J. Phys. Chem. 1984, 88, 5679-5683
5679
Acoustic Absorption and Proton-Exchange Kinetics in Aqueous Bovine Pancreatic Ribonuclease A L. J. Slutsky,* L. Madsen, Department of Chemistry, University of Washington, Seattle, Washington 981 95
and R. D. White Upjohn Co., Kalamazoo, Michigan 49003 (Received: May 10, 1984)
Acoustic absorption in solutions of bovine pancreatic ribonuclease A has been studied in unbuffered solutions and in the presence of phosphate buffer. In the absence of buffer, a single discrete relaxation (r = 3 X l(r7 s at 4 “C) plus an uncharacterized process (or processes) with characteristic time less than lo4 s together give a good account of the data over the experimental frequency range (0.3-152 MHz). In the presence of buffer an additional relaxation, with amplitude appropriate to the perturbation of a proton-exchange equilibrium between a single histidine residue and the inorganic phosphate buffer, is found. The rate constant for the reaction of dihydrogen phosphate ion with the unprotonated residue is (at 4 “C) 1.7 X lo8 M-’ 8,that is diffusion controlled with a modest orientational constraint. The volume change ( A T = -22.6 cm3/mol) is typical of that found for small molecules. A plausibility argument is offered in support of the proposition that proton exchange at H105 is observed in these experiments. The contribution of the perturbation of proton-transfer equilibria to ultrasonic absorption in biological media at the frequencies commonly employed in medical diagnostic imaging is briefly discussed.
Introduction Reactions of the form -I,H+
+~
k ~
0
~
kb
+ H~PO~-
2-I, -
(1)
where -I,H+ and -Ii are respectively the protonated and unprotonated forms of the ith histidyl or N-terminal amino residue of a peptide or protein, are more than usually amenable to study by ultrasonic techniques.’ In the case of the peptide antibiotic bacitracin A (molecular weight = 1421) which has a single histidyl residue, a discrete acoustic relaxation associated with perturbation of the equilibrium represented by eq 1, superimposed on a broad relaxation spectrum associated with processes intrinsic to the peptide, is readily observed, and it has proven fairly straightforward to deduce from acoustic data’ the rate constants and the volume change for eq 1 and thus implicitly the rate of phosphatecatalyzed intefmolecular proton exchange. In a protein with several groups of similar pKa, it will not in general be possible to resolve the acoustic relaxation spectrum into contributions associated with the perturbation of protontransfer equilibria at individual residues. It is perhaps unusual that in the case investigated h e r e b o v i n e pancreatic ribonuclease A (four histidyl residues) in 0.1 M KH2P04-K2HP04buffer at 4 OC-the portion of the excess ultrasonic absorption which may be attributed to bimolecular processes is described by a single relaxation time which is very close to that implied by the rate constants for eq 1 observed in bacitracin and close to that which would be predicted by the elementary theory of diffusion-controlled reactionse2 The relaxation amplitude observed in these experiments is appropriate for a single residue with the pKa of histidine 105 and a volume change equal to that observed in bacitracin and more generally in small molecule^.^ Histidine 48 of ribonuclease A is presumed to be “buriedv4and thus to exchange too slowly to contribute to the relaxation spectrum at megahertz frequencies. At the concentrations employed in these experiments inorganic phosphate is a competitive inhibitor of ribonuclease A. Thus a naive interpretation of the unusual simplicity of the acoustic absorption spectrum would be that the binding of phosphate to (1) Slutsky, L. J.; Madsen, L.; White, R. D.; Harkness, J. J. Phys. Chem. 1980,84, 1325. ( 2 ) Debye, P. Trans. Electrochem. SOC.1942,82, 265. (3) Kauzmann, W.; Bodansky, A.; Rasper, J. J. Am. Chem. SOC.1962,84, 1777. (4) Markley, J. Acc. Chem. Res. 1975, 8, 70.
0022-3654/84/2088-5679$01.50/0
ribonuclease restricts the access of additional phosphate to the two histidyl residues, H12 and H119, commonly considered to participate in the active site, sufficiently so that these residues no longer exchange at the diffusion limit. The presumption that proton exchange between inorganic phosphate and H105 of ribonuclease A is the principal bimolecular process contributing to the observed ultrasonic relaxation gives a good account of the data without any ad hoc adjustment of parameters, but, as is usual with acoustic relaxation in chemically complex systems, other explanations involving perturbation of the dissociation equilibrium of the enzyme-phosphate complex or a fast concomitant of the internal relaxation peculiar to the complex observed by Walz and ham me^^^ cannot be conclusively rejected. In the absence of significant concentrations of small ions, aqueous solutions of most proteins exhibit acoustic absorption, roughly proportional to the protein toncentration at concentrations less than 10% by weight, characterized by a broad spectrum of relaxation timesas The microscopic processes responsible for this absorption remain an object of conjecture; conformational change,sc perturbation of internal pr~ton-transfer~~ equilibria, and perturbation of “solvationnSaequilibria having been nominated in individual cases. The results in dilute solutions of ribonuclease in the absence of phosphate buffer are again unusual in that it does appear to be possible to resolve the absorption into two discrete relaxations well separated in frequency. Nonetheless, the ultrasonic data do not in themselves strongly nominate any of the alternative explanations, and the admittedly speculative discussion of possible sources of that portion of the acoustic absorption which is not associated with perturbation of intermolecular protontransfer equilibria rests on the results of other techniques.
Ultrasonic Absorption General. The ultrasonic absorption (a)at frequencyf associated with the perturbation of a single chemical equilibrium with relaxation time r is6
wheref, = 1/(27rr) and A represents the attenuation associated with the viscosity and thermal conductivity of the medium as well (5) (a) Carstensen, E. L.; Schwan, H. P. J. Acoust. SOC.A m . 1959, 31, 305. (b) White, R. D.; Slutsky, L. J. Biopolymers 1972,11, 1973. (c) Kessler, L. W.; Dum, F. J. Phys. Chem. 1970, 74,2736.
( 6 ) Herzfeld, K.F.;Litovitz, T. A. “Absorption and Dispersion of Ultra-
sonic Waves”; Academic Press: New York, 1959.
0 1984 American Chemical Society
5680
The Journal of Physical Chemistry, Vol. 88, No. 23, 1984
as that due to any processes with relaxation frequencies much higher than fr for the process in question. For a reaction with enthalpy change AH and volume change AV proceeding in a medium of density p and coefficient of thermal expansion 0 in which the heat capacity (per unit volume) is cp and the velocity of sound is u (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, if the activity of the ith species is expressed in terms of its molar concentration as ai = rimi, and if the activity coefficients depend on the chemical composition only through the ionic strength I , then for a reaction such as eq 1 where Cui = 0 (4) where zi is the charge, in units of the electronic charge (e), of the ith species. If the activity coefficient may be approximated by the Debye-Huckel equation or Davies7 semiempirical modification thereof
where e is the dielectric constant of the solvent and N is Avogadro's number, then
In the subsequent discussion each protonated residue will be treated as an independent singly charged species and the activity coefficients of the various ionic species will be estimated from eq 5 with the constant B = 0.033 being estimated from Alpert's study* of the effect of strong electrolytes on the dissociation of H2P04-. For an elementary reaction the rates of the forward and reverse reactions at equilibrium (respectively Rf and Rb)may be expressed in terms of the rate constants and the equilibrium (respectively R f and Rb) may be expressed in terms of the rate constants and the equilibrium activities as R f = kpr,ufiI = &, = kbriulY'where the continued products extends, in the case of Rf, only over reactant species and, in the case of Rb,only over products. The relaxation time or relaxation frequency may then be obtained from the relationg 7-l = RJ-' = Rbr-l = w,. Explicity for eq 1 wr
=
kf(rIH')(rHP04z-)(mIH+)(~HPO~z~)
=
kb(rH,P04-)(mI)(mH,P04-)r-
(7a)
For an ideal solution, eq 7a becomes wr
= 2rf, = kb(K(mIHt + mHP042-)+ mI
+ mH,PO4-) (7b)
where K is the equilibrium constant of the reaction as written. More generally, when there are several residues per molecule the system of linearized kinetic equations corresponding to eq 1 may be solved numerically, for any known or presumed values of the equilibrium chemical composition and rate constants, to determine the normal reactions and relaxation frequencies. The acoustic absorption is then a sum of terms of the form of eq 2. In the particularly simple case of three distinguishable sites per molecule with identical values of kf for which K = 1, the normal reactions are proton exchange between protein and inorganic phosphate and (7) Davies, C. W. "Ion Association"; Butterworths: London, 1962. (8) Alpert, M. Dissertation, Yale University, 1944; cited by: King, E. J. "Acid-Base Equilibrium"; Pergamon Press: Oxford, 1965. (9) Castellan, G. W. Ber. Bunsenges. Phys. Chem. 1963, 67, 898.
Slutsky et al. two degenerate modes corresponding to phosphate-catalyzed proton transfer between residues. In terms of the total concentration of inorganic phosphate (mJ, the relaxation frequencies of the two modes are respectively 2?rf, = kb(mo + mp) and 2rfr = kbm,. The Ionization Reactions of Ribonuclease. The effective equilibrium constants (K,') for the acid ionization reactions of the histidyl residues of bovine pancreatic ribonuclease A at 25 OC in 0.3 M NaCl have been determined by M a r k l e ~ .Histidine ~ 105 titrates with a pK,' of 6.72 with no strong evidence of interaction with any other group which titrhtes near pH 7. The effective pK,'s, at room temperature, of H12, H119, and the N-terminal amino group are respectively 6.17: 6.01: and 8.14,'O the pKa's of the two histidyls shifting of 6.9 and 6.6 on binding of inorganic phosphate." Under the conditions of these experiments there should be 1 mol of inorganic phosphate bound per mole of ribonuclease. Finally, if the pK,'s are adjusted to 4 OC with the aid of the measured heats of ionization of the residues in questionI2 values of 7.3, 7.1, and 7.2 for H105, H119, and H12 result. The pKa of H2PO4- at 4 "C is 7.286. If all three residues are equally accessible to solvent one might expect the simplifying assumptions of the immediately preceeding paragraph to adequately describe the proton-transfer reactions of the three rapidly exchanging histidyl residues of ribonuclease. It is clear from eq 4 that r will not exceed the concentration of the least abundant reactant and thus that large ultrasonic absorption due to chemical relaxation can be expected principally from reactions in which all participants are present at equilibrium in appreciable concentrations. The pK,'s of the lysyl and tyrosyl groups in ribonuclease A are respectively 9.1-10.213 and 9.9.14 At the temperature and pH employed here these groups, as well as the NTA, will be almost completely protonated and perturbation of proton-exchange equilibria at these residues will not contribute significantly to the absorption. At 4 O C the coefficient of thermal expansion of water is very small, the first term in the curly brackets in eq 3 can usually be neglected and the ultrasonic attenuation is approximately proportional to The volume change for the reaction of protonated imidazole with HPOZ- is large (-26 ~ r n ~ / m o l ) Insofar . ~ + ~ as intramolecular proton transfer can be looked upon as the independent ionization and recombination at equivalent residues, the volume change would be expected to be zero. The question of whether or not there is acoustic absorption due to electrostrictive volume changes associated with changes in the mean square dipole moment on internal proton transfer remains, we believe, an interesting one, but no plausible dielectric model of the protein interior will predict volume changes comparable in magltitude with those for exchange with the phosphate buffer. ~
Experimental Section and Results The ultrasonic absorption at frequencies less than 4 MHz was measured in a pressurized cylindrical resonator15 with 5-MHz, 1-in.-diameter X-cut quartz crystals. At higher frequencies a variable-path length pulse-echo spectrometer of conventional design operating on the odd harmonics of a 10-MHz X-cut crystal was employed. The excess acoustic absorption in solutions of bovine pancreatic ribonuclease A (Sigma Chemicals) in 0.1 M K2HP04-KH2P04,in ribonuclease in the absence of buffer, and the absorption in the buffer in the absence of protein, all at pH 6.62 and 4 OC, are displayed in the lower panel of Figure 1. The points in the upper panel of Figure 1 represent the difference between the attenuation in buffered and unbuffered solutions of ribonuclease less the small excess absorption in the buffer itself. (10) Carty, R. P.; Hirs, C. H. W. J . Bioi. Chem. 1968, 243, 5254. (1 1) Meadows, D. H.; Roberts, G. C. K.; Jardetzky, 0.J . Mol. Bioi. 1969, 45, 491. (12) Roberts, G. C. K.; Meadows, D. H.; Jardetzky, 0.Biochemistry 1969, 8, 2053. (13) Tanford, C.; Hauenstein, J. D. J. Am. Chem. Sac. 1956, 78, 5254. (14) Tanford, C.; Hauenstein, J. D.; Randa, D. G. J. Am. Chem. Sac. 1955, 77, 6409.. (15) Eggers, F.; Funk, Th. J . Acoust. Sac. Am. 1975,57, 331. Eggers, F.; Funk, Th.; Richman, K. H . Rev. Sci. Instrum. 1976, 47, 361.
Ultrasonic Study of Proton-Transfer Kinetics
The Journal of Physical Chemistry, Vol. 88, No. 23, 1984 5681
300
TABLE I: Rate Constants, Volume Changes, and Standard Volume Changes for the Reaction of Hydrogen Phosphate Ion with Protonated Imidazole Groups at 4 OC in 0.1 M Phosphate Buffer“
200
K
IO0
kkexpt)b kdexpOb
&i-
klb
i I. g
o
k3b
T 800
kb(calcd)b AV, cm3/mol AVO, cm3/mol
5
pc 0600
400
200
0
-0.5
bacitracin
ribonuclease
0.619 4.0 6.5 26.0 1.6 6.5 21.7 20.0
1 1.4 1.4 15.0 4.4 3.4 26.0 24.3
0.95 1.6 1.7 15.0 4.4 3.3 24.3 22.6
‘The experimental data constants are in terms of activities. * X M-1 s-l
\
a
imidazole
0
0.5
I .o
l o g f (MHz) Figure 1. The absorption coefficient (u/fZ) in 3.3 wt % bovine ribonuclease A in water (circles) and 0.1 M KH2P04-K2HP04buffer (squares) at 4 OC and pH 7 as a function of the logarithm of the frequency (in MHz). The squares in the upper panel represent the difference in the absorption between the buffered and unbuffered solutions less the small excess absorption (triangles) observed in 0.1 M buffer in the absence of protein. The solid curve in the upper panel represents the best single-relaxationfit to the data.
The solid curve in the upper panel of Figure 1 represents the best single relaxation fit to these data, the parameters of eq 2 being CT = 323 X lo-’’ cm-l s 2 , f , = 1.35 MHz. In these experiments the molar concentration of the phosphate buffer is necessarily considerably greater than that of the protein, thus the value of kb deduced from the relaxation frequency and eq 7a (kb = 1.7 X lo8 M-’ s-l) will be essentially the same whether it is assumed that the acoustic relaxation displayed in Figure 1 represents the contribution of one or of three equivalent histidyl residues. The experimental rate constants in Table I are deduced from the experimental relaxation frequencies in 0.1 M phosphate buffer with eq 7a. The values of kb in terms of concentrations rather than activities would be less by a factor 0.71, that is the activity coefficient of a univalent ion as deduced by eq 5. The principal source of uncertainty in kf,within the general interpretative framework offered here, is in the adequacy of the activity coefficient of HP04*-as calculated from eq 5. If kfwere, for example, calculated from eq 7b, the result would be approximately 1 X lo8 M-‘ The deduction of the volume change per residue does of course depend on the number of rapidly exchanging imidazole groups per molecule. If it is assumed that only proton transfer at H105 contributes to the observed relaxation then AV = 24.2 cm3/mol a typical value for the titration of imidazole in small molecules. If all three histidines exchange rapidly with inorganic phosphate then the value of AV for eq 1 deduced from the experimental relaxation amplitude and eq 2-6 is 13.4 cm3/mol, a value without precedent in observations on small molecules. The simplest interpretation of the observed relaxation amplitude and the fact that only a single relaxation time observed is then that the presence of a bound phosphate slows the exchange rate between HPOd2and protons bound to the imidazole ring of H12 and H 119 sufficiently that acoustic relaxation due to this process is not observed in these experiments. A relaxation time greater than lo6 s would be unobservable. When, as in these experiments, the molar concentration of the buffer is large compared to both the concentration of the enzyme and the dissociation constant ( K I )of the enzyme inhibitor complex,
the relaxation frequency for the binding of phosphate to RNase is, as is the relaxation frequency for proton exchange, proportional to the concentration of the buffer and independent of the concentration of the protein. Rate constants of 2.1 X lo7 M-’ s? have been reported for the binding of cytidine 3’-monophosphate to ribonuclease at 12.5 “C and pH 6.5;33it does not strain credulity to postulate that inorganic phosphate might bind ca. five times faster. Thus it is not possible, on the basis of either the magnitude of the relaxation time or its dependence on concentration, to exclude the possibility that the observed relaxation may be wholly or in part due to perturbation of the dissociation equilibrium of the ribonuclease-phosphate complex. On the other hand, although it is difficult to demonstrate conclusively that perturbation of the dissociation equilibrium does not contribute to the relaxation spectrum, it is not hard to rationalize the absence of such a contribution. Meadows, Roberts, and Jardetzky” find 0.08 M phosphate sufficient to “saturate” ribonuclease in the pH range 5.5-7. At 25 “C the value of K,, the equilibrium constant for the dissociation of the enzymephosphate complex, is 0.0065 M at pH 6.5. The value of F for the dissociation of the complex is thus significantly smaller than that for the proton-transfer reaction and there is no evidence for a comparably large volume change. Given the accessibility of H105 to the solvent,34one would expect to observe the relaxation of the proton-transfer equilibrium at this particular residue, in addition to whatever other processes might occur, in the 0.3-152-MHz frequency range. The fact that only a single process, with amplitude appropriate to proton transfer a t a single residue, is observed is the primary basis for the attribution of the 1.34-MHz relaxation. This attribution is supported by a plausibility argument suggesting that exchange at the “buried” H48 and at the active site, when the enzyme is nearly saturated, might be slower than the diffusion limit and that under the experimental conditions the concentration of free enzyme is low enough to suppress the effect of perturbation of binding equilibrium even though the rate may well be comparable with the rate of proton exchange. The excess attenuation in 1 wt % unbuffered aqueous ribonuclease at pH 7.08 and pH 6.47 at 4 “C is presented, in the frequency-range 0.3-131 MHz, in Figures 2 and 3. The highfrequency data in the lower panel of Figure 2 serves to determine, fairly reliably, the parameter A of eq 2 ( A = 18.2 X cm-’ s2). The results in Figure 2 are presented both in the form of a conventional plot of alp vs. log f and in the upper panel, with expanded scale, as a - A p . Perhaps unexpectedly, a single relaxation with Cr = 112 X cm-’ s* andf, = 0.55 MHz gives a satisfactory account of the data. The solid curve in Figure 2 is generated from eq 2 and the relaxation parameters in the immediately foregoing. As in any case where the apparent relaxation frequency lies near one extreme of the experimental range, the error in f,,although difficult to estimate, is large. For example, if the value of a/f rather than a were made the basis of a least-squares optimization, the agreement between calculated and experimental values at low frequencies would be improved to some degree at the expense of agreement at higher frequencies and the optimum relaxation frequency would decrease to 0.46 MHz.
5682 The Journal of Physical Chemistry, Vol. 88, No. 23, 1984
“r
-(I-H2P04)- are small, then the rate constants of eq 1 in terms of the rate constants of eq 8 are
I20
kf =
IO0 80
‘E Y
60
-.2
-.4
-.6
0
,“ c
klk3K
klk3
- kb = kl
+ k3K
kl
+ k3K
(9)
where K is the equilibrium constant for the reaction represented by eq 1. The Debye-Smoluchowski equation is
1
N
-2
Slutsky et al.
.2
0
.4
40
\
20 0“
I
0
I
I
I
I
I
2
log f (MHz) Figure 2. The excess acoustic absorption vs. frequency in 1 wt % aqueous ribonuclease at p H 7 and 4 OC in the absence of phosphate buffer. In the lower panel the difference between the absorption of the solution and that of pure water at the same temperature is displayed in the form of a plot of cy/f vs. log 0. In the upper panel the relaxational absorption, cy - ,-if is given. 1
120,
- 0.4
0
0.4
0.8
log f (MHz) Figure 3. The pH dependence of the ultrasonic absorption in 1% aqueous ribonuclease at 4 O C . The experimental points are at p H 6.47; the solid curve is a least-squares single relaxation fit to the data at pH 7.08.
Experimental values of a/J”for 1 wt % aqueous ribonuclease at pH 6.47 in the absence of buffer are compared with the smooth curve through the data at pH 7.08 in Figure 3. The pH dependence of the acoustic absorption in this range of pH is seen to be small.
Discussion Proton Transfer Kinetics. A reaction such as eq 1 can, at least formally, be divided into a diffusional encounter, a reversible proton transfer, and separation of the products, that is -IH+
k + HP042- & -(IH-HP04)-
-(IH-HP04)- + -(I-HzP04)-(I-H2P04)-
k3
-I
+ H2PO4-
@a) (8b) (8c)
where k l and k3 might be estimated from the Debye-Smoluchowski equationZor more recent and sophisticated treatments of the rates of diffusion-controlled reactions between chemically asymmetric If it is further assumed that the concentrations of the intermediate species (-IH-HP04)- and (16) Solc, K.; Stockmayer, W. H. In?. J . Chem. Kine?. 1972, 4, 733. (17) Schmitz, K. S.; Schurr, J. M. J . Phys. Chem. 1972, 76, 534. (18) Shoup, D.; Lipari, G.; Szabo, A. Biophys. J . 1981, 36, 697.
k =
4 7 T N z ~ z ~ e o ~+( DB)a D~ CkT[eXp(ZAZBeoz/ wdkT) - 1]
(10)
N being Avogadro’s number, u a steric factor, eo the electronic charge, zA and zB the algebraic charges of the reacting species, t the dielectric constant of the solvent, DA and DB the diffusion coefficients of the reacting species, and rd the effective radius for reactions. In ref 1, rd was taken to be 4.5 A, a reasonable distance between a nitrogen atom hydrogen bonded to an -OH group of a dihydrogen phosphate ion and the central P atom of that ion. The steric factor appropriate to k3 of eq 8c was assumed to be 1/4 since presumably one of the protonated O s of the HzPO; ion must be oriented toward the imidazole and the bulk of the protein would restrict the approach of a calculation based on these parameters and eq 9 and 10 is compared with experiment for ribonuclease, bacitracin, and imidazole in Table I where it is assumed that diffusion coefficients scale as the temperature divided by the viscosity of water so that the diffusion coefficients of H2PO4- and HPOZ- (0.45 X cmz/s) and ribonuclease (0.07 X cm2/s) at 4 O C can be estimated from their values at 20 0C,19920 The model advanced here is sufficiently naive so that it is perhaps unnecessary to rationalize disagreement by a factor of two between the calculated and experimental values of the rate constants although it would not be hard to justify an additional factor of 1 / 2 in the orientational constraints. The volume change derived from the observed relaxation amplitude and the experimental p 6 s by means of eq 3-6 is given in Table I. The standard volume change is calculated by differentiating the expression for the excess free energy represented by eq 5 with respect to pressure’ and making use of the known compressibility and the pressure dependence of the dielectric constant of water.37 Acoustic Absorption in the Absence of Buffer. Any microscopic interpretation of the observed relaxation parameters is purely speculative. It might, however, be noticed that French and ham me^^^ rationalize the pH dependence of the relaxation time for the isomerization of ribonuclease, on the 10-3-104-s time scale, in terms of a proton transfer between histidine and an aspartyl or glutamyl residue as a step in the overall process. A single two-state internal charge transfer equilibrium of the form -IH+-A= -1-HA with both states equally populated and a volume change appropriate to a classical zwitterion transition (-13.5 cm3/mol) would be sufficient to account for the amplitude associated with the 0.55-MHz relaxation frequency. It would then be consistent to attribute this relaxation to a fast internal proton-transfer step in the process which eventually leads to the release of the proton observed in the temperature-jump kinetics. Other equally consistent attributions are doubtless possible. Large-amplitude librational motions of side chains with correlation times of 10-9-10-11 s39,40appear to be fairly general features of the internal dynamics of proteins. These motions, insofar as they alter packing or partially expose hydrophobic groups to solvent, could contribute to the very high-frequency ultrasonic attenuation. In the presence of the specific alternative offered by nuclear magnetic resonance it does not seem that ultrasonics offers a useful insight into the subnanosecond internal dynamics of proteins. (1 9) “Landolt-Bornstein Tabellen”, 6th ed.;Springer-Verlag: Berlin, 1964; Vol. 11, Part 2. (20) Tanford, C. ‘Physical Chemistry of Macromolecules”;Wiley: New York, 1961; pp 357-358.
The Journal of Physical Chemistry, Vol. 88, No. 23, 1984 5683
Ultrasonic Study of Proton-Transfer Kinetics
I
T
-
0.2
-
I
-5 U
"
0
2
4
6
IO
8
f (MHz) Figure 4. The calculated acoustic absorption at 37 "C in a medium which is 0.05 M in histidyl residues and either 0.04 M (upper curve) or 0.008 M (lower curve) in low-molecular-weight phosphates with pK, near 7. The experimental points are for beef heart muscle.
Acoustic Absorption in Biological Media. An estimate of the contribution of the perturbation of the equilibrium represented by eq 1 to the acoustic absorption in intact tissue requires an estimate of the equilibrium concentrations of the various species. The net concentration21*22 of the more easily identified low-molecular-weight phosphates in muscle (AMP ADP ATP creatine phosphate (Pcr) phosphoglycerates and sugar phosphates inorganic phosphate (Pi)) is roughly 0.04 M. Pcr does not titrate near p H 7, the sum of the concentration of the remaining species is about 0.017 M. The equilibrium constant for the association of Mg2+ with either Pcr or inorganic phosphate is23approximately 40 M-l, and a t a presumed cytosolic [Mgz+] of 0.0025 M only about 10% of these species are expected to be present as the Mg2+ complex. The portion of the buffer capacity of muscle associated with protein, carnosine, and a n ~ e r i n ewould ~ ~ , ~imply ~ [-IH+] = [-I] rr 0.025 M. The purely geometrical factors in eq 10 (rd and CT) would not be expected to depend on the composition of the medium. The calculated value of the rate constant is relatively insensitive to the presumably small diffusion coefficient of the
+
+
+
+
+
(21) Veech, R. L.; Randolph-Lawson,J. W.; Correll, N. W.; Krebs, H. A. J . Biol. Chem. 1979, 254, 6538. (22) McGilvery, R. W.; Murray, T. W. J. Biol. Chem. 1974, 249, 5845. (23) Wu, S. T.; Pieper, G. M.; Salhany, J. M.; Eliot, R. S.Biochemistry 1981, 20, 7399. (24) Woodbury, J. W. In "Physiology and Biophysics II", 20th ed.; Rush, T. C.. Patton. H. D..Eds.: Saunders: Philadebhia. 1974: D 508. (25) Van Slyke, D. D.;Hastings, A. B.; M i l k , A:; Sendroy, Jr., J. J. Bid. Chem. 1928, 79, 769.
protein. The diffusion coefficients of a variety of small ions (Na+, K+, Ca2+, SOP, and ATP3-)2628in muscle fiber have been found to be about 'I2those in water and in the subsequent discussion it will be assumed that kl, k3, and hence kb, in the intracellular fluid are correspondingly about those in water. The experimental values of the acoustic absorption in heart muscle shown in Figure 4 were determined in tissue which had been stored in saline solution at room temperature for 1-2 h after e x c i s i ~ n . ~Under ~ , ~ ~ these conditions Pcr and ATP would be largely converted to inorganic phosphate and the upper solid curve corresponding to a total phosphate concentration of 0.04 M might be appropriate. Only a rough order-of-magnitude estimate is possible, but it is at least plausible that chemical relaxation associated with eq 1 is a major contributor to the ultrasonic absorption in excised or anoxic tissue where the concentration of inorganic phosphate is relatively high. In healthy resting muscle the contribution of the equilibrium represented by eq 1 to the chemical relaxation spectrum is likely to be considerably smaller. Among the alternate reactions between small ions which might be important in normal conditions, the complexation of K+ by Pcr, Pi, and ATP is perhaps an interesting object of speculation. The intracellular concentration of K+ is about 0.150 M; the equilibrium constant is about 3 M-l; thus the free ion, the complex, and free phosphate should be present in appreciable concentration. The volume change for this process is not known, a possible analogous reaction is K+ S042-= KS04- where31 A V = -5.9 cm3/mol. The relaxation amplitude is thus potentially fairly large; the kinetics have not been investigated. Registry No. RNase, 9001-99-4.
+
(26) Kushmeric, M. J.; Podolski, R. J. Science 1969, 166, 1297. (27) Pauly, H. Biophysik (Berlin) 1972, 10, 7. (28) Edzes, H. T.; Berendsen, H. J. C. Annu. Rev. Biophys. Bioeng. 1975, 4, 265. (29) Goss, S. A,; Frizzell, L. A.; Dum, F. Ultrasound Its Appl. Med. Biol. 1979, 5, 181. (30) Goss, S. A.; Johnston, R. L.; Dunn, F. J. Acoust. Soc. Am. 1980, 68, 93. (31) Fisher, F. H.; Fox, A. P. J. Solution Chem. 1978, 7, 561. (32) White, A,; Handler, P.; Smith, E. "Principles of Biochemistry"; 6th ed., McGraw-Hill: New York, 1970. (33) Cathou, R. E.; Hammes, G. G. J . Am. Chem. SOC.1965,87,4674. (34) Wyckoff, H.W.; Handman, K. D.;Allewell, N. M.; Inagami, T.; Johnson, L. N.; Richards, F. M. J. Biol. Chem. 1967, 242, 3985. (35) French. T. C.: Hammes. G. G. J. Am. Chem. SOC.1965.87. 4669. (36) Nelson; C. A.f Humme1,'J. P.; Swenson, C. A,; Friedman,'L. ? . Biol. Chem. 1962, 237, 1575, 3384. (37) Owen, B. B.; Miller, R. C.; Cogan, M. L. J. Phys. Chem. 1961, 65, 21-16s.
(38) Smith, G. A.; Hesketh, R. T.; Metcalfe, J. C.; Feeney, J.; Morris, R. G. Proc. Natl. Acad. Sci. U.S.A. 1983, 80, 7178-7182. (39) Richarz, R.; Nagayama, K.; Wuthrich, K. Biochemistry 1980, 19, 5189. (40) Wittebort, R. J.; Rothgeb, T. M.; Szabo, A.; Gurd, F. R. N. Proc. Natl. Acad. Sci. U.S.A. 1979, 76, 1059. (41) Lipari, G.; Szabo, A. J. Am. Chem. SOC.1982, 104, 4547, 4559.
