A Cardiac Muscle Model Relating Sarcomere Dynamics to Calcium Kinetics

A muscle model establishing the link between cross-bridge dynamics and intracellular Ca2+kinetics was assessed by simulation of experiments performed in isolated cardiac muscle. The model is composed by the series arrangement of muscle units formed by inextensible thick and thin filaments in parallel with an elastic element. Attached cross-bridges act as independent force generators whose force is linearly related to the elongation of their elastic structure. Ca2+kinetics is described by a four-state system of sites on the thin filament associated with troponin C: sites with free troponin C (T), sites with Ca2+bound to troponin C (TCa); sites with Ca2+bound to troponin C and attached cross-bridges (TCa*); and sites with troponin C not associated with Ca2+and attached cross-bridges (T*). The intracellular Ca2+concentration ( [Ca2+] ) is controlled solely by the sarcoplasmic reticulum through an inflow function and a saturated outflow pump function. All the simulations were performed using the same set of parameters. The model was able to reproduce the following experiments in cardiac muscle: (a) time course of isometric force (peak force: 46.5 mN/mm2), intracellular [Ca2+] (peak [Ca2+]: 1.5μ ); (b) force–length–[Ca2+] relations; (c) transient response of force to step changes in length; (d) force–velocity relation (maximum velocity: 3μm/s); (e) the force response to length pulses to estimate the time course of [TCa]; (f ) force response to quick releases showing the superactivating and deactivating effects of shortening; (g) stiffness response to sinusoidal length changes; and (h) time course of active state. The good accordance of the simulations with experimental results indicates that the model is an adequate representation of the link between cross-bridge dyamic behaviour and Ca2+kinetics.