A kinetic model linking protein conformational motions, interflavin electron transfer and electron flux through a dual-flavin enzyme – simulating the reductase activity of the endothelial and neuronal nitric oxide synthase flavoprotein domains
D. J. Stuehr, Department of Pathobiology, Lerner Research Institute (NC22), The Cleveland Clinic, 9500 Euclid Avenue, Cleveland, OH 44195, USA Fax: +1 216 636 0104 Tel: +1 216 445 6950 E-mail: firstname.lastname@example.org
NADPH-dependent dual-flavin enzymes provide electrons in many redox reactions, although the mechanism responsible for regulating their electron flux remains unclear. We recently proposed a four-state kinetic model that links the electron flux through a dual-flavin enzyme to its rates of interflavin electron transfer and FMN domain conformational motion [Stuehr DJ et al. (2009) FEBS J276, 3959–3974]. In the present study, we ran computer simulations of the kinetic model to determine whether it could fit the experimentally-determined, pre-steady-state and steady-state traces of electron flux through the neuronal and endothelial NO synthase flavoproteins (reductase domains of neuronal nitric oxide synthase and endothelial nitric oxide synthase, respectively) to cytochrome c. We found that the kinetic model accurately fitted the experimental data. The simulations gave estimates for the ensemble rates of interflavin electron transfer and FMN domain conformational motion in the reductase domains of neuronal nitric oxide synthase and endothelial nitric oxide synthase, provided the minimum rate boundary values, and predicted the concentrations of the four enzyme species that cycle during catalysis. The findings of the present study suggest that the rates of interflavin electron transfer and FMN domain conformational motion are counterbalanced such that both processes may limit electron flux through the enzymes. Such counterbalancing would allow a robust electron flux at the same time as keeping the rates of interflavin electron transfer and FMN domain conformational motion set at relatively slow levels.
A family of structurally-related dual-flavin reductases is widely expressed in animals and includes cytochrome P450 reductase (CPR), methionine synthase reductase, the novel reductase 1 and nitric oxide synthase (NOS) [1,2]. Dual-flavin reductases comprise a domain that binds NADPH and FAD, which is ancestrally related to ferredoxin/flavodoxin reductases [ferredoxin-NADP+-reductase (FNR)-like domain], and a domain that binds FMN, which is related ancestrally to flavodoxins (the FMN domain) .
Dual-flavin reductases typically transfer electrons from NADPH to various metalloprotein acceptors [1,2]. The FAD receives two electrons from NADPH through a hydride transfer reaction that occurs within the FNR domain. Single electrons are then passed to the FMN domain via interflavin electron transfer. The reduced FMN can then transfer an electron to other protein acceptors. During this process, the FMN cofactor cycles between its one- and two-electron reduced states, namely the one-electron reduced (semiquinone) FMN (FMNsq), which accepts an electron from FAD, and the two-electron reduced (hydroquinone) FMN (FMNhq), which donates an electron to the acceptor. The FMN domain is assumed to undergo relatively large conformational motion to shuttle electrons between the FNR and the protein acceptors [4–7]. A three-state, two equilibrium model can describe FMN domain function within dual-flavin enzymes (Fig. 1) . In equilibrium A, the FMN domain alternates between an ‘FMN-shielded’ or ‘closed’ conformation that allows it to receive an electron from the FNR domain, and an ‘FMN deshielded’ or ‘open’ conformation where the FMN domain has moved away and can transfer an electron to a metalloprotein acceptor. Once in an open conformation, the FMN domain is subject to equilibrium B, which involves its interaction with a metalloprotein acceptor (oxygenase domain of NOS, cytochrome P450, heme oxygenase, methionine synthase, cytochrome c). During steady-state catalysis, the FMN domain shuttles back and forth between the three conformational states, as dictated by equilibriums A and B, to deliver the electrons required for catalysis. Thus, the control of electron import into the FMN domain, and its conformational motions, are central to catalysis by dual-flavin enzymes.
To understand how protein conformational motions relate to electron flux through a dual-flavin enzyme, a simple kinetic model was proposed (Fig. 2) . The model relies on cytochrome c reductase activity to assess the electron flux through the flavoprotein. Assuming that the rates of electron transfer to cytochrome c (k4) are very fast and not rate limiting, the electron flux is only dependent on the rates of conformational motion of the FMN domain (k1, k−1, k3, k−3) and the rate of interflavin electron transfer between the FAD and FMN cofactors (k2). The model incorporates the one-electron redox cycling of the FMNhq and FMNsq that occurs within the dual-flavin enzymes during catalysis, and therefore includes two temporally-separate equilibrium terms (KAsq and KAhq) that differ according to the reduction state of the FMN (FMNhq versus sq). We define KAsq = k−1/k1 and KAhq = k−3/k3 (Fig. 2) such that higher values of KA indicate a higher tendency towards open conformations. The equilibrium described by KAhq involves a conformational opening step that allows bound FMNhq to reduce an acceptor (cytochrome c in this case) and consequently become oxidized to FMNsq. The equilibrium described by KAsq involves a conformational closing step that allows the FMNsq to receive another electron from the FNR domain, and thus continue the catalytic cycle. For simplicity, the model assumes that the interflavin electron transfer step (k2) is irreversible. Other assumptions are that the reduction of cytochrome c by FMNhq (k4 step) is irreversible and very rapid relative to all the other kinetic parameters, and that the same applies to the reduction of FNR by NADPH. These conditions are met under typical experimental conditions [8,9].
Recent crystal structures of CPR and the NOS reductase domain (NOSr) help to visualize how dual-flavin reductases may exist in their FMN-shielded and FMN-deshielded conformations [10–14]. These structures and related studies [15–17] make it clear that the FMN domain needs to be in an open conformation to interact with cytochrome c for electron transfer. Recently, Ilagan et al.  utilized this concept and deployed cytochrome c in stopped-flow spectroscopic experiments to measure the KAhq conformational equilibrium setpoint for the fully-reduced endothelial and neuronal NOSr (nNOSr and eNOSr). This represented the first equilibrium setpoint measures obtained for any member of the dual-flavin reductase family. Two observations from the study Ilagan et al.  were: (a) the eNOSr and nNOSr have markedly different KAhq setpoints and (b) they likely also have different speeds of conformational motion for their FMN domains. In the present study, we ran computer simulations of the kinetic model presented in Fig. 2, utilizing the measured KAhq values of eNOSr and nNOSr , aiming to better understand the factors that control electron flux in these enzymes. The computer simulations of the model were able to fit the experimental data well, and this allowed us to estimate ensemble rates for the conformational motions of the FMN domain and the rate interflavin electron transfer in nNOSr and eNOSr. Other techniques and methods have been unable to estimate these rates, making the model and computer simulations powerful analytic tools. Additionally, the reported results have interesting mechanistic implications and generally increase our understanding of how domain conformational motions and interflavin electron transfer may combine to govern electron flux through dual-flavin enzymes.
General relationships between the KA setpoint, interflavin electron transfer rate and electron flux
We ran computer simulations of the kinetic model using the computer software gepasi, version 3.30 (for details, see Doc. S1) under the simplest condition, which is to assume that the KA setpoint stays constant during the catalytic redox cycle of the flavoprotein, and is therefore not influenced by the changes in the FMN redox state (i.e. the value of KAsq is equivalent to KAhq, k1 = k3, and k−1 = k−3) (Fig. 2). Figure 3A shows how electron flux through a dual-flavin enzyme (equivalent to the cytochrome c reductase activity) would vary over a range of KA settings, which we created by varying the rates of conformational change within the range 0.5–9.5 s−1, and over the indicated range of interflavin electron transfer rates (k2). The simulations show that maximal electron flux through the enzyme to cytochrome c is achieved at KA settings near 1, particularly when k2 is relatively fast. This is expected because, at KA = 1, the association and dissociation rates of the FMN–FNR complex are balanced. The simulations also show that the maximally-achievable electron flux is always less than the rate of conformational change that represents the opening of the fully-reduced protein (k−3).
A second plot of the simulated data shows these relationships from a different perspective (Fig. 3B). Again, it is apparent that the electron flux through the enzyme to cytochrome c never achieves the conformational opening rate k−3 at any KA setting (indicated by the 1.0 value on the y-axis). The discrepancy is smallest when the KA setting is low (i.e. where the dual-flavin reductase predominantly favours a closed or FMN-shielded conformation) and becomes progressively greater as the KA setting increases (i.e. as the percentage of the reductase favouring an open or FMN-deshielded conformation increases). This is because, as the KA setting increases, the association rate of the FMNsq (k1) with the FNR domain becomes slower and plays an increasingly larger role in limiting the electron flux through the enzyme. Also indicated in Fig. 3B are the KAhq positions that have been reported for the fully-reduced eNOSr and nNOSr enzymes . The eNOSr has a low KAhq setting and thus exists predominantly in an FMN-shielded conformation. Thus, its rate of FMNhq dissociation (k−3) may not be too different from the maximal electron flux that eNOSr could achieve (depending on the speed of k2). By contrast, nNOSr has a KAhq setting close to 1, and thus its maximum electron flux should only be 50% or less than the rate of its FMNhq dissociation (k−3), according to the kinetic model.
Summary of the NOSr experimental data
Before describing the simulations that we ran for nNOSr and eNOSr in the present study, it is useful to review the experimental results of Ilagan et al.  that utilized pre-steady-state and steady-state measures of electron flux to cytochrome c, and, from these measures, estimated the KAhq positions of the fully-reduced eNOSr and nNOSr. Figure 4 contains the kinetic traces adapted from Ilagan et al.  that follow the cytochrome c reduction versus time in reactions where excess cytochrome c was mixed with fully-reduced nNOSr or eNOSr in a stopped flow spectrophotometer at 10 °C. The traces cover a time frame that includes the first catalytic turnover completed by each enzyme (transfer of an electron from the four-electron reduced (hydroquinone) FAD (FADhq)/FMNhq form of the reductase to one molar equivalent of cytochrome c, as indicated by the the dashed box in Fig. 4), and also includes the subsequent period where the reactions shift into multiple turnover and achieve a steady-state. The experimental traces show that both enzymes quickly reduced some cytochrome c within the mixing dead-time of the instrument. This initial reaction is assumed to have been carried out by the fraction of each NOSr enzyme that is in the open or FMN-deshielded conformation; essentially, the reaction that involves species a as indicated by the k4 step in the kinetic model (Fig. 2). The extent of cytochrome c reduction that occurs in this phase (moles) relative to the total moles of NOSr enzyme that are present in the reaction is indicated by the brackets on the y-axis in Fig. 4. This was used by Ilagan et al.  to calculate the proportion of each NOSr that was in the FMN-deshielded versus FMN-shielded conformation at the time of mixing, and thus to determine the KAhq setting of either fully-reduced NOSr enzyme . After the fast reaction that occurs in the mixing dead-time is finished, the absorbance trace for either enzyme reaction deflects and then continues to increase in a near-linear manner during the rest of the single turnover phase (designated as period p in Fig. 4). The absorbance then continues to increase almost unchanged as each enzyme goes beyond the first turnover equivalent of cytochrome c and enters the multiple turnover, steady-state phase of the reaction. This behaviour implies that whatever factors limit the electron flux to cytochrome c during period p in the first turnover continue to do so during the steady-state. Reasoning that electron flux to cytochrome c during period p must reflect the conformational opening rate k−3 of the fully-reduced, FMN-shielded NOSr, Ilagan et al.  concluded that electron flux through NOSr was dependent on this conformational opening step during the steady-state reaction.
Simulations of nNOSr using the kinetic model
With the above concepts in mind, we ran computer simulations of the kinetic model using the experimentally-determined KAhq setpoints for nNOSr and eNOSr , aiming to reproduce the published experimental traces of electron flux to cytochrome c (Fig. 4) and, in so doing, to obtain rate estimates for conformational change and for interflavin electron transfer from fits of the experimental data.
Figure 5A shows the absorbance trace generated from a simulated reaction of nNOSr with cytochrome c, using a KAhq setting of 1 and assuming a relatively fast interflavin electron transfer rate (k2) of 200 s−1, which is at least four-fold faster than the reported estimates of interflavin electron transfer rates [18–20]. The use of a fast k2 setting assures that the electron flux will be primarily limited by the rate of conformational motion in this particular simulation. We then set the conformational kinetic values to equal the 8 s−1 cytochrome c reduction rate that was observed by Ilagan et al.  during phase p in the nNOSr experimental data set in Fig. 4. All conformational rates are assumed to be the same in this case: k1 = k−1 = k3 = k−3 = 8 s−1. This simulation generated a reaction trace that qualitatively mimics the experimental data with respect to an initial fast cytochrome c reduction (similar to what occurs during the mixing dead-time) in Fig. 4, followed by a slower and linear increase in A550 that represents the cytochrome c reduction taking place during the remainder of the first turnover and into the steady-state phase. However, this simulation does not match the magnitude of electron flux through nNOSr that was observed in the experimental data during phase p or in the steady-state. Specifically, in the simulation, the electron flux to cytochrome c during these time frames was 3.85 s−1, which is only 48% of the 8 s−1 value that was experimentally-observed for nNOSr at 10 °C. This mismatch is consistent with the simulation results shown in Fig. 3A,B, which indicated the electron flux through nNOSr cannot go beyond 50% of its k−3 rate of conformational opening of the FMN hydroquinone, which was set at 8 s−1 in this simulation.
We next attempted a better fit by increasing the rates of conformational motion in nNOSr at the same time as keeping the KAhq and the k2 settings unchanged. Figure 5B shows that using a faster rate of conformational motion (k1 = k−1 = k3 = k−3 = 17.5 s−1) can more accurately simulate the observed electron flux of 8 s−1 through nNOSr. However, there is still a discrepancy in the simulated trace of Fig. 5B with respect to it taking a longer time to complete the first turnover (62 ms) compared to the experimental trace (37 ms) reported by Ilagan et al.  (Fig. 4). The simulated trace also shows a sharp break instead of a more rounded transition between the fast and slow phases of the reaction. We next repeated the simulation using a series of slower interflavin electron transfer rates (k2) and by selecting corresponding faster rates of conformational change that would still maintain an electron flux through nNOSr at 8 s−1. Figure 5C–E shows the traces that we obtained at k2 settings of 30, 25 and 20 s−1, respectively. In general, these traces created at slower k2 settings better match the experimental data. The very best match between the simulated and experimental traces was achieved using a k2 of 25 s−1 and a corresponding rate of conformational change of 45 s−1 (Fig. 5D). This provided a close match regarding the rounded transition between the two phases of cytochrome c reduction, and also accurately matched the time required to reduce one equivalent of cytochrome c (time for first catalytic turnover of 37 ms).
In the above simulations, we found that to maintain a steady electron flux through nNOSr as we slowed down the rate of interflavin electron transfer (k2), we had to invoke corresponding increases in the rate of conformational motion. Figure 6 shows the results obtained from many simulations, which provide a range of combinations of interflavin electron transfer rates and conformational change rates that fit the experimentally-determined electron flux through nNOSr (8 s−1 at 10 °C). At the highest interflavin electron transfer rate (k2), a horizontal tangent to the graphed line provides the lower boundary rate of conformational change that would be needed to maintain the observed electron flux, which, in the case of nNOSr, is approximately 17 s−1. Similarly, a vertical tangent to the graphed line indicates the lower boundary value for the interflavin electron transfer rate (k2) of approximately 20 s−1 because, below this value, the corresponding rate of conformational motion that would be needed to maintain the observed electron flux becomes prohibitively fast or even unattainable.
Traces in Fig. 7 were derived from the same simulations that we ran for Fig. 5B–E but, in this case, show how the distributions of the four enzyme species (Fig. 2) change as a function of reaction time under each setting. In the reaction that we simulated using a fast interflavin electron transfer (k2 = 200 s−1) and a correspondingly slow rate of conformational change (17.5 s−1) (Fig. 7A), the steady-state enzyme distribution is reached very quickly (within 30 ms) and is characterized by an almost equivalent build up of only two species of nNOSr, namely the deshielded FMNsq form (species b) and the shielded FMNhq form (species d). Together, these two species account for approximately 90% of the enzyme distribution in the steady-state under this condition. The build up of these two species makes sense because the further transition of either species depends on the relatively slow rate of conformational change. A somewhat different pattern emerges for reactions that were simulated using slower k2 values and correspondingly faster rates of conformational change (Fig. 7B–D). Under these circumstances, it takes longer to reach the steady-state, with final enzyme distribution requiring times even beyond the time required for the first turnover (marked by the vertical dashed line). The deshielded FMNsq species (species b) remains predominant in steady-state, accounting for 50% of the total enzyme distribution. However, build up of the shielded FMNhq species (species d) becomes compromised, and there is a corresponding increase in build up of the shielded FMNsq species (species c), such that species c overtakes species d when the k2 value falls below 30 s−1. In general, this distribution change is expected to occur as electron flux through nNOSr becomes more and more limited by its interflavin electron transfer rate (k2). How the distribution of the four enzyme species changes as a function of k2 and the conformational rate (both values were balanced in all cases to maintain the observed 8 s−1 electron flux through nNOSr) is shown in Fig. 8. Interestingly, the relative distribution of the total FMNsq and FMNhq enzyme species (the FMN-shielded plus the FMN-unshielded conformations) changes considerably across the range, going from a minimum of 50% total FMNsq species present at the fastest k2 to approximately 90% total FMNsq species present at the slowest allowable k2. Thus, the simulations predict that nNOSr should contain 50–90% of its FMN in the FMNsq state (with the remainder in the FMNhq state) during steady-state cytochrome c reduction. This range in FMNsq/hq redox distribution arises from the offsetting rise and fall of the two FMN-shielded forms of nNOSr (the FMNsq and FMNhq species) (Fig. 8) whose build up depends on whether the electron flux is limited primarily by the rate of interflavin electron transfer (i.e. favours build up of the FMNsq species) or by the rate of conformational change (i.e. favours build up of the FMNhq species).
Another notable feature is the enzyme re-distribution that occurs during the time required to reduce one molar equivalent of cytochrome c (the area marked within dashed boxes in Figs 4 and 5). In all reactions, there is an immediate enzyme distribution change that reflects the very fast reaction of cytochrome c with the proportion of the nNOSr FMNhq that is in the open conformation (species a), converting it instantly to the open FMNsq form (species b). In nNOSr, this fast reaction involves approximately 50% of the total enzyme molecules, as stipulated by KAhq = 1. As this fast reaction occurs, the nNOSr FMNhq molecules that are in the closed conformation begin to open according to rate k−3 and react with cytochrome c. However, at the same time, the 50% of nNOSr molecules that have already reacted with cytochrome c begin to redistribute to the closed conformation (species c) according to rate k1, and some of these molecules undergo interflavin electron transfer to form the closed form of nNOSr FMNhq (species d). These enzyme ‘recycling’ transitions take place even within the first turnover to ultimately create a relatively steady concentration of species d, which in turn helps determine the observed rate of cytochrome c reduction during phase p and enables this rate to remain relatively unchanged as the reaction proceeds beyond the first turnover.
Simulations of eNOSr using the kinetic model
Compared to nNOSr, the KAhq setting of eNOSr is eight-fold shifted toward the FMN-shielded state and its electron flux to cytochrome c is approximately 16-fold slower . Figure 9 shows four kinetic traces that we generated by simulating eNOS cytochrome c reduction, using the experimentally-determined KAhq setting of 0.125 , and different combinations of interflavin electron transfer rates (k2) and corresponding rates of FMN domain conformational motion that all maintain the experimentally-observed electron flux value of 0.5 s−1 at 10 °C. The simulated traces A–C generally mimic the experimental trace obtained for eNOSr (Fig. 4) with respect to the general line shape and the time required to catalyze a single turnover (1.8 s). These traces cover k2 settings of 100, 10 and 5 s−1, respectively. Only at a very low k2 setting (0.75 s−1) (Fig. 9D) does the shape of the trace, and the time required to complete the first turnover, deviate significantly from the experimental trace obtained for eNOSr. Thus, unlike for nNOSr, the electron flux through eNOSr can be accurately simulated over a relatively broad range of conformational motion and interflavin electron transfer rate pairings.
The graphs shown in Fig. 10 indicate the pairings of conformational motion and interflavin electron transfer rates that would maintain the experimentally-measured electron flux of 0.5 s−1 through eNOSr . These curves give lower boundary values for the rates of conformational change, k1 = k3 ≥ 4.5 s−1 and k−1 = k−3 ≥ 0.56 s−1, and also give a lower boundary value for the rate of interflavin electron transfer, k2 ≥ 0.5 s−1.
Figure 11 shows traces derived from the eNOSr reactions simulated in Fig. 9 and, in this case, shows how the distribution of eNOSr species would change as a function of reaction time under the different allowable kinetic settings. In all cases, initiating the reaction causes the 10% of reduced eNOSr that exists in the open conformation (according to the KAhq) to react instantly and convert to the open FMNsq form of eNOSr (species b). In the reaction that we simulated with relatively fast interflavin electron transfer (k2 =100 s−1) (Fig. 11A), the steady-state enzyme distribution is reached within 0.5 s, which is far before the single turnover is finished (1.8 s). During the steady-state (Fig. 11A), almost all of eNOSr populates only two forms: the closed FMNhq form (species d; 88.5%) and the open FMNsq form (species b; 11%). This distribution pattern is consistent with the relative slowness of the conformational opening step (k−1) in eNOSr, and also reflects the very different rates of conformational opening (k−1 and k−3) and closing (k1 and k3) as dictated by the value of KA. In the reactions that we simulated using slower interflavin electron transfer rates (k2 = 10, 5, or 3 s−1) (Fig. 11B–D), the steady-state enzyme distribution is reached more slowly, although it is still achieved well before the single turnover is finished (1.8 s). Thus, under all cases, a considerable extent of enzyme recycling occurs to form species d even before the first equivalent of cytochrome c is reduced by eNOSr. However, at slower k2 rates, a greater proportion of the closed FMNhq form (species d) becomes redistributed once the reaction starts, predominantly distributing into the closed FMNsq form (species c; changing from almost 0% to 5%, 10% and 17% in Fig. 11A–D, respectively). This shift reflects a growing influence of the FMNsq reduction step in limiting electron flux through eNOSr as the k2 value decreases. However, even at a relatively slow interflavin electron transfer rate (k2 = 3 s−1) (Fig. 11D), the k2 does not become the major factor limiting electron flux because the KAhq setting of eNOSr still constrains the enzyme to exist predominantly as the closed FMNhq species whose inherent reactivity toward cytochrome c is masked by its very slow rate of conformational opening. Thus, our simulations predict that 70–95% of eNOSr will exist in the FMNhq state during its steady-state cytochrome c reduction. By contrast, only 20–30% of nNOSr is predicted to be in its FMNhq state under identical reaction circumstances (see above). Their different enzyme distributions in the steady-state can be primarily attributed to their widely dissimilar KAhq settings, as well as to their different rates of conformational change.
Electron flux through the NADPH-dependent dual-flavin enzymes presents several thermodynamic, conformational, and kinetic challenges [1,2,7]. We have focused on the challenges inherent to the FMN domain performing electron acceptor and electron donor roles in tandem to shuttle electrons from NADPH to an acceptor protein, which, in the present study, was cytochrome c. Through computer simulations of a simple kinetic model that describes interflavin electron transfer and FMN domain conformational motions in a dual-flavin enzyme  (Fig. 2), we fit data obtained from previous experimental measures (KAhq, time required to complete a single turnover, and steady-state cytochrome c reductase activity)  to obtain predicted rates and lower boundary values for the interflavin electron transfer and the FMN domain conformational opening and closing steps that occur during catalysis by eNOSr and nNOSr. To our knowledge this is the first study to model electron flux through NOS enzymes or through dual-flavin enzymes. Practically speaking, the estimated rate values and enzyme distribution patterns that we report in the present study will be useful for guiding further experiments that aim to probe how electron transfer is linked to the protein conformational equilibrium in NOS enzymes. In addition, the general applicability of our approach makes it useful to study interflavin electron transfer and conformational motion in the other members of the dual-flavin enzyme family.
Relationship with protein structural aspects
It is important to consider how the rate measures and estimates that we describe in the present study may relate to the molecular-level events that occur in the NOSr proteins or in dual-flavin enzymes during electron flux to cytochrome c. Our kinetic model (Fig. 2) assumes that the FMNhq has a binary reactivity (highly reactive versus unreactive) that is linked to two general conformational states of the FMN domain (open versus closed conformations, respectively). Clearly, a binary model is a simplification because there are likely to be many conformational states that the FMN domain can populate during catalysis. Nevertheless, the crystal structures of nNOSr and the related CPR establish what a closed conformational state is likely to look like in a dual-flavin enzyme [11,13,14]. In these structures, the FMN domain is cradled by the FNR domain, with the FMN cofactor buried near the domain interface and shielded from solvent. In this conformation, the bound FMN is closely aligned with the FAD cofactor bound in the FNR domain. As discussed previously [13–15], the relatively large size of cytochrome c (minimum diameter of 35 Å, which is similar to that of the FMN domain) constrains its approach and should prevent it from accepting an electron from the FMN cofactor unless the FMN domain moves from its position as seen in these crystal structures. Support for this concept was recently provided in experiments with a CPR mutant whose FMN domain was held in place against the FNR domain by the introduction of a disulfide bond . Thus, the rates of conformational motion that we report (k3 and k−3) likely reflect any conformational movements of the FMN domain that would allow its bound FMNhq to transfer an electron to cytochrome c, or prevent it from doing so. Interestingly, recent crystallography and small angle x-ray scattering studies have visualized some of the possible open conformational states of CPR [10,12,16]. These studies suggest that the FMN domain undergoes a twisting motion to free itself from the FNR domain. The FMN domain can also undergo further movement that completely separates it from the FNR domain, and can populate conformations that place its bound FMN as far as 60 Å away from the bound FAD. All open conformational states described for CPR in these studies would be capable of rapid cytochrome c reduction. Which open conformations are populated during catalysis remains unclear, although evidence suggests that the most open conformation seen in these studies may be catalytically detrimental . A recent study that mapped the energy landscape of the conformational equilibrium in CPR also found that discreet conformations become populated during catalysis . A similar array of open complexes is likely to be populated by NOSr enzymes, and the individual formation rates and lifetimes would blend to create the ensemble kinetic values that we report in the present study for FMN domain motion in nNOSr and eNOSr.
Estimating the most probable rate values for nNOSr and eNOSr
Our simulations showed that reasonable fits of nNOSr or eNOSr electron flux to cytochrome c could be achieved over a range of combined interflavin electron transfer and conformational motion rate pairs (represented by the lines in Figs 6 and 10). Can we further determine which rate pair along these fit lines is the most likely combination for either enzyme? In the present analysis, the KAhq = 1 setting of nNOSr makes two other fitting parameters (i.e. the time required for the first turnover and the curvature of the line; Fig. 5) sufficiently sensitive to the magnitudes of any given rate pair such that these parameters become useful for estimating the most probable rates of interflavin electron transfer and conformational motion in nNOSr. With this in mind, the kinetic pair that best describes nNOSr electron flux to cytochrome c (at 10 °C) has the rate of interflavin electron transfer set at 25 s−1 and the rate of conformational motion set at 45 s−1 (Figs 5D and 7C). The position of this kinetic pair on the fit line is boxed in Fig. 6. The best fit rate estimate for interflavin electron transfer in nNOSr (25 s−1 at 10 °C) is close to the observed rates measured for nNOSr by T-jump or stopped-flow methods, which were in the range 14–55 s−1 [18–20].
For eNOSr, the experimental trace describing electron flux to cytochrome c has almost no curvature (Fig. 4) and the time required for completing the first turnover is relatively insensitive to the magnitude of the kinetic pair values that we used in the simulations (Fig. 9). This prevents us from estimating the most probable kinetic pair rates for eNOSr as we did above for nNOSr. However, if we consider that it is generally easier for enzymes to support slower transitions than faster ones (to a point), this implies that eNOSr, similar to nNOSr, may operate using a blend of relatively slow rate values that are found near the corners of the fit lines in Fig. 10. Indeed, one could consider that the rate pairs located in the corner positions, which represent the slowest possible pairs, may generally be the most efficient means for a dual-flavin enzyme to achieve a given electron flux. For the nNOSr and eNOSr, having slower setpoints for their rates of interflavin electron transfer and conformational motion could help minimize their uncoupled reduction of O2 and would also be consistent with their function because such circumstances give either enzyme room to improve the electron flux when calmodulin binds and activates electron transfer [6,21].
Relationship with other multi-domain redox enzymes
Domain conformational switching operates during electron transfer in several multi-domain enzymes, including sulfite oxidase, phthalate dioxygenase reductase, cytochrome bc1 and various flavo-heme enzymes [22–27]. Catalysis by these enzymes involves relatively large-scale movements of flavin, iron-sulfur or even heme-containing domains. The kinetics of the domain conformational motions or electron transfer events has been studied in some of these systems. For example, the rate of conformational shuttling by the FeS subdomain in cytochrome bc1 is considered to be near 300 s−1 . Estimated rates of interdomain electron transfer are in the range 50–1500 s−1 among flavo-heme enzymes [25,27] and, in sulfite oxidase, this is likely to be ≥ 400 s−1 . In comparison, our estimates for the rates of conformational motion and inter-flavin electron transfer in eNOSr and nNOSr would be in the slower part of the range. However, interdomain electron transfer in the related enzyme CPR is also slow, with estimates in the range 20–55 s−1 depending on the measurement method [28,29]. Relatively slow interflavin electron transfer and conformational motions in dual-flavin enzymes may reflect them having evolved to supply electrons to protein domains or partners whose catalytic activities are also relatively slow. In addition, for the NOS enzymes, their NO synthesis places a selective pressure to keep heme reduction from becoming too fast, which otherwise can cause problems in catalytic turnover related to heme-NO binding . In the case of nNOS, FMN domain conformational motion appears to be a major factor in limiting cytochrome c reduction, although it only partially limits heme reduction in nNOS . By contrast, the very slow rate of FMN conformational opening in eNOS could certainly limit its rate of heme reduction. These concepts may explain the findings reported in an earlier study with eNOS-nNOS chimeras that showed the identity of the flavoprotein domain determines the NOS heme reduction rate .
Our estimates for interflavin electron transfer rates in eNOSr and nNOSr, as well as the measured estimates for nNOSr and for CPR [18–20,28,29], are much slower than that predicted based on the close proximity of the FAD and FMN cofactors in the CPR and nNOSr crystal structures [11,13]. As discussed previously , this likely indicates that protein conformational factors and an inherently weak thermodynamic driving force combine to limit the interflavin electron transfer in dual-flavin enzymes. The close flavin positioning that is seen in the crystal structures is probably difficult to achieve during catalysis, such that a majority of the interflavin electron transfer may proceed through alternative, less optimally-positioned complexes . The protein conformational motions that help determine inter-flavin electron transfer in semi-closed complexes may be relatively rapid small-scale fluctuations (i.e. conformational sampling)  that are distinct from the slower, large-scale motions that the FMN domain must undergo to transfer electrons to cytochrome c .
Possible mechanistic implications
Our model for electron flux through a dual-flavin enzyme (Fig. 2) is perhaps the simplest conceivable model because it involves only four enzyme states. The model has the FNR domain serving as a monophasic source of electrons to reduce the FMNsq. Despite its simplicity, simulations of the model created accurate fits of the experimental traces obtained for cytochrome c reduction by nNOSr and eNOSr  during the initial and steady-state phases of the reaction. This outcome is unexpected and may have mechanistic implications. Consider the complexity inherent in the system: the two flavin cofactors (FAD + FMN) in dual-flavin enzymes contain a total of three, two and one electrons when they cycle during catalysis. This cycling and the known midpoint potentials of the FAD and FMN couples  constrain the enzyme to populate five main electron distributions among the flavin cofactors during catalysis, two of which are reactive toward cytochrome c (i.e. that contain FMNhq) (Fig. S1). In the FNR domain, the FAD cycles between all three of its possible redox states (FADox, FADsq, FADhq) with both the FADsq and FADhq forms being capable of reducing FMNsq during catalysis (Fig. S1). In addition, electron transfer from the FNR domain to FMNsq may be influenced by a number of factors, including NADP(H) binding site occupancy, the redox state of the bound NADP(H) (i.e. NADP+ versus NADPH) and FNR conformational changes [34–36]. In CPR or NOS enzymes, NADP(H) binding site occupancy can also influence the KA setpoint [37–39], and the reduction of FAD by NADPH may even be gated by the movement of the FMN domain . Conceivably, such complexity could create a very complicated kinetic model for electron flux where the interflavin electron transfer step is beholden to a multitude of separate FNR species, which are all subject to multiple equilibrium events. However, we found no need to invoke such complexity in FNR modes to successfully model electron flux through a dual-flavin enzyme such as NOS. Indeed, in our simulations, we found that an interflavin electron transfer rate (k2) that fitted the initial portion of the experimental trace of cytochrome c reduction (in which the reduced NOSr enzyme is undertaking its first interflavin electron transfer during the reduction of the first equivalent of cytochrome c) can continue to fit the observed electron flux trace in the multiple-turnover phase of the reaction, where all the aforementioned complexities come into play. This implies that, as far as electron flux through nNOSr or eNOSr is concerned, the interflavin electron transfers from FADhq or FADsq are equivalent, and the FNR redox state or NADP(H) occupancy is unimportant. In our simulations, we also did not need to include an FMN redox state bias on the conformational equilibrium (i.e. KAsq ≠ KAhq) to obtain good fits of the experimental data. This suggests that the redox state (FMNsq versus FMNhq) may not significantly impact the conformational equilibrium. However, our model and simulations do not allow any definitive judgment to be made, which will ultimately require better and more direct measurements, as discussed recently . There is indirect evidence suggesting that the FMN redox state can influence the conformational equilibrium in CPR under certain circumstances . In any case, we chose to propose the simplest model that can fit the data. Finally, it is curious that the best fit that we obtained for electron flux through nNOSr gave rate values for the interflavin electron transfer (k2) and conformational opening (k−3) steps that were very close in magnitude. Whether this equivalence indicates that the FMNsq reduction step (k2) is gated with the conformational opening step (k−3) represents an interesting possibility that remains to be explored.
Materials and methods
The kinetic model describing electron flux through NOSr, as measured by cytochrome c reductase activity (Fig. 2), was simulated using the computer software gepasi, version 3.30 . Cytochrome c was set to be in 100-fold molar excess relative to the flavoprotein. Values for each of the four conformational rates (k1, k−1, k3 and k−3) and the interflavin electron transfer rate (k2) were input into the software. Each simulated reaction began with 100% of the enzyme in the fully reduced state (represented by species d and a in Fig. 2). For simulations of the nNOSr and eNOSr reactions, the initial concentrations of species d and a were determined based on the published KAhq values for nNOSr and eNOSr . In some cases, we used an iterative procedure to obtain best-fit rate values and rate combinations to match a given rate of electron flux through nNOSr or eNOSr.
The ‘electron flux’ is defined as the rate of cytochrome c reduction in the steady-state. This is calculated by fitting the simulated traces for the cytochrome c reduction to a straight line (i.e. omitting the initial, nonlinear portion). Linear fittings were carried out using the software origin pro, version 7.5 (OriginLab, Northampton, MA, USA). The rationale for this calculation is that these traces resemble the experimental results obtained when studying the reactions of NOS reductase domains with cytochrome c. Further details concerning the simulation procedures are provided in Doc. S1.
We thank members of the Stuehr laboratory for helpful discussions. This work was supported by National Institutes of Health Grants GM51491 and HL58883 to D.J.S.