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 and frees hidden chain length 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 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 running force exceeds it, the bond snaps, freeing ~0.5 nm of hidden backbone into the amorphous pool and instantly lowering x/Lc — the force drops even though the strain keeps rising, producing the sawtooth. Five repeat units are pulled to the same nominal strain (the same simplification used by this simulator's 3D twin — a true series arrangement shares force, not strain — but each unit's bonds still rupture independently and stochastically).
Once every sacrificial bond in a unit has ruptured, further strain has nowhere left to go but the covalent backbone itself. This simulator applies a single shared backbone/crystallite failure force (500 pN) to both chains: the first unit whose fully-exhausted backbone reaches it ends the whole fibril, exactly as the weakest link in a series chain would. The control chain has the identical worm-like-chain elasticity and the identical backbone failure force, but no sacrificial bonds to rupture first — its fixed contour length reaches the same backbone force at a much lower strain, and with none of the intervening plateaus that let the real fibril keep absorbing energy. Toughness is the trapezoidal area under each force–strain curve, in pN·nm, up to that curve's own failure point — a direct, computed measure of how much mechanical energy each chain absorbs before it breaks.
- Applied strain — how far the fibril is stretched, as a fraction of one repeat unit's resting length. "Pull to failure" ramps it automatically and stops at the first backbone rupture.
- H-bonds per crystallite — more bonds means more sacrificial capacity (tougher, more extensible) but rebuilds the fibril and resamples every threshold.
- 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.
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 — the same approach used by this simulator's 3D twin, so the two stay physically consistent with each other.