  Active colloids and externally actuated semi-flexible filaments provide basic
building blocks for designing autonomously motile micro-machines. Here, we show
that a passive semi-flexible filament can be actuated and transported by
attaching an active colloid to its terminus. We study the dynamics of this
assembly when it is free, tethered, or clamped using overdamped equations of
motion that explicitly account for active fluid flow and the forces it
mediates. Linear states are destabilized by buckling instabilities to produce
stable states of non-zero curvature and writhe. We demarcate boundaries of
these states in the two-dimensional parameter space representing dimensionless
measures of polar and apolar activity. Our proposed assembly can be used as a
novel component in the design of micro-machines at low Reynolds number and to
study elastic instabilities driven by "follower" forces.
