Past exam of the biological physics course of the University of Oxford / 2015 / 4 / a / Solution

In single-molecule force spectroscopy of titin, one end of the protein is attached to a surface and the other to an atomic force microscope cantilever. Moving the support stretches the molecule; a calibrated cantilever deflection measures the force through $f=k_c\delta$. The molecular extension is the imposed separation minus cantilever deflection and other instrumental offsets, rather than the uncorrected support displacement.

At first, increasing extension removes conformational slack from unstructured segments. Their conformational entropy decreases and the resisting force rises. A folded protein domain then unfolds when a thermally activated transition becomes likely under load. Its residues join the stretched chain, increasing the available polymer contour length. At almost the same imposed separation, the newly released segment has slack: the force drops. Further pulling straightens this longer chain until another domain unfolds. Repetition produces a sawtooth sequence; each rising branch mainly measures stretching between unfolding events, and a peak marks the end of such a branch.

The peak height measures the resistance to unfolding under the particular loading history, not a direct equilibrium free energy or an invariant breaking force. Random unfolding times, loading rate, domain identity, attachments, and cantilever compliance affect the record. Releasing tension can allow protein folding, but refolding has its own kinetics and need not retrace the loading curve. Distinct unfolding events explain how a long protein can absorb extension in steps rather than failing at a single threshold.

Source illustration TODO: Figures A and B are absent in the held source and archive parent. This explanation uses the surviving sawtooth description; it supplies no recovered peak heights, spacings, or domain counts.