Actin filaments are far stiffer than DNA: a typical measured persistence length is

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

Forces, Machines and Signals, Ch The elastic polymer: DNA from random walk to worm-like chain

Problem

Actin filaments are far stiffer than DNA: a typical measured persistence length is ξp≈17 μm\xi_p\approx17\,\mathrm{\mu m}. Consider a short actin filament of contour length L=680 nmL=680\,\mathrm{nm}, described as a worm-like chain with this persistence length and tangent correlation ⟨t^(s)⋅t^(s′)⟩=e−∣s−s′∣/ξp\langle\hat{\mathbf t}(s)\cdot\hat{\mathbf t}(s')\rangle=e^{-|s-s'|/\xi_p}. ((a)) Starting from R=∫0Lt^(s) ds\mathbf R=\int_0^L\hat{\mathbf t}(s)\,\mathrm ds, derive⟨R2⟩=2ξpL−2ξp2(1−e−L/ξp).\langle R^2\rangle=2\xi_pL-2\xi_p^2\left(1-e^{-L/\xi_p}\right). ((b)) Show that this reduces to ⟨R2⟩→L2\langle R^2\rangle\to L^2 for L≪ξpL\ll\xi_p and to ⟨R2⟩→2ξpL\langle R^2\rangle\to2\xi_pL for L≫ξpL\gg\xi_p, and state which limit matches a freely jointed chain of Kuhn length b=2ξpb=2\xi_p. ((c)) Evaluate ⟨R2⟩1/2\langle R^2\rangle^{1/2} for the actin filament above and express it as a percentage of the contour length LL.

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