Dynamics of undulatory fluctuations of semiflexible filaments in a network
Abstract
We study the dynamics of a single semiflexible filament coupled to a Hookean spring at its boundary. The spring produces a fluctuating tensile force on the filament, the value of which depends on the filament's instantaneous endtoend length. The spring thereby introduces a nonlinearity, which mixes the undulatory normal modes of the filament and changes their dynamics. We study these dynamics using the MartinSiggiaRoseJanssenDe Dominicis formalism, and compute the timedependent correlation functions of transverse undulations and of the filament's endtoend distance. The relaxational dynamics of the modes below a characteristic wavelength √{κ /τ_{R} }, set by the filament's bending modulus κ and springrenormalized tension τ_{R}, are changed by the boundary spring. This occurs near the crossover frequency between tension and bendingdominated modes of the system. The boundary spring can be used to represent the linear elastic compliance of the rest of the filament network to which the filament is cross linked. As a result, we predict that this nonlinear effect will be observable in the dynamical correlations of constituent filaments of networks and in the networks' collective shear response. The system's dynamic shear modulus is predicted to exhibit the wellknown crossover with increasing frequency from ω^{1 /2} to ω^{3 /4}, but the inclusion of the network's compliance in the analysis of the individual filament dynamics shifts this transition to a higher frequency.
 Publication:

Physical Review E
 Pub Date:
 December 2020
 DOI:
 10.1103/PhysRevE.102.062406
 arXiv:
 arXiv:2006.10251
 Bibcode:
 2020PhRvE.102f2406K
 Keywords:

 Condensed Matter  Soft Condensed Matter
 EPrint:
 20 pages, 11 figures