It has been found in several in vitro experiments that cytoskeletal filaments driven by molecular motors show finite diffusion in sliding movement even in the long filament limit (Imafuku et al., 1996a, 1997; Noda et al., 2005). This anomalous fluctuation can be evidence that there exists some cooperativity among the motors in action because fluctuation should be averaged out if the action of each motor is independent. In order to understand the nature of the cooperativity in existing models of molecular motors, we perform numerical simulations and analyze velocity correlation on three models that are known to show some kind of cooperativity and/or large diffusion coefficient in the long filament limit. It is shown that Prost model (1994) and Duke model (1999) do not give a finite diffusion in the long filament limit in spite of collective action of motors. Quenched randomness in Sekimoto-Tawada model (1995) has been shown to give constant diffusion coefficient independent of filament length because of long time correlation proportional to filament length, but such a long correlation time is found to conflict with the experimental time scales. We conclude that none of the three models represent experimental findings, and a mechanism to be understood should allow both the amplitude and the time scale of the velocity correlation to be independent of the filament length.
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