Spider dragline silk is a semi-crystalline protein fibre: short, rigid β-sheet nanocrystals (stacked antiparallel polypeptide strands held together by hydrogen bonds) are embedded in a much longer, disordered amorphous matrix. Pulling the fibre first straightens the entropic amorphous chains; only once they are nearly taut does load reach the crystallites, whose H-bonds break one at a time as sacrificial bonds — each rupture is a tiny local failure that releases stored elastic energy as heat instead of snapping the whole fibre. This is what gives silk both high stiffness and enormous toughness.
Each amorphous segment is modelled with the interpolated worm-like chain formula (Marko–Siggia):
F(x) = (kT/Lp) · [ 1/4·(1−x/Lc)⁻² − 1/4 + x/Lc ]
where x/Lc is the extension as a fraction of the segment's contour length Lc and Lp is its persistence length (≈0.4 nm for a disordered polypeptide). Force diverges as x→Lc — the steep upturn you feel near full extension.
Each hydrogen bond ruptures stochastically under load, following the Bell–Evans dynamic force-spectroscopy model. Under a constant loading rate r, the rupture-force distribution has closed form:
F* = (kT/xβ) · ln[ 1 − (r·xβ)/(k₀·kT) · ln(1−U) ], U ~ Uniform(0,1)
with intrinsic off-rate k₀, reactive compliance xβ ≈ 0.2 nm. Each bond is assigned its own random threshold F* at reset time; whenever the instantaneous chain force exceeds it, the bond snaps. Releasing a bond frees a short length of hidden backbone (~0.5 nm) into the amorphous pool, instantly lowering the extension ratio x/Lc of that unit — the force drops even though you haven't released the slider, producing the characteristic sawtooth. Summing force × released-length over every rupture gives the dissipated (hysteresis) energy, shown in units of kT.
- Applied strain — how far the fibril is stretched, as a fraction of one repeat unit's resting length.
- H-bonds per crystallite — more bonds means more sacrificial capacity (tougher, more extensible) but rebuilds the fibril.
- H-bond strength — raises each bond's characteristic rupture force (lower intrinsic off-rate k₀).
- Temperature — softens the worm-like-chain elasticity and lowers effective bond stability, both live, matching kT's role in both formulas above.
The five repeat units shown are each pulled to the same nominal strain — a simplification of a true series arrangement, where the shared quantity would be force, not strain — but their bonds still rupture independently and stochastically, exactly the asynchronous staggering seen in real single-fibre and single-molecule silk pulling experiments. Simulated time is not real molecular kinetics: rupture is decided by comparing force to a pre-drawn threshold, not by integrating rates frame-by-frame.