F_oF₁-ATPase, rotary motor and biosensor

Abstract

F_oF₁-ATPase is an amazing molecular rotary motor at the nanoscale. Single molecule technologies have contributed much to the understanding of the motor. For example, fluorescence imaging and spectroscopy revealed the physical rotation of isolated F₁ and F_o, or F_oF₁ holoenzyme. Magnetic tweezers were employed to manipulate the ATP synthesis/hydrolysis in F₁, and proton translation in F_o. Here, we briefly review our recent works including a systematic kinetics study of the holoenzyme, the mechanochemical coupling mechanism, reconstituting the δ-free F_oF₁-ATPase, direct observation of F_o rotation at single molecule level and activity regulation through external links on the stator.

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Yao-Gen Shu

Y.-G. Shu was born on January 4, 1964 in Zhejiang province, China. He received his Bachelor of Electronic Engineering in July 1985 at Zhejiang University, and then worked on industrial automation till 1999. He received his Ph. D. in 2004 at the Department of Physics of Xiamen University. From 2004 to 2009, he worked with Prof. Zhong-Can Ou-Yang at the Institute of Theoretical Physics (Chinese Academy of Sciences) and Prof. Pik-Yin Lai at the National Central University (Taiwan), respectively. Currently, he is a research fellow at the Institute of Theoretical Physics. His research focuses on molecular motors, cell motion, biosensor, nanodevices, and so on.

Jia-Chang Yue

Prof. Jia-Chang Yue is the leader of the molecular motor group at the Institute of Biophysics at the Chinese Academy of Sciences. He has held positions as a visiting scholar at Tohoku University, Japan and Hong Kong Polytechnic University. Previously he researched at the Department of Engineering Physics, Tsinghua University, China. Current research interests include: the structure and function of the rotary molecular motor FoF1-ATPase, and developing biosensors based on FoF1-ATPase.

Zhong-Can Ou-Yang

Prof. Zhong-Can Ou-Yang was born on January 25, 1946 in Fujian province, China. He received his Ph.D. in 1984 from Tsinghua University (Beijing). From 1987–1988, he worked with Prof. W. Helfrich at the Freie University (Berlin) as an Alexander von Humboldt fellow. He has been a professor at the Institute of Theoretical Physics, Chinese Academy of Sciences since 1992, and Director from 1998–2007. His research focuses on soft condensed matter physics and theoretical biophysics. He received the Achievement in Asia Award from the Overseas Chinese Physics Association in 1993 and is a member of Chinese Academy of Sciences and the Third Word Academy of Sciences.

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I. Introduction

F_oF₁-ATPase is a ubiquitous rotary motor that uses the transmembrane electrochemical potential to synthesize ATP in the plasma membrane of bacteria, chloroplasts and mitochondria. The holoenzyme is a complex of two rotary motors, F_o and F₁, which are mechanically coupled by a common central stalk (“rotor”), c_nεγ. The membrane embedded F_o unit converts the proton motive force (p.m.f.) into mechanical rotation of the “rotor”, thereby causing cyclic conformational change of α₃β₃ crown (“stator”) in F₁ and driving ATP synthesis. A striking characteristic of this motor is its reversibility. It may rotate in the reverse direction for ATP hydrolysis and utilize the excess energy to pump protons across the membrane.^1–6

The basic hypothesis, “binding change mechanism”,⁷ however, had not been confirmed until direct observation of the rotation of F₁-ATPase at the single molecule level in 1997,⁸ although it was partly proven by the eccentric structure of the γ subunit in 1994.⁹ Single molecule technologies have contributed much to the understanding of the motor. For example, fluorescence imaging and spectroscopy revealed the physical rotation of isolated F₁^8,10–12 and F_o,^13,14 or F₁F_o holoenzyme.^15–17 Magnetic tweezers also be employed to manipulate the ATP synthesis/hydrolysis in F₁,^18,19 and proton translation in F_o.²⁰ Nevertheless, the fundamental relation between the rotation speed and substrate/product concentrations, transmembrane p.m.f. and damping coefficient is important in the time frame of enzymatics.²¹

II. Systematic kinetics of the holoenzyme

A few theoretical approaches have been proposed, aiming for a better understanding of the operating mechanism of this reversible motor. Some work focused on the hydrolysis or synthesis of F₁. For example, Oster et al. constructed a 4³ states model for the couplings among three catalytic sites and provided a physical view of the dynamics.^22–24 However, this model is too sophisticated to be investigated analytically. Some other models studied the mechanism of torque generation of F_o with a turbine or all-atom model.^25–27 The kinetics of the motor have also been investigated by Pänke et al. with simulations or storage of elastic energy model.^28,29 Here, we focus on an analytical investigation of the systematic kinetics of the holoenzyme, that is, the fundamental relation between the rotation speed and substrate/product concentrations, transmembrane p.m.f. and damping coefficient.²¹

It is well established that the mechanical process in F_o and the chemical reactions in F₁ are tightly coupled. Therefore, it is possible to construct a theory which can systematically describe the whole machine. From the view point of enzymatics, conventional theory generally concerned with irreversible reaction on a single substrate which can be described by Michaelis–Menten kinetics. But ATP can be reversibly synthesized and hydrolyzed in F_oF₁-ATPase, and the reaction involves several substrates/products, thus there is an need for a quantitative theory which describes the multi-substrate/product enzymatics. Furthermore, analytical results could presumably allow for a deeper insight for the working principles of the motor.

F_oF₁-ATPase, in particular, is an amazing reversible motor. ATP hydrolysis does spontaneously occur in F₁, whereas the thermodynamically unfavorable reaction, ATP synthesis, has to be driven by harnessing the transmembrane proton flow in F_o. If the motor functions as a synthase, the two substrates, ADP and P_i, are recombined into one product, ATP. The binding order of the two substrates is a characteristic attribute of the synthase. On the basis of inhibition studies, a compulsory order with binding of ADP preceding that of P_i was proposed.³⁰ Enzyme kinetic analysis, on the other hand, indicated a random order in their binding.^31,32

Another challenging question is whether the main kinetic enhancement occurs upon filling the second or the third site. Based on measurements of the dependence of ATP synthesis rate on ADP concentration, Boyer and Cross proposed that rapid net synthesis of MF₁ is attained when a second catalytic site is filled.^33,34 Results from the laboratories of Senior,³⁵ Allison³⁶ and Kinosita,¹¹ however, provided evidence that three catalytic sites are filled when sufficient ATP is present for rapid catalysis by EcF₁ or TF₁. A crystal structure³⁷ also indicated that all three sites are filled, one with ATP, one with ADP and P_i and one half closed site with ADP and P_i.

Different from the bi-site scenario, the tri-site one guarantees that the synthesis and the hydrolysis follow the same reaction pathway, which corresponds to the basic scheme that is proposed by Nakamoto, Senior and Kinosita.^12,38–40 Here, we propose a tri-site filled scenario with random order of ADP and P_i binding (shown in Fig. 1) and systematically investigate the kinetics of F_oF₁-ATPase with p.m.f. The following details are taken into account:

Fig. 1 The detailed coupling reaction scheme of the holoenzyme F_oF₁-ATPase. Synthesis pathway runs from right to left (red solid line), whereas hydrolysis one runs from left to right (blue dashed dots). T, D and P represent ATP, ADP and P_i respectively. The green, blue and red β subunits denote “open”, “loose” and “tight” conformations (labeled by the superscripts O, L and T of β respectively) and correspond to β_E, β_DP and β_T in the Walker structure.⁹ The inset shows the reversible reaction pathways of the enzyme F₁.²¹

1. The synthesis and hydrolysis follow the same reaction pathway. One ATP is consumed if the motor moves 120° counterclockwise (CCW, blue pathway). Conversely, one ATP is synthesized if it moves 120° clockwise (CW, red pathway).

2. Before each step, all three αβ pairs display different conformations depicted as “open” (green), “loose” (blue) and “tight” (red). The exchange of substrates is practically restricted to the “open” conformation.

3. The binding of ATP and ADP/P_i to the “open” site is taken to be competitive while that of ADP and P_i is random.

4. CCW 120° movement of γ drives conformational changes of the three sites as “open” → “tight”, “tight” → “loose” and “loose” → “open” respectively.

5. Chemical reaction, ADP + P_i ⇌ ATP + H₂O, takes place during the “tight” ⇌ “loose” conformational change, and is tightly coupled with transmembrane proton transport in F_o by the rotation of “rotor”.

Five states involved in this model are denoted by E, ET, EDP, ED and EP respectively. E is a two-site filled state and it has been indicated in the crystal structure⁹ that one site binds ATP and the other grips ADP and P_i. All others are three-site filled states. The structure of EDP has also been crystallized.³⁷ Different from the bi-site model, the present model suggests that ATP synthesis, in the presence of adequate p.m.f., requires ADP and P_i to occupy the third (open) site; while for ATP hydrolysis, if the p.m.f. is low or absent, it requires that ATP occupies the same site.

The kinetics of this reversible reaction (shown in Fig. 1)²¹ may be described by the equations governing the probabilities (denoted by P_E, P_ET, P_EDP, P_ED, and P_EP) of these five states

where the square bracket [ ] denotes the concentration, T, D and P represent ATP, ADP and P_i respectively, and k⁺ (k⁻) is the binding (unbinding) constant. The steady-state reaction rate has been derived as second order in [D] and [P], and cannot be treated in terms of a Michaelis–Menten form. However, if the bindings and unbindings of ADP and P_i are completely independent and there is no mutual interaction, i.e. k^±_D1 = k^±_D2 ≡ k^±_D and k^±_P1 = k^±_P2 ≡ k^±_P, it can be put into an apparent Michaelis–Menten equation. In addition, clamped ΔpH experiment⁴¹ has shown that binding and unbinding of a substrate (at cosubstrate saturation) are rapid processes as compared to the synthesis/hydrolysis step (mechanical rotation), which means that k_s/h ≪ k_L ≡ k⁺_P[P] + k⁺_D[D] + k⁻_P + k⁻_D. Within the framework of steady-state conditions for eqn (1), the clockwise revolution rate of the motor at steady state is given by ⅓(k_sP_EDP − k_hP_ET) and is computed to be

the definition and meaning of various quantities in the above equation are given below:

v ^s_M and v^h_M are the saturated rates of synthesis and hydrolysis and are given by

respectively, where the maximum rates are v^s_max ≡ k⁻_T and v^h_max ≡ k⁻_Pk⁻_D/(k⁻_P + k⁻_D).

The corresponding Michaelis constants are given by

The equilibrium constant is given by , where K^b_e ≡ K^T_d/(K^D_dK^P_d) and the dissociations constant are K¹_d = k⁻₁/k⁺₁ with the subscript I = T, D, P respectively. The equilibrium constant varies exponentially with p.m.f.

The inhibitions between substrates and products are complicated because ATP or ADP/P_i binds competitively to the same “open” site no matter which motor functions as the synthase or hydrolase. For convenience, we express the inhibitions in an uncompetitive hydrolysis form with the parameter: σ ≡ 1 + [P]/K^TP₁ + [D]/K^TD₁ + [D][P]/K^TDP₁, where K^TP₁ ≡ K^P_dχk⁻_D/k⁻_P, K^TD₁ ≡ K^D_dχk⁻_P/k⁻_D, , and .

Eqn (2) implies that the motor is a synthase if r_c > 0, a hydrolase if r_c < 0, and at equilibrium if r_c = 0. However, the relation between the rotation speed, p.m.f. and damping coefficient is still unclear. Now we use a stochastic mechanochemical coupling model to set the relation between k_h/k_s, ΔpH and the damping coefficient of the “rotor”.

III. Stochastic mechanochemical coupling model

The ensemble average behavior of F_oF₁-ATPase can be described phenomenologically by standard chemical kinetics if the reaction rates and mechanical rotation rate are related and their dependence on proton translocation is known. On the microscopic scale, F_oF₁-ATPase is more naturally described as a small mechanical device driven by a series of cyclic conformational states including rapid chemical events, such as binding and unbinding of substrates/products, and incessant, fast, thermal fluctuations which is essential to the molecular mechanism.^42–44 It is at this level of microscopic fluctuations that the mechanical reversible rotation speed and chemical quantities such as concentrations of substrates/products and p.m.f. can be most naturally connected.

It is rather well-established that different phenomena, such as the reversible chemical transition ET ⇌ EDP, the cyclic conformational changes of α₃β₃ crown, the couplings/communications among the three catalytic sites, and the stochastic 2π/3 rotation of the “rotor”, originate from the same process and occur simultaneously. In our model, E is the substrate “waiting” state, ED and EP are also substrate “waiting” states if the motor functions as a synthase. In these states, the barrier is too high for the chemical transition ET ⇌ EDP in β₂ to take place (dashed curve in Fig. 2). According to the binding change mechanism,^7,45 catalysis at one of the three sites is strongly promoted by additional substrate binding. For the hydrolysis pathway, ATP binding to the nucleotide-free site (β₁) opens the gate by reducing the barrier as shown in Fig. 2(solid curve), which allows another ATP in β₂ to be hydrolyzed. The free energy change of this step is given by:

ΔG = ΔG₀ − mΔ[small mu, Greek, tilde]_H⁺ (8)

where ΔG₀ ≈ 20k_BT⁴², ΔG is merely related to the ATP hydrolysis reaction, and is independent of entropic and enthalpic contributions. m is the H⁺/ATP ratio of proton transport-coupled ATP synthesis and hydrolysis, an important parameter for the energy balance of all cells. A straightforward interpretation of rotational catalysis predicts that m coincides with the ratio of the c-subunits to β-subunits, implying that m = n/3, while n ranges from 10 to 15 for different species.^46–51 The transmembrane electrochemical energy, Δ[small mu, Greek, tilde]⁺_H, is usually expressed in terms of the transmembrane pH difference, ΔpH ≡ pH_in − pH _out, and the transmembrane electric potential, Δϕ ≡ ϕ_out − ϕ_in, as

Δ[small mu, Greek, tilde]_H⁺ = 2.3k_BTΔpH + eΔϕ (9)

where k_B, T and e are Boltzmann constant, absolute temperature and elementary charge respectively. At room temperature, 2.3k_BT/e ≈ 59 mV. The p.m.f. ΔP ≡ Δ[small mu, Greek, tilde]_H⁺/e = Δϕ + 59ΔpH. Eqn (9) shows that ΔpH and Δϕ are energetically equivalent, which is an essential feature of chemiosmotic theory.⁵² Experimental results on steady-state synthesis rates obtained with reconstituted ATP synthase from both spinach chloroplasts^53,54 and chromatophores of R. capsulatus⁵⁵ also indicated this feature.

Fig. 2 Model energy landscape with a periodic tilt, ΔG > 0. The drop in the barrier from the red dotted curve to the black solid curve takes place once the corresponding substrate binds to the substrate “waiting” site.²¹

Here, we introduce a two-dimensional energy landscape, V(x₁, x₂), with chemical and position variables. The kinetics of the enzyme may then be investigated by a random walk on the energy surface. As required for cyclic chemical turnovers and mechanical rotations, the surface is periodic along the chemical and position axes except for a uniform tilt of ΔG. In the tight mechanochemical coupling step, ET ⇌ EDP, however, the two-dimensional V(x₁, x₂) may be reduced to an one-dimensional V(θ), where θ represents the relative position between the “rotor” and the “stator”. The energy difference, ΔG, is periodically coupled into V(θ) completely due to the tight coupling between the γ rotation and α₃β₃ crown conformational changes. The stochastic theory, thereby, makes it possible to obtain the rates of hydrolysis and synthesis as a function of p.m.f. since ΔG is included in V(θ).

At steady state, all quantities about the stochastic rotation of the “rotor”, including the probability density of the “rotor” at an angle θ, ρ(θ), and the associated probability current, J, are constant in time, namely

where the diffusion constant D = k_BT/ξ_r, in accordance with the Einstein relation between D and ξ_r. ξ_r is the rotational damping coefficient of “rotor” assembly. We solved for ρ(θ) with constant J, then set the probabilities of biochemical states ET and EDP to be and respectively. Finally, J is derived and compared with the form expected for a first-order chemical reaction at steady state, k_hP_ET − k_sP_EDP. The desired expressions for the rates of hydrolysis and synthesis as a function of ΔG can therefore be obtained:^56–60where
and

For a potential with two wells separated by a barrier, as in Fig. 2, the rate constants are most sensitive to the distances from the well bottoms to the barrier top, the size of each well, the barrier height (U), and the energy difference between wells (ΔG). Once these parameters are specified, the detailed shape of the potential has relatively little effect.

At equilibrium the net probability current, J, must be zero, and

because of V(θ + π/3) = V(θ) − ΔG. Eqn (13) is the simple and familiar Arrhenius form, though the ΔG no longer has the same simple physical interpretation of free energy. ΔG is merely related to the ATP hydrolysis reaction, transmembrane ΔpH and Δϕ, and is independent of entropic and enthalpic contributions of substrates and products.

In order to calculate the rates of hydrolysis and synthesis that are tightly coupled to the diffusive rotation of the “rotor”, the one-dimensional energy landscape is phenomenologically constructed as (see Fig. 2):

where λ = ΔG/(4ΔG₀), V₀ and θ₀ depend on the barrier U and free energy ΔG as follows:

This asymmetric ratchet potential can be used to describe simultaneously the chemical transition between the two metastable states, ET and EDP, and the stochastic rotation of the “rotor” because the chemical transition ET ⇌ EDP is tightly coupled to the 2π/3 step rotation. The potential is constructed so that the barrier position can shift with varying ΔG. Under the conditions favoring ATP hydrolysis, that is, the p.m.f. is so low that ΔG > 0, the barrier position approaches the state ET. On the other hand, under conditions favoring ATP synthesis, the barrier position is close to the state EDP. If ΔG = 0, the ratchet potential will become symmetric. Such a construction is phenomenologically reasonable for the reversible motor.

Eqn (3), (6) and (7) can be directly used to quantitatively interpret the ensemble synthesis experiment of the holoenzyme²⁸ as shown in Fig. 3. For an isolated TF₁ with an attached long actin filament on the “rotor”,¹⁰ the hydrolysis step is the rate-limiting step because of the large damping of the long filament. Thus the hydrolysis kinetics can be easily analyzed by our model. Here, k_s ≈ 0, and σ ≈ 1 due to v^h_M ≈ k_h ≪ k_L. Eqn (2) may be simplified into a normal Michaelis form:

where r_cc is the CCW rotational rate of the motor, and the apparent Michaelis constant K′^T_M ≈ K^T_d{1 + [P]/K^P_d + [D]/K^D_d + [P][D]/(K^P_dK^D_d)}. Thus, K′ ^T_M is almost independent of the length of the actin filament. The CCW rotational rate of the motor can be directly related to the actin filament length L through the damping coefficient: ξ_r = (π/3)ηL³/[ln(L/2r) − 0.447],⁶¹ where r is the radius of the attached filament and η is the medium viscosity. Then one obtains where F(U) = [k_BT/(πη)][Π_EDP0/(Π_ET0Π_EDP − Π_EDP0Π_ET)]. The single-molecule experimental results of r_cc as a function of L at different [T]¹⁰ can be fitted from eqn (16). These results are shown in Fig. 4. The parameter F(U) may be used to estimate the scale of the reduced barrier (black solid curve in Fig. 2) which gives U ≈ 2k_BT. In contrast to Oster's 64 states model,²⁴ the analytical results from our model can directly fit the single-molecule experimental data with just two parameters, one being the hydrolysis Michaelis constant and the other is the barrier of the mechanochemical coupling potential.

Fig. 3 Experimental data²⁸ of v^s_M, K^D_M and K^P_Mversus ΔpH fitted by our model with v^s_max = 250 s⁻¹(≪ k⁻_P), K^D_d = 57μM, K^P_d = 2.65 mM and k⁻_D = 500 s⁻¹. Here, Δϕ = 0 mV, m = 4,^62,63 and U = 3k_BT. Damping coefficient ξ_r = 6πη_bhr², is mainly contributed by the friction between c-ring and membrane, where h = 10 nm, is the “rotor” height, and r = 5 nm, is its radius.⁶⁴ The bilayer viscosity is taken to be η_b = 10⁻⁷ pN s nm⁻².^21,25

Fig. 4 The CCW rotational rate of an isolated TF₁versus L at different ATP concentrations. Symbols come from experiment¹⁰ while curves are fitted by our model with parameters K′^M_T = 0.8 μM and U = 2k_BT. Here ξ_r = (π/3)ηL³/[ln(L/2r) − 0.447]⁶¹ with the radius of filament r = 5 nm and the medium viscosity η = 10⁻⁹ pN s nm⁻².²¹

IV. Direct observation of the light-driven rotation of F_o motor

Single molecule experiments had indicated the rotation of the F₁ motor with a fluorescent filament attached the γ subunit.^8,10 The relative rotation between the stator and rotor of the holoenzyme also had been detected by the FRET between the ε and b subunits.¹⁶ F_o is an ion-driven rotary motor. Its “rotor” is the proton channels c_n and is connected the γ subunit by the ε subunit. Its “stator” consists of the a and b₂ subunits and is fixed to the α₃β₃ crown of F₁ by the δ subunit. Once the δ subunit is deleted, the two “stators” are no longer coupled, and the α₃β₃ crown will accompany the “rotor” on rotation. This is named δ-free F_oF₁-ATPase. We had developed a method to reconstitute the hybrid δ-free F_oF₁-ATPase and bacteriorhodopsins (BRs) into a liposome.^13,65 BR converts light energy into transmembrane p.m.f., while the liposome functions as a battery to drive the motor. Employing a fluorescent actin filament attached to the β subunit, we have observed the light-driven rotation of δ-free F_oF₁-ATPase motor directly at the single molecule level.¹³

The procedure of δ subunit deletion of F_oF₁-ATPase is briefly shown in Fig. 5. The proteoliposome containing F_oF₁-ATPase and BR was incubated with 2 M LiCl, 0.1 mM tricine-NaOH, 10 mM MgCl₂, and 1 mM ATP for 20 min at 4 °C. Then the proteoliposome was washed and isolated by centrifuging. Because some α and β subunits may also be removed during δ deletion, the LiCl-treated proteoliposome needs incubation with purified α₃β₃γ(or β) subunits at 4 °C for 60 min (for each divided subunit of F₁ with buffer 0.1 mM tricine-NaOH, 10 mM MgCl₂, 50 mM KCl, 0.5 mM NaCl, and 1 mM ATP), and then is cultured at 37 °C for 60 min (for reconstituting the δ-free F_oF₁-ATPase). The proteoliposome needs to be isolated to obtain the reconstituted δ-free F_oF₁-ATPase.^66–68

Fig. 5 The procedure for reconstituting δ-free F_oF₁-ATPase motor. (A) F_oF₁-ATPase; (B) F_oF₁-ATPase is treated by LiCl to remove δ subunit; (C) rebinding of purified β and α subunits; (D) the reconstituted δ-free F_oF₁-ATPase motor.¹³

To visualize the rotation of F_o in proteoliposome, a fluorescently labeled actin filament was attached to β subunits through His-tag, and the proteoliposome was immobilized onto the glass surface through the biotin–streptavidin–biotin complexes (Fig. 6A). The sample was exposed under the cooled light source with a 570 nm filter for 30 min to initiate the rotation of the F_o motor. Before illumination, the buffer containing 2 mM NaN₃ and 2 mM ADP was infused into the chamber. The clockwise rotation of the actin filament was traced directly by an Olympus IX71 fluorescent microscope equipped with an ICCD camera (Roper Scientific, Pentamax EEV 512 × 512 FT) viewing from F_o side to the F₁ side. Fig. 6B shows an example of the sequential clockwise rotation images with 100 ms interval. We have selected six rotational data points with different length filaments to show in Fig. 6C. The rotation displays occasional pause or even reversal due to Brownian fluctuation. The rotation speed decreases with the increasing length of filament , which is in agreement with the results of single molecule experiments of F₁^8,10 as expected.

Fig. 6 (A) The system used for observation of the F_o in the proteoliposome which was immobilized on the cover glass with biotin–streptavidin–biotin. (B) The sequential images of a clockwise rotating fluorescent actin filament. Time interval is 100 ms. (C) Time courses of the actin filament rotation with different lengths. The fluorescent filament was attached to the β subunits through His-tag. The length of filaments denoted L1, L2, L3,L4 ,L5 and L6 are 1.7, 1.9, 2.0, 2.3, 2.8 and 3.3 μm respectively. (D) The rotation was inhibited by adding CCCP, which verified the motor was indeed driven by transmembrane ΔpH.¹³

Several control experiments were performed to confirm that the observed rotation is driven by transmembrane proton flow. As shown in Fig. 6D, the rotation stopped immediately once 5 μl of 10 μM CCCP was added. It was also found that if the sample is in the dark or is incubated with DCCD before illumination, no rotation was observed (data not shown) because CCCP destroyed the transmembrane p.m.f. as well as DCCD blocked the proton channels. Furthermore, if NaN₃ and ADP disappeared in the buffer, no rotation of filament was found because NaN₃ and ADP prevented the α₃β₃ crown from sliding to the γ subunit.⁶⁹ These results demonstrated that the rotation of filaments depended on the p.m.f. produced in proteoliposome. It is interesting that the ΔpH transmembrane of proteoliposome can persist for a long time. After the illumination, some filaments rotated continuously for more than 20 min. Therefore, the proteoliposome functions as a recharge battery to supply energy to the rotary motor.

V. F_oF₁-ATPase activity regulated by external links on the stator

The activity regulation of the holoenzyme is an interesting topic. Traditional methods are chemical, which depend on either the concentration of substrate or the transmembrane electrochemical potential.^12,28,62,63 In fact, F_oF₁ motor actively converts a chemical reaction (ATP hydrolysis in F₁ or proton transfer in F_o) into unidirectional physical rotation of the “rotor”, which is accompanied by the cyclic conformational change of the “stator”. Single molecule assays have indicated that the activity of F₁^10,18 or the speed of F_o (δ free F_oF₁ motor)^13,20 can be regulated by varying the load on the “rotor” and the eccentric rotation of γ subunit is mechanically coupled with the cyclic conformational change of α₃β₃ crown at a high efficiency. However, how to regulate the holoenzyme (including F_o and F₁) activity with a physical method instead a chemical one is still challenging. One of the reasons is that the “rotor” of F_oF₁ motor is mostly enwrapped by the “stator” α₃β₃ crown. The other reason is that the exposed fraction of the “rotor” is also partly shaded by the b₂ subunit. Thus, it becomes very difficult to directly regulate the holoenzyme activity by a load on the “rotor”.

Considering that the unidirectional rotation of “rotor” is tightly coupled with the cyclic conformational change of the “stator”, what will happen to the activity of the rotary motor if external complexes bind to the “stator”? To study regulation of the F_oF₁-ATPase activity by a simple physical method, the influenza H9 virus and its special antibody were employed as external links on the β subunit. Firstly, the chromatophore was prepared from the cells of Rhodopseudomonas palustris according to ref. 70, in which F_o was embedded in the chromatophore,⁷¹ whereas F₁ protruded outside (structure 0).⁷² Next, the β antibody was bound to each β subunit (structure 1); then, streptavidin was connected to the β antibody (structure 2), and the H9 antibody was bound to the streptavidin in series via biotin (structure 3). Finally, the H9 virus was captured specifically by the H9 antibody (structure 4) (see Fig. 7). The holoenzyme activities of the five structures were measured by the luciferin–luciferase method with a computerized ultra-weak luminescence analyzer. All structures with different external links were treated as coordinates.^73–76

Fig. 7 A schematic illustration of the activity regulation assay. The holoenzyme is a complex of two rotary motors F_o and F₁. F_o motor was constituted by a subunit (stator) and n channel (c_n, rotor). α₃β₃ crown (stator) and γ subunit (rotor) formed the F₁ motor. The complex of b₂ and δ subunits fixed the two stators, whereas the two rotors are mechanically coupled by the ε subunit. External complexes are linked on β subunits to regulate the holoenzyme activity.

The activity of native F_oF₁-ATPase was used as a control and other structures were compared with the native value. When the β antibody was bound, the F_oF₁-ATPase (structure 1) activities in both synthesis and hydrolysis decreased, and its relative value was about 85% of the native form (structure 0). If streptavidin was joined to the β antibody (structure 2), the enzyme synthesis/hydrolysis activities decreased to 87% of the activity of structure 1. After the H9 antibody was connected to streptavidin (structure 3), the enzyme activity was inhibited continuously, with a relative value of 75% of structure 2. Once H9 virus was captured by its antibody (structure 4), however, the motor was activated, and its relative synthesis and hydrolysis activities were about 210% of that of structure 3. It is amazing that the activity of the modified holoenzyme, in which a series of external complexes are linked on the stator, can exceed the native level. These results are indicated in Fig.8.⁷⁷

Fig. 8 Relative synthesis (red) and hydrolysis (green) activities of the holoenzyme with different links on the β subunit as shown in Fig. 7. The statistical value (mean s.e.m.) of each structure was computed from 50–60 samples. The experiment has been repeated independently more than five times (10 samples each time). The native F_oF₁-ATPase (structure 0) activity was taken as a control and others were expressed in proportion to the control. Structures 1, 2, 3 and 4 represent the F_oF₁-ATPase linking in series on the β antibody, streptavidin, H9 antibody and H9 virus respectively. 0 + H9 represents the holoenzyme mixed directly with the H9 virus.

To identify whether the H9 virus directly affects F_oF₁-ATPase activity, we measured the activity of native buffer (structure 0) incubated with H9 virus. The results shown in Fig. 8 prove that the H9 virus doesn't have any direct effect on the holoenzyme activity no matter if the enzyme functions as a synthase or hydrolase.

The abnormal regulation from structure 3 to 4 implied that structure 3 has great potential in design of a rapid, unlabeled, sensitive and selective biosensor⁷⁸ though the underlying mechanism is still unclear.

VI. Conclusions

In contrast to human-made machines, motor proteins operate in a world where Brownian motion and viscous forces dominate. The relevant energy scale is k_BT, which amounts to 4 pN nm. This may be compared to the ∼80 pN nm of energy derived from hydrolysis of a single ATP molecule at physiological conditions. Thermal, nondeterministic motion is thus an important aspect of the dynamics of molecular motors.

ATP hydrolysis does spontaneously occur in F₁, whereas the thermodynamically unfavorable reaction, ATP synthesis, has to be driven by harnessing the transmembrane proton flow in F_o. The mechanism of ATP formation in the F₁ part is well described by the “binding change mechanism”. This has been developed in great detail by many techniques, and understanding of the mechanism has been claimed to be “almost complete”. However, if the motor functions as a synthase, the two substrates, ADP and P_i, are recombined into one product, ATP. The binding order of the two substrates is still unclear. Another challenging question is whether the main kinetic enhancement occurs upon filling the second or the third site. For F_o, the torque generation between a and c_n in F_o is still covered. In addition, It has remained unsettled whether the entropic (chemical) component of Δ[small mu, Greek, tilde]⁺_H relates to the difference in the proton activity between two bulk water phases (ΔpH^B) or between two membrane surfaces (ΔpH^S).⁷⁹

It is of interest to ponder whether we can employ F_oF₁-ATPase nanomachines in artificial environments outside the cell to perform tasks that we design to our benefit.⁸⁰ One striking demonstration is the construction of a nickel nanopropeller that rotates through the action of an engineered F₁-ATPase motor.⁸¹ A metal-binding site was engineered into the motor and acted as a reversible on–off switch by obstructing the rotation upon binding of a zinc ion,⁸² similar to the action of putting a stick between two cogwheels. Other examples worth highlighting are the sol–gel packaging of vesicles containing bacteriorhodopsin, a light driven proton pump, and F_oF₁-ATP synthase,^83,84 or F_oF₁-ATPase embedded chromatophore.⁷⁶ Upon illumination, protons are pumped into the vesicles and ATP is created outside the vesicle by the ATP synthase. Besides the excellent stability of these gels (bacteriorhodopsin continued functioning for a few months), this technology provides a convenient packaging method and a way to use light energy for fuelling devices. Therefore, these nanodevices with a battery can be employed to design a rapid, unlabeled, sensitive and selective biosensor,^73–75,77 or construct a micro-mixer to accelerate thrombolysis.⁶⁷ Of course, many of these applications are little more than proof-of-principle examples.

Acknowledgements

This work was supported by the National Basic Research Program of China (973 Program) under the grant No. 2007CB935903 and No. 2007CB935901

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