A Model of Canine Purkinje Cell Electrophysiology and Ca²⁺ Cycling: Rate Dependence, Triggered Activity and Comparison to Ventricular Myocyte

Abstract

Rationale

Purkinje cells (Pcell) are characterized by different electrophysiologic properties and Ca²⁺ cycling processes than ventricular myocytes (Vcell), and are frequently involved in ventricular arrhythmias. Yet, the mechanistic basis for their arrhythmic vulnerability is not completely understood.

Objective

(1) Characterize Pcell electrophysiology, Ca²⁺ cycling and their rate dependence. (2) Investigate mechanisms underlying Pcell arrhythmogenicity. (3) Compare Pcell and Vcell electrophysiology, Ca²⁺ cycling and arrhythmic properties.

Methods and Results

We developed a new mathematical model of Pcell. The Ca²⁺ subsystem includes spatial organization and receptors distribution unique to Pcell. Results: (1) in Pcell and Vcell, Na⁺ accumulation via its augmentation of repolarizing I_NaK dominates APD adaptation; in Pcell, I_NaL contributes additional APD shortening at short CL; (2) Steep Pcell restitution is due to slow recovery of I_NaL; (3) Pcell's biphasic CaT reflects delay between Ca²⁺ release from JSR and CSR; (4) Pcell Ca²⁺ alternans, unlike Vcell, can develop without inducing AP alternans; (5) Pcell AP alternans develops at a shorter CL than Vcell, with increased subcellular heterogeneity of Ca²⁺ cycling due to refractoriness of Ca²⁺ release from CSR and JSR; (6) Greater Pcell vulnerability to DADs is due to higher SR Ca²⁺ content and ionic currents that reduce excitation threshold and promote triggered activity; (7) EAD generation in Pcell is mostly due to reactivation of I_NaL2, while I_CaL plays this role in Vcell.

Conclusions

Steeper rate dependence of AP and CaT, central-peripheral heterogeneity of Ca²⁺ cycling and distinct ion channel profile underlie greater arrhythmic vulnerability of Pcell compared to Vcell.

It has been suggested that under similar conditions, cardiac Purkinje cells (Pcell) are more vulnerable to development of delayed afterdepolarizations (DAD) and arrhythmic activity than ventricular myocytes (Vcell)¹. Pcell participation in arrhythmia was recently reported in studies of catecholaminergic polymorphic ventricular tachycardia (CPVT)^2,3 and ventricular fibrillation⁴. On cessation of rapid pacing (5Hz) to load the sarcoplasmic reticulum (SR), Pcell exhibits higher frequency and amplitude of spontaneous Ca²⁺ release events than Vcell¹. It is unclear why Pcell is more arrhythmogenic than Vcell and what is the role of electrophysiologic properties and Ca²⁺ handling in its greater arrhythmogenicity. Answering these questions requires quantitative comparison of specific ionic mechanisms that underlie the action potential (AP) and calcium cycling in Pcell and Vcell.

Electrophysiologic characteristics and intracellular Ca²⁺ handling of Pcell are considerably different from Vcell. Pcell AP is distinguished from Vcell by its faster depolarization upstroke, sloping repolarization time course during phase-2, and longer AP duration (APD)^5–7. Ultrastructurally, Pcell is devoid of transverse tubular (T-tubule) network⁸. Pcell exhibits biphasic Ca²⁺ transients (CaT) in response to normal membrane depolarization^9,10; it has a complex, triple-layered spatial distribution of Ryanodine receptor subtype 2 (RyR2) and subtype 3 (RyR3), and Inositol trisphosphate receptor subtype 1 (IP₃R1)¹¹ (Figure 1B). These unique electrophysiological and ultra-structural characteristics likely underlie the differences in rate dependence and arrhythmic vulnerability between Pcell and Vcell.

Figure 1.

(A) Canine cardiac Purkinje cell (PRd) model. Model details and parameter definitions are provided in Supplement. The compartmental cell model contains the following compartments (from periphery to center): PCS (peripheral coupling subspace), SSL (sub-sarcolemma), Myo (bulk myoplasm), SR (sarcoplasmic retibulum), JSR (junctional SR), NSR (network SR) and CSR (corbular SR). (B) Comparison of ultra-structure between canine cardiac Purkinje and ventricular cells. Intracellular Ca²⁺ cycling components are based on Stuyvers et al¹¹ (Pcell) and Decker et al¹⁴ (Vcell). Lack of T-tubular network and compartmental localization of RyR2, RyR3 and IP₃R, create spatial heterogeneity of Ca²⁺ cycling in Purkinje cells.

Computational modeling of cardiac myocytes has been an important tool in advancing our understanding of cardiac electrophysiology and excitation-contraction (EC) coupling. Current cardiac Purkinje cell models^12,13 are limited by lacking a realistic description of intracellular Ca²⁺ dynamics. They adopt the ventricular Ca²⁺ cycling models and do not incorporate the receptor types and spatial organization that are unique to Pcell. This can lead to inaccurate simulation of electrophysiological processes due to the strong coupling between the electrical and Ca²⁺ subsystems via Ca²⁺ dependent ionic currents and dynamic ionic concentrations. In this study, we developed a mathematical model (the PRd model) of the canine cardiac Purkinje AP and Ca²⁺ cycling (Figure 1A). The model includes an accurate representation of sarcolemmal ionic currents and a detailed description of the distinct Pcell intracellular Ca²⁺ dynamics. Formulation was based on careful validation over a wide range of pacing rates. The model was used to gain new mechanistic insights into specific ionic processes underlying rate-dependent AP and CaT properties of Pcell. Through a comparative simulation study of Pcell and Vcell behaviors, we identified Pcell properties that could explain its greater vulnerability to arrhythmogenesis.

METHODS

General Approach

The newly developed canine cardiac Purkinje cell model (P-model) includes a physiologically-based representation of intracellular Ca²⁺ cycling specific to Pcell, and of major membrane ionic currents. The model is compartmental (Figure 1) and its formulation is based on un-diseased canine experimental data at 37 °C. Description and validation of model formulation, equations and parameter definitions are provided in Supplement (validation is in Online Figures I–VII). The model code can be downloaded from the research section of http://rudylab.wustl.edu. The recent canine ventricular epicardial cell model (V-model)¹⁴ is used in Purkinje-ventricular comparative simulation studies.

Cell geometry and subcellular compartments

The Pcell is represented as a cylinder, 164 µm in length and 17.5 µm in radius, based on experimental measurements¹⁵. The SR is divided into three compartments: junctional SR (JSR), corbular SR (CSR) and network SR (NSR)⁸. The cytoplasm is divided into the peripheral coupling subspace (PCS), sub-sarcolemmal region (SSL), and bulk myoplasm (Myo) (Figure 1A). PCS is the functional coupling domain between sarcolemmal Ca²⁺ entry (via I_CaL) and peripheral JSR Ca²⁺ release (mostly via RyR3 and IP₃R); it is the equivalent of a dyad in ventricular myocytes. The term "dyad" does not apply in Purkinje cells due to absence of a T-tubular network⁸. The SSL compartment is the layer of cytoplasm underneath the sarcolemmal membrane (about 2µm deep)¹¹. All membrane ionic currents that are not in PCS are located in SSL. There is a "void" region (about 2 µm) between SSL and Myo, with virtually no expression of RyR2 and IP₃R¹¹, and reduced expression of RyR3 compared to SSL (Figure 1B). Based on the model compartmental structure, each receptor type is placed in the model compartment where its expression level is high. With this compartmental design, the void region is modeled functionally by Ca²⁺ diffusion flux (J_gap) that connects the SSL and Myo compartments. CSR, located in Myo, represents SR terminal cisternae that are not in close proximity to the cell membrane. CSR Ca²⁺ receptors are not exposed to sarcolemmal Ca²⁺ influxes; they can only respond to cytoplasmic Ca²⁺ elevation in the Myo compartment. The P-model compartmentalization is based on the "triple-layered" structure introduced by Stuyvers et al¹¹ (Figure 1B, left); compartmentalization of Ca²⁺ cycling in the V-model¹⁴ is depicted in Figure 1B, right, for comparison.

Intracellular Ca²⁺ fluxes

Three types of Ca²⁺ receptors are included in the P-model: IP₃R, RyR2 and RyR3. RyR2 is located on the membrane surface of CSR and responds to [Ca²⁺]_i elevation in Myo. RyR3 is co-localized with IP₃R in PCS (Figure 1). Bidirectional Ca²⁺ diffusion fluxes, J_diff (between SSL and PCS) and J_gap (between SSL and Myo), connect the cytoplasmic compartments. J_SERCA is Ca²⁺ uptake (via SERCA) into NSR. Ca²⁺ translocation from NSR to JSR and CSR is via J_tr,j and J_tr,c, respectively.

Membrane ionic currents

P-model membrane ionic currents (Figure 1) were formulated using the Hodgkin-Huxley (HH) scheme, based on un-diseased canine-specific experimental data at 37 °C (Supplement).

Simulation protocols

Steady state results are for 60 minutes of pacing at a given cycle length (CL). Restitution curve is obtained with an additional paced beat at variable coupling intervals from the last steady state AP. APD is determined as APD₉₀ (90% repolarization). State variable clamp protocols were used to quantify individual contributions of selected ion channels or ionic concentrations to the AP. Standard programming language C was used. Forward Euler method with an adaptive time step was used for numerical integration.

RESULTS

AP morphology and rate adaptation

In Figure 2A, simulated Pcell AP morphology and APD during steady state pacing (CL of 500ms) reproduce closely experimental recordings^16–18, with APD₉₀ of 293.2ms, maximum upstroke velocity (dV/dt_max) of 461Vs⁻¹ and membrane resting potential of −84.6mV. Simulated drug effects (TTX, nifedipine and TEA) on Pcell AP morphology are consistent with experiments (Online Figure VIII). Simulated Pcell APD adaptation curve (Figure 2B; CLs from 300ms to 2000ms) is also in agreement with experimental measurements^19–20,6.

Figure 2.

AP morphology and APD rate dependence. (A) Simulated Purkinje AP (solid line) during steady state pacing at cycle length (CL) = 500ms and corresponding experimental recordings (symbols)^16–18. (B) APD rate adaptation curves for Pcell (simulated and measured) and Vcell. (C) Effects of [Na⁺]_i clamp at 14mM or 9mM on Pcell APD rate adaptation. (D) Effects of [Na⁺]_i clamp at 12mM on Vcell APD rate adaptation. (E) Changes in Pcell APD (ΔAPD) when [Na⁺]_i and selected currents (I_Na, I_NaL, I_to1, I_Kr, I_CaL, I_Ks and I_NaK) at steady-state CL of 2000ms are reset to their values at CL of 500ms. (F) Same as (E) for Vcell.

Specific ionic mechanisms of APD rate adaptation in Pcell and Vcell were investigated using state variable clamp protocols (Figure 2C–2F). In control (no clamp), steady sate intracellular [Na⁺]_i is 9.4mM at CL=2000ms and 13.5mM at CL=500ms (Online Figure IX). In Figure 2C, [Na⁺]_i clamp to either 9mM or 14mM considerably alters Pcell APD adaptation. For [Na⁺]_i clamp at 9mM, APD alternans develops at CL=300ms due to excessive prolongation of APD and short diastolic interval between APs. In Vcell (Figure 2D), [Na⁺]_i is 7.4mM at CL=2000ms, and 8.8mM at CL=500mM; [Na⁺]_i clamp at 12mM largely reduces the steepness of APD adaptation. To quantify the role of individual ionic currents or concentrations in APD adaptation, values of state variables (channel gates or ionic concentrations) at CL=2000ms were reset to their values at CL=500ms. ΔAPDs (difference between control APD at CL=2000ms and APD at CL=2000ms with selected state variables reset to their values at CL=500ms) are presented. In Pcell (Figure 2E), intracellular Na⁺ accumulation is most important in causing APD shortening at short CL ([Na⁺]_i reset shortens APD by 15%). The [Na⁺]_i-dependent APD shortening is mediated via an increased outward I_NaK. However, I_NaK clamp alone, without [Na⁺]_i reset, causes only 8% APD shortening, indicating additional contribution from I_NCX ([Na⁺]_i reset causes only 10% APD shortening when I_NCX is clamped to its value at CL=2000ms). I_NaL clamp causes 9% APD shortening. Thus, I_NaK, I_NaL and I_NCX participate in Pcell APD shortening at short CLs. In Vcell (Figure 2D and 2F), intracellular [Na⁺]_i accumulation (13% shortening with [Na⁺]_i reset) and I_NaK (6.7% shortening with I_NaK clamp alone) are the major determinants of APD shortening between CL=2000ms and CL=500ms. Effects of clamping other currents are small. Thus, APD adaptation in both Pcell and Vcel is mostly determined by [Na⁺]_i accumulation and I_NaK; however, in Pcell, I_NaL is also a major participant in APD shortening at short CL, due to its slower recovery from inactivation in this cell²¹.

APD restitution

For S1 pacing at CL_S1=500ms, simulated Pcell APD restitution agrees well with experimental data in isolated canine Purkinje cells¹⁷ (Figure 3A, top panel). At short S2 coupling interval (CL_S2 =340ms), Pcell APD and AP plateau potentials are considerably decreased from the CL_S1 AP. The simulated Pcell APD restitution curve matches experimental data^18,20 (Figure 3B). Pcell APD depends strongly on CL_S2 variation between 340ms and 1000ms. However, this dependence is much weaker in Vcell (Figure 3A, bottom). Figure 3C compares Pcell and Vcell APD restitution curves for CL_S1 of 500ms, 1000ms and 2000ms. More pronounced APD shortening at DI<300ms is observed in Pcell compared to Vcell (box in Figure 3C). Pcell dynamic restitution curve is provided in Online Figure X.

Figure 3.

APD restitution. (A) After steady state was reached during pacing at CL of 500ms (S1), an additional stimulus (S2) was applied at a coupling interval of 340ms or 1000ms from the last S1 stimulus. Simulated Pcell S1 and S2 APs (top) are compared with experimental recordings (middle)¹⁷ and with Vcell APs (bottom). (B) Simulated and experimentally measured^20,18 Pcell APD restitution curves (CL_S1=500ms). (C) Comparison of APD restitution in Pcell (black) and Vcell (gray) for S1 pacing at 500ms, 1000ms and 2000ms. Restitution is steep for S2 coupling interval <300ms in Pcell (box). (D) Top: Changes in Pcell (top) and Vcell (bottom) APD (ΔAPD) when I_Na, I_CaL, I_Ks, I_Kr, I_to1, and I_NaL at diastolic interval (DI) of 300ms were reset to their values at DI of 30ms, for CL_S1= 500ms. Bottom: same as top for Vcell.

Specific ionic mechanisms of APD restitution in Pcell and Vcell were examined using state variable clamp protocols (Figure 3D). At CL_S1=500ms, values of selected state variables at DI=300ms were reset to their values at DI=30ms. ΔAPDs (the difference between control APD at DI=300ms and APD with selected state variables clamped to their values at DI=30ms) are presented. In Pcell (Figure 3D, top), I_NaL clamp shortens APD the most (by 19.6%). I_CaL (3.3%) and I_Kr (4.3%) clamps also contribute. Intracellular Ca²⁺ concentration or SR Ca²⁺ content clamp lead to minor APD abbreviation by 2% or 0.8%, respectively (not shown). In Vcell, I_to1 clamp contributes most to APD shortening (8.3%). I_Kr, I_NaL and I_Ks clamp cause APD shortening of 3.7%, 2.7% and 1.3%, respectively. The much greater maximal APD shortening in Pcell (19.6%; I_NaL clamp) compared to Vcell (8.3%; I_to1 clamp) at CL_S1=500ms is consistent with the steeper Pcell restitution.

CaT morphology and rate dependence

Hess and Wier⁹ measured intracellular Ca²⁺ using aequorin fluorescence in canine cardiac Purkinje fibers. The aequorin fluorescence signal provides an estimate of spatially-averaged CaT; its time course has two components, L1 and L2 (Figure 4B, inset). At CL of 1000ms, simulated steady state [Ca²⁺]_avg (spatially averaged Ca²⁺ concentration in PCS, SSL and Myo), exhibits similar L1–L2 morphology (Figure 4B, top). The L1 and L2 components of CaT appear 25ms and 85ms after the stimulus, respectively. These delays are in quantitative agreement with experimental measurements (30ms for L1 and 80ms for L2⁹). For [Ca²⁺]_o=2.0mM at CL=1000ms, the simulated amplitude of CaT (0.24 µM) is consistent with calibrated fluorescence imaging measurements (0.27 µM) by Boyden et al¹⁰. The simulated CaT decay rate (time constant for half relaxation τ=156ms) is also in agreement with Boyden et al's confocal microscopic recordings (τ = 150ms)¹⁰. Interestingly, the simulated [Ca²⁺]_avg displays much slower decay than the Hess and Wier⁹ aequorin signal (τ = 40ms) (Figure 4B, inset), likely due to the sensitivity threshold of aequorin to local Ca²⁺.

Figure 4.

Purkinje CaT morphology and rate dependence. (A) Simulated steady state (CL=1000ms) AP, CaT ([Ca²⁺]_avg, the spatial average of Ca²⁺ in PCS, SSL and Myo), and [Ca²⁺]_i (Myoplasmic Ca²⁺) during the AP. (B) Comparison of simulated CaT with Aequorin luminescent signal (an estimate for spatially averaged CaT) and of simulated [Ca²⁺]_i with force recorded from canine Purkinje fibers (gray box)⁹. τ is time constant for half relaxation. (C) Contributions of RyR2 and RyR3 to CaT. During steady state pacing (CL=1000ms) RyR2 and RyR3 are either blocked individually or together. (D) Rate dependence of CaT (top), [Ca²⁺]_NSR,max (middle), [Na⁺]_i,max (bottom) in Pcell (black); corresponding simulated data for Vcell are shown for comparison (dash-grey).

To investigate the specific roles of RyR2 and RyR3 in determining the L1–L2 morphology of Pcell CaT, RyR2 and RyR3 were blocked individually or in combination during steady state pacing at CL of 1000ms. The simulations in Figure 4C identify Ca²⁺ release from RyR3 (in PCS) and RyR2 (in Myo) as the major contributors to the L1 and L2 components of [Ca²⁺]_avg, respectively. Interestingly, there is "cross talk" between these processes - RyR3 block has a strong effect on L2. This is because Ca²⁺ release via RyR3 from JSR in PCS is required for Ca²⁺-induced-Ca²⁺-release from RyR2 in Myo. In other words, Ca²⁺ influx from SSL to Myo acts as both a source of Ca²⁺ and a trigger of Ca²⁺ release from CSR.

Rate dependence of CaT is shown in Figure 4D. Generally, Pcell has a smaller CaT than Vcell (peak CaT Pcell=0.45 µM; Vcell=0.67 µM). The stronger rate dependence of Pcell CaT and SR loading (Figure 4D, top and middle) shows strong correlation with the faster intracellular [Na⁺]_i accumulation (Figure 4D, bottom). Pcell has a higher [Na⁺]_i concentration than Vcell, about 9mM in quiescent cells and 11mM during pacing at CL of 1000ms²². As CL decreases, [Na⁺]_i accumulates faster in Pcell due to larger Na⁺ influx via I_NaL. For CL below 500ms, [Na⁺]_i plateaus (Figure 4D, bottom), mostly due to a smaller I_NaL at short CL. The correlation between [Na⁺]_i and CaT rate dependence is due to coupling via I_NCX and SR loading; at high [Na⁺]_i, intracellular Ca²⁺ extrusion via I_NCX is reduced, leading to Ca²⁺ loading, greater SR Ca²⁺ content and larger CaT.

AP and Ca²⁺ alternans

CaT alternans (stimulus-to-response ratio of 2:2) develops in Pcell at CL = 300ms. At this rate, AP alternans is not present, and the CaT alternans is driven by refractoriness of SR Ca²⁺ release (Figure 5A). The L2 (gray) component of [Ca²⁺]_avg occurs every other beat, indicating high amplitude of alternans. The L1 (black) component appears on every beat and alternates with a smaller amplitude. Simulated traces of Ca²⁺ in JSR and CSR during CaT alternans show that Ca²⁺ depletion of JSR alternates with a small amplitude, while Ca²⁺ depletion of CSR (stimulus-to-response ratio of 2:1) occurs only every other beat. These compartment-specific alternations correspond to the alternans of the L1 and L2 components of CaT. It is interesting that subcellular Ca²⁺ alternans with such large amplitude (occurrence of L2 component every other beat) is not affecting the Pcell AP. Lack of t-tubular system in Pcell is probably responsible for the Ca²⁺-AP dissociation, because it spatially dissociates Ca²⁺ variations in the center of the cell from the membrane ionic transport subsystem.

Figure 5.

(A) Subcellular Ca²⁺ alternans develops in Pcell at CL of 300ms without APD alternans. The L1 component (black dots) of [Ca²⁺]_avg alternates with small amplitude from beat to beat, while the L2 component (gray dots) is only present on every other beat. (B) At CL=200ms, AP alternans also develops. Both L1 and L2 components of [Ca²⁺]_avg appear only every other beat. (C) At CL=170ms, the L1 component of [Ca²⁺]_avg occurs every other beat, while the L2 component only every fourth beat. Pacing stimuli are indicated by gray vertical bars on top. Black or gray dots indicate L1 or L2 component of CaT (and associated processes), respectively. Stimulus-to-response ratios are indicated in brackets in each panel.

During steady state pacing at CL=200ms, APD alternans develops with a large amplitude (Figure 5B, top), and is accompanied by very large CaT alternans (stimulus-to-response ratio of 2:2) (Figure 5B, second row). Ca²⁺ depletion of JSR alternates with a large amplitude and CSR release occurs only every other beat. At CL=170ms (Figure 5C), [Ca²⁺]_avg exhibits a more complex pattern (4:4), where the L1 component of CaT occurs every other beat (black dots) and L2 only every fourth beat (gray dots), reflecting increased subcellular heterogeneity of Ca²⁺ cycling. In summary: (1) [Ca²⁺]_CSR is more responsive to CL shortening than [Ca²⁺]_JSR, but has minimal effect on AP due to spatially mediated Ca²⁺-AP dissociation; (2) AP and [Ca²⁺]_JSR always display the same stimulus-to-response ratio due to strong coupling between the JSR and the cell membrane; (3) As pacing rate increases, subcellular heterogeneity of Ca²⁺ cycling increases as well.

DAD and arrhythmic vulnerability of Pcell

Ionic mechanisms underlying Pcell arrhythmic vulnerability due to the development of DAD and triggered activity are investigated in Figure 6. Hypersensitivity of RyR2 (e.g. due to RyR2 or calsequestrin mutation)²³ in Pcell and Vcell is phenomenologically modeled by a decrease of release time constant (by 66%) and increased sensitivity to luminal Ca²⁺ content (by 75%). With normal RyR2, after cessation of steady state pacing at CL=300ms, no spontaneous depolarizations are observed in either Pcell or Vcell (Figure 6A). With hypersensitive RyR2 at the same pacing rate, Pcell develops afterdepolarizations and triggered activity (7 subthreshold DADs and 5 triggered APs) after cessation of pacing, but Vcell does not (Figure 6B). Occurrence of DADs in Pcell exhibits positive rate dependence, mostly due to higher SR content at short CL, which is consistent with experiments^{23, 24}. In Figure 6C, to investigate the underlying cause of the Pcell greater arrhythmic vulnerability, selected Pcell ionic currents or concentrations (I_CaT, I_NaL, I_K1, I_f and [Ca²⁺]_NSR) are modified (individually or in combination) to be "ventricular-like". Specifically, relative to Pcell, Vcell has a mucher smaller I_NaL, larger I_K1, smaller SR Ca²⁺ content, and no I_CaT and I_f currents. In the simulations, block of I_CaT reduced the number of spontaneous events (6 DADs and 3 triggered APs), while block of I_NaL eliminated all triggered APs. 50% increase of I_K1 or block of I_f also eliminated triggered APs. 30% reduction of SR Ca²⁺ content reduced the number of spontaneous events by 60%. Combination of all above changes ("ventricular-like" cell) led to quiescent and stable resting potential. From these simulations, we conclude that the greater Pcell vulnerability to DADs and triggered activity is due to: (1) higher SR Ca²⁺ content; (2) membrane ion channel profile that reduces excitation threshold and resting potential stability (i.e. reduced I_K1 expression and presence of I_f); (3) depolarizing ion channels that promote triggered activity (i.e. presence of I_CaT and larger I_NaL).

Figure 6.

DADs and triggered activity. (A) After cessation of steady state pacing at CL=300ms, no spontaneous activity is observed in Pcell or Vcell under control conditions. (B) With increased RyR2 sensitivity, Pcell develops DADs and triggered APs, while Vcell remains quiescent. (C) Ionic currents or concentrations (Top to bottom: I_CaT, I_NaL, I_K1, I_f and [Ca²⁺]_NSR) are ajusted either individually or together to resemble their ventricular counterparts. * indicates triggered AP; # indicates sub-threshold DAD. See details in text.

Early afterdepolarization (EAD) and its underlying mechanisms

With application of quinidine^25–27 or I_Kr block¹⁹ during slow pacing, canine Purkinje fibers develop EADs that depolarize from plateau potentials of about −20mV. Earlier studies suggested that recovery from inactivation of I_CaL is responsible for genesis of EADs in both Pcell^26,28 and Vcell²⁹. However, recent experimental reports proposed a role for I_NaL in Purkinje fibers EADs^{30, 31}. The ionic mechanism of EADs is investigated in Figure 7. At CL=4000ms with complete block of I_Kr, large amplitude EADs develop starting from the 127^th beat (Figure 7A, top). Simulated tracings of I_NaL2, I_NaL3 and I_CaL are shown in Figure 7A (bottom three traces). Reactivation of I_NaL2 coincides with the EADs. In panel B, with only 50% I_Kr block, 80% reduction of I_to1 (simulating reduced i_to1 expression in heart failure³² or myocardial infarction³³) elevates the plateau potentials, leading to more severe EAD activity that starts earlier (at the 17^th beat, Figure 7B, top). Persistent EAD events are observed starting at the 42^th beat (Figure 7B, middle). Again, EAD occurrences and patterns are in synchrony with I_NaL2 reactivation (Figure 7B, bottom). Two consecutive APs (#41 and #42) and ionic currents (I_NaL2 and I_CaL) are overlaid in Figure 7C. Recovery and reactivation of I_NaL produce current of much larger amplitude than I_CaL. Furthermore, I_NaL2 reactivation always precedes both I_CaL reactivation (by 10ms) and the EAD upstroke (by 50ms) (Figure 7C, right), providing depolarizing charge for EAD generation. These results indicate that I_NaL2 plays the major role in the genesis of EADs in canine Purkinje cells, due to its high current density and voltage range for activation (I–V curve peaks at about −20mV, the EADs takeoff potential). I_CaL also reactivates during the EAD upstroke, but its contribution is much smaller than that of I_NaL. Thus, EAD formation in Pcell or Vcell relies on recovery and reactivation of different ion channels during a prolonged plateau; I_NaL is the major depolarizing current of Pcell EAD, while for Vcell EAD it is I_CaL.

Figure 7.

Purkinje EADs and underlying mechanism. (A) At CL=4000ms with complete I_Kr block, EADs develop starting from beat #127 (top panel). Simulated tracings of I_NaL2, I_NaL3 and I_CaL (bottom panel) identify reactivations of I_NaL2 as the mechanism of EAD generation. (B) 80% block of I_to1 and 50% block of I_Kr lead to increased EAD activity due to elevation of plateau potential. EADs are observed starting from beat #18 and persist from beat #42. (C) Two consecutive APs (beats #41 and #42 in (B)) are overlaid with I_NaL2 and I_CaL. A portion of beat #42 (box in left panel) is enlarged in the right panel. Reactivated I_NaL2 is of much larger amplitude than I_CaL and precedes the reactivation of I_CaL and the EAD upstroke.

DISCUSSION

We present a new mathematical model for the canine cardiac Purkinje AP and Ca²⁺ cycling, validated with recent experimental data. Importantly, the model incorporates not only electrophysiological components that are specific to Purkinje cell, but also Ca²⁺ cycling properties that differ greatly from those of ventricular myocyte, both in receptor types and spatial organization. These properties, which affect the amplitude and time courses of the CaT and consequently the AP, were not incorporated in recently published Purkinje cell models^12,13, which retained the calcium cycling representation from models of ventricular myocytes (see Models Comparison table in Supplement). The model is used to investigate mechanisms of AP and CaT rate dependence, including APD adaptation and restitution, SR loading, and alternans. Arrhythmic triggered activity due to DADs and EADs is also explored.

Through a comparative study of behaviors and mechanisms between a Purkinje cell and ventricular myocyte, we found that: (1) In both Pcell and Vcell, intracellular Na⁺ accumulation at fast rate and its enhancement of outward I_NaK dominate rate-dependent APD shortening during steady state pacing (adaptation). In Pcell, I_NaL contributes additional APD shortening at short CL due to incomplete recovery from inactivation, causing steeper adaptation than Vcell; contributions to APD adaptation from currents other than I_NaK are minimal in Vcell. (2) Pcell APD restitution is steeper than that of Vcell. At short coupling intervals, I_NaL inactivation is most important in causing APD shortening in Pcell; in Vcell, I_to1 underlies APD shortening. (3) Pcell exhibits a biphasic CaT, reflecting a delay between Ca²⁺ release from JSR (via RyR3 and IP₃R) and CSR (via RyR2). Rate dependence of CaT and SR loading is stronger in Pcell than Vcell, mostly due to faster [Na]_i accumulation. (4) In contrast to Vcell, Pcell Ca²⁺ alternans can occur without causing AP alternans because of spatial dissociation between [Ca²⁺]_i and membrane ion channels. (5) Pcell AP alternans develops at a shorter CL than Vcell, with an increased subcellular heterogeneity of Ca²⁺ cycling. (6) Greater Pcell vulnerability to DADs is due to higher SR content, and the presence of membrane currents that reduce excitation threshold and rest potential stability (I_K1, I_f) and currents that promote triggered activity (I_CaT, I_NaL). (7) EAD generation in Pcell is mostly due to reactivation of I_NaL2, while I_CaL plays this role in Vcell.

The above findings provide new insights into the arrhythmogenic potential of Purkinje fibers. Recent studies have demonstrated greater arrhythmic vulnerability in Purkinje compared to ventricular myocardium^1–4. This could result from properties at the tissue scale, such as high expression of connexin, loading conditions due to frequent branching and highly variable fiber cross-sections, and asymmetrical electrical properties at Purkinje-muscle junctions³⁴. The single cell results presented here show that Purkinje fibers are intrinsically more arrhythmogenic than ventricular myocytes. The Purkinje cell has a steeper rate dependence of AP and CaT, it operates at a higher SR Ca²⁺ load, and is more prone to develop triggered activity due to its different ion-channel profile.

A recent study in isolated canine Purkinje cells by Lee et al³⁵ reported complex beat-to-beat variations of CaT at fast pacing rate and negative rate dependence of CaT and SR loading. Consistent with the complex beat-to-beat CaT pattern, our simulations demonstrate increased subcellular heterogeneity of Ca²⁺ cycling at short CL, mostly due to Ca²⁺-AP dissociation and refractoriness of Ca²⁺ release from both CSR and JSR (Figure 5). However, unlike the experiment³⁴, the model exhibits positive rate dependence of both CaT and SR loading. This dependence is stronger in Pcell than in Vcell (for CLs between 2000ms and 500ms) due to faster Na⁺ accumulation. There is paucity of direct measurements of CaT rate dependence in canine Purkinje fibers. Indirect evidence supports a positive relationship; for example, DADs appear earlier with greater amplitudes as pacing rate is increased²⁴, suggesting an increased SR content. A positive CaT rate dependence was observed experimentally in sheep Purkinje fibers³⁶. The different results of Lee et al³⁵ could possibly reflect different temperature in model (37 °C, body temperature) and experiment (22–24 °C, room temperature), as reduced Na⁺ current at lower temperature decreases Na⁺ accumulation and consequently Ca²⁺ loading.

The Pcell model was formulated as a compartmental model, capturing properties of Ca²⁺ cycling in distinct compartments. While this constitutes an important step forward in modeling Pcell physiology, it does not represent spatially distributed processes at the scale of Ca²⁺ release units and spark formation. Further model development is required to simulate spatially distributed phenomena such as formation of Ca²⁺ waves and their electrophysiologic consequences.

NOVELTY AND SIGNIFICANCE.

What Is Known?

• Cardiac Purkinje cells (Pcell) are thought to be more prone to arrhythmic activity than ventricular myocytes (Vcell).

• Documented Pcell participation in arrhythmia includes catecholaminergic polymorphic ventricular tachycardia (CPVT) and ventricular fibrillation (VF).

• The electrophysiologic profile and calcium (Ca) cycling properties of Pcell are considerably different from Vcell.

What New Information Does This Article Contribute?

• We developed a mathematical model of Pcell that represents its unique electrophysiologic and Ca handling properties, and conducted a Pcell – Vcell comparison.

• Rate dependence of action potential (AP) and Ca transient (CaT) is steeper in Pcell; consistent with greater vulnerability to arrhythmia.

• Pcells are more prone to the development of arrhythmogenic delayed afterdepolarizations (DADs).

• Pcell mechanisms and properties of AP and CaT alternans, and of early afterdepolarizations (EADs) differ from those of Vcell.

The cardiac Pcell is thought to be more prone to develop arrhythmic activity than Vcell. The P cell has been implicated as an important contributor to CPVT and VF. However, the mechanistic basis for its greater arrhythmia vulnerability is not completely understood. Electrophysiologic characteristics and intracellular Ca handling of Pcell are considerably different from Vcell. Importantly, Pcell is devoid of transverse tubules and has a complex spatial distribution of Ca release sites. We developed a mathematical model of the canine Pcell that incorporates these unique properties. The model was used to obtain new mechanistic insights into rate-dependence of Pcell AP and CaT, and to compare Pcell and Vcell properties. The simulations demonstrated that Pcell is intrinsically more arrhythmogenic than Vcell. It has steeper rate dependence of AP (due to contribution from the late sodium current) and CaT (due to stronger rate dependence of sarcoplasmic reticulum (SR) Ca loading). It operates at higher SR Ca load, which together with its different ion-channel profile, makes it more prone to develop DADs and triggered activity than Vcell. Recognizing the important role of Pcell in arrhythmogenesis and understanding its underlying mechanisms is a first step towards the development of novel antiarrhythmic strategies.

Abbreviations

AP

Action Potential

APD₉₀

Action Potential Duration (at 90% repolarization) (ms)

CL

Cycle Length (ms)

DI

Diastolic Interval (ms): time from 90% repolarization of previous AP

CaT

Ca²⁺ Transient (µM/L)

PCS

Peripheral Coupling Subspace

SSL

Sub-Sarcolemmal compartment

Myo

Bulk Myoplasm compartment

JSR

Junctional Sarcoplasmic Reticulum

CSR

Corbular Sarcoplasmic Reticulum

NSR

Network Sarcoplasmic Reticulum

RyR

Ryanodine Receptor

IP₃R

Inositol trisphosphate receptor

CPVT

Catecholaminergic polymorphic ventricular tachycardia

DAD

Delayed afterdepolarization

EAD

Early afterdepolarization

Pcell

Cardiac Purkinje cell

Vcell

Ventricular myocyte