A much longer actin filament fragment

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Soft condensed matter · Soft condensed matter

Soft Matter at the Thermal Scale, Ch The size and shape of a polymer chain

Problem

A much longer actin filament fragment, of contour length L=60 μmL = 60\,\mu\mathrm{m}, is tracked by fluorescence microscopy; its mean-square end-to-end distance is measured to be ⟨R2⟩=1440 μm2\langle R^2\rangle = 1440\,\mu\mathrm{m}^2. ((a)) Estimate the persistence length lpl_p from the long-contour-length (random-coil) limit of the worm-like chain, ⟨R2⟩≈2lpL\langle R^2\rangle \approx 2l_pL, and find L/lpL/l_p for your estimate. ((b)) LL is only a few persistence lengths here. Refine the estimate with the worm-like chain result ⟨R2⟩=2lpL[1−lpL(1−e−L/lp)]\langle R^2\rangle = 2l_pL\left[1 - \frac{l_p}{L}\left(1 - e^{-L/l_p}\right)\right], dropping only the exponential, and check that the dropped term is small. Was the random-coil limit adequate?

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