Single turnover kinetics of the reaction between oxycytochrome P-450cam and reduced putidaredoxin.

A study of the single turnover kinetics of the reaction between oxycytochrome P-450cam and reduced putidaredoxin was performed using the inhibitor metyrapone to trap the cytochrome immediately after release of the product, 5-exo-hydroxycamphor. EPR determinations of the concentrations of reduced putidaredoxin and ferric metyrapone-bound cytochrome at the same time points showed that there is no time lag between the oxidation of reduced putidaredoxin and the appearance of metyrapone-bound cytochrome. This implies that the rate constant for electron transfer is smaller than the rate constant for the later processes involved in product formation and release, lumped into a single step. Taking this restriction into account and doing computer simulation of absorbance versus time curves, previously obtained at various putidaredoxin concentrations using stopped-flow spectrophotometry, allowed bounds to be determined for rate constants of the processes within the reaction. At 4 degrees C in buffer at pH 7.4 with 0.50 M KCl, the rate constant for the bimolecular association of the two enzymes is between 3 and 20/microM.s; the rate constant for dissociation is between 12 and 600/s; the rate constant for electron transfer is between 60 and 100/s; and the rate constant for the later processes is at least 200/s.

Although the basic groups of reactions catalyzed by the family of enzymes called cytochrome P-450 were discovered more than 2 decades ago, there is still very little known about the precise chemistry of these reactions. In an effort to define more clearly the chemistry of this important enzyme, our laboratory and others have attempted to investigate the individual steps which constitute the catalytic cycle.
In the normal catalytic cycle of cytochrome P-450,,,,' the enzyme first binds camphor, its substrate, then accepts one electron from the iron-sulfur protein putidaredoxin, and then reversibly binds molecular oxygen to form oxycytochrome P-450,.,. This species, in the presence of reduced putidaredoxin, accepts another electron and catalyzes the 5-exo-hydroxylation of the bound camphor molecule. The product is then released, and the enzyme is ready to bind another camphor molecule (Estabrook et al., 1972;Gunsalus et al., 1972).
In our study of the kinetics of the oxygenating step of this * The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact. 'The abbreviations and trivial names used are: cytochrome P-450,.,, the soluble cytochrome P-450 isolated from P. putida; oxycytochrome-P-450,.,, the form of cytochrome P-450,., which is camphor-bound, one-electron reduced, and oxygenated; metyrapone, 2methyl-1,2-di-3-pyridyl-l-propanone; MOPS, 4-morpholinepropanesulfonic acid. reaction, we have made separate solutions of oxycytochrome P-450,., and reduced putidaredoxin and then rapidly mixed them. The putidaredoxin solution contained a high concentration of metyrapone to trap rapidly and irreversibly the camphor-free enzyme Griffin and Peterson, 1972) after product release, preventing the continuation of the reaction cycle. In previous experiments using this experimental scheme, we have demonstrated the hyperbolic dependence of initial reaction rate upon putidaredoxin concentration (Brewer and Peterson, 1986). This relationship shows that the reaction mechanism includes the formation of a complex of reduced putidaredoxin and oxycytochrome P-450,,, and that its formation is not rate-limiting, a t least at higher putidaredoxin concentrations. This finding is in accord with the "effector" kinetics of reactions of oxycytochrome P-450,,, with the nonphysiological reactant dihydrolipoic acid or oxidized putidaredoxin (Lipscomb et al., 1976). It is also in agreement with the results of experiments done at subzero temperatures in a mixture of phosphate buffer and ethylene glycol (Hui Bon Hoa et al., 1978). These authors concluded that the catalytic step of the reaction cycle is rate-limited by the first-order decomposition of an intermediate formed by the rapid binding of reduced putidaredoxin and oxycytochrome P-450,,,.
We now address the question of which of the first-order processes in this ''final'' step of the cycle is rate-limiting: electron transfer, product formation, or product release. Cleland (1975) has argued convincingly that enzyme-catalyzed reactions are generally rate-limited by product release; the argument is supported both by known examples and by some theoretical considerations. On the other hand, preliminary experiments from two laboratories have suggested that electron transfer is rate-limiting in the catalytic reaction step of cytochrome P-450,,, (Peterson and Mock, 1975b;Pederson et al., 1977). In this paper, we report experiments which show that electron transfer is indeed rate-limiting. We also present a model reaction sequence with approximate rate constants obtained by curve-fitting procedures.

MATERIALS AND METHODS
Commercial Reagents-Crystallized Tris base and lyophilized glucose oxidase (Grade I) were obtained from Boehringer-Mannheim. Metyrapone, (lR)-(+)-camphor, and MOPS were products of Aldrich. Catalase in 0.1% thymol, myoglobin, and the disodium salt of NADH were obtained from Sigma. Purified gases (oxygen, nitrogen, and argon) were supplied by the Linde Division of Union Carbide. Sodium dithionite was the purest grade available, Mannox brand, from Hardman and Holdman (Manchester, England). All reagents were used without further purification except glucose oxidase and myoglobin, which were dialyzed against buffer. Solutions containing catalase were filtered (0.22-pm filter) to remove particulate matter.
Enzyme Purification-Cultures of Pseudomonas putida (ATCC 17453) were grown, and the cytochrome P-450,., was purified from them as previously described (O'Keeffe et nl., 1978). Aliquots of the enzyme were stored at -20 "C until needed. The samples used in this 79 1 study had a 392 to 280 nm absorbance ratio of greater than 1.3 (Yu et al., 1974). Putidaredoxin was purified from the same cell cultures essentially as described by Mock (1977) with minor modifications. The diluted putidaredoxin fraction was not concentrated by pressure ultrafiltration as before, but was loaded directly onto the second DEAE-cellulose column. Since this may require 24-36 h, sodium azide was added to the solution to a final concentration of 1 mM in had a 455 to 280 nm absorbance ratio of 0.44 or greater (Mock, 1977), order to prevent contamination by bacteria. Putidaredoxin samples and they were stored at -170 "C. Putidaredoxin reductase was purified from the P. putz'du cells by the method developed in this laboratory (Roome et al., 1983) and was stored at -170 "C.
was 20 mM MOPS brought to pH 7.4 at 4 "C with Tris base. The Solution Preparation-The buffer used for all of the experiments standard buffer solution contained 0.50 M KC1, and all experiments were done at this KC1 concentration except those for which other concentrations are mentioned. All solutions were kept either on ice or thermostatted to 4 "C during preparation and use. Solutions were deaerated when necessary in sealed vessels by repetitive exposure to vacuum and prepurified argon which had been further scrubbed of oxygen, as previously described in detail (Hintz and Peterson, 1980). All transfers into deaerated solutions were performed within a glove bag filled with an atmosphere of purified nitrogen.
Putidaredoxin solutions were made in the buffer described above and were deaerated. Each putidaredoxin solution contained the desired amount of putidaredoxin, about 0.1 p~ putidaredoxin reductase, and a concentration of NADH which was at least 20 times the concentration of putidaredoxin. The buffer for putidaredoxin solutions also included a catalytic oxygen-scavenging system consisting of glucose, glucose oxidase, and catalase (Peterson and Mock, 1975a), and it contained metyrapone to give a final concentration of 2.5 mM after mixing in the stopped-flow spectrophotometer. Putidaredoxin reduction was initiated by the addition of NADH inside the glove bag and was monitored spectrophotometrically at 455 nm. The rate of reduction was limited by the amount of putidaredoxin reductase; complete reduction required 15-20 min. After complete reduction, the putidaredoxin solution was drawn into a cold Hamilton gas-tight syringe and used immediately.
Cytochrome P-450,., solutions were made in the standard buffer with a final camphor concentration (after mixing in the stopped-flow instrument) of 20 p~. Each solution was deaerated as described above and then titrated with 1.5 mM sodium dithionite until completely reduced; the course of the titration was followed spectrophotometrically. Immediately before use, the reduced cytochrome was oxygenated by the addition of an equal volume of oxygen-saturated buffer at 4 "C.
Each series of reactions was performed using aliquots from at least two preparations of cytochrome P-450,,, and at least two preparations of putidaredoxin. For each of the experiments using 28 WM putidaredoxin and 30 pM cytochrome, cytochrome stocks from three or four preparations were mixed together in each solution, and putidaredoxin stocks from two preparations were mixed. These measurements at high enzyme concentrations were made in the presence of 40 p~ camphor and 7.4 mM metyrapone. Throughout this paper, the concentrations of enzymes and other reagents in mixing experiments are expressed as concentrations after mixing.
Spectrophotometric Measurements-The spectrophotometer used to record spectra and to follow enzyme reductions was a Cary Model 118, with cuvette holders temperature-controlled via connection to a Haake water bath. The stopped-flow spectrophotometer was an Aminco-Chance duochromator used in the single-wavelength mode with an Aminco-Morrow stopped-flow attachment. In the early experiments, data collection and display were done using either a PDP 11/10 minicomputer, as described by Peterson and Mock (1975a), or a DEC LSI 11 with similar hardware and software. For later experiments, an IBM PC/XT with a Tecmar Lab Master data acquisition and control board was used. Elements of the software design for the IBM PC/XT version have been discussed (Roome et al., 1985).
Rapid-quench Measurements-Reaction samples at discrete time points were prepared for EPR measurements using a Ballou-type rapid-quench device (Ballou, 1971). One-ml reaction mixtures were rapidly quenched and frozen by spraying them into 60 ml of isopentane at -140 k 5 "C. The frozen samples were then packed into EPR tubes whose relative EPR-detectable volumes had previously been determined using a standard CuS04 solution. The validity of this EPR was verified in Ballou's extensive study (Ballou, 1971). To freeze-quenching method of sample preparation for low-temperature determine our efficiency and repeatability in packing the mixtures into EPR tubes, we performed packing tests (see Ballou, 1971). Samples of ferric myoglobin fluoride (80 W M before freezing) were rapidly frozen by the usual freeze-quenching procedure and packed into EPR tubes. The EPR signals of these samples were then divided by the signals of samples which had been introduced directly into EPR tubes and then frozen. A mean packing efficiency of 0.72 and a standard deviation of 0.07 were found. The concentration of a given species in a reaction mixture before freeze-quenching was calculated by dividing its measured concentration in the EPR tube by 0.72.
Electron Paramagnetic Resonance-The EPR measurements were made on a Varian E-4 EPR spectrometer. Data collection and averaging were under the control of an IBM personal computer with the IBM PC data acquisition and control adapter. The IBM-supplied software interface made it possible to write a compiled BASIC program to collect, average, correct for EPR tube size, and store on diskette the EPR data. The EPR sample chamber was cooled by flowing nitrogen gas chilled by passage through a coil immersed in liquid nitrogen. The temperature of the chamber was maintained at -170 "C by a Varian variable temperature controller. The temperature variation was not measured, but the variation in signal for the same samples at several times was about 53%.
Quantitation of reduced putidaredoxin by EPR was done using the following instrument settings: frequency = 9.152 GHz, power = 100 milliwatts, modulation amplitude = 12.5 G, and time constant = 0.3 s. Gain was either 400, 800, or 2000. Magnetic field was repeatedly scanned from 3175 to 3575 G at 2 min/scan, and from 2 to 8 scans were computer-averaged for each determination. The amount of reduced putidaredoxin in each sample was determined by measuring the peak-to-peak height of the signal at g = 1.94 (3372 G), dividing by the instrument gain, and comparing the result with a standard curve.
EPR measurements of ferric metyrapone-bound cytochrome P-450,,, were made using the following instrument parameters: frequency = 9.152 GHz, power = 100 milliwatts, modulation amplitude = 12.5 G, time constant = 0.3 s, and gain = 6200. Field strength was repeatedly scanned from 2100 to 3100 G at 1 min/scan, and 50 scans were computer-averaged for each measurement. The method of quantitation of ferric metyrapone-bound cytochrome P-450,,, was similar to that used for reduced putidaredoxin. Because the signal from the cytochrome is inherently much weaker than the putidaredoxin signal, a higher recorder gain was required for the cytochrome. Therefore, in experimental samples containing a mixture of the two enzymes, part of the EPR spectrum of the cytochrome which overlaps the putidaredoxin signal was not scanned. Since the amount of ferric metyrapone-bound cytochrome P-450,-was determined by measurement of the peak-to-peak height at g = 2.25 (2900 G), not having the entire spectrum did not present a problem.
The quantitation of an EPR signal by peak-to-peak height measurements, shown to be valid by Aasa and Vanngird (19751, requires that the standards and the experimental samples have the same line shape. There is theoretically a possibility that interactions between putidaredoxin and cytochrome P-450,, in the experimental samples could change their signals from the line shapes seen for each protein separately (see, for example, Peterson and Mock, 197513). However, it was verified for these experiments that no such differences can be detected (data not shown) by scaling standard and experimental signals to the same peak height and overlaying them for direct comparison.

RESULTS AND DISCUSSION
As previously reported (Brewer and Peterson, 19861, the time course of the reaction between oxycytochrome P-450,., and reduced putidaredoxin in the presence of metyrapone consists of two spectrophotometrically observable phases. The first phase, which is quite rapid, includes in sequence the binding of reduced putidaredoxin to oxycytochrome P-45OCam, transfer of an electron from putidaredoxin to the cytochrome, formation and release of 5-exo-hydroxycamphor, and the more rapid irreversible binding of metyrapone to the ferric cytochrome. The second phase is much slower and includes the reversible reduction of ferric metyrapone-bound cytochrome by excess reduced putidaredoxin in the solution. A reaction scheme representing the physiologically relevant first phase of the reaction is shown in Fig. 1. In this scheme, the product formation and release and the metyrapone binding were lumped into one reaction step because they are kinetically indistinguishable. Initially, the electron transfer step was treated as irreversible for the sake of simplicity. The correctness of that treatment will be discussed later. A set of rate equations for the given reaction sequence is shown: d[Al]/dt

[A2]-k-,.[B]-kb.[B];d[C]/dt=kb.[B]-k~.[C];andd[D1]
/dt = kc. [C]. A trial-and-error curve-fitting procedure was used to find sets of rate constants k,, k,, kb, and kc that were consistent with the experimental results previously reported (Brewer and Peterson, 1986) for a range of putidaredoxin concentrations from 4 to 60 p~. Using the computer program MLAB (obtained from the National Institutes of Health and run on a DEC System 10 computer) to perform numerical integrations, we found several sets of rate constants that were consistent with the data.
Fitting Method and Results-A theoretical value of k, was estimated for use as a starting point in the curve-fitting procedure. First, a rate constant of 6 0 0 0 / p~. s was calculated for collisions between the oxycytochrome and tht reduced putidaredoxin using the Stokes radii of 28 and 17 A, respectively (Gunsalus and Wagner, 1978). Then, it was estimated that between 1/80 and 1/3000 of all collisions would occur with the proteins in the correct orientation for productive binding. This estimate is based on the product of the estimated fraction of collisions with the cytochrome in the correct orientation (1/10 to 1/100) times the estimated fraction of collisions with the putidaredoxin in the correct orientation (1/8 to 1/30). These fractions were obtained from an approximate correlation between molecular sizes and fractions of molecular surface areas which must be in contact for appropriate reaction (Hiromi, 1979). Thus, it was predicted that k, would be between 2 and 75/pM. s. Examples of experimentally derived association rate constants for two protein molecules include a constant of 3/pM. s for RNA polymerase u subunit + core enzyme a t 22 "C (Wu et al., 1976) and a constant of 6/ [Al]-p~. s for soybean trypsin inhibitor + trypsin at 21 "C (Luthy et al., 1973). For oxycytochrome P-450,,, and reduced putidaredoxin at 4 "C in 0.50 M KC1, values from 1 to 5/pM -s were used in initial modeling trials.
Three specific features of the experimental absorbance versus time curve were selected as criteria for matching by the computer-generated values: 1) the slope of the initial linear portion, 2) the duration of linearity, and 3) the time of occurrence of the peak absorbance. These three quantities were chosen because they varied systematically with variation in putidaredoxin concentration, they were repeatable at a given putidaredoxin concentration, and they did not involve assuming an initial absorbance value which could not be directly measured because of the instrumental dead time. The time of the beginning of the reaction was known to be 2 ? 1 ms before the stopping-switch-generated zero time. Hence, the times of the specified events can be compared with the theoretical times based on the rate equations. The maximum deviations allowed for an acceptable match of a computed time course with experimental data were +lo% for slope and duration of linearity and +20% for time of the peak absorbance value. Fig. 2 shows an example of a fit which was considered to be acceptable and another which was considered unacceptable by a very small margin. Representative sets of suitable rate constants are given in the legend to Fig. 3; the figure shows both experimental and calculated results. From a doublereciprocal replot of the experimental data were calculated a kcat of 53 p~/ p~. s and a K,,, of 33 WM. The term ''kCat)l as used here refers to the maximum turnover rate of the cytochrome in the partial reaction starting with oxycytochrome and ending with the dissociation of hydroxycamphor from the cytochrome. Its value is a composite of the values of kb and kc in Fig. 1. The K,,, for reduced putidaredoxin represents the concentration at which the turnover rate of the cytochrome is half the maximal value. Its value is a function of all of the This set of parameters was rejected because the calculated initial slope is more than 10% higher than it should be. rate parameters shown in Fig. 1.
Comparison of the Time Course of Electron Transfer with the Time Course of the Overall Reaction-We then narrowed down the possibilities for rate constants by determining whether electron transfer was slower than a subsequent step of the reaction. T o do this, we compared the time course of electron transfer with the time course of appearance of metyrapone-bound cytochrome, i.e. the time course of the overall product-forming reaction.
The general design of this experiment was to freeze-quench reaction samples at several times less than 0.1 s and to measure by EPR the amount of reduced putidaredoxin remaining and the amount of ferric metyrapone-bound cytochrome formed in each sample tube.
If a relatively slow process were occurring after the electron transfer, there would be, at early reaction times, a lag between the electron transfer and the completion of the overall reaction. The sets of possible rate constants obtained from the modeling results were used to aid in choosing enzyme concentrations a t which to perform these experiments. Enzyme concentrations were required which, for any of the possible sets of rate constants, would ensure that the hypothetical lag could be measured if it existed. Thus, concentrations were to be high enough for accurate measurements of their changes but not so high that any lag would occur within the 15-ms dead time of the freezequench method. Concentrations of 28 p~ putidaredoxin and 30 p~ cytochrome were chosen based on computer calculations of the time courses of accumulation of species D2 in Fig.  1 (oxidized putidaredoxin) and of species D l (metyraponebound cytochrome) using several different sets of rate constants, all compatible with the stopped-flow data. With these enzyme concentrations, for any values of k, and k-, that were consistent with the stopped-flow data, there were calculated to be measurably different ratios of D2 to D l at times of 15, 25, 40, and 80 ms, depending only on the relative magnitudes of kb and kc. Fig. 4 shows the computer-calculated time courses for these two species and the resulting ratios for four sets of rate constants which are representative of cases in which 1) kb << kc, 2) kb kc, 3) kb = kc, and 4) kb > kc. The experiment was then performed to allow some of these four cases to be ruled out.
Reactions between 28 p~ reduced putidaredoxin and 30 p~ oxycytochrome P-450,., were freeze-quenched at 15, 26, 40, or 82 ms and packed into EPR tubes. The concentration of camphor was 40 pM, and the metyrapone concentration was 7.4 mM. In each EPR tube, the amount of metyrapone-bound ferric cytochrome and the amount of reduced putidaredoxin were measured as described under "Materials and Methods." The initial amount of reduced putidaredoxin in each experiment was determined by freeze-quenching each putidaredoxin solution mixed with buffer instead of the oxycytochrome just before the freeze-quenching of the actual reaction mixture. The amount of reduced putidaredoxin oxidized was calculated as the difference between the amount measured in the buffermixed sample and the amount measured in the reaction sample. A control experiment was performed to determine how much, if any, metyrapone-bound cytochrome could be detected in a 15-ms mixture of buffer containing metyrapone with the oxycytochrome under the usual reaction conditions, with no putidaredoxin present. The amount of metyraponebound cytochrome present was above the limit of detection but was too small for very accurate quantitation. It was estimated to be approximately 1 pM by comparison with the 4 p~ standard, and this concentration was subtracted from the final concentration found in each reaction mixture to obtain the change due to the reaction. The presence of metyrapone-bound cytochrome in the absence of catalytic turnover ideally would not occur and probably did not occur when the experiments were performed at low concentrations of cytochrome. But, in the experiments at 30 p~ cytochrome, the camphor concentration (40 p M ) presumably was not sufficient to saturate the high concentration of cytochrome. Thus, it is reasonable to suppose that 1 p~ cytochrome may have remained substrate-free and would have bound metyrapone immediately upon being exposed to it. The results of the freeze-quench experiments, performed in triplicate, are shown in Table I. Comparison of these experimental results with the expected results for different relative values of kb and k, (Fig.   4) reveals that the conditions kb > kc and kb = kc are inconsistent with the results. Thus, k b , the rate constant of electron transfer, is at least 2-fold smaller than kc, the rate constant of product formation and release, and is most likely severalfold smaller.
A stopped-flow, spectrophotometric measurement was made at the same concentrations of reduced putidaredoxin and oxycytochrome as were used in the freeze-quench experiments. A wavelength of 555 nm was used for this measurement, which gave a total absorbance change of almost 0.1 with a background absorbance of about 0.5. Wavelengths in the 400-500-nm range were not suitable because of extremely high background absorbances at such high enzyme concentrations. Although the absorbance at 555 nm decreases during the reaction, a conversion factor of -O.o05/pM was used to convert the absorbance change into a positive change in concentration of metyrapone-bound ferric cytochrome P-450,,,. The time course of this change, along with the average values of putidaredoxin change and cytochrome change from the freeze-quench experiments, is presented in Fig. 5. There is good agreement between the spectrophotometric and the EPR results; however, it may be noted that the overall reaction rate shown in Fig. 5 is less than the rate predicted in Fig 4. This is caused by a dependence of the apparent value of one or more rate constants upon the initial concentration of cytochrome P-450,,,. It has been observed at lower concentrations (data not shown) that when the cytochrome concentration is increased, the overall reaction rates are slightly less than expected. Likewise, the rate constants used to generate the curves of Fig. 4 give an excellent match to the data collected at 3.3 p~ cytochrome over a range of putidaredoxin concentrations, but the same sets of rate constants overestimate the overall rate at 30 pM cytochrome.
The initial modeling trials allowed some limits to be placed on the magnitudes of the rate constants. The finding that kb is significantly smaller than k, places additional restrictions on the values that are possible for all of the rate constants because of the interdependence of these parameters in the fitting procedure. The final estimates of the rate constants are as follows: k, is between 3 and 20/pM s; k-, is between 12 and 600/s; kb is between 60 and 1OO/s; and kc is at least 200/ s. The fact that step b in Fig. 1 (the electron transfer step) is followed by a relatively fast and practically irreversible step means that the possibility of the reversibility of step b is no longer important; that is, even if step b is theoretically reversible, the next step will minimize the accumulation of species C (in Fig. 1) and thus prevent any significant rate of back reaction.
Effects of Varying KCZ Concentration-The effect of KC1 concentration upon the reaction was examined by determin-ing the relationship between initial rate and putidaredoxin concentration a t 20 and 100 mM KCl, for comparison to the earlier data at 500 mM KCl. The results of these initial rate measurements are given in Figs. 6 and 7, and again they show a hyperbolic dependence of initial rate on putidaredoxin concentration. Calculated kcat and k,,,/K, values at the three concentrations of KC1 are plotted together in Fig. 8. Fig. 8A shows ln(kcat) plotted against the square root of KC1 concentration. The relationship is not linear but deviates from linearity in a manner which is consistent with the expected deviation of electrostatic effects from Debye-Hiickel theory at ionic strengths from 0.1 to 0.5 M (Barrow, 1979). This suggests that the mechanism of the intramolecular portion of this reaction step, which determines kat, may involve an electrostatic interaction. Since parallel experiments using salts other than KC1 have not yet been done, the possibility of a specific ion effect upon kc,,, as opposed to a general ionic strength effect, has not been ruled out. Fig. 8B shows ln(kJK,,J plotted against the square root of KC1 concentration. These data are indicative of the effects of KC1 upon ko, the rate constant for the association of oxycytochrome P-450,., with reduced putidaredoxin. There is no significant change in k,.,/K, between 20 and 100 mM KC1, but there is a large decrease between 100 and 500 mM. In contrast with these results, an increase might be expected based on the fact that both of these proteins have rather acidic PI values, 4.7 and 3.4 (Dus et al., 1970;Gunsalus and   In each case, camphor concentration was 40 yM and metyrapone concentration was 7.4 mM. The reactions were in standard buffer at 4 "C. The line represents the time course of appearance of ferric metyrapone-bound cytochrome calculated from a stopped-flow experiment at 555 nm. The diamonds represent the average at each time point of EPR measurements of putidaredoxin oxidized in freeze-quench experiments, and the squares represent the averages of EPR measurements of metyrapone-bound ferric cytochrome P-450,,, in the same freeze-quench experiments. Lipscomb, 1973); and therefore, both are negatively charged at p H 7.4. Such an increase in rate constant with increased ionic strength has been seen, for example, in the oxidation of Chromatium vinosum high-potential iron-sulfur protein by ferricyanide (Feinberg and Johnson, 1980). T h e negative charges on both species cause electrostatic repulsion at low ionic strength, but these charges are shielded at high ionic strength, permitting a faster reaction rate.
In the case of reduced putidaredoxin and oxycytochrome P-450,,,, there is apparently no net electrostatic repulsion limiting the rate of association. Indeed, the decrease in k,,,/K,,, at high KC1 concentration might be interpreted as arising from small regions of opposite charges on the surfaces of the two enzymes, which would provide local electrostatic attraction at low, but not high, ionic strength. Alternatively, the decrease might be attributed to either a specific ion effect or an electrostatic effect on the conformation of one or both of the proteins, resulting in a loss of binding efficiency. In any case, the nonlinear relationship seen in Fig. 8B argues against electrostatic shielding as the sole effect of KC1 upon Iz,.
Modeling of the experiments at 20 a n d 100 mM KC1 was performed as described for the experiments at 500 mM. T h e modeling results imply a minimum ka = 1 7 / p~. s for the low and medium salt cases, compared with a minimum of 3/pM. s in high salt. This difference is consistent with the higher values of k,,,/K, in low and medium KCl. The minimum calculated values of kb are 2OO/s at 20 mM KC1 and 140/s at 100 mM KCI, compared with 60,' s a t 500 mM KCl. These values are consistent with the pattern of kc,, variation with KCl. A minimum value of kc = 200/s is estimated for all three salt concentrations. Maximum values of the rate constants could not be found for the low and medium salt cases.

Comparison with Rate Data for the First Electron Transfer
Step in the Cytochrome P-450,,, Cycle-The rate data for the first cytochrome P-450,,, reduction step (Hintz, 1981) have several points of dissimilarity to the rate data obtained for the second electron transfer. First, the time courses of the first reduction reactions were exponential, apparently indicative of first-order kinetics. Second, the effect of KC1 upon kc,, for the second reduction (Fig. 8A) is quite different from its effect upon kobs for the first reduction. In that case, experiments done at a higher range of KC1 concentrations showed no effect upon kobs until the KC1 concentration reached about 0.5 M, above which the ln(kobs) declined linearly with the square root of KC1 concentration. Third, the relationship between concentration of reduced putidaredoxin and rate constant was not hyperbolic in the case of the first reduction, although saturation was reached at about 20-30 p~ putidaredoxin. This saturation behavior permits the identification of a putidaredoxin concentration at which the rate is half-maximal, even though no formal K, can be calculated. For reaction conditions of 10 "C and ionic strength of 0.16 M, a half-maximal reaction rate was achieved a t slightly greater than 1 p~ putidaredoxin. This compares with a K , of about 7 p~ for the second reduction at 4 "C and 0.1 M KCl. Comparing the maximal turnover rates under the same two sets of conditions, the rate of the first reduction at saturating putidaredoxin was about 10-15/s, and the rate of the second reduction at saturating putidaredoxin was about 75-80/s. At 4 "C under optimal conditions, the turnover rate for the entire catalytic cycle is 10-2O/s (Ishimura et al., 1971). The differences between the kinetic characteristics of the first and second reductions support the argument (Peterson and Mock, 1975b) that at high reduced putidaredoxin concentrations, the first reduction may limit the overall turnover rate of the catalytic cycle; whereas at lower reduced putidaredoxin concentrations, with the same concentration of the cytochrome, the second reduction may be no faster than the first. As mentioned by Peterson and Mock (1975b), carbon monoxide inhibition of the overall reaction would not be expected when the first reduction is rate-limiting but should be observed when the second reduction is partially rate-limiting. The maximal rates of the two electron transfer steps (kcat) are significantly different, whereas the ratios of maximal rate to the putidaredoxin concentration at half-maximal rate (kcat/ K,) are not. This suggests that kinetically the most significant difference between the mechanisms of these two steps is probably in the electron transfer process and not in the cytochrome-putidaredoxin binding process.