We aimed to evaluate the relative role of membrane and [Ca2+]i dynamics in the formation of early afterdepolarisations (EADs). We analysed the membrane system (i.e. with all intra- and extra-cellular ionic concentrations clamped) of a Luo-Rudy ventricular cell model (LRd00; [1]) using continuation algorithms with the maximal conductance of the slow delayed rectifying K+ current (g*Ks) as the bifurcation parameter (Fig. 1a). A stable equilibrium existed at membrane potential V ≈ -88.5 mV for all g*Ks. Unstable oscillations states (OS) were found in between 0.105 < g*Ks < 0.223 mS μF−1, within the physiological range. These OS originated from a subcritical Hopf bifurcation (HB) at g*Ks ≈ 0.18 mS μF−1. Two equilibria coexisted (bistability) for g*Ks below the HB. The g*Ks of a LRd00 epi-: mid-: endocardial cells are 0.433: 0.125: 0.289 mS μF−1 [2]. The LRd00 mid-myocardial membrane model is bistable, whereas the epicardial and endocardial membrane models have a single stable equilibrium. This is confirmed by numerical integration from different initial conditions (Fig. 1b). The addition of [Ca2+]i dynamics to the mid-myocardial membrane restored the model to a single equilibrium (Fig. 1d). Action potentials and EADs in the cell model (Fig. 1c) showed similar plateau and repolarization dynamics as the transients in Fig. 1d. [Ca2+]i dynamics prevents the bistability of the mid-myocardial membrane model, and accounts for the EAD family of waveforms.
University College London 2006 (2006) Proc Physiol Soc 3, C22
Oral Communications: Intracellular calcium dynamics alters the membrane stability of a virtual ventricular mid-myocardial cell
Wing Chiu Tong1, Arun V Holden1
1. Institute of Membrane and Systems Biology, University of Leeds, Leeds, United Kingdom.
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Figure 1. (a) Bifurcation diagram of the membrane system (LRd00, clamped ionic concentrations) for g*Ks shows the membrane potential (V) at which dV/dt = 0: stable equilibria (black line) unstable equilibria (grey line) unstable periodic (grey circles) and Hopf bifurcation (HB). Stable equilibria for epicardial (triangle) mid-myocardial (black circles) and endocardial membrane (square) are indicated. (b) For the mid-myocardial membrane after 2 s at holding V V(t) converge into two stable equilibria but (d) addition of [Ca2+]i dynamics with the mid-myocardial membrane leaves one stable equilibrium. (c) Overlay of solitary action potentials in a simulated LRd00 cell with [Ca2+]i dynamics and g*Ks decreased from left to right: 0.433 0.289, 0.163 0.150 0.137 0.125 mS μF−1 show prolonged action potential duration with EADs.
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