a model of canine purkinje cell electrophysiology...

A Model of Canine Purkinje Cell Electrophysiology andCa2� Cycling

Rate Dependence, Triggered Activity, and Comparison toVentricular Myocytes

Pan Li and Yoram Rudy

Abstract: Purkinje cells (Pcell) are characterized by different electrophysiological properties and Ca2� cyclingprocesses than ventricular myocytes (Vcell) and are frequently involved in ventricular arrhythmias. Yet, themechanistic basis for their arrhythmic vulnerability is not completely understood. The objectives were to: (1)characterize Pcell electrophysiology, Ca2� cycling, and their rate dependence; (2) investigate mechanismsunderlying Pcell arrhythmogenicity; and compare Pcell and Vcell electrophysiology, Ca2� cycling, andarrhythmic properties. We developed a new mathematical model of Pcell. The Ca2� subsystem includes spatialorganization and receptors distribution unique to Pcell. Results were: (1) in Pcell and Vcell, Na� accumulationvia its augmentation of repolarizing INaK dominates action potential duration adaptation and, in Pcell, INaL

contributes additional action potential duration shortening at short cycle length; (2) steep Pcell restitution isattributable to slow recovery of INaL; (3) biphasic Ca2� transients of Pcell reflect the delay between Ca2� releasefrom junctional sarcoplasmic reticulum and corbular sarcoplasmic reticulum; (4) Pcell Ca2� alternans, unlikeVcell, can develop without inducing action potential alternans; (5) Pcell action potential alternans develops at ashorter cycle length than Vcell, with increased subcellular heterogeneity of Ca2� cycling attributable torefractoriness of Ca2� release from corbular sarcoplasmic reticulum and junctional sarcoplasmic reticulum; (6)greater Pcell vulnerability to delayed afterdepolarizations is attributable to higher sarcoplasmic reticulum Ca2�

content and ionic currents that reduce excitation threshold and promote triggered activity; and (7) early afterdepolarizations generation in Pcell is mostly attributable to reactivation of INaL2, whereas ICaL plays this rolein Vcell. Steeper rate dependence of action potential and Ca2� transients, central peripheral heterogeneityof Ca2� cycling, and distinct ion channel profile underlie greater arrhythmic vulnerability of Pcell comparedto Vcell. (Circ Res. 2011;109:71-79.)

Key Words: arrhythmia � calcium � electrophysiology � modeling � Purkinje

It has been suggested that under similar conditions, cardiacPurkinje cells (Pcell) are more vulnerable to development

of delayed afterdepolarizations (DAD) and arrhythmic activ-ity than ventricular myocytes (Vcell).1 Pcell participation inarrhythmia was recently reported in studies of catechol-aminergic polymorphic ventricular tachycardia2,3 and ventric-ular fibrillation.4 On cessation of rapid pacing (5 Hz) to loadthe sarcoplasmic reticulum (SR), Pcell exhibits higher fre-quency and amplitude of spontaneous Ca2� release eventsthan Vcell.1 It is unclear why Pcell is more arrhythmogenicthan Vcell, and what is the role of its electrophysiologicalproperties and Ca2� handling in its greater arrhythmogenic-ity. Answering these questions requires quantitative compar-ison of specific ionic mechanisms that underlie the actionpotential (AP) and calcium cycling in Pcell and Vcell.

Electrophysiological characteristics and intracellular Ca2�

handling of Pcell are considerably different from Vcell. PcellAP is distinguished from Vcell by its faster depolarizationupstroke, sloping repolarization time course during phase 2, andlonger AP duration (APD).5–7 Ultrastructurally, Pcell is devoidof transverse tubular (T-tubular) network.8 Pcell exhibits bipha-sic Ca2� transients (CaT) in response to normal membranedepolarization;9,10 it has a complex, triple-layer spatial distribu-tion of Ryanodine receptor subtype 2 (RyR2) and subtype 3(RyR3), and inositol trisphosphate receptor subtype 1 (IP3R1)11

(Figure 1B). These unique electrophysiological and ultrastruc-tural characteristics likely underlie the differences in rate depen-dence and arrhythmic vulnerability between Pcell and Vcell.

Computational modeling of cardiac myocytes has been animportant tool in advancing our understanding of cardiac

Original received April 12, 2011; revision received April 28, 2011; accepted May 3, 2011. In April 2011, the average time from submission to firstdecision for all original research papers submitted to Circulation Research was 15 days.

From the Department of Biomedical Engineering and Cardiac Bioelectricity and Arrhythmia Center, Washington University in St. Louis, St. Louis,MO 63112.

Correspondence to Yoram Rudy, PhD, Department of Biomedical Engineering and Cardiac Bioelectricity and Arrhythmia Center, Campus Box 1097,Washington University in St. Louis, 1 Brookings Drive, St. Louis, MO 63112. E-mail [email protected]

© 2011 American Heart Association, Inc.

Circulation Research is available at http://circres.ahajournals.org DOI: 10.1161/CIRCRESAHA.111.246512

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electrophysiology and excitation–contraction coupling. Cur-rent cardiac Purkinje cell models12,13 are limited by lacking arealistic description of intracellular Ca2� dynamics. Theyadopt the ventricular Ca2� cycling models and do notincorporate the receptor types and spatial organization thatare unique to Pcell. This can lead to inaccurate simulation ofelectrophysiological processes because of the strong couplingbetween the electric and Ca2� subsystems via Ca2�-dependent ionic currents and dynamic ionic concentrations.In this study, we developed a mathematical model (the PRdmodel) of the canine cardiac Purkinje AP and Ca2� cycling(Figure 1A). The model includes an accurate representation ofsarcolemmal ionic currents and a detailed description of thedistinct Pcell intracellular Ca2� dynamics. Formulation wasbased on careful validation over a wide range of pacing rates.The model was used to gain new mechanistic insights intospecific ionic processes underlying rate-dependent AP and CaTproperties of Pcell. Through a comparative simulation study ofPcell and Vcell behaviors, we identified Pcell properties thatcould explain its greater vulnerability to arrhythmogenesis.

Materials and MethodsGeneral ApproachThe newly developed canine cardiac Purkinje cell model includes aphysiologically based representation of intracellular Ca2� cyclingspecific to Pcell and of major membrane ionic currents. The modelis compartmental (Figure 1) and its formulation is based on undis-eased canine experimental data at 37°C. Description and validationof model formulation, equations, and parameter definitions areprovided in the Supplement (also see Supplemental Figures I–VIIavailable online at http://www.circresaha.org). The model code canbe downloaded from the research section of http://rudylab.wustl.edu.The recent canine ventricular epicardial cell model14 is used inPurkinje–ventricular comparative simulation studies.

Cell Geometry and Subcellular CompartmentsThe Pcell is represented as a cylinder, 164 �m in length and 17.5 �min radius, based on experimental measurements.15 The SR is divided

into three compartments: junctional SR (JSR), corbular SR (CSR),and network SR (NSR).8 The cytoplasm is divided into the peripheralcoupling subspace (PCS), subsarcolemmal region (SSL), and bulkmyoplasm (Myo; Figure 1A). PCS is the functional coupling domainbetween sarcolemmal Ca2� entry (via ICaL) and peripheral JSR Ca2�

release (mostly via RyR3 and IP3R); it is the equivalent of a dyad inventricular myocytes. The term “dyad” does not apply in Purkinjecells because of absence of a T-tubular network.8 The SSL compart-ment is the layer of cytoplasm underneath the sarcolemmal mem-brane (�2 �m deep).11 All membrane ionic currents that are not inPCS are located in SSL. There is a “void” region (�2 �m) betweenSSL and Myo, with virtually no expression of RyR2 and IP3R11 andwith reduced expression of RyR3 compared to SSL (Figure 1B).Based on the model compartmental structure, each receptor type isplaced in the model compartment where its expression level is high.With this compartmental design, the void region is modeled func-tionally by Ca2� diffusion flux (Jgap) that connects the SSL and Myocompartments. CSR, located in Myo, represents SR terminal cister-nae that are not in close proximity to the cell membrane. CSR Ca2�

receptors are not exposed to sarcolemmal Ca2� influxes; they canonly respond to cytoplasmic Ca2� elevation in the Myo compart-ment. The Purkinje cell model compartmentalization is based on thetriple-layer structure introduced by Stuyvers et al11 (Figure 1B, left);compartmentalization of Ca2� cycling in the ventricular epicardialcell model14 is depicted (Figure 1B, right) for comparison.

Intracellular Ca2� FluxesThree types of Ca2� receptors are included in the Purkinje cell model:IP3R, RyR2, and RyR3. RyR2 is located on the membrane surface ofCSR and responds to [Ca2�]i elevation in Myo. RyR3 is colocalizedwith IP3R in PCS (Figure 1). Bidirectional Ca2� diffusion fluxes, Jdiff(between SSL and PCS) and Jgap (between SSL and Myo), connect thecytoplasmic compartments. JSERCA is Ca2� uptake via sarco/endoplas-mic reticulum Ca2�-ATPase (SERCA) into NSR. Ca2� translocationfrom NSR to JSR and CSR is via Jtr,j and Jtr,c, respectively.

Membrane Ionic CurrentsPurkinje cell model membrane ionic currents (Figure 1) wereformulated using the Hodgkin-Huxley scheme based on undiseasedcanine-specific experimental data at 37°C (Supplemental Materialsavailable online at http://www.circresaha.org).

Simulation ProtocolsSteady-state results are for 60 minutes of pacing at a given cyclelength (CL). Restitution curve is obtained with an additional pacedbeat at variable coupling intervals from the last steady-state AP.APD is determined as APD90 (90% repolarization). State-variableclamp protocols were used to quantify individual contributions ofselected ion channels or ionic concentrations to the AP. Standardprogramming language C was used. Forward Euler method with anadaptive time step was used for numeric integration.

ResultsAP Morphology and Rate AdaptationIn Figure 2A, simulated Pcell AP morphology and APDduring steady-state pacing (CL of 500 ms) reproduce closelyexperimental recordings,16–18 with APD90 of 293.2 ms, max-imum upstroke velocity of 461 Vs�1, and membrane restingpotential of �84.6 mV. Simulated drug effects (tetrodotoxin[TTX], nifedipine, and tetraethylammonium [TEA]) on PcellAP morphology are consistent with experiments (Supplemen-tal Figure VIII available online at http://www.circresaha.org).Simulated Pcell APD adaptation curve (Figure 2B; CL from300 ms to 2000 ms) is also in agreement with experimentalmeasurements.6,19,20

Specific ionic mechanisms of APD rate adaptation in Pcelland Vcell were investigated using state-variable clamp pro-

Non-standard Abbreviations and Acronyms

DI diastolic interval (ms): time from 90% repolarization of previousaction potential

AP action potential

APD90 action potential duration (at 90% repolarization) (ms)

CaT Ca2� transient (�M/L)

CL cycle length (ms)

CSR corbular sarcoplasmic reticulum

DAD delayed after depolarization

EAD early after depolarization

IP3R inositol trisphosphate receptor

JSR junctional sarcoplasmic reticulum

Myo bulk myoplasm compartment

Pcell cardiac Purkinje cell

PCS peripheral coupling subspace

RyR ryanodine receptor

SSL subsarcolemmal compartment

Vcell ventricular myocyte

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tocols (Figure 2C–2F). In control (no clamp), steady-stateintracellular [Na�]i is 9.4 mmol/L at CL of 2000 ms and13.5 mmol/L at CL of 500 ms (Supplemental Figure IXavailable online at http://www.circresaha.org). In Figure 2C,[Na�]i clamp to either 9 mmol/L or 14 mmol/L considerablyalters Pcell APD adaptation. For [Na�]i clamp at 9 mmol/L,APD alternans develop at CL of 300 ms because of excessiveprolongation of APD and short diastolic interval betweenAPs. In Vcell (Figure 2D), [Na�]i is 7.4 mmol/L at CL of2000 ms and 8.8 mmol/L at CL of 500 mmol/L; [Na�]i clampat 12 mmol/L largely reduces the steepness of APD adapta-tion. To quantify the role of individual ionic currents orconcentrations in APD adaptation, values of state variables(channel gates or ionic concentrations) at CL of 2000 ms werereset to their values at CL of 500ms. The difference betweencontrol APD at CL of 2000 ms and APD at CL of 2000 mswith selected state variables reset to their values at CL of 500ms are presented. In Pcell (Figure 2E), intracellular Na�

accumulation is most important in causing APD shortening atshort CL ([Na�]i reset shortens APD by 15%). The [Na�]i-dependent APD shortening is mediated via an increasedoutward INaK. However, INaK clamp alone, without [Na�]i

reset, causes only 8% APD shortening, indicating additionalcontribution from INCX ([Na�]i reset causes only 10% APDshortening when INCX is clamped to its value at CL of 2000ms). INaL clamp causes 9% APD shortening. Thus, INaK, INaL,and INCX participate in Pcell APD shortening at short CL. InVcell (Figure 2D, 2F), intracellular Na� accumulation (13%shortening with [Na�]i reset) and INaK (6.7% shortening withINaK clamp alone) are the major determinants of APDshortening between CL of 2000 ms and CL of 500 ms. Effectsof clamping other currents are small. Thus, APD adaptationin both Pcell and Vcell is mostly determined by [Na�]i

accumulation and INaK; however, in Pcell, INaL is also a majorparticipant in APD shortening at short CL, because of itsslower recovery from inactivation in this cell.21

Figure 1. A, Canine cardiacPurkinje cell (PRd) model.Model details and parameterdefinitions are provided in theSupplement. The compartmen-tal cell model contains the fol-lowing compartments (fromperiphery to center): peripheralcoupling subspace (PCS), sub-sarcolemma (SSL), bulk myo-plasm (Myo), sarcoplasmicretibulum (SR), junctional SR(JSR), network SR (NSR), andcorbular SR (CSR). B, Compar-ison of ultrastructure betweencanine cardiac Purkinje cells(Pcell) and ventricular cells(Vcell). Intracellular Ca2�

cycling components are basedon Stuyvers et al11 (Pcell) andDecker et al14 (Vcell). Lack ofT-tubular network and com-partmental localization ofRyR2, RyR3, and IP3R createspatial heterogeneity of Ca2�

cycling in Purkinje cells.

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APD RestitutionFor S1 (steady-state) pacing at CLS1 of 500 ms, simulatedPcell APD restitution agrees well with experimental data inisolated canine Purkinje cells17 (Figure 3A, top). At short S2(additional premature beat) coupling intervals (CLS2�340ms), Pcell APD and AP plateau potentials are considerablydecreased from the CLS1 AP. The simulated Pcell APD resti-tution curve matches experimental data18,20 (Figure 3B). PcellAPD depends strongly on CLS2 variation between 340 ms and1000 ms. However, this dependence is much weaker in Vcell(Figure 3A, bottom). Figure 3C compares Pcell and Vcell APDrestitution curves for CLS1 of 500 ms, 1000 ms, and 2000 ms.More pronounced APD shortening at diastolic interval (DI)�300 ms is observed in Pcell compared to Vcell (Figure 3C,box). Pcell dynamic restitution curve is provided in Supplemen-tal Figure X available online at http://www.circresaha.org).

Specific ionic mechanisms of APD restitution in Pcell andVcell were examined using state-variable clamp protocols (Fig-ure 3D). At CLS1 of 500 ms, values of selected state variables atDI of 300 ms were reset to their values at DI of 30ms. Thedifference between control APD at DI of 300 ms and APD withselected state variables clamped to their values at DI of 30 ms are

presented. In Pcell (Figure 3D, top), INaL clamp shortens APDthe most (by 19.6%). ICaL (3.3%) and IKr (4.3%) clamps alsocontribute. Intracellular Ca2� concentration or SR Ca2� contentclamp lead to minor APD abbreviation by 2% or 0.8%, respec-tively (not shown). In Vcell, Ito1 clamp contributes most to APDshortening (8.3%). IKr, INaL, and IKs clamp cause APD shorten-ing of 3.7%, 2.7%, and 1.3%, respectively. The much greatermaximal APD shortening in Pcell (19.6%; INaL clamp) com-pared to Vcell (8.3%; Ito1 clamp) at CLS1 of 500 ms is consistentwith the steeper Pcell restitution.

CaT Morphology and Rate DependenceHess and Wier9 measured intracellular Ca2� using aequorinfluorescence in canine cardiac Purkinje fibers. The aequorinfluorescence signal provides an estimate of spatially averagedCaT; its time course has two components, L1 and L2 (Figure4B, inset). At CL of 1000 ms, 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 25 ms and 85ms after the stimulus, respectively. These delays are in quanti-tative agreement with experimental measurements (30 ms for L1and 80 ms for L29). For [Ca2�]o of 2.0 mmol/L at CL of 1000ms, the simulated amplitude of CaT (0.24 �mol/L) is consistentwith calibrated fluorescence imaging measurements(0.27 �mol/L) by Boyden et al.10 The simulated CaT decay rate(time constant for half relaxation: ��156 ms) is also in agree-ment with the confocal microscopic recordings (��150 ms) ofBoyden et al.10 Interestingly, the simulated [Ca2�]avg displaysmuch slower decay than the Hess and Wier9 aequorin signal(��40 ms; Figure 4B, inset), likely because of the sensitivitythreshold of aequorin to local Ca2�.

To investigate the specific roles of RyR2 and RyR3 indetermining the L1–L2 morphology of Pcell CaT, RyR2 andRyR3 were blocked individually or in combination duringsteady-state pacing at CL of 1000 ms. The simulations in Figure4C identify Ca2� release from RyR3 (in PCS) and RyR2 (inMyo) as the major contributors to the L1 and L2 components of[Ca2�]avg, respectively. Interestingly, there is “cross-talk” be-tween these processes; RyR3 block has a strong effect on L2.This is because Ca2� release via RyR3 from JSR in PCS isrequired for Ca2�-induced Ca2� release from RyR2 in Myo. Inother words, Ca2� influx from SSL to Myo acts as a source ofCa2� and as 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 CaTPcell�0.45 �mol/L; Vcell�0.67 �mol/L). The stronger ratedependence of Pcell CaT and SR loading (Figure 4D, top andmiddle) shows strong correlation with the faster intracellular[Na�]i accumulation (Figure 4D, bottom). Pcell has a higher[Na�]i concentration than Vcell, approximately 9 mmol/L inquiescent cells and 11 mmol/L during pacing at CL of 1000ms.22 As CL decreases, [Na�]i accumulates faster in Pcellbecause of larger Na� influx via INaL. For CL �500 ms, [Na�]i

plateaus (Figure 4D, bottom), mostly because of a smaller INaL

at short CL. The correlation between [Na�]i and CaT ratedependence is attributable to coupling via INCX and SR loading;at high [Na�]i, intracellular Ca2� extrusion via INCX is reduced,leading to Ca2� loading, greater SR Ca2� content, and larger CaT.

Figure 2. Action potential (AP) morphology and AP duration(APD) rate dependence. A, Simulated Purkinje AP (solid line) dur-ing steady-state pacing at cycle length (CL) of 500 ms and corre-sponding experimental recordings (symbols).16–18 B, APD rateadaptation curves for Purkinje cells (Pcell) (simulated and mea-sured) and ventricular cells (Vcell). C, Effects of [Na�]i clamp at14 mmol/L or 9 mmol/L on Pcell APD rate adaptation. D, Effects of[Na�]i clamp at 12 mmol/L on Vcell APD rate adaptation. E,Changes in Pcell APD (�APD) when [Na�]i and selected currents(INa, INaL, Ito1, IKr, ICaL, IKs, and INaK) at steady-state CL of 2000 msare reset to their values at CL of 500 ms. F, Same as (E) for Vcell.



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AP and Ca2� AlternansCaT alternans (stimulus-to-response ratio of 2:2) developsin Pcell at CL of 300 ms. At this rate, AP alternans is notpresent, and the CaT alternans is driven by refractorinessof SR Ca2� release (Figure 5A). The L2 component of[Ca2�]avg occurs every other beat, indicating high ampli-tude of alternans. The L1 component appears on every beatand alternates with a smaller amplitude. Simulated tracesof Ca2� in JSR and CSR during CaT alternans show that

Ca2� depletion of JSR alternates with a small amplitude,whereas Ca2� depletion of CSR (stimulus-to-responseratio of 2:1) occurs only every other beat. Thesecompartment-specific alternations correspond to the alter-nans of the L1 and L2 components of CaT. It is interestingthat subcellular Ca2� alternans with such large amplitude (oc-currence of L2 component every other beat) is not affecting thePcell AP. Lack of T-tubular system in Pcell is probably respon-sible for the Ca2�–AP dissociation, because it spatially dissoci-

Figure 3. Action potential duration (APD) restitution. A, After steady-state was reached during pacing at cycle length (CL) of 500 ms(S1), an additional stimulus (S2) was applied at a coupling interval of 340 ms or 1000 ms from the last S1 stimulus. Simulated Purkinjecell (Pcell) S1 and S2 action potential (AP; top) are compared with experimental recordings (middle)17 and with ventricular cell (Vcell)AP (bottom). B, Simulated and experimentally measured20,18 Pcell APD restitution curves (CLS1�500 ms). C, Comparison of APD resti-tution in Pcell (black) and Vcell (gray) for S1 pacing at 500 ms, 1000 ms, and 2000 ms. Restitution is steep for S2 coupling interval�300 ms in Pcell (box). D, Changes in Pcell (top) and Vcell (bottom) APD (�APD) when INa, ICaL, IKs, IKr, Ito1, and INaL at diastolic inter-val (DI) of 300 ms were reset to their values at DI of 30 ms for CLS1 of 500 ms. Bottom shows same as top but for Vcell.

Figure 4. Purkinje Ca2� transients (CaT) mor-phology and rate dependence. A, Simulatedsteady-state (cycle length [CL]�1000 ms) actionpotential (AP), CaT ([Ca2�]avg, the spatial averageof Ca2� in peripheral coupling subspace [PCS],subsarcolemmal region [SSL], and bulk myoplasm[Myo]), and [Ca2�]i (myoplasmic Ca2�) during theAP. B, Comparison of simulated CaT with aequorinluminescent signal (an estimate for spatially aver-aged CaT) and of simulated [Ca2�]i with force rec-orded from canine Purkinje fibers (gray box).9 � istime constant for half relaxation. C, Contributionsof ryanodine receptor subtype 2 (RyR2) and ryano-dine receptor subtype 3 (RyR3) to CaT. Duringsteady-state pacing (CL�1000 ms), RyR2 and RyR3are either blocked individually or together. D, Ratedependence of CaT (top), [Ca2�]NSR,max (middle),and [Na�]i,max (bottom) in Pcell (black); correspond-ing simulated data for Vcell are shown for compari-son (gray dash).



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ates Ca2� variations in the center of the cell from the membraneionic transport subsystem.

During steady-state pacing at CL of 200 ms, APD alternansdevelops with a large amplitude (Figure 5B, top) and areaccompanied by large CaT alternans (stimulus-to-responseratio of 2:2; Figure 5B, second row). Ca2� depletion of JSRalternates with a large amplitude and CSR release occurs onlyevery other beat. At CL of 170 ms (Figure 5C), [Ca2�]avg

exhibits a more complex pattern (4:4), in which the L1component of CaT occurs every other beat and L2 only everyfourth beat, reflecting increased subcellular heterogeneity ofCa2� cycling. In summary, [Ca2�]CSR is more responsive toCL shortening than [Ca2�]JSR but has minimal effect on APbecause of spatially mediated Ca2�–AP dissociation, AP and[Ca2�]JSR always display the same stimulus-to-response ratiobecause of strong coupling between the JSR and the cellmembrane, and as pacing rate increases, subcellular hetero-geneity of Ca2� cycling increases.

DAD and Arrhythmic Vulnerability of PcellIonic mechanisms underlying Pcell arrhythmic vulnerabilityattributable to the development of DAD and triggered activityare investigated in Figure 6. Hypersensitivity of RyR2 (eg,because of RyR2 or calsequestrin mutation)23 in Pcell andVcell is phenomenologically modeled by a decrease ofrelease time constant (by 66%) and increased sensitivity toluminal Ca2� content (by 75%). With normal RyR2, aftercessation of steady-state pacing at CL of 300 ms, no sponta-neous depolarizations are observed in either Pcell or Vcell(Figure 6A). With hypersensitive RyR2 at the same pacingrate, Pcell develops DADs and triggered activity (7 sub-threshold DADs and 6 triggered APs) after cessation ofpacing, but Vcell does not (Figure 6B). Occurrence of DADin Pcell exhibits positive rate dependence, mostly because ofhigher SR content at short CL, which is consistent withexperiments.23,24 In Figure 6C, to investigate the underlying

cause of the Pcell greater arrhythmic vulnerability, selectedPcell ionic currents or concentrations (ICaT, INaL, IK1, If, and[Ca2�]NSR) are modified (individually or in combination) tobe “ventricular-like.” Specifically, relative to Pcell, Vcell has

Figure 5. A, Subcellular Ca2� alternans developsin Purkinje cells (Pcell) at cycle length (CL) of 300ms without action potential duration (APD) altern-ans. The L1 component (black dots) of [Ca2�]avgalternates with small amplitude from beat to beat,whereas the L2 component (gray dots) is onlypresent on every other beat. B, At CL of 200 ms,AP alternans also develop. Both L1 and L2 com-ponents of [Ca2�]avg appear only every other beat.C, At CL of 170 ms, the L1 component of[Ca2�]avg occurs every other beat, whereas the L2component occurs only every fourth beat. Pacingstimuli are indicated by gray vertical bars on top.Black or gray dots indicate L1 or L2 componentof CaT (and associated processes), respectively.Stimulus-to-response ratios are indicated inbrackets in each panel.

Figure 6. Delayed afterdepolarizations (DAD) and triggeredactivity. A, After cessation of steady-state pacing at cyclelength (CL) of 300ms, no spontaneous activity is observed inPurinje cells (Pcell) or ventricular cells (Vcell) under control con-ditions. B, With increased ryanodine receptor subtype 2 (RyR2)sensitivity, Pcell develops DADs and triggered action potentials(AP), whereas Vcell remains quiescent. C, Ionic currents or con-centrations (top to bottom: ICaT, INaL, IK1, If, and [Ca2�]NSR) areadjusted either individually or together to resemble their ventric-ular counterparts. *Triggered AP; #subthreshold DAD.



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a much smaller INaL, larger IK1, smaller SR Ca2� content, andno ICaT and If currents. In the simulations, block of ICaT

reduced the number of spontaneous events (6 DADs and 3triggered APs), whereas block of INaL eliminated all triggeredAPs. A 50% increase of IK1 or block of If also eliminatedtriggered APs. A 30% reduction of SR Ca2� content reducedthe number of spontaneous events by 60%. Combination ofall these changes (ventricular-like cell) led to quiescent andstable resting potential. From these simulations, we concludethat the greater Pcell vulnerability to DAD and triggeredactivity is attributable to: (1) higher SR Ca2� content; (2)membrane ion channel profile that reduces excitation thresh-old and resting potential stability (ie, reduced IK1 expressionand presence of If); and (3) depolarizing ion channels thatpromote triggered activity (ie, presence of ICaT and largerINaL).

Early After Depolarization and ItsUnderlying MechanismsWith application of quinidine25–27 or IKr block19 during slowpacing, canine Purkinje fibers develop early afterdepolariza-tions (EAD) that depolarize from plateau potentials of ap-proximately �20 mV. Earlier studies suggested that recoveryfrom inactivation of ICaL is responsible for genesis of EADsin both Pcell26,28 and Vcell.29 However, recent experimentalreports proposed a role for INaL in Purkinje fibers EADs.30,31

The ionic mechanism of EADs is investigated in Figure 7. AtCL of 4000 ms with complete block of IKr, large amplitudeEADs develop starting from beat 127 (Figure 7A, top).Simulated tracings of INaL2, INaL3, and ICaL are shown inFigure 7A (bottom three traces). Reactivation of INaL2 coin-cides with the EADs. In Figure 7B, with only 50% IKr block,80% reduction of Ito1 (simulating reduced Ito1 expression inheart failure32 or myocardial infarction33) elevates the plateaupotentials, leading to more severe EAD activity that startsearlier (at beat 17; Figure 7B, top). Persistent EAD events areobserved starting at beat 42 (Figure 7B, middle). Again, EADoccurrences and patterns are in synchrony with INaL2 reacti-vation (Figure 7B, bottom). Two consecutive APs (41 and 42)

and ionic currents (INaL2 and ICaL) are overlaid in Figure 7C.Recovery and reactivation of INaL produce current of muchlarger amplitude than ICaL. Furthermore, INaL2 reactivationalways precedes both ICaL reactivation (by 10 ms) and theEAD upstroke (by 50 ms; Figure 7C, right), providingdepolarizing charge for EAD generation. These results indi-cate that INaL2 plays the major role in the genesis of EADs incanine Purkinje cells because of its high current density andvoltage range for activation (I-V curve peaks at ��20 mV,the EADs take-off potential). ICaL also reactivates during theEAD upstroke, but its contribution is much smaller than thatof INaL. Thus, EAD formation in Pcell or Vcell relies onrecovery and reactivation of different ion channels during aprolonged plateau; INaL is the major depolarizing current ofPcell EAD, whereas for Vcell EAD it is ICaL.

DiscussionWe present a new mathematical model for the canine cardiacPurkinje AP and Ca2� cycling that is validated with recentexperimental data. Importantly, the model incorporates notonly electrophysiological components that are specific toPurkinje cell but also Ca2� cycling properties that differgreatly from those of ventricular myocyte, both in receptortypes and spatial organization. These properties, which affectthe amplitude and time courses of the CaT and consequentlythe AP, were not incorporated in recently publishedPurkinje cell models12,13 that retained the calcium cyclingrepresentation from models of ventricular myocytes (seeModels Comparison Table in Supplement available onlineat http://www.circresaha.org). The model is used to investigatemechanisms of AP and CaT rate dependence, including APDadaptation and restitution, SR loading, and alternans. Arrhyth-mic triggered activity attributable to DAD and EAD is alsoexplored.

Through a comparative study of behaviors and mecha-nisms between a Purkinje cell and ventricular myocyte, wefound the following. In both Pcell and Vcell, intracellularNa� accumulation at fast rates and its enhancement ofoutward INaK dominate rate-dependent APD shortening dur-

Figure 7. Purkinje early afterdepolarizations(EAD) and underlying mechanism. A, At cyclelength (CL) of 4000 ms with complete IKr block,EADs develop starting from beat 127 (top). Simu-lated tracings of INaL2, INaL3, and ICaL (bottom)identify reactivations of INaL2 as the mechanism ofEAD generation. B, An 80% block of Ito1 and 50%block of IKr lead to increased EAD activity becauseof elevation of plateau potential. EADs areobserved starting from beat 18 and persist frombeat 42. C, Two consecutive action potentials (AP)(beats 41 and 42; B) are overlaid with INaL2 andICaL. A portion of beat 42 (box in left panel) isenlarged in the right panel. Reactivated INaL2 is ofmuch larger amplitude than ICaL and precedes thereactivation of ICaL and the EAD upstroke.



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ing steady-state pacing (adaptation). In Pcell, INaL contributesadditional APD shortening at short CL because of incompleterecovery from inactivation, causing steeper adaptation thanVcell; contributions to APD adaptation from currents otherthan INaK are minimal in Vcell. Pcell APD restitution issteeper than that of Vcell. At short coupling intervals, INaL

inactivation is most important in causing APD shortening inPcell; in Vcell, Ito1 underlies APD shortening. Pcell exhibitsa biphasic CaT, reflecting a delay between Ca2� release fromJSR (via RyR3 and IP3R) and CSR (via RyR2). Ratedependence of CaT and SR loading is stronger in Pcell thanVcell, mostly because of faster [Na]i accumulation. In con-trast to Vcell, Pcell Ca2� alternans can occur without causingAP alternans because of spatial dissociation between [Ca2�]i

and membrane ion channels. Pcell AP alternans develops at ashorter CL than Vcell, with an increased subcellular heteroge-neity of Ca2� cycling. Greater Pcell vulnerability to DAD isattributable to higher SR content and the presence of membranecurrents that reduce excitation threshold and rest potentialstability (IK1, If) and currents that promote triggered activity(ICaT, INaL). EAD generation in Pcell is mostly attributable toreactivation of INaL2, whereas ICaL plays this role in Vcell.

These findings provide new insights into the arrhythmo-genic potential of Purkinje fibers. Recent studies have dem-onstrated greater arrhythmic vulnerability in Purkinje com-pared to ventricular myocardium.1–4 This could result fromproperties at the tissue scale, such as high expression ofconnexin, loading conditions attributable to frequent branch-ing and highly variable fiber cross-sections, and asymmetricalelectric properties at Purkinje–muscle junctions.34 The singlecell results presented here show that Purkinje fibers areintrinsically more arrhythmogenic than ventricular myocytes.The Purkinje cell has a steeper rate dependence of AP andCaT, it operates at a higher SR Ca2� load, and it is moreprone to development of triggered activity because of itsdifferent ion channel profile.

A recent study in isolated canine Purkinje cells by Lee etal35 reported complex beat-to-beat variations of CaT at a fastpacing rate and negative rate dependence of CaT and SRloading. Consistent with the complex beat-to-beat CaT pat-tern, our simulations demonstrate increased subcellular het-erogeneity of Ca2� cycling at short CL, mostly because ofCa2�–AP dissociation and refractoriness of Ca2� releasefrom both CSR and JSR (Figure 5). However, unlike theexperiment,34 the model exhibits positive rate dependence ofboth CaT and SR loading. This dependence is stronger inPcell than in Vcell (for CL between 2000 ms and 500 ms)because of faster Na� accumulation. There is a paucity of directmeasurements of CaT rate dependence in canine Purkinje fibers.Indirect evidence supports a positive relationship; for example,DAD appear earlier with greater amplitudes as pacing rate isincreased,24 suggesting an increased SR content. A positive CaTrate dependence was observed experimentally in sheep Purkinjefibers.36 The different results of Lee et al35 could possibly reflectdifferent temperature in models (37°C, body temperature) andexperiments (22°C to 24°C, room temperature), because reducedNa� current at a lower temperature decreases Na� accumulationand consequently Ca2� loading.

The Pcell model was formulated as a compartmental model,capturing properties of Ca2� cycling in distinct compartments.Although this constitutes an important step forward in modelingPcell physiology, it does not represent spatially distributedprocesses at the scale of Ca2� release units and spark formation.Further model development is required to simulate spatiallydistributed phenomena such as formation of Ca2� waves andtheir electrophysiological consequences.

AcknowledgmentsThe authors thank the following members of the Rudy LaboratoryLeonid M. Livshitz, Thomas O’Hara, Namit Gaur, Ali Nekouzadeh,Ashwin Mohan, Jiajing Xu, and Smiruthi Ramasubramanian formost helpful discussions.

Sources of FundingThis work was supported by National Institutes of Health NationalHeart, Lung, and Blood Institute grants RO1-HL-49054-19 andRO1-HL-33343-26, by the National Science Foundation under grantCBET-0929633, and by Foundation Leducq Award to the Alliancefor Calmodulin Kinase Signaling in Heart Disease (grant 08CVD01)to Y. Rudy. Y. Rudy is the Fred Saigh Distinguished Professor atWashington University.

DisclosuresNone.

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calcium dysregulation is the cellular mechanism that underlies catechol-aminergic polymorphic ventricular tachycardia. Heart Rhythm. 2010;7:1122–1128.

2. Cerrone M, Noujaim SF, Tolkacheva EG, Talkachou A, O’Connell R,Berenfeld O, Anumonwo J, Pandit SV, Vikstrom K, Napolitano C, PrioriSG, Jalife J. Arrhythmogenic mechanisms in a mouse model of catechol-aminergic polymorphic ventricular tachycardia. Circ Res. 2007;101:1039.

3. Kang G, Giovannone SF, Liu N, Liu FY, Zhang J, Priori SG, Fishman GI.Purkinje cells from RyR2 mutant mice are highly arrhythmogenic butresponsive to targeted therapy. Circ Res. 2010;107:512–519.

4. Tabereaux PB, Walcott GP, Rogers JM, Kim J, Dosdall DJ, RobertsonPG, Killingsworth CR, Smith WM, Ideker RE. Activation patterns ofPurkinje fibers during long-duration ventricular fibrillation in an isolatedcanine heart model. Circulation. 2007;116:1113–1119.

5. Dun W, Boyden PA. The Purkinje cell; 2008 style. J Mol Cell Cardiol.2008;45:617–624.

6. Balati B, Varro A, Papp JG. Comparison of the cellular electrophysiologicalcharacteristics of canine left ventricular epicardium, M cells, endocardiumand Purkinje fibres. Acta Physiol Scand. 1998;164:181–190.

7. Burashnikov A, Antzelevitch C. Differences in the electrophysiologicresponse of four canine ventricular cell types to �1-adrenergic agonists.Cardiovasc Res. 1999;43:901.

8. Sommer JR, Johnson EA. Cardiac muscle. J Cell Biol. 1968;36:497.9. Hess P, Wier WG. Excitation-contraction coupling in cardiac Purkinje

fibers. Effects of caffeine on the intracellular [Ca2�] transient, membranecurrents, and contraction. J Gen Physiol. 1984;83:417.

10. Boyden PA, Pu J, Pinto J, Keurs H. Ca2� transients and Ca2� waves inpurkinje cells: role in action potential initiation. Circ Res. 2000;86:448.

11. Stuyvers BD, Dun W, Matkovich S, Sorrentino V, Boyden PA, ter KeursH. Ca2� sparks and waves in canine purkinje cells: a triple layered systemof Ca2� activation. Circ Res. 2005;97:35.

12. Aslanidi OV, Stewart P, Boyett MR, Zhang H. Optimal velocity andsafety of discontinuous conduction through the heterogeneous Purkinje-ventricular junction. Biophys J. 2009;97:20–39.

13. Sampson KJ, Iyer V, Marks AR, Kass RS. A computational model ofPurkinje fibre single cell electrophysiology: implications for the long QTsyndrome. J Physiol. 2010;588:2643–2655.

14. Decker KF, Heijman J, Silva JR, Hund TJ, Rudy Y. Properties and ionicmechanisms of action potential adaptation, restitution, and accommo-dation in canine epicardium. Am J Physiol Heart Circ Physiol. 2009;296:H1017.



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15. Sheets MF, January CT, Fozzard HA. Isolation and characterization ofsingle canine cardiac purkinje cells. Circ Res. 1983;53:544.

16. Han W, Wang Z, Nattel S. A comparison of transient outward currents incanine cardiac Purkinje cells and ventricular myocytes. Am J PhysiolHeart Circ Physiol. 2000;279:H466.

17. Robinson RB, Boyden PA, Hoffman BF, Hewett KW. Electrical resti-tution process in dispersed canine cardiac Purkinje and ventricular cells.Am J Physiol Heart Circ Physiol. 1987;253:H1018.

18. Knilans TK, Varro A, Nanasi PP, Murray RJ, Kaiser FC, Lathrop DA.Electrophysiologic effects of FPL 13210 on canine Purkinje fiber actionpotential duration and Vmax comparison to disopyramide. CardiovascDrugs Ther. 1991;5:139–146.

19. Kondo M, Tsutsumi T, Mashima S. Potassium channel openersantagonize the effects of class III antiarrhythmic agents in canine Purkinjefiber action potentials. Implications for prevention of proarrhythmiainduced by class III agents. Jpn Heart J. 1999;40:609–619.

20. Varro A, Nakaya Y, Elharrar V, Surawicz B. Effect of antiarrhythmic drugson the cycle length-dependent action potential duration in dog Purkinje andventricular muscle fibers. J Cardiovasc Pharmacol. 1986;8:178.

21. Bocchi L, Vassalle M. Characterization of the slowly inactivating sodiumcurrent INa2 in canine cardiac single Purkinje cells. Exper Physiol. 2008;93:347–361.

22. Lee CO, Dagostino M. Effect of Strophanthidin on Intracellular Na ionactivity and twitch tension of constantly driven canine cardiac Purkinjefibers. Biophys J. 1982;40:4.

23. Liu N, Rizzi N, Boveri L, Priori SG. Ryanodine receptor and calse-questrin in arrhythmogenesis: what we have learnt from genetic diseasesand transgenic mice. J Mol Cell Cardiol. 2009;46:149–159.

24. Moak JP, Rosen MR. Induction and termination of triggered activity bypacing in isolated canine Purkinje fibers. Circulation. 1984;69:149.

25. Davidenko JM, Cohen L, Goodrow R, Antzelevitch C. Quinidine-inducedaction potential prolongation, early afterdepolarizations, and triggeredactivity in canine Purkinje fibers. Effects of stimulation rate, potassium,and magnesium. Circulation. 1989;79:674.

26. Nattel S, Quantz MA. Pharmacological response of quinidine inducedearly afterdepolarisations in canine cardiac Purkinje fibres: insights intounderlying ionic mechanisms. Cardiovasc Res. 1988;22:808.

27. Roden DM, Hoffman BF. Action potential prolongation and induction ofabnormal automaticity by low quinidine concentrations in canine Purkinjefibers. Relationship to potassium and cycle length. Circ Res. 1985;56:857.

28. January CT, Riddle JM. Early afterdepolarizations: mechanism ofinduction and block. A role for L-type Ca2� current. Circ Res. 1989;64:977.

29. Zeng J, Rudy Y. Early afterdepolarizations in cardiac myocytes:mechanism and rate dependence. Biophys J. 1995;68:949–964.

30. Orth PM, Hesketh JC, Mak CKH, Yang Y, Lin S, Beatch GN, Ezrin AM,Fedida D. RSD1235 blocks late INa and suppresses early afterdepolar-izations and torsades de pointes induced by class III agents. CardiovascRes. 2006;70:486.

31. Fedida D, Orth PM, Hesketh JC, Ezrin AM. The role of late I andantiarrhythmic drugs in EAD formation and termination in Purkinjefibers. J Cardiovasc Electrophysiol. 2006;17:S71–S78.

32. Kaab S, Nuss HB, Chiamvimonvat N, O’Rourke B, Pak PH, Kass DA,Marban E, Tomaselli GF. Ionic mechanism of action potential prolon-gation in ventricular myocytes from dogs with pacing-induced heartfailure. Circ Res. 1996;78:262.

33. Jeck C, Pinto J, Boyden P. Transient outward currents in subendocardialPurkinje myocytes surviving in the infarcted heart. Circulation. 1995;92:465.

34. Kleber AG, Rudy Y. Basic mechanisms of cardiac impulse propagationand associated arrhythmias. Physiol Rev. 2004;84:431.

35. Lee YS, Dun W, Boyden PA, Sobie EA. Complex and rate-dependentbeat-to-beat variations in Ca2� transients of canine Purkinje cells. J MolCell Cardiol. 2011;50:662–669.

36. Lado MG, Sheu SS, Fozzard HA. Changes in intracellular Ca2� activitywith stimulation in sheep cardiac Purkinje strands. Am J Physiol HeartCirc Physiol. 1982;243:H133.

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 catechol-

aminergic polymorphic ventricular tachycardia and ventricularfibrillation (VF).

● The electrophysiological profile and calcium (Ca) cycling properties ofPcell are considerably different from Vcell.

What New Information Does This Article Contribute?● We developed a mathematical model of Pcell that represents its

unique electrophysiological and Ca handling properties, and weconducted a Pcell–Vcell comparison.

● Rate dependence of action potential (AP) and Ca transient (CaT) issteeper in Pcell, consistent with greater vulnerability to arrhythmia.

● Pcell is more prone to the development of arrhythmogenic delayedafterdepolarizations (DAD).

● Pcell mechanisms and properties of AP and CaT alternans and ofearly afterdepolarizations (EAD) differ from those of Vcell.

The cardiac Pcell is thought to be more prone to development ofarrhythmic activity than Vcell. The Pcell has been implicated as

an important contributor to catecholaminergic polymorphic ven-tricular tachycardia and VF. However, the mechanistic basis forits greater arrhythmia vulnerability is not completely understood.Electrophysiological characteristics and intracellular Ca handlingof Pcell are considerably different from Vcell. Importantly, Pcellis devoid of transverse tubules and has a complex spatialdistribution of Ca release sites. We developed a mathematicalmodel of the canine Pcell that incorporates these uniqueproperties. The model was used to obtain new mechanisticinsights into rate dependence of Pcell AP and CaT, and tocompare Pcell and Vcell properties. The simulations demon-strated that Pcell is intrinsically more arrhythmogenic than Vcell.It has steeper rate dependence of AP (because of contributionfrom the late sodium current) and CaT (because of stronger ratedependence of sarcoplasmic reticulum [SR] Ca loading). Itoperates at higher SR Ca load that, together with its different ionchannel profile, makes it more prone to development of DAD andtriggered activity than Vcell. Recognizing the important role ofPcell in arrhythmogenesis and understanding its underlyingmechanisms are first steps toward the development of novelantiarrhythmic strategies.



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Pan Li and Yoram RudyTriggered Activity, and Comparison to Ventricular Myocytes

Cycling: Rate Dependence,2+A Model of Canine Purkinje Cell Electrophysiology and Ca

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SUPPLEMENT

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

Pan Li and Yoram Rudy

I. Definitions and Abbreviations (Page 2-4)

II. Model Parameters (Page 5-6)

III. Model Equations and Validation (Page 7-25)

IV. Supplemental Figures S8, S9, S10 (Page 26-27)

V. Models Comparison Table (Page 28-29)

VI. Supplemental References (Page 30-32)

Revised to correct minor typos and equation errors on November 19, 2012.

I DEFINITIONS AND ABBREVIATIONS

Abbreviations Definitions General parameters AP Action Potential APD90 Action Potential Duration (at 90% repolarization) (ms) CL Cycle Length (ms) DI Diastolic Interval (ms) CaT Ca2+ Transient (mmol/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 V Membrane Voltage (mV) Ex Reversal potential of current x (mV) Gx Maximum conductance of current x (ms/µF) x∞ Steady state value of variable x xτ Time constant of variable x αx Opening rate constant of gate x βx Closing rate constant of gate x Px Permeability to ion x (cm/s) Px,y Permeability ratio of ion x to ion y zx Valence of ion x vx Volume of compartment x R Gas constant (8314 J/kmol/K) T Temperature (310K) F Faraday constant (96487 C/mol) ACap Capacitive membrane area (cm2) AGeo Geometric membrane area (cm2) CAMKII Ca2+/calmodulin-dependent protein kinase II CAMKbound Fraction of CAMKII binding sites bound to Ca2+/calmodulin CAMKtrap Fraction of autonomous CAMKII binding sites with trapped calmodulin CAMKactive Fraction of active CAMKII binding sites CAMK0 Fraction of active CAMKII binding sites at equilibrium αCAMK, βCAMK Phosphorylation and dephosphorylation rates of CAMKII (ms-1)

PLB Phospholamban Currents, Pumps, Exchangers (µA/µF) INa Fast Na+ current INaL Slowly inactivating late Na+ current INaL,2 Type 2 component of INaL with its I-V curve peaked at -20mV INaL,3 Type 3 component of INaL in the pacemaker range ICaL Ca2+ current through the L-type Ca2+ channel ICaT Ca2+ current through the T-type Ca2+ channel IpCa Sarcolemmal Ca2+ pump ICab Background Ca2+ current IKr Rapid delayed rectifier K+ current IKs Slow delayed rectifier K+ current IK1 Inward rectifier K+ current If Hyper-polarization activated Na+-K+ current If,Na Hyper-polarization activated Na+ current If,K Hyper-polarization activated K+ current Ito1 4-AP sensitive transient outward K+ current INaK Na+-K+ pump current INCX Na+-Ca2+ exchanger current ICa,tot Total transmembrane Ca2+ current ICa,tot=ICaL+ICab+IpCa+ICaT - 2(INCX,SSL+INCX,PCS) IK,tot Total transmembrane K+ current IK,tot=IKr+IKs+IK1-2INaK+Ito1+If,k INa,tot Total transmembrane Na+ current INa,tot=INa+INaL +INab+3INaK+If,Na+3(INCX,SSL+INCX,PCS) Itot Total transmembrane current Itot=ICa,tot+ IK,tot+ INa,tot

Gates m,h,j Activation gate, fast inactivation gate, and slow inactivation gate of INa,

respectively mL2,hL2 Activation gate and slow inactivation gate of INaL,2, respectively mL3,hL3 Activation gate and slow inactivation gate of INaL,3, respectively d, f, f2 Activation gate, fast voltage-dependent inactivation gate, and slow

voltage dependent inactivation gate of ICaL, respectively fCa, fCa2 Fast Ca2+-dependent inactivation gate and slow Ca2+-dependent

inactivation gate of ICaL, respectively X1s , X2s Fast activation gate and slow activation gate of IKs, respectively xr Activation gate of IKr

rkr Time-independent rectification gate of IKr K1 Inactivation gate of IK1 a,i,i2 Activation gate, fast inactivation gate, and slow inactivation gate of Ito,

respectively asus,isus Activation gate and inactivation gate of Isus, respectively y Activation gate of If

Fluxes (mmol /L /ms) JRyR3 Ca2+ release from RyR3 JIP3R Ca2+ release from IP3R JRyR2 Ca2+ release from RyR2 Jtr,j Ca2+ translocation from NSR to JSR Jtr,c Ca2+ translocation from NSR to CSR Jleak Ca2+ leak from NSR to Myo Jleak,s Ca2+ leak from NSR to SSL JSERCA Ca2+ uptake from Myo to NSR via SERCA Jdiff Ionic diffusion from PCS to SSL Jgap Ionic diffusion from SSL to Myo τdiff Time constant for diffusion from PCS to SSL (ms) τgap Time constant for diffusion from SSL to Myo (ms) τtr Time constant for Ca2+ translocation from NSR to JSR/CSR (ms)

Calcium Buffers CMDNMyo Calmodulin, Ca2+ buffer in Myo TRPNMyo Troponin, Ca2+ buffer in Myo CMDNSSL Calmodulin, Ca2+ buffer in SSL TRPNSSL Troponin, Ca2+ buffer in SSL BSR Anionic SR binding sites for Ca2+ buffer in PCS BSL Anionic sarcolemmal binding sites for Ca2+ buffer in PCS 𝛽𝑃𝐶𝑆 Buffer factor for PCS CSQNJSR Calsequestrin, Ca2+ buffer in JSR CSQNCSR Calsequestrin, Ca2+ buffer in CSR

Ionic Concentrations (mmol/L) [Ca2+]x Ca2+ concentration in compartment x,

(e.g. x=i indicates the Myoplasmic compartment) [Na+]x Na+ concentration in compartment x [K+]x K+ concentration in compartment x

II MODEL BASIC PARAMETERS

Stimulus

Current stimulus of amplitude -80.0 𝜇𝐴/𝜇𝐹 and duration 0.5 ms is applied during pacing protocols.

External concentrations

[𝑁𝑎+]𝑜 = 140 𝑚𝑀; [𝐶𝑎2+]𝑜 = 1.8 𝑚𝑀; [𝐾+]𝑜 = 5.4 𝑚𝑀

Initial conditions

V -85.0 m 0.0 h 0.9 j 0.9 d 0.0 f 0.9 f2 0.9 fca 0.9 fca2 0.9 xs1 0.0 xs2 0.0 xr 0.0 a 0.0 i 0.9 i2 0.9 aa 0.0 mL2 0.0 mL3 0.0 hL2 0.9 hL3 0.9 b 0.0 g 0.9 u 0.0 y 0.0 [Ca2+]PCS 0.0001 [Ca2+]JSR 1.0 [Ca2+]CSR 1.0 [Ca2+]NSR 1.0 [Ca2+]SSL 0.0001 [Ca2+]i 0.0001 [Na+]i 8.0 [K+]i 140 [CAMK]trap 0.0

Reversal potentials

𝐸𝑁𝑎 =𝑅𝑇𝐹∙ ln(

[𝑁𝑎+]𝑜[𝑁𝑎+]𝑆𝑆𝐿

)

𝐸𝐾 =𝑅𝑇𝐹∙ ln(

[𝐾+]𝑜[𝐾+]𝑖

)

𝐸𝐶𝑎 =𝑅𝑇𝐹∙ ln(

[𝐶𝑎2+]𝑜[𝐶𝑎2+]𝑆𝑆𝐿

)

III MODEL EQUATIONS AND VALIDATION

Experimental Data Selection Criteria

1. Validation of ionic currents: Experimental data used to validate the Pcell model were either from un-diseased canine Purkinje fibers or isolated cells at 37oC. For the validation of individual ionic currents, we preferred experimental studies (Han et al1) that provided measurements of multiple ionic currents, recoded under the same experimental conditions. Among voltage-clamp studies that provided measurements of the same ionic current (i.e. IK1

1,2), preference was given to those providing additional information that allowed for more rigorous validation, (e.g. dependence on extracellular ionic concentrations). For instance, we validated Pcell IK1 current using data from Shah et al2, where I-V relationship and [K+]o dependence are both available.

2. Validation of ionic concentrations: Although it is well accepted that intracellular Na content in Pcell is higher than that of Vcell3, there is paucity of experimental data that directly quantify steady-state Na accumulation during pacing at different cycle lengths (CL). Validation of the intracellular Na content is based on experimental measurements of Na ion activity of constantly driven canine cardiac Purkinje fibers4. For validation of simulated Pcell Ca dynamics, we used both earlier and more recent experimental data. Early Ca measurements using Aequorin5 revealed the biphasic L1-L2 morphology of the Ca2+ transient (CaT) and described the dynamic response of L1 and L2 to drug application. Despite the relatively low sensitivity of Aequorin to local Ca, these experiments are well suited for validation of the model subcellular organization of Ca cycling. Importantly, recent data from confocal microscopic studies6 using fluorescence imaging were used for the validation of other CaT properties, including diastolic concentration, magnitude during the AP and time course of relaxation.

3. Validation of the Action Potential (AP): 3.1 AP Morphology: Even under similar experimental conditions, morphology of AP recorded from isolated canine Purkinje cells demonstrates large differences (probably related to the isolation procedure1). With these differenecs, canine Purkinje AP morphology can be characterized by the following consistent properties: fast upstroke (dV/dtmax of about 500 v/s; faster than Vcell), sloping repolarization time course during phase-2, slower repolarization during phase-3 compared to Vcell, and similar resting potential to that of Vcell. The Pcell model formulated here reproduces these characteristics that are distinct and typical to Purkinje AP (Figure 2A, main text). 3.2 AP rate dependence: Most experimental data of Purkinje AP rate dependence are based on measurements in Purkinje fibers. While more consistent than single-cell recordings, results still vary. For example, steady-state measurements of APD in isolated canine Purkinje fibers at CL=2000ms range from 350ms to 450ms7,8. Such variation (100ms) in APD is much larger than the differences between fiber and single cell measurements due to electrotonic influences (10ms9). Thus, the more consistent experimental measurements in Purkinje fibers were used to validate the simulated Purkinje AP rate dependence (Figure 2B, main text).

Fast Sodium Current (INa)

Formulation of INa is modified from the Hund-Decker-Rudy (HRd) model9 to achieve maximum upstroke velocity (dV/dtmax) and amplitude of Purkinje AP that are consistent with experimental measurements7.

Equations:

𝛼𝑚 =0.64 ∙ (𝑉 + 37.13)1 − 𝑒−0.1∙(𝑉+37.13)

𝛽𝑚 = 0.16 ∙ 𝑒−( 𝑉11)

If 𝑉 ≥ −40.0𝑚𝑉

𝛼ℎ = 0.0

𝛽ℎ =1

0.13 ∙ (1 + e−(V+10.6611.1 ))

𝛼𝑗 = 0.0

𝛽𝑗 =0.3 ∙ e−2.535×10−7∙V

1 + e−(V+3210 )

else

𝛼ℎ = 0.135 ∙ 𝑒−(𝑉+706.8 )

𝛽ℎ = 3.56 ∙ 𝑒0.079∙𝑉 + 3.1 × 105 ∙ 𝑒0.35∙𝑉

𝛼𝑗 =(−1.2714 × 105 ∙ e0.2444∙V − 0.003474 ∙ 𝑒−0.04391∙𝑉) ∙ (𝑉 + 37.78)

1 + e0.311∙(Vm+79.23)

𝛽𝑗 =0.1212 ∙ e−0.01052∙V

1 + e−0.1378∙(v+40.14)

��𝑁𝑎= 18 mS/µF

𝐼𝑁𝑎 = ��𝑁𝑎 ∙ 𝑚3 ∙ ℎ ∙ 𝑗 ∙ (𝑉 − 𝐸𝑁𝑎)

Late Sodium Current (INaL)

Two populations of INaL (INaL,2 and INaL,3) are included in the model, based on canine purkinje data from Vassalle and coworkers10,11. It was shown using voltage clamp that INaL,2 activated at -50mV and reached its peak at -20mV. Time constant for activation of INaL is the same as that of INa. INaL,2 voltage dependence of activation, inactivation and the time constant for inactivation were fitted to the data of Vassalle et al10 (Figure S1). The INaL,2 I-V curve is in agreement with experimental recordings (Figure S1 A). Compared to INaL,2, INaL,3 is characterized by smaller current density, faster inactivation and left-shifted voltage-dependent activation (35mV)11.

Equations:

𝑚𝐿2,𝜏 =1

0.64 ∙ (𝑉 + 37.13)1 − 𝑒−0.1∙(𝑉+37.13) + 0.16 ∙ 𝑒−( 𝑉11)

𝑚𝐿2,∞ =1

1 + e−(V+28)

7

𝑚𝐿3,𝜏 = 𝑚𝐿2,𝜏

𝑚𝐿3,∞ =1

1 + e−(V+63)

7

ℎ𝐿2,𝜏 = 162 +132

1 + 𝑒−(𝑉+28)5.5

ℎ𝐿2,∞ =1

1 + e(V+28)12

ℎ𝐿3,𝜏 = 0.5 ∗ ℎ𝐿2,𝜏

ℎ𝐿3,∞ =1

1 + e(V+63)12

𝑗𝐿2,𝜏 = 411

𝑗𝐿2,∞ = ℎ𝐿2,∞

𝑗𝐿3,𝜏 = 0.5 ∙ 𝑗𝐿2,𝜏

𝑗𝐿3,∞ = ℎ𝐿3,∞

��𝑁𝑎𝐿,2= 0.052 mS/µF; ��𝑁𝑎𝐿,3= 0.018 mS/µF

𝐼𝑁𝑎𝐿,2 = ��𝑁𝑎𝐿,2 ∙ 𝑚𝐿2 ∙ ℎ𝐿2 ∙ 𝑗𝐿2 ∙ (𝑉 − 𝐸𝑁𝑎)

𝐼𝑁𝑎𝐿,3 = ��𝑁𝑎𝐿,3 ∙ 𝑚𝐿3 ∙ ℎ𝐿3 ∙ 𝑗𝐿3 ∙ (𝑉 − 𝐸𝑁𝑎)

𝐼𝑁𝑎𝐿 = 𝐼𝑁𝑎𝐿,2 + 𝐼𝑁𝑎𝐿,3

Figure S1. INaL,2 Model Validation. Experimental data are from Vassalle et al10 (dots). Simulation results are shown as solid gray lines. (A) I-V curve (B) Inactivation time constant.

L-type Calcium Current (ICaL)

ICaL is a smaller current in canine Purkinje cells compared to ventricular myocytes. Steady state activation and inactivation, and fast and slow inactivation time constants are fitted using data from canine purkinje cells published by Han et al1 (Figure S2). I-V curve of ICaL is in agreement with experimental measurements (Figure S2 C). Calcium dependent inactivation and CAMKII dependence of ICaL are the same as in HRd model.

Equations:

𝑑∞ =1

1 + e−(V−2)7.8

𝑑𝜏 = 0.59 + 0.8 ∙𝑒0.052∙(𝑉+13)

1 + 𝑒0.132∙(𝑉+13)

𝑓∞ =1

1 + eV+16.59.5

𝑓𝜏 =0.92

0.125 ∙ e−0.00261∙(V−2.5)2 + 0.1

𝑓2,∞ = 𝑓∞

𝑓2,𝜏 =0.9

0.02 ∙ e−0.0018∙(V−18.6)2 + 0.005

𝑓𝐶𝑎,∞ =0.3

1 − 𝐼𝐶𝑎𝐿0.05

+0.55

1 + [𝐶𝑎2+]𝑃𝐶𝑆0.003

+ 0.15

𝑓𝐶𝑎,𝜏 =10

1 + 𝐾𝑚𝐶𝑎𝑀𝐶𝐴𝑀𝐾𝑎𝑐𝑡𝑖𝑣𝑒

+ 0.5 +1

1 + [𝐶𝑎2+]𝑃𝐶𝑆0.003

A B

𝑓𝐶𝑎,2,∞ =1

1 − 𝐼𝐶𝑎𝐿0.01

𝑓𝐶𝑎,2,𝜏 =300

1 + 𝑒−(0.175+𝐼𝐶𝑎𝐿)

0.04+ 125

𝑃𝐶𝑎 = 1.9926 × 10−4 𝑐𝑚/𝑠

𝛾𝑐𝑎𝑖 = 1

𝛾𝑐𝑎𝑜 = 0.341

𝐼��𝑎𝐿 = 𝑃𝐶𝑎 ∙ 𝑧𝐶𝑎2 ∙(𝑉 − 15) ∙ 𝐹2

𝑅𝑇∙𝛾𝐶𝑎𝑖 ∙ [𝐶𝑎2+]𝑃𝐶𝑆 ∙ 𝑒

𝑧𝑐𝑎∙(−15)∙𝐹𝑅𝑇 − 𝛾𝐶𝑎𝑜 ∙ [𝐶𝑎2+]𝑜

𝑒𝑧𝑐𝑎∙(𝑉−15)∙𝐹

𝑅𝑇 − 1

𝐼𝐶𝑎𝐿 = 𝐼��𝑎𝐿 ∙ 𝑑 ∙ 𝑓 ∙ 𝑓2 ∙ 𝑓𝑐𝑎 ∙ 𝑓𝑐𝑎,2

Figure S2. ICaL Model Validation. Experimental data are from Han et al1 (dots). Simulation results are shown as gray lines. (A) voltage dependence of steady state activation and inactivation. (B) slow and fast inactivation time constants . (C) I-V curve.

τslow

τfast

T-type Calcium Current (ICaT)

ICaT is a larger current in canine Purkinje cells compared to ventricular myocytes. Steady state activation and inactivation are fitted using canine Purkinje cell data from Han et al1 (Figure S3 A). I-V curve of ICaT is in agreement with experimental measurements (Figure S3 B). It should be noted that the T/L ratio (the ratio between maximum T type and L type Ca current densities) measured by Han et al1 and computed in the model is 0.8. This ratio is larger than earlier reported values (0.6) (Hirano et al12, Tseng and Boyden13). The difference could be accounted for by differences between voltage clamp protocols (in holding potential and [Ca2+]o). However, this difference has minimal effect on the Pcell AP ( reduction of T/L ratio to 0.6 in the model does not change AP morphology and shortens APD by only 1ms). We chose Han et al1 data for ICaT validation because this publication provides data for several other currents, recorded under the same experimental conditions.

Equations:

𝑏∞ =1

1 + e−(V+30)

7

𝑏𝜏 =1

1.068 ∙ e−(V+16.330 ) + 1.068 ∙ e

V+16.330

𝑔∞ =1

1 + e(V+61)

5

𝑔𝜏 =1

0.015 ∙ e−(V+71.783.3 ) + 0.015 ∙ e

V+71.715.4

��𝐶𝑎𝑇 = 0.07875 mS/µF

𝐼𝐶𝑎𝑇 = ��𝐶𝑎𝑇 ∙ 𝑏 ∙ 𝑔 ∙ (𝑉 − 𝐸𝐶𝑎)

Figure S3. ICaT Model Validation. Experimental data are from Han et al1 (dots). Simulation results are shown as gray lines. (A) steady state voltage dependence of steady-state activation and inactivation. (B) I-V curve.

Transient Outward Potassium Current (Ito1)

Formulation of Ito1 is fitted to canine Purkinje cell data from Han et al1 and Dumaine and Cordeiro14 (Figure S4). Ito1 consists of a transient outward current with slow time-dependent recovery (Ito) and an instantaneous sustained current (Isus).

Ito is more rate dependent in Purkinje cells than in ventricular myocytes15. Voltage dependent activation and inactivation, slow and fast inactivation time constants and I-V curve are in agreement with experimental measurements1 (Figure S4 A-C). Simulated Ito reactivation time course (Figure S4 D) is in agreement with experimental data from Han et al1.

The formulation of Isus is modified from previous modeling studies16,17, assuming instantaneous activation. This is consistent with experimental recordings that show no rate dependence of this current (Jeck et al18 and Han et al15). The simulated I-V curve is in agreement with experimental measurements by Dumaine and Cordeiro14 (Figure S4 E).

Equations:

𝑎𝜏 =1

25 ∙ eV−8218

1 + eV−8218

+ 25 ∙ e−�V+5218 �

1 + e−�V+5218 �

𝑖𝜏 =1

0.1 ∙ e−(V+12515 ) + 0.1 ∙ eV+226.5

+ 2.86

𝑖2,𝜏 =1

0.005 ∙ e−(V+138.252 ) + 0.003 ∙ e

V+1812.5

+ 21.5

𝑎∞ =1

1 + e−(V−8.9)10.3

𝑖∞ =1

1 + eV+3011

𝑖2,∞ = 𝑖∞

𝑎𝑠𝑢𝑠 = 1

1+e−(V−3.0)19.8

��𝑡𝑜 = 0.1414mS/µF

��𝑠𝑢𝑠 = 0.042 mS/µF

𝐼𝑡𝑜,𝑠 = ��𝑡𝑜 ∙ 𝑎 ∙ 𝑖 ∙ 𝑖2 ∙ (𝑉 − 𝐸𝐾)

𝐼𝑡𝑜,𝑓 = ��𝑠𝑢𝑠 ∙ 𝑎𝑠𝑢𝑠 ∙ (𝑉 − 𝐸𝐾)

𝐼𝑡𝑜1 = 𝐼𝑡𝑜 + 𝐼𝑠𝑢𝑠

Figure S4. Ito and Isus Model Validation. Experimental data are from Han et al1 (Ito) and Dumaine and Cordeiro14 (Isus) (dots). Simulation results are shown as gray lines. (A) voltage dependence of steady-state activation and inactivation. (B) I-V curve. (C) fast (solid) and slow (dashed) inactivation time constants. (D) Simulated Ito reactivation time course obtained from a double-pulse (P1-P2) protocol. (E) Isus I-V curve.

Slow Delayed Rectifier Potassium Current (IKs)

Formulation of IKs is fitted to canine Purkinje cell data from Han et al1 (Figure S5). Slow and fast activation time constants, and I-V relationship are in agreement with experimental measurements.

Equations:

𝐸𝐾𝑠 =𝑅𝑇𝐹∙ ln(

[𝐾+]𝑜 + 𝑃𝑁𝑎,𝐾 ∙ [𝑁𝑎+]𝑜[𝐾+]𝑖 + 𝑃𝑁𝑎,𝐾 ∙ [𝑁𝑎+]𝑆𝑆𝐿

)

��𝐾𝑠 = 0.053 ∙

⎝

⎜⎛

1 +0.6

1 + �3.8 × 10−5[𝐶𝑎2+]𝑆𝑆𝐿

�1.4

⎠

⎟⎞

𝑋1𝑠,∞ = 𝑋2𝑠,∞ =1

1 + e−(V−913.7)

B C

D

E

A

τfast

τslow

𝑋1𝑠,𝜏 =200

e−(V+106 ) + eV−6255

𝑋2𝑠,𝜏 = 1500 + 350

e−(V+104 ) + eV−9058

𝐼𝐾𝑠 = ��𝐾𝑠 ∙ 𝑋1𝑠 ∙ 𝑋2𝑠 ∙ (𝑉 − 𝐸𝐾𝑠)

Figure S5. IKs Model Validation. Experimental data are from Han et al1 (dots). Simulation results are shown as gray lines. (A) slow and fast activation time constants. (B), (C) I-V curves for step and tail currents, respectively.

Rapid Delayed Rectifier Potassium Current (IKr)

Formulation of IKr is fitted to canine Purkinje cell data from Han et al1 (Figure S6). Simulated I-V curve is in agreement with experimental measurements1 (Figure S6).

Equations:

𝑥𝑟∞ =1

1 + e−V15

𝑥𝑟𝜏 = 100 +400

1 + ev10

𝑟𝑘𝑟 =1

1 + eV35

��𝐾𝑟 = 0.03262 ∙ �[𝐾+]𝑜

5.4

𝐼𝐾𝑟 = ��𝐾𝑟 ∙ 𝑥𝑟 ∙ 𝑟𝑘𝑟 ∙ (𝑉 − 𝐸𝐾)

τslow

τfast

A B C

Figure S6. IKr Model Validation. Experimental data are from Han et al1 (dots). Simulation results are shown as gray lines. I-V curves for step current (A) and tail current (B).

Hyper-polarization Activated Current (If) Formulation of If is modified from Maltsev and Lakatta17. If is carried by HCN (Hyperpolarization-activated, cyclic nucleotide-gated) channels19. Steady state activation is adjusted to fit experimental data for HCN2 channels19, reflecting the high expression level of HCN2 in canine Purkinje cells20. The time constant for activation and the current density are fitted to canine Purkinje data from Yu et al21.

Equations:

𝑦∞ =1

1 + eV+879.5

𝑦𝜏 =2000

e−(V+132)

10 + eV+5760

𝐼fNa = 0.012 ∙ 𝑦2 ∙ (𝑉 − 𝐸𝑁𝑎)

𝐼fK = 0.024 ∙ 𝑦2 ∙ (𝑉 − 𝐸𝐾)

𝐼f = 𝐼fNa + 𝐼fK

Time-independent inward rectifier potassium current (IK1) Formulation of IK1 is modified from the HRd model. I-V curve and its dependence on [K+]o are fitted to experimental data from Shah et al2, where IK1 was measured as 10mM Cs+ sensitive current (Figure S7).

Equations:

𝐾1 =1

1 + 𝑒𝑉+100.1−2.175∙[𝐾+]𝑜

10.15

��𝐾1 = 0.12 ∙ �[𝐾+]𝑜

𝐼𝐾1 = ��𝐾1 ∙ 𝐾1 ∙ (𝑉 − 𝐸𝐾)

Figure S7. IK1 Model Validation. (A) Experimental data are from Shah et al2 ([𝐾+]𝑜 = 4mM (open circles) and 12mM (filled circles). Simulation results are shown as gray ([𝐾+]𝑜 = 4mM) and black ([𝐾+]𝑜 = 12mM) lines. (B) Comparison of simulated IK1 [𝐾+]𝑜 dependence in canine Purkinje (Black) and Ventricular (Red) cells; [𝐾+]𝑜 = 4mM (solid) and [𝐾+]𝑜 =12mM (dashed).

Sodium-Calcium Exchanger (INCX) Formulation of INCX is the same as in the HRd model, with a reduced current density based on reduced expression level of Na+-Ca2+ exchanger protein (NCX1) in canine Purkinje cells compared to ventricular myocytes20.

Equations:

𝑣𝑚𝑎𝑥 = 2.52 𝜇𝐴/𝜇𝐹; 𝑘𝑠𝑎𝑡 = 0.27; 𝜂 = 0.35

𝐾𝑚,𝑁𝑎𝑖 = 12.3 𝑚𝑀/𝐿; 𝐾𝑚,𝑁𝑎𝑜 = 87.5 𝑚𝑀/𝐿;

𝐾𝑚,𝐶𝑎𝑖 = 0.0036 𝑚𝑀/𝐿; 𝐾𝑚,𝐶𝑎𝑜 = 1.3 𝑚𝑀/𝐿;

𝐾𝑚𝐶𝑎,𝑎𝑐𝑡 = 1.25 × 10−4 𝑚𝑀/𝐿;

𝐼𝑁𝑎𝐶𝑎𝑥 = 𝐴𝑙𝑙𝑜𝑥 ∙ ∆𝐸𝑥

𝐴𝑙𝑙𝑜𝑥 =1

1 + (𝐾𝑚𝐶𝑎,𝑎𝑐𝑡

1.5 ∙ [𝐶𝑎2+]𝑥)2

∆𝐸𝑥

=𝑣𝑚𝑎𝑥 ∙ ([𝑁𝑎+]𝑥3 ∙ [𝐶𝑎2+]𝑜 ∙ 𝑒

𝜂∙𝑉𝐹𝑅𝑇 − [𝑁𝑎+]𝑜3 ∙ 1.5 ∙ [𝐶𝑎2+]𝑥 ∙ 𝑒(𝜂−1)∙𝑉𝐹𝑅𝑇)

�1 + 𝑘𝑠𝑎𝑡 ∙ 𝑒(𝜂−1)∙𝑉𝐹

𝑅𝑇 � ∙ (𝐾𝑚,𝐶𝑎𝑜 ∙ [𝑁𝑎+]𝑥3 + 𝐾𝑚,𝑁𝑎𝑜3 ∙ 1.5 ∙ [𝐶𝑎2+]𝑥 + 𝐾𝑚,𝑁𝑎𝑖

3 ∙ [𝐶𝑎2+]𝑜 ∙ �1 + 1.5 ∙ [𝐶𝑎2+]𝑥𝐾𝑚,𝐶𝑎𝑖

�

+

𝐾𝑚,𝐶𝑎𝑖 ∙ [𝑁𝑎+]𝑜3 ∙ �1 + [𝑁𝑎+]𝑥3𝐾𝑚,𝑁𝑎𝑖3 � + [𝑁𝑎+]𝑥3 ∙ [𝐶𝑎2+]𝑜 + [𝑁𝑎+]𝑜3 ∙ 1.5 ∙ [𝐶𝑎2+]𝑥)

𝐼𝑁𝑎𝐶𝑎 = 0.8 ∙ 𝐼𝑁𝑎𝐶𝑎𝑆𝑆𝐿 + 0.2 ∙ 𝐼𝑁𝑎𝐶𝑎𝑃𝐶𝑆

A B

Sodium-Potassium Pump (INaK) Formulation of INaK is modified from the HRd model. Half saturation coefficient for extracellular potassium is ajusted to 0.8 mM, as suggested by Cohen et al22. Gao et al23 reported identical dependence of INaK on both voltage and intracellular sodium in canine Epi- and Endo- myocardium. Here, we assume similar dependence for Purkinje INaK. Current density of INaK is reduced based on reduced expression level of Na+/K+ ATPase in Purkinje cells compared to ventricular myocytes24 (human data). We assume that the relative difference between expression levels of Na+/K+ ATPase in human Purkinje and ventricular cells is similar in canine25. With intracellular sodium of 10mM and resting membrane potential at -78 mV, simulated resting Na/K pump current is 0.3 pA/pF, which is within the range of experimental measurements (0.27 pA/pF (Cohen et al22); 0.6 pA/pF (Boyden et al26)). Differences in experimental measurements are likely due to different intracellular Na and resting membrane potential.

Equations:

𝐼��𝑎𝐾 = 1.1004 𝜇𝐴/𝜇𝐹

𝑓𝑣 =1

1 + 𝑒−(𝑉+92)∙𝐹

𝑅∙𝑇

𝑃𝑁𝑎 = ([𝑁𝑎+]𝑆𝑆𝐿

[𝑁𝑎+]𝑆𝑆𝐿 + 2.6)3

𝑃𝐾 =[𝐾+]𝑜

[𝐾+]𝑜 + 0.8

𝐼𝑁𝑎𝐾 = 𝐼��𝑎𝐾 ∙ 𝑓𝑣 ∙ 𝑃𝑁𝑎 ∙ 𝑃𝐾

Sarcolemmal Calcium Pump (IpCa), Background Calcium Current (ICab) and Background Sodium Current (INab)

Formulations of these two currents are the same as in the HRd model, with adjusted current amplitudes.

Equations:

��𝑝𝐶𝑎 = 0.0115 𝑚𝑆/𝜇𝐹

𝐾𝑚,𝑝𝐶𝑎 = 0.0005 𝑚𝑀

𝐼𝑝𝐶𝑎 =��𝑝𝐶𝑎

1 +𝐾𝑚,𝑝𝐶𝑎

[𝐶𝑎2+]𝑆𝑆𝐿

𝑃𝐶𝑎𝑏 = 3.99 × 10−8 𝑐𝑚/𝑠; 𝛾𝐶𝑎𝑖 = 1; 𝛾𝐶𝑎𝑜 = 0.341

𝐼𝐶𝑎𝑏 = 𝑃𝑐𝑎𝑏 ∙ 𝑧𝐶𝑎2 ∙𝑉 ∙ 𝐹2

𝑅𝑇∙𝛾𝐶𝑎𝑖 ∙ [𝐶𝑎2+]𝑆𝑆𝐿 ∙ 𝑒

𝑧𝐶𝑎∙𝑉𝐹𝑅𝑇 − 𝛾𝐶𝑎𝑜 ∙ [𝐶𝑎2+]𝑜

𝑒𝑧𝐶𝑎∙𝑉𝐹𝑅𝑇 − 1

𝑃𝑁𝑎𝑏 = 0.64 × 10−8 𝑐𝑚/𝑠

𝐼𝑁𝑎𝑏 = 𝑃𝑁𝑎𝑏 ∙𝑉 ∙ 𝐹2

𝑅𝑇∙

[𝑁𝑎+]𝑆𝑆𝐿 ∙ 𝑒∙𝑉𝐹𝑅𝑇 − [𝑁𝑎+]𝑜

𝑒𝑉𝐹𝑅𝑇 − 1

SR Ca2+ Fluxes

Formulation for Ca2+ release via RyR (RyR3 and RyR2) is modified from Livshitz and Rudy27. Localization of RyR2 and RyR3 is according to their spatial distribution in canine Purkinje cells28. RyR3 responds to Ca2+ fluxes in the PCS, including ICaL, JRyR3, JIP3R and Jdiff; while RyR2 responds to Ca2+ fluxes in Myo, including JSERCA, Jleak, Jgap and JRYR2. 𝜏𝑅𝑦𝑅 and 𝑅𝑦𝑅∞ are fitted to experimental data5,6, to reproduce accurate morphology, decay and amplitude of the Ca transient ([Ca2+]avg) during steady-state pacing at 1Hz.

For validation of simulated Pcell Ca dynamics, we used both earlier and more recent experimental data. Early Ca measurements using Aequorin5 revealed the biphasic L1-L2 morphology of CaT and described the dynamic response of L1 and L2 to application of drugs. These experiments are well suited for validation of the Pcell model subcellular organization of Ca2+ cycling. Recent confocal microscopic studies using fluorescence imaging6 were used for the validation of other CaT properties, including diastolic concentration, magnitude during the AP and time course of relaxation.

During pacing at CL=1000ms, regions of interest (ROI) of canine Purkinje cell aggregate (Boyden et al6) showed an increase of fluorescent signal intensity from 30 units to 90 units (assuming that each ROI represents equal portion of the cell aggregate). The 60 units difference can be calibrated to represent an increase of free Ca2+ by 260 nM/L. With [Ca2+]o of 2mM at CL=1000ms, simulated resting and peak levels of [Ca2+]avg are 70nM/L and 310nM/L, respectively. This amounts to an increase of free Ca2+ by 240nM/L. Thus, the simulated amplitude of CaT during pacing at CL=1000ms is in agreement with experimental data. Simulated rate dependence curve of CaT (slope = 0.485 with linear fitting) is consistent with measurements of rate dependence of intracellular Ca activity (slope = 0.5 with linear fitting) recorded from sheep Purkinje strand (Lado et al29).

Average time of CaT half decay (τ) measured by fluorescent signal, is ~150ms (Boyden et al6) during pacing at CL=1000ms. Simulated τ of [Ca2+]avg during steady-state pacing at CL=1000ms is 156ms, consistent with experiments. The simulated L1 component of peak CaT occurs 25ms after the stimulus, while the L2 component occurs after 85ms. This is in good agreement with experimental measurements ( 30ms for L1 and 80ms for L2; Hess et al5). Value of τdiff is the same as for diffusion between subspace and myoplasm in the HRd model9. For τgap = 12ms, the simulated delay between the L1 and L2 components of CaT is consistent with the delay measured experimentally5.

CAMKII regulation of Ca2+ release via RyR is the same as in the HRd model9.

Equations:

o RyR3 Ca2+ Release:

𝑅𝑒𝑙𝑅𝑦𝑅3 = −(𝐼𝐶𝑎𝐿 ∙𝐴𝐶𝑎𝑝

𝑉𝑃𝐶𝑆 ∙ 2 ∙ 𝐹− �𝐽𝑅𝑦𝑅3 + 𝐽𝐼𝑃3𝑅�

𝑉𝐽𝑆𝑅𝑉𝑃𝐶𝑆

+ 𝐽𝑑𝑖𝑓𝑓)

𝜏𝑅𝑦𝑅3 =

2 ∙ (1 + 11 + ( 0.28

[𝐶𝐴𝑀𝐾]𝑎𝑐𝑡𝑖𝑣𝑒)8

)

1 + 0.0123[𝐶𝑎2+]𝐽𝑆𝑅

if (𝑅𝑒𝑙𝑅𝑦𝑅3 > 0)

𝑅𝑦𝑅3∞ =

15 ∙ 𝑅𝑒𝑙𝑅𝑦𝑅3 ∙ (1 + 11 + ( 0.28


)

1 + ( 1[𝐶𝑎2+]𝐽𝑆𝑅

)8

else

𝑅𝑦𝑅3∞ = 0

d𝐽𝑅𝑦𝑅3dt

=𝑅𝑦𝑅3∞ − 𝐽𝑅𝑦𝑅3

𝜏𝑅𝑦𝑅3

o RyR2 Ca2+ Release:

𝑅𝑒𝑙𝑅𝑦𝑅2 = −𝐽𝑆𝐸𝑅𝐶𝐴𝑉𝑁𝑆𝑅𝑉𝑀𝑦𝑜

+ 𝐽𝑔𝑎𝑝𝑉𝑆𝑆𝐿𝑉𝑀𝑦𝑜

+ 𝐽𝑅𝑦𝑅2𝑉𝐶𝑆𝑅𝑉𝑀𝑦𝑜

𝜏𝑅𝑦𝑅2 =

6 ∙ (1 + 11 + ( 0.28


)

1 + 0.0123[𝐶𝑎2+]𝐶𝑆𝑅

if (𝑅𝑒𝑙𝑅𝑦𝑅2 > 0)

𝑅𝑦𝑅2∞ =

91 ∙ 𝑅𝑒𝑙𝑅𝑦𝑅2 ∙ (1 + 11 + ( 0.28


)

1 + ( 1[𝐶𝑎2+]𝐶𝑆𝑅

)8

else

𝑅𝑦𝑅2∞ = 0

d𝐽𝑅𝑦𝑅2dt

=𝑅𝑦𝑅2∞ − 𝐽𝑅𝑦𝑅2

𝜏𝑅𝑦𝑅2

o IP3R Ca2+ Release:

Formulation for Ca2+ release via IP3R is based on Bugrim and Zhabotinsky30 (a simplification of the DeYong and Keizer model31). The model of IP3R considers a ligand binding site for IP3 and two ligand binding sites for Ca2+ (activating and inactivating), and assumes that the rate constants of binding and dissociation of the ligands do not depend on the state of the receptor30. IP3R is co-localized with RyR3 in the PCS, and both its activation and inactivation depend on the local Ca2+ concentration ([Ca2+]PCS) and Ca2+ in the JSR ([Ca2+]JSR) for a fixed level of [IP3].

𝑘0 = 96000 𝑚𝑀−1𝑠−1; 𝑘0𝑎 = 9.6𝑠−1; 𝑘1 = 150000𝑚𝑀−1𝑠−1;𝑘1𝑎 = 16.5𝑠−1;

𝑘2 = 1800𝑚𝑀−1𝑠−1; 𝑘2𝑎 = 0.21𝑠−1; 𝜏𝐼𝑃3𝑅 = 3.7𝑠−1;

[𝐼𝑃3] = 0.001𝑚𝑀/𝐿;

d𝑢𝐼𝑃3𝑅dt

= [𝐶𝑎2+]𝑃𝐶𝑆 ∙ 𝑘2 ∙ �1 − 𝑢𝐼𝑃3𝑅� − 𝑘2𝑎 ∙ 𝑢𝐼𝑃3𝑅

𝐽𝐼𝑃3𝑅 = 10.92 ∙𝜏𝐼𝑃3𝑅 ∙ [𝐼𝑃3] ∙ [𝐶𝑎2+]𝑃𝐶𝑆 ∙ �1 − 𝑢𝐼𝑃3𝑅�

�1 + [𝐼𝑃3] ∙ 𝑘0𝑘0𝑎

� ∙ �1 + [𝐶𝑎2+]𝑃𝐶𝑆𝑘1𝑘1𝑎

��[𝐶𝑎2+]𝐽𝑆𝑅 − [𝐶𝑎2+]𝑃𝐶𝑆�

o Ca2+ Uptake via SERCA: Formulation for SR Ca2+ ATPase (JSERCA) is modified from the HRd model. Maximum uptake via JSERCA (𝐽��𝐸𝑅𝐶𝐴) is reduced based on the reduced expression of SERCA2 in Purkinje cells compared to ventricular myocytes20. A small population of JSERCA (JSERCA,s) is located in the SSL.

∆𝐾�𝑚,𝑃𝐿𝐵 = 0.00017𝑚𝑀/𝐿; ∆𝐽��𝐸𝑅𝐶𝐴,𝑃𝐿𝐵 = 0.75; 𝐾𝑚,𝐶𝐴𝑀𝐾 = 0.15 𝐽��𝐸𝑅𝐶𝐴 = 0.0026𝑚𝑀/𝐿 𝑝𝑒𝑟 𝑚𝑠; 𝐽��𝐸𝑅𝐶𝐴,𝑠 = 0.0002𝑚𝑀/𝐿 𝑝𝑒𝑟 𝑚𝑠; 𝐾𝑚,𝑆𝐸𝑅𝐶𝐴 = 0.00028𝑚𝑀/𝐿 NSR�� = 15 mM/L

∆𝐾𝑚,𝑃𝐿𝐵 = ∆𝐾�𝑚,𝑃𝐿𝐵 ∙𝐶𝐴𝑀𝐾𝑎𝑐𝑡𝑖𝑣𝑒

𝐾𝑚,𝐶𝐴𝑀𝐾 + 𝐶𝐴𝑀𝐾𝑎𝑐𝑡𝑖𝑣𝑒

∆𝐽𝑆𝐸𝑅𝐶𝐴,𝐶𝐴𝑀𝐾 = ∆𝐽��𝐸𝑅𝐶𝐴,𝐶𝐴𝑀𝐾 ∙𝐶𝐴𝑀𝐾𝑎𝑐𝑡𝑖𝑣𝑒

𝐾𝑚,𝐶𝐴𝑀𝐾 + 𝐶𝐴𝑀𝐾𝑎𝑐𝑡𝑖𝑣𝑒

𝐽𝑆𝐸𝑅𝐶𝐴 = 𝐽��𝐸𝑅𝐶𝐴 ∙�1 + ∆𝐽𝑆𝐸𝑅𝐶𝐴,𝐶𝐴𝑀𝐾�

1 +𝐾𝑚,𝑆𝐸𝑅𝐶𝐴 − ∆𝐾𝑚,𝑃𝐿𝐵

[𝐶𝑎2+]𝑖

− 0.00105 ∙[𝐶𝑎2+]𝑁𝑆𝑅

NSR��

𝐽𝑆𝐸𝑅𝐶𝐴,𝑠 = 𝐽��𝐸𝑅𝐶𝐴,𝑠 ∙�1 + ∆𝐽𝑆𝐸𝑅𝐶𝐴,𝐶𝐴𝑀𝐾�

1 +𝐾𝑚,𝑆𝐸𝑅𝐶𝐴 − ∆𝐾𝑚,𝑃𝐿𝐵

[𝐶𝑎2+]𝑆𝑆𝐿

− 0.0042 ∙[𝐶𝑎2+]𝑁𝑆𝑅

NSR��

o Ca2+ Translocation Fluxes:

Formulation of Ca2+ translocation fluxes (from NSR to CSR and JSR) is from the HRd model9.

τtr = 120ms

𝐽𝑡𝑟,𝑗 =([𝐶𝑎2+]𝑁𝑆𝑅 − [𝐶𝑎2+]𝐽𝑆𝑅)

τtr

𝐽𝑡𝑟,𝑐 =([𝐶𝑎2+]𝑁𝑆𝑅 − [𝐶𝑎2+]𝐶𝑆𝑅)

τtr

Ionic Concentrations

𝜏𝑑𝑖𝑓𝑓 = 0.2 𝑚𝑠; 𝜏𝑔𝑎𝑝 = 12𝑚𝑠

𝐽𝑑𝑖𝑓𝑓 =[𝐶𝑎2+]𝑃𝐶𝑆 − [𝐶𝑎2+]𝑆𝑆𝐿

𝜏𝑑𝑖𝑓𝑓

𝐽𝑔𝑎𝑝 =[𝐶𝑎2+]𝑆𝑆𝐿 − [𝐶𝑎2+]𝑖

𝜏𝑔𝑎𝑝

o [𝑪𝒂𝟐+]𝑷𝑪𝑺 :

𝛽𝑃𝐶𝑆 =1

1 + 𝐵𝑆𝑅�� ∙𝐾𝑚,𝐵𝑆𝑅

�[𝐶𝑎2+]𝑃𝐶𝑆 + 𝐾𝑚,𝐵𝑆𝑅�2 + 𝐵𝑆𝐿�� ∙

𝐾𝑚,𝐵𝑆𝐿

�[𝐶𝑎2+]𝑃𝐶𝑆 + 𝐾𝑚,𝐵𝑆𝐿�2

d[𝐶𝑎2+]𝑃𝐶𝑆dt

= 𝛽𝑃𝐶𝑆 ∙ (−�𝐼𝐶𝑎𝐿 − 2 ∙ 𝐼𝑁𝑎𝐶𝑎,𝑃𝐶𝑆� ∙𝐴𝐶𝑎𝑝

𝑉𝑃𝐶𝑆 ∙ 2 ∙ 𝐹+ �𝐽𝑅𝑦𝑅2 + 𝐽𝐼𝑃3𝑅� ∙

𝑉𝐽𝑆𝑅𝑉𝑃𝐶𝑆

− 𝐽𝑑𝑖𝑓𝑓)

o [𝑪𝒂𝟐+]𝑺𝑺𝑳 :

d[𝐶𝑎2+]𝑆𝑆𝐿dt

= −�𝐼𝐶𝑎𝑇 + 𝐼𝑝𝐶𝑎 + 𝐼𝐶𝑎𝑏 − 2 ∙ 𝐼𝑁𝑎𝐶𝑎,𝑆𝑆𝐿� ∙𝐴𝐶𝑎𝑝

𝑉𝑆𝑆𝐿 ∙ 2 ∙ 𝐹+ 𝐽𝑑𝑖𝑓𝑓

𝑉𝑃𝐶𝑆𝑉𝑆𝑆𝐿

− 𝐽𝑆𝐸𝑅𝐶𝐴,𝑠 ∙𝑉𝑁𝑆𝑅𝑉𝑆𝑆𝐿

− 𝐽𝑔𝑎𝑝

𝑇𝑅𝑃𝑁𝑆𝑆𝐿 = 𝑇𝑅𝑃𝑁��𝑆𝑆𝐿 ∙[𝐶𝑎2+]𝑆𝑆𝐿

[𝐶𝑎2+]𝑆𝑆𝐿 + 𝐾𝑚,𝑇𝑅𝑃𝑁

𝐶𝑀𝐷𝑁𝑆𝑆𝐿 = 𝐶𝑀𝐷𝑁��𝑆𝑆𝐿 ∙[𝐶𝑎2+]𝑆𝑆𝐿

[𝐶𝑎2+]𝑆𝑆𝐿 + 𝐾𝑚,𝐶𝑀𝐷𝑁

[𝐶𝑎2+]𝑆𝑆𝐿,𝑡𝑜𝑡 = [𝐶𝑎2+]𝑆𝑆𝐿 + 𝑇𝑅𝑃𝑁𝑆𝑆𝐿 + 𝐶𝑀𝐷𝑁𝑆𝑆𝐿 + 𝑑[𝐶𝑎2+]𝑆𝑆𝐿

𝑏𝑆𝑆𝐿 = 𝑇𝑅𝑃𝑁��𝑆𝑆𝐿 + 𝐶𝑀𝐷𝑁��𝑆𝑆𝐿 − [𝐶𝑎2+]𝑆𝑆𝐿,𝑡𝑜𝑡+𝐾𝑚,𝑇𝑅𝑃𝑁 + 𝐾𝑚,𝐶𝑀𝐷𝑁

𝑐𝑆𝑆𝐿 = 𝐾𝑚,𝑇𝑅𝑃𝑁 ∙ 𝐾𝑚,𝐶𝑀𝐷𝑁 − [𝐶𝑎2+]𝑆𝑆𝐿,𝑡𝑜𝑡 ∙ �𝐾𝑚,𝑇𝑅𝑃𝑁+𝐾𝑚,𝐶𝑀𝐷𝑁� + 𝑇𝑅𝑃𝑁��𝑆𝑆𝐿 ∙ 𝐾𝑚,𝐶𝑀𝐷𝑁 + 𝐶𝑀𝐷𝑁��𝑆𝑆𝐿 ∙ 𝐾𝑚,𝑇𝑅𝑃𝑁

𝑑𝑆𝑆𝐿 = −𝐾𝑚,𝑇𝑅𝑃𝑁 ∙ 𝐾𝑚,𝐶𝑀𝐷𝑁 ∙ [𝐶𝑎2+]𝑆𝑆𝐿,𝑡𝑜𝑡

[𝐶𝑎2+]𝑆𝑆𝐿 =23∙ �𝑏𝑆𝑆𝐿

2 − 3 ∙ 𝑐𝑆𝑆𝐿 ∙ cos(13

cos−1(9𝑏𝑆𝑆𝐿𝑐𝑆𝑆𝐿 − 2𝑏𝑆𝑆𝐿

3 − 27𝑑𝑆𝑆𝐿2(𝑏𝑆𝑆𝐿

2 − 3𝑐𝑆𝑆𝐿)1.5)) −

𝑏𝑆𝑆𝐿3

o [𝑪𝒂𝟐+]𝒊 (Ca2+ concentration in Myo):

d[𝐶𝑎2+]𝑖dt

= 𝐽𝑔𝑎𝑝𝑉𝑆𝑆𝐿𝑉𝑀𝑦𝑜

− 𝐽𝑆𝐸𝑅𝐶𝐴 ∙𝑉𝑁𝑆𝑅𝑉𝑀𝑦𝑜

+ 𝐽𝑅𝑦𝑅2𝑉𝐶𝑆𝑅𝑉𝑀𝑦𝑜

𝑇𝑅𝑃𝑁𝑀𝑦𝑜 = 𝑇𝑅𝑃𝑁��𝑀𝑦𝑜 ∙[𝐶𝑎2+]𝑖

[𝐶𝑎2+]𝑖 + 𝐾𝑚,𝑇𝑅𝑃𝑁

𝐶𝑀𝐷𝑁𝑀𝑦𝑜 = 𝐶𝑀𝐷𝑁��𝑀𝑦𝑜 ∙[𝐶𝑎2+]𝑖

[𝐶𝑎2+]𝑖 + 𝐾𝑚,𝐶𝑀𝐷𝑁

[𝐶𝑎2+]𝑖,𝑡𝑜𝑡 = [𝐶𝑎2+]𝑖 + 𝑇𝑅𝑃𝑁𝑀𝑦𝑜 + 𝐶𝑀𝐷𝑁𝑀𝑦𝑜 + 𝑑[𝐶𝑎2+]𝑖

𝑏𝑀𝑦𝑜 = 𝑇𝑅𝑃𝑁��𝑀𝑦𝑜 + 𝐶𝑀𝐷𝑁��𝑀𝑦𝑜 − [𝐶𝑎2+]𝑖,𝑡𝑜𝑡+𝐾𝑚,𝑇𝑅𝑃𝑁 + 𝐾𝑚,𝐶𝑀𝐷𝑁

𝑐𝑀𝑦𝑜 = 𝐾𝑚,𝑇𝑅𝑃𝑁 ∙ 𝐾𝑚,𝐶𝑀𝐷𝑁 − [𝐶𝑎2+]𝑖,𝑡𝑜𝑡 ∙ �𝐾𝑚,𝑇𝑅𝑃𝑁+𝐾𝑚,𝐶𝑀𝐷𝑁� + 𝑇𝑅𝑃𝑁��𝑀𝑦𝑜 ∙ 𝐾𝑚,𝐶𝑀𝐷𝑁 + 𝐶𝑀𝐷𝑁��𝑀𝑦𝑜 ∙ 𝐾𝑚,𝑇𝑅𝑃𝑁

𝑑𝑀𝑦𝑜 = −𝐾𝑚,𝑇𝑅𝑃𝑁 ∙ 𝐾𝑚,𝐶𝑀𝐷𝑁 ∙ [𝐶𝑎2+]𝑖,𝑡𝑜𝑡

[𝐶𝑎2+]𝑖 =23∙ �𝑏𝑀𝑦𝑜

2 − 3 ∙ 𝑐𝑀𝑦𝑜 ∙ cos(13

cos−1(9𝑏𝑀𝑦𝑜𝑐𝑀𝑦𝑜 − 2𝑏𝑀𝑦𝑜

3 − 27𝑑𝑀𝑦𝑜2(𝑏𝑀𝑦𝑜

2 − 3𝑐𝑀𝑦𝑜)1.5)) −

𝑏𝑀𝑦𝑜3

o [𝑪𝒂𝟐+]𝒂𝒗𝒈 (Averaged Ca2+ concentration):

[𝐶𝑎2+]𝑎𝑣𝑔 =[𝐶𝑎2+]𝑖 ∙ 𝑉𝑀𝑦𝑜 + [𝐶𝑎2+]𝑆𝑆𝐿 ∙ 𝑉𝑆𝑆𝐿 + [𝐶𝑎2+]𝑃𝐶𝑆 ∙ 𝑉𝑃𝐶𝑆

𝑉𝑀𝑦𝑜 + 𝑉𝑆𝑆𝐿 + 𝑉𝑃𝐶𝑆

o [𝑪𝒂𝟐+]𝑱𝑺𝑹 :

d[𝐶𝑎2+]𝐽𝑆𝑅dt

= 𝐽𝑡𝑟,𝑗 − 𝐽𝑅𝑦𝑅3 − 𝐽𝐼𝑃3𝑅

𝐶𝑆𝑄𝑁𝐽𝑆𝑅 = 𝐶𝑆𝑄𝑁��𝐽𝑆𝑅 ∙[𝐶𝑎2+]𝐽𝑆𝑅

[𝐶𝑎2+]𝐽𝑆𝑅 + 𝐾𝑚,𝐶𝑆𝑄𝑁

𝑏𝐽𝑆𝑅 = 𝐶𝑆𝑄𝑁��𝐽𝑆𝑅 − 𝐶𝑆𝑄𝑁𝐽𝑆𝑅 − [𝐶𝑎2+]𝐽𝑆𝑅 − d[𝐶𝑎2+]𝐽𝑆𝑅+𝐾𝑚,𝐶𝑆𝑄𝑁

𝑐𝐽𝑆𝑅 = 𝐾𝑚,𝐶𝑆𝑄𝑁 ∙ (𝐶𝑆𝑄𝑁𝐽𝑆𝑅 + [𝐶𝑎2+]𝐽𝑆𝑅 + 𝑑[𝐶𝑎2+]𝐽𝑆𝑅)

[𝐶𝑎2+]𝐽𝑆𝑅 =(�𝑏𝐽𝑆𝑅

2 + 4𝑐𝐽𝑆𝑅 − 𝑏𝐽𝑆𝑅)

2

o [𝑪𝒂𝟐+]𝑪𝑺𝑹 :

d[𝐶𝑎2+]𝐶𝑆𝑅dt

= 𝐽𝑡𝑟,𝑐 − 𝐽𝑅𝑦𝑅2

𝐶𝑆𝑄𝑁𝐶𝑆𝑅 = 𝐶𝑆𝑄𝑁��𝐶𝑆𝑅 ∙[𝐶𝑎2+]𝐶𝑆𝑅

[𝐶𝑎2+]𝐶𝑆𝑅 + 𝐾𝑚,𝐶𝑆𝑄𝑁

𝑏𝐶𝑆𝑅 = 𝐶𝑆𝑄𝑁��𝐶𝑆𝑅 − 𝐶𝑆𝑄𝑁𝐶𝑆𝑅 − [𝐶𝑎2+]𝐶𝑆𝑅 − d[𝐶𝑎2+]𝐶𝑆𝑅+𝐾𝑚,𝐶𝑆𝑄𝑁

𝑐𝐶𝑆𝑅 = 𝐾𝑚,𝐶𝑆𝑄𝑁 ∙ (𝐶𝑆𝑄𝑁𝐶𝑆𝑅 + [𝐶𝑎2+]𝐶𝑆𝑅 + 𝑑[𝐶𝑎2+]𝐶𝑆𝑅)

[𝐶𝑎2+]𝐶𝑆𝑅 =(�𝑏𝐶𝑆𝑅

2 + 4𝑐𝐶𝑆𝑅 − 𝑏𝐶𝑆𝑅)

2

o [𝑪𝒂𝟐+]𝑵𝑺𝑹 :

d[𝐶𝑎2+]𝑁𝑆𝑅dt

= 𝐽𝑆𝐸𝑅𝐶𝐴 + 𝐽𝑆𝐸𝑅𝐶𝐴,𝑠 − 𝐽𝑡𝑟,𝑐 ∙𝑉𝐶𝑆𝑅𝑉𝑁𝑆𝑅

− 𝐽𝑡𝑟,𝑗 ∙𝑉𝐽𝑆𝑅𝑉𝑁𝑆𝑅

o [𝑵𝒂+]𝑷𝑪𝑺 :

𝐽𝑑𝑖𝑓𝑓,𝑁𝑎 =[𝑁𝑎+]𝑃𝐶𝑆 − [𝑁𝑎+]𝑆𝑆𝐿

𝜏𝑑𝑖𝑓𝑓

𝐽𝑔𝑎𝑝,𝑁𝑎 =[𝑁𝑎+]𝑆𝑆𝐿 − [𝑁𝑎+]𝑖

𝜏𝑔𝑎𝑝

d[𝑁𝑎+]𝑃𝐶𝑆dt

= −3 ∙ 𝐼𝑁𝑎𝐶𝑎,𝑃𝐶𝑆 ∙𝐴𝐶𝑎𝑝

𝑉𝑃𝐶𝑆 ∙ 𝑧𝑁𝑎 ∙ 𝐹− 𝐽𝑑𝑖𝑓𝑓,𝑁𝑎

o [𝑵𝒂+]𝑺𝑺𝑳 :

d[𝑁𝑎+]𝑆𝑆𝐿dt

= −(3 ∙ 𝐼𝑁𝑎𝐾 + 𝐼𝑁𝑎 + 𝐼𝑁𝑎𝐿 + 3 ∙ 𝐼𝑁𝑎𝐶𝑎,𝑆𝑆𝐿 + 𝐼fNa + 𝐼Nab) ∙𝐴𝐶𝑎𝑝

𝑉𝑆𝑆𝐿 ∙ 𝑧𝑁𝑎 ∙ 𝐹+ 𝐽𝑑𝑖𝑓𝑓,𝑁𝑎 ∙

𝑉𝑃𝐶𝑆𝑉𝑆𝑆𝐿

− 𝐽𝑔𝑎𝑝,𝑁𝑎

In the following (and throughout), subscript "i" indicates the myoplasmic compartment (Myo).

o [𝑵𝒂+]𝒊 :

d[𝑁𝑎+]𝑖dt

= 𝐽𝑔𝑎𝑝,𝑁𝑎 ∙𝑉𝑆𝑆𝐿𝑉𝑀𝑦𝑜

o [𝑲+]𝒊 :

d[𝐾+]𝑖dt

= −𝐼𝐾,𝑡𝑜𝑡 ∙𝐴𝐶𝑎𝑝

(𝑉𝑆𝑆𝐿 + 𝑉𝑀𝑦𝑜 + 𝑉𝑃𝐶𝑆) ∙ 𝑧𝐾 ∙ 𝐹

Calcium/Calmodulin-Dependent Protein Kinase (CAMKII)

The CAMK model is equivalent to that used in the HRd model9. We assume that CAMK kinetics are similar in Purkinje and ventricular cells.

𝛼𝐶𝐴𝑀𝐾 = 0.05 𝑚𝑠−1; 𝛽𝐶𝐴𝑀𝐾 = 0.00068 𝑚𝑠−1;

𝐶𝐴𝑀𝐾0 = 0.05; 𝐾𝑚𝐶𝑎𝑀 = 0.0015 𝑚𝑀

𝑑𝐶𝐴𝑀𝐾𝑡𝑟𝑎𝑝𝑑𝑡

= 𝛼𝐶𝐴𝑀𝐾 ∙ 𝐶𝐴𝑀𝐾𝑏𝑜𝑢𝑛𝑑 ∙ �𝐶𝐴𝑀𝐾𝑏𝑜𝑢𝑛𝑑 + 𝐶𝐴𝑀𝐾𝑡𝑟𝑎𝑝� − 𝛽𝐶𝐴𝑀𝐾 ∙ 𝐶𝐴𝑀𝐾𝑡𝑟𝑎𝑝

𝐶𝐴𝑀𝐾𝑏𝑜𝑢𝑛𝑑 = 𝐶𝐴𝑀𝐾0 ∙1 − 𝐶𝐴𝑀𝐾𝑡𝑟𝑎𝑝

1 + 𝐾𝑚𝐶𝑎𝑀[𝐶𝑎2+]𝑃𝐶𝑆

𝐶𝐴𝑀𝐾𝑎𝑐𝑡𝑖𝑣𝑒 = 𝐶𝐴𝑀𝐾𝑏𝑜𝑢𝑛𝑑 + 𝐶𝐴𝑀𝐾𝑡𝑟𝑎𝑝

Cell Geometry

Purkinje cell geometry is determined based on experimental measurements of isolated canine Purkinje cells32. The subcellular compartments and their volumes are based on the histological studies by Sommer and Johnson33. Due to lack of t-tubular network, 𝑅𝐶𝐺 (ratio of capacitive to geometric area) is set to 1.5422 (instead of 2 in the HRd ventricular cell model).

Length (L) = 0.0164 cm; radius (r) =0.00175 cm

Cell volume: Vcell = 𝜋 ∙ 𝑟2 ∙ 𝐿 = 1.57 × 10−4𝜇𝐿

Geometric membrane area: Ageo = 2 ∙ 𝜋 ∙ 𝑟2 + 2 ∙ 𝜋 ∙ 𝐿 = 1.9957 × 10−4𝑐𝑚2

Capacitive membrane area: Acap = 𝑅𝐶𝐺 ∙ 𝐴𝑔𝑒𝑜 = 1.9957 × 10−4𝑐𝑚2

Myoplasm volume: 𝑉𝑀𝑦𝑜 = 𝑉𝑐𝑒𝑙𝑙 ∙ 60%

Mitochondria volume: 𝑉𝑚𝑖𝑡𝑜 = 𝑉𝑐𝑒𝑙𝑙 ∙ 18%

SR volume: 𝑉𝑆𝑅 = 𝑉𝑐𝑒𝑙𝑙 ∙ 5%

NSR volume: 𝑉𝑆𝑅 = 𝑉𝑐𝑒𝑙𝑙 ∙ 4%

JSR volume: 𝑉𝑆𝑅 = 𝑉𝑐𝑒𝑙𝑙 ∙ 0.2%

CSR volume: 𝑉𝑆𝑅 = 𝑉𝑐𝑒𝑙𝑙 ∙ 0.8%

Peripheral coupling subspace volume: 𝑉𝑃𝐶𝑆 = 𝑉𝑐𝑒𝑙𝑙 ∙ 2%

Subsarcolemmal region volume: 𝑉𝑆𝑆𝐿 = 𝑉𝑐𝑒𝑙𝑙 ∙ 15%

Species Specificity

Purkinje cell electrophysiologic properties are species dependent39. Given the availability of experimental data from canine Purkinje fibers or cells, our model is constructed to be canine-specific.

IV SUPPLEMENTAL FIGURES

Figure S8. Drug effects on Purkinje AP during pacing at CL=1000ms. Response to TTX (blocker of INaL), Nifidipine (blocker of ICaL) and TEA (blocker of Ito1) are shown (left to right). Experimental data are shown in top panels. Middle and bottom panels show simulations in Purkinje and ventricular cell, respectively.

Figure S9. Simulated rate dependence of intracellular K+ (red), Na+ (green) and SR Ca2+ (blue) in Purkinje cell.

Figure S10. T Simulated S1-S2 (blue) and dynamic (red) APD restitution curves for Purkinje cell. The dynamical restitution curve is generated by plotting steady-state APD against steady-state DI at different pacing CLs.

V MODELS COMPARISON TABLE

The table below presents an overview of recent computational models36-38 of cardiac Purkinje cells. Model properties are obtained from performing computer simulations36,37 or from the literature38. H-H, Hodgkin-Huxley formalism; SR, sarcoplasmic reticulum; NSR, network SR; JSR, junctional SR; CSR, corbular SR; PCS, peripheral coupling subspace; SSL, sub-sarcolemmal region; Myo, myoplasm; RyR, ryanodine receptor; RyR2, type 2 RyR; RyR3, type 3 RyR; IP3R, inositol trisphosphate receptor; GCaL, conductance of L-type calcium channal; DI, diastolic interval.

Study Aslanidi et al Biophys J 2009 [36]

Sampson et al J Physiol 2010 [37]

Corrias et al AJP 2011 [38]

PRd (Present study)

Species Canine Human Rabbit Canine

Model Formulation H-H Markov; H-H H-H H-H

Subcellular Ca2+ Compartments

4 (NSR, JSR,

Subspace, Myo)

4 (NSR, JSR,

Subspace, Myo)

3 (Peripheral Myo,

bulk Myo, SR)

6 (NSR, JSR, CSR, PCS, SSL, Myo)

Purkinje-specific Ca2+ Cycling No No Yes Yes

Steady-State No Yes N/Aa Yes

SR Ca2+ Release SR Ca2+ release to Subspace

Ca2+ release via RyR to Subspace

SR Ca2+ release to Peripheral Myo

Ca2+ release via RyR3 and IP3R to PCS;

Ca2+ release via RyR2 to Myo

CaMKII Signaling Yes No No Yes

AP Morphology (CL=500ms)

Steady-state Steady-state After pacing for 10s

After pacing for 10s

APD Rate Adaptation N/Ab

APD Restitution N/Ab

N/Ac

AP and Ca2+ Alternans

(CL=200ms) Yes No N/Ac Yes

EAD Nod Nod Yese Yesd

aSimulation results of APD rate adaptation in Corrias et al38 are provided after pacing for 10s. bNot available since the model presented in Aslanidi et al36 cannot reach steady state. cNot provided in Corrias et al38. dSimulation protocol: CL = 4000ms; initial [Ca2+]NSR =1.0mM/L; initial [Na+]i = 8.0mM/L; complete block of IKr. eSimulation protocol: increased ICaL conductance; GCaL × 3.5, CL-N/A38

After pacing for 10s

Steady-state Steady-state

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