Analysis of molecular mechanisms of ATP synthesis from the standpoint of the principle of electrical neutrality

Biophysical Chemistry 224 (2017) 49–58

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Review

Analysis of molecular mechanisms of ATP synthesis from the standpoint of the principle of electrical neutrality Sunil Nath Department of Biochemical Engineering and Biotechnology, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi 110016, India

H I G H L I G H T S

G R A P H I C A L

A B S T R A C T

• Theories of biological energy coupling and mechanisms of ATP synthesis are reviewed. • Current ATP theories are evaluated based on the principle of electrical neutrality. • Mitchell's chemiosmotic theory is shown to violate the electroneutrality principle. • A dynamically electrogenic but overall electroneutral mode of ion transport is proposed. • Nath's torsional mechanism satisfies electroneutrality and is a more complete theory.

a r t i c l e

i n f o

Article history: Received 13 February 2017 Received in revised form 6 March 2017 Accepted 6 March 2017 Available online 8 March 2017 Keywords: Principle of electrical neutrality Electroneutrality ATP synthesis Bioenergetics Oxidative phosphorylation Biological energy coupling Nonequilibrium thermodynamics Mitchell's chemiosmotic theory Nath's torsional mechanism of energy transduction and ATP synthesis F1FO Ion transport

a b s t r a c t Theories of biological energy coupling in oxidative phosphorylation (OX PHOS) and photophosphorylation (PHOTO PHOS) are reviewed and applied to ATP synthesis by an experimental system containing purified ATP synthase reconstituted into liposomes. The theories are critically evaluated from the standpoint of the principle of electrical neutrality. It is shown that the obligatory requirement to maintain overall electroneutrality of bulk aqueous phases imposes strong constraints on possible theories of energy coupling and molecular mechanisms of ATP synthesis. Mitchell's chemiosmotic theory is found to violate the electroneutrality of bulk aqueous phases and is shown to be untenable on these grounds. Purely electroneutral mechanisms or mechanisms where the anion/countercation gradient is dissipated or simply flows through the lipid bilayer are also shown to be inadequate. A dynamically electrogenic but overall electroneutral mode of ion transport postulated by Nath's torsional mechanism of energy transduction and ATP synthesis is shown to be consistent both with the experimental findings and the principle of electrical neutrality. It is concluded that the ATP synthase functions as a proton-dicarboxylic acid anion cotransporter in OX PHOS or PHOTO PHOS. A logical chemical explanation for the selection of dicarboxylic acids as intermediates in OX PHOS and PHOTO PHOS is suggested based on the pioneering classical thermodynamic work of Christensen, Izatt, and Hansen. The nonequilibrium thermodynamic consequences for theories in which the protons originate from water vis-a-vis weak organic acids are compared and contrasted, and several new mechanistic and thermodynamic insights into biological energy transduction by ATP synthase are offered. These considerations make the new theory of energy coupling more complete, and lead to a deeper understanding of the molecular mechanism of ATP synthesis. © 2017 Elsevier B.V. All rights reserved.

E-mail addresses: [email protected], [email protected].

http://dx.doi.org/10.1016/j.bpc.2017.03.002 0301-4622/© 2017 Elsevier B.V. All rights reserved.

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S. Nath / Biophysical Chemistry 224 (2017) 49–58

Contents 1. 2.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Classical theories of energy coupling in OX PHOS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. The ongoing debate on OX PHOS since the 1960s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. New conceptual framework for energy coupling in OX PHOS and PHOTO PHOS . . . . . . . . . . . . . . . . . . . . . . . 4. The issue of electrical neutrality and its biological implications for energy coupling and ATP synthesis . . . . . . . . . . . . . 4.1. The principle of electrical neutrality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Experimental system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Violation of the principle of electrical neutrality by Mitchell's chemiosmotic theory . . . . . . . . . . . . . . . . . . 4.4. Other important consequences for the chemiosmotic theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1. Protonmotive force, Δp is not an essential intermediate in ATP synthesis. . . . . . . . . . . . . . . . . . . 4.4.2. Delocalized electrical potential, Δφ is not an essential intermediate in ATP synthesis . . . . . . . . . . . . . 4.5. A dynamically electrogenic but overall electroneutral mode of ion transport as a new paradigm in bioenergetics . . . . . 4.6. Sites of entry and exit of the dicarboxylic acid anion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Possible chemical logic for the selection of dicarboxylic acids as intermediates of energy coupling in OX PHOS and PHOTO PHOS . 6. Further details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1. Estimation of electrogenic H+ charge transfer required by chemiosmosis in mitochondrial OX PHOS . . . . . . . . . . 6.2. Energy transduction by a Mitchellian fuel cell versus a Nathean biological molecular machine . . . . . . . . . . . . . 6.3. The issue of H+/2e− and H+/ATP stoichiometries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4. Usage of the term “electrogenic” and stationary vs. transient electrical fields . . . . . . . . . . . . . . . . . . . . . 6.5. Relationship to the Nernst equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6. Transient departure from electrical neutrality as an ordering principle for transport and reaction steps and the stringency of electrical neutrality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. Introduction The synthesis of adenosine-5′-triphosphate (ATP), the universal biological energy currency, catalyzed by the enzyme F1FO-ATP synthase is the fundamental means of cellular energy production in animals, plants and microorganisms. It is among the most important and frequently occurring enzyme reactions in biology. ATP synthesis is achieved by coupling of the reactions of oxidation and phosphorylation in the process of oxidative phosphorylation (OX PHOS) or light reactions and phosphorylation (PHOTO PHOS) in photosynthesis. The prevailing theory of energy coupling serves as a guiding compass for several sectors of biochemical and biophysical research. Hence, the mechanism underlying the coupling of chemical reactions on the redox/photo and ATP sides is among the most important questions of physical and biophysical chemistry. In this invited article, the major theories of biological energy coupling are briefly delineated (Sections 2 and 3). In Section 4, these theories of energy coupling and molecular mechanisms of ATP synthesis are critically examined from the standpoint of the principle of electrical neutrality. It is shown that the principle imposes strong constraints on possible mechanisms of energy transduction, coupling, and ATP synthesis. 2. Classical theories of energy coupling in OX PHOS The first theory of energy coupling in OX PHOS proposed by Slater [1] envisaged a chemical high-energy intermediate as the link between oxidation and phosphorylation. The theory was abandoned after a massive and lengthy search (lasting ~20 years) for the elusive chemical intermediate proved futile, and was eventually replaced by Mitchell's chemiosmotic theory of energy coupling [2,3]. The chemiosmotic theory postulated that energy coupling was achieved in OX PHOS by a “protonmotive force” Δp [Eq. (1), where Δp is in units of mV] obtained by addition of the bulk-to-bulk ΔpH and a delocalized electrical potential, Δφ between bulk aqueous phases created by translocation of uncompensated protons across the membrane by the redox complexes in the respiratory chain.

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coupling oxidation and phosphorylation [3,4]. According to the theory, the membrane itself plays no active role in the energy transduction, serving only as “insulation material” for separating two bulk phases, and Mitchell repeatedly emphasized this point and the key role of such “energized bulk aqueous media” [4]. The chemiosmotic theory is an equilibrium theory lying in the realm of classical equilibrium thermodynamics, and the Δp is considered by the theory to equilibrate both with the respiratory chain and the high-energy squiggle (the ~) in ATP [2–4]. 2.1. The ongoing debate on OX PHOS since the 1960s The chemiosmotic theory itself had a contentious history, with part of the accumulated body of experimental evidence supporting the theory, and part of it in conflict with it [summarized in refs. 5–7]. The theory was severely criticized by many stalwarts of 20th century biochemistry, including E. C. Slater [8], R. J. P. Williams [9], Albert Lehninger [10], Gregorio Weber [11], and David Green [12] on the grounds of it either being “physically unsound,” involving “unrealistic assumptions,” or being “unsupported by experiments” and having “no basis in fact” [8–12], and specifically of violating “the necessity to observe charge neutrality in chemical reactions” [12]. However, despite long and heated debates, among the most acrimonious in modern science, and commonly known as “the OX PHOS wars” [13], the controversies were never resolved [5–7]. Even the scientific ingenuity of the above stalwarts of biochemistry and biophysics and the efforts of a large number of researchers in the field of bioenergetics in the 20th century could not formulate a theory of energy coupling that might be put in place of chemiosmosis. Moreover, the design of experiments and the interpretation of data failed to offer any guidance either in devising a rational substitute. The chemiosmotic theory was incorporated into the textbooks more by erosion of the opposition than by any decisive experimentation or theoretical analysis.

ð1Þ

3. New conceptual framework for energy coupling in OX PHOS and PHOTO PHOS

In the theory of chemiosmosis, the electrogenic Δp created across bulk aqueous phases is considered as the obligatory energy intermediate

Following a fresh molecular systems biology/engineering approach to the problem, an alternative theory of energy coupling and molecular

Δp ¼ Δφ−60ΔpH

S. Nath / Biophysical Chemistry 224 (2017) 49–58

mechanism of ATP synthesis has been formulated and embellished by the author during the last two decades [5–7,14–21]. Nath's torsional mechanism of energy transduction and ATP synthesis has also been extensively discussed by other authors [22–28]. The molecular mechanism appealed to E. C. Slater and R. J. P. Williams (who, among the stalwarts mentioned above, were the only ones alive or scientifically active during the author's time), as evidenced by a long 15-year correspondence. In this new conceptual framework for energy coupling, the overall driving force for ATP synthesis is postulated to be the sum of the electrochemical potential difference of protons and anions/ countercations that translocate through the access channels at the interface of the a-c subunits, i.e., Δμ̃H + Δμ̃A/C, or equivalently, ΔpH and ΔpA/ C (or because the driving force has to change form to act, ΔpH and ΔψA/ C, or ΔψH and ΔψA/C, depending on the stage of the conformational cycle and where one draws the boundary surface). In other words, the driving force for ATP synthesis is created by two independent sources of energy, i.e., FO-permeable anions/countercations and protons respectively, in contrast to all other mechanisms, including chemiosmosis, that postulate a single energy source only (e.g., protons). Both molecular driving forces are thermodynamically intensive properties, related to the discrete, ordered and sequential elementary events of proton and anion/ countercation translocations (binding and unbinding) through the FO portion of the F1FO-ATP synthase at the a-c interface. New terminology of symsequenceport and antisequenceport was coined to enable a more perceptive understanding of the temporal sequence of events in the new paradigm in order to extract energy from anion/countercation translocation in addition to proton translocation. The Δψ in this mechanism is local and transient in the access half-channels of FO and has no relationship with the delocalized potential, Δφ [Eq. (1)] postulated by chemiosmosis across bulk aqueous phases [6,17,18,20]. The mechanism is step-wise or dynamically electrogenic but overall electroneutral on both redox/photo and ATP sides, and hence does not violate overall electroneutrality of bulk media. These principles were postulated to be of a general and universal nature in biological systems, and applicable also to the related P-type, V-type, and A-type ATPases and to other biological molecular machines such as the bacterial flagellar motor. Following a ten-year search [summarized in Ref. 7], the anion involved in biological energy coupling has been identified as a dicarboxylic acid anion by the torsional mechanism – succinate in mitochondrial OX PHOS, malate in PHOTO PHOS by chloroplasts, and fumarate in the bacterial flagellar motor. This is a major experimental accomplishment of the work. The identity of the countercation to H+ (in certain bacterial and other systems) was found to be either Na+ or K+. Hence the F1FOATP synthase is a proton-dicarboxylic acid monoanion cotransporter in mitochondria and chloroplasts, and not simply an electrogenic H+ conductor. 4. The issue of electrical neutrality and its biological implications for energy coupling and ATP synthesis 4.1. The principle of electrical neutrality The principle of overall electrical neutrality in condensed media has been covered in various textbooks of thermodynamics and biophysical chemistry [29–31]. For a bulk liquid phase it can be expressed by the condition ∑ zi n i ¼ 0 i

ð2Þ

where zi is the charge number of the ionic species i, and ni is the number of moles of the ith species. The electroneutrality principle is a cornerstone in generalization of Wyman's classical linked functions [32] and was used by Record and Anderson to arrive at a theory of preferential interactions applicable to electrolyte ions [33–35]. The principle has major implications for molecular mechanisms of ATP synthesis and offers

51

Fig. 1. The experimental model system containing purified F1FO-ATP synthase reconstituted into a liposome.

great assistance in discriminating between various theories of energy coupling. It can be profitably applied to the routinely-used purified, reconstituted F1FO-ATP synthase experimental system shown in Fig. 1. 4.2. Experimental system Depicted in Fig. 1 is the purified F1FO-ATP synthase reconstituted into a tight phospholipid membrane, the biochemist's choice of experimental system. The system was first introduced by Ephraim Racker in the early 1970s [36] and was therefore available during Mitchell's time; however, today, liposome technology has advanced to a level where routine preparations contain a single molecule of the enzyme per vesicle embedded in the membrane and plugged through it in a defined orientation (F1 sector facing out in Fig. 1) [37]. No other contaminating protein is present in the liposomal system of Fig. 1. Both “inside” and “outside” aqueous phases are macroscopic bulk phases that are spatially of large extent, and may be figuratively likened to the Atlantic and Pacific oceans respectively, pursuing the analogy first adumbrated by Williams [4,9]. This system enables study of ATP synthesis in a single enzyme and single vesicle mode, although for our purposes in this invited review, no difference exists even if the experimental system contains more than one F1FO molecule per vesicle or organelle. Such experimental systems have been shown to produce physiological rates of ATP synthesis per F1FO molecule, e.g. when incubated typically in a succinic acid bath, and the characteristics of the system have been documented in a number of previous reports [38–41]. This experimental observation creates insurmountable hurdles for the operation of a proton-only Mitchellian chemiosmotic mechanism (Fig. 2a). 4.3. Violation of the principle of electrical neutrality by Mitchell's chemiosmotic theory Fig. 2a shows that uncompensated H+ movement that lies at the heart of the explanation of ATP synthesis by the chemiosmotic theory will violate the electroneutrality of both the inside and outside bulk

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S. Nath / Biophysical Chemistry 224 (2017) 49–58

Fig. 2. Simplified representation of various models of energy coupling in OX PHOS and PHOTO PHOS based on a) the chemiosmotic theory, b) the torsional mechanism of energy transduction and ATP synthesis, with the bold arrow denoting the primary dicarboxylic acid monoanion translocation, and the dashed arrow showing the succeeding secondary proton translocation at the a-c stator-rotor interface in the membrane-bound FO portion of ATP synthase, and c) a mechanism in which overall electroneutrality is maintained by transporting the anion through the membrane lipid bilayer.

aqueous phases, as also pointed out by Wray [28], and earlier by Green [12]. Thus, the outside bulk aqueous phase will incessantly accumulate H+ ions, while the inside bulk aqueous phase will contain an excess of OH– ions (Fig. 2a), and both bulk phases will violate the principle of electrical neutrality as given by Eq. (2). One can perhaps imagine that if sufficient energy is supplied to the system, it might be possible to move protons in an uncompensated way. However, it should be stressed that in the experiment, no external energy is being supplied to

the system, for instance in the form of light or redox energy, and the thermodynamic system containing only the tight phospholipid coupling membrane, the F1FO molecule(s), and different concentrations of uncharged and anionic components of the dicarboxylic acid and protons in the two bulk compartments “in” and “out” is well-defined, and the problem is well-posed. Such gross, spontaneous violation of electroneutrality of bulk aqueous phases that is required by chemiosmosis and is central to its view of energy coupling is unprecedented in nature. In

S. Nath / Biophysical Chemistry 224 (2017) 49–58

fact, the author is not aware of any natural process that violates bulk electroneutrality in this way and to this extent. Hence the chemiosmotic theory cannot be the correct theory of energy coupling in OX PHOS and PHOTOPHOS. Therefore, an alternative theory of energy coupling that is consistent with the principle of electrical neutrality is needed. 4.4. Other important consequences for the chemiosmotic theory 4.4.1. Protonmotive force, Δp is not an essential intermediate in ATP synthesis ATP synthesis by the clean experimental liposome system of Fig. 1 has several other important consequences for the chemiosmotic theory. Interestingly, in these and other experiments [7,42] no protonmotive force, Δp [Eq. (1)] has been imposed on the system; yet ATP is synthesized at physiological rates under specific experimental conditions, for instance when use of a succinate or malate bath is made. As is wellknown, the chemiosmotic theory postulates uncompensated protons in an electrogenic mode of translocation as the source of the protonmotive force [3], not compensated protons, as for example in the form of succinic acid or malic acid [7,18–20,38–42] imposed by the experimentalist as gradient in a liposomal system (Fig. 1). Such experiments do not provide proof of the driving power of a protonmotive force, as generally believed, because in reality, no protonmotive force was applied in these experiments. In fact, since physiological ATP synthesis occurs without application of a protonmotive force, these biochemical experiments in reconstituted liposomes prove that, contrary to chemiosmotic dogma, the protonmotive force is not an obligatory intermediate in ATP synthesis. Hence Δp is not the primary form in which energy is conserved in these experiments and it is absolutely essential to consider alternatives to Δp as the intermediate in energy coupling. 4.4.2. Delocalized electrical potential, Δφ is not an essential intermediate in ATP synthesis A delocalized electrical potential between two bulk aqueous phases, Δφ created upon electrogenic H+ pumping by the redox complexes (Complexes I–IV) in animal mitochondria and bacteria at the expense of free energy provided by the oxidation process in OX PHOS is a strict requirement of the chemiosmotic theory. Yet ATP synthesis occurs in the purified reconstituted system of Fig. 1 in a succinic acid/malic acid bath even in the absence of redox enzymes or photosystems, complexes that are supposedly responsible for the creation of the delocalized Δφ according to the chemiosmotic theory! Hence the delocalized electrical potential, Δφ is not an essential intermediate in ATP synthesis. Further, once the central thesis of this article is accepted – that the electroneutrality of bulk aqueous phases cannot be violated by an electrogenic mode of ion transport involving incessant uncompensated proton translocation from one bulk phase to another (Section 4.3) – then, increasing the magnitude of ΔpH between the phases cannot compensate for the absence of the delocalized Δφ, and the ΔpH alone cannot sustain ATP synthesis and act as its sole driving force. Hence a new paradigm was needed to understand the energetics of energy coupling in the FO portion of ATP synthase. 4.5. A dynamically electrogenic but overall electroneutral mode of ion transport as a new paradigm in bioenergetics As discussed above, physiological ATP synthesis has been shown to occur under specific experimental conditions with the enzyme molecule purified and reconstituted into liposomes, which do not contain any redox/photo complexes. Further, since bulk electroneutrality is inviolable, an extensive study was needed in order to provide new insights into energy coupling in OX PHOS and PHOTO PHOS. In particular, a reappraisal of the mode of ion transport across the membrane through the FO portion of ATP synthase was felt to be absolutely necessary when the development of the torsional mechanism of energy transduction and ATP synthesis was a work in progress [17–19]. One possibility was that no electrical potential

53

is created, which was the view of Tedeschi and colleagues [43–45]; another was a completely electroneutral transport across the membrane, which would also lead to zero potential. However, the present author found it very difficult to conceive how a mechanical torque could be produced in the FO motor of the ATP synthase in the absence of a local electrical potential generated at or in the vicinity of the strictly conserved binding sites of the two ions (the a-subunit Arg-210 and the c-subunit Glu/Asp-61 for the anion and the proton respectively) in the half-access channels at the a-c interface of FO, which he considered to be an obligatory requirement for rotation. Hence, both the above alternatives were considered highly unlikely, if not impossible, and therefore eliminated from further consideration. The logically promising alternative suggested itself that the electrical potential is created at the a-c interface within the FO portion of the ATP synthase enzyme molecule itself (in other words, the electrical potential, Δψ is local) by an independent source other than protons. Energetic considerations indicated that ΔpH supplied only part of the energy requirement (~50%) for ATP synthesis; therefore the rest had to be supplied by a locally present but independent source of Δψ. The overall driving forces for ATP synthesis are the ion concentration gradients due to protons and counterions (anions transported through symsequenceport or cations transported through antisequenceport), and a dynamically electrogenic but overall electroneutral mode of ion transport was proposed in this context [17]. This mode of ion transport involves a permeant anion (succinate in mitochondria, malate in chloroplasts, fumarate in the bacterial flagellar motor) that is translocated in the same direction as the proton (Fig. 2b), or a cation (Na+ in certain bacterial ATPase/redox systems [46,47], or K+ in the presence of valinomycin in vitro) being transported in a direction opposite to the direction of proton translocation [7]. However, both proton and anion (or countercation) do not move together or simultaneously or concurrently as in electroneutral ion transport mechanisms but sequentially (Fig. 2b). Hence, the ion transport is step-wise or dynamically electrogenic, but overall electroneutral. The discrete, sequential ion translocations in the half-access channels of FO transiently generate (for a time interval between the primary and secondary ion translocation events) a local Δψ, that is immediately destroyed by the succeeding (H+) translocation, and thus involve a change in local electrical potential, Δ(Δψ) as an intermediate step for energy transduction and rotation of the c-rotor in this novel mode of ion transport. Yet, bulk electroneutrality is not violated and the energy of both the ion gradients are harnessed and jointly utilized for rotation by the FO motor. These central concepts can be written in the form of mathematical equations that govern the torsional mechanism and describe its operation, and also include the constraint imposed on the overall process by the principle of electrical neutrality (Section 4.1). According to the torsional mechanism, the overall driving force (d.f.), i.e. the energy supplied to synthesize one molecule of ATP by coupled ion translocation [6,7] is given by d:f : ¼ nH Δμ̃H þ nA=C Δμ̃A=C

ð3Þ

where nH and nA/C represent the number of proton and anion/ countercation translocations required to make one ATP molecule, and Δμ̃H and Δμ̃A/C are the electrochemical potential differences of proton and anion/countercation respectively. Eq. (3) is general and is valid under nonequilibrium conditions at which coupled proton and anion/ countercation transport occurs in biological systems. Since overall electroneutrality has to be maintained during the coupled ion translocation process, nH ¼ nA=C ¼ n

ð4Þ

Hence, in general, for nonequilibrium flow conditions,   d:f : ¼ n Δμ̃H þ Δμ̃A=C

ð5Þ

Eq. (5) is the principal equation, as per the torsional mechanism, for describing physiological ATP synthesis by the F1FO-ATP synthase.

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S. Nath / Biophysical Chemistry 224 (2017) 49–58

For the dead-end condition of equilibrium, the net d.f. = 0, ion transport ceases to occur, and ATP is not synthesized. The general Eq. (5) reduces to the special case of 

 Δμ̃H þ Δμ̃A=C ¼ 0

ð6Þ

Eq. (6), though not useful under the prevailing physiological conditions of nonequilibrium steady states, can however be utilized to obtain the ionic distributions under conditions of thermodynamic equilibrium. However, in order to extract energy from the anion/countercation, it is important to understand the temporal sequence of ion translocation events. The possibilities of simultaneous transport of proton and anion (or countercation) or proton transport preceding anion (or countercation) translocation through access pathways at the a-c stator-rotor interface in FO are ruled out because in either case, the energy of the anion (or countercation) gradient is not made available to the proton, and therefore complete rotation of the c-rotor in the FO portion of ATP synthase cannot occur. Thus anion (or countercation) translocation (bold arrow in Fig. 2b) must precede proton translocation (dashed arrow in Fig. 2b) through the proton half-access channels at the a-c interface in FO. In other words, anion or countercation translocation is primary and proton translocation is secondary on the ATP side; primary and secondary events are interchanged on the redox/photo sides where proton translocation in response to electron transfer is the primary event, followed by secondary anion or countercation translocation. A strictly conserved Arg-Leu-Asn-Ala (RLNA) sequence on helix 4 of the a-subunit has been identified as the signature of an anion-binding sequence in mitochondria and chloroplasts, with the essential aArg-210 forming the dicarboxylate anion binding site in the immediate vicinity of the cGlu/Asp-61 proton-binding site at the a-c interface of FO [7]. In summary, the huge problem of violation of electrical neutrality of bulk aqueous phases is avoided in Nath's torsional mechanism of ATP synthesis by postulating a dynamically electrogenic but overall electroneutral mode of ion transport. This unique mode of ion transport has been quantified, and the principal result [Eq. (5)] is shown to be valid for general nonequilibrium states, and incorporates within it the constraint of overall electroneutrality arising from the coupling of proton and anion/countercation translocation. Because of the sequential translocation of anion (or countercation) and proton through contiguous transport access channels in the a- and c-subunits respectively to/ from their binding sites at the a-c stator-rotor interface of FO, a transient local field is created and subsequently destroyed, leading to the generation of a mechanical torque that is ultimately transduced through a cascade of events into torsional energy in the γ-subunit of the F1 portion of ATP synthase [15–20], and hence the name of the mechanism. This torsional energy is used at the three catalytic β-sites in F1 to competently bind ADP and Pi, forcibly condense them to form ATP, and release preformed ATP respectively by a novel catalytic cycle in which all three catalytic sites are occupied by bound nucleotide and every elementary step requires energy [17], contradicting the fundamental tenets of Boyer's binding change mechanism [48]. The fifteen novel predictions made in 2002 [see pp. 79–80 of Ref. 17] for the physiologically important mode of ATP synthesis by the F1FO-ATP synthase (as opposed to ATP hydrolysis by F1-ATPase, a wasteful process in both mitochondria and chloroplasts) were well ahead of their time and are still relevant today. 4.6. Sites of entry and exit of the dicarboxylic acid anion Depending on the sites of entry and exit of the dicarboxylic acid monoanion, other ways of energy coupling are perhaps possible. Kaim and Dimroth [41] showed experimentally that succinate monoanion is indeed translocated in the purified reconstituted system of Fig. 1. However, unlike the torsional mechanism that localized the translocation of succinate monoanion through the aqueous access half-channels at the

a-c interface of the FO portion of the F1FO-ATP synthase transporter molecule itself (Fig. 2b), these workers postulated that the succinate is transported through the membrane (Fig. 2c). While this model overcame the problem of violation of bulk electroneutrality, it created a host of other serious difficulties. A major difficulty for this variant is that the lipid bilayer is known to be impermeable to ions; hence postulating a flux of succinate through the membrane (Fig. 2c) runs counter to our knowledge of membrane biophysics. Basically, the lipid bilayer is a barrier to all charged species, and the real question evolutionarily was how to circumvent such a tenacious barrier to charged species, which is why nature devised membrane-bound transporters. Further, allowing such bulk-to-bulk passage of the succinate monoanion will collapse the delocalized Δφ created by primary proton movement and dissipate the driving force of chemiosmosis in OX PHOS. Moreover, such ion translocation (Fig. 2c) is inconsistent with a central postulate of the chemiosmotic theory, as discussed previously [p. 302 of Ref. 6]. Such ion translocation would anyhow require modification of the fundamental postulates of the chemiosmosis, or the proposal of a new theory of energy coupling. Further, the acute mechanistic difficulties of transmitting the driving force to the FO sites in the a-stator and crotor, where they are required, are not addressed in a model such as that shown in Fig. 2c. These difficulties do not arise in the proposals of the torsional mechanism (Fig. 2b) because the molecular driving forces are created by anion and proton binding/unbinding to/from the strictly conserved Arg-210 and Glu/Asp-61 binding sites in the a-stator and crotor respectively; such collimated molecular driving forces act exactly at the sites where they are required for torque production and rotation in the FO motor, and therefore they can be readily utilized for performing useful work. Finally, postulating that the energy of succinate translocation through the membrane is not employed for performance of useful work but serves only as a means to maintain electroneutrality is not adequate either: it essentially implies that the succinate ion gradient is dissipated, and that the efficiency of energy conversion is halved. Such a model is also incompatible with comprehensive nonequilibrium thermodynamic analyses of ATP synthesis [14,21]. In summary, the only three models of energy coupling possible in the context of ATP synthesis are clearly delineated and depicted in Fig. 2. Following the arguments made in Sections 4.3–4.4, and Section 4.6 respectively, the alternatives shown in Fig. 2(a) and Fig. 2(c) appear indefensible to the author. From the detailed analysis in Section 4.5, the theory of energy coupling proposed by Nath's torsional mechanism of energy transduction and ATP synthesis (Fig. 2b) emerges as the only available theory that is consistent with the principle of electrical neutrality, and it is by far the best conceptual framework available for logical interpretation of experimental data and guidance in the design of future experiments in this highly interdisciplinary field. 5. Possible chemical logic for the selection of dicarboxylic acids as intermediates of energy coupling in OX PHOS and PHOTO PHOS Following the detailed analysis in Section 4, the obvious question that arises in the reader's mind is what the underlying chemical reasons could be for the evolutionary selection of dicarboxylic acids as intermediates in biological energy coupling. A possible and attractive chemical explanation can be offered thanks to the pioneering classical thermodynamic research work of Christensen, Izatt, and Hansen. These workers conducted a broad research program to measure the thermodynamic quantities associated with proton ionization in dilute aqueous solution from various donor atom types. Initially, these studies were performed at 298 K [49], but later, temperature studies were also carried out by calorimetry and the results tabulated in a Handbook [50]. Inspection of their results shows that weak dicarboxylic acids such as succinic and malic acids are among the few chemical systems that have a fairly small standard enthalpy of ionization, ΔH° (compared to water or strong acids) and their ionic fractions at the operating conditions and the values of the first and second ionization enthalpies are tuned such

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that the net ΔH° approaches zero at 310 K [21,49,50]. In other words, virtually no input of external enthalpy is needed to dissociate these dicarboxylic acids; the first proton is almost completely disassociated in aqueous solution at physiological pH and the enthalpy change for disassociation of the second proton is near zero. Gibbs free energies for disassociation of carboxylic acids are almost entirely entropic. By contrast, the protons in Mitchell's chemiosmotic theory originate from water [51], which has a large standard enthalpy of ionization of 57.3 kJ/mol. Thus the mitochondrial respiratory chain needs to additionally expend 57.3 × 10 = 573 kJ per pair of electrons in order to generate 10H+ and 10 OH– ions (assuming the consensus value of stoichiometry of 10H+/2e− in animal mitochondria) [21,52] from water by the hypothetical fuel cell in mitochondria that release H+ on one side of the membrane and the OH– on the other side and ensure the “charge separation across the membrane” required by chemiosmosis [3,4,51]. However, a pair of electrons moving down the respiratory chain in OX PHOS can generate 220 kJ/mol only. Moreover, in addition to synthesizing ATP, the energy of 220 kJ/mol per 2e− also needs to compensate for active transport losses in the electrogenic H+ pumps, leaks in the membrane, respiratory slip, and other losses at the coupling sites. The extremely steep costs of ionization/dissociation of water (that have not been included previously by any energy balance of the OX PHOS process) are inconsistent with the nonequilibrium thermodynamics of energy coupling [14,21,52,53]. Needless to say, inclusion of the high thermodynamic costs owing to the large ionization enthalpy of water renders impossible the operation of a Mitchellian charge-separating chemiosmotic engine in which water is the origin of the translocated protons. These difficulties do not arise in the torsional mechanism of energy transduction and ATP synthesis according to which a weak dicarboxylic acid is the source of the proton and the anion, and the energies of both proton and anion translocations in the membranebound FO portion of ATP synthase are collaboratively utilized to synthesize ATP in the hydrophilic F1 headpiece. The above thermodynamic arguments lend us even greater confidence in the superiority of the concept of energy coupling proposed in the framework of the torsional mechanism of ATP synthesis over other alternatives.

6. Further details While it is satisfying to be assured by one of the referees that “bulk electroneutrality is indeed broken in Mitchell's theory” and by another that “use of the principle of electrical neutrality has convincingly shown the flaw in Mitchell's chemiosmotic theory,” it is nonetheless important to quantify the extent of electrogenic charge transfer postulated by chemiosmosis under physiological conditions, as suggested.

6.1. Estimation of electrogenic H+ charge transfer required by chemiosmosis in mitochondrial OX PHOS In order to achieve a bulk-to-bulk delocalized Δφ of 200 mV by the macroscopic process of chemiosmotic coupling, a charge transfer of 0.8 μeq H+/g protein in rat liver mitochondria was estimated [3]. Classical morphological data shows that 1 mg mitochondrial protein contains 7.2 × 109 mitochondria [54]. Hence, in order to reach a delocalized Δφ of 240 mV required by the chemiosmotic theory during OX PHOS, the number of protons translocated per mitochondrion corresponds to [0.8 × (240/200) × 10−9 × 6.0 × 1023]/7.2 × 109 = 80,000 H+/mitochondrion. Thus, in chemiosmosis, where the potential energy depends on a macroscopic charge transfer process, 8000 cycles of transfer of a pair of electrons in OX PHOS are required in a single mitochondrion for the formation of a protonmotive force, Δp compatible with the thermodynamic requirements imposed by the Gibbs free energy of phosphorylation.

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6.2. Energy transduction by a Mitchellian fuel cell versus a Nathean biological molecular machine In the Mitchellian view [51] where energy-transducing membranes in mitochondrial OX PHOS are fuel cells that split water, transfer of a large number of electrons (8000·2e− cycles) and protons (80,000 H+ per mitochondrion) are required to attain a Δp competent to synthesize ATP. Transfer of 2e− creates only a negligible delocalized Δφ and Δp in Mitchell's model, and consequently does not lead to ATP synthesis. By contrast, a Nathean biological molecular machine is characterized by the involvement of nonequilibrium states and an irreversible mode of operation [17,18] (though the molecular machine/enzyme can be reversed by imposing a different set of initial and boundary conditions, and in that sense the system is indeed reversible [20]), and a mechanism of e− transfer and ATP synthesis where ΔG is equal to or close to ΔH. In a Nathean model where the potential energy depends on microscopic events and the driving forces of ATP synthesis are molecular in nature, the translocation of only a few protons and anions/ countercations (arising from a single cycle of 2e− transfer) is sufficient to reach a potential energy level compatible with the Gibbs free energy of phosphorylation and produce a nonequilibrium energized state of a submolecular component of a single F1FO-ATP synthase molecule involved in the energy transduction. This stored internal energy within the single molecule is subsequently utilized to synthesize ATP. The two alternative models (fuel cell vs. biological molecular machine) are diagrammatically compared in Fig. 3. In the molecular energy model of Nath's torsional mechanism, first the c-subunits of the c-rotor in FO and subsequently the γ-subunit in F1 store an internal potential energy (of ~54–58 kJ/mol as twist/torsion). This is contrasted with the equivalent energy of the Δp attained by a macroscopic electrogenic process in Mitchell's chemiosmosis model (Fig. 3). Hence, in conclusion, it is unrealistic to retain the analogy of energy-transducing membranes as watersplitting Mitchellian fuel cells, and the analogy of the ATP synthase to a Nathean biological molecular machine is far superior.

6.3. The issue of H+/2e− and H+/ATP stoichiometries Mitchell postulated an H+/2e− stoichiometry of 6 and an H+/ATP stoichiometry of 2 in his theory, stoichiometries that he obdurately hung on to until his dying day even in the face of adverse experimental evidence that unequivocally showed higher values of redox and ATPase stoichiometries in mitochondrial OX PHOS (Section 5) [13]. However, he never gave any explanation, or offered even a hint of the reasons for his defiance. Following the detailed thermodynamic considerations in Sections 5 and 6.2, it can be easily calculated that Mitchell's watersplitting fuel cell model [51] in the mitochondrion could provide only 220/57.3 or approximately four H+ per 2e−, with another 2H+/2e− arising from the QH2 → Q + 2H+ + 2e− redox reaction, i.e., he could obtain at most 6 H+/2e− from his theory. Acceptance of the

Fig. 3. Comparison of macroscopic fuel cell and molecular energy transduction models of energy coupling. Consult the text in Section 6.2 for details.

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experimentally obtained higher OX PHOS redox stoichiometries of 10 H+/2e− created an energy crisis for the chemiosmotic theory, because it meant that water could not be the source of the coupling protons, that the chemiosmotic theory would violate the first law of thermodynamics, and that his (hypothetical) fuel cell could not operate in a manner competent to generate the obligatory delocalized intermediate, Δp envisaged in chemiosmosis. Mitchell would have known that accepting the higher consensus stoichiometry would strike at the root of his redox loop concept, and definitely invalidate his chemiosmotic theory because of the steep energy shortfall. Similarly, a stoichiometry on the ATP-side of 2 H+/ATP is required by and central to the direct coupling between H+ and ATP formation postulated by Mitchell [4]. In this model (contrary to a model [16,17] involving conformational changes in F1), it is envisaged that, at the F1 active site, binding of ADP and phosphate is arranged so that the substrates are oriented perpendicular to the plane of membrane at the interface between FO and F1, thereby permitting the terminal oxygen atom from phosphate to accept 2H+ from FO, i.e. two positive charges move inward to finally reside in water. Acceptance of higher values of three to four for the H+/ATP ratio would also have invalidated direct coupling schemes between H+ and ATP formation postulated by the chemiosmotic theory. Hence, we have explained for the first time the underlying reasons for Mitchell's apparently irrational and dogmatic refusal to accept the higher stoichiometry values definitively revealed by various experiments in bioenergetics. The new higher stoichiometry values have now been accepted as the “consensus” values [21], but it is ironical that the theory of energy coupling remains of the old, and one that cannot be reconciled with the new experiments. 6.4. Usage of the term “electrogenic” and stationary vs. transient electrical fields In this paper, the word “electrogenic” refers to the internal potential differences appearing inside FO due to discrete sequential proton and anion/countercation translocation events to and from their respective binding sites in the a-c half-access channels. It should not be confused with the transfer of electrical charge across the membrane or to the build-up of electrical potential across the membrane in the bulk or at the membrane surface. It should also be understood that the chemiosmotic process of proton transfer does not cause acidification of an external medium or bulk region per se as happens extensively for instance in PHOTO PHOS; however for acidification and measurement of the pH difference by probes that always access a larger space than the immediate membrane surface, a second ion such as a dicarboxylic acid anion or chloride etc. is also necessary. An interesting aspect of the liposome experiments (Fig. 1; Section 4.2) is that it is not possible to take refuge in explanations based on creation of a localized or delocalized field by other redox/photosystem pumps present in natural experimental mitochondria/chloroplast systems or other transporters present in partially purified systems, and collapse of the field by other agents such as K+ in the presence of valinomycin or a general H+ movement on the ATP-side. Of course, H+ translocation can generate a field in the liposome system of Fig. 1, but without destroying the field it is not possible to synthesize ATP. Moreover, the same source (e.g. H+) moving unidirectionally (“in” to “out” in Fig. 2a) cannot be the agent that creates as well as destroys the electrical field in a liposome system containing only the ATP synthase (Fig. 1, Fig. 2a). The above analysis also implies that a stationary electrical field Δφ associated with a concentration gradient of ions cannot be converted into useful work and therefore direct field-driven chemistry cannot take place as postulated in the theory of chemiosmosis. This point was also emphasized by R. J. P. Williams [55] in his last paper on the subject [56]. In his words, “Mitchell's mechanism of ATP

formation was electrolytic field driven and is impossible” [see p. 148, col. 1 in Ref. 55] and “Both Mitchell and I failed to give a good description of the ATP synthetases” [p. 149, col. 2 in Ref. 55]. Energy conservation requires that useful work be done at the expense of a reduction in electrical field strength, in which case the stationary field has to take on a lower value of field strength. This reduction in the electrical potential can only be brought about by an actual ion current of differing character from the one that created the field in the first place. Hence localized models [9,57,58] where protonic charge build-up is confined to a thin surface region adjacent to the membrane are also inadequate, not because they violate electroneutrality (since a membrane surface can accumulate ionic charge and a membrane potential can be built up), but because they cannot be coupled to rotation in FO and performance of useful work. The above difficulties are avoided in the torsional mechanism because only closely bound H+ and A− at their respective binding sites can be coupled to rotation due to destructive interference by an ion of opposite charge from the one that created the transient electrical field, and further, the electrical imbalance and its return to a balanced charge configuration occurs only at the restricted site of the ion binding/unbinding process. Electrostatic interaction between the essential a-c residues upon electrical imbalance produced by ion binding/unbinding is the driving force for c-ring rotation and ATP synthesis in the torsional mechanism. Since inception, it was predicted that the geometry of the a- and c-subunits should be such that “while c is a complete cylinder, the a-subunit (containing the key Arg-210 and His-245 residues) is part of a cylinder coaxial to c, covering two subunits of c (each containing a Glu/Asp-61 H+ binding site). Thus, the interacting region of a- and c-subunits can be considered as the surfaces of two coaxial cylinders in close proximity to each other” [15], a prediction supported by the recent cryoelectron microscopy (cryo-EM) structure of the a-c interface in an F-type ATPase [59]. The a-subunit access channels translocate anions to their binding site located at the a-c interface. This would bring the dicarboxylate anion very close to the proton, as repeatedly emphasized by the torsional mechanism and italicized (see pp. 2222–2223 of Ref. 19; p. 433 of Ref. 7]. Interestingly, the important side chains in the horizontal helices of the a-subunit have also been interpreted to approach the protonation site in the c-subunit more closely (than would be the case if the helices were vertical) in the cryo-EM structure, and also enable the Arg-210 and His-245 to interact with two adjacent c-subunits simultaneously with a constant distance of interaction [59], exactly as predicted by Nath's torsional mechanism of energy transduction and ATP synthesis since 1998. The close approach predictions of the torsional mechanism were made to account for the interaction of the anion with the proton and thereby enable their coupled symsequenceport translocation as separate charges without recombination in the membrane, and for energy addition, joint energy utilization, and ATP synthesis. However, in the absence of any role ascribed to the anion, the rationale for such a close approach (of 1.1 nm – 1.35 nm depending on the diameter of the c-ring in different organisms) is very difficult to explain. Hence a functional role and significance for the close approach of the side chains of the essential Arg-210 and His-245 a-subunit residues located on the long horizontal helix hairpin with the Glu/Asp-61 protonation site on the c-subunit is provided by the torsional mechanism. 6.5. Relationship to the Nernst equation For an uncoupled process involving a single ion, assuming that the ion species distributes at electrochemical equilibrium, the Nernst equation can be applied and a value of the electrical potential can be calculated. However, the field stays as such and cannot be coupled to rotation and mechanical torque (Section 6.4). In a nonequilibrium transport process involving coupling of proton and anion flows,

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where two ions are involved in energy-linked transport, it is invalid to assume that any one given ionic species is in sole equilibrium with the membrane potential, and thus there is no solid theoretical basis for using the Nernst equation in this case. It would therefore be quite impossible to calculate the presumed transmembrane electrical potential from the concentration gradients of a particular ion without knowing for certain that one ion or the other (or none!) is in passive equilibrium with the electrical potential. In fact, as explained in Sections 4.5 and 6.4, a transient field is created and then destroyed by discrete ion translocation, and hence the electrical potential is not long-lasting, and therefore it is incorrect to interpret the calculated electrical potential obtained on application of the Nernst equation as a stationary electrical potential that remains as such and continues to exist at all times. This important aspect requires a separate and more detailed analysis based on the principles of nonequilibrium thermodynamics and transport [53] that is beyond the scope of this work. However, it can be safely concluded that failure to consider the second ion in an ion-coupled mechanism of transport is a lacuna of all previous theories of biological energy coupling. Therefore it is recommended that the torsional mechanism be utilized for scientific and technological progress in the field as a matter of course, instead of considering only outmoded and misinformed theories that were postulated more than half-a-century ago and have now been surpassed by a more detailed and superior alternative. 6.6. Transient departure from electrical neutrality as an ordering principle for transport and reaction steps and the stringency of electrical neutrality The regulating principle that emerges at the molecular level (the level at which driving forces are defined in the torsional mechanism of ATP synthesis) is that charge imbalance can (and needs to) be created at conserved, restricted transport sites in the membrane for biological energy transduction, but that the imbalance cannot be sustained for long. Hence a discrete step-by-step mechanism of transport has evolved in which translocation of a counterion is favored over translocation of another co-ion, which implies that the requirement of electrical neutrality is very stringent. In the overall sense, the entire transport process is initiated by the concentration gradients of the species to which the membrane is permeable. These concentration differences are therefore of fundamental importance and constitute the main factors that differentiate the internal and external compartments of the cell or organelle, and thus all voltages and electrical potentials result from these concentration differences. The above ideas are also supported in a self-consistent way structurally by the fact [59] that there exists only one ion-binding site per a- and c-subunit in an F1FO molecule. We can apply the dynamically electrogenic but overall electroneutral ion transport to the complete process of oxidative phosphorylation in mitochondria. ATP synthesis is regulated by its demand in various cellular processes; when ATP4 − is required, it is transported out from the intracristal space to the cytoplasm along its concentration gradient. The local electrical potential thus created drives ADP3 − along its concentration gradient to the mitochondrial intracristal space in exchange for ATP4 − by the adenine nucleotide transporter. The resulting unbalanced local electrical potential causes HPO 24 − to move into the crista, and the OH – produced during ATP synthesis in the F1 portion of ATP synthase is driven out of the mitochondria in exchange for the HPO24 − by the HPO24 −/ OH– antiporter, and overall electrical neutrality is restored. The same exchanges occur between the intracristal space and the matrix space of the mitochondrion, and thus the substrates MgADP− and Pi are made available to the ATP synthase F1 portion that protrudes into the matrix space. The binding of MgADP − to the β-catalytic site 3 in the F1 portion is the rate limiting step of the process according to the torsional mechanism of ATP synthesis, and until MgADP− binding occurs in F 1 (and the single negative charge of MgADP− is

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occluded by the β-catalytic site 3 in F1), the anion and proton access channels in the FO portion of ATP synthase are closed, and the energy of the ion gradients is not wasted. The electrical imbalance created upon binding of MgADP − is the signal for the anion pathway to open and conduct an anion, and an interesting inter-access channel communication develops that leads to anion and proton cotransport, that continues upon subsequent phosphate binding, and only ceases upon restoration of electrical neutrality after release of product MgATP2 − from the F1 catalytic site along with OH−. The self-regulatory cycle repeats, with the transient departure from and restoration back to electrical neutrality acting as an ordering principle for the elementary steps of transport and chemical reaction. In order to prevent dissipation of ion gradient energies until the substrate(s) is/are bound in F1, Boyer's binding change mechanism has proposed long-range interactions between β-catalytic sites and site-site cooperativity in F1 [48] based on oxygen exchange studies. However, owing to the complexity of the intermediate Pi-HOH and intermediate ATP-HOH exchange reactions and the difficulties in their interpretation [18], supramolecular structural effects and coupling between FO and F1 mediated by the energy-transducing membrane could provide an alternative explanation. Such an explanation for a number of puzzling features of the mitochondrial intermediate exchange reactions [18] is more elegant and attractive, and one that is more likely to be correct in the light of a dynamically electrogenic but overall electroneutral mode of ion transport. Hence the incorporation additionally of key regulatory aspects within the self-consistent conceptual framework of energy coupling in the torsional mechanism can be considered to be another merit of the new biochemical theory. 7. Conclusions A systematic reappraisal of the modes of ion transport proposed by various theories of energy coupling in oxidative phosphorylation and photosynthetic phosphorylation and molecular mechanisms of ATP synthesis has been undertaken for the routinely-used reconstituted liposome experimental system containing purified F1FO-ATP synthase. The chemiosmotic theory involving uncompensated proton translocation has been shown to violate the principle of electrical neutrality of bulk aqueous phases, and on these grounds it has been concluded to be indefensible, and therefore unsound as a theory of biological energy coupling. Experiments suggest the movement of succinate/malate monoanion in OX PHOS or PHOTO PHOS (or countercations Na+ or K+ in other bioenergetic systems) in addition to protons. However, attempts to save the chemiosmotic theory by postulating movement of these anions/countercations through the barrier of the membrane lipid bilayer have been shown to be plagued by a host of insurmountable problems, and such models are therefore inadequate, as are other purely electroneutral mechanisms. The dynamically electrogenic but overall electroneutral mode of ion transport postulated by Nath's torsional mechanism of energy transduction and ATP synthesis has been quantified and shown to be consistent both with the experimental evidence and the principle of electrical neutrality. This mode of ion transport involves an ordered and sequential translocation of dicarboxylic acid monoanion (or countercation) through the aqueous access halfchannels known to be located at the a-c stator-rotor interface of the membrane-bound FO portion of ATP synthase and the creation transiently of a local electrical potential, Δψ in these access channels that can be transduced into mechanical torque and rotation by the FO motor. The energies of the ΔpH and Δψ contributed by the two ions are jointly utilized for rotation and converted finally into a store of torsional energy in the γ-subunit of F1 through a mechanoelectrochemical process by ion-protein interactions. It is concluded that the ATP synthase functions as a proton-dicarboxylic acid anion cotransporter in the processes of OX PHOS or PHOTO PHOS. Several novel mechanistic and thermodynamic insights into biological energy transduction by the ATP synthase in the FO and F1 portions have been offered based on

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the new vistas of energy coupling within the conceptual framework of Nath's torsional mechanism of ATP synthesis. These considerations make the new theory of energy coupling more complete, and take our fundamental understanding of these vital life processes a step deeper. Acknowledgements The funding and constant support of the Department of Science and Technology, India to the author's research program on the mechanism and thermodynamics of biological molecular machines by various grants for the past 25 years (1992–2016) is gratefully acknowledged. The author thanks all three reviewers for their detailed comments and constructive suggestions that have greatly helped to clarify and elaborate several physicochemical aspects in this work. References [1] E.C. Slater, Mechanism of phosphorylation in the respiratory chain, Nature 172 (1953) 975–978. [2] P. Mitchell, Coupling of phosphorylation to electron and hydrogen transfer by a chemi-osmotic type of mechanism, Nature 191 (1961) 144–148. [3] P. Mitchell, Chemiosmotic coupling in oxidative and photosynthetic phosphorylation, Biol. Rev. 41 (1966) 445–502. [4] P. Mitchell, Bioenergetic aspects of unity in biochemistry: evolution of the concept of ligand conduction in chemical, osmotic and chemiosmotic reaction mechanisms, in: G. Semenza (Ed.), Of Oxygen, Fuels and Living Matter, Part 1, John Wiley, New York 1981, pp. 30–56. [5] S. Nath, Beyond the chemiosmotic theory: analysis of key fundamental aspects of energy coupling in oxidative phosphorylation in the light of a torsional mechanism of energy transduction and ATP synthesis – invited review part 1, J. Bioenerg. Biomembr. 42 (2010) 293–300. [6] S. Nath, Beyond the chemiosmotic theory: analysis of key fundamental aspects of energy coupling in oxidative phosphorylation in the light of a torsional mechanism of energy transduction and ATP synthesis – invited review part 2, J. Bioenerg. Biomembr. 42 (2010) 301–309. [7] S. Nath, J. Villadsen, Oxidative phosphorylation revisited, Biotechnol. Bioeng. 112 (2015) 429–437. [8] E.C. Slater, The mechanism of the conservation of energy of biological oxidations, Eur. J. Biochem. 166 (1987) 489–504. [9] R.J.P. Williams, Some unrealistic assumptions in the theory of chemi-osmosis and their consequences, FEBS Lett. 102 (1979) 126–132. [10] B. Reynafarje, A. Alexandre, P. Davies, A.L. Lehninger, Proton translocation stoichiometry of cytochrome oxidase: Use of a fast-responding oxygen electrode, Proc. Natl. Acad. Sci. U. S. A. 79 (1982) 7218–7222. [11] G. Weber, Energetics of ligand binding to proteins, Adv. Protein Chem. 29 (1975) 1–83. [12] D.E. Green, A critique of the chemosmotic model of energy coupling, Proc. Natl. Acad. Sci. U. S. A. 78 (1981) 2240–2243. [13] J. Prebble, Peter Mitchell and the ox phos wars, Trends Biochem. Sci. 27 (2002) 209–212. [14] S. Nath, A thermodynamic principle for the coupled bioenergetic processes of ATP synthesis, Pure Appl. Chem. 70 (1998) 639–644. [15] H. Rohatgi, A. Saha, S. Nath, Mechanism of ATP synthesis by protonmotive force. Curr. Sci. 1998, 75, 716-718. Erratum, Curr. Sci. 78 (2000) 201. [16] S. Nath, H. Rohatgi, A. Saha, The torsional mechanism of energy transfer in ATP synthase, Curr. Sci. 77 (1999) 167–169. [17] S. Nath, The molecular mechanism of ATP synthesis by F1F0-ATP synthase: a scrutiny of the major possibilities, Adv. Biochem. Eng. Biotechnol. 74 (2002) 65–98. [18] S. Nath, The torsional mechanism of energy transduction and ATP synthesis as a breakthrough in our understanding of the mechanistic, kinetic and thermodynamic details, Thermochim. Acta 422 (2004) 5–17. [19] S. Nath, A novel systems biology/engineering approach solves fundamental molecular mechanistic problems in bioenergetics and motility, Process Biochem. 41 (2006) 2218–2235. [20] S. Nath, The new unified theory of ATP synthesis/hydrolysis and muscle contraction, its manifold fundamental consequences and mechanistic implications and its applications in health and disease, Int. J. Mol. Sci. 9 (2008) 1784–1840. [21] S. Nath, The thermodynamic efficiency of ATP synthesis in oxidative phosphorylation, Biophys. Chem. 219 (2016) 69–74. [22] S. Jain, R. Murugavel, L.D. Hansen, ATP synthase and the torsional mechanism: resolving a 50-year-old mystery, Curr. Sci. 87 (2004) 16–19. [23] J. Villadsen, J. Nielsen, G. Lidén, Bioreaction Engineering Principles, third ed. New York, Springer, 2011 136–145. [24] C. Channakeshava, New paradigm for ATP synthesis and consumption, J. Biosci. 36 (2011) 3–4.

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