An AFM force-extension trace of a single titin molecule at shows a sawtooth with five…

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

Forces, Machines and Signals, Ch Measuring one molecule: traps, tweezers and single-molecule fluorescence

Problem

An AFM force-extension trace of a single titin molecule at

298\,\mathrm{K}

shows a sawtooth with five rupture peaks. Worm-like chain fits to the segments before each peak give contour lengths

28

56

84

112

and

140\,\mathrm{nm}

for the successive peaks (each

28\,\mathrm{nm}

longer than the last). The final peak occurs at an extension

x = 126\,\mathrm{nm}

(contour length

L = 140\,\mathrm{nm}

) with a rupture force

f = 195\,\mathrm{pN}

. Take every peak to mark a domain unfolding; the molecule detaches from the tip only later, beyond the stretch described here. ((a)) How many folded domains unfolded during the stretch recorded here, and what does the

28\,\mathrm{nm}

increment between successive contour lengths represent? ((b)) Using the worm-like chain force law (Chapter 5, restated here)

f = \frac{k_BT}{\xi_p}\left[\frac{1}{4}\left(1 - \frac{x}{L}\right)^{-2} - \frac{1}{4} + \frac{x}{L}\right]

estimate the persistence length

\xi_p

consistent with the final peak, and say whether it agrees with titin's persistence length of about

0.4\,\mathrm{nm}

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