Partitioning Ratios and a Biochemical Kinetic Dilemma The pH Dependence of Chymotrypsin Catalysis Ronald Breslow Columbia Universlty. New York, NY 10027
The enzyme a-chvmotrypsin catalvzes the hydrolytic cleavageof peptide honds; i t can also cleave variousartifikal substrates ( I , 2).The overall process involves the formation of an acyl-enzyme intermediate in which serine-195 of the enzyme is first acylated. The resulting serine ester is then hydrolyzed. With natural peptide substrates the acylation sequence is rate determining, and hydrolysis of the intermediate is rapid. The generally accepted mechanism (3) for the acylation reaction is shown in Figure 1.The pH dependence of kcat,the rate constant for acylation of the enzyme within the enzvme-substrate com~lex,is shown in Fimre 2. Earlier s u e &stions that kcatdrops on ionization of group with pK, of about 8.5 have been shown to involve instead a weakening of the enzyme-substrate binding when isofeucine-16is titrated (4,5);kat itself does not decrease as the pH is raised. The low nH section of the curve is easilv understood. since the basic and cannot kidazole of His-57 is protonked at low perform its function as a base catalyst. However, many people find it surprising that kcat does not drop at high pH, producing a hell-shaped curve. In the second step of Figure 1,with rate constant kz, an imidazolium ion ImHf is acting as an acid to protonate the leaving group nitrogen. Since ImHf has a pK, near 7.0, it should lose its proton at higher pH, and one might expect the overall process to slow. There are many enzymatic (6) and nonenzymatic (7) examples of such bell-shaped pH vs. rate profiles that are the result of titration of acid and hase catalytic groups. One way out of this dilemma is to suggest that the ImH+ does not lose its proton to the solvent fast enough but performs the needed proton transfer of step 2 before it has a chance to equilbrate. It is the purpose of this note to point out that the pH curve of Figure 2 is exactly as expected for the mechanism of Figure 1euen if the proton equilibration is rapid. Furthermore, if proton equilibration is rapid the observed pH independence at high pH is actually direct evidencefor the participation of the His-57 ImH+ in step 2 of the sequence. This participation is completely reasonable but lacks other direct evidence. The kinetic expression (eq 1) can be derived by use of the steady state treatment, but amoreinstructive approach is to consider partitioning ratios (8). This approach gives the same result as the steady-state method, but it is easier for students (and others) to apply. The rate of formation of a product is simply equal to the rate of formation of a precursor that does not build up (the steady-state assumption) multiplied by the fraction of that precursor that goes to product, by partitioning in the forward direction. In a multistep sequence, the kinetic expression can also he written down on inspection (8). In the case at hand, formation of the steady-state intermediate I- requires His-57 in its basic form; so we symbolize that with [Im] in the part of eq 1that expresses formation of I-. The Im is converted to ImH+ in this first step, so in the reverse reaction with rate constant k-, the ImHf reacts with I-. However, in the forward direction with rate constant kl there is also a reaction of I- with ImH+; the partitioning of I-
a
Figure 1. Acylation of the enzyme chymobypsin by a peptide substrale. In a later step the resulting w i n e ester is hydrolyzed, leadingto overall hydrolysis bond. e Ser-195 and His-57 are serine and hirtidine residues of of lk ~ e ~ l i d the en;y& im is the imidazole ring of the histidins side chain, a general base; ImH+ is mat ricg with a proton lhat acts as a general acid.
p~
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Journal of Chemical Education
Figure 2. The dependence of lhe overall catalytic rate constam lor the acylation sequence of Figure 1 on lhe pH of the medium.
in the forward direction involves a ratio with [ImH+]in every term, so the [ImH+] cancels. Thus above pH 8 or so, when His-57 is initiallv entirelv in the Im form. the overall reaction rate is independent "f the concentration of ImH7 relative to Im, and raising the DH does not slow the rate. Rate of formationif thk acyl enzyme product = rate of formation of the intermediate I- times the fraction of the intermediate that goes to product.
At a high enough pH the kllk-l equilibrium of step 1could be shifted to the right by titrating away the ImH+ that is part of the equilibrium, but the steady-state treatment as-
sumes that 1- is an unstable intermediate that will not accumulate even when the concentration of ImH' is low. This assumption is certainly reasonable in this case ('3, with an intermediate that breaks up a conjugated amide grouping. 'I'husas the pH is raised hoth thek.] stepand theklstep will slow, but the partitioning ratio is unchanged. The flat k.., vs. nH curve of Fieure 2 at hiah ~H'sactuallv ~ + a s a catalyst. tells us that%he k; step uses t h e ~ m gro;p We know that ImH+ must be involved in the k-I step, the microscopic reverse of the kl step; if the k 2 step did not also use ImH+. the ~artitioninaratio would have ImHf in the denominator a i d not be & independent. Thus, if the enzyme is at p H eauilibrium throughout the reaction (which of course ma; not b e true), the pH-vs. kat curve of Figure 2 is not only consistent with the mechanism of Figure 1but is actually strong support in its favor.
This example shows the attractiveness and ease of the partitioning ratio alternative to the commonly used steadystate method. It also shows that there is no substitute for actually working through the kinetic arguments for a particular mechanism. Literature Clted 1. Hess. G.P. In The Enzymes; Ed. 3rd ed.; Boyer. P. D.; Aredemie: New Yolk, 1911:Vol. 111, Chapter 7. 2. Zubay, G. Biorhrmistry:Addison-Wwwley: Reading, MA, 1984: p 144-156. 3. Metzler. D. B i o c h e m i a w Academic: New York, 1977; p 375. 4. Rot I . p 236. 5. Himoe, A : P a r k , P. C.; He-, G. P. J. B i d . Chem. 1967,242,919. 6. E.g., panercafic ribonucleese; cf. ref2, pp 164-169. 7. Brerlaw. R.; BbPlla. M,J , Am. C h e m Soc. 1386.108.2655:Anslyn. E.: Bredow, R. J. Am. Chem.Soc., 1989,111,4473. 8. Cleland. W. W.Biochemisfry 1375,14,3220. 9. Ferrht, A.R.: Renard, M.Blochemisfv 1974.13,1416.
Volume 67
Number 3 March 1990
229
