Kinetic analysis of the inhibition mechanism of bovine mitochondrial F₁-ATPase inhibitory protein using biochemical assay

Abstract

ATPase inhibitory factor 1 (IF₁) is a mitochondrial regulatory protein that blocks ATP hydrolysis of F₁-ATPase, by inserting its N-terminus into the rotor–stator interface of F₁-ATPase. Although previous studies have proposed a two-step model for IF₁-mediated inhibition, the underlying molecular mechanism remains unclear. Here, we analysed the kinetics of IF₁-mediated inhibition under a wide range of [ATP]s and [IF₁]s, using bovine mitochondrial IF₁ and F₁-ATPase. Typical hyperbolic curves of inhibition rates with [IF₁]s were observed at all [ATP]s tested, suggesting a two-step mechanism: the initial association of IF₁ to F₁-ATPase and the locking process, where IF₁ blocks rotation by inserting its N-terminus. The initial association was dependent on ATP. Considering two principal rotation dwells, binding dwell and catalytic dwell, in F₁-ATPase, this result means that IF₁ associates with F₁-ATPase in the catalytic-waiting state. In contrast, the isomerization process to the locking state was almost independent of ATP, suggesting that it is also independent of the F₁-ATPase state. Further, we investigated the role of Glu30 or Tyr33 of IF₁ in the two-step mechanism. Kinetic analysis showed that Glu30 is involved in the isomerization, whereas Tyr33 contributes to the initial association. Based on these findings, we propose an IF₁-mediated inhibition scheme.

Graphical Abstract

ATP synthase, also termed as F_oF₁-ATP synthase (F_oF₁), is ubiquitously found in bacterial plasma membranes, chloroplast thylakoid membranes and mitochondrial inner membranes (1–5). It catalyzes ATP synthesis from ADP and inorganic phosphate (P_i) using proton motive force (pmf) across membranes. F_oF₁-ATP synthase consists of two reversible rotary motors, F_o and F₁. F_o, the membrane-embedded portion of ATP synthase, conducts proton translocation across the membrane, whereas F₁, the water-soluble portion, contains the catalytic centre domain for ATP synthesis. In the F_oF₁ complex, F_o and F₁ are connected by the common rotary shaft and the peripheral stalk, enabling the interconversion of pmf and the chemical potential of ATP. Under physiological conditions with sufficiently high pmf level, F_o reverses the rotation of F₁, inducing ATP synthesis. When pmf is low or diminished, F₁ hydrolyzes ATP to rotate F_o in the opposite direction, resulting in active proton pumping to form pmf.

F₁ hydrolyzes ATP to ADP and P_i when isolated from F_o (6, 7). α₃β₃γ is the minimum component of a rotary molecular motor. Three α subunits and three β subunits are arranged alternately to form the α₃β₃ stator ring, of which the central rotary shaft, the γ subunit, is inserted into the central cavity (8, 9). The catalytic reaction centres are located on the αβ interface, mainly on the β subunit. During ATP hydrolysis, the γ subunit of F₁ rotates against the α₃β₃-ring in anticlockwise direction when viewed from the F_o side (5). Crystal structures of bovine mitochondrial F₁-ATPase (bMF₁) showed asymmetric features of nucleotide occupancy and the conformational states of the three β subunits (8, 10–12). One β subunit, designated β_TP, preferentially binds to an ATP analogue, AMP-PNP, whereas another one, β_DP, binds to ADP and P_i or P_i analogues, representing the catalytically active state. The third one, β_E, has no nucleotides, although some crystal structures show that it has phosphate (9), thiophosphate (11) or sulfate ions (12), suggesting that β_E represents the phosphate releasing state (13). Both β_TP and β_DP adopt a closed conformational state in which the C-terminal domain swings toward the γ subunit, wrapping the bound nucleotide, whereas β_E assumes an open conformation.

The coupling reaction scheme for the rotation and catalysis of bMF₁ was recently studied in a single-molecule rotation study (14). Similar to the reaction scheme for thermophilic F₁ (TF₁), bMF₁ makes rotation with 120° steps, each resolved into 80° and 40° substeps. The 80° and 40° substeps are triggered by ATP binding and hydrolysis, respectively. Therefore, the dwelling states before the 80° and 40° substeps are referred to as ‘binding dwell’ and ‘catalytic dwell’, respectively. In addition, bMF₁ exhibits a short transient pause between the binding dwell and the catalytic dwell. The reaction step involved in the short transient pause remains to be identified. Previous studies have shown that the crystal structures of bMF₁ in the ground state or relevant states correspond to the catalytic dwell in the rotation assay (14–16).

There are diverse mechanisms for the suppression of ATP hydrolysis by F₁, which is generally detrimental to cells (17–19). The self-inhibition of F₁, termed ADP inhibition, is the most universal mechanism for F₁ inhibition (14, 20, 21). Inhibitory factor 1 (IF₁) of mitochondrial F₁ inhibits unfavourable ATPase. Under inhibitory conditions, IF₁ associates with F₁ to block ATP hydrolysis by inserting its N-terminal region into F_oF₁-ATP synthase, which results in mechanical blockage of rotation and catalysis. Bovine mitochondrial IF₁ is composed of 84 amino acid residues. IF₁ inhibits the function of F_oF₁-ATP synthase under hydrolytic condition to prevent wasteful consumption of ATP. Thus, it is an unidirectional inhibitor of F_oF₁-ATP synthase (22, 23), although several reports have suggested that IF₁ also has an inhibitory effect under synthesized condition (24, 25). Among the 84 residues in bovine IF₁, the N-terminus is responsible for the inhibition of F_oF₁-ATP synthase, forming a long α-helix when bound to F₁. When isolated from F₁, the N-terminus of IF₁ is intrinsically disordered (26). Native IF₁ forms a homodimer associating at the C-terminal region (27, 28). Deletion of C-terminus residues 61–84 produces a stable monomeric form of IF₁ without the loss of inhibition activity (28, 29). Thus, the C-terminus deleted form of IF₁ (termed ${\text{IF}}_1^{1-60}$ hereafter) provides a simple platform for biochemical and structural analyses of IF₁ (28, 30, 31). Biochemical assay showed that the fusion of green fluorescent protein (GFP) and 6 histidine tag (His-tag) to the C-terminus in ${\text{IF}}_1^{1-60}$ (${\text{IF}}_1^{1-60}$GFPHis) has little impact on its inhibitory capacity (30).

The first crystal structure of the complex of bMF₁ and ${\text{IF}}_1^{1-60}$ showed that the N-terminal helix of ${\text{IF}}_1^{1-60}$ was deeply buried in the α_DP/β_DP interface in its locked state (28). Following this, the crystal structure of the bMF₁-(${\text{IF}}_1^{1-60}$)₃ complex was resolved, revealing that each of the three α/β interfaces was occupied with IF₁ (31). Each IF₁ bound to the α/β interface differed in conformation: IF₁ at the α_DP/β_DP interface showed the most folded state, as found in the first bMF₁-IF₁ structure; IF₁ at α_TP/β_TP showed partially folded α-helix with unfolded N-terminal region; and IF₁ at α_E/β_E was largely disordered. These findings suggest progressive conformational isomerization of IF₁ from a disordered state to the α-helical state, accompanying the conformational transition of the α/β pair from α_E/β_E to α_DP/β_DP. As the conformational transition of the α/β pair is tightly coupled with γ rotation, the progressive conformational isomerization model inevitably assumes that IF inhibition accompanies γ rotation (Fig. 1A). Comprehensive studies of mutagenesis based on the crystal structure revealed that Glu30 and Tyr33 of IF₁ are particularly critical for IF₁ inhibition. Glu30 and Tyr33 form a salt bridge and hydrophobic interaction with a residue of the β subunit, respectively. Ala substitution causes a loss of the inhibitory activity of IF₁ (30). However, the roles of these residues in the proposed progressive conformational change model remain to be elucidated.

Fig. 1.

Experimental concept and procedure. (A) Schematic image of inhibition by IF₁. IF₁ loosely associates with the α_E and β_E subunits. Then, IF₁ is deeply inserted into the α_DPβ_DP interface (PDB: 2JDI and 4TT3). The initial association and the following isomerization are represented by three rate constants, $k_{\mathrm{on}}$, $k_{\mathrm{off}}$ and $k_{\mathrm{lock}}$. (B) Time course of 340 nm NADH absorbance at 1 mM ATP and 1 μM ${\text{IF}}_1^1$^–60. At 180 s after F₁ addition, ${\text{IF}}_1^1$^–60 was added to the reaction mixture and ATPase activity decreased. To see this figure in colour, go online.

Biochemical studies have revealed that IF₁ inhibition requires catalytic turnover of F₁; in the absence of ATP, IF₁ only shows slow and partial inhibition of F₁ (32, 33). In the presence of ATP, IF₁ shows rapid inhibition during turnover (34). Kinetic analyses showed that the rate constant of IF₁-mediated inhibition increases with [ATP], although some complex behaviours of IF₁ inhibition were observed, such as a decrease in the inhibition rate at the mM range of [ATP] (32, 33, 35). The correlation of IF₁ inhibition with occupancy of the catalytic site was also studied (32, 33, 36). Based on kinetic analyses, an ATP-dependent two-step model has been proposed for IF₁-mediated inhibition (35, 37, 38). The two-step model suggests that the rate constant of IF₁-mediated inhibition should increase with [IF₁], reaching an ATP-dependent plateau. However, comprehensive kinetic analysis covering a wide range of IF₁ and ATP concentrations to confirm the expected hyperbolic curves has not been performed yet.

In this study, we studied the kinetics of bMF₁ inhibition by bovine mitochondrial IF₁ with an NADH-coupled ATP-regenerating system, using a wide range of [ATP] from 100 nM to 1 mM with [IF₁] from 0.05 to 40 µM. The resultant rate constant of IF₁-mediated inhibition showed typical hyperbolic curves for [IF₁] at each [ATP], consistent with the two-step model. We then investigated the IF₁ mutants IF₁(E30A) and IF₁(Y33A) to study the effects of Glu30 and Tyr33, respectively, on the kinetics of IF₁ inhibition. Based on the results as well as the established reaction scheme for catalysis and rotation of bMF₁ (14), we propose an IF₁ inhibition scheme.

Materials and Methods

Construct and purification of IF₁

An expression plasmid encoding residues 1–60 of bovine IF₁ was constructed as follows: His-tag and TEV site were fused to the N-terminal region, and the linker and mScarlet sequences were fused to the C-terminal region. The resulting artificially synthesized construct was introduced into the pRSET-B plasmid, which encoded the protein ${\text{IF}}_1^{1-60}$mScarlet (hereafter referred to as wild-type ${\text{IF}}_1^{1-60}$ or ${\text{IF}}_1^{1-60}$).

${\text{IF}}_1^{1-60(\Delta \text{mS})}$ was generated by deleting the linker and mScarlet sequences from the wild-type ${\text{IF}}_1^{1-60}$ plasmid. The single-point amino acid mutants, E30A and Y33A, were introduced into the wild-type ${\text{IF}}_1^{1-60}$ plasmid. The sequence encoding ${\text{IF}}_1^{1-60}$ or a mutation was amplified by PCR. After gel electrophoresis and purification, the product was digested with two restriction enzymes and cloned into the vector wild-type ${\text{IF}}_1^{1-60}$ plasmid, digested with the same restriction enzymes. The sequences of the recombinant plasmids for IF₁ were confirmed by Fasmac sequencing service (Fasmac, Japan).

Cells of Escherichia coli C43 were transformed with the constructed plasmids and grown in LB medium containing 100 µg/mL carbenicillin at 37°C for 4 h as a preculture. The culture medium was then transferred to SB medium containing 100 µg/mL carbenicillin at 37°C. When the absorbance of the culture was 0.6 at 600 nm (for ∼4 h), isopropyl-β-D-thiogalactopyranoside (IPTG) was added at a final concentration of 1 mM to induce protein expression. After 24 h of growth at 20°C, cells were harvested by centrifugation (7000×g, 8 min, 4°C). Subsequent procedures were performed at 4°C, except for the gel-filtration process. The harvested cells were suspended in buffer A [50 mM KP_i (pH 7.5), 200 mM KCl, 10% Glycerol and 25 mM Imidazole], disrupted by an ultrasound disintegrator and subjected to ultracentrifugation (81,000×g, 20 min). The supernatant was applied to Ni-Sepharose FF resin (GE Healthcare) equilibrated in buffer A. After binding IF₁ to the resin, it was washed with 10 volumes of buffer A. IF₁ was eluted with elution buffer [50 mM KP_i (pH 7.5), 200 mM KCl, 10% glycerol and 500 mM imidazole].

To remove His-tag, TEV protease was used. The eluted fractions containing the proteins were concentrated with a centrifugal concentrator (3 kDa for ${\text{IF}}_1^{1-60(\Delta \text{mS})}$ and 10 kDa for wild-type ${\text{IF}}_1^{1-60}$ and mutants; Centricon50; Millipore Corp.). The concentrated fractions were diluted 20-fold with TEV treatment buffer [20 mM KP_i (pH 8.0), 50 mM NaCl 0.04% 2-mercaptoethanol, and 0.1 mg/mL TEV protease]. After treatment for 16 h at 4°C, the solution was concentrated with a centrifugal concentrator and diluted 30-fold with buffer A. The resultant solution was applied to a Ni-Sepharose FF resin. The flow-through and wash fractions were concentrated with a centrifugal concentrator after adding DTT at a final concentration of 5 mM. The resulting samples were further purified by passing through a gel-filtration column (Superdex 75 for ${\text{IF}}_1^{1-60(\Delta \text{mS})}$, and Superdex 200 for wild-type ${\text{IF}}_1^{1-60}$ and mutants; GE Healthcare) equilibrated with Gel-filtration buffer [20 mM HEPES-KOH (pH7.5), 100 mM KCl and 10% glycerol]. If necessary, the fractions were concentrated with a centrifugal concentrator. The concentration of IF₁ was determined based on the absorbance at 280 nm. The purified samples were flash-frozen in liquid nitrogen and stored at −80°C before use. Their molecular masses were verified by SDS-PAGE (sodium dodecyl sulfate polyacrylamide gel electrophoresis) analysis (Supplementary Fig. S1). Further confirmation of the molecular masses for wild-type ${\text{IF}}_1^{1-60}$ and ${\text{IF}}_1^{1-60(\Delta \text{mS})}$ was performed by MALDI‐TOF/TOF mass spectrometry (Genomine. Inc., Korea) (Supplementary Table S1).

Construct and purification of bMF₁

bMF₁ was prepared as previously described (14) with slight modifications. We removed ATP from buffers A, B and gel-filtration buffer for measurements of ATPase activity at low ATP conditions because the carryover ATP from the purified bMF₁ sample to the cuvette was not negligible under these conditions. The ATPase activity of bMF₁ purified without ATP was identical to that purified with ATP.

Biochemical assay with NADH-coupled ATP-regenerating system

As previously reported (14), the ATPase activity of bMF₁ was measured using a spectrometer at 25°C in HEPES-KOH (pH 7.5) containing KCl, MgCl₂ and an ATP-regenerating system supplemented with NADH and lactate dehydrogenase. The ATPase reaction was initiated by adding purified bMF₁.

IF₁ was added 180 s after the addition of bMF₁ to avoid ADP inhibition. The change in NADH absorbance was monitored for over 10 min. All data points were measured at least in triplicate. The apparent rate constants for IF₁ inhibition ($k_{\mathrm{inhibition}}^{\mathrm{app}}$) were measured from the exponential decay of ATPase activity after IF₁ addition, using the following equation:

$$y\left(t\right)-y_0=V_{\mathrm{\infty }}t+\frac{V_0-V_{\mathrm{\infty }}}{k_{\mathrm{inhibition}}^{\mathrm{app}}}\left\{1-\exp \left(-k_{\mathrm{inhibition}}^{\mathrm{app}}t\right)\right\}\#$$ (1)

where $y\left(t\right)$ and $y_0\mathrm{ }$are the absorbances at time points t and 0 after IF₁ addition, respectively, and $V_0$ and $V_{\mathrm{\infty }}$ are the initial and final rates of reaction, respectively. For precise fitting, we have fitted the time course 60 s after IF₁ injection to remove noise caused by solution injection. Examples of $V_0$ and $V_{\mathrm{\infty }}$, estimated in Fig. 2B at 1 mM ATP, were shown in Supplementary Fig. S6.

Fig. 2.

Kinetic analysis of IF₁ inhibition in bMF₁. (A) Time course of IF₁ inhibition at 1 mM ATP. Colour represents different ${\text{IF}}_1^{1-60}$ concentrations; (Red) 1 μM, (Blue) 0.65 μM, (Green) 0.3 μM, and (Orange) 0.1 μM. The final concentration of bMF₁ was 10 nM. (B) Determined $k_{\mathrm{inhibition}}^{\mathrm{app}}$ plotted against [${\text{IF}}_1^{1-60}$]s. The mean value and SD for each data point in (B) are shown with circles and error bars, respectively (n = 3 for each measurement). Solid line represents the fitting curve of Eq. 2. For wider [${\text{IF}}_1^{1-60}$] range of wild-type bMF₁ at 100 nM ATP and bMF₁(βE188D) at 1 mM ATP, see Supplementary Fig. S4. To see this figure in colour, go online.

Modelling the two-step reaction of IF₁ inhibition

The kinetic scheme is as follows:

$${\mathrm{F}}_1+{\mathrm{IF}}_1\underset{k_{\mathrm{off}}}{\overset{k_{\mathrm{on}}}{\rightleftarrows }}{\mathrm{F}}_1\cdot {\mathrm{IF}}_1\stackrel{k_{\mathrm{lock}}}{\to }{\mathrm{F}}_1\cdot {\mathrm{IF}}_1^{\mathrm{lock}} \left(\mathrm{Scheme}\mathrm{ }1\right)$$

where $k_{\mathrm{on}}$ is the rate constant for IF₁ binding to F₁, $k_{\mathrm{off}}$ is the rate constant for IF₁ release from F₁, and $k_{\mathrm{lock}}$ is the rate constant for isomerization to the locked state. F₁ and ${\mathrm{F}}_1·\mathrm{I}{\mathrm{F}}_1$ are active and ${\mathrm{F}}_1·\mathrm{I}{\mathrm{F}}_1^{\mathrm{lock}}$ is inactive. In the first step, IF₁ loosely binds to F₁, forming an intermediate state. Following this, IF₁ is irreversibly locked, forming a dead-end complex. For derivation of $k_{\mathrm{inhibition}}^{\mathrm{app}}$, see the Supplemental text.

Results

Preparation of IF₁protein

C-terminal residues of ${\text{IF}}_1^{1-60}$ in bovine IF₁ were fused with mScarlet, a bright monomeric red fluorescent protein with a short linker sequence, to enhance its expression in E. coli, as previously described (30). The fusion IF₁ is hereafter referred to as wild-type ${\text{IF}}_1^{1-60}$ or ${\text{IF}}_1^{1-60}$ for simplicity, unless mentioned otherwise. For comparison, we also purified ${\text{IF}}_1^{1-60(\Delta \text{mS})}$ lacking the linker sequence and the mScarlet domain. For the preparation of ${\text{IF}}_1^{1-60}$(E30A) or ${\text{IF}}_1^{1-60}$(Y33A), a single point mutation was introduced into the wild-type ${\text{IF}}_1^{1-60}$ plasmid. For purification with an Ni-Sepharose column, the His-tag and TEV recognition sequences were fused to the N-terminal region of the IF₁ proteins. After collecting the eluted fractions from the Ni-Sepharose column, the His-tag was cleaved with TEV-protease. The resultant products were identified by SDS-PAGE analysis (Supplementary Fig. S1) and mass spectroscopy (Supplementary Table S1).

Time course of IF₁-mediated inhibition

ATP hydrolysis activity of bMF₁ was monitored using an ATP regenerating system. The decay of NADH absorbance at 340 nm represents ATP hydrolysis leading to NADH oxidation. Upon injection, bMF₁ initially showed rapid catalysis, followed by slow deceleration to reach steady-state catalysis (Fig. 1B). The slow auto-inactivation is a typical feature of ADP inhibition. Under the present conditions, bMF₁ activity almost reached steady state within 180 s (Supplementary Fig. S2). Subsequently, IF₁ was injected at 180 s after F₁ injection. Since the time constant for ADP inhibition at 1 µM ATP was longer than 400 s, ADP inhibition did not reach an equilibrium state at the time of IF₁ injection. However, additional analysis of IF₁ inhibition including ADP inhibition (Supplementary text and Supplementary Fig. S3) revealed that it has little impact on IF₁ kinetics, probably due to the slow and modest suppression at 1 µM ATP.

Fig. 2A shows the typical time courses of IF₁-mediated inhibition at 1 mM [ATP]. Immediately after the injection of ${\text{IF}}_1^{1-60}$_, ATPase activity decreased, reaching almost zero activity. The time course of IF₁-mediated inhibition was well fitted with an exponential function (Eq. 1), giving the apparent rate constant of the inhibition, $k_{\mathrm{inhibition}}^{\mathrm{app}}$. The inhibition rate increased with [${\text{IF}}_1^{1-60}$], reaching a plateau when [${\text{IF}}_1^{1-60}$] was over 0.65 µM. We also measured the time courses of IF₁-mediated inhibition to determine $k_{\mathrm{inhibition}}^{\mathrm{app}}$ at all [ATP]s ranging from 100 nM to 1 mM. In Fig. 2B and Supplementary Fig. S4, data points of $k_{\mathrm{inhibition}}^{\mathrm{app}}$ are plotted against [${\text{IF}}_1^{1-60}$] at all [ATP]s. At a given [ATP], $k_{\mathrm{inhibition}}^{\mathrm{app}}$ always increases with [${\text{IF}}_1^{1-60}$] and reaches a plateau, following a hyperbolic curve. Further, we tested the inhibitory capacity of a monomer IF₁ without mScarlet (${\text{IF}}_1^{1-60(\Delta \text{mS})}$) and found that the result was almost identical to that of wild-type ${\text{IF}}_1^{1-60}$ (Supplementary Fig. S5), suggesting that mScarlet in the C-terminal region did not affect the kinetics of IF₁-mediated inhibition. It should be noted that previous biochemical assay based on mutagenesis (30) showed monotonous enhancement of $k_{\mathrm{inhibition}}^{\mathrm{app}}$, whereas clear hyperbolic curve was observed in our assay. Such an apparent difference is attributable to low [IF₁] employed in the assay (30), which enabled to visualize the limited region of the hyperbolic curve in the two-step inhibition mechanism. Another possible reason for this discrepancy is the difference in experimental conditions: including pH, temperature and chemicals.

The observed hyperbolic curves suggest a two-step model, where IF₁ reversibly associates with F₁, and the resulting ${\mathrm{F}}_1·\mathrm{I}{\mathrm{F}}_1$ complex isomerizes to the final locked state. Thus, we assume the following reaction scheme for IF₁-mediated inhibition:

$${\mathrm{F}}_1+{\mathrm{IF}}_1\underset{k_{\mathrm{off}}}{\overset{k_{\mathrm{on}}}{\rightleftarrows }}{\mathrm{F}}_1\cdot {\mathrm{IF}}_1\stackrel{k_{\mathrm{lock}}}{\to }{\mathrm{F}}_1\cdot {\mathrm{IF}}_1^{\mathrm{lock}} \left(\mathrm{Scheme}\mathrm{ }1\right)$$

where, ${\mathrm{F}}_1·\mathrm{I}{\mathrm{F}}_1^{\mathrm{lock}}$ represents the catalytically locked state of the ${\mathrm{F}}_1·\mathrm{I}{\mathrm{F}}_1$ complex. $k_{\mathrm{on}}$ and $k_{\mathrm{off}}$ represent the rate constants of association and dissociation, respectively. $k_{\mathrm{lock}}$ is the rate constant of isomerization to the locked state. This scheme calculates the apparent rate constant of IF₁ inhibition, $k_{\mathrm{inhibition}}^{\mathrm{app}}$, as follows:

$$k_{\mathrm{inhibition}}^{\mathrm{app}}=\frac{\left[\mathrm{I}{\mathrm{F}}_1\right]}{K_M^{\mathrm{I}{\mathrm{F}}_1}+\left[\mathrm{I}{\mathrm{F}}_1\right]}·k_{\mathrm{lock}}\#$$ (2)

$$K_{\mathrm{M}}^{\mathrm{I}{\mathrm{F}}_1}\equiv \frac{k_{\mathrm{off}}+k_{\mathrm{lock}}}{k_{\mathrm{on}}}\#$$ (3)

The experimentally obtained data points at each [ATP] were well fitted with Eq. 2, giving $k_{\mathrm{lock}}$ and $K_{\mathrm{M}}^{\mathrm{I}{\mathrm{F}}_1}$.

[ATP] dependence of ${\mathit{k}}_{\mathbf{lock}}\mathrm{ }\mathrm{and}\mathrm{ }{\mathit{K}}_{\mathbf{M}}^{\mathbf{I}{\mathbf{F}}_1}$

Fig. 3A shows the plot of $k_{\mathrm{lock}}$ against [ATP]s. Although not well constant, $k_{\mathrm{lock}}$ was around 0.02 s⁻¹ irrespective of [ATP]; this value is almost consistent with that estimated from previous studies (39, 40). $k_{\mathrm{lock}}$ is evidently lower than the catalytic turnover rate, 1–200 s⁻¹, indicating that IF₁ transforms into the inhibitory locking state during the rotation of the γ subunit. Fig. 3B shows the plot of $K_{\mathrm{M}}^{\mathrm{I}{\mathrm{F}}_1}$ against [ATP]. $K_{\mathrm{M}}^{\mathrm{I}{\mathrm{F}}_1}$ was determined to be in the sub-µM to µM range, consistent with that of previous biochemical studies with isolated F₁ and sub-mitochondrial particles (32–35, 39). $K_{\mathrm{M}}^{\mathrm{I}{\mathrm{F}}_1}$ reveals a clear [ATP] dependence, decreasing from 27 to 0.1 µM when [ATP] is over 10 µM. Considering constant $k_{\mathrm{lock}}$ over [ATP], this means that the rate constant of IF₁ association to F₁ follows a hyperbolic increment with [ATP].

Fig 3.

Fitted parameters derived fromFig. 2Band Supplementary Fig. S4. (A) $k_{\mathrm{lock}}$ and (B) $K_{\mathrm{M}}^{\mathrm{I}{\mathrm{F}}_1}$. In (A) and (B), the circles and error bars in each data point represent the fitted parameter and fitting error determined in Fig. 2B and Supplementary Fig. S4. (C) The effective binding constant $k_{\mathrm{on}}^{\mathrm{ }\mathrm{eff}}\equiv k_{\mathrm{lock}}/K_{\mathrm{M}}^{\mathrm{I}{\mathrm{F}}_1}$. The gray line represents the fitting curve of Eq. 5 and the orange line represents the duty ratio of catalytic dwell against overall reaction time. The circles and error bars in each data point represent the mean value and the SD calculated from Fig. 3A and B. In Fig. 3A–C, grey and blue points represent the results for bMF₁(wild-type) at 0.1–1000 μM and bMF₁(βE188D) at 1 mM ATP, respectively. To see this figure in colour, go online.

Here, we define the effective rate constant of IF₁ association to F₁ as follows:

$$k_{\mathrm{on}}^{\mathrm{eff}}\equiv \frac{k_{\mathrm{lock}}}{K_{\mathrm{M}}^{\mathrm{I}{\mathrm{F}}_1}}\#$$ (4)

Fig. 3C shows the plot of $k_{\mathrm{on}}^{\mathrm{eff}}$ against [ATP]. As expected, $k_{\mathrm{on}}^{\mathrm{eff}}$ shows a typical hyperbolic saturation curve. Considering that IF₁ cannot bind ATP by itself, it is reasonable to attribute the ATP binding to F₁, c.f. IF₁ is predominantly associated with F₁ in the post-ATP-bound state. In light of the reaction scheme for rotation and catalysis, this means that IF₁ is not associated with F₁ in the binding dwell, but it preferentially associates with F₁ in the catalytic dwell.

With the assumption that IF₁ preferentially binds to F₁ in the catalytic dwell, we tested the mutant bMF₁(βE188D). Previous studies have shown that Glu188 of bMF₁ or the corresponding glutamic residues of other F₁s are the most critical residues for catalysis (8, 16, 41). Mutagenic substitution of Glu188 with aspartic acid largely retarded bMF₁ catalysis, lengthening the catalytic dwell by 400 times (14). We investigated IF₁-mediated inhibition of bMF₁(βE188D) at 1 mM [ATP] (Supplementary Fig. S7). Contrary to the expectation, bMF₁(βE188D) did not exhibit enhanced IF₁ inhibition rate compared with wild-type bMF₁ at saturating [ATP]s. The hyperbolic inhibition curve of bMF₁(βE188D) at 1 mM [ATP] was similar to that of wild-type bMF₁ at 100 nM [ATP], where the binding dwell is dominant (Fig. 2B and Supplementary Fig. S4). Considering that F₁ mediates two reactions through the catalytic dwell, hydrolysis and presumably inorganic phosphate release, the catalytic state and the conformation of bMF₁(βE188D) at the catalytic dwell maybe different from that of the wild-type in some aspects.

Mutation of Glu30 and Tyr33

A previous comprehensive mutagenetic study identified E30 and Y33 as the most critical residues for the inhibitory function of IF₁ (31). Although the mutants created by substituting these residues with alanine suppressed the activity down to an undetectable level (30), we reinvestigated these mutants, ${\text{IF}}_1^{1-60}$(E30A) and ${\text{IF}}_1^{1-60}$(Y33A), in our experimental setup.

Experiments were conducted using 1 mM [ATP]. Fig. 4A shows the time course of its inhibition by ${\text{IF}}_1^{1-60}$(E30A) at 0.5, 1 and 3 µM concentrations, which are similar to the range for wild-type ${\text{IF}}_1^{1-60}$. ATPase activity showed slight decay and reached steady state with some activity remaining. Compared to wild type, where the complete inhibition was observed (Fig. 2A), the inhibition by ${\text{IF}}_1^{1-60}$(E30A) was not irreversible. Based on the exponential fitting of the time courses in Eq. 1, $k_{\mathrm{inhibition}}^{\mathrm{app}}$ of ${\text{IF}}_1^{1-60}$(E30A) was determined (Fig. 4B, green) and found to be quite similar to that of wild-type ${\text{IF}}_1^{1-60}$ (Fig. 4B, grey) at each [${\text{IF}}_1^{1-60}$(E30A)]. The resultant $k_{\mathrm{lock}}$ and $k_{\mathrm{on}}^{\mathrm{eff}}$ were almost consistent with those for the wild-type ${\text{IF}}_1^{1-60}$ (Supplementary Table S2). These results show that the E30A mutant also follows a two-step mechanism for inhibition. However, ${\text{IF}}_1^{1-60}$(E30A)-mediated inhibition is evidently less efficient, as seen in the partial inhibition of ATPase activity. Fig. 4C shows the final ATPase activity observed at the end of the measurement (360 s after IF₁ injection). While wild-type IF₁ suppresses ATPase activity down to almost zero at each [${\text{IF}}_1^{1-60}$], ${\text{IF}}_1^{1-60}$(E30A) suppresses ATPase activity down to only 20–40% at [${\text{IF}}_1^{1-60}$(E30A)]s lower than 1 µM. Even at 3 µM [${\text{IF}}_1^{1-60}$(E30A)], where $k_{\mathrm{inhibition}}^{\mathrm{app}}$ reached a plateau, a fraction of bMF₁ retained its activity.

Fig. 4.

Analysis of (A–C) ${\text{IF}}_1^{1-60}$(E30A) and (D–F) ${\text{IF}}_1^{1-60}$(Y33A) at 1 mM ATP. (A), (D) Time course of IF₁ inhibition for (A) ${\text{IF}}_1^{1-60}$(E30A) and (D) ${\text{IF}}_1^{1-60}$(Y33A). The final concentration of bMF₁ was 10 nM. (B), (E) Determined $k_{\mathrm{inhibition}}^{\mathrm{app}}$ plotted against [${\text{IF}}_1^{1-60}$]s. Solid line represents the fitting curve of Eq. 2. (C), (F) Relative ATPase activity at the end of the measurement. The mean value and SD for each data point are shown with circles and error bars, respectively (n = 3 for each measurement). To see this figure in colour, go online.

The Y33A mutant, ${\text{IF}}_1^{1-60}$(Y33A), was also examined at 1 mM ATP. Fig. 4D shows the time course of its inhibition. This mutant required a significantly higher concentration of [${\text{IF}}_1^{1-60}$(Y33A)], at least 10 µM [${\text{IF}}_1^{1-60}$(Y33A)], to induce clear inhibition. However, in contrast to the E30A mutant, the Y33A mutant suppressed ATPase activity to almost zero (Fig. 4F). These observations suggest that the Y33A mutant has high inhibitory activity, although the time scale for its association with F₁ was significantly longer than that for the wild-type ${\text{IF}}_1^{1-60}$. Fig. 4E shows $k_{\mathrm{inhibition}}^{\mathrm{app}}$ of ${\text{IF}}_1^{1-60}$(Y33A), which follows a hyperbolic curve consistent with the two-step model of IF₁ inhibition. The plateau determined the $k_{\mathrm{lock}}$ of ${\text{IF}}_1^{1-60}$(Y33A) to be 0.019 s⁻¹, which is very similar to that of wild-type ${\text{IF}}_1^{1-60}$. The significant difference was observed for $K_{\mathrm{M}}^{\mathrm{I}{\mathrm{F}}_1}$, which was 25 µM in case of ${\text{IF}}_1^{1-60}$(Y33A), 160 times higher than that of wild-type ${\text{IF}}_1^{1-60}$ (Table S2).

Thus, the effect of the mutations contradicted each other. Although the E30A mutant had normal $k_{\mathrm{inhibition}}^{\mathrm{app}}$, it was evidently deficient in locking the catalysis of F₁. The Y33A mutant was quite slow for the association with F₁ and had lower $k_{\mathrm{inhibition}}^{\mathrm{app}}$ and higher $K_{\mathrm{M}}^{\mathrm{I}{\mathrm{F}}_1}$, although this mutant finally locked the catalysis almost completely.

Discussion

[ATP] dependence of $k_{\mathrm{on}}^{\mathrm{eff}}$

The present study showed that the effective binding rate of$\mathrm{ }$IF₁ to bMF_1,$k_{\mathrm{on}}^{\mathrm{eff}}$, evidently followed an [ATP]-dependent saturation curve (Fig. 3C). As IF₁ itself cannot bind ATP, the [ATP] dependence of $k_{\mathrm{on}}^{\mathrm{eff}}$ can be attributed to bMF₁. As IF₁ inhibition requires catalytic turnover of bMF₁, it is reasonable to assume that the [ATP] dependence is the result of the Michaelis–Menten kinetics of ATPase activity. Kinetic analysis of bMF₁ rotation (14) shows that F₁ principally has two conformational states: binding dwell and catalytic dwell. Here, we neglect the short dwell between the binding dwell and the catalytic dwell because its duration is significantly shorter than those of the other dwells. The duration of the binding dwell is inversely proportional to [ATP]$\mathrm{ }(=1/\left(k_{\mathrm{on}}^{\mathrm{ATP}}\right[\mathit{ATP}\left]\right)$, whereas that of the catalytic dwell is constant at approximately 0.3 ms, irrespective of [ATP] (14). Thus, we consider the following two states of F₁:

$$F_1\left(\mathrm{binding}\hspace{0.17em}\mathrm{dwell}\right)\underset{k_{\mathrm{cat}}^{\mathrm{ATP}}}{\overset{k_{\mathrm{on}}^{\mathrm{ATP}}[\mathrm{ATP}]}{\rightleftarrows }}{F}_1\left(\mathrm{catalytic}\hspace{0.17em}\mathrm{dwell}\right)$$

where, $k_{\mathrm{cat}}^{\mathrm{ATP}}$ represents the rate of the catalytic dwell (∼2100 s⁻¹) and$\mathrm{ }{k}_{\mathrm{on}}^{\mathrm{ATP}}\left[\mathrm{ATP}\right]$ is the rate of ATP binding to bMF₁. The simplest assumption to explain the [ATP] dependence of $k_{\mathrm{on}}^{\mathrm{eff}}$ is that IF₁ preferentially associates with F₁ in the catalytic dwell. Here, we calculate the duty ratio of the catalytic dwell in the overall reaction time ($R_{\mathrm{c}}$) as follows:

$$R_c=\frac{\left[\mathrm{ATP}\right]}{K_m^{\mathrm{ATP}}+\left[\mathrm{ATP}\right]}\#$$ (5)

where, $K_{\mathrm{m}}^{\mathrm{ATP}}$ is defined as $k_{\mathrm{cat}}^{\mathrm{ATP}}/k_{\mathrm{on}}^{\mathrm{ATP}}$ from the Michaelis–Menten fitting of the rotation speed, 77 µM (14). Along with Eq. (4) and Eq. (5), we redefine $k_{\mathrm{on}}\mathrm{ }$and $k_{\mathrm{on}}^{\mathrm{eff}}$ as follows:

$$k_{\mathrm{on}}=R_c·k_{\mathrm{on}}^{\mathrm{\text{'}}}\#$$ (6)

$$k_{\mathrm{on}}^{\mathrm{eff}}=\frac{\mathrm{ }{k}_{\mathrm{lock}}}{k_{\mathrm{off}}+k_{\mathrm{lock}}}·k_{on}=\frac{k_{\mathrm{lock}}}{k_{\mathrm{off}}+k_{\mathrm{lock}}}\mathrm{ }·R_{\mathrm{c}}·k_{\mathrm{on}}^{\mathrm{\text{'}}}\#$$ (7)

where, $k_{\mathrm{on}}^{\mathrm{\text{'}}}$ is the genuine rate constant of IF₁ binding to F₁ in the catalytic dwell. In Fig. 3C, the calculated $R_{\mathrm{c}}$ (orange) is plotted with the experimental data points of $k_{\mathrm{on}}^{\mathrm{eff}}$ (gray) after normalization. The experimental data points were fitted to determine $k_{\mathrm{on}}^{\mathrm{\text{'}}}$ and $K_{\mathrm{m}}^{\mathrm{ATP}}$. Since we have not estimated $k_{\mathrm{off}}$ from our experimental data, we simply assume $k_{\mathrm{off}}$ as 0.0017 s⁻¹, which was previously estimated (30). The resultant $k_{\mathrm{on}}^{\mathrm{\text{'}}}$ was determined to be 1.5 × 10⁵ M⁻¹s⁻¹, in good agreement with previous studies that determined $k_{\mathrm{on}}^{\mathrm{\text{'}}}$ in the order of 10⁴–10⁶ M⁻¹s⁻¹ (30, 32, 33, 35). However, $K_{\mathrm{m}}^{\mathrm{ATP}}$ was determined to be 9 µM, which was obviously lower than the expected concentration of 77 µM. One of the possible explanations for this is the difference in experimental conditions: the rotation assay that determined $K_{\mathrm{m}}$ to be 77 µM selectively analysed actively rotating particles, whereas this study was based on a solution experiment where the value was averaged over molecules including those in the ADP-inhibited form. However, since the determined $K_{\mathrm{m}}$ from ATPase measurement was 218 µM (14), we do not have convincing interpretations at this moment. Future single-molecule analysis of IF₁ inhibition is required to overcome this limitation.

Proposed IF₁ inhibition scheme and correlation with crystal structures

The present study observed hyperbolic curves at different [ATP]s that allows us to discuss the IF₁ inhibition mechanism based on the rotary catalysis of bMF₁. We also carefully examined the mutant IF₁s with a mutation at critical points: Glu30 and Tyr33. These mutants significantly affect the IF₁ inhibition at different processes. Taking the present results into account, together with those of previous single-molecule analyses (14) and structural studies (31), we propose the following IF₁-mediated inhibition mechanism (Fig. 5), where the role of Glu30 and Tyr33 in the two-step inhibition by IF₁ was clarified as well as the catalytic state of bMF₁. Initially, IF₁ weakly associates with F₁ in the catalytic dwell. This weakly bound state corresponds to the intermediate state in the two-step model, as represented ${\mathrm{F}}_1·\mathrm{I}{\mathrm{F}}_1$ in Scheme 1, which undergoes reversible association and dissociation. We assume that this state represents IF₁ bound to the α_Eβ_E site in the crystal structure of the bMF₁-(${\text{IF}}_1^{1-60}$)₃ complex (31), where only a small part of the N-terminal helix is folded and associates with β_E via a few interactions at distal points to the γ subunit. In this state, a large part of the N-terminal helix remains unfolded and IF₁ principally does not interfere with γ rotation and catalysis. Tyr33 of IF₁ interacts with Lys401 of β_E in its crystal structure. The present study showed that Y33A mutation of IF₁ slows the association step of IF₁, in consistent with the crystal structure. Therefore, it is reasonable that the Y33A mutation largely suppresses the formation of the initial F₁-IF₁ complex.

Fig. 5.

The possible IF₁ inhibition scheme. Each circle represents the catalytic state of the β subunit. The asterisks following “ATP” represent the catalytically active state to undergo hydrolysis of a bound ATP. All nucleotide binding states of bMF₁ in this figure represent catalytic dwell, where bMF₁ executes cleavage of ATP. To see this figure in colour, go online.

After the formation of the initial F₁-IF₁ complex, IF₁ slowly transforms its conformation to the fully folded state, inserting the N-terminal helix deeply into the αβ interface, as seen in IF₁ at the α_DPβ_DP site in its crystal structure. This state completely locks the rotation and catalysis of F₁ (${\mathrm{F}}_1·\mathrm{I}{\mathrm{F}}_1^{\mathrm{lock}}$ in Scheme 1). In the crystal structure, Glu30 of IF₁ forms a salt bridge with Arg408 of β_DP or β_TP but not with Arg408 of β_E, indicating that Glu30 is involved in the isomerization of IF₁ to the fully stretched state. Consistent with this, the present study shows that the Ala mutant of Glu30 significantly destabilizes the locked state, without affecting formation of the initial F₁-IF₁ complex.

Notably, the mean duration for this isomerization from the initial F₁-IF₁ complex to the final locked state is 50 s (${=1/k}_{\mathrm{lock}}$), which is significantly longer than the meantime for rotation (5–1000 ms). This suggests that F₁ drives thousands of γ rotation with a hanging IF₁. In other words, IF₁ almost always fails to isomerize to the locking state in each catalysis or each turn.

However, this contradicts the observation that IF₁ preferentially associates with F₁ in the catalytic dwell to form an initial complex. The contention that F₁ can drive many turns while associated with IF₁ indicates that F₁ has some affinity to IF₁ in any state besides the catalytic dwell. Although we do not have clear explanations for this contradiction, simplification of the reaction scheme may be a possible cause. Nevertheless, the crystal structure suggests that IF₁ can have several conformations, and our model assumes only two states, neglecting intermediate states. Another possible reason for the contradiction is that some minor states were neglected through ensemble averaging and curve fitting of the time courses of IF₁ inhibition. Considering the intrinsic heterogeneity of the F₁ states among molecules, different experimental approaches that can assess molecular heterogeneity are required to resolve this problem and to elucidate the molecular mechanism of IF₁-mediated inhibition.

Supplementary Data

Supplementary Data are available at JB Online.

Abbreviations

bMF₁

F₁ from bovine mitochondria

F₁

F₁-ATPase

F_oF₁

F_oF₁-ATP synthase

GFP

green fluorescent protein

His-tag

histidine tag

HEPES

2-[4-(2-hydroxyethyl)piperazin-1-yl]ethanesulfonic acid

IF₁

ATPase Inhibitory factor 1

KPi

potassium phosphate buffer

MALDI-TOF/TOF

Matrix Assisted Laser Desorption/Ionization—Time-of-Flight/Time-of-Flight mass spectrometer

pmf

proton motive force

SDS-PAGE

sodium dodecyl sulfate polyacrylamide gel electrophoresis

TEV

tobacco etch virus

TF₁

F₁ from thermophilic Bacillus PS3.