Arrhythmia mechanisms and spontaneous calcium release: Bi-directional coupling between re-entrant and focal excitation
Fig 3
Derivation of the Spontaneous Release Functions.
A–Traces of open RyR (NRyR_O/NRyR) associated with 250 simulations of SCRE at different SR-Ca2+ concentrations (low = 1125 mM, purple; and high = 1200 mM, blue; 100 traces for each condition shown) in the 3D cell model. Each trace represents an individual simulation, and two simulations are highlighted for each of the two SR-Ca2+ values (note the two blue traces overlap, but are separate simulations); A(inset)–spontaneous Ca2+ transients which correspond to the four highlighted RyR traces. B–Histogram describing the initiation time for SCRE and C–the corresponding cumulative frequency plots, associated with 250 simulations of each condition. Inset–example of fitting the cumulative frequency with two sigmoidal functions (F1(ti) and F2(ti), orange and green), separated at a specific point (ti_Sep, F(ti)|ti = ti_Sep, red triangular marker). D–Examples of two types of waveform, corresponding to those highlighted in A (upper panel) and the SRF which approximate them (lower panel). Labelled are the parameters which fully describe the waveforms: the initiation time (ti), peak time (tp), final time (tf), initiation time of spike during plateau (tispike), peak open RyR (NRyR_Opeak), plateau open RyR (NRyR_Oplateau). E–Histogram illustrating the distribution of RyR waveform duration for the two conditions, with the median duration (MD) and width of distribution either side of the median (DW1, DW2) labelled for Distribution 1 (upper panel); relationship between the distribution widths and median (lower panel, points–data; lines–fit by Eqs (18 and 19)). F–Correlation between peak of open RyR and the duration, shown for the two conditions featured in the Figure (purple, blue) and all other simulations (yellow). Low amplitude SCRE occurring near the threshold SR-Ca2+ are shown in orange. Fit by Eq (12) is shown by the red line.