Human Atrial Action Potential and Ca²⁺ Model: Sinus Rhythm and Chronic Atrial Fibrillation

Abstract

Rationale

Understanding atrial fibrillation (AF) requires integrated understanding of ionic currents and Ca²⁺ transport in remodeled human atrium, but appropriate models are limited.

Objective

To study AF we developed a new human atrial action potential (AP) model, derived from atrial experimental results and our human ventricular myocyte model.

Methods and Results

Atria vs. ventricles have lower I_K1, resulting in more depolarized resting membrane potential (~7mV). We used higher I_to,fast density in atrium, removed I_to,slow, and included an atrial-specific I_Kur. I_NCX and I_NaK densities were reduced in atrial vs. ventricular myocytes according to experimental results. SERCA function was altered to reproduce human atrial myocyte Ca²⁺ transients. To simulate chronic AF, we reduced I_CaL, I_to, I_Kur and SERCA, and increased I_K1, I_Ks and I_NCX. We also investigated the link between Kv1.5 channelopathy, [Ca²⁺]_i, and AF. The sinus rhythm model showed a typical human atrial AP morphology. Consistent with experiments, the model showed shorter APs and reduced AP duration shortening at increasing pacing frequencies in AF or when I_CaL was partially blocked, suggesting a crucial role of Ca²⁺ and Na⁺ in this effect. This also explained blunted Ca²⁺ transient and rate-adaptation of [Ca²⁺]_i and [Na⁺]_i in chronic AF. Moreover, increasing [Na⁺]_i and altered I_NaK and I_NCX causes rate-dependent atrial AP shortening. Blocking I_Kur to mimic Kv1.5 loss-of-function increased [Ca²⁺]_i and caused early-afterdepolarizations under adrenergic stress, as observed experimentally.

Conclusions

Our study provides a novel tool and insights into ionic bases of atrio-ventricular AP differences, and shows how Na⁺ and Ca²⁺ homeostasis critically mediate abnormal repolarization in AF.

Introduction

Atrial fibrillation (AF) is the most common cardiac arrhythmia observed clinically, and is the main cause of embolic stroke ¹. The mechanisms underlying AF remain unclear, and AF is thought to be maintained either via ectopic foci, multiple wavelets, or fibrillatory conduction emanating from a small number of stable rotors ². Electrical and structural remodeling have emerged as key elements in the development of the AF substrate (e.g., the tendency for persistence of AF)³. Electrical remodeling includes changes in Ca²⁺ and K⁺ currents leading to shortening of the action potential (AP) duration (APD) and loss of APD rate-dependent adaptation, whereas structural remodeling leads to changes in atrial myocyte and tissue morphology (e.g. cell hypertrophy, fibrosis) ^3-5.

At present mechanisms leading to perpetuation of AF are still undetermined. Growing experimental evidence points to abnormal intracellular Ca²⁺-handling as a key mediator in AF-pathophysiology ^{6, 7}, but the mechanism through which Ca²⁺-related abnormalities can lead to the occurrence and maintenance of AF are poorly understood. Models of human atrial myocytes have been developed and used to gain mechanistic insights into human atrial cell physiology and pathophysiology ^8-10, however none of these included detailed descriptions of Ca²⁺ (or Na⁺) regulatory processes. A recent simulation study incorporated and studied the sub-cellular nature of Ca²⁺ homeostasis and its relation to human atrial action potentials ¹¹; however the role of Ca²⁺ in mediating AF was not investigated.

We recently developed a model of the human ventricular myocyte AP and Ca²⁺ transient (CaT) ¹², a major advance over prior human ventricular models in robustly describing excitation-contraction coupling, and the model was extensively validated against a broad range of experimental data.

The aims of the present study were two fold: 1) to derive a new human atrial cell model with detailed Ca²⁺ handling, by implementing experimentally documented structural and ionic differences in atrial vs. ventricular cells ¹³ and starting from our recently published model of human ventricular myocytes¹²; 2) to study how Ca²⁺ homeostasis is involved in abnormal APs seen in chronic AF (cAF), and AF related to adrenergic stress in patients with Kv1.5 mutations ¹⁴. Ionic currents in the ventricular model were modified based on experimental data comparing protein expression and function in atrial vs. ventricular myocytes. Importantly, we utilized new experimental data addressing the poorly understood molecular basis of impaired atrial Ca²⁺ signaling in cAF to constrain our model parameters.

We validated our model by testing its ability to recapitulate a wide range of physiological behaviors observed in experiments. We next investigated the mechanisms of APD and CaT rate-adaptation in sinus rhythm and cAF, and assessed the effects of blocking the atrial-specific ultrarapid K⁺ current (I_Kur) in the absence and presence of β-adrenergic activation, to understand arrhythmogenesis in AF related to Kv1.5 channelopathy and adrenergic stress. Finally, right-to-left gradients in repolarizing currents were also included in the model, since in a number of instances the driving source of the AF (reentry or foci) is located in the left atrium ².

Methods

Cellular [Ca²⁺]_i and electrophysiological methods are described in the Online Supplement and were used to tune our model and for validation. Table 1 shows key changes made in our new human atrial model vs. our ventricular myocyte model, ¹² to account for ionic remodeling in cAF, and to simulate the effects of β-adrenergic and cholinergic stimulation. Further details are in Online Supplement, including formulation of I_Kur block by AVE0118.

Table 1.

Main changes to our human ventricular model to generate the human atrial model, simulate cAF, and β-adrenergic stimulation.

	Atrial vs. Ventricular	cAF vs. Sinus Rhythm	Adrenergic Stimulation
Ionic Currents
INa	Unchanged	-10% peak density 56	Unchanged
INaL	None	Added late component 56	Unchanged
IKs	Unchanged	Increased 2-fold 33	Enhanced maximal conductance (3 fold) and leftward shift in IV relationship (by 40 mV) 57
IKr	Unchanged	Unchanged	Unchanged
IKur	Added	-55% in the RA	Enhanced maximal conductance (3 fold) 58
		-45% in the LA 4, 33
IK1	85% reduction 43	Upregulated +100% 4, 21	Unchanged
Ito	No Ito,slow
	Ito,fast: activation and inactivation negatively shifted and slower inactivation; larger amplitude 59	Ito,fast	Unchanged
		-80% in the RA
		-45% in the LA4, 33
Ca and Na handling
ICaL	Matched amplitude and kinetics at 37°C from our data and 20	Current density is reduced by 50% in cAF 4, 17, 18 (and present data)	Increased fraction of available channels (+50%), and channel availability shifted leftward (by 3mV) 57
		No changes in voltage dependence of activation and inactivation 19
INCX	Atrium<ventricle (-30%)60	Upregulated in cAF (+40%) 17, 25, 61, 62	Unchanged
	kd,act increased by 50%
SERCA	No changes in maximal pump rate	Reduced maximal pump rate 17	Forward mode km reduced by 50% 57
	Kmf increased 2-fold 17,42, 63
RyR	Unchanged	Increased sensitivity for luminal Ca (2-fold) 17, 61	Sensitivity to [Ca2+]SR enhanced twofold 57
SR Ca2+ leak	Unchanged	Increased by 25%	Unchanged
TnI	Unchanged	Unchanged	Affinity for Ca2+ decreased 57
INKA	Atrium<ventricle (-30%)60	Unchanged 64	Affinity for [Na+]i increased by 25% 65

Model differential equations were implemented in Matlab (Mathworks Inc., Natick, MA, USA) and solved numerically using a variable order solver (ode15s). APDs were obtained after pacing digital cells at indicated frequencies at steady-state. APD was measured as the interval between AP upstroke and 90% repolarization level (APD₉₀).

Results

The baseline alterations to our ventricular cell model resulted in a typical Type-3 human atrial AP morphology¹⁵ (Figure 1A, right panel). The higher density of K⁺ currents that are active in AP phase 1 (early repolarization, I_to+I_Kur) confers the AP a triangular shape lacking a plateau phase. We have investigated the impact on AP shape of varying I_to and I_Kur densities, and quantified the changes in the plateau potential, which gets more depolarized as the degree of K⁺ channel blockade increases (Online Figure I, Online Supplement). AP waveform also feeds back onto ion channel gating determining notable differences in atrial currents. For example, although atrial I_to is almost twice as large in voltage clamp experiments (see Online Figure II), in current clamp conditions it is comparable to ventricular I_to,fast (Figure 1G, right vs. left panel). Maximal velocity of AP upstroke was comparable to that measured in experiments of ~140 V/s (vs. 250 V/s in cAF) ¹⁶, and was smaller than in the ventricular cell model (372 V/s in the epicardial cell model paced at 1 Hz ¹²). In fact, I_Na is remarkably reduced in atrial vs. ventricular cells (Figure 1C, right vs. left panel) during the AP, due to more inactivated channels (because of slower recovery from inactivation at more depolarized atrial resting membrane potential). Although I_Kr or I_Ks were not modified vs. ventricular myocytes, the spiky AP reduced net I_Kr and I_Ks (Fig. 1E and F). It is noteworthy that the reduction of I_NCX from the ventricular model resulted in larger I_NCX in the atrial model (Fig. 1K). This is presumably because of the short early repolarization in atrium and the slightly larger CaT, both favoring inward I_NCX. I_CaL is similar in atria and ventricle in voltage-clamp conditions, but the AP shape causes I_CaL to be much larger in atrial vs. ventricular myocyte model (Fig. 1D). I_K1 is smaller in atria, consistent with its lower maximal conductance. I_NaK is decreased (not as much as its pump rate because the higher [Na⁺]_i, 9.1 in atrium vs. 8.2 mmol/L in ventricle at 1 Hz pacing rate, activates the pump more).

Figure 1.

Steady-state human cardiac AP and major underlying currents and CaT at 1 Hz pacing (A-K) for ventricle (left) and atrium (right). Thicker traces represent currents for which density was increased (in atria vs. ventricle or vice versa) because of altered maximal conductance or pump rate to generate the atrial cell model from the ventricular cell model.

A typical Ca²⁺ transient is shown in Figure 1B (right panel): at 1 Hz pacing rate, diastolic [Ca²⁺]_i is 207 nmol/L and peaks at 462 nmol/L. Simultaneous I_CaL and [Ca²⁺]_i measurements in human atrial myocytes at physiological temperature are shown in Figure 2D-G and compared to simulated traces (Figure 2A-B; 0.5 Hz). Simulated CaT amplitude and rate of CaT decay matched the experimental data (Fig. 2B grey line vs. E, and Fig. 2H-I), as did peak I_CaL (-6.47 A/F vs. -6.78±0.36 in experiments, Fig. 2A grey line vs. D). When cAF was simulated, by accounting for ion channel remodeling as illustrated in the methods, I_CaL was greatly diminished (Fig. 2A, black vs. grey lines), as shown in experiments (Fig. 2D vs. F) ^{4, 17, 18}. The reduced I_CaL could explain the reduced sarcoplasmic reticulum (SR) Ca²⁺ release and CaT amplitude (Fig. 2B,E,G,H), even if SR Ca²⁺ content were unaltered. However, the reduced I_CaL and SERCA function (rate of twitch [Ca²⁺]_i decline; Fig. 2I) and the elevated SR Ca²⁺ leak and NCX function (greater I_NCX for a given [Ca²⁺]_i; Fig. 3A-G) all tend to lower SR Ca²⁺ content in cAF, which is apparent in the model (but not significantly so in the experiments; Fig. 3H).

Figure 2.

Ca²⁺ current (A) and transient (B) were simulated for a voltage clamp protocol (A, inset) where membrane potential was stepped to +10 mV for 100 ms after a 100 ms duration ramp to -40mV to inactivate fast I_Na from a holding potential of -80 mV (pacing at 0.5 Hz). For cAF Ca²⁺ current amplitude is small compared to sinus rhythm (A, grey vs. black traces), as in experiments at physiological temperature in human atrial cells (D vs. F, protocol in D, inset). This leads to a strong reduction in CaT amplitude (B and H), also observed experimentally (E vs. G, H), which also limits the increase in junctional [Ca²⁺] (C). Twitch [Ca²⁺]_i decline rate (indicative of SERCA function) is slowed in cAF, in agreement with experiments (I).

Figure 3.

Caffeine-induced CaT and I_NCX in sinus rhythm (A and C) and cAF (B and D) reveal a smaller SR Ca²⁺ content in cAF compared to sinus rhythm (H). The slope of NCX current vs. [Ca²⁺]_i during the decaying phase of the caffeine-evoked CaT (E-F) was higher in cAF vs. sinus rhythm (G).

We next tested the response of our model to changes in pacing frequency. Simulated human atrial cell APs under baseline conditions (Fig. 4D) shorten with faster pacing rates (Figure 4J, black circles) as shown in atrial myocytes from patients in normal sinus rhythm (Fig. 4A and 4M, black circles) ¹⁹. To illustrate the effect of a reduction in I_CaL Van Wagoner et al. ¹⁹ recorded APs from the same myocytes at various cycle lengths in the presence of the I_CaL blocker nifedipine (10 μM), showing little rate–dependent change in APD (Fig. 4C and 4M, grey open circles). Li and Nattel ²⁰ obtained analogous results. Similarly, simulated APs following 50% I_CaL block (Figure 4F) exhibited impaired APD rate-adaptation (Figure 4J, grey open circles). Myocytes from chronic AF patients (Figure 4B) are characterized by shorter APD₉₀ values ^{16, 19, 21-23}, with less variation as a function of cycle length than control (sinus rhythm) myocytes (Figure 4M, squares) ^{4, 16, 19, 22, 23}. Analogously, our cAF model predicts shorter APs than sinus rhythm (solid vs. dashed line in Fig. 4D inset), and reduced adaptation to changes in pacing frequency (Figure 4J, squares). At 4 Hz pacing AP duration alternates (Fig. 4E, and so does [Ca²⁺]_i in Fig. 4H). The sinus rhythm model exhibits this behavior at higher frequency (Fig. 4O at 6 Hz pacing rate).

Figure 4.

APs recorded at different cycle lengths in a control human atrial myocyte (A), in a cell from cAF patient (B), and in the same control myocyte exposed to Ca²⁺ channel block (10 μmol/L nifedipine, C). ¹⁹ Simulated steady-state AP and CaT traces are shown for pacing frequencies 0.5, 1, 2, 3, and 4 Hz, for sinus rhythm (sr, D and G), cAF (E and H), and sr with 50% I_CaL block (F and I). Simulated APD₉₀ (J) decreases at increasing pacing frequency in sr, but rate-adaptation is impaired in cAF or with I_CaL partially inhibited. Experimental results ¹⁹ are also reported (M). Predicted CaT amplitude (K) and [Na⁺]_i (L) increase with frequency in sr cells, in agreement with changes in aequorin signals in human atrial muscle strips (N, grey circles). Frequency-dependence of [Ca²⁺]_i, [Na⁺]_i and force is limited in cAF or when I_CaL is partially inhibited (K,L,N). Alternating long and short APs and CaTs (O) are predicted in sr and cAF cells paced at 6 Hz.

The model predicts a positive dependency of CaT amplitude on the pacing rate in sinus rhythm (Figure 4G and K, black circles), which is in agreement with intracellular [Ca²⁺] measurements via aequorin light signals (Figure 4N, grey circles and dashed line) ²⁴ and twitch force measurements (Figure 4N, open circles and solid line) ^{24, 25}. Positive dependency is impaired when I_CaL is partially inhibited (Figure 4F and K, grey open circles) and in cAF (Figure 4E and K, squares). Similarly, atrial myocytes from patients with cAF show impaired contractility (Figure 4N, squares)²⁵. Our model also predicts the increase of intracellular [Na⁺] with increasing pacing frequency, as shown in Figure 4L (and Online Figure IIIA), which is more limited in cAF and with inhibition of I_CaL compared to sinus rhythm (squares and grey open circles vs. black circles).

Figures 5 and Online Figure III show that [Na⁺]_i is critical for APD rate-adaptation. Time courses of APD₉₀ and [Na⁺]_i changes subsequent to an increase in pacing frequency from 0.5 to 1 Hz (Online Figure IIIC) suggest that non steady-state measurements (before [Na⁺]_i slowly reaches steady-state) may give rise to highly variable experimental APD adaptation curves. Moreover, if [Na⁺]_i is clamped in the model, the APD rate adaptation is nearly abolished (Fig. 5A). Simulation of partial block of NKA causes a biphasic APD response (Figure 5D): first, APD prolongation by acute NKA current block, then as [Na⁺]_i rises it increases outward NKA causing APD shortening. Importantly, we validated these model predictions in isolated human atrial myocytes challenged with strophanthidin (10 μmol/L). Acute NKA inhibition was confirmed by abrupt and relatively sustained depolarization of resting membrane potential (Figure 5C). Figure 5C shows a typical time course of APD₉₀ from a representative cell and pooled data (n=10). Strophanthidin application produces an initial marked increase and subsequent decrease in APD₉₀ (Figure 5C, right). Similar behavior has been described in guinea pig ventricular myocytes, ²⁶ human atrial fibers, ²⁷ and rabbit atrial myocytes (not shown).

Figure 5.

A) APD₉₀ decreases with increasing pacing frequency from 0.5 to 2 Hz and [Na⁺]_i changes freely (black circles). If the atrial myocyte is paced at low frequency, but with [Na⁺]_i clamped at 10.5 mmol/L (level predicted at fast rate), APD₉₀ shortens (white circles) to APD₉₀ value at 2 Hz. Similarly, when the atrial myocyte is paced at fast rate and [Na⁺]_i is clamped to the low level predicted with slow pacing, APD₉₀ lengthens (gray circles) to APD₉₀ value at 0.5 Hz. B) NKA and NCX currents at 0.5 and 2 Hz pacing rate. Experimental and simulated time courses of APD₉₀ (C and D), resting membrane potential (C) and [Na⁺]_i (D) following application of strophanthidin (C) and partial (50%) I_NaK block (D, at time 0) at 0.5 Hz pacing rate. Effect of strophanthidin on mean APD₉₀ (C, right). p<0.05 and **p<0.001 with paired t-test and Bonferroni correction (n = 10 myocytes from 5 patients).

Blockade of the atrial specific current I_Kur has been proposed to improve atrial contractility without increasing the risk of ventricular arrhythmias. In fact, in human atrial myocardium, block of I_Kur results in a prolongation and elevation of the AP plateau, which elicit a positive inotropic effect ^{28, 29}. Thus, we assessed the impact of I_Kur block (modeled as shown in Online Methods and Online Figure IV) on APD and CaT (Figure 6 and Online Figure V). Moderate blockade of I_Kur (by 25-50%) increases CaT amplitude (Figure 6B) with little effects on APD (Figure 6A) both in sinus rhythm and cAF models, in agreement with experimental results (Figure 6A and B, insets) ^{28, 29}. Enhancement of CaT amplitude is greatly increased when I_Kur is more fully (75-100%) blocked (Figure 6B), paralleled by AP prolongation (Figure 6A) in agreement with ¹⁴ (see also Figure 6D, inset). A more moderate increase in CaT amplitude is also predicted in cAF. In Figure 6C the predicted impact of various degrees of I_Kur block on sinus rhythm and cAF CaT amplitude (grey symbols and axis) shows good agreement with the reported effect of the I_Kur inhibitor AVE0118 on contractile force of atrial trabeculae from patients in sinus rhythm and in AF (black symbols and axis) ²⁹.

Figure 6.

Effect of different degrees of I_Kur block on simulated human atrial APD (A) and CaT (B-C) in sr and cAF is compared with experimental AP recordings ²⁸ (A, inset) and twitch force measurements ²⁹ (B inset and C). D) ISO application causes EADs (green dashed line) in the presence of I_Kur blockade, as shown experimentally by Olson et al. (D, inset) ¹⁴. Blocking I_Ks does not have the same deleterious effect (red solid line).

To study AF associated with Kv1.5 mutation during β-adrenergic activation, we also investigated the effect of adrenergic stimulation on atrial AP (Figure 6D) by incorporating steady-state effects of PKA-dependent phosphorylation on I_Ca, I_Ks, I_Kur, PLN-SERCA2a, RyR2, troponin Ca²⁺ affinity and Na/K-ATPase (see Online Supplement). In our simulations, administration of isoproterenol (ISO) causes the CaT amplitude to increase (by ~ 65%, not shown) without major changes in the duration of repolarization (Figure 6D, solid black vs. blue lines), in agreement with data from human atrial preparations ³⁰. When simulating the block of I_Kur (which is enhanced during adrenergic activation) in the presence of ISO, early after-depolarizations (EADs) occurred (Figure 6D, green dashed line). These results are in agreement with data from Olson et al. ¹⁴ (Figure 6D, inset) showing that 4-AP (50 μmol/L) prolonged APD in human atrial myocytes and caused EADs and triggered activity upon ISO (1 μmol/L) challenge. Notably, simulation of I_Ks (also increased by ISO) blockade (50%) did not affect atrial AP markedly (Figure 6D, red line almost completely overlaps black line).

To reflect parasympathetic effects we also now include an I_KACh model (fitted with human data) and demonstrate a dose-dependent reduction in human atrial AP and CaT in response to the parasympathetic transmitter acetylcholine (Online Figure VI). The APD shortening is consistent with experiments in human atria. We did not integrate crosstalk between β-adrenergic and acetylcholine or CaMKII pathways, or develop compartmentalized dynamic G-protein coupled receptor models as done recently for animal myocyte models,^31,32 but those would be a logical extensions of our model.

There is only limited data available concerning intra-atrial heterogeneities in repolarizing currents in human atrial myocytes. Caballero et al. found a gradient of I_Kur with 20% higher density in right atrium (RA) vs. left atrium (LA) ³³. We incorporated such heterogeneity to simulate RA and LA APs and CaT (Figure 7A). The slightly higher I_Kur density in RA has negligible effects on AP and mildly decreases CaT amplitude (Fig. 7A, left; see also Fig. 6). cAF decreases I_to and I_Kur differentially in right vs. left atrium ³³. Indeed, cAF greatly reduced I_to in the RA (~80%) and to a lesser extent in the LA (~45%), thus generating RA-LA I_to gradient. In contrast, I_Kur was more markedly reduced in the RA (-55%) than in the LA (-45%), thus abolishing the atrial right-to-left I_Kur gradient observed in sinus rhythm. We simulated these perturbed left-to-right gradients in cAF. I_K1 in LA was 2-fold higher in both paroxysmal AF and cAF than in SR, with a left-to-right gradient in paroxysmal AF only ³⁴. Thus, we did not simulate such gradient here. The model predicted a longer AP in the RA during cAF, similar to experimental data ³⁵, with slightly larger CaT amplitude (Figure 7A, right, solid vs. dashed lines), but reduced APD adaptation (Figure 7A, right, solid grey to black vs. dashed grey to black lines). Thus, these changes modify the left-to-right gradients and may contribute to the perpetuation of arrhythmia. To account for variability in AP morphology between and within atria, we also varied K⁺ and Ca²⁺ current densities (reduced I_Kur by 50%, increased I_CaL and I_Kr by 50% and 400% respectively) to produce a Type-1 AP, i.e., similar to the manipulation attempted in an earlier modeling study by Nygren and co-workers. ⁹ This results in a larger I_K and I_K/I_to ratio, more depolarized plateau potential, and steeper phase 3 repolarization (Figure 7B, left) as reported by the Nattel group ³⁶ (Figure 7B, right). Importantly, as in experiments,^28,37 we show that when I_Kur is blocked Type-3 AP prolongs (7C, left), whereas Type-1 APD is almost unaltered (7C, right).

Figure 7.

A) Simulated APs and CaTs from right and left atria (RA and LA) at 1Hz and 3 Hz are shown in sinus rhythm (left) and cAF (right). B) Type-1 AP (dashed and bottom panel) was obtained by modifying K⁺ and Ca²⁺ current densities in the nominal Type-3 AP (top panel, solid line). C) I_Kur block prolongs Type-3 APs (left) but has little effect on APD₉₀ of Type-1 APs (right), as shown experimentally (insets) ^{28, 37}. CaTs are shown in bottom panels.

Discussion

We developed a new mathematical model of human atrial myocyte with detailed electrophysiology and Ca²⁺ handling, including ionic and Ca²⁺ handling remodeling in cAF. This places our present understanding of atrial myocyte function in a useful quantitative framework to understand how changes in ion channel and Ca²⁺ handling influence function.

Atrial vs. ventricular cell models

Understanding atrio-ventricular ionic differences is important, has been investigated in simulations and experiments ^{38, 39}, and may lead to safer therapy as a result of targeting atrial-specific ion channels for AF ^{1, 40}. We used the Grandi-Pasqualini-Bers model of the human ventricular AP and CaT ¹² as a framework for model development. As a result, the two models have a common format and similar aspects that may be convenient for integrating into whole heart models. Similarities include the Ca²⁺ handling processes, which is also based on the Shannon-Bers model of the rabbit ventricular myocyte ⁴¹. However, appropriate changes to many model parameters were introduced to recapitulate experimental findings in atrial samples from patients in sinus rhythm and cAF. Specific amalgams of ion channel expression and function confers differential AP characteristics for various cardiac regions ^{42, 43}. For example, it is well known that atrial I_K1 density is smaller than ventricular I_K1, explaining the slightly less negative atrial diastolic membrane potential (by ~5 to 10 mV), reduced Na⁺ channel availability and slower phase-3 repolarization ⁴³. Again, in humans, I_Kur is present in atria but not in ventricles ⁴⁴, and in human atrium, I_to is encoded entirely by Kv4.3 (responsible for I_to,fast) ⁴⁵, whereas both fast and slow I_to components are detected in human ventricle. We also simulated different AP morphologies and included right-to-left gradients in I_to and I_Kur as reported recently in human myocytes from the RA and the LA from patients in sinus rhythm or with cAF. This new set of models accounting for tissue-specific ion current differences will be useful for understanding regional electrophysiology, Ca²⁺ handling and arrhythmia mechanisms.

Novelties of the model compared to previous models

Computational cell modeling has been widely used to understand how individual ionic/molecular components (often studied in isolation) interact in the integrated environment of the cardiac myocyte. For human atrial myocyte models, the Courtemanche ¹⁰ and Nygren ⁹ models, which focused primarily on ion channels generating the atrial AP, have been useful to investigate physiological ^{46, 47} and pathophysiological ^{48, 49} mechanisms of the human atrium. However, those models have vastly different properties, especially in their rate-dependent behavior ⁵⁰. Recently, Maleckar et al. ⁸ incorporated new experimental K⁺ current data into the Nygren model, including formulations of I_Kur and I_to that we have also adopted here. They also studied the early and late phase of atrial repolarization and improved the rate-dependent properties of the AP model.

However, no previous model focused on Ca²⁺ handling properties of human atrial myocytes, and it is increasingly clear that Ca²⁺-handling and electrophysiology are intimately linked with respect to arrhythmias⁷. Cherry et al. ⁵⁰ showed CaT differences between the two above models, with a more gradual longer lasting transient in the Courtemanche compared to a much sharper CaT in the Nygren/Maleckar models. Our human model uses the Ca²⁺ handling framework developed by Shannon et al. for rabbit ventricular myocytes ⁴¹, which was the first to introduce both a junctional cleft (where ryanodine receptor, RyR, and most I_CaL function) and also a subsarcolemmal Ca²⁺ compartment, where Ca²⁺-dependent currents (e.g. I_NCX and I_Cl(Ca)) sense different local [Ca²⁺]_i compared to bulk [Ca²⁺]_i ⁵¹. We have characterized Ca²⁺ handling properties in atrial myocytes from patients in sinus rhythm and with cAF, and modified the Ca²⁺ handling parameters in our model accordingly. This recapitulates experimental data including simultaneous measurements of I_CaL and CaT, caffeine-induced CaT amplitude (i.e., SR content) and decay time (i.e., SERCA and NCX function) and SR Ca²⁺ leak at physiological temperature. Our human atrial model provides an accurate representation of Ca²⁺ homeostasis in human atrial myocytes.

Recently, the Tavi group proposed a model describing heterogeneous subcellular Ca²⁺ dynamics for human atrial cells presumed to lack of t-tubules.¹¹ They produced a biphasic rise of [Ca²⁺]_i, as seen at 22°C in human atrial myocytes.⁵² In their model the biphasic [Ca²⁺]_i rise resulted from delay between peripheral and central SR Ca²⁺ release. An extensive t-tubular network has been reported in atrial myocytes from large mammals.⁵³ Because we did not observe biphasic [Ca²⁺]_i rise in our human atrial myocytes at 37°C (time to peak ~60 ms) and quantitative data on t-tubule organization in human atrial myocytes is lacking, we did not assume slow propagating Ca²⁺ release toward the cell center.

Rate-dependent APD adaptation

Using our human ventricular myocyte model, we found that the increase in [Na⁺]_i at fast pacing rates feeds back to shorten APD via outward (repolarizing) shifts in Na⁺/K⁺ pump (NKA) and NCX currents¹². Our human atrial model (Figure 5) and that of the Tavi group¹¹ exhibit analogous behavior. The model showed negligible APD-rate adaptation when [Na⁺]_i was clamped to a certain value (Figure 5A). Notably, we confirmed experimentally in human atrial myocytes the prediction of our model that acutely blocking NKA causes AP prolongation followed by APD shortening (Figure 5C and D), thus supporting the involvement of [Na⁺]_i in APD (via shift in NKA current, Fig. 5B) and rate-dependent APD adaptation in human atrial cells. Furthermore, we show that I_CaL block has a similar effect on normal (sinus rhythm) and cAF human atrial action potentials (Figure 4), and in fact similar reductions in APD and APD rate-dependence occur in atrial myocytes isolated from patients with chronic AF. If I_CaL is blocked, APD is shorter (less depolarizing current), but also the CaT is greatly diminished, causing less extrusion of Ca²⁺ and less Na⁺ entry via NCX. In addition, the positive inotropy observed in normal atrial myocytes is lost in cAF, also limiting NCX-dependent Na⁺ accumulation at fast rates (as in Fig. 3I). Thus, our model recapitulated experimental results and point to [Na⁺]_i and I_CaL as critical components of the normal rate–dependent modulation of atrial APD. While direct effects of [Na⁺]_i on APD are compelling and logical, additional experimental validation of these effect would be valuable. We have discussed previously the role of delayed-rectifier K⁺ currents in APD rate adaptation ¹², and showed in Online Figure VII that I_Kr block has little effect on APD. Here we ruled out an important role of the atrial-predominant I_Kur (see Online Figure VIII).

Role of [Ca²⁺]_i in mediating AF in presence of I_Kur channelopathies

Atrial contractility is decreased in cAF, largely due to electrical remodeling that is associated with downregulation of I_CaL ^{28, 29}, which reduces CaT amplitude. Our simulation demonstrated that block of I_Kur enhances CaT amplitude of human atrial myocytes, both in patients in sinus rhythm or AF (Figure 6), thus pointing to I_Kur as an atrial-specific target to counteract hypocontractility associated to cAF. Indeed, experiments have shown that I_Kur blockers in ventricle did not appreciably alter APD or CaT ²⁹.

We hypothesize that I_Kur in the atrium may serve the same function as I_Ks in the ventricle, that is opposing AP prolongation expected from larger inward I_CaL and I_NCX during β-adrenergic stress ⁵⁴. Indeed, our simulations showed that block of I_Kur (to mimic Kv1.5 mutation that leads to non-functional current, and AF) in the presence of adrenergic challenge causes EADs (Figure 6D). That agrees with experimental data¹⁴, where I_Kur inhibition led to EADs in human atrial myocytes challenged with ISO. On the other hand, I_Ks block did not appreciably affect APD. Administration of ISO also led to cellular arrhythmic depolarizations when stimulating our model at low pacing frequency (not shown), in accordance with experimental work ^{14, 55}.

Conclusions

We developed a new computational framework to study the contribution of individual ionic pathway differences between atrial and ventricular cells to AP phenotype difference in the human atrium vs. ventricle. It also established that Ca²⁺ and Na⁺ handling processes are major contributors to atrial APD and its rate-related behavior in both normal and cAF conditions, and identified the role of I_Kur in helping prevent EADs in the presence of adrenergic stress. This model (freely available at https://somapp.ucdmc.ucdavis.edu/Pharmacology/bers/) will also be useful for integrating into multicellular models of the human heart.

Novelty and Significance.

What is Known?

• Atrial cells exhibit electrophysiological characteristics that differ from those of ventricular cells due to structural differences and specific combinations of ion channel/transporters expression and function.

• During chronic atrial fibrillation (AF), electrical and structural remodeling contributes to the development of the AF substrate, and abnormalities in intracellular Ca²⁺ cycling has emerged as key mediators in AF pathophysiology.

• Detailed models of myocyte Ca²⁺ cycling have typically focused on ventricular rather than atrial myocytes, in part because of limited appropriate experimental data (especially from human atrial myocytes).

What New Information Does This Article Contribute?

• Based on recent data from human atrial cells, we have developed a new mathematical model of the human atrial myocyte that accounts for the electrophysiological and Ca²⁺ handling properties of atrial cells in both normal and chronic AF conditions.

• Simulations indicate that heart rate-dependent action potential duration (APD) shortening in healthy atrial cells involves the accumulation of intracellular [Na⁺] at high frequencies that causes outward shifts in Na⁺/Ca²⁺ exchange and Na⁺/K⁺ pump currents, whereas ionic and Ca²⁺ handling remodeling lead to reduced Na⁺ accumulation in chronic AF, which causes a blunted APD rate-dependent response.

• Our modeling suggests that I_Kur is a key component of the adrenergic response of human atrial cells, as its loss (such as in Kv1.5 channelopathy) results in predisposition to early-afterdepolarizations in presence of isoproterenol, and may help explain the bouts of stress mediated AF observed in these patients.

It is increasingly clear that Ca²⁺-handling and electrophysiology are intimately linked to the development and perpetuation of AF. Thus, understanding AF requires an integrated quantitative understanding of ionic currents and Ca²⁺ transport in healthy and remodeled human atrium. However, no previous model focused on Ca²⁺ transport in human atrial myocytes in chronic AF. We developed a new human atrial myocyte model that incorporates the latest experimental data and modern concepts relating to intracellular Ca²⁺ homeostasis and related electrophysiology, including ionic and Ca²⁺ handling remodeling seen in chronic AF. Our simulation showed that I_Kur block enhances the amplitude of the Ca²⁺ transient of human atrial myocytes, representing an atrial-specific target to counteract hypocontractility associated to cAF. This current is also predicted to oppose APD prolongation expected from larger inward I_CaL and I_NCX during β-adrenergic stress. Our model provides novel insights into the mechanism of APD rate-dependent adaptation, by showing that accumulation of [Na⁺]_i at fast heart rates feeds back to shorten APD via outward shifts in Na⁺/Ca²⁺ exchange and Na⁺/K⁺ pump currents. This human atrial model provides a useful tool to investigate atrio-ventricular differences with respect to arrhythmogenesis and therapeutical approaches.

Non-standard Abbreviations and Acronyms

AF

Atrial Fibrillation

AP

Action Potential

APD

Action Potential Duration

APD₉₀

Action Potential Duration at 90% repolarization

cAF

chronic Atrial Fibrillation

CaT

Ca²⁺ transient

EAD

Early After Depolarization

G_NaL

Late Na⁺ current maximal conductance

I_CaL

L-type Ca²⁺ current

I_Cl(Ca)

Ca²⁺-activated Cl^- current

I_KACh

Acetylcholine-activated K⁺ current

I_Kr

Rapidly activating delayed rectifier K⁺ current

I_Ks

Slowly activating delayed rectifier K⁺ current

I_Kur

Ultrarapid delayed rectifier K⁺ current

I_K1

Inward rectifier K⁺ current

I_Na

Fast Na⁺ current

I_NCX

Na⁺/Ca²⁺ exchange current

I_NaK

Na⁺/K⁺ pump current

ISO

Isoproterenol

I_to

Transient outward K⁺ current

LA

Left Atrium

NCX

Na⁺/Ca²⁺ exchange

NKA

Na⁺/K⁺ ATPase

PKA

Protein Kinase A

RA

Right Atrium

RyR

Ryanodine Receptor

SERCA

Sarcoplasmic Reticulum Ca²⁺ ATPase

SK2

Ca²⁺-activated K⁺ channels

sr

sinus rhythm

SR

Sarcoplasmic Reticulum