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. 2018 Nov 26;14(11):e1006382.
doi: 10.1371/journal.pcbi.1006382. eCollection 2018 Nov.

Determinants of early afterdepolarization properties in ventricular myocyte models

Affiliations

Determinants of early afterdepolarization properties in ventricular myocyte models

Xiaodong Huang et al. PLoS Comput Biol. .

Abstract

Early afterdepolarizations (EADs) are spontaneous depolarizations during the repolarization phase of an action potential in cardiac myocytes. It is widely known that EADs are promoted by increasing inward currents and/or decreasing outward currents, a condition called reduced repolarization reserve. Recent studies based on bifurcation theories show that EADs are caused by a dual Hopf-homoclinic bifurcation, bringing in further mechanistic insights into the genesis and dynamics of EADs. In this study, we investigated the EAD properties, such as the EAD amplitude, the inter-EAD interval, and the latency of the first EAD, and their major determinants. We first made predictions based on the bifurcation theory and then validated them in physiologically more detailed action potential models. These properties were investigated by varying one parameter at a time or using parameter sets randomly drawn from assigned intervals. The theoretical and simulation results were compared with experimental data from the literature. Our major findings are that the EAD amplitude and takeoff potential exhibit a negative linear correlation; the inter-EAD interval is insensitive to the maximum ionic current conductance but mainly determined by the kinetics of ICa,L and the dual Hopf-homoclinic bifurcation; and both inter-EAD interval and latency vary largely from model to model. Most of the model results generally agree with experimental observations in isolated ventricular myocytes. However, a major discrepancy between modeling results and experimental observations is that the inter-EAD intervals observed in experiments are mainly between 200 and 500 ms, irrespective of species, while those of the mathematical models exhibit a much wider range with some models exhibiting inter-EAD intervals less than 100 ms. Our simulations show that the cause of this discrepancy is likely due to the difference in ICa,L recovery properties in different mathematical models, which needs to be addressed in future action potential model development.

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Conflict of interest statement

The authors have declared that no competing interests exist.

Figures

Fig 1
Fig 1. EAD properties.
A. Definitions of AEAD, TEAD, LEAD, Vpeak, and Vtakeoff. B. Vpeak versus Vtakeoff from a short segment of sheep Purkinje fiber [1], a short segment of canine Purkinje fiber [1], and a human-induced pluripotent stem cell-derived cardiomyocyte [2]. The dashed straight lines were added as references for the slopes of the negative linear correlations of the data.
Fig 2
Fig 2. Bifurcation and EAD amplitude in the LR1 model.
A. Bifurcations in the fast subsystem when treating the slow subsystem (X) as a parameter. Q, S, and R are the three equilibria in the fast subsystem. The green bell-shaped envelope is the steady state oscillation amplitude (from Vtakeoff to Vpeak) from the Hopf bifurcation point to the homoclinic bifurcation point. The lowest possible takeoff potential is at the homoclinic bifurcation point, which is around -41.5 mV. The red trace (arrows indicate the time course) is an AP from the whole system where X is a variable. Open red circle is the resting state. Note: the bifurcations and simulations shown in this panel and panel B were done without the presence of INa. B. The steady-state oscillation period from the Hopf bifurcation point to the homoclinic bifurcation point. C. AEAD versus Vtakeoff. The parameters were randomly drawn from the assigned intervals as described in Methods. For each parameter set, the amplitudes of all EADs in the AP were included. The inset shows representative AEAD versus Vtakeoff from individual APs distinguished by colors. D. Same as C but for shifted Isi kinetics (d and f). The green data points are for d and f shifted 8 mV toward more negative voltages and the blue ones are for d and f shifted 8 mV toward more positive voltages. The inset shows the corresponding shifts. Panels A and B were replots from Tran et al [12]. The dashed straight lines in C and D are references for slopes.
Fig 3
Fig 3. Dependence of EAD amplitude on ionic currents in the LR1 model.
A. AEAD versus fold of control Gsi [labeled as α(Gsi)]. The colored arrows mark the α(Gsi) values for the traces shown in B-D: red, α = 0.658; green, α = 0.7; blue, α = 0.74; magenta, α = 0.7425; and black, α = 0.8. The numbers mark the EAD order in an AP as indicated in B-D. For example, in B, there is only one EAD in both APs, then the EAD is labeled as the 1st EAD. In C, a new EAD appears in the magenta AP, and this EAD is labelled the 2nd EAD while the old one is labeled as the 1st EAD. The number increases as more EADs appear in the AP. B. APs with one EAD as α indicated by the red and green arrows in A. C. APs in the transition from one EAD to two EADs as α indicated by the blue and magenta arrows in A. D. APs with two EADs as α indicated by the magenta and black arrows in A. E. AEAD versus fold of control GK. F. AEAD versus fold of control τd and τf. In these simulations, τd and τf are multiplied by the same α. G. AEAD versus DI. α(Gsi) = 0.95 and other parameters are their control values.
Fig 4
Fig 4. Linking the dual Hopf-homoclinic bifurcation to the EAD amplitude behavior.
A. AEAD versus fold change (α) of τX. B. APs correspond to the parameters indicated by the arrows with the same colors. Red: α = 8.24; Blue: α = 8.29; Magenta: α = 8.78. C. Bifurcation in the fast subsystem, the same as in Fig 2A except that INa was present. The blue and red traces are V versus X for the corresponding blue and red APs in B. Inset is the blowup of the EAD window. D. Same as C but for the blue and magenta APs in B. Open arrows in the inset mark the takeoff location of the 5th EAD with respect to the homoclinic bifurcation point. Note that both APs exhibit 5 EADs but the ones in the magenta AP take off at smaller X values.
Fig 5
Fig 5. AEAD versus Vtakeoff in the physiologically more detailed models.
A. LRd. B. HUCLA. C. TP04. D. ORd. E. GB. Parameters were randomly drawn from assigned intervals (as described in Methods). AEAD was measured for all EADs in an AP. Black dots are AEAD for control steady-state activation and inactivation curves of ICa,L; blue dots are for both curves being shifted toward negative voltage; and green dots are for both curves being shifted toward more positive voltages. The voltage shifts are indicated by the open arrows in each panel in the same way as in Fig 2D. Dashed lines are reference lines for the slopes.
Fig 6
Fig 6. Theoretical predictions and simulation results of TEAD using the LR1 model.
A. TEAD versus Gsi. The numbers mark the order of TEAD as defined in B. B. AP traces for Gsi indicated by the two arrows in A with two EADs and one TEAD in the green AP (α = 0.741) while four EADs and three TEAD in the blue AP (α = 0.9). C. TEAD versus GK. D. TEAD versus GK1. E. TEAD versus τf. F. Histogram of TEAD obtained from a large number of simulations using randomly selected parameter sets and all TEAD in an AP. Control τf (α = 1) was used. The total number of TEAD is 13317 in the histogram.
Fig 7
Fig 7. Dependence of TEAD on maximum conductance and kinetics of ionic currents in different models.
A. LRd. B. HUCLA. C. TP04. D. ORd. E. GB. Only the first TEAD (the interval between the first and the second EAD) are plotted. One parameter (indicated by color) was changed while the others were set at their control values.
Fig 8
Fig 8. Distributions of TEAD in different models.
A. LRd. B. HUCLA. D. TP04. E. ORd. F. GB. In these distributions, the ionic conductance (see SI for the specific ones for each model) were randomly drawn from the assigned intervals. C. τf versus V in the original LRd (black) and the modified one (red). The same τf was used in the HUCLA model as in the LRd model.
Fig 9
Fig 9. Dependence of EAD latency on ionic current conductance in different AP models.
A. LR1. B. LRd. C. HUCLA. D. TP04. E. ORd. F. GB. One parameter (indicated by color) was changed while the others were set as their control values.
Fig 10
Fig 10. Distributions of TEAD in different models.
A. LR1. B. LRd. C. HUCLA. D. TP04. E. ORd. F. GB. In these distributions, the ionic conductance (see SI for the specific ones for each model) were randomly drawn from the assigned intervals.

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