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.
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