Calcium homeostasis in a local/global whole cell model of permeabilized ventricular myocytes with a Langevin description of stochastic calcium release

Population density approaches to modeling local control of Ca²⁺- induced Ca²⁺ release in cardiac myocytes can be used to construct minimal whole cell models that accurately represent heterogeneous local Ca²⁺ signals. Unfortunately, the computational complexity of such “local/global” whole cell models scales with the number of Ca²⁺ release unit (CaRU) states, which is a rapidly increasing function of the number of ryanodine receptors (RyRs) per CaRU. Here we present an alternative approach based on a Langevin description of the collective gating of RyRs coupled by local Ca²⁺ concentration ([Ca²⁺]). The computational efficiency of this approach no longer depends on the number of RyRs per CaRU. When the RyR model is minimal, Langevin equations may be replaced by a single Fokker- Planck equation, yielding an extremely compact and efficient local/ global whole cell model that reproduces and helps interpret recent experiments that investigate Ca²⁺ homeostasis in permeabilized ventricular myocytes. Our calculations show that elevated myoplasmic [Ca²⁺] promotes elevated network sarcoplasmic reticulum (SR) [Ca²⁺] via SR Ca²⁺-ATPase-mediated Ca²⁺ uptake. However, elevated myoplasmic [Ca²⁺] may also activate RyRs and promote stochastic SR Ca²⁺ release, which can in turn decrease SR [Ca²⁺]. Increasing myoplasmic [Ca²⁺] results in an exponential increase in spark-mediated release and a linear increase in nonspark-mediated release, consistent with recent experiments. The model exhibits two steady-state release fluxes for the same network SR [Ca²⁺] depending on whether myoplasmic [Ca²⁺] is low or high. In the later case, spontaneous release decreases SR [Ca²⁺] in a manner that maintains robust Ca²⁺ sparks.