J, Phys. Chem. 1980, 84, 1325-1329
charged species out of the photochemical cage. The back reaction occurring in the acid pH range seems to be the first such reaction t o be observed between photoredox products returning directly to the ground state reactants in a polyelectrolyte system. In alkaline solutions the possibility of using the photoelectron transfer product R ~ ( b p y ) , ( c N ) ~for + the production of oxygen was investigated, although totally conclusive results could not be obtained. Such a system as that investigated above may be potentially useful in the conversion and storage of solar energy either by operating a photogalvanic cell based on the back reaction of the charge-separated products or by converting the high yields of the high-energy charge-separated products into more convenient synthetic fuels. Work is continuing in this laboratory on searching for new improved polyelectrolyte systems where the bulk back reaction is further hindered allowing for easier extraction of the stored energy.
Acknowledgment. The authors gratefully acknowledge the financial support given to this work by the Israel Ministry of Energy. The authors are indebted to M. Ottolenghi and Z. Aizenshtat for useful discussions. References and Notes (1) H. Morawetz, Acc. Chem. Res., 3, 354 (1970). (2) (a) H. Morawetz and B. Vogel, J . Am. Chem. Soc., 91, 563 (1969); (b) H. Morawetz and G. Gordiner, ibid., 92, 7532 (1970). (3) (a) N. Ise and Y. Matsuda, J . Chem. SOC.,Faraday Trans. 1 , 8% 99 (1973); (b) S. Kunugi and N. Ise, Z . Phys. Chem. (Frankfurtam Main), 91, 174 (1974). (4) C. D. Jonah, M. S. Matheson, and D. Meisel, J . Phys. Chem., 81, 1805 (1977). (5) I. A. Taha and H. Morawetz, J . Am. Chem. Sac., 93, 829 (1971). (6) D. Meisel, J. Rabani, D. Meyerstein, and M. S. Matheson, J . Phys. Chem., 82, 985 (1978). (7) C. D Jonah, M. S.Matheson, and D. Meisel, J. Phys. Chem., 83, 257 (1979). (8) D. Melsel and M. S. Matheson, J. Am. Chem. Soc., 99,6577 (1977). (9) D. Meisel, M. S. Matheson, and J. Rabani, J. Am. Chem. Soc., 100, 117 (1978). (10) Y. Usui, S. Kodera, and Y. Nishida, Chem. Left., 1329 (1976). (11) D. Meyerstein, J. Rabani, M. S. Matheson, and D. Meisel, J. Phys. Chem., 82, 1879 (1978).
1325
(12) (a) Y. Moroi, A. Braun, and M.Gratzel, J . Am. Chem. Soc., 101, 567 (1979); (b) Y. Moroi, P. P. Infelta, and M. Gratzei, ibld., 101, 573 (1979). (13) F. Boiieta, M. Maestri, and V. Baizani, J. Phys. Chem., 80, 2499 (1976). (14) J. N. Demas and G. A. Crosby, J. Am. Chem. Soc.,93, 2841 (1971). (15) S. Raffia and M. Ciano, J . Nectroanal. Chem., 77, 349 (1977). (16) J. N. Demas, J. W. Addington, S. H. Peterson, and E. W. Harris, J. Phys. Chem., 81, 1039 (1977). (17) J. N. Demas, T. F. Turner, and 0. A. Crosby, Inorg. Chem., 8, 674 (1969). (18) C. R. Goldshmidt, M. Ottoienghi, and 0. Stein, Israel J. Chem., 8, 29 (1970). (19) D. Lougnot, G. Dolan, and C. R. GoidshmMt, J. Phys. E, 12, 1051 (1979). (20) (a) C. T. Lin and N. Sutin, J. phys. Chem., 80,97 (1976); (b) D. Melsel, M. Matheson, W. Mulac, and J. Rabani, ibid., 81, 1449 (1977); (c) C. T. Lin, W. Bottcher, M. Chou, C. Creutz, and N. Sutin, J. Am. Chem. Soc., 98, 6536 (1976). (21) S. H. Peterson and J. N. Demas, J . Am. Chem. Soc., 98, 7880 (1976). (22) Ce(1V) and PbO, in HC104were found to produce no change in the visible absorption spectrum of Ru(bpy)dCN), after sthing the solution for several hours and then centrifuging. It was concluded therefore that no oxidation, indeed no reaction whatsoever, occus under these conditions. However, when the acid m e d i i was replaced by H M 4 , reaction with PbO, was observed. After stirring the mixture for 3 h a ruthenium(II1) product was in fact formed which on addition of OH- gave back a ruthenium(I1) compound (absorption maximum at 640 nm) and then proceeded on to give a further product (absorption maximum at 453 nm). lhls final product was atso conftmed to wntain ruthenium in oxidation state (11). However, since neither of these two products gave an absorption or emission spectrum identical with Ru(bpy)&N), it was assumed that the origlnal oxidation reaction with PbO, also involved partial decomposition of the complex. It should also be noted that addition of cyanide ions to the final ruthenium(I1) products caused no change in their absorption spectra. Ozone passed through a sokrtion of Ru(bpy)dCNk gave results indicating that it caused complete decomposition of the Ru(bpy)dCN), complex, the reaction possibly proceeding via OH radical attack on the bipyridine ring. Ru(bpy):+, formed by PbO, oxidation of Ru(bpy)t+ in the presence of 1 M H2SO4,when added to a solution of R$bpy)&Nk immediately gave the well-known spectrum of Ru(bpy): (A, = 452 nm, E = 14400 M' cm-l) but this unfortunately made any identification of the possible Ru(bpy)&Nk+ product in thls wavelenglh twqlon very difficult. The final method of oxidatbn attempted involved Mn formed in situ by pulse radblysls of a sokition of Mn2+bns and Ru(bpy&N)n. Again no reaction with the ruthenium complex appeared to take place, however, it did disproportionate to Mn2+and MnO,. (23) Variation of up to 10% in peak absorbance could be observed both in the dark and under illumination. (24) C. Creutz and N. Sutin, hoc. Natl. Acad. Sci. U.S.A., 72, 2858 (1975). +
Kinetics of the Exchange of Protons between Hydrogen Phosphate Ions and a Histidyl Residue L. J. Slutsky, L. Madsen, Department of Chemistry, University of Washington, Seattle, Washington 98 195
R. D. White," and J.
Harkness
Department of Chemistty, University of Idaho, Moscow, Idaho 83843 (Received August 8, 1979) Publication costs assisted by the University of Idaho
The rate constants and the volume changes for the reaction of HP0:- with the protonated imidazole ring of the histidyl residue in bacitracin, and with imidazole itself, have been determined at 4 "C.The rate constants are 1.4 X lo8 M-' s-l for bacitracin and 4.0 X lo8 M-l s-l for imidazole. The rate constants are used to estimate the spectrum of relaxation times and acoustic relaxation amplitudes associated with intermolecular and intramolecular proton-exchange reactions in biological media. It is concluded that the magnitude of the acoustic absorption reasonably attributableto the perturbation of proton-transfer equilibria between proteins and inorganic phosphate is comparable in magnitude with the acoustic absorption observed in some intact tissues.
I. Introduction The peptide antibiotic bacitracin (molecular weight = 1420) has a single histidyl residue with a PK,, at room temperature, of 6.9. If AH" for the ionization of the imidazole group in the antibiotic is close to the heat of ion0022-3654/80/2084-1325$01 .OOlO
ization of imidazole2 (8 kcal), then at 4 "C the pKa of the histidyl residue will be 7.3. At 4 O C the pK, of H$'04- is 7.286.2 Thus, the equilibrium constant for eq 1 (where
-IH+
k + HPQt- & -I + H2P04kb
0 1980 American Chemical Society
(1)
1326
The Journal of Physical Chemistry, Vol. 84, No. 11, 1980
-IHS and -I represent, respectively, the protonated and neutral forms of the imidazole ring) will be rather close to one. Bacitracin contains two carboxyl groups with pKa)s of 3.9 and 4.6 and two -NH2 groups with pK,'s presumably greater than 9. There is thus no group other than the histidyl which titrates near neutrality. From the volume change for the reaction of protonated imidazole with hydroxide ion3 (23.9 cm3), for H 2 0 H+ OH- (-21.3 cm3),4and for H2P04-- HP02-+ H+ (-21.4 cm3),6the volume change for the reaction represented by eq 1would be estimated to be 24 cm3. The large volume change, convenient equilibrium constant, and the absence of competing proton-transfer reactions at other residues combine to make the reaction represented by eq 1 unusually amenable to study by ultrasonic techniques. We report a determination of the rate constants and volume changes for eq 1 for imidazole and for the imidazole ring in the histidyl residue of bacitracin and very briefly discuss the possible utility of the results in the estimation of the rates and relaxation amplitudes associated with intermolecular and intramolecular proton-transfer processes in biological media. 11. Ultrasonic Absorption The ultrasonic absorption ( a )at frequency f associated with the perturbation of a single chemical equilibrium with relaxation time T is6
-
+
where f, = 1 / 2 m and A represents the attenuation associated with the viscosity and thermal conductivity of the medium as well as that due to any processes with relaxation frequencies much higher than f r for the process in question. When the high-frequency limit of ( a / f ) is accurately determined it is often more convenient to display the excess absorption per wavelength ( a , = a - A f ) and thus to rewrite eq 2a in the form
uc
(f/fr)
a,h = 2* 1 + ( f / f r ) 2
and if the activity coefficient may be approximated by the Debye-Huckel equation or Davies7 semiempirical modification thereof
where D is the dielectric constant of the solvent and N is Avogadro's number, then
For an elementary step the rate (Rf) of the forward reaction at equilibrium may be expressed in terms of the rate constant (kf) and the equilibrium activities of the reactants (ai) bys Rf = kfIlallvil (8) 1
where the continued product extends only over reactant species (vi C 0). The relaxation time may be obtained from the relation8 7-l = RJ-' = wr E 2xfr (9) Or, explicitly for the reaction represented by eq 1 ar
= kf(YIHt)(YHP042-)(IT11Ht)(mHP042-)r-1 (lo)
Introducing the abbreviations cb for the total concentration of the buffer (cb = mHzp04-+ mHpoz-), c, for the total concentration of antibiotic or imidazole (c, = m-I + m-H+), y for the activity coefficient of a univalent ion as calculated from eq 6, Rb = aHp04z-/aH2p04-, and R, = a-I/a-IH+, eq 10 becomes
(2b)
where u is the velocity of sound. For a reaction with enthalpy change AH and volume change A V proceeding in a medium with density p and coefficient of thermal expansion 8 in which the heat capacity (per unit volume) is cp (3) If the equation for the reaction in question is written in the form CiviAi = 0 where vi, the stoichiometric coefficient of the species Ai,is taken to be positive for products and negative for reactants, and if the activity of the ith species is expressed in terms of its molar concentration (mi) as ai = Timi, then
Equation 4 as written here is specialized to the class of reactions for which, as for eq 1, = 0 and presumes, as is the case in this study, that the volume change for the reaction is small compared to the reciprocal concentrations of the less abundant reacting species. If it is further assumed that the activity coefficients depend on the chemical composition only through the ionic strength Z defined by I = 1/2ximizipwhere ziis the charge of the ith species in units of the charge of the electron (3),then eq 4 may be simplified to
xiv;
Slutsky et al.
The values of R,, Rb, and the equilibrium constant for the overall reaction are readily calculated from the pH and the pKa's of the buffer and the histidyl residue. If one works near 4 " C where the coefficient of thermal expansion of the solution is small, then the term in AH in eq. 3 may be neglected and a determination of C and 7 at a single set of conditions will suffice to determine the forward and reverse rate constants and the volume change. We have determined the acoustic absorption in 0.01 M solutions of bacitracin at 4 " C and pH 7 as a function of potassium phosphate buffer concentration in the range c b = 0 to c b = 0.5. We have relied on the data at cb = 0.1, where the relaxation frequency is conveniently situated experimentally and where one may calculate activity coefficients from eq 6, with some expectation of success, to deduce the rate constants and AV. We have used the data at other concentrations to test the presumption that the observed acoustic absorption is primarily due to perturbation of a proton-transfer equilibrium between the antibiotic and the hydrogen phosphate ion. Similarly, in the case of imidazole, we have deduced the kinetic and thermodynamic constants from data at cb = 0.1 M and an imidazole concentration of 0.03 M. Experimental Section and Results The excess acoustic absorption in 0.01 M bacitracin is displayed in the form of plots of a,/f as a function of
The Journal of Physical Chemistry, Vol. 84, No. 11, 1980
Proton Exchange between HP04'- and Histidyi
5@ $ %E 32000 0 0
Q
:;Aoi;*e
].
****0
~
s
0
e/,. 1000
AAA
-05
o t
1
A A
0 0
%:!& -0 5
a
A.
O0
a
05.a
1327
&%*
4,
b.. 0 5 log ( f i n MHz)
1
0 log ( f in MHz)
Flgure 1. The excess acoustic absorption divided by the frequency squared (alf') in 0.01 M bacitracin at pH 7 and 4 O C as a function of frequency (f) and the molar concentration of potassium phosphate buffer (cb), The excess absorption here denotes the difference between the absorption exhibited by a solution of bacitracin in aqueous buffer and the absorption in the buffer itself. Solid circles correspond to cb = 0.0, 0 to cb = 0.001, 0 to cb = 0.01, and A to cb = 0.1. The upper right panel contains data for cb = 0.5.
frequency and concentration of the buffer in Figures 1 and 3. The excess absorption in the unbuffered solution is relatively small, but not altogether negligible, and it is clear that there is a process other than proton exchange between bacitracin and the buffer which contributes to the absorption. If one might assume that this process is not altered by the presence of the protonated phosphate ion, then it would be advantageous to display the difference between the absorption in buffered and unbuffered solution. Such a display is given in the form of a plot of the excess absorption per wavelength (a& vs. f . The continuous curve through the data in 0.1 M phosphate buffer represents the excess absorption due to a single relaxation with CT = 2016 X :LO1' sz/cm and f, = 1.2 MHz. These relaxation parameters give quite a good account of the experimental results. The rate constant kfcalculated from the observed relaxation frequency in 0.1 M buffer with eq 6 and 11 is 1.4 X lo8 M-l s-l. Since K = 1.0, k b is also 1.4 X lo8 M-l s-l. The volume change for the reaction represented by eq 1 deduced from the experimental relaxation amplitude by eq 3,6,and 7 is 26 crn3and is thus rather close to the value to be expected if AV for the protonation of the imidazole in bacitracin is the same as that in small molecules. Equation 6 and the known pressure dependence of the dielectric constant of waterg predict a small but not altogether negligible dependence of AV on the ionic strength since
10
Figure 2. The difference between the ultrasonic absorption per wavelength at buffer concentration c ( a ( c ) X )and the absorption in the absence of buffer (a(0)X)in 0.01 M bacitracin at 4 O C and pH 7. The upper set of soli circles corresponds to cb = 0.1 M, the open circles to cb = 0.01 M, and the lower set of solM circles to cb = 0.001. The curve through the data at cb = 0.1 represents the best slngle-relaxation fit to that data. The remaining continuous curves are calculated from the rate constant and volume change deduced from the relaxation parameters in 0.1 M buffer.
,*e***
Q
Q
i z -
B
a
200 100 -.5
5
0
10
1.5
log ( f i n MHz)
Flgure 3. The excess acoustlc absorption in 0.01 M bacitracin in 0.5 M phosphate buffer at pH 7 and 4 O C as a function of frequency. 25
2 VI
8 %
$
15
1
5
I
0
1 log ( f inMHz)
2
Figure 4. The excess acoustic absorption per wavelength for 0.03 M imidazole in 0.1 M potasslum phosphate buffer at pH 7 and 4 O C . The solid circles represent data obtained in a pressurized spherical resonator, the squares measurements in a pulse-echo apparatus of conventional design.
where AVO is the standard volume change, @theisothermal compressibility of water, and (a In DldP), = 4.7 X ~ m ~ / d y nAt. ~4 "C and the ionic strength of the 0.1 M potassium phosphate buffer, eq 12 predicts AV = AVO + 1.7 cm3 or AVO = 24.3 cm3. The remaining continuous curves in Figures 2 and 3 are calculated from the rate constant and AVO deduced from the results at cb = 0.1 M by eq 12,11, 7, 6,3,and 2. The agreement with experiment is quite good except perhaps
in the 0.5 M phosphate solution where the ionic strength is sufficiently high so that the adequacy of eq 6 as a basis for the calculation of the activity coefficients is questionable. Thus, the variation of the acoustic absorption with chemical composition is such as to nominate perturbation of the equilibrium represented by eq 1 as the principal source of absorption. A plot of a,X vs. frequency for 0.03 M imidazole in 0.1 M buffer is given in Figure 4 where the continuous curve corresponds to a single relaxation with f, = 4.5 MHz and
1328
The Journal of Physical Chemistry, Vol. 84, No. 11, 1980
CT = 1000 X s-z/cm. The rate constant kf derived from these parameters is 4.0 X lo8 M-l s-l. The volume change is 21.7 cm3/mol and AVO N 20.0 cm3/mol. In the case of imidazole at 4 "C the equilibrium constant for eq 1 is 0.619,2 thus kb = 6.5 X lo8 M-l s-l. Schwarzmhas determined relaxation parameters for the reaction of HP042-with imidazole between 10 and 40 "C a t an ionic strength of 0.2 M presuming the activity coefficients to be 1 and relying on the kinetic data to determine the equilibrium constant. He finds, at 10 "C, kb = 3.7 X lo8 s-l M-l, kf = 6.5 X los s-l M-l, and AV = 20 cm3/mol. Aqueous solutions of bacitracin are not stable upon prolonged storage at room temperature and neutral pH. Therefore, we have not repeated these studies at 25 "C. If, as is usual, it is assumed that the volume change for a simple proton-transfer reaction such as eq 1is primarily electrostrictive in origin, then the temperature dependence of the volume change might be approximately calculated from the ionic radii (RJ of the reacting species and the temperature and pressure dependence of the dielectric constant of waterg by means of the relation
The standard volume change at 25 "C estimated with eq 13 (with the radii of HP02- and H2P04both taken to be 2 A) is 25.4 cm3/mol for bacitracin and 22.8 cm3/mol for imidazole.
Discussion A . Volume Changes. These results imply a AVO of 26 cm3/mol for the reaction of the protonated imidazole in bacitracin with hydroxide ion at 4 "C and 23.5 cm3/mol at 25 "C. The room temperature volume changes are thus rather close to those which have been determined for small molecules such as imidazole (23.g3) and histidinate (23.61°) and significantly greater than the 15-18 cm3/mol which has been found for larger proteins such as lysozyme,ll ribonuclease,'l bovine serum albumin,ll and hemoglobin.12 B. Rate Constants. The rationalization of the observed rate constants would seem to be present no difficulty. For a simple diffusion-controlled reaction of the form
-I
+ H2P04
k
-IHf
+ HP042-
the rate constant may be estimated by means of the Debye-Smoluchowski13 equation k = ~RuN(D-I DH2p04-)rd (14)
+
where N is Avogadro's number, rd an effective radius for reaction, u a steric factor, and Di the diffusion coefficient of the ith species. We have taken rd to be a reasonable distance between an N atom hydrogen bonded to an OH of a dihydrogen phosphate ion and the central P atom of that ion (4.5 A) and u to be 1 / 4 since presumably one of the protonated 0's of the HzP04-ion must be oriented toward the imidazole and the bulk of the protein would restridt the approach of the H2P04ion to a solid angle of 27r.
The limiting equivalent conductance (A) of H2PO4- at 18 "C is 27.5 cm2/(ohm mol).14 The diffusion coefficient at 18 "C calculated from D = RTX/32 (where R is the gas constant and 3 the Faraday) is 0.71 X cmz/s. Assuming that the temperature dependence of D below 18 OC is typical of the small ions which have been more extensively investigated,15 one would estimate D N 0.45 X cm2/s at 4 "C. For the case of an imidazole bound
Slutsky et al.
to a rather large peptide framework as in bacitracin D-* + D~,po,-.N DHzpo4-and the estimated value of the rate constant is kf = 3.8 X lo8 s-l. The diffusion coefficient of imidazole should be roughly comparable with that of H2P04- and kf for the reaction of H2P04-with imidazole would be estimated at 7.6 X lo8 s-l. One would expect that the rate constant for a reaction with an equilibrium constant close to one would be somewhat less than that predicted by the Debye-Smoluchowski equation which presumes that reaction proceeds at every encounter. A reaction such as that represented by eq 1can at least formally be divided into a diffusional encounter, a reversible proton transfer, and separation of the products; that is, if H P and P represent respectively the protonated and unprotonated forms of the phosphate buffer k
-1H
+ P ? -1H--P
-1H- -P + -1- -HP -I--HP
e -I + H P k3
(15a) (15b) (15~)
where kl and k3 may be estimated from eq 14. If the coupled relaxation equations corresponding to the kinetic scheme represented by eq 15 are solved for the case of interest here where the concentration of the intermediate species are small compared to the concentrations of reactants and products, then the rate constants of eq 1in terms of the constants of parts a and c of eq 15 and K the k3) equilibrium constant for eq 15b are kf = klk&/(klK and k b = klk3/(k1K + k3). Since K N 1the predicted rate constants for imidazole and bacitracin are 3.8 X lo8 and 1.9 X lo8 s-l, respectively. Thus, the elementary theory of diffusion-controlled reactions with plausible values of the geometrical parameters gives a rather satisfactory account of our results.
+
Inter- and Intramolecular Proton-Transfer Kinetics and Relaxation Amplitudes in Biological Media If A and B represent the unprotonated forms of two equivalent independent proton-binding sites on a single proton molecule (here written AB) and if the charges of the various species are not made explicit, then the equations for proton-exchange between the various forms of AB and the buffer may be written k
HABH + P -PIHAB + HP
(164
+
(16b)
kbl
HABH + P
k
kbz
k
ABH + HP
HAB + P + A B kb3
k
+ HP
ABH + P 2 AB + HP kbi
(16~) (16d)
In the case where the pK,'s of AH, BH, and PH are identical and the forward rate constants of parts a-d of eq 16 the same, at the midpoint of the titration of the three groups the normal reactions and normal relaxation frequencies are w = kf(2co+ cb) HABH + 2P + AB + 2PH (17a) w = 2k$b HABH + AB + HAB + ABH (17b) ABH + HAB w = kfCb (17~) where c,, is the protein concentration and cb the buffer concentration.
Proton Exchange between HP0:-
The Journal of Physical Chemistry, Vol. 84, No. 11, 1980 1320
and Histidyl
The rate constant, kf should exhibit roughly the same temperature dependence as the diffusion coefficient thus at 37 OC one would expect kf N 3 X lo8 and, if in the intracellular medium the concentration of inorganic phosphate is roughly 0.14 M16and the pH is approximately s and 2.4 X s for 7, then relaxation times of 1.2 X phosphate-catalyzed intermolecular and intramolecular proton exchange between pairs of residues which titrate near pH 7 are predicted. In the extracellular fluid the concentration of phosphate is approximately160.002 M and the corresponding times are 0.8 X lo4 and 1.6 X lo* s. When the number of binding sites per molecule is large, it is not practical to write explicitly a system of equations analogous to eq 17 for the reaction of buffer with each of the large number of different states of the protein molecule nor, in the case where the sites are equivalent and independent, is such a procedure necessary. The rates of overall exchange between protein and buffer and the rates of phosphate catalyzed intermolecular proton exchange for molecules with N sites can in this simple case be obtained from the normal modes of the system of reactions H,Z
+P
kbn
H,-lZ
+ PH
+
(18)
where kf, = kfn and Ftb, = kb(N - n l),that is the rate of the forward reaction for a molecule with n sites is the rate at a single site times the number of protonated sites. When the linearized rate equations corresponding to eq 18 are solved, the relaxation frequency of the mode which may be described as proton exchange between protein and buffer is found to be kf(Nco+ cb) where Ncocorresponds to the total concentration of sites. If the intracellular fluid is approximately 25% by weight proteid6 and if about 5% of the protein fraction consists of residues which titrate near pH 7 (histidyls, N-terminal amino groups, etc.) then Neo N 0.08 M and the relaxation time for proton exchange with the phosphate buffer is approximately 1.5 X lo-* s. The corresponding time in the extracellular medium (7% s. protein, c b = 0.002 M)16is 1.3 X When Nco = 0.08 M and cb = 0.14 M, the relaxation amplitude CT for proton exchange between protein and s2/cm. If one assumes that 70% of buffer is 1500 X the mass of a “typical tissue” is intracellularleb the predicted absorption coefficients at 1,4, and 7 MHz are respectively 0.011, 0.16, and 0.37 cm-l. Experimental valu e ~ at~1MHzl9 ~ - ~are~0.015 (testis), 0.023 (liver), and 0.033 cm-l (heart and kidney). At 4 MHz, experimental absorption coefficient are 0.079 (testis) and 0.14 cm-l (liver), and at 7 MHz 0.12 (testis), 0.2 (heart and kidney), and 0.24 cm-’ ( l i ~ e r ) . l ~ - ~ ~
The absorptions calculated here are perhaps large since it is assumed that the pKa)s of the imidazole residues and H2P04-coincide exactly as for bacitracin at 40 O C . If, for example, it were assumed that the histidyl residues titrate 1 pH unit on the acid side of neutrality, the calculated absorptions would be smaller but still appreciable with the results at 1,4, and 7 MHz being 0.007,0.084, and 0.18 cm-l. Thus, a case can be made for the proposition that perturbation of the equilibrium represented by eq 1is a significant source of acoustic absorption in tissues a t frequencies commonly employed in medical diagnostic ultrasonics. In addition to exchange with buffer, there are N - 1 solutions of the linearized kinetic equations corresponding to eq 18 with relaxation frequencies given by w = kfncb (2 < n < N) associated with interm6Iecular proton exchange. If the volume changes for these normal reactions are assumed to be electrostrictive in origin, the estimated absorption due to intermolecular proton exchange does not exceed 1% of the absorption due to exchange with buffer and is therefore thought to be insignificant in tissue.
References and Notes J. M. Lyerla and M. H. Freedman, J. Bb/. Chem., 247, 8183 (1972). “Handbook of Biochemistry and Molecular Biology”, G. Fasman, Ed., CRC Press, Cleveland, 1976. K. Understromlang and C. F. Jacobsen, C . R. Trav. Lab. Carlsberg, Ser. Chlm., 24, 1 (1941). S. D. Hammann and S. C. Lim, Austr. J . Chem., 7 , 329 (1954). F. J. Milero In “Water and Aqueous Solutions”, R. A. Home, Ed., Wlley, New York, 1972. K. F. Herzfeld and T. A. Litovitz, “Absorption and Dispersion of Ultrasonic Waves”, Academic Press, New York, 1959. C. W. Davies, “Ion Association”, Butterworths, London, 1962. G. W. Castellan, Ber. Bunsenges. Phys. Chem., 67, 898 (1963); R. D. White, Ph.D. Thesis, University of Washington, Seattle, Wash., 1971. B. B. Owen, R. C. Miller, and M. L. Cogan, J. phys. Chem., 65, 2065 (1961). W. Kauzrnann, A. Bodansky, and J. Rasper, J. Am. Chem. Soc., 84, 1777 (1962). J. Rasper and W. Kauzmann J. Am. Chem. Soc.,84, 1771 (1962). S. Katz, J. A. Beall, and J. K. Crissman, Bkxhsmkby, 12,4180 (1973). P. Debye, Trans. Necrrochem. SOC.,82, 265 (1942); M. V. Srnoluchowski, Z . Phys. Chem. (Lelpzg),92, 129 (1917). “Landolt Bornstein Tabellen”, 6th ed., Vol. 11, Part 2. L. G. Longsworth, “American Institute of Physics Handbook”, D. E. Gray, Ed., McGraw-Hill, New York, 1957. (a) E. Muntwyler, “Water and ElectroiyteMetabolism”,C. V. Mosby, St. LOUIS,1968. (b) A. White, P. Handler, and E. Smith, “Prlnciples of Biochemistry”, 3rd ed, McGraw-Hill, New York, 1964. J. K. Brady, S. A. Goss, R. L. Johnston, W. D. O’Brlen, Jr., and F. Dunn, J . Acoust. SOC.Am., 60, 1407 (1976). S. A. Ooss, R. L. Johnston, and F. Dunn, J. Acoust. SOC.Am., 64, 423 (1978). S. A. Goss, L. A. Frizzell, and F. Dunn, in press. C. U. Nicoia, A. Labhardt, and 0 . Schwarz, Ber. Bunsenges. Phys. Chem., 83, 43 (1979).
