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Three-dimensional modeling of Ca2+ dynamics in single cardiac cells

M.S. Imtiaz, D.F. van Helden and D.R. Laver, School of Biomedical Sciences and Pharmacy, University of Newcastle, Callaghan, NSW 2308, Australia.

Ca2+ release from the sarcoplasmic reticulum (SR) contributes to the cardiac rhythm under resting and stimulated conditions (Lakatta et al., 2003; Imtiaz et al., 2010). We have developed a detailed three-dimensional mathematical model to study Ca2+ sparks and waves in single cardiac cells.

The fundamental building block of our three-dimensional model is a calcium cycling unit (CCU). Each CCU is composed of: 1) a ryanodine receptor (RyR) cluster - formulation of the RyR in the cluster is based on experimental data from lipid bi-layer measurements; 2) terminal SR; 3) network SR; 4) SERCA which transports Ca2+ from the bulk cytoplasm to the network SR; 5) various Ca2+ buffers in all the compartments of the CCU. Geometric dimensions and other parameter values were based on available experimental data.

A cardiac cell was formulated by defining a three dimensional bulk cytoplasmic space which also contained cytoplasmic buffers. An algorithm was developed to distribute CCUs in the three-dimensional space in required density and arrangement. The cardiac cell model could be stimulated locally and globally to study emergence of sparks, and generation and propagation of Ca2+ waves.

Our model provides the ability to incorporate experimental data characterizing RyRs during resting and stimulated conditions into detailed three dimensional simulations. This model can be used in further studies investigating role of Ca2+ in cardiac pacemaking and contraction.

Imtiaz MS, von der Weid PY, Laver DR, van Helden DF. (2010) SR Ca2+ store refill - a key factor in cardiac pacemaking. Journal of Molecular and Cellular Cardiology 49, 412-426.

Lakatta EG, Maltsev VA, Bogdanov KY, Stern MD, Vinogradova TM. (2003) Cyclic variation of intracellular calcium: a critical factor for cardiac pacemaker cell dominance. Circulation Research 92: e45-50.