Hopping and stalling of processive molecular motors.

When a two-headed molecular motor such as kinesin is attached to its track by just a single head in the presence of an applied load, thermally activated head detachment followed by rapid re-attachment at another binding site can cause the motor to 'hop' backwards. Such hopping, on its own, would produce a linear force-velocity relation. However, for kinesin, we must incorporate hopping into the motor's alternating-head scheme, where we expect it to be most important for the state prior to neck-linker docking. We show that hopping can account for the backward steps, run length and stalling of conventional kinesin. In particular, although hopping does not hydrolyse ATP, we find that the hopping rate obeys the same Michaelis-Menten relation as the ATP hydrolysis rate. Hopping can also account for the reduced processivity observed in kinesins with mutations in their tubulin-binding loop. Indeed, it may provide a general mechanism for the breakdown of perfect processivity in two-headed molecular motors.

Direction and speed of microtubule movements driven by kinesin motors arranged on catchin thick filaments.

Conventional kinesin (Kinesin-1) is a microtubule-based molecular motor that supports intracellular vesicle/organelle transport in various eukaryotic cells. To arrange kinesin motors similarly to myosin motors on thick filaments in muscles, the motor domain of rat conventional kinesin (amino acid residues 1-430) fused to the C-terminal 829 amino acid residues of catchin (KHC430Cat) was bacterially expressed and attached to catchin filaments that can attach to and arrange myosin molecules in a bipolar manner on their surface. Unlike the case of myosin where actin filaments move toward the center much faster than in the opposite direction along the catchin filaments, microtubules moved at the same speed in both directions. In addition, many microtubules moved across the filaments at the same speed with various angles between the axes of the microtubule and catchin filament. Kinesin/catchin chimera proteins with a shorter kinesin neck domain were also prepared. Those without the whole hinge 1 domain and the C-terminal part of the neck helix moved microtubules toward the center of the catchin filaments significantly, but only slightly, faster than in the opposite direction, although the movements in both directions were slower than those of the KHC430Cat construct. The results suggest that kinesin has substantial mechanical flexibility within the motor domain, possibly within the neck linker, enabling its interaction with microtubules having any orientation.

Anomalous fluctuations in sliding motion of cytoskeletal filaments driven by molecular motors: model simulations.

It has been found in in vitro experiments that cytoskeletal filaments driven by molecular motors show finite diffusion in sliding motion even in the long filament limit [Imafuku, Y. et al. Biophys. J. 1996, 70, 878-886. Noda, N. et al. Biophysics 2005, 1, 45-53]. This anomalous fluctuation can be evidence for cooperativity among the motors in action because fluctuation should be averaged out for a long filament if the action of each motor is independent. In order to understand the nature of the fluctuation in molecular motors, we perform numerical simulations and analyze velocity correlation in three existing models that are known to show some kind of cooperativity and/or large diffusion coefficient, i.e., the Sekimoto-Tawada model [Sekimoto, K.; Tawada, K. Phys. Rev. Lett. 1995, 75, 180], the Prost model [Prost, J. et al. Phys. Rev. Lett. 1994, 72, 2652], and the Duke model [Duke, T. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 2770]. It is shown that the Prost model and the Duke model do not give a finite diffusion in the long filament limit, in spite of the collective action of motors. On the other hand, the Sekimoto-Tawada model has been shown to give a diffusion coefficient that is independent of filament length, but it comes from the long time correlation whose time scale is proportional to filament length, and our simulations show that such a long correlation time conflicts with the experimental time scales. We conclude that none of the three models represent experimental findings. In order to explain the observed anomalous diffusion, we have to search for a mechanism that will allow both the amplitude and the time scale of the velocity correlation to be independent of the filament length.

Fluctuation of actin sliding over myosin thick filaments in vitro.

It is customarily thought that myosin motors act as independent force-generators in both isotonic unloaded shortening as well as isometric contraction of muscle. We tested this assumption regarding unloaded shortening, by analyzing the fluctuation of the actin sliding movement over long native thick filaments from molluscan smooth muscle in vitro. This analysis is based on the prediction that the effective diffusion coefficient of actin, a measure of the fluctuation, is proportional to the inverse of the number of myosin motors generating the sliding movement of an actin filament, hence proportional to the inverse of the actin length, when the actions of the motors are stochastic and statistically independent. Contrary to this prediction, we found the effective diffusion coefficient to be virtually independent of, and thus not proportional to, the inverse of the actin length. This result shows that the myosin motors are not independent force-generators when generating the continuous sliding movement of actin in vitro and that the sliding motion is a macroscopic manifestation of the cooperative actions of the microscopic ensemble motors.

Kinesin: a molecular motor with a spring in its step.

A key step in the processive motion of two-headed kinesin along a microtubule is the 'docking' of the neck linker that joins each kinesin head to the motor's dimerized coiled-coil neck. This process is similar to the folding of a protein beta-hairpin, which starts in a highly mobile unfolded state that has significant entropic elasticity and finishes in a more rigid folded state. We therefore suggest that neck-linker docking is mechanically equivalent to the thermally activated shortening of a spring that has been stretched by an applied load. This critical tension-dependent step utilizes Brownian motion and it immediately follows the binding of ATP, the hydrolysis of which provides the free energy that drives the kinesin cycle. A simple three-state model incorporating neck-linker docking can account quantitatively for both the kinesin force-velocity relation and the unusual tension-dependence of its Michaelis constant. However, we find that the observed randomness of the kinesin motor requires a more detailed four-state model. Monte Carlo simulations of single-molecule stepping with this model illustrate the possibility of sub-8 nm steps, the size of which is predicted to vary linearly with the applied load.