Muscle contraction is cooperative. Calcium binds to regulatory sites on the thin filament (actin), exposing binding sites for the motor protein (myosin). But a single calcium binding event does more than expose one site — it increases the probability that neighboring sites also become available. The filament switches from off to on not site by site but in coordinated stretches. This cooperativity is what makes muscle contraction sharp: a small change in calcium concentration produces a large change in force. Without cooperativity, the force-calcium curve would be a gentle sigmoid. With it, the curve is steep — almost a switch.
Saadat, Caruel, Gherardini, and colleagues (arXiv:2603.03866, March 2026) show that this cooperativity is exactly the one-dimensional Ising model. Each regulatory unit on the thin filament is a spin — on or off. Calcium concentration is the external field, biasing spins toward the on state. The force exerted by an attached myosin motor modulates the coupling between neighboring spins, and this coupling is temperature-dependent. Two parameters: field strength (calcium) and coupling constant (myosin force, modified by temperature). The partition function, the correlation length, the susceptibility — all the apparatus of the Ising model — map directly onto experimental measurements of muscle activation.
The model predicts the force-calcium relationship quantitatively. It captures the cooperativity — measured by the Hill coefficient — with no free parameters beyond the two physical couplings. And it predicts the effect of a real drug: Omecamtiv Mecarbil, used clinically to treat heart failure, works through anti-cooperativity. The drug stabilizes myosin in its force-generating state, increasing the number of attached motors. But more attached motors reduce the coupling between neighboring actin sites — the force from each motor partially substitutes for the cooperative activation, and the cooperativity drops. The Hill coefficient decreases. The force-calcium curve becomes shallower. More force at low calcium, less sharp transition at high calcium. The drug works by making the muscle less like a magnet.
The mapping is not metaphor. The thin filament is a one-dimensional chain of coupled binary units in an external field. The mathematics is identical because the physics is identical: nearest-neighbor coupling in a linear chain, broken by thermal fluctuations, biased by an external field. The Ising model was not designed for muscle. Muscle is an Ising system that biology built before Ising wrote it down.
Saadat, Caruel, Gherardini, Morotti, Marcello, Caremani, Linari, Latella, and Ruffo, "Ising Models of Cooperativity in Muscle Contraction," arXiv:2603.03866 (March 2026).