Characterization of amylin-induced calcium dysregulation in rat ventricular cardiomyocytes
Bradley D. Stewart, Caitlin E. Scott, Thomas P. McCoy, Guo Yin, Florin Despa, Sanda Despa, Peter M. Kekenes-Huskey
CCharacterization of amylin-induced calciumdysregulation in rat ventricular cardiomyocytes
Bradley D. Stewart Caitlin E. Scott Thomas P. McCoy Guo Yin Florin Despa Sanda Despa ∗ Peter M. Kekenes-Huskey ∗ Department of Chemistry, University of Kentucky, Lexington, KY,USA 40506 Department of Family & Community Nursing, University of NorthCarolina - Greensburo, Greensburo, NC, USA Department of Pharmacology and Nutritional Sciences, Universityof Kentucky, Lexington, KY, USA 40506April 12, 2017 a r X i v : . [ q - b i o . M N ] A p r bstract Hyperamylinemia, a condition characterized by above-normal blood levelsof the pancreas-derived peptide amylin, accompanies obesity and precedestype II diabetes. Human amylin oligomerizes easily and amylin oligomersdeposit in the pancreas (1), brain (2), and heart (3), where they have beenassociated with calcium dysregulation. In the heart, accumulating evidencesuggests that human amylin oligomers form modestly cation-selective (4, 5),voltage-dependent ion channels that embed in the cell sarcolemma (SL).The oligomers increase membrane conductance in a dose-dependent man-ner (5), which is correlated with elevated cytosolic Ca . These effectscan be reversed by pharmacologically disrupting amylin oligomerization (6).These findings motivated our core hypothesis that non-selective inward Ca conduction afforded by human amylin oligomers increase cytosolic and sar-coplasmic reticulum (SR) Ca load, which thereby magnifies intracellularCa transients. Questions remain however regarding the mechanism ofamylin-induced Ca dysregulation, including whether enhanced SL Ca influx is sufficient to elevate cytosolic Ca load (7), and if so, how mightamplified Ca transients perturb Ca -dependent cardiac pathways. Toinvestigate these questions, we modified a computational model of cardiomy-ocytes Ca signaling to reflect experimentally-measured changes in SLmembrane permeation and decreased Sarcoplasmic/endoplasmic reticulumcalcium ATPase (SERCA) function stemming from acute and transgenic hu-man amylin peptide exposure. With this model, we confirmed the hypothesisthat increasing SL permeation alone was sufficient to enhance Ca transientamplitudes without recruitment of prominent SL-bound Ca transporters,such as the L-type Ca . Our model indicated that amplified cytosolic tran-sients are driven by increased Ca loading of the sarcoplasmic reticulumand may contribute to the Ca -dependent activation of calmodulin. Thesefindings suggest that increased membrane permeation induced by depositionof amylin oligomers contributes to Ca dysregulation in pre-diabetes. mylinmylin
Bradley D. Stewart Caitlin E. Scott Thomas P. McCoy Guo Yin Florin Despa Sanda Despa ∗ Peter M. Kekenes-Huskey ∗ Department of Chemistry, University of Kentucky, Lexington, KY,USA 40506 Department of Family & Community Nursing, University of NorthCarolina - Greensburo, Greensburo, NC, USA Department of Pharmacology and Nutritional Sciences, Universityof Kentucky, Lexington, KY, USA 40506April 12, 2017 a r X i v : . [ q - b i o . M N ] A p r bstract Hyperamylinemia, a condition characterized by above-normal blood levelsof the pancreas-derived peptide amylin, accompanies obesity and precedestype II diabetes. Human amylin oligomerizes easily and amylin oligomersdeposit in the pancreas (1), brain (2), and heart (3), where they have beenassociated with calcium dysregulation. In the heart, accumulating evidencesuggests that human amylin oligomers form modestly cation-selective (4, 5),voltage-dependent ion channels that embed in the cell sarcolemma (SL).The oligomers increase membrane conductance in a dose-dependent man-ner (5), which is correlated with elevated cytosolic Ca . These effectscan be reversed by pharmacologically disrupting amylin oligomerization (6).These findings motivated our core hypothesis that non-selective inward Ca conduction afforded by human amylin oligomers increase cytosolic and sar-coplasmic reticulum (SR) Ca load, which thereby magnifies intracellularCa transients. Questions remain however regarding the mechanism ofamylin-induced Ca dysregulation, including whether enhanced SL Ca influx is sufficient to elevate cytosolic Ca load (7), and if so, how mightamplified Ca transients perturb Ca -dependent cardiac pathways. Toinvestigate these questions, we modified a computational model of cardiomy-ocytes Ca signaling to reflect experimentally-measured changes in SLmembrane permeation and decreased Sarcoplasmic/endoplasmic reticulumcalcium ATPase (SERCA) function stemming from acute and transgenic hu-man amylin peptide exposure. With this model, we confirmed the hypothesisthat increasing SL permeation alone was sufficient to enhance Ca transientamplitudes without recruitment of prominent SL-bound Ca transporters,such as the L-type Ca . Our model indicated that amplified cytosolic tran-sients are driven by increased Ca loading of the sarcoplasmic reticulumand may contribute to the Ca -dependent activation of calmodulin. Thesefindings suggest that increased membrane permeation induced by depositionof amylin oligomers contributes to Ca dysregulation in pre-diabetes. mylinmylin Introduction
Amylin, a 3.9 kilodalton peptide produced by the pancreatic β cells (8), issecreted along with insulin into the blood stream (9). Increased circula-tion of human amylin peptide preceding the onset of type II diabetes hasbeen correlated with amylin deposits in the heart (10). These deposits havebeen shown to induce diastolic dysfunction (7), hypertrophy, and dilation(6). While the amylin peptide in humans is amyloidogenic, that is, it poly-merizes into amyloid-like fibrils, rodents secret a non-amyloidogenic form ofamylin that does not accumulate in cells or tissue. However, rodents ex-pressing human amylin in the pancreatic β cells develop late onset type-2diabetes (1, 10). While studies correlating human amylin depositing withthe onset of pathological states typical of diabetic cardiomyopathy (11) arebeginning to emerge (3), molecular mechanisms linking amylin insult withcellular dysfunction remain poorly understood. Gaining momentum, how-ever, is the notion that amylin oligomerization in cardiac tissue may disruptnormal calcium homeostasis (7), stemming from its modestly cation-selectiveconductance properties. (4, 5, 12). While this conductance is small rela-tive to predominant sarcolemma (SL) Ca currents including the LCC andNa + /Ca exchanger (NCX), it nevertheless exhibits largely unexplained ef-fects on perturbing intracellular Ca signals and recruiting Ca -dependentpathways associated with pathological, hypertrophic remodeling (13).To motivate the interrelationship between amylin and potential Ca dysregulation in the heart, we first summarize key aspects of cardiac Ca signaling. In the healthy heart, the Ca -dependent excitation-contraction(EC) coupling cycle begins with a depolarizing action potential (AP) thatmodulates SL Ca fluxes, including the L-type calcium channel (LCC),Na + /Ca exchanger (NCX), and sarcolemmal Ca leak (14). Ca entryvia LCC and NCX triggers (15) sarcoplasmic reticulum (SR) Ca releasevia RyRs, leading to a rapid increase in intracellular Ca (Ca transient)that ultimately activates and regulates competent myocyte contraction (14).The cycle completes as SR Ca uptake via the Sarcoplasmic/endoplasmicreticulum calcium ATPase (SERCA), as well sarcolemmal Ca extrusionvia NCX and the sarcolemmal Ca ATPase, collectively restore diastolicCa levels. Recently, we reported that this process was perturbed in ratstransgenic for human amylin (human amylin transgenic (HIP)), as well asin isolated cardiomyocytes acutely exposed to the peptide (acute amylin-exposed rats (+Amylin)) (7). In particular, both rat models exhibited largercytosolic Ca transients and faster rates of sarcolemmal Ca leak thancontrol. Furthermore, we found that in HIP rats, SERCA function was mylinmylin
Amylin, a 3.9 kilodalton peptide produced by the pancreatic β cells (8), issecreted along with insulin into the blood stream (9). Increased circula-tion of human amylin peptide preceding the onset of type II diabetes hasbeen correlated with amylin deposits in the heart (10). These deposits havebeen shown to induce diastolic dysfunction (7), hypertrophy, and dilation(6). While the amylin peptide in humans is amyloidogenic, that is, it poly-merizes into amyloid-like fibrils, rodents secret a non-amyloidogenic form ofamylin that does not accumulate in cells or tissue. However, rodents ex-pressing human amylin in the pancreatic β cells develop late onset type-2diabetes (1, 10). While studies correlating human amylin depositing withthe onset of pathological states typical of diabetic cardiomyopathy (11) arebeginning to emerge (3), molecular mechanisms linking amylin insult withcellular dysfunction remain poorly understood. Gaining momentum, how-ever, is the notion that amylin oligomerization in cardiac tissue may disruptnormal calcium homeostasis (7), stemming from its modestly cation-selectiveconductance properties. (4, 5, 12). While this conductance is small rela-tive to predominant sarcolemma (SL) Ca currents including the LCC andNa + /Ca exchanger (NCX), it nevertheless exhibits largely unexplained ef-fects on perturbing intracellular Ca signals and recruiting Ca -dependentpathways associated with pathological, hypertrophic remodeling (13).To motivate the interrelationship between amylin and potential Ca dysregulation in the heart, we first summarize key aspects of cardiac Ca signaling. In the healthy heart, the Ca -dependent excitation-contraction(EC) coupling cycle begins with a depolarizing action potential (AP) thatmodulates SL Ca fluxes, including the L-type calcium channel (LCC),Na + /Ca exchanger (NCX), and sarcolemmal Ca leak (14). Ca entryvia LCC and NCX triggers (15) sarcoplasmic reticulum (SR) Ca releasevia RyRs, leading to a rapid increase in intracellular Ca (Ca transient)that ultimately activates and regulates competent myocyte contraction (14).The cycle completes as SR Ca uptake via the Sarcoplasmic/endoplasmicreticulum calcium ATPase (SERCA), as well sarcolemmal Ca extrusionvia NCX and the sarcolemmal Ca ATPase, collectively restore diastolicCa levels. Recently, we reported that this process was perturbed in ratstransgenic for human amylin (human amylin transgenic (HIP)), as well asin isolated cardiomyocytes acutely exposed to the peptide (acute amylin-exposed rats (+Amylin)) (7). In particular, both rat models exhibited largercytosolic Ca transients and faster rates of sarcolemmal Ca leak thancontrol. Furthermore, we found that in HIP rats, SERCA function was mylinmylin leak leads to Ca dysregulation in pre-diabetes and ultimately the activation of hypertrophic remodeling pathways.Cardiac computational models are particularly well-suited for explor-ing intracellular mechanisms of Ca signaling and their dysregulation incardiac tissue (16–19). We extended one such model, the Shannon-Bersmodel of ventricular myocyte Ca dynamics (20), to unravel the influenceof amylin in the HIP phenotype. Specifically, the revised model reflects ourexperimentally-measured changes in SL membrane Ca permeation as wellas decreased SERCA function consistent with acutely-exposed and trans-genic human amylin rats (7). We find that increased Ca background leakconductance via amylin was sufficient to reproduce enhanced Ca tran-sients previously measured in HIP rats (7). These simulations implicate in-creased SR loading as the primary mechanism of increasing Ca transientamplitude for the amylin phenotypes, which in turn elevates cytosolic Ca load. Finally, we show higher propensities for calmodulin (CaM) activationunder conditions of elevated diastolic Ca , which we speculate may trig-ger the CaM-dependent NFAT remodeling pathway. These findings lead toour hypothesized model of amylin-induced Ca dysregulation summarizedin Fig. 1. Materials and Methods
Experimental animals
N=12 Sprague-Dawley rats were used in this study. All animal experimentswere performed conform to the NIH guide for the care and use of laboratoryanimals and were approved by the Institutional Animal Care and Use Com-mittee at University of Kentucky. Ventricular myocytes were isolated byperfusion with collagenase on a gravity-driven Langendorff apparatus (7).
Measurements of Ca transients and sarcolemmal Na + /Ca leak Myocytes were plated on laminin-coated coverslips, mounted on the stageof a fluorescence microscope and loaded with Fluo4-AM (10 µ mol/L, for 25min). Ca transients were elicited by stimulation with external electrodes at mylinmylin
Measurements of Ca transients and sarcolemmal Na + /Ca leak Myocytes were plated on laminin-coated coverslips, mounted on the stageof a fluorescence microscope and loaded with Fluo4-AM (10 µ mol/L, for 25min). Ca transients were elicited by stimulation with external electrodes at mylinmylin in acuteamylin-exposed rats (+Amylin) increases sarcoplasmic reticulum Ca load-ing, amplifies intracellular Ca transients and increases the Ca -boundstate of proteins including calmodulin (CaM) (PDB codes 1DBM and3CLN).a frequency of 1 Hz. The passive trans-sarcolemmal Ca leak was measuredas the initial rate of Ca decline upon reducing external Ca from 1 to 0mM. In these experiments, Ca fluxes to and from the SR were blockedby pre-treating the cells with 10 µ M thapsigargin for 10 min whereas theNCX and sarcolemmal Ca - ATPase were abolished by using 0 Na + /0Ca solution (Na + replaced with Li + ) and adding 20 µ M carboxyeosin,respectively. The outward sarcolemmal Ca leak was measured in theabsence and presence of the membrane sealant poloxamer 188, which isa surfactant that stabilizes lipid bilayers and thus protects against amylin-induced sarcolemmal damage.Na + influx was measured as the initial rate of the increase in intracellularNa + concentration ([Na + ] i ) immediately following Na + /K + atpase (NKA)pump inhibition with 10 mM ouabain. As described previously (21), [Na + ] i was measured using the fluorescent indicator SBFI (TefLabs). The SBFIratio was calibrated at the end of each experiment using divalent-free solu-tions with 0, 10, or 20 mmol/L of extracellular Na + in the presence of 10 µ mol/L gramicidin and 100 µ mol/L strophanthidin. mylinmylin
Measurements of Ca transients and sarcolemmal Na + /Ca leak Myocytes were plated on laminin-coated coverslips, mounted on the stageof a fluorescence microscope and loaded with Fluo4-AM (10 µ mol/L, for 25min). Ca transients were elicited by stimulation with external electrodes at mylinmylin in acuteamylin-exposed rats (+Amylin) increases sarcoplasmic reticulum Ca load-ing, amplifies intracellular Ca transients and increases the Ca -boundstate of proteins including calmodulin (CaM) (PDB codes 1DBM and3CLN).a frequency of 1 Hz. The passive trans-sarcolemmal Ca leak was measuredas the initial rate of Ca decline upon reducing external Ca from 1 to 0mM. In these experiments, Ca fluxes to and from the SR were blockedby pre-treating the cells with 10 µ M thapsigargin for 10 min whereas theNCX and sarcolemmal Ca - ATPase were abolished by using 0 Na + /0Ca solution (Na + replaced with Li + ) and adding 20 µ M carboxyeosin,respectively. The outward sarcolemmal Ca leak was measured in theabsence and presence of the membrane sealant poloxamer 188, which isa surfactant that stabilizes lipid bilayers and thus protects against amylin-induced sarcolemmal damage.Na + influx was measured as the initial rate of the increase in intracellularNa + concentration ([Na + ] i ) immediately following Na + /K + atpase (NKA)pump inhibition with 10 mM ouabain. As described previously (21), [Na + ] i was measured using the fluorescent indicator SBFI (TefLabs). The SBFIratio was calibrated at the end of each experiment using divalent-free solu-tions with 0, 10, or 20 mmol/L of extracellular Na + in the presence of 10 µ mol/L gramicidin and 100 µ mol/L strophanthidin. mylinmylin L-type Ca current measurement L-type Ca current ( i Ca) was measured under voltage-clamp in whole cellconfiguration. i Ca was determined as the nifedipine-sensitive current recordedduring depolarization steps from -40 mV (where the cell was held for 50 msto inactivate Na + channels), to -35 to +60 mV. The patch-pipette was filledwith a solution containing (in mM) 125 Cs-methanesulfonate, 16.5 TEA-Cl,1 MgCl , 10 EGTA, 3.9 CaCl , 5 Hepes, and 5 Mg-ATP (pH=7.2). The ex-ternal solution contained (in mM) 150 NMDG, 1 CaCl , 5 4-aminopyridine,1 MgCl , 10 Hepes, and 10 glucose (pH=7.4). Simulation and analysis protocols
Summary of Shannon-Bers-Morotti rat Ca handling model To examine the relationship between increased sarcolemmal Ca entry andelevated Ca transients reported in rats (7), we adapted a rabbit ven-tricular myocyte model of Ca signaling to reflect handling terms specificto mice and rats. Our choice of a mouse model was based on the initiallack of rat-specific Ca handling models available in the literature andthe similar rates of Ca relaxation via SERCA, NCX, and other minorcontributions (sarcolemmal) shared by rat and mice (92, 8 and 1%, versus90.3, 9.2 and 0.5%, respectively) shared by both species (22, 23). Mouse-specific parameter and potassium current changes were introduced into theShannon-Bers rabbit cardiomyocyte Ca model (20) according to Morotti et al. . (24) (summarized in Supplement). The resulting model is hereafterreferred to as the Shannon-Bers-Morroti (SBM) model. Model equations,’state’ names, current names and initial conditions are provided in the sup-plement. As noted in (24), four predominant changes in potassium channelswere included: 1) the transient outward potassium current expression forrabbits was replaced with fast component ( i tof) for mice, 2) the slowing ac-tivating delayed rectifier current was substituted with a slowly inactivatingdelayed rectifier current ( i Ks), 3) a non-inactivating potassium steady-statecurrent ( i ss) was added 4) the inward rectifier potassium current ( i K1) wasreduced. Other distinctions between the two species are the elevated intra-cellular sodium load and sodium ion current in murine versus rabbit species,which we optimized to match experimental data collected in this study. InFig. S1-Fig. S3, we compare metrics such as Ca transients, action po-tentials, potassium currents and prominent Na + /Ca currents for rabbitsversus mice, for which we report excellent agreement with data from Morotti et al. . (24). mylinmylin
Summary of Shannon-Bers-Morotti rat Ca handling model To examine the relationship between increased sarcolemmal Ca entry andelevated Ca transients reported in rats (7), we adapted a rabbit ven-tricular myocyte model of Ca signaling to reflect handling terms specificto mice and rats. Our choice of a mouse model was based on the initiallack of rat-specific Ca handling models available in the literature andthe similar rates of Ca relaxation via SERCA, NCX, and other minorcontributions (sarcolemmal) shared by rat and mice (92, 8 and 1%, versus90.3, 9.2 and 0.5%, respectively) shared by both species (22, 23). Mouse-specific parameter and potassium current changes were introduced into theShannon-Bers rabbit cardiomyocyte Ca model (20) according to Morotti et al. . (24) (summarized in Supplement). The resulting model is hereafterreferred to as the Shannon-Bers-Morroti (SBM) model. Model equations,’state’ names, current names and initial conditions are provided in the sup-plement. As noted in (24), four predominant changes in potassium channelswere included: 1) the transient outward potassium current expression forrabbits was replaced with fast component ( i tof) for mice, 2) the slowing ac-tivating delayed rectifier current was substituted with a slowly inactivatingdelayed rectifier current ( i Ks), 3) a non-inactivating potassium steady-statecurrent ( i ss) was added 4) the inward rectifier potassium current ( i K1) wasreduced. Other distinctions between the two species are the elevated intra-cellular sodium load and sodium ion current in murine versus rabbit species,which we optimized to match experimental data collected in this study. InFig. S1-Fig. S3, we compare metrics such as Ca transients, action po-tentials, potassium currents and prominent Na + /Ca currents for rabbitsversus mice, for which we report excellent agreement with data from Morotti et al. . (24). mylinmylin I iBK = F x iBk G iBk ( V − E i ) (1)where F x represents leak density, G c is the max conductance for Ca i , V is voltage and E i is the Nernst potential of ion i . In rats acutely exposed toamylin (+Amylin), amylin oligomer deposition was correlated with a roughly70% increased rate of Ca leak in hypotonic solution (see Figure 3D ofDespa et al. (7)). We accordingly increased G c for Ca by a commensurateamount (see Table S3) to reflect this observation. Although amylin poresexhibit poor cation selectivity (5), we maintained G c for Na + at baselinevalues, given that we observed no detectable change in Na + load (Fig. 2).Furthermore, though we assume that the increased Ca influx scaled withapplied voltage ( V ), given the short duration of the action potential thisapproximation did not significantly affect the model. The magnitude ofenhanced SL Ca leak, I Cab , is depicted in Fig. S4. Lastly, we fit ourmodel outputs Na + transients and τ values to mimic the rat using a geneticalgorithm (GA) (detailed in the Supplement) that varied the parameters ofthe NKA current and the SERCA Vmax values respectively. This fittingwas necessary to capture Ca and Na + transients reported in the HIP,+Amylin and an ’activated LCC’ condition that mimics enhanced SL Ca leak. We compare our predicted normalized Ca transients to control datain Fig. ?? and report excellent agreement. For our +Amylin configuration,the GA increased NKA Vmax by 14% to maintain normal Na + levels (seeTable S3), which concurs with a study indicating agonized NKA functionin skeletal muscle (25). For the human amylin transgenic model (HIP),it was observed that Ca transient decay time increased by nearly 30%relative to control (7)), for which the GA determined a reduction in SERCAVmax by 47% was necessary. Lastly, we introduced an ’LCC’ configurationfor which Ca permeation is increased, to elucidate potential differencesbetween Ca -entry via non-selective leak as opposed to via Ca -selectivechannels (see Table S3). Numerical model of Ca handling The Shannon-Bers cellML model was converted into a Python module viathe Generalized ODE Translator gotran (https://bitbucket.org/johanhake/gotran).The mouse-specific alterations summarized in the previous section were im-plemented into the resulting module. In our numerical experiments, theSBM model was numerically integrated by the scipy function odeint , which mylinmylin
Summary of Shannon-Bers-Morotti rat Ca handling model To examine the relationship between increased sarcolemmal Ca entry andelevated Ca transients reported in rats (7), we adapted a rabbit ven-tricular myocyte model of Ca signaling to reflect handling terms specificto mice and rats. Our choice of a mouse model was based on the initiallack of rat-specific Ca handling models available in the literature andthe similar rates of Ca relaxation via SERCA, NCX, and other minorcontributions (sarcolemmal) shared by rat and mice (92, 8 and 1%, versus90.3, 9.2 and 0.5%, respectively) shared by both species (22, 23). Mouse-specific parameter and potassium current changes were introduced into theShannon-Bers rabbit cardiomyocyte Ca model (20) according to Morotti et al. . (24) (summarized in Supplement). The resulting model is hereafterreferred to as the Shannon-Bers-Morroti (SBM) model. Model equations,’state’ names, current names and initial conditions are provided in the sup-plement. As noted in (24), four predominant changes in potassium channelswere included: 1) the transient outward potassium current expression forrabbits was replaced with fast component ( i tof) for mice, 2) the slowing ac-tivating delayed rectifier current was substituted with a slowly inactivatingdelayed rectifier current ( i Ks), 3) a non-inactivating potassium steady-statecurrent ( i ss) was added 4) the inward rectifier potassium current ( i K1) wasreduced. Other distinctions between the two species are the elevated intra-cellular sodium load and sodium ion current in murine versus rabbit species,which we optimized to match experimental data collected in this study. InFig. S1-Fig. S3, we compare metrics such as Ca transients, action po-tentials, potassium currents and prominent Na + /Ca currents for rabbitsversus mice, for which we report excellent agreement with data from Morotti et al. . (24). mylinmylin I iBK = F x iBk G iBk ( V − E i ) (1)where F x represents leak density, G c is the max conductance for Ca i , V is voltage and E i is the Nernst potential of ion i . In rats acutely exposed toamylin (+Amylin), amylin oligomer deposition was correlated with a roughly70% increased rate of Ca leak in hypotonic solution (see Figure 3D ofDespa et al. (7)). We accordingly increased G c for Ca by a commensurateamount (see Table S3) to reflect this observation. Although amylin poresexhibit poor cation selectivity (5), we maintained G c for Na + at baselinevalues, given that we observed no detectable change in Na + load (Fig. 2).Furthermore, though we assume that the increased Ca influx scaled withapplied voltage ( V ), given the short duration of the action potential thisapproximation did not significantly affect the model. The magnitude ofenhanced SL Ca leak, I Cab , is depicted in Fig. S4. Lastly, we fit ourmodel outputs Na + transients and τ values to mimic the rat using a geneticalgorithm (GA) (detailed in the Supplement) that varied the parameters ofthe NKA current and the SERCA Vmax values respectively. This fittingwas necessary to capture Ca and Na + transients reported in the HIP,+Amylin and an ’activated LCC’ condition that mimics enhanced SL Ca leak. We compare our predicted normalized Ca transients to control datain Fig. ?? and report excellent agreement. For our +Amylin configuration,the GA increased NKA Vmax by 14% to maintain normal Na + levels (seeTable S3), which concurs with a study indicating agonized NKA functionin skeletal muscle (25). For the human amylin transgenic model (HIP),it was observed that Ca transient decay time increased by nearly 30%relative to control (7)), for which the GA determined a reduction in SERCAVmax by 47% was necessary. Lastly, we introduced an ’LCC’ configurationfor which Ca permeation is increased, to elucidate potential differencesbetween Ca -entry via non-selective leak as opposed to via Ca -selectivechannels (see Table S3). Numerical model of Ca handling The Shannon-Bers cellML model was converted into a Python module viathe Generalized ODE Translator gotran (https://bitbucket.org/johanhake/gotran).The mouse-specific alterations summarized in the previous section were im-plemented into the resulting module. In our numerical experiments, theSBM model was numerically integrated by the scipy function odeint , which mylinmylin load or the action potential, as well as ’currents’ that include majorCa , Na + , K + , and Cl − -conducting proteins. Model fitting proceeded bya genetic algorithm (reviewed in (27)) that iteratively improved parametervalues, such as LCC Ca conductance, membrane leak, and NKA con-ductance over several generations of ’progeny’ (Fig. S18). Experimentally-measured outputs, such as Ca transient decay time and amplitude, weremeasured for each of the progeny; those that reduced output error relativeto the experimentally-measured equivalent with stored for future genera-tions (see Sect. ) for more details). To validate our implementation, wepresent comparisons of action potentials, intracellular Ca and Na + tran-sients, as well as ionic currents for rabbit versus murine cardiac ventricularmyocytes in Sect. , and we report good agreement. Steady-state action po-tentials and intracellular Ca oscillations were generally observed within6000 ms. We additionally stimulated the model at several frequencies rang-ing from 0.25 to 2.0 Hz, with the reference frequency at 1.0 Hz, subject todefault (control) parameters as case-specific values listed in Methods. Sensi-tivity of Ca transients to sarcolemmal leak rates and Vmax for NKA andSERCA were probed as described in Sect. . All data processing was per-formed using scipy and the ipython notebook; source code will be provided mylinmylin
Summary of Shannon-Bers-Morotti rat Ca handling model To examine the relationship between increased sarcolemmal Ca entry andelevated Ca transients reported in rats (7), we adapted a rabbit ven-tricular myocyte model of Ca signaling to reflect handling terms specificto mice and rats. Our choice of a mouse model was based on the initiallack of rat-specific Ca handling models available in the literature andthe similar rates of Ca relaxation via SERCA, NCX, and other minorcontributions (sarcolemmal) shared by rat and mice (92, 8 and 1%, versus90.3, 9.2 and 0.5%, respectively) shared by both species (22, 23). Mouse-specific parameter and potassium current changes were introduced into theShannon-Bers rabbit cardiomyocyte Ca model (20) according to Morotti et al. . (24) (summarized in Supplement). The resulting model is hereafterreferred to as the Shannon-Bers-Morroti (SBM) model. Model equations,’state’ names, current names and initial conditions are provided in the sup-plement. As noted in (24), four predominant changes in potassium channelswere included: 1) the transient outward potassium current expression forrabbits was replaced with fast component ( i tof) for mice, 2) the slowing ac-tivating delayed rectifier current was substituted with a slowly inactivatingdelayed rectifier current ( i Ks), 3) a non-inactivating potassium steady-statecurrent ( i ss) was added 4) the inward rectifier potassium current ( i K1) wasreduced. Other distinctions between the two species are the elevated intra-cellular sodium load and sodium ion current in murine versus rabbit species,which we optimized to match experimental data collected in this study. InFig. S1-Fig. S3, we compare metrics such as Ca transients, action po-tentials, potassium currents and prominent Na + /Ca currents for rabbitsversus mice, for which we report excellent agreement with data from Morotti et al. . (24). mylinmylin I iBK = F x iBk G iBk ( V − E i ) (1)where F x represents leak density, G c is the max conductance for Ca i , V is voltage and E i is the Nernst potential of ion i . In rats acutely exposed toamylin (+Amylin), amylin oligomer deposition was correlated with a roughly70% increased rate of Ca leak in hypotonic solution (see Figure 3D ofDespa et al. (7)). We accordingly increased G c for Ca by a commensurateamount (see Table S3) to reflect this observation. Although amylin poresexhibit poor cation selectivity (5), we maintained G c for Na + at baselinevalues, given that we observed no detectable change in Na + load (Fig. 2).Furthermore, though we assume that the increased Ca influx scaled withapplied voltage ( V ), given the short duration of the action potential thisapproximation did not significantly affect the model. The magnitude ofenhanced SL Ca leak, I Cab , is depicted in Fig. S4. Lastly, we fit ourmodel outputs Na + transients and τ values to mimic the rat using a geneticalgorithm (GA) (detailed in the Supplement) that varied the parameters ofthe NKA current and the SERCA Vmax values respectively. This fittingwas necessary to capture Ca and Na + transients reported in the HIP,+Amylin and an ’activated LCC’ condition that mimics enhanced SL Ca leak. We compare our predicted normalized Ca transients to control datain Fig. ?? and report excellent agreement. For our +Amylin configuration,the GA increased NKA Vmax by 14% to maintain normal Na + levels (seeTable S3), which concurs with a study indicating agonized NKA functionin skeletal muscle (25). For the human amylin transgenic model (HIP),it was observed that Ca transient decay time increased by nearly 30%relative to control (7)), for which the GA determined a reduction in SERCAVmax by 47% was necessary. Lastly, we introduced an ’LCC’ configurationfor which Ca permeation is increased, to elucidate potential differencesbetween Ca -entry via non-selective leak as opposed to via Ca -selectivechannels (see Table S3). Numerical model of Ca handling The Shannon-Bers cellML model was converted into a Python module viathe Generalized ODE Translator gotran (https://bitbucket.org/johanhake/gotran).The mouse-specific alterations summarized in the previous section were im-plemented into the resulting module. In our numerical experiments, theSBM model was numerically integrated by the scipy function odeint , which mylinmylin load or the action potential, as well as ’currents’ that include majorCa , Na + , K + , and Cl − -conducting proteins. Model fitting proceeded bya genetic algorithm (reviewed in (27)) that iteratively improved parametervalues, such as LCC Ca conductance, membrane leak, and NKA con-ductance over several generations of ’progeny’ (Fig. S18). Experimentally-measured outputs, such as Ca transient decay time and amplitude, weremeasured for each of the progeny; those that reduced output error relativeto the experimentally-measured equivalent with stored for future genera-tions (see Sect. ) for more details). To validate our implementation, wepresent comparisons of action potentials, intracellular Ca and Na + tran-sients, as well as ionic currents for rabbit versus murine cardiac ventricularmyocytes in Sect. , and we report good agreement. Steady-state action po-tentials and intracellular Ca oscillations were generally observed within6000 ms. We additionally stimulated the model at several frequencies rang-ing from 0.25 to 2.0 Hz, with the reference frequency at 1.0 Hz, subject todefault (control) parameters as case-specific values listed in Methods. Sensi-tivity of Ca transients to sarcolemmal leak rates and Vmax for NKA andSERCA were probed as described in Sect. . All data processing was per-formed using scipy and the ipython notebook; source code will be provided mylinmylin https://bitbucket.org/huskeypm/wholecell . Analyses
To examine potential mechanisms that link increased SL Ca permeationto SR-loading and elevated Ca transients, we present a simple method,State Decomposition Analysis (SDA), that monitors and identifies promi-nent changes in key ’state’ variables (including the action potential, SR-load, channel gate probabilities among others) as well as ion channel cur-rents, relative to control conditions. The key benefit of this approach is theautomated identification of modulated EC coupling components that canmotivate model refinements and additional experiments. The SDA methodconsists of the following steps: 1) numerically solve the time-dependent or-dinary differential equations (ODE)s governing all components (the statevariables) of the EC coupling model for trial and control parameter config-urations 2) ’score’ the time-dependent state values according to metrics likeamplitude 3) calculate percent differences between trial and control statevariable scores 4) rank order states by either the percent difference with areference state or by the amplitudes in the reference. mylinmylin
To examine potential mechanisms that link increased SL Ca permeationto SR-loading and elevated Ca transients, we present a simple method,State Decomposition Analysis (SDA), that monitors and identifies promi-nent changes in key ’state’ variables (including the action potential, SR-load, channel gate probabilities among others) as well as ion channel cur-rents, relative to control conditions. The key benefit of this approach is theautomated identification of modulated EC coupling components that canmotivate model refinements and additional experiments. The SDA methodconsists of the following steps: 1) numerically solve the time-dependent or-dinary differential equations (ODE)s governing all components (the statevariables) of the EC coupling model for trial and control parameter config-urations 2) ’score’ the time-dependent state values according to metrics likeamplitude 3) calculate percent differences between trial and control statevariable scores 4) rank order states by either the percent difference with areference state or by the amplitudes in the reference. mylinmylin Results
Effects of human amylin on intracellular Ca transients inrat cardiac ventricular myocytes The accumulation of human amylin aggregates in rat cardiomyocyte SL waspreviously correlated with increased rates of sarcolemmal Ca conductionand amplified Ca transient amplitudes (7). Increased Ca sarcolemmalconduction was originally attributed to permeation across the bilayer, asopposed to direct modulation of ion channels, based on observations of anamylin dose-dependent outward Ca leak (7). This led to the hypothesisthat sarcolemma-localized human amylin oligomers have the primary effectof increasing the inward Ca leak, although the mechanism linking Ca leak and transient amplitudes was not established. We first validate thishypothesis by measuring the effect of human amylin (50 µ M; 2 hours incu-bation) on SL Ca leak and Ca transient amplitude in the absence andin the presence of poloxamer 188 (P188), a surfactant that stabilizes lipidbilayers through hydrophobic interactions (28). As reported previously, hu-man amylin significantly increased both passive SL Ca leak and Ca transient amplitude (Fig. 3A). When amylin was applied in the presence ofP188 (50 µ M), however, SL Ca leak and transient amplitudes were statis-tically comparable to control (Fig. 3). Similar behavior was observed uponco-incubation with epoxyeicosatrienoic acids (14,15-EETs; 5 µ M), whichhave anti-aggregation effects and reduce amylin deposition at the SL (6).These results support the hypothesis that amylin primarily influences my-ocyte Ca cycling through poration of the sarcolemma.To investigate how membrane poration via human amylin leads to ampli-fied Ca transients, we numerically solved the SBM whole-cell model at 1Hz pacing under control conditions and with enhanced SL leak (+Amylin).Our simulations confirmed that Ca transients for the +Amylin config-uration were 46% higher than control (Fig. 4), consistent with experiment(Fig. 3b and Fig, 3C of (7)). We further modeled the pre-diabetic (HIP) ratsexamined in (7) by assuming increased SL leak and decreased SERCA func-tion. Similar to +Amylin the HIP model predicted elevated Ca transientamplitudes (36% relative to control), although they were somewhat atten-uated compared to the +Amylin conditions. In contrast to the +Amylinconfiguration, however, the HIP model presented 27% slower diastolic re-laxation and a 92 % increase in diastolic intracellular Ca load rela-tive to control, as would be expected with reduced SERCA function (29).We further note that the enhancement of Ca transient amplitudes for mylinmylin
Effects of human amylin on intracellular Ca transients inrat cardiac ventricular myocytes The accumulation of human amylin aggregates in rat cardiomyocyte SL waspreviously correlated with increased rates of sarcolemmal Ca conductionand amplified Ca transient amplitudes (7). Increased Ca sarcolemmalconduction was originally attributed to permeation across the bilayer, asopposed to direct modulation of ion channels, based on observations of anamylin dose-dependent outward Ca leak (7). This led to the hypothesisthat sarcolemma-localized human amylin oligomers have the primary effectof increasing the inward Ca leak, although the mechanism linking Ca leak and transient amplitudes was not established. We first validate thishypothesis by measuring the effect of human amylin (50 µ M; 2 hours incu-bation) on SL Ca leak and Ca transient amplitude in the absence andin the presence of poloxamer 188 (P188), a surfactant that stabilizes lipidbilayers through hydrophobic interactions (28). As reported previously, hu-man amylin significantly increased both passive SL Ca leak and Ca transient amplitude (Fig. 3A). When amylin was applied in the presence ofP188 (50 µ M), however, SL Ca leak and transient amplitudes were statis-tically comparable to control (Fig. 3). Similar behavior was observed uponco-incubation with epoxyeicosatrienoic acids (14,15-EETs; 5 µ M), whichhave anti-aggregation effects and reduce amylin deposition at the SL (6).These results support the hypothesis that amylin primarily influences my-ocyte Ca cycling through poration of the sarcolemma.To investigate how membrane poration via human amylin leads to ampli-fied Ca transients, we numerically solved the SBM whole-cell model at 1Hz pacing under control conditions and with enhanced SL leak (+Amylin).Our simulations confirmed that Ca transients for the +Amylin config-uration were 46% higher than control (Fig. 4), consistent with experiment(Fig. 3b and Fig, 3C of (7)). We further modeled the pre-diabetic (HIP) ratsexamined in (7) by assuming increased SL leak and decreased SERCA func-tion. Similar to +Amylin the HIP model predicted elevated Ca transientamplitudes (36% relative to control), although they were somewhat atten-uated compared to the +Amylin conditions. In contrast to the +Amylinconfiguration, however, the HIP model presented 27% slower diastolic re-laxation and a 92 % increase in diastolic intracellular Ca load rela-tive to control, as would be expected with reduced SERCA function (29).We further note that the enhancement of Ca transient amplitudes for mylinmylin leak and intracellular Ca transient am-plitude. a) Outward sarcolemmal Ca leaks are reported for control andamylin-incubated rats. Significantly higher leak rates were found for amylin-incubated rats relative to control. Introduction of membrane sealants EETand P188 maintained Ca leak rates at levels comparable to control con-ditions. b) Ca transients under analogous conditions are elevated foramylin-incubated rats, while control and sealant-exposed myocytes exhibitequivalent amplitudes+Amylin/HIP rats relative to control diminished with increased pacing (upto 2 Hz), in accordance with experimental findings (see Fig. S6). Ca tran-sient relaxation rates remained unchanged over this range, as our model doesnot currently include factors governing frequency dependent acceleration ofrelaxation, such as the involvement of Ca2+/calmodulin-dependent proteinkinase II (CaMKII)(30).A distinctive feature of murine species is the dominant role of the SRin managing Ca homeostasis, with nearly 90% of the intracellular Ca transient originating from SR (14). In contrast, in higher species, sarcolem-mal derived Ca plays a significantly larger role; in rabbits, for instance,inward sarcolemmal Ca currents account for roughly 40% of the intracel-lular Ca transient (14). As a proof of principle, we augmented the originalShannon-Bers (SB) formulation of cardiac Ca cycling in rabbits (20) withincreased Ca leak. In Fig. S11 , we demonstrate similar trends of increasedcytosolic and SR Ca load under conditions of increased sarcolemmal Ca leak. ). mylinmylin
Effects of human amylin on intracellular Ca transients inrat cardiac ventricular myocytes The accumulation of human amylin aggregates in rat cardiomyocyte SL waspreviously correlated with increased rates of sarcolemmal Ca conductionand amplified Ca transient amplitudes (7). Increased Ca sarcolemmalconduction was originally attributed to permeation across the bilayer, asopposed to direct modulation of ion channels, based on observations of anamylin dose-dependent outward Ca leak (7). This led to the hypothesisthat sarcolemma-localized human amylin oligomers have the primary effectof increasing the inward Ca leak, although the mechanism linking Ca leak and transient amplitudes was not established. We first validate thishypothesis by measuring the effect of human amylin (50 µ M; 2 hours incu-bation) on SL Ca leak and Ca transient amplitude in the absence andin the presence of poloxamer 188 (P188), a surfactant that stabilizes lipidbilayers through hydrophobic interactions (28). As reported previously, hu-man amylin significantly increased both passive SL Ca leak and Ca transient amplitude (Fig. 3A). When amylin was applied in the presence ofP188 (50 µ M), however, SL Ca leak and transient amplitudes were statis-tically comparable to control (Fig. 3). Similar behavior was observed uponco-incubation with epoxyeicosatrienoic acids (14,15-EETs; 5 µ M), whichhave anti-aggregation effects and reduce amylin deposition at the SL (6).These results support the hypothesis that amylin primarily influences my-ocyte Ca cycling through poration of the sarcolemma.To investigate how membrane poration via human amylin leads to ampli-fied Ca transients, we numerically solved the SBM whole-cell model at 1Hz pacing under control conditions and with enhanced SL leak (+Amylin).Our simulations confirmed that Ca transients for the +Amylin config-uration were 46% higher than control (Fig. 4), consistent with experiment(Fig. 3b and Fig, 3C of (7)). We further modeled the pre-diabetic (HIP) ratsexamined in (7) by assuming increased SL leak and decreased SERCA func-tion. Similar to +Amylin the HIP model predicted elevated Ca transientamplitudes (36% relative to control), although they were somewhat atten-uated compared to the +Amylin conditions. In contrast to the +Amylinconfiguration, however, the HIP model presented 27% slower diastolic re-laxation and a 92 % increase in diastolic intracellular Ca load rela-tive to control, as would be expected with reduced SERCA function (29).We further note that the enhancement of Ca transient amplitudes for mylinmylin leak and intracellular Ca transient am-plitude. a) Outward sarcolemmal Ca leaks are reported for control andamylin-incubated rats. Significantly higher leak rates were found for amylin-incubated rats relative to control. Introduction of membrane sealants EETand P188 maintained Ca leak rates at levels comparable to control con-ditions. b) Ca transients under analogous conditions are elevated foramylin-incubated rats, while control and sealant-exposed myocytes exhibitequivalent amplitudes+Amylin/HIP rats relative to control diminished with increased pacing (upto 2 Hz), in accordance with experimental findings (see Fig. S6). Ca tran-sient relaxation rates remained unchanged over this range, as our model doesnot currently include factors governing frequency dependent acceleration ofrelaxation, such as the involvement of Ca2+/calmodulin-dependent proteinkinase II (CaMKII)(30).A distinctive feature of murine species is the dominant role of the SRin managing Ca homeostasis, with nearly 90% of the intracellular Ca transient originating from SR (14). In contrast, in higher species, sarcolem-mal derived Ca plays a significantly larger role; in rabbits, for instance,inward sarcolemmal Ca currents account for roughly 40% of the intracel-lular Ca transient (14). As a proof of principle, we augmented the originalShannon-Bers (SB) formulation of cardiac Ca cycling in rabbits (20) withincreased Ca leak. In Fig. S11 , we demonstrate similar trends of increasedcytosolic and SR Ca load under conditions of increased sarcolemmal Ca leak. ). mylinmylin transients (concentration versus time) pre-dicted using the Shannon-Bers-Morroti (SBM) Ca cycling model following300s of 1.0 Hz pacing. Transients are reported for model conditions repre-senting control (black), acute amylin-exposed rats (+Amylin) (blue), humanamylin transgenic (HIP) (red) and L-type calcium channel (LCC) (green).Comparisons between simulation and experiment from 0.5 through 2 Hzpacing are shown in Fig. S6 Effects of acute amylin-induced modulation of sarcolemmalion handling
Cytosolic and sarcoplasmic reticulum Ca load While background sarcolemmal Ca leak is evidently enhanced for +Amylinand HIP, the corresponding Ca current over a single beat does not con-tribute significantly to the total cytosol Ca content. Hence, the leakalone is insufficient to directly account for the observed increase in Ca amplitude for the amylin models on a beat-to-beat basis. Rather, our dataindicate that the Ca transients required nearly 20 seconds of pacing toreach steady state (Fig. 4), which suggests that Ca transient amplifica- mylinmylin
Cytosolic and sarcoplasmic reticulum Ca load While background sarcolemmal Ca leak is evidently enhanced for +Amylinand HIP, the corresponding Ca current over a single beat does not con-tribute significantly to the total cytosol Ca content. Hence, the leakalone is insufficient to directly account for the observed increase in Ca amplitude for the amylin models on a beat-to-beat basis. Rather, our dataindicate that the Ca transients required nearly 20 seconds of pacing toreach steady state (Fig. 4), which suggests that Ca transient amplifica- mylinmylin released on a beat-to-beat basis originates in the SR (14), we hy-pothesized that the increased intracellular Ca transient amplitudes forthe amylin rats stemmed from elevated SR Ca loading owing to increasedsarcolemmal Ca leak. For this scenario, we would expect that Ca tran-sient amplitudes should scale proportionally with SL leak rates. Therefore,we examined how the control model responded to variations SL Ca leak(Amylin Leak %), as well in SERCA function. These effects are summa-rized in Fig. 5a-c, for which we report predicted cytosolic Ca transients(a., ∆ Cai ), SR Ca transients (b., ∆ Ca SR ) and diastolic SR Ca loads(c., max Ca SR ). These data strongly indicate that the SR Ca load is pos-itively correlated with increasing sarcolemmal Ca leak and to a lesser ex-tent, SERCA function. More importantly, the increased sarcolemmal Ca leak assumed for +Amylin and HIP relative to control largely accounted forthe elevated Ca transients and SR load.In other words, SERCA appeared to play a minor role in tuning the Ca transient in our amylin model, as the reduced SERCA Vmax for HIP relativeto +Amylin maintained enhanced, albeit modestly reduced, Ca transientsand load. Instead, SERCA control the extent to which altered sarcolemmalCa leak modulates Ca transient amplitude. This was most apparent aspacing rates were varied from 0.5 to 2 Hz in our model, which essentiallydetermined the time during which SERCA could recover SR Ca load fol-lowing a release event. Specifically, our model predicted that amylin-inducedCa transient enhancement diminished with increased pacing and nearlyapproached control transient amplitudes at 2 Hz (see Fig. S6). Further, thedecline in transient amplitude with pacing was faster for HIP relative to+Amylin, which expectedly suggests that amylin’s inotropic effects are atleast partially modulated by the efficiency of SERCA Ca handling. Maintenance of Na + load in +Amylin and HIP myocytes To determine whether amylin induced appreciable changes in cardiomyocyteNa + handling, we measured Na + load and influx in control and amylin-incubated myocytes following the inhibition of the NKA pump. NKA isa sarcolemma-bound ATPase that extrudes Na + by exchanging the cationwith extracellular K + , thus its inhibition would be expected to demonstrateany differences in Na + load and influx due to +Amylin. We found thatboth Na + handling metrics were indistinguishable between the control and+Amylin cells when the NKA was allowed to compensate for the Ca leak(Fig. S7c). However, when we assumed NKA activity in our +Amylin model mylinmylin
Cytosolic and sarcoplasmic reticulum Ca load While background sarcolemmal Ca leak is evidently enhanced for +Amylinand HIP, the corresponding Ca current over a single beat does not con-tribute significantly to the total cytosol Ca content. Hence, the leakalone is insufficient to directly account for the observed increase in Ca amplitude for the amylin models on a beat-to-beat basis. Rather, our dataindicate that the Ca transients required nearly 20 seconds of pacing toreach steady state (Fig. 4), which suggests that Ca transient amplifica- mylinmylin released on a beat-to-beat basis originates in the SR (14), we hy-pothesized that the increased intracellular Ca transient amplitudes forthe amylin rats stemmed from elevated SR Ca loading owing to increasedsarcolemmal Ca leak. For this scenario, we would expect that Ca tran-sient amplitudes should scale proportionally with SL leak rates. Therefore,we examined how the control model responded to variations SL Ca leak(Amylin Leak %), as well in SERCA function. These effects are summa-rized in Fig. 5a-c, for which we report predicted cytosolic Ca transients(a., ∆ Cai ), SR Ca transients (b., ∆ Ca SR ) and diastolic SR Ca loads(c., max Ca SR ). These data strongly indicate that the SR Ca load is pos-itively correlated with increasing sarcolemmal Ca leak and to a lesser ex-tent, SERCA function. More importantly, the increased sarcolemmal Ca leak assumed for +Amylin and HIP relative to control largely accounted forthe elevated Ca transients and SR load.In other words, SERCA appeared to play a minor role in tuning the Ca transient in our amylin model, as the reduced SERCA Vmax for HIP relativeto +Amylin maintained enhanced, albeit modestly reduced, Ca transientsand load. Instead, SERCA control the extent to which altered sarcolemmalCa leak modulates Ca transient amplitude. This was most apparent aspacing rates were varied from 0.5 to 2 Hz in our model, which essentiallydetermined the time during which SERCA could recover SR Ca load fol-lowing a release event. Specifically, our model predicted that amylin-inducedCa transient enhancement diminished with increased pacing and nearlyapproached control transient amplitudes at 2 Hz (see Fig. S6). Further, thedecline in transient amplitude with pacing was faster for HIP relative to+Amylin, which expectedly suggests that amylin’s inotropic effects are atleast partially modulated by the efficiency of SERCA Ca handling. Maintenance of Na + load in +Amylin and HIP myocytes To determine whether amylin induced appreciable changes in cardiomyocyteNa + handling, we measured Na + load and influx in control and amylin-incubated myocytes following the inhibition of the NKA pump. NKA isa sarcolemma-bound ATPase that extrudes Na + by exchanging the cationwith extracellular K + , thus its inhibition would be expected to demonstrateany differences in Na + load and influx due to +Amylin. We found thatboth Na + handling metrics were indistinguishable between the control and+Amylin cells when the NKA was allowed to compensate for the Ca leak(Fig. S7c). However, when we assumed NKA activity in our +Amylin model mylinmylin + increased by 0.3mM (Fig. S7c), though the predicted difference in Na + load was likely belowthe limits of experimental detection. The increased Na + load appearedto arise due to higher NCX exchange rates (Fig. 6) brought about by theelevated diastolic Ca load for +Amylin. In order to maintain Na + loadat control levels for the +Amylin model, our fitting procedure revealed thatthe NKA current should be increased by 14%. Interestingly, it has beenreported (25) that rat soleus muscle exposed to 10 µM amylin increased Rbcation uptake by 24% relative to control (25), which is commensurate withour predicted Vmax for maintaining cytosolic Na + load.To further elucidate the potential contribution of NKA exchange to Ca and Na + homeostasis, we present in Fig. S8 cytosolic and SR Ca transientamplitudes as well as Na + load as a function of sarcolemmal leak rates andNKA activity. In Fig. S8d we confirm that Na + load decreases with in-creasing NKA Vmax and increases with sarcolemmal Ca leak. Our modelassumes amylin does not change sarcolemmal Na + leak relative to control,therefore we attribute the positive correlation between Na + load and sar-colemmal Ca leak to NCX exchange activity. Specifically, as cytosolicCa load increases with sarcolemmal leak rates, NCX exchange of cytoso-lic Ca with extracellular Na + would contribute to increased intracellularNa + . Analogously, as increased NKA activity depletes cytosolic Na + , Ca influx via the NCX reverse mode would be expected to decrease and therebyultimately reduce intracellular Ca . Our simulated data reflect these trendsfor several metrics of Ca transients in Fig. S8a-c, which we discuss furtherin the Supplement. Ion channel activity and Ca handling It was expected that amylin-driven increases in cytosolic and SR Ca loading would culminate in the modulation of multiple downstream Ca -dependent signaling pathways (21). In this regard, we leveraged the com-putational model to systematically probe the response of its outputs, suchas the activity of various Ca handling components, to changes in modelinputs including SL Ca leak. Accordingly, we depict in Fig. 6 relativechanges 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 Ca leak ( i CaB) for+Amylin and HIP, as we assumed increased leak conductance parametersfor both cases. Interestingly, i Na was predicted to increase for both cases rel-ative to control, which in principle could influence the AP upstroke velocity mylinmylin
Cytosolic and sarcoplasmic reticulum Ca load While background sarcolemmal Ca leak is evidently enhanced for +Amylinand HIP, the corresponding Ca current over a single beat does not con-tribute significantly to the total cytosol Ca content. Hence, the leakalone is insufficient to directly account for the observed increase in Ca amplitude for the amylin models on a beat-to-beat basis. Rather, our dataindicate that the Ca transients required nearly 20 seconds of pacing toreach steady state (Fig. 4), which suggests that Ca transient amplifica- mylinmylin released on a beat-to-beat basis originates in the SR (14), we hy-pothesized that the increased intracellular Ca transient amplitudes forthe amylin rats stemmed from elevated SR Ca loading owing to increasedsarcolemmal Ca leak. For this scenario, we would expect that Ca tran-sient amplitudes should scale proportionally with SL leak rates. Therefore,we examined how the control model responded to variations SL Ca leak(Amylin Leak %), as well in SERCA function. These effects are summa-rized in Fig. 5a-c, for which we report predicted cytosolic Ca transients(a., ∆ Cai ), SR Ca transients (b., ∆ Ca SR ) and diastolic SR Ca loads(c., max Ca SR ). These data strongly indicate that the SR Ca load is pos-itively correlated with increasing sarcolemmal Ca leak and to a lesser ex-tent, SERCA function. More importantly, the increased sarcolemmal Ca leak assumed for +Amylin and HIP relative to control largely accounted forthe elevated Ca transients and SR load.In other words, SERCA appeared to play a minor role in tuning the Ca transient in our amylin model, as the reduced SERCA Vmax for HIP relativeto +Amylin maintained enhanced, albeit modestly reduced, Ca transientsand load. Instead, SERCA control the extent to which altered sarcolemmalCa leak modulates Ca transient amplitude. This was most apparent aspacing rates were varied from 0.5 to 2 Hz in our model, which essentiallydetermined the time during which SERCA could recover SR Ca load fol-lowing a release event. Specifically, our model predicted that amylin-inducedCa transient enhancement diminished with increased pacing and nearlyapproached control transient amplitudes at 2 Hz (see Fig. S6). Further, thedecline in transient amplitude with pacing was faster for HIP relative to+Amylin, which expectedly suggests that amylin’s inotropic effects are atleast partially modulated by the efficiency of SERCA Ca handling. Maintenance of Na + load in +Amylin and HIP myocytes To determine whether amylin induced appreciable changes in cardiomyocyteNa + handling, we measured Na + load and influx in control and amylin-incubated myocytes following the inhibition of the NKA pump. NKA isa sarcolemma-bound ATPase that extrudes Na + by exchanging the cationwith extracellular K + , thus its inhibition would be expected to demonstrateany differences in Na + load and influx due to +Amylin. We found thatboth Na + handling metrics were indistinguishable between the control and+Amylin cells when the NKA was allowed to compensate for the Ca leak(Fig. S7c). However, when we assumed NKA activity in our +Amylin model mylinmylin + increased by 0.3mM (Fig. S7c), though the predicted difference in Na + load was likely belowthe limits of experimental detection. The increased Na + load appearedto arise due to higher NCX exchange rates (Fig. 6) brought about by theelevated diastolic Ca load for +Amylin. In order to maintain Na + loadat control levels for the +Amylin model, our fitting procedure revealed thatthe NKA current should be increased by 14%. Interestingly, it has beenreported (25) that rat soleus muscle exposed to 10 µM amylin increased Rbcation uptake by 24% relative to control (25), which is commensurate withour predicted Vmax for maintaining cytosolic Na + load.To further elucidate the potential contribution of NKA exchange to Ca and Na + homeostasis, we present in Fig. S8 cytosolic and SR Ca transientamplitudes as well as Na + load as a function of sarcolemmal leak rates andNKA activity. In Fig. S8d we confirm that Na + load decreases with in-creasing NKA Vmax and increases with sarcolemmal Ca leak. Our modelassumes amylin does not change sarcolemmal Na + leak relative to control,therefore we attribute the positive correlation between Na + load and sar-colemmal Ca leak to NCX exchange activity. Specifically, as cytosolicCa load increases with sarcolemmal leak rates, NCX exchange of cytoso-lic Ca with extracellular Na + would contribute to increased intracellularNa + . Analogously, as increased NKA activity depletes cytosolic Na + , Ca influx via the NCX reverse mode would be expected to decrease and therebyultimately reduce intracellular Ca . Our simulated data reflect these trendsfor several metrics of Ca transients in Fig. S8a-c, which we discuss furtherin the Supplement. Ion channel activity and Ca handling It was expected that amylin-driven increases in cytosolic and SR Ca loading would culminate in the modulation of multiple downstream Ca -dependent signaling pathways (21). In this regard, we leveraged the com-putational model to systematically probe the response of its outputs, suchas the activity of various Ca handling components, to changes in modelinputs including SL Ca leak. Accordingly, we depict in Fig. 6 relativechanges 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 Ca leak ( i CaB) for+Amylin and HIP, as we assumed increased leak conductance parametersfor both cases. Interestingly, i Na was predicted to increase for both cases rel-ative to control, which in principle could influence the AP upstroke velocity mylinmylin i Na amplitude appear to be of little consequence. Beyond these currents,increased SL leak had opposing effects on the currents for the +Amylin andHIP data. For +Amylin, for instance, we observed enhanced SR release anduptake amplitudes ( j relSR, j pumpSR and j leakSR in Fig. 6) that are ex-pected to contribute to larger cytosolic Ca transients. For HIP, we foundmodestly higher i NaCa and i Cap relative to control and +Amylin, whichreflects a redistribution of sarcolemmal Ca extrusion versus SR Ca up-take. Similar redistributions are known to occur when SERCA function isreduced (32).In Fig. S13 we depict the relative change in activity for the top twentymodulated model ’states’ upon increasing SL Ca leak. Unique to +Amylinwere nearly 2.5- and 1.5-fold increases in the inactive (I) and open (O)states of the Ryanodine receptor model (33, 34) relative to control, whichis consistent with elevated dyadic junction Ca that acts to both promoteand terminate ryanodine receptor (RyR) opening. More importantly, thegreater RyR open probability translates to an increased rate of SR Ca re-lease and commensurate increase in cytosolic Ca transients. Apparent toboth +Amylin and HIP conditions are 30-75% increases in states represent-ing intracellular Ca and Ca -bound buffers, including CaM, Troponin C(TnC), and myosin, which can be expected with Ca loading. Comparison with non-amylin-induced increases in sarcolem-mal Ca -specific currents and sarcoplasmic reticulum Ca handling Our main hypothesis was that the +Amylin phenotype is primarily drivenby non-specific SL Ca leak. This mechanism would be in contrast todirect modulation of Ca conducting channels, as has been demonstratedfor LCC and TRPV4 in neurons (35). To investigate these hypotheses, we fitthe LCC conductance to reproduce the cytosolic Ca transients exhibitedfor +Amylin. The fitting procedure yielded an increased PCa value relativeto control (180%) that in turn increased peak i CaL. These conditions,which we refer to as the LCC configuration, were found to present many ofthe same trends observed for the +Amylin conditions, including increasedintracellular SR Ca transients and SR load (see Fig. S10). Our analysesin Fig. S12 revealed some differences in sarcolemmal channel currents forLCC relative +Amylin. Firstly, the data reflect the model assumptions of mylinmylin
Cytosolic and sarcoplasmic reticulum Ca load While background sarcolemmal Ca leak is evidently enhanced for +Amylinand HIP, the corresponding Ca current over a single beat does not con-tribute significantly to the total cytosol Ca content. Hence, the leakalone is insufficient to directly account for the observed increase in Ca amplitude for the amylin models on a beat-to-beat basis. Rather, our dataindicate that the Ca transients required nearly 20 seconds of pacing toreach steady state (Fig. 4), which suggests that Ca transient amplifica- mylinmylin released on a beat-to-beat basis originates in the SR (14), we hy-pothesized that the increased intracellular Ca transient amplitudes forthe amylin rats stemmed from elevated SR Ca loading owing to increasedsarcolemmal Ca leak. For this scenario, we would expect that Ca tran-sient amplitudes should scale proportionally with SL leak rates. Therefore,we examined how the control model responded to variations SL Ca leak(Amylin Leak %), as well in SERCA function. These effects are summa-rized in Fig. 5a-c, for which we report predicted cytosolic Ca transients(a., ∆ Cai ), SR Ca transients (b., ∆ Ca SR ) and diastolic SR Ca loads(c., max Ca SR ). These data strongly indicate that the SR Ca load is pos-itively correlated with increasing sarcolemmal Ca leak and to a lesser ex-tent, SERCA function. More importantly, the increased sarcolemmal Ca leak assumed for +Amylin and HIP relative to control largely accounted forthe elevated Ca transients and SR load.In other words, SERCA appeared to play a minor role in tuning the Ca transient in our amylin model, as the reduced SERCA Vmax for HIP relativeto +Amylin maintained enhanced, albeit modestly reduced, Ca transientsand load. Instead, SERCA control the extent to which altered sarcolemmalCa leak modulates Ca transient amplitude. This was most apparent aspacing rates were varied from 0.5 to 2 Hz in our model, which essentiallydetermined the time during which SERCA could recover SR Ca load fol-lowing a release event. Specifically, our model predicted that amylin-inducedCa transient enhancement diminished with increased pacing and nearlyapproached control transient amplitudes at 2 Hz (see Fig. S6). Further, thedecline in transient amplitude with pacing was faster for HIP relative to+Amylin, which expectedly suggests that amylin’s inotropic effects are atleast partially modulated by the efficiency of SERCA Ca handling. Maintenance of Na + load in +Amylin and HIP myocytes To determine whether amylin induced appreciable changes in cardiomyocyteNa + handling, we measured Na + load and influx in control and amylin-incubated myocytes following the inhibition of the NKA pump. NKA isa sarcolemma-bound ATPase that extrudes Na + by exchanging the cationwith extracellular K + , thus its inhibition would be expected to demonstrateany differences in Na + load and influx due to +Amylin. We found thatboth Na + handling metrics were indistinguishable between the control and+Amylin cells when the NKA was allowed to compensate for the Ca leak(Fig. S7c). However, when we assumed NKA activity in our +Amylin model mylinmylin + increased by 0.3mM (Fig. S7c), though the predicted difference in Na + load was likely belowthe limits of experimental detection. The increased Na + load appearedto arise due to higher NCX exchange rates (Fig. 6) brought about by theelevated diastolic Ca load for +Amylin. In order to maintain Na + loadat control levels for the +Amylin model, our fitting procedure revealed thatthe NKA current should be increased by 14%. Interestingly, it has beenreported (25) that rat soleus muscle exposed to 10 µM amylin increased Rbcation uptake by 24% relative to control (25), which is commensurate withour predicted Vmax for maintaining cytosolic Na + load.To further elucidate the potential contribution of NKA exchange to Ca and Na + homeostasis, we present in Fig. S8 cytosolic and SR Ca transientamplitudes as well as Na + load as a function of sarcolemmal leak rates andNKA activity. In Fig. S8d we confirm that Na + load decreases with in-creasing NKA Vmax and increases with sarcolemmal Ca leak. Our modelassumes amylin does not change sarcolemmal Na + leak relative to control,therefore we attribute the positive correlation between Na + load and sar-colemmal Ca leak to NCX exchange activity. Specifically, as cytosolicCa load increases with sarcolemmal leak rates, NCX exchange of cytoso-lic Ca with extracellular Na + would contribute to increased intracellularNa + . Analogously, as increased NKA activity depletes cytosolic Na + , Ca influx via the NCX reverse mode would be expected to decrease and therebyultimately reduce intracellular Ca . Our simulated data reflect these trendsfor several metrics of Ca transients in Fig. S8a-c, which we discuss furtherin the Supplement. Ion channel activity and Ca handling It was expected that amylin-driven increases in cytosolic and SR Ca loading would culminate in the modulation of multiple downstream Ca -dependent signaling pathways (21). In this regard, we leveraged the com-putational model to systematically probe the response of its outputs, suchas the activity of various Ca handling components, to changes in modelinputs including SL Ca leak. Accordingly, we depict in Fig. 6 relativechanges 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 Ca leak ( i CaB) for+Amylin and HIP, as we assumed increased leak conductance parametersfor both cases. Interestingly, i Na was predicted to increase for both cases rel-ative to control, which in principle could influence the AP upstroke velocity mylinmylin i Na amplitude appear to be of little consequence. Beyond these currents,increased SL leak had opposing effects on the currents for the +Amylin andHIP data. For +Amylin, for instance, we observed enhanced SR release anduptake amplitudes ( j relSR, j pumpSR and j leakSR in Fig. 6) that are ex-pected to contribute to larger cytosolic Ca transients. For HIP, we foundmodestly higher i NaCa and i Cap relative to control and +Amylin, whichreflects a redistribution of sarcolemmal Ca extrusion versus SR Ca up-take. Similar redistributions are known to occur when SERCA function isreduced (32).In Fig. S13 we depict the relative change in activity for the top twentymodulated model ’states’ upon increasing SL Ca leak. Unique to +Amylinwere nearly 2.5- and 1.5-fold increases in the inactive (I) and open (O)states of the Ryanodine receptor model (33, 34) relative to control, whichis consistent with elevated dyadic junction Ca that acts to both promoteand terminate ryanodine receptor (RyR) opening. More importantly, thegreater RyR open probability translates to an increased rate of SR Ca re-lease and commensurate increase in cytosolic Ca transients. Apparent toboth +Amylin and HIP conditions are 30-75% increases in states represent-ing intracellular Ca and Ca -bound buffers, including CaM, Troponin C(TnC), and myosin, which can be expected with Ca loading. Comparison with non-amylin-induced increases in sarcolem-mal Ca -specific currents and sarcoplasmic reticulum Ca handling Our main hypothesis was that the +Amylin phenotype is primarily drivenby non-specific SL Ca leak. This mechanism would be in contrast todirect modulation of Ca conducting channels, as has been demonstratedfor LCC and TRPV4 in neurons (35). To investigate these hypotheses, we fitthe LCC conductance to reproduce the cytosolic Ca transients exhibitedfor +Amylin. The fitting procedure yielded an increased PCa value relativeto control (180%) that in turn increased peak i CaL. These conditions,which we refer to as the LCC configuration, were found to present many ofthe same trends observed for the +Amylin conditions, including increasedintracellular SR Ca transients and SR load (see Fig. S10). Our analysesin Fig. S12 revealed some differences in sarcolemmal channel currents forLCC relative +Amylin. Firstly, the data reflect the model assumptions of mylinmylin leak for the +Amylin case and larger magnitude i CaL for LCC.More importantly, +Amylin and LCC were found to have different effectson i Na, as the former indicated an amplified sodium channel current, whilethe i Na for LCC was similar to control. Conversely, the most prominent K + channel currents ( i tof, i kur, and i K1) were for the most part moderatelyenhanced for LCC, compared to modest suppression of those current for+Amylin. Despite these opposing effects on i Na and K + currents, therewere negligible differences in the AP relative to control (see Fig. S4i). mylinmylin
Cytosolic and sarcoplasmic reticulum Ca load While background sarcolemmal Ca leak is evidently enhanced for +Amylinand HIP, the corresponding Ca current over a single beat does not con-tribute significantly to the total cytosol Ca content. Hence, the leakalone is insufficient to directly account for the observed increase in Ca amplitude for the amylin models on a beat-to-beat basis. Rather, our dataindicate that the Ca transients required nearly 20 seconds of pacing toreach steady state (Fig. 4), which suggests that Ca transient amplifica- mylinmylin released on a beat-to-beat basis originates in the SR (14), we hy-pothesized that the increased intracellular Ca transient amplitudes forthe amylin rats stemmed from elevated SR Ca loading owing to increasedsarcolemmal Ca leak. For this scenario, we would expect that Ca tran-sient amplitudes should scale proportionally with SL leak rates. Therefore,we examined how the control model responded to variations SL Ca leak(Amylin Leak %), as well in SERCA function. These effects are summa-rized in Fig. 5a-c, for which we report predicted cytosolic Ca transients(a., ∆ Cai ), SR Ca transients (b., ∆ Ca SR ) and diastolic SR Ca loads(c., max Ca SR ). These data strongly indicate that the SR Ca load is pos-itively correlated with increasing sarcolemmal Ca leak and to a lesser ex-tent, SERCA function. More importantly, the increased sarcolemmal Ca leak assumed for +Amylin and HIP relative to control largely accounted forthe elevated Ca transients and SR load.In other words, SERCA appeared to play a minor role in tuning the Ca transient in our amylin model, as the reduced SERCA Vmax for HIP relativeto +Amylin maintained enhanced, albeit modestly reduced, Ca transientsand load. Instead, SERCA control the extent to which altered sarcolemmalCa leak modulates Ca transient amplitude. This was most apparent aspacing rates were varied from 0.5 to 2 Hz in our model, which essentiallydetermined the time during which SERCA could recover SR Ca load fol-lowing a release event. Specifically, our model predicted that amylin-inducedCa transient enhancement diminished with increased pacing and nearlyapproached control transient amplitudes at 2 Hz (see Fig. S6). Further, thedecline in transient amplitude with pacing was faster for HIP relative to+Amylin, which expectedly suggests that amylin’s inotropic effects are atleast partially modulated by the efficiency of SERCA Ca handling. Maintenance of Na + load in +Amylin and HIP myocytes To determine whether amylin induced appreciable changes in cardiomyocyteNa + handling, we measured Na + load and influx in control and amylin-incubated myocytes following the inhibition of the NKA pump. NKA isa sarcolemma-bound ATPase that extrudes Na + by exchanging the cationwith extracellular K + , thus its inhibition would be expected to demonstrateany differences in Na + load and influx due to +Amylin. We found thatboth Na + handling metrics were indistinguishable between the control and+Amylin cells when the NKA was allowed to compensate for the Ca leak(Fig. S7c). However, when we assumed NKA activity in our +Amylin model mylinmylin + increased by 0.3mM (Fig. S7c), though the predicted difference in Na + load was likely belowthe limits of experimental detection. The increased Na + load appearedto arise due to higher NCX exchange rates (Fig. 6) brought about by theelevated diastolic Ca load for +Amylin. In order to maintain Na + loadat control levels for the +Amylin model, our fitting procedure revealed thatthe NKA current should be increased by 14%. Interestingly, it has beenreported (25) that rat soleus muscle exposed to 10 µM amylin increased Rbcation uptake by 24% relative to control (25), which is commensurate withour predicted Vmax for maintaining cytosolic Na + load.To further elucidate the potential contribution of NKA exchange to Ca and Na + homeostasis, we present in Fig. S8 cytosolic and SR Ca transientamplitudes as well as Na + load as a function of sarcolemmal leak rates andNKA activity. In Fig. S8d we confirm that Na + load decreases with in-creasing NKA Vmax and increases with sarcolemmal Ca leak. Our modelassumes amylin does not change sarcolemmal Na + leak relative to control,therefore we attribute the positive correlation between Na + load and sar-colemmal Ca leak to NCX exchange activity. Specifically, as cytosolicCa load increases with sarcolemmal leak rates, NCX exchange of cytoso-lic Ca with extracellular Na + would contribute to increased intracellularNa + . Analogously, as increased NKA activity depletes cytosolic Na + , Ca influx via the NCX reverse mode would be expected to decrease and therebyultimately reduce intracellular Ca . Our simulated data reflect these trendsfor several metrics of Ca transients in Fig. S8a-c, which we discuss furtherin the Supplement. Ion channel activity and Ca handling It was expected that amylin-driven increases in cytosolic and SR Ca loading would culminate in the modulation of multiple downstream Ca -dependent signaling pathways (21). In this regard, we leveraged the com-putational model to systematically probe the response of its outputs, suchas the activity of various Ca handling components, to changes in modelinputs including SL Ca leak. Accordingly, we depict in Fig. 6 relativechanges 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 Ca leak ( i CaB) for+Amylin and HIP, as we assumed increased leak conductance parametersfor both cases. Interestingly, i Na was predicted to increase for both cases rel-ative to control, which in principle could influence the AP upstroke velocity mylinmylin i Na amplitude appear to be of little consequence. Beyond these currents,increased SL leak had opposing effects on the currents for the +Amylin andHIP data. For +Amylin, for instance, we observed enhanced SR release anduptake amplitudes ( j relSR, j pumpSR and j leakSR in Fig. 6) that are ex-pected to contribute to larger cytosolic Ca transients. For HIP, we foundmodestly higher i NaCa and i Cap relative to control and +Amylin, whichreflects a redistribution of sarcolemmal Ca extrusion versus SR Ca up-take. Similar redistributions are known to occur when SERCA function isreduced (32).In Fig. S13 we depict the relative change in activity for the top twentymodulated model ’states’ upon increasing SL Ca leak. Unique to +Amylinwere nearly 2.5- and 1.5-fold increases in the inactive (I) and open (O)states of the Ryanodine receptor model (33, 34) relative to control, whichis consistent with elevated dyadic junction Ca that acts to both promoteand terminate ryanodine receptor (RyR) opening. More importantly, thegreater RyR open probability translates to an increased rate of SR Ca re-lease and commensurate increase in cytosolic Ca transients. Apparent toboth +Amylin and HIP conditions are 30-75% increases in states represent-ing intracellular Ca and Ca -bound buffers, including CaM, Troponin C(TnC), and myosin, which can be expected with Ca loading. Comparison with non-amylin-induced increases in sarcolem-mal Ca -specific currents and sarcoplasmic reticulum Ca handling Our main hypothesis was that the +Amylin phenotype is primarily drivenby non-specific SL Ca leak. This mechanism would be in contrast todirect modulation of Ca conducting channels, as has been demonstratedfor LCC and TRPV4 in neurons (35). To investigate these hypotheses, we fitthe LCC conductance to reproduce the cytosolic Ca transients exhibitedfor +Amylin. The fitting procedure yielded an increased PCa value relativeto control (180%) that in turn increased peak i CaL. These conditions,which we refer to as the LCC configuration, were found to present many ofthe same trends observed for the +Amylin conditions, including increasedintracellular SR Ca transients and SR load (see Fig. S10). Our analysesin Fig. S12 revealed some differences in sarcolemmal channel currents forLCC relative +Amylin. Firstly, the data reflect the model assumptions of mylinmylin leak for the +Amylin case and larger magnitude i CaL for LCC.More importantly, +Amylin and LCC were found to have different effectson i Na, as the former indicated an amplified sodium channel current, whilethe i Na for LCC was similar to control. Conversely, the most prominent K + channel currents ( i tof, i kur, and i K1) were for the most part moderatelyenhanced for LCC, compared to modest suppression of those current for+Amylin. Despite these opposing effects on i Na and K + currents, therewere negligible differences in the AP relative to control (see Fig. S4i). mylinmylin transients and loads as a function of SERCAVmax activity (% of control) and SL Ca leak (% of control). a) intracel-lular Ca , b) SR Ca transient c) maximum SR Ca load and d) sodiumload. A black point is representative of the Control case, a blue square isrepresentative of the Amy case, and a red square is representative of theHIP case. mylinmylin
Cytosolic and sarcoplasmic reticulum Ca load While background sarcolemmal Ca leak is evidently enhanced for +Amylinand HIP, the corresponding Ca current over a single beat does not con-tribute significantly to the total cytosol Ca content. Hence, the leakalone is insufficient to directly account for the observed increase in Ca amplitude for the amylin models on a beat-to-beat basis. Rather, our dataindicate that the Ca transients required nearly 20 seconds of pacing toreach steady state (Fig. 4), which suggests that Ca transient amplifica- mylinmylin released on a beat-to-beat basis originates in the SR (14), we hy-pothesized that the increased intracellular Ca transient amplitudes forthe amylin rats stemmed from elevated SR Ca loading owing to increasedsarcolemmal Ca leak. For this scenario, we would expect that Ca tran-sient amplitudes should scale proportionally with SL leak rates. Therefore,we examined how the control model responded to variations SL Ca leak(Amylin Leak %), as well in SERCA function. These effects are summa-rized in Fig. 5a-c, for which we report predicted cytosolic Ca transients(a., ∆ Cai ), SR Ca transients (b., ∆ Ca SR ) and diastolic SR Ca loads(c., max Ca SR ). These data strongly indicate that the SR Ca load is pos-itively correlated with increasing sarcolemmal Ca leak and to a lesser ex-tent, SERCA function. More importantly, the increased sarcolemmal Ca leak assumed for +Amylin and HIP relative to control largely accounted forthe elevated Ca transients and SR load.In other words, SERCA appeared to play a minor role in tuning the Ca transient in our amylin model, as the reduced SERCA Vmax for HIP relativeto +Amylin maintained enhanced, albeit modestly reduced, Ca transientsand load. Instead, SERCA control the extent to which altered sarcolemmalCa leak modulates Ca transient amplitude. This was most apparent aspacing rates were varied from 0.5 to 2 Hz in our model, which essentiallydetermined the time during which SERCA could recover SR Ca load fol-lowing a release event. Specifically, our model predicted that amylin-inducedCa transient enhancement diminished with increased pacing and nearlyapproached control transient amplitudes at 2 Hz (see Fig. S6). Further, thedecline in transient amplitude with pacing was faster for HIP relative to+Amylin, which expectedly suggests that amylin’s inotropic effects are atleast partially modulated by the efficiency of SERCA Ca handling. Maintenance of Na + load in +Amylin and HIP myocytes To determine whether amylin induced appreciable changes in cardiomyocyteNa + handling, we measured Na + load and influx in control and amylin-incubated myocytes following the inhibition of the NKA pump. NKA isa sarcolemma-bound ATPase that extrudes Na + by exchanging the cationwith extracellular K + , thus its inhibition would be expected to demonstrateany differences in Na + load and influx due to +Amylin. We found thatboth Na + handling metrics were indistinguishable between the control and+Amylin cells when the NKA was allowed to compensate for the Ca leak(Fig. S7c). However, when we assumed NKA activity in our +Amylin model mylinmylin + increased by 0.3mM (Fig. S7c), though the predicted difference in Na + load was likely belowthe limits of experimental detection. The increased Na + load appearedto arise due to higher NCX exchange rates (Fig. 6) brought about by theelevated diastolic Ca load for +Amylin. In order to maintain Na + loadat control levels for the +Amylin model, our fitting procedure revealed thatthe NKA current should be increased by 14%. Interestingly, it has beenreported (25) that rat soleus muscle exposed to 10 µM amylin increased Rbcation uptake by 24% relative to control (25), which is commensurate withour predicted Vmax for maintaining cytosolic Na + load.To further elucidate the potential contribution of NKA exchange to Ca and Na + homeostasis, we present in Fig. S8 cytosolic and SR Ca transientamplitudes as well as Na + load as a function of sarcolemmal leak rates andNKA activity. In Fig. S8d we confirm that Na + load decreases with in-creasing NKA Vmax and increases with sarcolemmal Ca leak. Our modelassumes amylin does not change sarcolemmal Na + leak relative to control,therefore we attribute the positive correlation between Na + load and sar-colemmal Ca leak to NCX exchange activity. Specifically, as cytosolicCa load increases with sarcolemmal leak rates, NCX exchange of cytoso-lic Ca with extracellular Na + would contribute to increased intracellularNa + . Analogously, as increased NKA activity depletes cytosolic Na + , Ca influx via the NCX reverse mode would be expected to decrease and therebyultimately reduce intracellular Ca . Our simulated data reflect these trendsfor several metrics of Ca transients in Fig. S8a-c, which we discuss furtherin the Supplement. Ion channel activity and Ca handling It was expected that amylin-driven increases in cytosolic and SR Ca loading would culminate in the modulation of multiple downstream Ca -dependent signaling pathways (21). In this regard, we leveraged the com-putational model to systematically probe the response of its outputs, suchas the activity of various Ca handling components, to changes in modelinputs including SL Ca leak. Accordingly, we depict in Fig. 6 relativechanges 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 Ca leak ( i CaB) for+Amylin and HIP, as we assumed increased leak conductance parametersfor both cases. Interestingly, i Na was predicted to increase for both cases rel-ative to control, which in principle could influence the AP upstroke velocity mylinmylin i Na amplitude appear to be of little consequence. Beyond these currents,increased SL leak had opposing effects on the currents for the +Amylin andHIP data. For +Amylin, for instance, we observed enhanced SR release anduptake amplitudes ( j relSR, j pumpSR and j leakSR in Fig. 6) that are ex-pected to contribute to larger cytosolic Ca transients. For HIP, we foundmodestly higher i NaCa and i Cap relative to control and +Amylin, whichreflects a redistribution of sarcolemmal Ca extrusion versus SR Ca up-take. Similar redistributions are known to occur when SERCA function isreduced (32).In Fig. S13 we depict the relative change in activity for the top twentymodulated model ’states’ upon increasing SL Ca leak. Unique to +Amylinwere nearly 2.5- and 1.5-fold increases in the inactive (I) and open (O)states of the Ryanodine receptor model (33, 34) relative to control, whichis consistent with elevated dyadic junction Ca that acts to both promoteand terminate ryanodine receptor (RyR) opening. More importantly, thegreater RyR open probability translates to an increased rate of SR Ca re-lease and commensurate increase in cytosolic Ca transients. Apparent toboth +Amylin and HIP conditions are 30-75% increases in states represent-ing intracellular Ca and Ca -bound buffers, including CaM, Troponin C(TnC), and myosin, which can be expected with Ca loading. Comparison with non-amylin-induced increases in sarcolem-mal Ca -specific currents and sarcoplasmic reticulum Ca handling Our main hypothesis was that the +Amylin phenotype is primarily drivenby non-specific SL Ca leak. This mechanism would be in contrast todirect modulation of Ca conducting channels, as has been demonstratedfor LCC and TRPV4 in neurons (35). To investigate these hypotheses, we fitthe LCC conductance to reproduce the cytosolic Ca transients exhibitedfor +Amylin. The fitting procedure yielded an increased PCa value relativeto control (180%) that in turn increased peak i CaL. These conditions,which we refer to as the LCC configuration, were found to present many ofthe same trends observed for the +Amylin conditions, including increasedintracellular SR Ca transients and SR load (see Fig. S10). Our analysesin Fig. S12 revealed some differences in sarcolemmal channel currents forLCC relative +Amylin. Firstly, the data reflect the model assumptions of mylinmylin leak for the +Amylin case and larger magnitude i CaL for LCC.More importantly, +Amylin and LCC were found to have different effectson i Na, as the former indicated an amplified sodium channel current, whilethe i Na for LCC was similar to control. Conversely, the most prominent K + channel currents ( i tof, i kur, and i K1) were for the most part moderatelyenhanced for LCC, compared to modest suppression of those current for+Amylin. Despite these opposing effects on i Na and K + currents, therewere negligible differences in the AP relative to control (see Fig. S4i). mylinmylin transients and loads as a function of SERCAVmax activity (% of control) and SL Ca leak (% of control). a) intracel-lular Ca , b) SR Ca transient c) maximum SR Ca load and d) sodiumload. A black point is representative of the Control case, a blue square isrepresentative of the Amy case, and a red square is representative of theHIP case. mylinmylin mylinmylin
Cytosolic and sarcoplasmic reticulum Ca load While background sarcolemmal Ca leak is evidently enhanced for +Amylinand HIP, the corresponding Ca current over a single beat does not con-tribute significantly to the total cytosol Ca content. Hence, the leakalone is insufficient to directly account for the observed increase in Ca amplitude for the amylin models on a beat-to-beat basis. Rather, our dataindicate that the Ca transients required nearly 20 seconds of pacing toreach steady state (Fig. 4), which suggests that Ca transient amplifica- mylinmylin released on a beat-to-beat basis originates in the SR (14), we hy-pothesized that the increased intracellular Ca transient amplitudes forthe amylin rats stemmed from elevated SR Ca loading owing to increasedsarcolemmal Ca leak. For this scenario, we would expect that Ca tran-sient amplitudes should scale proportionally with SL leak rates. Therefore,we examined how the control model responded to variations SL Ca leak(Amylin Leak %), as well in SERCA function. These effects are summa-rized in Fig. 5a-c, for which we report predicted cytosolic Ca transients(a., ∆ Cai ), SR Ca transients (b., ∆ Ca SR ) and diastolic SR Ca loads(c., max Ca SR ). These data strongly indicate that the SR Ca load is pos-itively correlated with increasing sarcolemmal Ca leak and to a lesser ex-tent, SERCA function. More importantly, the increased sarcolemmal Ca leak assumed for +Amylin and HIP relative to control largely accounted forthe elevated Ca transients and SR load.In other words, SERCA appeared to play a minor role in tuning the Ca transient in our amylin model, as the reduced SERCA Vmax for HIP relativeto +Amylin maintained enhanced, albeit modestly reduced, Ca transientsand load. Instead, SERCA control the extent to which altered sarcolemmalCa leak modulates Ca transient amplitude. This was most apparent aspacing rates were varied from 0.5 to 2 Hz in our model, which essentiallydetermined the time during which SERCA could recover SR Ca load fol-lowing a release event. Specifically, our model predicted that amylin-inducedCa transient enhancement diminished with increased pacing and nearlyapproached control transient amplitudes at 2 Hz (see Fig. S6). Further, thedecline in transient amplitude with pacing was faster for HIP relative to+Amylin, which expectedly suggests that amylin’s inotropic effects are atleast partially modulated by the efficiency of SERCA Ca handling. Maintenance of Na + load in +Amylin and HIP myocytes To determine whether amylin induced appreciable changes in cardiomyocyteNa + handling, we measured Na + load and influx in control and amylin-incubated myocytes following the inhibition of the NKA pump. NKA isa sarcolemma-bound ATPase that extrudes Na + by exchanging the cationwith extracellular K + , thus its inhibition would be expected to demonstrateany differences in Na + load and influx due to +Amylin. We found thatboth Na + handling metrics were indistinguishable between the control and+Amylin cells when the NKA was allowed to compensate for the Ca leak(Fig. S7c). However, when we assumed NKA activity in our +Amylin model mylinmylin + increased by 0.3mM (Fig. S7c), though the predicted difference in Na + load was likely belowthe limits of experimental detection. The increased Na + load appearedto arise due to higher NCX exchange rates (Fig. 6) brought about by theelevated diastolic Ca load for +Amylin. In order to maintain Na + loadat control levels for the +Amylin model, our fitting procedure revealed thatthe NKA current should be increased by 14%. Interestingly, it has beenreported (25) that rat soleus muscle exposed to 10 µM amylin increased Rbcation uptake by 24% relative to control (25), which is commensurate withour predicted Vmax for maintaining cytosolic Na + load.To further elucidate the potential contribution of NKA exchange to Ca and Na + homeostasis, we present in Fig. S8 cytosolic and SR Ca transientamplitudes as well as Na + load as a function of sarcolemmal leak rates andNKA activity. In Fig. S8d we confirm that Na + load decreases with in-creasing NKA Vmax and increases with sarcolemmal Ca leak. Our modelassumes amylin does not change sarcolemmal Na + leak relative to control,therefore we attribute the positive correlation between Na + load and sar-colemmal Ca leak to NCX exchange activity. Specifically, as cytosolicCa load increases with sarcolemmal leak rates, NCX exchange of cytoso-lic Ca with extracellular Na + would contribute to increased intracellularNa + . Analogously, as increased NKA activity depletes cytosolic Na + , Ca influx via the NCX reverse mode would be expected to decrease and therebyultimately reduce intracellular Ca . Our simulated data reflect these trendsfor several metrics of Ca transients in Fig. S8a-c, which we discuss furtherin the Supplement. Ion channel activity and Ca handling It was expected that amylin-driven increases in cytosolic and SR Ca loading would culminate in the modulation of multiple downstream Ca -dependent signaling pathways (21). In this regard, we leveraged the com-putational model to systematically probe the response of its outputs, suchas the activity of various Ca handling components, to changes in modelinputs including SL Ca leak. Accordingly, we depict in Fig. 6 relativechanges 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 Ca leak ( i CaB) for+Amylin and HIP, as we assumed increased leak conductance parametersfor both cases. Interestingly, i Na was predicted to increase for both cases rel-ative to control, which in principle could influence the AP upstroke velocity mylinmylin i Na amplitude appear to be of little consequence. Beyond these currents,increased SL leak had opposing effects on the currents for the +Amylin andHIP data. For +Amylin, for instance, we observed enhanced SR release anduptake amplitudes ( j relSR, j pumpSR and j leakSR in Fig. 6) that are ex-pected to contribute to larger cytosolic Ca transients. For HIP, we foundmodestly higher i NaCa and i Cap relative to control and +Amylin, whichreflects a redistribution of sarcolemmal Ca extrusion versus SR Ca up-take. Similar redistributions are known to occur when SERCA function isreduced (32).In Fig. S13 we depict the relative change in activity for the top twentymodulated model ’states’ upon increasing SL Ca leak. Unique to +Amylinwere nearly 2.5- and 1.5-fold increases in the inactive (I) and open (O)states of the Ryanodine receptor model (33, 34) relative to control, whichis consistent with elevated dyadic junction Ca that acts to both promoteand terminate ryanodine receptor (RyR) opening. More importantly, thegreater RyR open probability translates to an increased rate of SR Ca re-lease and commensurate increase in cytosolic Ca transients. Apparent toboth +Amylin and HIP conditions are 30-75% increases in states represent-ing intracellular Ca and Ca -bound buffers, including CaM, Troponin C(TnC), and myosin, which can be expected with Ca loading. Comparison with non-amylin-induced increases in sarcolem-mal Ca -specific currents and sarcoplasmic reticulum Ca handling Our main hypothesis was that the +Amylin phenotype is primarily drivenby non-specific SL Ca leak. This mechanism would be in contrast todirect modulation of Ca conducting channels, as has been demonstratedfor LCC and TRPV4 in neurons (35). To investigate these hypotheses, we fitthe LCC conductance to reproduce the cytosolic Ca transients exhibitedfor +Amylin. The fitting procedure yielded an increased PCa value relativeto control (180%) that in turn increased peak i CaL. These conditions,which we refer to as the LCC configuration, were found to present many ofthe same trends observed for the +Amylin conditions, including increasedintracellular SR Ca transients and SR load (see Fig. S10). Our analysesin Fig. S12 revealed some differences in sarcolemmal channel currents forLCC relative +Amylin. Firstly, the data reflect the model assumptions of mylinmylin leak for the +Amylin case and larger magnitude i CaL for LCC.More importantly, +Amylin and LCC were found to have different effectson i Na, as the former indicated an amplified sodium channel current, whilethe i Na for LCC was similar to control. Conversely, the most prominent K + channel currents ( i tof, i kur, and i K1) were for the most part moderatelyenhanced for LCC, compared to modest suppression of those current for+Amylin. Despite these opposing effects on i Na and K + currents, therewere negligible differences in the AP relative to control (see Fig. S4i). mylinmylin transients and loads as a function of SERCAVmax activity (% of control) and SL Ca leak (% of control). a) intracel-lular Ca , b) SR Ca transient c) maximum SR Ca load and d) sodiumload. A black point is representative of the Control case, a blue square isrepresentative of the Amy case, and a red square is representative of theHIP case. mylinmylin mylinmylin Discussion
Shannon-Bers-Morotti myocyte model
We revised the Shannon-Bers model of rabbit ventricular myocyte Ca cycling (20) to reflect Ca handling in murine species, as a close approx-imation to the human amylin transgenic/amylin-exposed rats used in (7).The predominant changes implemented in our model primarily entailed in-creasing the rates of SR Ca uptake and release to mirror the larger roleof SR Ca handling in murine relative to higher order animals, as well asmodulating potassium channel current profiles. The SBM model capturedkey distinguishing features of murine cardiomyocyte Ca handling, includ-ing shorter AP and Ca transient duration relative to rabbit, as well as agreater role of Ca release and uptake via the SR, as opposed to NCX(36).When we included sarcolemmal Ca leak data from Despa et al. . (7) ap-propriate for the +Amylin and HIP phenotypes in rats, as well as reducedSERCA Ca uptake rates for HIP, the computational model reproduced thealtered Ca transient amplitudes across a broad range of pacing intervals.With this model, we conclude that • increased rates of Ca influx through the sarcolemma, for instance asa result of amylin-induced membrane poration, promotes the amplifi-cation of cytosolic Ca transients. • the increase in Ca transient amplitude arises due to greater SR Ca load relative to control • elevated cytosolic Ca load stemming from higher rates of sarcolem-mal Ca influx (+Amylin), and especially when SERCA function isreduced (HIP), significantly increases the proportion of Ca -boundproteins. Of these proteins, CaM activation in particular may triggerremodeling via the calcineurin/NFAT pathway (37)(see Fig. 1). • the concerted relationship between amylin-induced increased sarcolem-mal Ca leak, intracellular Ca transients, and SR loading gives riseto similar Ca transient amplification in the Shannon-Bers model ofEC coupling in rabbit (20), which suggests similar mechanisms of dys-regulation in pre-diabetes may be manifest in higher order mammals. Enhanced SL Ca fluxes are sufficient to elevate cytosolicCa load in absence of altered SR Ca handling Recently, it was established that pre-diabetic rats transgenic for humanamylin peptide presented a high density of oligomerized amylin deposits mylinmylin
We revised the Shannon-Bers model of rabbit ventricular myocyte Ca cycling (20) to reflect Ca handling in murine species, as a close approx-imation to the human amylin transgenic/amylin-exposed rats used in (7).The predominant changes implemented in our model primarily entailed in-creasing the rates of SR Ca uptake and release to mirror the larger roleof SR Ca handling in murine relative to higher order animals, as well asmodulating potassium channel current profiles. The SBM model capturedkey distinguishing features of murine cardiomyocyte Ca handling, includ-ing shorter AP and Ca transient duration relative to rabbit, as well as agreater role of Ca release and uptake via the SR, as opposed to NCX(36).When we included sarcolemmal Ca leak data from Despa et al. . (7) ap-propriate for the +Amylin and HIP phenotypes in rats, as well as reducedSERCA Ca uptake rates for HIP, the computational model reproduced thealtered Ca transient amplitudes across a broad range of pacing intervals.With this model, we conclude that • increased rates of Ca influx through the sarcolemma, for instance asa result of amylin-induced membrane poration, promotes the amplifi-cation of cytosolic Ca transients. • the increase in Ca transient amplitude arises due to greater SR Ca load relative to control • elevated cytosolic Ca load stemming from higher rates of sarcolem-mal Ca influx (+Amylin), and especially when SERCA function isreduced (HIP), significantly increases the proportion of Ca -boundproteins. Of these proteins, CaM activation in particular may triggerremodeling via the calcineurin/NFAT pathway (37)(see Fig. 1). • the concerted relationship between amylin-induced increased sarcolem-mal Ca leak, intracellular Ca transients, and SR loading gives riseto similar Ca transient amplification in the Shannon-Bers model ofEC coupling in rabbit (20), which suggests similar mechanisms of dys-regulation in pre-diabetes may be manifest in higher order mammals. Enhanced SL Ca fluxes are sufficient to elevate cytosolicCa load in absence of altered SR Ca handling Recently, it was established that pre-diabetic rats transgenic for humanamylin peptide presented a high density of oligomerized amylin deposits mylinmylin leak rates and amplified Ca tran-sients. These effects on sarcolemmal Ca conductance and transient am-plitudes were recapitulated in isolated myocytes that were incubated withhuman amylin, which suggested that the phenotypical changes likely pre-cede any significant changes in protein expression that might otherwise pro-duce similar effects. Further, disruption of amylin oligomers via increasingeicosanoid serum levels (6) and the application of membrane sealant P188(Fig. 3) were both found to restore normal Ca handling. These exper-iments together firmly establish the link between oligomer-induced mem-brane poration and Ca dysregulation. Similarly, in our implementationof the Morotti-Shannon-Bers Ca cycling model, we found that amplifiedCa transients could be induced solely by increasing the sarcolemmal Ca conductance parameter (see Eq. 1).The enhancement of intracellular Ca transient amplitudes by amylinbears similarity to agonism of the sarcolemmal Ca channels LCC and P2X.It is well-established, for instance, that activation of LCC via β -adrenergicreceptor ( β AR) agonists promote larger Ca transients that are accompa-nied by elevated SR Ca load (14). Further, P2X receptor activation hascomparable effects on Ca transients and SR load (38), albeit without themultifarious changes in Ca handling associated with β AR stimulation.While we defer the topic of SR load to later in the Discussion, our simula-tions present strong evidence that increased inward sarcolemmal Ca aloneis sufficient to explain amylin dose-dependent effects on Ca transients in(7).For pacing intervals at 1 Hz and greater, our predictions of the controlCa transient using the SBM model (see Fig. S6) follow a neutral tran-sient amplitude/frequency relationship, as is frequently exhibited in mice(39) and the Despa et al. rat control data (7). Further, the computationalmodel captures the negative Ca transient relationships with pacing fre-quency reflected in the Despa et al. HIP rat data, including the diminishingdifference in transient amplitude relative to control at 2 Hz pacing. Thedecline in transient amplitude for HIP can be ascribed to the inability tomaintain elevated SR load as pacing increases, given the reduced SERCAactivity evident for these rats (7). Our data also reflect a negative transientamplitude/frequency relationship for the +Amylin conditions, which mayarise because the model does not reflect phosphorylation-dependent effectson relaxation, including CaMKII activation (40). Nevertheless, given thatour model captures the predominant changes in Ca handling exhibitedin +Amylin and HIP pre-diabetic rats (7) chiefly through modulating sar- mylinmylin
We revised the Shannon-Bers model of rabbit ventricular myocyte Ca cycling (20) to reflect Ca handling in murine species, as a close approx-imation to the human amylin transgenic/amylin-exposed rats used in (7).The predominant changes implemented in our model primarily entailed in-creasing the rates of SR Ca uptake and release to mirror the larger roleof SR Ca handling in murine relative to higher order animals, as well asmodulating potassium channel current profiles. The SBM model capturedkey distinguishing features of murine cardiomyocyte Ca handling, includ-ing shorter AP and Ca transient duration relative to rabbit, as well as agreater role of Ca release and uptake via the SR, as opposed to NCX(36).When we included sarcolemmal Ca leak data from Despa et al. . (7) ap-propriate for the +Amylin and HIP phenotypes in rats, as well as reducedSERCA Ca uptake rates for HIP, the computational model reproduced thealtered Ca transient amplitudes across a broad range of pacing intervals.With this model, we conclude that • increased rates of Ca influx through the sarcolemma, for instance asa result of amylin-induced membrane poration, promotes the amplifi-cation of cytosolic Ca transients. • the increase in Ca transient amplitude arises due to greater SR Ca load relative to control • elevated cytosolic Ca load stemming from higher rates of sarcolem-mal Ca influx (+Amylin), and especially when SERCA function isreduced (HIP), significantly increases the proportion of Ca -boundproteins. Of these proteins, CaM activation in particular may triggerremodeling via the calcineurin/NFAT pathway (37)(see Fig. 1). • the concerted relationship between amylin-induced increased sarcolem-mal Ca leak, intracellular Ca transients, and SR loading gives riseto similar Ca transient amplification in the Shannon-Bers model ofEC coupling in rabbit (20), which suggests similar mechanisms of dys-regulation in pre-diabetes may be manifest in higher order mammals. Enhanced SL Ca fluxes are sufficient to elevate cytosolicCa load in absence of altered SR Ca handling Recently, it was established that pre-diabetic rats transgenic for humanamylin peptide presented a high density of oligomerized amylin deposits mylinmylin leak rates and amplified Ca tran-sients. These effects on sarcolemmal Ca conductance and transient am-plitudes were recapitulated in isolated myocytes that were incubated withhuman amylin, which suggested that the phenotypical changes likely pre-cede any significant changes in protein expression that might otherwise pro-duce similar effects. Further, disruption of amylin oligomers via increasingeicosanoid serum levels (6) and the application of membrane sealant P188(Fig. 3) were both found to restore normal Ca handling. These exper-iments together firmly establish the link between oligomer-induced mem-brane poration and Ca dysregulation. Similarly, in our implementationof the Morotti-Shannon-Bers Ca cycling model, we found that amplifiedCa transients could be induced solely by increasing the sarcolemmal Ca conductance parameter (see Eq. 1).The enhancement of intracellular Ca transient amplitudes by amylinbears similarity to agonism of the sarcolemmal Ca channels LCC and P2X.It is well-established, for instance, that activation of LCC via β -adrenergicreceptor ( β AR) agonists promote larger Ca transients that are accompa-nied by elevated SR Ca load (14). Further, P2X receptor activation hascomparable effects on Ca transients and SR load (38), albeit without themultifarious changes in Ca handling associated with β AR stimulation.While we defer the topic of SR load to later in the Discussion, our simula-tions present strong evidence that increased inward sarcolemmal Ca aloneis sufficient to explain amylin dose-dependent effects on Ca transients in(7).For pacing intervals at 1 Hz and greater, our predictions of the controlCa transient using the SBM model (see Fig. S6) follow a neutral tran-sient amplitude/frequency relationship, as is frequently exhibited in mice(39) and the Despa et al. rat control data (7). Further, the computationalmodel captures the negative Ca transient relationships with pacing fre-quency reflected in the Despa et al. HIP rat data, including the diminishingdifference in transient amplitude relative to control at 2 Hz pacing. Thedecline in transient amplitude for HIP can be ascribed to the inability tomaintain elevated SR load as pacing increases, given the reduced SERCAactivity evident for these rats (7). Our data also reflect a negative transientamplitude/frequency relationship for the +Amylin conditions, which mayarise because the model does not reflect phosphorylation-dependent effectson relaxation, including CaMKII activation (40). Nevertheless, given thatour model captures the predominant changes in Ca handling exhibitedin +Amylin and HIP pre-diabetic rats (7) chiefly through modulating sar- mylinmylin leak, our simulations support the hypothesis that increasedSL Ca entry alone (without recruiting cation-specific channels like LCC)promotes the development of enhanced Ca transients (see Fig. 1). Contributions of SR loading to amylin phenotype
We demonstrated in Fig. S14 a positive correlation of increasing Ca SLleak rates with elevated SR Ca loading and transients, respectively, withpreserved SERCA function. This configuration is analogous to the +Amylinconditions assumed in this study. Therefore, the predicted amplification ofthe cytosolic Ca transients appears to be driven by Ca -loading of theSR, which in turn affords greater RyR Ca flux per release event. We notethat diastolic SR Ca load was modestly increased by approximately 10%relative to control under the +Amylin conditions. The increased SR load ap-peared to be of little consequence, as steady-state behavior was maintainedthrough several minutes of simulated pacing without evidence of DADs.These results concur with those of Campos et al. , for which computationalstudies of rabbit ventricular myocytes indicated considerable tolerance to SRCa overload before abnormal AP behavior was evident (41). Further, ourhypothesis is congruent with a study examining triggering of the SL Ca channel P2X4, which was found to yield both elevated Ca transients andSR Ca load (42).An interesting finding from our simulations, is that both +Amylin andHIP rats presented amplified Ca transients, despite the latter of whichhaving predicted diastolic SR Ca loads commensurate with the control(see Fig. S15). The notion that diastolic SR Ca loads are comparable forHIP and control has precedent, as insignificant changes in SR load relativeto control were reported in (7). We speculate that the higher diastoliccytosolic Ca exhibited in HIP may amplify RyR release (Fig. S4) viaCa -induced Ca release (43), which would ultimately yield larger Ca transients despite unchanged SR Ca load. Implications of elevated cytosolic Ca load An interesting consequence of elevated Ca transients and in the case ofHIP, increased diastolic Ca load, is the potential for activating Ca -dependent pathways that are normally quiescent during normal Ca han-dling. We observed in Fig. S13 for instance, that greater levels of Ca -bound CaM and TnC are evident relative to control. Under normal condi-tions, Ca activation of TnC is the critical substrate for force development mylinmylin
We demonstrated in Fig. S14 a positive correlation of increasing Ca SLleak rates with elevated SR Ca loading and transients, respectively, withpreserved SERCA function. This configuration is analogous to the +Amylinconditions assumed in this study. Therefore, the predicted amplification ofthe cytosolic Ca transients appears to be driven by Ca -loading of theSR, which in turn affords greater RyR Ca flux per release event. We notethat diastolic SR Ca load was modestly increased by approximately 10%relative to control under the +Amylin conditions. The increased SR load ap-peared to be of little consequence, as steady-state behavior was maintainedthrough several minutes of simulated pacing without evidence of DADs.These results concur with those of Campos et al. , for which computationalstudies of rabbit ventricular myocytes indicated considerable tolerance to SRCa overload before abnormal AP behavior was evident (41). Further, ourhypothesis is congruent with a study examining triggering of the SL Ca channel P2X4, which was found to yield both elevated Ca transients andSR Ca load (42).An interesting finding from our simulations, is that both +Amylin andHIP rats presented amplified Ca transients, despite the latter of whichhaving predicted diastolic SR Ca loads commensurate with the control(see Fig. S15). The notion that diastolic SR Ca loads are comparable forHIP and control has precedent, as insignificant changes in SR load relativeto control were reported in (7). We speculate that the higher diastoliccytosolic Ca exhibited in HIP may amplify RyR release (Fig. S4) viaCa -induced Ca release (43), which would ultimately yield larger Ca transients despite unchanged SR Ca load. Implications of elevated cytosolic Ca load An interesting consequence of elevated Ca transients and in the case ofHIP, increased diastolic Ca load, is the potential for activating Ca -dependent pathways that are normally quiescent during normal Ca han-dling. We observed in Fig. S13 for instance, that greater levels of Ca -bound CaM and TnC are evident relative to control. Under normal condi-tions, Ca activation of TnC is the critical substrate for force development mylinmylin β -adrenergic stimulation (45). However, it isalso implicated in the activation of pathways associated with remodeling andfailure (13). In particular, activation of the CaM-regulated CaMKII is at-tributed to cardiac remodeling via the HDAC pathway Concurrently, activa-tion of the phosphatase calcineurin via CaM is known to promote transcrip-tional changes by way of NFAT activation (46), which together contribute tothe hypertrophic response to dysregulated Ca handling (47). Indeed, inpre-diabetic HIP there was evidence that CaMKII-HDAC and calciuneurin-NFAT remodeling were simultaneously activated (7). In this regard, whilethe increased Ca transients stemming from amylin oligomerization mayinitially have beneficial inotropic effects, activation of CaM and its depen-dent hypertrophic pathways may contribute to cardiac decline. Limitations
Our model was based on a rather modest set of changes in Ca , Na + andK + handling to a rabbit ventricular cardiomyocyte formulation. Furtherrefinement of rat electrophysiology (48, 49) and implementation of a recentrat /catwo/ handling model (50), could provide improved predictive powerfor our model of amylin-induced dysregulation. In the greater context ofdiabetes, it is likely that the Ca dysregulation and subsequent activationof CaMKII sets forth a cascade of maladaptive events that drive heart failure.As such, our simulation results could be improved by including the impactof altered protein kinase A (PKA) and CaMKII activity on Ca handling.Here, tuning the full Morotti model (24), which explicitly considers PKAand CaMKIIsignaling, to reflect excitation-contraction coupling in rats maybe appropriate. Conclusions
Our predictions of elevated calcium transients under enhanced SL Ca leak(via amylin oligomers) relative to control are in qualitative agreement withfindings from Despa et al. (7). Further, these simulations suggest a potentialmechanism linking human amylin infiltration of cardiac sarcolemma, am-plification of intracellular Ca transients and potential activation of CaM-dependent remodeling pathways; namely, amylin-induced increases in SLCa leak potentially dually elevate Ca load in the cytosol and sarcoplas-mic reticulum. Increased sarcoplasmic reticulum Ca content facilitatesCa release, while elevated cytosolic Ca levels promote the activation of mylinmylin
Our predictions of elevated calcium transients under enhanced SL Ca leak(via amylin oligomers) relative to control are in qualitative agreement withfindings from Despa et al. (7). Further, these simulations suggest a potentialmechanism linking human amylin infiltration of cardiac sarcolemma, am-plification of intracellular Ca transients and potential activation of CaM-dependent remodeling pathways; namely, amylin-induced increases in SLCa leak potentially dually elevate Ca load in the cytosol and sarcoplas-mic reticulum. Increased sarcoplasmic reticulum Ca content facilitatesCa release, while elevated cytosolic Ca levels promote the activation of mylinmylin -dependent proteins, including CaM. The latter effect may potentiallycontribute to the CaM-dependent activation of NFAT/HDAC pathways re-ported in (7). Given that human amylin oligomers have been shown todeposit in cell types including cardiac, neuronal, microglia, and beta cells(2, 7, 10, 35), the effects of amylin-induced Ca dysregulation may gener-alize to a variety of pathologies in higher animals. Acknowledgments
PKH thanks the University of Kentucky for pilot grant support, as wellas a grant from the National Institute of General Medical Science (P20GM103527) of the National Institutes of Health. This work was also sup-ported by the National Institutes of Health (R01HL118474 to FD and R01HL109501to SD) and The National Science Foundation (CBET 1357600 to FD). mylinmylin
PKH thanks the University of Kentucky for pilot grant support, as wellas a grant from the National Institute of General Medical Science (P20GM103527) of the National Institutes of Health. This work was also sup-ported by the National Institutes of Health (R01HL118474 to FD and R01HL109501to SD) and The National Science Foundation (CBET 1357600 to FD). mylinmylin References
1. Westermark, P., A. Andersson, and G. T. Westermark, 2011. Islet amy-loid polypeptide, islet amyloid, and diabetes mellitus.
Physiological re-views β Synthesis in Brains of Alzheimer’sDisease Patients with Type-2 Diabetes and in Diabetic HIP Rats.
Jour-nal of Alzheimer’s Disease β Synthesis in the Heartvia Peroxidative Sarcolemmal Injury.
Diabetes β through membrane fragmentation and pore formation. Biophys-ical journal
Journal of BiologicalChemistry
Journal of the American Heart Association
Circulation Research
Proceedings of the NationalAcademy of Sciences of the United States of America mylinmylin
Proceedings of the NationalAcademy of Sciences of the United States of America mylinmylin
The American journal of physiology
Endocrine reviews
Diabetologia β Species on LipidBilayers.
Biochemistry
Biochemical Societytransactions
Biophysical Journal
Journal of Molecular and CellularCardiology
Current Opinion inStructural Biology
ScienceTranslational Medicine mylinmylin
ScienceTranslational Medicine mylinmylin
AJP: Heart and CirculatoryPhysiology
Biophysical Journal
Circulation
The American journal of physiology
The Journal of Physiology
The Journal of physiology
The Journal ofPhysiology
Siam Journal onScientific and Statistical Computing
Computer
Biochimica et biophysica acta mylinmylin
Biochimica et biophysica acta mylinmylin
Diabetes
Journal of molecular and cellular cardiology
The Journal of cell biology
Biophysical Journal
The Journal of general physiology
The Journal of generalphysiology
Neuropharmacology
Nature
Biochemical and BiophysicalResearch Communications
The FASEB Journal mylinmylin
The FASEB Journal mylinmylin
The Journal ofphysiology
The American journal of physiology
Cardiovascular research
Chemical Engineering Science
The Journal of general physiology
Physiological Reviews
Journal ofmolecular and cellular cardiology
Journal of molecular and cellular cardiology
Annual review of physiology
The Japanese journal of phys-iology
Comparativebiochemistry and physiology. Part A, Molecular & integrative physiology mylinmylin
Comparativebiochemistry and physiology. Part A, Molecular & integrative physiology mylinmylin
The Journal of Physiology δ c in RyR2R4496C+/ Knock-In MiceLeads to Altered Intracellular Ca2+ Handling and Increased Mortality. Journal of the American College of Cardiology < i > Serca2 < /i > knockout. The Journalof Physiology
Journal of molecular and cellularcardiology
TheJournal of Physiology
Cardiovascular Research
Circulationresearch
BiophysicalJournal mylinmylin
BiophysicalJournal mylinmylin
Frontiers in physiology
Bio-physical Journal
Journalof the American Heart Association
Molecules and Cells mylinmylin
Molecules and Cells mylinmylin Supplement
Supplemental Results
Validation of murine SB modelPotassium channel equations
Among the most significant changes inthe murine-specific Morotti model relative to the Shannon-Bers rabbit ven-tricular myocyte system are the phenomological representations of K + chan-nel currents. In Fig. S2 we compare time-dependent current profiles for nineof the prominent K + channels. Nearly all channels required minor param-eter changes to correspond to murine species ( i Kp, i NaK, i K1, i Kr, i tof, i Ks,and i tos, of which the latter two were inactive in mice); however, two chan-nels, i ss and i kur, were not included in the Shannon-Bers model and arethus implemented here. Following Morotti et al. (24), i ss (Eq. S4d) and i kur (Eq. S1a) were parameterized as follows: IKur (S1a) i KurP KAp = y i KurtotBA (S1b) a Kur = 0 . − fIKurpISOfIKurp (S1c) f IKuravail = 1 − a Kur + a Kur f IKurp i KurP KAp (S1d) f IKuravail = 1 (S1e) i kur = Gkur Kcoef f f IKuravail ( − E K + V ) X Kurslow Y Kurslow (S1f) i kur = Gkur Kcoef f ( − E K + V ) X Kurslow Y Kurslow (S1g) i kur = i kur + i kur Xkur gate mylinmylin
Among the most significant changes inthe murine-specific Morotti model relative to the Shannon-Bers rabbit ven-tricular myocyte system are the phenomological representations of K + chan-nel currents. In Fig. S2 we compare time-dependent current profiles for nineof the prominent K + channels. Nearly all channels required minor param-eter changes to correspond to murine species ( i Kp, i NaK, i K1, i Kr, i tof, i Ks,and i tos, of which the latter two were inactive in mice); however, two chan-nels, i ss and i kur, were not included in the Shannon-Bers model and arethus implemented here. Following Morotti et al. (24), i ss (Eq. S4d) and i kur (Eq. S1a) were parameterized as follows: IKur (S1a) i KurP KAp = y i KurtotBA (S1b) a Kur = 0 . − fIKurpISOfIKurp (S1c) f IKuravail = 1 − a Kur + a Kur f IKurp i KurP KAp (S1d) f IKuravail = 1 (S1e) i kur = Gkur Kcoef f f IKuravail ( − E K + V ) X Kurslow Y Kurslow (S1f) i kur = Gkur Kcoef f ( − E K + V ) X Kurslow Y Kurslow (S1g) i kur = i kur + i kur Xkur gate mylinmylin X Kurslowss = 11 + 0 . e − . × − V (S2b) τ Xkur = 0 .
95 + 50 × − e − × − V (S2c) dX Kurslow dt = 1 τ Xkur ( − X Kurslow + X Kurslowss ) Ykur gate (S3a) Y Kurslowss = 11 + 2 . × e . V (S3b) τ Y kur = 400 − × − e − . V + 900 e − ( . . × − V ) (S3c) dY Kurslow dt = 1 τ Y kur ( − Y Kurslow + Y Kurslowss ) (S3d) τ Y kur = 400 + 5501 + 553 × − e − . V + 900 e − ( . . × − V ) (S3e) dY Kurslow dt = 1 τ Y kur ( − Y Kurslow + Y Kurslowss ) Xss gate (S4a) xssss = X Kurslowss (S4b) tauxss = 14 + 70 e − ( . . × − V ) (S4c) dXssdt = 1 tauxss ( − Xss + xssss ) (S4d) i ss = GssKcoef f ( − E K + V ) Xss mylinmylin
95 + 50 × − e − × − V (S2c) dX Kurslow dt = 1 τ Xkur ( − X Kurslow + X Kurslowss ) Ykur gate (S3a) Y Kurslowss = 11 + 2 . × e . V (S3b) τ Y kur = 400 − × − e − . V + 900 e − ( . . × − V ) (S3c) dY Kurslow dt = 1 τ Y kur ( − Y Kurslow + Y Kurslowss ) (S3d) τ Y kur = 400 + 5501 + 553 × − e − . V + 900 e − ( . . × − V ) (S3e) dY Kurslow dt = 1 τ Y kur ( − Y Kurslow + Y Kurslowss ) Xss gate (S4a) xssss = X Kurslowss (S4b) tauxss = 14 + 70 e − ( . . × − V ) (S4c) dXssdt = 1 tauxss ( − Xss + xssss ) (S4d) i ss = GssKcoef f ( − E K + V ) Xss mylinmylin transients(a-b), as well as sodium load (c) and action potential (d). The SBM imple-mentation exhibits, for instance, modestly higher Ca transients in both thecytosol and SR, higher intracellular Na + load and a significantly shorter AP,in comparison to data predicted for rabbit Ca handling. The decreasedaction potential largely stems from reparameterization of the potassium cur-rents defined above, the currents of which we summarize in Fig. S2. Thesemodel predictions are in quantitative agreement with corresponding currentprofiles presented in the Morotti et al. supplemental data (24), which werebased on transient data from Dybkova et al. (51). We present analogouscurrent data for i Na, i CaL, and i NaCa, which again are in quantitativeagreement with Morotti et al. . Altogether, these predictions indicate thatour implementation of the Morotti model faithfully reproduces the murineelectrophysiology and Ca handling. This implementation serves as thebasis for our further refinement to reflect the rat Ca dynamics. Maintenance of sodium load
In the context of Ca handling, Na + serves an important role in both ex-truding cytosolic Ca in its ’forward’ mode, as well as promoting Ca influx during its brief ’reverse’ mode (14). Sodium load exceeding normalphysiological ranges (approximately 9-14 mM in rodents), for instance, cancontribute to diastolic dysfunction (52, 53), predominantly by impairingNCX Ca extrusion (54). Conversely, the NCX reverse mode may leverageNa + gradients to amplify sarcolemmal Ca transients and thereby prime SRCa release (15, 55–58).While our measurements of Na + -load in +Amylinrats indicated that intracellular Na + was within normal ranges, numericalpredictions suggested that loading may be elevated under conditions of in-creased sarcolemmal Ca leak with constant NKA function. Therefore tomaintain predicted Na + transients within control levels, a modest increasein NKA Vmax was predicted. On one hand, there is precedent for smallpeptides like insulin partitioning into the rat skeletal transverse tubule sys-tem (59), as well agonism of NKA activity due to amylin (25). However,for rat cardiac ventricular tissues, these changes in NKA function may benon-existent or below the limits of experimental detection at least in fully-developed diabetes (60). mylinmylin
In the context of Ca handling, Na + serves an important role in both ex-truding cytosolic Ca in its ’forward’ mode, as well as promoting Ca influx during its brief ’reverse’ mode (14). Sodium load exceeding normalphysiological ranges (approximately 9-14 mM in rodents), for instance, cancontribute to diastolic dysfunction (52, 53), predominantly by impairingNCX Ca extrusion (54). Conversely, the NCX reverse mode may leverageNa + gradients to amplify sarcolemmal Ca transients and thereby prime SRCa release (15, 55–58).While our measurements of Na + -load in +Amylinrats indicated that intracellular Na + was within normal ranges, numericalpredictions suggested that loading may be elevated under conditions of in-creased sarcolemmal Ca leak with constant NKA function. Therefore tomaintain predicted Na + transients within control levels, a modest increasein NKA Vmax was predicted. On one hand, there is precedent for smallpeptides like insulin partitioning into the rat skeletal transverse tubule sys-tem (59), as well agonism of NKA activity due to amylin (25). However,for rat cardiac ventricular tissues, these changes in NKA function may benon-existent or below the limits of experimental detection at least in fully-developed diabetes (60). mylinmylin Up-regulated SL currents (via LCC) have dissimilar phenotype toamylin action
The dominant effect of amylin appears to be its enhancement of non-selectiveSL Ca currents, although there are reports that amyloidogenic peptidescan alter LCC regulation (61). To delineate this contribution from sec-ondary agonism of SL Ca channel activity, we performed simulations us-ing an amplified i CaL sufficient to reproduce the Ca transients observedfor enhanced SL Ca leak. We emphasize here that LCC current/volt-age relationship is indeed preserved in HIP rats (as shown in Fig. S16).Similar to +Amylin, increased LCC current yielded increased intracellularCa transients, elevated SR Ca load, and increased diastolic Ca load.Nevertheless, we identified distinct patterns of modulated channel activityfor increased LCC relative to those presented for the +Amylin configura-tion. Namely, our models indicate amylin-induced Ca leak amplifies i Na,whereas in contrast, increased LCC conductance inflates the amplitudes ofseveral prominent K + channels. While the predicted channel currents havea complex dependence on ion-sensitive gating probabilities, these findingsraise interesting possibilities that different modes of Ca entry could inprinciple yield distinct influences on channels controlling the action poten-tial. Nevertheless, under the conditions considered in this study, our mod-eling data (see Fig. S9 and Fig. S15) suggest that the modest perturbationsin ion channel conductance under the +Amylin and LCC configurations didnot appreciably impact the action potential duration (APD). These findingsare consistent with preserved APD upon P2X stimulation reported in Fig 6of (42). Genetic algorithm for fitting
In order to optimize model fitting to the experimentally measured cases, agenetic algorithm was written to fit the model to various cases. For example,in regards to the Amylin case, we randomized the NKA current parameterto find what value that gave the closest steady state value of 12 mM forthe intracellular Na + over 30s of simulation time. A starting value for NKAcurrent (5 µ A µ F − ) was given with a generous starting standard deviation(0.5) to randomize within. The standard deviation value was done as alognormal distribution to ensure that reductions and increases of N% wereequally probable. A total of 30 random draws were made. Once the randomdraws were made, they were submitted to be run using CPUs. After the jobfinished, an error value was calculated for comparing an output of the system mylinmylin
In order to optimize model fitting to the experimentally measured cases, agenetic algorithm was written to fit the model to various cases. For example,in regards to the Amylin case, we randomized the NKA current parameterto find what value that gave the closest steady state value of 12 mM forthe intracellular Na + over 30s of simulation time. A starting value for NKAcurrent (5 µ A µ F − ) was given with a generous starting standard deviation(0.5) to randomize within. The standard deviation value was done as alognormal distribution to ensure that reductions and increases of N% wereequally probable. A total of 30 random draws were made. Once the randomdraws were made, they were submitted to be run using CPUs. After the jobfinished, an error value was calculated for comparing an output of the system mylinmylin + ) against the experimentally determined valueby squaring the result minus the experiment value.This gave a ”job fitness” score that was used to determine which randomdraw was the best. jobF itness = ( X i,exp − X i,truth ) (S5)The job that had the best ”job fitness” score was now selected as the newstarting value to have jobs randomized around for the next iteration. Thestandard deviation was then adjusted by multiplying the input standarddeviation by e to the negative iteration number times a scaler. σ i = σ e − iσ scaler (S6)This new standard deviation determined the range of random draws aroundthe new starting value given from the first iteration of the code. This processwas then continued for several different iterations (20) to converge to asingle value of the NKA current which would also give an output value forintracellular Na + to match that of the experimentally given value. Anexample plot of the convergence of the NKA current value over number ofiterations can be seen in Fig. S18. The graph shows how after the amount ofiterations increased, the value of the NKA current converged. This value ofthe NKA current was then used within the simulation and the intracellularNa + value was compared to the baseline case to match experiment. Thisplot can be see in Fig. S9. Since the value found for the NKA currentusing the genetic algorithm gave an intracellular Na + comparable to that ofexperiment, it can be seen that the generic algorithm worked as expected. Comparison of parameter sensitivitySensitivity analyses
We determined the sensitivity of SBM model out-puts including Ca amplitude, cytosolic Na + , SR Ca , diastolic Ca ,APD, and Ca transient decay ( τ ) to the model parameters, by randomiz-ing model parameters temperature, background Ca leak, background Na + leak, SERCA function, NKA function, and PCa. Each parameter was ran-domized independently, while holding all other parameters at their defaultvalues for the rat model.The random draw was done within a standard deviation value of 10%of the given input value based on the baseline rat data. This was done fora total of 10 times to get 10 random draws for the parameter. Once the10 random draws were done for the chosen parameter, the program moved mylinmylin
We determined the sensitivity of SBM model out-puts including Ca amplitude, cytosolic Na + , SR Ca , diastolic Ca ,APD, and Ca transient decay ( τ ) to the model parameters, by randomiz-ing model parameters temperature, background Ca leak, background Na + leak, SERCA function, NKA function, and PCa. Each parameter was ran-domized independently, while holding all other parameters at their defaultvalues for the rat model.The random draw was done within a standard deviation value of 10%of the given input value based on the baseline rat data. This was done fora total of 10 times to get 10 random draws for the parameter. Once the10 random draws were done for the chosen parameter, the program moved mylinmylin < Sensitivity results
Inputs that had at least one significant associationwith any of the outputs included: Background Ca leak (Λ = 0.039,F(5,49) = 242.804, η = 0.961), background Na + leak (Λ = 0.009, F(5,49)= 1,097.591, η = 0.991), NKA Vmax (Λ = 0.001, F(5,49) = 12,009.757, η = 0.999), PCa (Λ = 0.002, F(5,49) = 5,906.809, η = 0.998), T (Λ = 0.002,F(5,49) = 5,145.939, η = 0.998), and SERCA Vmax (Λ = 0.014, F(5,49)= 708.322, η = 0.986). Thus, inputs respectively accounted for 96% ormore variation in the best linear combination of outputs (all η (cid:61) leak and increasing backgroundNa + leak, there was only a significant association with increasing Nai (partial η ( η p ) = 0.568, p < η p = 0.829, p < η p = 0.981, p < η p = 0.929, p < η p = 0.694, p < η p = 0.951, p < ( η p = 0.058, p = 0.076).Increased SERCA Vmax was significantly associated with increased APD( η p = 0.166, p = 0.002), increased SR Ca ( η p = 0.138, p = 0.005), anddecreased Nai ( η p = 0.354, p < mylinmylin
Inputs that had at least one significant associationwith any of the outputs included: Background Ca leak (Λ = 0.039,F(5,49) = 242.804, η = 0.961), background Na + leak (Λ = 0.009, F(5,49)= 1,097.591, η = 0.991), NKA Vmax (Λ = 0.001, F(5,49) = 12,009.757, η = 0.999), PCa (Λ = 0.002, F(5,49) = 5,906.809, η = 0.998), T (Λ = 0.002,F(5,49) = 5,145.939, η = 0.998), and SERCA Vmax (Λ = 0.014, F(5,49)= 708.322, η = 0.986). Thus, inputs respectively accounted for 96% ormore variation in the best linear combination of outputs (all η (cid:61) leak and increasing backgroundNa + leak, there was only a significant association with increasing Nai (partial η ( η p ) = 0.568, p < η p = 0.829, p < η p = 0.981, p < η p = 0.929, p < η p = 0.694, p < η p = 0.951, p < ( η p = 0.058, p = 0.076).Increased SERCA Vmax was significantly associated with increased APD( η p = 0.166, p = 0.002), increased SR Ca ( η p = 0.138, p = 0.005), anddecreased Nai ( η p = 0.354, p < mylinmylin Supplemental Tables mylinmylin
Inputs that had at least one significant associationwith any of the outputs included: Background Ca leak (Λ = 0.039,F(5,49) = 242.804, η = 0.961), background Na + leak (Λ = 0.009, F(5,49)= 1,097.591, η = 0.991), NKA Vmax (Λ = 0.001, F(5,49) = 12,009.757, η = 0.999), PCa (Λ = 0.002, F(5,49) = 5,906.809, η = 0.998), T (Λ = 0.002,F(5,49) = 5,145.939, η = 0.998), and SERCA Vmax (Λ = 0.014, F(5,49)= 708.322, η = 0.986). Thus, inputs respectively accounted for 96% ormore variation in the best linear combination of outputs (all η (cid:61) leak and increasing backgroundNa + leak, there was only a significant association with increasing Nai (partial η ( η p ) = 0.568, p < η p = 0.829, p < η p = 0.981, p < η p = 0.929, p < η p = 0.694, p < η p = 0.951, p < ( η p = 0.058, p = 0.076).Increased SERCA Vmax was significantly associated with increased APD( η p = 0.166, p = 0.002), increased SR Ca ( η p = 0.138, p = 0.005), anddecreased Nai ( η p = 0.354, p < mylinmylin Supplemental Tables mylinmylin T a b l e S : C o m p a r i s o n o f S B d e f a u l t p a r a m e t e r s w i t h m o u s e - s p ec i fi c v a r i a t i o n s i n a cc o r d a n ce t o M o r o tt i e t a l. ( ) P l a ce s w i t h * r e p r e s e n tt h e v a l u e w a s fi tt e du s i n go u r G A t o m a t c h c o rr e s p o nd i n g e x p e r i m e n t a l d a t a . P a r a m e t e r [ un i t s ] N a m e R a bb i t M o u s e R a t M e m b r a n ec a p a c i t a n ce [ F ] C m . × − . × − - C e ll v o l u m e [ L ] V C e ll . × − . × − ( ) - I n t r a ce ll u l a r N a + [ m M ] N a i . . . F r eec o n ce n t r a t i o n o f C a + [ C a ] o . . - i n e x t r a ce ll u l a r c o m p a r t m e n t [ m M ] M a x i m a l c o ndu c t a n ce o f flu x f o r G I N a - f a s t N a + c u rr e n t [ m S µ F − ] J un c t i o n a l p a r t i t i o n i n g F X i j un c t i o n . . - S a r c o l e mm a l p a r t i t i o n i n g F X i s a r c o l e mm a l . . - B a c k g r o und N a + l e a k [ m S µ F − ] G N a B k . × − . × − - K ˙ m o f N a + - C a + e x c h a n g e r f o r N a + [ m M ] K m N a i - M a x c u rr e n t o f t h e N a + - K + pu m p [ µ A µ F − ] I N a K m a x . . S l o w a c t i v a t i n g d e l a y e d r ec t i fi e r c u rr e n t G K s . . - S l o w i n a c t i v a t i n g d e l a y e d r ec t i fi e r c u rr e n t [ nSp F − ] G k u r N / A . - S l o w i n a c t i v a t i n g d e l a y e d r ec t i fi e r c u rr e n t [ nSp F − ] G k u r N / A . - i ss c o ndu c t a n ce [ nSp F − ] G ss N / A . - V e l o c i t y m a x f o r N a + - C a + e x c h a n g e r [ µ A µ F − ] V m a x I N a C a - A ll o s t e r i c C a + a c t i v a t i o n c o n s t a n t [ m M ] K d − A c t . × − . × − - B a c k g r o und C a + l e a k [ m S µ F − ] G C a B k . × − . × − - S R C a + c o n ce n t r a t i o nd e p e nd e n t a c t i v a t i o n o f S R C a + r e l e a s e [ m M ] E C − S R . . - P a ss i v e l e a k i n t h e S R m e m b r a n e [ m s − ] K S R l e a k . × − . × − - V e l o c i t y m a x f o r S R C a + pu m pflu x [ m M m s − ] V m a x J p u m p . × − ** K m S R C a + pu m p f o r w a r d m o d e [ m M ] K m f . × − × − - K m S R C a + pu m p r e v e r s e m o d e [ m M ] K m r . . - L - t y p e C a + c h a nn e l C a + p e r m e a b ili t y [ L F − m s − ] P C a . × − . × − - L - t y p e C a + c h a nn e l N a + p e r m e a b ili t y [ L F − m s − ] P N a . × − . × − - L - t y p e C a + c h a nn e l K + p e r m e a b ili t y [ L F − m s − ] P K . × − . × − - B a c k g r o und C a + l e a k [ m S µ F − ] G C a B k . × − . × − - mylinmylin
Inputs that had at least one significant associationwith any of the outputs included: Background Ca leak (Λ = 0.039,F(5,49) = 242.804, η = 0.961), background Na + leak (Λ = 0.009, F(5,49)= 1,097.591, η = 0.991), NKA Vmax (Λ = 0.001, F(5,49) = 12,009.757, η = 0.999), PCa (Λ = 0.002, F(5,49) = 5,906.809, η = 0.998), T (Λ = 0.002,F(5,49) = 5,145.939, η = 0.998), and SERCA Vmax (Λ = 0.014, F(5,49)= 708.322, η = 0.986). Thus, inputs respectively accounted for 96% ormore variation in the best linear combination of outputs (all η (cid:61) leak and increasing backgroundNa + leak, there was only a significant association with increasing Nai (partial η ( η p ) = 0.568, p < η p = 0.829, p < η p = 0.981, p < η p = 0.929, p < η p = 0.694, p < η p = 0.951, p < ( η p = 0.058, p = 0.076).Increased SERCA Vmax was significantly associated with increased APD( η p = 0.166, p = 0.002), increased SR Ca ( η p = 0.138, p = 0.005), anddecreased Nai ( η p = 0.354, p < mylinmylin Supplemental Tables mylinmylin T a b l e S : C o m p a r i s o n o f S B d e f a u l t p a r a m e t e r s w i t h m o u s e - s p ec i fi c v a r i a t i o n s i n a cc o r d a n ce t o M o r o tt i e t a l. ( ) P l a ce s w i t h * r e p r e s e n tt h e v a l u e w a s fi tt e du s i n go u r G A t o m a t c h c o rr e s p o nd i n g e x p e r i m e n t a l d a t a . P a r a m e t e r [ un i t s ] N a m e R a bb i t M o u s e R a t M e m b r a n ec a p a c i t a n ce [ F ] C m . × − . × − - C e ll v o l u m e [ L ] V C e ll . × − . × − ( ) - I n t r a ce ll u l a r N a + [ m M ] N a i . . . F r eec o n ce n t r a t i o n o f C a + [ C a ] o . . - i n e x t r a ce ll u l a r c o m p a r t m e n t [ m M ] M a x i m a l c o ndu c t a n ce o f flu x f o r G I N a - f a s t N a + c u rr e n t [ m S µ F − ] J un c t i o n a l p a r t i t i o n i n g F X i j un c t i o n . . - S a r c o l e mm a l p a r t i t i o n i n g F X i s a r c o l e mm a l . . - B a c k g r o und N a + l e a k [ m S µ F − ] G N a B k . × − . × − - K ˙ m o f N a + - C a + e x c h a n g e r f o r N a + [ m M ] K m N a i - M a x c u rr e n t o f t h e N a + - K + pu m p [ µ A µ F − ] I N a K m a x . . S l o w a c t i v a t i n g d e l a y e d r ec t i fi e r c u rr e n t G K s . . - S l o w i n a c t i v a t i n g d e l a y e d r ec t i fi e r c u rr e n t [ nSp F − ] G k u r N / A . - S l o w i n a c t i v a t i n g d e l a y e d r ec t i fi e r c u rr e n t [ nSp F − ] G k u r N / A . - i ss c o ndu c t a n ce [ nSp F − ] G ss N / A . - V e l o c i t y m a x f o r N a + - C a + e x c h a n g e r [ µ A µ F − ] V m a x I N a C a - A ll o s t e r i c C a + a c t i v a t i o n c o n s t a n t [ m M ] K d − A c t . × − . × − - B a c k g r o und C a + l e a k [ m S µ F − ] G C a B k . × − . × − - S R C a + c o n ce n t r a t i o nd e p e nd e n t a c t i v a t i o n o f S R C a + r e l e a s e [ m M ] E C − S R . . - P a ss i v e l e a k i n t h e S R m e m b r a n e [ m s − ] K S R l e a k . × − . × − - V e l o c i t y m a x f o r S R C a + pu m pflu x [ m M m s − ] V m a x J p u m p . × − ** K m S R C a + pu m p f o r w a r d m o d e [ m M ] K m f . × − × − - K m S R C a + pu m p r e v e r s e m o d e [ m M ] K m r . . - L - t y p e C a + c h a nn e l C a + p e r m e a b ili t y [ L F − m s − ] P C a . × − . × − - L - t y p e C a + c h a nn e l N a + p e r m e a b ili t y [ L F − m s − ] P N a . × − . × − - L - t y p e C a + c h a nn e l K + p e r m e a b ili t y [ L F − m s − ] P K . × − . × − - B a c k g r o und C a + l e a k [ m S µ F − ] G C a B k . × − . × − - mylinmylin i Cl(Ca) Ca -activated chloride current i Clb Background Cl current i Cap SL-Ca pump i CaB Background Ca leak i NaB Background Na + leak i NaK NKA current i tof fast Cardiac transient outward potassium i tos slow Cardiac transient outward potassium i Kr the ’rapid’ delayed rectifier current i Ks slowly activating K+ current i K1 inward rectifier K+ current i Kp plateau potassium current i kur slowly inactivating outward i ss non-inactivating steady-state K+ current i CaL LCC channel current i NaCa NCX current i Na Na + current SL Na SL Na + jct + I RyR inactive gateO RyR open gateCai cytosolic Ca V Action potentialTable S2: Model terms. mylinmylin
Inputs that had at least one significant associationwith any of the outputs included: Background Ca leak (Λ = 0.039,F(5,49) = 242.804, η = 0.961), background Na + leak (Λ = 0.009, F(5,49)= 1,097.591, η = 0.991), NKA Vmax (Λ = 0.001, F(5,49) = 12,009.757, η = 0.999), PCa (Λ = 0.002, F(5,49) = 5,906.809, η = 0.998), T (Λ = 0.002,F(5,49) = 5,145.939, η = 0.998), and SERCA Vmax (Λ = 0.014, F(5,49)= 708.322, η = 0.986). Thus, inputs respectively accounted for 96% ormore variation in the best linear combination of outputs (all η (cid:61) leak and increasing backgroundNa + leak, there was only a significant association with increasing Nai (partial η ( η p ) = 0.568, p < η p = 0.829, p < η p = 0.981, p < η p = 0.929, p < η p = 0.694, p < η p = 0.951, p < ( η p = 0.058, p = 0.076).Increased SERCA Vmax was significantly associated with increased APD( η p = 0.166, p = 0.002), increased SR Ca ( η p = 0.138, p = 0.005), anddecreased Nai ( η p = 0.354, p < mylinmylin Supplemental Tables mylinmylin T a b l e S : C o m p a r i s o n o f S B d e f a u l t p a r a m e t e r s w i t h m o u s e - s p ec i fi c v a r i a t i o n s i n a cc o r d a n ce t o M o r o tt i e t a l. ( ) P l a ce s w i t h * r e p r e s e n tt h e v a l u e w a s fi tt e du s i n go u r G A t o m a t c h c o rr e s p o nd i n g e x p e r i m e n t a l d a t a . P a r a m e t e r [ un i t s ] N a m e R a bb i t M o u s e R a t M e m b r a n ec a p a c i t a n ce [ F ] C m . × − . × − - C e ll v o l u m e [ L ] V C e ll . × − . × − ( ) - I n t r a ce ll u l a r N a + [ m M ] N a i . . . F r eec o n ce n t r a t i o n o f C a + [ C a ] o . . - i n e x t r a ce ll u l a r c o m p a r t m e n t [ m M ] M a x i m a l c o ndu c t a n ce o f flu x f o r G I N a - f a s t N a + c u rr e n t [ m S µ F − ] J un c t i o n a l p a r t i t i o n i n g F X i j un c t i o n . . - S a r c o l e mm a l p a r t i t i o n i n g F X i s a r c o l e mm a l . . - B a c k g r o und N a + l e a k [ m S µ F − ] G N a B k . × − . × − - K ˙ m o f N a + - C a + e x c h a n g e r f o r N a + [ m M ] K m N a i - M a x c u rr e n t o f t h e N a + - K + pu m p [ µ A µ F − ] I N a K m a x . . S l o w a c t i v a t i n g d e l a y e d r ec t i fi e r c u rr e n t G K s . . - S l o w i n a c t i v a t i n g d e l a y e d r ec t i fi e r c u rr e n t [ nSp F − ] G k u r N / A . - S l o w i n a c t i v a t i n g d e l a y e d r ec t i fi e r c u rr e n t [ nSp F − ] G k u r N / A . - i ss c o ndu c t a n ce [ nSp F − ] G ss N / A . - V e l o c i t y m a x f o r N a + - C a + e x c h a n g e r [ µ A µ F − ] V m a x I N a C a - A ll o s t e r i c C a + a c t i v a t i o n c o n s t a n t [ m M ] K d − A c t . × − . × − - B a c k g r o und C a + l e a k [ m S µ F − ] G C a B k . × − . × − - S R C a + c o n ce n t r a t i o nd e p e nd e n t a c t i v a t i o n o f S R C a + r e l e a s e [ m M ] E C − S R . . - P a ss i v e l e a k i n t h e S R m e m b r a n e [ m s − ] K S R l e a k . × − . × − - V e l o c i t y m a x f o r S R C a + pu m pflu x [ m M m s − ] V m a x J p u m p . × − ** K m S R C a + pu m p f o r w a r d m o d e [ m M ] K m f . × − × − - K m S R C a + pu m p r e v e r s e m o d e [ m M ] K m r . . - L - t y p e C a + c h a nn e l C a + p e r m e a b ili t y [ L F − m s − ] P C a . × − . × − - L - t y p e C a + c h a nn e l N a + p e r m e a b ili t y [ L F − m s − ] P N a . × − . × − - L - t y p e C a + c h a nn e l K + p e r m e a b ili t y [ L F − m s − ] P K . × − . × − - B a c k g r o und C a + l e a k [ m S µ F − ] G C a B k . × − . × − - mylinmylin i Cl(Ca) Ca -activated chloride current i Clb Background Cl current i Cap SL-Ca pump i CaB Background Ca leak i NaB Background Na + leak i NaK NKA current i tof fast Cardiac transient outward potassium i tos slow Cardiac transient outward potassium i Kr the ’rapid’ delayed rectifier current i Ks slowly activating K+ current i K1 inward rectifier K+ current i Kp plateau potassium current i kur slowly inactivating outward i ss non-inactivating steady-state K+ current i CaL LCC channel current i NaCa NCX current i Na Na + current SL Na SL Na + jct + I RyR inactive gateO RyR open gateCai cytosolic Ca V Action potentialTable S2: Model terms. mylinmylin T a b l e S : P a r a m e t e r s u s e d i nS B M c o m pu t a t i o n a l m o d e l t o r e fl ec t c o n t r o l a ndh y p e r a m y li n e m i a/ p r e - d i a b e t i c r a t . P e r ce n t ag e s i np a r e n t h e s e s a r e r e l a t i v e t o c o n t r o l r a t . I f r o m ( ) . II f r o m ( ) . III fi tt e d t o ( ) . I V fi tt e d t o ( ) . C a s e S a r c o l e mm a ll e a k S E R C AN K A P C a G C a V m a x I N K A m a x ( m S / µ F )( m M / m s )( µ A / µ F ) c o n t r o l II . × − I V . × − III . + A m y li n III . × − , ( % ) III . × − III . , ( % ) H I P III . × − , ( % ) III . × − , ( % ) III . , ( % ) L CC II . × − I V . × − III . III . × − , ( % ) mylinmylin
Inputs that had at least one significant associationwith any of the outputs included: Background Ca leak (Λ = 0.039,F(5,49) = 242.804, η = 0.961), background Na + leak (Λ = 0.009, F(5,49)= 1,097.591, η = 0.991), NKA Vmax (Λ = 0.001, F(5,49) = 12,009.757, η = 0.999), PCa (Λ = 0.002, F(5,49) = 5,906.809, η = 0.998), T (Λ = 0.002,F(5,49) = 5,145.939, η = 0.998), and SERCA Vmax (Λ = 0.014, F(5,49)= 708.322, η = 0.986). Thus, inputs respectively accounted for 96% ormore variation in the best linear combination of outputs (all η (cid:61) leak and increasing backgroundNa + leak, there was only a significant association with increasing Nai (partial η ( η p ) = 0.568, p < η p = 0.829, p < η p = 0.981, p < η p = 0.929, p < η p = 0.694, p < η p = 0.951, p < ( η p = 0.058, p = 0.076).Increased SERCA Vmax was significantly associated with increased APD( η p = 0.166, p = 0.002), increased SR Ca ( η p = 0.138, p = 0.005), anddecreased Nai ( η p = 0.354, p < mylinmylin Supplemental Tables mylinmylin T a b l e S : C o m p a r i s o n o f S B d e f a u l t p a r a m e t e r s w i t h m o u s e - s p ec i fi c v a r i a t i o n s i n a cc o r d a n ce t o M o r o tt i e t a l. ( ) P l a ce s w i t h * r e p r e s e n tt h e v a l u e w a s fi tt e du s i n go u r G A t o m a t c h c o rr e s p o nd i n g e x p e r i m e n t a l d a t a . P a r a m e t e r [ un i t s ] N a m e R a bb i t M o u s e R a t M e m b r a n ec a p a c i t a n ce [ F ] C m . × − . × − - C e ll v o l u m e [ L ] V C e ll . × − . × − ( ) - I n t r a ce ll u l a r N a + [ m M ] N a i . . . F r eec o n ce n t r a t i o n o f C a + [ C a ] o . . - i n e x t r a ce ll u l a r c o m p a r t m e n t [ m M ] M a x i m a l c o ndu c t a n ce o f flu x f o r G I N a - f a s t N a + c u rr e n t [ m S µ F − ] J un c t i o n a l p a r t i t i o n i n g F X i j un c t i o n . . - S a r c o l e mm a l p a r t i t i o n i n g F X i s a r c o l e mm a l . . - B a c k g r o und N a + l e a k [ m S µ F − ] G N a B k . × − . × − - K ˙ m o f N a + - C a + e x c h a n g e r f o r N a + [ m M ] K m N a i - M a x c u rr e n t o f t h e N a + - K + pu m p [ µ A µ F − ] I N a K m a x . . S l o w a c t i v a t i n g d e l a y e d r ec t i fi e r c u rr e n t G K s . . - S l o w i n a c t i v a t i n g d e l a y e d r ec t i fi e r c u rr e n t [ nSp F − ] G k u r N / A . - S l o w i n a c t i v a t i n g d e l a y e d r ec t i fi e r c u rr e n t [ nSp F − ] G k u r N / A . - i ss c o ndu c t a n ce [ nSp F − ] G ss N / A . - V e l o c i t y m a x f o r N a + - C a + e x c h a n g e r [ µ A µ F − ] V m a x I N a C a - A ll o s t e r i c C a + a c t i v a t i o n c o n s t a n t [ m M ] K d − A c t . × − . × − - B a c k g r o und C a + l e a k [ m S µ F − ] G C a B k . × − . × − - S R C a + c o n ce n t r a t i o nd e p e nd e n t a c t i v a t i o n o f S R C a + r e l e a s e [ m M ] E C − S R . . - P a ss i v e l e a k i n t h e S R m e m b r a n e [ m s − ] K S R l e a k . × − . × − - V e l o c i t y m a x f o r S R C a + pu m pflu x [ m M m s − ] V m a x J p u m p . × − ** K m S R C a + pu m p f o r w a r d m o d e [ m M ] K m f . × − × − - K m S R C a + pu m p r e v e r s e m o d e [ m M ] K m r . . - L - t y p e C a + c h a nn e l C a + p e r m e a b ili t y [ L F − m s − ] P C a . × − . × − - L - t y p e C a + c h a nn e l N a + p e r m e a b ili t y [ L F − m s − ] P N a . × − . × − - L - t y p e C a + c h a nn e l K + p e r m e a b ili t y [ L F − m s − ] P K . × − . × − - B a c k g r o und C a + l e a k [ m S µ F − ] G C a B k . × − . × − - mylinmylin i Cl(Ca) Ca -activated chloride current i Clb Background Cl current i Cap SL-Ca pump i CaB Background Ca leak i NaB Background Na + leak i NaK NKA current i tof fast Cardiac transient outward potassium i tos slow Cardiac transient outward potassium i Kr the ’rapid’ delayed rectifier current i Ks slowly activating K+ current i K1 inward rectifier K+ current i Kp plateau potassium current i kur slowly inactivating outward i ss non-inactivating steady-state K+ current i CaL LCC channel current i NaCa NCX current i Na Na + current SL Na SL Na + jct + I RyR inactive gateO RyR open gateCai cytosolic Ca V Action potentialTable S2: Model terms. mylinmylin T a b l e S : P a r a m e t e r s u s e d i nS B M c o m pu t a t i o n a l m o d e l t o r e fl ec t c o n t r o l a ndh y p e r a m y li n e m i a/ p r e - d i a b e t i c r a t . P e r ce n t ag e s i np a r e n t h e s e s a r e r e l a t i v e t o c o n t r o l r a t . I f r o m ( ) . II f r o m ( ) . III fi tt e d t o ( ) . I V fi tt e d t o ( ) . C a s e S a r c o l e mm a ll e a k S E R C AN K A P C a G C a V m a x I N K A m a x ( m S / µ F )( m M / m s )( µ A / µ F ) c o n t r o l II . × − I V . × − III . + A m y li n III . × − , ( % ) III . × − III . , ( % ) H I P III . × − , ( % ) III . × − , ( % ) III . , ( % ) L CC II . × − I V . × − III . III . × − , ( % ) mylinmylin Supplemental Figures
Figure S1: Predicted intracellular Ca (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for mouse (black) andrabbit (red) conditions mylinmylin
Figure S1: Predicted intracellular Ca (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for mouse (black) andrabbit (red) conditions mylinmylin i kur, steady-state current, i ss, fast transient outward current, i tof. Middle row: slowtransient outward current, i tos, slowly activating current, i Ks, rapidly ac-tivating current, i Kr. Bottom row: inward rectifier current, i K1, sodi-um/potassium exchanger, i NaK mylinmylin
Figure S1: Predicted intracellular Ca (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for mouse (black) andrabbit (red) conditions mylinmylin i kur, steady-state current, i ss, fast transient outward current, i tof. Middle row: slowtransient outward current, i tos, slowly activating current, i Ks, rapidly ac-tivating current, i Kr. Bottom row: inward rectifier current, i K1, sodi-um/potassium exchanger, i NaK mylinmylin i Na, L-type Ca chan-nel current (middle), i CaL, and sodium/Ca -exchanger current (right), i NaCa, predicted for rabbit (black) and mouse (blue) ventricular cardiomy-ocytes via the SB and SBM models, respectively. mylinmylin
Figure S1: Predicted intracellular Ca (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for mouse (black) andrabbit (red) conditions mylinmylin i kur, steady-state current, i ss, fast transient outward current, i tof. Middle row: slowtransient outward current, i tos, slowly activating current, i Ks, rapidly ac-tivating current, i Kr. Bottom row: inward rectifier current, i K1, sodi-um/potassium exchanger, i NaK mylinmylin i Na, L-type Ca chan-nel current (middle), i CaL, and sodium/Ca -exchanger current (right), i NaCa, predicted for rabbit (black) and mouse (blue) ventricular cardiomy-ocytes via the SB and SBM models, respectively. mylinmylin mylinmylin
Figure S1: Predicted intracellular Ca (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for mouse (black) andrabbit (red) conditions mylinmylin i kur, steady-state current, i ss, fast transient outward current, i tof. Middle row: slowtransient outward current, i tos, slowly activating current, i Ks, rapidly ac-tivating current, i Kr. Bottom row: inward rectifier current, i K1, sodi-um/potassium exchanger, i NaK mylinmylin i Na, L-type Ca chan-nel current (middle), i CaL, and sodium/Ca -exchanger current (right), i NaCa, predicted for rabbit (black) and mouse (blue) ventricular cardiomy-ocytes via the SB and SBM models, respectively. mylinmylin mylinmylin transient data at 1 Hz formouse (a)(24, 51) and rat (b)(50) (purple) with our predicted control data(black) . Ca transients predicted for +Amylin (blue) and HIP (red) areadditionally provided. mylinmylin
Figure S1: Predicted intracellular Ca (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for mouse (black) andrabbit (red) conditions mylinmylin i kur, steady-state current, i ss, fast transient outward current, i tof. Middle row: slowtransient outward current, i tos, slowly activating current, i Ks, rapidly ac-tivating current, i Kr. Bottom row: inward rectifier current, i K1, sodi-um/potassium exchanger, i NaK mylinmylin i Na, L-type Ca chan-nel current (middle), i CaL, and sodium/Ca -exchanger current (right), i NaCa, predicted for rabbit (black) and mouse (blue) ventricular cardiomy-ocytes via the SB and SBM models, respectively. mylinmylin mylinmylin transient data at 1 Hz formouse (a)(24, 51) and rat (b)(50) (purple) with our predicted control data(black) . Ca transients predicted for +Amylin (blue) and HIP (red) areadditionally provided. mylinmylin transient amplitude (∆ Ca [uM],left axis,solid) and diastolic Ca load (right axis, dashed) versus pacing fre-quency [Hz] for control (black) and HIP (red) conditions. Data are providedbased on SBM model predictions (a) and Despa et al (7) (b). mylinmylin
Figure S1: Predicted intracellular Ca (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for mouse (black) andrabbit (red) conditions mylinmylin i kur, steady-state current, i ss, fast transient outward current, i tof. Middle row: slowtransient outward current, i tos, slowly activating current, i Ks, rapidly ac-tivating current, i Kr. Bottom row: inward rectifier current, i K1, sodi-um/potassium exchanger, i NaK mylinmylin i Na, L-type Ca chan-nel current (middle), i CaL, and sodium/Ca -exchanger current (right), i NaCa, predicted for rabbit (black) and mouse (blue) ventricular cardiomy-ocytes via the SB and SBM models, respectively. mylinmylin mylinmylin transient data at 1 Hz formouse (a)(24, 51) and rat (b)(50) (purple) with our predicted control data(black) . Ca transients predicted for +Amylin (blue) and HIP (red) areadditionally provided. mylinmylin transient amplitude (∆ Ca [uM],left axis,solid) and diastolic Ca load (right axis, dashed) versus pacing fre-quency [Hz] for control (black) and HIP (red) conditions. Data are providedbased on SBM model predictions (a) and Despa et al (7) (b). mylinmylin and Na + load. Predicted a) Ca and b)Na + intracellular transients under control (black, solid line), control withincreased NKA to match +Amylin level NKA current(black, dashed line),+Amylin (blue, solid line), and +Amylin with decreased NKA to matchcontrol level NKA current (blue, dashed line). See Table S3 for parameters. mylinmylin
Figure S1: Predicted intracellular Ca (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for mouse (black) andrabbit (red) conditions mylinmylin i kur, steady-state current, i ss, fast transient outward current, i tof. Middle row: slowtransient outward current, i tos, slowly activating current, i Ks, rapidly ac-tivating current, i Kr. Bottom row: inward rectifier current, i K1, sodi-um/potassium exchanger, i NaK mylinmylin i Na, L-type Ca chan-nel current (middle), i CaL, and sodium/Ca -exchanger current (right), i NaCa, predicted for rabbit (black) and mouse (blue) ventricular cardiomy-ocytes via the SB and SBM models, respectively. mylinmylin mylinmylin transient data at 1 Hz formouse (a)(24, 51) and rat (b)(50) (purple) with our predicted control data(black) . Ca transients predicted for +Amylin (blue) and HIP (red) areadditionally provided. mylinmylin transient amplitude (∆ Ca [uM],left axis,solid) and diastolic Ca load (right axis, dashed) versus pacing fre-quency [Hz] for control (black) and HIP (red) conditions. Data are providedbased on SBM model predictions (a) and Despa et al (7) (b). mylinmylin and Na + load. Predicted a) Ca and b)Na + intracellular transients under control (black, solid line), control withincreased NKA to match +Amylin level NKA current(black, dashed line),+Amylin (blue, solid line), and +Amylin with decreased NKA to matchcontrol level NKA current (blue, dashed line). See Table S3 for parameters. mylinmylin transients and loads as a function of NKAactivity (% of control) and SL Ca leak (% of control). a) intracellularCa , b) SR Ca transient c) maximum SR Ca load and d) sodiumload. A black point is representative of the Control case, a blue square isrepresentative of the Amy case, and a red point is representative of the HIPcase. Measurements are taken at 55 s mylinmylin
Figure S1: Predicted intracellular Ca (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for mouse (black) andrabbit (red) conditions mylinmylin i kur, steady-state current, i ss, fast transient outward current, i tof. Middle row: slowtransient outward current, i tos, slowly activating current, i Ks, rapidly ac-tivating current, i Kr. Bottom row: inward rectifier current, i K1, sodi-um/potassium exchanger, i NaK mylinmylin i Na, L-type Ca chan-nel current (middle), i CaL, and sodium/Ca -exchanger current (right), i NaCa, predicted for rabbit (black) and mouse (blue) ventricular cardiomy-ocytes via the SB and SBM models, respectively. mylinmylin mylinmylin transient data at 1 Hz formouse (a)(24, 51) and rat (b)(50) (purple) with our predicted control data(black) . Ca transients predicted for +Amylin (blue) and HIP (red) areadditionally provided. mylinmylin transient amplitude (∆ Ca [uM],left axis,solid) and diastolic Ca load (right axis, dashed) versus pacing fre-quency [Hz] for control (black) and HIP (red) conditions. Data are providedbased on SBM model predictions (a) and Despa et al (7) (b). mylinmylin and Na + load. Predicted a) Ca and b)Na + intracellular transients under control (black, solid line), control withincreased NKA to match +Amylin level NKA current(black, dashed line),+Amylin (blue, solid line), and +Amylin with decreased NKA to matchcontrol level NKA current (blue, dashed line). See Table S3 for parameters. mylinmylin transients and loads as a function of NKAactivity (% of control) and SL Ca leak (% of control). a) intracellularCa , b) SR Ca transient c) maximum SR Ca load and d) sodiumload. A black point is representative of the Control case, a blue square isrepresentative of the Amy case, and a red point is representative of the HIPcase. Measurements are taken at 55 s mylinmylin (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for control (black) and+Amylin (blue) conditions. Results are presented for 0 to 60s for clarity,although action potentials for up to 300s are reported in Fig. S17 mylinmylin
Figure S1: Predicted intracellular Ca (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for mouse (black) andrabbit (red) conditions mylinmylin i kur, steady-state current, i ss, fast transient outward current, i tof. Middle row: slowtransient outward current, i tos, slowly activating current, i Ks, rapidly ac-tivating current, i Kr. Bottom row: inward rectifier current, i K1, sodi-um/potassium exchanger, i NaK mylinmylin i Na, L-type Ca chan-nel current (middle), i CaL, and sodium/Ca -exchanger current (right), i NaCa, predicted for rabbit (black) and mouse (blue) ventricular cardiomy-ocytes via the SB and SBM models, respectively. mylinmylin mylinmylin transient data at 1 Hz formouse (a)(24, 51) and rat (b)(50) (purple) with our predicted control data(black) . Ca transients predicted for +Amylin (blue) and HIP (red) areadditionally provided. mylinmylin transient amplitude (∆ Ca [uM],left axis,solid) and diastolic Ca load (right axis, dashed) versus pacing fre-quency [Hz] for control (black) and HIP (red) conditions. Data are providedbased on SBM model predictions (a) and Despa et al (7) (b). mylinmylin and Na + load. Predicted a) Ca and b)Na + intracellular transients under control (black, solid line), control withincreased NKA to match +Amylin level NKA current(black, dashed line),+Amylin (blue, solid line), and +Amylin with decreased NKA to matchcontrol level NKA current (blue, dashed line). See Table S3 for parameters. mylinmylin transients and loads as a function of NKAactivity (% of control) and SL Ca leak (% of control). a) intracellularCa , b) SR Ca transient c) maximum SR Ca load and d) sodiumload. A black point is representative of the Control case, a blue square isrepresentative of the Amy case, and a red point is representative of the HIPcase. Measurements are taken at 55 s mylinmylin (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for control (black) and+Amylin (blue) conditions. Results are presented for 0 to 60s for clarity,although action potentials for up to 300s are reported in Fig. S17 mylinmylin (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for control (black) andincreased LCC current (green) conditions. Results are presented for 0 to 60sfor clarity mylinmylin
Figure S1: Predicted intracellular Ca (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for mouse (black) andrabbit (red) conditions mylinmylin i kur, steady-state current, i ss, fast transient outward current, i tof. Middle row: slowtransient outward current, i tos, slowly activating current, i Ks, rapidly ac-tivating current, i Kr. Bottom row: inward rectifier current, i K1, sodi-um/potassium exchanger, i NaK mylinmylin i Na, L-type Ca chan-nel current (middle), i CaL, and sodium/Ca -exchanger current (right), i NaCa, predicted for rabbit (black) and mouse (blue) ventricular cardiomy-ocytes via the SB and SBM models, respectively. mylinmylin mylinmylin transient data at 1 Hz formouse (a)(24, 51) and rat (b)(50) (purple) with our predicted control data(black) . Ca transients predicted for +Amylin (blue) and HIP (red) areadditionally provided. mylinmylin transient amplitude (∆ Ca [uM],left axis,solid) and diastolic Ca load (right axis, dashed) versus pacing fre-quency [Hz] for control (black) and HIP (red) conditions. Data are providedbased on SBM model predictions (a) and Despa et al (7) (b). mylinmylin and Na + load. Predicted a) Ca and b)Na + intracellular transients under control (black, solid line), control withincreased NKA to match +Amylin level NKA current(black, dashed line),+Amylin (blue, solid line), and +Amylin with decreased NKA to matchcontrol level NKA current (blue, dashed line). See Table S3 for parameters. mylinmylin transients and loads as a function of NKAactivity (% of control) and SL Ca leak (% of control). a) intracellularCa , b) SR Ca transient c) maximum SR Ca load and d) sodiumload. A black point is representative of the Control case, a blue square isrepresentative of the Amy case, and a red point is representative of the HIPcase. Measurements are taken at 55 s mylinmylin (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for control (black) and+Amylin (blue) conditions. Results are presented for 0 to 60s for clarity,although action potentials for up to 300s are reported in Fig. S17 mylinmylin (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for control (black) andincreased LCC current (green) conditions. Results are presented for 0 to 60sfor clarity mylinmylin (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for control (black) and300 % increased Ca background leak (blue) conditions using the rabbitSB model. mylinmylin
Figure S1: Predicted intracellular Ca (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for mouse (black) andrabbit (red) conditions mylinmylin i kur, steady-state current, i ss, fast transient outward current, i tof. Middle row: slowtransient outward current, i tos, slowly activating current, i Ks, rapidly ac-tivating current, i Kr. Bottom row: inward rectifier current, i K1, sodi-um/potassium exchanger, i NaK mylinmylin i Na, L-type Ca chan-nel current (middle), i CaL, and sodium/Ca -exchanger current (right), i NaCa, predicted for rabbit (black) and mouse (blue) ventricular cardiomy-ocytes via the SB and SBM models, respectively. mylinmylin mylinmylin transient data at 1 Hz formouse (a)(24, 51) and rat (b)(50) (purple) with our predicted control data(black) . Ca transients predicted for +Amylin (blue) and HIP (red) areadditionally provided. mylinmylin transient amplitude (∆ Ca [uM],left axis,solid) and diastolic Ca load (right axis, dashed) versus pacing fre-quency [Hz] for control (black) and HIP (red) conditions. Data are providedbased on SBM model predictions (a) and Despa et al (7) (b). mylinmylin and Na + load. Predicted a) Ca and b)Na + intracellular transients under control (black, solid line), control withincreased NKA to match +Amylin level NKA current(black, dashed line),+Amylin (blue, solid line), and +Amylin with decreased NKA to matchcontrol level NKA current (blue, dashed line). See Table S3 for parameters. mylinmylin transients and loads as a function of NKAactivity (% of control) and SL Ca leak (% of control). a) intracellularCa , b) SR Ca transient c) maximum SR Ca load and d) sodiumload. A black point is representative of the Control case, a blue square isrepresentative of the Amy case, and a red point is representative of the HIPcase. Measurements are taken at 55 s mylinmylin (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for control (black) and+Amylin (blue) conditions. Results are presented for 0 to 60s for clarity,although action potentials for up to 300s are reported in Fig. S17 mylinmylin (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for control (black) andincreased LCC current (green) conditions. Results are presented for 0 to 60sfor clarity mylinmylin (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for control (black) and300 % increased Ca background leak (blue) conditions using the rabbitSB model. mylinmylin mylinmylin
Figure S1: Predicted intracellular Ca (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for mouse (black) andrabbit (red) conditions mylinmylin i kur, steady-state current, i ss, fast transient outward current, i tof. Middle row: slowtransient outward current, i tos, slowly activating current, i Ks, rapidly ac-tivating current, i Kr. Bottom row: inward rectifier current, i K1, sodi-um/potassium exchanger, i NaK mylinmylin i Na, L-type Ca chan-nel current (middle), i CaL, and sodium/Ca -exchanger current (right), i NaCa, predicted for rabbit (black) and mouse (blue) ventricular cardiomy-ocytes via the SB and SBM models, respectively. mylinmylin mylinmylin transient data at 1 Hz formouse (a)(24, 51) and rat (b)(50) (purple) with our predicted control data(black) . Ca transients predicted for +Amylin (blue) and HIP (red) areadditionally provided. mylinmylin transient amplitude (∆ Ca [uM],left axis,solid) and diastolic Ca load (right axis, dashed) versus pacing fre-quency [Hz] for control (black) and HIP (red) conditions. Data are providedbased on SBM model predictions (a) and Despa et al (7) (b). mylinmylin and Na + load. Predicted a) Ca and b)Na + intracellular transients under control (black, solid line), control withincreased NKA to match +Amylin level NKA current(black, dashed line),+Amylin (blue, solid line), and +Amylin with decreased NKA to matchcontrol level NKA current (blue, dashed line). See Table S3 for parameters. mylinmylin transients and loads as a function of NKAactivity (% of control) and SL Ca leak (% of control). a) intracellularCa , b) SR Ca transient c) maximum SR Ca load and d) sodiumload. A black point is representative of the Control case, a blue square isrepresentative of the Amy case, and a red point is representative of the HIPcase. Measurements are taken at 55 s mylinmylin (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for control (black) and+Amylin (blue) conditions. Results are presented for 0 to 60s for clarity,although action potentials for up to 300s are reported in Fig. S17 mylinmylin (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for control (black) andincreased LCC current (green) conditions. Results are presented for 0 to 60sfor clarity mylinmylin (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for control (black) and300 % increased Ca background leak (blue) conditions using the rabbitSB model. mylinmylin mylinmylin ( Ca SL , Cai , Ca jct ) for +Amylin(blue), HIP(red) and increased LCC (green). A list ofstate labels is provided in Table S2 mylinmylin
Figure S1: Predicted intracellular Ca (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for mouse (black) andrabbit (red) conditions mylinmylin i kur, steady-state current, i ss, fast transient outward current, i tof. Middle row: slowtransient outward current, i tos, slowly activating current, i Ks, rapidly ac-tivating current, i Kr. Bottom row: inward rectifier current, i K1, sodi-um/potassium exchanger, i NaK mylinmylin i Na, L-type Ca chan-nel current (middle), i CaL, and sodium/Ca -exchanger current (right), i NaCa, predicted for rabbit (black) and mouse (blue) ventricular cardiomy-ocytes via the SB and SBM models, respectively. mylinmylin mylinmylin transient data at 1 Hz formouse (a)(24, 51) and rat (b)(50) (purple) with our predicted control data(black) . Ca transients predicted for +Amylin (blue) and HIP (red) areadditionally provided. mylinmylin transient amplitude (∆ Ca [uM],left axis,solid) and diastolic Ca load (right axis, dashed) versus pacing fre-quency [Hz] for control (black) and HIP (red) conditions. Data are providedbased on SBM model predictions (a) and Despa et al (7) (b). mylinmylin and Na + load. Predicted a) Ca and b)Na + intracellular transients under control (black, solid line), control withincreased NKA to match +Amylin level NKA current(black, dashed line),+Amylin (blue, solid line), and +Amylin with decreased NKA to matchcontrol level NKA current (blue, dashed line). See Table S3 for parameters. mylinmylin transients and loads as a function of NKAactivity (% of control) and SL Ca leak (% of control). a) intracellularCa , b) SR Ca transient c) maximum SR Ca load and d) sodiumload. A black point is representative of the Control case, a blue square isrepresentative of the Amy case, and a red point is representative of the HIPcase. Measurements are taken at 55 s mylinmylin (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for control (black) and+Amylin (blue) conditions. Results are presented for 0 to 60s for clarity,although action potentials for up to 300s are reported in Fig. S17 mylinmylin (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for control (black) andincreased LCC current (green) conditions. Results are presented for 0 to 60sfor clarity mylinmylin (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for control (black) and300 % increased Ca background leak (blue) conditions using the rabbitSB model. mylinmylin mylinmylin ( Ca SL , Cai , Ca jct ) for +Amylin(blue), HIP(red) and increased LCC (green). A list ofstate labels is provided in Table S2 mylinmylin load as a functionof sarcolemma (SL) Ca leak rates (scaled relative to control) at 1 Hzpacing to approximate dose-dependent amylin incubation effects in rats.Left axis: maximum Ca (at diastole) and minimum (at systole, magentadashed). Right axis: SR Ca transient amplitudes (magenta dots) andsquares indicating the SL leak rates assumed for control (black), +Amylin(blue), and HIP (red) conditions mylinmylin
Figure S1: Predicted intracellular Ca (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for mouse (black) andrabbit (red) conditions mylinmylin i kur, steady-state current, i ss, fast transient outward current, i tof. Middle row: slowtransient outward current, i tos, slowly activating current, i Ks, rapidly ac-tivating current, i Kr. Bottom row: inward rectifier current, i K1, sodi-um/potassium exchanger, i NaK mylinmylin i Na, L-type Ca chan-nel current (middle), i CaL, and sodium/Ca -exchanger current (right), i NaCa, predicted for rabbit (black) and mouse (blue) ventricular cardiomy-ocytes via the SB and SBM models, respectively. mylinmylin mylinmylin transient data at 1 Hz formouse (a)(24, 51) and rat (b)(50) (purple) with our predicted control data(black) . Ca transients predicted for +Amylin (blue) and HIP (red) areadditionally provided. mylinmylin transient amplitude (∆ Ca [uM],left axis,solid) and diastolic Ca load (right axis, dashed) versus pacing fre-quency [Hz] for control (black) and HIP (red) conditions. Data are providedbased on SBM model predictions (a) and Despa et al (7) (b). mylinmylin and Na + load. Predicted a) Ca and b)Na + intracellular transients under control (black, solid line), control withincreased NKA to match +Amylin level NKA current(black, dashed line),+Amylin (blue, solid line), and +Amylin with decreased NKA to matchcontrol level NKA current (blue, dashed line). See Table S3 for parameters. mylinmylin transients and loads as a function of NKAactivity (% of control) and SL Ca leak (% of control). a) intracellularCa , b) SR Ca transient c) maximum SR Ca load and d) sodiumload. A black point is representative of the Control case, a blue square isrepresentative of the Amy case, and a red point is representative of the HIPcase. Measurements are taken at 55 s mylinmylin (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for control (black) and+Amylin (blue) conditions. Results are presented for 0 to 60s for clarity,although action potentials for up to 300s are reported in Fig. S17 mylinmylin (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for control (black) andincreased LCC current (green) conditions. Results are presented for 0 to 60sfor clarity mylinmylin (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for control (black) and300 % increased Ca background leak (blue) conditions using the rabbitSB model. mylinmylin mylinmylin ( Ca SL , Cai , Ca jct ) for +Amylin(blue), HIP(red) and increased LCC (green). A list ofstate labels is provided in Table S2 mylinmylin load as a functionof sarcolemma (SL) Ca leak rates (scaled relative to control) at 1 Hzpacing to approximate dose-dependent amylin incubation effects in rats.Left axis: maximum Ca (at diastole) and minimum (at systole, magentadashed). Right axis: SR Ca transient amplitudes (magenta dots) andsquares indicating the SL leak rates assumed for control (black), +Amylin(blue), and HIP (red) conditions mylinmylin (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for control (black) andHIP (red) conditions. Results are presented for 0 to 60s for clarity, we reportfull 300s simulations in Fig. S17 mylinmylin
Figure S1: Predicted intracellular Ca (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for mouse (black) andrabbit (red) conditions mylinmylin i kur, steady-state current, i ss, fast transient outward current, i tof. Middle row: slowtransient outward current, i tos, slowly activating current, i Ks, rapidly ac-tivating current, i Kr. Bottom row: inward rectifier current, i K1, sodi-um/potassium exchanger, i NaK mylinmylin i Na, L-type Ca chan-nel current (middle), i CaL, and sodium/Ca -exchanger current (right), i NaCa, predicted for rabbit (black) and mouse (blue) ventricular cardiomy-ocytes via the SB and SBM models, respectively. mylinmylin mylinmylin transient data at 1 Hz formouse (a)(24, 51) and rat (b)(50) (purple) with our predicted control data(black) . Ca transients predicted for +Amylin (blue) and HIP (red) areadditionally provided. mylinmylin transient amplitude (∆ Ca [uM],left axis,solid) and diastolic Ca load (right axis, dashed) versus pacing fre-quency [Hz] for control (black) and HIP (red) conditions. Data are providedbased on SBM model predictions (a) and Despa et al (7) (b). mylinmylin and Na + load. Predicted a) Ca and b)Na + intracellular transients under control (black, solid line), control withincreased NKA to match +Amylin level NKA current(black, dashed line),+Amylin (blue, solid line), and +Amylin with decreased NKA to matchcontrol level NKA current (blue, dashed line). See Table S3 for parameters. mylinmylin transients and loads as a function of NKAactivity (% of control) and SL Ca leak (% of control). a) intracellularCa , b) SR Ca transient c) maximum SR Ca load and d) sodiumload. A black point is representative of the Control case, a blue square isrepresentative of the Amy case, and a red point is representative of the HIPcase. Measurements are taken at 55 s mylinmylin (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for control (black) and+Amylin (blue) conditions. Results are presented for 0 to 60s for clarity,although action potentials for up to 300s are reported in Fig. S17 mylinmylin (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for control (black) andincreased LCC current (green) conditions. Results are presented for 0 to 60sfor clarity mylinmylin (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for control (black) and300 % increased Ca background leak (blue) conditions using the rabbitSB model. mylinmylin mylinmylin ( Ca SL , Cai , Ca jct ) for +Amylin(blue), HIP(red) and increased LCC (green). A list ofstate labels is provided in Table S2 mylinmylin load as a functionof sarcolemma (SL) Ca leak rates (scaled relative to control) at 1 Hzpacing to approximate dose-dependent amylin incubation effects in rats.Left axis: maximum Ca (at diastole) and minimum (at systole, magentadashed). Right axis: SR Ca transient amplitudes (magenta dots) andsquares indicating the SL leak rates assumed for control (black), +Amylin(blue), and HIP (red) conditions mylinmylin (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for control (black) andHIP (red) conditions. Results are presented for 0 to 60s for clarity, we reportfull 300s simulations in Fig. S17 mylinmylin mylinmylin
Figure S1: Predicted intracellular Ca (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for mouse (black) andrabbit (red) conditions mylinmylin i kur, steady-state current, i ss, fast transient outward current, i tof. Middle row: slowtransient outward current, i tos, slowly activating current, i Ks, rapidly ac-tivating current, i Kr. Bottom row: inward rectifier current, i K1, sodi-um/potassium exchanger, i NaK mylinmylin i Na, L-type Ca chan-nel current (middle), i CaL, and sodium/Ca -exchanger current (right), i NaCa, predicted for rabbit (black) and mouse (blue) ventricular cardiomy-ocytes via the SB and SBM models, respectively. mylinmylin mylinmylin transient data at 1 Hz formouse (a)(24, 51) and rat (b)(50) (purple) with our predicted control data(black) . Ca transients predicted for +Amylin (blue) and HIP (red) areadditionally provided. mylinmylin transient amplitude (∆ Ca [uM],left axis,solid) and diastolic Ca load (right axis, dashed) versus pacing fre-quency [Hz] for control (black) and HIP (red) conditions. Data are providedbased on SBM model predictions (a) and Despa et al (7) (b). mylinmylin and Na + load. Predicted a) Ca and b)Na + intracellular transients under control (black, solid line), control withincreased NKA to match +Amylin level NKA current(black, dashed line),+Amylin (blue, solid line), and +Amylin with decreased NKA to matchcontrol level NKA current (blue, dashed line). See Table S3 for parameters. mylinmylin transients and loads as a function of NKAactivity (% of control) and SL Ca leak (% of control). a) intracellularCa , b) SR Ca transient c) maximum SR Ca load and d) sodiumload. A black point is representative of the Control case, a blue square isrepresentative of the Amy case, and a red point is representative of the HIPcase. Measurements are taken at 55 s mylinmylin (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for control (black) and+Amylin (blue) conditions. Results are presented for 0 to 60s for clarity,although action potentials for up to 300s are reported in Fig. S17 mylinmylin (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for control (black) andincreased LCC current (green) conditions. Results are presented for 0 to 60sfor clarity mylinmylin (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for control (black) and300 % increased Ca background leak (blue) conditions using the rabbitSB model. mylinmylin mylinmylin ( Ca SL , Cai , Ca jct ) for +Amylin(blue), HIP(red) and increased LCC (green). A list ofstate labels is provided in Table S2 mylinmylin load as a functionof sarcolemma (SL) Ca leak rates (scaled relative to control) at 1 Hzpacing to approximate dose-dependent amylin incubation effects in rats.Left axis: maximum Ca (at diastole) and minimum (at systole, magentadashed). Right axis: SR Ca transient amplitudes (magenta dots) andsquares indicating the SL leak rates assumed for control (black), +Amylin(blue), and HIP (red) conditions mylinmylin (a), sarcoplasmic reticulum Ca (b), intracellular sodium (c), and action potential (d) for control (black) andHIP (red) conditions. Results are presented for 0 to 60s for clarity, we reportfull 300s simulations in Fig. S17 mylinmylin mylinmylin V , for control, +Amylin, HIPandLCC conditions over five minutes of 1 Hz pacing to demonstrate modelstability mylinmylin