  We consider the dynamics of a rigid filament in a motor protein assay under
external loading. The motor proteins are modeled as active harmonic linkers
with tail ends immobilized on a substrate. Their heads attach to the filament
stochastically to extend along it, resulting in a force on the filament, before
detaching. The rate of extension and detachment are load dependent. Here we
formulate and characterize the governing dynamics in the mean field
approximation using linear stability analysis, and direct numerical simulations
of the motor proteins and filament. Under constant loading, the system shows
transition from a stable configuration to instability towards detachment of the
filament from motor proteins. Under elastic loading, we find emergence of
stable limit cycle oscillations via a supercritical Hopf bifurcation with
change in activity and the number of motor proteins. Numerical simulations of
the system for large number of motor proteins show good agreement with the mean
field predictions.
