  We consider a model of an extensible semiflexible filament moving in two
dimensions on a motility assay of motor proteins represented explicitly as
active harmonic linkers. Their heads bind stochastically to polymer segments
within a capture radius, and extend along the filament in a directed fashion
before detaching. Both the extension and detachment rates are load-dependent
and generate an active drive on the filament. The filament undergoes a first
order phase transition from open chain to spiral conformations and shows a
reentrant behavior in both the active extension and the turnover, defined as
the ratio of attachment-detachment rates. Associated with the phase transition,
the size and shape of the polymer changes non-monotonically, and the relevant
autocorrelation functions display double-exponential decay. The corresponding
correlation times show a maximum signifying the dominance of spirals. The
orientational dynamics captures the rotation of spirals, and its correlation
time decays with activity as a power law.
