Arrhythmogenic transient dynamics in cardiac myocytes - PubMed (original) (raw)

Arrhythmogenic transient dynamics in cardiac myocytes

Yuanfang Xie et al. Biophys J. 2014.

Abstract

Cardiac action potential alternans and early afterdepolarizations (EADs) are linked to cardiac arrhythmias. Periodic action potentials (period 1) in healthy conditions bifurcate to other states such as period 2 or chaos when alternans or EADs occur in pathological conditions. The mechanisms of alternans and EADs have been extensively studied under steady-state conditions, but lethal arrhythmias often occur during the transition between steady states. Why arrhythmias tend to develop during the transition is unclear. We used low-dimensional mathematical models to analyze dynamical mechanisms of transient alternans and EADs. We show that depending on the route from one state to another, action potential alternans and EADs may occur during the transition between two periodic steady states. The route taken depends on the time course of external perturbations or intrinsic signaling, such as β-adrenergic stimulation, which regulate cardiac calcium and potassium currents with differential kinetics.

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Figures

Figure 1

Transient APD alternans is induced by sudden, but not by gradual, application of ISO. (a and b) Protocol of ISO application and its effect on GCa (red) and GK (black) in sudden (a) and gradual (b) application. τGCa = 500 ms and τGK = 4000 ms. (c and d) APD traces and slope of APD restitution in sudden (red) and gradual (black) application of ISO at PCL 250 ms. (Insets) Voltage trace (c) and slope with its corresponding APD (d) in the case of sudden application of ISO. To see this figure in color, go online.

Figure 2

(a) Diagram of APD alternans onset in the _G_Ca-G_K parameter space. Three states were mapped in the diagram: the steady states before (1) and after (3) ISO application and the transient state at the eighth beat after sudden ISO application (2). Red and blue arrows indicate the routes of sudden and gradual application, respectively, as in Fig. 1. The dotted line is the PCL used in Fig. 1_b. (b) Bifurcation of APD before ISO (1, black), after ISO (3, blue), and in the transient state (2, red) shown in a. To see this figure in color, go online.

Figure 3

Transient EADs are induced by sudden (a), but not by gradual (b), application of ISO. The protocol of ISO application is the same as in Fig. 1. Red dots in a indicate EADs (see inset). τGCa = 1000 ms; τGK = 8000 ms; PCL = 1000 ms. To see this figure in color, go online.

Figure 4

Dynamical mechanism of EADs. (a) Steady-state I/V curve plots of ICa (red) and IK (blue). The black dotted line (V c) indicates the bifurcation for bistability. Green dots are fixed points. (b) Eigenvalue analysis of FP3 in the (V,τf) parameter space. The purple area (intersection of red (tr>0) and blue areas (Δ<0)) indicates the Hopf bifurcation (cyan dashed line). Red (small τf) and blue (large τf) arrows mark two bifurcation scenarios shown in c and d. (c and d) Mechanism of EAD illustrated by the fast ((V,f))-slow (x) subsystem analysis at small (τf =18 ms) and large τf (τf =80 ms), respectively, showing stable-focus FP3 (blue circles) and unstable-focus FP3 (red circles). (Inset) The voltage trace (green line) is mapped into the _V_-x plane, and its time course is indicated (black arrows). τx =100 ms (c) and 300 ms (d). (e and f) I/V plots corresponding to the AP plateaus in c and d, respectively, indicating the existence of bistability for EADs. Numbers 1–4 labeled with asterisks indicate the reversal points of voltage for EADs. To see this figure in color, go online.

Figure 5

Mechanism of transient EADs induced by sudden ISO application. (a) Basin of attraction for FP3 (red) decreases as x increases. Fixed point (green dot) is the intersection of V nullcline (black line) and f nullcline (red line). Plateau voltage (white line and arrows) evolves toward (at small x) or bypasses (at large x) FP3. (B) Schematic plot shows evolution route of I/V plots of ICa and IK in sudden (upper) and gradual (lower) ISO application. Green dot represents FP3. To see this figure in color, go online.

Figure 6

Attractors and trajectories in the phase space in sudden (left) and gradual (right) ISO application of Fig. 3. Green and red curves are the steady-state APs before and after ISO application, respectively. Black curves represent the transient states. To see this figure in color, go online.

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Arrhythmogenic transient dynamics in cardiac myocytes - PubMed (original) (raw)