Efficiency Of Free Energy Transduction Research Articles

Mechanism of a high free-energy transduction efficiency of Bacillus PS3 F1-ATPase from the perspective of solvent entropy

Bacillus PS3 F1-ATPase is a rotary molecular motor with a 100% free-energy transduction efficiency (The 100% efficiency means that the free-energy change upon hydrolysis of adenosine triphosphate (ATP) is almost completely consumed by the external dissipation arising from the rotation of the central stalk (γ subunit) of F1-ATPase.). In this work, to elucidate the mechanism of 100% free-energy transduction efficiency, the rotation of Bacillus PS3 F1-ATPase was investigated from the perspective of solvent entropy. The two F1-ATPase structures of the catalytic- and binding-dwell states recently published were used to compute the solvation entropy (The γ subunit of the F1-ATPase structure at the binding-dwell state is rotated by 44° relative to the structure of the catalytic-dwell state). To compute the solvation entropy, the integral equation theory was used. It was found that the change in the solvent entropy of the F1-ATPase upon 44° rotation of the γ subunit is approximately zero, which is surprising because a large structural change occurs in F1-ATPase upon rotation. The present result indicated the compensation of solvent entropy in the F1-ATPase. The compensation behavior was discussed by decomposing the solvent entropy of F1-ATPase into the components of the solvent entropy of subunits and that at the interfaces between the adjacent subunits. We also discussed that the system energy and conformational entropy would also remain unchanged upon the 44° rotation of the γ subunit. Based on the results and discussion, the following rotation mechanism was proposed: the free energy of Bacillus PS3 F1-ATPase is unchanged upon rotation; and the ATP binding, hydrolysis of ATP, and release of products lead to the rotation. This mechanism is consistent with the 100% free-energy transduction efficiency of F1-ATPase.

Optimal Control of the F1-ATPase Molecular Motor

F1-ATPase is a rotary molecular motor that in vivo is subject to strong nonequilibrium driving forces. There is great interest in understanding the operational principles governing its high efficiency of free-energy transduction. Here we use a near-equilibrium framework to design a nontrivial control protocol to minimize dissipation in rotating F1 to synthesize adenosine triphosphate. We find that the designed protocol requires much less work than a naive (constant-velocity) protocol across a wide range of protocol durations. Our analysis points to a possible mechanism for energetically efficient driving of F1 in vivo and provides insight into free-energy transduction for a broader class of biomolecular and synthetic machines.

Molecular dynamics simulation of proton-transfer coupled rotations in ATP synthase FO motor

The FO motor in FOF1 ATP synthase rotates its rotor driven by the proton motive force. While earlier studies elucidated basic mechanisms therein, recent advances in high-resolution cryo-electron microscopy enabled to investigate proton-transfer coupled FO rotary dynamics at structural details. Here, taking a hybrid Monte Carlo/molecular dynamics simulation method, we studied reversible dynamics of a yeast mitochondrial FO. We obtained the 36°-stepwise rotations of FO per one proton transfer in the ATP synthesis mode and the proton pumping in the ATP hydrolysis mode. In both modes, the most prominent path alternatively sampled states with two and three deprotonated glutamates in c-ring, by which the c-ring rotates one step. The free energy transduction efficiency in the model FO motor reached ~ 90% in optimal conditions. Moreover, mutations in key glutamate and a highly conserved arginine increased proton leakage and markedly decreased the coupling, in harmony with previous experiments. This study provides a simple framework of simulations for chemical-reaction coupled molecular dynamics calling for further studies in ATP synthase and others.

Is F1-ATPase a Rotary Motor with Nearly 100% Efficiency? Quantitative Analysis of Chemomechanical Coupling and Mechanical Slip.

We present a chemomechanical network model of the rotary molecular motor F1-ATPase which quantitatively describes not only the rotary motor dynamics driven by ATP hydrolysis but also the ATP synthesis caused by forced reverse rotations. We observe a high reversibility of F1-ATPase, that is, the main cycle of ATP synthesis corresponds to the reversal of the main cycle in the hydrolysis-driven motor rotation. However, our quantitative analysis indicates that torque-induced mechanical slip without chemomechanical coupling occurs under high external torque and reduces the maximal efficiency of the free energy transduction to 40-80% below the optimal efficiency. Heat irreversibly dissipates not only through the viscous friction of the probe but also directly from the motor due to torque-induced mechanical slip. Such irreversible heat dissipation is a crucial limitation for achieving a 100% free-energy transduction efficiency with biological nanomachines because biomolecules are easily deformed by external torque.

Energy-based analysis of biomolecular pathways.

Decomposition of biomolecular reaction networks into pathways is a powerful approach to the analysis of metabolic and signalling networks. Current approaches based on analysis of the stoichiometric matrix reveal information about steady-state mass flows (reaction rates) through the network. In this work, we show how pathway analysis of biomolecular networks can be extended using an energy-based approach to provide information about energy flows through the network. This energy-based approach is developed using the engineering-inspired bond graph methodology to represent biomolecular reaction networks. The approach is introduced using glycolysis as an exemplar; and is then applied to analyse the efficiency of free energy transduction in a biomolecular cycle model of a transporter protein [sodium-glucose transport protein 1 (SGLT1)]. The overall aim of our work is to present a framework for modelling and analysis of biomolecular reactions and processes which considers energy flows and losses as well as mass transport.

Thermodynamic efficiency and mechanochemical coupling of F 1 -ATPase

F(1)-ATPase is a nanosized biological energy transducer working as part of F(o)F(1)-ATP synthase. Its rotary machinery transduces energy between chemical free energy and mechanical work and plays a central role in the cellular energy transduction by synthesizing most ATP in virtually all organisms. However, information about its energetics is limited compared to that of the reaction scheme. Actually, fundamental questions such as how efficiently F(1)-ATPase transduces free energy remain unanswered. Here, we demonstrated reversible rotations of isolated F(1)-ATPase in discrete 120° steps by precisely controlling both the external torque and the chemical potential of ATP hydrolysis as a model system of F(o)F(1)-ATP synthase. We found that the maximum work performed by F(1)-ATPase per 120° step is nearly equal to the thermodynamical maximum work that can be extracted from a single ATP hydrolysis under a broad range of conditions. Our results suggested a 100% free-energy transduction efficiency and a tight mechanochemical coupling of F(1)-ATPase.

Efficiency of Free Energy Transduction in Autonomous Systems

We consider the thermodynamics of chemical coupling from the viewpoint of free energy transduction efficiency. In contrast to an external parameter-driven stochastic energetics setup, the dynamic change of the equilibrium distribution induced by chemical coupling, adopted, for example, in biological systems, is inevitably an autonomous process. We found that the efficiency is bounded by the ratio between the non-symmetric and the symmetrized Kullback-Leibler distance, which is significantly lower than unity. Consequences of this low efficiency are demonstrated in the simple two-state case, which serves as an important minimal model for studying the energetics of biomolecules.

Energetic analysis of the growth of Methanobrevibacter arboriphilus A2 in hydrogen‐limited continuous cultures

Hydrogen-limited chemostat cultures of Methanobrevibacter arboriphilus A2 were carried out. The available electron balance and carbon balance in M. arboriphilus A2 and other methanogenic strains grown on various substrates were well satisfied. This indicates that no extracellular organic products were formed during methanogenic growth. The molar growth yields for methane (Y(X/CH(4) )) were calculated as 1.06-1.42 g cell/mol CH(4) at dilution rate (0.21-0.43 day(-1)). The smaller Y(X/CH(4) ) of M. arboriphilus A2 compared with that of the other methanogenic strains was probably owing to the low growth rate of M. arboriphilus A2. The low value of Y(X/CH(4) ) may be favorable for methane fermentation because less sludge accumulation is expected. The efficiency of free energy transduction to ATP during methane formation from H(2) + CO(2) was 12-17% at the dilution rate (0.21-0.43 day(-1)) assuming that Y(ATP) was 6.5 g/mol and the free energy change of CO(2) reduction to methane with H(2) was -62.8 kJ/mol under physiological conditions.