Computational modeling of amylin-induced calcium dysregulation in rat ventricular cardiomyocytes

Abstract

Hyperamylinemia is a condition that accompanies obesity and precedes type II diabetes, and it is characterized by above-normal blood levels of amylin, the pancreas-derived peptide. Human amylin oligomerizes easily and can deposit in the pancreas [1], brain [2], and heart [3], where they have been associated with calcium dysregulation. In the heart, accumulating evidence suggests that human amylin oligomers form moderately cation-selective [4, 5] channels that embed in the cell sarcolemma (SL). The oligomers increase membrane conductance in a concentration-dependent manner [5], which is correlated with elevated cytosolic Ca²⁺. These findings motivate our core hypothesis that non-selective inward Ca²⁺ conduction afforded by human amylin oligomers increase cytosolic and SR Ca²⁺ load, which thereby magnifies intracellular Ca²⁺ transients. Questions remain however regarding the mechanism of amylin-induced Ca²⁺ dysregulation, including whether enhanced SL Ca²⁺ influx is sufficient to elevate cytosolic Ca²⁺ load [6], and if so, how might amplified Ca²⁺ transients perturb Ca²⁺-dependent cardiac pathways. To investigate these questions, we modified a computational model of cardiomyocytes Ca²⁺ signaling to reflect experimentally-measured changes in SL membrane permeation and decreased sarcoplasmic/endoplasmic reticulum calcium ATPase (SERCA) function stemming from acute and transgenic human amylin peptide exposure. With this model, we confirmed the hypothesis that increasing SL permeation alone was sufficient to enhance Ca²⁺ transient amplitudes. Our model indicated that amplified cytosolic transients are driven by increased Ca²⁺ loading of the sarcoplasmic reticulum (SR) and the greater fractional release may contribute to the Ca²⁺-dependent activation of calmodulin. Importantly, elevated Ca²⁺ in the SR and dyadic space collectively drive greater fractional SR Ca²⁺ release for human amylin expressing rats (HIP) and acute amylin-exposed rats (+Amylin) mice, which contributes to the inotropic rise in cytosolic Ca²⁺ transients. These findings suggest that increased membrane permeation induced by oligomeratization of amylin peptide in cell sarcolemma contributes to Ca²⁺ dysregulation in pre-diabetes.

1 Introduction

Amylin, a 3.9 kilodalton peptide produced by the pancreatic β cells [7], is secreted along with insulin into the blood stream [8]. Human amylin is amyloidogenic, i.e. at high concentrations it aggregates into amyloid and fibrils. In contrast, the amylin isoform found in rodents is non-amyloidogenic [6]. Secretion of amylin (and insulin) is increased in individuals with insulin resistance, a metabolic abnormality that precedes the onset of type II diabetes. Enhanced amylin secretion leads to accumulation of amylin aggregates in the pancreas [9] and other organs, including the heart [6]. These amylin deposits have been shown to induce diastolic dysfunction [6], hypertrophy, and dilation [10]. While studies correlating human amylin oligomerization in tissue with the onset of pathological states typical of diabetic cardiomyopathy [11] are beginning to emerge [3], the molecular mechanisms linking amylin insult with cellular dysfunction remain incompletely understood. Gaining momentum, however, is the notion that amylin oligomers in cardiac tissue may disrupt normal calcium homeostasis [6], stemming from amylin’s moderately cation-selective conductance properties [4, 5, 12]. While this conductance is small relative to predominant sarcolemmal Ca²⁺ currents including the L-type calcium channel (LCC) and Na⁺/Ca²⁺ exchanger (NCX), it nevertheless exhibits largely unexplained effects on perturbing intracellular Ca²⁺ signals and recruiting Ca²⁺-dependent pathways associated with pathological, hypertrophic remodeling [13].

In the healthy heart, the Ca²⁺-dependent excitation-contraction (EC) coupling cycle begins with a depolarizing action potential (AP) that modulates sarcolemma (SL) Ca²⁺ fluxes, including contributions from LCC and NCX [14]. Ca²⁺ entry via LCC and NCX triggers [15] sarcoplasmic reticulum (SR) Ca²⁺ release via ryanodine receptors (RyRs), leading to a rapid increase in intracellular Ca²⁺(Ca²⁺ transient) that ultimately activates and regulates competent myocyte contraction [14]. The cycle completes as SR Ca²⁺ uptake via the sarcoplasmic/endoplasmic reticulum calcium ATPase (SERCA), as well sarcolemmal Ca²⁺ extrusion via NCX and the sarcolemmal Ca²⁺ ATPase, collectively restore diastolic Ca²⁺ levels. Recently, we reported that this process is perturbed in hearts from rats that express human amylin in the pancreas (HIP), as well as in isolated cardiomyocytes acutely exposed to the peptide (+Amylin conditions) [6]. In both cases, measurements of a passive, trans-sarcolemmal Ca²⁺ leak from isolated myocytes were faster relative to control [6], which suggested that amylin oligomers insert into the membrane to facilitate a non-selective Ca²⁺ current that correlated with increased cytosolic Ca²⁺ transients. Furthermore, in HIP rat myocytes SERCA function was impaired, and the hypertrophic remodeling associated with nuclear factor of activated T-cells (NFAT) and histone deacetylase (HDAC) pathways were activated. Both properties are strongly associated with the progression toward heart failure [13]. In this study, therefore, we seek to clarify whether and through which mechanisms the human amylin-induced sarcolemmal Ca²⁺ leak leads to myocyte Ca²⁺ dysregulation.

Cardiac computational models are routinely used for exploring intracellular mechanisms of Ca²⁺ signaling and their dysregulation in cardiac tissue [16–22]. We extended one such model, the Shannon-Bers model of ventricular myocyte Ca²⁺ dynamics [23], to unravel the influence of amylin in the HIP phenotype. Specifically, the revised model reflects our experimentally-measured changes in SL membrane Ca²⁺ permeation as well as decreased SERCA function consistent with acutely-exposed myocytes and transgenic human amylin rats [6]. We find that increased a sarcolemmal Ca²⁺ background current (’leak’) arising from human amylin oligomerization was sufficient to reproduce enhanced Ca²⁺ transients previously measured in HIP rats [6]. These simulations implicate increased SR loading and fractional SR Ca²⁺ release work in tandem to magnify Ca²⁺ transient amplitude for the amylin phenotypes, which in turn elevates cytosolic Ca²⁺ load. Accompanying enhanced SR Ca²⁺ loading is an increased fractional release, stemming from both SR and dyadic cleft Ca²⁺ content. Finally, we show higher propensities for CaM activation under conditions of elevated diastolic Ca²⁺, which we speculate may trigger the CaM-dependent NFAT remodeling pathway. These findings lead to our hypothesized model of amylin-induced Ca²⁺ dysregulation summarized in Fig. 1.

Figure 1.

Hypothesized model. Increased sarcolemmal Ca²⁺ in acute amylin-exposed rats (+Amylin) increases sarcoplasmic reticulum Ca²⁺ loading, amplifies intracellular Ca²⁺ transients and increases the Ca²⁺-bound state of proteins including calmodulin (CaM). Blue arrows represent Ca²⁺ fluxes.

2 Materials and Methods

2.1 Experimental animals

N=12 Sprague-Dawley rats were used in this study. All animal experiments were performed conform to the NIH guide for the care and use of laboratory animals and were approved by the Institutional Animal Care and Use Committee at University of Kentucky. Ventricular myocytes were isolated by perfusion with collagenase on a gravity-driven Langendorff apparatus [6].

2.2 Measurements of Ca²⁺ transients and passive, trans-sarcolemmal sarcolemmal Na⁺ and Ca²⁺ leaks

Myocytes were plated on laminin-coated coverslips, mounted on the stage of a fluorescence microscope and loaded with either Fluo4-AM (10 µmol/L, for 25 min) for Ca²⁺ transient recordings or Fura2-AM (10 µmol/L, for 25 min) for measurements of sarcolemmal Ca²⁺ leak. Ca²⁺ transients were elicited by stimulation with external electrodes at a frequency of 1 Hz. The passive trans-sarcolemmal Ca²⁺ leak was measured as the initial rate of Ca²⁺ decline upon reducing external Ca²⁺ from 1 to 0 mM. In these experiments, Ca²⁺ fluxes to and from the SR were blocked by pre-treating the cells with 10 µM thapsigargin for 10 min whereas the NCX and sarcolemmal Ca²⁺- ATPase were abolished by using 0 Na⁺/0 Ca²⁺ solution (Na⁺ replaced with Li⁺) and adding 20 µM carboxyeosin, respectively. Sarcolemmal Ca²⁺ leak was measured in control cells and in myocytes incubated with human amylin (50 µM for 2 hrs) in the absence and presence of the membrane sealant poloxamer 188 (P188, 50 µM) or epoxyeicosatrienoic acid (14,15-EET, 5 M). Data for HIP rats are from Despa et al. [6].

Na⁺ influx was measured as the initial rate of the increase in intracellular Na⁺ concentration ([Na⁺]_i) immediately following Na⁺/K⁺ ATPase (NKA) inhibition with 10 mM ouabain. As described previously [24], [Na⁺]_i was measured using the fluorescent indicator SBFI (TefLabs). The SBFI ratio was calibrated at the end of each experiment using divalent-free solutions with 0, 10, or 20 mmol/L of extracellular Na⁺ in the presence of 10 µmol/L gramicidin and 100 µmol/L strophanthidin.

2.3 Statistical analysis

Data are expressed as mean ± SEM. Statistical discriminations were performed using (1) 2-tailed unpaired Student t-test when comparing 2 groups and 1-way ANOVA when comparing multiple groups Statistical analysis was done in GraphPad Prism version 5.0 for Windows (GraphPad Software, La Jolla, CA). P<0.05 was considered significant.

2.4 Simulation and analysis protocols

2.4.1 Summary of Shannon-Bers-Morotti rat Ca²⁺ handling model

To examine the relationship between increased sarcolemmal Ca²⁺ entry and elevated Ca²⁺ transients reported in rats [6], we adapted a rabbit ventricular myocyte model of Ca²⁺ signaling to reflect handling terms specific to rodents. This choice was based on the initial lack of rat-specific Ca²⁺ handling models available in the literature. Recent computational models of rat cardiomyocyte Ca²⁺ handling have been published [25, 26], and are in qualitative agreement with our implementation, as we will discuss below. Myocytes from rats and mice have similar rates of Ca²⁺ relaxation via SERCA, NCX, and minor contributors such as sarcolemmal Ca²⁺-ATPase and mitochondrial Ca²⁺ uptake (92, 8 and 1%, versus 90.3, 9.2 and 0.5%, respectively) [27, 28]. Accordingly, mouse-specific parameters and potassium current changes were introduced into the Shannon-Bers rabbit cardiomyocyte Ca²⁺ model [23] according to Morotti et al. [29] (summarized in Supplement). The resulting model is hereafter referred to as the Shannon-Bers-Morroti (SBM) model. Model equations, ’state’ names, current names and initial conditions are provided in the supplement. As noted in [29], four predominant changes in potassium channels were included: 1) the transient outward potassium current expression for rabbits was replaced with fast component (i_tof) for mice, 2) the slowly activating delayed rectifier current was substituted with a slowly inactivating delayed rectifier current (i_Ks), 3) a non-inactivating potassium steady-state current (i_ss) was added 4) the inward rectifier potassium current (i_K1) was reduced. Other distinctions between the two species are the elevated intracellular sodium load and sodium ion current in murine versus rabbit species, which we optimized to match experimental data collected in this study. In Fig. S2–Fig. S4, we compare metrics such as Ca²⁺ transients, action potentials, potassium currents and prominent Na⁺/Ca²⁺ currents for rabbits versus mice predicted using the ’Numerical model of Ca²⁺ handling’ described below, for which we report excellent agreement with data from Morotti et al. [29].

The prominent adjustment required to then match rat Ca²⁺ collected at 310 K (98.3° F) from Gattoni et al. [25] was optimization of SERCA V_max (Fig. S5) via a genetic algorithm (GA) we describe in the Supplement. The decision to use the Gattoni Ca²⁺ transient data was based on the common temperature of 310K used in their data and the fitting of the Shannon-Bers model, whereas transients reported by Despa et al were measured at 298K (76.7° F). Thus, all simulations were conducted at 310 K. After fitting the Ca²⁺ transient, NKA V_max was varied to maintain intracellular Na⁺ content at 12 mM, as was measured in this study Fig. S16.

In rat myocytes incubated with human amylin (+Amylin), amylin oligomer deposits was correlated with a roughly 73% higher rate of sarcolemmal Ca²⁺ leak (see Figure 3D of Despa et al. [6]). We indicate in the supplement that amylin does not significantly impact LCC current in our experiments (see Sect. S.3.1 and Fig. S15), thus the computational model assumed amylin only impacts sarcolemmal Ca²⁺ leak when acutely applied to isolated myocytes. Therefore, to reflect increased SL leak due for the +Amylin condition, we increased by 73% (see Table S3) the Ca²⁺ conductance term, G_Ca, in the Shannon-Bers leak model described by Eq. 1

$$I_{\mathit{\text{ibk}}}={\rho }_i{G}_i(V-E_i)$$ (1)

where ρ_i represents sarcolemmal leak density of ion i, G_i is the max conductance for ion i, V is voltage, and E_i is the Nernst potential of ion i. It is important to emphasize that the leak model assumed in the Shannon-Bers model balances Ca²⁺ entry (via LCC and NCX) with extrusion mechanisms to ensure physiologically-reasonable resting diastolic Ca²⁺ levels [23]. For simplicity, we utilized Eq. 1 to account for the additional trans-sarcolemmal Ca²⁺ leak due to amylin oligomerization, though we discuss in Limitations how this model might be improved. Although amylin pores exhibit poor cation selectivity [5], we maintained G_Na at baseline values, given that we observed no detectable change in Na⁺ load (Fig. S16, discussed in Sect. S.3.2). This required a slight reoptimization of NKA max to remain in agreement with the consistent 12 mM loading reported in Fig. S16. Specifically, the GA determined that increasing NKA Vmax by 14% was required to maintain normal Na⁺ levels (see Table S3), which interestingly concurs with a study indicating amylin-agonized NKA function in skeletal muscle [30]. For the human amylin transgenic rat model (HIP), the SL leak rate is unknown, therefore we fit G_CA to reproduce the approximately 40% higher Ca²⁺ transients observed in the Despa et al. rats paced at 0.5 Hz (Fig 5 of [6]). It was also observed that Ca²⁺ transient decay time increased by nearly 30% in HIP rats relative to control [6], for which the GA determined that a reduction in SERCA Vmax by 38% was necessary.

Figure 3.

Predicted Ca²⁺ transients and loads as a function of SERCA V_max activity (% of control) and SL Ca²⁺ leak (% of control). a) intracellular Ca²⁺, b) SR Ca²⁺ transient c) maximum SR Ca²⁺ load and d) sodium load. A black circle is representative of the Control case, a blue square is representative of the +Amylin case, and a red square is representative of the HIP case.

Figure 5.

Percent change in SBM-predicted a) ion current amplitudes and b) model state variables for +Amylin (blue) and HIP (red) configurations relative to control (black, normalized to 100%). A list of current labels is provided in the supplement Table S2

2.4.2 Numerical model of Ca²⁺ handling

The Shannon-Bers cell ML model was converted into a Python module via the Generalized ODE Translator gotran (https://bitbucket.org/johanhake/gotran) to make use of our Python-based routines for simulation and analyses. The mouse-specific alterations summarized in the previous section were implemented into the resulting module. In our numerical experiments, the SBM model was numerically integrated by the scipy function odeint, which utilizes the LSODA algorithm for stiff ordinary differential equations [31]. The numerical model was integrated using a timestep of 0.1 ms for a total simulation time of up to 5 minutes. These simulations provide as output the time-dependent values of the SBM ’states’, such as intracellular Ca²⁺ load or the action potential, as well as ’currents’ that include major Ca²⁺, Na⁺, K⁺, and Cl⁻-conducting proteins. Model fitting proceeded by a genetic algorithm (reviewed in [32]) that iteratively improved parameter values, such as LCC Ca²⁺ conductance, sarcolemmal Ca²⁺ leak, and NKA conductance over several generations of ’progeny’ (Fig. S6). Experimentally-measured outputs, such as Ca²⁺ transient decay time and amplitude, were measured for each of the progeny; those that reduced output error relative to the experimentally-measured equivalent with stored for future generations (see Sect. S.3.5 for more details). To validate our implementation, we present comparisons of action potentials, intracellular Ca²⁺ and Na⁺ transients, as well as ionic currents for rabbit versus murine cardiac ventricular myocytes (see Sect. S.2), for which we report good agreement across these model outputs.

We additionally stimulated the model at several frequencies ranging from 0.1 to 2.0 Hz, to ensure that our model predictions were consistent with transient data recorded by Despa et al. [6]. Sensitivity analyses were additionally performed to determine relative correlations between model input parameters and predicted outputs (see Supplement). Data processing was performed using scipy and the ipython notebooks, with exception to the sensitivity analyses described in the supplement. Source code will be provided at HTTPS://BITBUCKET.ORG/HUSKEYPM/WHOLECELL. Since the initiation of this project, an additional rat cardiomyocyte model has been published. This model is based on the 2001 Pandit model of the rat LV cardiomyocyte [33] and includes recalibrated Ca²⁺ fluxes parameters to provide more consistent fitting with experimental data. We discuss later that the Devenyi et al [26] model reproduces trends discussed in this paper, which we obtained using the above described SBM formulation.

2.4.3 Analyses

To examine potential mechanisms that link increased SL Ca²⁺ permeation to elevated Ca²⁺ transients, we present a simple method, State Decomposition Analysis (SDA), that monitors and identifies prominent changes in key ’state’ variables (including the action potential, SR-load, channel gate probabilities among others) as well as ion channel currents, relative to control conditions. The key benefit of this approach is the automated identification of modulated EC coupling components that can motivate model refinements and additional experiments. The SDA method consists of the following steps: 1) numerically solve the time-dependent ordinary differential equations (ODE)s governing all components (the state variables) of the EC coupling model for trial and control parameter configurations 2) ’score’ the time-dependent state values according to metrics like amplitude 3) calculate percent differences between trial and control state variable scores 4) rank order states by either the percent difference with a reference state or by the amplitudes in the reference.

3 Results

3.1 Effects of human amylin on intracellular Ca²⁺ transients in rat cardiac ventricular myocytes

Accumulation of human amylin aggregates in rat cardiomyocyte SL was previously correlated with increased rates of sarcolemmal Ca²⁺ leak and amplified Ca²⁺ transient amplitudes [6]. However, the mechanism linking sarcolemmal Ca²⁺ leak and Ca²⁺ transient amplitudes is not established. We first validate the hypothesis that amylin oligomerization has the primary effect of elevating sarcolemmal Ca2+ leak. This was evaluated by measuring the effect of human amylin on the Ca²⁺ leak and Ca²⁺ transients in the absence and in the presence of poloxamer 188 (P188), a surfactant that stabilizes lipid bilayers and seals sarcolemmal lesions [34] through hydrophobic interactions [35]. As in previous reports, human amylin significantly increased both passive SL Ca²⁺ leak and Ca²⁺ transient amplitude (Fig. S1A). When amylin was applied in the presence of P188, however, SL Ca²⁺ leak and transient amplitudes were statistically comparable to control (Fig. S1). Similar behavior was observed upon co-incubation of amylin with epoxyeicosatrienoic acids (EET), which have anti-aggregation effects and reduce amylin oligomerization at the SL [10], though they are reported to have opposing effects on the regulation inward Ca²⁺ entry via voltage-gated and L-type Ca²⁺ channels [36, 37]. These results support the hypothesis that amylin primarily acts to increase trans-sarcolemmal Ca²⁺ conductance potentially through poration of the membrane, without significant recruitment of transmembrane Ca²⁺ channels or transporters.

To investigate the mechanism linking membrane poration via human amylin to amplified Ca²⁺ transients, we numerically solved the SBM whole-cell model at 1 Hz pacing under control conditions and with 73% increased SL leak (+Amylin) in accordance with the experimental results of Despa et al. [6]. Our simulations confirmed that Ca²⁺ transients for the +Amylin configuration were higher than control (65% in Fig. 2), consistent with increases observed in experimental data collected in this study (Fig. S1b), as well as Fig. 3C of [6]). We further modeled the HIP rats examined in [6] by additionally considering decreased SERCA function, which together with SL Ca²⁺ leak rate, we fitted to reproduce the experimentally measured relative increase in Ca²⁺ transient amplitudes and decay. We note here that the absolute rates of the Ca²⁺ declines in our model (solved at 310K) were consistent with experimental data recorded at 310K by Gattoni et al [25] (see Fig. S5), but were faster than those obtained at 298K by Despa et al [6]. Similar to +Amylin the HIP model predicted elevated Ca²⁺ transient amplitudes that were higher than control (approximately 30%).

Figure 2.

(a) Intracellular Ca²⁺ transients (concentration versus time) predicted using the Shannon-Bers-Morroti (SBM) Ca²⁺ cycling model following 300s of 1.0 Hz pacing. Transients are reported for model conditions representing control (black), acute amylin-exposed rats (+Amylin, blue) and human amylin transgenic (HIP, red). (b,c) Predicted intracellular Ca²⁺ transient amplitude (ΔCa [uM], left axis, solid) and diastolic Ca²⁺ load (right axis, dashed) versus pacing frequency [Hz] for control (black) and HIP (red) conditions. Data are provided based on SBM model predictions at 310 K (b) and data collected by Despa et al at 298 K [6] (c).

In contrast to the +Amylin configuration, however, the HIP model presented 27% slower diastolic relaxation and a 33% increase in diastolic intracellular Ca²⁺ load relative to control, as would be expected with reduced SERCA function [38]. Intracellular Ca²⁺, Ca²⁺ SR, intracellular Na⁺, and AP are shown for +Amylin and HIP relative to control in Fig. S7–Fig. S8. We further note that the enhancement of Ca²⁺ transient amplitudes for +Amylin/HIP rats relative to control diminished with increased pacing (up to 2 Hz), in accordance with experimental findings (see Fig. 2). Ca²⁺ transient relaxation rates remained unchanged over this range, as our model does not currently include factors governing frequency dependent acceleration of relaxation, such as the involvement of Ca2+/calmodulin-dependent protein kinase II (CaMKII) [39].

3.2 Effects of acute amylin-induced modulation of sarcolemmal ion handling

The rate of Ca²⁺ entry directly due to amylin oligomerization in the sarcolemma is small relative to contributions from the prominent sarcolemmal Ca²⁺ currents, namely LCC and NCX. Hence, the SL leak alone is insufficient to directly account for the observed increase in Ca²⁺ amplitude for the amylin models on a beat-to-beat basis. This implicates other indirect mechanisms in driving the increased Ca²⁺ transients observed in HIP and +Amylin rats. Since the majority of the Ca²⁺ released during a single beat originates in the SR [14], we hypothesized that the increased intracellular Ca²⁺ transient amplitudes for the amylin-incubated myocytes and HIP rats stemmed from elevated SR Ca²⁺ loading owing to increased sarcolemmal Ca²⁺ leak. Under these conditions, we would expect that Ca²⁺ transient amplitudes should scale proportionally with SL leak rates. Therefore, we examined how the control model responded to variations SL Ca²⁺ leak (Amylin Leak %), as well in SERCA function. These effects are summarized in Fig. 3a–c, for which we report predicted cytosolic Ca²⁺ transients (a., ΔCai), SR Ca²⁺ transients (b., ΔCa_SR) and diastolic SR Ca²⁺ loads (c., max Ca_SR). These data indicate that under the parameters considered in this study, the SR Ca²⁺ load is positively correlated with increasing sarcolemmal Ca²⁺ leak and to a lesser extent, SERCA function. More importantly, the increased sarcolemmal Ca²⁺ leak assumed for +Amylin and HIP relative to control largely accounted for the elevated Ca²⁺ transients and SR load in our model. In other words, SERCA appeared to play less of a role in tuning the Ca²⁺ transient over the V_max and SL leak values we considered, as the reduced SERCA V_max for HIP relative to +Amylin maintained enhanced, albeit modestly reduced, Ca²⁺ transients and load.

It is important, though, to distinguish the modest changes in SERCA function we considered from complete SERCA knockout, for which mice subject to the latter conditions develop heart failure, manifesting in reduced twitch and caffeine-induced Ca²⁺ transients, as well as Na⁺ dysregulation [40]. Similarly, it has been reported [41] that thapsigargin dose-dependent reductions in SERCA activity as measured by Ca²⁺ transient decline rate correlate with reduced Ca²⁺ transient amplitudes, and SR load to some extent. Indeed, we find that more significant reductions in V_max (beyond a 50% reduction) attenuate the Ca²⁺ transient, but in our model this would present a Ca²⁺ decay rate incongruent with data used for fitting.

These results raise the question of why the modest modulation of SERCA V_max seems to have lesser impact on Ca²⁺ transient amplitude than sarcolemmal Ca²⁺ leak rates (Fig. 3). First, assuming normal sarcolemmal Ca²⁺ leak, modestly reduced V_max will expectedly slow the rate of replenishing the SR diastolic Ca²⁺ load; however, the time interval for 1 Hz pacing rate was still sufficiently long for cytosolic and SR Ca²⁺ to approach steady state (e.g. when ${\mathit{\text{Ca}}}_{\text{cyto}}^{2+}/K_{\mathit{\text{mf}}}={\mathit{\text{Ca}}}_{\text{SR}}^{2+}/K_{\mathit{\text{mr}}}$ in our model). As pacing frequency is increased, the time interval during which to reestablish diastolic SR Ca²⁺ load is diminished. When the SL Ca²⁺ leak is increased by way of amylin oligomerization, the total Ca²⁺ content of the cell is increased, which manifests in both increased cytosolic and SR Ca²⁺ load. Both Ca²⁺ pools are coupled to the cleft (junctional) Ca²⁺ compartment, which in part controls ryanodine receptor (RyR) gating by favoring the RyR open state at higher cleft Ca²⁺ concentrations. We support this assertion in Sect. S.3.7, wherein we demonstrate that both higher SR and cleft Ca²⁺ independently lead to increased intracellular Ca²⁺ transient amplitudes, although SR Ca²⁺ load has the largest effect. In other words, higher cleft Ca²⁺ for HIP despite nearly normal SR load is still sufficient to increase Ca²⁺ transient amplitudes, which we rationalize below is due to increased SR fractional Ca²⁺ release. Nevertheless, the amylin-induced Ca²⁺ transient enhancement diminished with increased pacing and nearly approached control transient amplitudes at 2 Hz (see Fig. 2) Further, since the decline in transient amplitude with pacing was faster for HIP relative to +Amylin, this expectedly suggests that amylin’s inotropic effects are at least partially modulated by the efficiency of SERCA Ca²⁺ handling.

It is apparent from our data that modest changes in SR load permit significant changes in Ca²⁺ transient amplitudes, as has been demonstrated by Bode et al in thapsigargin-treated rat ventricular myocytes [41]. To investigate the mechanism of this effect in our models of human amylin-induced Ca²⁺ leak, we report in Fig. 4 for control, HIP and +Amylin conditions the SR Ca²⁺ load, cleft Ca²⁺(’junctional’ Ca²⁺ localized to the dyadic cleft, which triggers RyR activation [42]), fractional Ca²⁺ release

$$\mathit{\text{fr}}=({\text{Ca}}_{\text{SR},\text{diastolic}}^{2+}-{\text{Ca}}_{\text{SR},\text{systolic}}^{2+})/{\text{Ca}}_{\text{SR},\text{diastolic}}^{2+}$$ (2)

where ${\text{Ca}}_{\text{SR},\text{diastolic}}^{2+}$ and ${\text{Ca}}_{\text{SR},\text{systolic}}^{2+}$ are the diastolic and systolic SR Ca²⁺ loads, respectively), the RyR open probability with respect to cleft Ca²⁺. These data indicate that cleft Ca²⁺ is elevated for +Amylin and HIP relative to control, and this trend appears to be insensitive to pacing. Additionally, we report that SR Ca²⁺ load is marginally elevated for +Amylin and HIP relative to control, but all conditions present loads that monotonically decrease with pacing frequency. As a result, fractional Ca²⁺ release for the amylin-treated cases is generally larger than that which is observed for control. These data therefore suggest that 1) higher cleft Ca for HIP/+Amylin prime RyR activation for SR Ca release and 2) faster pacing reduces the SR load available for RyR Ca²⁺ release, which manifests in increased fractional release for +Amylin/HIP that is frequency-dependent. This interpretation is supported by our predictions of RyR open probability (P_o) means and maxima, which demonstrate that P_o monotonically increase with cleft Ca²⁺ over the ranges predicted by our control and HIP/+Amylin conditions. Further, we discuss in Sect. S.3.7 and Fig. S17 that peak cytosolic Ca²⁺ transient amplitudes, which are indicative of fractional SR release, are positively correlated with increases in both SR Ca²⁺ diastolic load as well as cleft Ca²⁺. In other words, the increased fractional release exhibited in our +Amylin and HIP models likely arises from both increased SR Ca²⁺ load as well as higher cleft Ca²⁺ relative to control.

Figure 4.

(Upper left) ’Junctional’ Ca²⁺ localized to the LCC/RyR dyadic space as a function of pacing for control (black), +Amylin (blue) and HIP (red) rat cardiac ventricular myocytes. upper right) fractional release as measured by Eq. 2. bottom left) Diastolic (solid) and systolic (dashed) SR Ca content. bottom right) Mean/maximum ryanodine open probability with respect to junctional Ca²⁺, assuming constant SR content. Junctional Ca²⁺ characteristic of the control, +Amylin and HIP are marked with symbols.

It was expected that amylin-driven increases in cytosolic and SR Ca²⁺ loading would culminate in the modulation of multiple downstream Ca²⁺-dependent signaling pathways [24]. In this regard, we leveraged the computational model to systematically probe the response of its outputs, such as the activity of various Ca²⁺ handling components, to changes in model inputs including SL Ca²⁺ leak. Accordingly, we depict in Fig. 5 relative changes in all ion channel amplitudes described in the SBM model for the +Amylin and HIP configurations, ranked by their absolute magnitudes. These data expectedly reflect increased sarcolemmal Ca²⁺ leak (i_CaB) for +Amylin and HIP, as we assumed increased leak conductance parameters for both cases. Interestingly, i_Na was predicted to increase for both cases relative to control, which in principle could influence the AP upstroke velocity [43]. However, the AP waveform is largely unchanged in the amylin cases relative to control, thus the predicted effects on i_Na amplitude appear to be of little consequence (See Fig. S7d). Common to both HIP and +Amylin, we found modestly higher i_NaCa and i_Cap relative to control, which reflect redistribution of sarcolemmal Ca²⁺ extrusion versus SR Ca²⁺ uptake. Similar redistributions are known to occur when SERCA function is reduced [44].

In Fig. 5 we depict the relative change in activity for the top twenty modulated model ’states’ upon increasing SL Ca²⁺ leak. Unique to +Amylin, and HIP to a lesser extent, were increases in the inactive (I) and open (O) states of the Ryanodine receptor model [45, 46] relative to control. These increases are consistent with elevated junctional (cleft) and SR Ca²⁺ that together both promote and terminate RyR opening. More importantly, the greater RyR open probability translates to an increased SR Ca²⁺ release flux and commensurate increase in cytosolic Ca²⁺ transients. Apparent to both +Amylin and HIP conditions are 30–75% increases in states representing intracellular Ca²⁺ and Ca²⁺-bound buffers, including CaM, Troponin C (TnC), and myosin, which can be expected with increased Ca²⁺ loading.

3.3 Sensitivity analyses

Following the protocol outlined in Sect. S.3.6, we determined the sensitivity of SBM model outputs including Ca²⁺ amplitude, cytosolic Na⁺, SR Ca²⁺, diastolic Ca²⁺, action potential duration (APD), and Ca²⁺ transient decay (τ) to the model parameters, by randomizing model parameters temperature, background Ca²⁺ leak, background Na⁺ leak, SERCA function, NKA function, and LCC Ca²⁺ permeability. An advantage of this approach is to potentially isolate a small number of contributions that disproportionally modulate a given physiological output, which can serve as a basis for experimental testing of novel model prediction as done recently by Devenyi et al [26]. Here we present Spearman correlations in Table S4 as a measure of the relative monotonicity between parameter/model output pairs. These statistical analyses revealed substantial correlations for background Ca²⁺ leak with APD (r_s = −0.61, p < 0.01), SR Ca²⁺ (r_s = 0.60, p < 0.01), Ca²⁺ amplitude (r_s = 0.58, p < 0.01), diastolic Ca²⁺ (r_s = 0.59, p < 0.01), cytosolic Na⁺ (r_s = 0.41, p < 0.01), and Ca²⁺ transient decay (τ) (r_s = −0.50, p < 0.01). These analyses confirm that an increase in background calcium leak correlates with increased cellular Ca²⁺ content, as well as increased SR Ca²⁺, Ca²⁺ amplitude, and diastolic Ca²⁺. Other notable associations were between: background Na⁺ leak and cytosolic Na⁺ (r_s = 0.46, p < 0.01) and max NKA current and cytosolic Na⁺ (r_s = −0.61, p < 0.01) (greater NKA activity reduces intracellular Na⁺ content). We emphasize that the correlations reported are inclusive of all sampled parameters. As an example, Ca²⁺ amplitude (the calcium transient amplitude) is controlled not only by the background calcium leak, but also other parameter inputs including LCC Ca²⁺ permeability. For this reason, the moderate correlation of background leak with calcium transient amplitude (r_s = 0.58, p < 0.01) indicates that other parameters significantly contribute to the variation in Ca²⁺ amplitude. If we instead consider a dataset for which only background Ca²⁺ leak is modulated, the r_s increases to > 0.95. Further details concerning correlation magnitudes and significances are reported in Sect. S.3.6.

3.4 Extension of findings to higher mammals

A distinctive feature of murine species is the dominant role of the SR in managing Ca²⁺ homeostasis, with nearly 90% of the intracellular Ca²⁺ transient originating from SR [14]. In contrast, in higher species, including humans, sarcolemmal derived Ca²⁺ plays a significantly larger role; in rabbits, for instance, inward sarcolemmal Ca²⁺ currents account for roughly 40% of the intracellular Ca²⁺ transient [14]. As a proof of principle, we augmented the original Shannon-Bers (SB) formulation of cardiac Ca²⁺ cycling in rabbits [23] with increased sarcolemmal Ca²⁺ leak. In Fig. S9, we demonstrate similar trends of increased cytosolic and SR Ca²⁺ load under conditions of increased sarcolemmal Ca²⁺ leak.

4 Discussion

4.1 Shannon-Bers-Morotti myocyte model

We revised the Shannon-Bers model of rabbit ventricular myocyte Ca²⁺ cycling [23] to reflect Ca²⁺ handling in murine species, as a close approximation to the human amylin transgenic/amylin-exposed rats used in [6]. The predominant changes implemented in our model primarily entailed increasing the rates of SR Ca²⁺ uptake and release to mirror the larger role of SR Ca²⁺ handling in murine relative to higher order animals, as well as modulating potassium channel current profiles. The SBM model captured key distinguishing features of murine cardiomyocyte Ca²⁺ handling, including shorter AP and Ca²⁺ transient duration relative to rabbit, as well as a greater role of Ca²⁺ release and uptake via the SR, as opposed to NCX [47]. When we included sarcolemmal Ca²⁺ leak data from Despa et al. [6] appropriate for the +Amylin and HIP phenotypes in rats, as well as reduced SERCA Ca²⁺ uptake rates for HIP, the computational model reproduced the altered Ca²⁺ transient amplitudes across a broad range of pacing intervals. With this model, we conclude that

• increased rates of Ca²⁺ influx through the sarcolemma, for instance as a result of amylin-induced membrane poration, promotes the amplification of cytosolic Ca²⁺ transients.

• the increase in Ca²⁺ transient amplitude arises due to greater SR Ca²⁺ load relative to control

• elevated cytosolic Ca²⁺ load stemming from higher rates of sarcolemmal Ca²⁺ influx (+Amylin), and especially when SERCA function is reduced (HIP), significantly increases the proportion of Ca²⁺-bound proteins. Of these proteins, CaM activation in particular may trigger remodeling via the calcineurin/NFAT pathway [48](see Fig. 1).

• the concerted relationship between amylin-induced increased sarcolemmal Ca²⁺ leak, intracellular Ca²⁺ transients, and SR loading gives rise to similar Ca²⁺ transient amplification in the Shannon-Bers model of EC coupling in rabbit [23], which suggests similar mechanisms of dysregulation in pre-diabetes may manifest in higher order mammals.

Since the initiation of this project, an additional rat cardiomyocyte model has been published (Devenyi et al [26]). This model is based on the 2001 Pandit model of the rat ventricular cardiomyocyte [33] and included optimized Ca²⁺ fluxes parameters to further refine its reproduction of experimental data, including the Ca²⁺ transient. We discuss in the next section that the Devenyi et al [26] model reproduces trends discussed in this paper, which we obtained using the above described SBM formulation.

4.2 Enhanced SL Ca²⁺ fluxes are sufficient to elevate cytosolic Ca²⁺ load in absence of altered SR Ca²⁺ handling

Recently, it was established that pre-diabetic rats transgenic for human amylin peptide presented a high density of oligomerized amylin deposits in ventricular tissue [6]. Cells containing these deposits were additionally found to have greater sarcolemmal Ca²⁺ leak rates and amplified Ca²⁺ transients. These effects on sarcolemmal Ca²⁺ conductance and transient amplitudes were recapitulated in isolated myocytes that were incubated with human amylin, which suggested that the phenotypical changes likely precede any significant changes in protein expression that might otherwise produce similar effects. Further, disruption of amylin oligomers via increasing eicosanoid serum levels (EET) [10] and the application of membrane sealant P188 (Fig. S1) were both found to restore normal Ca²⁺ handling. These experiments together firmly establish the link between oligomer-induced membrane poration and Ca²⁺ dysregulation. Similarly, in our implementation of the Morotti-Shannon-Bers Ca²⁺ cycling model, we found that amplified Ca²⁺ transients could be induced solely by increasing the sarcolemmal Ca²⁺ conductance parameter (see Eq. 1). Indeed, the trend of increasing Ca²⁺ transient amplitude with increased sarcolemmal Ca²⁺ leak was also captured in the Devenyi et al [26] model (Fig. S14), which suggests the effect is not limited to our choice of EC coupling model.

The enhancement of intracellular Ca²⁺ transient amplitudes by amylin bears similarity to agonism of the sarcolemmal Ca²⁺ channels LCC and P2X. It is well-established, for instance, that activation of LCC via β-adrenergic receptor (βAR) agonists promote larger Ca²⁺ transients that are accompanied by elevated SR Ca²⁺ load [14], which has also recently been demonstrated for human amylin expressed in rat hippocampal neurons [49]. Further, P2X receptor activation has comparable effects on Ca²⁺ transients and SR load [50], albeit without the multifarious changes in Ca²⁺ handling associated with βAR stimulation. In fact, though our characterization of LCC in amylin-incubated revealed no significant changes in its current/voltage profile relative to control, our modeling results indicate similar amplification of Ca²⁺ transients can be obtained by increasing the peak LCC Ca²⁺ conductance term (see). While we defer the topic of SR load to later in the Discussion, our simulations present strong evidence that increased inward sarcolemmal Ca²⁺ alone is sufficient to explain amylin dose-dependent effects on Ca²⁺ transients in Despa et al. [6].

For pacing intervals at 1 Hz and greater, our predictions of the control Ca²⁺ transient using the SBM model (see Fig. 2) follow a neutral transient amplitude/frequency relationship, as is frequently exhibited in mice [51] and the Despa et al. rat control data [6]. Further, the computational model captures the negative Ca²⁺ transient relationships with pacing frequency reflected in the Despa et al. HIP rat data, including the diminishing difference in transient amplitude relative to control. The decline in transient amplitude for HIP can be ascribed to the inability to maintain elevated SR load as pacing increases, given the reduced SERCA activity evident for these rats [6]. Our data also reflect a negative transient amplitude/frequency relationship for the +Amylin conditions, which may arise because the model does not reflect phosphorylation-dependent effects on relaxation, including CaMKII activation [52]. Nevertheless, given that our model captures the predominant changes in Ca²⁺ handling exhibited in +Amylin and HIP pre-diabetic rats [6] chiefly through modulating sarcolemmal Ca²⁺ leak, our simulations support the hypothesis that increased SL Ca²⁺ entry alone, without recruiting cation-specific channels like L-type calcium channel (LCC), promotes the development of enhanced Ca²⁺ transients (see Fig. 1).

4.3 Contributions of SR loading to amylin phenotype

We demonstrated in Fig. S17 a positive correlation of increasing Ca²⁺ SL leak rates with elevated SR Ca²⁺ loading and transients, respectively, with preserved SERCA function. This configuration is analogous to the +Amylin conditions assumed in this study. Therefore, the predicted amplification of the cytosolic Ca²⁺ transients appears to be driven by Ca²⁺-loading of the SR, which in turn affords greater RyR Ca²⁺ flux per release event. We note that diastolic SR Ca²⁺ load was modestly increased relative to control under the +Amylin conditions (see Fig. S8) The increased SR load appeared to be of little consequence to spontaneous Ca²⁺ release associated with SR Ca²⁺ overload [53], as steady-state behavior was maintained through several minutes of simulated pacing without evidence of delayed after-depolarizations. These results concur with those of Campos et al., for which computational studies of rabbit ventricular myocytes indicated considerable tolerance to SR Ca²⁺ overload before abnormal AP behavior was evident [54]. Further, our hypothesis is congruent with a study examining triggering of the SL Ca²⁺ channel P2X4, which was found to yield both elevated Ca²⁺ transients and SR Ca²⁺ load [50].

An interesting finding from our simulations, is that both +Amylin and HIP rats presented amplified intracellular Ca²⁺ transients, despite the latter having predicted diastolic SR Ca²⁺ loads that were commensurate with the control (see Fig. S8). The notion that diastolic SR Ca²⁺ loads are comparable for HIP and control has precedent, as insignificant changes in SR load relative to control were reported in Despa et al. [6]. We demonstrate that the higher diastolic cytosolic Ca²⁺ exhibited in HIP amplifies RyR release, as measured by SR fractional release, prominently through elevated Ca²⁺ in the dyadic cleft, which would ultimately yield larger Ca²⁺ transients despite unchanged SR Ca²⁺ load.

Our model indicates that the increased Ca²⁺ transient amplitudes arise in part due to higher relative fractional release rates. Firstly, all conditions considered reported reduced fractional release at higher pacing in line with experimental findings from Antoons et al [51], for which they found 50% fractional release at 1 Hz, versus 40 percent at 2 Hz. Second, our model reflects that fractional Ca²⁺ release is increased for the +Amylin and HIP phenotypes relative to control, which we attribute to increased Ca²⁺ cleft Ca²⁺. These predictions bear resemblance to transgenic LCC overexpression models, for which higher amplitude i_CaL supports increased fractional release [55]. An important distinction here, however, is that the increase in fractional release for LCC overexpression is likely due to elevated cleft Ca²⁺ only during electrical stimulation, whereas for our +Amylin/HIP models elevated cleft Ca²⁺ persists during diastole. This behavior is also analogous to effects of CaMKII activation on promoting RyR SR Ca²⁺ leak, for which higher fractional release rates [56] with preserved SR Ca²⁺ loads are reported [57]. Progression toward transverse tubule (TT) remodeling may further exacerbate this effect [58] though such remodeling is not evident in +Amylin/HIP rats [6]. At a minimum, given the preponderance of data suggesting that CaMKII activity is enhanced in heart failure (HF), the effects of human amylin on increasing fractional release could synergize SR Ca²⁺ dysregulation.

4.4 Implications of elevated cytosolic Ca²⁺ load

An interesting consequence of elevated Ca²⁺ transients and in the case of HIP, increased diastolic Ca²⁺ load, is the potential for activating Ca²⁺-dependent pathways that are normally quiescent during normal Ca²⁺ handling. We observed in Fig. 5 for instance, that greater levels of Ca²⁺-bound CaM and TnC are evident relative to control. Under normal conditions, Ca²⁺ activation of TnC is the critical substrate for force development in contractile tissue [59], while CaM in part regulates normal force-frequency relationships and responses to β-adrenergic stimulation [60]. However, it is also implicated in the activation of pathways associated with remodeling and failure [13]. In particular, activation of the CaM-regulated CaMKII is attributed to cardiac remodeling via the histone deacetylase (HDAC) pathway. Concurrently, activation of the phosphatase calcineurin via CaM is known to promote transcriptional changes by way of NFAT activation [61], which together contribute to the hypertrophic response to dysregulated Ca²⁺ handling [62]. Indeed, in pre-diabetic HIP rats there was evidence that CaMKII-HDAC and calcineurin-NFAT remodeling were simultaneously activated [6]. In Sect. S.4, we present computational evidence based on the calmodulin/calcineurin/NFAT computational model from Cooling et al [63] that increased intracellular Ca²⁺ transients analogous to those predicted for HIP and +Amylin conditions, as well as increased diastolic Ca²⁺ load consistent with HIP, increase total nuclear NFAT concentration (see Fig. S19. In this regard, while the increased Ca²⁺ transients stemming from amylin oligomerization may initially have beneficial inotropic effects, activation of CaM and its dependent hypertrophic pathways may contribute to diastolic dysfunction. While this model has not been fitted to quantitatively reproduce changes in nuclear NFAT reported in [6], the predictions nevertheless qualitatively indicate +Amylin and HIP induced Ca²⁺ dysregulation can activate a transcriptional pathway associated with hypertrophy, consistent with experiment.

Additionally, the positive correlation between sarcolemmal Ca²⁺ leak and Na⁺ load we identified via our sensitivity analysis parallels findings from Louch et al indicating sodium accumulation upon SERCA knock-out [40, 64]. In mice, they found that seven week old SERCA KO mice presented elevated Na⁺ among other signs of cardiac failure, which in part was attributed to increased NCX Na⁺/Ca²⁺ exchange. Our model demonstrates that persistent increased SL Ca²⁺ leak alone may raise cytosolic Ca²⁺ and Na⁺ levels, in a manner that may activate the NFAT/HDAC remodeling pathways associated with cardiac dysfunction.

4.5 Limitations

Our model was based on a rather modest set of changes in Ca²⁺, Na⁺ and K⁺ handling to a rabbit ventricular cardiomyocyte formulation. Further refinement of rat electrophysiology [65, 66] and implementation of a recent rat Ca²⁺ handling model [25], could provide improved predictive power for our model of amylin-induced dysregulation. In the greater context of diabetes, it is likely that the Ca²⁺ dysregulation and subsequent activation of CaMKII sets forth a cascade of maladaptive events that drive heart failure. As such, our simulation results could be improved by including the impact of altered protein kinase A (PKA) and CaMKII activity on Ca²⁺ handling. Here, tuning the full Morotti model [29], which explicitly considers PKA and CaMKII signaling, to reflect excitation-contraction coupling in rats may be appropriate. Moreover, while the computational model used in this study assumes distinct intracellular compartments, such as the subsarcolemmal and cleft spaces, it is well-established that spatially heterogeneous factors, including transverse tubule organization and RyR subcellular distribution, profoundly influence EC coupling (reviewed in [67]). An intriguing hypothesis is that amylin may distribute non-uniformly in the cell sarcolemma and thereby disproportionately impact local Ca²⁺ homeostasis. Given the similar sizes of amylin and insulin, as well as the precedent for insulin signaling within skeletal TT networks [68, 69], in principle amylin could distribute within analogous invaginations in cardiac myocytes. There they might interfere with normal Ca²⁺ homeostasis in the critical dyadic compartments that dictate EC coupling. Describing these Ca²⁺ signaling against a backdrop of potential alterations in TT microstructure and redistribution of Ca²⁺ handling proteins could benefit from three-dimensional modeling.

5 Conclusions

Our predictions of elevated calcium transients under enhanced SL Ca²⁺ leak (via amylin oligomers) relative to control are in qualitative agreement with findings from Despa et al. [6]. Further, these simulations suggest a potential mechanism linking human amylin infiltration of cardiac sarcolemma, amplification of intracellular Ca²⁺ transients and potential activation of CaM-dependent remodeling pathways; namely, amylin-induced increases in SL Ca²⁺ leak potentially dually elevate Ca²⁺ load in the cytosol and sarcoplasmic reticulum. Increased sarcoplasmic reticulum Ca²⁺ content facilitates Ca²⁺ release, while elevated cytosolic Ca²⁺ levels enhance SR fractional Ca²⁺ release, as well as the activation of Ca²⁺-dependent proteins, including CaM. The latter effect may potentially contribute to the CaM-dependent activation of NFAT/HDAC pathways reported in [6]. Given that human amylin oligomers have been shown to deposit in cell types including cardiac, neuronal, microglia, and beta cells [2, 6, 9, 49], the effects of amylin-induced Ca²⁺ dysregulation may generalize to a variety of pathologies in higher animals.

Highlights.

• Rats expressing or subject to human amylin peptide, exhibit moderate Ca²⁺ dysregulation including larger cytosolic Ca²⁺ transients and activation of hypertrophic remodeling pathways.

• Our computational model of Ca²⁺ handling in rat cardiac ventricular myocytes implicate greater sarcoplasmic reticulum (SR) Ca²⁺ load and increased fractional Ca²⁺ release gives rise to amylin-induced Ca²⁺ dysregulation.

• Elevated cytosolic Ca²⁺ is accompanied by increased Ca²⁺ binding to calmodulin (CaM), a substrate for activation of the calcineurin/nuclear factor of activated T-cells (NFAT) remodeling pathway.

• Similar results were found for a rabbit model, suggesting human amylin may have analogous effects in higher order mammals.

Abbreviations

SL

sarcolemma

SR

saroplasmic reticulum

SERCA

sarcoplasmic/endoplasmic reticulum calcium ATPase

NCX

Na⁺/Ca²⁺ exchanger

EC

excitation-contraction

AP

action potential

LCC

L-type calcium channel

HIP

human amylin transgenic

NFAT

Nuclear factor of activated T-cells

HDAC

histone deacetylases

CaM

calmodulin

P188

poloxamer 188

NKA

Na⁺/K⁺ ATPase

L-type Ca²⁺ channel current (i_Ca)

L-type Ca²⁺ current

SBM

Shannon-Bers-Morroti

i_tof

fast component outward potassium current

i_Ks

slowly inactivating delayed rectifier current

i_ss

non-inactivating potassium steady-state current

i_K1

inward rectifier potassium current

GA

genetic algorithm

V

voltage

SDA

state decomposition analysis

ODE

ordinary differential equations

CaMKII

Ca²⁺/calmodulin-dependent protein kinase II

SB

Shannon-Bers

TnC

troponin C

TRPV4

transient receptor potential cation channel subfamily V member

βAR

β-adrenergic receptor