Torsional elasticity and energetics of F
            <sub>1</sub>
            -ATPase

Czub, Jacek; Grubmüller, Helmut

doi:10.1073/pnas.1018686108

Cited by 50 publications

(78 citation statements)

References 39 publications

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“…This figure was originally presented in (Mukherjee & Warshel, 2011). problem far beyond anything that has been obtained so far from other studies of the system, and can provide consistent insight into the events occurring in the F 1 -ATPase system. Now several works have proposed a steric mechanism (Koga & Takada, 2006 ;Pu & Karplus, 2008), or a somewhat related elastic spring model (Czub & Grubmueller, 2011), and asserted that such a mechanism emerged from their calculations. However, these works forced the system to move in the desired direction (by applying very large forces) rather than allowing the system to be driven by the chemical potential or by the proper external torque.…”

Section: The Coupling Between the Subunitsmentioning

confidence: 99%

“…Moreover, these models cannot predict the observed unidirectionality but just impose it. The use of a microscopic model (Czub & Grubmueller, 2011), which only applied torque on the c-subunits, has provided instructive information on the response of the other subunits to the c-motion, but again this was done by use of a very large force.…”

Section: The Coupling Between the Subunitsmentioning

confidence: 99%

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Why nature really chose phosphate

Kamerlin

Sharma

Prasad

et al. 2013

Quart. Rev. Biophys.

340

448

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Phosphoryl transfer plays key roles in signaling, energy transduction, protein synthesis, and maintaining the integrity of the genetic material. On the surface, it would appear to be a simple nucleophile displacement reaction. However, this simplicity is deceptive, as, even in aqueous solution, the low-lying d-orbitals on the phosphorus atom allow for eight distinct mechanistic possibilities, before even introducing the complexities of the enzyme catalyzed reactions. To further complicate matters, while powerful, traditional experimental techniques such as the use of linear free-energy relationships (LFER) or measuring isotope effects cannot make unique distinctions between different potential mechanisms. A quarter of a century has passed since Westheimer wrote his seminal review, ‘Why Nature Chose Phosphate’ (Science 235 (1987), 1173), and a lot has changed in the field since then. The present review revisits this biologically crucial issue, exploring both relevant enzymatic systems as well as the corresponding chemistry in aqueous solution, and demonstrating that the only way key questions in this field are likely to be resolved is through careful theoretical studies (which of course should be able to reproduce all relevant experimental data). Finally, we demonstrate that the reason that naturereallychose phosphate is due to interplay between two counteracting effects: on the one hand, phosphates are negatively charged and the resulting charge-charge repulsion with the attacking nucleophile contributes to the very high barrier for hydrolysis, making phosphate esters among the most inert compounds known. However, biology is not only about reducing the barrier to unfavorable chemical reactions. That is, the same charge-charge repulsion that makes phosphate ester hydrolysis so unfavorable also makes it possible to regulate, by exploiting the electrostatics. This means that phosphate ester hydrolysis can not only be turned on, but also be turned off, by fine tuning the electrostatic environment and the present review demonstrates numerous examples where this is the case. Without this capacity for regulation, it would be impossible to have for instance a signaling or metabolic cascade, where the action of each participant is determined by the fine-tuned activity of the previous piece in the production line. This makes phosphate esters the ideal compounds to facilitate life as we know it.

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Section: The Coupling Between the Subunitsmentioning

confidence: 99%

Section: The Coupling Between the Subunitsmentioning

confidence: 99%

Why nature really chose phosphate

Kamerlin

Sharma

Prasad

et al. 2013

Quart. Rev. Biophys.

340

448

View full text Add to dashboard Cite

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“…Is Steric Mechanism Driving the System? As stated in the Introduction, several works proposed a steric mechanism (18,20) or a somewhat related elastic spring model (19) and asserted that such mechanism emerged from their calculations. However, these works forced the system to move in the desired direction (by applying very large forces) rather than allowing the system to be driven by the chemical potential coupled by the proper external torque.…”

Section: 3mentioning

confidence: 99%

“…Recent molecular dynamics simulation aimed at understanding the effect of the γ-subunit rotation (18,19) was instructive but could not capture the relevant energy of the actual millisecond process of the complete F1-ATPase motor. Attempts to understand the rotary mechanism, using coarse-grained models (18,20), forced the rotation rather than reproduce it from structurally based energetics (see Background).…”

mentioning

confidence: 99%

Electrostatic origin of the mechanochemical rotary mechanism and the catalytic dwell of F1-ATPase

Mukherjee

Warshel

2011

Proc. Natl. Acad. Sci. U.S.A.

102

152

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Understanding the nature of energy transduction in life processes requires a quantitative description of the energetics of the conversion of ATP to ADP by ATPases. Previous attempts to do so have provided an interesting insight but could not account for the rotary mechanism by a nonphenomenological structure/energy description. In particular it has been very challenging to account for the observations of the 80°and 40°rotational substates, without any prior information about such states in the simulation procedure. Here we use a coarse-grained model of F1-ATPase and generate, without the adjustment of phenomenological parameters, a structure-based free energy landscape that reproduces the energetics of the mechanochemical process. It is found that the landscape along the relevant rotary path is determined by the electrostatic free energy and not by steric effects. Furthermore, the generated surface and the corresponding Langevin dynamics simulations identify a hidden conformational barrier that provides a new fundamental interpretation of the catalytic dwell and illuminate the nature of the energy conversion process.bioenergetics | chemical-conformational coupling | molecular motors | coarse grain model U nderstanding the energetics of the biological conversion of ATP to ADP is crucial for elucidating the nature of energy transduction in life processes and also for practical understanding of the action of molecular motors (1, 2). At present it seems that the detailed nature of this biological energy conversion process has remained a major puzzle (1-7). For example, despite the fact that the structures of several ATPases have been elucidated (e.g., refs. 4 and 8) and recent advances in detailed elucidation of some key steps have been made (9-11), it is not completely clear at what stage in the reaction energy is actually released and, in turn, what is the nature of the energy conversion process. Some workers have suggested that the major source of the energy release is the conversion of the free energy of ATP binding into elastic strain, which is subsequently released by a coordinated and tightly coupled conformational mechanism (6). It was also postulated that the energy conversion involves an inertial energy release (12), whereas our works (13, 14) have suggested that the energetics is associated with the electrostatic work, and the origin of the free energy change involves a significant contribution from the charge separation in solution outside the ATPase active sites. Furthermore, biochemical and structural studies have provided a molecular model for the action of ATPases (1-4), and remarkable phenomenological analyses (6, 7) indicated what are the conditions for effective action. However, we still do not have a clear structure function correlation that involves both the chemistry and the conformational coupling. The challenge became even more exciting in view of the remarkable progress in single-molecule studies that directly visualized the γ-subunit rotation in a unidirectional way, while revealing several...

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“…Previous modeling studies of the F-ATPase have addressed structural and mechanistic questions about the rotary mechanism (e.g., refs. [11][12][13][14][15][16][17][18][19][20], but not the metaissue of the mechanism itself compared with alternatives.…”

mentioning

confidence: 99%

Biophysical comparison of ATP synthesis mechanisms shows a kinetic advantage for the rotary process

Anandakrishnan

Zhang

Donovan-Maiye

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

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The ATP synthase (F-ATPase) is a highly complex rotary machine that synthesizes ATP, powered by a proton electrochemical gradient. Why did evolution select such an elaborate mechanism over arguably simpler alternating-access processes that can be reversed to perform ATP synthesis? We studied a systematic enumeration of alternative mechanisms, using numerical and theoretical means. When the alternative models are optimized subject to fundamental thermodynamic constraints, they fail to match the kinetic ability of the rotary mechanism over a wide range of conditions, particularly under low-energy conditions. We used a physically interpretable, closed-form solution for the steady-state rate for an arbitrary chemical cycle, which clarifies kinetic effects of complex free-energy landscapes. Our analysis also yields insights into the debated "kinetic equivalence" of ATP synthesis driven by transmembrane pH and potential difference. Overall, our study suggests that the complexity of the F-ATPase may have resulted from positive selection for its kinetic advantage.ATP synthase | kinetic mechanism | free-energy landscape | nonequilibrium steady state | evolution T he F-ATPase performs molecular-level free-energy (FE) transduction to phosphorylate ADP and yield ATP, the primary energy carrier that drives a vast range of cellular processes. It spurred Mitchell's chemiosmotic hypothesis (1) and Boyer's now-validated proposal for the binding-change mechanism (2) in which a proton electrochemical gradient is transduced to rotationbased mechanical energy and then back to chemical FE as ADP is phosphorylated. The F-ATPase's two-domain uniaxial rotary structure is conserved across all three domains of life (3-6), and details of its function have been the subject of a multitude of studies (e.g., refs. 7-30).Here, we address a relatively narrow question with potentially significant evolutionary implications: Why is ATP synthesized by a rotary mechanism instead of a potentially much simpler alternating-access mechanism (Fig. 1)? Using thermodynamic and kinetic constraints, we address the question of whether evolution tends to arrive at optimal molecular processes (31), building on established concepts of optimality-derived evolutionary convergence (32, 33). Presumably, performance advantages in the central task of ATP synthesis would be under significant evolutionary pressure. Previous modeling studies of the F-ATPase have addressed structural and mechanistic questions about the rotary mechanism (e.g., refs. 11-20), but not the metaissue of the mechanism itself compared with alternatives.To assess whether the rotary mechanism possesses any intrinsic performance advantage, we constructed a series of kinetic models abstracted from known mechanisms (Fig. 1). Beyond the rotarybased model, we considered a series of alternating-access analogs (Fig. 2), building on the demonstrated capacity for ATP-hydrolyzing transporters to be driven in reverse to synthesize ATP (34, 35). The discrete-state models do not include structural details, bu...

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Torsional elasticity and energetics of F ₁ -ATPase

Cited by 50 publications

References 39 publications

Why nature really chose phosphate

Why nature really chose phosphate

Electrostatic origin of the mechanochemical rotary mechanism and the catalytic dwell of F1-ATPase

Biophysical comparison of ATP synthesis mechanisms shows a kinetic advantage for the rotary process

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Torsional elasticity and energetics of F 1 -ATPase

Cited by 50 publications

References 39 publications

Why nature really chose phosphate

Why nature really chose phosphate

Electrostatic origin of the mechanochemical rotary mechanism and the catalytic dwell of F1-ATPase

Biophysical comparison of ATP synthesis mechanisms shows a kinetic advantage for the rotary process

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Torsional elasticity and energetics of F ₁ -ATPase