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Register a new userF1 rotary motor of ATP synthase is driven by the torsionally-asymmetric drive shaft
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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 against the concentration gradient across the membrane. ATPase is composed of two rotary motors, F0 and F1, which generate the opposing rotation and compete for control of their shared central gamma-shaft. Here we present a self-consistent physical model of the F1 motor as a simplified two-state Brownian ratchet based on the asymmetry of torsional elastic energy of the coiled-coil gamma-shaft. This stochastic model unifies the physical description of linear and rotary motors and explains the stepped unidirectional rotation of the $gamma$-shaft, in agreement with the `binding-change ideas of Boyer. Substituting the model parameters, all independently known from recent experiments, our model quantitatively reproduces the ATPase operation, e.g. the `no-load angular velocity is ca. 400~rad/s anticlockwise at 4 mM ATP, in close agreement with experiment. Increasing the pmf torque exerted by F0 can slow, stop and overcome the torque generated by F1, switching from ATP hydrolysis to synthesis at a very low value of `stall torque. We discuss the matters of the motor efficiency, which is very low if calculated from the useful mechanical work it produces - but is quite high when the `useful outcome is measured in the number of H+ pushed against the chemical gradient in the F1 ATP-driven operation.
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Generation of mechanical oscillation is ubiquitous to wide variety of intracellular processes. We show that catchbonding behaviour of motor proteins provides a generic mechanism of generating spontaneous oscillations in motor-cytoskeletal filament complexes. We obtain the phase diagram to characterize how this novel catch bond mediated mechanism can give rise to bistability and sustained limit cycle oscillations and results in very distinctive stability behaviour, including bistable and non-linearly stabilised in motor-microtubule complexes in biologically relevant regimes. Hitherto, it was thought that the primary functional role of the biological catchbond was to improve surface adhesion of bacteria and cell when subjected to external forces or flow field. Instead our theoretical study shows that the imprint of this catch bond mediated physical mechanism would have ramifications for whole gamut of intracellular processes ranging from oscillations in mitotic spindle oscillations to activity in muscle fibres.
A discrete-state model of the F1-ATPase molecular motor is developed which describes not only the dependences of the rotation and ATP consumption rates on the chemical concentrations of ATP, ADP, and inorganic phosphate, but also on mechanical control parameters such as the friction coefficient and the external torque. The dependence on these mechanical parameters is given to the discrete-state model by fitting its transition rates to the continuous-angle model of P. Gaspard and E. Gerritsma [J. Theor. Biol. 247 (2007) 672-686]. This discrete-state model describes the behavior of the F1 motor in the regime of tight coupling between mechanical motion and chemical reaction. In this way, kinetic and thermodynamic properties of the F1 motor are obtained such as the Michaelis-Menten dependence of the rotation and ATP consumption rates on ATP concentration and its extension in the presence of ADP and Pi, their dependences on friction and external torque, as well as the chemical and mechanical thermodynamic efficiencies.
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 motor in real time. We studied the formation of adenosine triphosphate, ATP, from ADP and phosphate by FoF1-ATP synthase. The reaction is performed by a stepwise internal rotation of subunits of the lipid membrane-embedded enzyme. Using fluorescence resonance energy transfer, FRET, we detected rotation of this biological motor by sequential changes of intramolecular distances within a single FoF1-ATP synthase. Prolonged observation times of single enzymes were achieved by functional immobilization to the glass surface. The stepwise rotary subunit movements were identified by Hidden Markov Models (HMM) which were trained with single-molecule FRET trajectories. To improve the accuracy of the HMM analysis we included the single-molecule fluorescence lifetime of the FRET donor and used alternating laser excitation to co-localize the FRET acceptor independently within a photon burst. The HMM analysis yielded the orientations and dwell times of rotary subunits during stepwise rotation. In addition, the action mode of bactericidal drugs, i.e. inhibitors of FoF1-ATP synthase like aurovertin, could be investigated by the time resolved single-molecule FRET approach.
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. We monitor subunit rotation by a single-molecule fluorescence resonance energy transfer (FRET) approach using two fluorophores specifically attached to the enzyme. To identify the stepsize of rotary movements by the motors of ATP synthase we simulated the confocal single-molecule FRET data of freely diffusing enzymes and developed a step finder algorithm based on Hidden Markov Models (HMM). The HMM is able to find the proximity factors, P, for a three-level system and for a five-level system, and to unravel the dwell times of the simulated rotary movements. To identify the number of hidden states in the system, a likelihood parameter is calculated for the series of one-state to eight-state HMMs applied to each set of simulated data. Thereby, the basic prerequisites for the experimental single-molecule FRET data are defined that allow for discrimination between a 120 degree stepping mode or a 36 degree substep rotation mode for the proton-driven Fo motor of ATP synthase.
In cells and in vitro assays the number of motor proteins involved in biological transport processes is far from being unlimited. The cytoskeletal binding sites are in contact with the same finite reservoir of motors (either the cytosol or the flow chamber) and hence compete for recruiting the available motors, potentially depleting the reservoir and affecting cytoskeletal transport. In this work we provide a theoretical framework to study, analytically and numerically, how motor density profiles and crowding along cytoskeletal filaments depend on the competition of motors for their binding sites. We propose two models in which finite processive motor proteins actively advance along cytoskeletal filaments and are continuously exchanged with the motor pool. We first look at homogeneous reservoirs and then examine the effects of free motor diffusion in the surrounding medium. We consider as a reference situation recent in vitro experimental setups of kinesin-8 motors binding and moving along microtubule filaments in a flow chamber. We investigate how the crowding of linear motor proteins moving on a filament can be regulated by the balance between supply (concentration of motor proteins in the flow chamber) and demand (total number of polymerised tubulin heterodimers). We present analytical results for the density profiles of bound motors, the reservoir depletion, and propose novel phase diagrams that present the formation of jams of motor proteins on the filament as a function of two tuneable experimental parameters: the motor protein concentration and the concentration of tubulins polymerized into cytoskeletal filaments. Extensive numerical simulations corroborate the analytical results for parameters in the experimental range and also address the effects of diffusion of motor proteins in the reservoir.
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