Mitochondrial depolarization promotes calcium alternans: Mechanistic insights from a ventricular myocyte model

Vikas Pandey; Lai-Hua Xie; Zhilin Qu; Zhen Song

doi:10.1371/journal.pcbi.1008624

Abstract

Mitochondria are vital organelles inside the cell and contribute to intracellular calcium (Ca²⁺) dynamics directly and indirectly via calcium exchange, ATP generation, and production of reactive oxygen species (ROS). Arrhythmogenic Ca²⁺ alternans in cardiac myocytes has been observed in experiments under abnormal mitochondrial depolarization. However, complex signaling pathways and Ca²⁺ cycling between mitochondria and cytosol make it difficult in experiments to reveal the underlying mechanisms of Ca²⁺ alternans under abnormal mitochondrial depolarization. In this study, we use a newly developed spatiotemporal ventricular myocyte computer model that integrates mitochondrial Ca²⁺ cycling and complex signaling pathways to investigate the mechanisms of Ca²⁺ alternans during mitochondrial depolarization. We find that elevation of ROS in response to mitochondrial depolarization plays a critical role in promoting Ca²⁺ alternans. Further examination reveals that the redox effect of ROS on ryanodine receptors and sarco/endoplasmic reticulum Ca²⁺-ATPase synergistically promote alternans. Upregulation of mitochondrial Ca²⁺ uniporter promotes Ca²⁺ alternans via Ca²⁺-dependent mitochondrial permeability transition pore opening. Due to their relatively slow kinetics, oxidized Ca²⁺/calmodulin-dependent protein kinase II activation and ATP do not play significant roles acutely in the genesis of Ca²⁺ alternans after mitochondrial depolarization, but their roles can be significant in the long term, mainly through their effects on sarco/endoplasmic reticulum Ca²⁺-ATPase activity. In conclusion, mitochondrial depolarization promotes Ca²⁺ alternans acutely via the redox effect of ROS and chronically by ATP reduction. It suppresses Ca²⁺ alternans chronically through oxidized Ca²⁺/calmodulin-dependent protein kinase II activation.

Author summary

Mitochondrial dysfunction has been implicated in life-threatening cardiac arrhythmias. Experimentalists have shown that mitochondrial depolarization could cause period-doubling behavior in cytosolic Ca²⁺ transient (i.e., Ca²⁺ alternans). However, the underlying mechanisms behind these experimental observations remain unclear. Here, we focus on revealing the underlying mechanisms of cellular Ca²⁺ alternans in the context of mitochondrial depolarization. Using our newly developed action potential model that incorporates a 3D network of Ca²⁺ release unit with a 3D network of mitochondria, we dissect out individual roles of mitochondrial Ca²⁺ and complex signaling pathways (e.g., reactive oxygen species, oxidized Ca²⁺/calmodulin-dependent protein kinase II activation, and ATP) in the genesis of cellular Ca²⁺ alternans. The key finding is that mitochondrial depolarization promotes Ca²⁺ alternans acutely via the redox effect of ROS and chronically by ATP reduction, and oxidized Ca²⁺/calmodulin-dependent protein kinase II activation may suppress Ca²⁺ alternans chronically. We believe that this study reveals insightful information for understanding the mechanisms of the genesis of Ca²⁺ alternans in the context of mitochondrial depolarization and provides valuable simulation results to guide future experiments.

Citation: Pandey V, Xie L-H, Qu Z, Song Z (2021) Mitochondrial depolarization promotes calcium alternans: Mechanistic insights from a ventricular myocyte model. PLoS Comput Biol 17(1): e1008624. https://doi.org/10.1371/journal.pcbi.1008624

Editor: Daniel A. Beard, University of Michigan, UNITED STATES

Received: August 18, 2020; Accepted: December 10, 2020; Published: January 25, 2021

Copyright: © 2021 Pandey et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: All relevant data are within the manuscript and its Supporting Information files.

Funding: ZQ receives R01 HL134709 from National Institutes of Health. ZQ and LHX receive R01 HL133294 from National Institutes of Health. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: The authors have declared that no competing interests exist.

Introduction

Calcium (Ca²⁺) is a critical regulator of excitation-contraction coupling in cardiac myocytes [1]. Ca²⁺ enters a cardiac myocyte mostly through the L-type Ca²⁺ channels (LCCs), which open in response to membrane depolarization. The resulting rise in the intracellular Ca²⁺ concentration activates ryanodine receptors (RyRs) to release a large amount of Ca²⁺ from the sarcoplasmic reticulum (SR), an internal Ca²⁺ store in cardiac myocytes. RyRs are clustered on the membrane of SR, forming discrete Ca²⁺ release units (CRUs). The SR Ca²⁺ release causes a transient increase in cytosolic Ca²⁺, which binds to myofilament to cause contraction. Ca²⁺ in the cytosol is extruded outside the cell via Na⁺-Ca²⁺ exchangers (NCX) and transported back to the SR through the sarco/endoplasmic reticulum Ca²⁺-ATPase (SERCA) pump. The normal Ca²⁺ cycling is essential to maintain the normal function of excitation-contraction coupling due to the bi-directional coupling through nonlinear interactions of ion channels, transporters, and pumps. Disturbances in the complex regulations of these components of the cell can lead to various nonlinear dynamics that underlie life-threatening cardiac arrhythmias [2]. Ca²⁺ alternans is one of the most studied phenomena for cardiac arrhythmias. Ca²⁺ alternans can cause action potential duration (APD) alternans due to the bi-directional coupling of the membrane voltage and Ca²⁺ [2,3]. Ca²⁺ and APD alternans are known to occur in acute myocardial ischemia and other diseased conditions [4–9]. APD alternans gives rise to T-wave alternans, which is a risk marker for sudden cardiac death [10,11]. Besides SR, mitochondria are also internal Ca²⁺ stores, and Ca²⁺ enters into and moves out of the mitochondria during a cardiac cycle, directly affecting intracellular Ca²⁺ signaling [8,12–17]. Moreover, mitochondria produce ATP and reactive oxygen species (ROS), which affect Ca²⁺ dynamics via their effects on the Ca²⁺ cycling proteins. Recent studies have shown that mitochondrial Ca²⁺ cycling plays a key role in cardiac diseases [18–22]. The goal of this work is to investigate mitochondrial contributions to the genesis of Ca²⁺ alternans.

Experimental studies have shown that metabolic stress or impaired mitochondrial function promotes Ca²⁺ alternans [14,23–26]. However, the complex effects of mitochondria on Ca²⁺ cycling, energy metabolism, and signaling make it difficult to dissect out the underlying mechanisms in experiments. Ca²⁺ enters mitochondria via the mitochondrial Ca²⁺ uniporter (MCU) [27,28], and exits mitochondria via mitochondrial sodium-calcium exchanger (mNCX) [29] or the mitochondrial permeability transition pore (mPTP). The mPTP open probability is very low under normal conditions but can be high under pathophysiological conditions. In addition to the direct mitochondrial Ca²⁺ cycling, mitochondria are coupled with intracellular Ca²⁺ cycling in several other ways. ROS signaling and the redox regulation affect the opening of RyRs and the activity of the SERCA pump [30,31]. Mitochondria provide ATP to the SERCA pump and other sarcolemmal ion pumps, and a shortage of ATP may impair the function of these pumps [32,33]. Moreover, there is a positive feedback loop between mitochondrial ROS production and SR Ca²⁺ release, i.e., leaky RyRs trigger more Ca²⁺ release resulting in more Ca²⁺ sequestered in mitochondria, which can trigger the opening of mPTP, leading to mitochondria depolarizations [34,35]. Mitochondrial depolarization produces ROS, which regulates SR Ca²⁺ uptake and release. The oxidized Ca²⁺/calmodulin-dependent protein kinase II (CaMKII) activation enhances the sensitivity of the SERCA pump through phosphorylation of phospholamban [36]. Concurrently, CaMKII also affects the activation of LCCs [37].

Therefore, mitochondria play complex roles in intracellular Ca²⁺ cycling via different pathways. These pathways can either promote or suppress alternans depending on their properties [38,39], making it very difficult to experimentally dissect out the key pathways responsible for alternans. We recently developed a physiologically detailed ventricular myocyte model that incorporated mitochondrial Ca²⁺ cycling, mPTP, ROS production, and oxidized CaMKII signaling [40]. We showed that this model could exhibit Ca²⁺ alternans and spontaneous Ca²⁺ release mediated delayed afterdepolarizations (DADs) under mitochondrial depolarization. In the present study, we use computer simulations of this model to investigate the underlying mechanisms for the genesis of Ca²⁺ alternans in response to mitochondrial depolarization induced by mPTP opening. Taking advantage of computer simulations, we can differentiate the effects of direct mitochondrial Ca²⁺ cycling, the redox regulation of RyRs and SERCA by ROS, oxidized CaMKII signaling, and ATP reduction on Ca²⁺ alternans. We demonstrate that mitochondrial depolarization promotes Ca²⁺ alternans acutely via the redox effect of ROS and chronically by ATP reduction, and may suppress Ca²⁺ alternans chronically by oxidized signaling, mainly via their effects on SERCA activity.

Results

Ca²⁺ alternans caused by mitochondrial depolarization due to mPTP opening

To show the effects of mPTP opening on Ca²⁺ alternans, we carried out simulations under the control condition (where the mPTP open probability is very low) and a high mPTP open probability condition (by increasing the transition rate from the closed state, C₁, to the open state, O, to 60-fold of the control value, i.e., α_mPTP = 60) for PCL = 500 ms (Fig 1A). Under the control condition (black lines), no alternans occurred. Under the condition of high mPTP open probability (red lines), Ca²⁺ alternans occurred. And the Ca²⁺ alternans was abolished when all the mPTPs within the cell were commanded to be in the closed state, which also recovered Δψ (S1 Fig). These observations were consistent with our previous experimental results using either mPTP inhibitor or cyclophilin D knockout mouse model [41] in which mitochondrial depolarization was prevented. Note that the corresponding APD alternans appears small (see the enlarged one in S2A Fig), since the Ca²⁺ alternans amplitude is small (~0.2 μM) at PCL = 500 ms. At a faster pacing rate (PCL = 300 ms), the APD alternans becomes more significant due to greater Ca²⁺ alternans amplitude (S2B Fig). Note that for this α_mPTP value, the open probability of mPTP was about 30%. Also, note that at t = 30 s CaMKII activity and cytosolic ATP are still changing slowly. When we ran the simulations for a much longer time (e.g., 1000 s), the CaMKII activity and the cytosolic ATP became ~74% and ~2 mM, respectively. Since these two variables change extremely slowly over time, we treated them as quasi-steady state variables for the half-minute long simulation. For the same reason, we investigated the acute effect of mitochondrial depolarization on the genesis of Ca²⁺alternans in this study by performing free-running simulations for 30 s. Fig 1B shows a bifurcation diagram plotting the peak values of cytosolic Ca²⁺ transient against the pacing cycle length (PCL) for both conditions. The high mPTP open probability condition changed the onset of Ca²⁺ alternans to a longer PCL, from 450 ms to 550 ms.

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Fig 1. Mitochondrial depolarization promotes Ca²⁺ alternans.

A. Time traces of membrane potential V, whole-cell averaged cytosolic Ca²⁺ concentration , SR Ca²⁺concentration , SERCA uptake flux, SR Ca²⁺ release flux via RyRs, mitochondrial free Ca²⁺ , open probability of mPTP , mitochondrial membrane potential , cytosolic ROS concentration , cytosolic CaMKII activation , cytosolic ATP concentration for normal control (α_mPTP = 1) in black and mitochondrial depolarization (α_mPTP = 60) conditions in red, respectively. PCL is 500 ms. Note that the horizontal bar above each variable means that the quantity is an averaged value over all the CRUs or mitochondria within the myocyte. B. Bifurcation diagrams of peak values of in the last two consecutive beats vs. PCL for control (black) and mitochondrial-depolarization (red) cases.

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Since mPTP opening and mitochondrial depolarization can affect the intracellular Ca²⁺ dynamics directly or indirectly via changing the properties of Ca²⁺ handling proteins (e.g., RyRs and SERCA) or altering CaMKII and other signaling pathways [30,31], it becomes difficult to reveal the roles of each process experimentally. In the following sections, we take advantage of computer simulation to examine the individual roles of cytosolic ROS, mitochondrial Ca²⁺, CaMKII activation, and cytosolic ATP in the genesis of Ca²⁺ alternans.

Effects of ROS on the genesis of Ca²⁺ alternans

To determine the effect of ROS on Ca²⁺ alternans, we carried out simulations in the conditions of the free-running ROS (i.e., the ROS dynamics obeys the differential equations) and a clamped ROS (i.e., the ROS was fixed to a constant) at PCL = 500 ms, shown in Fig 2A as bifurcation diagrams. Under the free-running case, increasing α_mPTP above certain threshold promotes alternans, but when ROS was clamped at a low level (0.1 μM), no alternans occurs. Therefore, our simulation results here suggest that Ca²⁺ alternans was predominantly mediated by the cytosolic ROS. Also, note that increasing α_mPTP increases the open probability of mPTP, and under the setting of the free-running ROS, we found that Ca²⁺ alternans became obvious when the open probability of mPTP is above ~20% (S3 Fig).

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Fig 2. Effect of cytosolic ROS signaling on the genesis of Ca²⁺ alternans.

A. Bifurcation diagram of peak values of Ca²⁺ transients vs. α_mPTP for free-running ROS (black) and fixed ROS = 0.1 μM (red), respectively. B. Bifurcation diagram of peak values of Ca²⁺ transient vs. α_mPTP with free-running ROS, but the redox effect of ROS only exerted on RyRs (green) or SERCA (blue), respectively. The PCL is 500 ms. The total simulation time for each simulation is 30 sec.

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To further dissect out how ROS promotes Ca²⁺ alternans, we first investigate its redox effect on RyRs and SERCA separately. Fig 2B shows the bifurcation diagrams for the redox effect of ROS on RyRs only (green, by setting f_up,ros = 1 in Eq 5) or for the redox effect of ROS on SERCA only (blue, by setting Δk_ros = 0 in Eq 2). We then performed the same simulations as in Fig 2A for these two cases (Fig 2B). When the redox effect on SERCA was removed, the amplitude of Ca²⁺ alternans was greatly reduced (Fig 2B, green). When the redox effect on RyRs was removed, the amplitude of Ca²⁺ alternans was also decreased (Fig 2B, blue) compared to the case of free-running ROS (Fig 2A, black). Note that the onsets of alternans for these two cases are about the same as in the case of free-running ROS (Fig 2A, black). These results suggest that the redox effect of ROS on RyRs and SERCA synergistically promotes Ca²⁺ alternans.

Effects of mitochondrial Ca²⁺ on the genesis of Ca²⁺ alternans

Under certain pathological conditions, such as nonischemic cardiomyopathy, MCU has been reported to dramatically upregulated [17], which may markedly increase the mitochondrial free Ca²⁺. Although our previous simulation study [40] has shown that the release of mitochondrial Ca²⁺ to the cytosol may only transiently affect the cytosolic Ca²⁺, the elevation of mitochondrial free Ca²⁺ is believed to promote the opening of mPTP and thus the production of ROS. Here we performed simulations to investigate how the MCU activity affects the genesis of Ca²⁺ alternans. For simplicity, we multiplied a pre-factor, α_MCU, to the maximal MCU conductance. Therefore, α_MCU = 1 represents the control MCU conductance and increasing α_MCU increases the maximal MCU activity. Fig 3 shows the dependence of Ca²⁺ alternans amplitude on α_MCU and α_mPTP. When the close-to-open rate of mPTP is low (α_mPTP<20), no Ca²⁺ alternans occurs even if the maximal MCU activity is increased to 50-fold (α_MCU = 50). However, as mPTP open probability increases (i.e., as α_mPTP increases), the value of α_MCU required to generate Ca²⁺ alternans decreases. Furthermore, when the close-to-open rate of mPTP further increases (α_mPTP>80), the effect of α_MCU on the genesis of Ca²⁺ alternans becomes less important. In addition, we found that inhibition of either MCU or mNCX in the setting of these simulations was unable to abolish Ca²⁺ alternans (S4 Fig). In conclusion, these results suggest that MCU upregulation may play an important role in generating Ca²⁺ alternans through mitochondrial Ca²⁺ mediated mPTP opening under certain pathological conditions.

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Fig 3. MCU upregulation promotes Ca²⁺ alternans through Ca²⁺- dependent opening of mPTP.

Dependence of Ca²⁺ alternan amplitude on α_MCU and α_mPTP. is calculated as the difference between the last two Ca²⁺ transient peaks in a simulation of 30 sec. PCL = 500 ms.

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Effects of oxidized CaMKII signaling on Ca²⁺ alternans

Since mitochondrial depolarization activates oxidized CaMKII signaling via ROS, we then evaluate the importance of CaMKII activation in the genesis of Ca²⁺ alternans during mitochondrial depolarization. As discussed earlier, CaMKII activation dynamics is a very slow process in the model and thus it can be treated as a quasi-steady state variable. Therefore, we clamped the CaMKII activation at different levels and examined the corresponding effects on the genesis of Ca²⁺ alternans. Fig 4 shows the bifurcation diagrams of the peak values of cytosolic Ca²⁺ transient against α_mPTP for CaMKII activity clamped at 1%, 10%, and 30% levels. These results show that Ca²⁺ alternans is suppressed as the CaMKII activation level increases. However, as shown in Fig 1A, the CaMKII activation level is about 1% for both control and the high mPTP open probability conditions within the 30 sec total simulation time. Therefore, our simulation results suggest that for the acute effect of mitochondrial depolarization on the genesis of Ca²⁺ alternans, CaMKII may not exhibit a big effect. However, for the long-term effect, CaMKII may play a more significant role, suppressing Ca²⁺ alternans via its regulation of SERCA.

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Fig 4. Effect of CaMKII activation on the genesis of the Ca²⁺ alternans.

Bifurcation diagrams of peak values of Ca²⁺ transients in the last two beats vs. α_mPTP for clamped CaMKII activation level 1% (A), 10% (B) and 30% (C), respectively. PCL = 500 ms.

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Effects of ATP depletion on Ca²⁺ alternans due to mitochondrial depolarization

When a mitochondrion depolarizes, it stops producing ATP, and as more mitochondria depolarize in the cell due to the increased mPTP open probability, the cytosolic ATP decreases. Since ATP is required for the SERCA pump, a low ATP level could impair the SERCA activity to promote Ca²⁺ alternans. As shown in Fig 1A, in our model, the cytosolic ATP level decays very slowly during mitochondrial depolarization. Similar to what we did for CaMKII, we clamped the cytosolic ATP concentration to different values and examined the consequences of ATP depletion during mitochondrial depolarization on the genesis of Ca²⁺ alternans.

Fig 5 shows the bifurcation diagram of the peak values of Ca²⁺ transient vs. the clamped cytosolic ATP concentration. The result shows that reducing the cytosolic ATP concentration promotes Ca²⁺ alternans during mitochondrial depolarization (α_mPTP = 30). This result suggests that the cytosolic ATP indeed has a great impact on the genesis of Ca²⁺ alternans. However, considering its slow decay during the process of mitochondrial depolarization, ATP may not play a central role in inducing Ca²⁺ alternans at least at the scale of sub-minute evolution. Therefore, similar to CaMKII, during mitochondrial depolarization, ATP may not exhibit a significant effect on the genesis of Ca²⁺ alternans acutely, but may promote alternans in a much longer time scale when the cytosolic ATP level reduces dramatically to impair the SERCA activity.

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Fig 5. Effect of ATP on the genesis of Ca²⁺ alternans.

Bifurcation diagrams of peak values of Ca²⁺ transients in the last two beats vs. clamped whole-cell average ATP level in the cytosol. α_mPTP = 30. The PCL = 500 ms.

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Discussion

In this study, we used a physiologically-detailed ventricular myocyte model consisting of a 3D network of coupled CRUs and mitochondria to investigate the roles of mitochondrial depolarization via mPTP opening in the genesis of Ca²⁺ alternans. We showed that the effects of mitochondrial depolarization on Ca²⁺ alternans mainly via the ROS induced redox regulation of SERCA and RyRs. ROS induced oxidized CaMKII signaling and ATP decay exhibit little effect acutely but can exhibit large effects chronically via their regulations of SERCA. Mitochondrial Ca²⁺ cycling alone exhibits little effect on Ca²⁺ alternans but can exhibit a large effect via the Ca²⁺-dependent opening of mPTP.

Role of ROS in the genesis of Ca²⁺ alternans

We have shown that an increase in the cytosolic ROS concentration in response to mitochondrial depolarization plays a key role in generating Ca²⁺ alternans. By judicious manipulation of the redox effects of ROS on RyRs and SERCA, we have been able to demonstrate that there is a synergy effect of the ROS redox regulation on both SERCA and RyRs in generating Ca²⁺ alternans. Our results show that only enhancing the RyR activity (Fig 2B, green) or reducing SERCA pump ability (Fig 2B, blue) via the ROS redox regulation causes a much smaller amplitude of Ca²⁺ alternans compared to the case where the ROS redox regulation effect is turned on for both RyRs and SERCA (Fig 2A, black). A previous study by Belevych et al. [23] has shown that an increase in ROS increases the RyR open probability, producing leaky RyR channels, and in turn resulting in Ca²⁺ alternans. Our findings here extend those of Belevych et al. [23], suggesting that the ROS redox regulation on SERCA is also crucial for promoting Ca²⁺ alternans. In fact, these findings well agree with the unified alternans theory developed in our previous study [42], since either hyperactivating RyRs or reducing the SERCA pump ability contributes to the increased steepness of the SR release-load relationship in cardiac myocytes, and therefore it is not surprising that the combined effect of the two factors synergistically promotes Ca²⁺ alternans.

Besides the redox effect, ROS is known to activate CaMKII, PKA and PKC pathways [30,31], which could affect the genesis of Ca²⁺ alternans. The model used in this study takes into account the effect of ROS on the activation of CaMKII by incorporating the oxidized CaMKII signaling formulation developed by Foteinou et al. [37]. The effect of CaMKII activation on Ca²⁺ handling proteins and ion channels has been simulated here following Hund and Rudy [36]. However, the kinetics of CaMKII appears to be very slow as seen in Fig 1A, since the percentage of CaMKII activation merely changes from 0.4% to 1.2%, whereas the mPTP open probability increases from ~0% to ~32% in response to the mitochondrial depolarization. These results therefore indicate that in the case of acute and severe metabolic insults, CaMKII activation may not be the cause of the genesis of Ca²⁺ alternans. In fact, our simulations of clamping CaMKII activation to different levels even suggest that higher CaMKII activation tends to suppress Ca²⁺ alternans (Fig 4) due to CaMKII phosphorylation of phospholamban, which reduces the half-maximal value of SERCA to increase SERCA pump activity. This agrees with our previous theoretical prediction that increasing SERCA pump activity can move the cell system out of the alternans regime [42]. However, that does not mean oxidized CaMKII activation during mitochondrial depolarization is beneficial, since CaMKII activation enhances LCC, RyRs and SERCA, which are known factors promoting arrhythmogenic Ca²⁺ waves, DADs and EADs [43–45].

Clinically, ischemia/reperfusion injury of myocardium is associated with both mitochondrial depolarization and repolarization phases. During the repolarization phase, Ca²⁺ homeostasis is disrupted, which is believed via opening of mPTP because of high ROS and mitochondrial Ca²⁺ accumulation [46–48]. However, some experiment showed that sustained depolarization of mitochondrial membrane potential did not occur even after 10 min of reperfusion [48], which requires more comprehensive future studies to explain. Nevertheless, our simulations suggest that ROS is the main factor for mitochondrial depolarization induced Ca²⁺ alternans, and targeting mPTP or ROS may prevent Ca²⁺ alternans in acute myocardial ischemia.

Mitochondrial Ca²⁺ cycling and intracellular Ca²⁺ alternans

We have shown that MCU upregulation combined with the increased C₁-to-O transition rate of mPTP gating kinetics promotes Ca²⁺ alternans (Fig 3). In our previous study [40], we found that mitochondrial Ca²⁺ released into the cytosol due to severe mitochondrial depolarization (100%) can only transiently change the cytosolic Ca²⁺ dynamics, but not the steady state. Therefore, our findings here indicate that mitochondrial Ca²⁺ may not directly affect the intracellular Ca²⁺ homeostasis, but it can enhance mPTP opening, which in turn causes Ca²⁺ alternans via ROS induced signaling pathways or lowering ATP. However, in nonischemic cardiomyopathy, MCU upregulation, together with other electrophysiological remodeling changes in heart failure conditions, can result in an all-or-none behavior or bistability, corresponding to the no EAD and EAD states in AP without mitochondrial depolarization [17]. Furthermore, the Ca²⁺ alternans in our simulations is driven by the cytosolic Ca²⁺, not the mitochondrial Ca²⁺. As shown in S5 Fig, when the mitochondrial Ca²⁺ was clamped to fixed values, the cytosolic Ca²⁺ alternans still exists (S5A Fig), but when cytosolic Ca²⁺ was clamped to fixed values, the mitochondrial Ca²⁺ alternans disappeared (S5B Fig).

ATP level and Ca²⁺ alternans

Previous experimental studies have documented that a reduced cellular ATP level is linked to Ca²⁺ alternans[14,24,25], presumably via the reduced SERCA pump activity. Here, we have shown that the ATP level during acute mitochondrial depolarization (30%) only changes slightly in our simulation (Fig 1A). If that is the case in experiment, then it is unlikely that the Ca²⁺ alternans occurring during acute mitochondrial depolarization is associated with the cellular ATP change. However, in experiment, whether the cellular ATP level is reduced has been shown to depend on the concentration of FCCP and treatment time [49]. Because the newly developed experimental technology can now be used to measure the ATP level in living functioning cells [50,51], future work should therefore include the fine-tuning of the ATP computer model to match the dynamics of ATP in individual experiments. Here, in order to evaluate the role of the ATP level in the genesis of Ca²⁺ alternans, we have performed simulations to clamp the cytosolic ATP concentration at different levels during mitochondrial depolarization. We show that when ATP is low enough, it can promote alternans via its effect on SERCA. However, it could work in synergy with the redox effect of ROS on SERCA even at much higher levels. Note that the effect of ATP on the genesis of Ca²⁺ alternans under mitochondrial depolarization is also mPTP dependent, since different mPTP open probabilities would cause different levels of cytosolic ROS, thereby affecting the cytosolic Ca²⁺ dynamical regime, which is on top of the ATP effect on Ca²⁺ alternans (S6 Fig). Also, the cytosolic ATP concentration itself depends on the mPTP activity; the opening of mPTP depolarizes the mitochondrial membrane potential, malfunctioning the ATP synthases.

Limitations

Several limitations should be noted in this study. The AP model and the 3-dimensional CRU network used in this study can successfully simulate the basic excitation-contraction-metabolism coupling in a ventricular myocyte, but it cannot capture all the aspects of electrophysiology of a real myocyte, such as heterogeneities in T-tubule networks and distribution of ion channels and Ca²⁺ handling proteins [52,53]. Such heterogeneities may alter the propensity of a cardiac myocyte for alternans [9]. Moreover, in this study the opening of mPTP was only mitochondrial free Ca²⁺ dependent, and the open probability was increased by increasing the C₁ to O transition rate constant. However, mPTP could open via a ROS-induced ROS release mechanism [54,55]. This mechanism is important for modeling mitochondrial depolarization waves [56–58], which are not the focus of this study. Furthermore, mitochondria have been found to constantly divide and fuse in cardiac myocytes, and in heart failure conditions, mitochondrial fusion could be depressed, which may contribute to the genesis of cardiac arrhythmias [59]. Therefore, further advanced computer models should be developed in the future to incorporate the feature of mitochondrial fusion and fission. Lastly, mitochondria have a special BK channels (mBKs), which is a voltage-dependent and Ca²⁺-activated K⁺ channel with a conductance ~100–300 pS. It has been known that the opening of mBK brings in K⁺ into the mitochondrion, depolarizing Δψ. It then reduces the driving force of MCU, which in turn attenuates the overload of mitochondrial Ca²⁺ (Stowe et al. [60]). The cardioprotective role of the mBK channel has been proposed to be similar to the mKATP channel (Stowe et al. [60]). The opening of these channels may prevent mPTP from opening by reducing mitochondrial Ca²⁺ overload. Therefore, in future studies, models of mBK and mKATP channels will be developed and incorporated in the mitochondrion model.

Methods

The details of this model, including mathematical formulation, values of parameters, and experimental validation, can be found in Song et al. [40]. Here we describe some of the key components of the model that are important for this study.

The overall ventricular myocyte model structure

This rabbit ventricular myocyte model contains a 3-dimensional coupled network of CRUs and mitochondria. There are 21504 (64×28×12) CRUs and 5376 (64×14×6) mitochondria (see Song et al. [40] for the details on the arrangement of these networks.).The membrane potential (V) of the cell is described by (1) where C_m = 1 μF/cm² is cell membrane capacitance, and I_sti is the stimulus pulse with the current density being -80 μA/cm² and the duration being 0.5 ms. The formulations of the ionic currents are referred to Song et al. [40].

The Gilespie method was used to simulate the random transitions of LCCs, RyRs, and mPTPs. The Euler method was used to solve the differential equations, and an adaptive time step method was used to compute the AP upstroke [61] with a time step 0.001 ms. The time step for computation for the rest of the AP was 0.01 ms. The computer model was programmed in CUDA C++ with double precision on Nvidia Tesla K20c and K80 GPU cards.

ROS and CaMKII regulation of RyRs

Both oxidized CaMKII signaling and the redox regulation of ROS increase the RyRs open probability [30,31,62–64]. To model these effects, we formulated the close-to-open rate (k₁₂) of RyRs as follows: (2) where Δk_CaMKII and Δk_ROS are the CaMKII-dependent and ROS-dependent components, respectively. The equations of Δk_CaMKII and Δk_ROS are formulated in Song et al. [40].

(3)

(4)

In Fig 2B, when we examined the effect of ROS via SERCA alone on inducing Ca²⁺ alternans, we set Δk_ROS = 0 to remove the effect of ROS on RyR activity. Other than that, Δk_ROS was calculated using Eq 4. k_base and k_u are rate constants. [Ca²⁺]_p is the Ca²⁺ concentration in the dyadic space. k₁₂ represents a closed-to-open rate of the RyR model [40] incorporated in the cell model. Increasing k₁₂ increases the open probability of RyRs.

ROS and CaMKII regulation of SERCA pump

Direct redox regulation slows the SERCA pump activity [31], and CaMKII phosphorylation of the phospholamban reduces the half maximum value [36]. Hence, the CaMKII effect on the activity of SERCA competes with the ROS effect on the SERCA activity. SERCA activity is also influenced by the ATP [65], i.e., reducing ATP impairs the SERCA pump function. Thus, the formulation of SERCA activity incorporating the ATP, CaMKII and ROS dependency is as follows: (5) where f_up,ATP, and f_up,ROS are ATP and ROS-dependent functions, which are detailed in Song et al. [40].

(6)

(7)

Eq 6 was adopted from Cortassa et al. [65]. Eq 7 was formulated in our previous study [40] to account for the redox effect of ROS on SERCA. In Fig 2B, when we examined the effect of ROS via RyR on inducing the Ca²⁺ alternans, we set f_up,ROS = 1 to eliminate the redox effect of ROS on SERCA in our model. Other than that, f_up,ROS was calculated using Eq 7 in this study. v_up and k_i is the maximum SERCA strength and the half maximum value, respectively. PLB([CaMKII]_act) is a CaMKII dependent function affecting the half maximum value of SERCA, where [CaMKII]_act is the local CaMKII activation in the cytosol.

The mPTP model

A 3-state (two close states C₀ and C₁, and an open state O) model of the mPTP (S7 Fig) was used. The transition from the C₀ state to the C₁ state is mitochondrial free Ca²⁺ dependent as shown below: (8)

Where h_mPTP is the Hill coefficient, [Ca²⁺]_m is the mitochondrial free Ca²⁺ in the corresponding mitochondrion, and [Ca²⁺]₀ is the half maximum value. Other transition rates are assumed to be constant. To simulate different levels of mPTP open probability, we multiplied a pre-factor, α_mPTP, to the C₁ to O transition rate, , (9)

The relationship between α_mPTP and the steady state open probability of mPTP is the following, (10)

Eq 10 suggests that P_mPTP~0 when α_mPTP~0, and P_mPTP~1 when α_mPTP~ ∞. Therefore, by simply increasing α_mPTP, we were able to increase the level of the open probability of mPTP.

Supporting information

S1 Fig.

From top to bottom, time traces of mitochondrial membrane potential, whole-cell averaged cytosolic ROS level, whole-cell averaged cytosolic Ca²⁺ concentration. The red bar indicates the time period when all the mPTPs in the cell were commanded to be closed.

https://doi.org/10.1371/journal.pcbi.1008624.s001

(TIF)

S2 Fig.

A. Time traces of voltage and Ca for control and mitochondrial depolarization cases at PCL = 500 ms. B. Time traces of voltage and Ca for mitochondrial depolarization case at PCL = 300 ms. Note that we plot two consecutive beats on top of each other to better observe the alternans.

https://doi.org/10.1371/journal.pcbi.1008624.s002

(TIF)

S3 Fig.

Bifurcation diagram of peak values of Ca²⁺ transients vs. the whole-cell averaged open probability of mPTP. The open probability of mPTP was measured at the end of each simulation of Fig 2A. We can see that the threshold for mPTP open probability is ~20% in this model. However, this specific value of the threshold depends on many factors, such as what we discussed in the Limitation section.

https://doi.org/10.1371/journal.pcbi.1008624.s003

(TIF)

S4 Fig.

A. Time traces of whole-cell averaged cytosolic Ca²⁺ transient and mitochondrial Ca²⁺ for α_MCU = 1 (red) and 0.5 (black). α_mPTP = 60. B. Same as A, but mitochondrial NCX was at control (red) and 50% reduction (black). α_mPTP = 60, PCL = 500 ms.

https://doi.org/10.1371/journal.pcbi.1008624.s004

(TIF)

S5 Fig.

A. Time traces of the whole-cell average cytosolic Ca²⁺, mitochondrial Ca²⁺, where the mitochondrial Ca²⁺ was clamped to 0.4 (black), 0.5 (red), and 0.6 (blue) μM at t = 25 sec. B. Same as A, but the cytosolic Ca²⁺ was clamped to 0.2 (black), 0.5 (red), and 1 (blue) μM at t = 25 sec.

https://doi.org/10.1371/journal.pcbi.1008624.s005

(TIF)

S6 Fig.

Dependence of Ca²⁺ alternans amplitude on α_mPTP and was calculated as the difference between the last two Ca²⁺ transient peaks in a simulation of 30 sec. PCL = 500 ms.

https://doi.org/10.1371/journal.pcbi.1008624.s006

(TIF)

S7 Fig.

Three-state mPTP model. C₀ and C₁ are the two closed states. O represents the open state.

https://doi.org/10.1371/journal.pcbi.1008624.s007

(TIF)

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Figures

Abstract

Author summary

Introduction

Results

Ca2+ alternans caused by mitochondrial depolarization due to mPTP opening

Effects of ROS on the genesis of Ca2+ alternans

Effects of mitochondrial Ca2+ on the genesis of Ca2+ alternans

Effects of oxidized CaMKII signaling on Ca2+ alternans

Effects of ATP depletion on Ca2+ alternans due to mitochondrial depolarization

Discussion

Role of ROS in the genesis of Ca2+ alternans

Mitochondrial Ca2+ cycling and intracellular Ca2+ alternans

ATP level and Ca2+ alternans

Limitations

Methods

The overall ventricular myocyte model structure

ROS and CaMKII regulation of RyRs

ROS and CaMKII regulation of SERCA pump

The mPTP model

Supporting information

References

Ca²⁺ alternans caused by mitochondrial depolarization due to mPTP opening

Effects of ROS on the genesis of Ca²⁺ alternans

Effects of mitochondrial Ca²⁺ on the genesis of Ca²⁺ alternans

Effects of oxidized CaMKII signaling on Ca²⁺ alternans

Effects of ATP depletion on Ca²⁺ alternans due to mitochondrial depolarization

Role of ROS in the genesis of Ca²⁺ alternans

Mitochondrial Ca²⁺ cycling and intracellular Ca²⁺ alternans

ATP level and Ca²⁺ alternans