= Solution
In <spectrin unfolding by force spectroscopy>, the <cantilever> measures <Tension>[tension] through its calibrated deflection, while <displacement> of the pulling point increases the separation of the <protein> attachments. The <protein> extension is obtained after allowing for <cantilever> compliance and any linker extension; it is not simply the commanded <displacement>.
A folded <spectrin> repeat stores much of its backbone in a compact domain. Between <Protein denaturation>[unfolding] events, the already released chain is stretched: increasingly straight conformations have fewer accessible configurations, and the resisting <entropic force> rises nonlinearly. A peak is reached when a still-folded domain crosses an <Protein denaturation>[unfolding] barrier on the timescale of the imposed loading. Its released backbone increases the available <Polymer contour length>[contour length] abruptly. At nearly the same end-to-end distance the fractional extension $x/L$ is then smaller, so <Tension>[tension] drops. Pulling resumes on the next, longer-chain elastic branch. Repeated release of domains produces the saw-tooth sequence.
The record is therefore evidence for sequential mechanical <Protein denaturation>[unfolding] of modular structure, not repeated stretching of a fixed-length rod. For the nominal eight-domain construct, successive branches correspond to increasing numbers of unfolded repeats. The order and rupture <Force>[forces] can fluctuate because barrier crossing is thermally activated and depends on loading rate, structural heterogeneity and pulling geometry; equivalent repeats need not rupture at identical <force>.
The horizontal separation between worm-like-chain fits at the same <force> estimates the added <Polymer contour length>[contour length], whereas the vertical <force> drop at one extension reflects redistribution of <Tension>[tension]. These are distinct measurements. A repeat increment near the specified $31.7\,\mathrm{nm}$ is consistent with repeated similar structural units. The gain is a net release relative to the folded span and attachment geometry; $31.7/106\,\mathrm{nm}$ is not automatically the universal <Polymer contour length>[contour length] of a <peptide> residue.
During unloading, relaxation and possible refolding can restore compact domains. <Hysteresis> would indicate dissipative or kinetically delayed processes. Neither the peak <force> alone nor an arbitrary saw-tooth area directly equals an equilibrium <Protein denaturation>[unfolding] <Gibbs free energy>[free energy]: one must separate chain <Elasticity (physics)>[elasticity], <cantilever> storage, irreversible loss and pulling-rate effects. The worm-like-chain branches describe released-chain <Elasticity (physics)>[elasticity], not the molecular transition state responsible for a rupture peak.
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