Zipping mechanism for force-generation by growing filament bundles

We investigate the force generation by polymerizing bundles of filaments, which form because of short-range attractive filament interactions. We show that bundles can generate forces by a zipping mechanism, which is not limited by buckling and operates in the fully buckled state. The critical zipping force, i.e. the maximal force that a bundle can generate, is given by the adhesive energy gained during bundle formation. For opposing forces larger than the critical zipping force, bundles undergo a force-induced unbinding transition. For larger bundles, the critical zipping force depends on the initial configuration of the bundles. Our results are corroborated by Monte Carlo simulations. Introduction. – Filamentous polymers play an important role in biological and chemical physics. Both cytoskeletal filaments such as filamentous actin and microtubules and chemically synthesized polymers such as dendronized polymers have diameters in the range from 2 to 25 nanometers which leads to a considerable bending rigidity, i.e. the persistence length is comparable or larger than the polymer’s contour length. The most important building blocks of the cytoskeleton are actin filaments with a persistence length of Lp ∼ 15μm and microtubules with a much larger persistence length Lp ∼ 5mm. Such semiflexible polymers are governed by several competing energy scales in the system: the bending energy and the thermal energy of the filaments, the interaction energy between the filaments, and biochemical forces. In biological systems, such biochemical forces are generated by the activity of molecular motors proteins or the polymerization dynamics of cytoskeletal filaments [1]. Force generation by polymerizing cytoskeletal filaments is essential for various cellular processes, such as motility [1] or the formation of cell protrusions including filopodia, lamellipodia, or acrosomal extensions [2, 3], where filaments push against a planar obstacle. Single polymerizing filaments can generate forces in the piconewton range, which arise from the gain in chemical bonding energy upon monomer attachment [4]. This process also involves shape fluctuations of the filament [5], which exerts entropic forces on the planar obstacle [6]. Polymerizing filaments buckle at some critical length under the action of their own polymerization force [7], which limits force generation by single filaments. Filament bundles support cell protrusions and serve as stress fibres [8, 9]. Filament bundles have a higher bending rigidity and are, thus, more stable against buckling if a compressive load is applied [10]. The formation of filament bundles is governed by the competition of thermal fluctuations and attractive interactions, which can arise from crosslinking proteins or unspecific interactions. Crosslinker-mediated interactions allow a reversible formation of actin bundles, which can be regulated by the concentration of crosslinkers in solution [11]. Cellular force generating structures are typically made of polymerizing bundles rather than single filaments. One reason is the enhanced stability of crosslinked stiffer bundles against buckling. Moreover, ensembles of N filaments could share a compressive load force suggesting that the maximally generated force increases by a factor of N , similar to protofilaments in a microtubule [12]. In addition, crosslinking within filament bundles can allow the bundle to generate higher forces by exploiting the additional interaction energy [13, 14]. As a result, the mechanism of force generation by polymerizing bundles is difficult to understand because it involves several types of forces: chemical polymerization forces from monomer bonding,