  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 [Y. Imafuku et al., Biophys. J. 70 (1996) 878-886; N. Noda et
al., Biophys. 1 (2005) 45-53]. This anomalous fluctuation can be an 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 analyse velocity correlation in three
existing models that are known to show some kind of cooperativity and/or large
diffusion coefficient, i.e. Sekimoto-Tawada model [K. Sekimoto and K. Tawada,
Phys. Rev. Lett. 75 (1995) 180], Prost model [J. Prost et al., Phys. Rev. Lett.
72 (1994) 2652], and Duke model [T. Duke, Proc. Natl. Acad. Sci. USA, 96 (1999)
2770]. It is shown that Prost model and Duke model do not give a finite
diffusion in the long filament limit in spite of collective action of motors.
On the other hand, Sekimoto-Tawada model has been shown to give the 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 do not
represent experimental findings. In order to explain the observed anomalous
diffusion, we have to seek for the mechanism that should allow both the
amplitude and the time scale of the velocity correlation to be independent of
the filament length.
