Coupled Shear-bending Effects on Energy Dissipation in Thermally Fluctuating Biofilaments

Thermally fluctuating biofilaments including microtubules, chromosomes, and actin filaments exhibit energy dissipation from internal friction associated with viscoelastic conformational changes or fluid flow through internal filament pores, as well as external friction from hydrodynamic drag. Poirier and Marko (2002) introduced a physical model of the internal friction for thermally fluctuating biofilaments based on Langevin formulation of Euler-Bernoulli beam theory that considers deformation only due to bending. In this study, we present an extended model based on Timoshenko beam theory that explicitly considers the effects of shear deformation in addition to bending on both internal and external dissipation mechanisms. Our results reveal that shear deformation leads to dissipation dynamics on two time scales associated with internal friction (in lieu of a single time scale predicted by bending alone) and two length scales associated with external friction. This extended model successfully describes the experimental behavior for thermally fluctuating chromosomes and microtubules, and consequently, yields the superior estimates of energy dissipation deriving from internal and external frictions.