Analysing cardiac excitation-contraction coupling with mathematical models of local control.

Cardiac excitation-contraction (E-C) coupling describes the process that links sarcolemmal Ca2+ influx via L-type Ca2+ channels to Ca2+ release from the sarcoplasmic reticulum via ryanodine receptors (RyRs). This process has proven difficult to study experimentally, and complete descriptions of how the cell couples surface membrane and intracellular signal transduction proteins to achieve both stable and sensitive intracellular calcium release are still lacking. Mathematical models provide a framework to test our understanding of how this is achieved. While no single model is yet capable of describing all features of cardiac E-C coupling, models of increasing complexity are revealing unexpected subtlety in the process. In particular, modelling has established a general failure of 'common-pool' models and has emphasized the requirement for 'local control' so that microscopic sub-cellular domains can separate local behaviour from the whole-cell average (common-pool) behaviour. The micro-architecture of the narrow diadic cleft in which the local control takes place is a key factor in determining local Ca2+ dynamics. There is still considerable uncertainty about the number of Ca2+ ions required to open RyRs within the cleft and various gating models have been proposed, many of which are in reasonable agreement with available experimental data. However, not all models exhibit a realistic voltage dependence of E-C coupling gain. Furthermore, it is unclear which model features are essential to producing reasonable gain properties. Thus, despite the success of local-control models in explaining many features of cardiac E-C coupling, more work will be needed to provide a sound theoretical basis of cardiac E-C coupling.