Torque-coupled thermodynamic model for FoF1 -ATPase

Abstract

F o F 1 -ATPase is a motor protein complex that utilizes transmembrane ion flow to drive the synthesis of adenosine triphosphate (ATP) from adenosine diphosphate (ADP) and phosphate (Pi). While many theoretical models have been proposed to account for its rotary activity, most of them focus on the F o or F 1 portions separately rather than the complex as a whole. Here, we propose a simple but new torque-coupled thermodynamic model of F o F 1 -ATPase. Solving this model at steady state, we find that the monotonic variation of each portion's efficiency becomes much more robust over a wide range of parameters when the F o and F 1 portions are coupled together, as compared to cases when they are considered separately. Furthermore, the coupled model predicts the dependence of each portion's kinetic behavior on the parameters of the other. Specifically, the power and efficiency of the F 1 portion are quite sensitive to the proton gradient across the membrane, while those of the F o portion as well as the related Michaelis constants for proton concentrations respond insensitively to concentration changes in the reactants of ATP synthesis. The physiological proton gradient across the membrane in the F o portion is also shown to be optimal for the Michaelis constants of ADP and phosphate in the F 1 portion during ATP synthesis. Together, our coupled model is able to predict key dynamic and thermodynamic features of the F o F 1 -ATPase in vivo semiquantitatively, and suggests that such coupling approach could be further applied to other biophysical systems.

Activated barrier crossing dynamics of a Janus particle carrying cargo

“…Thanks to selfpropulsion, Janus particles can diffuse orders of magnitude faster than a normal Brownian particles of the same size (e.g., a silica sphere of radius 2.13 mm, half-coated with 20 nm thick gold caps, diffuses 7.84 µm 2 per second when the particle is exposed to a laser pulse of intensity 161 nW per micro meter square , where as a silica sphere of the same size (without gold coating) has diffusivity of 0.03 µm 2 per second [10]). Transport properties of Janus particles are unusual as well as very interesting, e.g., they can exhibit autonomous motion when they encounter potential (due to interaction with substrate) or confinement of asymmetric and periodic nature [15][16][17][18], in some special non-equilibrium situations JPs can move opposite to the driving force [25], JPs can transiently drift towards the high fuel density or intense light [26][27][28][29]. All these features fascinate researchers to learn more precisely about motion of the particle so that they can be used in targeted drug delivery and other purposes in medical sciences.…”

Energy and information flows in autonomous systems

“…Increasingly, researchers are modeling molecular machines as multi-component systems with internal flows of energy and information. Examples are the molecular motor F o −F 1 ATP synthase [66,160,161] that can be modeled using two strongly coupled subsystems [54, [162][163][164][165][166], or molecular motor-cargo collective systems where sometimes hundreds of motors (such as kinesin, dynein [167], and myosin [168]) work in concert [68,69], leading to different performance trade-offs [169][170][171][172][173][174].…”

Nonequilibrium Energy Transduction in Stochastic Strongly Coupled Rotary Motors

“…A common assumption in modeling F o F 1 -ATP synthase-and more generally in modeling molecular machines-is tight coupling, where two coordinates are perfectly correlated, moving in lockstep. In F o F 1 -ATP synthase this typically means tight mechanical coupling between the F o and F 1 subsystems, 13 tight mechanochemical coupling between F o and the proton current, and tight mechanochemical coupling between F 1 and ATP synthesis and hydrolysis. Tight coupling is not always mentioned explicitly, but instead a fixed stoichiometry between the number of protons translocated and each ATP synthesis/hydrolysis event is assumed.…”