  Biological systems are among the most challenging subjects for theoretical
physicists, as well as experimentalists or simulationists. Physical principles
should have been both constraints and guide-lines for the evolution of living
systems over billions of years. One generally aims at clarifying what physical
principles, possibly new ones, are behind the phenomena of biological interest
and at understanding how they work within the entire biological world. In the
present talk we describe an example of such an effort.
  Since the discovery of `superprecipitation' by Szent-Gyorgyi's group in
1940's, it has been a long puzzle how an assemblage of actin filaments with
random orientation can contract in the presence of the two-headed myosin
molecules undergoing actin-activated ATP-hydrolysis reaction. It is widely
accepted that during the contraction the two-headed myosin mediates the
relative sliding of two actin filaments whose polarity directions are not
parallel but rather anti-parallel. But this fact solely does not account for
the shortening. We propose a dynamical model which, upon numerical simulation,
exhibits the shortening of an bundle of the actin filaments which are initially
dirstributed randomly both in space along a line and in polarity direction. In
the course of shortening several clusters of actins appears along the bundle.
The model also shows the sorting of the actin filaments according to their
polarity in the late stage. These findings are in accordance with the recent
experiment by Takiguchi.
