Each titin Ig domain is a compact folded module. Under tension the chain behaves as a worm-like chain (WLC) between unfolding events — the Marko–Siggia interpolation formula:
F(x) = (kBT/p) · [ 1/4·(1−x/L)⁻² − 1/4 + x/L ]
where p ≈ 0.4 nm is the persistence length of unfolded polypeptide and L is the current contour length. As force ramps up, each folded domain has a force-dependent unfolding rate given by Bell's model:
k(F) = k₀ · exp(F·Δx‡ / kBT)
k₀ is the spontaneous (zero-force) unfolding rate and Δx‡ is the distance to the transition state along the pulling axis. Higher force sharply increases the unfolding probability per unit time — a Monte Carlo draw each frame decides whether the currently most-loaded folded domain snaps open.
- Each unfolding event releases ≈25 nm of extra contour length (the domain's folded core unravels into an extended coil) and the WLC force instantly drops, since the same extension now stretches a longer, floppier chain.
- The chain re-stiffens as extension approaches the new (longer) contour length, so force climbs again — producing the characteristic sawtooth pattern seen in real single-molecule AFM and optical-tweezer pulls of titin (Rief et al., 1997).
- Pulling speed sets how fast the cantilever base moves; faster pulls need higher force to unfold each domain in time (loading-rate dependence of Bell's model).
- ΔF‡ (force sensitivity) sets how sharply the unfolding rate rises with force — a mechanical proxy for the domain's individual stability.
Real-world relevance: this exact sawtooth signature, measured by Rief, Gaub, Fernandez and others with AFM cantilevers and optical tweezers, was the first direct proof that titin's elasticity in muscle sarcomeres comes from sequential domain unfolding rather than simple polymer stretching — and the technique now underlies single-molecule force spectroscopy of proteins genome-wide.