An AFM force-extension trace of a multidomain protein shows a sawtooth of unfolding events

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

An AFM force-extension trace of a multidomain protein shows a sawtooth of unfolding events. One rip releases a contour-length increment ΔL=32 nm\Delta L = 32\,\mathrm{nm}. Each residue contributes 0.38 nm0.38\,\mathrm{nm} of fully extended backbone, and the folded domain that opens up already spans about 4 nm4\,\mathrm{nm} end-to-end before it unfolds. Take T=298 KT=298\,\mathrm{K}, kBT=4.11 pN nmk_BT=4.11\,\mathrm{pN\,nm}. ((a)) Using ΔL≈0.38n nm−4 nm\Delta L \approx 0.38n\,\mathrm{nm} - 4\,\mathrm{nm}, estimate the number of residues nn in the domain that unfolded. ((b)) The newly released, still-unfolded segment (contour length L=0.38n nmL=0.38n\,\mathrm{nm}, using your answer to part (a) with no subtraction) is observed, before the next rip, sitting at relative extension z/L=0.60z/L=0.60 under a pulling force f=20 pNf=20\,\mathrm{pN}. Using the Marko-Siggia formula, estimate the persistence length ξpprotein\xi_p^{\rm protein} of the unfolded backbone, and compare it with the value ξp≈0.4 nm\xi_p\approx0.4\,\mathrm{nm} quoted for an unfolded polypeptide. What would the low-force limit z/L=2ξpf/(3kBT)z/L = 2\xi_pf/(3k_BT) have given from the same point, and why is it not to be trusted here?

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