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Home » Biology Articles » Biophysics » Medical Biophysics » 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 » Fundamental Consequences of the Torsional Mechanism, the Rotation-Uncoiling-Tilt EnergyStorage Mechanism, and the Unified Theory for Molecular Mechanisms of ATPSynthesis/Hydrolysis and Muscle Contraction


As discussed in Sections 2.1, 2.3, 2.4.2 and 3.2.2, previous mechanisms of ATP synthesis and muscle contraction have not felt the necessity to include definite aspects of energy storage within the enzyme molecule, which is of central importance in the torsional mechanism of energy transduction and ATP synthesis, the rotation-uncoiling-tilt energy storage mechanism of muscle contraction, and the unified theory. This has fundamental consequences [10] because previous mechanisms can be shown to violate the first and second laws of thermodynamics.

4.1. Violations of the First Law of Thermodynamics by Previous Mechanisms of ATP Synthesis and Muscle Contraction

In the binding change mechanism of ATP synthesis, the γ-subunit rotates freely (“spins like a top” in one of the descriptions). However, it is not possible to transduce the rotational kinetic energy of the spinning shaft into the stored internal energy/potential energy of ATP, as discussed in Section 2.3. In fact, as the shaft slows down (as it must, every 120o, since the rotation is in discrete steps), the rotational kinetic energy will be thermalized and dissipated as heat, and not converted to useful work or transduced to another form of stored energy. We are then left with binding energy alone as the sole source of useful external work. But calculation based on experimental nucleotide binding affinity values (Section 3.1.1) and use of the expression ΔG = RT ln (Kd2 / Kd1) shows clearly that the binding free energy difference between loose and tight catalytic sites in the F1 portion of ATP synthase is only ~7-10 kJ/mol and is thus grossly insufficient to account for the required stabilization of ~55 kJ/mol postulated in the previous mechanism, or, for that matter, of even the standard state value of ~35-36 kJ/mol in the synthesis mode. Further, additional energy is required to weaken subunit-catalytic site (e.g. ε-β) interactions, and to bind inorganic phosphate to the F1 catalytic site in the complete enzymatic cycle. Thus, the binding energy of MgADP/MgATP to the catalytic sites is grossly insufficient to make ATP and unless another source of energy is added, the overall energy balance is not satisfied, and therefore the first law of thermodynamics is violated. This violation of the law is removed if internal energy, specifically as torsional energy stored in the γ-subunit of F1FO-ATP synthase as in the torsional mechanism, is added to the MgADP binding energy. However, it will not be sufficient for previous mechanisms to add an energy source in a vague way to satisfy the first law of thermodynamics (e.g. “protonmotive force,” which has already been used for free rotation of γ); moreover, to be complete theories, it will be necessary to specify how the energy from a particular energy source is transduced, how and where it is accumulated and stored, what is the mode of transmission of that stored energy to the catalytic sites, how that energy is utilized, and above all, what is the mechanism by which all these events occur? These are basically the very details that have been addressed within the grand framework of the torsional mechanism of energy transduction and ATP synthesis. Thus, previous theories have not synthesized ATP but have only made ADP/ADP + Pi, but since these claim to have made ATP, they could only have done so by violating the first law of thermodynamics.

The above paragraph implies the binding change mechanism of ATP synthesis constitutes a perpetual motion machine of the first kind. It should be clearly recognized that these are fundamental difficulties with the concepts of previous theories of the ATP mechanism, and are not related to the way in which the ATP synthase enzyme actually works. We should clearly distinguish between these two. In any case, the previous mechanisms are incomplete, have not been cast in molecular terms, are not sufficiently detailed to permit a proper evaluation, and the process of energy transduction in these mechanisms remains a black box. In contrast, the new paradigms of the torsional mechanism and the unified theory open this black box of energy transduction and convert it into a white box, and, without exception, none of these inconsistencies and violations of the universal laws of nature arise [10].

Similar difficulties arise with previous models of muscle contraction, such as the lever arm model. If the energy quanta released at various steps of the ATP cycle are not conserved and stored in the myosin molecule, then the energy whose release would have produced the contractile force and lifted a load a certain distance will be dissipated, and will be unavailable for performing useful external work. Yet, in these models, muscle is supposed to have contracted, lifted a load a certain distance, and done useful work, even though the energy of ATP has been wasted and was not available for performance of that work, in violation of the first law of thermodynamics.

4.2. Violations of the Second Law of Thermodynamics by Previous Mechanisms of ATP Synthesis and Muscle Contraction

Fundamentally, as analyzed in Section 4.1, if the energy of the ion gradients or that of ATP binding and hydrolysis is not conserved and stored within the enzyme, then that energy must be dissipated as heat and was not used to perform useful mechanical work. We are then left with thermal energy only as the source of the useful work. Thus, all previous mechanisms of ATP synthesis and muscle contraction (other than Nath’s mechanisms) imply that the electrochemical gradients of ions or the energy of ATP is first converted into thermal motions, and only subsequently is it used to carry out useful work [10]. This would violate the second law of thermodynamics since all known biological machines are isothermal. This violation of the second law occurs because it would mean that useful work has been done cyclically using heat energy under isothermal conditions. This is forbidden by the second law of thermodynamics because, according to the law, heat cannot be an energy source unless it flows between a source and a sink at different temperatures. To date, nobody has conceived of thermal gradients in such a small system (a nanomachine enzyme construction), because such gradients, even if they could be produced in the first place, would even out extremely fast, and moreover, it is very difficult to conceive how such thermal gradients in such a small system could ever be directed to the right places/contacts/interaction points to perform useful work, because fundamentally, at the molecular level, heat energy and Brownian motion are random in character. In any case, we aver that biological energy-transducing machines are not heat engines. The above fundamental difficulties do not arise in Nath’s mechanisms because there the intermediates are electrostatic/mechanical, and not thermal, and sufficient torsional energy (~54 kJ/mol in the entire process) is stored in γ-subunit, energetically competent to make the ATP, or sufficient free energy (~36 kJ/mol) is stored in an uncoiled high-energy state of the S-2 coiled coil in myosin, energetically competent to cause a powerstroke by each head of a double-headed molecule of muscle myosin on actin.

We now see that for a single molecule, it is impossible, according to the second law, to convert energy that has spread over the thermal (rotational, vibrational and translational) degrees of freedom and equilibrated with the surroundings and reached a Boltzmann distribution very fast (in a time t < τ) to a longer-living form of stored energy in a molecular device that lasts or stays stored in the device for a time t > τ. What is thus forbidden by the second law of thermodynamics for single molecules is to take a form of stored energy, allow it to spread over the thermal degrees of freedom, and then try to transduce this thermalized energy, Q, under isothermal conditions, to another form of stored energy, i.e., to an energy that remains stored and lasts longer than the time of thermal exchange. The design principle operative in energy-transducing biological nanomachines, call it the trick of biology, is to directly transduce stored energy from one form to another, and not to allow stored energy to spread over and exchange freely with the thermal degrees of freedom of the surrounding bath or reservoir. These fundamental concepts show that biological machines and constructions of molecular dimensions do not work in the same way as heat engines, and in turn enable us to achieve a true understanding of the meaning of the second law of thermodynamics at the molecular level. It shows that it is not sufficient for a fluctuation (e.g. Brownian motion) or other perturbation to lift a microscopic or molecular load; it has to keep the load lifted (or store energy in a device) for a time t > τ, and not lose it to the surroundings as heat within that time. This is because the concepts discussed here and earlier [2, 10, 11] allowed us to make a distinction between heat and work (or stored energy) at the molecular level on the basis of timescales applicable at even a single molecule level. A suitable and concise statement of the second law of thermodynamics applicable to single molecules performing useful work under isothermal conditions then is, “Single molecules perform useful work by direct transduction of energy from one form to another, and energy once thermalized cannot be transduced into stored energy.” Previous theories and models of ATP synthesis, muscle contraction, and other related energy transductions, including the binding change mechanism of ATP synthesis and the lever arm model of muscle contraction are Maxwell’s demon machines that violate the second law of thermodynamics because, in all these models, in effect, heat is being converted to work in a cyclic isothermal process. Therefore these theories cannot be correct and need to be replaced by the new paradigm, which will lead to rapid scientific progress in this important interdisciplinary field of science.

4.3. Mechanistic H+/O, H+/ATP and P/O Ratios, Efficiency of Oxidative Phosphorylation, and the Overall Energy Balance of Cellular Bioenergetics

The important question of mechanistic H+/O, H+/ATP and P/O ratios in oxidative phosphorylation has been the subject of extensive studies for 65 years [1]. To address this aspect, let us consider the dynamically electrogenic but overall electroneutral ion transport proposed within the torsional mechanism of energy transduction and ATP synthesis [1, 2, 13] for the complete process of oxidative phosphorylation in vivo in mitochondria. ATP synthesis is regulated by its demand for various cellular processes; when ATP4- is required, it is transported out from the mitochondrial matrix to the cytoplasm along its concentration gradient. The local electrical potential thus created drives ADP3- along its concentration gradient to the mitochondrial matrix in exchange for ATP4- by the adenine nucleotide transporter (ANT) [1]. The resulting unbalanced local potential is the signal that causes HPO4 2- to move into the matrix along its concentration gradient, and the OH- produced during ATP synthesis in the F1 portion of ATP synthase [1, 17] is driven out of the mitochondria in exchange for the HPO4 2- by the Pi/OH- antiporter. The OH- released per ATP produced is neutralized by a proton from the external medium, forming water. Thus, we need ten protons (and not twelve protons as taken earlier [2]) to synthesize three molecules of ATP as clearly seen from the structure of the F1-c10 complex from yeast mitochondrial F1FO-ATP synthase [46], i.e., on the average, 3.33 protons to synthesize one molecule of ATP (see Section 2.4.1) and one proton to neutralize the released OH-, i.e. 4.33 H+/ATP in vitro. However, in the in vivo demand process utilizing the ATP transported out of the mitochondrion, the reverse process operates, i.e. the ATP consumes an OH- and is cleaved into ADP and Pi. Thus a proton is given back to the external medium (balancing the proton used for neutralization of the OH- in the external medium), and therefore in the overall oxidative phosphorylation process in vivo, a mean of 3.33 protons is needed to synthesize one molecule of ATP, i.e. H+/ATP = 3.33, assuming the same c10 ring stoichiometry in mammalian ATP synthase as in the ATP synthase from S. cerevisiae mitochondria [46]. This then is the value of the mechanistic stoichiometry in vivo on the ATPase side. On the redox side, as per the consensus stoichiometry that has evolved after considerable systematic experimental investigation of mechanistic P/O ratios in mitochondrial oxidative phosphorylation [47], ten protons are pumped out by the redox complexes per 2 electrons with NADH-related substrates such as 3-hydroxybutyrate, and six protons are transported from the matrix to the inner membrane against the concentration gradient per 2 electrons with succinate as substrate. Thus the mechanistic H+/O stoichiometry in vivo is 10 with NADH-related substrates that use site 1, site 2 and site 3 on the redox side, and 6 with succinate that employs only site 2 and site 3. This implies that the mechanistic P/O ratio equals 10/3.33 (= 3.0) and 6/3.33 (= 1.8) for NADH-related substrates and succinate respectively for the overall oxidative phosphorylation process in vivo. This P/O ratio corresponds to the physiological steady-state mode of operation. The above analysis also carries the important biological implication that the ANT, the Pi/OH- antiporter and the F1FO-ATP synthase lie physically close to each other, or in other words form a supercomplex (an ATP synthasome) such that the local potential created by one complex (e.g. ANT) can be sensed by the other complex (e.g. the Pi/OHantiporter) and the OH- produced due to the operation of the ATP synthase is immediately funnelled out by the Pi/OH- antiporter in exchange for the HPO4 2-. This has always been an important prediction inherent in the torsional mechanism [1, 13]. Recently, Pedersen and colleagues have isolated and characterized the mitochondrial ATP synthasome, a 1:1:1 supercomplex of ANT, Pi/OH- and F1FO located near one another in an oblong membrane basepiece, and have provided its first low-resolution (2.3 nm) EM/immuno EM structural model [48]. This important finding of co-localization contradicts the classical view that regards these components as separate entities in the energy-transducing membrane and it is significant that only the torsional mechanism of energy transduction and ATP synthesis is in accord with the new data on membrane association of these entities to form the ATP synthasome supercomplex.

The above has important implications for previous theories of energy coupling, such as the chemiosmotic theory. In chemiosmosis, for each pair of electrons transferred in mitochondrial respiration, up to a maximum of six protons may be produced (H+/O = 6) and the number of H+ ions transported per O consumed cannot exceed the number of hydrogen carriers present in the respiratory chain. Thus, the number of H+ transported per O atom (= 6) includes two transported over NAD, two over flavins and two over quinones and two protons are required for each mole of ATP synthesized from ADP and Pi (H+/ATP = 2). Several experiments, the energy balance in the torsional mechanism, as well as a nonequilibrium thermodynamic analysis [2, 20, 24, 25] show that these stoichiometries need to be approximately doubled to account for the coupling protons [H+/O = 10, H+/ATP = 3.33]. These numbers have important thermodynamic consequences because the smaller values of the stoichiometries in chemiosmosis require a larger so-called protonmotive force (in this case by a factor of ~1.5-2) to make the free energy change energetically competent for ATP synthesis. This poses a formidable problem of energy shortfall for the chemiosmotic theory. The moment experimental evidence and basic nonequilibrium thermodynamic computation that the active proton transport machinery on the redox side must be an ion pump that works with higher stoichiometries than that postulated in chemiosmosis is accepted, the chemiosmotic mechanism of redox loop transport along the respiratory chain breaks down, because there are simply not enough hydrogen carriers to transport 10 protons per oxygen atom. Basically, chemiosmosis does not provide a mechanism to obtain the balance of (10 - 6), i.e. 4 protons per O atom. Obtaining these extra protons for coupling presents another insurmountable problem for the chemiosmotic theory. With this background, it is now possible to historically understand why Mitchell refused to accept the higher values of H+/O and H+/ATP ratios than the ones he had postulated in his theory, even in the face of the most incontrovertible experimental evidence, as documented by Prebble [49]. These stoichiometries were central and fundamental to chemiosmosis, and acceptance of the higher numbers would have created a severe energy crisis for the chemiosmotic theory and sounded the death-knell for it. Workers in the field accepted the new, higher stoichiometries obtained repeatedly by experiment, but did not ask the chemiosmotic theory to account for these higher stoichiometries and failed to take cognisance that the theory contradicted the experimental facts, despite the herculean efforts of Slater [50], Lehninger [51], Williams [52], Green [53] and other stalwart workers, probably because no alternative theory of the scope of the chemiosmotic theory was available at that time. Hence the old theory and the new experimental facts have co-existed uneasily, but the old theory cannot explain the new facts; therefore it is absolutely necessary to go beyond chemiosmosis, if we have to solve the fundamental discrepancies that exist between theory and experiment.

Any mechanism should finally also be able to withstand the ultimate challenge of satisfying the overall, macroscopic energy balance of cellular metabolism (keeping the constraints imposed by the oxidative phosphorylation process intact). Thus, we should investigate whether the overall energy balance for the complete oxidation of glucose and the cytoplasmic ATP yield in the cell is satisfied from the sides of energy supply and energy production [54]. For a basis of 1 mole of glucose, the energy available from the supply side for ATP synthesis is 672 kcal/(mol glucose). On the user side 38 ATP molecules are produced per mole of glucose. The efficiency of the oxidative phosphorylation machinery on the redox side, ηredox, is the product of the mechanistic P/O ratio and the ratio of the affinity of phosphorylation and the affinity of oxidation (AP/AO), in accordance with the principles of nonequilibrium thermodynamics when the degree of coupling, q → 1 [20, 55, 56]. Taking the consensus experimental values of the mechanistic P/O ratio as 3.0 [2, 46, 47], as discussed in this section, and the experimentally obtained operating (AP/AO) affinity ratio in mitochondria in state 3 as – 0.26 [20, 57], we obtain the efficiency on the redox side, ηredox as 0.78. This value can also be derived theoretically from the torsional mechanism. The value of the affinity of oxidation, AO for the respiratory chain in mitochondria is 2280 meV per two electrons, or 220 kJ/mol. The value of the affinity of phosphorylation, AP, according to the torsional mechanism is the 54 kJ/mol of stored energy in the entire process plus losses, especially due to untwisting of an α-helix in the inlet half-access channel of FO upon its protonation (see Section 5.4 also), and the entry of the untwisted helix carrying the bound proton into the membrane, which was a required conformational change for rotation of the c-rotor [1, 12]. This is estimated to be approximately one-ninth of the energy donated by ion translocation in the inlet half-access channel for a c-ring with ten c-subunits, and since there is no corresponding loss in the exit half-access channel, it is approximately 1/18 of 54 kJ/mol or ~3 kJ/mol. Hence the value of AP is estimated from the torsional mechanism to measure 54 + 3 = 57 kJ/mol. Therefore, the estimated value of ηredox from the torsional mechanism is 3.0 × (57/220) = 0.777 (77.7%).

Now we are in a position to perform the overall energy balance of cellular bioenergetics. For a basis of 1 mol glucose, we have an energy production of 57 kJ/mol per ATP × 38 ATP per mol glucose = 2166 kJ/mol glucose. On the supply side, the energy available is 672 kcal × 4.18 kJ/kcal × 0.777 = 2182.5 kJ/mol glucose, which is exactly adequate, because making the next integral number of ATP molecules (39) would have required 2223 kJ/mol, which is more than the energy available from the supply side. Thus the overall balance of cellular bioenergetics is perfectly satisfied. The torsional mechanism can be employed to go further in that it can offer us an excellent estimate of the efficiency on the ATP side, ηATP. Since the value of AP of 57 kJ/mol includes the energy required to torsionally strain a bond so that MgADP can bind, the energy required to bind Pi, the energy required to make the ATP plus the small irreversible loss in the cycle, the efficiency of ATP synthesis is 36/57 or 0.632 (63.2%). This value of ηATP is also in agreement with the experimentally measured efficiency of lightdriven production of ATP catalyzed by F1FO-ATP synthase in a liposome-based artificial photosynthetic membrane [58]. Thus the overall efficiency of oxidative phosphorylation in mitochondria (from donation of energy by the redox processes to the energy finally stored in ATP), ηoverall is the product of ηredox and ηATP, or 0.777 × 0.632 = 0.491, i.e. 49.1%. All the various aspects discussed in this and previous sections of the paper serve to give us complete confidence in the correctness of the mechanistic, thermodynamic and kinetic proposals within the framework of torsional mechanism of energy transduction and ATP synthesis/hydrolysis and the unified theory

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