  We study force generation by a set of parallel actin filaments growing
against a non-rigid obstacle, in presence of an external load. The filaments
polymerize by either moving the whole obstacle, with a large energy cost, or by
causing local distortion in its shape which costs much less energy. The
non-rigid obstacle also has local thermal fluctuations due to which its shape
can change with time and we describe this using fluctuations in the height
profile of a one dimensional interface with Kardar-Parisi-Zhang dynamics. We
find the shape fluctuations of the barrier strongly affects the force
generation mechanism. The qualitative nature of the force-velocity curve is
crucially determined by the relative time-scale of filament and barrier
dynamics. The height profile of the barrier also shows interesting variation
with the external load. Our analytical calculation within mean-field theory
shows reasonable agreement with our simulation results.
