A microtubule embedded in the cytoskeletal network of a living cell buckles into a…

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Biophysics & Medical Physics · Macromolecules, membranes and cell architecture

Forces, Machines and Signals, Ch Filaments, networks and the mechanics of whole cells

Problem

A microtubule embedded in the cytoskeletal network of a living cell buckles into a short wavelength

\lambda = 4.0\,\mathrm{\mu m}

instead of along its whole length, because the surrounding elastic network resists sideways deflection with a stiffness per unit length

k_m

. Its bending rigidity is

\kappa = 2.1\times10^{-23}\,\mathrm{N\,m^2}

, and the reinforced-buckling relations are

\lambda = 2\pi(\kappa/k_m)^{1/4}

and

F_c = 8\pi^2\kappa/\lambda^2

. ((a)) Find the critical load

F_c

the microtubule can carry before buckling at this wavelength. ((b)) Find the stiffness per unit length

k_m

of the surrounding network implied by this wavelength.

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