Abstract
Thermally fluctuating biofilaments possessing porous structures or viscoelastic properties exhibit energy losses from internal friction as well as external friction from drag. Prior models for internal friction account for energy dissipation solely from the dynamic bending of filaments. In this paper, we present a new energy dissipation model that captures the important effects of dynamic shear in addition to bending. Importantly, we highlight that shear-induced friction plays a major role in energy dissipation for shorter filaments and for shorter wavelengths (larger wavenumbers). The new model exhibits coupled shear-bending energy relaxation on two distinct time scales in lieu of a single time scale predicted by bending alone. We employ this model to interpret results from prior experiments on the internal friction of thermally fluctuating chromosomes and the drag-induced friction of thermally fluctuating microtubules. The examples confirm the energy relaxation on two time scales associated with internal friction and on two length scales associated with external friction. Overall, this new model that accounts for shear deformation yields superior estimates of energy dissipation for fluctuating biofilaments.
Highlights
Biofilaments including microtubules, DNA, and actin filaments are semiflexible micro-scale polymer structures that perform essential functions in living cells
Results demonstrate that shear deformation leads to qualitatively new energy dissipation behaviors including dissipation dynamics on two time scales associated with internal friction and on two length scales associated with external friction
We reveal the significant influence of shear deformation in the energy dissipation of thermally fluctuating biofilaments
Summary
Biofilaments including microtubules, DNA, and actin filaments are semiflexible micro-scale polymer structures that perform essential functions in living cells. For short filaments (L/2r < 10)[14,17] or short wavelength fluctuations (λ/r < 10)[14], the effect of shear deformation becomes important relative to bending deformation At these length scales, the filament exhibits direct shear deformation and the filament cross sections no longer remain perpendicular to the filament centerline (see Fig. 1b) as assumed in the WLC model (see Fig. 1a). Results demonstrate that shear deformation leads to qualitatively new energy dissipation behaviors including dissipation dynamics on two time scales associated with internal friction and on two length scales associated with external friction These new theoretical predictions successfully describe the experimental trends observable in studies of fluctuating chromosomal fragments[12] and microtubules[13]
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