Statistical and Biological Physics

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Mechanics of bundled semiflexible polymer networks

Oliver Lieleg, Mireille M.A.E. Claessens, Claus Heussinger, Erwin Frey, and Andreas R. Bausch

To ensure adaptability of cytoskeletal organization cells exploit the dynamic interplay between semi-flexible filamentous polymers such as microtubules or F-actin using a multitude of associated binding proteins. In particluar, the local elastic properties are regulated by the activation of auxiliary proteins which e.g. cross-link and/or bundle the filamentous networks into complex scaffolds. In this Letter we show that above a critical concentration of the actin binding protein (ABP) fascin, a solution of actin filaments organizes into a homogeneous network whose building blocks are bundles only. So far the mechanical response of highly cross-linked actin networks, also in the presence of bundles and composite phases, has mainly been described assuming affine stretching deformations. However, an applied tension can stretch a thermally undulating polymer only as far as there is excess contour length available. As the maximal amount of stored length is inversely proportional to the persistence length, this deformation mode is suppressed in networks of stiff polymer bundles, where the persistence length grows with bundle size. As an alternative we find that the recently introduced concept of the ''floppy modes'' is better suited to describe the network mechanical properties. While the above mentioned entropic models assume affine polymer stretching as the main source of elasticity, the floppy modes constitute energetic bending excitations, which retain a highly non-affine character. With this new theory it is possible to rationalize the observed rheological properties of the actin/fascin model system, which therefore provides a benchmark for addressing the further challenge of the mechanics of more complex in vivo networks as formed in the cytoskeleton.

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