An actin filament's tangent-tangent correlation is measured along its contour at

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

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

Problem

An actin filament's tangent-tangent correlation is measured along its contour at T=298 KT = 298\,\mathrm{K}, giving ⟨cos⁡θ(s)⟩=0.89\langle\cos\theta(s)\rangle = 0.89 at arclength s=2.0 μms = 2.0\,\mathrm{\mu m}, following the worm-like chain relation ⟨cos⁡θ(s)⟩=e−s/ξp\langle\cos\theta(s)\rangle = e^{-s/\xi_p}. ((a)) Find the persistence length ξp\xi_p of the filament. ((b)) At the barbed end of this same filament, growing against a load, the free monomer concentration is c=1.2 μMc = 1.2\,\mathrm{\mu M}, the critical concentration is cc=0.12 μMc_c = 0.12\,\mathrm{\mu M}, and each monomer adds a step δ=2.7 nm\delta = 2.7\,\mathrm{nm}. Find the Brownian ratchet stall force per filament.

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