A kinetic simulation model that describes catalysis and regulation in nitric-oxide synthase.

After initiating NO synthesis a majority of neuronal NO synthase (nNOS) quickly partitions into a ferrous heme-NO complex. This down-regulates activity and increases enzyme K(m,O(2)). To understand this process, we developed a 10-step kinetic model in which the ferric heme-NO enzyme forms as the immediate product of catalysis, and then partitions between NO dissociation versus reduction to a ferrous heme-NO complex. Rate constants used for the model were derived from recent literature or were determined here. Computer simulations of the model precisely described both pre-steady and steady-state features of nNOS catalysis, including NADPH consumption and NO production, buildup of a heme-NO complex, changes between pre-steady and steady-state rates, and the change in enzyme K(m,O(2)) in the presence or absence of NO synthesis. The model also correctly simulated the catalytic features of nNOS mutants W409F and W409Y, which are hyperactive and display less heme-NO complex formation in the steady state. Model simulations showed how the rate of heme reduction influences several features of nNOS catalysis, including populations of NO-bound versus NO-free enzyme in the steady state and the rate of NO synthesis. The simulation predicts that there is an optimum rate of heme reduction that is close to the measured rate in nNOS. Ratio between NADPH consumption and NO synthesis is also predicted to increase with faster heme reduction. Our kinetic model is an accurate and versatile tool for understanding catalytic behavior and will provide new perspectives on NOS regulation.

Three main NOSs are expressed in mammals. Neuronal NOS (nNOS or NOS-1) and endothelial NOS (eNOS or NOS-3) are constitutively expressed and largely participate in signal cascades. Inducible NOS (iNOS or NOS-2) is primarily regulated by transcriptional mechanisms and functions as a regulator and effector of the immune response. The counterpart to this diversity of localization and function is a specific regulation of each isoform. In this regard, nNOS appears unique because it is the only isoform for which a rapid (within seconds) and stable buildup of a ferrous heme-NO complex has been observed (14,15). This differs from that reported for iNOS and eNOS (16 -19), where partial buildup of a ferric heme-NO complex, if it occurs at all, takes minutes. Moreover, ferric heme-NO complex formation in eNOS and iNOS is directly linked to the exogenous NO concentration and can be suppressed by NO scavengers like oxyhemoglobin (18,19), whereas ferrous heme-NO complex formation in nNOS is independent of external NO (15,21).
The kinetics of heme-NO complex formation in nNOS and its effect on steady-state activity has been extensively studied (14,15,22,23). During steady-state catalysis, a majority of nNOS (up to 80%) is present as its ferrous heme-NO complex. Buildup of this complex is linked to a decrease in catalytic activity. Moreover, it induces a significant increase in the apparent K m,O 2 of the enzyme (14), which has important implications regarding function in cells or tissues (24,25). Different mechanisms have been suggested to explain this phenomenon (14,23). However, simulation of these early models (14,15) failed to reproduce precisely the pre-steady and steady-state behavior of nNOS.
Here we describe a kinetic model for nNOS catalysis that is built from rate constants derived from the literature or completed here. The model incorporates our recent finding that a ferric heme-NO complex is generated prior to release of free NO (26). This ferric heme-NO product partitions between two pathways to regenerate ferric enzyme, but only one of these pathways efficiently releases NO. The kinetic model is shown to simulate correctly behaviors of wild-type nNOS or nNOS mutants that display greater activity in the steady state (22,23). The general utility of the model in visualizing the effect of enzyme modifications and in understanding the different catalytic behaviors of the three NOS isoforms is discussed.

EXPERIMENTAL PROCEDURES
Materials-All reagents and materials were obtained from Sigma or sources as previously reported (22,25).
Protein Expression and Purification-Wild-type nNOS protein was expressed in Escherichia coli and purified as described previously (23,27). UV-visible spectra were recorded on a Hitachi U3110 Spectrophotometer in the absence or presence of 20 M H 4 B and 1 mM Arg. Enzyme concentration was quantified using the absorption of the ferrous-CO adduct at 444 nm and an extinction coefficient of 74 mM Ϫ1 cm Ϫ1 (A 444 -A 500 ).
Citrulline Binding Assay-nNOS was incubated in a solution containing 40 mM EPPS, pH 7.6, 300 M DTT, 10% glycerol, and 4 M H 4 B plus different L-citrulline concentrations ranging from 100 M to 166 mM for 10 min at room temperature. Spectra were recorded, and the absorption increase at 420 nM was monitored to follow citrulline binding. Citrulline release was monitored in a stopped-flow instrument equipped with a rapid-scanning diode array detector (HI-Tech MG 6000). Solutions containing 2 M nNOS in 40 mM EPPS, pH 7.6, 300 M DTT, 10% glycerol, 4 M H 4 B, and 100 mM citrulline were rapidly mixed with the same buffer containing 100 mM Arg. Two sets of 10 mixings were run. In each run 96 spectra were recorded within 144 or 288 ms. The decrease in absorption at 417 nm and increase at 387 nm were fit to a mono-exponential curve using software provided by the instrument manufacturer for the first data set. The second set was simultaneously fitted to a mono-exponential curve using the multifit program of Origin 5.0.
nNOS Activity Assays-NADPH oxidation and NO formation at steady-state were measured at room temperature by spectroscopic assays as described previously (15).
Ferrous-Nitrosyl Complex Formation during NO Synthesis-For experiments done without an NADPH-regenerating system, a cuvette containing 1 M nNOS was incubated for 10 min at room temperature in an air-saturated solution containing 40 mM EPPS, pH 7.6, 0.5 mM EDTA, 2 M CaM, 2.5 mM Ca 2ϩ , 400 M DTT, 20 M H 4 B, and 1 mM Arg. NO synthesis was triggered by NADPH addition (40 M final concentration) at 10°C. In the presence of an NADPH-regenerating system (9 units of glucose-6-phosphate dehydrogenase and 1 mM glucose 6-phosphate), NADPH was added prior to the reaction, and NO synthesis was triggered by addition of excess Ca 2ϩ . Spectra were recorded before, during, and after NO synthesis was initiated. The same reactions were also done using a stopped-flow instrument and monitored by a rapidscanning diode array detector. The buffer containing the enzyme was rapidly mixed at 10°C with the same buffer containing the triggering agent (NADPH or Ca 2ϩ ). Absorbance change at 436, 395, and 340 nm were used to follow the formation of ferrous heme-NO complex, the decay of ferric enzyme, and the oxidation of NADPH, respectively. Spectra were recorded in a time scale ranging from 144 ms to 7.22 s. A set of eight representative experiments (with and without the NADPHregenerating system) was simultaneously fitted using the multifit option of Origin 5.0. The buildup of Fe(II) heme-NO complex and the decay of Fe(III) enzyme were fit to a double exponential curve. NADPH oxidation rates were fit to a linear function in both a 0 -500-ms and 2-8-s range.
Model Simulations-The simulation was based on rate equations derived from the kinetic model in Scheme 1. The equations are defined under the "Appendix." See text for details about the rate constants and their dimension. For simulation the rate equations were treated by simultaneous iterative calculation. The iteration step was typically 1 ms and up to 100,000 points were calculated. Percentages of each intermediate were determined at steady state. Initial rates of NADPH oxidation and citrulline production were calculated between 0 and 0.1 s. The same iterative treatment was applied for the abbreviated kinetic model in the inset of Fig. 3.

RESULTS
General Considerations of the Model-We chose the simplified sequence "Fe(III) to Fe(II) to Fe(II)O 2 to Product" to describe heme transitions in both steps or NO synthesis (Arg hydroxylation to NOHA, NOHA oxidation to NO plus citrulline). As recently shown with the nNOS oxygenase domain in single turnover experiments by Boggs et al. (26), the Fe(III) heme-NO complex forms as the first observable product of NOHA oxidation, with subsequent NO release from the enzyme occurring through its dissociation from the heme. A comparable buildup of Fe(II) heme-NO complex has been observed by Abu-Soud et al. (15) within the first second of initiating a multiple turnover reaction in nNOS. In both cases, heme-NO complex buildup is not linked to enzyme binding solution NO because there is no effect of added NO scavengers. It also differs from NO inhibition as originally described by Ignarro and colleagues (20), which occurs in nNOS only after a high number of catalytic turnovers (15 min at 37°C) and at high concentrations of exogenous NO (complete inhibition required 100 M of NO). Rather, heme-NO complex formation during the initial phase of NO synthesis is probably linked to a geminate-type combination of Fe(III) heme and NO generated in the active site. This process was proposed by Kominami et al. (28), who found through EPR experiments that NO rebinds quickly to nNOS after photo-dissociation from the ferric heme even at 5 K. A complete study of NO geminate recombination in eNOS has been achieved by Negrerie et al. (29); geminate rebinding of NO to heme after photo-dissociation consists in fact of both picosecond and nanosecond phases. This phenomenon was also described by Scheele and colleagues (30) through photo-dissociation experiments with nNOS. Their kinetic characterization showed a low dissociation efficiency of NO after photolysis, suggesting its escape from the heme pocket is relatively slow compared with direct rebinding (30). The k on derived from their experiments (1.2 ϫ 10 7 M Ϫ1 s Ϫ1 at 23°C) is close to the values observed by Abu-Soud et al. (31) and Huang et al. (32) when iNOS or nNOS was mixed with NO in a stopped-flow instrument (k on around 10 6 M Ϫ1 s Ϫ1 at 10°C). These values are consistent with a slow step being NO entry into the heme pocket and a subsequent very fast binding (30). This was confirmed by the absence of effects on rates of NO binding to ferric or ferrous NOS by bound substrate or H 4 B, as is also the case with O 2 binding (27). Although it has not been directly observed, most current mechanisms for NO synthesis predict that the NOS heme will end up in a low spin, six-coordinate aqua form immediately after generating NO from NOHA. Thus, NO binding has to occur after water dissociation. During the single turnover stopped-flow experiments of Boggs et al. (26), this water-bound intermediate is not seen. Instead, there is a quantitative buildup of the ferric-NO complex. Therefore, it appears that the speed of water release and NO binding is such that essentially all of the NO molecules bind before they leave the heme pocket. Thus, a nearly instantaneous and quantitative binding of NO probably occurs in all NOS to generate a Fe(III) heme-NO complex as the first observable product.
After forming the ferric heme-NO complex, NO can be re-SCHEME 1. Kinetic model of nNOS catalysis. Catalysis is approximated by 10 steps. Each number refers to rate constants displayed in Table I. Single arrows indicate that each step was assumed to be irreversible. The values of rate constants for wild-type or mutant nNOS are detailed in the legends of Tables I and II. See text for details. leased at a relatively high dissociation rate (the k off for NO from ferric nNOS varies between 3 and 5 s Ϫ1 depending on the reports) (22,26,30). This represents a "productive" pathway to release NO and regenerate ferric enzyme for a second catalytic cycle. Nevertheless, during the steady-state nNOS exists mainly as a ferrous heme-NO complex (14,15). This was confirmed recently by Adak et al. (22) and by experiments we will report here. This implies that reduction of the heme-NO complex occurs, which is likely because the rate of ferric heme reduction in nNOS (3-4 s Ϫ1 at 10°C) is within the same range as NO dissociation from the ferric heme. In contrast, NO dissociation from the ferrous heme-NO complex is quite slow (29,30), and ferric enzyme is mainly regenerated by direct reaction with O 2 (14). However, because NO is not released in this reaction (the product is nitrate), the ferrous heme-NO species represents an intermediate in a "futile" pathway that regenerates ferric enzyme for the next catalytic cycle. Thus, NO binding to the ferric heme results in a circumstance where the enzyme can partition between NO dissociation versus reduction of the heme-NO complex.
This concept allows us to propose a simplified kinetic model for nNOS catalysis (Scheme 1). Our model contains 10 steps and is characterized by a forward pathway that leads to the production of citrulline and NO (steps 1-6) and two regenerating pathways as follows: the first involves direct release of NO from ferric heme (step F), and the second involves reduction of the ferric heme-NO complex (step G) followed either by a slow NO release (step 10) or oxidation of the ferrous heme-NO complex (step 9). Our purpose was to simulate both the initial and steady-state behaviors of nNOS and to understand how NO regulates enzyme activity and oxygen response. We did not try to model precisely the forward pathway and assumed some simplifications concerning this sequence. The validity of these simplifications will be judged on the ability of the model to reproduce the principal parameters and particularly NADPH oxidation, NO synthesis, and oxygen response. Considering the concentration of oxygen and NO, oxygen binding and NO release steps are assumed to be irreversible in the model, and we considered only forward rate constants. The constants we used to build this model were all determined at 10°C and were obtained from the literature or determined here when necessary.
Substrate Binding and Citrulline Release-At the Arg concentrations typically used in our experiments, the association rate is sufficiently high to neglect Arg binding in the kinetic analysis (apparent binding rate constant around 300 s Ϫ1 considering a k on between 2 and 8 ϫ 10 5 M Ϫ1 s Ϫ1 (33,34)). The Arg k off is also slow enough to assume that no substrate molecule is likely to leave the binding site once it is bound (k off ϭ between 0.8 and 1.6 s Ϫ1 (33)(34)(35)). Similar arguments can be made for NOHA after it forms in the active site (34,35). However, release of citrulline could affect the overall kinetics if it is slow relative to k cat . The only published value for citrulline k off was indirectly derived from single turnover and steady-state data (36) and led to an estimate of 0.32 s Ϫ1 , which would be ratelimiting. To check the reliability of this value, we studied citrulline binding by equilibrium and stopped-flow methods. Based on the changes observed in the UV and resonance Raman spectra for citrulline (37,39) or thiocitrulline binding (34,38,39), we followed citrulline binding to nNOS as a shift in Soret absorbance from 393 to 417 nm (Fig. 1A). The K d derived from the equilibrium titration is 7 Ϯ 2.5 mM. We then measured the rate of citrulline release in a stopped-flow chase experiment using excess Arg. An nNOS sample containing 100 mM citrulline was rapidly mixed with a solution containing 100 mM Arg, and 96 spectra were recorded during the first 144 or 288 ms. As shown in Fig. 1B, there was a progressive decrease in absorption at 417 and an increase at 393, which reflects dissociation of the ferric-citrulline complex and buildup of the ferric-Arg complex. The kinetics of spectral change at 387 and 417 nm are displayed in Fig. 1C. The traces fit well to single exponential curves and give an apparent off rate of 17 Ϯ 2 s Ϫ1 . At the Arg concentration used in this experiment the binding rate of Arg is maximum. Therefore, we can assume that the k off of citrulline is no slower than 17 Ϯ 2 s Ϫ1 . By using our experimentally determined k off and K d values, the citrulline k on is calculated to be 2 ϫ 10 3 M Ϫ1 s Ϫ1 , which is significantly slower than the Arg k on . Thus, citrulline in the range of concentrations typically generated during NOS activity assays (0 -20 M) will not compete with Arg binding. This is confirmed by Frey et al. (38), Rogers and Ignarro (20), and Sennequier and Stuehr (39), who did not see a change in steady-state activity with added citrulline up to concentrations of 1 mM. We conclude that binding and release of amino acid substrates or products will not impact the kinetic characteristics of nNOS catalysis under our experimental conditions.
Flavin and Heme Reduction-The rate of flavin reduction in CaM-bound nNOS is relatively high (bimolecular reduction constants ranged from 0.3 to 2 ϫ 10 6 M Ϫ1 s Ϫ1 according to Gachhui et al. (40) and Abu-Soud et al. (41)) and leads to apparent monomolecular constants higher than 70 s Ϫ1 in the range of NADPH concentrations that we used. Thus, we assume that flavin reduction is sufficiently fast to neglect this step, and we only consider the rate of electron transfer between the reductase domain and oxygenase domain heme, which is a monomolecular process. Because flavin reduction is fast, the rate of heme reduction under aerobic conditions can be inferred from the initial rate of NADPH consumption. We obtain then a pseudo-first order rate constant independent of the NADPH concentration that characterizes heme reduction. We checked this hypothesis with stopped-flow experiments in which nNOS catalysis was triggered by NADPH addition to CaM-bound enzyme or by adding excess Ca 2ϩ to an NADPH-reduced enzyme. NADPH consumption was followed as a decrease in absorption at 340 nm. The initial slope was ϳ2.4 s Ϫ1 in the NADPH-triggered reaction (Fig. 2, Table I). In experiments where the initial rate of heme reduction was followed at 395 nm after initiating by Ca 2ϩ addition, absorption loss followed a double exponential decay, with a slow phase characterized by a rate constant of about 2 s Ϫ1 . This value, which represents heme reduction (and is the rate-limiting step of the process, as seen later), coincides well with the initial rate of NADPH consumption. Moreover, both values are close to rates obtained for nNOS heme reduction by Adak et al.  (40)) through anaerobic experiments at similar temperature. This validates our simplification and allows us to derive the rate of heme reduction from the initial NADPH oxidation rate, whose signal remains largely unaffected by changes in heme or flavin absorption. Similar results were obtained in experiments with NOHA (data not shown), where the initial slope of NADPH consumption gave a pseudo-first order rate constant of 2.5 s Ϫ1 . Thus, we assume in our model that the heme reduction rate is the same for enzyme containing Arg or NOHA. In addition, based on our unpublished results 2 (data not shown), we assumed that reduction of the ferric heme proceeds at the same rate whether NO is bound or not.
O 2 Binding to Heme-The O 2 concentration in our experiments is relatively high (ϳ150 M in half-air-saturated solution at 10°C), and little O 2 is consumed during the rate measurement. Thus, we assumed a constant oxygen concentration and binding rate in the model. We used a pseudo-first order rate based on results obtained by Boggs and colleagues (26) at the same oxygen concentration and temperature. Their pseudofirst order binding rate (pseudo-k on ) varies between 8 and 10 ϫ 10 5 M Ϫ1 s Ϫ1 , consistent with more extensive O 2 binding studies by Abu Soud et al. (27) who for nNOS determined a k on for O 2 of 9 ϫ 10 5 M Ϫ1 s Ϫ1 . The high association rate and similarity between these estimates validates our considering O 2 binding as an irreversible step in the model. We neglected superoxide or H 2 O 2 release due to autooxidation of Fe(II)-O 2 . No direct kinetic data are available concerning the release of superoxide in the presence of Arg and H 4 B, the only rates reported concern conversion of the Fe(II)-O 2 species to ferric enzyme (27,43,44), which may involve reduction of the complex by H 4 B. Moreover, Arg seems to suppress completely superoxide generation (45)(46)(47)(48). In the same manner, H 2 O 2 formation (direct release from the heme or through superoxide dismutation) is typically absent in assays run in presence of Arg and H 4 B (49). Catalytic Step-We assumed that both steps of the reaction (conversion of Arg to NOHA and then NOHA to citrulline) could be approximated by the same rate constants. This assertion is supported by the results of Iwanaga et al. (36) who found similar rate constants for the Arg to NOHA and NOHA to citrulline transitions in nNOS (7 and 6 s Ϫ1 , respectively). Although this simplification may modify the overall rate of catalysis in our model, it will not affect the characteristics that are linked to heme-NO binding. Boggs and colleagues (26) have studied the NOHA to citrulline catalytic step in a single turnover at 10°C starting with pre-reduced ferrous nNOS oxygenase domain. The transformation rate of Fe(II)-O 2 into Fe(III)-NO product was 26 s Ϫ1 . Few other reports are available. Iganawa et al. (36) found global forward constants between 6 and 7 s Ϫ1 for nNOS, but this rate included heme reduction. However, the weighted reciprocal mean of the three constants we used for describing the same phenomenon is 7 s Ϫ1 , which coincides with their value.
NO Release from Heme or Oxidation of the Fe(II) Heme-NO Complex-We used a rate constant for NO dissociation from ferrous nNOS of 1 ϫ 10 Ϫ4 s Ϫ1 based on the measurements of Scheele et al. (30). For O 2 reaction with the Fe(II) heme-NO complex we used a pseudo-first order rate constant (0.19 s Ϫ1 ) that was reported by Adak et al. (22) at a single O 2 concentration (half-air-saturated) at 10°C. NO dissociation from ferric nNOS corresponds to rate of 5 s Ϫ1 in our model (22,26,30). Thus, the Fe(III) heme-NO complex can be reduced or have NO dissociate at similar rates, which allows near equivalent partitioning of this species between the two recycling pathways in Scheme 1. In contrast, NO dissociation from the Fe(II) heme-NO complex or its reaction with O 2 is comparatively slow, which explains why the Fe(II) heme-NO complex accumulates during the steady state.
Mathematic Simulation of the Kinetic Model-We used a simultaneous iterative calculation based on rate equations derived from the kinetic model in Scheme 1. Rate equations are described under the "Appendix." These calculations were achieved using Mathcad 7.0 software. A single catalytic turnover takes about 1 s for nNOS at 10°C. Thus, for the calculations we chose a time step of 1 ms, which should be small enough given that the fastest step in the process (O 2 binding) is around 100 s Ϫ1 . Indeed, no changes were seen if we shortened the time step for analysis to 0.1 ms (data not shown). As described below, this model can simulate the concentrations of all the heme intermediates depicted in Scheme 1, the rates of NADPH consumption and citrulline, NO, or nitrate production at pre-steady state and steady state, the various ratios of these rates, and how all these parameters change as a function of time, O 2 concentration, or rate of heme reduction. NADPH consumption rates were derived from the slope between 0 and 500 ms (burst phase) and then between 10 and 50 s (steadystate phase). The latter time scale was used to determine the steady-state formation rate of citrulline and NO.
Comparing Experimental and Simulated Behavior of nNOS-We first confirmed the basic behavior of nNOS regarding its partitioning during steady-state NO synthesis. In Fig.  2A, NO synthesis was triggered by adding excess Ca 2ϩ to NADPH-reduced nNOS in the presence of CaM and an NADPH-regenerating system. As previously reported (14,22), the reaction at steady state was characterized by an absorbance increase at 436 nm and an absorbance decrease at 395 nm, due to the presence of the Fe(II) heme-NO species and a loss of the ferric species. The relative proportion of these two species was calculated based on standard spectra of ferric, ferrous, ferrous heme-NO, and ferric heme-NO nNOS as published by Wang et al. (50,51) and Abu-Soud et al. (14). This led us to redefine our estimated extinction coefficient for the ferrous heme-NO complex to 60 mM Ϫ1 s Ϫ1 at 436 nm. In our experiment the percentage of Fe(III) enzyme that remained during steady state was ϳ28%, and the percentage of ferrous heme-NO species present was about 72% (Table I). This falls within estimates reported in literature (14,15,22), which range between 67 and 85% ferrous heme-NO complex.
We also confirmed nNOS behavior during the initial phase of NO synthesis using rapid-scanning stopped-flow spectroscopy. Here, the reaction was triggered with NADPH and did not include an NADPH-regenerating system so we could follow consumption of NADPH. As shown in Fig. 2B, there was a time-dependent absorbance increase at 436 nm and decrease at 395 nm to levels that were similar to those in Fig. 2A and to results reported previously (14,15,22). We also observed an inflection in the NADPH oxidation rate that corresponded to buildup of the 436 nm species (Fig. 2C). The first rate of NADPH consumption was derived from the slope between 0 and 0.5 s, and the second rate of NADPH consumption was calculated between 4 and 14 s. A multifit of eight similar experiments gave an NADPH oxidation rate of 2.4/s for the first phase and 0.48/s for the second phase, i.e. a ratio of 5. This is in the same range of values reported by Adak et al. (22) (Table I). We also determined the rate constants of Fe(II) heme-NO formation and loss of Fe(III) enzyme through a multifit of traces from several similar experiments. For Fe(II) heme-NO buildup, the curves best fit to a double exponential equation, giving rate constants that vary from 15 to 10 s Ϫ1 for the fast phase and from 2.5 to 0.9 s Ϫ1 for the slow phase. Again, this is close to values obtained for nNOS by Adak et al. (22) and Abu-Soud et al. (14,15) (Table I). For loss of Fe(III) enzyme, the traces also follow a double exponential decay, with rate constants of 12 s Ϫ1 for the fast phase and from 2 to 0.8 s Ϫ1 for the slow phase. This confirms that loss of the ferric species is kinetically coupled to heme-NO complex formation after NO synthesis is started.
We next simulated the NO synthesis reaction according to our kinetic model in Scheme 1, using kinetic values and concentration of enzyme, O 2 , Arg, and NADPH derived for wildtype nNOS as discussed above. Traces in Fig. 2, D and E, show that the simulation faithfully reproduces the behavior of nNOS. Within the correct time period after catalysis is initiated, the Fe(II) heme-NO species builds up to represent 67% of the total enzyme, whereas the Fe(III) species decreases to 25% of total enzyme. The remaining 8% of nNOS mainly distributes between two other enzyme species (Fe(II)-O 2 and Fe(III) heme-NO; data not shown). The simulation also gives NADPH consumption rates of 2.35 and 0.55 turnovers/s in the initial and steady-state phases of NO synthesis, respectively. Thus, the simulated change in NADPH oxidation rate occurs within the correct time frame, corresponds to buildup of the Fe(II) heme-NO species, and is of a magnitude (5-fold decrease) that is very close to our experimental value. As shown in Fig. 2E, the simulation also predicts a deflection in the rate of citrulline accumulation and has NO release delayed until heme-NO complex buildup nears completion.
The simulated rate of Fe(III) loss is biphasic with rate constants of 22.8 and 0.61 s Ϫ1 which approximates our experimental values. However, simulated buildup of the Fe(II) heme-NO species best fit to a mono-exponential equation with a rate constant corresponding to the slower rate component that was experimentally observed (Table I). Thus, our model does not predict the fast phase of Fe(II) heme-NO buildup. One explanation may be that absorption at 436 does not characterize only the buildup of Fe(II)-NO but can also reflect absorption changes linked to Fe(III) heme-NO that forms prior to the Fe(II) heme-NO species (26) and could contribute to the fast phase. The purpose of our model was not to reproduce precisely the kinetics within the first 50 ms. Indeed, the simplification of the forward pathway and the limitation of the mathematical simulation forbid it. But the resolution of this ultra-rapid phase is of no use, and our model faithfully reproduces changes that occur within the 1st s.
The simulation also predicts an NADPH per citrulline ratio of 1.67, which is greater than the theoretical minimum value (1.5 NADPH oxidized per citrulline formed) (7, 8, 11) but actually matches several experimental values (53,54). It also predicts that nNOS will release somewhat less NO than citrulline during the steady state. Both of these effects derive from a portion of the Fe(III) heme-NO species being reduced to the corresponding ferrous species, which wastes an NADPH-derived electron because it leads the enzyme to generate citrulline without releasing free NO (see Scheme 1). Thus, our model gives insight into the functioning and efficiency of catalysis.
Partitioning of nNOS between productive and futile regenerating cycles is a key aspect of our model. The relative enzyme flux through the two different paths can be appreciated through different ratios. For example, the ratio of nitrate versus citrulline reflects the flux of nNOS through the futile cycle. The simulation gives a ratio of 0.34, which means about a third of the enzyme cycles through this futile pathway in unit time. The ratio of NADPH-oxidized versus NO-formed depends also on the partitioning between both regenerating pathways. The simulation gives a ratio of 2.54, which is a bit high but close to several reported values (from 1.7 to 2.2, see Table I). Because this ratio is quite sensitive to the heme reduction rate, slight changes can modify it drastically and make it difficult to obtain a perfect fit between experimental and simulated substrate/ product ratios.
The Effect of NO Synthesis on nNOS Apparent K m,O 2 -One remarkable characteristic of nNOS is that NO synthesis greatly increases its apparent K m,O 2 . A K m,O 2 of 350 M was obtained when nNOS was synthesizing NO, whereas a value of about 38 M was obtained when nNOS oxidized NADPH in the absence of substrate (15). This shift cannot be derived from a direct competition between NO and O 2 , because it would require NO concentrations (20 -40 M) that are out of reach for steady-state experiments. In fact, this behavior appears to involve formation of the Fe(II) heme-NO complex, which influences the apparent K m,O 2 through its O 2 -dependent oxidation reaction (see Scheme 1). Thus, we tested if our kinetic model could simulate how catalysis in the presence and absence of NO synthesis affects enzyme K m,O 2 . We simplified our model into a substrate-free one, where one-electron reduction of the heme leads only to superoxide generation (Fig. 3, inset) (48). The numerical treatment was achieved by the same iterative method discussed above (see "Appendix"). The rate constants used here were the same as noted above except for the release of superoxide. We used the values of Boggs et al. (26) who reported a general k cat of 20 s Ϫ1 for ferrous nNOS in the absence of substrate. For O 2 -dependent decay of the Fe(II) heme-NO complex, we varied the single rate constant obtained for this reaction (see above) in direct proportion to the simulated O 2 concentration. We then calculated the rate of catalysis (NADPH oxidation) as a function of O 2 concentration in the presence or absence of substrate (Fig. 3). The K m,O 2 obtained in the absence of substrate (no NO synthesis) was 2.5 M. Although this is somewhat lower than our experimentally determined value (14), it is close to values generally reported for O 2 -binding heme proteins and primarily reflects ferrous heme affinity for O 2 (50). In the presence of substrate (and NO synthesis) the K m,O 2 was 271 M, which is close to the measured value of Abu-Soud et al. (15). Thus, our model can accurately simulate how NO synthesis shifts the K m,O 2 of nNOS.
Simulating Behavior of Hyperactive nNOS Mutants-We next tested if our kinetic model could simulate the initial and steady-state behavior of nNOS W409F and W409Y mutants, which have been characterized by Adak et al. (22,23). These mutants have lower levels of Fe(II) heme-NO complex buildup in the steady-state, a negligible deflection between their initial and steady-state rates of NADPH oxidation, and an increased rate of NO synthesis during the steady state as compared with wild-type nNOS. Only two kinetic steps appear to be changed in the mutants (22,23). Their rates of heme reduction are 2-3 times slower compared with wild type, and their rates of Fe(II) heme-NO complex oxidation are 7-8 times faster.
We performed two different simulations based on W409F mutation. In the first we increased the rate of Fe(II) heme-NO oxidation and left the heme reduction rate constant (Fig. 4A and Table II), whereas in the second we both increased Fe(II) heme-NO oxidation and slowed the heme reduction rate (Fig.  4B and Table II). In both cases, we obtain a smaller percentage of Fe(II) heme-NO complex during steady state (21.5 and 9.5%) compared with wild-type nNOS. These reduced levels are close to percentages directly estimated from experiments (25% for W409F and 14% W409Y; Ref. 23). Moreover, the simulation correctly predicts that only a small change occurs between the initial and steady-state rates of NADPH consumption in W409F and W409Y, and their steady-state rates are predicted to be faster than wild type (1.3 and 0.9 turnover/s for the mutants compared with 0.55 for wild type). These simulated rates of NADPH turnover are almost identical to those measured for W409F and W409Y at 10°C (1.4 and 0.8 turnover/s, Ref. 22).
Other parameters derived from the simulation match those determined experimentally (see Table II for general comparison). In particular, the model correctly simulates a slower buildup of the Fe(II) heme-NO complex in the mutants (23). The ratio of NADPH oxidized versus NO produced is also predicted to be smaller for the Trp-409 mutants than for wild type, as confirmed experimentally by Adak et al. (23). The slight overestimation of this parameter in the simulation highlights the sensitivity of the outcome toward modifications in heme reduction rate. In general, slowing heme reduction favors enzyme partitioning toward the active cycle (NO dissociation from the Fe(III) heme-NO complex) and disfavors partitioning toward the futile cycle (reduction to form the Fe(II) heme-NO complex) (see Scheme 1). We also simulated catalysis at different O 2 concentrations to derive K m,O 2 values for the W409F mutant. The simulations were run as described for wild type except we included appropriate heme reduction and Fe(II) heme-NO oxidation rates as noted above. We obtained K m,O 2 values of 41 Ϯ 1 and 16 Ϯ 1 M for W409F depending on whether one or both parameters were modified (data not shown). These values clearly differ from the wild-type K m,O 2 (271 M) but actually match the values determined experimentally for Trp-409 mutants by Adak et al. (K m,O 2 around 40 M). 3 Together, this highlights how our model can correctly simulate complex effects of a mutation on both pre-steady-state and steady-state catalysis.
Influence of Heme Reduction Rate-Our kinetic model can also predict how graded changes in any kinetic parameter will affect nNOS catalysis. To examine the influence of heme reduction rate, we ran simulations at heme reduction rates that 3 S. Adak and D. J. Stuehr, manuscript in preparation. Values were calculated respectively from the kinetic models depicted in Scheme 1 or the inset. The simulation process is described under "Experimental Procedures" and "Appendix." The curves were fit using a single binding site equation with Origin© software. Inset, kinetic scheme used to simulate nNOS catalysis in the absence of substrate. Single arrows indicate assumption that each step is irreversible. Bold numbers refer to rate constants listed in Table I. See text for details.

FIG. 4. Simulated pre-and steady-state behavior of the nNOS W409F mutant.
Both panels show simulated concentration changes as a function of time for the Fe(III) nNOS, Fe(II) heme-NO complex, and NADPH after initiating NO synthesis at 10°C. These were calculated using the kinetic model in Scheme 1 and the reaction conditions for wild-type nNOS in Fig. 2. A, results using one different rate constant compared with wild-type nNOS (a faster Fe(II) heme-NO oxidation rate of 9 ϫ 10 3 M Ϫ1 s Ϫ1 ). B, results incorporating two different rate constants (the faster Fe(II) heme-NO oxidation rate and a slower heme reduction rate of 1.2 s Ϫ1 ). The buildup of Fe(II) heme-NO complex and decay of Fe(III) nNOS were fit to single-or two-exponential equations as described under "Experimental Procedures." ranged from 0 to 10 s Ϫ1 . Fig. 5A shows how the distribution of three nNOS species varies in the steady state as a function of heme reduction rate. At rates below 1 s Ϫ1 , most of the enzyme is present in its Fe(III) form. However, as heme reduction gets faster, the proportion of Fe(III) species goes down and there is a concomitant gain in Fe(II) heme-NO species, which predominates at rates above 2 s Ϫ1 . Clearly, the relative proportion of these species is quite sensitive to the heme reduction rate. In contrast, the simulation predicts that the Fe(II)-O 2 species builds up to a relatively minor but stable level. In general, the steady-state concentrations of Fe(III) and Fe(II) heme-NO species as predicted by the model match experimental data obtained for nNOS (this report and Ref. 15). Fig. 5B predicts that a surprising relationship exists between heme reduction rate and steady-state catalysis. Regardless of how nNOS activity is measured (rates of NADPH oxidation, citrulline, or NO synthesis) the simulation shows that there is an optimum rate of heme reduction beyond which activity falls. Although this seems counterintuitive, it makes sense when one considers that faster rates of heme reduction favor greater reduction of the Fe(III) heme-NO product complex, and thus favor cycling of enzyme through the futile pathway (see Scheme 1). This eventually decreases the rate of NO release in the steady state. On the other hand, for slower rates of heme reduction, product formation (the Fe(III) heme-NO complex) becomes the rate-limiting step and can result in a decreased rate of NO synthesis. It appears that the system can set the rate of heme reduction to optimally counterbalance these two effects.
To ensure the robustness of our model, we checked if this surprising and unexpected regulation feature is not linked to particular values of the kinetic parameters. Three main parameters qualitatively and quantitatively control the outcome of the simulation as follows: (i) the heme reduction rate, which influences the biosynthetic pathway and enzyme partitioning between the two regenerating cycles; (ii) the dissociation rate of Fe(III)-NO, which influences enzyme partitioning and controls the rate of the productive regenerating cycle; (iii) the rate of Fe(II)-NO oxidation, which controls the rate of the futile regenerating cycle. As can be seen in Fig. 5B, a variation of 4-fold in the simulated rate of heme reduction (between 1 and 4 s Ϫ1 ; experimental values ranged between 2.4 and 3.6 s Ϫ1 ) only moderately alters the simulated NO synthesis rate (0.225 s Ϫ1 Ϯ 20%). The same variation alters rates of citrulline production and NADPH consumption by 10 and 8%, respectively. We also ran simulations for extreme changes in parameters ii and iii noted above (Fig. 5C). We chose rates of Fe(III)-NO dissociation of 1 and 10 s Ϫ1 (experimental values range between 3.5 and 5 s Ϫ1 ). The optimum rate for heme reduction in this case shifts between 1 and 3 s Ϫ1 , along with an obvious increase in the rate of NO synthesis (4-fold versus a 10-fold change in Fe(III)-NO dissociation rate). When we varied the simulated rate of Fe(II)-NO oxidation between 0.05 and 1 s Ϫ1 (experimental value is  0.19 s Ϫ1 ), the optimum rate for heme reduction shifts between 0.8 to 2 s Ϫ1 , and the NO synthesis activity is multiplied by 2 (for a 20-fold increase of Fe(II)-NO oxidation rate). Clearly, extreme changes of these essential parameters (up to 20-fold) do not alter drastically the results of the simulation. In all cases, NO synthesis versus heme reduction rate is described by a bell-shaped curve with an optimum between 1 and 3 s Ϫ1 . Although such changes also altered the predicted rate of NO synthesis, it is encouraging to note that the experimental rate values we used for i-iii above in our simulation actually predict a steady-state rate of NO synthesis that is quite close to the experimentally observed value. Therefore our kinetic model appears robust and is not overly sensitive to inaccuracies in any particular rate measurement. Fig. 5D simulates how the rate of heme reduction influences catalytic efficiency in nNOS. The NADPH/NO ratio climbs continuously from an initial value of 1.5 as the heme reduction rate increases. NO release becomes less probable as the heme reduction rate increases because a greater percentage of the Fe(III) heme-NO complex is channeled into the futile cycle (see Scheme 1). Because of this lowering in catalytic efficiency, citrulline and NO release become increasingly uncoupled from NADPH consumption as the heme reduction rate increases. The uncoupling profile is less accentuated for citrulline because citrulline is made when enzyme partitions into either the active or futile cycle, whereas NO is only released by enzyme molecules that partition into the active cycle. Because the futile cycle generates nitrate instead of NO, the nitrate/citrulline ratio also increases with the heme reduction rate (Fig. 5D). This ratio has a maximum value of 1, and the simulation suggests that a significant percentage of total enzyme will cycle through the futile cycle at high heme reduction rates. DISCUSSION We developed a kinetic model to understand the unique behavior of nNOS. This involves a fast buildup of ferrous-NO complex includes about 80% of the steady-state population, with an associated change between initial and steady-state activities. In the past we proposed models for nNOS partitioning which typically invoked direct competition between NO and O 2 binding to ferrous heme (15). Nevertheless, none of the earlier models when simulated were able to mimic closely the behavior of nNOS, and the competition binding concept eventually did not fit well with relative rates of heme reduction and ligand binding that were determined later. Our current model integrates the latest results in the literature, particularly the concept of fast recombination between ferric heme and NO formed in the active site (26,30). Simulations of our kinetic model closely mimic all catalytic features of wild-type or mutant nNOS, including their initial and steady-state behaviors, populations of heme species, and apparent K m,O 2 values. Together, this strongly argues that the fundamental features of our current model are correct.
In our model catalytic turnover is regulated by the following two distinct features: 1) partitioning of an immediate Fe(III) heme-NO product between a futile and productive regenerating pathway, and 2) the relative rate of the futile regenerating pathway. These two features share no common influences and thus operate completely independent of one another. Partitioning simply reflects the relative rates of NO dissociation versus reduction of the immediate Fe(III) heme-NO product. Because these are fundamental characteristics of the enzyme, they are immune to the external environment when the enzyme operates under V max conditions (i.e. sufficient NADPH, Arg, etc.). However, because they oppose each other, small changes in these two rates can have a relatively large effect on enzyme partitioning. For our model we assumed that reduction of the Fe(III) heme-NO complex was identical to reduction of the ferric enzyme, whose extent and rate is known (40,41). Because NO binding to hemeproteins typically raises their midpoint potential (55), the assumption is probably valid at least from a thermodynamic standpoint. The accuracy of our model in simulating several aspects of nNOS catalytic behavior also supports the assumption. Nevertheless, a direct measure of this rate may enable finer refinement. In contrast to the partitioning step, the rate of the futile regenerating cycle is clearly influenced by factors that are both extrinsic and intrinsic to the enzyme. For example, the rate of Fe(II) heme-NO oxidation is directly related to the O 2 concentration, and enzyme mutations at residue Trp-409 greatly increase the rate at any given O 2 concentration. Given the multiple opportunities for "fine-tuning" both intrinsic and extrinsic parameters, our kinetic model should be useful to guide and interpret further investigation of catalysis and regulation.
One imagines that intrinsic parameters of nNOS have been set for its proper physiologic function. This may be illustrated by its measured rate of heme reduction corresponding to the activity optimum predicted in our model (see Fig. 5B). Intrinsic parameters can also govern the relative impact of extrinsic factors such as O 2 concentration. This is illustrated by the high apparent K m,O 2 that is unique to nNOS (14,56). Our model reveals that a relatively fast heme reduction, coupled with a relatively slow cycling through the futile pathway, creates this special regulation in nNOS. Functionally, this allows the enzyme to minimize its catalytic sensitivity to O 2 concentration changes, while generating NO in a near-linear manner as a function of O 2 concentration. Why this evolved is still unclear (14). However, it must be physiologically important, because our model clearly shows that the enzyme sacrifices catalytic efficiency to create this response.
For iNOS (17,18,57), eNOS (16,19), and nNOS (16,20), a loss of activity occurs if heme binds NO that accumulates in solution. However, this occurs only when relatively high NO concentrations are achieved, can be prevented by NO scavenging, and involves trapping the heme in a ferric NO complex. It is important to stress that this phenomenon corresponds to a simple equilibrium between ferric heme and free NO and is therefore quite different from the kind of regulation described in this report. This phenomenon occurs quite late during NO synthesis (15 min at 37°C) and therefore was not taken into account by our model that focused on initial and steady-state phases.
Negrerie and colleagues (29), who thoroughly studied the NO recombination process in eNOS, suggested on the basis of results by Abu-Soud et al. (14) that the Fe(II) heme-NO species may form via reduction of the Fe(III) heme-NO species. However, the Fe(II) heme-NO species is not observed during steadystate catalysis in eNOS or iNOS. At this point, our model can provide an explanation for this difference. eNOS is distinguished by a low steady-state activity, a slow heme reduction, and an undetectable level of Fe(II) heme-NO species (19). Its low catalytic activity is therefore not linked to eNOS cycling through the futile regenerating pathway. In fact, according to our simulations, the slow heme reduction rate in eNOS (19,58,59) is sufficient to explain its low proportion of Fe(II) heme-NO species during the steady state (Fig. 5A) and its overall lower activity (Fig. 5B). This suggests that eNOS follows the same kinetic model as nNOS, but the slower heme reduction minimizes partitioning into the futile regenerating cycle and diminishes the global speed of catalysis. In iNOS, one observes a similar catalytic activity and a slightly slower heme reduction rate compared with nNOS (19, 60) but little or no Fe(II) heme-NO complex formation in the steady state. 4 This phenotype is similar to what is seen for the Trp-409 nNOS mutants. Indeed, our preliminary data suggest that iNOS exhibits accelerated Fe(II) heme-NO oxidation, 5 as occurs in the Trp-409 nNOS mutants (23), and this can account for such results. Thus, although several kinetic parameters remain to be determined for iNOS and eNOS, our kinetic model seems capable of simulating their behavior as well.
So far, the different behaviors of the three NOS isoforms appear to be linked to differences in their heme reduction and Fe(II) heme-NO oxidation rates. But what structural and physical parameters control these processes? The Trp-409 mutations achieved by Adak et al. (22,23) suggest one controlling factor is the heme reduction potential. Crystal structures show that a Trp-409 indole nitrogen forms a strong hydrogen bond with the heme thiolate (61,62). Suppression of this hydrogen bond through mutation is expected to lower the reduction potential of the heme, which we suspect inhibits heme reduction while speeding oxidation of the Fe(II) heme-NO complex. This hypothesis also arises from the comparison of the results of Wang et al. (51), who observed a faster rate of Fe(II) heme-NO complex oxidation in the absence of Arg, and Presta et al. (63), who showed that Arg binding increases the reduction potential of the NOS heme. Consequently, it seems possible that catalytic differences among NOS isoforms arise in part from their differential control of heme reduction potential. Our kinetic model provides a basis to investigate this hypothesis and better understand the structure-function relationships in the three NOS.  Mathematical Simulation of the Simplified Model in Absence of Substrate (Fig. 3, Inset)-The model used to depict catalytic turnover in absence of substrate is a simplification of the previous one (see . The values of the constants are detailed in main text. Oxygen concentration is set at 140 M.