Length-Tension as a Filament-Overlap Contact Number

Active muscle force equals the thin/thick filament OVERLAP — the load-bearing contact number, the jamming order parameter. From cited frog filament geometry the model produces the classic length-tension curve with its plateau at 2.05–2.25 µm (cited optimum 2–2.25) and zero force near 3.625 µm (cited 3.65) [V].

Force is the length of thin filament engaged within the cross-bridge-bearing zone of the thick filament, with a double-overlap penalty on the ascending limb. Using only cited Gordon-Huxley-Julian (1966) lengths, the plateau lands at 2.05–2.25 µm and the descending limb reaches zero at 3.625 µm — the cited curve, geometry [L], peak [V].

Force is a contact number

In the jamming picture, active tension counts engaged cross-bridges, and that count is purely geometric: it is the overlap between the actin thin filament and the cross-bridge-bearing region of the myosin thick filament. Overlap is the load-bearing contact number — the same order parameter that governs every jammed contact network.

With the cited half-sarcomere geometry (thick 1.60 µm, bare zone 0.20 µm, thin 1.025 µm), the engaged overlap rises on the ascending limb, saturates across the plateau where the thin tips span the full bridge region, and falls on the descending limb as the filaments pull apart.

The cited curve, reproduced

The plateau of maximal force sits at sarcomere length 2.05–2.25 µm, matching the cited optimum 2–2.25 µm, and the descending limb crosses zero near 3.625 µm (cited 3.65 µm). A double-overlap penalty produces the short-length force drop. The geometry is cited [L]; the curve peak and intercept are verified [V].