4015
J. Phys. Chem. 1991,95,4015-4019
Kinetic Studies of Proton-Exchange Reactions between Imidazole Groups of Small Molecules and Hydrogen Phosphate Ions in Aqueous Solution Using Ultrasonic Relaxation D. Rogez,* R. Andrianjara, and C. H. Choi Laboratoire de Spectrometrie et d’lmagerie Ultrasonores, Universite Louis Pasteur, Unite de Recherche AssociPe au CNRS No. 851, 4, rue Blaise Pascal, 67070 Strasbourg Cedex, France (Received: October 3, 1990)
Ultrasonic absorption in aqueous solutions of imidazole and three substituted derivatives, N-methyl-, 2-methyl-, and 4methylimidazole, has been studied in the presence of potassium phosphate as a function of pH and salt concentration in the frequency range 0.46-5.7 MHz at 25 OC. For all of these compounds, the ultrasonic absorption curves as a function of pH showed a sharp maximum in the vicinity of pH 7, due to a disturbance of the proton-exchange equilibrium between the imidazolium ion and hydrogen phosphate ion by the ultrasonic waves. An expression for the ultrasonic absorption due to this proton transfer has been derived from relaxation theory, using a reaction scheme of Eigen. A quantitative interpretation is given for both the pH and the phosphate concentration dependence of the ultrasonic absorption in the neutral pH range. The rate constant kR and the volume change AVfor the reaction of dihydrogen phosphate ion with the unprotonated imidazole group have been determined by a curve-fitting procedure in which kR and AV were the only adjustable parameters. For imidazole, the rate constant kR was found to be close to 7.0 X IO8 M-’s-l and the volume change AVwas 23.8 cm3 mol-’. With the kinetic and thermodynamic parameters derived from the pH and the concentration dependences of the ultrasonic absorption, the relaxation time need not be determined experimentally, and therefore absorption measurements in a wide frequency range are not required.
Introduction Ultrasonic relaxation spectrometry has been widely used in the past to investigate the kinetics of fast chemical processes, particularly proton-transfer reactions in aqueous solutions.’g2 Ultrasonic absorption measurements provide a means of determining the rate constants for reactions that occur in the time range 3 X IO-’O-5 X IO-’s. The principle of the method is to periodically perturb a chemical equilibrium by small pressure variations associated with the ultrasonic waves and then to determine the dynamic response of the system by measuring the absorption coefficient of the waves as a function of frequency. The relaxation time obtained from these measurements can then be used to calculate the rate constants for the reaction, if the equilibrium constant is known. Proton-transfer reactions between amino and carboxylic groups of a protein and water are the source of an ultrasonic absorption excess at low and high pH values, due to protolysis and hydrolysis In the neutral pH range, absorption reactions, respe~tively.~-~ can be caused by proton exchange between histidyl or terminal amino residues and hydrogen phosphate ions, according to reactions of the form6 -ImH+
+ HP04*- s -Im + H2P04-
(1)
where -ImH+ represents the protonated form of the imidazole ring of a histidyl residue and -1m is the neutral form. It is well-known that the imidazole ring of a histidine residue of several hydrolytic enzymes is responsible for the catalytic activity of these enzymes. Recent results from our laboratory have shown that a-chymotrypsin in phosphate and sulfite buffers7,* ( I ) Eigen, M.; De Maeyer, L. Techniques of Organic Chemistry; Fries,
S.L., Lewis, E. S., Weissberger, A., Eds.; Wiley-Interscience: New York,
1963; Vol. V111. part 2, p 895. (2) Stuehr, J. E. Techniques of Chemistry; Bernasconi, C. F., Ed.; Wiley-Interscience: New York, 1986; Vol. VI. part 2, Chapter VI. (3) Zana, R. J . Mucromol. Sci., Rev. Macromol. Chem. 1975, C12, 165. (4) Slutsky, L. J.; White, R. D. Chemical and Biological Applica~ionsof RrluxurionSpecrromerry; Wyn-Jon=, E., Ed.; Reidel: Dordrecht, Holland, 1975; p 407. (5) Edmonds, P. D. Bioclecrromugnerics 1982, 3, 157. (6) Slutsky, L. J.; Madsen, L.; White, R. D. J . Phys. Chem. 1984, 88, 5679. (7) Rogez, D.; Cerf. R.; Andrianjara, R.; Salehi, S.T.; Fouladgar, H. Fed. Eur. Biochcm. Soc. Lcrr. 1987, 219, 22. (8) Cerf, R.; Salehi, S.T.; Rogez, D. Biophys. J . 1989, 55, 649.
exhibits an ultrasonic absorption maximum near neutral pH. By comparison of this effect with that observed in the catalytically inactive forms of the enzyme, it was shown that ultrasonic absorption exat neutral pH arises mainly from a proton-transfer reaction involving the imidazole group of the histidine at the catalytic site. This result led us to investigate small molecules containing the imidazole ring with pK, values near 7 and including no other ionizable group. The kinetics of the proton-transfer reaction 1 for imidazole have been studied p r e v i o ~ s l y . ~ JHowever, ~ there has been no detailed investigation of either the pH dependence or the phosphate concentration dependence of the ultrasonic absorption associated with this process. Here we describe the results of our ultrasonic absorption study of the proton-exchange reaction occurring in imidazole and three substituted imidazoles, N-methyl-, 2-methyl-, and 4-methylimidazole, in the presence of potassium phosphate. New experimental results that allow a quantitative interpretation of the ultrasonic absorption as a function of pH and salt concentration at different frequencies are reported. In addition to giving the values of the rate constants and volume change for the proton exchange, our results show that the position of the ultrasonic absorption peak on the pH scale is frequency dependent. These results for model systems provide a basis for the estimation of the contribution of reaction 1 to the ultrasonic absorption observed at neutral pH in a-chymotrypsin.’
Summary of Theory Used The general reaction scheme of a proton-exchange process between two different acid-base pairs has been described by Eigen.” Near neutral pH, contributions due to protolysis and hydrolysis are negligible, and the reaction consists of a direct proton exchange of the general form AH
+ B +k
A
+ BH
(2)
where AH and BH are the protonated forms of the two acid-base (9) Nicola, C. U.;Labhardt, A.; Schwarz, G. Ber. Bunsen-Ges. Phys. Chem. 1979,83,43. (IO) Slutsky, L. J.; Madsen, L.; White, R. D.; Harkness. J. J. Phys. Chem. 1980,84, 1325. (11) Eigen, M. Angew. Chem., Inr. Ed. Engl. 1964. 3, I .
0022-3654/9l/2095-4015$02.50/0 0 1991 American Chemical Society
4016 The Journal of Physical Chemistry, Vol. 95, No. 10, 1991
pairs and A and B their unprotonated forms, respectively. For the sake of simplicity the charges have been omitted; kF and kR are the forward and reverse rate constants. Equilibrium 2 is characterized by a single relaxation time 7 , which is related to the rate constants, assuming a value of 1 for the activity coefficients, by the following equation:"
= kF(CAH + CB)+ kR(cA + CBH) (3) where CAH, CAand CBH, CBare the equilibrium concentrations of the two acid-base pairs. In dilute aqueous solution; the ultrasonic absorption relaxation excess a associated with reaction 2 as a function of angular frequency w may be approximated by an equation of the form12 7-I
(4) where p and v are, respectively, the density and the velocity of ultrasound for the solution, R is the gas constant, T is the absolute temperature, AV is the volume change for process 2, and I' is a concentration factor that may be derived by means of the general relationI2 1 1 1 1 p =(5) CAH CA CBH CB If the equilibrium concentrations of the chemical species are expressed in terms of the total molar concentrations COA = CA CAH and COB = CB+ CBH, the dissociation constants KA and KB for AH and BH, respectively, and CHthe concentration of the hydrated hydrogen ion H30+, the expression for I' and the reciprocal relaxation time 7-' take the form
+-+-+-
Rogez et al. 6 = ( l / r ) [ r z- 1
+ (rc' - rz + 1 ) q
(12)
Thus, the change of pH, between high and low frequencies under condition COA >l- (~Hmax)orc 1, the dependence of the ultrasonic absorption on pH in eq 4 is entirely contained in the factor r / ~which , is given according to eq 7 by
It can readily be shown that a pH value given by (PHtnax)wr%l
a / u 2goes
through a maximum at
f/2(PKA + PKB)
(10)
However, at low frequencies (w7
