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 10 4 times 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.he long-standing quest to understand why the mobility of entangled linear polymers is ultraslow normally considers the diffusion of a single average macromolecule in its average surrounding environment, most prominently envisioned as a polymer reptating through the confining Edwards-de Gennes tube composed of the identical polymers that surround it (1-6). Although differing in important respects according to polymer geometry (e.g., flexible and semiflexible chains, rigid rods, and branched polymers), all share the peculiarity that because the size of the macromolecule vastly exceeds the size of individual units along it, adjoining segments on a tagged polymer become correlated over large separations simply because they are covalently bonded and cannot cross other macromolecules. In this paper, our focus is not on the familiar single-polymer problem (1-13) but rather on the open question of how the motion of a given reptating macromolecule is coupled in space and time with others that reptate within its pervaded volume. The fractal and strongly interpenetrating nature of linear polymers in dense liquids causes the number of "correlated neighbors" on the macromolecular length scale to grow strongly as the polymer size increases (1-3, 14). The dynamical consequences of such a feature are not addressed by the classical r...

Quenched and annealed disorder mechanisms in comb models with fractional operators

“…Thus, we observed that the interplay between two subdiffusion mechanisms (geometrical restrictions and memory effects) may lead to the usual Brownian motion. This crossover and its physical explanation also appear consistent with experimental results of anisotropic diffusion of entangled biofilaments [84] and the mobility of water molecules on protein surfaces [85]. On the other hand, when an exponential memory kernel acts on the backbone, we obtained a crossover from subdiffusion to confined diffusion.…”

“…This interpretation is somehow in agreement with the results on anisotropic diffusion of entangled biofilaments reported in Ref. [84], where the authors have written:…”

Single-crosslink microscopy in a biopolymer network dissects local elasticity from molecular fluctuations

“…Next, we consider the cross-correlations between crosslinks. Hydrodynamic arguments for a continuum anticipates C rr r 0 to be constant regardless of separation 13,17 , whereas our data is massively scattered (Fig. 4e) with negative points highlighted by the pink background.…”

“…A protocol was designed to polymerize the filaments and to fluorescently label the crosslinks by exploiting the fragmentation/fusion nature of actin filaments (Fig. 1b, see Methods section for details) 16,17 . The resulting network is composed of a “sea” of unlabeled filaments and a few labeled ones (ratio ~1000:1), in which green segments with biotin are most likely to be crosslinked to unlabeled filaments (Fig.…”

Profile of Steve Granick

“…"With those instrumental capabilities, it became very natural to look not just at interfaces, but also at bulk mobility, the dynamics of how molecules move from point to point in space in crowded environments, and what are the mechanisms," he says. For example, Granick and his colleagues used single-molecule fluorescence imaging to elucidate correlations between neighboring actin biofilaments and colloids rather than take the conventional mean-field approach (7,8).…”