THE SEMECQMQUC‘FWIW OF HEMOGLQEEN-AD‘SWA'EE WSTEMS like“: foe {Em Dawn :25. NM D. MICHIGAR STAR WWERSETY Elliot Pes‘cow 1968 (11”.: This is to certify that the thesis entitled THE SEMICONDUCTIVITY 0F HEMOGLOBIN- ADSORBATE SYSTEMS presented by Elliot Postow has been accepted towards fulfillment of the requirements for M degree inw$l DP“ YSiCxS 31M Pewxw Major professor ‘ Date &Q‘T Q‘6 J 199:2 0-169 LIBRARY Michigan State ' University ductor follow] conduc‘ I U0 is :I tempera h hemoglil temper: F with t; for set | the COR by the COnStax adsorpt and amz BET (Ty: Sults i: m0190u15 On the { ABSTRACT THE SEMICONDUCTIVITY OF HEMOGLOBIN- ADSORBATE SYSTEMS By Elliot Postow Hemoglobin may be operationally defined as a semicon- ductor because the temperature dependence of its conductivity follows the equation: 0 = exp(-E/2kT) where o is the Go conductivity, E is the activation energy for semiconduction, 00 is a constant, k is Boltzmann's constant and T is the temperature. As water, ethanol or methanol are adsorbed on hemoglobin the conductivity is found to increase but its temperature dependence is of the same form. Concomitant with the increased conductivity a decreased activation energy for semiconduction is found. The pre-exponential factor in the conductivity equation is observed to remain unchanged by the adsorption process. Measurements of the dielectric constant of hemoglobin demonstrate increases caused by the adsorption of water, ethanol or methanol. Adsorption isotherms of water, methanol, ethanol and ammonia adsorbed on hemoglobin are shown to be of the BET (Type II) form. Interpretation of the experimental re- sults in terms of BET theory indicates that the solvent molecules are adsorbed at the polar sites which are located on the exterior surface of the protein molecule. Elliot Postow The dependence of the activation energy on the quan- tity of vapor adsorbed and the independence of the pre- exponential factor from this quantity demonstrate that the adsorbant is not acting as an impurity in the classical sense of inorganic semiconductors. Adsorption-induced decreases in the activation energy are the result of increases in the polarization relaxation energy. The energy gained when the dielectric medium relaxes, after the creation of a new charge center, is dependent upon the dielectric constant of the medium. As the amount of vapor adsorbed increases the dielec- tric constant increases. This increases the dielectric re- laxation energy which decreases the semiconduction activation energy. Decreased activation energy results in increased conductivity. The observed conductivity of hemoglobin with adsorbed ammonia cannot be explained by the same theory. These results more closely resemble those of the classical impurity model of semiconductivity. However, the amount of ammonia adsorbed on the hemoglobin is much greater than the amount of dOpant commonly used in doped inorganic semiconductors. A possible enzymatic model utilizing semiconductive pr0perties of biomolecules is discussed. THE SEMICONDUCTIVITY OF HEMOGLOBIN- ADSORBATE SYSTEMS BY Elliot Postow A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Biophysics 1968 TO MY PARENTS ACKNOWLEDGMENTS I wish to express my graditude to Professor Barnett Rosenberg whose interest in and enthusiasm for this work has been a source of encouragement and inspiration. I wish to thank also Drs. D. W. Bonniface, R. G. Leffler and J. 0. Williams and Messrs. M. R. Powell and L. Su for many fruit- ful discussions. The financial assistance of the United States Atomic Energy Commission is gratefully acknowledged. iii TABLE OF CONTENTS ACKNOWLEDGMENTS O O O C O O O O O O O O O O C O C C 0 LIST OF TABLES. O O O O O C C O O C O O O O O O O O 0 LIST OF FIGURES O O O I O O O I O O O O O I O O O O 0 SECTION I. II. III. IV. INTRODUCTION. 0 O O O O O O O O O O O O O O O C Semiconductive Biological Materials . . . . . Parameters and Mechanisms of Conductivity . . Adsorption Isotherms. . . . . . . . . . . . . Hemoglobin. . . . . . . . . . . . . . . . . . THEORY. O O O O O O O O O O O O O O O O O O O 0 Biological Semiconductivity . . . . . . . . . Adsorption Isotherms. . . . . . . . . . . . . EXPERIMENTAL METHODS. . . . . . . . . . . . . . Sample Preparation Techniques . . . . . . . . Conductivity Measurements . . . . . . . . . . Dielectric Measurements . . . . . . . . . . . Adsorption Isotherm Measurements. . . . . . . EXPERIMENTAL RESULTS 0 D O O O C O O O O O O C O Conductivity Measurements . . . . . . . . . . Dielectric Studies. . . . . . . . . . . . . . Adsorption Measurements . . . . . . . . . . . DISCUSSION. 0 O O O O O O O O O I O O O O O O O Impurities in Biological Semiconductors . . . The Effect of Inter-granular Spaces on Conductivity. . . . . . . . . . . . . . . . The Pre-exponential Factor in Hemoglobin Conductivity. . . . . . . . . . . . . . . . Apparent Low Frequency Dielectric Dispersion. Comparison of Results with Dielectric Theory. iv Page iii vi vii l3 17 22 22 25 31 31 31 36 39 43 43 60 7O 87 87 92 93 95 98 Page Comparison of Quantum Calculations with Experimental Results. . . . . . . . . . . . . 106 Adsorption Studies. . . . . . . . . . . . . . . 109 VI. SOME THOUGHTS ON THE BIOLOGICAL RELEVANCE OF SOLID STATE SEMICONDUCTION. C O O O C O O O O O O 115 BIBLIOGRAPHY. O O O O O C O O O O O O O O O O C O O I O 123 Table 1. LIST OF TABLES Page Microwave Hall mobilities of hemoglobin and DNA. 0 O I O I O O O O O O O I O O O O O O O I 0 14 The equilibrium relative humidity over some saturated salt solutions. . . . . . . . . . . . 34 Vapor pressure of alcohols as a function of temperature. . . . . . . . . . . . . . . . . . . 35 Conductivity of hemoglobin with adsorbed water, methanol and ethanol. . . . . . . . . . . . . . 56 Dielectric constant and activation energy of hemoglobin with adsorbed water, methanol and ethanol. . . . . . . . . . . . . . . . . . . 69 BET parameters for water, methanol, ethanol and ammonia adsorbed on hemoglobin.. . . . . . . . . 72 a for water, methanol, ethanol and ammonia adsorbed on hemoglobin. . . . . . . . . . . . . 72 Heat of vaporization calculations for water, methanol, ethanol and ammonia adsorbed on hemoglObin. O O O I O O O O O O O O I O I I O O 112 Activation energies (l/2kT basis) calculated from Arrhenius plots of maximum turnover rates of enzymes showing configurational transitions. 119 vi 10. ll. 12. LIST OF FIGURES Band, hopping and tunneling models of semiconduction. . . . . . . . . . . . . . . . Six different isotherms descriptive of physical adsorption processes. . . . . . . . Schematic diagram of the apparatus used to measure conductivity and semiconduction acti- vation energy. . . . . . . . . . . . . . . . Schematic diagram of the capacitance bridge assembly. . . . . . . . . . . . . . . . . . . Schematic diagram of the vacuum micro- balance apparatus. . . . . . . . . . . . . . Ohm's law plot for hydrated hemoglobin. . . . Semiconduction activation energy of hemo- globin at several difference hydration States. . . . . C . . . . . . . . . . O . . . Variation of conductivity with semiconduction activation energy for hemoglobin at various hydration states. . . . . . . . . . . . . . . Semiconduction activation energy of hemo- globin in equilibrium with various partial pressures of methanol. . . . . . . . . . . . Variation of conductivity with semiconduction activation energy for hemoglobin with various quantities of adsorbed methanol. . . Semiconduction activation energy of hemo- globin in equilibrium with various partial pressures of ethanol. . . . . . . . . . . . . Variation of conductivity with semiconduction activation energy for hemoglobin with various quantities of adsorbed ethanol. . . . vii Page 15 33 38 41 44 46 47 49 51 53 55 Figure l3. l4. l6. l7. l8. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. mg Figure Page 13. Semiconduction activation energy of hemo- globin in equilibrium with various partial pressures of ammonia. . . . . . . . . . . . . . 58 14. Frequency dependence of the apparent dielec- tric constant of hemoglobin with various quantities of adsorbed water. . . . . . . . . . 61 15. Frequency dependence of the apparent dielec- tric constant of hydrated hemoglobin as determined by the contact method and by the air gap method. . . . . . . . . . . . . . . . . 64 16. Frequence depence of the capacitance of hydrated hemoglobin at very low frequencies. . 65 17. Frequency dependence of the capacitance of hydrated hemoglobin. . . . . . . . . . . . . . 68 18. Adsorption isotherm of water on hemoglobin at 24° C. O . . . . . . . . . . . . . . . . . . 73 19. Adsorption isotherm of methanol on hemo- glObin at 24° C. . . . . . . . . . . . . O . . 74 20. Adsorption isotherm of ethanol on hemo- glObj—n at 24° C. . . . . . . . . . . . . . . . 75 21. Adsorption isotherm of ammonia on hemo- glObj-n at 0° C. . . . . . . O . . . . . . . . . 76 22. BET curve of water adsorption on hemoglobin. . 77 23. BET curve of methanol adsorption on hemo- glObin. . . . . . . . . O . . O . . . . . . I O 78 24. BET curve of ethanol adsorption on hemo- glObin. . . . . . . . . . . . . . . . . I O O O 79 25. BET curve of ammonia adsorption on hemo- glObin. . . . . . . . . . . . . . . . . . O . O 80 26. Conductivity of hemoglobin as a function of water adsorbed. . . . . . . . . . . . . . . . . 81 27. Conductivity of hemoglobin as a function of methanol adsorbed. . . . . . . . . . . . . . . 82 28. Conductivity of hemoglobin as a function of ethanol adsorbed. . . . . . . . . . . . . . . . 83 viii Figure 29. 30. 31. 32. 33. 34. Figure Page 29. Conductivity of hemoglobin as a function of ammonia adsorbed. . . . . . . . . . . . . . . . 84 30. Conductivity of hemoglobin as a function of mole % adsorbate. . . . . . . . . . . . . . . . 85 31. A. Schematic diagram of classical impurity semiconductivity. B. Schematic diagram of semiconductivity found in hemoglobin-adsorbate systems. . . . . 89 32. Variation of conductivity with dielectric constant. . . . . . . . . . . . . . . . . . . . 101 33. Variation of activation energy with dielectric constant. . . . . . . . O . . . . . . . . . . . 103 34. Variation of dielectric constant with the adsorption of water on hemoqlobin. . . . . . . 105 35. Illustration of the semiconduction model of . enzyme activity. . . . . . . . . . . . . . . . 120 ix cepts 0 He pro; structu approac in prot Cal int in bioc impert whEre C Energy Tis t:- define: Old ark tors '1 Of COnc I . INTRODUCTION Semiconductive Biological Materials In 1941 Albert Szent-Gyorgi suggested that the con- cepts of solid state physics be applied to biological systems. He proposed the existence of conduction bands in protein structures. This interesting suggestion has since been approached from both theoretical and experimental directions in proteins as well as in several other substances of biologi- cal interest. The generality of solid state semiconduction in biochemical substances is now evident. The biological import of this prOperty, however, is still only hypothesis. Substances whose electrical conductivity follows: 0(T) = eXp(-E/2kT) (l) C1‘0 where o is the electrical conductivity; E is the activation energy for semiconduction; k is the Boltzmann constant; and T is the temperature in degrees Kelvin; are Operationally defined as semiconductors. This definition eliminates the old arbitrary distinction between semiconductors and insula- tors while maintaining the distinction between semiconductors and metals, which exhibit a negative temperature dependence of conductivity. ”mete tL repres comple A rece chemic which « measure activa1 3 eV. tors dc mechani tivity, general conduct of adSO biOCheyl the rest Charge ( tronic I lOnic n5 Employing the simple criterion of Equation (1), representatives of every class of biomolecules, and even complex organelles, have been shown to be semiconductors. A recent review by Gutmann and Lyons (1967) lists 116 bio- chemical substances, ranging from adenine to wool, upon which conductivity and semiconductivity activation energy measurements have been made. In all but three cases the activation energy for'semiconduction varies between 1 and 3 eV. The fact that all of these materials are semiconduc- tors does not, of course, suggest that the conductivity mechanism, or even that any of the parameters of conduc- tivity, are the same in all systems. An experimental generalization which does indicate a certain uniformity of conductivity mechanisms is the similar effect of a variety of adsorbants and complexing agents with several different biochemicals. This will be discussed below. Parameters and Mechanisms of Conductivity An electrical current is, in the most general case, the result of the movement of several different species of charge carriers. These charge carriers may be of an elec- tronic nature, either electrons or positive holes, or of an ionic nature, either positive or negative ions. In general, therefore, the conductivity is given by: = u 0 8(Zhnhuh + izini i) (2) where the summation over h includes both electrons and holes; semicon mobilit materia barge to the Carrier density therefo tration trOlei prOtOnS from io in the : Can, til t hrolgh the summation over i includes the several species of ions present in the substance; u is the mobility of the charge carrier indicated by its subscript; n is the density of the charge carrier indicated by its subscript; z is the valence of the apprOpriate ion; and e is the electronic charge. All species of charge carriers present in a substance contribute to its conductivity. An important problem in biological semiconductivity is the determination of the density and mobility of each species of charge carrier present in the material. Then the contributions of the several species of charge carrier to the total conductivity may be evaluated. It is seen from Equation (2) that the contribution to the total conductivity of a single species of charge carrier is determined by the product of the carrier species' density and mobility. Conductivity measurements cannot, therefore, distinguish between the contributions of concen- tration and mobility to the product. If the charge carriers are ionic in nature, elec- trolysis will occur at metal electrodes (which do not inject protons) where an electrode reaction is necessary to change from ionic carriers in the material to electronic carriers in the metal. Electronic carriers in the sample would not produce such an electrode reaction. Solid state electrolysis can, therefore, be used to distinguish between the two varie- ties of charge carriers. Electronic charge carriers passing through a hydrated sample for an extended period of time will decrease the amount of adsorbed water because electrolysis will h Either remane; monito; hydrat; determ: ionic < tivity adsorbé globin conduct time ir 7.5% ad least 9 'n will have converted some of the water to hydrogen and oxygen. Either the increase in evolved gas or the decrease in the remanent water, in the case of a hydrated sample, can be monitored. Conductivity is a very sensitive measure of the hydration state of a protein and can therefore be used to determine the amount of water adsorbed on the protein. If ionic charge carriers pass through the sample, the conduc- tivity will decrease as a function of time as the amount of adsorbed water decreases. Rosenberg (1962) observed hemo- globin with 7.5% adsorbed water in such an experiment. The conductivity was found to remain constant over a period of time in which ionic conductivity would have decreased one order of magnitude. It was concluded, therefore, that at 7.5% adsorbed water the conductivity of hemoglobin is at least 95% electronic. Keratin films containing greater than 15% adsorbed water were examined by King and Medley (1949). They found hydrogen evolution sufficient to account for the conductivity as entirely ionic. Oxygen evolution was not found, but the oxygen may have been chemically sorbed onto the hemoglobin. MariEiE, Pifat and Pravdid (1964a) impressed 150 V across a sample of crystalline hemoglobin with 9% adsorbed water for seven days. The evolution of gas could not be detected, thus indicating electronic conductivity. However, when hemoglobin with 15% water adsorbed was examined (Maridid and Pifat, 1966) hydrogen evolution sufficient to assign 90% of the conductivity to ionic carriers was found. observe usedja hydroge was ele detects by an i contrib tors wc that me The results described above all depend on the visual observation of hydrogen evolution. If tritiated water is used)a proportional counter can monitor the evolution of hydrogen. Hemoglobin with 30% tritiated water adsorbed was electrolized by Rosenberg (1964). The quantity of tritium detected was sufficient to account for 44% of the conductivity by an ionic mechanism. This is a lower limit on the ionic contribution to the total conductivity because exchange fac— tors would cause the ionic contribution to be greater than that measured. Riehl (1957) reported the activation energy of gela- tin with somewhat less than 10% adsorbed water to be 1.8 eV. Drawing on the similarity between this value and the acti- vation energy for conduction in ice, which is now known to be somewhat lower, Riehl argued for protonic conduction in the ice-like layer of water adsorbed on the protein. How— ever, it is questionable that an ice-like array of water molecules exists at so low a hydration state, as will be discussed in a later section. Similar results have been found in nucleic acid con- ductivity (MariEiE and Pifat, 1966). Electronic conductivity is indicated in Na—DNA with less than 50% adsorbed water. However, when greater quantities of water are adsorbed onto the DNA the evolution of hydrogen indicates a contribution of ionic conductivity. It appears that at low hydration states the conduc- tivity of proteins is predominantly, if not entirely, electrc 'hen er acid 5: tein, c then pr. protein conduct the act water a conduct hydrati vestiga ealCula netwOrk HEaSure Protein electronic in nature. Ionic conductivity becomes significant when enough water is adsorbed onto the protein or nucleic acid so that hydrogen bond bridges are formed over the pro— tein, or nucleic acid molecule. The conduction process may then proceed via water molecules without passing through the protein. The protein must, however, influence the process of charge generation because the activation energy for semi— conductivity in fully hydrated proteins is not the same as the activation energy for either water or ice. 0.2-0.3 gm water are bound to each gm of dry protein in solution. Ionic conductivity becomes significant near the completion of this hydration shell. The nature of the charge carrier has not been in- vestigated in adsorbate systems other than water. The dominant charge carriers in the substance may arise from an impurity or adsorbant (extrinsic), it may be indigenous to the biological material (intrinsic), or it may be injected from the electrode (in the case of electronic carriers). The inapplicability of classical impurity semi- conductivity to biochemical systems, where only short range order pervails, is discussed in Section V. Suard-Sender (1965) has argued that, in proteins, an extrinsic semiconduct- ing mechanism must apply. She reached this conclusion after calculating the energy band gap, in a two dimensional peptide network, to be 5 eV. This is significantly higher than the measured value of the semiconduction activation energy in proteins, i.e. ~2.4 eV. A possible explanation for this dis- crepancy is considered in Section V. protei: action verselj fore, R is t1 the in dence t data c. jected the eng bioche: Conduc materi; Where ' Chemic‘. C 0. the Eley and Leslie (1963) proposed that for the hydrated protein system water acts as an electron donor. The inter- action energy between impurity atoms is assumed to be in— versely proportional to the distance between them. There- fore, the impurity mechanism predicts: E = E0 - aNl/B; where N is the number of impurity atoms and a is a constant. In the intrinsic model discussed in Section II a linear depen- dence of activation energy on hydration is assumed. Extant data cannot definitely distinguish between these possibilities. Eley (1967) suggests that the electrons may be in- jected from the metal electrodes. If this is the case then the energy required to transfer an electron from an intrinsic biochemical semiconductor to a metal electrode (p-type semi— conductor) or from the metal electrode to the biochemical material (n—type semiconductor) are respectively: (3) where IC is the solid state ionization potential of the bio- chemical material; AC is the solid state electron affinity of the biochemical material; and o is the work function of the metal electrode. Nine different metals have been used as electrodes by workers in the Nottingham and Michigan State laboratories. In all cases the results were independent of the electrode material. The work functions of the various metals used as electrodes differed by several electron volts. Therefc must be trode. the met the int the ser abstit tion e: this cc metal 6 sured a Therefore, the measured semiconduction activation energy must be independent of the work function of the metal elec- trode. If, as is suggested by Eley, the Fermi levels in the metal electrode and in the semiconductor are equal at the interface, without any bending of the energy bands in the semiconductor then we have: 9 ll (Ic + AC>/2 . (4) Substituting Equation (4) in Equation (3) we find the activa- tion energy to be independent of the work function ¢. Under this condition the process of injecting electrons from a metal electrode into the sample can give rise to the mea- sured activation energy. In the hydration region where electronic charge carriers are believed to dominate, several mechanisms of conductivity can be considered. Charge carriers may be localized on a given site for long periods of time and then, in a short period of time, 'hOp' or 'tunnel' to a second site where again they remain for some period of time. A second model visualizes the charge carriers drifting in a conduc- tion band to which they have been thermally excited from either the valence band or an impurity center. These several models are depicted in Figure 1. Typical values of the mobility, the average velocity of a carrier in the direction of an electric field of unit strength, will vary with the model chosen. Hopping or tunneling models predict low mobil— ities, <1 cmZ/(volt-sec), while in systems in which the band .GOHDUSUGOUHEom Mo mHoUoE mcflamccsu cam mcwmmo: .Usmm .H musmflm JMOOS— 023wZZDF Jun—OS. OZEn—OI Jun—OS. 024m emsmkwmmhu ncom 85:5 0 o as o o o o R 0 i axottaklwlal 00 L . a _ a .2 MIL HESS sketch Mci i \oxaoxofisoxS QueSxm_ 3. or team cozosvcoo 10 model is applicable higher mobilities, >1 cmaflvolt-sec), are expected. Mobilities in the band model are very dependent on the band width. As the band width decreases the expected mobility likewise decreases. Eley (1967) has shown that an electron possessing a mean free path of 70 A in a band of 0.01 eV will have a mobility of ~0.2 cmgflvolt-sec). It is possible that mobility measurements can determine which model is apprOpriate to describe protein semiconductivity. Conductivity measures the product of mobility and carrier density, as can be seen in Equation (2), and is therefore insufficient to determine the mobility. If, how— ever, the density of conducting states is estimated, an in— dication of the mobility may be found from: o = ueN exp(-E/2kT) (5) 0 where N0 is the effective density of conducting states. (It has been assumed in Equation (5) that mobility is not an activated process. This is not true in the case of a hOpping' model of conductivity.) However, this method of obtaining a value for the mobility of the charges cannot be used because reasonable estimates of the density of conducting states, N0, do not exist for biomolecules. Mobilities can be determined from eXperiments in which a pulse of charge carriers is created at a temporal and spatial point. The charges then drift, in an electric field, to a second point there they are monitored and the time recorded. If the charges are photo-created the method 11 is essentially that of LeBlanc (1959) and Kepler (1960). This method of mobility determination was attempted in B-carotene (Bonniface, 1968). Most biochemicals are not photoconductors (Liang and Scalco (1964), reported photo- conduction in DNA but it can be demonstrated that this was probably the result of a bolometer effect) therefore, this method of mobility determination is rarely applicable. An alternative method of carrier injection is via an electron beam. Recently Delany and Hirsch (1968) have used the electron bombardment technique to determine carrier mobilities in anthracene crystals. Using 10-60 keV electrons they obtained values for the drift mobilities of electrons and holes as 0.92 and 0.38 cm2/(volt-sec) respectively. These values compare favorably with the uv flash measure- ments of Kepler (1960). This method has not been applied to biochemical materials. A third method of mobility determination is by use of the Hall effect or magnetoresistance which, in the case of inorganic semiconductors, is the simplest means. The Hall mobility is not necessarily the same as the drift mobil- ity (which is measured by the charge injection methods dis— cussed above). Traps do not reduce the Hall mobility but they do reduce the drift mobility. A Hall effect is produced when a transverse magnetic field is impressed across a con— ductor or semiconductor. A potential difference which is perpendicular to both the direction of the current and the direction of the impressed magnetic field is then produced. The not tected does no electrc tected. tronic indicat or hole Leffler sistanc lipids. UR mag dent, 4 Hall ef; Where b. time de; field t. Cently. detemi ‘iodine This me 12 The mobilities of ionic carriers are too small to be de- tected by the Hall effect. The absence of a Hall effect does not, however, indicate ionic conductivity because electrons may also possess mobilities too small to be de- tected. Observation of a Hall effect indicates the elec- tronic nature of the carrier. The sign of the Hall effect indicates the sign of the dominant carrier, i.e. electrons or holes. Although attempts have been made (Jendrasiak, Leffler and Rosenberg, 1967) dc Hall voltages or magnetore- sistance effects have not been observed in proteins or lipids. In the above discussion it was assumed that neither the magnetic field nor the applied voltage was time depen- dent. Although usually true this is not a condition of the Hall effect. Hermann and Ham (1965) have developed a system where both the magnetic field and the applied potential are time dependent. The sample is rotated in a static magnetic field thus simulating an alternating magnetic field. Re- cently, Hermann and Ham (1967) have used this technique to determine an ac Hall mobility for poly (n-vinyl-carbozole) -iodine, a donor-acceptor complex, as 0.5 cmZ/volt-sec. This method, although most promising, has not yet furnished mobility measurements for any biomolecules. A field in the microWave region, 1010 Hz, is im— pressed across the sample in the method of Trukhan (1966). At these high frequencies the capacitative effects of intergranular spaces are of no consequence. This effect hemoglci nated b; l which ti The effl to decr' detecte ) first r= ments, Stances tions C 13 is discussed in Section V. Trukhan investigated hemoglobin and DNA in both the dry and hydrated states. Measurements were made in the light as well as in darkness. These re- sults are summarized in Table 1. Illumination, as is ex- pected, does not appreciably change the mobility of mmvdemsin hemoglobin, which is about 2 cmZ/volt-sec or in DNA which is less than 1 cmz/volt—sec. Trukhan finds that hydrating hemoglobin changes it from a p-type semiconductor, domi- nated by hole conduction, to an n-type semiconductor, in which the majority of the charge carriers are electrons. The effect of denaturation, in both hemoglobin and DNA, is to decrease the mobility to values which then could not be detected by the apparatus. As the data of Trukhan is the first report of protein, or nucleic acid, mobility measure- ments, corroboration is necessary. The conductivity properties of biochemical sub- stances are only beginning to be understood. Basic ques- tions concerning the origin, nature and mobility of the dominant charge carriers are still unresolved. Adsorption Isotherms Several types of adsorption isotherms have been reported. Brunauer (1945) has considered the six principal shapes as illustrated in Figure 2. Type I is the familiar Langmuir isotherm which may be roughly characterized by a monotonic approach to a limiting adsorption which presumably corresponds to the adsorption of a single complete monolayer. .m30H0H2 .H QHQMB 14 mmaoz moaoc moaos mconuooao mconuooao mom wow wow wow mom 0 sue mmoo HMEHOC +I HMEHOQ +| Ln 0 0 Doom Op Umumwn +l N ooom ou emumms Em\mmHoE m.o +l N . m +l N Em\mmHoE m.o. xume umaoa> Imuuac xmms xyme xnmc xnme ucmfla gnaw £29 consumcoo dZQ <25 GHQOHmOEmm consumcma GHQonoEmm CHQOHmOEmm cHnonoamm mmwommm Hmwuumo AoomluHo>\NEov suaaanoz mpmum aoflumucmm conumaassaaH magnumnsm .«za cam canoamoEms mo monuuaflnoe Hams m>mzouoflz .H magma 15 o .ucofianomxm can mo musumnomEop can um oudmmonm uomm> may ma m .mommmooum coaumHOmwm Hmoammnm ucanauomoc mEHoQDOma ucoummmac xam .N mufimam ousmmoed (3 CL <3 CL (3 CL ---------d a on»... -------------— ------------d panosqv awn/0A V H 2;... a on»... H 22:. P-------------- --_ _----—---------- ----- 16 Type II isotherms, generally referred to as BET isotherms (Brunauer, Emmett and Teller, 1938), are very common in the case of physical adsorption. The BET isotherm.cor- responds to multilayer formation. Prior to the theoreti— cal contribution of Brunauer 32 31. it was the practice to take a point at the knee of the curve as the point of completion of a monolayer. Surface areas calculated using the knee point method were found to be consistent with those obtained by using adsorbates which give a BET ad— sorption isotherm. Type III is relatively rare and is characterized by a heat of adsorption equal to or less than the heat of liquefaction of the adsorbate. Both Types IV and V are the result of capillary condensation phenomena in that they level off before saturation pressure is at- tained. They often exhibit pronounced hysteresis effects. Type VI is descriptive of chemisorption and usually referred to as a Freundlich isotherm. This process is described by the equation: x = mpl/n (6) where x is the weight increase caused by adsorption; p is the pressure of the adsorbate; m and n are constants, n always being greater than unity. Isotherms for the adsorption of water, methanol, ethanol, and ammonia, on hemoglobin as illustrated in Figures 18—21 are of the BET type. A careful analysis of this type of isotherm according to the method developed in hig} found : The ove a lengt It is a two dif The 1-c 146 res is very 17 by Brunauer 33 El' (1938) can yield both the surface area of the monolayer and the heat of adsorption of the first layer of adsorbed molecules. This is developed in Sec- tion II. Hemoglobin Hemoglobin, the most important respiratory pigment in higher vertebrates, is not found in solution but is found in a highly concentrated form in the erythrocytes. The overall shape of the molecule resembles a spheroid with a length of 64 A, a width of 55 A and a height of 50 A. It is a tetramer of molecular weight 64,450 consisting of two different types of chains known as d- and B-chains. The d-chains contain 141 residues each and the B-chains 146 residues each. The configuration of each of the chains is very similar to that of myoglobin. Hemoglobin molecules are packed in a pseudo-face-centered—cubic crystal. Con- tact between neighboring tetramers exists only at‘a few points. Water fills the volume between molecules in the fully hydrated crystal. A 2.8 A resolution model of horse oxyhemoglobin has recently been constructed from 100,000 x-ray reflections of three isomophous replacements (Perutz 33 31. l968a,b). In hemoglobin the non-polar cavities of the chains shelter the hemes. Excluding the covalent bond between iron and histidine, there are about sixty cases where O atoms of the globin are within 4 A of heme atoms. In all but thl’ the int three p invaria indica: heme grl for the nantly a- and like ch ESpecia Hm mo; 18 but three cases, one in the d-chain and two in the B-chain, the interaction is non-polar (Perutz gt 31., l968b). The three polar contacts are exposed to water. A relative invariance is found in the residues in contact with the heme group. Only two exceptions are known. This would indicate that nearly all of these residues are necessary for the functioning of the hemoglobin molecule. The interaction between unlike chains is predomi- nantly non-polar. The few hydrogen bonds found between a- and B-chains are all exposed to water. Contact between like chains may possibly occur through salt bridges. An internal cavity lined with polar residues, especially serine and threonine, extends all the way down the molecular dyad axis. The shape of this cavity can be represented by two boxes each 25 A deep, along the axis of the molecular dyad, 20 A long and 8—10 A wide. These two spaces separate like chains. Polar residues are located either on the exterior of the molecule or in the large internal cavity along the dyad axis. In both cases they are in contact with water. Exception is made in the case of an occasional serine or threonine whose hydroxyl group is hydrogen bonded to a carbonyl group within the same a-helix. Large non-polar groups may occupy the interior of the chain, be situated in the surface crevices of the subunits, or reside at the boundary between unlike subunits. The surface crevices minimize the contact of non-polar groups with water. 19 Two non-polar side chains, a cysteine and a leucine, are however found to protrude into the surrounding water. Perutz gt a1. (1965) suggest that the presence of a single, non-hydrogen-bonded group with a large dipole moment in the interior of a hemoglobin subunit would be sufficient to make the tertiary structure unstable. Mutations which cause the replacement of an interior non- polar residue by a polar residue would therefore probably be lethal. No such replacements have been observed in any of the several abnormal human hemoglobins thus far. The change in free energy arising from the introduction of a polar group in the interior of a hemoglobin subunit has been estimated by Perutz (1965) as 3,500 cal./mole. This figure may be a bit high but it does indicate that the instability created by a single uncompensated polar group may be of the same magnitude as the weak bond ener- gies which stabilize tertiary configuration. Clearly the general distribution of side chains in hemoglobin is in accord with the principles of protein structure formulated by Kauzmann (1959). The free ener— gies of protein molecules are minimized if their exteriors are polar and their interiors non-polar, as in soap micelles. Groups carrying a net charge, or strong dipoles, produce strong potential fields around them. This effect can be mitigated by placing these groups in an environment of high dielectric constant, i.e. water on the exterior of the molecule. If hydrophobic groups are found on the 20 exterior surface of the molecule, they tend to immobilize the water molecules in their vicinity reducing the entrOpy of the system. Tanford (1962) has estimated the increase in unitary free energy caused by exposing one mole of non- polar side chains to water as: tryptophan 3, tyrosine 2.9, phenylalanine 2.65, leucine 2.4, and valine 1.7 kilocalories. The packing of non-polar side-chains in such a manner that they are not in contact with water adds additional stability to the hemoglobin molecule. This is mainly the result of entropy changes connected with alterations of the water structure around the side chains (Nemethy and Scheraga, 1962). Klotz (1960) has proposed that the stability of hydr0phobic interaction arises from the ice-like water structure formed around exposed hydrophobic side chains. This is similar to the ice-like structures formed about argon or methane in water. The creation of polar hydrates produces a negative enthalpy change. It is therefore argued that the stability of hydrophobic interactions is the result of this favorable enthalpy change. As indicated above, only two non-polar side-chains extend from hemoglobin. Structured water, other than that bound to polar groups, has not been observed on the surface of protein molecules. Thus, ice-like structures, at best, provide only a small degree of structural stability to hemoglobin. Reduced iron, in the ferrous state, is in the cen— ter of a square planer heme group. It is further coordinated 21 to one strong field ligand, histidine, and one weak field ligand, water. The introduction of one strong, nitro— genous, ligand to a heme group facilitates the introduc- tion of a second strong ligand. It is only because the heme is protein bound, i.e. in a medium of low dielectric strength of the surrounding globin, that such a complex as reduced hemoglobin can exist at all. n-bonding sub- stances, e.g. 0 CO or CN_, readily substitute for the 2: water at the sixth coordinate position. The binding of 02 to heme does not cause the oxidation of iron to the ferric state, methemoglobin, something readily accomplished by oxidizing agents. Again it is the hydrophobic environ- ment of the heme group, as provided by the globin portion of hemoglobin, which is believed to permit the reversible oxygenation of hemoglobin. Each of the subunits is capable of binding one molecule of oxygen. The binding constants for the addition of each successive molecule of oxygen to the hemoglobin tetramer is different. The ratio of the four stepwise constants is approximately 1 : 4 : 24 : 9. Addition of the first molecule of oxygen produces a conformation transition, allosteric effect, which favors the associa- tion of a second molecule of oxygen at a second heme group in the tetramer etc. Oxygenation dependent changes in the orientation of the a‘ and B-chains with respect to each other have been found by Perutz (l968b). II . THEORY Biological Semiconductivity At constant temperature the conductivity of a pro- tein will increase with hydration as found by King and Medley (1949), Eley and Spivey (1960) and Rosenberg (1962). In the region of hydration where conductivity is believed to be principally electronic in nature, a good fit to the observed data is provided by: o(m) = OD exp(dm) (7) where CD is the dry state conductivity; m is the % water adsorbed onto the protein; and a is a constant. Cutomary usage is to state m in weight % of water adsorbed. How- ever if several adsorbates are to be compared, as is the case in Sections IV and V, it is more meaningful to state m in terms of mole %. This change serves only to alter the value of the constant a. In the region where ionic conductivity is believed to dominate, a saturation of conductivity with respect to hydration is observed and Equation (7) does not apply. Dry proteins obey the operational definition of semiconductors, Equation (1), i.e.: 22 23 CD = 00 exp(-ED/2kT) (8) where o is the conductivity of the dry protein; and E D D is the activation energy of the dry protein. Similarly hydrated proteins are operational semiconductors because they obey the relation: 0 = 00 eXp(-EH/2kT) (9) where EH is the activation energy of the hydrated sample. The pre-exponential factor, 00’ does not change with hydra- tion of hemoglobin. This is perhaps atypical of biochemical systems and will be discussed in Section V. Combining Equations (8) and (9) we obtain: -E D + am (10) o(T,m) = 00 exp 2ET Equating Equation (9) with Equation (10) we observe that: EH = ED -2kTam (11) Some basic concepts of solid state theory may pro- vide a degree of physical insight to better understand these results. As a first approximation the hydrated crystalline protein is considered to be represented by a continuous medium which can be described by a single dielectric constant K. In this medium the work necessary to relocate a charge from a neutral portion of the protein molecule to a previously neutral portion of another, or 24 distant part of the same molecule, can be calculated. If the charge is moved a considerable distance, then the Coulomb interaction between the charges may be neglected and the charges are essentially free. The energy required for such a process is: E=I—A-2P (12) where Ig is the gas state ionization potential of the sub- stance; A9 is the gas state electron affinity; and P is the stabilization resulting from polarization relaxation _at each site of ionization (Lyons, 1957). The polariza- tion stabilization is the result of the relaxation of the dielectric media in a spherical region around each of the two newly created charges and is given by: 2 _ e P - 2R (1 - 1/K) (13) where R is the radius of the spherical region in which the relaxation occurs; and K is the effective dielectric con- stant of the medium considered as a bulk prOperty. Com— bining Equations (12) and (13) we obtain: 2 _ e ED - Ig - Ag - fi— (1- l/K) (14) Hydrated protein possesses a higher effective dielectric constant K'. Since hydration cannot alter either the gas state ionization potential or the gas 25 state electron affinity of the protein we may write for the hydrated protein: 2 _ _ _ E— _ . ED - Ig Ag R (l l/K ) (15) Eliminating<£g - AéJbetween Equations (14) and (15) yields: 2 _. e ' EH — ED - fi— (l/K - l/K ) (16) Comparing Equations (11) and (16) we obtain: 2 2dem = (l/K — l/K') (17) SUI“) Introducing this result into Equation (10) yields: -E 2 — D . e .— O(T,K') - 00 exp 2kT exp 'Efiffi (l/K l/K') (18) (Rosenberg, 1962a). In this model the effect of hydration, or more generally adsorption, is to increase the conductivity of the protein by increasing the effective dielectric con- stant of the medium. This serves to increase the polariza- tion relaxation energy which then decreases the activation energy for semiconduction. Adsorption Isotherms BET theory extends Langmuir's approach to multi- layer adsorption. It is assumed that the Langmuir equation 26 applies to each adsorbed layer. Furthermore it is pos- tulated that the heat of adsorption for the first layer E1 may have some special value, whereas for all succeeding layers the heat of adsorption is equal to the heat of vaporization of the liquid adsorbate, L, i.e. E = E ... = 2 3 Ei = L. It is also assumed that the average time of so- journ of a molecule on each of the layers, excluding the first, is the same. The average time a molecule remains in a given surface layer is identical with the reciprocal of the frequency of oscillation perpendicular to that surface. This development further assumes that evapora- tion, or condensation, can occur only from, or on, exposed surfaces. The model is then one in which the surface of the adsorbent can be divided into a portion, SO, which is uncovered, a portion, 81’ which is covered by a single layer of adsorbed molecules, a portion, 82, which is cov- ered by two layers, etc. Equilibrium demands that the amount of each type of surface reaches a steady value with respect to the next deeper level. Then for the first molecular layer we have: alps0 = slbl exp(-El/RT) (19) where al is a constant given by kinetic theory; p is the vapor pressure of the adsorbate species; bl is a constant which depends on the frequency of oscillations (perpen— dicular to the surface) of the molecules in the first layer. Similarly for the second and succeeding layers of adsorbed molecules we may write: 27 asz1 = Szb2 exp(-E2/RT) (20) aipSi-l = Sibi exp(—Ei/RT) (21) aip exp(Ei/RT) where aZ/b2 = ai/bi' Setting b equal to a new i constant y, we may rewrite Equations (20) and (21) as: S. = y. S (22) s. = y. —— s eXp(El/RT) (23) a b. By defining a new constant C as aifii eXp{(El — Ei)/RT}, i 1 this may be rewritten as: _ i Si - Cy S0 (24) The total number of molecules adsorbed is: z = zm(Sl + 282 + 383 + ... 1Si + ...) (25) where zm is the total number of molecules adsorbed in a square cm of complete monolayer. The total number of molecules adsorbed per cm2 is giVen by: 28 (26) If the surface area of one gram of the adsorbent is A cmz, then the total number of molecules adsorbed on one gram of co adsorbent is Az/ Si‘ The corresponding number of i=0 molecules adsorbed in a completed monolayer is Az . If x m is the adsorption per gram of adsorbent at a partial pres- sure p and xm is the corresponding term for a monolayer, then from Equation (26) we obtain: i 1 ) (27) Substituting Equation (24) in Equation (27), we obtain: (28) 29‘ Both sums are infinite geometric progressions. Rewriting therefore yields: csoy/(l - y)2 = so{1 + Cy/(l — y)? (29’ Xlx m which may be rewritten as: _ .Ey " (l - yT(l-y+CyT (30) XIX At saturation the amount adsorbed on a free surface is infinite. Then at p = p x + m or y = 1. When y = p/p0 0 we obtain the familiar BET equation (Brunauer, Emmett and Teller, 1938) pp = 1 C-1 2_ EYPO _ p) §;C + [£353 po (31) a b It is assumed that 5152.~ l which simplifies the expression for 2 1 C to: C = exp{(El-L)/RT} (32) According to Equation (31) a plot of p/ x(p0 - p) vs. p/pO should yield a straight line of slope (C - l)/me and inter— cept l/me. Thus from the lepe and the intercept it is possible to obtain both the monolayer adsorption(3Qn) per gram of adsorbent and, if the latent heat of 30 condensation (L) is known, the heat of adsorption of the monolayer[E, ). Equation (31) cannot be used to describe the ad- sorption isotherm.at relative pressures (p/po) above 0.35. This has been explained (Gregg, 1961) as arising from the effect of narrow pores in limiting the thickness of the film. The BET model implicitly assumes that upon con- densation, in any layer after the first, the molecule gives up its full latent heat of liquefaction. In the case of a molecule condensing into a liquid it will have a coordination number, number of nearest neighbors, of 12. But in the absence of horizontal neighbors, as is often the case in physical adsorption, the coordination number is much less than 12 (Hirst, 1948). When this is true the heat evolved should be only a fraction of the latent heat of liquefaction. Halsey (1948), therefore, believes BET theory capable of explaining only monolayer adsorption. III. EXPERIMENTAL METHODS Sample Preparation The protein used in this study was dialyzed (salt free), twice recrystallized bovine hemoglobin processed by Servac and obtained from Gallard-Schlesinger. It was used without further purification. A compacted tablet was formed by pressing the hemoglobin crystallites in a die which had been teflon coated to avoid sticking. Pres- sures of 103Kgm per cm2 were applied to the die with a pneumatic press. In order to avoid localized heating which serves to denature the hemoglobin the pressure was increased slowly. Denaturation could be determined by visual observa— tion of the compacted table as denatured portions of the hemoglobin are of a very much darker color than is native hemoglobin. Conductivity Measurements Compacted tablets having a surface area of 4 cm2 and a thickness of 0.03 - 0.05 cm were fastened between solid metal electrodes with the aid of Spring clips. Stainless steel, copper, brass or tin oxide coated glass electrodes were used at various times with no discernable difference in the conductive properties of the hemoglobin 31 32 sample. Teflon was used for insulation throughout. One electrode was in contact with a mercury pool which was, in turn, connected to a stout copper rod. The rod which projects out of the chamber was used as a thermal sink. The apparatus is illustrated in Figure 3. A copper—constantan thermocouple, inserted in the mercury pool, was used to monitor the temperature. The sample completed an electrical circuit between a battery and a vacuum tube electrometer (Keithley model 610BR). At times higher voltages were supplied with a regulated dc power supply (Keithley model 230). The sample was dried by heating it to 95°C for a minimum of 12 hours. Heating was in a dry nitrogen atmosphere. This procedure was found to be entirely equivalent, as far as electrical measurements are con- cerned, to drying in vacuum. After the sample was cooled to room temperature, a fixed partial pressure of an ad- sorbent was introduced into the chamber. Saturated salt solutions were used to establish various relative humidities in the sealed chamber. At constant temperature, 24 i 1°C in the case of these exper- iments, a saturated salt solution will reach equilibrium with the atmosphere above it at some relative humidity. The equilibrium relative humidity will depend on the salt chosen as seen in Table 2 (O'Brein, 1948). The saturated salt solution fixes the relative humidity in the sealed chamber. At this fixed relative humidity the hemoglobin 33 e/YYVVVQOOQQOOOOééé/ ELECTROMETER SAMPLE ‘- I'l P0TEMH0METER~ MERCURY SATURATED SALT o SOLUTTON , TEMPERATURE CONTROL BATH % Figure 3. Schematic diagram of the apparatus used to measure conductivity and semiconduction activation energy. The sample makes thermal contact with the temperature con— trol rod via a cup of mercury. All insulation indicated by the symbol a is of teflon. 34 Table 2. Equilibrium relative humidity over some saturated salt solutions, Salt Equilibrium Relative Humidity at 24°C Lithium Chloride Potassium Acetate Magnesium Chloride Potassium Carbonate Magnesium Nitrate Sodium Nitrite Sodium Chloride Barium Chloride Potassium Nitrate Potassium Sulfate Water 12 23 33 44 54 65 76 88 92 97 100 35 sample adsorbs a given quantity of water which was deter- mined with an electro-microbalance. A relatively long period of time, on the order of days, was required to establish an equilibrium between the saturated salt solu— tion, the atmosphere within the chamber, and the sample. The atmosphere in the conductivity chamber was regulated to various partial pressures of ethanol or methanol by slowly exchanging the nitrogen atmosphere in the chamber for the nitrogen atmosphere over a thermo- statically controlled reservoir of the desired alcohol. If this process is continued for 12 hours, the partial pressure of the alcohol in the conductivity chamber very closely approximates the equilibrium vapor pressure of the alcohol at the temperature of the alcohol reservoir as given in Table 3. Table 3. Vapor pressure of alcohols as a function of temperature. Alcohol Temperature 0°C 15°C 24°C Methanol 30 mm 76 mm 130 mm Ethanol 12 mm 33 mm 56 mm Mixed streams of nitrogen and anhydrous ammonia were introduced into the dry conductivity chamber. By altering the relative flow rates of the two gases the con- centration of ammonia in the chamber could be regulated. 36 The conductivity of the sample was monitored throughout the adsorption process. After the conductivity was found to be constant, the chamber, in the case of alcohol adsorption, was sealed. As the temperature of the sample was altered, by cooling or heating the copper rod, simultaneous measurements of temperature and current were made using the thermocouple-potentiometer and the electrometer. It is not desirable to use an equilibrium method of determining the semiconduction activation energy of samples with adsorbed vapors because during the interval required to establish thermal equilibrium the adsorption equilibrium will be altered. If equilibrium conductivity measurements are made, the adsorbtion state of the sample will change between conductivity measurements in which case each conductivity measurement is descriptive of a sample at a different adsorption state. The reproducibility with which the system can be recycled, when dynamic measure— ments are made, indicates that the adsorption state of the system is not significantly changed when the sample tem- perature is changed rapidly, i.e. 1.5°C per minute. Dielectric Measurements Compacted tablets, 3.5 cm diameter 0.02 - 0.05 cm thick, are measured in a stainless steel dielectric cell (Balsbaugh Laboratories model LD-3). The high electrode is connected to a micrometer drive. Electrode separation, therefore, may be accurately determined. The ground 37 electrode, 2.5 cm diameter, is guarded. Insulation throughout the chamber is of teflon. Regulation of the relative vapor pressure of the adsorbates in the dielec- tric chamber was effected in the same manner as in the con- ductivity chamber. Capacitance measurements in the frequency range of 30 Hz - 100 KHz were made with a General Radio model l610-B Capacitance Measuring Assembly. The assembly con— sists of: l. The Type 716 Capacitance Bridge, A Schering Bridge which is direct reading in capacitance from 30 Hz to 100 KHz, and in dissipation factor at 100 Hz, 1 KHz, 10 KHz and 100 KHz. 2. The Type 716—P4 Guard Circuit, which permits measure- ments using a guard electrode with the dielectric cell. This is sometimes called a Wagner-ground circuit. 3. The Type l302—A Oscillator which has a frequency range of 10 Hz to 100 KHz. 4. The Type 1231-B Amplifier and Null Detector, a com— bination solid state amplifier and sensitive visual null detector. A 100 pF capacitor was placed in parallel with the sample capacitance. Figure 4 provides a schematic illustra- tion of the capacitance measuring assembly including the dielectric cell. The direct reading method of determining capacitance was used throughout. In this mode, capacitance of the magnitude measured, could be determined to an 38 sGENuP is: C” ”BOOfEf CN I IDIELECTRIEI 4) DETG Figure 4. Schematic diagram of the capacitance bridge assembly. The Schering bridge consists of the variable air capacitors CA and CN, the fixed capacitor CB and the fixed resistors RA and RB. The guard on the lower elec- trode is connected to the Wagner ground circuit which con- sists of three variable resistors, RC, RF and RG and a variable capacitor CG’ 39 accuracy of i 0.8 pF. Dissipation factors could be deter- mined to an accuracy of i 2%. Some extremely low frequency, 0.1 - 10 Hz, measure— ments of capacitance were made with a guarded bridge de- signed by Nakajima and Saito (1958). The assembly, built by the Ando Electric Co. Ltd. of Tokyo, Japan consists of: l. The Type ULO-S Oscillator, a multi—wave form oscillator operating in the range of 8 x 10.4! - 1.2 x 103 Hz. 2. The Type TR-4 Bridge consisting of a variable con- denser and a conductance shifter. A Wagner potential bal- ancing circuit is also included. 3. The Type EC-3 Null Detector which is a directly coupled dc amplified with 100 megohm input resistance. The capacitance of the sample was measured in a vacuum, 10-2 torr, by enclosing the dielectric sample chamber in an outer brass chamber which was evacuated with a mechanical pump. All insulation in the outer chamber was of teflon and all leads were shielded. The outer chamber was at ground potential. Adsorption Isotherm Measurements A portion of a compacted tablet weighing ~30 mgm was placed on a Cahn electrobalance (Model RG). The electro- balance was placed in a glass vacuum chamber and connected to a recorder (Bausch and Lomb Model VOM-S). The sample was weighed on a Mettler balance under laboratory atmo- spheric conditions and then reweighed on the electrobalance list?" 40 when the balance chamber was at atmospheric humidity. Counter balancing a portion of the sample weight in— creases the accuracy with which adsorption induced weight increases can be determined. After the sample chamber had been evacuated and the sample heated to 95°C for a minimum of 12 hours, a "dry reading" was ob- tained. From these three measurements the dry weight of the sample was obtained. Buoyancy corrections were calculated both for the determination of the dry weight and for the weight of the adsorbed vapors. In all cases, excepting that of ammonia adsorption, buoyancy corrections were small when compared to the weight of the quantities being deter— mined. Ammonia results presented in Section IV have been corrected for buoyancy. Calibration measurements, made on counter balanced pans with no sample, showed that water and ethanol vapors affected the system while methanol and ammonia had little effect. In the Cahn electrobalance some electronic apparatus is included in the balance chamber and is exposed to the vapors intro- duced for adsorption studies. The negative balance cor- rections for water and ethanol adsorption studies have been added to the results presented in Section IV. In the cases of water, ethanol and methanol the liquid was placed in the liquid reservoir as illustrated in Figure 5. After degassing, a small amount of the vapor over the liquid was introduced into the evacuated balance . Ii! Ill {92. r... 47.55.15 ' 41 .moumummmm oocmamolonoaa Essom> mo Emummflo oaumeonom m _o>mmmmm mt>fil+$ru uoaazoo ampuzozas E35: 6 *ID‘» .m ousmflm m¢3oszOm an no_ _ .va auswflm .1 13‘" ~() 4|! I / o\o ®_ $1 1 1 4 O m 8 9 1NV1SNOO OIHLOHWBICI I 6 q. 63 gap measurements the moveable electrode is not in contact with the hemoglobin tablet. The equivalent capacitance of the tablet in series with an air capacitor is measured by the bridge. Measurements are made with a variety of air gaps. The capacitance of the tablet is then obtained by extrapolation to the zero air gap condition. The results of such measurements with and without an air gap are illus- trated in Figure 15. An air gap or a sheet of teflon would act as a blocking electrode and should greatly diminish elec- trode polarization. If electrode polarization is diminished the low frequency dispersion would be altered. As this was not the case it is believed that electrode polarization is not responsible for the low frequency dielectric dispersion in hydrated hemoglobin. A large positive temperature coefficient is found to be associated with the low frequency dielectric dispersion. This is in agreement with studies of O'Konski, Moser and Shirai (1964) on nucleic acids. At relatively low temper- atures (N -25° C) the low frequency dielectric dispersion is not found and the capacitance of a hydrated hemoglobin pellet is found to vary inversely with the thickness of the sample. In Figure 15 it appears that, at low frequencies, the capacitance of hydrated hemoglobin varies inversely as a power of the frequency. However, before this can be verified by plotting the log of both variables it is neces- sary to demonstrate that setting one variable to zero causes the other variable to be zero simultaneously i.e. the re- lation between the variables does not contain an additive 64 .Ammamcmfluuv oocuae mom Hem asp >3 can Amoaouflov pocumfi uomucoo an» an pocflanmump mo caboamofimc pmumnpms mo unopmcoo oauuomaoflo ucoummmm on» NO mocapcmmap mocmzwoum aha .ma mHSmHm 3.: 35:52... no. v n N _ _ A Grit IIAVI! 1.0 o 1o. m. m. -2 x u. nu. . w 10w 0 c. If D U .lmuN 1! .mmflocozganm 30H hua> um cabonoEmn pmumupmc mo mOQMUH tommmo may mo Hmoonmflomu asp mo mocmpcmmmp wocosvmum .mH musmflm 66 TEE no. x ..oocozooaoo m m c .mH musmflm « — ,fi L “3 (2H) A‘ouanbay 1 O 67 constant. Low frequency capacitance measurements, obtained using the Ando TR-4 dielectric bridge, of a compacted hemo- globin tablet in equilibrium with an atmosphere of 76% relative humidity, have been plotted against the frequency in Figure 16. The curve intercepts the origin indicating that the data may be displayed on a log—log graph without a change of variable. When this data is plotted on a log-log graph, as in Figure 17, it is found that the capacitance varies as w-0'35. This frequency dependence continues to 200 - 500 Hz for the data at 76% relative humidity. At lower hydration states this effect terminates at lower frequencies. An examination of the dielectric data of Marididz Pifat and Pravdi5’(l964b) indicates that the same frequency dependence was found, but not discussed, by these workers. The ad- sorption of methanol and ethanol on hemoglobin produces similar results. The apparent low frequency dielectric dispersion of hemoglobin with various adsorbates is believed to be the result of a polarization effect, probably of the Maxwell- Wagner variety. A further discussion of this point will be found in Section V. It can be seen in Figure 14 that in the region 104-105 Hz, polarization effects are negligible. Therefore, in the following discussion the dielectric con- stant has been calculated from the capacitance as measured at 105 Hz. The dielectric constant, as defined in Equation (31), is corrected for the air filled intersticies found in 68 -10 .cflboamoEoc woumupmc mo moonwaommmo any mo aocapcommp mocosgoum .na ousmflm 3.: 3532... no. . o T ‘ d N (yd) oauouaadog 60/ 69 Table 5. Dielectric constant and activation energy of hemoglobin with adsorbed water, methanol and ethanol. Adsorbate m(mole %) E (eV) Dielectric Constant none 0 2.35 2.3 water ' .355 1.95 2.9 .656 1.77 3.4 1.01 1.55 4.2 2.2 1.44 5 5 - 1.23 7.4 methanol 0.203 1.75 3.2 0.53 1.45 4.6 - 1.20 5.9 ethanol 0.073 1.8 3.1 0.35 1.6 4.5 70 compacted tablets. This is done by extending Bottcher's (1962) treatment of a powder to the case of a compacted tablet. One then obtains for the dielectric constant of the crystallite material: 3KP6 + 2KP(K-l) _ ___ (34) — 3KP6 - (KP-l) where K is the dielectric constant of the crystalline mate- rial; KP is the dielectric constant of the tablet (given as K in Equation (33)) and 6 is the packing fraction, or partial volume of crystalline material in the pellet. The dielectric constants of hemoglobin with adsorbed water, ethanol and methanol are presented in Table 5. Water, methanol and ethanol, when adsorbed on hemoglobin increase the effective dielectric constant of the sample. Concomitant with this increased dielectric constant a decrease is found in the activation energy for semiconduction. Although the dielectric constant of hemoglobin increases with the ad- sorption of ammonia these redeUstcannot.be correlated with the activation energy or the molar adsorption. They have therefore been omitted at this time. Adsorption Measurements The adsorption of water vapor, methanol, ethanol, and ammonia on hemoglobin follows Type II, or BET, isotherm as can be seen in Figure 18, 19, 20 and 21. In each case the data was plotted according to the BET equation and a straight line obtained in the region p/po < 0.3 as 71 illustrated in Figures 22, 23, 24, and 25. As discussed above the BET equation contains two constants, Yfi the mono- layer coverage, and C which is a function of the heat of adsorption of the first layer and of the heat of liquefaction of the vapor. In the case of a compacted hemoglobin tablet, values for Ym and C were calculated from Figures 22, 23, 24 and 25 and are given in Table 6. Simultaneous with, and under the same conditions as, the adsorption studies)conductivity experiments were con- ducted on a second sample of hemoglobin. The results of these conductivity experiments are presented in Figures 26, 27, 28, and 29. In order to better compare the effect of these several vapors on the conductivity of hemoglobin the results were redrawn on a mole %, rather than a weight %, basis in Figure 30. An exponential dependence of the con- ductivity on the quantity of vapor adsorbed, as is indicated in Equation (5), is found to hold in most of the region studied. Values of a, as given in Equation (5), have been calculated from Figure 30 and are presented in Table 7. 72 ea mascafifl ma. Hosanna mm Hosanna: ha Hmumz Am mHoEV CH 5 mumnhompd HI. .GHQOHmoEmc co UmQHOmUm mflcoafim Una .Hocmcpm .Hocmcuma .Hmpm3 How a .h magma s.H ne.o o.m mflaossa o.~ oa.o m.e Hosanna m.m m¢.o m.mH Hosanna: m.ma nv.o m.m “mom: a .rcugnflououa em ooa\moaosvsx Anamooua em ooa\smvsx aumonomoa - .caboamoemn co UmbHOmpm macofifim paw Hocmcom .Hocmcpoa .Hawm3 How mHauoEMHmm 5mm .0 manna 73 '0 o .o 3 1» 30 ' 1: < O b 2 o P 3 o\° .. 20 P z .9 o 3 /0 I0 " O l L l l .2 .4 .6 .8 P / P0 Water Figure 18. Adsorption isotherm of water on hemoglobin at 24° C. [Q L 74 Weight 95 Methanol Absorbed 1 1 1 1 .2 4 6 .8 P/ Po (Methanol) Figure 19. Adsorption isotherm of methanol on hemoglobin at 24° C. 75 50F o 401- 113210 b .D b O a ‘O < '3 C E o “‘20 ' 39 E .3 o 3 l0 ' o o/ o/ /O/ l l J l l 4 l 1 l l .2 4 .6 .8 P/Po Ethanol Figure 20. Adsorption isotherm of ethanol on hemoglobin at 24° C. 76 Weight 2: Ammonia Adsorbed l l Figure 21. at 0° C. 1 .2 P/Po (Ammonia) Adsorption isotherm of ammonia on hemoglobin 77 VmIPo-P) l l I J0 .20 .30 P/Po Water Figure 22. BET curve of water adsorption on hemoglobin. 78 .o4 - A .03 - m(Po-P) .02 - .0I '- l l l l l l .05 .l0 .15 .20 .25 .30 P/Po Methanol Figure 23. BET curve of methanol adsorption on hemoglobin. 79 .04F' .02" l l l l l l .1 .2 .3 P/Po Ethanol Figure 24. BET curve of ethanol adsorption on hemoglobin. 8O .03 B? .02 - ° I O O. \— E .01 2 l l .2 P/ Po Ammonia Figure 25. BET curve of ammonia adsorption on hemoglobin. 81 '61- e~ o .- / 2 - ° 3 o c/ .3..- f d E- 1 l 1 1 l l 1 5 l0 I5 20 25 30 35 Weight % Water Adsorbed Figure 26. Conductivity of hemoglobin as a function of water adsorbed. .UmnHOmUm Hocmcpme mo coauocsM a mo canoamoamc mo mufl>fluospcou .bm muzmfim on 82584 .2252 x. 23»; ON 0. 82 A A u _ .4 :ueung 00/ 83 VI log Current '-"-I l l l 1 1 IO 20 3o 40 Weight ‘71. Ethanol Adsorbed Figure 28. Conductivity of hemoglobin as a function of ethanol adsorbed. 84 log Current e .‘o L 2'0 Weight % Ammonia Adsorbed Figure 29. Conductivity of hemoglobin as a function of ammonia adsorbed. Figure 30. Conductivity of hemoglobin as a function of mole % adsorbate. Ammonia adsorption is illustrated in curve A, methanol adsorption in curve B, water adsorption in curve C and ethanol adsorption in curve D. The vertical line indi- cates monolayer coverage (see Section V). 86 mt log Current SI l l (15 MOIC °/0 Figure 30. L0 Adsorbate V. DISCUSSION Impurities in Bioloqical Semiconductors Some inorganic semiconductors are of "electronic ”“2 grade" purity, i.e. less than one impurity molecule for each 1010 substrate molecules. Although a few organic crystals can be greatly purified by zone refining techniques, biolog- ical substances are not obtainable at purity levels even i“; approaching "electronic grade." "Electronic grade" biochem- icals, particularly those of the polymeric variety, are not possible in the forseeable future. The cell contains many "impurities." Therefore, a relative insensitivity of the conductivity mechanism to general impurities is demanded of semiconductive models postulated in biological systems. The difference in sensitivity to impurities is not between inorganic and biochemical semiconductors but between covalent crystalline semiconductors on the one hand and mole- cular crystals on the other. Tauc (1967) has reported that the incorporation of impurities, at low concentration levels, influences the conductivity of amorphous germanium but very little. This is in contradistinction to crystalline german— ium where low concentration impurities dominate the semi- conductive process. Covalent crystals possess a long range order which may extend over a distance as great as 1000 87 88 unit cells. This provides for a long range interaction not found in amorphous materials, polymers, or molecular crys— tals. In covalent crystals, any alteration of the long range order, such as the introduction of an impurity, will have widespread ramifications. The same is not the case for a system possessing only short-range order. In such a sys- tem impurities, until their concentration becomes rather high, exhibit only local effects which do not statistically *‘7 affect the short range order of the system (Gutmann and Lyons, . 1967). . The experimental evidence presented in Figures 7, 9 i and 11 indicates that hemoglobin with adsorbed water, methanol 11w or ethanol is not an impurity dominated process. In the case of hemoglobin with adsorbed ammonia, however, an impurity mechanism could well explain the results of Figure 13. A classic example of inorganic impurity semiconductivity is given in Figure 31A. Each region of the curve can'be described by an equation of the same form as Equation (1). However, both the activation energy for semiconduction and the pre- exponential factor differ in the two regions. The temperature dependence of the conductivity can therefore be described by an equation of the form: a = a exp(-E1/2kT) + a 1 exp(-E2/2kT) (35) 2 The pre-exponential factor in the impurity conductivity term is a function of the concentration of impurities. At low temperatures, and hence low conductivity, im— purity conductivity will dominate because of the lower Figure 31. A. Schematic diagram of classical impurity semiconductivity. B. Schematic diagram of semiconductivity found in hemoglobin-adsorbate systems. F33 90 363.3231 egoxxg \staufix b.3323 23$ AllAllOflClNOO 90'I Figure 31. 91 activation energy needed to promote the charge to the con- duction band from the impurity center, while at higher tem- peratures the intrinsic conductivity of the substrate mate- rial will dominate because of its higher activation energy and hence its faster increase with temperature. As the im- purity concentration is increased the dominance of impurity conductivity is extended to a higher temperature region. Alteration of the impurity concentration does not change the activation energy of impurity conductivity because only the number of carriers is affected by such a change. (If im- purity band conduction results from an increased impurity concentration, then a concomitant change will be found in the semiconduction activation energy.) Varying the impurity concentration yields parallel curves, indicating a changing pre-exponential factor but constant activation energy. The semiconduction curve for hemoglobin with adsorbed ammonia may be of this form. However, the conductivity data for hemoglobin with adsorbed water, ethanol and methanol are not of this form. In the latter cases increased adsorbate con- centration alters the activation energy of the system but does not affect the pre-exponential factor. Thus, a com— pensation effect, as discussed below, is not found in hemo- globin. A linear relation is found between the activation energy and the amount of adsorbate present in the system. This indicates that the adsorbate is not behaving as an im- purity but is in some way altering the intrinsic semicon- ductive pr0perties of the hemoglobin. The property which 92 is altered is the magnitude of the polarization relaxation of the matrix. The Effect of Inter:granular Spaces on Conductivity A micro—crystalline powder was compacted to form tablets which contain inter-granular spaces. The capacitance of inter-granular Spaces often causes the dc resistance to be significantly greater than the resistance which is mea- sured at high frequencies. High frequencies short out the capacitance of the inter-crystalline barrier. The acti— vation energy was determined from measurements of do con- ductivity. It is therefore important to investigate the role of inter-granular effects on the activation energy determinations. Siemons, Bierstedt and Kepler (1963) have compared the semiconduction activation energy for single crystals and compressed tablets of the highly conducting charge—transfer complex C52(TCNQ)3. Compressed tablets exhibit an activation energy for semiconduction of 0.07 eV while the activation energy of single crystals is 0.01 eV. In the case of the CsZ(TCNQ)3 compressed tablet nearly all of the activation energy results from inter-granular impedances. If this value, 0.07 eV, is generally indicative of the activation energy resulting from inter-granular impedance, then the activation energy measurements reported herein, 1.2 - 2.4 eV, are indi- cative of processes occurring in the bulk of the material. 93 The Pre-exponential Factor in Hemoglobin Conductivity The solid state electrical conductivity of organic substances is generally thought of as having a temperature dependence given by Equation (1). For many polynuclear hydrocarbons there exists a correlation between the activation energy and the pre-exponential factor (Many, Harnik and Ger- 1ach, 1955). The data can be seen (Gutmann and Lyons, 1967) to fit roughly the relationship: logoo = a E + B (36) where a and B are constants for all of the compounds con- sidered. Recently Rosenberg 32 31. (1968) have shown that a compensation effect is exhibited by several bioloqical com- pounds when they are treated in different ways. Several organic semiconductors exhibit a compensation effect as well (Eley, Fawcett and Willis, 1968). These results are similar to the Meyer-Neldel (1937) rule for inorganic semiconductors. In both cases a single compound is capable of exhibiting a variety of activation energies depending on its method of preparation or pretreatment. The activation energy and the pre-exponential factor vary as described in Equation (36). Among the biological substances which exhibit a compensation effect are oxidized cholesterol, nucleic acids and retinal. Melanin with adsorbed water, hemoglobin with several adsorbed vapors and bovine plasma albumen complexed with various carcinogens (Snart, 1968) do not follow the compensation relationship. 94 If it is assumed that most semiconductive materials exhibit a compensation effect, then it is of interest to investigate the implications of a given substance not fol- lowing such a relationship. We may rewrite Equation (1) as: logo = logoO - E/ZkT (37) Substituting Equation (36) we obtain: logo = E/2kTo + B - E/2kT (38) where we have replaced a in Equation (36) by l/2kTo. To is then that temperature at which two samples which have differ- ent activation energies will exhibit the same conductivity. In the case of hemoglobin with various adsorbed vapors this temperature is infinity. The most general interpretation of Equation (38) is in terms of activated complex theory (Eley, 1967). The ex- ponential terms then take on thermodynamic significance as an analogy is drawn between Equation-(38) and: kF = (kT/h)exp(AS/R) ° exp-(AH/RT) (39) where kF is a rate constant; AS and‘AH are the entropy and enthalpy of activation respectively. If this analogy is drawn we are confronted with the perplexing statement that conductivity in hemoglobin conserves entrOpy but conductivity in DNA does not. Another interpretation of Equation (38) is that the process measured, i.e. conductivity, is a two step process, only one of the steps being thermally activated. The step which is not thermally activated may be, for example, 95 intermolecular quantum tunneling. In the case of protein conductivity the probability of the second step is so high that its effective rate constant is unity. If indeed the second step is intermolecular tunneling, as suggested by Kemeny (1968), then the intermolecular barrier in proteins would be very low. Apparent Low Frequency Dielectric Dispersion Low frequency dielectric dispersions attributed to electrode polarization, in aqueous solution measurements, possesses a frequency dependence which is very different from that found for hydrated compacted tablets. Electrode polarization, in the former case, varies as the -l.5 to -l.7 power of the frequency. Employing Scheider's (1962) model of a lumped polarization capacitance in series with the specimen conductance, which is in turn in parallel with the specimen capacitance: JICs ”7 . A. I II CP The admittance of the netwprk is given by: l wZC 2» P G2 ( i where G is the sample conductance, C Y_= G + iwcS + {1 + (-G + iwCP) (40) S is the sample capaci- tance, CP is the polarization and w is the frequency of the impressed voltage. The real part of the admittance is the 96 conductance and the imaginary part is the capacitance. In the case of measurements of biomolecules in aqueous solutions it is assumed that: >> 1 (41) Under this condition the apparent parallel polarization capacitance, C the second imaginary term in Equation (40), A, is: C = (42) According to Wolff's (1936) direct measurement of low fre— quency polarization capacitance in aqueous solutions CP varies as the -0.5 to -O.3 power of the frequency. C the A’ apparent polarization capacitance should then vary as the -1.5 to -l.7 power of the frequency which is found to be the case in the measurement of the capacitance of aqueous solu- tions of biomolecules. However, in the case of hydrated hemoglobin tablets typical low frequency values would be -10 -7 C = 10 farad and G = 10 mho at w = lOOHz. Therefore, it is more reasonable to assume: (11ch2 2 << 1 (43) G in which case: Y.= iw(CS + CP) (44) The measured capacitance should then be the arithmetic sum of the specimen capacitance and the polarization capacitance. 97 If, in the low frequency region the sample capacitance does not exhibit a disperison, the frequency region dependence of the mea- sured capacitance will be that of the polarization capacitance. This is the experimental result which is found, i.e.: Cum-l/3 (45) as illustrated in Figure 17. When these polarization effects are subtracted the low frequency dielectric dispersion in hydrated hemoglobin tablets disappears. Low frequency dielectric dispersion is most probably the result of a Maxwell-Wagner type of process. This type of polarization arises at the boundary between two materials which do not possess the same conductivity to dielectric constant ratio. If a specimen composed of two such mate- rials, is initially in the completely uncharged state, then when a potential is instantaneously impressed across it the dielectric displacement, D, at the first moment, will be constant throughout the specimen. The charges have not yet penetrated into the sample. However, current density is determined by: D (46) nun j=OE= where j is the current density and E is the field strength. An accumulation of charges at boundaries which separate regions of different a/K must then occur. The buildup of charge at the boundary will continue until j is constant. This building up process requires time because it depends upon a finite conduction thrOugh the media on both sides of 98 the boundary considered. It is then a process which may be characterized by a relaxation time (Schwan, 1957). This boundary polarization may be associated either with the interface between the electrode and the hydrated pellet or with the interface between the crystallites and-the inter- sticies. Comparison of Results with Dielectric Theory The adsorption of water, ethanol or methanol alters the conductivity of hemoglobin in such a way that the con- ductivity increases while the semiconduction activation energy decreases. The pre-exponential factor in the con- , ductivity equation is unchanged by the adsorption process. These results can be interpreted in terms of the theory developed in Section II. It appears that the adsorption of ammonia has a dif- ferent effect on the conductivity of hemoglobin. In this case the results resemble classical impurity semiconductivity. The increased conductivity of hemoglobin with ammonia cannot be accurately correlated with the quantity of ammonia ad- sorbed because the partial pressure of the gas in the con- ductivity chamber could not be determined. However, as the rate of flow of ammonia, relative to that of nitrogen, is increased the conductivity of the specimen is increased in- dicating dependence of the conductivity on the quantity of ammonia adsorbed. The results of Figure 13 can be understood either if ammonia is acting as an impurity donating charge 99 carriers to the hemoglobin or if the charge carriers both originate from and move through the ammonia, i.e. conducti- vity of ammonia on a hemoglobin substrate. In the latter case the activation energy measured, 0.8 eV, should be that of ammonia. From the data of Cuelleron and Chariet (1954) the semiconduction activation energy of liquid ammonia can be calculated. A value of 0.1 eV is obtained. At present, therefore, it appears that ammonia is behaving as an impurity in the classical sense. The concentration of ammonia in the hemoglobin tablet is, however, much greater than concentra- tions of impurities in inorganic semiconductors. The im- purity nature of the conductivity could be verified by fol- lowing the temperature dependence of the conductivity of hemoglobin with adsorbed ammonia in order to determine if at higher temperatures intrinsic conductivity, i.e. the conductivity of hemoglobin with an activation energy of 2.35 eV, is found. But at higher temperatures the ammonia desorbes producing anomalous results. Very small quantities of ad- sorbed ammonia must be used which will decrease the temper- ature at which intrinsic conductivity will dominate. How- ever, hemoglobin with small quantities of adsorbed ammonia has relatively low conductivity and the present apparatus can not be used for these measurements. A vibrating reed elec- trometer, and therefore static measurements, must be used. to investigate this conductivity region. When water, ethanol or methanol is adsorbed on hemoglobin the conductivity increases and the semiconduction activation energy decreases in a manner inconsistent with 100 classical impurity semiconductivity. These solvents do not affect the value of the pre-exponential factor. The theory deve10ped in Section II predicts a linear dependence of activation energy on the reciprocal of the effective dielec- tric constant. Since the log of the conductivity varies linearly with activation energy, a similar relation should exist between the log of the conductivity and dielectric constant. In Figure 32 the reciprocal of the dielectric con- stant is plotted against the log of the conductivity. Data for water, ethanol and methanol all fit the same straight line. Interpreted in terms of the theory outlined in Section II this indicates that, according to Equation (18), R, the polarization radius, is independent of the adsorbate. The reciprocal of the dielectric constant is plotted against the activation energy in Figure 33. This is according to Equation (16) and has the same significance as Figure 32. From these figures a value of R may be calculated. In both cases R = 4.3 A. The relaxation of the dielectric medium within a region of radius 4.3 A is responsible for the de- creased activation energy and hence higher conductivity of hemoglobin samples with adsorbed water, ethanol or methanol. The effective dielectric constant of hemoglobin with the same mole percent of the various solvents adsorbed does not vary as the dielectric constant of the solvent. Since R is the same constant for water, ethanol and methanol ad- sorption, it can be seen from Equation (17) that a does not 7...: Figure 32. Variation of conductivity with dielectric con- stant. The circles indicate water, the triangles ethanol and the filled circles methanol adsorption on hemoglobin respectively. log Conductivity (ohm-cm)" 5 Figure 102 l l 0.1 0.2 01.3 (Dielectric Constant)" 32. (14 103 F0 Activation Energy (eV) I I I I 0.1 o.2 0.3 0.4 0.5 (Dielectric Constant)’| Figure 33. Variation of activation energy with dielectric constant. The circles indicate water adsorption, the tri- angles indicate ethanol adsorption and the filled circles indicate methanol adsorption. 104 ° vary directly with the dielectric constant of the adsorbed phase. Equation (17) specifies a linear relation between the quantity of vapor adsorbed on the hemoglobin and the reciprocal of the effective dielectric c0nstant of the hemo- globin-adsorbate system. The data for the adsorption of water on hemoglobin is shown in Figure 34. In the region of hydration where the conductivity is believed to be elec- tronic, i.e. <2BET monolayers of adsorbed water, this re- lation is seen to hold. When hemoglobin is further hydrated deviation from this linearity is found. From Equation (17) and a knowledge of a, which was determined in Section IV, R, the radius of polarization, can be calculated. A value of 3.7A is obtained. This is in close agreement with the value of 4.3A calculated above. The data for ethanol and methanol adsorption are insufficient to draw any conclusions regarding the variation of dielectric constant with the quantity of vapor adsorbed. In both the theoretical develOpment of Section II and the experimental presentation no assumptions were made concerning either the nature of the charge carriers or the mechanism of conduction. (Activation energies have been calculated on a l/2kT basis which does indicate the con- ceptual framework of a band theory. The elimination of the troublesome 2 will, however, only halve the activation en- ergy values and double the polarization radius. Neither of these changes negate any of the preceeding discussion.) Neither the experimental nor the theoretical considerations 105 24- b6“ PZI' ‘7. Water Absorbed Male 5. I .11 r o .| -Z '3 '4 (Dielectric Constant)" Figure 34. Variation of dielectric constant with the ad- sorption of water on hemoglobin. l I l l . 106 presented herein can distinguish from amongst the several possibilities indicated in Section I. However, both the theoretical and experimental discussions (except for the anomalous results with ammonia adsorption) indicate a con- stancy of mechanism over the range of environments consid- ered. Comparison of Quantum Calculations with Experimental Results A number of theorectical calculations have attempted to evaluate the possible band structures of energy levels in a protein system. 'In all such cases the protein has been Ly treated as a repeating structure linked by hydrogen bonds across the peptide chains. The n electrons are considered to be delocalized across the hydrogen bonds. This is essen- tially the method used by Evans and Gergely (1949) who em- ployed Hfickel LCAO molecular orbital calculations. Yomosa (1964) extended the analysis to HMO-SCF and ASMO-SCF cal- culations. A further modification was made by Suard et 31. (1961) to include the oxygen lone pair electrons as well. Suard-Sender (1965) has extended the calculation to include an infinite two dimensional network. Using the results of this latter calculation, a semiconductivity band gap of 5 eV was calculated (as compared with 3 eV calculated by Evans and Gergely). It was stated that this band gap is too large for intrinsic electronic conductivity to be significant and, therefore, measured band gaps of 2.4 eV must refer to some extrinsic processes. 107 A value of the ionization potential minus the electron affinity for a protein can be calculated. Rewriting Equation (14) we obtain: 2 .— e — Ig - Ag — ED + '13—. (l 1/K) (47) In Section III we have obtained values of the dry state activation energy (2.35 eV) and dry state dielectric con- stant (2.3) of hemoglobin. Furthermore, earlier in this section a value of R, the cavity radius, has been calculated as 4.3 A. Substituting this value in Equation (47) we obtain Ig - Ag = 4.3 eV. It is difficult to specify exactly what this means, but presumably it refers to vertical ionization and electron attachment processes in a small isolated polypeptide region of the protein molecule, i.e. a gas of peptide bonds. This would correspond to the general usage of Ig and Ag as gas state values. Simpson (1964) has estimated that the ioniza- tion potential (19) of an isolated amide group is 8.5 eV and that the electron affinities are usually 1 - 2 eV. This value of I9 is close to values of Ig listed by Gutmann and Lyons (1967) for N, N-diethylacetamide (8.60 eV) and N- methylacetamide (8.9 eV). It is believed that these com- pounds more closely resemble a peptide bond than does forma- mide (10.25 eV). Suard et 31. suggest that in going from a monOpeptide linkage to a polypeptide linkage the value of Ig would decrease by 1 eV and Ag would increase by 0.6 eV. From these rough estimates a value for (I - A ) 9 q 9 protein' 4.9 - 5.9 eV is calculated. This is in better agreement with of the experimental value of 4.3 eV. 108 From band theory, if such a model is applicable, it is expected that the semiconduction band gap, E, is equal to IC - AC where IC and AC are the solid state values of the ionization energies and electron affinities. The difference between the gas values and the solid state values are the result of polarization stabilization energy, P, arising from relaxation of the lattice around the new charge centers. Thus, I = I - P and A = A + P or: C 9 C 9 E=IC-AC=Ig-Ag-2P (48) as in Equation (12). In the case of protein this relaxation may take place in secondary, tertiary or quaternary structure. Quantum calculations are inherently vapor state cal- culations (Kasha, 1962). Therefore, the calculations of Evans and Gergely, Yomosa, Suard, gt gt._and of Suard-Sender do not explicitly take into account polarization of the medium when charges are separated. Quantum calculations.are for a medium with dielectric constant of l. The experiments, however, are executed in a medium of dry state dielectric constant 2.3. It is, therefore, suggested that the value of 5 eV calculated by Suard-Sender should be compared with the experimental value of Ig - Ag and that when a proper account- ing is made of the dielectric constant of the medium the discrepancies between theory and experiment are diminished. As far as Optical transitions are concerned the quantum calculations are not questioned by the experimental results herein under discussion. That is, an optical tran— sition is not expected at 2.35 eV (band to band transitions), 109 or at even lower energies in the case of hydrated proteins, which is the measured activation energy. It would then ap- pear that the excitation states of a protein lie at higher energies than the conducting states. This is not an unusual condition for organic molecules. Adsorption Studies Determinations of Vm,the monolayer coverage, have been presented in Table 6. These values are somewhat larger than 5.76 gm water per 100 gm of ox hemoglobin reported by Cardew and Eley (1958). The differences between the values herein reported and those of Cardew and Eley cannot be at- tributed to protein denaturation. Cardew and Eley, as well as Eley and Leslie (1966) have shown that denaturation has a small effect on the value of Vm. Differences between the amino acid composition or tertiary structure of ox and bovine hemoglobins could not be great enough to account for these differences in Vm' The values of Vm reported herein, 430 - 470 moles/105 gm protein are very close to the number of polar side chains, including proline, found for hemoglobin, 435 moles/105 gm protein (Tristam, 1949). It would appear that water, methanol and ammonia are adsorbed predominantly on the polar sites of the hemoglobin molecule. The majority of the polar side chains of amino acids are on exposed portions of the mole- cule, as discussed in Section I, and form the bulk of the adsorption sites. One BET layer is completed when a mole- cule of vapor is adsorbed on each of these polar sites. 110 An apparent anomaly exists in the case of ethanol adsorption. Because of the larger size of the ethanol mole- cule, as compared to water or ammonia, the diffusion of ethanol into the sample is at a much slower rate than the diffusion of the other vapors discussed. This decreases the accuracy with which the adsorption isotherm can be obtained but could hardly explain a 300% variation in the determination of a BET adsorption. If the Cross-sectional areas of adsorbed water and O 2 and 14.6 A2 ammonia are taken as 10.8 A respectively (Liv- ingstone, 1949) and the surface area of a dry spheroid of hemoglobin is taken as 8,350 A2 (Bragg, Howells and Perutz, 1954), then at a coverage of one BET monolayer of water 39% of the surface area of the protein molecule is covered. The coverage for one BET monolayer of ammonia is 53%. The cross-sectional areas of methanol and of ethanol may be calculated from the formula given by Emmett and Brunauer (1953): 2/3 — E. Area — 1.09 [ON] (49) where M is the molecular weight of the vapor; p is the den- sity of the vapor and N is Avogadro's number. This yields 0 2 for methanol, and 18 A2 for a cross-sectional area of 14 A ethanol. One BET monolayer of methanol then occupies 46% of the surface area of the hemoglobin molecule. If it is as- sumed that one BET monolayer of ethanol is adsorbed at 0.16 moles/100 gms of hemoglobin, then 22% of the surface of the hemoglobin molecule is covered at the monolayer. However, if 111 one molecule of ethanol is adsorbed at each polar site the coverage is about 65%. It may be argued that all of the polar sites are not occupied by‘ethanol molecules at the apparent BET monolayer because the polar sites are on the average clumped and the adsorption of an ethanol molecule at each site is sterically impossible. The difference between the cross-sections of methanol and ethanol is not, however, large enough to explain the large difference in the BET calculations. A convincing explanation of the apparent anomaly escapes the present author. If the polar sites are distributed uniformly on the surface of the hemoglobin, then each site will have asso- ciated with it 29 A2. When one BET monolayer of water is adsorbed,the average center-to-center distance between nearest neighbor water molecules will be W 6 A. The diameter of the water molecule is W 3.8 A; therefore, a single mole- cule of water can, on the average, bridge the gap between nearest neighbor water molecules. When this gap is bridged, and a contiguous path of water molecules can be found, it is expected that protonic conductivity, through these water molecules, will dominate the conductive process. This may occur when less than two BET layers of water are adsorbed, which is consistent with the results of Maricic and Pifat (1966) who found 90% ionic conductivity in hemoglobin with 15% adsorbed water. Values for the constant C calculated from the BET equation are given in Table ‘; Eley and Leslie (1966) Pg 72 .12 .n .Iu'Im 112 report a value of 8 To 12 for water adsorbed on hemoglobin. The value of 12.3 reported herein is in close agreement with the published results. They, however, obtain a value of 22 for methanol adsorbed on bovine plasma albumen compared with 3.5 found for the adsorption of the same vapor on bovine hemoglobin. The value of C is very sensitive to small errors in the adsorption isotherm and should only be taken as an indication of the difference between the heat of liquefaction of the first BET monolayer and the heat of liquefaction of the bulk. Equation (30) defines C which may be rewritten as: RT log c = El - L (50) Calculations of(El - Elalong with accepted values of L,are given in Table 8. In all cases the heat of liquefaction in the first BET layer differs only slightly from the heat of liquefaction in the bulk. Table 8. Heat of vaporization calculations of water, methanol, ethanol and ammonia. r Jr _‘ r Adsorbate C L(cal/mole) E1 - L(cal/mole) Water 12.3 10,500 2,820 Methanol 3.5 8,400 735 Ethanol 1.7 9,400 287 Ammonia 2.0 5,100 374 113 The parameter, a, is defined by Equation (5) and computed in Table 7. This parameter is a measure of the ef- fectiveness of the adsorbate in increasing the conductivity of the substrate, in this case hemoglobin. Although it has been shown, see Figure 32, that adsorption induced conducti- vity increments are related to the effective dielectric con- stant of the system, it is interesting to note that the ef- ficiency with which an adsorbate increases the conductivity is not a simple function of its dielectric constant. If the tablet is assumed to consist of spherical particles of hemoglobin and spherical adsorbate particles then a relation can be derived which relates the measured dielectric constant of the tablet, KP, the dielectric con- stant of hemoglobin, the dielectric constant of the KH , adsorbate, the partial volume of hemoglobin, 6 and the H’ The measured dielectric partial volume of the adsorbate, 6A. constant of the tablet is considered to be a continuous prop- erty of the tablet, then the electric field inside the hemo- globin, EH, and the electric field inside the adsorbate, EA' are given by: 3KP E = E (51) H ZKP + KH K K A 2.P + A The polarization of the tablet is limited to the polarization of hemoglobin and the polarization of the adsorbate. The polarization of the tablet (per cm3) is then: 114 K - 1 _6H(KH - l) 6A(KA - l) P = ———_—_E‘— 4n EH + 4n EA (53) Eliminating EH and EA between Equations (51), (52) and (53) we obtain: K-l 1<.—1 .KA-l ___._=____a +_—:—_5 (54) 3KP KH + ZKP H KA ZKP A If the bound nature of the adsorbate is considered, then the measured dielectric constant of the tablet, KP, may be con- sistant with Equation (54). In this case adsorbate-adsorbent interactions need not necessarily be postulated. VI. SOME THOUGHTS ON THE BIOLOGICAL RELEVANCE OF SOLID STATE SEMICONDUCTION The semiconductive prOperties of biologically impor- tant molecules may be related to their functions. The transport of charge over relatively long distances is an important process in biology. Several tentative models which utilize the semiconductive prOperties of biological molecules have been proposed. These models are most often hypothesized in organelles where electron microsc0py or x—ray diffraction studies have indicated extensive order on the molecular level. Some years ago Arnold and Sherwood (1957) proposed a solid state model for the action of chloroplast grana in the photosynthetic apparatus. It was proposed that free electrons and holes are generated by the adsorption of light in the chlorOphyll. The electrons and holes then move in- dependently to different trapping centers where the dark chemistry of photosynthesis proceeds. The visual pigments in the highly organized lamellar structures of the outer segments of rods and cones is another system. Rosenberg (1962b) has prOposed that photoexcitation leads to the creation a free charge carrier (probably elec- tronic in nature) which is injected from the chromophore into the attached protein moiety. The drifting of free charges 115 116 in the protein constitutes an electric current which can change the potential across a neural membrane. This model establishes a causal chain from the adsorption of a light quanta to the initiation of the neural response. The semiconductive nature of lipids has been demon- strated by Leslie gt gt. (1967) and by Rosenberg and Jendrasiak (1968). The temperature dependence of the conductivity of lipid bilayers, 50 - 100 A thick, follows Equation (1) and hence they are semiconductors. It has been prOposed (Rosen- berg and Bhowmik, 1968) that lipid bilayers are electronic semiconductors. This opens up an entirely new area of semi- conductive models. The membrane mediated oxidation-reduction scheme of Mitchell (1961) may then proceed via electronic carriers. Solid state models of neural transmission, e.g. the model of Wei (1967), must now be viewed in a new context. All of the above systems are characterized by an intermolecular transport of charge carriers. Semiconductive models can also be employed in systems where the movement of charge is within a single macromolecule. In enzymes which involve the transfer of an electron the protein molecule may act as the path of the electronic charge carrier between the sites of oxidation and reduction. Attempting to test the feasibility of this model Cardew and Eley (1959) calculated the conductivity expected on a molecular level. The conductivity parameters of dry hemoglobin were used. For a sea urchin egg the respiration rate would be equivalent to a current of 1.68 x 10.10 amp. If this current, as assumed by Cardew and Eley, flows through 117 a 1 micron fiber of 50 A diameter under a tension of 1 V, then the conductivity of hemoglobin is 16 orders of magnitude too small to explain the oxidation mechanism. The activation energy of dry hemoglobin (data from Cardew and Eley on a l/kT basis) is 1.4 eV while the activation energy for res- piration is about 0.5 eV. Therefore, they conclude that a semiconductive model can not explain biolOgical respiratory processes. Rosenberg and Postow (1968) have amended this cal- culation by employing the conductivity parameters of hydrated hemoglobin. They assumed intra-molecular electron transport .and therefore considered a conductor of 25 A diameter and 36 A length, the approximate dimensions of a cytochrome c molecule. The resistivity was taken as that of hydrated hemoglobin, i.e. 108 ohm-cm. For a l V redox potential a current of 10-15 amp/molecule is expected. This would re- quire a concentration of 105 molecules of cytochrome per sea urchin egg which is a reasonable figure. The conductivity' corresponds to a maximum turnover rate of 104 electrons/sec/ molecule which is above that typical of most enzymes. The activation energy of hydrated protein, 0.6 eV (on a l/kT basis) is close to the activation energy of respiration. It must therefore be concluded that the assumption of elec- tronic conductivity in protein molecules as the rate lim- iting step in electron transfer processes is consistant with biological data. The kinetics of electronic conduction through a particle has been examined by Cope (1965). The kinetics 118 predicted under the assumption of electronic conductivity are consistent with those observed in the cytochrome oxidase system. Anomalous Arrhenius plots of enzymatic activity have recently been reported for several different enzymes shown in Table 9. The transition temperatures range from 13° C to 24° C for the different enzymes. Activation energies for enzymatic activity calculated at temperatures above the transition temperature are in all cases smaller than those calculated below the transition point. The activation en- ergies calculated from Arrhenius plots (on a l/2kT basis), shown in Table 9, are very similar to those which would be. expected for dry (or partially hydrated) and hydrated pro- teins. Optical rotatory disPersion, ultra violet difference spectra, flourescence studies and visible spectra all indi— cate a conformational change at the transition temperature. If it is hypothesized that, for these several enzymes, the rate limiting step for enzymatic activity is intra- molecular electronic transport, then the extant data can be explained with the aid of Figure 35. The conformational change may so alter one portion of the protein (site A in Figure 35) as to permit its extensive hydration in one con- figuration while demanding a hydrOphobic environment in the other configuration. When site A is in a hydrOphobic envi— ronment, low dielectric region, the activation energy for semiconduction is high. In a hydrOphilic environment, high dielectric medium, after the conformational change, the activation energy is decreased. 119 Amomav ocmmm o.a >.H «a ommcflx oumusuhm maomsfi panhmu Amomavamm mm mo>mna m.H Amvo.e ma .h_ammamuonamonm ammooaam loomav.mm mm mmmmmz H.H H.~ em Amumoumnsm acohnoms as ammoflxo meow OCHEM1© Aomaac.mm mm sommmz m.o m.H «a Aanmuumnsm mahcmamuec mmmpflxo ofloa OGHEMIU Ammaac.mm mm m>aq H.H H.N ea came»: onfipmumm mnsumumm 1&0» goes lamp 30H Loco mosmummom A>ovm mucumummEoB cofluflmcmna mamncm .mcoHuHmGMHu HMGOHuMHsmHchO mcfl3ocm mmE>Ncm mo moumu Hm>ocusp EdEmeE mo muon msficocuum Eoum wouaasoamo Amflmmn me\av moflmuocm coaum>fluo¢ .m magma Figure 35. Illustration of the semiconduction model of enzyme activity. When site A is in a hydrophobic environ- ment the activation energy for semiconduction will be high. If the protein conformation changes so as to place site A in a hydrophilic environment the activation energy for semiconduction will be lowered. ' 121 >0mmzw 22.22.54 30... m whdmkmmam .mm musmwm >Gmmzm ZO_._.<>_._.O< 10.1 d. mh