Environ. Sci. Technol. 2002, 36, 4199-4200
Response to Comment on “Peroxidase-Catalyzed Oxidative Coupling of Phenols in the Presence of Geosorbents: Rates of Non-extractable Product Formation” SIR: The singular concern raised by Dr. Aitken in his thoughtful and generally positive Comment relates to the rigor of the rate analysis applied to the reversible phenoxy radical (AH‚) generation process we proposed. In addressing that concern, Aitken misconstrues the mechanistic character of the process and inappropriately translates the schematic representation given in Figure 3 of the paper into the chemical reaction forms of eqs a and b of the Comment. This radical generation process is complex, and full development in the paper of all elementary reactions involved was precluded by space limitations. We thus simplified the mathematical derivations by presenting them on the basis of compositereaction effects. Based on the misconceptions inherent in eqs a and b of his Comment, Aitken questions the correctness of this approach, suggesting that a different result may be obtained from an elementary-reaction-based rate analysis. We demonstrate here that such an analysis yields exactly the same result. Peroxidase facilitates the generation of phenoxy radicals via the Chance-George mechanism presented schematically in Figure 1 (1-3). This catalytic cycle includes three sequential steps, each mediated by one of three different forms of the enzyme; i.e., the native enzyme E0 and the two enzyme intermediates Ei and Eii. Hydrogen peroxide functions as the substrate in the first enzymatic step and phenol(s) in the latter two. The rate constants for these enzymatic reactions are designated kE0, kEi, and kEii . Two phenoxy radicals, AH‚i and AH‚ii, are generated in steps 2 and 3 of the cycle by single-electron transfers from the phenol substrate (AH2) to the enzyme intermediates. An important feature of this cycle is that the reactions involving formation of Ei and Eii are much faster than conversion of Eii to E0 (i.e., kEii , kE0, kEi), thus allowing a steady-state approximation for the enzyme intermediate concentrations (1, 3). This is equivalent to assuming that a specific distribution of the three different forms (E0, Ei, and Eii) of total active enzyme (E) is quickly established and maintained, with the ratio [E0]:[E] approaching zero and the ratio [Ei]:[Eii] maintaining a constant value determined by the intrinsic rate constants of the enzyme conversion reactions. Taraban et al. (4) demonstrated that, as indicated in steps 2 and 3 in Figure 1, electron transfer from the enzymes to the phenoxy radicals also occurs before the latter are scavenged, essentially reversing each radical generation reaction. The respective rate constants for the reverse reactions are designated kri and krii. The radicals may leave the enzyme by direct radical scavenging reactions or by diffusion into bulk solution prior to being scavenged. The rates of these radical-enzyme separation processes are designated rsi and rsii for [AH‚i] and [AH‚ii], respectively. Figure 3 of the original paper presented the reversible radical generation comprised by steps 2 and 3 in Figure 1 schematically but did not describe the complete catalytic cycle. It is inappropriate to isolate that schematic representation and put it in the chemical reaction form as Aitken did in eq a. When both H2O2 and phenol substrates are present in excess, the steady-state distribution of Ei and Eii allows the overall rate of radical generation in steps 2 and 3 to be represented in terms of a first-order rate expression with 10.1021/es020817n CCC: $22.00 Published on Web 08/31/2002
2002 American Chemical Society
FIGURE 1. The peroxidase catalysis mechanism with reverse electron transfer taken into account. respect to the total active enzyme concentration; i.e., rE ) kE[E] in eq 2 of the original paper. The overall rate of the phenoxy radical reverse electron transfer was expressed as rr ) - kr[AH‚] in our eq 3. Equations 2 and 3 were then coupled, assuming that reverse electron transfer is the dominant mechanism for radical disappearance, to give eq 4, which describes the pseudo-steady-state radical concentration in this reaction system at any instant in time; i.e.,
[AH‚] )
kE [E] kr
(4)
To elaborate the fundamental correctness of the analysis presented in the original paper, a rate analysis is performed here on the basis of elementary reactions under conditions and assumptions consistent with those given in the paper; i.e., (i) both substrates (H2O2 and phenol) are present in excess, (ii) reverse electron transfer is the predominant radical-disappearance route, and (iii) concentrations of the enzyme intermediates (Ei, Eii) and the radical species (AH‚i, AH‚ii) are at steady-state. The following equation can then be obtained through the detailed derivation process presented in Part 1 of the Supporting Information provided with this Response.
[AH‚] )
2kEikEii [E] krikEii + kriikEi + 2kEikEii
(c)
Equation c is functionally equivalent to eq 4 in that they both describe the appropriate proportionality between phenoxy radical and active enzyme concentrations at any instant in time. As evident in the schematic presented in Figure 1, the overall rate of radical generation is the sum of the rates of the forward reactions in steps 2 and 3; i.e. rE ) rEi + rEii. Similarly, the overall reverse reaction rate is given by rr ) rri + rrii. From these relationships, the rate constants for the overall reaction effects, kE and kr, can be written in terms of the rate constants for the elementary reactions (a detailed derivation is provided in Part 2 of the Supporting Information) as
kE )
kEikEii(kri + krii) krikEii + kriikEi + 2kEikEii
(d)
1 (k + krii) 2 ri
(e)
kr )
Substitution of eqs d and e into eq 4 then yields precisely the same relationship as given in eq c. VOL. 36, NO. 19, 2002 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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Equation 4 was used in the original paper for rate analyses of the postenzymatic reactions involving phenoxy radicals shown in Figure 3; i.e., enzyme inactivation and formation of nonextractable products. Inherent to this strategy is the entirely justifiable simplification effected by omitting the process of radical diffusion from enzyme to solution (see Part 3 of the Supporting Information). For example, enzyme inactivation resulting from radical attack was expressed in eq 5 as -d[E]/dt ) kin[E][AH‚]. Substituting eq 4 into eq 5 and combining rate constants leads to eq 6, -d[E]/dt ) k′in[E]2, which we demonstrated (as Aitken notes) provides good mathematical descriptions of the experimentally observed enzyme inactivation rate behaviors. Because eqs c above and 4 of the paper are equivalent, it can be concluded that the rate analysis strategy presented here on the basis of elementary reactions leads to exactly the same results as those presented in our paper. The inappropriate translation of the schematic representation of the reversible radical generation process given in Figure 3 of the paper into the chemical reaction equation form of eq a is compounded in the Comment by extension of eq a to eq b, which does not capture the irreversible reaction step 1. This then leads to Aitken’s erroneous conclusion that, because the net rate of composite enzymatic reactions for both cases can be represented by the Michaelis-Menten equation, it is irrelevant whether reverse electron transfer is included in the rate analysis. While it is true that both cases can be described by rate equations of similar form, it does not logically follow that reverse electron transfer can be ignored. A detailed analysis of this issue in Part 4 of the Supporting Information indicates that the rate equations for scenarios with and without reverse electron transfer converge only when radical scavenging reactivity is constant. The study described in our paper and in ensuing work (5), conversely, is specifically designed to investigate systems containing reactive sorbents having different cross-coupling reacitivties.
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ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 36, NO. 19, 2002
As such, it is one in which reverse electron-transfer reaction must be incorporated in the rate analysis.
Supporting Information Available Derivation of eq c (Part 1), derivation of eqs d and e (Part 2), rationalization of radical diffusion (Part 3), and differences in rate analyses with and without reverse electron transfer considered (Part 4). This material is available free of charge via the Internet at http://pubs.acs.org.
Literature Cited (1) Nicell, J. A. J. Chem. Technol. Biotechnol. 1994, 60, 203-215. (2) Wu, Y.; Taylor, K. E.; Biswas, N.; Bewtra, J. K. J. Environ. Eng. 1999, 125, 451-458. (3) Choi Y-J.; Chae, H. J.; Kim, E. Y. J. Biosci. Bioeng. 1999, 88, 368-373. (4) Taraban, M. B.; Leshina, T. V.; Anderson, M. A.; Grissom, C. B. J. Am. Chem. Soc. 1997, 119, 5768-5769 (5) Huang, Q.; Weber, W. J., Jr. Peroxidase-catalyzed oxidative coupling of phenols in the presence of geosorbents: Effects of sorbent chemical characteristics; American Chemical Society, Environmental Chemistry Awards Symposia, 224th ACS National Meeting (ext. abs.), Boston, MA, 2002.
Qingguo Huang, Hildegarde Selig, and Walter J. Weber, Jr.* Environmental and Water Resources Engineering Department of Civil and Environmental Engineering Department of Chemical Engineering The University of Michigan Ann Arbor, Michigan 48109-2125 ES020817N * Corresponding author phone: (734)763-2274; fax: (313)936-4391; e-mail:
[email protected].
