Cooperative thin filament activation of a kinetic model of cardiac sarcomere dynamics

Actin-myosin crossbridges form in a sarcomere under the control of calcium ions binding to the thin filament. Crossbridges first form weak attachments before they transform into strong bonds that generate force. An appropriately simplified model of this action is critical for developing higherlevel models of cardiac function. Models can be simplified by separating slower from faster processes, where the fast processes have achieved equilibrium. Processes in equilibrium can also be analyzed using the Ising model of statistical mechanics, which allows us to study a row of cooperatively interacting units - as occurs along the thin filament. Using these concepts, the sarcomere model was simplified to 3 states: (1) strong crossbridges attached to a regulatory unit (RU) on the thin filament that had calcium bound to it; (2) strong crossbridges attached to an RU without calcium; (3) an equilibrium mixture of detached and weakly attached crossbridges with and without calcium bound. This simplified model predicted steady-state relationships between force and calcium that reproduced the experimentally seen trend toward less cooperativity as force rises to more than half maximum. It also predicted a trend for clustering of strong crossbridges along the thin filament due to cooperative interactions.