J. Phys. Chem. 1993,97, 9259-9262
9259
Evolution of Enzyme Activity: Is Diffusion Control Important? Activation Parameters in the Reactions of Ferric Heme Species with Hydrogen Peroxide Dominique Job,? Peter Jones,* and H. Brian Dunford'*t Laboratoire Mixte, Centre National de la Recherche ScientifiquelRhone-Poulenc (UM 41). Rhone-Poulenc Agrochimie, 14-20 rue Pierre Baizet, 69263 Lyon cedex 9 France; Department of Chemistry, University of Newcastle upon Tyne, Newcastle upon Tyne, England NE1 7RU; and Department of Chemistry, University of Alberta, Edmonton, Alberta, Canada T6G 2G2 Received: April 28, 1993'
There is a finite energy of activation for a diffusion-controlled reaction. I t can be calculated by comparing a combination of the Stokes-Einstein relation between the diffusion coefficient of a solute molecule and the viscosity of a solvent and the Smoluchowski equation for a diffusion-controlled rate constant to the rate equation of simple transition state theory. The entropy of activation for a diffusion-controlled reaction can also be obtained. Comparison is made of the enthalpy and entropy of activation for a diffusion-controlled reaction to the enthalpies and entropies of reaction of a series of heme-containing proteins and a simple heme with hydrogen peroxide. For nonenzymatic species the enthalpy of activation is greater than that for the ionization of hydrogen peroxide, indicating that they react with the conjugate base of hydrogen peroxide. For the peroxidases and catalases, both the enthalpy and entropy of activation are less than that for both hydrogen peroxide ionization and a diffusion-controlled reaction. The latter result indicates reaction with unionized hydrogen peroxide, which gives the enzymes a huge advantage over the nonenzymatic species at physiological pH. It also indicates that the peroxidases and catalases do not operate by a diffusion-controlled mechanism. Our conclusion is that the hypothesis of the diffusion-controlled limit being the ultimate criterion of a perfectly evolved enzyme is too restrictive. Rather, enzymes evolve in such a manner that they ultilize the binding energy of the substrate to lower the enthalpy of activation below that for a diffusion-controlled reaction, in compensation for the necessary low entropy of activation required to form a transition state which is much more highly ordered than that of the separated reactants.
Introduction Some aspects of two overlapping problems in enzymology will be discussed in the context of the kinetic behavior of heme species in their reactions with hydrogen peroxide. How did enzyme activity evolve? And, is a diffusion-controlledrate the ultimate upper limit in the rate of an enzyme reaction, or must some sacrifice of speed be made for specificity?
Theory The basic rate law, expressed in terms of the thermodynamic form of transition state theory,' is
given temperature there are a series of values of AH*and Ms which yield the same value of AG*. If eq 2 is rearranged into the form
+ AG*
+ HOC
AHi = 34.3 kJ/mol
(4) then one sees that for a fixed value of AG*, one can plot AH* versus AS*and obtain a straight line with a slope of T. Two such parallel plots for T = 298 K are shown in Figure 1. For one, k = 104 M-l s-1 (In k = 9.2, AG* = 50.6 kJ/mol), and for the other, k = lo8 M-1 s-1 (In k = 18.4, AG* = 27.5 kJ/mol). There are two other reference points on Figure 1. One is the enthalpy of ionization of hydrogen peroxide:2
H,O, where k is the rate constant, R is the universal gas constant, T is the Kelvin temperature, N is Avogadro's number, h is Planck's constant, and AS* and AH* are the entropy and enthalpy of activation. The latter two quantities are related through
AH*= TAS'
-
H+
(5)
(2)
The other is the enthalpy of activation for a diffusion-controlled reaction. According to the Stokes-Einstein relation, a diffusion coefficient of a solute molecule is dependent upon the inverse of the coefficient of viscosity of the solvent. Combination with the Smoluchowski equation' for the rate constant for a diffusioncontrolled reaction, kdiR, leads to eq 64
-AGS + In R T (3) RT Thus eq 3 tells us that, at any given temperature, the value of In kdetermines thevalueof AG*,or viceversa. However, thevalues of AH* and AS*are not fixed by AG*, According to eq 2, at any
where TJ is the coefficient of viscosity of water and r is the radii of the reactants (assumed here to be equal). The value of k a in water at 25 OC accordingto eq 6 is 7.4 X lo9M-1 s-1. Equation 6 can be rearranged to
AG* = AH*- TM* Combination of eqs 1 and 2 leads to Ink=-
* Author to whom correspondence should be addressed.
Rhone-Poulenc Agrochimie. $University of Newcastle upon Tyne. f University of Alberta. *Abstract published in Aduance ACS t
Abstracts, August IS, 1993.
kdiff 8R In -= In T 30007
(7)
For a diffusion-controlledreaction eq 1 can be put into the form
0022-365419312097-9259$04.00/0 0 1993 American Chemical Society
Job et al.
9260 The Journal of Physical Chemistry, Vol. 97, No. 36, 1993
25°C
170
40 -
k 0
Y
-c
165
Diffusion Control
-
-100
-50
0
+50
AS', JK-lmo1-l Figure 1. Enthalpies and entropies of activation for ferric heme species reacting with hydrogen peroxide at 25 OC. Abbreviations and references: Mb, sperm whale myoglobin; Lb, leghemoglobin isoenzymes a and c (new data on the globins); BC, beef liver catalase;8 HEC, horse erythrocytecata1ase;a MLC, Micrococcus lysodeikticus catalase;*HRP, horseradish peroxidase isoenzymes C2 and TP, turnip peroxidase isoenzymes P1 and P7;1° DFH, deuterioferriheme." The diagonal lines show allowed values of AH* and rls* for & = 104 M-I s-l and lo8 M-I s-I. The target for diffusion control is in the range 2 X lo8 M-l s-l < & d i d 1 X lo9 M-I s-l and covers the temperature range from 0 to 40 OC. Theupper dashedlineindicatestheenthalpyofionizationofhydrogen peroxide.
Thusone sees that a plot of ln(kdm/ T),obtained from eq 7 ,versus 1 / T yields a slope from which the enthalpy of activation for a diffusion-controlled reation AH*dn can be obtained (eq 8 and Figure 2). Values of 1 from 0 to 40 OC were used,5 which covers the temperature range for most living systems. The result is u * d i f f = 17.9 kJ/mol for water at 298 K. There is a small curvature in the plot in Figure 2 which changes AH*by 7% over the 0-40 OC range. Other assumptions can be made concerning properties of the reactants such as the diffusion coefficient of the enzyme being neglibible compared to that of the substrate, the radius of the substrate being negligible compared to that of the enzyme, and theactivesiterepresentingonly a fractionof the enzyme surface.617 These may reduce the value of kdiff from 7.4 X lo9 M-Ls-l to as low as 2.0 X lo8 M-I s-l which is reflected in a change of h S * d f l , but the value of AH*dffremains the same. The range of values for M * d i f f and h S * d i f f , corresponding to the probable range for enzyme-catalyzed diffusion-controlled reactions of 2 X 108 to 1 X lo9 M-l s-l, are shown on Figure 2 for the 0-40 OC range. Experiment A compilation of AH* and AS*data for deuterioferriheme and a series of heme proteins is shown in Figure 2,&12 which includes hitherto unpublished data on the globins. The results for deuterioferriheme have been corrected for its small amount of dimerization.13J4
I
I
I
32
34
36
1 io3 ( K 1 ) T Figure 2. Plot of In(&/T ) versus 1 / T for a diffusion-controlled reaction according to eqs 7 and 8. The slope at 25 OC yields AZf" 17.9 5
kJ/mol.
Discussion The catalases and peroxidasesare well-known for their reactions with hydrogen peroxide to form compound I which contains the two oxidizing equivalents obtained by oxygen atom transfer.lsJ6 On the other hand, the globins17-19 and heme itselPo appear to react by a different mechanism, in which a compound 11-like species is formed containing only one extra oxidizing equivalent. Compounds I and I1 are the intermediate oxidized species in a normal peroxidatic cycle: native enzyme compound I compound I1 native enzyme. It can be seen from Figure 1 that there are two groups of results. All of the nonenzymatic species have rate constants of lo4 M-l s-1 or less, enthalpies of activation in excess of that for the ionization of hydrogen peroxide, and entropies of activation scattered around a value of zero, suggestingthat they are incapable of reaction with hydrogen peroxide. Rather, they react with the stronger nucleophile H02-.21 In contrast the peroxidases and catalases (with the exception of turnip peroxidase isoenzyme7 ,the dominant form in the winter storage of turnips) all have rate constants of the order of lo7 M-1 s-l. Their enthalpies of activation are less than that for diffusion of a solute species and much less than the enthalpy of ionization of hydrogen peroxide. This suggests that the enzymes react with unionized hydrogen peroxide, which gives them a huge advantage over the nonenzymes. Since the pKafor the ionization of hydrogen peroxidez2 is 11.6, the concentration of unionized hydrogen peroxide is larger than that of HO2- by a factor of 4.6 log units at pH 7.0. The results in Figure 1 may also provide an indication of the kinetic evolution of enzymes. Viable samples of enzymes and their protein precursors from prehistoric times are not available. However, it is widely accepted that the evolutionaryprocess leads to greater catalytic efficiency. The problem is in defining the ultimate efficiency. Properly placed distal catalytic groups capable of interacting with ferric heme-bound hydrogen peroxide would appear to explain the ability of peroxidases and catalases to react with unionized hydrogen peroxide. What is the nature of ultimate catalytic efficiency? It has been argued that it is the diffusion-controlledlimit, which implies that the perfectly evolved enzymecan convert substrate to product as fast as it arrives at the active site. Using this criterion an
-
-
-
Is Diffusion Control Important?
The Journal of Physical Chemistry, Vol. 97, No. 36, 1993 9261
“efficiency function” of 0.6 was deduced for triose phosphate isomera~e.23-~5It was also concluded that a requirement of the ultimate efficiency is to have an internal equilibrium constant of unity between enzyme-substrate and enzyme-product complexes. Three types of mutant effects on free energy profiles were described in terms of “uniform binding”, “differential binding”, and the most difficult: loweringof the free energy of the transition state without affecting the energy of reactive intermediates. This work has attracted a great deal of attention. Recently it has been criticized on the basis of experimental resultsz.27 and subjected to a thorough critical analysis.28 In the most recent paper in the series,25free energy profiles have been replaced with kinetic barrier diagrams, but it is still assumed that the diffusion-controlled limit is the ultimate target of evolutionary improvement. To the best of our knowledge, ours is the first attempt to break the free energy profile down into enthalpy of activationand entropy of activation terms and to compare the results to that predicted by simple diffusioncontrol. The study of the elementary reaction with hydrogen peroxide,part of theoverall enzymecycle,simplifies the interpretation of the results. It is our hypothesis that the diffusion-controlled limit is roo limiting. The diffusion-controlledlimit for an enzyme-catalyzed reaction appears to lie in the range in the range 2 X lo8 to 1 X 109 M-l s-l which corresponds to a AH* value of 17.9 kJ mol-’, and AS* values between 17.3 and 18.5 J mol-’ K-l at 25 OC (Figure 1). The peroxidasesand catalasesactually have enthalpies of activation below that for a diffusion-controlledreaction. How is this possible? For the formation of an encounter complex ki
E
+ S a ES k-i
k2
products
(9)
If k-1 >> k2 then E and S diffuse apart faster than they react.29 The rate of reaction is then chemically controlled by the value of kz. d[products] /dt = k2[ES] (10) Formation of the encountercomplex is governed by the equilibrium constant Kr:
Therefore and the rate of product formation (eq 10) becomes d[products]/dt = k2Kr[E][SI (13) Therefore the experimentally determined rate constant k,, is given by kapp = k2Kf The Gibbs-Helmholtz equation is d(ln K,)/dT = AHo/Rp and the kinetic analog is sufficiently accurately given by d(ln k2)/dT = AH2*/Rp Upon taking logs of eq 14 and differentiating with respect to temperature one obtains the following expression for the experimentally measured activation energy AH*,,:
AHsapp = AH2* + AiP AHo is the standard heat of formation of the encounter complex which can be negative, and the value of A H 2 * could be as low as zero for an exothermic reaction. Therefore the measured
activation energy could in principle have a negativevalue. In the case of bovine liver catalase an overall enthalpy of activation of zero is observed (Figure 1). On the other hand if k2 >> k-1, the reaction is truly diffusion controlled, there is no population of encounter complexes, and the reaction is simply
ki
E + S products In this case k,, = kl, and MSa, = MI*= 17.9 kJ mol-’. Thus diffusion control is unnecessarily restrictive. It limits the enthalpy of activation to an unnecessarily high value, and the enzyme is incapable of fully utilizing the enthalpy of binding to facilitate reaction. Recent work on phosphoglucomutase shows the importance of binding energy.30 We have maintained that some speed must be sacrificed for specificity.31J2 If there is zero lifetime to the encounter complex then there is zero time for enzyme and substrate rearrangement into the most favorableconformation for reaction. Not only must reaction occur immediately upon contact of reactants but the initial contact must be perfectly oriented! There is a general trend displayed in Figure 1 as one goes from deuterioferriheme to catalase. Both the enthalpy and entropy of activation decrease. The catalases are more specific in their reactions of compound I than are the peroxidases. They are also bigger with more complicated tetrameric structures. It would appear with longer polypeptide chains, more suitable configurations are more readily obtained.33 However, nature has paid a price in biosynthetic energy to obtain these more specific catalysts. Both the enthalpies and entropies of activation are much less for the catalases than is predicted by the theory for diffusioncontrolled reactions. The large negative entropies of activation for the catalases slow the reaction rate and indicate that the transition state for compound I formation is much more ordered in structure than are the reactants. This may be the price which it is necessary for nature to pay, which is partially compensated by the very low enthalpy of activation. In the next millennium a catalase may evolve with a faster rate of reaction, but it would appear unlikely that it will react by a strict diffusion-controlled mechanism. Rather, the enzyme will continue to utilize the negative enthalpy of formation of the enzyme-substrate precursor complex to lower the overall activation enthalpy of compound I formation, in compensation for the necessary large negative entropy of activation, a result of forming a highly ordered transition state. Acknowledgment. We thank Dr. Steve Withers for helpful suggestions. References and Notes (1) Eyring, H. J. Chem. Phys. 1935, 3, 107. (2) Evans, M.G.; Uri, N. Trans. Faraday Soc. 1949, 45, 224. (3) von Smoluchowski, M.W. Z . Phys. Chem. 1917,92, 129. (4) Caldin, E. F. Fast Reactions in Solution; Wiley: New York, 1963; pp 11-12. (5) Hardy, R. C.; Cottingham, R. L. J . Res. Narl. Bur. Stand. 1949,42, 473. (6) Nakatani, H.; Dunford, H. B. J . Phys. Chem. 1979,83, 2662. (7) Dunford, H. B.; Hasinoff, B. B. J . Inorg. Biochem. 1986, 28,263. (8) Beers. R. F.: Sizer. I. W. J. Phvs. Chem. 1953, 57. 290. (95 Markiund,S:;Ohladon,P.-I.;Opara,A.;Paul, K.-G.Biochim. Biophys. Acta 1974. 350. 304. (10) J0GD.t Ricard, J.; Dunford, H. B. Can. J . Biochem. 1978,56,702. ( 1 1) Mantle, D. Ph.D. Thesis, University of Newcastle upon Tyne, 1976. (12) George, P.; Irvine, D. H. J . ColloidSci. 1956, 1 1 , 327. (13) Kelly, H. C.; Davies, D. M.;King, M. J.; Jones, P. Biochemistry 1977, 16, 3543. (14) Jones, P.;Prudhoe, K.; Brown, S . B. J . Chem. Soc., Dalton Trans. 1974, 911. (15) Frew, J.; Jones, P. In Advances in Inorganic and Bioinorganic Mechanisms;Sykes, A. G., Ed., Academic Press: New York, 1984; pp 175212.
9262 The Journal of Physical Chemistry, Vol. 97, No. 36, 1993 (1 6) Dunford, H. B. In Peroxidases in Chemistry and Biology; Everse, J., Everee, K.E., Grisham, M. B., Eds.; CRC Press: Boca Raton, FL, 1992; Vol. 11, Chapter 1, pp 1-24. (17) George, P. Ado. Cat. 1952, I, 367. (18) Yonetani, T.; Schleyer, H. 1.Biol. Chem. 1967, 242, 1974. (19) Job, D.; Zeba, B.;Puppo, A.; Rigaud, J. Eur. J. Biochem. 1980,107, 491. (20) Frew, J. E.; Jones, P. J . Inorg. Biochem. 1983, 18, 33. (21) Jones, P. In Oxidases and Related Redox Systems; King, T. E., Mason, H. S.,Morrison, M., Eds.; University Park Press: Baltimore, 1973; VOl. 1, pp 333-343. (22) Schumb, W.C.; Satterfield, C. N.;Wentworth, R. L. In Hydrogen Peroxide; ACS Monograph No. 128; American Chemical Society: Washington, DC,1955; p 393.
Job et al. (23) Albery, W. J.; Knowles, J. R. Biochemistry 1976,15, 5631. (24) Knowles, J. R.;Albery, W . J. Acc. Chem. Res. 1977, 10, 105. (25) Bumbaum, J. J.; bines, R. T.; Albery, J. A.; Knowles, J. R. Biochemistry 1989, 28, 9293. (26) Elliott, A. C.; Sinnott, M. L.; Smith, P.J.; Bommuswamy, J.; Guo, 2.;Hall, B. G.; Zhang, Y . Biochem. J . 1992, 282, 155. (27) Li, B. F. L.; Holdup, D.; Morton, C. A. J.; Sinnott, M. L. Biochem. J . 1989, 260, 109. (28) Benner, S . A. Chem. Rev. 1989, 89, 789. (29) Eigen, M. 2.Phys. Chem. N.F. 1954, I , 176. (30) Percival, M. D.; Withers, S . G. Biochemistry 1992, 31, 498. (31) Hewson, W. D.; Dunford, H. B. Can. J . Chem. 1975, 53, 1928. (32) Jones, P.; Dunford, H. B. J . Theor. Bid. 1977, 69, 457. (33) Koshland, D. E. Fed. Proc. 1976, 35, 2104.
