J. Chem. SOC., Faraday Trans. 1, 1985,81, 91-104 Reaction of Catalase with Ethylhydrogen Peroxide BY MORDECHAI L. KREMER Department of Physical Chemistry, The Hebrew University of Jerusalem, Jerusalem 9 1904, Israel Received 14th March, 1984 C,H,OOH reacts with catalase in a basically irreversible reaction in the course of which the species called compound (I) is formed and decomposed. The formation of compound (I) is preceded by the formation of a precursor complex which is able to react with a further molecule of C,H,OOH to yield an inactive biperoxy complex. The biperoxy complex causes a diminution of the extent of formation of compound (I) at hgh [C,H,OOH]. As a consequence, compound (I) can never be formed quantitatively. Some of its physical constants can, nevertheless, be evaluated.Compound (I) with C,H,OOH appears to retain C,H,OH in its structure. The study of the reactions of enzymes with pseudosubstrates has played an important role in efforts to elucidate the mechanism of enzyme action. It has often been hoped that the deviation of the enzyme reaction from its natural path will provide clues regarding certain steps in the otherwise unresolvable (or only partially resolvable j complexity of steps which comprise the natural course of enzyme catalysis. With this purpose in mind, the reactions of catalase with H202 and substituted peroxides have been studied, the former being the natural substrate for ~atalase.l-~ By using derivatives of H202 as substrates, the course of the reaction changes, resulting, when alkyl groups are used as substituents, in oxidation of the alkyl C,H,OOH -+ CH,CHO + H20 (A) and no evolution of oxygen.A characteristic feature of the reaction of catalase with both H202 and substituted peroxides is the formation of optically distinct intermedi- ates. In the commonly accepted interpretation, the (green) primary intermediates [called compound (I) (C,) because they are the first to appear in the spectrum], which are formed with mono- or un-substituted hydrogen peroxide, are regarded as essen- tially identical. Moreover, the decrement of the molar absorptivity of catalase upon formation of C, with CH,OOH or with C2H,00H has been used to determine the concentration of CI formed with H202.8* In the present investigation the basis of this cross-determination will be examined in some detail.One of the assumptions on which the above procedure is based concerns the possibility of a complete saturation of catalase by excess alkylhydroperoxide to form C,. This assumption was questioned by Brill and Williams, who found that the degree of saturation of catalase by C2H,00H depended in a complex fashion on the excess of C2H,00H applied.1° Details of their observations will be given in the experimental section. The study of the model reaction with the pseudo-substrate created some additional problems which have to be solved before any conclusions can be drawn regarding various aspects of the enzymic reaction of catalase with H202. First and foremost among these problems is the question of the detailed mechanism of the catalase + C2H,00H reaction. It is the objective of the present work to construct a 91 4-292 REACTION OF CATALASE WITH C,H,OOH scheme for the reaction.On the basis of this scheme the degree of saturation of catalase and the question of the determination of the physical constants of CI will be discussed. EXPERIMENTAL The basic experimental observations on the reaction can be summarized as follows. By adding a dilute solution of C,H,OOH, with an initial concentration (x,) < ca. 50 pmol dm-3, to a dilute solution of catalase, its total concentration on a haematin basis (e,) being ca. 5 pmol dm-3, there is a transient decrement of the optical absorption (AA) at the Soret peak of catalase (A. = 405 nm). After AA has reached a maximum (A&,,) there is a gradual regeneration of the original catalase spectrum.The time scale of events is ca. 1-5 min. There is a variation of the rate of regeneration of the spectrum with the type of catalase used, it being higher with horse-liver catalase and lower with bacterial catalase.ll9 l2 With x, > 50 pmol dm-3, the original catalase spectrum is not restored. Instead, a new species, denoted ethylhydroperoxicatalase, compound (11), is formed to a varying extent, depending on the conditions of the experiment. These changes occur on a time scale of several tens of minutes. Therefore, the best conditions for a saturation of catalase haematins (E) by C,H,OOH to form C, quantitatively were considered to be (a) short times (< 2 min) and (b) x, 50 pmol dm-3.10 Using this strategy, Brill and Williams undertook a systematic investigation of the catalase C,H,OOH reaction.’, They found that AA,,, first increased with increasing x,, but above x, x 300 pmol dm-3, a further increase of x, caused a decrease of AA,,,.Furthermore, they could show that even under optimal conditions for the formation of C, (largest AA,,,), at x, x 300 pmol dm-3 (a large excess of C,H,OOH over E), there was still free cutaluse haematin in the system. No explanation for this observation was offered. Also, no specific mechanism of the reaction was forwarded. It was suggested that the reactions which occurred in the system were basically irreversible. This suggestion contradicted an earlier assumption of Chance and Schonbaum, who considered the analogous reaction of catalase with CH300H to be a reversible, equilibrium reaction.12 Later work of Chance and Schonbaum supported the hypothesis of irreversibility, as they were able to show the formation of acetaldehyde from ethylhydrogen peroxide during its reaction with catalase.,9 1 3 9 l4 Irreversibility will be assumed also in the present analysis, the immediate aim of which is the construction of a mechanism which can account for the observations of Brill and Williams.Details of the method of calculation applied are given in the following section. METHOD OF CALCULATION A certain mechanism was assumed and the relevant set of rate equations was integrated numerically, using the DGEAR routine of the IMSL computer program library. By inserting a given set of initial concentrations, rate constants and molar absorptivity parameters, the routine calculated the instantaneous concentrations of the various species and of the optical absorption decrements (AA) at a preset array of points of time. The calculations were continued until AA reached a maximum (AAmax).At this point the calculations were stopped and a check was made to make sure that the program reached AA,,, in no less than 50 steps. In case this condition was not met, the calculations were repeated with a more densely set array of time points. In this manner it was ensured that the program did not miss the largest value of AA during a given run. Calculations were performed for the set of values of e, and x, used by Brill and Williams [ref. (lo), table 13. The quantity m,,, = AAmax/eo was evaluated and compared with the experimental results (column 3 of table 1, vide infra).The parameters were then varied in order to reach agreement between the calculations and the experiment. The standard optimization procedure, based on the method of ‘least residual squares’, was applied. In order to avoid the simultaneous variation of all parameters, which makes such calculations extremely difficult, the followingM. L. KREMER 93 procedure was adopted. First, it was assumed that at most two absorbing species (C,,C,) were formed in the system and that the deviations of their respective molar absorption coefficients from that of catalase were AE, and A E ~ . Next, the expression log m,ax(calc) = log + log ([PI + (AE~/AEJP~I/~OI (1) was evaluated. p1 and p 2 are the respective concentrations of C, and C,.By choice, C, was taken to be the species responsible for the major part of the absorbance change. [Eqn (1) could be simplified in cases in which the absorbance change was attributed to a single species only.] In a series of calculations AE,/AE, was held constant, whereas the factor log AE, appeared as an additive constant, which did not influence the shape of the log~,,x(calc) against x, curves. (Strictly speaking, the data of Brill and Williams do not lie on a single curve, since e, was not held strictly constant in their experiments, but they can be said to do so in an approximate sense.) Regarding the group of rate-constant parameters, their number could always be reduced by one, since the value of the computed maxima depended only on the ratios of rate constants and not on their absolute values.Consequently, the value of one of them (chosen as the rate constant of formation of the principal intermediate) could be arbitrarily fixed ( I dm3 mol-1 s-l). The other rate constants were then evaluated relative to this reference value. As the mechanisms considered involved, at most, three independent rate constants, the usual fitting procedure consisted of the adjustment of two rate parameters and of a coordinate shift parameter, representing log A&,. In this manner a partial minimum, corresponding to the chosen value of AE~/AE,, was found. The calculations were repeated for different values of AE~/AE, until a true minimum was found. The converged values of the parameters were then further refined and their standard deviations determined using the BMDPAR program of the BMDP computer program library.DERIVATION OF THE MECHANISM The criterion for a successful mechanism was seen in an explanation of the fact that as x, increased at constant e,, the values of AA,,, (reached in each experiment) passed through a maximum (AAMAX). First, the assumption was made that the phenomenon was caused by ethanol contamination of the ethylhydrogen peroxide reagent. Assuming a minimal set of reactions involving the formation and decomposition of an intermediate C, and its additional reaction with C2H50H, it was found that such a scheme could not account for the existence of AA,,,. An increase of the fraction of ethanol in the reagent caused a decrease of AA,,, at all values of x,, without causing the appearance of AAMAx.Next, catalatic-type reactions were tried, i.e. schemes which involve a reaction of CI with C2H500H to free catalase haematin. These reactions also failed to predict the existence of AAMAX. (An increase in the rate of freeing catalase increased the rate of its combination with C2H,00H, so that there was no net effect on [C,].) This result is in accordance with the lack of 0, evolution in the system.? These negative results indicated that the maximum was probably caused by an irreversible inactivation of catalase during the reaction with C,H,OOH. It could occur either via a direct reaction with C, or through a reaction involving a precursor of C,. First, the direct reaction of C, (I) with C,H,OOH was investigated. The details of this mechanism [mechanism (A)] are given in Appendix A.As this mechanism failed ZC,H,OH + 0,. t A catalatic reaction is equivalent to the disproportionation of C,H,OOH : 2C,H,OOH +94 REACTION OF CATALASE WITH C,H,OOH to account for the existence of AA,,,, the other possibility, involving a precursor complex, was investigated. The mechanism considered consisted of the following steps : where C,,, denotes a precursor complex to C,, C,, is an (inactive) biperoxy derivative of catalase haematin and lower-case letters denote concentrations. By assuming a rapid equilibrium between E, C,H,OOH and CPRC and further that at any instant only a small fraction of E is tied up in CPRC, we can write the rate equations as follows : = k;(e - p - q) (x, - p - 2q-S) - k , p dt dq - = ki(e - p - q) (x, - p - 24 - s), dt ds dt = k2P - (3) (4) where ki = kJK, kj = k3/K and The results of computer simulations based on mechanism (B) are summarized in table 1 and shown in fig.1. In fig. 1 , AAmax/eO is plotted as a function of the ratio of the concentrations of C,H,OOH and catalase haematin. Both the experimental and the calculated data show that AAmax/e, first increases then decreases with increasing x,/e,, having a maximum at x,/e, z 55. The rate constants were determined only up to a common multiplication factor (see Appendix B). The following values were calculated relative to the chosen reference of k; = 1 dm3 mol-l s-l: k, = (4.16k0.72) x s-l, ki = (8+ 12) x lo2 dms rnol-, s-l and eE-cI = (8.02f0.65) x lo4 dm3 mol-1 cm-l. The data show that while k, and cI, referring to the main catalytic path and intermediate, could be determined with reasonable accuracy, the accuracy achieved in the determination of ki and cBp, being representative of a minor branch of the reaction path under the experimental conditions, was considerably worse. The value of cE-cBP could not be determined with any degree of accuracy. The calculated standard deviation was much larger than the value itself [cE-cBP = - (8 & 70) x lo3 dm3 mol-l cm-l].It may be assumed that cBP has a value very near cE itself at 1 = 405 nm. Thus, according to the present explanation, the decrease of AAmax/eO at high x,/e, is due to the increased formation of CBP. As EE-EBP is much smaller than cE -c1 (and possibly has a negative sign), the formation of CBp causes an increase in the absorbance.In order to determine the absolute values of the rate constants, at least one AA against time curve must be known. Brill and Williams made a recording of AA as K = (e, - p - 4) (x, - p - 2q - s)/z.M. L. KREMER " 5- E d I 0 4 E E P 4 - E! m 0 --- n 0 u -. X il 9 'f 95 0 6 6 @ 3 - 3 I I I I I I I I 10 20 30 40 50 60 70 80 90 Fig. 1. Plot of AAmaX/eo as a function of xo/eo: 0, experimental results; +, calculated results. Experimental data of Brill and Williams [ref. (lo), table 13; T = 25 "C, pH 7.25 and A = 405 nm; calculations based on mechanism (B); k', = 1 dm-3 mol-l s-l, k, = 4.16 x s--l , and E ~ - E ~ ~ = ki = 7.87 x 10, dms rnol-, s-l, E ~ - E ~ = 8.02 x lo4 dm3 mol-l cm-l -7.9 x lo3 dm3 mo1-I cm-l. Table 1.Maximum optical adsorption decrements per unit concentration of catalase haematin. Data of Brill and Williams [ref. (lo), table 11. pH 7.25, T = 25 "C, A = 405 nm. Parameters used in calculations: k', = 1 dm3 mol-1 s-l, k, = 4.16 x lop5 s-l, ki = 7.87 x 10, dms rnol-, s-l, E ~ - E ~ = 8.02 x lo4 dm3 mol-l cm-l and E ~ - E ~ ~ = -7.9 x lo3 dm3 mol-1 cm-l 5.04 32 5.08 98 6.36 29 5 5.25 286 6.32 560 3.05 4.93 5.30 5.43 4.80 3.05 4.93 5.36 5.37 4.80 a function of time using e, = 6.32 pmol dmp3 and x, = 295 pmol dm-3 [fig. 1. of ref. (lo)]. No entirely satisfactory simulation of this curve could be achieved by taking the above set of relative rate constants and absorption coefficient parameters and adjusting the scaling factor of the rate constants.It is thought that the initiation of the reaction by Brill and Williams was not fast enough to ensure instantaneous mixing of the reactants. In fact, 65% of the total absorbance change had already occurred before the first observation was made (10 s). This factor may have influenced some96 REACTION OF CATALASE WITH C,H,OOH of their absorbance readings. Therefore, their measurement of the total absorbance change is considered to be more accurate than their recording of its temporal behaviour . Approximate values of the absolute rate constants which optimized, within limitations, the fit between the experimental and calculated curves, were as follows : k; = 1.7 x lo2 dm3 mol-1 s-l, k, = 7.1 x s-l and ki = 1 x lo5 dm6 rnol-, s-l.DISCUSSION The overall decomposition of C,H,OOH is, in effect, a dehydration process C,H,OOH -+ CH,CHO + H20 and it is remarkable that it is catalysed by an oxidation-reduction catalyst like catalase. With the participation of a catalyst, however, the dehydration reaction can be resolved into steps which do involve oxidation and reduction a C,H,OOH + E -+ EO + C,H,OH b EO + C,H50H -+ E + CH3CH0 + H,O or C C,H,OOH + E -+ {EO * C,H,OH} d (EO - C,H,OH)-+ E + CH3CH0 + H20. Mechanism (B) involves steps (c) and (d) as the path of catalysis, but an alternative mechanism, based on reactions (a) and (b) may also be envisaged: K E + C,H,OOH CpRC kz C; + C,H,OH -+ E + CH,CHO + H20 A series of calculations, based on mechanism (C), has been carried out. They have shown that the residual square sum, defined as {S = Z[logbAmax(calc.) - log aA,,,(e~ptl)]~}, was considerably higher for mechanism (C) (1.42 x lo-*) than for mechanism (B) (4.49 x became 1.37 x lo5 dm3 mol-1 cm-l, which implies a negative molar absorption coefficient for compound (I).[The molar absorption coefficient of free catalase haematin at 405 nm is 1.01 x lo5 dm3 mo1-l cm-l, from fig. 2 of ref. (lo)]. From this failure of mechanism (C), in contrast to mechanism (B), to provide an adequate basis for an interpretation of the experimental data we conclude that C,, rather than C;, is the correct description of compound (I), i.e. that compound (I) from C,H500H retains C,H,OH as part of its structure. This conclusion agrees with the statement of Nicholls and Schonbaum Furthermore, the converged value of E~M.L. KREMER 97 that no evidence has been found for the liberation of alcohol upon the formation of compound (I).3 Mechanisms (B) and (C) contain the essential elements of scheme (11) of Schonbaum and Chance with path 2 or 3 ~ p e r a t i n g : ~ ~ E+CH,CHO+H,O 1 E+CH,CH,OOH e ( E . C H , C H , O O H ) EO + CH,CH,OH scheme (I) E+CH,CH,OOH + (E.CH,CH,OOH) + (EO.CH,CH,OH) ‘ k / k3 E + CH,CHO + H,O E O+ CH,CH,OH scheme (11) The present analysis shows that, at least in the case of C,H,OOH, only path 2 of scheme (11) is operative. (Also the reverse transformation EO * CH,CH,OH -, E.CH,CH,OOH, questioned by Schonbaum and Chance, is now ruled out.) The precursor complex C,,, = E * CH3CH200H becomes significant kinetically only at high x,, where it presents a point of branching off from the catalytic path to form the inactive intermediate CBp.Another question concerns the extent of conversion of catalase into compound (I) during the reaction. To investigate this point a series of computer runs was performed at a constant e, and at increasing x,. In each of these runs pmax and the simultaneous values of q and of free catalase haematin remaining in the reaction mixture were determined. (Note that p and AA reach their maxima at different times during the reaction.) Calculations were based on mechanism (B) and on the set of (relative) rate constants obtained in the previous section. The results obtained at e, = 5 pmol dmW3 are shown in fig. 2. Fig. 2 shows that as x, increases, the values of pmax pass through a maximum (pMAX).The values OfpMAX obtained at different e, are shown in table 2, where qMAX, and [&AX, are the concentrations of the respective species when p = PMAX. The data in table 2 show that there is an inherent limitation to the extent of formation of C,. When e, is in the range 2.5 - 10 pmol dm-3 only cu. 69% of catalase haematins can be converted under optimal conditions into compound (I). Cu. 18% of the haematins are in the inactive biperoxy complex, while nearly 13 % of the haematins are free. An important point to be considered concerns the fact that the value of p at the maximum of AA is always less than pmax, since at the maximum of AA, p is already decreasing. Thus, the values of p, corresponding to AAmax, are even lower than those given by the curve in fig.2. By adding 0.085 cm3 0.013 mol dm-3 KCN to a ‘steady-state mixture’ (i.e. when AA has reached its maximum) of 3.00 cm3 4.2 pmol dmP3 catalase haematin and 0.052 cm3 0.017 mol dm-3 C2H,00H, Brill and Williams found that cu. 5-10% of catalase haematins were free. A separate computer simulation was run with the appropriate initial concentrations of the above experiment (e, = 4.17 pmol dm-3, x, = 290 pmol dm-3). The calculations were stopped when AA reached its maximum98 REACTION OF CATALASE WITH C,H,OOH 1 I00 xo /pmol dm-3 200 300 400 Fig. 2. Maximum concentration of compound (I) as a function of x,; e, = 5 pmol dm-3; mechanism (B), rate parameters as in fig. 1. rable 2. Maximum formation of compound (I) [calculated on the basis of mechanism (B: ki = 1 dm3 mol-l 0, k, = 4.16 x lo5 s-l and k; = 7.87 x 10, dms rnol-, s-l e0 X O PMAX QMAX, p p PMAX QMAX.p IE1MAX, /pmol dmW3 /pmol dmP3 /pmol dm-3 /pmol dm-3 /pmol dm-3 / e , l e , /e0 2.5 230 1.734 0.447 0.323 0.694 0.179 0.129 5 23 5 3.464 0.905 0.63 1 0.693 0.181 0.126 10 240 6.914 1.821 1.265 0.691 0.182 0.127 value. At this point the following results were obtained: p = 2.873 and q = 0.868 pmol dm-3, giving [Elfree = 0.429 pmol dm-3, i.e. 10.3% of e,. This result is in excellent agreement with the above estimate of Brill and Williams.? The decrease of the molar absorption coefficient accompanying the change E + C, was found to be 8 . 0 2 ~ 104dm3mol-1cm-1 at d =405nm. Thus, E, becomes 2.1 x lo4 dm3 mol-1 cm-l, which is considerably lower than the value of 4.5 x lo4 dm3 mol-l cm-l given by Brill and Williams (their fig.2). The difference stems from the different values of the degree of conversion of E into C, used in the two calculations. Brill and Williams, on the basis of their CN- binding experiments, used a value of 92.5 % as the degree of conversion of catalase, by ignoring any species other than E or CI in the system. The present value also differs from that given by Chance [4.9 x lo4 dm3 mol-1 cm-l, ref. (8), fig. 2, calculated on haematin basis], who assumed 100% conversion into C,. t The results of Brill and Williams should be corrected slightly upward, if the finite dissociation constant of the E-CN complex [KECN = 22 pmol dm-3, ref. (9)] is considered. Thus, for example, a calculated value of 7.5% free catalase haematin should become 8%.M.L. KREMER 99 c a t a l y t i c range non-catalytic range I < n 3 50 100 I 5 0 xo /pmol dm-' Fig. 3. Concentrations of the components of the reaction mixture at the end of the reaction; eo = 5 pmol dm-3; mechanism (B), k; = 1 dm3 mol-1 s-l, k, = 4.33 x s-' and kj = 1.17 x lo3 dms rnol-, s-l. 50 100 150 xo/pmol dm-3 c a t a l y t i c range n o n - c a t a l y t i c range , Fig. 4. Relative concentrations of the components of the reaction mixture at the end of the reaction; e = 5 pmol dm-3; mechanism (B), all parameters as in fig. 3.100 REACTION OF CATALASE WITH C2H,00H The decrease of the molar absorption coefficient of bacterial catalase upon forming the analogous ‘Compound (I)’ species with H202 is 2.5 x lo4 dm3 mol-l cm-l at 1 = 405 nm.15 It differs substantially from AcI = 8.02 x 104 dm3 mol-1 cm-1 calculated above for the catalase-thylhydroperoxi-compound (I).This result does not support the view that there is an identical depression of the Soret band absorption of catalase upon forming different compound (I) species with alkyl hydrogen peroxides and with H202.8 According to the present discussion [retainment of C2H50H by ethylhydroperoxi-compound (I) and differences in the spectra], it appears that ‘compound (I) ’ species obtained with different substrates are not identical. The various steps and rate constants describe only the first part of the reaction, up to the maximum of the decrease in the absorbance. In spite of the inherent uncertainty, it is of interest to discuss the predicted course of the reaction in its later stages.In the following calculations it will be assumed that E~ - E ~ , has a small positive value. This assumption is not excluded by the above results and seems to agree with observations made on the system during the later phases of the reaction. (The parameters used in the calculations are those obtained before the BMDPAR refinement procedure. There has been only a slight change of the rate parameters as a result of this refinement so that the essential features of the following results remain unaffected by it.) In fig. 3 and 4 the final concentrations of the various constituents of the reaction mixture are plotted as a function of x,, and s,, x, and qe denote the final concentrations of CH3CH0, C,H,OOH and CBP, respectively. The ‘end of the reaction’ was defined here as a state in which either x became < 0.1 % of x, (low x, range), or the concentration of free catalase haematin falls to < 0.01% of e, (high x, range).(Under these conditions no substantial changes in the system could further take place.) Fig. 3 shows the absolute concentrations of the various components of the system at varying x,. In fig. 4 the concentrations relative to x, and e,, respectively, are given. Fig. 3 and 4 show that around x, = 100 pmol dm-3, where the formation of C,, becomes, to a good approximation, quantitative, there is a striking change in the distribution of the products of the reaction. There is an abrupt decrease in the final concentration of aldehyde (s,).Its formation is not quantitative even at x, < 100 pmol dm-2 (its curve of formation lags behind the straight line r which corresponds to the quantitative formation of CH3CH0 from C2H500H), but at x, = 100 pmol dm-3 there starts a sharp decline of s, as x, is further increased. At the same time, peroxide appears in the final state of the system in increasing concentrations. If we regard the reaction as essentially catalytic when > 90% of C2H,00H is converted to CH3CH0, then there is a sharply defined region when the reaction is essentially catalytic (x, < 100 pmol dm-3) and another region (x, > 100 pmol dmP3) where it is essentially non-catalytic. At low x,, the formation of CBp in the system can be neglected. Under these circumstances, the absorbance of the system will return at the end of the reaction to that of the free enzyme [fig.5, curves (a) and (b)]. Note the relatively flat maxima of curves (a) and (b), which in some interpretations of the corresponding experimental curves were thought to represent a ‘steady state, existing for a limited amount of time’. In reality, the system is far removed from any such situation. As noted above, the system is also not in an equilibrium. Consequently, the initial part of the curves cannot be treated as being a pre-steady state or an approach to an equilibrium or to represent quantitative bimolecular formation of compound (I). Any evaluation of the rate constant for the formation of CI on these assumptions must lead to erroneous r e s ~ l t s .~ ~ l1 Considering the run with x, = 5 pmol dm3, the curve x(a) shows that there is a considerable drop in the concentration of ethylhydrogen peroxide until the maximumM. L. KREMER 101 0.20 0 15 - I 5 2 0.10 Q 0 0 5 \ I 3 4 m 3 2 - 0 2 3 Y I I I I I t l s Fig. 5. Time dependence of AA at various x,; e, = 5 pmol dmP3; x, = (u) 5, (b) 10, (c) 20 and ( d ) 50 pmol dm-3; mechanism (B), k; = 6.0 x 10, dm3 mol-l s-l, k , = 2.6 x lop2 s-l, kh = 7.0 x lo5 dm6 mo1F2 s-l, C ~ ; - - E ~ = 8.17 x lo4 dm3 mol-l cm-' and E~~ = 8.2 x lo3 dm3 mol-l cm-'. 100 200 300 400 500 decrement of the absorption is reached (ca. 90 s). According to the calculations, ca. 77% of the original ethylhydroperoxide are still present. This feature of the reaction differs from that observed with the catalase-H,O, system, where at the maximum of AA, [H,O,] is practically nil.,? 18* l9 As x, is increased, the concentration of C,, in the system increases. Beyond a certain value of x,, the absorbance at the end of the reaction will not return to that of free catalase, but will remain at some residual value corresponding to the permanent typing up of part of the catalase haematins in the inactive biperoxy complex [curves In general, the calculated curves of fig.5 agree qualitatively with the behaviour of various alkylhydroperoxikcatalase systems, at low as well as at high initial concen- trations of the alkylhydroperoxides.ll9 l6 There is an interesting parallelism between the conditions of formation of C,, and of compound (11) (high x, and long reaction times).16 There may thus exist a relationship between these two species.? It should also be added that the present analysis cannot distinguish between the existence of an actual biperoxy complex or (4 and (41.t In the case of H,O,, the rate constant of reaction of the precursor complex with H,O, is probably very low. In the course of many catalytic cycles C,, may, however, accumulate. These are exactly the conditions under which compound (11) is observed in the catalase-H,O, system. Repeated cycles of reaction are provided here by continuously generating H,O, with the notatin-glucose-0, system.''102 REACTION OF CATALASE WITH C,H,OOH of some products of a reaction between the constituents of this complex, as long as the enzyme remains in an inactive form. Summarizing, the present investigation shows that the catalase-ethylhydrogen peroxide system is complex and that it is not possible to convert catalase quantitatively, under any circumstances, into compound (I).(At low x, the concentration of the alkylhydroperoxide is insufficient to saturate catalase, and at high x, part of the catalase is converted into the inactive biperoxy complex.) The formation of compound (I) can, however, be optimized and (at least some of) its physical constants can be determined. APPENDIX A The reactions comprising mechanism (A) are as follows: ki E +C,H,OOH 4 C, (e0-P-q) X ke C, --+ E + CH,CHO + H20 P s k3 C, + C2H5OOH + CBp. 4 At low x , step (2) predominates over step (3): the scheme is then a catalytic mechanism for the decomposition of C2H500H with a gradual inactivation of the catalyst through step (3).By increasing x , the catalytic step (2) becomes suppressed and the scheme becomes a two-step mechanism for the formation of C,, via the intermediate C,. We are interested in an analytical solution of the rate equations at high x (compared with eo). This condition is fulfilled in most of the experiments. By assuming that x remains constant during the reaction at its initial value (xo) and by introducing the variable u = eo - q, we can write the following matrix representation of the rate equations: This is a set of simultaneous linear first-order differential equations whose solutions are and The reduced absorbance decrement 6 = A A / ( E ~ - E , ) can be written as 6 = p + t r q (A 4) where E, = ( E ~ - E , ~ ) / ( E ~ - E ~ ) .By introducing the expressions for p and q from eqn (A 2) and (A 3) into (A 4), we obtain 6 = Er eo + (eo/ v'B) [(kl xo + Er 12) ~ X P (4 1) - (k1 xo + Er A) ~ X P (22 t)l- (A 5 ) By differentiating 6 with respect to time, and equating the time derivative to zero, we obtain the following expression for t,,,, the time when 6 has reached its maximum: In(=)M. L. KREMER 103 where u = k,/k,, a = t [ v + ( v 2 - 4a):] b = k,/k,, u = 1 +a+ (b/xo), and p = t [ u - (u2 - 4a):I. By introducing t,,, into eqn (A 5 ) we obtain an expression for 6,,, 6max = Er eo + S,,, depends on the ratios of rate constants a and b and on xo. By differentiating 6,,, with respect to u (and hence with respect to x,) we obtain where 2+2 2(1 +z) F(z) = z-'ln(l+z)-- and z = (a-p)/(P-a&,). It follows from eqn (A 9) that - 1 is the lower limit of z.Since tmax must be real and positive, (a-m,)/(P-ae,) must be positive (and greater than one). F(z), on the other hand, is always negative, in the allowed range of z. Thus, dS,,,/du is always negative, and because of the inverse relationship between xo and u, d6,,,/dx0 is positive. Mechanism (A) predicts, therefore, a monotonous increase of a,,, with x,, in contradiction to the experiment. To complete the proof, direct numerical integrations of the rate equations were carried out under conditions in which constancy of x during a run could not be assumed. The computations have shown that for all values of rate constants and extinction coefficients tried, 6,,, increased monotonously with increasing xo, in the same way as found in the analytical solution.APPENDIX B The reduced absorbance decrement is given by 6 = p+crq. The condition for the maximum of 6 is given by dP dq --f&,- = 0 dt dt which can be written in the alternative form Since at finite times dq/dt > 0, the condition for the maximum becomes dP -+&, = 0. d4 dp/dq can be obtained from eqn (1) and (2) and s can also be expressed as a function of q Eqn (B 5 ) and (B 6) are first-order linear differential equations for the calculation of p and s104 REACTION OF CATALASE WITH C,H,OOH as functions of q. From the form of these equations it can be deduced that the solution will depend on the ratios of the rate constants but not on their absolute values. Prof. Shalom Baer and Prof. Maurice Cohen are thanked for helpful discussions. B. Chance, in The Enzymes, ed. J. B. Sumner and K. 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