  The formation, maintenance and reorganization of the cytoskeletal filament
network is essential for a number of cellular processes. While the crucial role
played by active forces generated by motor proteins has been studied
extensively, only recently the importance of passive forces exerted by
non-enzymatic crosslinkers has been realized. The interplay between active and
passive proteins manifests itself, e.g., during cell division, where the
spindle structure formed by overlapping microtubules is subject to both active
sliding forces generated by crosslinking motor proteins and passive forces
exerted by passive crosslinkers, such as Ase1 and PRC1. We propose a minimal
model to describe the stability behaviour of a pair of anti-parallel
overlapping microtubules resulting from the competition between active motors
and passive crosslinkers. We obtain the stability diagram which characterizes
the formation of stable overlap of the MT pair, identify the controlling
biological parameters which determine their stability, and study the impact of
mutual interactions between motors and passive crosslinkers on the stability of
these overlapping filaments.
