 Solution

An inextensible worm-like chain describes entropic elasticity and diverges as $x\to L$. Real protein backbones and folded protein domains also deform energetically under large forces. For an axial stretch modulus $K_s$, a simple extensible-chain correction isThe last term supplies extension through bond and structural deformation that the inextensible model excludes. It becomes especially noticeable on the high-force ends of rising branches.^[ref] An unfolding transition itself is also outside a single equilibrium fixed-$L$ branch. These mechanisms explain why the source explicitly distinguishes energetic and entropic elasticity.

Source-dependent TODO: the arrows and actual deviations at the first four peaks in Figure B are unavailable. Energetic stretching is the natural explanation of a high-force excess-extension deviation, but its direction, onset, and uniqueness cannot be checked against the missing curves. No particular arrow-marked feature or numerical stretch modulus is invented. This source-dependent identification remains incomplete; the recoverable model limitation is explained above.