Functional interactions between nitrite reductase and nitric oxide reductase from Paracoccus denitrificans

Abstract

Denitrification is a microbial pathway that constitutes an important part of the nitrogen cycle on earth. Denitrifying organisms use nitrate as a terminal electron acceptor and reduce it stepwise to nitrogen gas, a process that produces the toxic nitric oxide (NO) molecule as an intermediate. In this work, we have investigated the possible functional interaction between the enzyme that produces NO; the cd₁ nitrite reductase (cd₁NiR) and the enzyme that reduces NO; the c-type nitric oxide reductase (cNOR), from the model soil bacterium P. denitrificans. Such an interaction was observed previously between purified components from P. aeruginosa and could help channeling the NO (directly from the site of formation to the side of reduction), in order to protect the cell from this toxic intermediate. We find that electron donation to cNOR is inhibited in the presence of cd₁NiR, presumably because cd₁NiR binds cNOR at the same location as the electron donor. We further find that the presence of cNOR influences the dimerization of cd₁NiR. Overall, although we find no evidence for a high-affinity, constant interaction between the two enzymes, our data supports transient interactions between cd₁NiR and cNOR that influence enzymatic properties of cNOR and oligomerization properties of cd₁NiR. We speculate that this could be of particular importance in vivo during metabolic switches between aerobic and denitrifying conditions.

Introduction

Denitrification is an anaerobic process in which nitrate (NO₃⁻) is reduced stepwise to nitrogen gas (N₂) via the intermediates nitrite, nitric oxide and nitrous oxide. There is widespread interest in denitrification because it limits the amount of nitrogen available to crops by decreasing the amount of nitrate and nitrite in the soil and because incomplete denitrification yields nitrous oxide which is a potent green-house gas. In Paracoccus (P.) denitrificans, a model organism for both aerobic respiration and denitrification, the enzymes that catalyze these reactions are: nitrate reductase (NAR), reducing nitrate to nitrite, nitrite reductase (NiR) which reduces nitrite to nitric oxide, nitric oxide reductase (NOR), reducing nitric oxide to nitrous oxide and finally nitrous oxide reductase (N₂OR), which reduces nitrous oxide to nitrogen gas (for a review on denitrification enzymes, see¹).

The stepwise reduction of nitrate requires the product of one enzyme to be the substrate for the next enzyme in the pathway and as a consequence the expression of all four enzymes should be coordinated and regulated in such way that the concentrations of nitrite and nitric oxide are kept at concentrations that are not toxic to the cell². Lethal nitric oxide concentrations have been shown to vary between organisms, with some bacteria such as Agrobacterium tumefaciens accumulating µM NO concentrations during rapid switches between oxic and anoxic conditions, but in P. denitrificans nitric oxide is kept at (or below) ~30 nM³.

The enzyme catalyzing the reduction of nitrite to nitric oxide (NO₂⁻ + e⁻ + 2 H⁺ →NO + H₂O) in P. denitrificans is cytochrome cd₁ nitrite reductase (cd₁NiR), a soluble protein located in the periplasm (for a recent review on cd₁NiR and nitrite, see⁴). The almost identical (97% sequence identity) and well characterized cd₁NiR from Paracoccus pantotrophus is purified⁵ and crystallized as a dimer⁶. Each cd₁NiR monomer consists of one small heme c domain and one large d₁ domain, where NO₂⁻ reduction takes place. The heme c domain receives electrons from one of two soluble donors; either cytochrome c⁵⁵⁰ or the copper protein pseudoazurin⁷. The heme d₁ in the catalytic domain has an unusual ability (as compared to other hemes) to rapidly release NO, thereby lowering the degree to which the cd₁NiR enzyme activity is inhibited by its product NO⁸.

The well-characterized cd₁NiRs from P. pantotrophus and Pseudomonas (Ps) aeruginosa (see e.g.⁹ and⁴) have many properties in common including a similar overall fold especially in the larger, catalytic d₁ domain. They also use similar electron donors; a soluble c cytochrome or a blue copper protein. However, there are also striking differences, such as the ‘domain swapping’ that occurs only in the Ps. aeruginosa cd₁NiR dimer, where the N-terminal arm (in the cyt. c domain) of one monomer crosses over to interact with the d₁ domain of the second monomer.

Nitric oxide, produced from cd₁NiR, is further reduced to nitrous oxide (2NO + 2e⁻ + 2 H⁺ →N₂O + H₂O), by nitric oxide reductase (NOR). NORs are members of the heme-copper oxidase (HCuO) superfamily. This superfamily (comprising the cytochrome c oxidase in mitochondria) is large and diverse and some of its members are capable of NO-reduction^10,11,12, and all that have been investigated also show that the physiological O₂-reduction reaction is inhibited by NO (reviewed in^13,14, see also¹⁵), an effect which is linked to the use of NO as a signaling molecule in mammals¹⁶.

The NOR from P. denitrificans is a cytochrome c-dependent NOR (cNOR) that, as purified, is composed of two subunits; NorB and NorC. The NorB is an integral membrane protein and harbors a low-spin heme b and the active site, composed of a high-spin heme b₃ and a non-heme iron, Fe_B. NorC is membrane-anchored and contains a periplasmic heme c, which receives electrons from soluble donors such as cytochrome c or pseudoazurin (the same as for cd₁NiR). The enzyme uses protons and electrons from the same side of the membrane (periplasmic, see^17,18) and is thus non-electrogenic^19,20, which differs from the O₂-reducing HCuOs. The crystal structure of the cNOR from P. aeruginosa supports this as putative proton transfer pathways are only found leading from the periplasm into the active site²¹.

Respiratory chain complexes in mitochondria commonly form higher-order complexes, so-called supercomplexes. Such supercomplexes have also been found in bacteria (see e.g.^22,23), but the functional advantage of them is not always fully understood. Recently, the crystal structure of a complex between separately purified cd₁NiR and cNOR from Ps. aeruginosa was presented²⁴. The complex has a 2:2 stoichiometry (dimer of cd₁NiR with two monomers of cNOR), and the interaction was suggested to be present also under native conditions, but then in a 2:1 stoichiometry since the membrane-location of cNOR is not compatible with the 2:2 complex observed. Such a cd₁NiR-cNOR complex could confer advantages in vivo as the toxic NO molecule would, instead of being released into the periplasmic solution, rather be ‘channeled’ into the membrane in which it is more soluble. From the membrane, NO could directly enter the gas channel suggested for cNOR^21,25, see Fig. 1.

Figure 1

Structure of the co-complex of the P. aeruginosa cNOR and the cd₁NiR dimer (PDB ID: 5GUW²⁴). (a) The full 2:2 structure with the two cNOR molecules in light green (NorC) and teal (NorB) and the cd₁NiR dimer in blue/gray. (b) Enlargement of the co-complex interaction area for cd₁NiR and a single cNOR, with the interaction between Arg-71 (cd₁NiR, blue stick) and Glu-119 (cNOR, green stick) shown. Also shown are schematic outlines of the cytoplasmic membrane in which cNOR sits and the path for NO from the release from the d₁ heme of cd₁NiR (pink) into the membrane from which it would travel through the suggested gas channel (indicated by green sticks) to the active site heme b₃ (pink) in cNOR²⁵. Also highlighted is the initial electron-accepting heme c in NorC (pink), other heme groups in grey.

The aim of this work was to determine whether the P. denitrificans cd₁NiR and cNOR form a molecular complex in vivo and/or in vitro and to study potential functional interactions in vitro. To this end we investigated the localization of cd₁NiR in P. denitrificans, and we also used the cNOR catalyzed reaction as an in vitro ‘handle’ to report on a possible complex with cd₁NiR. We also used fluorescence spectroscopy to investigate cd₁NiR dimerization and the interactions of cd₁NiR with artificial and native membranes as well as with cNOR. Our data implies interference from cd₁NiR binding on electron donation to cNOR, consistent with an overlapping interaction surface. This effect of cd₁NiR on cNOR activity shows a titration profile consistent with an interaction primarily with a single cd₁NiR monomer. Our fluorescence data is consistent with this dimerization occurring in the relevant concentration range (20–40 nM cd₁NiR). However, we could not observe any clear long-lived high-affinity binding between cd₁NiR and cNOR going beyond the rather high affinity cd₁NiR showed to artificial membranes, nor could we observe a large fraction of the cd₁NiR associated with the membrane-bound cNOR in P. denitrificans membranes. Potential in vivo consequences of our results are discussed.

Results

The influence of cd ₁NiR on catalytic activity of cNOR

If cNOR and cd₁NiR interact with each other, they could influence each other’s catalytic parameters, therefore we measured the influence of the presence of cd₁NiR on NO-reduction by cNOR (which is straightforward to measure). Surprisingly, we observed clear inhibition of cNOR-catalyzed NO-reduction in the presence of cd₁NiR, see Fig. 2a. NO-reduction by the P. denitrificans cNOR exhibits a sigmoidal curve, due to substrate inhibition^26,27 at NO > 10 µM. The value we report for cNOR activity is the maximum activity (k_max, note that this k_max is not a k_cat since there is substrate inhibition at higher [NO]) observed at ~5 µM NO. In the presence of cd₁NiR (Fig. 2a), two effects are observed; the maximum activity is lowered and the substrate inhibition pattern changes, see below.

Figure 2

The inhibitory effect of cd₁NiR on cNOR catalysis. (a) NO reduction profile of P. denitrificans cNOR in the absence (black line) and presence (red line) of cd₁NiR. Experimental conditions: 50 mM HEPES pH 7.0, 50 mM KCl, 0.05% DDM, 30 mM glucose, 1 U/ml glucose oxidase, 20 U/ml catalase. Once the chamber was anaerobic, cyt. c (15 µM), TMPD (0.5 mM), and 5 times 10 µM NO (from NO-saturated water) was added. At t ~250 s, ascorbate (3 mM) and cNOR (80 nM) were added. For the trace with cd₁NiR (80 nM), it was added before the addition of NO. (b) Titration of the inhibitory effect of cd₁NiR on cNOR catalysis. Experimental conditions as in A, except the cNOR concentration was 40 nM, and the cd₁NiR concentration varied between 0–200 nM. cNOR activity (black circles) refers to the k_max at ~5 µM NO, with the k_max in the absence of cd₁NiR set at 100%. Also shown is the effect of adding cd₁NiR on substrate inhibition (blue circles) for NO-reduction by cNOR. The right y-axis refers to the [NO] where k_max/2 is reached (termed K_i^app in the text, note that this is higher than for k_max).

We investigated the inhibitory effect as a function of cd₁NiR concentration added, the raw data is shown in Supporting Fig. 1, and a plot of the maximum rate as a function of added cd₁NiR is shown in Fig. 2b (and Supporting Fig. 2). The maximum activity of cNOR decreases gradually the more cd₁NiR is added and the effect reaches a maximum level of inhibition (~50%) at ~30 nM cd₁NiR (approximately equimolar to cNOR). Surprisingly, at higher concentrations of cd₁NiR, the inhibition is released (Fig. 2b), the possible reasons for this are discussed further below (see Fluorescence section). For the investigations of the influence of the electron donor described in the next section, we used the cd₁NiR concentration (and cNOR/cd₁NiR ratio) giving the maximum inhibition.

Electron donation to cNOR in the presence of cd ₁NiR

In the co-crystal structure of the complex between the cd₁NiR and cNOR from P. aeruginosa²⁴, the interaction surface (see Fig. 1) could possibly overlap with interaction of the electron donor to cNOR. Thus, one reason for the inhibition observed with cd₁NiR could be that it interferes with electron donation, and we therefore studied the titration behavior of electron donors for cNOR catalysis in the absence and presence of cd₁NiR.

As a pre-requisite for the investigation of possible interference of electron donation caused by cd₁NiR binding to cNOR, we determined the K_m for cytochrome c (horse heart) during NO reduction by cNOR. For these titrations, we always used the maximum activity, k_max at ~5 µM NO. The results are shown in Fig. 3a and can be fitted with a k_max = 6 ± 1 e⁻s⁻¹ (electrons/(s•cNOR)) and K_m = 0.8 ± 0.3 µM. As seen in this graph, the data is scattered and the standard deviation in the K_m quite large. We therefore instead measured the activity with cNOR reconstituted into liposomes. The aim of this was two-fold, first the activity of P. denitrificans cNOR is higher in liposomes^17,28, giving us a larger total change in activity during titration and hence smaller relative errors. Secondly, the presence of a membrane might influence a putative cNOR-cd₁NiR interaction, as suggested for the P. aeruginosa complex²⁴. In liposome-reconstituted cNOR, we determined the k_max to 15 ± 1 e⁻s⁻¹ and the K_m for cyt. c to 0.8 ± 0.2 µM (Fig. 3a), i.e. no change in K_m was observed.

Figure 3

Determinations of the K_m for cytochrome c for NO reduction by cNOR. (a) Comparison between cNOR in detergent (blue) and reconstituted in liposomes (grey). Experimental conditions as in Fig. 2, except for with liposomes, DDM was omitted. cNOR activity refers to the k_max at ~5 µM NO with the k_max obtained without cyt. c subtracted. The lines shown are fits giving k_cat = 6 ± 1 (e^-/(s•cNOR)), K_m = 0.8 ± 0.3 µM cyt. c (blue, detergent) and k_cat = 15 ± 1 (e^-/(s•cNOR)), K_m = 0.8 ± 0.2 µM cyt. c (dark grey, liposomes). (b) Comparison between liposome-reconstituted cNOR in the absence (black) and presence (red) of cd₁NiR. cNOR activity refers to the k_max at ~5 µM NO, with the k_max at 3 µM cyt. c in the absence of cd₁NiR set at 100%. The curves were fitted as in a, giving K_m = 0.20 ± 0.05 µM cyt. c (black, cNOR only) and k_cat = 46 ± 4%, K_m = 0.15 ± 0.05 µM cyt. c (red, + cd₁NiR). Experimental conditions as in (a).

Side by side experiments were conducted to determine the K_m for cyt. c of liposome-reconstituted cNOR in the absence or presence of ∼30 nM cd₁NiR (Fig. 3b). This is the cd₁NiR concentration which maximally inhibits detergent-solubilized cNOR (Fig. 2b; see also corresponding data for liposome-reconstituted cNOR in Supporting Fig. 2). Surprisingly the observed K_m was unchanged in the presence of cd₁NiR (K_m = 0.15 ± 0.05 µM) compared to the control (K_m = 0.20 ± 0.05 µM) as shown in Fig. 3b. However, the relative k_max in the presence of cd₁NiR was ~50% of the control. Thus, only the k_max and not the K_m value is affected, indicating that the cd₁NiR and cyt. c do not bind at the same place to cNOR.

We note that the K_m value determined (in the absence of cd₁NiR) in this experiment is different from that determined in the previous experiment (Fig. 3a). This is probably due to the K_m values being low and therefore the data obtained possibly not represented well by a simple Michaelis-Menten fit. Also, the concentration of cd₁NiR is about equimolar to cNOR and small differences in the relative concentrations between experiments might affect the data. These considerations are the reasons for doing comparative experiments ‘side-by-side’.

Since the K_m for cyt. c does not change significantly in the presence of cd₁NiR, we scrutinized the raw data used for Fig. 3b, and re-plotted it without subtracting the background rate (with Ascorbate (Asc)/tetramethyl-p-phenylenediamine (TMPD)) (see Supporting Fig. 3A). This shows that there is inhibition of the basal activity by cd₁NiR with only Asc/TMPD to provide electrons that does not change significantly when cyt. c is added. This observation suggests that cd₁NiR inhibits the electron donation from TMPD rather than that from cyt. c. To verify this, we studied the effect of titrating cd₁NiR on cNOR catalysis in the absence of TMPD (with only cyt. c and Asc), see Supporting Fig. 3B which shows that in the absence of TMPD, there is no inhibition.

We then studied the cNOR activity as a function of the TMPD concentration (with ascorbate, but in the absence of cyt. c), both in the absence and presence of cd₁NiR, see Fig. 4. Here there is a clear inhibition by cd₁NiR. The data indicates that there might be more than one interaction with TMPD, but assuming a single binding site, the obtained constants are; in the absence of cd₁NiR: k_max = 31 ± 2 e⁻s⁻¹ and K_m = 1.2 ± 0.2 mM, and in the presence of cd₁NiR: k_max = 12 ± 2 e⁻s⁻¹ and K_m = 0.7 ± 0.2 mM. In this scenario, both the k_max and K_m are affected (so-called mixed inhibition). Our data does not allow for any unambigous fit to a more complex behaviour.

Figure 4

Determination of the K_m for TMPD for NO reduction by liposome-reconstituted cNOR in the absence (black) and presence (red) of cd₁NiR. Experimental conditions, and data treated as in Fig. 3. The black line is a single-hyperbolic fit to the cNOR data giving k_cat = 31 ± 3 (e⁻/(s•cNOR)), K_m = 1.2 ± 0.2 mM TMPD. The red line is the same fit for the cNOR + cd₁NiR data, giving k_cat = 10 ± 2 (e⁻/(s•cNOR)), K_m = 0.6 ± 0.2 mM TMPD.

We also observe inhibition by cd₁NiR when PMS is used as an electron mediator instead of TMPD (see Supporting Fig. 4). Thus, there is an inhibition of cNOR activity by the presence of cd₁NiR with both TMPD and PMS, indicating that the interaction surface (or part of it, cf. the data with TMPD) on cNOR is similar for TMPD and PMS, and that this surface overlaps with cd₁NiR binding.

As controls for the measurements described above, we studied the possibility that TMPD directly affects auto-reduction of NO, as well as the possibility that small amounts of nitrite formed (from NO) in the buffer could have effects interfering with our results. However, we found no effects that were significant enough to influence the data presented. For nitrite, we see that it can inhibit cNOR activity, but only at high (mM) concentrations, consistent with previous studies²⁹.

Substrate inhibition in cNOR in the presence of cd ₁NiR

As described above, adding cd₁NiR during NO-reduction by cNOR has two effects; both reducing the maximum activity investigated above, and in changing the pattern of substrate inhibition, see Fig. 2 and Fig. S1. Thus, a plot of the NO concentration where k_max/2 is reached as a function of cd₁NiR added is shown in Fig. 2b (together with the corresponding effects on the k_max). Note that this refers to the NO concentration at higher NO (than that which gives k_max) where k_max/2 is reached, and therefore refers to an apparent K_i (rather than an apparent K_m). We note that the decrease in maximum rate at low cd₁NiR correlates well to the decrease in the K_i^app for NO (that is a higher apparent affinity for NO at an inhibitory site), whereas the K_i^app for NO then roughly saturates at ~40 nM cd₁NiR. It is thus clear that even though the inhibition on the maximum rate is released at higher cd₁NiR, there is still an influence also at higher cd₁NiR concentrations, indicating an interaction between cNOR and cd₁NiR that persists (see Discussion).

SDS page analysis for localization of cd ₁NiR in P. denitrificans

To investigate the localization of cd₁NiR in P. denitrificans cells grown under denitrifying conditions, cells were fractionated, and the presence of cd₁NiR analyzed using Western blot with a specific antibody for cd₁NiR. The results, shown in Supporting Fig. 5, demonstrate that although cd₁NiR is present mainly in the periplasm, it is also found in the membrane fraction. We investigated many different conditions for this analysis including different detergents and ionic strength, but although using a milder detergent (digitonin) for solubilisation of the membrane fraction gave a somewhat larger fraction of cd₁NiR bound to it, this fraction is still small, see Discussion.

Figure 5

Fluorescently labeled cNOR (ATTO 594) and cd₁NiR (STAR 635) visualized with a laser scanning confocal microscope. (a) cNOR was reconstituted in giant unilamellar vesicles (GUVs) and cd₁NiR was added to the GUV solution. cNOR was detected in the membrane (green GUV) and cd₁NiR was found to be highly associated with the membrane (red GUV). (b) Fluorescence intensity scan across the membrane (Z-plane), from the inside (−) to the outside (+) of a GUV after adding cd₁NiR or BSA, labeled with STAR 635. cd₁NiR (in contrast to BSA) is highly enriched at the membrane surface. For experimental conditions, see Material and Methods.

Interactions of cd ₁NIR and cNOR investigated by fluorescence spectroscopy

Purified cd₁NiR and cNOR proteins were fluorescently labeled with ATTO 594 and STAR 635, respectively. cNOR was successfully reconstituted in giant unilamellar vesicles (GUVs), anchored to a biotin-covered glass surface imaged using a confocal laser scanning microscope (see Fig. 5a, green GUVs). cd₁NiR was then added in equimolar concentration (to cNOR) to the GUV solution. The cd₁NiR was also added to ‘empty’ GUVs. The cd₁NiR was found to be highly associated with the membrane (Fig. 5a, red GUV). A scan across the membrane (Z-plane, Fig. 5b) showed an increase in fluorescence intensity in the membrane plane (Z = 0), i.e. the concentration of cd₁NiR is higher at the membrane surface than in the surrounding solution. A control with STAR 635-labeled BSA protein (Fig. 5b) showed no such increase in the membrane plane.

The possible interaction between cd₁NiR and cNOR was then assayed using fluorescence correlation spectroscopy (FCS, see Methods) in combination with the confocal setup. First, we measured FCS on the reconstituted cNOR-ATTO 594 and cd₁NiR-STAR 635 simultaneously on the membrane surface and looked for interaction by using two-color FCS and cross-correlation analysis (FCCS). However, no significant interaction could be distinguished by this approach (Supporting Fig. 6). In agreement with this, there was no significant difference in the degree of cd₁NiR binding between the GUVs with or without cNOR reconstituted.

Figure 6

Interactions between cd₁NiR and liposomes, cNOR-liposomes and native membranes. (a) Fluorescence autocorrelation curves measured on a sample containing 5 nM cd₁NiR-STAR 635 (red), and after addition of LUVs containing 2.5 nM cNOR (green). The dashed (black) line is a fit of the data using a model with two diffusion times. As references, measurements of a sample containing free dye STAR 635 (red dotted line) and a sample with LUVs containing cNOR labelled with ATTO 594 are also shown. (b) Titration of 5 nM cd₁NiR-STAR 635 with increasing concentrations of LUVs containing unlabeled cNOR in buffer containing 2 mM KCl (black) or 100 mM KCl (green), and titration with the same amount of LUVs without protein (white). The plot shows the amplitude of the slow component where F_max has been set to 1. The data for LUVs with and without protein were fitted with a simple binding model (see text for details). (c) FCS curves from titration experiments with native membranes from P. denitrificans grown under aerobic (green) or anaerobic denitrifying (red) conditions. Sonicated membranes were added to a solution of 50 nM cd₁NiR-STAR 635 (black dotted line). A sample with DOPC-liposomes produced in the same way containing cNOR labelled with ATTO 594 is shown as reference (black line).

To further probe potential interactions, cNOR was reconstituted in DOPC liposomes (LUVs) and the interaction with cd₁NiR was assayed by monitoring changes in diffusion of labelled cd₁NiR upon binding. The diffusion time of the liposomes containing cNOR labelled with ATTO 594 was 2.6 ms determined with FCS (Fig. 6b, black trace). This would correspond to a liposome size of approximately 90 nm (corresponding well to the 100 nm expected from the LUV-forming protocol). Liposomes containing unlabeled cNOR were added in increasing concentrations to a solution containing 5 nM cd₁NiR-STAR 635. The diffusion of cd₁NiR-STAR 635 alone was 0.34 ms, corresponding to a hydrodynamic radius of ~100 Å. The addition of liposomes changed the apparent diffusion time of cd₁NiR indicating that cd₁NiR binds to the LUVs containing cNOR (Fig. 6). The fraction of bound cd₁NiR was determined by fitting the FCS data with a two-component diffusion model (Eq. 1), where the amplitude of the component with a long (2.6 ms) diffusion time was taken to represent liposome-bound cd₁NiR. The amplitudes of the 2.6 ms component (Fig. 6b) were fitted with a simple ligand-binding model (Eq. 2). The same experiment was repeated with ‘empty’ LUVs, and the binding constant for liposome binding to cd₁NiR, compared on the basis of lipid concentration, was ~13 ± 1 μM with and ~22 ± 2 μM (see Fig. 6b) without cNOR present in the membrane. This difference is likely within the experimental uncertainties and cd₁NiR has a similar, rather high, affinity to the liposomes independently of the presence or absence of cNOR.

We also increased the ionic strength in the buffer from 2 to 100 mM (KCl) in order to shield purely electrostatic interactions between cd₁NiR and the membrane. However, no decrease in the fraction bound cd₁NiR was observed (green circles in Fig. 6b) which indicates that the association of cd₁NiR to the DOPC membrane is not purely electrostatic in nature (see Discussion).

Although diffusion of both cd₁NiR and cNOR was detected when measuring FCS on the GUV membrane surface, there was no interaction observed using cross-correlation analysis. Thus, neither the titration experiment using small liposomes, nor the FCCS, measured directly on the membrane surface, could detect an interaction between cd₁NiR and cNOR going beyond the interaction between cd₁NiR and the membrane under these experimental conditions. However, it should be noted that the rather high-affinity interaction between cd₁NiR and the DOPC liposomes themselves might ‘hide’ a relatively weak interaction between cNOR and cd₁NiR, see Discussion.

Since cd₁NiR showed such significant interaction with the pure DOPC liposomes, we also wanted to investigate whether an interaction between cd₁NiR and the membrane (with or without cNOR expressed) could be observed using native P. denitrificans membranes. Small membrane vesicles were made from cells grown under either aerobic or anaerobic denitrifying conditions and mixed with a solution containing 50 nM cd₁NiR-STAR 635. Although cNOR expresses only during denitrifying conditions no differences were observed. The diffusion time of cd₁NiR-STAR 635 (Fig. 6c) was partly slowed down in both cases with a fraction matching the diffusion time (~1.5 ms) of sonicated DOPC liposomes containing cNOR-ATTO 594. In both cases the slow fraction was maximum ~ 25% of the total cd₁NiR-STAR 635 population, in comparison to up to 85% when using pure DOPC liposomes. Although these fractions do not necessarily correspond directly to the fraction bound cd₁NiR, we can conclude that cd₁NiR interacts much more strongly with artificial ‘lipid-only’ liposomes than it does with native membranes, see Discussion.

Dimerization of cd ₁NiR

From the functional cNOR-catalyzed NO-reduction data presented above, the observed effect of adding increasing amounts of cd₁NiR (see Fig. 2b) made us consider that this dependence could be linked to dimerization of cd₁NiR. cd₁NiR is a dimer in the X-ray crystal structures from both P. aeruginosa^9,24 and P. denitrificans⁶ and also reported to be a dimer in solution^5,30, but to our knowledge, there is no reported value for the dimerization constant. To further investigate if there is such a cd₁NiR dimer dissociation/association in the concentration range used, we analyzed the fluorescence intensity from labeled cd₁NiR as a function of its concentration. The fluorescence intensity as well as the particle number of cd₁NiR-STAR 635 obtained by FCS (parameter N in Eq. 1) was used to determine the photon count-rate per molecule (CPM). Figure 7 shows that the CPM increases with increasing concentrations when adding cd₁NiR-STAR 635 alone. Assuming that the majority of cd₁NiR-STAR 635 is present as a monomer at very low concentrations (<1 nM) an increase in CPM at higher concentrations indicates dimerization. In comparison, the CPM of cNOR labelled with the same fluorophore (cNOR-STAR 635) showed only a small increase, indicating that there is no change in its oligomeric state in this region.

Figure 7

Fluorescence intensity (count per molecule (CPM)) when adding increasing amounts of cd₁NIR-STAR 635 to a solution with (green circles) or without (red circles) 40 nM cNOR. The fluorescence intensity measured with increasing concentrations of cNOR-STAR 635 alone is also shown (white circles). The black lines are ligand-binding fits for cd₁NiR dimerization, giving K_D = 3.5 ± 0.1 nM (without) and 5.3 ± 0.2 nM (with cNOR) respectively.

This cd₁NiR titration was done both in the presence and absence of cNOR. Interestingly, both the maximum CPM for cd₁NiR-STAR 635 and its concentration dependence changed when 40 nM cNOR (unlabeled) was present in the solution. The CPM data could be fitted using the ligand-binding model (Eq. 2) allowing for a simple comparison; the apparent binding constants for the suggested dimerization of cd₁NiR-STAR 635 was 3.5 ± 0.1 nM without and 5.3 ± 0.2 nM with cNOR present. We observed a slight decrease in CPM at cd₁NiR-STAR 635 concentrations above 15 nM, but only in the case when cNOR was not present and these data points were not included in the fit (dashed line). The maximum CPM reached was lower in the presence of cNOR, indicating either a quenching effect, or that even when dimerized, the cd₁NiR is influenced by/binds cNOR, or that there is a fraction of cd₁NiR that cannot dimerize in the presence of cNOR.

Discussion

The denitrification process is tightly controlled in P. denitrificans, in order to avoid release and accumulation of toxic intermediates; nitric oxide and (to a lesser degree) nitrite. This control occurs on the level of transcription, by a tight coupling of the expression of the enzymes involved (see e.g.^31,32). It has also been suggested that in vivo, kinetic parameters for cNOR are significantly different from those obtained in vitro, with e.g. a very high NO affinity thereby helping to keep the steady-state NO levels low³. A different way to minimize toxic intermediates would be to control the enzymes themselves, by e.g. forming a functional complex between cd₁NiR and cNOR that shuttles the NO produced from cd₁NiR directly to cNOR without release into the bulk phase. Support for this hypothesis was recently presented in the form of a co-complex structure of the cd₁NiR and cNOR from P. aeruginosa obtained from separately purified components²⁴, see Fig. 1. It should be noted that in aerobic respiration in both eukaryotes and prokaryotes, supercomplexes of individual enzyme components involved are frequently found (see e.g.^22,23,33 and references therein).

In this work, we investigated the possibility of a cNOR/cd₁NiR complex for P. denitrificans, a denitrification model bacterium. The two enzymes cd₁NiR and cNOR from P. denitrificans share 48% (cNOR) and 61% (cd₁NiR) overall sequence identity with their counterparts from P. aeruginosa. We purified the cd₁NiR from Paracoccus pantotrophus and not denitrificans, but these two enzymes are 97% identical.

The addition of cd₁NiR during NO-reduction by cNOR shows some intriguing effects. First, both the substrate inhibition pattern and maximum rate of NO reduction is affected by cd₁NiR (Fig. 2). Since both these parameters are presumed to be linked to the effective electron donation (see ref. ³⁴ for a discussion on substrate inhibition), it seems plausible that a complex of cd₁NiR and cNOR forms and that the complex interface interferes with the access of the electron donor to cNOR. This conclusion is supported by the co-crystallised Ps. aeruginosa cd₁NiR/cNOR complex²⁴, which shows that the cd₁NiR interacts with the NorC subunit (see Fig. 1) that harbors the initial electron acceptor (a heme c) of cNOR. As is clear from Fig. 3b (and Supporting Fig. 3) however, the observed K_m for cyt. c does not change in the presence of cd₁NiR but direct electron donation by TMPD is clearly affected (see Fig. 4). Although we have not used the presumed physiological c⁵⁵⁰ cytochrome^7,35, but the readily available horse heart (hh) cyt. c, the structures align very well and hh cyt. c works well as electron donor to cNOR. The small TMPD molecule (MW: 164 g/mol) presumably has a less defined or multiple interaction surfaces on cNOR, as indicated by our titration data (Fig. 4), and these (or some of them) presumably overlap with the interaction surface for cd₁NiR. We also observe inhibition by the presence of cd₁NiR with the electron mediator PMS (instead of TMPD, see Supporting Fig. 4).

An interesting parallel is that the antibody used for crystallisation of the Ps. aeruginosa cNOR (only)²¹, was shown to interfere with electron donation from cytochrome c, but not from PMS²¹. The binding site for this antibody has some, albeit small, overlap with the binding of cd₁NiR in the co-crystal complex²⁴.

The inhibition of cNOR activity observed upon addition of cd₁NiR shows a clear correlation in extent to the concentration of added cd₁NiR up until approximately equimolar amounts to cNOR (20–40 nM), but at higher concentrations of cd₁NiR, the inhibition is relieved. This is a surprising but highly reproducible observation which we suggest could be due to an effect of dimerization of cd₁NiR, which is purified and crystallized in the dimeric form both in P. pantotrophus⁶ and P. aeruginosa⁹. Our fluorescence intensity measurements with labeled cd₁NiR showed a fluorescence ‘count-rate per particle’ (CPM) increase (Fig. 7), consistent with dimerization with an apparent K_D of ~3.5 nM. To our knowledge, an apparent dimerization constant for cd₁NiR has not previously been determined. In the P. aeruginosa cd₁NiR dimer there is domain ‘swapping’ between the monomers, leading to a presumably obligatory dimer, whereas no such swapping occurs in the P. pantotrophus (and hence denitrificans) cd₁NiR. This difference is likely to affect the stability of the dimer and also the propensity to interact with cNOR. Also consistent with our functional data is that this K_D is affected (increases) in the presence of cNOR, from 3.5 nM to ~5 nM, supporting an interaction between cNOR and cd₁NiR in the same concentration range as used in the functional assay. The total CPM for cd₁NiR is also affected by cNOR, and the 40 nM cNOR used in this experiment might not be enough to saturate the effects, such that the influence of cNOR for cd₁NiR dimerization might be somewhat underestimated.

The Ps. aeruginosa co-complex structure, where each cd₁NiR monomer binds a cNOR on opposite ‘ends’ (Fig. 1) is a structure that cannot be formed in vivo because of the restrictions imposed by the cytoplasmic membrane. This is thus consistent with a cNOR/cd₁NiR interaction that is stronger when both proteins are in their monomeric forms. In this context, we do see differences in the inhibition patterns when adding cd₁NiR to cNOR in detergent versus in liposomes, but qualitatively, the results are similar (see Supporting Fig. 2).

Although the effect cd₁NiR has on the maximum rate of NO-reduction was interpreted above in terms of only occurring for the monomer of cd₁NiR, even at higher cd₁NiR concentrations (i.e. when cd₁NiR is predominantly a dimer) it still influences cNOR catalysis as seen in the plots of the K_i^app (Fig. 2b). A possible interpretation for this is that cd₁NiR still interacts with cNOR even in its dimeric form, but that the interaction surface changes. It’s also possible that the effect on the cNOR substrate inhibition pattern originates from structural changes occurring in cd₁NiR itself as a response to changes in [NO] or in reduction levels (as seen in³⁶, see below).

Even though there are clear influences on the function of cNOR by the presence of cd₁NiR, we could not find evidence for a high-affinity, constant complex between the P. denitrificans cd₁NiR and cNOR, as indicated e.g. by the Western Blot results (Supporting Fig. 5) and the lack of clear differences between the interactions of (fluorescently labeled) cd₁NiR with either the native aerobic or anaerobic (denitrifying) P. denitrificans membranes shown in Fig. 6c. Interpreting this data is complicated by the observation that there is a rather high affinity of the cd₁NiR for lipid membranes (see Figs. 5 and 6), as reported also previously^37,38. This interaction is not purely electrostatic in nature, whereas only electrostatic interactions between the d₁ domain and the membrane were discussed for the P. aeruginosa cd₁NiR-cNOR co-complex simulations²⁴. An interaction between cd₁NiR and the cytoplasmic membrane would enable the NO produced to directly dissolve into the membrane bilayer from which it can migrate to the gas channel in cNOR (see Fig. 1) without equilibrating with the bulk water phase even with no direct contact between the two enzymes.

Since a co-complex structure of cd₁NiR-cNOR exists only for the P. aeruginosa proteins, we overlayed the potential interaction between the two homologous proteins from P. denitrificans. For the P. denitrificans cNOR, we constructed a model based on the P. aeruginosa structure (to which it has 54% (NorB) and 47% (NorC) sequence identity), as shown in Supporting Fig. 8A, and the Glu-119 of P. aeruginosa cNOR that forms the main interaction with the P. aeruginosa cd₁NiR overlays well with the corresponding Asp-123 in P. denitrificans cNOR. However, the P. pantotrophus cd₁NiR structure (sequence identity 97% to P. denitrificans cd₁NiR) shows significant differences to the cd₁NiR from P. aeruginosa, and there is no Arg equivalent to the R-96 (numbering from our alignment (Supporting Fig. 7), corresponds to the R-71 in the alignment from Terasaka et al.²⁴) that interacts with the E-119 on cNOR (in P. denitrificans and P. pantotrophus cd₁NiR, the corresponding residue is a Leu). The structural overlay of the P. pantotrophus and P. aeruginosa cd₁NiRs (see Supporting Fig. 8B) further shows that the cyt. c domain is more different than the d₁ domain and specifically the region on cd₁NiR that is interacting with cNOR in the Ps. aeruginosa co-crystal structure is markedly different in P. pantotrophus cd₁NiR, there is a small N-terminal helix that would ‘clash’ with the cNOR, as shown in Fig. 8, whereas in Ps. aeruginosa cd₁NiR, the N-terminal is involved in ‘domain swapping’ and forms part of the d₁ domain (see Supporting Fig. 8C).

Figure 8

(a) The model of the P. denitrificans cNOR (NorB in magenta, NorC in salmon) and the P. pantotrophus cd₁NiR monomer structure (blue, PDB ID: 1QKS⁶) overlapped on the cd₁NiR/cNOR co-complex structure from P. aeruginosa (PDB ID: 5GUW²⁴ (not shown)). The cd₁NiR helix that interacts with NorC (in the co-complex) in light blue and the ‘extra’ N-terminal helix in purple. Note that this ‘extra’ helix would clash into the NOR/NiR interface. Shown is also the D123 (stick) of NorC (equivalent to the E-119 in Ps. aeruginosa) and the heme groups of the proteins. (b) Zoom-in of interface. The picture outlines also the surface (transparent) of the proteins except for the ‘extra’ helix.

However, it is also known that the P. pantotrophus cd₁NiR c domain structure is significantly different in the reduced state³⁶, and thus suggested to undergo large-scale conformational changes upon reduction (Supporting Fig. 9). Such changes could affect both the cNOR interaction and the dimerization constant, since the c domain of cd₁NiR ‘swings’ out of dimer contact in the reduced state. It is difficult to predict what would happen to a putative cd₁NiR/cNOR complex when cd₁NiR is reduced since the N-terminal ‘clashing’ helix (Fig. 8), is not even resolved in the reduced cd₁NiR structure³⁶, and there is hardly any overlap between the oxidised and reduced c domain structures (Supporting Fig. 9). Presumably the interaction between P. denitrificans cNOR and cd₁NiR, if it occurs using a similar interaction surface as in Ps. aeruginosa, would affect this cd₁NiR conformational change and hence could be involved in controlling cd₁NiR activity. We also note that in our functional cNOR assays, cd₁NiR is presumably predominantly in the reduced state (depending on if it has turned over, see³⁹) since there is an excess reductant and no nitrite added.

So, are there physiological consequences of having an interaction between the cd₁NiR monomer and cNOR that becomes much less pronounced once the cd₁NiR dimerizes? It is possible that such regulation on the enzyme level (on top of the major transcriptional regulation) is there to fine tune flux through denitrification in response to rapidly fluctuating environmental conditions and is especially important when expression levels are low.

Materials and Methods

cd ₁NiR; growth of bacteria and purification

Paracoccus pantotrophus (G6) was grown anaerobically and cd₁NiR purified essentially as in⁵. Briefly, bacteria were grown until OD₆₀₀ ~0.8 in a medium containing nitrate as electron acceptor and acetate as carbon source, supplemented with 50 µg/ml kanamycin. To obtain the periplasmic fraction, the cell pellet was resuspended in 200 mL buffer containing 0.5 M sucrose, 3 mM EDTA, 100 mM Tris-HCl, pH 8.0, and 400 mg of lysozyme was added. The solution was then incubated with constant stirring at 30 °C for 40 minutes. The cell solution was then centrifuged at 25000 g for 10 min. The supernatant (containing the periplasm) was applied to a DEAE anionic-exchange column (GE Healthcare), from which bound fractions were eluted with a 0–300 mM NaCl gradient in 100 mM Tris/HCl pH 8.0. The brown-colored fractions were pooled, solid ammonium sulfate was added to 40% (w/v) and the precipitated protein removed by centrifugation at 30000 g for 30 min.

The solution was applied to a phenyl-sepharose column (GE Healthcare), and a 40-0% ammonium sulfate gradient was applied. The fractions that contained pure cd₁NiR (A⁴⁰⁶/A²⁸⁰ ~1.25)⁸ were pooled and concentrated. The concentration of cd₁NiR was determined by using ε⁴¹⁸ = 268 mM⁻¹ cm⁻¹. For antibody generation the enzyme was further purified using size exclusion chromatography in 100 mM Tris/HCl pH 7.0 on a Superose 10/300 column (GE-Healthcare).

cNOR; growth of bacteria, protein purification and model building

Purification of cNOR (P. denitrificans overexpressed in E. coli) was performed as described in¹⁸, based on the original protocol from⁴⁰. Briefly, the plasmid pNOREX was transformed in to a JM109 strain which contained the pEC86 vector⁴⁰. cNOR expression was induced by IPTG. The membranes were solubilized in 100 mM Tris, pH 7.6, 50 mM NaCl, 1 mM EDTA and 1% n-dodecyl-β-D-maltoside (DDM). The membrane solution was incubated with constant stirring for 1 hour at 4 °C. The unsolubilized membranes were removed by centrifugation, and the supernatant was applied to a Q-Sepharose high performance (GE-HealthCare) column, which was equilibrated in 20 mM Tris/HCl pH 7.6, 0.04% DDM and 5 mM NaCl. The column was washed with the same buffer but containing 250 mM NaCl and cNOR was eluted with a 250 mM-500 mM NaCl gradient in 20 mM Tris/HCl pH 7.6, 0.04% DDM.

The pure fractions of cNOR were pooled, diluted 3 times in 100 mM Tris/HCl, 50 mM NaCl, and the concentration of NaCl was lowered to below 50 mM by repeated dilution and reconcentration in concentrating vials (Millipore Merck, Ltd). Aliquots were flash frozen in liquid nitrogen and stored in −80 °C.

The structural model of P. denitrificans cNOR was constructed with SWISS-MODEL (https://swissmodel.expasy.org) using the default parameters and refinement procedure. The crystal structure of Pseudomonas aeruginosa cNOR (PDB ID: 3o0r²¹, sequence identity 54% for NorB and 47% for NorC) was used as the structural template. The P. denitrificans cNOR could also be modelled on the Roseobacter denitrificans cNOR (sequence identity 75% for NorB and 69% for NorC) structure⁴¹, but since this cNOR, unlike P. denitrificans cNOR, was found to bind a Cu⁺ ion in the NorC subunit, which could potentially influence the region around the presumed interaction with cd₁NiR, we chose to use the P. aeruginosa cNOR–derived model.

Detection of cd ₁NiR in anaerobically grown (on nitrate) P. denitrificans cells

P. denitrificans (Pd1222) cells were grown anaerobically on nitrate (32 mM) as electron acceptor at 37 °C, the cells were harvested and the periplasm was obtained by osmotic shock as described above. The pellet was sonicated, and the membranes were extracted by high-speed centrifugation (100 000 g). The different cell components (whole cell, periplasm (PL) and membrane (M) fractions) were subjected to SDS-PAGE (Invitrogen, 4–12%) analysis followed by Western blot using a PDVF membrane and an antibody against cd₁NiR, obtained from Biogenes GmbH (Germany).

Protein reconstitution in vesicles

For the generation of small unilamellar vesicles (SUVs), a solution of 40 mg/ml soybean lipids in 50 mM Tris/HCl pH 7.0, 50 mM KCl was sonicated until it became clear. 2–4 µM cNOR was added to the liposomes in the presence of 0.6% Na-cholate and the mixture was incubated for 1 hour at 22 °C. The detergent was then removed on a PD-10 column (GE-Healthcare). For generation of large unilamellar vesicles (LUVs), DOPC (1,2-dioleoyl-sn-glycero-3-phosphocholine) lipids dissolved in CHCl₃ were dried and then rehydrated to 2 mM in a 10 mM phosphate buffer (pH 7.4) with 2 mM KCl. Unilammelar liposomes were made by passing the lipid solution trough a filter with a 100 nm pore size 21 times. cNOR was reconstituted into the liposomes by gently solubilizing the vesicles with 0.6% Na-Cholate before adding the protein at a 10:1 molar ratio (protein: liposome), giving a protein to lipid ratio of ca. 1:3500 in the outer monolayer. The detergent was then slowly removed by dialysis at 4 °C over night.

For generation of giant unilamellar vesicles (GUVs), a 1 mM stock solution of DOPC supplemented with 1% DPPE-biotinyl (2-dioleoyl-sn-glycero-3-phosphoethanolamine-N-biotinyl) (Avanti Polar Lipids) was used according to the procedure described in⁴². cNOR labelled with ATTO 594 (see below) was reconstituted into the GUVs using a mild detergent treatment with DDM; the protein solution containing 1 mM DDM was mixed with 20 μl GUV-solution to a final concentration of 0.05–0.25 μM protein and 0.05 mM DDM and incubated at room temperature for 30 min. The proteo-GUVs were then diluted 20 times in a 100 mM buffered glucose solution (10 mM phosphate buffer pH 7.4, 2 mM KCl) and transferred to a LabTek microscope chamber coated with streptavidin and further incubated at room temperature for 2 h. The dilution gave a final detergent concentration of 2.5 μM DDM in the sample.

Steady-state activity measurements

The interaction between cNOR and cd₁NiR was investigated by studying the multiple turnover activity of cNOR, either in detergent (0.05% DDM) or incorporated in vesicles, using a Clark-type electrode (World Precision Instruments, WPi) as in¹⁸. Briefly, the activity was measured in 50 mM HEPES at pH 7.0 with 50 mM KCl at room temperature. The buffer in the reaction chamber (total volume = 1 ml) was made anaerobic by adding the glucose (30 mM)/glucose oxidase (1 U/ml)/catalase (20 U/ml) system. Substrates were added with a syringe in the following order, horse heart (hh) cyt. c (varying concentrations), TMPD at varying concentrations, 5 equal additions of 10 µM NO (from NO-saturated water), and 3 mM sodium ascorbate. cNOR was added at various concentrations (20–80 nM) either prior to (cNOR in vesicles) or after all substrate additions (detergent solubilized). cd₁NIR was added prior to the addition of NO, when specified. The data was recorded with the LabScribe2 software (WPi), and the maximum NO-reduction rate was calculated (at ~5 µM NO).

Fluorescence labelling

cd₁NiR and cNOR were fluorescently labelled using amino-reactive dyes. The protein concentration was set to 3 mg/ml and a 1/20 volume of NaHCO₃ (pH 9.0) was added. cd₁NiR was labelled with a 5-fold molar excess of Abberior STAR 635 (Abberior GmbH) and cNOR was labelled with a 3-fold molar excess of ATTO 594 (ATTO Tec GmbH) by incubating at room temperature while gently shaking for 1.5 h. Unbound dye was removed using a PD-10 column (GE Healthcare), equilibrated with a 10 mM phosphate buffer (pH 7.4) supplemented with 100 mM sucrose, 2 mM KCl and 1 mM (~0.05%) DDM.

Fluorescence correlation spectroscopy (FCS) measurements and analyses

FCS measurements were performed on an instrument from Abberior Instruments (Göttingen, Germany), built on a stand from Olympus (IX83), and modified for two-color imaging (see⁴² for a detailed desciption of the experimental set up). Two fiber-coupled, pulsed (20 MHz) diode lasers emitting at 637 nm (PicoQuant AG, Berlin) and 594 nm (Abberior Instruments) were used for excitation, with the excitation pulses of the two lasers out of phase, to minimize cross-talk and enable fluorescence cross correlation of cd₁NiR-STAR 635 on the membrane surface of the GUVs containing cNOR-ATTO 595. For details on the correlation and cross correlation analysis, see^42,43.

The diffusion time of cd₁NiR-STAR 635 (5 nM) was determined with FCS in the presence of increasing concentration of LUVs, with or without reconstituted cNOR. Normalized autocorrelation curves of the recorded fluorescence intensity fluctuations, G(τ), were calculated using a MatLab script, and the recorded G(τ) curves were then fitted using a model for 3D-diffusion, including two diffusional components and a population of a non-fluorescent triplet state (T) with a relaxation time τ_T:

$$G(\tau )=\frac{1}{N(1-T)}\times a[{[1+\frac{\tau }{{\tau }_{D1}}]}^{-1}{[1+\frac{\tau }{{\beta }^{2}{\tau }_{D1}}]}^{-1/2}]+b[{[1+\frac{\tau }{{\tau }_{D2}}]}^{-1}{[1+\frac{\tau }{{\beta }^{2}{\tau }_{D2}}]}^{-1/2}]\times [1-T+T{e}^{-\frac{\tau }{{\tau }_{T}}}]$$

(1)

Here, τ_D1 is the diffusion time of free cd₁NiR-STAR 635 and τ_D2 is the diffusion time of LUV-bound cd₁NiR-STAR 635. β = ω₂/ω_1, where ω₂ and ω₁ denote the 1/e² extension of the FCS detection volume in along and perpendicular to the excitation beam direction, respectively. N is the average number of fluorescent molecules in the detection volume, and a and b the fractions of fluorescent molecules belonging to each of the two different diffusion components (with a + b = 1) The amplitudes of the component with diffusion time τ_D2 were fitted with the binding model:

$${F}_{m}=\frac{{F}_{m}^{{\rm{\max }}}\times {c}_{{\rm{sol}}}}{{K}_{D}+{c}_{{\rm{sol}}}}$$

(2)

where F_m represents fraction of liposomes bound to cd₁NiR-STAR 635, c_sol represents non-bound liposomes (plotted as number of free lipids), and K_D is the binding constant defined by the concentration at which half of the liposomes are bound (F_m = 0.5). The value of ${F}_{m}^{max}$ was set to unity.