Conditions for optimal mechanical power generation by a bundle of growing actin filaments

Bundles of actin filaments are central to a large variety of cellular structures, such as filopodia, stress fibers, cytokinetic rings or focal adhesions. The mechanical properties of these bundles are critical for proper force transmission and force bearing. Previous mathematical modeling efforts have focused on bundles rigidity and shape. However, it remains unknown how bundle length and thickness are controlled by external physical factors, and how the attachment of the bundle to a load affects its ability to transmit forces. In this paper, we present a biophysical model for dynamic bundles of actin filaments that takes into account individual filaments, their interaction with each other and with an external load. In combination with in vitro motility assays of beads coated with formins, our model allowed us to characterize conditions for bead movement and bundle buckling. From the deformation profiles, we determined key biophysical properties of tethered actin bundles, such as their rigidity and filament density. Our model also demonstrated that filaments undulate under lateral constraints applied by external forces or by neighboring filaments of the bundle. Last, our model allowed us to identify optimum conditions in filament density and barbed end tethering to the load for a maximal yield of mechanical power by a dynamic actin bundle.