A Mechanochemical Model for Frequency Entrainment and Bursting Transitions in Cardiac Calcium Oscillations

Rhythmic contraction of cardiomyocytes is driven by self-sustained intracellular calcium oscillations. While these oscillations are typically attributed to intrinsic calcium cycling, increasing experimental evidence indicates that external mechanical forces can modulate calcium oscillation frequency and lead to frequency entrainment. However, the physical mechanisms underlying such mechanical entrainment remain unclear. Here, we develop a minimal mechanochemical model that couples intracellular calcium cycling, adaptive ryanodine receptor (RyR) gating, and strain-induced reactive oxygen species (ROS) signaling to investigate how external mechanical forces reshape the nonlinear dynamics of autonomous calcium oscillations in cardiomyocytes. Linear stability analysis reveals that RyR inactivation is a slow adaptive variable that sets the intrinsic calcium oscillation timescale and stabilizes limit-cycle dynamics. Within this framework, external mechanical forces act as a parametric perturbation that reshapes the phase-space structure of the oscillator. We show that periodic forces induce frequency entrainment within a finite locking range, followed by a transition to a bursting-like regime as the force frequency exceeds a critical threshold. This transition boundary is further tunable by the balance between ROS production and clearance, which controls the effective sensitivity of the oscillator. These results thus establish a quantitative dynamical framework linking RyR channel kinetics to the stability and synchronization of cardiac calcium oscillations, and provide mechanistic insight into frequency-dependent mechanochemical coupling in cardiomyocytes.