The loose coupling mechanism in molecular machines of living cells

Oosawa, Fumio

doi:10.1046/j.1365-2443.2000.00304.x

Cited by 58 publications

(51 citation statements)

References 37 publications

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“…Our set of torque-speed curves is an order of magnitude bigger than any previous torque-speed dataset and allowed a systematic exploration of the parameter space of a minimal four-state kinetic model of the BFM mechanochemical cycle. The four-state kinetic model derives from the simplest possible representation of a carrier-like ion transport mechanism (29,30) and has been extensively used to model the BFM (31). Rather than choosing a single set of model parameters by educated guesswork, as in all previous attempts to model the flagellar motor, we performed a comprehensive search for sets of values of the 25 model parameters that were consistent with our measured torque-speed curves.…”

Section: Significancementioning

confidence: 99%

Mechanism and kinetics of a sodium-driven bacterial flagellar motor

Sowa

Pilizota

et al. 2013

Proc. Natl. Acad. Sci. U.S.A.

104

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The bacterial flagellar motor is a large rotary molecular machine that propels swimming bacteria, powered by a transmembrane electrochemical potential difference. It consists of an ∼50-nm rotor and up to ∼10 independent stators anchored to the cell wall. We measured torque-speed relationships of single-stator motors under 25 different combinations of electrical and chemical potential. All 25 torque-speed curves had the same concave-down shape as fully energized wild-type motors, and each stator passes at least 37 ± 2 ions per revolution. We used the results to explore the 25-dimensional parameter space of generalized kinetic models for the motor mechanism, finding 830 parameter sets consistent with the data. Analysis of these sets showed that the motor mechanism has a "powerstroke" in either ion binding or transit; ion transit is channel-like rather than carrier-like; and the rate-limiting step in the motor cycle is ion binding at low concentration, ion transit, or release at high concentration. where V m is the membrane voltage and Δμ = k B T ln(C in /C out ) and q are the transmembrane chemical potential difference and charge of the ions, respectively, with C in and C out the internal and external ion concentrations. In most species the primary form of biological free energy is the proton-motive force (PMF), the IMF for H + ions (1). Physiological PMF is typically in the range −150 mV to −200 mV, with the inside electrically negative and slightly alkaline relative to the outside. Some organisms use sodium-motive force (SMF) to drive numerous cellular processes, such as bacterial motility (2), ATP synthesis (3), and active membrane transport (4). Arguably the most important process driven by IMF is ATP synthesis, which generates cellular ATP by forced rotation of the F 1 part of F 1 F O ATP-synthase. F 1 is mechanically coupled to and rotated by F O , which like the bacterial flagellar motor (BFM) is an ion-driven rotary motor. Understanding the mechanism of these and other ion-driven molecular machines is a fundamental challenge in cellular energetics and biophysics. The BFM (Fig. 1A) is a rotary molecular machine that propels many species of swimming bacteria. It couples ion flow, for example protons (H + ) in Escherichia coli or sodium ions (Na + ) in Vibrio alginolyticus, to the rotation of extracellular helical flagellar filaments at hundreds of revolutions per second (Hz) (2, 5, 6). Torque is generated by interactions between stator complexes (containing the proteins MotA and MotB in E. coli and PomA and PomB in V. alginolyticus) and the rotor protein FliG (7). In E. coli, each motor can be powered by any number between 1 and at least 11 functionally independent stators (8), which exchange with a membrane-bound pool of "spare" stators on a timescale of minutes (9).The most important biophysical method for studying the torque-generating mechanism of the BFM has been to measure its torque-speed curves. This has been done using varying viscous load (10-14) or external torque (15, 16) to control the speed. Fu...

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Section: Significancementioning

confidence: 99%

Mechanism and kinetics of a sodium-driven bacterial flagellar motor

Sowa

Pilizota

et al. 2013

Proc. Natl. Acad. Sci. U.S.A.

104

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“…Thus, only coordination of nucleotide kinetics among the three stator magnets needs be programmed. This could be done without postulating switches, as shown in ¢gure 13, which is one version of the general model of Oosawa & Hayashi (1986).…”

Section: (B) Analogy Might Helpmentioning

confidence: 99%

“…Because ATP hydrolysis on b is reversible (the free-energy di¡erence between b binding ATP and b binding ADP + phosphate is small), the a¤nity for the hydrolysis products has to be lower in order for b to act as ATPase. In the original model of Oosawa & Hayashi (1986), near 100% e¤ciency was achieved for both hydrolysis and synthesis.…”

Section: (B) Analogy Might Helpmentioning

confidence: 99%

A rotary molecular motor that can work at near 100% efficiency

Kinosita

Yasuda

Noji

et al. 2000

Phil. Trans. R. Soc. Lond. B

225

141

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A single molecule of F 1 -ATPase is by itself a rotary motor in which a central g-subunit rotates against a surrounding cylinder made of a 3 b 3 -subunits. Driven by the three bs that sequentially hydrolyse ATP, the motor rotates in discrete 1208 steps, as demonstrated in video images of the movement of an actin ¢lament bound, as a marker, to the central g-subunit. Over a broad range of load (hydrodynamic friction against the rotating actin ¢lament) and speed, the F 1 motor produces a constant torque of ca. 40 pN nm. The work done in a 1208 step, or the work per ATP molecule, is thus ca. 80 pN nm. In cells, the free energy of ATP hydrolysis is ca. 90 pN nm per ATP molecule, suggesting that the F 1 motor can work at near 100% e¤ciency. We con¢rmed in vitro that F 1 indeed does ca. 80 pN nm of work under the condition where the free energy per ATP is 90 pN nm. The high e¤ciency may be related to the fully reversible nature of the F 1 motor: the ATP synthase, of which F 1 is a part, is considered to synthesize ATP from ADP and phosphate by reverse rotation of the F 1 motor. Possible mechanisms of F 1 rotation are discussed.

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“…Furthermore, in the case of the molecular motors, the energy supplied by the hydrolysis of adenosine triphosphate (ATP), which is to be converted to the mechanical work, is only an order of magnitude larger than the thermal energy at room temperature (∼20k B T), and hence it seems likely that the molecular machines harness the thermal noise, instead of suppressing it as the human-made machines do (1). This distinct feature of the molecular machines should arise from the atomic structures of the constituent proteins, which is reflected in the current focus of interest in the structural aspect of the molecular machines.…”

mentioning

confidence: 99%

Unidirectional Brownian motion observed in an in silico single molecule experiment of an actomyosin motor

Takano

Terada

Sasai

2010

Proc. Natl. Acad. Sci. U.S.A.

120

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The actomyosin molecular motor, the motor composed of myosin II and actin filament, is responsible for muscle contraction, converting chemical energy into mechanical work. Although recent single molecule and structural studies have shed new light on the energy-converting mechanism, the physical basis of the molecular-level mechanism remains unclear because of the experimental limitations. To provide a clue to resolve the controversy between the lever-arm mechanism and the Brownian ratchet-like mechanism, we here report an in silico single molecule experiment of an actomyosin motor. When we placed myosin on an actin filament and allowed myosin to move along the filament, we found that myosin exhibits a unidirectional Brownian motion along the filament. This unidirectionality was found to arise from the combination of a nonequilibrium condition realized by coupling to the ATP hydrolysis and a ratchet-like energy landscape inherent in the actin-myosin interaction along the filament, indicating that a Brownian ratchet-like mechanism contributes substantially to the energy conversion of this molecular motor. M olecular machines in living organisms are nanometer-sized small systems working robustly and efficiently in the presence of the severely disturbing thermal noises. Furthermore, in the case of the molecular motors, the energy supplied by the hydrolysis of adenosine triphosphate (ATP), which is to be converted to the mechanical work, is only an order of magnitude larger than the thermal energy at room temperature (∼20k B T), and hence it seems likely that the molecular machines harness the thermal noise, instead of suppressing it as the human-made machines do (1). This distinct feature of the molecular machines should arise from the atomic structures of the constituent proteins, which is reflected in the current focus of interest in the structural aspect of the molecular machines. However, it should be remembered that the structural aspect is not everything but is inseparably linked to the dynamical and energetical aspects. Therefore, a unified description of structure, dynamics, and energetics is the step necessary to understand the molecular-level physical principle of how the molecular machines work.The actomyosin molecular motor, the system composed of myosin II and actin molecules, is responsible for muscle contraction, and is the most extensively studied molecular motor. It has been shown by single molecule experiments (SME) that a single myosin molecule and an actin filament (polymerized actin) constitute the minimal force-generating unit of this motor (2-4) (see Fig. 1A). Although SME has been a powerful approach to study the dynamical aspect of the force-generating unit (2-4), the limitation of the spatiotemporal resolution of SME has inhibited us from developing the full atomistic picture of the force-generating process. On the other hand, since the currently available high-resolution structures of myosin (5-7) are those obtained in the crystalline environment and in the absence of actin, it remains unc...

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The loose coupling mechanism in molecular machines of living cells

Cited by 58 publications

References 37 publications

Mechanism and kinetics of a sodium-driven bacterial flagellar motor

Mechanism and kinetics of a sodium-driven bacterial flagellar motor

A rotary molecular motor that can work at near 100% efficiency

Unidirectional Brownian motion observed in an in silico single molecule experiment of an actomyosin motor

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