Multiscale stochastic modeling for calcium dynamics in cardiac electrophysiology: assessing whole-cell model reliability under phosphorylation and LCC downregulation

Intracellular calcium (Ca²⁺) dynamics drives contractile function in cardiac myocytes. In particular, L-type Calcium Channels (LCCs) and Ryanodine Receptors (RyRs) are organized in microdomains, where LCCs trigger substantial Ca²⁺ release from the Sarcoplasmic Reticulum (SR) via RyRs. Different microdomains can be coupled at different length scales by calcium diffusion or common external activation. We present a Scalable Aggregate Calcium Release Unit (SA-CaRU) model for human ventricular myocytes that integrates a recently developed Markov Chain (MC)-based description of LCCs, replacing classical Hodgkin-Huxley gates. Our approach is based on previously published MC-based frameworks for the human heart, enabling stochastic gating and reproducing evoked local Ca²⁺ release statistics across different effective levels of microdomain aggregation. Our single-SA-CaRU system captures, within a unified framework, key features of microscale and macroscale Ca²⁺ cycling and allows, for the first time, systematic exploration of variability in SR Ca²⁺ release as a function of effective microdomain size and coupling. Simulations with increasing numbers of channels reveal that the transition from stochastic to deterministic-like Ca²⁺ behavior is typically sharp at a specific cluster size. Under normal (healthy) conditions, this occurs at $O\left(10^2\right)$ LCCs (with mild sensitivity to the RyR:LCC scaling). However, under high phosphorylation or LCC upregulation, stochasticity persists and convergence to deterministic-like behavior is absent or markedly delayed even for total LCC numbers as large as 20,000. In these conditions, whole-cell deterministic models become doubtful, since their behavior can be qualitatively different from that arising from any plausibly mediated coordination of subcellular calcium release units.