title: Dynamic cross-correlations between entangled biofilaments as they diffuse.
abstract: Entanglement in polymer and biological physics involves a state in which linear interthreaded macromolecules in isotropic liquids diffuse in a spatially anisotropic manner beyond a characteristic mesoscopic time and length scale (tube diameter). The physical reason is that linear macromolecules become transiently localized in directions transverse to their backbone but diffuse with relative ease parallel to it. Within the resulting broad spectrum of relaxation times there is an extended period before the longest relaxation time when filaments occupy a time-averaged cylindrical space of near-constant density. Here we show its implication with experiments based on fluorescence tracking of dilutely labeled macromolecules. The entangled pairs of aqueous F-actin biofilaments diffuse with separation-dependent dynamic cross-correlations that exceed those expected from continuum hydrodynamics up to strikingly large spatial distances of ≈15 µm, which is more than 104times the size of the solvent water molecules in which they are dissolved, and is more than 50 times the dynamic tube diameter, but is almost equal to the filament length. Modeling this entangled system as a collection of rigid rods, we present a statistical mechanical theory that predicts these long-range dynamic correlations as an emergent consequence of an effective long-range interpolymer repulsion due to the de Gennes correlation hole, which is a combined consequence of chain connectivity and uncrossability. The key physical assumption needed to make theory and experiment agree is that solutions of entangled biofilaments localized in tubes that are effectively dynamically incompressible over the relevant intermediate time and length scales.
authors.affiliation: Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801.
authors.forename: Boyce
authors.initials: B
authors.lastname: Tsang
authors.affiliation: Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801.
authors.forename: Zachary E
authors.initials: ZE
authors.lastname: Dell
authors.affiliation: Department of Materials Science and Engineering, Jinan University, Guangzhou 510632, China.
authors.forename: Lingxiang
authors.initials: L
authors.lastname: Jiang
authors.affiliation: Department of Materials Science, University of Illinois at Urbana-Champaign, Urbana, IL 61801.|Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, IL 61801.
authors.forename: Kenneth S
authors.initials: KS
authors.lastname: Schweizer
authors.affiliation: IBS Center for Soft and Living Matter, Ulsan National Institute of Science and Technology, Ulju-gun, Ulsan 689-789, South Korea sgranick@illinois.edu.
authors.forename: Steve
authors.initials: S
authors.lastname: Granick
keywords: biofilament; cross-correlation; entangled; imaging; reptation