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F$_1$-ATPase (F$_1$) is central to cellular energy transduction. Forcibly rotated by another motor F$_\mathrm{o}$, F$_1$ catalyzes ATP synthesis by converting mechanical work into chemical free energy stored in the molecule ATP. The details…
F$_{1}$-ATPase is a rotary molecular motor that \emph{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…
F$_\mathrm{o}$F$_1$-ATP synthase is a factory for synthesizing ATP in virtually all cells. Its core machinery is the subcomplex F$_1$-motor (F$_1$-ATPase) and performs the reversible mechanochemical coupling. Isolated F$_1$-motor hydrolyzes…
F1F0 ATP synthase (ATPase) either facilitates the synthesis of ATP in the mitochondrial membranes and bacterial inner membranes in a process driven by the proton moving force (pmf), or uses the energy from ATP hydrolysis to pump protons…
We demonstrate asymmetric enzyme kinetics of a biomolecular motor F1-ATPase between synthesis and hydrolysis of adenosine triphosphate (ATP). Our experiments show that ATP hydrolysis follows Michaelis-Menten kinetics, but ATP synthesis,…
Two simple (rotator and one-particle) mechanistic models are suggested to describe simultaneously at a minimal level of sophistication two basic functions of F$_1$-ATPase: a motor regime driven by ATP hydrolysis and its inverted function as…
Molecular motors drive mechanical motions utilizing the free energy liberated from chemical reactions such as ATP hydrolysis. Although it is essential to know the efficiency of this free energy transduction, it has been a challenge due to…
Confocal time resolved single-molecule spectroscopy using pulsed laser excitation and synchronized multi channel time correlated single photon counting (TCSPC) provides detailed information about the conformational changes of a biological…
Bartussek, Hanggi and Kissner studied a rocking ratchet system, in which a Brownian particle is subject to an asymmetric periodic potential together with an oscillating force, and found that the direction of the macroscopic current can be…
F1-ATPase is the soluble portion of the membrane-embedded enzyme FoF1-ATP synthase that catalyzes the production of adenosine triphosphate in eukaryotic and eubacterial cells. In reverse, the F1 part can also hydrolyze ATP quickly at three…
We have developed a novel method to evaluate the potential profile of a molecular motor at each chemical state from only the probe's trajectory and applied it to a rotary molecular motor F$_1$-ATPase. By using this method, we could also…
Biological molecular machines convert free energy between different forms in cells, often at high efficiency. Optimal control theory provides a framework to elucidate design principles governing energetically efficient driving. Here, we use…
F1-ATPase catalyses ATP hydrolysis and converts the cellular chemical energy into mechanical rotation. The hydrolysis reaction in F1-ATPase does not follow the widely believed Michaelis-Menten mechanism. Instead, the hydrolysis mechanism…
The diffusion of a molecular motor in the presence of a constant external force is considered on the basis of a simple theoretical model. The motor is represented by a Brownian particle moving in a series of parabolic potentials placed…
F1-ATPase (or F1), the highly-efficient and reversible biochemical engine, has motivated physicists as well as biologists to imagine the design principles governing machines in the fluctuating world. Recent experiments have clarified yet…
The enzyme FoF1-ATP synthase provides the 'chemical energy currency' adenosine triphosphate (ATP) for living cells. Catalysis is driven by mechanochemical coupling of subunit rotation within the enzyme with conformational changes in the…
Single-molecule experiments have found near-perfect thermodynamic efficiency in the rotary motor F1-ATP synthase. To help elucidate the principles underlying nonequilibrium energetic efficiency in such stochastic machines, we investigate…
FoF1-ATP synthase is the enzyme that provides the 'chemical energy currency' adenosine triphosphate, ATP, for living cells. The formation of ATP is accomplished by a stepwise internal rotation of subunits within the enzyme. Briefly, proton…
The pump process of the ratchet model inspired by the $F_o$ rotatory motor of ATP synthase is investigated. In this model there are two kinds of characteristic time. One is dynamical, the relaxation time of the system. Others are chemical,…
Fueled by the hydrolysis of ATP, the motor protein kinesin literally walks on two legs along the biopolymer microtubule. The number of accidental backsteps that kinesin takes appears to be much larger than what one would expect given the…