb. Measurements of the complex dielectric constant of these solutions were made in the frequency range of 1-1200 MHz. This dielectric behavior is described in terms of the dipolar nature of the molecule, the dipolar nature of side chains extending out from the surface, and by a relaxation of a shell of water bound to the surface. The amount of bound water leading to the most reasonable dielectric behavior is 0.2 0.05 g/g of Hb. This bound water is characterized by a change of enthalpy of abou t7 kcal/mol and a characteristic frequency of 500-1000 MHz.
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Introduction The purpose of this paper is to relate the measured values of the complex dielectric constant of the globular protein, hemoglobin, in solution, to certain structural features of the hemoglobin molecule (namely, water bound to the surface and polar side chains extending out from the surface). This paper is an extension of the paper by SchwanS2 History of Protein Measurements Oncley3 measured the dielectric dispersions of hemoglobin, albumin, and other protein solutions. The hemoglobin dispersion was described by a characteristic frequency near 2 MHz. Oncley attributed this dispersion to the polar nature of the protein molecule and interpreted the characteristic frequency in terms of an ellipsoidal molecular shape. The highest frequency of measurement used by Oncley was 20 MHz. Subsequently, Haggis, et uL14measured the dielectric constant of the protein, serum albumin, in solution at frequencies above 3 GHz. He found that the dielectric constant of the solution was lower than that predicted from an extrapolation of the dispersion studied by Oncley . Buchanan, et uLJ5measured the dielectric constant of six other proteins at frequencies above 3 GHz. They found a discrepancy with the prediction of Oncley similar to that noted by Haggis. Both of these investigators [Haggis and Buchanan) interpreted the lowering of the solution’s dielectric constant in terms of a shell of water bound to the surface of the protein. They reasoned as follows. The dielectric constant of naturally occurring water is completely described by a dispersion with a characteristic frequency of about 20 GHz, a low-frequency dielectric constant, BO, of about 80, and a high-frequency dielectric constant, E,, of near 5. The protein molecule has a constant dielectric constant of about 2.5 at The Journal of Physical Chemistry
frequencies above 20 M H z . ~ Thus, at frequencies between 20 MHz and about 5 GHz a mixture of water (e N 80) and protein (e = 2.5) will have a dielectric constant between 2.5 and 80, the exact value depending on the volume of each component and the mixture equation (see Appendix). Haggis and Buchanan derived a mixture equation for the protein in water, calculated the volume fraction of protein from the dry weight and known specific volume, and found that t,he calculated mixture dielectric constant was higher than their measured value. They attributed the discrepancy to the calculated molecular volume fraction and corrected it by assuming that a layer of water was bound to the protein surface making the protein volume appear larger than previously assumed. (The “bound water” was assumed to have a dielectric constant of about 5 in the frequency range of interest (>3 GHz).) Schwan7 discussed the critical dependence of the hydration value calculated by Haggis and Buchanan on the assumed dielectric constant of the water shell and protein arid thus the resultant difficulty in obtaining hydration values from microwave measurements. Schwan and Li8 and Schwan7 have observed an (1) Woman’s Medical College, Philadelphia, Pa. 19129. (2) H. P. Schwan, Ann. N . Y . Acad. Sci., 125,344 (1965). (3) J. L. Oncley, “Proteins, Amino Acids, and Peptides,” Reinhold Publishing Co., New York, N. Y.,1943. (4) G. H.Haggis, T. J. Buchanan, and J. B. Hasted, Nature, 167, 607 (1951). (5) T.J. Buchanan, G. H. Haggis, J. B. Hasted, and B. G. Robinson, Proc. Roy. SOC.,A213,379 (1952). (6) S. Takashima and H. P. Schwan, J . Phys. Chem., 69, 4176 (1965). (7) H.P. Schwan, “Electrical Properties of Tissue and Cell Suspensions” in “Advances in Biological and Medical Physics,” Vol. V,
C. A. Tobias and J. H. Lawrence, Ed., Academic Press, New York, N. Y.,1957,p 61. (8) H. P. Schwan and K. Li, Proceedings of the First National Biophysics Conference, Columbus, Ohio, 1957 (Pub. 1959),p 355.
ELECTRICAL PROPERTIES OF HEMOGLOBIN-BOUND WATER additional dielectric dispersion of hemoglobin solutions in the frequency range of 10 to 1000 MHz. This dispersion was attributed to the rotation of polar subunits or to the relaxation of a shell of water bound to the hemoglobin. Schwan2 again considered the dielectric dispersion of hemoglobin solutions and cited reasons for preference of the interpretation of the results in terms of the bound water shell. Grant9 suggested that part of the reason for the discrepancy between the values obtained by extrapolating the microwave and radiofrequency (rf) measurements was due to the choice of a single relaxation time for the former dispersion. By measurements on egg albumen (the only protein common to the investigations of both Oncley and Buchanan, et al.) the existence of a subsidiary dispersion at hundreds of MHz was revealed,'O thus supporting Schwan's conclusion for hemoglobin. Further work on serum albumen showed a similar dispersion" with a characteristic frequency near 500 MHz. This dispersion was interpreted in terms of the bound water shell. Purpose The dielectric dispersion observed by Schwan, with hemoglobin, and by Grant, with the albumins, might be attributed to (1) the surface charges which develop as a result of the presence of a mixture of several substances (electrolyte, bound water, protein) of different complex dielectric constant (Maxwell-Wagner dispersion) ; (2) a frequency dependence of ep*, the complex dielectric constant of the protein, in the frequency range of interest (10 MHz-1 GHz), probably as a result of the presence of polar side chains on the surface of the protein or a spread of time constants of the rf dispersion first studied by O n ~ l e y ; ~ (3) a frequency variation of q,*, the complex dielectric constant of the bound water shell. This dispersion would bc analogous to the dispersion of ice at lower frequencies and of water at higher frequencies. An attempt will be made to determine the relative contribution of these effects to the observed dielectric relaxation behavior. The measured dielectric conscant will be compared with that expected from a reference model consisting of unhydrated hemoglobin molecules (e, = 2.5) in an electrolyte (ew N 80) using the Maxwell mixture equation (eq 4). A dielectric increase (measured E > expected e) is to be expected from a polar relaxation (item 2 above) and a dielectric decrease (measured E < expected E ) may be expected to result from the presence of a shell of hound water (item 3 above) if it is assumed that the dielectric constant of the bound water is smaller than that of free water. Precise measurements of the dielectric constant of solutions of hemoglobin shall be reported indicating that the former result] occurs at frequencies below 100-500 MHz. We shall then adopt a model consisting of hydrated hemoglobin molecules in an electrolyte and calculate the
2601 complex dielectric constant of the bound water shell. The temperature dependence of the characteristic frequency of its dispersion will be used to calculate the energies associated with the bound water's relaxational behavior. Materials and Method Horse hemoglobin was crystallized out of solution by slowly introducing ethyl alcohol.l* The crystals were resuspended in dilute KOH solution and crystallized a second time. The solution of these crystals in dilute KOH (pH
