Polymerising filaments generate force against an obstacle, as in, e.g., microtubule-kinetochore interactions in the eukaryotic cell. Earlier studies of this problem have not included explicit three-dimensional monomer diffusion, and consequently, missed out on two important aspects: (i) the barrier, even when it is far from the polymers, affects free diffusion of monomers and reduces their adsorption at the tips, while (ii) parallel filaments could interact through the monomer density field (“diffusive coupling”), leading to negative interference between them. In our study, both these effects are included and their consequences investigated in detail. A mathematical treatment based on a set of continuum Fokker-Planck equations for combined filament-wall dynamics suggests that the barrier-induced monomer depletion reduces the growth velocity and also the stall force, while the total force produced by many filaments remains additive. However, Brownian dynamics simulations show that the linear force-number scaling holds only when the filaments are far apart; when they are arranged close together, forming a bundle, sublinear scaling of force with number appears, which could be attributed to diffusive interaction between the growing polymer tips.

Polymers growing against a barrier generate force and push it forward. We study here force generation by a bundle of N rigid polymers growing in parallel against a diffusing, rigid, flat barrier, resembling a bundle of microtubules. To estimate the polymerization force, the barrier is subjected to a force f acting against the direction of growth of the polymers and the mean velocity VN (f ) of the filament assembly is computed. The maximum polymerization force (alias stall force) f N s is deduced from the condition VN (f N s ) = 0. This problem has been studied in the literature earlier, but two important aspects have escaped attention: (a) free diffusion of monomers is hindered by the barrier, even when it is far from the growing tips and (b) parallel filaments could interact through the monomer density field ("diffusive coupling"), leading to negative interference between them. In our model, both these effects are investigated in detail. A mathematical treatment based on a set of continuum Fokker-Planck equations for combined filament-wall dynamics suggests that the barrier reduces the influx of monomers to the growing polymer tip, thereby reducing the growth velocity and also the stall force, but it doesn't affect the scaling of the stall force with number, i.e., f N s = N f 1 s . However, Brownian dynamics simulations show that the linear scaling holds only when the filaments are far apart; when they are arranged close together, forming a bundle, sublinear scaling of force with number appears. We argue that the nonlinear scaling could be attributed to diffusive interaction between the growing tips which becomes significant when the tips are close together. These conclusions, initially established for simple flat-faced polymers, are also found to hold true for microtubules with their characteristic hollow cylindrical geometry and rugged tip structure. In particular, simulations show conclusively that the stall force of a single microtubule is a fraction of the combined stall force of the 13 protofilaments. This result is supported by a simple analytical estimate of the force using diffusive coupling theory, and is in agreement with earlier experimental observations.