Thermal contour analysis of an actin filament of contour length at decomposes its…

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

Thermal contour analysis of an actin filament of contour length L=10.0 μmL = 10.0\,\mathrm{\mu m} at T=298 KT = 298\,\mathrm{K} decomposes its tangent angle into cosine bending modes normalised as in the text, with mean-square amplitudes ⟨an2⟩=L2/(π2n2ξp)\langle a_n^2\rangle = L^2/(\pi^2 n^2 \xi_p). Three modes give ⟨a12⟩=0.596 μm\langle a_1^2\rangle = 0.596\,\mathrm{\mu m}, ⟨a22⟩=0.149 μm\langle a_2^2\rangle = 0.149\,\mathrm{\mu m}, ⟨a32⟩=0.0662 μm\langle a_3^2\rangle = 0.0662\,\mathrm{\mu m}. ((a)) Explain what should be plotted against what to give a straight line through the origin, and identify the slope in terms of LL and ξp\xi_p. ((b)) Use the data to extract the persistence length ξp\xi_p. ((c)) Hence find the bending rigidity κ\kappa.

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