PROTEIN MOTOR F1 AS A MODEL SYSTEM FOR FLUCTUATION THEORIES OF NON-EQUILIBRIUM STATISTICAL MECHANICS

2012 ◽  
Vol 11 (03) ◽  
pp. 1241001 ◽  
Author(s):  
KUMIKO HAYASHI ◽  
RYUNOSUKE HAYASHI
Keyword(s):  
Statistical Mechanics ◽  
Single Molecule ◽  
Nonequilibrium Statistical Mechanics ◽  
Model System ◽  
Fluctuation Theorem ◽  
Biological Model ◽  
Equilibrium Statistical Mechanics ◽  
Γ Subunit ◽  
Protein Motor ◽  
Rotary Motor

F1-ATPase (F1) is a rotary motor protein in which the rotor γ subunit rotates in the α3β3 ring hydrolyzing adenosine-5′-triphosphate (ATP). Several fluctuation theories of nonequilibrium statistical mechanics have been applied recently to the single-molecule experiments on F1. For example, the fluctuation theorem, a recent achievement in the field of nonequilibrium statistical mechanics, has been suggested to be useful for measuring the rotary torque of F1. In this paper, we introduce F1 as a good biological model for experimentally testing the theories of nonequilibrium statistical mechanics.

scholarly journals Elasticity, friction, and pathway of γ-subunit rotation in FoF1-ATP synthase

2015 ◽  
Vol 112 (34) ◽  
pp. 10720-10725 ◽  
Author(s):  
Kei-ichi Okazaki ◽  
Gerhard Hummer
Keyword(s):  
Atp Synthase ◽  
Single Molecule ◽  
Viscoelastic Model ◽  
Thermodynamic Efficiency ◽  
Γ Subunit ◽  
Frictional Dissipation ◽  
Rotary Motors ◽  
Subunit Rotation ◽  
Dynamics Simulations ◽  
Rotary Motor

We combine molecular simulations and mechanical modeling to explore the mechanism of energy conversion in the coupled rotary motors of FoF1-ATP synthase. A torsional viscoelastic model with frictional dissipation quantitatively reproduces the dynamics and energetics seen in atomistic molecular dynamics simulations of torque-driven γ-subunit rotation in the F1-ATPase rotary motor. The torsional elastic coefficients determined from the simulations agree with results from independent single-molecule experiments probing different segments of the γ-subunit, which resolves a long-lasting controversy. At steady rotational speeds of ∼1 kHz corresponding to experimental turnover, the calculated frictional dissipation of less than kBT per rotation is consistent with the high thermodynamic efficiency of the fully reversible motor. Without load, the maximum rotational speed during transitions between dwells is reached at ∼1 MHz. Energetic constraints dictate a unique pathway for the coupled rotations of the Fo and F1 rotary motors in ATP synthase, and explain the need for the finer stepping of the F1 motor in the mammalian system, as seen in recent experiments. Compensating for incommensurate eightfold and threefold rotational symmetries in Fo and F1, respectively, a significant fraction of the external mechanical work is transiently stored as elastic energy in the γ-subunit. The general framework developed here should be applicable to other molecular machines.

scholarly journals High-resolution single-molecule characterization of the enzymatic states in Escherichia coli F 1 -ATPase

2013 ◽  
Vol 368 (1611) ◽  
pp. 20120023 ◽  
Author(s):  
Thomas Bilyard ◽  
Mayumi Nakanishi-Matsui ◽  
Bradley C. Steel ◽  
Teuta Pilizota ◽  
Ashley L. Nord ◽  
...  
Keyword(s):  
Escherichia Coli ◽  
Single Molecule ◽  
Room Temperature ◽  
Atp Hydrolysis ◽  
Chemical Processes ◽  
Atp Binding ◽  
Γ Subunit ◽  
Rotary Motor ◽  
Resolution Single

The rotary motor F 1 -ATPase from the thermophilic Bacillus PS3 (TF 1 ) is one of the best-studied of all molecular machines. F 1 -ATPase is the part of the enzyme F 1 F O -ATP synthase that is responsible for generating most of the ATP in living cells. Single-molecule experiments have provided a detailed understanding of how ATP hydrolysis and synthesis are coupled to internal rotation within the motor. In this work, we present evidence that mesophilic F 1 -ATPase from Escherichia coli (EF 1 ) is governed by the same mechanism as TF 1 under laboratory conditions. Using optical microscopy to measure rotation of a variety of marker particles attached to the γ-subunit of single surface-bound EF 1 molecules, we characterized the ATP-binding, catalytic and inhibited states of EF 1 . We also show that the ATP-binding and catalytic states are separated by 35±3°. At room temperature, chemical processes occur faster in EF 1 than in TF 1 , and we present a methodology to compensate for artefacts that occur when the enzymatic rates are comparable to the experimental temporal resolution. Furthermore, we show that the molecule-to-molecule variation observed at high ATP concentration in our single-molecule assays can be accounted for by variation in the orientation of the rotating markers.

scholarly journals Long-term behavior of Hertzian chains between fixed walls is really equilibrium

2017 ◽  
Vol 31 (10) ◽  
pp. 1742011 ◽  
Author(s):  
Michelle Przedborski ◽  
Surajit Sen ◽  
Thad A. Harroun
Keyword(s):  
Heat Capacity ◽  
Statistical Mechanics ◽  
Thermal Equilibrium ◽  
Nonequilibrium Statistical Mechanics ◽  
Quasi Equilibrium ◽  
Equilibrium Statistical Mechanics ◽  
Hertz Potential ◽  
Long Term Behavior ◽  
Opening Up

We examine the long-term behavior of nonintegrable, energy-conserved, 1D systems of macroscopic grains interacting via a contact-only generalized Hertz potential and held between stationary walls. Existing dynamical studies showed the absence of energy equipartitioning in such systems, hence their long-term dynamics was described as quasi-equilibrium. Here, we show that these systems do in fact reach thermal equilibrium at sufficiently long times, as indicated by the calculated heat capacity. This phase is described by equilibrium statistical mechanics, opening up the possibility that the machinery of nonequilibrium statistical mechanics may be used to understand the behavior of these systems away from equilibrium.

Sign in / Sign up

Export Citation Format

Share Document