  To theoretically understand force generation properties of actin filaments,
many models consider growing filaments pushing against a movable obstacle or
barrier. In order to grow, the filaments need space and hence it is necessary
to move the barrier. Two different mechanisms for this growth are widely
considered in literature. In one class of models (type $A$), the filaments can
directly push the barrier and move it, thereby performing some work in the
process. In another type of models (type $B$), the filaments wait till thermal
fluctuations of the barrier position create enough space between the filament
tip and the barrier, and then they grow by inserting one monomer in that gap.
The difference between these two types of growth seems microscopic and rather a
matter of modelling details. However, we find that this difference has
important effect on many qualitative features of the models. In particular, how
the relative time-scale between the barrier dynamics and filament dynamics
influences the force generation properties, are significantly different for
type $A$ and $B$ models. We illustrate these differences for three types of
barrier: a rigid wall-like barrier, an elastic barrier and a barrier with
Kardar-Parisi-Zhang dynamics. Our numerical simulations match well with our
analytical calculations. Our study highlights the importance of taking the
details of filament-barrier interaction into account while modelling force
generation properties of actin filaments.
