Nonequilibrium fluctuations of lipid membranes by the rotating motor protein F₁F₀-ATP synthase

Significance

The shape of biological membranes is constantly remodeled and maintained out of equilibrium by active proteins. The functional capacity of membrane deformation is mainly determined by the mechanical interplay between protein activity and bending elasticity. In our experiments, we find that ATP synthase, a rotating membrane protein that synthesizes the biochemical energy in cells through proton-pumping activity across the membrane, promotes localized nonequilibrium membrane fluctuations when reconstituted in giant lipid vesicles. The large membrane deformations emerge from the pumping action of rotating proteins clustered at specific emplacements in the membrane. Our results pave the way to new experimental realizations to explore the collective effects of rotating ATP synthases and their possible biological implications for biomembrane organization and protein functionality.

Abstract

ATP synthase is a rotating membrane protein that synthesizes ATP through proton-pumping activity across the membrane. To unveil the mechanical impact of this molecular active pump on the bending properties of its lipid environment, we have functionally reconstituted the ATP synthase in giant unilamellar vesicles and tracked the membrane fluctuations by means of flickering spectroscopy. We find that ATP synthase rotates at a frequency of about 20 Hz, promoting large nonequilibrium deformations at discrete hot spots in lipid vesicles and thus inducing an overall membrane softening. The enhanced nonequilibrium fluctuations are compatible with an accumulation of active proteins at highly curved membrane sites through a curvature−protein coupling mechanism that supports the emergence of collective effects of rotating ATP synthases in lipid membranes.

The rotating F₁F₀-ATP synthase (F₁F₀-ATPase) is the transmembrane protein complex responsible for the cellular ATP production, a nonspontaneous chemical reaction that is catalyzed in the presence of an electrochemical proton gradient across the lipid membrane (1). The electrochemical gradient or proton-motive force is composed of an electric charge gradient (ΔΨ) and a chemical proton gradient (ΔpH), which regulate the optimal functionality of the F₁F₀-ATPase. This mechanism for ATP biosynthesis is functionally and structurally conserved in all kingdoms of life (2). In recent decades, ATP synthesis function has been artificially reconstituted using several model systems. An important achievement was the combined reconstitution of the chloroplast F₁F₀-ATPase together with a light-inducible proton pump (3). ATP synthesis has been also reconstituted in vitro on different support substrates such as silica particles (4), polymersomes (5), electrode surfaces (6, 7) and nanowires (8), which are potentially exploitable in technological applications. Recently, the Escherichia coli bo3 proton transporter and the E. coli F₁F₀-ATPase have been functionally reconstituted into giant unilamellar vesicles (GUVs) by using oppositely charged liposome fusion techniques (9).

GUVs are suitable model membranes that allow the performance of cytomimetic studies using microscopy-assisted methods, where micropipette manipulation techniques (10) and flickering spectroscopy analysis (11, 12) extract the mechanical properties of membranes. In particular, fast video microscopy makes membrane dynamics easily accessible from the stochastic analysis of the membrane fluctuations (12). The GUV model has been exploited in recent years to get quantitative descriptions of the mechanical impact of different transmembrane proteins or supramolecular assemblies on lipid bilayers (13–16). However, the mechanical influence of the rotating F₁F₀-ATPase on its embedding lipid membrane has not been explored yet. This important issue is of particular interest, as a curvature-inducing mechanism has been suggested for this protein complex in the formation of membrane invaginations (cristae) in the inner mitochondrial membrane (17–19).

Here, we report the functional reconstitution of E. coli F₁F₀-ATPase into GUVs composed of a native E. coli lipid extract (F₁F₀-GUVs). By using flickering spectroscopy, we show that F₁F₀-ATPase activity induces nonequilibrium membrane fluctuations additional to thermal motions at discrete regions of the membrane. Thus, the rotating F₁F₀-ATPase promoted an overall membrane softening that is detected as a significant decrease of the effective bending modulus and a lowering of surface tension (15). Furthermore, we found an additional relaxation process characterized with a constant rate of Γ_act = 20 s⁻¹, which is found independent of the spatial scale probed. This active relaxation rate coincides with the rotational dynamics of the ATPase enzyme. The nonequilibrium character of the membrane fluctuations accounts for active membrane motions arising from the coupling between the pumping activity of clustered proteins and the bending modes of the membrane.

Materials and Methods

Electroformation of GUVs.

Giant vesicles were prepared using the standard electroformation protocol using indium-tin-oxide (ITO)-covered slides (20). GUVs made of E. coli total lipid extract (TLE) (EcGUVs) were prepared by transferring on each ITO slide two 5-μL drops of 20 mg/mL E. coli TLE. Electroformed F₁F₀-GUVs (E-F₁F₀-GUVs) were prepared by spreading on each ITO slide 10 μL of F₁F₀ small unilamellar vesicles (F₁F₀-SUVs) (see Supporting Information for details). Then, the films were rehydrated in sucrose solution (200 mM, pH 6), and the electrodes were connected to an AC power supply (500 Hz, 1.1 V; Agilent) for at least 3 h. E-F₁F₀-GUVs were almost spherical and unilamellar. The size and unilamellarity distributions are shown in Fig. S1.

Fig. S1.

Size and unilamellarity distribution of E-F₁F₀-GUVs. Over a population of 204 vesicles, 70% of the giant vesicles were unilamellar, and the average size was 15 μm.

Detergent-Based Reconstitution of the F₁F₀-ATPase in GUVs.

EcGUVs were prepared by electroformation in the presence of 200 mM sucrose, 0.2 mM of n-Dodecyl-$\mathrm{\beta }$-d-maltoside (DDM), and 150 μM pH-sensitive fluorescent probe pyranine. Then, F₁F₀-GUVs produced by detergent removal (D-F₁F₀-GUVs) were formed by incubating 10 nM purified F₁F₀-ATPase with 0.25 mg/mL EcGUVs for 2 h at 4 °C. The excess of detergent was removed with SM2 Bio-Beads (Biorad) according to manufacturer’s instructions (21).

Activation of F₁F₀-ATPase On Addition of Valinomycin.

Twenty-five microliters of F₁F₀-GUVs were diluted three times in an iso-osmolar reaction buffer (50 mM KCl, 10 mM K₂HPO₄, 10 mM Na₂ADP, 5 mM MgCl₂, and 30 mM Hepes pH 7.2) and incubated for 15 min at 20 °C to let pH equilibrate. F₁F₀-GUVs were activated on addition of 10 μM valinomycin in ethanol (≤1% vol final concentration) (22). For control experiments, F₁F₀-GUVs were incubated with the triggering solvent in the absence of valinomycin.

Fluctuation Spectroscopy and Membrane Mechanics.

To obtain the spectrum of the membrane fluctuation modes P(q), movies of the fluctuating GUVs are recorded at their equatorial plane by high-velocity video microscopy in the phase contrast mode (see Supporting Information for details). At a given time t, the shape fluctuations are described as discrete Fourier modes, that is, $h\left(t\right)={\displaystyle {\sum }_q{h}_q\left(t\right)e^{iqx}}$, where q = l/R₀ is the equatorial projection of the fluctuation wave vector (l = 2, 3, 4, … ∞). The spectrum is given by the variance of the mode amplitudes, which is $P\left(q\right)={\mathrm{ℒ}}^2\langle h_q^2\rangle$ (${\mathrm{ℒ}}^2$ is the area of the membrane); for thermal fluctuations (11),

$$P_{th}^{\left(pass\right)}\left(q\right)=\frac{k_{B}T}{2\sigma }\left[\frac{1}{q}-\sqrt{\frac{\kappa }{\sigma +\kappa q^2}}\right],$$ [1]

where k_BT is the thermal energy, the bending modulus (κ) and the surface tension (σ) can be obtained by fitting to the experimental mode amplitudes. The case of nonequilibrium modes driven by protein activity has been studied by Prost and coworkers (13, 23, 24). For the equatorial spectrum, they deduced (24)

$$P_q^{\left(\exp \right)}\left(q_x\right)=P_q^{\left(\text{pass}\right)}\left({\sigma }_{eff},{\kappa }_{eff}\right)+\frac{A{k}_{B}T\hspace{0.17em}}{4{\kappa }_{eff}^2{\left(q^2+\frac{{\sigma }_{eff}}{{\kappa }_{eff}}\right)}^{3/2}}\hspace{0.17em},$$ [2]

with effective mechanical parameters depending on the activity of the protein, and

$$A=\left(F_0^2-\mathrm{\Xi }{F}_0\right)/4\zeta$$ [3]

being an effective amplitude for the active term. Here, $F_0$ is a generalized force stressed by the active components, and $\mathrm{\Xi }$ is a coupling constant that accounts for the energy involved in creating local curvature by a net imbalance of pumping activity between the two sides of the membrane. The susceptibility involved in creating such imbalance is denoted by $\zeta$ (see Supporting Information for details). Within the active vesicle theory, this curvature−protein coupling induces a softening that is described as a decrease of the effective bending modulus as (13)

$${\kappa }_{eff}=\kappa -{\mathrm{\Xi }}^2/\zeta .$$ [4]

Membrane dynamics can be studied by probing the experimental autocorrelation function (24)

$$\langle h_q\left(t\prime -t\right)h_q(t\prime )\rangle ={\langle h_q^2\rangle }_{\text{pass}}{e}^{-{\mathrm{\Gamma }}_{0}t}+{\langle h_q^2\rangle }_{\text{act}}{e}^{-{\mathrm{\Gamma }}_{\text{act}}t},$$ [5]

which consists of the ordinary time relaxation of the thermal mechanical mode (passive), plus an extraordinary term that describes correlations within the nonequilibrium (active) fluctuations. For a passive membrane fluctuating in a fluid of viscosity $\eta$, the autocorrelation function (ACF) is found as a single-exponential decay for thermal modes with a relaxation rate (25),

$${\mathrm{\Gamma }}_0=\left(\sigma q+\kappa q^3\right)/4\eta .$$ [6]

Results

Reconstitution of the E. coli F₁F₀-ATPase in GUVs.

F₁F₀-GUVs were formed either by electroformation of F₁F₀-SUVs (26) or by detergent-mediated (27) incorporation of the purified F₁F₀ complex into preformed EcGUVs (Fig. S2 A and B; see Materials and Methods for details). For both types of GUVs, the incorporation of the F₁F₀-ATPase was confirmed by Western blotting using specific antibodies that specifically recognize the beta (∼50 kDa) and b subunit (∼17 kDa) of F₁ and F₀, respectively (Fig. S3). Additionally, we checked the reconstitution of the F₁F₀ complex into the detergent-mediated GUVs with Alexa-647 labeled F₁F₀-ATPase. Confocal microscope images show the fluorescence signal of proteins in the GUV membrane (Fig. S2C). After quantification, we found two protein density ranges: n₀ = 10¹³ proteins per square meter (corresponding to an area fraction of 0.15%) for D-F₁F₀-GUVs and n₀ = 10¹⁴ proteins per square meter (corresponding to an area fraction of 1.5%) for E-F₁F₀-GUVs.

Fig. S2.

(A) EcGUVs. Green channel, pyranine; orange channel, Rh-PE. (B) D-F₁F₀-GUVs after detergent removal. Green channel, pyranine; orange channel, Rh-PE. (C) Incorporation of F₁F₀ proteins into GUVs. Orange channel, Alexa-647 labeled F₁F₀-ATPase. (Scale bars: 10 microns.)

Fig. S3.

Western blot analysis of F₁F₀-ATPase incorporation into GUVs. Western blot analyses with specific antibodies that recognize the beta (∼50 kDa) and b subunit (∼17 kDa) of the F₁ and F₀, respectively, reveal the presence of F₁F₀-ATPase at different stages of protein incorporation into GUVs; (A) 20-s and (B) 5-min exposure with: IMV, E. coli inner membrane vesicles; DDM-F₁F₀, purified F₁F₀-ATPase in presence of 0.05% DDM; F₁F₀-SUV, F₁F₀–ATPase reconstituted into SUVs of total E. coli lipid extract; F₁F₀-GUV, GUVs electroformed from F₁F₀-SUVs; DDM-GUV, purified F₁F₀-ATPase in presence of 0.05% DDM; and F₁F₀-GUV, GUVs grown as D-F₁F₀-GUVs.

Then we checked the enzymatic activity of F₁F₀-ATPase in GUVs (Fig. 1A). ATP synthesis is triggered by the addition of the selective K⁺ transporter valinomycin (22). As a consequence of K⁺ internalization, protons are pumped out through the rotating proton channel of the F₀ subunit. The presence of the pH-sensitive fluorescent probe pyranine is used as a reporter to visualize luminal basification (28), which is indicative for ATP synthesis, as both enzymatic processes are strictly correlated. After valinomycin addition, we observed an average increase of fluorescence in the lumen of F₁F₀-GUVs (Fig. 1B, Top). The green luminal fluorescence increased until it reached a plateau after several minutes of incubation. In contrast, we did not observe any pyranine fluorescence intensity increase in EcGUVs experiments performed in the absence of F₁F₀ proteins (Fig. 1B, Bottom). The average increase of fluorescence corresponded to a ΔpH of 1.5 to 2 units (Fig. S4) as measured from the calibration curves shown in Fig. S5 (see Supporting Information for details). The distribution of the basification rates is shown in Fig. S6. Both E-F₁F₀-GUVs and D-F₁F₀-GUVs displayed similar distributions, as a vast majority of vesicles had a basicity rate of k_b ≈ 0.01 min⁻¹. This indicates that both F₁F₀-GUVs presented similar protein activity. Despite a more efficient reconstitution of the F₁F₀ complex in E-F₁F₀-GUVs, the electroformation process in the absence of salts may be harmful for proteins, and the effective concentration of proteins could be reduced. Even so, a small fraction of E-F₁F₀-GUVs showed larger basicity rates in comparison with D-F₁F₀-GUVs, in agreement with a higher protein/lipid ratio on reconstitution.

Fig. 1.

Reconstitution of the E. coli F₁F₀-ATPase in GUVs. (A) Schematic cartoon of F₁F₀-ATPase reconstitution into giant vesicles (Left). ATP synthesis is triggered on valinomycin incubation that creates a membrane potential, positive in the lumen of the vesicle. Proton outward translocation through F₁F₀-ATPases is monitored by the pH-sensitive fluorophore pyranine (green). The lipid bilayer was doped with 0.5% mol RhPE (orange dye). (B) Proton efflux kinetics of E. coli GUVs on valinomycin incubation as observed under fluorescence microcopy, in the presence (Top) and in the absence (Bottom) of F₁F₀-ATPases. (Scale bar: 10 microns.)

Fig. S4.

Proton efflux kinetics of D-F₁F₀-GUVs on valinomycin incubation (circles, n = 27), lipid EcGUVs (squares, n = 63) and (Inset) electroformed E-F₁F₀-GUVs (n = 16). Red and blue patterned areas are the SD obtained over each vesicle population.

Fig. S5.

(A) Calibration curve of fluorescence intensity of pyranine vs. pH as measured by confocal microscopy at different initial concentration of pyranine. The curves show a linear variation of fluorescence intensity in the pH 6.0 to 8.5 range. (B) Slope of the linear regime shown in A, with m_RL as a function of the concentration of pyranine, c₀. (C) Calibration curve of fluorescence intensity of pyranine vs. concentration of pyranine as measured by confocal microscopy at pH = 7.2.

Fig. S6.

Histogram of the basicity rate distribution for D-F₁F₀-GUVs and (Inset) E-F₁F₀-GUVs.

Although the lumen increase of pH adjusts to the expected ΔpH as calculated by the Nernst potential due to K⁺ internalization, an independent measurement of the membrane potential by the fluorescent probe Rhodamine 123 indicates that the reconstituted F₁F₀ complexes are not able to completely compensate the membrane potential triggered by the valinomycin molecules (Fig. S7). After the initial regime of rapid ATP synthesis rate, the protein activity is expected to be maintained, as ΔΨ is not completely dissipated and the ATP synthesis by F₁F₀-ATPase of E. coli depends on the presence of an electric membrane potential (29).

Fig. S7.

Valinomycin-induced electrochemical potential measurements in D-F₁F₀-GUVs. Electrochemical potential experiments were visualized with the sensitive pH fluorescent probe pyranine (empty circles), and ΔΨ experiments were independently performed with the membrane potential fluorescent probe Rhod 123 (full circles). Note that the activity of F₁F₀ pumps is not able to fully compensate the rapid inward translocation of K⁺ promoted by valinomycin. As ATP synthesis rate of F₁F₀-ATPase of E. coli depends on the electric membrane potential, the dashed region represents the time period in which the protein activity increases. This time range was chosen to evaluate the membrane fluctuations at 20 °C.

Membrane Fluctuations.

To directly observe the impact of the ATP synthesis on the bending properties of lipid membranes, we performed single-vesicle fluctuation spectroscopy on F₁F₀-GUVs under ATP-producing (active) and non-ATP-producing (passive) conditions (Movie S1). Fig. 2 illustrates the membrane fluctuation maps of single GUVs, which are obtained as the root mean SD (RMSD =${\sigma }_h={\langle h^2\rangle }^{1/2}$) of the local fluctuation time traces recorded at different time intervals counted from the beginning of the reaction. On the addition of valinomycin, F₁F₀-GUVs membrane fluctuations became larger during protein activity and were characterized as membrane displacements far away from the equilibrium position (Fig. 2A). This observation correlates with the increasing protein activity established by the increasing ΔΨ during the first 20 min after the addition of valinomycin (Fig. S7). Moreover, active F₁F₀-GUVs showed enhanced fluctuations at discrete regions of the membrane, whose relative position varied from one time interval to another. The passive F₁F₀-GUVs exhibited initially similar but low fluctuations than active F₁F₀-GUVs (Fig. 2B). In this case, the fluctuations remained weak in amplitude along time and were characterized by a low value of the SD (σ_h^(pass) ≈ 15 nm). Nonetheless, the active vesicles displayed increasing enhanced fluctuations when tracked for the same time intervals as in the passive case (σ_h^(act) (t) ≥ σ_h^(pass)). Unlike passive vesicles, which remained fluctuating for longer times, active vesicles lose optical contrast and become unstable.

Fig. 2.

Membrane fluctuations of single D-F₁F₀-GUVs. Typical membrane fluctuation maps of a single D-F₁F₀-GUV at different time intervals (Ht, handling time) under (A) active conditions and (B) passive conditions. Scale bar represents the SD value (RMSD in nanometers) of the local membrane fluctuations measured in real space at the equatorial vesicle plane as h(i,t) − h₀, where h accounts for the time membrane position i and h₀ is the time average value. For illustration, see Movie S1.

The statistical characterization of the membrane fluctuations was performed using the ensemble-averaged probability density function (PDF) (Supporting Information), which was calculated over all of the points in the contour profile and over a statistically significant population of single vesicles (n ≥ 20). For passive F₁F₀-GUVs, the ensemble-averaged PDF is found to be nearly Gaussian (with a narrow and nearly symmetric quadratic signature in the logarithmic plot, Fig. S8A) as expected for thermal fluctuations. The membrane fluctuations were characterized by an RMSD value, σ₀ = 16.3 ± 0.3 nm, which remains unchanged over time. However, active F₁F₀-GUVs exhibited enhanced fluctuations, and the PDFs were found to progressively broaden over time (Fig. S8B). In this case, we found that the SD values shifted to higher values with increasing times: σ_{Ht + 4} = 25.6 ± 0.1 nm, σ_{Ht + 8} = 32.1 ± 0.3 nm, and σ_{Ht + 12} = 32.7 ± 0.3 nm. Regarding the higher PDF moments, they remained essentially compatible with the Gaussian characteristics in both cases (the third moment, or skewness, S = 0, and the fourth one, or kurtosis, K = 3; Fig. S8, Insets).

Fig. S8.

Ensemble-averaged PDF of D-F₁F₀-GUVs. (A) Ensemble-averaged PDF of passive D-F₁F₀-GUVs (n = 26) at different time intervals. (Inset) Skewness and kurtosis values for the explored time intervals. (B) Ensemble-averaged PDF of active D-F₁F₀-GUVs (n = 23) at different time intervals. (Inset) Skewness and kurtosis values for the explored time intervals. A Guassian distribution is characterized by a zero skewness and kurtosis K = 3.

Further, we explored the presence of locally non-Gaussian distributions (Fig. 3) at the specific membrane sites with magnified levels of membrane fluctuations, or hot spots (Fig. 2A). For the passive case, F₁F₀-GUVs were systematically characterized by almost normal Gaussian distributions along the membrane contour (Fig. 3 A and B), in agreement with the intrinsically symmetric nature of the thermal fluctuations. However, under active conditions, a non-Gaussian distribution of the membrane displacements is observed for different hot spots, which are generally right-skewed (S > 0) and leptokurtic (K > 3), as revealed by the longer tails than expected for the normal distribution (Fig. 3 C and D, respectively). The positive skew is compatible with a vectorized protein pumping toward the outer side of the membrane. As a representative example of this asymmetric behavior, we zoom on the mechanical hot spot 1 (S = 1.2, and K = 5.8) and hot spot 3 (S = 0.5, and K = 4), whereas the fluctuations in the low-activity sites (spots 2 and 4) distribute almost Gaussian (S ≈ 0; K ≈ 3). Because the majority of the membrane contour points display a Gaussian behavior, they mask the non-Gaussian signature of the hot spots when ensemble-averaged by the rest of the thermalized contour membrane points (Fig. S8B). Note that, according to the measured n₀, the protein area fraction is 0.15 to 1.5%, so that the number of active hot spots per contour GUV should be 3 to 30, in agreement with our observations.

Fig. 3.

Mechanical hot-spots of D-F₁F₀-GUVs. (A) Fluctuation map of passive D-F₁F₀-GUV from B (t = Ht + 12 min). Points indicate the membrane positions where the PDF is calculated in B. (B) PDF at different points highlighted in A. Dashed line represents the ensemble-averaged PDF as calculated for all contour points of the vesicle. (C) Active D-F₁F₀-GUV from A (t = Ht + 12 min). Points indicate membrane positions where the PDF is calculated in D. (D) PDF at different points highlighted in C. Dashed line represents the ensemble-averaged PDF as calculated for all points of the vesicle. PDFs from points 1 and 3 deviate from Gaussianity. Note that B and D have different scales to highlight the probable out-of-equilibrium signature of hot spots.

Membrane Mechanical Properties.

The experimental fluctuation spectra were obtained at different time intervals for both active and passive cases (Fig. 4A). Regarding q scaling, an evident difference is observed between passive and active cases. Helfrich-like scaling is observed for the passive vesicles (Fig. 4A, Top Right), which is characterized by a regular crossover between tension-dominated (P ≈ q⁻¹ at low q) down to a bending regime (P ≈ q⁻³ at high q) (Eq. 1). However, the spectral amplitudes of the active vesicles are characterized by a low-q pseudoplateau (P ≈ q⁰), which is characteristic of the tension-dominated regime of the active spectrum (Eq. 2 for A > 0 at ${\sigma }_{eff}\gg {\kappa }_{eff}{q}^2$). A decrease in the bending energy is pointed out as a progressive increase of the fluctuation amplitudes at low wave vectors, where the fluctuation modes are mainly driven by an active force exceeding the thermal energy and mainly restored by surface tension (Fig. 4A, Left). By contrast, only the thermal contribution is observed in this region of the fluctuation spectra under nonactive conditions (Fig. 4A, Top Right).

Fig. 4.

Fluctuation spectrum and mechanical properties. (A) Experimental fluctuation spectra obtained for a typical active D-F₁F₀-GUV at different time intervals after valinomycin incubation. Solid lines represent the best fit to Eq. 2. The dashed line represents the fit to Eq. 1 for the passive case (t = Ht) as shown in Top Right. (Top Right) Experimental fluctuation spectra obtained for a typical passive D-F₁F₀-GUV at different time intervals. Solid lines represent the best fit to Eq. 1. (Bottom Right) Variation of the effective surface tension σ at different time intervals after valinomycin incubation. (B) Variation of the population-averaged bending rigidity, κ, of active (red, n = 23) and passive (blue, n = 33) D-F₁F₀-GUVs measured at different time intervals. Bending rigidity is normalized to the bending rigidity measured for pure lipid EcGUVs, κ_TLE. The dashed region represents the dispersity on the lipid bending modulus, κ_TLE. (C) (Left) Variation of the effective activity, A, of active (red, n = 23) D-F₁F₀-GUVs at different time intervals. (Right) Variation of the coupling parameter (Ξ) at different time intervals after valinomycin incubation.

The effective values of the mechanical parameters can be obtained by fitting the experimental equatorial spectra to Eqs. 1 and 2. The progressive membrane softening observed under ATP synthesis was quantified as a decrease of the effective bending modulus due to protein activity (Eq. 4). The elastic parameters for active and passive F₁F₀-GUVs and EcGUVs are shown in Fig. 4B. EcGUVs represented the basal level of membrane fluctuation that corresponds to the rigidity of the bare lipid membrane with a statistically averaged bending modulus of κ_lipid = (13 ± 2) k_BT. The incorporation of proteins at low density (up to 1.5% in our case) into lipid membranes is not expected to produce significant compositional impact on the membrane rigidities (30); thus the measured value of bending stiffness in F₁F₀-GUVs was similar to that in EcGUVs and remained unchanged over time (Fig. 4B). Remarkably, on F₁F₀ activation, the value of bending rigidity significantly decreased by a quarter of the initial value compatible with the passive case. This mechanical softening can be understood as a dynamical effect that connects the F₁F₀ activity with the overall membrane softening. With respect to surface tension, no significant changes of the averaged population values were detected during protein activity. The high variability of this mechanical parameter among different vesicle specimens is due to the broadly variable excess area that is created in every single vesicle using electroformation (25) (see Supporting Information for a detailed explanation). However, a systematic decrease of the effective value is observed for individual specimens undergoing nonequilibrium fluctuations (Fig. 4A, Bottom Right), in agreement with similar active systems with protein pumps (15, 31).

The quantitative spectral analysis in terms of active vesicle theory allows for a discrimination of a nonequilibrium fluctuation regime. Particularly, the amplitude of the active component A was evaluated (Fig. 4C, Left). On average, we measured initial values of A ≈ 400 k_BT that decreased over time to values close to 150 k_BT. The global decrease observed in the active term, which is concomitant with a monotonical decrease in the bending modulus, reflects the nontrivial dependence of the effective amplitude A on activity. In effect, A is proportional to the force, F₀, exerted by the active proteins according to Eq. 3, but also decreases with the strength of the coupling term $\mathrm{\Xi }$, which might depend itself on the pumping activity. From Eq. 4, higher values of $\mathrm{\Xi }$ are obtained under continuous fluctuation enhancement (Fig. 4C, Right). Thus, the observed decrease of A over time indicates the progressive dominance of the coupling term, whereas F₀ remains essentially constant. From the fits, the value of F₀ can be deduced, which is of the order of F₀ = 10⁻²⁵ to 10⁻²⁶ J m (taking our experimental value for n₀ = 10¹³ m⁻² and 10¹⁴ m⁻², respectively). This estimation for F₁F₀-ATPase seems higher than previous values obtained from micropipette and shape fluctuation experiments with GUVs containing the pumping membrane protein bacteriorhodopsin (13, 31). However, once the protein densities are considered, similar values of A are obtained for the two proteins. This energy can be related to the energy barrier that the pumping proteins must overcome during the proton transfer process. Whereas this barrier is of the order of 10 kcal/mol for bacteriorhodopsin (32), the torque required for a full rotation of the ATPase motor corresponds to a free energy barrier of 14 kcal/mol, which is supplied by the proton gradient (Discussion). Finally, note that the increasing of the coupling constant $\mathrm{\Xi }$ can be interpreted in terms of localized protein activity, which may eventually reach the onset of instability predicted in ref. 24, a fact compatible with the presence of localized nonequilibrium fluctuations at the hot spots where the protein could be clustered.

Time Correlation Function and Relaxation Dynamics.

Additional evidence on the nonequilibrium character of the membrane fluctuations during ATP synthesis arises from the analysis of the relaxation dynamics of the membrane fluctuations that are obtained from the height-to-height time ACF (Materials and Methods). Fig. 5 A and B shows typical experimental ACFs calculated for the first equatorial fluctuation modes for passive and active F₁F₀-GUVs, respectively. In Fig. 5C, we show the relaxation rates obtained from the single-exponential fittings for the passive case (Eq. 5 for ${\langle h_q^2\rangle }_{\text{act}}=0$, when $A=0$). The mechanical parameters were obtained by fitting the experimental relaxation rates to Eq. 6 (see Supporting Information for details). We obtained κ_pass = 14 ± 3 k_BT (n = 10 vesicles), in agreement with the values previously obtained from the time-averaged fluctuation spectra (Fig. 4). However, ACFs from active F₁F₀-GUVs exhibited the two-exponential decay predicted by Eq. 5 from active vesicle theory (Fig. 5B), which describes two relaxation modes. As in passive F₁F₀-GUVs, the relaxation rate of the faster mode showed the same power-law dependence as described by the thermal mode (Fig. 5D). Note that, in the active theory, both the surface tension and the bending modulus contain the active contribution to the relaxation rates (13). From our experiments, an effective value of the bending rigidity κ_eff = 2 ± 1 k_BT < κ_pass is obtained (n = 7 vesicles), whereas a systematic decrease of the effective value of surface tension is detected in every single vesicle after protein activation. This result is in quantitative agreement with the effective decrease in the bending modulus and the tension lowering observed from the fluctuation spectra in active F₁F₀-GUVs, as shown in Fig. 4. Furthermore, whereas the thermal mode is found to be dispersive, the second relaxation mode appears always with a nearly q-independent relaxation rate, which suggests a metabolic origin that could be related to the characteristic rate of the enzymatic activity of the protein (15). The relaxation dynamics of active F₁F₀-GUVs was characterized by a constant rate, at Γ_act = 20 ± 5 s⁻¹.

Fig. 5.

Time correlation function and relaxation dynamics. Experimental ACFs of a D-F₁F₀-GUV in the (A) passive and (B) active cases for azimuthal wave vectors 2 ≤ l ≤ 10. Solid lines correspond to fits of the experimental data to Eq. 5. Only the thermal contribution of Eq. 5 was necessary under passive conditions, whereas the bimodal function of Eq. 5 was required for active D-F₁F₀-GUVs. Relaxation rates of a D-F₁F₀-GUV in the (C) passive and (D) active cases. Thermal frequencies, Γ₀, were fitted using Eq. S8 with η = 1 cP (solid lines). For comparison, dashed line in D corresponds to the thermal rate shown in C. Γ_act is the characteristic rate of the metabolic active mode.

As a main outcome of our results, we have demonstrated the functional reconstitution of F₁F₀-ATPase in GUVs, and evidenced that the ATP synthesis activity of the F₁F₀-ATPase promotes enhanced nonequilibrium membrane fluctuations that modify the mechanical properties of the embedding lipid bilayer.

Discussion

According to the conventional Helfrich theory (33, 34), the amplitudes of the thermal fluctuations become progressively smaller at higher wave vectors. Thus, bending-mediated fluctuations prevent large-amplitude deformations at the nanoscale if excited by passive thermal agitation alone. However, cell membranes exhibit a plethora of morphologies in the nanometric scale, including highly curved membranes of some organelles, such as the Golgi, the endoplasmic reticulum, and the inner mitochondrial membrane. Cells take advantage of membrane-associated proteins to promote and stabilize these local membrane deformations either by scaffolding (35, 36) or by wedging (37, 38) mechanisms.

Bending-effector proteins stress membrane distortion that affects the mechanical behavior of the hosting bilayer. Protein activity can contribute to decrease the bending energy of lipid bilayers, as already detected in giant vesicles containing bacteriorhodopsin (13, 31), Ca²⁺ ATPase (14), Na⁺ ATPase (15), or K⁺ ATPase (37). Our observational results with active vesicles containing F₁F₀-ATPase reveal enhanced fluctuations at localized hot spots in the vesicle membrane that translate into a global lowering in surface tension, which is predominant over long distances, and a decrease in the bending modulus of the membrane at high wave vectors. As F₁F₀-ATPase is not only a proton pump but also a rotating motor through the membrane-spanning component, F_0, two possible effecting modes can be attributed to F₁F₀-ATPase to explain the enhanced membrane fluctuations: a transverse mode connected with the proton-pumping activity of the enzyme, and an in-plane rotating mode connected to the directional torque of the protein rotor.

Pumping.

The coupling mechanism existing between transverse flow of protons across the membrane and the lateral stresses explains the observed lowering in surface tension, as shown for the case of the proton-pumping activity of bacteriorhodopsin (31). Likewise, the coupling between the protein density and the bending elasticity of the membrane can be invoked to explain the observed membrane softening (24). Indeed the nonequilibrium fluctuations found at hot spots are compatible with a pumping-driven undulation of the membrane due to the action of clustered proteins (24). In structural terms, the ability of conic-like ATP synthase dimers to partition into highly curved membranes has been also proposed to induce membrane curved shapes characterized by a wedge angle within the range of 55° and 120° (18, 19). This wedged configuration gives structural support to a positive spontaneous curvature (C₀ > 0) and thus to a localized membrane softening [κ_eff = κ (1−C₀R)² < κ] (39). Furthermore, above a given concentration threshold for protein clustering, the dynamic coupling between protein and curvature can elicit a membrane instability through localized high-amplitude fluctuations (24), as observed at long times in our experimental realization.

Rotation.

The pumping-driven clustering of F₁F₀-ATPases might possibly involve a facilitated protein diffusion of rotating motors through a long-range hydrodynamic interaction mediated by the viscoelastic substrate (40). Indeed, active rotation in a dense medium gives rise to effective interactions between rotors that promote clustering, phase separation, spatial ordering, and synchronization (41–45). These effects remain experimentally unexplored in the case of F₁F₀-ATPase, but the localized nonequilibrium membrane fluctuations we report here can be explained as a consequence of the collective behavior of simultaneous pumping protein clusters mediated by molecular rotation. To identify the characteristic rotation time for an individual rotor, the generated torque by F₀-ring rotation can be estimated as T = ξ × ω = 6πμR² ω; where ξ is the drag force of a disk embedded in 2D medium, ω is the angular velocity, μ is the surface membrane viscosity, and R is the radius of the F₀ ring. Taking previously reported values for μ = 10⁻⁵ N s⋅m⁻¹ (46), R = 5 nm (47), and the experimentally measured characteristic rate ω = Γ_act = 20 ± 5 s⁻¹, we obtain a frictional torque of about 100 ± 25 pN nm. This value is similar to that reported previously for E. coli F₁F₀-ATPase (6, 48, 49) and corresponds to the metabolic energy put into play in a rotating cycle of the F₁F₀-ATPase to hydrolyze/synthetize three molecules of ATP. The agreement of these estimations with biochemical information suggests that the time correlation of the active component actually corresponds to the rotational movements of the F₀ ring during ATP synthesis. Therefore, we identify dynamical correlations at a mesoscopic scale, which may correspond to the F₀-ring rotation time in lipid membranes and in the absence of any probe that may eventually drag its rotatory motion.

Furthermore, the correlation decay time of the active component, Γ_act, might be predicted from an alternative bending energy formulation. The rotational movements of the F₀ ring during ATP synthesis could be transmitted to the lipid membrane environment by a torsional−curvature coupling mechanism, as lipid reorganization can take place at the vicinity of rotating proteins (50). In a simple dynamical modeling, a metabolic rotator is coupled with the bending mode of the membrane, causing an additional susceptibility, χ_act ≈ (T/V₀)∇²h, where T is the torque power stroke of the rotor and V₀ is the molecular volume where rotation takes place. Thus, whereas the thermal mode relaxation depends on the bulk viscosity, the active mode due to metabolic activity of the rotator might relax through the shear viscosity of the embedding membrane, with the hydrodynamic compliance Λ_memb = 4μq². Consequently, the active mode is expected to relax at a q-independent constant rate Γ_act ≈ χ_act/Λ_memb ≈ Τ/(μA₀) ≈ 10 s⁻¹ in agreement with our experimental observations (here, A₀ ≈ V₀/h is the molecular area of the rotor).

In summary, we present experimental evidence that the coupled pumping and rotation activities of F₁F₀-ATPase promote localized nonequilibrium membrane fluctuations where the active proteins might be clustered. The activity of F₁F₀-ATPase favors the decrease in the bending stiffness of the membrane and the concomitant lowering of its surface tension. Our results point out the existence of a functional connection between microscopic protein activity, supramolecular organization, and macroscopic mechanics, which could be not only operating as a protein activity modulator or as an effector of membrane remodeling in vivo but also exploited in synthetic realizations containing F₁F₀-ATPase within viscoelastic media.

Chemicals

Potassium chloride (KCl), magnesium chloride (MgCl₂), glucose, sucrose, Tris(hydroxymethyl)aminomethane (Tris), 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid (Hepes), hydroxypyrene-1,3,6-trisulfonic acid (Pyranine), valinomycin, dibasic potassium phosphate (K₂HPO₄), and adenosine-5′-diphosphate (Na₂ADP) were supplied by Sigma-Aldrich. DDM was purchased from VWR. Ultrapure water was produced from a Milli-Q unit (Millipore, conductivity lower than 18 MΩ cm).

Lipids

The fluorescent probe 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine-N- (lissamine rhodamine B sulfonyl) (Rh-PE) and E. coli TLE were purchased from Avanti Polar and suspended in chloroform at 1 mg/mL and 20 mg/mL, respectively. Lipids were stored at −20 °C.

Purification and Reconstitution of the E. coli F₁F₀-ATPase into SUVs

The E. coli F₁F₀-ATPase was purified from native E. coli MG1655 cytoplasmic membranes as previously described (7) and reconstituted together with E. coli TLE into SUVs by rapid dilution. Briefly, 100 μL of purified F₁F₀-ATPase (0.5 mg/mL) was incubated with 20 μL of E. coli TLE (20 mg/mL) for 30 min on ice and rapidly diluted to a volume of 4 mL with 50 mM Tris⋅HCl (pH 8) and 3 mM KCl. Proteoliposomes carrying the F₁F₀-ATPase (F₁F₀-SUVs) were collected by ultracentrifugation (MLA 80 rotor; 30 min at 298,906 × g) and resuspended in 100 μL of H₂O.

Fluorescent Labeling of F₁F₀-ATPase

Before reconstitution, the purified F₁F₀-ATPase complex was incubated with 1 mM fluorescent Alexa 647-NHS at 4 °C for 120 min. The reaction was quenched by the addition of 10 mM Lysine, and the unreacted label was removed by ion exchange chromatography.

Protein Density Quantification

The phospholipid to protein ratio of the F₁F₀-GUVs was estimated on the determination of the phospholipid concentration according to Rouser et al. (51) and the protein concentration by comparative Western blot (52) using known concentrations of purified F₁F₀ complex as a reference and a specific monoclonal antibody of the F₁-beta subunit for protein detection. The protein concentration was quantified from nonsaturated Western blot signals with the ImageJ software package (53).

Confocal Microscopy

Confocal microscopy images of F₁F₀-GUVs were collected with a Nikon Ti-E inverted microscope equipped with a Nikon C2 confocal scanning confocal module, 488-nm and 561-nm continuous lasers, emission band-pass filters, and a Nikon Plan Apo 100× NA 1.45 oil immersion objective. Images were processed with the Nikon NIS-Elements software and further processed with MATLAB R2013b (The MathWorks Inc.).

Valinomycin-Induced Electrochemical Potential Measurements in GUVs

In our experimental setup, ATP synthesis is triggered by the addition of the selective K⁺ transporter valinomycin. In the presence of valinomycin, K⁺ ions from the outer medium ([K⁺]_out = 30 mM) enter the lumen of vesicles ([K⁺]_in = 1 mM) and produce an electrical transmembrane potential (ΔΨ ≈ $\log {\left[K\right]}_{\text{out}}/{\left[K\right]}_{\text{in}}$), positive inside, which triggers the ATP synthesis by the F₁F₀ proteins. The vectorial proton transport across the membrane eventually leads to the luminal basification of the GUV and promotes the synthesis of ATP by the F₁ subunit that binds ADP and inorganic phosphate (P_i) on the external side of the GUV.

The luminal basification of GUVs was recorded over time as the increase in fluorescence intensity from the encapsulated pyranine (28), a pH-sensitive probe whose fluorescence intensity increases linearly with the pH of the solution within the range of 6.5 to 8.5. Out of this range, the fluorescence intensity becomes nearly constant (Fig. S5A). The linear regime is characterized by a slope m_LR, which depends also linearly on the initial concentration of the probe, c₀, as m_LR = m_pH c₀ (Fig. S5B). As electroformation does not reach a 100% encapsulation yield of the pyranine in GUVs, the initial concentration was determined for each vesicle using the calibration curve $I_0^{\left(7.2\right)}=m_{c_0}{c}_0$ measured at pH = 7.2 (Fig. S5C). After valinomycin incubation, the time course of the pH increase can be described by $\mathrm{\Delta }pH\left(t\right)=I\left(t\right)-I_0^{\left(7.2\right)}/m_{LR}=I\left(t\right)-I_0^{\left(7.2\right)}/m_{pH}{c}_0=\left(I\left(t\right)-I_0^{\left(7.2\right)}\right)m_{c_0}/m_{pH}{I}_0^{\left(7.2\right)}$, where I(t) is the instantaneous intensity and $I_0^{\left(7.2\right)}$ accounts for the initial fluorescence intensity, both measured in the lumen of each GUV.

Similar but independent experiments were performed to estimate the time evolution of the valinomycin-dependent membrane potential in F₁F₀-GUVs using the increase of membrane fluorescence of Rhodamine 123 (Fig. S7). Rho 123 is a cationic membrane potential probe whose fluorescence intensity increases as it accumulates the lipid bilayer of the vesicle by the presence of a membrane potential (54). It is worth noting that, 20 min after the addition of valinomycin, ΔΨ still continues to increase linearly. The protein activity is assumed to increase during this period, as the rate of ATP synthesis by F₁F₀-ATPase of E. coli depends on the electric membrane potential. After 30 min of incubation with valinomycin, both ΔpH and ΔΨ reached steady values.

High-Velocity Video Microscopy

Phase contrast microscopy images and movies of the F₁F₀-GUVs were recorded with an inverted microscope (Nikon Eclipse 2000Ti) equipped with a 100 W TI-12 DH Pillar Illuminator, an LWD 0.52 collimator, and a 100× oil immersion objective (PlanApoVC, N.A. 1.4; Nikon). Fluctuation movies (see Movie S1 for a representative example) were captured with a FASTCAM SA3 camera (Photron), with an effective pixel size of 50 × 50 nm². To provide optimal signal-to-noise ratio (SNR), the movies were recorded during 1 s of tracking time at a sampling frequency of 500 Hz (n = 500 frames). Experiments on membrane fluctuations were made at 22 °C. The GUV equatorial positions were digitally segmented using a custom-made algorithm that combines accurate instantaneous positioning of the membrane contour with respect to the GUV center (55) and optimal contour imaging with respect to the background noise (11).

The radial positions of the contour points R_j(x_j, t) (j = 1, … n = 2,048) are determined for each frame of the recorded movie. The statistics of the membrane fluctuations is built as a real-space ensemble, which is constituted by the local displacements of each point in the equatorial contour of the vesicle membrane, h_j(x, t) = R_j(x_j, t) − R₀, with R₀ being the contour-averaged radius measured with respect to the instantaneous position of the vesicle barycenter.

To statistically characterize the membrane fluctuations on F₁F₀ activity, the ensemble-averaged PDF was built from the normalized histograms of the membrane height displacements, which were time-averaged over all of the points in the equatorial profile and over a statistically significant population of individual vesicles (n ≥ 20, typically). The PDF is used to calculate the three first consecutive moments, that is, the SD, the skewness, and the kurtosis, respectively, which allows the analysis of a possible deviation from Gaussianity.

Membrane Fluctuation Spectroscopy

At a given time t, the equatorial fluctuations h(t) = {h_j (x_j,t} with j = 1…n are described as discrete Fourier modes h(t) = Σ_(l)h_l(t) exp(iq_xx), where q_x = l/R₀ is the equatorial projection of the fluctuation wave vector (l = 2, 3, 4, … ∞, with l as the azimuthal number; l = 1 corresponds to the breathing mode, which does not contribute to change the spherical shape). The fluctuation spectrum P(q) is defined as the amplitude variance of the thermal fluctuation modes; this is ${\langle h_q^2\rangle }_{th}={\langle h_q\left(t\right)h_q\left(t\right)\rangle }_{th}$. By comparison with the theoretical spectrum, the Fourier-space decomposition of the vesicle fluctuations allows the calculation of the mechanical parameters of the membrane. At equilibrium conditions, according to the fluctuation−dissipation theorem, the spectrum reads

$$P_{th}\left(q\right)={\mathrm{ℒ}}^2{\langle h_q^2\rangle }_{th}={\mathrm{ℒ}}^2\frac{k_{B}T}{{\chi }_{th}},$$ [S1]

where ${\mathrm{ℒ}}^2$ is the area of the fluctuating membrane, $\langle \cdot \rangle$ denotes the time average on the time ensemble h_q(t_k); k = 1…N, and ${\chi }_{th}$ is the elastic susceptibility of the thermal membrane modes, as described by the Helfrich Hamiltonian (HH) (33, 34).

$$\delta E_{\text{Helf}}=\frac{1}{2}\left[\sigma {\left(\nabla h\right)}^2+\kappa {\left({\nabla }^{2}h\right)}^2\right].$$ [S2]

From HH, the formation of thermal modes is opposed by membrane stiffness, which restores changes both in membrane area through surface tension (σ) and in membrane curvature by bending rigidity (κ). For planar modes in Fourier space, the thermal elastic susceptibility associated with HH reads as ${\chi }_{th}=\sigma q^2+\kappa q^4$. This is the usual description used to analyze thermal modes in passive membranes, that is, lipid vesicles (11, 12). Here, the mechanical parameters κ and σ are obtained by fitting the experimental mode amplitudes to the Helfrich theoretical spectrum particularized to the equatorial fluctuations; in the case of a passive membrane, this equatorial spectrum is given by (11)

$$P_{th}^{\left(\text{pass}\right)}\left(q_x\right)={\displaystyle \int P_{th}\left(q_x,q_y\right)d{q}_y}=\frac{k_{B}T}{2\sigma }\left[\frac{1}{q_x}-\sqrt{\frac{\kappa }{\sigma +\kappa q_x^2}}\right],$$ [S3]

where the x component of the wave vector q = (q_x, q_y) is chosen as the equatorial projection of the fluctuation wave vector; this is q_x (=l/R₀, with l = 2, 3, 4, … ∞). Since our experiments only deal with equatorial fluctuations described in terms of the azimuthal modes with wave vectors q_x, in the following, they will be renamed as q for simplicity, and the equatorial spectrum will be simply P(q). Thus, Eq. S3 is rewritten as Eq. 1.

Experimental spectra are often analyzed in terms of q scaling. For the passive membrane, two regimes can be distinguished in the equatorial spectrum depending on q; a tension-dominated regime P ≈ q⁻¹ at q << (σ/κ)^1/2, and P ≈ q⁻³ in the bending dominated regime at q >> (σ/κ)^1/2.

Relaxation Dynamics, Time Correlations, and Active Vesicle Theory

GUV dynamics is experimentally probed through the time ACF of the membrane height fluctuations (transverse fluctuations), which, in Fourier space, is defined as

$${\text{ACF}}_q\left(t\right)=\frac{\langle h_q\left(t\prime -t\right)h_q(t\prime )\rangle }{\langle h_q^2\rangle }.$$ [S4]

This ACF is normalized, with a normalization constant given by the height variance$\langle h_q^2\rangle$. From a theoretical standpoint, the ACF can be calculated from solving the equation of motion (EoM) of the membrane thermal fluctuations, which describes a generalized stochastic diffusive transport, where the fluctuation field h evolves driven by the gradient in elastic energy δE/δh; usually, EoM is written with the Langevin form (56),

$$\frac{\partial h}{\partial t}+\mathrm{\Lambda }\frac{\delta E}{\delta h}={\xi }_{th}\left(t\right),$$ [S5]

where $\mathrm{\Lambda }$ is a generalized hydrodynamic compliance, and ${\xi }_{th}\left(t\right)$ is a stochastic velocity function of variance $\langle {\xi }_{th}\left(t\right){\xi }_{th}(t\prime )\rangle =2\mathrm{\Lambda }{k}_{B}T\delta \left(t-t\prime \right)$.

For elastic systems in the linear regime, $\delta E/\delta h=\chi h$, with $\chi$ being a generalized elastic susceptibility; for thermal modes in an elastic membrane, ${\chi }_{th}=\sigma q^2+\kappa q^4$. If membrane relaxation occurs exclusively via bulk viscosity (against the surrounding fluid of shear viscosity $\eta$), then ${\mathrm{\Lambda }}_0=1/4\eta q$ (56). Under these conditions, EoM takes the form $\dot{h}+{\mathrm{\Gamma }}_{0}h={\xi }_{th}\left(t\right)$, where ${\mathrm{\Gamma }}_0={\mathrm{\Lambda }}_0{\chi }_{th}$ is a decay rate determined by the balance between elastic stresses and hydrodynamic friction; thus, time correlations of the ordinary (passive) fluctuation modes are found with a single-exponential decay as (25)

$$\langle h_q\left(t\prime -t\right)h_q(t\prime )\rangle ={\langle h_q^2\rangle }_{\text{pass}}{e}^{-{\mathrm{\Gamma }}_{0}t}$$ [S6]

with height variance

$${\langle h_q^2\rangle }_{\text{pass}}=\frac{k_{B}T}{\sigma q^2+\kappa q^4}$$ [S7]

and relaxation rates

$${\mathrm{\Gamma }}_0=\frac{\sigma q+\kappa q^3}{4\eta }.$$ [S8]

To describe the mechanical response of the vesicle membrane containing mechanically active proteins, we considered an effective HH framework combined with a permeability-modified relaxation dynamics (15, 22, 23). To account for the observed out-of-equilibrium membrane fluctuations that give rise to effective bending softening, we considered linear coupling between active protein motions and local curvature, similarly to the active permeation theory of Prost and collaborators, which was developed to account for the proton-pumping activity of bacteriorhodopsin (57). In that theory, a protein-dependent extension of the HH is given as

$$\delta E\left[h,\psi \right]=\delta E_{\text{Helf}}\left[h\right]+\frac{1}{2}\zeta {\psi }^2-\mathrm{\Xi }\psi {\nabla }^{2}h,$$ [S9]

where the additional field ψ accounts for the net imbalance in protein density that gives rise to nonequilibrium membrane activity.

Two additional terms due to protein are included in the modified membrane Hamiltonian: (i) the energy cost necessary to generate a protein density imbalance, which is quantified by the linear osmotic impedance ζ [for dilute protein density in the membrane, ζ ≈ k_BT/n₀, where n₀ is the average density of proteins; in the present work, n₀ ≈ 10¹³ m⁻² to 10¹⁴ m⁻², which represents a surface coverage as low as 0.15 to 1.5% (Supporting Information)]; and (ii) a stabilizing contribution from the active motions, which supports creation of nonequilibrium modes, and thus enhances membrane fluctuations (the last term in the right-hand side of Eq. S9). This term is written as a negative contribution to changes in elastic energy, which is proportional, through the coupling constant Ξ, to the crossed product between the local membrane curvature and the colocalized change in the protein density field.

Regarding diffusive dynamics of the height fluctuations, if an active protein is assumed to exert a force f₀ normal to the membrane, an additional term due to the transport of the protein density field must be considered; this is $\dot{h}+\mathrm{\Lambda }\left(\partial E/\partial h\right)+v_0\psi ={\xi }_{th}\left(t\right)$, where $v_0=\mathrm{\Lambda }{F}_0$ is the normal projection of the active velocity field (24). The presence of transverse membrane transport (e.g., due to passive membrane permeability, or to the pumping activity of membrane protein channels) is particularly relevant, as it makes the hydrodynamic compliance increase by a permeation flow term, $\mathrm{\Lambda }={\mu }_P+{\mathrm{\Lambda }}_0={\mu }_P+{\left(4\eta q\right)}^{-1}$ (with ${\mu }_P$ being a permeation rate (13, 24). Additionally, the dynamic evolution of the protein density field obeys the conservation law $\dot{\psi }-D\mathrm{\Delta }\psi +\mathrm{\Lambda }\left(\partial E/\partial \psi \right)={\xi }_{\psi }\left(t\right)$, where D is the lateral diffusion coefficient of the membrane protein.

In the stable dynamic regime, there is an intermediate q range of effective softening where several relevant features emerge from the active model (24):

• i)The “equilibrium” height variance of the (passive) mechanical modes varies as

$${\langle h_q^2\rangle }_{\text{pass}}=\frac{k_{B}T}{{\sigma }_{eff}{q}^2+{\kappa }_{eff}{q}^4}$$ [S10]

• with an effective bending rigidity

$${\kappa }_{eff}=\kappa -{\mathrm{\Xi }}^2/\zeta ,$$ [S11]

• that is, the larger the protein activity, the higher the bending softening undergone by the membrane.

• ii)There is a superposed nonequilibrium (active) mode of fluctuation with a strength depending on kinetic coefficients. This mode describes nonequilibrium fluctuations, which are a direct consequence of the force stressed by the active proteins, that is, ${\langle h_q^2\rangle }_{\text{act}}\propto F_0^2$, where (with $F_0=f_0/n_0$).
• iii)The longest fluctuations travel as nondispersive waves, that is, with time correlations independent of the wave vector, and exclusively set by the activity of the protein. Therefore, the ACF is expected in this regime with a bimodal form,

$$\langle h_q\left(t\prime -t\right)h_q(t\prime )\rangle ={\langle h_q^2\rangle }_{\text{pass}}{e}^{-{\mathrm{\Gamma }}_{1}t}+{\langle h_q^2\rangle }_{\text{act}}{e}^{-{\mathrm{\Gamma }}_{\text{act}}t},$$ [S12]

• which consists of the ordinary mechanical mode (passive) with equilibrium amplitude ${\langle h_q^2\rangle }_{\text{pass}}$ and relaxation rate, ${\mathrm{\Gamma }}_1=\mathrm{\Lambda }{\chi }_{th}\ge {\mathrm{\Gamma }}_0$, plus an active term, which describes nonequilibrium (active) fluctuations driven by the protein activity. If protein diffusional dynamics is neglected (4ηqD << κq² + σ), the amplitudes of these active fluctuations is expected to vary as (13, 24)

$${\langle h_q^2\rangle }_{\text{act}}={\langle h_q^2\rangle }_{\text{pass}}\left(1+\frac{A{q}^2}{{\sigma }_{eff}+{\kappa }_{eff}{q}^2}\right),$$ [S13]

• where $A$ enters the nonequilibrium contribution of protein activity to the height fluctuations, and the equatorial fluctuation spectrum used to fit the experimental data are taken with the general form (24)

$$P_{q_x}^{\left(\exp \right)}\left(q_x\right)=P_{q_x}^{\left(\text{pass}\right)}\left({\sigma }_{eff},{\kappa }_{eff}\right)+\frac{A\hspace{0.17em}}{4{\kappa }_{eff}^2}\frac{k_{B}T\hspace{0.17em}}{{\left(q^2+\frac{{\sigma }_{eff}}{{\kappa }_{eff}}\right)}^{3/2}},$$ [S14]

• where the passive term $P_{q_x}^{\left(\text{pass}\right)}=P_{th}^{\left(eq\right)}$ corresponds to the equilibrium expression in Eq. S3, and $A=F_0^2-\mathrm{\Xi }{F}_0/4\zeta$ describes the amplitude of the active term and $\zeta =k_{B}T/n_0$ for dilute protein density, $n_0$. Eq. S14 corresponds to the expression in Eq. 2, which is used to fit the experimental spectra.

Similarly, the normalized ACF obtained from experiments would be fitted to a bimodal exponential written as the sum of an equilibrium term ACF_q^(th) corresponding to the thermal fluctuations plus an active component ACF_q^(act),

$${\text{ACF}}_q\left(t\right)=A_q{\text{ACF}}_q^{\left(th\right)}\left(t\right)+\left(1-A_q\right){\text{ACF}}_q^{\left(\text{act}\right)}\left(t\right),$$ [S15]

where the normalized coefficient A_q accounts for the relative contribution of the passive component. Here, the active component ${\text{ACF}}_q^{\text{act}}\left(t\right)$ is formally described as a second relaxation mode, which is assumed to decay exponentially at a constant rate corresponding to the correlations of the active process (58); thus, ${\text{ACF}}_q^{\text{act}}\left(t\right)\approx \exp \left(-{\mathrm{\Gamma }}_{act}t\right)$, where Γ_act is the characteristic rate of the metabolic process, which produces correlations only at a characteristic timescale independently of the considered mode.