2.1 ATPase activities The dependence of the ATPase activity on the concentration of GSSG was measured for NaAtm1 reconstituted under three different conditions: a detergent mixture composed of 0.05% DDM and 0.05% C12E8 used in the crystallization studies.13, 14 nanodiscs composed of the membrane scaffolding protein MSP1D1 and the phospholipid 1-palmitoyl-2- oleoyl-glycero-3-phosphocholine (POPC).16 proteoliposomes composed of E.coli polar lipids and 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC).17 The ATPase rates were measured in sextuplicate for the detergent and proteoliposome samples, and triplicate for the nanodisc sample under varying concentrations of MgATP (8 concentrations: 0, 0.1, 0.2, 0.5, 1, 2, 5, and 10 mM) and GSSG (6 concentrations, 0, 1, 2.5, 5, 10, and 20 mM). The ATPase rate was measured by quantifying the amount of inorganic phosphate (Pi) released upon ATP hydrolysis over a 15-min period using a molybdate based colorimetric assay.18 For a given GSSG concentration, the dependence of the ATPase activity on (MgATP) was modeled by a Michaelis–Menten (hyperbolic) equation (Figure 1), yielding kcat and Km for ATP hydrolysis as a function of GSSG concentration (Table S1). In the absence of GSSG, the values of kcat characterizing the basal (uncoupled) ATPase rate were determined to be 18.0 ± 0.4, 30.9 ± 0.7, and 9.5 ± 0.4 min−1 in detergent, nanodiscs, and proteoliposomes, respectively. As the orientation effect in proteoliposomes was not taken into account, the actual ATPase rate in proteoliposomes may be ~2 times of the measured activity, or ~19 min−1. In each system, GSSG was observed to stimulate the ATPase activity of NaAtm1 in a concentration dependent fashion (Figure 1 and Table S1). The magnitude of the stimulation was dependent on the reconstitution conditions, as the kcats in 20 mM GSSG were increased above the basal rate in the absence of GSSG by factors of ~5, 14, and 11 (Table S1a), in detergent, nanodiscs, and proteoliposomes, respectively. Less pronounced, but statistically significant changes in Km were also observed between 0 and 20 mM GSSG, corresponding to a decrease of ~20% in detergent, and increases of 2.7 times and 1.9 times for nanodiscs and proteoliposomes, respectively (Table S1b).

Fit of the ATPase activities of NaAtm1 to the Michaelis–Menten kinetic model. ATPase activities of NaAtm1 as a function of (MgATP) in (a) detergent (DDM/C12E8), (b) nanodiscs, and (c) proteoliposomes, with stimulations by GSSG at various concentrations. ATPase activities of NaAtm1 in detergent and PLS were measured six times, and three times in nanodiscs, all with distinct samples. All of the extrapolated Vmax values are shown next to each GSSG concentration curve. Error bars represent the standard error of the mean for the replicates

2.2 Basic nonessential activator kinetic model To model this data, we used a nonessential activator model (Figure 2a), a steady-state, equilibrium binding model where the transported substrate GSSG is an activator that stimulates the ATPase rate above the basal level.19, 20 The key kinetic parameters in this model are: KT, the Michaelis binding constant for MgATP, KS, the Michaelis binding constant for the transported substrate, GSSG, which is also an activator of the ATPase rate, α, the interaction factor for how binding of MgATP influences the binding of GSSG (and vice versa); α < 1 or > 1 denote positive and negative cooperativity, respectively, k, the basal rate constant for MgATP hydrolysis in the absence of GSSG, and β, the acceleration factor for MgATP hydrolysis with bound GSSG. In this basic model, the ATPase sites are treated as independent since the dependence of the ATPase rate on ATP is reasonably well approximated by the hyperbolic Michaelis–Menten equation, except possibly at the lowest concentrations of ATP where some evidence for cooperativity was observed. For this scheme, expressions for the overall velocity, kobs and KTapp, may be derived (where ET denotes the total concentration of transporter).

v=ETkTKT+βSTαKSKT1+TKT+SKS+STαKSKT.(1)

kobs=k1+βSαKS1+SαKS.(2)

KTapp=KT1+SKS1+SαKS.(3)

The parameters (k, KT, KS, α, and β) of the nonessential activator model (Equation (1), Table 1) were fit against the 48 measured ATPase rates as a function of ATP and GSSG concentrations in detergent, nanodiscs, and proteoliposomes. The basal turnover rates observed for saturating MgATP in the absence of GSSG, k, were determined to be 17.6 min−1 in detergent, 32 min−1 in nanodiscs and 9 min−1 in proteoliposomes (Table 1), with the binding affinities of MgATP, KT), measured as 0.82 mM in detergent, 1.41 mM in nanodiscs and 1.6 mM in proteoliposomes. The determined values for KS, the binding constant of GSSG, were found to be ~10 mM under all reconstitution conditions. Extrapolating to saturating concentrations of GSSG, the acceleration factors β were determined to be 8.3, 77, and 29 in detergent, nanodiscs, and proteoliposomes, respectively (Table 1). With these values for the parameters of the nonessential activator model, the experimental values of kcat and Km as a function of (GSSG) were fit reasonably well (Figure 2bc), as were the fit of the individual ATPase measures as a function of MgATP and GSSG concentrations (Figure S1). Nonessential activator model of NaAtm1 ATPase kinetics. (a) Schematic of the nonessential activator kinetic model for the ATPase activities of NaAtm1. Fits of (b) the apparent rate constant, kobs, for ATP hydrolysis (Equation (2)) and (c) the Michaelis–Menten constant, KT, of MgATP binding (Equation (3)) as a function of (GSSG) based on the experimentally derived parameters (Table 1) for the nonessential activator model for NaAtm1 in detergent, nanodics, and proteoliposomes, respectively. In these schemes, E = NaAtm1, T = MgATP, D = ADP, S = GSSG, KT = binding constant for MgATP, KS = binding constants for GSSG, k = rate constant for MgATP hydrolysis, α = interaction factor of how ATP binding influences GSSG binding and vice versa, and β = acceleration factor for ATP hydrolysis with bound GSSG, Error bars represent the experimentally observed standard deviations TABLE 1. Kinetic parameters of the nonessential activator model Parameters Detergent Nanodiscs Proteoliposomes kobs (min−1) 17.58 ± 0.75 31.86 ± 1.04 9.49 ± 1.26 KT (mM) 0.82 ± 0.07 1.41 ± 0.08 1.64 ± 0.34 KS (mM) 13.34 ± 2.20 9.65 ± 0.74 12.79 ± 4.09 Αlpha (α) 1.03 ± 0.20 10.05 ± 1.73 2.64 ± 1.26 Beta (β) 8.30 ± 0.46 76.60 ± 8.68 28.69 ± 6.30 Note: Parameters calculated with the nonessential activator model shown in Figure 2 for the ATPase activities of NaAtm1 in detergent, nanodiscs, and proteoliposomes. The R2 values are in the range of 0.94 to 0.99 for the measurements in detergent, 0.99–1.00 for the measurements in nanodiscs and 0.91–0.95 for the measurements in proteoliposomes. Parameters are tabulated to two decimal places to accurately reproduce the calculations depicted in Figures 2 and S1.

The results of this analysis demonstrate the ATPase kinetics are dependent on the lipid environment, explored in this work as detergent, nanodiscs, and proteoliposomes, and that the basal ATPase rates are stimulated by GSSG under these reconstitution conditions. While the primary influence of GSSG is to accelerate kcat, the Km values for ATP are also impacted. These results provide the opportunity to explore the binding interactions between ATP and GSSG, as reflected in the cooperativity parameter α. While little cooperativity is evident in detergent (α ~ 1.025), in the lipid environment provided by reconstitution into nanodiscs and proteoliposomes, evidence for modest negative cooperativity is observed with α ~ 10 and 3, respectively. These trends are similarly reflected in the increases in KT, the Michaelis constant for ATP, between 0 and 20 mM observed for nanodiscs and proteoliposomes.

For an allosteric system described by a classical Monod–Wyman–Changeux model,21 a ligand that preferentially binds to the inactive conformation of a two-state system will function as an inhibitor. GSSG appears to bind preferentially to the inward-facing conformation of NaAtm1, while the catalytically competent conformation for ATP hydrolysis is the outward-facing conformation. Based on an equilibrium binding model, it would be anticipated that GSSG and MgATP should exhibit negative cooperativity towards each other. This expectation is reflected in the α > 1 values for NaAtm1 reconstituted in a lipid environment, corresponding to the increases in KT between 0 and 20 mM GSSG under those conditions. Nevertheless, GSSG significantly stimulates the ATPase rate, which suggests that the kinetics of forming the outward-facing conformations of NaAtm1 differ in important ways between the binary (with MgATP) and ternary (with MgATP and GSSG) complexes. A key mechanistic question is why the ternary complex has an accelerated ATPase rate. Structural studies have yet to provide any insights into this question as no structures of this ternary complex have been determined for an ABC exporter. Understanding how this species promotes ATP hydrolysis relative to the binary complex is at the heart of the coupling mechanism and emphasizes the importance of characterizing the structure and dynamics of this elusive transporter-ATP-substrate ternary state.