1980
J. Phys. Chem. 1995, 99, 1980-1987
New Reaction Mechanism for the Oscillatory Peroxidase-Oxidase Reaction and Comparison with Experiments Yu-Fen Hung, Igor Schreiber,?and John Ross* Department of Chemistry, Stanford University, Stanford, Califomia, 94305 Received: September I , 1994; In Final Form: November 23, 1994@
We present a new model for the oscillatory peroxidase-oxidase reaction, which is an extension of the recent model C (Aguda, B. D.; Larter, R.J. Am. Chem. SOC.1991, 113, 7913) and includes reaction steps involving 2,4-dichlorophenol and termination reactions for the superoxide radical and hydrogen peroxide. The calculations with this model compare well with measurements of temporal variations, including mixed-mode, chaotic, and bursting oscillations as well as tests for the assignment of roles of the species in the model and the categorization of the oscillator (Eiswirth, M.; Freund, A.; Ross, J. Adv. Chem. Phys. 1991, 80, 127). Of the 12 species considered in this model, six are essential, and the others nonessential. The essential species are oxygen, compound I, compound 11, compound 111, the NAD radical, and the superoxide radical. The nature of these essential species is also identified. Of the four species (oxygen, NADH, native HRP, and compound 111) measured experimentally, oxygen and compound I11 have been determined to be essential. The category of this model is lCW, in accordance with the experimental results. The new model reproduces better than the earlier models the temporal variations observed experimentally.
I. Introduction The peroxidase-oxidase (PO) reaction is a much studied reaction exhibiting many different types of dynamic behavior. A variety of models, abstract as well as detailed, has been proposed'-' for the PO reaction. The abstract models include the DOP model,' the Olsen model? and the Alexandre-Dunford modeL3 The Olsen model is a slight variation of the DOP model, while the Alexandre-Dunford model is a skeletonized version of the more detailed model A.4 The detailed models include the Yokota-Yamazaki m e c h a n i ~ m ,the ~ Fed'kinaAtaullakhanov-Bronnikova oscillatory mechanism: model A, and model C.' See ref 8 for a review of most of these models. The most extensive and recent of these is model C, shown in Figure 1 (thin lines). Although the detailed models mentioned here include most of the reactions involving the different intermediates of the horseradish peroxidase (HRP) enzyme, and the reactants, oxygen and reduced nicotinamide adenine dinucleotide (NADH), neither 2,4-dichlorophenol (DCP) nor methylene blue (MB) is considered due to the lack of understanding of their exact roles in the mechanism. In the absence of DCP and MB, the limit cycle oscillations are not stable, and the reaction decays after a few oscillations to a stationary state.' In the presence of these two chemicals, oscillations are sustained for a few hours. (However, only DCP is required for sustained oscillations under the experimental conditions commonly used. ') We wish to augment model C with possible reaction steps involving DCP since this compound is crucial for sustained oscillations in the system, but is not considered in the other detailed models. The thick lines in Figure 1 represent the five additional steps along with two more species, DCP and D C P , added to model C to form the new model (18 reactions and 12 dynamic species). These reactions include two steps recycling DCP, two termination steps involving the superoxide radical and hydrogen peroxide, and an autooxidation step in NADH: +Department of Chemical Engineering, Prague Institute of Chemical Technology, Prague, Czech Republic. * To whom correspondence should be addressed. Abstract published in Advance ACS Absrracts, January 15, 1995. @
Figure 1. Network diagram of model C (thin lines) and the new model (thinand thick lines). The number of feathers denotes the stoichiometric coefficient of the reactants and the number of barbs denotes the stoichiometric coefficient of the products. The left feather also indicates the kinetic exponent of the reactant. No feather is shown if the stoichiometric coefficient of the reactant and its kinetic exponent are both unity.g Model C is redrawn from ref 7, and the number notations follow those listed in Table 1.
+ DCP - Per2+ + 0;-+ DCP' DCP' + NADH - DCP + NAD' 20,'- + 2H+ - 0, -t H,O, NADH 4-H,O, 4-Hf - 2H,O + NAD' NADH + 0, + Hf - H,O, + NAD' COIII
0022-3654/95/2099-1980$09.00/0 0 1995 American Chemical Society
J. Phys. Chem., Vol. 99,No. 7, 1995 1981
The Oscillatory Peroxidase-Oxidase Reaction. 2
TABLE 1: Elementary Reactions and Rate Coefficients for the New Modela no. reaction Per3+ H202 coI 1. RI coI NADH coII NAD' 2. R7 COII NADH Pes+ NAD' 3. 4. Per3+ NAD' Pes' + NAD+ Perz+ 0 2 coIII 5. COIII NAD' H+- coI NAD' 6. Per3+ 02.7. COIII NAD' 0 2 NAD' + 0 2 ' 8. 9. 0 2 ' - + NADH + H+- H202 + NAD' 2NAD' (NAD)2 10. 202'- 2 H+- H202 + 0 2 11. NADH 0 2 H+ HzOz NAD' 12. NADH~ NADH (1.5 x 10-7 M S-1) 13. 14. Oz(g) Oz(aq) (7.5 X10-8 M s - I ) 15. Odaq) 02(g) NADH Hz02 H+ 2Hz0 NAD' 16. COIII DCP P e P + 0 2 ' - + DCP 17. DCP NADH DCP + NAD' 18.
+ + + +
+ + + +
--+
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+ + +
+
+
rate constant 4.0 x 107 M-' s-I 5.0 x 105 M-' s-I 1.0 x 1O6M-'s-I 1.0 x lo6M-I s - I 2.0 x 107 M-1 s-1 3.0 x 1O8M-I s-l 3.0 x 107 M-I s-I 2.0 x lo8M-' s-I 3.0 x 105 M-' s-1 1.0 x lo8M-' s-l 2.0 x 107 M-1 s-1 5.0 x M-' s-l flow rate varied flow rate varied k, = 5.0 x s-l 1.0 x 107 ~ - 1 s - 1 1.0 x 1 0 3 ~ - l s - ' 1.0 x 10' M-ls-I
+ +
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[H+] is constant, whereas NAD+, (NAD)2, and H20 are considered inert products. The number notation of the corresponding reactions in Figure 1 is also shown for reference. Reaction 16 here is actually a combination of R17 and Rl8 in Table 1 of ref 8. The reaction rates listed for the inflows of NADH, R19, and oxygen, R ~ oare , average values of those used in the simulations; they are varied in the simulations as in the experiments. The combination of these two flow rates, along with the concentrations of HRP and DCP, is important in determining the dynamics of the reaction, as is observed in experiments. The five reactions with an asterisk are not considered in model C. Experimental Results
Experimental Results 0 52
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Figure 2. Temporal variations of the oscillations of (a, left) oxygen, (b, middle) NADH, and (c, right) native enzyme and COIII.The top graph represents the experimental results (typical oscillations reprinted from ref 13) and the bottom graph represents the model calculations. Extemal constraints and initial conditions for the model calculations: 7.5 x M s-I for 0 2 inflow rate (15 pM of 0 2 initially, equivalent to 1.25% oxygen flow in experiments), 1.27 x M s-l for NADH inflow rate (equivalent to 22.9 p L h of NADH flow (0.15 M solution) in 7.5 mL of solution), 0.60 p M of HRP, 12 pM of DCP, and 1 x M of HzOz (emulates experimental conditions where small amounts of HzOz are required to initiate the The NADH concentration level stabilizes faster if the experiment is started with a trace amount of H202 at lower DCP concentrations (< 15 p M ) in this model. This is not necessary at higher DCP concentrations and does not affect the eventual NADH concentration level in the system but does affect the transient time necessary to reach that concentration. where COIII(compound 111) and Per2+ (ferroperoxidase) are, respectively, enzymatic intermediates, and D C P is the DCP radical. The set of reactions and rate constants for the new model is listed in Table 1. The rate constants are determined considering the reported values (see ref 8 and the references within) and fitting to experiments. Direct comparison between the rate constants used in the model and those found experimentally are not possible in most cases since the experimental conditions, such as pH, used for those experiments are not comparable to those used in the experiments with which the
model calculations are compared. [H+] is buffered in the model while NAD+ and H20 are inert products that do not interfere with the reaction, even when they accumulate in the reaction system. Except for the reactions involving DCP, all other reactions in the model have been postulated for the PO reaction8 Although the chemistry of DCP has been studied extensively,10-12 its exact chemical interaction with the other species in the PO reaction is still unknown. However, it has been shown that DCP somehow reduces COIIIto its native enzyme form, and that without DCP, the enzyme remains mainly in the COD form.1s10-12
Hung et al.
1982 J. Phys. Chem., Vol. 99, No. 7, 1995 Experimental Results
-Oxygen -----NADH
Experimental Results
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4000
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(sec) Figure 4. Comparison of the transition of oxygen from its low stationary state to the oscillatory state due to an increase in oxygen flow between experimental measurements (reproduced from ref 13) and the model calculations. Extemal constraints and initial conditions for the experimental measurements: 1.0% oxygen flow (2.0 m L / s total gas flow rate) increased to 1.5% (dashed line), 20.0 pL/h NADH flow (0.15 M solution), 0.44 p M of HRP, 10 p M of DCP, 0.1 p M of MB, and 7.0 mL of solution in reactor. Extemal constraints and initial conditions for the model calculations: 7.5 x lo-* M s-l for 02 inflow rate (15 p M of 02 initially, equivalent to 1.25% oxygen flow in experiments and increased to 1.5% at 3500 sec), 1.70 x lo-' M s-' for NADH inflow rate (equivalent to 30.6 pL/h of NADH flow (0.15 M solution) in 7.5 mL of solution), 0.10 pM of HRP,and 35 p M of DCP. Time
Time (sec)
Figure 3. Comparison of the relative amplitudes and phase shifts of the oscillations of the measurable species (reproducedfrom ref 13) with those calculated with the present model (same conditions as in Figure 2).
In this report, we present and compare some of the characteristic dynamics of the new model to experimental result^,^^^'^ as well as to other detailed model^.^-^ Further, this new model is analyzed with the systematic methods proposed in refs 15 and 16 in an attempt to categorize the oscillator. Several of the PO models are also analyzed by these methods in ref 17.
11. Computational Methods The dynamic simulations are performed with the LSODE p a ~ k a g e ' ~using , ' ~ a backward differentiation implicit multistep method up to the seventh order, specifically with a LSODA solver which automatically switches between stiff and nonstiff methods. The phase shift relations are calculated by accurately locating the Hopf bifurcation and extracting the information from the Jacobian of the system.17 The concentration shift matrix is calculated similarly but from a skeletonized system where the concentrations of all nonessential species are held constant at their stationary-state values. The Jacobian of this skeletonized system is nonsingular and may be inverted to obtain the concentration shift matrix.
III. Calculations of Some Dynamic Features of the New Model and Comparison with Experiments We report the results of calculations with the model presented here and compare them with those observed experimentally. We also employ some of the tests suggested in refs 15 and 16 to assign roles to the essential species involved in the model and to categorize the oscillator (section IV).
A. Temporal Variations. This model displays many of the dynamic characteristics observed in the experimental system. First, we compare the oscillatory waveforms of the concentrations of the species that can be measured experimentally (those of oxygen, NADH, native HRP,and C O I I I ~ ~toJthat ~ ) calculated by this model and find that the model satisfactorily reproduces the experimental findings. Second, the conditions under which oscillations are found in the experiments and this model are also similar, as are the transients leading to the oscillatory and the stationary states.I3 The temporal variations in the oscillations of the concentrations of the four species mentioned as calculated with the model are shown in Figure 2. The two enzymatic species are plotted together for comparison. The native HRP is antiphase with respect to COIIIas is observed in the experiments. We may also compare the relative amplitudes and phase shifts of these four species and the result of increasing oxygen flow at the stationary and the oscillatory states as calculated with the model to that of the experiment^.'^,'^ Figure 3 compares the experimental results of measuring the relative amplitudes along with the phase shifts of the four species with those calculated with the model. The trend of the relative amplitudes for these species is similar in both instances, except that oxygen is the largest in experiments while coIII is the largest in the
J. Phys. Chem., Vol. 99, No. 7, 1995 1983
The Oscillatory Peroxidase-Oxidase Reaction. 2
Model Calculations
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