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An inextensible freely jointed chain of $N$ links of Kuhn length $b$ has contour length $L_c=Nb$ and cannot be extended beyond it at any finite force. There is an explicit numerical contradiction in the printed parameters:The discrepancy is present in the original page, not introduced by digitization. To obtain $26\mu \mathrm{m}$ with $186$ links requires $b\simeq 140\mathrm{nm}$; to obtain it with $b=7\mathrm{nm}$ requires $N\simeq 3714$. No single inextensible FJC can satisfy all three stated numbers. The graph's much larger extension is an immediate counterexample to treating the literal $N,b$ as an accurate global fit.

Separately, accepting the graph's nominal $26\mu \mathrm{m}$ contour as an effective low-force model, its continuation to $32.7\mu \mathrm{m}$ is about $26\%$ beyond that contour. An inextensible ideal chain contains orientational entropy only; it excludes stretching of segments, energetic compliance of bonds, changes in helix structure or base pairing, and heterogeneous attachments. An extensible freely jointed chain or a semiflexible-chain model with appropriate energetic terms can describe some departures. Calibration or contour-length assignment can also be wrong. The graph alone does not identify which mechanism contributes, and its displayed moderate forces do not justify assigning a specific high-force DNA structural transition. Arithmetic inconsistency in $Nb$ is not explained away by these physical mechanisms.

The rigid-link freely jointed chain stores extension entirely in orientation. It predicts $⟨z⟩\to L=Nb$ and a divergent force as that limit is approached. Real chemical bonds and bond angles can deform, adding energetic compliance. This permits the measured chain to stretch farther at the same large force and removes the rigid-link vertical asymptote over the experimentally accessible range. Other limitations include segment correlations, solvent effects and eventual failure; a fit alone does not isolate their contributions.

Introduce one axial stretch modulus $S$ with units of force. A useful phenomenological extensible freely jointed chain law adds a linear strain contribution:Equivalently, if each aligned segment is a spring of stiffness $k_s$ in force per length, $S=b{k}_s$ and the additional extension is $Nf/k_s$. At high force, $⟨z⟩\simeq L-N{k}_{B}T/f+Lf/S$; the extra term supplies finite axial compliance. At small force, the compliances add: $d⟨z⟩/df=N{b}^2/(3k_{B}T)+L/S$.

This additive law is a simple requested one-term modification, rather than an exact angular average for harmonic links. Another common approximation is $L\mathcal{L}(fb/(k_{B}T))(1+f/S)$, which couples stretching to orientation. Neither should be extrapolated through bond rupture or claimed to predict a universal finite maximum for an extensible chain. A positive fitted $S$ could improve the high-force extension while leaving the entropic part largely intact.