Energy coupling mechanism of F O in a rotary ATP synthase: a model update

In nearly all living cells, rotary ATP synthases of the F1FO family are essential to inter-conversing of energy between the transmembrane electrochemical potential and the ATP form (Boyer 1997). During ATP synthesis, the FO sector of the ATP synthase machinery converts the electrochemical energy of either protons or sodium ions into mechanical energy of a rotor; in turn, this energy is converted into chemical energy of ATP by the F1 sector (Gruber et al. 2014; Nakamoto et al. 2008). A fundamental question here is as to why these driving substances are all electrically charged. The answer to this conundrum is likely to be related to the electric nature of the transmembrane potential. For a membrane protein whose functional cycle is driven by proton motive force (Dp), be it an FO complex (Boyer 1988) or a secondary transporter (Zhang et al. 2015b, 2017), the driving force includes two parts, namely the electrostatic membrane potential (DWM) and DpH. The corresponding energy terms are expressed as FDWM and 2.3RTDpH, respectively. Whereas DWM is influenced by the capacitance of the lipid bilayer, DpH depends on buffer strength on either side of the membrane. Furthermore, the DpH-associated energy term is equivalent to the Nernst voltage of protons (Benedek and Villars 2000), i.e., VN = 2.3(RT/F)DpH. Therefore, Dp itself can be represented by an overall, effective membrane potential DWp 1⁄4 DWM þ VN: Thus, the biophysics of the transmembrane proton wire in FO appears to be similar to that of selective ion channels (Zhang et al. 2018). In particular, the movement of protons along its transmembrane path is dictated by electrostatic forces. For instance, the repulsion forces between neighboring protons possibly serve as a medium to transduce concentration (i.e., pH) information between the source, path, and sink of protons. Based on moderate-resolution structures of F1FO ATP synthases, we previously proposed a model to illuminate the energy coupling mechanism of FO (Zhang et al. 2015a), which is in agreement with an earlier hypothesis put forward by Dimroth and coworkers (Dimroth et al. 2003). In both models, DWM plays a major role in driving the FO machinery during ATP synthesis. To enable the energy coupling process to proceed effectively, a large drop in the electrostatic potential of the driving substance (e.g., proton) at the interface between the stator (i.e., a-subunit) and the rotor (i.e., c-ring, the symmetric homo-oligomer formed by c-subunits) is essential and must be associated with unidirectional rotation of the rotor. Equivalently, the proton trajectory viewed in the rotor reference system (R-trajectory) must lag behind that viewed in the stator reference system (S-trajectory) so that catching up of the R-trajectory with the S-trajectory coincides with the unidirectional rotation of the c-ring. For instance, if DWM were uniformly distributed across the membrane in the interface region between the a-subunit and c-ring (a–c interface) where energy conversion occurs, the R-trajectory and S-trajectory of the protons might assume shapes of a straight line and a spiral curve, respectively (Zhang et al. 2015a). Although the actual shape of the trajectory depends on structural details of the a–c interface, the ‘‘ideal’’ spiral-shaped trajectory may qualitatively represent the energy landscape for the proton movement.


INTRODUCTION
In nearly all living cells, rotary ATP synthases of the F 1 F O family are essential to inter-conversing of energy between the transmembrane electrochemical potential and the ATP form (Boyer 1997). During ATP synthesis, the F O sector of the ATP synthase machinery converts the electrochemical energy of either protons or sodium ions into mechanical energy of a rotor; in turn, this energy is converted into chemical energy of ATP by the F 1 sector (Gruber et al. 2014;Nakamoto et al. 2008). A fundamental question here is as to why these driving substances are all electrically charged. The answer to this conundrum is likely to be related to the electric nature of the transmembrane potential. For a membrane protein whose functional cycle is driven by proton motive force (Dp), be it an F O complex (Boyer 1988) or a secondary transporter (Zhang et al. 2015b(Zhang et al. , 2017, the driving force includes two parts, namely the electrostatic membrane potential (DW M ) and DpH. The corresponding energy terms are expressed as FDW M and -2.3RTDpH, respectively. Whereas DW M is influenced by the capacitance of the lipid bilayer, DpH depends on buffer strength on either side of the membrane. Furthermore, the DpH-associated energy term is equivalent to the Nernst voltage of protons (Benedek and Villars 2000), i.e., V N = -2.3(RT/F)DpH. Therefore, Dp itself can be represented by an overall, effective membrane potential Thus, the biophysics of the transmembrane proton wire in F O appears to be similar to that of selective ion channels (Zhang et al. 2018). In particular, the movement of protons along its transmembrane path is dictated by electrostatic forces. For instance, the repulsion forces between neighboring protons possibly serve as a medium to transduce concentration (i.e., pH) information between the source, path, and sink of protons.
Based on moderate-resolution structures of F 1 F O ATP synthases, we previously proposed a model to illuminate the energy coupling mechanism of F O (Zhang et al. 2015a), which is in agreement with an earlier hypothesis put forward by Dimroth and coworkers (Dimroth et al. 2003). In both models, DW M plays a major role in driving the F O machinery during ATP synthesis. To enable the energy coupling process to proceed effectively, a large drop in the electrostatic potential of the driving substance (e.g., proton) at the interface between the stator (i.e., a-subunit) and the rotor (i.e., c-ring, the symmetric homo-oligomer formed by c-subunits) is essential and must be associated with unidirectional rotation of the rotor. Equivalently, the proton trajectory viewed in the rotor reference system (R-trajectory) must lag behind that viewed in the stator reference system (S-trajectory) so that catching up of the R-trajectory with the S-trajectory coincides with the unidirectional rotation of the c-ring. For instance, if DW M were uniformly distributed across the membrane in the interface region between the a-subunit and c-ring (a-c interface) where energy conversion occurs, the R-trajectory and S-trajectory of the protons might assume shapes of a straight line and a spiral curve, respectively (Zhang et al. 2015a). Although the actual shape of the trajectory depends on structural details of the a-c interface, the ''ideal'' spiral-shaped trajectory may qualitatively represent the energy landscape for the proton movement.

NEW STRUCTURAL OBSERVATIONS
Recently, a number of studies reported high-resolution, cryo-electron microscopy structures of F 1 F O ATP synthases (Guo et al. 2017;Hahn et al. 2018;Srivastava et al. 2018). In agreement with the reversibility of the functional cycle of ATP synthase, the F O sector, especially the a-c interface, shows a pseudo twofold symmetry with the axis parallel to the membrane plane. Two pieces of proton wire, which half-way penetrate into the lipid bilayer from opposite sides of the membrane, are well defined by polar and/or charged residues ( Fig. 1) and are symmetrically arranged relative to the pseudo-axis. According to the current mainstream ''double half-channel'' hypothesis (Junge et al. 1997), these two proton wire segments are referred to as halfchannels. It is reasonable to speculate that additional water molecules infiltrate into these half-channels, where they become coordinated by the polar groups from the stator, and remain titratable by protons moving from sites of lower pK a along the proton wire. The two half-channels comprise the static components of a complete proton wire, along which protons translocate across the membrane in the energy-descending direction. Intriguingly, these half-channels (especially the entrance one) are located between transmembrane helices of the a-subunit in such a manner that the corresponding segments of the proton wire are mostly buried inside the a-subunit, but are not in extensive contact with polar groups from the rotor. This structural feature dictates that proton movement inside these halfchannels is not directly involved in the energy conversion. Furthermore, at the middle level of the lipid bilayer, the two half-channels appear to be connected to the two ends of a dynamic proton wire formed by a set of titratable acidic residues of the c-ring. This latter imaginary proton wire may assume its role in carrying protons only when the c-ring rotates continuously. Despite support from newly reported structures, the current ''double half-channel'' hypothesis remains to be extended to formally take DW p into account.

FOCUSED ELECTRIC FIELDS
Because of the presence of the two half-channels, the dielectric constant of the F O complex cannot be treated as uniform. Thus, the above-mentioned ''ideal'' picture of the uniformly distributed electric field is severely distorted. In particular, the electric field around the a-c interface becomes focused (Fig. 2). More specifically, the electric field between the inner surface of a half-channel and its closest protein surface on the opposite side of the membrane is reinforced, as it is associated with patches of higher charge-densities compared to their surrounding areas. In addition, because of the much Positions of selected C a atoms are marked with spheres: D/E sites in the c-ring, red; Arg-finger in the a-subunit, blue; residues contributing sidechain or maintain polar groups to the entrance half-channel, cyan; and residues of the exit half-channel, rose color higher dielectric constant inside the half-channels relative to their surrounding nonpolar structure, the electric fields inside the half-channels are significantly weaker than that inside the remaining F O . Consequently, at the inner end of each half-channel, the electrostatic potential is roughly the same as that on the surface of the same leaflet of the lipid bilayer, depicted as V ? or V -(see Fig. 2). As first approximation, one may consider a scenario in which the effective membrane potential, DW p (i.e., V --V ? ), is directly applied between the tips of the two half-channels (Dimroth et al. 2003). A benefit of such a focused electric field is that proton movements inside the two stator-buried half-channels consume negligibly amount of energy, thus ensuring that ATP synthesis remains a highly efficient energy-generating process (Silverstein 2014). A conserved Arg-finger is located between the half-channels and on the pseudo twofold axis of F O (Lightowlers et al. 1987;Zhang et al. 2015a). This Arg-finger generates a formidable energy barrier for protons. As a result, futile discharge of protons directly across the ends of the two half-channels is prevented. Therefore, the dynamic proton wire created by the rotating c-ring becomes necessary and effective for discharging the energy potential acutely accumulated between the two half-channels.
The dynamic part of the proton wire in F O is comprised of a series of titratable acidic residues, referred to as D/E sites, around the circumference of the c-ring. In order to maintain both high speed and high efficiency of energy conversion in ATP synthesis, this proton wire should present low or no kinetic barriers. On the one hand, the multiple protonated D/E sites (positioned away from the a-c interface) experience a constant voltage, V 0 , which assumes a value between Vand V ? . Thus, a given D/E site senses a flat energy landscape when it moves from one position to the next during rotation of the c-ring. On the other hand, during the process of continuing ATP synthesis, the overall movement of protons does proceed from higher voltage sites to lower sites. Therefore, two drastic voltage drops likely exist at the a-c interface: one from the entrance half-channel to the c-ring (V ? -V 0 junction) and the other drop from the c-ring to the exit half-channel (V 0 -Vjunction). These jumps of protons across the two voltage gaps convert the electrostatic energy into the unidirectional rotation of the c-ring, similar to a ratchet-like movement. From a mechanistic point of view, a large energy drop in a small angular range obligatorily generates a strong torque, favoring a rotation along the energy-descending direction. Furthermore, by properly arranging the two half-channels relative to the proton loading/releasing subunits in the c-ring, the most likely scenario is that the pulses of energy conversion occur sequentially to generate smooth rotation of the c-ring. For instance, the proton release at the V 0 -Vjunction may slightly proceed of the proton loading at the V ? -V 0 junction (Srivastava et al. 2018).

THE PATH FOR PROTON TRANSLOCATION
In agreement with the monotonically descending energy landscape of the dynamic proton wire, the titratable D/E sites assume distinct pK a values in different phases of the function cycle of the c-ring. More specifically, the pK a value of a given D/E site (e.g., Glu c59 in the yeast mitochondrial F O ) transiently decreases when approaching the Arg-finger (Arg a176 ), as a result of which the proton is released. Since it is accompanied by a large energy drop, the proton release at the V 0 -Vjunction is a high probability event; so is the unidirectional rotation of the c-ring, because both events are in the same chain of Bayesian probabilities. Therefore, one can conclude that, analogous to a dropping chain at a table edge, the proton release drags the corresponding c-subunit to move toward the Arg-finger. Concurrently, the rigid-body rotation of the c-ring moves the neighboring c-subunit on the proton loading side away from the Arg-finger, and the pK a of the D/E site in this c-subunit starts returning to ''normal,'' permitting proton loading. Thus, the proton loading at the V ? -V 0 junction requires and drives the corresponding Fig. 2 Schematic diagram of the energy coupling mechanism of F O . The positive side of the membrane potential is shown in cyan, and the negative side in pink. For simplicity, we assume that the electric potential inside each half-channel equals to that of the surface of the same-side membrane leaflet. Selected electric lines of forces are represented as black arrows. For instance, in the lipid bilayer region away from the a-c interface, the membrane potential is uniformly distributed. In contrast, near the two halfchannels, the membrane potential becomes focused. The dynamic proton wire formed by the rotating c-ring is presented as a green curve, and the direction of the proton movement (i.e., rotation of the c-ring) during ATP synthesis is indicated by the yellow arrow. Energy coupling between Dp and the rotation of the c-ring occurs at both the V ? -V 0 and V 0 -Vjunctions. The conserved Arg-finger is represented with a blue sphere Energy coupling mechanism of F O in a rotary ATP synthase OPINION c-subunit to move away from the Arg-finger. Being buried in the lipid bilayer environment, the ''normal'' pK a of the D/E site seems to be sufficiently high to attract protons from the entrance side of the membrane. At this point, it is important to clarify a common, yet false belief about the role of the Arg-finger. It is often assumed that on the proton-releasing side of the Argfinger, the electrostatic attraction between the Argfinger of the stator and incoming deprotonated D/E site of the c-ring contributes to the overall driving force for the c-ring rotation. However, a second, similar attraction on the proton loading side would energetically disfavor the unidirectional rotation, thus canceling the first attraction. Unfortunately, this second attraction is usually selectively ignored. In agreement with the pseudo twofold symmetry of F O as well as the reversibility of the F 1 F O type of ATP synthase machinery, our arguments presented here are likely suitable for both the Dp-driven ATP synthesis and the ATP hydrolysis-driven proton pumping process.
In summary, we argue here that DW p is the sole driving force in ATP synthesis, maintaining the rotation of the c-ring via accelerating proton movements across the two junction points between the stator and the rotor. Any future attempt of a more complete understanding of the F O F 1 ATP synthase mechanism must take DW p into account; otherwise, the high efficiency of this elegant machinery would be left unexplained.