Muscle contraction requires activation of the thin filament — the actin strand that myosin motors grip to generate force. Activation works through calcium: calcium ions bind to troponin, which displaces tropomyosin, which exposes binding sites on actin for myosin to attach. One troponin complex regulates seven actin monomers — a single regulatory unit. The mechanism is well understood at the single-unit level.
What isn't straightforward is why activation is cooperative. A small increase in calcium concentration produces a disproportionately large increase in force. The response is steeper than any individual binding event can explain. Something along the filament amplifies the signal.
Saadat, Caruel, and collaborators (arXiv:2603.03866, March 2026) show that the cooperativity maps exactly onto a one-dimensional Ising model with two parameters. The first parameter encodes calcium concentration — the external field that biases each regulatory unit toward the active state. The second parameter encodes the coupling between neighboring units, which turns out to come from myosin itself: when a myosin motor attaches to actin, it displaces tropomyosin further than the calcium-induced shift alone, exposing binding sites in adjacent regulatory units. The motor's grip helps activate its neighbors.
The Ising model predicts that each myosin attachment activates 2-7 actin monomers beyond the 7 in its own regulatory unit. This spreading activation creates the cooperativity — a small increase in attached motors produces a cascade of additional exposed binding sites, which recruit more motors, which expose more sites. The steep calcium-force curve is a consequence of nearest-neighbor coupling propagating along a one-dimensional chain.
The model also captures something counterintuitive about the cardiac drug Omecamtiv Mecarbil. The drug increases force production in heart failure patients by stabilizing the myosin-actin interaction. The Ising model predicts this should produce anti-cooperativity: if every motor grips harder and stays attached longer, the spreading activation saturates. Each motor's contribution to its neighbors' activation becomes redundant because the neighbors are already active. More grip, less cooperativity. The drug increases total force but flattens the calcium-sensitivity curve. The model predicts both effects from the same parameter change.
Saadat, Caruel, et al., "Ising Models of Cooperativity in Muscle Contraction," arXiv:2603.03866 (March 2026).