Sarcomere Cross-Bridge Kinetics (2D)

This 2D companion to the 3D myofibril model replaces its length-tension lookup table with a real, numerically-integrated kinetic engine: A.F. Huxley's 1957 two-state cross-bridge model, tracking a population of myosin heads across a range of elastic strain states and advancing their attachment/detachment probabilities with an operator-split ODE solver every frame. Sarcomere length still sets filament overlap, but overlap here is derived from filament geometry with two extra interference terms — double thin-filament overlap and Z-disc jamming — that a simple zone-intersection integral misses. A Ca²⁺ slider gates cross-bridge attachment through a cooperative Hill-equation activation curve, and a new shortening-velocity control lets the same kinetic engine reproduce Hill's classic hyperbolic force-velocity relationship, a dimension the 3D original does not model at all.