UNDERSTANDING THE ROLES OF NCX-NAK COUPLING USING
COMPUTATIONAL TOOLS
by Lulu Chu
A dissertation submitted to Johns Hopkins University in conformity with the requirements for the degree of Doctor of Philosophy Baltimore, Maryland September, 2016
Abstract
Normal cardiac excitability depends on the coordinated activity of ion channels and
transporters. Mutations or dysregulation in ion channels affecting their biophysical
properties have been known for years as a root cause of fatal human electrical rhythm
disturbance (arrhythmias). Moreover, recent studies have shown that defects in ion channel associated protein, ankryin-B, results in a great loss of sodium (Na+)/calcium
(Ca2+) exchanger (NCX1) and sodium (Na+)/potassium (K+) ATPase (NaK) to the t- tubules and cause arrhythmia with beta-adrenergic stimulation. It is important to gain a good understanding of their modulation in ionic homeostasis and Ca2+ dynamics in
normal and pathological cardiac functions. A biophysically constrained computational
model of cardiac ventricular myocyte provides the framework for investigating the functional coupling of NCX1 and NaK and for identifying the underlying mechanisms for early-afterdepolarization generation in cardiomyocytes. The cardiac NCX1 is an
electrogenic membrane transporter that regulates Ca2+ homeostasis in cardiomyocytes, serving mainly to extrude Ca2+ during diastole. The direction of Ca2+ transport reverses at membrane potentials near that of the action potential plateau, generating an influx of Ca2+
into the cell. Therefore, there has been great interest in the possible roles of NCX1 in
cardiac Ca2+-induced Ca2+ release (CICR). Interest has been reinvigorated by a recent super-resolution optical imaging study suggesting that ~18% of NCX1 co-localize with ryanodine receptor (RyR2) clusters, and ~30% of additional NCX1 are localized to within ~120 nm of the nearest RyR2. NCX1 may therefore occupy a privileged position in which to modulate CICR. To examine this question, we have developed a mechanistic biophysically detailed model of NCX1 that describes both NCX1 transport kinetics and
ii Ca2+-dependent allosteric regulation. This NCX1 model was incorporated into a
previously developed super-resolution model of the Ca2+ spark as well as a computational
model of the cardiac ventricular myocyte that includes a detailed description of CICR
with stochastic gating of L-type Ca2+ channels and RyR2s, and that accounts for local
Ca2+ gradients near the dyad via inclusion of a peri-dyadic (PD) compartment. Both
models predict that increasing the fraction of NCX1 in the dyad and PD decreases spark
frequency, fidelity, and diastolic Ca2+ levels. On the other hand, there is mounting
evidence suggesting that there exists a Na+ fuzzy space that is regulated by NCX1, NaK, and neuronal Na+ channels. The model constraints suggest a similar distribution between
NaK and NCX1. Furthermore, upon voltage activation, neuronal Na+ channels can raise
+ the local [Na ]d to ~35-40mM and reverse NCX1 to enhance the CICR process.
Therefore, NCX1 plays an important role in promoting Ca2+ entry into the dyad, and hence contributing to the trigger for RyR2 release at depolarized membrane potentials and in the presence of elevated local Na+ concentration. In Ankyrin-B defect cells, pro- arrhythmic spontaneous release and afterdepolarizations are observed in the presence of beta-adrenergic stimulation. Model simulations demonstrates that local regulation of
[Ca2+] and [Na+] is compromised as a result of NCX1 and NaK reduction, which contribute to an elevation in Ca2+ spark activities and increased RyR2 opening
probability, which leads to further activation of NCX1 and results in imbalance of
currents. This underlies the early-afterdepolarization generation.
iii Thesis Committee Members
Raimond L. Winslow, The Raj and Neera Singh Professor, Department of Biomedical
Engineering, The Johns Hopkins University
Brian O’Rourke, Vice Chair of Basic and Translational Research, Department of
Medicine, The Johns Hopkins University
Gordon Tomaselli, Chief, Department of Medicine, Division of Cardiology, The Johns
Hopkins University
Joseph L. Greenstein, Associate research scientist, Department of Biomedical
Engineering, The Johns Hopkins University
iv
Acknowledgements
There are so many people who without which, this dissertation could not have
been completed. I really appreciate all the help and guidance that was provided to me
over the past 7 years, a really important time period of my life.
First and foremost, I must thank my advisor, Dr. Rai Winslow. I could not have asked for a better mentor. You not only taught me about science, research, scientific communication (cardiac electrophysiology, computational models of cardiomyocytes, etc.) but you have been a great role model and have shown me your persistence and passion for science. I have always enjoyed our meetings and discussion and thank you for your tremendous support through my most frustrated time during the experimental work and your help to push me in the right directions. Moreover, I have enjoyed our talks about continuing efforts and persistence in physical activities as well. You constantly inspire me in every single way.
To Joe Greenstein, I want to thank you for your patience and all your help with my Ph.D. studies here. You are always so calm and encouraging whenever I am stressed or frustrated with research. I have learned a lot from you from science, research to life attitude.
I must also express my gratitude to my committee, Dr. Brian O’Rourke and Dr.
Gordon Tomaselli, for their encouragement, guidance and review of my work.
To the rest of the Winslow and Mac Gabhann labs, I want to thank you all being a
great resource of both knowledge and encouragement. Yasmin, Laura, Rob, Pegy, Mark,
Bhaskar, Iraj, Lindsay, Feilim, Liz, An-Chi, Claire, it has been really great working with
v you all. In addition, I was thankful for the discussions I had with Dr. Jon Lederer and Dr.
G.S. Blair Williams for the early-stage discussion during my NCX1 project.
To Kyle Reynolds, I would love to thank you for your help with cluster and any other computer matters that happened over the years.
And to my family, in particular my parents, I want to thank you so much for your love and support over the years. Even though you are far away, you have always encouraged me to keep going and overcome any obstacles that come in my way. You are always there for me whenever I need someone to talk to during challenging times. All of the sacrafices you have made through the years to provide me with the best education have not gone unnoticed. Words cannot describe my gratitude for your constant love.
vi Table of Contents Chapter 1 - Introduction ...... 1 1.1 Objective ...... 1 1.2 Cardiac Action Potential ...... 1 1.3 Excitation-Contraction Coupling ...... 2 1.4 Cardiac dyad ...... 3 1.5 Sodium Calcium Exchanger ...... 4 1.6 Na+ Fuzzy Space ...... 5 1.7 Ankyrin-B and Localization of NCX1 and NaK ...... 6 1.8 Mathematical Modeling of Electrophysiology ...... 8 Chapter 2 - NCX1 regulation of CICR ...... 13 2.1 Background ...... 13 2.2 Methods ...... 16 2.2.1 NCX1 Kinetic Model with CBD12-mediated Allosteric Activation ...... 16 2.2.2 NCX1 in the Super-resolution Spark Model ...... 25 2.2.3 Spatial Localization of NCX1 in the Canine Whole-cell Model ...... 27 2.3 Results ...... 30 2+ 2+ 2.3.1 INCX1 driven by [Ca ]d and [Ca ]i ...... 31 2.3.2 Effect of NCX1 on Ca2+ sparks in the SRS model ...... 32 2.3.3 Role of NCX1 localization on Ca2+ sparks in the whole-cell model ...... 37 2.3.4 NCX1 localization and the cardiac action potential ...... 39 2.3.5 Does NCX1 play a role in CICR? ...... 44 2.3.6 Role of NCX1 localization on whole-cell INCX1 ...... 46 2.3.7 Role of NCX1 allosteric regulation on whole-cell physiology ...... 48 2.4 Discussion ...... 50 2.4.1 Spatial localization of NCX1 ...... 52 2.4.2 Interspecies differences ...... 54 2.4.3 The dual roles of NCX1 ...... 55 2.4.4 Role of NCX1 Ca2+-dependent allosteric regulation ...... 60 Chapter 3 – Na+ local control in cardiomyocytes ...... 63 3.1 Background ...... 63 3.2 Methods ...... 68 3.2.1 Implementation of Na+ local control in the whole cell model ...... 68 3.2.2 Implementation of Na+ dynamics in the super-resolution spark model ...... 73 3.2.3 Ankyrin-B+/- model and beta-adrenergic stimulation ...... 74 3.3 Results ...... 75 3.3.1 Validation of Na+ local control in the whole-cell model ...... 75 3.3.2 Model predicts the existence of Na+ sparks ...... 77 3.3.3 Redistribution of NaK and cardiac action potential ...... 80 3.3.4 Can neuronal INa trigger RyR2 release and contribute to CICR? ...... 84 3.3.5 Ankyrin-B+/- cardiomyocytes leads to increased Ca2+ spark activities and results in arrhythmia generation ...... 87 3.4 Discussion ...... 92 3.4.1 Similar spatial distribution of NCX1 and NaK ...... 93 3.4.2 Computational prediction of Na+ sparks suggests possible experiments ...... 95 3.4.3 Na+ microdomains and Na+ diffusion in fuzzy space ...... 96 3.4.4 The role of NCX1 to trigger or prime the local [Ca2+] during CICR process ...... 99 3.4.5 Na+ related other disease and potential therapeutic direction ...... 100
vii Chapter 4 – Conclusions and Future Direction ...... 102 4.1 Summary of Findings ...... 102 4.2 Limitations ...... 104 4.3 Future directions ...... 105 Appendix A Model Equations and Parameters ...... 108 A.1 Model equations and parameters for Chapter 2 ...... 108 A.1.1 NCX1 Model ...... 108 A.1.2 Model equations and parameters for SRS and whole-cell model for NCX1 incorporation ...... 110 A.2 Model equations and parameters for Chapter 3 ...... 112 A.2.1 Sodium/Potassium ATPase (NaK) formulation ...... 113 A.2.2 Neuronal Na+ channel ...... 115 A.2.3 Local Na+ dynamics in the whole-cell model ...... 117 A.2.4 3D super-resolution spark (SRS) model ...... 118 Bibliography ...... Error! Bookmark not defined.
viii List of Tables Table 2-1: NCX1 contribution in Ca2+ transient decay in Fig. 2-13...... 42 Table 2-2: NCX1 contribution in Ca2+ transient decay in Fig. 2-15...... 43 Table A1: NCX1 biological model parameters...... 108 Table A2: ...... 110 Table A3: ...... 112 SRS model and whole-cell parameters + SRS model and whole-cell parameters in Na local control
ix
List of Figures
Figure 1-1: Ca2+ and Na+ transport in ventricular myocytes and Ca2+-induced-Ca2+- release process Figure 2-1: NCX1 kinetic schemes and dyad model geometry. (A) State model for NCX1 transport kinetics...... (B) State model...... for CBD12 Ca...... 2+-dependent allosteric...... regulation.... 4 with partial activity coefficients (red). (C) 3D mesh from SRS model [39] showing a t-tubule modeled as a cylinder (blue) partially encircled by JSR (red) containing a cluster of RyR2s (green-blue), forming a dyadic space with a 15 nm gap between these membranes. (D) Illustration of flattened JSR from the SRS model with a centered 7x7 RyR2 lattice. (E) A t-tubule-JSR cleft (or CRU) of the whole-cell model (shown in cross-section) is composed of four dyadic subspace volumes arranged on a 2x2 grid, each containing 2 LCCs and 12 RyR2s. The PD is a single compartment that surrounds the subspace grid (i.e. the dyad). Figure 2-2: The electrochemical factor is constrained by experimental steady state NCX1 current-voltage (I-V) curves measured using fully-active NCX1 ...... in giant membrane...... 17 patches treated with chymotrypsin [51]. Experimental data (circles) and model fits 2+ (black solid lines) are shown. (A) Fits to NCX1 I-V curves at 1 µM [Ca ]i and a + 2+ + range of [Na ]i. (B) Fits to NCX1 I-V curves at 0.1 µM [Ca ]i and a range of [Na ]i.
Figure 2-3: The CBD12 Ca2+ binding and allosteric regulation model. (A) Simplification of ...... 7-state CBD12...... Ca2+ binding model...... to a reduced...... 3-state model...... (B) Model of 18 CBD12 Ca2+-dependent allosteric activation. Figure 2-4: Constraining the 7-state CBD12 sequential model (Fig. 2-3A). Experimental data in red, simulation results in black. (A) Equilibrium ...... Ca2+ binding...... curve from...... 20 isolated canine CBD12 protein was used to constrain the CBD12 model Ca2+ binding affinities [44, 86]. (B) The kinetic stop-flow experiment using Quin-2 to deprive Ca2+ from CBD12 proteins and to constrain the Ca2+ dissociation rate constants for the first three Ca2+ binding sites [44, 86] Figure 2-5: Model constraints for CBD12 Ca2+-dependent allosteric regulation. (A) Model fit to normalized peak INCX1 [52, 61]. (B) Model ...... fit for NCX1 CBD12...... 21 activation versus experimental data in which inward NCX1 current is activated by 2+ increasing [Ca ]i from 0 to 1, 3, or 5 µM in an inside-out giant membrane patch preparation [61]. A two-phase dynamical activation process is characterized with a very rapid current jump (achieves ~80% of its peak value in <500 ms) upon Ca2+ stimulation, followed by a secondary, slower development in current. The time courses of these phases of activation were used to constrain the rates (α2, β2, α4, β4) in conformational changes of CBD12 allosteric regulation in Fig. S3B. Figure 2-6: NCX1 model constraint and validation. (A) CBD12 model constraint: Ca2+ binding site steady state occupancy compares to experimental data of Giladi ...... et al. 22
x [44]. (B) Model NCX1 fractional activity compared with experimental data [54]. (C) Steady state NCX1 I-V curve validation against whole-cell patch clamp results 2+ under various [Ca ]i [87]. (D). Fast and slow phases of NCX1 model activation 2+ time-course in response to [Ca ]i clamp to indicated value at (at 1 s) resembles those of Fujioka et al. [54] (not shown). Figure 2-7: Dynamical properties of NCX1 allosteric activation. (A) and (D): Rapid cytosolic Ca2+ signals used in simulations ...... to drive the Ca...... 2+-dependent allos...... teric 24 activation process of NCX1. (B) and (E): NCX1 current activation in response to 2+ [Ca ]i step increase. NCX1 exhibits relatively slow activation kinetics upon a 2+ moderate [Ca ]i increase, as would be sensed in the cytosolic compartment. NCX1 2+ activation kinetics are very fast in response to high levels of [Ca ]i, as would be sensed within and near the dyad. (C) and (F): NCX1 allosteric factor in response to 2+ [Ca ]i step increase. Figure 2-8: Determination of transfer time constants τss2pd and τpd2c in the whole-cell model, with constraints ...... yielding Ca2+ ...... spark properties...... consistent with ...... those of the 25 SRS model. * represents the optimized model value in the whole-cell model. (A) 2+ 2+ τpd2c defines peak [Ca ]pd. Spark rate (B), peak [Ca ]d (C), and full spark duration (D) from SRS model constrain the value of τss2pd. 2+ Figure 2-9: NCX1 dynamics driven by AP and [Ca ] clamp. (A) Baseline AP-clamp Vm 2+ generated by a previous whole-cell model [93], and ...... (B) corresponding...... [Ca ]i and 29 2+ [Ca ]d signals. NCX1 allosteric factor, Allo (C), and INCX1 (D) underlying APs paced from rest. Figure 2-10: Effects of NCX1 on SRS model Ca2+ sparks. Spark fidelity simulations were initiated by ...... opening a single...... random RyR2...... NCX1s were placed...... in the dyad 31 only (blue bars), PD only (red bars), or both (yellow bars). (A) Predicted park 2+ fidelity. (B) Spark rate. (C) Spark amplitude measured as peak [Ca ]d, ** indicates statistically significant difference based on t-test (p < 0.05). (D) Spark duration measured as FDHM. Figure 2-11: Effects of NCX1 on SRS model Ca2+ sparks. Spark fidelity simulations were initiated by opening ...... a central RyR2...... NCX1s were...... placed in the dyad...... only 35 (blue bars), PD only (red bars), or both (yellow bars). (A) Predicted park fidelity. 2+ (B) Spark rate. (C) Spark amplitude measured as peak [Ca ]d, ** indicates statistically significant difference based on t-test (p < 0.05). Figure 2-12: Effects of NCX1 localization on spark properties in the whole-cell model. The role of NCX1 distribution between cytosol and dyad only ...... (fd+pd = fd since...... fpd = 36 0, solid lines), between cytosol and PD only (fd+pd = fpd since fd = 0, dashed lines), or among all three compartments with a fd:fpd ratio of 1:2 (fd+pd = fd + fpd with fpd = 2fd, 2+ dotted lines) on whole-cell spark rate (A), peak [Ca ]d (B), spark duration measured 2+ as FDHM (C), and diastolic [Ca ]d (D). The total number of NCX1s in the cell is the same in all cases. Figure 2-13: Effects of various dyadic NCX1 distributions (fd values of 0, 0.05, 0.10, 0.15, and 0.20) on APs ...... and Ca2+ handling...... with no PD ...... NCX1. (A) APs;...... and (B) 39 whole-cell INCX1. Arrows indicate time of ENCX1 crossing for fd = 0 (blue) and fd = 2+ 2+ 2+ 0.2 (red). (C) Cytosolic Ca transient [Ca ]i. (D) [Ca]jsr. (E) [Ca ]d. (F) Diastolic 2+ phase of [Ca ]d.
...... 41
xi Figure 2-14: Effects of dyadic NCX1 on ENCX1 during ECC. (A) ENCX1 in the cytosol. (B) ENCX1 in the dyad. Figure 2-15: Effects of PD NCX1 on ECC. (A) Action potential with NCX1 placement in 2+ 2+ the PD space. (B) Ca...... transient. (C)...... Total NCX1 currents...... (D) Cajsr...... (E) [Ca ]d. (F)42 2+ Diastolic phase of [Ca ]d is significantly reduced in the presence of PD NCX1. Figure 2-16: The CICR triggering capacity of NCX1. (A-D) Test potentials to 0 mv and 50 mV of 200 ms duration were applied to the whole-cell model from a holding ... 43 potential of -90 mV under NCX1c (control NCX1, black lines) or NCX1* (reverse mode NCX1 clamped to zero, red lines) conditions. (A) JNCX1, scale bar (black): 0.01 µM/ms. (B) JLCC, scale bar (blue): 0.1 µM/ms. (C) JRyR2, scale bar (green): 1 µM/ms. 2+ (D) Normalized peak Ca influx (JLCC + JNCX1) in response to test potentials from - 30 mV to 80 mV for NCX1c (black) and NCX1* (red). The results suggest that NCX1 can trigger CICR consistent with experiments [78]. (E) NCX1 fraction of CICR trigger. (F) JRyR2 during AP. Figure 2-17: NCX1 tail currents under AP-clamp. (A) AP clamp recording in a rabbit ventricular myocytes from Weber et ...... al. [87]. (B) Model...... prediction of...... NCX1 tail 46 currents upon AP-clamp interruption at various times (10, 25, 50, 100, 200, and 300 ms) with original Greenstein and Winslow [38] model. (C) Model prediction of NCX1 tail currents with fcyto = 1.0 (100% NCX1 in cytosol). (D) Model prediction of whole-cell NCX1 tail currents with fd, fpd, and fcyto values of 0.15, 0.30, and 0.55, respectively (dyad-to-PD ratio of 1:2). Figure 2-18: The beat-to-beat role of NCX1 Ca2+-dependent allosteric regulation. (A) CBD12 allosteric regulation of NCX1 ...... in cytosol (solid ...... line), PD (dashed...... line), and 48 2+ dyad (dotted line). (B) INCX1 in cytosol, PD, and dyad. (C) [Ca ]i and Vm (black) 2+ and (D) [Ca ]jsr comparisons between control (blue) and fully active NCX1 (Allo = 1, red). Figure 2-19: Effects of NCX1 spatial distribution between dyad and PD on CRT gain. All + values are ...... normalized to...... CRT gain at 10...... mM [Na ]i and ...... Vm = 0 mV. An ...... NCX1 50 dyad-to-PD ratio of 1:2 is most consistent with the experimental data of Litwin et al. [75]. This further supports a dyad-to-PD NCX1 ratio of 1:2 in agreement with the imaging data of Wang et al. [68]. + + + Figure 2-20: Effects of local [Na ] ([Na ]d and [Na ]pd) on ECC gain. (A) ECC gain with + 2+ 2+ local [Na ] set to 10, 20 and 40 mM ...... (initial condition...... for [Ca ]jsr and...... [Ca ]d 54 2+ + identical in all cases). (B) ECC gain with initial value of [Ca ]d arising from Na - 2+ dependent pre-conditioning but [Ca ]jsr identical in all cases. + + Figure 2-21: Effects of [Na ]d on CICR during AP-clamp with [Na ]cyto = 10 mM and + + [Na ]d = [Na ]pd = 10 (black lines), 40 mM between 10-20ms (red ...... lines) and 40...... mM 59 (blue lines). (A) AP clamp for the first 50ms. (B) JNCX1 during the first 50 ms during 2+ the AP-clamp. (C) JRyR2 fluxes. (D) RyR2 open probability. (E) [Ca ]d corresponding to the three values of local [Na+]. Figure 3-1: Schematics of Na+ local control in cardiomyocytes. (A) Model schematics for channel localization in the t-tubules in cardiomyocytes...... (B) A t-tubule...... -JSR cleft (or 60 CRU) of the whole-cell model (shown in cross-section) is composed of four dyadic subspace volumes arranged on a 2x2 grid, each containing 2 LCCs and 12 RyR2s. (C) Illustration of flattened JSR from the SRS model with a centered 7x7 RyR2 lattice and 7 LCC
...... 68
xii Figure 3-2: Surface plot for the cost function to constrain the whole-cell model. The minimum cost function value (red star) determines the optimized parameters of tauss2pd and fd to match experimental data in Despa et al. 2003 [137] and Su et al. 2001 [76]. + Figure 3-3: Model constraints. A. Normalized whole-cell INaK upon [K ]o activation. B. Cytosolic [Na ...... +] decay process...... upon NaK activation...... C. Voltage...... protocol with...... test 71 + + potential at 0 mV at 0.4Hz. Black line: [K ]o = 4mM; red line: [K ]o = 0.01 mM. D. 2+ An elevation in [Ca ]i upon inhibition of NaK. + 2+ Figure 3-4: Whole-cell model Na local control validation. A. [Ca ]i signals upon 2+ + caffeine application. [Ca ] decay is faster in the ...... presence of NaK...... ([K ]o = 6mM,.. 72 + black line) than with NaK inhibited ([K ]o = 0mM, red line), consistent with experimental measurement [124]. B. Dyadic [Na+] decay in the presence and absence of NaK. C. The magnitude of NCX1 current is smaller with NaK inhibition, which leads to the slow down of [Ca2+] decay. Figure 3-5: The existence of Na+ sparks generated by NCX1 during Ca2+ spark activity. A. [Ca2+] signal and [Na+] signal with 0% NaK ...... in the dyad. The...... dynamics of Na....+ 76 spark is slower than Ca2+ sparks. B. [Ca2+] signal and [Na+] signal with 13% NaK in the dyad space. The Na+ spark magnitude and half duration are smaller. Figure 3-6: Effects of NaK localization on Ca2+ and Na+ spark properties in the whole- cell model. The role of NaK distribution between cytosol and dyad only ...... (fd+pd = fd 77 since fpd = 0, solid lines), between cytosol and PD only (fd+pd = fpd since fd = 0, 2+ 2+ + dashed lines) on whole-cell Ca spark rate (A), peak [Ca ]d (B), peak [Na ]d (C), + 2+ + Na spark duration (D), diastolic [Ca ]d (E), diastolic [Na ]d (F). Figure 3-7: Effects of NaK on SRS model Ca2+ sparks and Na+ sparks. Spark fidelity simulations were initiated by opening a single random RyRs. NaKs ...... were placed in 79 the dyad only (blue bars), PD only (yellow bars). (A) Predicted Ca2+ spark rate. (B) Ca2+ spark amplitude. (C) Na+ spark amplitude. (D) Na+ spark duration measured as FDHM. Figure 3-8: Effects of various dyadic NaK distributions (fd values of 0, 0.10, 0.20, and 0.40) on ...... APs and Ca2+ handling...... with no PD...... NaK. (A) Aps...... (B) Cytosolic ...... Ca2+ 80 2+ transients [Ca ]i. (C) whole-cell INCX1. Arrows indicate time of ENCX1 crossing for 2+ 2+ NaK fd = 0 (blue) and fd = 0.40 (red). (D) Dyadic space Ca [Ca ]d. (E) whole-cell + INaK. (F) Dyadic space [Na ]d. Figure 3-9: Effects of NaK redistribution in PD on ECC. (fpd values of 0, 0.20, 0.40, 0.60 and 0.80) on APs and Ca2+ handling ...... with no dyadic...... NaK. (A) Action...... potential with. 82 NaK placement in the PD space. (B) Ca2+ transient. (C) Total NCX1 currents. (D) 2+ + [Ca ]d. (E) Total NaK currents. (F) [Na ]d. + Figure 3-10: [Na ]i drift rate as a function of NaK distribution. Figure 3-11: Neuronal INa contributes to the CICR ...... process. (A) Voltage...... protocol with...... test 83 potential at 0mV for 200ms from a holding potential of -80mV...... (B) Cytosolic...... Ca2+ 84 transients with control (black line), only neuronal INa inhibition (red line), only LCC inhibition (blue line), and both LCC and NCX1 inhibition (green line). (C) The sum of INCX1 in dyad and PD. (D) Dyadic space [Ca2+]. (E) RyR2 flux. (F) Dyadic space [Na+] dynamics. Figure 3-12: ECC gain comparison between control and neuronal INa inhibition with the same initial condition...... 86
...... 87
xiii Figure 3-13: Ca2+ spark analysis for control and ankyrin-B+/- following AP pacing at 0.5, 2+ 2+ 2+ 1, and 2 Hz. (A) Whole-cell Ca sparks. (B) [Ca ]jsr. (C) Whole-cell Ca sparks 2+ normalized to [Ca ]jsr. Figure 3-14: AP pacing properties comparison in control (black line), 50% NCX1 reduction in dyad+PD (blue ...... line), 50% NaK...... reduction in...... dyad+PD (green...... line), 88 ankryin-B+/- deficiency (both 50% reduction, red line). (A) Action potential. 50% 2+ 2+ NaK reduction prolongs APD. (B) [Ca ] transient. (C) [Ca ]d. (D) LCC current. 2+ (E) Zoom-in of [Ca ]d during the diastole phase. (F) Total NCX1 current. (G) + 2+ [Na ]d. (H) [Ca ]jsr. Figure 3-15: The existence of EADs in ankyrin-B+/-. (A) APs. (B) Ca2+ transients 2+ 2+ 2+ + 2+ [Ca ]i. (C) Dyadic space ...... Ca [Ca ]d...... (D) ILCC. (E) [Na...... ]d. (F) INCX1...... (G) [Ca ]jsr. 89 (H) INaK. Figure 3-16: Examination of the time sequence for EAD generation compared between control (black) ...... and ankryin...... -B+/- deficiency...... (red) under ISO...... stimulation. (A)...... Action 91 +/- 2+ potential. Ankryin-B remains in the depolarized phase. (B) [Ca ]d and (C) PRyRopen in ankryin-B+/- exhibits a diverging behavior before the reference time point 23.21 s. (D) LCC open probability diverges from the control condition after the reference time point. (E) The sum of NCX1 and NaK currents becomes more inward before the reference time point. (F) Total current of cell becomes more inward before reference time point. + Figure 3-17: An example of Na sparks generated by neuronal INa upon voltage step to 0 mM. Average Na+ spark ...... peak is ~26.7...... mM and half duration...... is ~4.3 ms...... 92 Figure 5-1: Model schematic for neuronal Na+ channel ...... 96 ...... 115
xiv
Chapter 1 - Introduction
1.1 Objective
Coronary heart disease claims approximately one life every minute and accounts
for more than 600,000 deaths per year in the United States. Arrhythmia is the primary
cause of death in these individuals ([1]). Clearly, it is crucial to understand the molecular mechanisms that cause the arrhythmic behavior. Despite advances in pharmaceutical and medical options to prevent arrhythmia and sudden deaths, there is clearly a specific need to gain a better understanding of the events that occur at the molecular and cellular level
that lead to those life-threatening conditions. Therefore, the overall goal of my research is
to investigate and understand the ion channel/pump functions in Ca2+ and Na+
homeostasis and the ionic mechanisms responsible for arrhythmia generation. In order to
achieve this goal, I use multi-scale mathematical modeling and computational
simulations, based on experimental data, to uncover the roles of NCX1 and NaK coupling
on cardiac functions in healthy and pathological conditions.
1.2 Cardiac Action Potential
The cardiac action potential (AP) is dependent upon electrical currents generated
by the flow of several different ions, including Na+, Ca2+, K+, and Cl-, across the cell
membrane. There are several different types of ion transporters, including ion channels,
ion pumps, and ion exchangers. Voltage-gated ion channels are a class of ion channels
that open and close in response to a change in the membrane potential (Vm). At the
resting Vm (~-90 mV in the ventricular cardiomyocytes), the membrane is nearly
1 + 2+ + impermeable to Na and Ca but slightly permeable to K . Therefore, the resting Vm is
close to the value of K+ Nernst potential.
With the application of an external, depolarizing stimulus, voltage-gated Na+
channels in the cell membrane open and allow Na+ ions to rapidly flow into the cell down its electrochemical gradient. This influx of positively charged Na+ ions further depolarizes the membrane, opening more sodium channels and increasing the flow of Na+
ions. The Na+ channels then rapidly inactivate. Meanwhile, the Ca2+ and K+ channels,
which have slower kinetics than Na+ channels, begin to open. The influx of positive Ca2+
ions is balanced by the efflux of positive K+ ions leading to the plateau phase of the
action potential. The Ca2+ channels then begin to inactivate while the K+ channels are still
open, allowing the cell to repolarize back toward the resting membrane potential. The
concentration gradients of the ions are re-established by ion pumps and exchangers[2].
1.3 Excitation-Contraction Coupling
Influx of Ca2+ during the cardiomyocyte action potential causes the cell to contract. Depolarization of myocardial cells stimulates the opening of the voltage-gated
L-Type Ca2+ channels (LCC) in the plasma membrane. This initial influx of Ca2+ down its concentration gradient into the dyad space, formed by opposing membranes of the transverse-tubules (t-tubules) and junctional sarcoplasmic reticulum (JSR), triggers process known as Ca2+-induced-Ca2+-release (CICR). Ca2+ ions entering the cell bind to
Ca2+ channels ryanodine receptors (RyR2) located on the JSR, which acts as a Ca2+
storage unit during muscle relaxation. When Ca2+ ion binds to RyR2, the channels open and Ca2+ from JSR is released into the dyadic space. The Ca2+ will diffuse from the dyad
2+ 2+ to the cytosol, which increases the intracellular Ca concentration ([Ca ]i). The free
2 Ca2+ in the cytosol binds with a protein called troponin-C. This complex is then bound to
tropomyosin which is attached to a thin filament of actin. These thin filaments surround
thick filaments composed of myosin. The binding of Ca2+ to troponin causes a
conformational change which allows the myosin heads along the think filament to bind to
the thin filament. Following another conformational change, a power stroke occurs that
pulls the filaments in opposite directions resulting in muscle contraction. The excitation-
contraction coupling ends as cytosolic [Ca2+] is cycled back into the network
sarcoplasmic reticulum (NSR) through sarcoplasmic reticulum Ca2+-ATPase (SERCA) or is pumped out of the cell via plasma membrane Ca2+-ATPase (PMCA) and Na+/Ca2+
exchanger (NCX1).
1.4 Cardiac dyad
The cell membrane of a ventricular cardiomyocyte contains a large number of
membrane invaginations (t-tubules). Membrane proteins necessary for excitation-
contraction coupling (ECC), specifically LCCs, are located in the t-tubules. As mentioned
above, the proximity of the t-tubule to the JSR membrane is known as the cardiac dyad,
shown in Fig. 1-1. The height of the dyad is ~15 nm.
3
2+ + 2+ 2+ Figure 1-1: Ca and Na transport in ventricular myocytes and Ca -induced-Ca -
release process
Located across from the LCCs are clusters of RyR2s on the JSR membrane. By
positioning the LCCs near the RyR2, the dyad allows for a very small influx of Ca2+ to
2+ trigger the release of Ca by JSR . Tomographic data of mouse ventricular myocyte has
provided surprising insights into the architecture of the dyad [3] . The average volume of
the dyadic cleft is ~2.9x10 5 nm 3 (ranging from 9.3x10 3 to 1.5x10 6 nm3). In addition, recent super -resolution fluorescence microscopy technique showed that the majority of
RyR2 channels are organized in clusters of ~25 RyR 2s in rat myocytes [4]. Several of the
proteins i n the cardiac dyad, including LCC and RyR2 s, are regulated by phosphorylation
and dephosphorylation. Phosphorylation of LCC and RyR2 by both protein kinase A
2+ (PKA) and Ca -calmodulin -dependent protein kinase II (CaMKII) regulates the
activities of those channels in the dyadic space.
1.5 Sodium Calcium Exchanger
4 The NCX1 is an active transporter, translocating three Na+ ions in exchange for one Ca2+ ion across the plasma membrane, and is the main route for Ca2+ extrusion.
+ 2+ Trans-sarcolemmal Na and Ca concentration gradients and Vm determine whether NCX1
functions in the forward mode (Ca2+ efflux, inward net current) or reverse mode (Ca2+
influx, outward net current). NCX1 plays a key role in the regulation of intracellular
[Ca2+] and [Na+] in cardiomyocytes, serving as the primary Ca2+ extrusion mechanism. In
larger mammals, NCX1 extrudes ~ 20-50% of the total Ca2+ comprising the intracellular
Ca2+ transient [5, 6], matching the amount of Ca2+ that enters through L-type Ca2+
channels (LCCs) at steady state. However, as a complex nexus integrating both Ca2+ and
Vm signals, there remain gaps in our understanding of the multiple physiological roles of
NCX1 in cardiac function in health and disease. The reversibility of NCX1 has naturally led to the question whether under some circumstances NCX1 can bring Ca2+ into the cell and directly trigger or enhance ECC. Immunofluorescence studies in ventricular myocytes have shown that a fraction of NCX1, ranging from 4-8 to 42%, is co-localized with RyR2 clusters in the t-tubules [7-9]. Physical co-localization potentially enables
NCX1 to have functional access to the dyadic cleft and modulate local Ca2+ dynamics.
1.6 Na+ Fuzzy Space
In addition to NCX1 localization in the dyadic space, other Na+ channels and pumps have been suggested to reside in the t-tubules and potentially modulates the Na+
concentration within/near the dyadic space. The Na+/K+-APTase (NaK) is the primary
membrane transporter regulating Na+ homeostasis in cardiomyocytes. Voltage-gated Na+
channels (INa) play an important role in the ECC process by causing the rapid upstroke of the action potential (AP) [10]. INas have traditionally been thought to be composed of
5 mainly by the cardiac Nav1.5 isoforms, but recent studies have demonstrated the
existence of neuronal Na channels isoforms (Nav1.1, Nav1.2, Nav1.3, Nav1.6) in
ventricular myocytes [11-14]. They can be inhibited by nano-moler levels of tetrodotoxin
(TTX), whereas cardiac INa is not affected. Neuronal INa makes up for 5-30% of the total
INa depending on cardiac preparations and animal species [12, 15, 16]. There is mounting
evidence to suggest that those Na+ channels can contribute to the existence of Na+
microdomains. A Na+ microdomain involving neuronal Na+ channels, NCX1 and RyR2 was first proposed by Lederer and coworkers and the [Na+] microdomain may exert an impact on the CICR process through the reverse mode of NCX1 [17, 18]. The concept of a subsarcolemmal space with NCX1 and NaK has also been proposed in previous electrophysiology and modeling studies and it was suggested that the [Na+] in this space can be several-fold higher than the cytosol [19, 20]. In addition, experiments using electron probe X-ray analysis also reported an existence of an elevated Na+ submembrane
[20, 21]. Here we are most interested in how NaK and neuronal INa work together with
NCX1 to regulate the Na+ microdomain that overlaps with the traditional Ca2+ dyadic
space.
1.7 Ankyrin-B and Localization of NCX1 and NaK
Ankyrin polypeptides are a family of multifunctional proteins responsible for the targeting and stabilization of ion channels, transporters, and signaling molecules at the cell membrane in cardiomyocytes [22-24]. Ankyrins link these integral membrane proteins and cell adhesion molecules to the actin/spectrin cytoskeleton. ANK2 encodes ankryin-B protein and it can be found in brain, heart, and thymus [25, 26]. Ankyrin-B has four major domains including a membrane binding domain, a spectrin binding domain, a
6 death domain, and a C-terminal domain [27]. The membrane binding domain is where
different membrane proteins bind to the ankyrin. It has been shown that NaK, NCX1, and
inositol 1,4,5 triphosphate (InsP3) receptor are bound to ankryin-B to be targeted to the t-
tubules [28]. Ankyrin-B has the ability to bind to multiple membrane proteins at the same
time, which allows large protein complexes to form.
Proper activity of ankyrin-B is necessary for normal cardiac activity. In particular,
ankyrin-B dysfunction has been linked to long QT syndrome. Dysregulation of ankyrin-B
protein was identified as the cause in Long QT type 4 syndrome by Mohler et al.
2003[29]. Mohler et al. 2005 then presented that ankyrin-B is localized in both the M-line
and Z-line/t-tubules. NCX1 and NaK are mainly co-localized with the t-tubular ankyrin-
B. In ankyrin-B+/- deficient cardiomyocytes, t-tubular ankyrin-B, as well as its associated
proteins NCX1 and NaK are preferentially targeted and markedly reduced. Several
ankyrin-B alternative splice isoforms have been identified [30-32] and it was suggested that the M-line ankyrin-B does not possess the NCX1 binding sites, which does not impact NCX1 localization to the t-tubules [31]. Furthermore, it was shown that the M-
line ankyrin-B interacts with obscurin, which targets and stabilizes ankyrin-B localization
to the M-lines [30]. Ankyrin-B defect cardiomyocytes exhibit higher Ca2+ spark activity
2+ and an increase in [Ca ]i despite no significant alteration in action potential duration
(APD) or LCC peak currents. It also has been linked with abnormal electrophysiology in ventricular myocytes with beta-adrenergic stimulation. The ways in which Ca2+ and Na+
dynamics change locally to enhance the propensity for arrhythmogenic behavior in
ankyrin-B+/- defect cells remains poorly understood.
7 In addition, ankyrin-B+/- dysfunction has been observed in acquired forms of heart disease. In a study by Hund et al., it was shown that ankyrin-B protein levels and localization are reduced following myocardial infarction [33]. Furthermore, a decrease of ankyrin-B protein expression levels is also observed in heart failure conditions [34]. This
further suggests the importance of proper targeting and localization of ion channels and
ion pumps in the process of normal cardiac functions.
In summary, the action potential is a highly controlled cellular process dependent
upon the proper regulation and movement of charged ions across the cell plasma
membrane. When this process is disrupted, life-threatening arrhythmic events and sudden
cardiac death may occur. Potential disruptions include the mishandling of Ca2+ dynamics,
mutations in ion channels or ion channel accessory protein such as ankyrin-B.
Both the NCX1 immunofluorescence studies and ankyrin-B studies suggest that
NCX1 and NaK are in a privileged position to regulate the local [Ca2+] and [Na+] within/near the dyadic space and potentially modulate the CICR process. However, there has been significant debate as to whether or not NCX1 current reverses and generates an influx of Ca2+ that contributes to the trigger for JSR Ca2+ release. Furthermore, how
NCX1 and NaK co-localization regulate the local [Na+] and the CICR properties through
NCX1 remains unclear. Therefore, my thesis research will focus on addressing these
questions.
1.8 Mathematical Modeling of Electrophysiology
As a result of the complex Ca2+ and Na+ microdomain regulation through NCX1,
NaK and neuronal INa in the dyad, it is hard to tease apart the role of each component in
8 this CICR process experimentally. Therefore, computational models can be used to help
us understand better of their modulation in ion homeostasis and during the CICR process.
While many different medical treatment options for arrhythmias are available, a
better understanding of what occurs at the molecular and cellular level may help explain
the initiation of the arrhythmia syndrome and lead to the development of new therapeutic
strategies. Using mathematical modeling, we could uncover the underlying changes of
local Ca2+ and Na+ dynamics and regulation that contribute to the arrhythmia generation in ankyrin-B+/- dysfunction.
Mathematical modeling of excitable cells began with Hodgkin and Huxley in the
1950s and their work has served as the foundation for modeling studies since then.
Hodgkin and Huxley formulated the first computational model of the action potential of a giant squid nerve axon. Since their work, ion channels were identified as a protein that allowed for the movement of ions across the membrane. Noble [35] was among the first to apply Hodgkin and Huxley’s theory to reproduce the plateau action potential seen in
+ + cardiomycoytes. However, it was assumed that [Na ]i and [K ]i remains constant during an action potential. Difrancesco and Noble 1985 [36] were able to lead next major advance in cardiac modeling by integrating ion channels, membrane transporters, and the dynamics of intracellular ions concentrations. This model established the conceptual framework on which all subsequent models of the myocyte have been built.
Mathematical models are dependent upon available experimental data. With development in single cell and single channels recording techniques, it allowed for description of individual channel kinetics and ionic current by many subsequent computational models
of ventricular myocytes [37]. These models accounted for dynamic concentration
9 changes of the intracellular ions, including Ca2+, Na+ and K+, and the effects they had on transmembrane currents. The model incorporated NaK, NCX1, PMCA in the sarcolemma, a two-compartment sarcoplasmic reticulum, and Ca2+ buffering. However, those models of the cardiomyocyte do not incorporate biophysical mechanisms of local
control of SR Ca2+. In these models all Ca2+ influx through sarcolemmal LCCs and Ca2+
release flux through RyR2 goes into a common Ca2+ compartment. A comprehensive
model of the ventricular based on the theory of local control of SR Ca2+ release was developed by Greenstein and Winslow 2002 [38]. This model included a population of dyadic Ca2+ release units. Local interactions of individual sarcolemmal LCCs with nearby
RyR2s in the JSR membrane are simulated stochastically. Ca2+ local control has been demonstrated to be important to reproduce the graded Ca2+ release phenomenon and also
plays a crucial role in establishing the integrative electrophysiological properties.
With advancement in microscopy/imaging techniques, individual Ca2+ release events, referred as Ca2+ sparks, can be visualized using fluorescent Ca2+ indicators and confocal microscopy. A Ca2+ spark occurs when a RyR2 opens in spontaneously and
2+ causes a rise in [Ca ]d that triggers the rest of the RyR2 clusters. Understanding the
regulation of Ca2+ dynamics in a single Ca2+-release unit that underlies the CICR process is important to understanding healthy and diseased. A three-dimensional (3D) biophysically constrained Ca2+ spark super-resolution (SRS) model has been previously
in the lab by Walker et al [39]. The model reproduced important physiological parameters
like Ca2+ spark kinetics and Ca2+ spark frequency.
Computational models have helped us gain a better understanding of cardiac
physiology. With mathematical modeling it is possible to run simulations for which
10 experiments are impossible. These models have already made significant contributions to
the study of cardiovascular physiology and disease with a great potential for future
modeling studies. As stated earlier, the regulation of Ca2+ and Na+ microdomains through
NCX1, NaK and neuronal Na+ channels are not yet investigated in those models. In order to address the questions of the roles NCX1-NaK functional coupling, we decide to employ a multi-scale modeling approach with both the SRS model as well as a whole-cell model of cardiomyocyte. We hypothesize that 1) NCX1 in the t-tubules regulates the
CICR progress but its roles differ during diastole and systole phases. It means that NCX1 suppresses Ca2+ spark generation at rest, whereas it augments the triggering current
during the CICR process at depolarized membrane potentials. 2) Co-localization of
NCX1 and NaK regulates local Na+ levels and the CICR properties. Ankyrin-B down- regulation disrupts NCX1-NaK coupling in the t-tubules, leading to arrhythmia generation. Important aspects of the modeling efforts in this thesis research will include:
1) Develop a biophysically-constrained markov chain model for NCX1 that characterizes both the transport kinetics as well as the dynamics of intracellular Ca2+-dependent allosteric regulation; 2) Incorporating NCX1 in the dyadic and PD spaces in both the SRS
Ca2+ spark model as well as a canine cardiomyocyte model with stochastic simulations of
LCCs and RyRs to investigate the dual roles of NCX1 in Ca2+ dynamics and the CICR process and to achieve validity of this multi-scale modeling approach; 3) Development of
Na+ local control dynamics in the dyad and PD with NaK and neuronal Na+ channels in
the dyad and PD to understand the roles of NaK and neuronal Na+ channels in local Na+ regulation; 4) application of the whole-cell model to mimic ankyrin-B+/- deficiency
11 condition to show that reduction in NCX1 and NaK in the t-tubules leads to an elevation in activities in Ca2+ spark and to increase susceptibility to early-afterdepolarizations.
12 Chapter 2 - NCX1 regulation of CICR
2.1 Background
NCX1 is an important Ca2+ extrusion mechanism in cardiomyocytes. Elevation of
2+ 2+ intracellular Ca concentration ([Ca ]i) allosterically activates NCX1 allowing ionic exchange to occur. The thermodynamically driven cycling of NCX1 as well as its allosteric activation are Ca2+-dependent mechanisms, therefore these underlying processes can be difficult to differentiate experimentally. Allosteric regulation of NCX1
2+ by [Ca ]i was originally demonstrated in mammalian cells by Kimura et al. [40] via two
high-affinity Ca2+ ion binding sites. These sites are distinct from the ion transport sites,
and exhibit high cooperativity of binding [41]. More recently it has been shown that there
are two Ca2+ binding domains (CBD1 and CBD2; jointly termed CBD12) that bind up to
six Ca2+ ions per protein [42-45]. CBD1 and CBD2 contain four (Ca1, Ca2, Ca3, and
Ca4) and two (CaI and CaII) Ca2+-binding sites, respectively [42, 46]. Measurements of
Ca2+ binding affinities in isolated CBD12 proteins in vitro [44] and analyses of transporter currents in NCX1 mutants with each Ca2+ binding site ablated have helped
2+ identify their regulatory roles [42, 47, 48]. These studies indicated that at low [Ca ]i the
two high affinity sites of CBD1, Ca3 and Ca4, act as the primary Ca2+ sensors [47].
2+ Elevated [Ca ]i may result in occupation of the CaI site at CBD2 [42, 49], further activating NCX1. The low affinity sites of CBD1, Ca1 and Ca2, and CBD2 site CaII are likely to be occupied only at very high [Ca2+], as would occur in the dyadic space
between the opposing membranes of the t-tubules and the junctional sarcoplasmic
reticulum (JSR) in cardiomyocytes [50]. Time constants of allosteric NCX1 activation
13 have been measured in the range of 0.1-10 s in membrane patches [47, 51-54] and
additional studies using caffeine application [55-57] or flash-photolysis [58, 59] to
2+ 2+ generate rapid elevation of [Ca ]i demonstrated rapid activation of NCX1 by [Ca ]i. The
2+ Ca half-activation concentration (KmAct) has been measured in the range of 25-600 nM in both membrane patches and intact cardiomyocytes [54, 55, 60-63]. Ottolia et al. [64] observed beat-to-beat conformational changes in CBD12 by measuring fluorescent
2+ resonance energy transfer in response to changes of [Ca ]i in cardiomyocytes, but how
these changes in CBD12 conformation lead to NCX1 activation remains unclear.
These data suggest that allosteric regulation of NCX1 may occur over a wide
range of [Ca2+] from as low as ~ 100 nM to as high as ~ 100 µM. Therefore, the spatial
distribution and localization of NCX1 will be an important factor in determining the
nature of its Ca2+-dependent allosteric regulation. If positioned in or near the dyad, NCX1 can potentially be strongly activated by high (> 100 µM) local [Ca2+] in the dyadic space
2+ ([Ca ]d). While multiple immunofluorescence labeling studies have suggested that up to
40-60% of NCX1 is localized in the t-tubular system [7-9, 65-67], it has been difficult to assess the degree to which NCX1 is co-localized within and/or near the dyad in imaging studies because of the high spatial resolution required to address this question. Early studies [7, 8] showed that only 4-8% of NCX1s are co-localized with type 2 ryanodine
receptors (RyR2s) in rat myocytes. However, using immuno-gold labeling methods,
Thomas et al. [65] estimated that the distribution of NCX1s and RyR2s were similar. This
debate has been re-invigorated by a recent study in which super-high resolution optical
imaging showed that ~18% of NCX1s co-localize (i.e., fluorescent labels targeted to
NCX1 and RyR2 share overlapping voxels) with RyR2s in the dyad, and that ~30% of
14 additional NCX1s are within 120 nm of the nearest RyR2 [68]. These important new
findings suggest that NCX1 may be in a privileged location to modulate cardiac CICR.
Experimental studies suggest that NCX1 may play multiple roles in CICR.
Several studies employing NCX1 inhibition or de-tubulation have demonstrated that forward mode NCX1-mediated Ca2+ extrusion may lower whole-cell Ca2+ spark frequency and Ca2+ spark amplitude [68-71]. There has been significant debate as to
whether or not NCX1 current reverses during the action potential (AP) and generates an
influx of Ca2+ that contributes to the trigger for JSR Ca2+ release. Some studies have
shown no role of reverse-mode NCX1-mediated Ca2+ entry on CICR [72-74]. Others
have demonstrated increased Ca2+ triggering currents or augmented Ca2+ release at
depolarized potentials attributable to reverse-mode NCX1 Ca2+ flux [75-79]. It has been suggested that voltage-dependent LCC openings following the AP upstroke provide Ca2+
for allosteric NCX1 activation, which in turn allows NCX1-mediated Ca2+ influx to enhance CICR during the AP plateau [78].
These results demonstrate how challenging it can be to experimentally tease apart the complex role of NCX1 in CICR. To help address this question of whether NCX1 can play dual roles in modulating the CICR process, this study presents a new biophysically based computational model of NCX1 describing both its transport kinetics and allosteric regulation by Ca2+. This model of NCX1 is integrated into a previously developed three-
dimensional (3D) model of the Ca2+ spark that includes high spatial resolution representations of the JSR, T-tubules, and the dyadic space [39], referred to as the super- resolution spark (SRS) model. The SRS model is used investigate how positioning NCX1 at specific locations within and near the dyad influences Ca2+ spark generation.
15 Furthermore, the Greenstein and Winslow model of the cardiac ventricular myocyte [38],
which reproduces independent (stochastic) local dyadic JSR Ca2+ release events underlying cell-wide excitation-contraction coupling (ECC), is extended to incorporate a spatial “peri-dyad” (PD) compartment that is immediately adjacent to and surrounding each dyad. The parameters that define Ca2+ fluxes both into and out of the PD, and hence
2+ 2+ PD Ca concentration ([Ca ]pd), are informed by the SRS model results in order to ensure validity of this multi-scale modeling approach. This whole-cell model is used to examine the ways in which differential placement of NCX1 into cytosolic, PD, and dyadic compartments influences properties of CICR and the cardiac AP.
2.2 Methods
2.2.1 NCX1 Kinetic Model with CBD12-mediated Allosteric Activation
16 Figure 2-1: NCX1 kinetic schemes and dyad model geometry. (A) State model for NCX1
transport kinetics. (B) State model for CBD12 Ca2+-dependent allosteric regulation with partial activity coefficients (red). (C) 3D mesh from SRS model [39] showing a t-tubule modeled as a cylinder (blue) partially encircled by JSR (red) containing a cluster of
RyR2s (green-blue), forming a dyadic space with a 15 nm gap between these membranes.
(D) Illustration of flattened JSR from the SRS model with a centered 7x7 RyR2 lattice.
(E) A t-tubule-JSR cleft (or CRU) of the whole-cell model (shown in cross-section) is composed of four dyadic subspace volumes arranged on a 2x2 grid, each containing 2
LCCs and 12 RyR2s. The PD is a single compartment that surrounds the subspace grid
(i.e. the dyad).
We present a novel model of NCX1 consisting of two modules [80]. The first,
shown in Fig. 2-1A, describes NCX1 electrochemical transport kinetics. The second,
shown in Fig. 2-1B, describes Ca2+-dependent allosteric regulation. NCX1 current is the product of an electrochemical factor (ΔE) and an allosteric factor (Allo), as shown in previous studies [55, 81]:
(1)
𝐼𝐼 = 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴×∆𝐸𝐸
ΔE represents the transport of Na+ and Ca2+ across the cell membrane and is modeled as a Markov process representation of the ping pong bi bi cyclic reaction scheme [82, 83], which is a consecutive ordered kinetic mechanism that has two membrane-crossing transitions. NCX1 is assumed to function at a non-equilibrium steady
17 state and the turnover rate is represented using the net reaction velocity through the
NCX1 cycle. The governing equations for ion transport are developed in the Appendix
A.1 (Eqs. A1.2-A1.14). The rates for membrane translocation reflect the rate-limiting
steps of NCX1 cycling, which are dependent on Vm and the unloaded exchanger charge
(~ -2.56e) [59, 84], as described by Keener and Sneyd [85]. The ion binding/dissociation rate constants and membrane translocation rate constants in the NCX1 transport model were constrained utilizing experimental steady state NCX1 current-voltage (I-V) curves measured using fully-active NCX1 in giant membrane patches [51] (Fig. 2-2).
Figure 2-2: The electrochemical factor is constrained by experimental steady state NCX1 current-voltage (I-V) curves measured using fully-active NCX1 in giant membrane patches treated with chymotrypsin [51]. Experimental data (circles) and model fits (black
2+ + solid lines) are shown. (A) Fits to NCX1 I-V curves at 1 µM [Ca ]i and a range of [Na ]i.
2+ + (B) Fits to NCX1 I-V curves at 0.1 µM [Ca ]i and a range of [Na ]i.
Allosteric regulation of NCX1 is mediated via Ca2+ binding to the CBD12 domain
[50, 64]. A sequential binding CBD12 model consisting of a linear set of seven states (A0
– A6) was first developed using data on the binding affinities for each site measured in
18 isolated CBD12 proteins [44, 86]. Each CBD12 protein can bind up to 6 Ca2+ ions. A sequential binding CBD12 model consisting of a linear set of seven states (A0 – A6) was
therefore developed (Fig. 2-3A) using data on the binding affinities for each site
measured in isolated CBD12 proteins [44, 86]. Association and dissociation rate
constants were determined by fitting in vitro experimental measurements of the CBD12
equilibrium Ca2+ binding curve and data from stop-flow experiments of Ca2+ dissociation
(for the first three Ca2+ dissociation constants). Model fits are shown in Fig. 2-4A-B. This initial model was then simplified using rapid equilibrium approximations. States A1 and
2+ A2 were coalesced since there are normally 2 Ca bound to CBD12 at physiological
2+ 2+ diastolic [Ca ]i (100 nM). The dissociation rates of the low-affinity Ca binding sites
(A4, A5, and A6) are ~ 100- to 1000-fold greater than those of the high-affinity sites.
Therefore, rapid equilibrium approximations were used to coalesce states A3-A6 into a single state, yielding the 3-state model of CBD12 Ca2+-binding in Fig. 2-3A. Transition
rates were derived using the fast equilibrium approximation (Eqs. A1.15-A1.18).
19
Figure 2-3: The CBD12 Ca2+ binding and allosteric regulation model. (A) Simplification of 7-state CBD12 Ca2+ binding model to a reduced 3-state model. (B) Model of CBD12
Ca2+-dependent allosteric activation.
20 Figure 2-4: Constraining the 7-state CBD12 sequential model (Fig. 2-3A). Experimental data in red, simulation results in black. (A) Equilibrium Ca2+ binding curve from isolated canine CBD12 protein was used to constrain the CBD12 model Ca2+ binding affinities
[44, 86]. (B) The kinetic stop-flow experiment using Quin-2 to deprive Ca2+ from CBD12
proteins and to constrain the Ca2+ dissociation rate constants for the first three Ca2+
binding sites [44, 86]
Time constants of allosteric NCX1 activation have been measured in the range of
0.1-10 s in membrane patches [47, 51-54] and additional studies using caffeine
2+ application [55-57] or flash-photolysis [58, 59] to generate rapid elevation of [Ca ]i have
2+ 2+ demonstrated rapid activation of NCX1 by [Ca ]i. The Ca half-activation concentration
(KmAct) has been measured in the range of 25-600 nM in both membrane patches and
intact cardiomyocytes [54, 55, 60-63]. These studies show that in response to a rapid
2+ increase in [Ca ]i, INCX1 exhibits an initial instantaneous increase followed by a slow secondary activation phase. This process was modeled by two steps of conformational transitions to represent the allosteric activation process, as shown in Fig. 2-3B. A partial activity coefficient F(state) is assigned to each activated state to represent fractional activity
of NCX1 in that state, and total allosteric activity of NCX1 is the weighted sum of
CBD12 state activities, given by Eq. (2).
A A A A (2)
2+ The𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 transition= 𝐹𝐹 rates+ 𝐹𝐹 α2, β2, +α4𝐹𝐹, β4 are constrained+ 𝐹𝐹 using both the dynamics of the Ca
2+ activation and normalized peak INCX1 as a function of Ca from membrane patch experiments [52, 61], as shown in Fig. 2-5. The NCX1 model reproduces rapid Ca2+-
21 2+ dependent allosteric activation in response to step increases of [Ca ]i. Ordinary
differential equations governing state occupancy probabilities are given in Eqs. A1.19-24.
Figure 2-5: Model constraints for CBD12 Ca2+-dependent allosteric regulation. (A)
Model fit to normalized peak INCX1 [52, 61]. (B) Model fit for NCX1 CBD12 activation
2+ versus experimental data in which inward NCX1 current is activated by increasing [Ca ]i
from 0 to 1, 3, or 5 µM in an inside-out giant membrane patch preparation [61]. A two-
phase dynamical activation process is characterized with a very rapid current jump
(achieves ~80% of its peak value in <500 ms) upon Ca2+ stimulation, followed by a secondary, slower development in current. The time courses of these phases of activation were used to constrain the rates (α2, β2, α4, β4) in conformational changes of CBD12 allosteric regulation in Fig. S3B.
Figure 2-6A shows that the equilibrium Ca2+ binding curve for the simplified
2+ model reproduces experimental data [44]. KmAct for CBD12 Ca -dependent allosteric regulation is estimated to be ~300 nM, consistent with experimental measurements in inside-out membrane patches and whole-cell patch clamp studies [52, 60, 62, 63]. The allosteric regulation model shows that there are always 2 Ca2+ ions bound to the CBD12
22 protein at physiological resting [Ca2+] (~100 nM), and there is a baseline NCX1
fractional activity of ~ 0.3.
The NCX1 model was then validated by comparison with experimental data not
included in the parameter fitting process. The model reproduced experimental
measurements of NCX1 fractional activity [54], steady state wild-type INCX1 [87], and dynamics of Ca2+-dependent activation [54], as shown in Fig. 2-6B-D. The fractional
activity of CBD12 saturates at [Ca2+] above ~30 µM, suggesting that its function remains sensitive to high levels of Ca2+ as predicted to occur in and near the dyad. A rapid
2+ increase in [Ca ]i results in rapid activation of NCX1 current, followed by a slow secondary phase (Fig. 2-6D), which is qualitatively similar to NCX1 Ca2+ activation dynamics measured in response to a step increase of [Ca2+] reported by Fujioka et al.
[54]. The model exhibits relatively slow activation kinetics in response to moderate
[Ca2+] steps, as would be sensed in the cytosolic compartment (Fig. 2-7A-C), but the
kinetic response of the exchanger is rapid in response to high [Ca2+], as would be sensed
within and near the dyad (Fig. 2-7D-F). To further investigate NCX1 behavior with Ca2+
allosteric regulation intact, additional Ca2+ clamps as well as Ca2+ signals simulated during AP pacing in the Greenstein and Winslow model [38] were applied as inputs to this NCX1 model.
23
Figure 2-6: NCX1 model constraint and validation. (A) CBD12 model constraint: Ca2+
binding site steady state occupancy compares to experimental data of Giladi et al. [44].
(B) Model NCX1 fractional activity compared with experimental data [54]. (C) Steady
state NCX1 I-V curve validation against whole-cell patch clamp results under various
2+ [Ca ]i [87]. (D). Fast and slow phases of NCX1 model activation time-course in
2+ response to [Ca ]i clamp to indicated value at (at 1 s) resembles those of Fujioka et al.
[54] (not shown).
24
Figure 2-7: Dynamical properties of NCX1 allosteric activation. (A) and (D): Rapid
cytosolic Ca2+ signals used in simulations to drive the Ca2+-dependent allosteric
2+ activation process of NCX1. (B) and (E): NCX1 current activation in response to [Ca ]i
2+ step increase. NCX1 exhibits relatively slow activation kinetics upon a moderate [Ca ]i
increase, as would be sensed in the cytosolic compartment. NCX1 activation kinetics are
2+ very fast in response to high levels of [Ca ]i, as would be sensed within and near the
2+ dyad. (C) and (F): NCX1 allosteric factor in response to [Ca ]i step increase.
2.2.2 NCX1 in the Super-resolution Spark Model
Walker et al. [39] recently developed the super-resolution spark (SRS) model in rat. This
model was used here to explore the potential roles of NCX1 in the dyadic space and
nearby regions. In the SRS model, the area of JSR membrane in contact with the t-tubule
25 is assumed to be a square with 465 nm edge length that wraps around a t-tubule, as shown
in Fig. 1C-D. A 7x7 lattice of RyR2s is positioned in the center of the JSR dyadic
surface. In order to facilitate comparison of SRS model spark properties in rat with those
obtained in the whole-cell model [38] used here, it was necessary to reduce spark
frequency from that measured in rat to that measured in canine. The ratio of spark
frequency in rat versus canine is ~ 2.3 (~133 cell-1 s-1 in rat vs. ~ 59 cell-1 s-1 in canine at
2+ 2+ 1 mM JSR [Ca ] ([Ca ]jsr)) [88, 89]. The RyR2 opening rate in the SRS model was adjusted to reproduce lower Ca2+ spark rate measured in canine versus rat. At rest, the adjusted canine whole-cell model produces a spark rate of ~1.3 cell-1 s-1 with 700 µM
2+ [Ca ]jsr.
As shown in Fig. 2-1D (red shaded region), the region bounded by the lateral edge
of the JSR and the outer edge of the centrally-located RyR2 lattice is defined as the peri-
dyad (PD). The profile of [Ca2+] declines very rapidly with distance outside this region,
2+ becoming comparable to [Ca ]i [90]. The model PD extends 124 nm beyond the RyR2
cluster, and has a height of 15 nm. Model simulations predict the average Ca2+ in this
2+ 2+ region is greatly elevated compared to [Ca ]i, with a peak of ~ 70 µM during a Ca
spark (Fig. 2-8D). Approximately 30% of non-dyadic NCX1s have been estimated to be
within 120 nm of the nearest RyR2 in the recent imaging study of Wang et al. [68]
(values estimated from their Fig. 5D).
NCX1s are treated as Ca2+ point sources arranged in the t-tubule membrane on a
lattice with 31 nm spacing (opposite RyR2s). To examine the effects of local INCX1 on
Ca2+ spark properties and spark fidelity (i.e. the probability that a spontaneous RyR2
2+ opening triggers a Ca spark), Vm was fixed at -80 mV and either the central or a
26 randomly selected RyR2 was opened. The spark rate (per release site) was determined by
the product of spark fidelity and RyR2 opening rate, and was then scaled to per cell
values. NCX1s were positioned only within the dyad and/or PD at various membrane
densities, and the effect of this positioning on Ca2+ sparks was investigated. Since RyR2s and NCX1s gate stochastically, more than 1,000 simulations were performed for each choice of NCX1 spatial distribution, and average responses were calculated. The methods used to estimate Ca2+ spark fidelity and rate are those previously described by Walker et
al. [39].
2.2.3 Spatial Localization of NCX1 in the Canine Whole-cell Model
In order to evaluate the roles of NCX1 and its spatial localization on whole
myocyte physiology, the NCX1 model was incorporated into the Greenstein and Winslow
[38] model of the canine ventricular myocyte, which incorporates stochastic simulations of LCC and RyR2 gating. In this model, the t-tubule-JSR cleft is represented as a four- compartment dyad (in which a single dyadic compartment is referred to as a subspace) surrounded by a single PD compartment (Fig. 2-1E), which taken together with their associated LCCs and RyR2s, is referred to as a Ca2+ release unit (CRU). Ca2+
concentration is assumed to be uniform within each compartment, and Ca2+ may diffuse passively between adjacent subspace compartments or across a subspace-PD boundary within the same CRU. Each dyadic subspace contains 2 LCCs and 12 RyR2s in the t- tubule and the JSR membranes, respectively (consistent with the SRS model). This yields a total of 8 LCCs and 48 RyR2s per CRU. A total of 6250 active CRUs were included per myocyte to give a total of 50,000 active LCCs, the ensemble current of which correspond to whole-cell measurements in canine myocytes [91]. A subset of CRUs (625 or 10%)
27 was used for all simulations in this study and all CRU Ca2+ fluxes were scaled to the total
number of CRUs to obtain whole-cell spark rate or whole-cell LCC currents and RyR2
Ca2+ fluxes. In addition, the whole-cell model was updated to incorporate the same 2- state RyR2 model [92] as that used in the SRS model. Ca2+-dependent allosteric
regulation of NCX1 in the dyad and PD was simulated stochastically while the
thermodynamically driven NCX1 transport rate was assumed to operate in steady-state at
all times. In the whole cell model, as a result of RyR2 formulation change, the forward rate
constants of LCC Ca2+-dependent inactivation (CDI) were modified to accommodate the high
2+ [Ca ]d in order to insure CDI occurs with the physiologically correct time-course during the AP
[38]. The modified equation for CDI transitions is given in Eq. A1.32) and the rate of changes of
2+ [Ca ]d are described as Eqs. A1.27-30.
As shown in Fig. 2-1E, the whole-cell model was extended such that each CRU
includes a single PD compartment immediately adjacent to and surrounding the dyad
which is a simplified representation of the PD space modeled in the SRS model. The
volume of the PD is ~ 4x that of the dyad, matching the SRS model PD volume. The PD
2+ 2+ 2+ is a single compartment with uniform Ca concentration ([Ca ]pd), and Ca can diffuse
between it, the cytosol, and each of the dyad subspace compartments. The PD model is
defined by two parameters; the Ca2+ diffusion (transfer) rate between a CRU subspace
and the PD (rss2pd); and the diffusion rate between the PD and cytosol (rpd2c). These two parameters were constrained to match SRS model PD Ca2+ profiles and average spark
properties under resting conditions (Fig. 2-8). These steps were taken in order to ensure
that the parameters that determine the nature of Ca2+ fluxes both into and out of the PD,
2+ and hence [Ca ]pd, are informed by the well-constrained SRS model results [39]. This is a critically important step in this multi-scale approach and enhances the validity of the
28 whole-cell model predictions. Spontaneous sparks were measured in the whole-cell
model with Vm held at -80 mV for 20 s and the simulated CRU release events were analyzed and used to estimate spark rate. A spark was determined to have occurred if the
[Ca2+] peak magnitude in a single dyadic subspace exceeded a threshold of 100 µM.
Figure 2-8: Determination of transfer time constants τss2pd and τpd2c in the whole-cell model, with constraints yielding Ca2+ spark properties consistent with those of the SRS model. * represents the optimized model value in the whole-cell model. (A) τpd2c defines
2+ 2+ peak [Ca ]pd. Spark rate (B), peak [Ca ]d (C), and full spark duration (D) from SRS model constrain the value of τss2pd.
In order to explore the physiological roles of Ca2+-dependent allosteric regulation
29 of NCX1 and the effects of NCX1 localization on ECC, NCX1 was positioned with
various distributions among the dyadic, PD, and cytosolic Ca2+ compartments of the cell
and both ECC gain and AP pacing protocols were performed. The distribution of NCX1
in the whole-cell model is defined by three parameters, fd, fpd, and fcyto, which represent the fraction of NCX1s that are localized to dyads, PDs, and the cytosol, respectively. By definition fd + fpd + fcyto = 1, and for notational convenience the combined fraction of
NCX1s localized to both dyad and PD is denoted fd+pd = fd + fpd. APs were generated by
2+ + pacing at 1 Hz for 15 - 20 beats until cytosolic Ca transients reached steady state. [Na ]i
is clamped to 10 mM for all simulations unless specified otherwise.
2.3 Results
30 2+ 2+ 2.3.1 INCX1 driven by [Ca ]d and [Ca ]i
2+ Figure 2-9: NCX1 dynamics driven by AP and [Ca ] clamp. (A) Baseline AP-clamp Vm
2+ 2+ generated by a previous whole-cell model [93], and (B) corresponding [Ca ]i and [Ca ]d signals.
NCX1 allosteric factor, Allo (C), and INCX1 (D) underlying APs paced from rest.
In order to investigate dynamics of NCX1 Ca2+-dependent allosteric regulation in
2+ response to physiologically relevant [Ca ] during the AP clamp, template Vm (Fig. 2-
2+ 2+ 9A), [Ca ]i (Fig. 2-9B, black line), and [Ca ]d (Fig. 2-9B, red line) waveforms were
generated using a previous whole-cell model [93]. The model was paced for at 1 Hz
starting from rest and these signals were then used to drive the NCX1 model presented
here. Figure 2-9C displays the NCX1 allosteric factor (Allo), and Fig. 2-9D shows INCX1.
31 2+ 2+ Driving NCX1 beat-to-beat with the higher [Ca ]d, as compared to [Ca ]i, leads to a
relatively more rapid allosteric activation of the exchanger and a greater level of NCX1
CBD12 activity is achieved. Similar simulation results are achieved in response to step
2+ increases of [Ca ] in conjunction with voltage-clamp (Fig. 2-7). INCX1 exhibits dramatically different responses to dyadic and cytosolic Ca2+ signals underlying the APs
st 2+ starting from the 1 beat. NCX1 current driven by [Ca ]i is primarily outward during the
2+ first ~200 ms of the AP. On the other hand, the NCX1 current driven by [Ca ]d exhibits a very brief outward current after the AP upstroke immediately followed by a rather large
2+ inward current arising from the elevation of [Ca ]d and the current remains inward for
the remainder of the AP.
2.3.2 Effect of NCX1 on Ca2+ sparks in the SRS model
To explore effects of NCX1 placement on spark morphology and frequency,
NCX1s were positioned in the dyad, PD, or both within the SRS model. The dyadic area of the t-tubule in this model is defined as a square patch of membrane directly opposed to the 7 x 7 array of RyR2s in the JSR membrane. This sarcolemmal membrane patch is similarly subdivided into a 7 x 7 array (where each element is 31 nm x 31 nm) such that
NCX1s can be placed directly across the cleft from RyR2s. The t-tubule surface of the
PD is defined by a concentric 15 x 15 array of similar membrane lattice elements excluding the central 7 x 7 array (which are within the dyad), on which NCX1s can be placed. To vary NCX1 membrane density, increasing numbers of NCX1 transporters (0 -
3) were allocated to the sarcolemmal membrane lattice sites within the dyad and/or PD. A spark was initiated by opening a random RyR2 in the dyad (Fig. 2-10). Figure 2-10A plots Ca2+ spark fidelity as a function of NCX1 membrane density when NCX1s are
32 placed only in the dyad (blue bars), only in the PD (red bars), or in both dyad and PD
(dyad + PD, yellow bars) under resting conditions. Spark fidelity decreases as NCX1
membrane density increases in all three cases. Exchangers placed in the dyad have a
greater impact on spark fidelity reduction than those placed in the PD. The model
predicts a ~ 32% reduction in spark fidelity when placing 2 NCX1s opposite each RyR2
in the dyad compared to the baseline case with no NCX1. Placement of NCX1 in dyad +
PD, compared with placement in the dyad alone, further contributes to the reduction of
spark fidelity, however the PD NCX1s only weakly influence local Ca2+ spark generation. An increasing presence of NCX1 in the dyad and/or PD reduced spark rate
(Fig. 2-10B), which is qualitatively consistent with experiments showing that NCX1 inhibition or de-tubulation leads to an increased spark rate [68, 69, 71]. Mean values of
2+ peak [Ca ]d (Fig. 2-10C) decrease with increasing density of NCX1 positioned in the
dyad, PD, or both. The mean Ca2+ spark amplitude is not significantly different from
control (no NCX1) when only 2 or fewer NCX1s are placed across each RyR2 in the
dyad, however with 3 NCX1s placed at each sarcolemmal lattice site, there is a small but
significant reduction in spark amplitude of ~ 20% (p < 0.05) compared to control (Fig. 2-
10C). These simulations support the idea that lower levels of dyadic NCX1 do not have a
significant effect on Ca2+ spark amplitude, but can effectively regulate spark fidelity and
rate. The former conclusion is in agreement with Hake et al. [94] who concluded that
2+ 2+ NCX1 has minimal impact on [Ca ]d once JSR Ca release is initiated due to the fact
that NCX1 Ca2+ flux is quite small relative to the RyR2 Ca2+ release flux. With 1 mM
2+ 2+ -7 [Ca ]jsr and 100 nM [Ca ]d, a single NCX1 current is calculated to be ~ 7.2 × 10 pA, which is at least 100,000 times smaller than a unitary RyR2 Ca2+ current (9.77 × 10-2
33 2+ 2+ pA). At 100 µM [Ca ]d (comparable to Ca spark amplitude), a single NCX1 current is
estimated to be ~ 2 × 10-4 pA, consistent with experimentally measured maximum unitary
NCX1 current [95] but still dwarfed by unitary RyR2 current. Therefore it is not
surprising that even when positioned in the dyad, NCX1 has little effect on Ca2+ release following spark initiation. However, at higher dyadic NCX1 densities (> 3 exchangers per lattice element) which are physiologically less likely to occur, there is a smaller Ca2+
gradient between JSR and dyad, and the NCX1 Ca2+ flux becomes comparable to Ca2+
flux through a single open RyR2, and therefore reduces Ca2+ spark amplitude. The reason this is physiologically unlikely is that these higher densities correspond to a localization of >50% of the cell NCX1 to the dyad, which is greater than the upper bound observed in
NCX1-RyR2 co-localization imaging studies [7, 9, 68]. Based on the observation that
~18% of NCX1 co-localize with RyR2 clusters [68], ~70 exchangers are calculated to reside in each dyad, which corresponds to 1-2 NCX1s per sarcolemmal lattice element. In contrast, NCX1s placed in the PD are by definition displaced from the dyad and therefore
2+ have less of impact on spark properties and [Ca ]d. NCX1 placement in the dyad and/or
PD leads to minor reductions in spark duration (measured as full duration at half
maximum amplitude, FDHM) (Fig. 2-10D) which is in qualitative agreement with
experimental findings [68, 70]. These results show that spark fidelity and rate are most
strongly affected by dyadic and PD placement of NCX1, while effects on spark amplitude
and duration are less significant. Simulations in which the spark was initiated by the
center RyR2 (Fig. 2-11) yielded similar results on NCX1-mediated modulation of spark
fidelity, rate, and morphology.
34
Figure 2-10: Effects of NCX1 on SRS model Ca2+ sparks. Spark fidelity simulations were initiated by opening a single random RyR2. NCX1s were placed in the dyad only
(blue bars), PD only (red bars), or both (yellow bars). (A) Predicted park fidelity. (B)
2+ Spark rate. (C) Spark amplitude measured as peak [Ca ]d, ** indicates statistically significant difference based on t-test (p < 0.05). (D) Spark duration measured as FDHM.
35 Figure 2-11: Effects of NCX1 on SRS model Ca2+ sparks. Spark fidelity simulations were initiated by opening a central RyR2. NCX1s were placed in the dyad only (blue bars), PD only (red bars), or both (yellow bars). (A) Predicted park fidelity. (B) Spark
2+ rate. (C) Spark amplitude measured as peak [Ca ]d, ** indicates statistically significant difference based on t-test (p < 0.05).
36 2.3.3 Role of NCX1 localization on Ca2+ sparks in the whole-cell model
As mentioned earlier, the SRS model was used to guide the whole cell model
building and parameter fitting to achieve consistency in whole cell spark frequency
between the two models (~60 cell-1s-1). In order to understand the effects of NCX1
localization on Ca2+ spark properties and CICR at the whole-cell level, a variety of NCX1 distributions were analyzed. In the first case, NCX1 was assumed to reside only in the dyad or cytosol, but not in the PD (i.e. fd+pd = fd = 1 – fcyto since fpd = 0) (Fig. 2-12, solid lines). In the second case, NCX1 was assumed to reside only in the PD or cytosol, but not in the dyad (i.e. fd+pd = fpd = 1 – fcyto since fd = 0) (Fig. 2-12, dashed lines). Finally,
NCX1 was assumed to reside in all three locations with a fd:fpd ratio of 1:2 as suggested by the imaging data of Wang et al. [68] (i.e. fd+pd = fd + fpd = 1 – fcyto where fpd = 2fd) (Fig.
2-12, dotted lines). In all cases, the total number of NCX1s in the cell was conserved.
2+ The effect of these different NCX1 distributions on spark rate (Fig. 2-12A), peak [Ca ]d
2+ (Fig. 2-12B), spark duration (Fig. 2-12C), and average diastolic [Ca ]d (Fig. 2-12D) were simulated in the whole-cell model. The results of redistributing NCX1 between the dyad and cytosol only (i.e. fpd = 0) are consistent with those obtained using the SRS model in that NCX1-mediated extrusion of Ca2+ at rest reduces whole-cell spark rate (Fig. 2-12A,
solid line). Simulations show that placing ~ 20% of NCX1 in the dyadic space (~ 80 % in
cytosol) results in ~ 40% reduction in spark rate and by placing ~ 80% of NCX1 in the
dyad (~ 20% in cytosol), spark activity is nearly eliminated. While spark rate is highly
dependent on spatial distribution of NCX1, the whole-cell model shows that dyadic
NCX1 plays less of a role in regulating individual Ca2+ spark properties, and that
redistributing NCX1 to PD and cytosol only (i.e. fd = 0) has much less impact on all spark
37 2+ properties (Fig. 2-12, dashed lines). Mean peak [Ca ]d and spark duration are reduced with increasing NCX1 distribution to the dyad and/or PD in a manner that matches the results of the SRS model. Furthermore, as predicted using the SRS model, spark duration is minimally influenced by redistribution of NCX1 to the dyad and/or PD (Fig. 2-12C).
2+ Diastolic [Ca ]d is greatly diminished with increasing NCX1 distribution to the dyad
and/or PD in the whole-cell model (Fig. 2-12D) consistent with SRS model behavior
(data not shown). This underlies the associated reduction on spark frequency and
suggests the spatial distribution of NCX1 plays an important role in resting cellular Ca2+
homeostasis.
38 Figure 2-12: Effects of NCX1 localization on spark properties in the whole-cell model.
The role of NCX1 distribution between cytosol and dyad only (fd+pd = fd since fpd = 0, solid lines), between cytosol and PD only (fd+pd = fpd since fd = 0, dashed lines), or among
all three compartments with a fd:fpd ratio of 1:2 (fd+pd = fd + fpd with fpd = 2fd, dotted lines)
2+ on whole-cell spark rate (A), peak [Ca ]d (B), spark duration measured as FDHM (C),
2+ and diastolic [Ca ]d (D). The total number of NCX1s in the cell is the same in all cases.
2.3.4 NCX1 localization and the cardiac action potential
APs were generated in the whole-cell model under various distributions of NCX1 between the cytosolic and dyadic compartments, with no NCX1 in the PD (fd values of 0,
2+ 0.05, 0.10, 0.15, and 0.20, all with fpd = 0) to examine underlying Ca dynamics. The
model was paced at 1 Hz to steady-state (15 beats) from the same initial condition for
each NCX1 distribution. Simulation results from the final paced beat in Fig. 2-13A show
that the AP notch becomes more depolarized from -20 mV to 0 mV, and APD prolongs
with increasing dyadic NCX1 distribution. Figure 2-13B demonstrates that increased fd
greatly enhances forward mode NCX1 operation, which underlies the depolarization of
the AP notch. With sufficient dyadic NCX1, INCX1 will be transiently inward during JSR
Ca2+ release, temporarily outward during the early AP plateau, and will finally reverse to
inward later in the AP plateau. There are therefore multiple times during the AP at which
Vm and the NCX1 reversal potential (ENCX1) intersect. With increasing fd, the late phase of INCX1 becomes increasingly inward, which shifts the NCX1 time-to-reversal from ~
270 ms to ~ 150 ms and helps to prolong APD. NCX1 localization has minimal impact
2+ 2+ 2+ on [Ca ]jsr (Fig. 6C) and [Ca ]i (Fig. 2-13D). Fig. 2-13E illustrates average [Ca ]d
during an AP whose peak is not significantly affected by redistribution of NCX1 to the
39 2+ dyad. Figure 2-13F displays the beginning of the diastolic phase of [Ca ]d following the decay of the Ca2+ transient where Ca2+ spark activity becomes more prevalent with fewer dyadic NCX1s (lower values of fd). As fd increases, NCX1 plays an increasing role in
2+ reducing the magnitude of [Ca ]d (Fig. 2-13E) and decreases diastolic spark rate (Fig. 2-
13F). The corresponding time-courses of NCX1 equilibrium potential (ENCX1) in the cytosol and dyad are illustrated in Fig. 2-14, and show that dyadic ENCX1 remains at a relatively high value (~ 40 mV) throughout the AP with NCX1 placement in dyad.
Furthermore, redistribution of NCX1 from cytosol to dyad leads to a modest prolongation of the Ca2+ transient decay time constant from ~185 ms to ~215 ms (Table 2-1), and an increase in the fraction of cycled Ca2+ extruded from the cell by NCX1 on each beat from
~ 24% to ~ 36%. Redistribution of NCX1 between only cytosolic and PD compartments yields similar trends (Fig. 2-15 and Table 2-1). Interestingly, placement of NCX1 in the
2+ PD has a stronger impact on [Ca ]i as compared to dyadic NCX1. With an fd:fpd ratio of
2+ 1:2 (i.e., fd = 0.15 and fpd = 0.3), the Ca transient decay time constant for 1 Hz AP pacing is quantified to be ~ 220 ms and NCX1 accounts for ~ 36% of Ca2+ extrusion during relaxation, which are both consistent with experimental measurements [6, 10, 96].
While these results clearly indicate that NCX1 plays an important role in extruding Ca2+
+ 2+ under physiological [Na ]i, it remains unclear whether the brief outward INCX1 (Ca
influx) that occurs upon AP upstroke plays a role in triggering RyR2s and JSR Ca2+
release.
40 Figure 2-13: Effects of various dyadic NCX1 distributions (fd values of 0, 0.05, 0.10,
0.15, and 0.20) on APs and Ca2+ handling with no PD NCX1. (A) APs; and (B) whole-
cell INCX1. Arrows indicate time of ENCX1 crossing for fd = 0 (blue) and fd = 0.2 (red). (C)
2+ 2+ 2+ 2+ Cytosolic Ca transient [Ca ]i. (D) [Ca]jsr. (E) [Ca ]d. (F) Diastolic phase of [Ca ]d.
41
Figure 2-14: Effects of dyadic NCX1 on ENCX1 during ECC. (A) ENCX1 in the cytosol. (B)
ENCX1 in the dyad.
NCX1 contribution to Ca2+ transient decay 2+ 2+ fd Ca decay time constant (s) Fractional contribution to Ca extrusion 0.0 0.185 0.2481 0.05 0.190 0.3144 0.10 0.200 0.3254 0.15 0.210 0.3349 0.20 0.215 0.3651 Table 2-1: NCX1 contribution in Ca2+ transient decay in Fig. 2-13.
42
Figure 2-15: Effects of PD NCX1 on ECC. (A) Action potential with NCX1 placement in
2+ 2+ the PD space. (B) Ca transient. (C) Total NCX1 currents. (D) Cajsr. (E) [Ca ]d. (F)
2+ Diastolic phase of [Ca ]d is significantly reduced in the presence of PD NCX1.
NCX1 contribution to Ca2+ transient decay 2+ 2+ fpd Ca decay time constant (ms) Fractional contribution to Ca extrusion 0.0 0.185 0.2481 0.20 0.195 0.3127 0.40 0.210 0.3727 0.60 0.220 0.3846 Table 2-2: NCX1 contribution in Ca2+ transient decay in Fig. 2-15.
43
2.3.5 Does NCX1 play a role in CICR?
Whether NCX1 in the dyad can underlie a significant portion of the triggering
current for CICR still remains controversial. In this model the NCX1 spatial distribution
follows those identified in the imaging study of Wang et al. [68] (as calculated from their
Fig. 5D) with fd, fpd, and fcyto values of 0.15, 0.30, and 0.55, respectively. AP simulations at 1 Hz pacing show that the reverse mode of NCX1 which occurs upon AP upstroke precedes the onset of LCC trigger and RyR2 Ca2+ release (data not shown), which suggests a potential role for NCX1 in contributing to CICR. Therefore, the triggering role of reverse mode NCX1 was further investigated by application of voltage clamp protocols and comparison of control NCX1 Ca2+ flux (NCX1c, Fig. 2-16, black lines) to that in which only the reverse mode of INCX1 was ablated by clamping it to zero (NCX1*,
Fig. 2-16, red lines). The model was pre-conditioned with ten 200-ms depolarizations to
40 mV from a holding potential of -90 mV applied at 1 Hz to load JSR Ca2+ prior to application of a test potential (from -30 mV to 80 mV in 10 mV increments). The sum of
2+ 2+ dyad and PD NCX1 Ca fluxes (JNCX1, Fig. 2-16A), LCC Ca flux (JLCC, Fig. 2-16B),
2+ and RyR2 Ca flux (JRyR2, Fig. 2-16C) during the test potentials are shown for 0 mV and
50 mV test potentials for both the NCX1c and NCX1* cases. Since JNCX1 remains in
forward mode (outward Ca2+ flux) during the entirety of the test potential at 0 mV, no
2+ difference is observed in the peaks of RyR2 Ca flux between JNCX1c and JNCX1*. In
contrast, the presence of inward JNCX1 in the dyad and PD can greatly augment RyR2
2+ Ca release at 50 mV while no apparent difference in peak JLCC is detected (Fig. 2-16B,
lower panel). The summary data showing peak CICR trigger Ca2+ influx in the presence
(JLCC + JNCX1c, black line) or absence (JLCC + JNCX1*, red line) of reverse mode NCX1 are
44 normalized and plotted in Fig. 2-16D and are consistent with experiments of Sobie et al.
2+ [78]. This result suggests that at more depolarized Vm (>30 mV), INCX1 augments the Ca
trigger flux in CICR and can play an important role in triggering JSR Ca2+ release.
Furthermore, the fractional contribution of NCX1 to the CICR trigger (i.e. 1-
JRyR2(NCX1c)/JRyR2(NCX1*)) is shown in Fig. 7E. Reverse mode NCX1 contributes
significantly to the CICR trigger at highly depolarized Vm, but does not contribute significantly when Vm is at more moderately depolarized potentials corresponding to the
AP plateau. This is further confirmed by investigation of the role of reverse mode INCX1
during AP pacing. During the AP upstroke, Vm briefly reaches >30 mV (lasting <5 ms), but for the remainder of the plateau phase it is closer to 0 mV. Blocking the reverse mode of NCX1 does not reduce the peak of JRyR2 (Fig. 2-16F) during the AP, which shows that
+ NCX1 does not have a significant contribution to CICR under physiological [Na ]I,
which is explained by limited NCX1-mediated Ca2+ entry during the brief AP upstroke.
45
Figure 2-16: The CICR triggering capacity of NCX1. (A-D) Test potentials to 0 mv and
50 mV of 200 ms duration were applied to the whole-cell model from a holding potential of -90 mV under NCX1c (control NCX1, black lines) or NCX1* (reverse mode NCX1 clamped to zero, red lines) conditions. (A) JNCX1, scale bar (black): 0.01 µM/ms. (B) JLCC, scale bar (blue): 0.1 µM/ms. (C) JRyR2, scale bar (green): 1 µM/ms. (D) Normalized peak
2+ Ca influx (JLCC + JNCX1) in response to test potentials from -30 mV to 80 mV for
NCX1c (black) and NCX1* (red). The results suggest that NCX1 can trigger CICR consistent with experiments [78]. (E) NCX1 fraction of CICR trigger. (F) JRyR2 during
AP.
2.3.6 Role of NCX1 localization on whole-cell INCX1
46 The AP clamp interruption protocols performed in the experiments of Weber et al.
[87] were applied to the whole-cell model to examine the role of NCX1 localization on
INCX1 morphology. The model was pre-conditioned with ten 200 ms depolarizations to 40 mV applied at 1 Hz prior to the application of the AP-clamp. Each AP was interrupted at various times with a clamp to -90 mV to reveal NCX1 tail currents (LCCs are inactivated at -90 mV). Figure 2-17A displays the AP clamp used experimentally in a rabbit ventricular myocytes by Weber et al. [87] and that was used as an AP template in model simulations with AP interruptions at 10, 25, 50, 100, 200, and 300 ms following the pre- conditioning protocol. Figure 2-17B presents the NCX1 tail currents upon AP interruption from the original Greenstein and Winslow [38] model. The simulated NCX1 tail currents are smaller than the tail currents measured by Weber et al. [87] and exhibit a maximal peak at 200 ms. In addition, the decay of the current is slow. After updating the
RyR2 formulation, incorporating the new PD compartment, and setting fcyto = 1.0 (i.e. no
NCX1 in dyad or PD), the simulated peak of NCX1 tail currents remains much smaller than those measured experimentally and the decay of current is faster (Fig. 2-17C). In contrast, with fd, fpd, and fcyto values of 0.15, 0.30, and 0.55, respectively (Fig. 2-17D),
INCX1 tail currents more closely resemble those measured experimentally by Weber et al.
[87] which displayed a maximal peak current for the 25 ms interrupted AP clamp (the
2+ approximate time of peak [Ca ]d). These findings further support the idea that NCX1 is not localized solely to the cytosolic sarcolemma.
47
Figure 2-17: NCX1 tail currents under AP-clamp. (A) AP clamp recording in a rabbit
ventricular myocytes from Weber et al. [87]. (B) Model prediction of NCX1 tail currents
upon AP-clamp interruption at various times (10, 25, 50, 100, 200, and 300 ms) with
original Greenstein and Winslow [38] model. (C) Model prediction of NCX1 tail currents
with fcyto = 1.0 (100% NCX1 in cytosol). (D) Model prediction of whole-cell NCX1 tail
currents with fd, fpd, and fcyto values of 0.15, 0.30, and 0.55, respectively (dyad-to-PD ratio
of 1:2).
2.3.7 Role of NCX1 allosteric regulation on whole-cell physiology
The physiological role of beat-to-beat Ca2+-dependent allosteric regulation of
NCX1 was investigated with 1 Hz current clamp simulations at steady-state with fd, fpd,
and fcyto values of 0.15, 0.30, and 0.55, respectively (dyad-to-PD ratio of 1:2). The
CBD12 model allows NCX1 allosteric activation to various levels of activity and enables
NCX1 to play a local functional role in each subcellular compartment. Exchangers in the
cytosol respond to a global Ca2+ signal, while those in the, PD, and dyad respond to a
2+ local Ca signal. This results in differing levels of regulation (Allo) and INCX1 behavior,
as shown in Fig. 2-18A and 2-18B, respectively. In addition, the physiological role of
NCX1 Ca2+-dependent activation was further studied by removing the allosteric
regulation (fully active NCX1, Allo = 1). Figure 2-18C displays a ~ 40% reduction in
48 2+ [Ca ]i with full NCX1 activity (red line) compared to control (blue line) and Fig. 2-18D
2+ shows a ~ 15% decrease in [Ca ]jsr in the absence of allosteric regulation. The control
AP is illustrated in Fig. 2-18C. No significant difference is observed for APs as a result of
removing the allosteric regulation (not shown). Full NCX1 activity associated with loss
of NCX1 regulation facilitates Ca2+ extrusion during diastole resulting in a reduction of
2+ 2+ 2+ diastolic [Ca ]i (Fig. 2-18C) and [Ca ]d (not shown), and JSR Ca load (Fig. 2-18D),
which reduces resting Ca2+ spark generation and impacts efficiency of local CICR. These simulations demonstrate that the Ca2+-dependent allosteric regulation of NCX1 is a
means by which the myocyte can tune the activation of these exchangers in a spatially
dependent manner. The ability of the cell to “functionally localize” NCX1 operation via
this regulatory mechanism ensures proper function in each Ca2+ compartment. The partial deactivation of cytosolic NCX1 during diastole is important for maintaining normal cellular Ca2+ load and physiological Ca2+ transient properties.
49
Figure 2-18: The beat-to-beat role of NCX1 Ca2+-dependent allosteric regulation. (A) CBD12 allosteric regulation of NCX1 in cytosol (solid line), PD (dashed line), and dyad (dotted line). (B)
2+ 2+ INCX1 in cytosol, PD, and dyad. (C) [Ca ]i and Vm (black) and (D) [Ca ]jsr comparisons between
control (blue) and fully active NCX1 (Allo = 1, red).
2.4 Discussion
In this study, a biophysically based model of NCX1 incorporating allosteric
regulation by Ca2+ is developed and analyzed. This NCX1 model captures properties of
NCX1 allosteric regulation by Ca2+ over a wide range of [Ca2+] levels spanning from that
in diastole (~ 100 nM) to those occurring at the peak of the dyadic Ca2+ transient (~ 100
µM or more). This improved model of NCX1 is incorporated into a super-resolution model of the Ca2+ spark that is based on realistic t-tubule and JSR geometry [39], as well
50 as an integrative model of the cardiac ventricular myocyte in which L-type Ca2+ channels
and RyR2s gate stochastically [38]. Parametric studies in both the SRS model and the
whole-cell model demonstrate that localization of NCX1 to the dyad enables it to closely
2+ 2+ modulate the local [Ca ]d, as well as Ca spark fidelity and rate during diastole. Using a multi-scale approach, the whole-cell model is extended to incorporate a spatial PD compartment that is immediately adjacent to and surrounding each dyad, with parameters that define trans-PD Ca2+ fluxes informed by the SRS model results. This allows for the
inclusion of NCX1s in various distributions within the PD and dyad compartments of
each CRU. During AP pacing in the whole-cell model, this study shows that the
dynamics of NCX1 activation depending on its localization to the cytosolic, PD, or
2+ dyadic compartments. Due to tight coupling between cellular Ca cycling and Vm, along with the potential interaction of NCX1s with LCCs during CICR, it is difficult to
2+ experimentally control and study the L-type Ca current and INCX1 independently. Model simulations enable isolation of the functional effects of NCX1, and show that INCX1 can
act as a mechanism for additional Ca2+ entry and trigger JSR Ca2+ release at depolarized potentials (> 30 mV) in response to voltage-clamp steps. Model simulations qualitatively reproduce experimentally measured NCX1-mediated triggering of CICR [78] as well as
NCX1 tail currents evoked by AP-clamp interruption protocols [87] when the NCX1
spatial distribution is adjusted to match the imaging results of Wang et al. [68], which
showed that a high percentage of NCX1s reside in the dyad and PD with a dyad-to-PD
ratio of roughly 1:2.
51 2.4.1 Spatial localization of NCX1
Optical imaging studies have quantified the co-localization between NCX1s and
RyR2s in a wide range between 4% and 30% and have indicated 40-60% of NCX1s
reside on the t-tubule membrane [7-9, 65-68], which suggests that this localization is
likely to be functionally important. In addition, inhibition of INCX1 or NCX1 knockout in
cardiomyocytes has been used to demonstrate the close proximity of NCX1 to RyR2
clusters and show the role of NCX1 in Ca2+ modulation at rest [68-71]. However, it
remains difficult to differentiate NCX1 subpopulations which sense spatially-dependent
differences in Ca2+ signals in intact cardiomyocytes. Several electrophysiology studies
[87, 97, 98] in which NCX1 tail currents were measured during voltage- and/or AP-
clamp indicated that the actual peak tail current is much larger than values calculated
2+ based on activation by [Ca ]i (i.e. assuming 100% NCX1 reside in the cytosol).
Furthermore, during an AP, the NCX1 tail current peaks at ~ 25 ms, which suggests that
2+ NCX1 is rapidly activated upon RyR2 Ca release and INCX1 reflects the dynamics of
2+ [Ca ]d [87, 97, 98]. Despite these data, the spatial distribution of NCX1 within, near, and/or far from the dyads remained unclear. Recent super-resolution optical imaging, which demonstrated NCX1 localization within the dyad and the nearby region, guided the distribution of NCX1 investigated in this model and simulation results are consistent with a number of experiments. The model simulations (Fig. 2-16D-E, Fig. 2-17B) adhering to a dyad-to-PD ratio of roughly 1:2 (fd, fpd, and fcyto values of 0.15, 0.30, and 0.55, respectively) reproduce the ECC NCX1 triggering capacity experiments of Sobie et al.
[78] and qualitatively match experimentally recorded NCX1 tail current magnitudes and time-to-peak during AP clamp [87]. These results provide additional evidence for the
52 idea that a high percentage of NCX1s reside within or near the dyad consistent with a
dyad-to-PD ratio of 1:2. Furthermore, three different NCX1 distributions with fd+pd of
2+ 0.45 were evaluated for [Ca ]i transient rise-time (CRT). CRT gain was defined by
Litwin et al. [75] as the maximum time rate of change of the Ca2+ transient divided by
peak LCC current. Model simulations of the CRT gain (Fig. 2-19), where fd+pd was
+ redistributed between dyad and PD, show that with fd = 0.45 and 10 mM [Na ]i, as fd
increases, CRT gain at depolarized membrane potentials increases compared to the 0 mM
+ [Na ]i case. However, the best reproduction of the relationship between CRT gain at 10
+ + mM [Na ]i vs. 0 mM [Na ]i at highly depolarized membrane voltages (> 30 mV) as measured by Litwin et al. [75] was achieved for the case with dyad-to-PD ratio of 1:2
(Fig. 2-19).
3 [Na+] =0mM i [Na+] = 10mM; NCX1 dyad-to-PD ratio 1:2 2.5 i [Na+] = 10mM; NCX1 45% in dyad only i [Na+] = 10mM; NCX1 45% in PD only i 2
1.5
1 Normalized CRT gain
0.5
0 0 10 20 30 40 50 60 V (mV)
53
Figure 2-19: Effects of NCX1 spatial distribution between dyad and PD on CRT gain. All
+ values are normalized to CRT gain at 10 mM [Na ]i and Vm = 0 mV. An NCX1 dyad-to-
PD ratio of 1:2 is most consistent with the experimental data of Litwin et al. [75]. This
further supports a dyad-to-PD NCX1 ratio of 1:2 in agreement with the imaging data of
Wang et al. [68].
2.4.2 Interspecies differences
Previous experimental data suggests that in small mammals (e.g. rats, mice),
NCX1 is responsible for extruding only 7-10% of the total Ca2+ comprising intracellular
Ca2+ transients, whereas in larger mammals (e.g. canine, guinea pig, rabbit), NCX1
extrudes 40-50% of the total Ca2+ [6, 10]. This interspecies difference in Ca2+ cycling could be attributed to species-dependent differences in NCX1 membrane density. Niggli
& Lederer [59] calculated NCX1 membrane density of ~250 µm-2 in mice, whereas
Hilgemann et al. suggested 400-500 µm-2 in guinea pig cardiomyocyte [99]. NCX1
membrane density in this model can be adjusted to study interspecies differences.
Another facet of species-dependent differences may be in the details of NCX1 spatial
distribution. Additional super-resolution imaging studies are needed to quantify NCX1
placement in dyad, PD, and cytosol in a species-specific manner. Furthermore, the KmActs in Ca2+-dependent allosteric activation can be species-dependent. This NCX1 model incorporates a Ca2+-dependent allosteric activation mechanism which is closely based on
CBD12 Ca2+-binding studies in order to capture Ca2+ activation dynamics in the
physiological range of [Ca2+]. This NCX1 formulation responds over a wider dynamic
54 2+ range of Ca signals than previous models, with a KmAct of ~300 nM. Early experimental
studies estimated NCX1 KmAct to be in the range of 22-47 nM in guinea pig myocytes
[60] or Chinese hamster ovary cells [100]. However, estimates of KmAct in guinea-pig myocyte excised membrane patches or in expressed canine NCX1 measured at steady- state have been shown to be much lower, in the range of 200-800 nM [52, 61, 101-103].
More recent experiments using rapidly alternating Ca2+ influx-efflux voltage-clamp protocols in intact cardiomyocytes reported a KmAct between in the range of 125-500 nM
[55, 62, 63]. The KmAct of this model agrees well with previous reports both in excised
membrane patches and whole-cell voltage clamp recordings. In mouse, however, Ca2+-
2+ dependent activation of NCX1 was not detected for [Ca ]i above 100 nM, therefore
2+ KmAct has been suggested to be well below physiological diastolic [Ca ] in this case [55].
This suggests the possibility that KmAct is species-dependent and relevant parameters of
the NCX1 model proposed here may need to be adjusted for use in other species.
However, additional experimental studies are needed to measure KmActs in different
animal species to guide further modeling studies.
2.4.3 The dual roles of NCX1
Spark fidelity is a measure of the probability that a single RyR2 opening leads to
a spark and reflects properties of spontaneous spark generation in the absence of LCC
activity at rest, whereas measures of ECC reflect excitability during LCC triggered CICR
during an AP or voltage clamp stimulation. NCX1 may play different roles in these two
different types of Ca2+ release events. Simulations with both the SRS and whole-cell
2+ models show that dyadic NCX1 plays an important role in extruding [Ca ]d at rest, thus
55 effectively limiting Ca2+ accumulation and preventing local CICR and Ca2+ spark generation. Accordingly, a decrease in dyadic expression of NCX1 may result in enhanced Ca2+ spark activity. This may occur in the presence of down-regulation of the
protein junctophilin-2 (JPH2), an anchor protein for RyR2s and possibly for NCX1s as
well. Wang et al. [68] demonstrated that JPH2 knockdown reduces NCX1-RyR2 co-
localization and functional INCX1 (even without altered NCX1 protein expression), and
this leads to increased JSR Ca2+ leak via increased resting Ca2+ spark activity. This was
compared with pharmacological impairment of NCX1, which resulted in a qualitatively
similar change in Ca2+ sparks. The result is further supported by Neco et al. [70] who demonstrated an increase in spark activity in NCX1 knockout mice compared to control.
Moreover, a recent study has linked the down-regulation of JPH2 to potentially arrhythmic behavior by showing that mutant JPH2 mice exhibit a higher incidence of inducible atrial fibrillation than wild-type [90]. The reduction of NCX1-RyR2 co- localization in JPH2 mutants may be a contributing factor in these findings. The simulations reported here highlight the important role of dyadic NCX1 in regulating resting Ca2+ and its ultimate impact on local CICR in cardiac dyads.
While there is consensus regarding the important role of NCX1 for Ca2+ extrusion
during diastole, the question still remains as to whether NCX1 cycling reverses and
contributes to the trigger for CICR during an AP. Experimental and modeling studies
have been unable to consistently identify whether NCX1 operates in forward or reverse
mode during the AP plateau. The experiments of Grantham and Cannell [104] suggested
that INCX1 was predominantly outward (reverse mode) during an AP clamp, however
INCX1 was measured under an AP waveform with highly depolarized plateau (> 50 mV)
56 and with JSR release minimized, a condition that promotes reverse mode operation of
NCX. In contrast, duBell et al. [105] showed in rat myocytes that INCX1 contributed to the net inward current that sustained the AP. Using a computational model of the guinea pig ventricular myocyte in which 100% of NCX1 was localized to the cytosol, Luo and Rudy
[106] showed that INCX1 becomes outward upon AP upstroke and this mode lasts ~100 ms
before reversing to forward mode operation for the remainder of the AP and the diastolic
inter-beat phase. On the other hand, in a computational model of the rabbit ventricular
myocyte in which NCX1 senses subsarcolemmal [Ca2+], Weber at al. [87] predicted that
the time of reversal of INCX1 is very early in the AP (~19 ms) and that NCX1 operates in
forward mode during the remainder of AP plateau. INCX1 is highly sensitive to AP shape
and [Ca2+] profiles of various subcellular compartments. Therefore variations in spatial distribution of NCX1 result in very different morphologies of the current as driven by an
AP. Simulations of the model presented here are consistent with the study of Sher et al.
[107] which showed that NCX1 mainly works in forward mode to extrude Ca2+ during
diastole, but functions in reverse mode transiently during the AP upstroke and the early
part of the AP plateau phase.
Analysis of the direction of NCX1 during the AP naturally leads to the question of
whether NCX1 impacts CICR. The whole-cell model simulation with reverse mode INCX1
inhibited (NCX1*) revealed that NCX1 contributes to trigger Ca2+ entry (and subsequent
2+ + JSR Ca release) only under highly depolarized Vm (>30 mV), at 10 mM [Na ]i.
+ Numerous studies have shown that [Na ]i plays a crucial role in determining the transport direction of NCX1, which can alter the role of NCX1 in CICR. Recently, Na+ currents
have been shown to play a role in ECC. Specifically, Na+ current block via either
57 tetrodotoxin (TTX) or a pre-pulse inactivation protocol reduces JSR Ca2+ release flux in
rabbit ventricular myocytes. This action is ablated in NCX1-knockout mice, supporting
the hypothesis that Na+ influx during the AP enhances reverse-mode NCX1 in a way that
2+ augments [Ca ]d in the vicinity of RyR2s [75, 108-110]. These results support the idea that a subpopulation of Na+ channels (possibly neuronal) [109], reside within or near the
2+ dyad and can modulate ECC via local activation of NCX1 to prime [Ca ]d just prior to
peak activation of LCCs and CICR. Localized domains of highly elevated [Na+] may
form as t-tubular NCX1 and fast Na+ channels introduce an influx of Na+ in this confined space [18, 19, 111], and this can be a potent mechanism to drive reversal of INCX1,
enhancing its contribution to the trigger for CICR. Therefore, microdomain [Na+] is
likely to play an important role in modulating Ca2+ dynamics and CICR via the nexus that is NCX1.
Electron probe microanalysis has indicated that local [Na+] may reach ~ 40 mM
+ within 20 nm of the inner side of the sarcolemma [21]. In order to investigate how [Na ]d
+ + + + and [Na ]pd affect CICR, we set [Na ]d and [Na ]pd to more elevated values than [Na ]i.
Fig. 2-20A demonstrates that ECC gain increases at all membrane potential in response to
+ + an acute elevation of [Na ]d and [Na ]pd at the moment of depolarization (i.e. initial
2+ 2+ + [Ca ]jsr and [Ca ]d are the same in all cases). In Fig. 2-20B, the Na -dependent role of
2+ 2+ local NCX1 on [Ca ]d and [Ca ]pd during the pre-conditioning protocol remain intact
2+ and only the initial [Ca ]jsr is identical in all cases (see Supplement for details). In this
+ 2+ case elevated [Na ]d primes [Ca ]d via NCX1 which further amplifies the contribution of
+ + NCX1 to CICR. In addition, elevation of [Na ]d and [Na ]pd from 10 mM (black lines) to
40 mM for a short time period (10ms) beginning upon AP upstroke (red lines) or during
58 the entirety of an AP-clamp (blue lines) leads to an amplified outward NCX1 current
(Fig. 2-21A and 2-21B) with no observed difference in peak LCC fluxes. This results in a
2+ 2+ ~ 20-30% increase in SR Ca release (Fig. S14C) and [Ca ]d (Fig. 2-21E), which is consistent with the experimental measurement of Ca2+ signal reduction upon TTX
application observed by Torres et al. [109]. The reverse mode of NCX1 (Ca2+-influx)
2+ preceding the peak of RyR2 release (10-20ms) is critical for increasing [Ca ]d (Fig. 2-
21E), which sensitizes the RyR2s and enhances their open probability (Fig. 2-21 D).
+ [Na ]d, through its influence on local NCX1, can therefore be a regulator of ECC. The
+ impact of [Na ]d on ECC saturates at levels above ~ 40 mM, suggesting that the relevant
+ range in which [Na ]d has functional impact is 10-40 mM, which is consistent with experimental estimates [21]. These findings indicate that further experimental studies of the role of local [Na+] in the regulation of CICR are needed.
+ + + Figure 2-20: Effects of local [Na ] ([Na ]d and [Na ]pd) on ECC gain. (A) ECC gain with
+ 2+ 2+ local [Na ] set to 10, 20 and 40 mM (initial condition for [Ca ]jsr and [Ca ]d identical in
2+ + all cases). (B) ECC gain with initial value of [Ca ]d arising from Na -dependent pre-
2+ conditioning but [Ca ]jsr identical in all cases.
59
+ + Figure 2-21: Effects of [Na ]d on CICR during AP-clamp with [Na ]cyto = 10 mM and
+ + [Na ]d = [Na ]pd = 10 (black lines), 40 mM between 10-20ms (red lines) and 40 mM
(blue lines). (A) AP clamp for the first 50ms. (B) JNCX1 during the first 50 ms during the
2+ AP-clamp. (C) JRyR2 fluxes. (D) RyR2 open probability. (E) [Ca ]d corresponding to
the three values of local [Na+].
2.4.4 Role of NCX1 Ca2+-dependent allosteric regulation
60 The beat-to-beat physiological role of NCX1 Ca2+-dependent allosteric regulation
has long been debated and remains unclear. Weber et al. [112] originally suggested that,
during an AP, allosteric regulation accelerates Ca2+ extrusion via NCX1 in response to
2+ 2+ the Ca transient and as [Ca ]i approaches diastolic levels, NCX1 deactivates partially
to limit diastolic Ca2+ extrusion. A recent study by Ginsburg et al. [81] suggested that deactivation is very slow (>10 s) such that the allosteric activity of NCX1 remains nearly constant from beat to beat during paced APs, but the degree of activation varies in a frequency-dependent manner. On the other hand, as a result of the high cooperativity of
Ca2+ dependence in the model formulation (hill coefficient = 4), the rate constant can be
2+ amplified exponentially with [Ca ]d, which is not physiological and can result in computational instability. This differs from the kinetic properties of activation/deactivation in the model presented here which contain both fast and slow components, allowing the level of activation to respond to intra-beat Ca2+ dynamics (Fig.
2-18A) in addition to multi-beat time scales (Fig. 2-9C). With respect to spark generation
and the role of NCX1 in the regulation of CICR and the AP, the findings presented here
may not be largely dependent on the kinetic property differences between this CBD12-
based model and an instantaneous formulation of allosteric NCX1 regulation [112].
However, the dynamical properties of NCX1 in this model, which differ substantially
from those of Ginsburg et. al. [81], are essential in order for it to play a physiological role
in Ca2+ modulation.
The Ca2+-dependent allosteric regulation mechanism of this NCX1 model enables
a range of activation levels that correspond to the operating ranges and waveforms of
[Ca2+] that occur across different subcellular compartments. Allosteric regulation
61 effectively reduces the operation of NCX1 in the cytosol, but this inhibitory mechanism
is relieved in the dyad and PD where [Ca2+] is high. The ability of the cell to
“functionally localize” NCX1 operation via this regulatory mechanism ensures cytosolic
NCX1 functions at a lower capacity compared to dyadic and PD NCX1, which is
important for maintaining normal cellular Ca2+ load and physiological Ca2+ transient properties.
62 Chapter 3 – Na+ local control in cardiomyocytes
3.1 Background
+ + Intracellular Na concentration ([Na ]i) in cardiomyocytes is a primary
+ determinant of cardiac contractility, and changes in [Na ]i have a large impact on
contractility [113, 114]. The cardiac sodium potassium ATPase pump (NaK) is the
primary mechanism for regulating the Na+ homeostasis in cardiac myocyte. It uses the
energy released by the hydrolysis of an ATP to actively transport three Na+ ions out of
the cell in exchange for two K+ ions. There are multiple isoforms of NaK including different α-unit isoforms, α1, α2 and α3, and their expression differs significantly
between species [115-118]. The different isoforms exhibit similar affinities for [Na+] but respond differently to cardiac glycoside [119]. Voltage-gated Na+ channels play an
important role in the excitation-contraction coupling (ECC) process by causing the rapid
+ upstroke of the action potential (AP) [10]. The fast Na current (INa) has traditionally
been thought to be generated mainly by the cardiac Nav1.5 isoforms, but recent studies
have demonstrated the existence of neuronal Na+ channels isoforms (Nav1.1, Nav1.2,
Nav1.3, Nav1.6) in the ventricular myocytes [11-14]. They can be inhibited by
nanomoler levels of tetrodotoxin (TTX), whereas cardiac INa is not affected. Neuronal
INa makes up for 5-30% of the total INa depending on cardiac preparations and animal species [12, 15, 16]. There is mounting evidence to suggest that those Na+ channels can contribute to the existence of Na+ microdomains.
A microdomain involving neuronal INa, NCX1 and ryanodine receptors (RyR2) was first proposed by Lederer and coworkers and the microdomain [Na+] may exert an
63 impact on the CICR process through the reverse mode of NCX1 [17, 18]. The concept of
a subsarcolemmal space with NCX1 and NaK has also been proposed in previous
electrophysiology and modeling studies and it was suggested that the [Na+] in this space can be several-fold higher than the cytosol [19, 20]. In addition, experiments using electron probe X-ray analysis also reported an existence of an elevated Na+ submembrane
[20, 21]. Here we are most interested in how NaK and neuronal INa work together with
NCX1 to regulate the Na+ microdomain that overlaps with the traditional Ca2+ dyadic
space, formed by opposing membranes of the t-tubules and junctional sarcoplasmic
reticulum (JSR).
NaK has been suggested to be a major regulator of excitation-contraction
coupling (ECC). Detubulation studies demonstrated that 40-60% of the total NaK current
is generated in the t-tubules [66, 119], which puts NaK in a privileged position to regulate
the local [Na+] in the t-tubules. Previous experiments show that α1 isoform makes up the majority of the total NaK pump current (>65%) and is relatively evenly distributed within the cells, which maintains the global [Na+]. On the other hand, α2 and/or α3 is much more concentrated in the t-tubules compared to sarcolemma, determines the [Na+] microenvironment and indirectly controls the myocardial contractility by influencing
NCX1 activity and indirectly setting SR Ca2+ load and contractility [119-122]. Rapid
NaK blockage can slow down the decline of caffeine induced Ca2+ transient and NCX1
+ 2+ current, under conditions such that [Na ]i and sarcoplasmic reticulum [Ca ] are not yet
changed or significantly altered [123, 124].
In addition to NaK regulation, neuronal INa has been suggested to contribute to the
2+ rise of dyadic [Ca ] through NCX1 upon activation [110, 125]. The effect of INa on ECC
64 was first characterized by Leblanc and Hume [110] and the study demonstrated that INa
2+ 2+ inhibition results in a reduction in cytosolic Ca transient ([Ca ]i). Several
immunofluorescence labeling studies reported that more than 80-90% of neuronal INa
resides in the t-tubules [126, 127] and potentially co-localized with RyR2 clusters [128,
129]. However, it is difficult to assess the degree to which INa is co-localized. Whether
+ neuronal INa opening upon voltage activation could introduce a large amount of Na into
the t-tubules and trigger RyR2 release through the reverse mode of NCX1 remains
controversial. No differences were observed in Ca2+ transients in cardiomyocyte with tetrodotoxin application to inhibit neuronal INa in Brette et al. 2006 [126]. However, other studies reported that the peak of intracellular Ca2+ is reduced ~10-14% with either voltage
2+ ramp or TTX to inhibit neuronal INa [76, 109]. Additional Ca spark experiments upon
AP activation using knockout NCX1 cardiomyocytes with Ca2+ buffering further suggests
+ 2+ that NCX1 serves as the bridge between local Na (INa) and Ca to prime the dyadic
[Ca2+] and increase ECC efficiency [70]. A computational model of the dyadic cleft
where both Ca2+ and Na+ diffusion are taken into account was used to investigate the contribution of NCX1 to the trigger Ca2+. The model indicates that if a Na+ channel is present in the fuzzy space and Na+ diffusion is substantially slow than in water (~4 orders
slower), NCX1 is able to influence the timing of RyR2 release [130]. However, the
NCX1 model used in the study exhibited a single exchanger current >100 fA, about
~1000 times bigger than experimental measurement of maximum unitary NCX1 current
[95], and did not incorporate intracellular Ca2+-dependent allosteric regulation. In addition, the changes in RyR2 release were not quantified in the study.
Ankyrin-B is a multivalent adapter in cardiac myocytes and is organized in an
65 intracellular tubular lattice in parallel with both the M-line and the t-tubules (Z-line) [28].
The t-tubular Ankyrin-B is important for the targeting for NCX1 and NaK colocalization
in the t-tubules [28, 31]. Loss-of-function mutations in ankyrin-B cause a dominantly
inherited cardiac arrhythmia with increased sudden cardiac death [29]. Mutation E1425G
(Exon 38) in the spectrin-domain of the protein can result in preferential loss of targeting
of Ankyrin-B to the t-tubule and results in arrhythmia generation [28]. Studies with
ankyrin-B+/- cardiomyocyte revealed that there is a 50% reduction in ankyrin-B protein expression levels and ~15-30% in NCX1 and NaK expression, particularly dramatic loss of localization at t-tubules [28, 29, 131]. It is puzzling why only t-tubular rather than M- line ankyrin-B was preferentially targeted. Several ankyrin-B alternative splicing isoforms have been identified [30-32] and it was suggested the M-line ankyrin-B does not possess the NCX1 binding sites and interacts with protein obscurin for its localization to the M-lines [30]. This potentially explains why ankyrin-B and its associated proteins are markedly reduced in the t-tubules. An elevation in Ca2+ transient is observed in ankyrin-
+/- 2+ 2+ + B but APD and resting [Ca ]i are not significantly altered. However, how Ca and Na
dynamics change locally to enhance the propensity for arrhythmogenic behavior in
ankyrin-B+/- remains poorly understood.
These experimental results demonstrate that it is challenging to tease apart the complex roles of the different components in the Na+ local control and its interaction with
local Ca2+ regulation. To help address those questions, this study presents a mechanistic canine cardiomyocyte model, which reproduces independent (stochastic) local dyadic
JSR Ca2+ release events underlying cell-wide ECC, as well as a three-dimensional (3D)
2+ + model of the Ca spark that describes local Na dynamics with NaK, neuronal INa and
66 NCX1. Dyadic and peri-dyadic (PD) Na+ spaces are constructed to characterize the local
+ Na dynamics and used to examine NaK and neuronal INa regulation on the CICR process
through NCX1. In addition, how dysregulation of NCX1-NaK coupling leads to
arrhythmia generation was investigated using the whole-cell model. The Na+ diffusion
coefficient in the SRS model was informed by the Na+ spark morphology from whole- cell model to achieve multi-scale modeling.
Using both the whole-cell model and the super-resolution Ca2+ spark (SRS)
model, the existence of Na+ sparks generated by NCX1 upon activation during Ca2+
sparks is demonstrated. The Na+ sparks present peaks around 32 mM and a half spark
duration around 200ms in the absence of NaK, which sustains much longer compared to
Ca2+ sparks (~7 ms). Dyadic and PD NaK both regulate the Na+ spark properties but play a minor role in modulating Ca2+ spark rate. Model predictions show that redistribution of
NaK plays a crucial role in modulating dyadic and PD [Na+] level, especially the diastolic phase, which regulates NCX1 current reversal time-point and affects the action potential duration (APD). On the other hand, neuronal INa is a key player during the systolic phase.
+ The model results confirm that neuronal INa can elevate dyadic [Na ] to 35-40mM upon
voltage activation, which reverses NCX1 to promote Ca2+ entry into the dyad, and hence
2+ contribute to the trigger for JSR Ca release. However, the triggering capacity of INa on its own is limited in the absence of LCC. Furthermore, the whole-cell model predicts that there is a higher probability of early-afterdepolarizations (EADs) occurrence in ankyrin-
B+/- compared to control during isoproterenol (ISO) stimulation. Reduced local NCX1
and NaK regulation of dyadic [Ca2+] and [Na+] results in an increase in Ca2+ spark
activities, which leads to a higher probability of RyR2 opening and then cellular
67 arrhythmias as a result of increased net inward current.
3.2 Methods
3.2.1 Implementation of Na+ local control in the whole cell model
Figure 3-1: Schematics of Na+ local control in cardiomyocytes. (A) Model schematics for channel localization in the t-tubules in cardiomyocytes. (B) A t-tubule-JSR cleft (or
CRU) of the whole-cell model (shown in cross-section) is composed of four dyadic subspace volumes arranged on a 2x2 grid, each containing 2 LCCs and 12 RyR2s. (C)
Illustration of flattened JSR from the SRS model with a centered 7x7 RyR2 lattice and 7
LCC
To investigate the effect of Na+ local control in Ca2+ dynamics, a stochastic local- control model previously developed by Chu et al. 2016 [80] that includes stochastic
gating of LCCs, RyR2s and NCX1s in each Ca2+ release unit was used in this study (Fig
3-1A and B). The Na+ local spaces are assumed to take the same spaces as the Ca2+
release units (CRUs) and PD (shown in Fig. 3-1A) since NCX1 transports three 3 Na+ in
68 exchange of 1 Ca2+ ion in the t-tubules and closely regulates the ion changes in both the
Ca2+ and Na+ microenvironments simultaneously. Activation of dyadic and PD NCX1 through Ca2+ spark generation can result in an elevation in Na+ in those spaces. This Na+
will free diffuse to PD and cytosol or can be extruded by NaK outside the cell. NaK
formulation was updated utilizing the steady-state formulation originally developed by
Smith and Crampin 2004 [132] and further updated by Oka et al. 2010 [133]. This formulation is characterized by Eqs. A2.1-19 in the appendenx and is implemented in the
dyadic and PD spaces, as illustrated in Fig. 1A. Neuronal INa is not currently taken into consideration in the whole cell model. A 14-state Markov chain model for neuronal INa
channel developed by Clancy et al. 2004 [134, 135] characterizes both the fast current
process as well as the small late current and is stochastically implemented in the dyadic
space with parameters from Sampson et al. [135], shown in Fig. 1A. The rate constants
and equations for the neuronal Na+ Channel Markov Chain model are given by Eqs.
A2.20-36. The current density of INa has been measured to be similar to that of L-type
2+ 2 Ca channels (ILCC) ~3-7/µm and no difference has been found between t-tubules and
sarcolemma [10, 130]. Therefore, each dyad is assumed to contain 4 neuronal Na+
channels and thus neuronal INa makes up ~25% of total INa in the cell, consistent with
+ experimental INa transcription patterns [136]. Na may diffuse freely between dyadic-PD boundary as well as the PD-cytosol boundaries. The time rate of change of Na+ for each
Na+ compartments is characterized using ordinary differential equations given in the
Appendix A2 (Eqs. A2.37-43). Despa et al. estimated the intracellular Na+ buffering
capacity is very minimal [137]. Therefore, no Na+ buffering was included in the Na+
dynamical formulation.
69 Four parameters including the transfer rate between subspace and peri-dyadic
(PD) space (rss2pd), transfer rate between PD and the cytosol (rpd2c), fraction of NaK in the
dyad space (fd) and fraction of NaK in PD (fpd). In order to systemically constrain the
parameters to describe, we assumed the ratio between Na+ diffusion from subspace
(dyad) to PD and from PD to cytosol is the same as Ca2+ dynamics, which was constrained using the Ca2+ properties of SRS model. Despa et al. 2003 presents a two- phase behavior in NaK current upon activation [137]. Su et al. 2001 demonstrate that
Ca2+ transient is increased by ~15% upon an immediate inhibition of NaK [76]. NaK
current experiment in Despa et al. simultaneously recorded NaK current as well as
+ + + cytosolic Na concentration [Na ]i through a Na fluorescent indicator, SBFI, upon NaK
+ activation by switching [K ]o from 0 to 4 mM. The NaK current exhibits an immediate
current decrease upon activation that potentially reflects the local Na+ depletion.
+ Preliminary parametric study shows that the rate of [Na ]i decay only depends on the fraction of NaK in the cytosol. Therefore, the sum of NaK in dyad and PD can be determined to be ~0.45, consistent with experimental measurements of NaK in the t- tubules [66]. This way, the four parameters were then reduced to two and can be systematically studied using a 2-D parametric study as functions of the time constant
τss2pd (the inverse of r ss2pd) and fd, to minimize the difference between model simulation and experimental data. The cost function is defined as the squared sum of the difference simulated data and experimental recordings and is displayed in Fig. 3-2. Red star represents the combination of parameters that produce the minimum cost function and are utilized in the whole-cell model.
70 1
0.8
0.6
0.4 Cost function
0.2
0
0.3 0.2 1500 0.1 500 1000 f 0 0 = d ss2pd ms
Figure 3-2: Surface plot for the cost function to constrain the whole-cell model. The minimum cost function value (red star) determines the optimized parameters of tauss2pd and fd to match experimental data in Despa et al. 2003 [137] and Su et al. 2001 [76].
+ Figure 3-3A and B exhibit normalized whole-cell INaK fit and [Na ]i dynamics
+ respectively upon NaK activation by switching [K ]o from 0 to 4 mM, matching the experimental measurement in Despa et al. 2003 [137]. The immediate INaK decrease upon activation is due to local depletion of Na+ in the dyad and PD space. In addition, the
2+ whole-cell model demonstrated a ~13.5% increase in [Ca ]i upon an immediate
+ inhibition in NaK (red) following steady state AP pacing in the presence of [K ]o (black), shown in Fig. 3-3C and D. Model constraints suggests ~13% of NaK is distributed in the dyadic space, ~32% of NaK reside in the PD, and the rest is in the cytosol, which is
71 similar to the spatial distribution of NCX1 in the dyad, PD and cytosol as suggested in
our previous model.
+ Figure 3-3: Model constraints. A. Normalized whole-cell INaK upon [K ]o activation. B.
Cytosolic [Na+] decay process upon NaK activation. C. Voltage protocol with test
+ + potential at 0 mV at 0.4Hz. Black line: [K ]o = 4mM; red line: [K ]o = 0.01 mM. D. An
2+ elevation in [Ca ]i upon inhibition of NaK.
In order to study the effects of NaK on Ca2+ sparks, 15% of NCX1 was distributed in the dyadic space, as suggested in the super-resolution optical imaging data for the fraction of NCX1 and RyR2 co-localization [68]. NaK was positioned with various
72 distributions between dyadic space and cytosol or PD and cytosol to study its effects on
Ca2+ spark rate and spark properties. Spontaneous sparks were measured and analyzed in
the whole-cell model with Vm held at -80mV for 20s. With the total NaK being
conserved, the distribution of NaK in the whole-cell model is defined by three
parameters, fd, fpd, and fcyto which presents the fraction of NaKs that are localized to
+ dyads, PDs, and the cytosol, respectively. (fd + fpd + fcyto = 1) NaK regulation on local Na
+ spark peak, half spark duration and diastolic [Na ]d in the simulated CRUs was analyzed as well.
Furthermore, to study the physiological roles of NaK in regulating AP and ECC,
NaK was similarly positioned with various distributions among the dyadic, PD, and cytosolic Na+ compartments of the cell. APs were generated by pacing at 1 Hz for 40 beats until cytosolic Ca2+ transients reached steady state.
3.2.2 Implementation of Na+ dynamics in the super-resolution spark model
To make the super-resolution Ca2+ spark (SRS) model consistent with the whole cell model, Na+ diffusion is implemented similarly to Ca2+ diffusion. The reaction-
diffusion for Na+ is given by
(1) [ ] = 𝐷𝐷 ∇ 𝑁𝑁𝑁𝑁 + 𝐽𝐽 + DNa is the diffusion coefficient for Na and Ji terms represent influx or efflux sources of
+ + Na including NCX1, NaK extrusion and neuronal INa. NaKs are treated as Na point sources in the t-tubular membrane with 31 nm spacing. They are placed in a square lattice in the dyadic and PD. The dyadic area of the t-tubule in this model is defined as a square patch of membrane directly opposed to the 7x7 array of RyR2s in the JSR membrane.
The sarcolemmal membrane patch is similarly subdivided into a 7x7 array such that
73 NaKs can be placed together with NCX1, directly across the cleft from the RyR2 cluster.
The t-tubule surface of the PD is defined by a concentric 15x15 array of similar
membrane lattice elements excluding the central 7x7 array (dyad), on which NaKs can be
placed. Neuronal Na+ channels are distributed at the same positions as LCCs.
In order to make the SRS model consistent with the whole-cell cardiac myocyte
model, two NCX1s per lattice point were used in the dyadic space to give 15% NCX1 in
2+ the dyad, matching the whole-cell model. To examine the effects of INaK on Ca spark frequency and properties, Vm was fixed at -80 mV and a random selected RyR2 was
2+ + opened to generate Ca sparks. DNa was parameterized to match the average Na spark amplitude and half duration produced by the whole-cell model in the absence of NaK in the dyad. NaKs were positioned within dyad or PD at various membrane densities and the effects of this positioning on Ca2+ sparks and local Na+ dynamics was investigated. Since
RyR2s and NCX1s gate stochastically, ~1,000 simulations were performed for each
2+ + + choice of NaK spatial distribution, and average [Ca ]d and [Na ]d peaks and Na spark
half duration were quantified to examine the effects of NaK.
3.2.3 Ankyrin-B+/- model and beta-adrenergic stimulation
The Ankyrin-B E1425G mutation was first characterized in Mohler et al. 2003
[29] and it preferentially targets t-tubular ankyrin-B and its associated proteins. Ankyrin-
B deficiency hearts have been shown to express reduced levels of 220-kDa ankyrin-B
(~50%), NaK (~15-30%) and NCX1 (~15-30%) [28, 29, 131]. 25-40% decrease in
functional activities of NaK and NCX1 have been characterized in ankyrin-B+/-
deficiency cardiomyocytes [131]. Therefore, in order to reproduce the ankyrin-B+/-
deficiency phenotype in the whole-cell model, 50% of NCX1 and 50% of NaK are
74 reduced in the dyad and PD. This results in a ~22% decrease of the whole-cell NCX1 and
NaK expression, which is consistent with experimental measurements [28, 131]. Whole- cell Ca2+ spark frequencies are investigated in control and ankyrin-B+/- following AP pacing at 0.5, 1 and 2Hz till [Ca2+] transients reach steady state.
Mohler et al. demonstrated with isoproterenol (ISO) stimulation, ankryin-B+/-
cells exhibited early-afterdepolarization (EADs) [29]. The modifications of ISO
stimulation follows the methods from Greenstein et al. 2004 [138]. L-type calcium
channel (LCC) open probability is increased by reducing the exit rate (g) from normal
open state by 6.5 times. Functional increase in sarcoplasmic reticulum Ca2+-ATPase
(SERCA) availability is modeled by simultaneous scaling of both the forward and reverse maximum pump rates Vmaxf and Vmaxr by a factor of 3.3. Reduction in the degree of
steady state inactivation of IKr is modeled by reducing rates entering the inactivation state
(αi and αi3) by a factor of four, and increasing the rates exiting the inactivation state (βi
and Ψ) by this same factor. Functional upregulation of IKs is modeled by scaling maximal
conductance by a factor of two.
AP pacing protocol was simulated for 80 seconds at 1Hz with ISO stimulation
and EAD probability was calculated for the last 70 seconds and compared between
control and ankryin-B+/- deficiency.
3.3 Results
3.3.1 Validation of Na+ local control in the whole-cell model
75 + 2+ Figure 3-4: Whole-cell model Na local control validation. A. [Ca ]i signals upon
2+ + caffeine application. [Ca ] decay is faster in the presence of NaK ([K ]o = 6mM, black
+ line) than with NaK inhibited ([K ]o = 0mM, red line), consistent with experimental
measurement [124]. B. Dyadic [Na+] decay in the presence and absence of NaK. C. The
magnitude of NCX1 current is smaller with NaK inhibition, which leads to the slow
down of [Ca2+] decay.
The whole cell model was validated against independent experimental data not included in the parameter fitting process. The model reproduced the experimental measurement time course of [Ca2+] decay upon caffeine application by Teracciano et al.
2+ + [124]. Figure 3-4A exhibits the [Ca ]i decay process in control ([K ]o = 6 mM, black
+ line) and with NaK inhibition by switching [K ]o to 0mM (red line) at -80 mV after pre-
76 conditioning with ten 200-ms depolarization to 40 mV from a holding potential of -80
mV applied at 1 Hz to load JSR Ca2+. NaK inhibition case presents a slower Ca2+
extrusion process upon NaK inhibition, consistent with the experimental recordings. The
phenomenon can be explained by the difference between dyadic [Na+] dynamics upon
+ caffeine application shown in Fig. 3-4B. The [Na ]d elevation attributes to the NCX1
+ placement in the dyadic and PD space. [Na ]d increases immediately upon caffeine
application as dyadic NCX1 is activated to extrude the dumped Ca2+ from JSR in exchange for Na+ into the cell. Inhibition of NaK results in a much slower decline of
[Na+] in the local spaces, which in turn decreases the electrochemical gradient for NCX1
and limits its ability to extrude Ca2+, displayed in Fig. 3-4C. The model simulation is consistent with experimental recordings of inward current comparison between control and NaK inhibition [124]. This suggests that local [Na+] can regulate [Ca2+] dynamics in the Na+ microenvironment through NCX1.
3.3.2 Model predicts the existence of Na+ sparks
Figure 3-5: The existence of Na+ sparks generated by NCX1 during Ca2+ spark activity.
A. [Ca2+] signal and [Na+] signal with 0% NaK in the dyad. The dynamics of Na+ spark is
77 slower than Ca2+ sparks. B. [Ca2+] signal and [Na+] signal with 13% NaK in the dyad
space. The Na+ spark magnitude and half duration are smaller.
To investigate effects of NaK on Ca2+ spark rates and morphology, NaKs were positioned in the dyad or PD within the whole-cell model. The model simulation predicts the existence of Na+ sparks that are generated by NCX1 influx of Na+ upon activation by
Ca2+ spark, as shown in Fig. 3-5A. The Na+ spark peaks around 35mM and its duration is
~200ms, much slower compared to Ca2+ spark dynamics. Inclusion of ~13% NaK in the dyad results in a reduction of Na+ spark magnitude (~25mM) and a decrease in the half duration (~140ms) but has no impact on Ca2+ spark morphology, displayed in Fig. 3-5B.
A variety of NaK distributions were simulated and analyzed in the whole-cell model.
NaK was first assumed to reside only in the dyad (fpd = 0) and then assumed to reside
only in the PD (fd = 0). In both cases, the total number of NaKs in the cell was conserved.
Model results show that NaK distribution in the dyad or PD has a minor impact on the spark rate, shown in Fig. 3-6A. The existence of ~20% NaKs in the dyad results in ~30% reduction in Ca2+ spark frequency, however, the reduction reaches a saturation beyond
20%. Similar results are observed with NaK placement in the PD space. NaK
redistribution in the dyad or PD has no effects on the Ca2+ spark magnitude, as illustrated
in Fig. 3-6B. In addition to NaK regulation on Ca2+ sparks, its modulation on Na+ spark
+ 2+ peak (Fig. 3-6C), half spark duration (Fig. 3-6D), diastolic [Na ]d (Fig. 3-6E) and [Ca ]d
(Fig. 3-6F) are examined as well. Na+ spark magnitude and duration are decreasing
2+ functions of fd. Interestingly, diastolic [Ca ]d reduces from 0.093 µM to 0.087 µM with
20% NaK placement in the dyad and reaches a saturated level as well with increasing
78 NaK placement in the dyad. This is attributed to the limited capacity of NCX1 at very low levels of [Na+] and [Ca2+]. The Ca2+ spark rate follows the same trend as the diastolic
2+ 2+ [Ca ]d because it is a function of diastolic [Ca ]d. NaK in the PD space has a less impact
2+ + on regulating Ca and Na local dynamics. DNa in the SRS model was constrained to match the Na+ spark magnitude and half spark duration to the values from the whole-cell model in the absence of NaK, in order to achieve consistency between to the two models.
Ca2+ spark simulations of SRS model take the steady state diastolic [Na+] and [Ca2+] values from the whole-cell model and exhibit a similar trend of NaK modulation on Ca2+
spark and Na+ sparks with increasing NaK density per lattice in the dyad, displayed in
Fig. 3-7.
Figure 3-6: Effects of NaK localization on Ca2+ and Na+ spark properties in the whole-
cell model. The role of NaK distribution between cytosol and dyad only (fd+pd = fd since
fpd = 0, solid lines), between cytosol and PD only (fd+pd = fpd since fd = 0, dashed lines) on
79 2+ 2+ + + whole-cell Ca spark rate (A), peak [Ca ]d (B), peak [Na ]d (C), Na spark duration (D),
2+ + diastolic [Ca ]d (E), diastolic [Na ]d (F).
A B ) 60 300 -1 M) s 7 -1 ( d
40 ] 200 2+
20 100 Peak [Ca
Spark rate (cell 0 0 0 1 2 3 4 5 6 0 1 2 3 4 5 6 NaK density (per lattice element) NaK density (per lattice element)
C 40 D 0.3 NaK in Dyad only
M) NaK in PD only 7
( 30
d 0.2 ] + 20 0.1 10 half width (ms) + Peak [Na Na 0 0 0 1 2 3 4 5 6 0 2 4 6 NaK density (per lattice element) NaK density (per lattice element)
Figure 3-7: Effects of NaK on SRS model Ca2+ sparks and Na+ sparks. Spark fidelity
simulations were initiated by opening a single random RyRs. NaKs were placed in the
dyad only (blue bars), PD only (yellow bars). (A) Predicted Ca2+ spark rate. (B) Ca2+
spark amplitude. (C) Na+ spark amplitude. (D) Na+ spark duration measured as FDHM.
3.3.3 Redistribution of NaK and cardiac action potential
APs were generated in the whole-cell model under various distributions of NaK
between the cytosolic and dyadic compartments, with no NaK in the PD (fd values of 0,
0.10, 0.20, and 0.40) to examine its regulation on Na+ dynamics and Ca2+ dynamics. The
80 model was paced at 1Hz to reach steady-state Ca2+ transients (40 beats) from the same
initial condition for each NaK distribution. Simulation results from the final paced beat in
Fig. 3-8A show that action potential duration (APD) prolongs with increasing dyadic
NaK distribution. Figure 3-8B demonstrates that with increasing fd, the late phase of
NCX1 current becomes more inward, which shifts the NCX1 time-to-reversal from ~220 to ~170ms and underlies the APD prolongation. Figure 3-8C displays the total NaK current with increasing placement of NaK in the dyad. NaK localization has a minimal
2+ 2+ impact on [Ca ]i (Fig. 3-8D) and [Ca ]d (Fig. 3-8E). Figure 3-8F illustrates the dyadic
+ + [Na ]i levels are closely modulated by NaK placement in the dyad and diastolic [Na ]d is reduced from ~15mM to 7mM, which helps to regulate the reversal time points of NCX1.
The model simulation shows that NaK and NCX1 are functionally coupled to regulate the
+ 2+ local [Na ]i, which in turn has an impact on Ca dynamics through NCX1 regulation of
local Ca2+. NaK distribution in the PD demonstrates a similar regulation on cardiac AP, shown in Fig. 3-9. Redistribution of NaK in the dyadic and PD spaces also has an impact
+ on the rate of [Na ]i drift during AP pacing and the results for dyadic placement are
displayed in Fig. 3-10. The constrained distribution of NaK with ~13% in the dyad, 32%
+ in the PD and the remaining NaK in cytosol results in a very small [Na ]i drift.
81 Figure 3-8: Effects of various dyadic NaK distributions (fd values of 0, 0.10, 0.20, and
0.40) on APs and Ca2+ handling with no PD NaK. (A) Aps. (B) Cytosolic Ca2+ transients
2+ [Ca ]i. (C) whole-cell INCX1. Arrows indicate time of ENCX1 crossing for NaK fd = 0
2+ 2+ (blue) and fd = 0.40 (red). (D) Dyadic space Ca [Ca ]d. (E) whole-cell INaK. (F)
+ Dyadic space [Na ]d.
82
Figure 3-9: Effects of NaK redistribution in PD on ECC. (fpd values of 0, 0.20, 0.40, 0.60 and 0.80) on APs and Ca2+ handling with no dyadic NaK. (A) Action potential with NaK
placement in the PD space. (B) Ca2+ transient. (C) Total NCX1 currents. (D) [Ca2+]d. (E)
+ Total NaK currents. (F) [Na ]d.
83 #10-3 2
0
-2
-4 rate change (mM/s) i ]
+ -6 [Na
-8
-10 fd = 0 0.10 0.20 0.40 fd=0.13,fpd=0.32
+ Figure 3-10: [Na ]i drift rate as a function of NaK distribution.
3.3.4 Can neuronal INa trigger RyR2 release and contribute to CICR?
Whether neuronal INa in/near the dyad can reverse the direction of NCX1 and contribute to the triggering current for CICR still remains controversial. In this model
NCX1 spatial distribution follows those in Chu et al. [80] with 15% NCX1 in the dyad,
30% in the PD. In addition, NaK distribution takes ~13% in the dyad, 32% in the PD and
55% in the cytosol. The role of neuronal INa was investigated by blocking the neuronal INa
in the presence or absence of LCC trigger during voltage clamp from -80mV to 0mV
(Fig. 3-11A) with the same initial condition. Figure 3-11B shows that upon neuronal INa
2+ inhibition (red line), peak of [Ca ]i is reduced by ~14% compared to the control
condition (black line), which is consistent with previous experimental data [76, 108, 109].
The study further investigated whether neuronal INa can trigger sufficient CICR on its
84 2+ own under LCC inhibition conditions and the model results show that [Ca ]i is much
2+ ablated (blue line). However, a slow rise in [Ca ]i is still observed, compared to
2+ completely elimination in [Ca ]i when NCX1 is blocked in addition to LCC inhibition
(green line). The sum of NCX1 in the dyad and peri-dyad space are illustrated in Fig. 3-
11C. In the presence of neuronal INa, NCX1 current reverses during the test potential,
2+ contributing to [Ca ]d changes and the CICR process. However, NCX1 current remains
2+ entirely in the Ca extrusion mode (forward mode) when neuronal INa is inhibited. LCC
inhibition alone results in NCX1 functions in the Ca2+ uptake mode (reverse mode),
2+ 2+ acting as the entire source for Ca trigger current. A ~20% difference in [Ca ]d (Fig. 3-
11D) and JRyR2 (Fig. 3-11E) was observed between control and neuronal INa. The
+ increase in RyR2 release is due to the opening of neuronal INa, which accumulates [Na ]d
up to ~35-40mM to reverse NCX1, shown in Fig. 3-11F. These model results suggest that
NCX1 serves as the bridge between local [Na+] and [Ca2+] to prime the local [Ca2+] and
enhance the CICR process but does not trigger RyR2 release efficiently. The ECC gain is
calculated for the 0 mV test potential and the presence of neuronal INa increases the ECC gain by ~20% compared with INa inhibition. The effects of neuronal INa on ECC gain from -20 to 50 mV from a holding potential at -80mV are examined between control
(black line) and INa block conditions (red line), displayed in Fig. 3-12. Accumulation of
Na+ increases ECC gain through NCX1 reverse mode in the dyad between -20 to 30mV, suggesting that INa plays an important role in the CICR process.
85 0 0.7 0.5 A B C 0.6 -20 0 M) 0.5 7 (pA/pF) ( i ]
(mV) -40 0.4 -0.5 m 2+ d+pd V 0.3 -60 [Ca -1 NCX1 0.2 I -80 0.1 -1.5 0 0.2 0.4 0 0.2 0.4 0 0.2 0.4 Time (s) Time (s) Time (s) #10-3 D 0.1 E 1.4 F 40 Control 1.2 I block 35 0.08 NaTTX I block 1 CaL 30 0.06 I &NCX1 block (mM) CaL
0.8 (mM) 25 d d (mM/s) ] ] + 2+ 0.04 0.6 20 RyR2 [Na
[Ca J 0.4 15 0.02 0.2 10 0 0 5 0 0.2 0.4 0 0.2 0.4 0 0.2 0.4 Time (s) Time (s) Time (s)
Figure 3-11: Neuronal INa contributes to the CICR process. (A) Voltage protocol with test
potential at 0mV for 200ms from a holding potential of -80mV. (B) Cytosolic Ca2+
transients with control (black line), only neuronal INa inhibition (red line), only LCC inhibition (blue line), and both LCC and NCX1 inhibition (green line). (C) The sum of
INCX1 in dyad and PD. (D) Dyadic space [Ca2+]. (E) RyR2 flux. (F) Dyadic space [Na+] dynamics.
86 18 Control 16 I block Na 14
12
10
ECC gain 8
6
4
2 -20 0 20 40 60 V (mV) m
Figure 3-12: ECC gain comparison between control and neuronal INa inhibition with the same initial condition.
3.3.5 Ankyrin-B+/- cardiomyocytes leads to increased Ca2+ spark activities and
results in arrhythmia generation
Ankyrin-B+/- cardiomyocytes have an increased susceptibility to stress-induced
arrhythmia [29]. Electrophysiology studies have demonstrated an increase in Ca2+ spark
rates following different pacing frequencies and shown an elevation in [Ca2+] transient.
AP pacing protocols were conducted at 0.5, 1 and 2 Hz for 40 beats and the Ca2+ spark rates following the pacing protocols were examined for the whole-cell. Figure 3-13A summarizes the whole-cell Ca2+ spark rates and a significant increase in Ca2+ spark rates
was observed in ankyrin-B+/- compared to control. The SR loads are increased in ankryin-
B+/- conditions, which potentially promotes Ca2+ spark generation (Fig. 3-13B). The Ca2+
2+ sparks were then normalized by [Ca ]jsr to account for the SR differences, illustrated in
87 Fig. 3-13C. The model results are consistent with experimental measurements [131, 139]
and increased Ca2+ spark activities could make cardiomyocytes more susceptible to
2+ generate arrhythmic behavior. AP simulations at 1Hz pacing were run till [Ca ]i reached till steady-state and ECC properties were compared between control (black line), only
NCX1 deficiency (50% reduction in dyad and PD, blue line), only NaK deficiency (50% reduction in dyad and PD, green line), and ankyrin-B+/- conditions (both 50% reduction in dyad and PD, red line) in Fig. 3-14. The NaK reduction case leads to a slight prolongation of APD (Fig. S7A) as a result of more net inward current into the cell, whereas NCX1 reduction case or ankyrin-B+/- case does not alter APD much. Both NCX1
2+ 2+ deficiency and NaK deficiency contribute to increase in [Ca ]i (Fig. 3-14B), [Ca ]d (Fig.
3-14C), and local Ca2+ activities during diastole (Fig. 3-14E) but ankyrin-B+/- deficiency
2+ +/- results in the largest impact on [Ca ]i. APD is not significantly altered in ankyrin-B
2+ deficiency simulation and a ~20% elevation in [Ca ]i is quantified, consistent with the
measurements in Mohler et al. 2003 [29]. No EADs are observed during 1Hz AP pacing.
Figure 3-13: Ca2+ spark analysis for control and ankyrin-B+/- following AP pacing at 0.5,
2+ 2+ 2+ 1, and 2 Hz. (A) Whole-cell Ca sparks. (B) [Ca ]jsr. (C) Whole-cell Ca sparks
2+ normalized to [Ca ]jsr.
88 Figure 3-14: AP pacing properties comparison in control (black line), 50% NCX1
reduction in dyad+PD (blue line), 50% NaK reduction in dyad+PD (green line), ankryin-
B+/- deficiency (both 50% reduction, red line). (A) Action potential. 50% NaK reduction
2+ 2+ 2+ prolongs APD. (B) [Ca ] transient. (C) [Ca ]d. (D) LCC current. (E) Zoom-in of [Ca ]d
+ 2+ during the diastole phase. (F) Total NCX1 current. (G) [Na ]d. (H) [Ca ]jsr.
In order to understand how reduction of ankyrin-B could lead to arrhythmia generation, both control and ankryin-B+/- models were paced at 1Hz for a total of 80s
with ISO stimulation. The probabilities of EADs are measured for both control and
ankyrin-B+/-. There is a 10% probability of EAD occurrence in ankyrin-B+/-
89 cardiomyocytes, whereas only 1.43% of APs exhibits EADs in control. This suggests a
much higher susceptibility of ankyrin-B+/- in generating arrhythmogenic behavior with
beta-adrenergic stimulation. Example traces of control and ankyrin-B+/- with an EAD are
2+ 2+ displayed in Fig. 3-15A. Model simulations show that [Ca ]i (Fig. 3-15B) and [Ca ]d
(Fig. 3-15C) are elevated but no differences of the peak LCC was observed (Fig. 3-15D).
+ As a result of NaK deficiency, local [Na ]d is increased during diastole phase, illustrated
2+ in Fig. 3-15E. Due to a larger RyR2 release and subsequently higher [Ca ]d under ISO
stimulation, NCX1 functions primarily in the forward mode to extrude Ca2+, which makes NCX1 more important of a role in regulation Ca2+ homeostasis. The total NCX1
current are shown in Fig. 3-15F and peak current peak is reduced by ~40%. As a result of
2+ reduction in both NaK and NCX1 in the local spaces, [Ca ]jsr is increased, displayed in
Fig. 3-15G, and can facilitate more RyR2 release. Reduction in NaK current is
demonstrated in Fig. 3-15H. To further understand why EADs originate in ankryin-B+/-
defect cardiomyocyte, the sequences of events were analyzed for several EADs between
control and ankryin-B+/- deficiency, displayed in Fig. 3-16 in the supplement. The divergence of RyR2 opening probability between control and ankyrin-B+/- occurs before
the divergence of LCC opening probability. As a result of reduced NCX1 and NaK, both
2+ 2+ 2+ diastolic [Ca ]d and [Ca ]jsr are elevated, which contributes to enhanced Ca release
2+ and increased [Ca ]d during the CICR process. Even though NCX1 current and NaK
2+ current are reduced to the same extent in the dyadic space, elevated [Ca ]d potentially activates NCX1 further and disturbs the balance between NCX1 current and NaK current in the dyadic space, thus resulting in a more net inward current overall. Therefore,
90 membrane voltage was sustained around relatively depolarized values and re-triggered
the opening of LCC and leads to generations of EADs.
Figure 3-15: The existence of EADs in ankyrin-B+/-. (A) APs. (B) Ca2+ transients
2+ 2+ 2+ + 2+ [Ca ]i. (C) Dyadic space Ca [Ca ]d. (D) ILCC. (E) [Na ]d. (F) INCX1. (G) [Ca ]jsr. (H)
INaK.
91
Figure 3-16: Examination of the time sequence for EAD generation compared between
control (black) and ankryin-B+/- deficiency (red) under ISO stimulation. (A) Action
+/- 2+ potential. Ankryin-B remains in the depolarized phase. (B) [Ca ]d and (C) PRyRopen in
ankryin-B+/- exhibits a diverging behavior before the reference time point 23.21 s. (D)
LCC open probability diverges from the control condition after the reference time point.
(E) The sum of NCX1 and NaK currents becomes more inward before the reference time point. (F) Total current of cell becomes more inward before reference time point.
3.4 Discussion
In this study, a biophysically constrained whole-cell cardiomyocyte model as well
+ as a SRS model that characterize the Na dynamics through NaK, neuronal INa and NCX1
in the dyad and PD spaces are developed. NaK presents a similar distribution as NCX1,
92 with ~13% in the dyad, 32% in PD and 55% in the cytosol. NaK couples with NCX1 to
+ + regulate the baseline/diastolic phase of [Na ] in the dyad as well as the [Na ]i drift rate.
+ On the other hand, neuronal INa contributes mainly to transient [Na ] accumulation during systolic phase. The whole-cell model reproduces the slow-down [Ca2+] decay upon an
immediate inhibition of NaK, which reflects the local [Na+] accumulation and a
decreased NCX1 activity in the t-tubules. Model predicts the existence of Na+ sparks in
the presence of NCX1 in the dyad upon Ca2+ spark generation and the Na+ sparks exhibit peaks around ~32mM and relatively slow dynamics compared to Ca2+ (half duration:
~200ms) as a result of slow dynamics of NCX1. Redistributing NaK in the dyad or PD regulates the local [Na+] and results in APD prolongation through shifting NCX1 reversal
time point. The model investigation of the roles of neuronal INa demonstrate that it
increases the ECC efficiency through promoting the reverse-mode of NCX1 to prime the
2+ [Ca ]d and enhancing the CICR process, consistent with experimental measurements.
However, it cannot trigger Ca2+ release effectively on its own in the absence of LCC. The
role of NCX1 and NaK functional coupling has been further examined in the ankryin-B+/-
deficiency setting. As a result of reduction of both NCX1 and NaK regulation of the dyad
and PD, local regulation of [Ca2+] and [Na+] dynamics is compromised and the whole- cell Ca2+ sparks are greatly elevated. Upon beta-adrenergic stimulation, ankyrin-B+/-
model exhibits a much higher EAD occurrence compared to control cardiomyocyte.
Similar spatial distribution of NCX1 and NaK
3.4.1 Similar spatial distribution of NCX1 and NaK
93 A great portion of NCX1 (40-60%) has been suggested to be distributed in the t-
tubules [66, 68, 80]. Many previous studies have shown that NaK activation directly
alters the activities of NCX1 [140, 141]. This suggests a potential physical co-localization of NCX1 and NaK. The model constraints suggested that there is an existence 13% NaK in the dyad, 32% in the PD and 55% in the cytosol, which matches with the model spatial distribution of NCX1 and is consistent with the imaging study of co-localization of
NCX1 and NaK in the t-tubules [28]. NCX1 brings in three Na+ for each Ca2+ ion extrusion and represents an important route for Na entry. More than 60% of Na+ influx
+ during the cardiac cycle enters the cell via NCX1 [142]. To maintain [Na ]i at a
physiological steady state, a similar amount of Na+ has to be extruded via NaK.
Therefore, the location of NaK with respect to NCX1 is important in [Na+] regulation and ultimately in ECC through NCX1. In addition, experimental data also suggests that NaK are preferentially located in the t-tubules and the percentage of NCX1 and NaK activities in the t-tubules or cytosol are comparable [66]. This suggests a functional coupling of these transporters. NCX1 closely regulates the local Ca2+ spark generation and ECC. The
+ model simulations in Fig. 3-8 and Fig. 3-9 demonstrate the significant decrease of [Na ]d
levels as a function of NaK placement in the dyad and PD. Therefore, the co-localization
of NaK in the dyad and PD can enable it to functionally interact with NCX1 within the
restricted Ca2+ and Na+ diffusion spaces and prevent a local accumulation of [Na+] near
NCX1 and RyR2, which potentially increase the local [Ca2+] and promote Ca2+ spark
+ activities. Furthermore, the [Na ]i drift as a function of NaK redistribution is displayed in
Fig. 3-10 and 100% NaK in the cytosol can results in a major imbalance between Na+
influx and efflux, leading to a 0.008 mM/s decrease drift over time.
94
3.4.2 Computational prediction of Na+ sparks suggests possible experiments
Much of the current knowledge of intracellular ionic dynamics has predominantly
focused on Ca2+ and signaling and many molecular probes for imaging Ca2+ in single cells provide information on its spatial dynamics ranging from nanomolar to millimolar levels. However, such information has not been able to be attained by other ion measurement (Na+, K+) techniques due to low detecting resolutions. The model simulations suggest that the existence of Na+ sparks and they are generated by dyadic
NCX1 upon Ca2+ spark generation. Dubach et al. [143, 144] synthesized a new Na+
fluorescent nanosensor, which is ~100nm in size, has a high selectivity over K+,
+ possesses a Km ~20mM, and a resolution ~370uM. This enables the Na indicator to
detect Na+ dynamical changes in the millimolar level. The study used this Na+
nanosensor to demonstrate the existence of transient and brief Na+ sparks (with peak ~20-
50mM) generated by INa upon voltage activation in the presence of 2,3-butanedione monoxime to decouple the excitation and coupling process and LCC and NCX1 can be largely blocked during this process too [145, 146]. The Na+ sparks generated by neuronal
INa are reproduced using our models, exhibiting peaks ~26.7mM and duration ~4.3ms. An
example trace of the Na+ spark is shown in Fig. 3-17. Therefore, this Na+ nanosensor potentially can be utilized to detect the local Na+ dynamics generated by NCX1 upon
Ca2+ spark activities.
95 30
28
26
24
22 (mM) d
] 20 + 18 [Na 16
14
12
10 0 5 10 15 20 25 30 Time (ms) + Figure 3-17: An example of Na sparks generated by neuronal INa upon voltage step to 0 mM. Average Na+ spark peak is ~26.7 mM and half duration is ~4.3 ms.
3.4.3 Na+ microdomains and Na+ diffusion in fuzzy space
Different types of Na+ microdomains have been proposed in previous literature. 1)
+ + Na fuzzy space. A Na microdomain including neuronal INa, NCX1 and RyR2 was originally proposed by Lederer and others [18]. It has been greatly debated whether INa
could be positioned near RyR2 cluster and/or contribute to accumulation enough Na+.
Scriven et al. [7] used indirect immunofluorescence imaging to show that the majority of
Na+ channels clustered are distributed outside the dyadic RyR2 cluster. In contrast, recent studies by Radwanski et al. [129] have demonstrated the co-localization of neuronal Na+
channels and RyR2 in the same subcellular regions. It is possible that due to the low
+ density of INa, it was difficult to detect their existence in the dyad. 2) The Na
subsarcolemmal space. Several electrophysiological studies focus submembrane regions,
which include NCX1 and NaK and they could potentially present a subsarcolemmal Na+
96 concentration gradient compared to the bulk Na+ concentration[19]. The size of
subsarcolemmal Na+ compartment has been suggested to take up ~1.6 – 14% of total cell volume depending on individual experimental approaches, larger than the predicted value for dyadic space [87, 137, 141].
This present study focuses on quantifying the nature of the Na+ fuzzy space and
how it modulates the local Ca2+ dynamics. The Na+ microdomain is assumed to take the
same space as the dyadic and PD spaces where NCX1 resides and simultaneously
modulate the local [Ca2+] and [Na+] dynamics. The model constraints suggest a very slow diffusion in the dyadic space and PD in order to reproduce the NaK current during Na+
local depletion experiment [137]. There are several reports that indicate that diffusion in
the Na+ fuzzy space is quite slow, and estimates of the diffusion constant in the dyadic space have been extensively debated [18, 19, 141, 147, 148]. Prior work by Kushmerick and Podolsky found that Na+ diffusion in frog skeletal muscle was 50% of that in water
[149]. However, several other investigations that addressed this question have raised
different opinions. Recent studies using X-Ray analysis showed that Na+ can accumulate close to the sarcolemma and a Na+ gradient can be established between the area beneath
sarcolemma and the cytosol [20, 21]. Despa et al. recently used a different technique and
estimated the sodium diffusion in the cytosol as well as the subsarcolemmal
compartments are much slower than previously measured (at least 102 (cytosol)-104
(subsarcolemmal compartment) smaller) [137, 150].
Some models have also attempted to address this issue. Shannon et al. developed
a detailed mathematical model Ca2+ dynamics and other ionic currents in the rabbit ventricular myocyte [151]. Diffusion of Na+ between the dyadic space and the
97 submembrane compartment and from submemebrane compartment to cytosol in the
model was close to the value in water. However, the model was not able to reproduce the
experimental observations of NaK current in response to Na+ local depletion or Ca2+
transient reduction upon INa inhibition. Another computational model that describes the
dyadic space Ca2+ and Na+ diffusion by Lines et al. showed that only with co-localization
2+ of NCX1 and INa and slow diffusion could result in earlier Ca release. With higher diffusion rate, not enough Na+ can accumulate locally to allow for reversal of NCX1.
However, the NCX1 model used in the study exhibited a single exchanger current >100 fA, about ~1000 times bigger than experimental measurement of maximum unitary
NCX1 current [95], and did not incorporate intracellular Ca2+-dependent allosteric
regulation. In addition, the changes in RyR2 release were not quantified in the study. The
model constraints and simulations in the present study demonstrate consistent results with
slow Na+ diffusion. Slow diffusion allows the model to be able to reproduce experimental observations as mentioned above and also enables NCX1 to contribute to CICR process.
It still remains unclear why such gradients of Na+ can be established. There could be several reasons for the slow diffusion in the Na+ fuzzy space. The dyadic space is
filled with channels and proteins that are part of the signaling cascades or serve to
stabilize local ion channels and transporters in the t-tubules and JSR membrane [152,
153]. Therefore, it is possible that macromolecular crowding ([154]) can contribute
significantly to slowing diffusion. Furthermore, the presence of negatively charged
phospholipids in the membrane may also cause a surplus of soluble anions to accumulate
[19, 155]. Therefore, it is possible that the Na+ diffusion in the restricted space in the t-
tubules is much slower than in cytosol.
98
3.4.4 The role of NCX1 to trigger or prime the local [Ca2+] during CICR process
The physiological roles of NCX1 have been discussed extensively. Dyadic NCX1
2+ has been shown to play an important role in extruding [Ca ]d at rest in our prior study
[80] and previous experimental work [68], limiting local Ca2+ accumulation. While there
is consensus regarding the important role of NCX1 for Ca2+ extrusion during diastole, whether the reverse mode of NCX1 could trigger or enhance the CICR process remains controversial. The model simulation in Fig. 3-11 show that the presence of INa in the dyad
is important for local Na+ accumulation, which is a prerequisite for reversing NCX1 and
+ contributing to additional RyR2 release with physiological [Na ]i conditions at 0mV
membrane voltage. This is consistent with our previous ECC gain investigation with
+ fixed elevated [Na ]d values. The peak of LCC current is reduced slightly as a result of
NCX1 reverse mode bringing in Ca2+ to decrease the Ca2+ gradient for LCC Ca2+ influx.
2+ On the other hand, the additional [Ca ]d influx through NCX1 induces more RyR2 release, which results in an increase in the peak JRyR2. Consequently, ECC gain at 0 mV is increased in the presence of INa. The investigation of INa and NCX1 with testing potential from -20 – 50mV further present their impact on augmenting the triggering current at Vm
around AP plateau phase, displayed in Fig. 3-12 in the supplement material. This priming
effect of NCX1 has been examined and confirmed in NCX1 knockout cardiomyocytes in
comparison with control under strong EGTA buffering conditions to understand the
contribution of NCX1 to ECC [70]. The knockout mice exhibit reduced coupling
efficiency upon AP pacing but the wild-type mice display normal EC coupling as a result
of NCX1 contribution during the CICR process. In the absence of LCC, NCX1 reversal
99 2+ through the fast opening of INa only ineffectively induces small and slow Ca release, shown in Fig. 3-11. Thus, it can be concluded from our simulation results that a small
+ subpopulation of neuronal INa and NCX1 in the dyad are crucial for Na regulation and
2+ they prime [Ca ]d to enhance the CICR process. However, the capacity of INa alone to
trigger RyR2 release is very limited. Dysregulation in any of the Na+ regulation
components can potentially result in dysregulation of dyadic [Ca2+] and [Na+] and lead to arrhythmogenic behavior.
3.4.5 Na+ related other disease and potential therapeutic direction
The model simulations in this study show that reduction of NCX1 and NaK leads
to a higher probability of EADs occurrence compared to control cardiomyocytes with
ISO stimulation. This is attributed to an elevation in local Ca2+ spark activities and a higher [Ca2+]d triggers reopening of RyR2 (Fig. 3-16C), which later on induces the
reopening of LCC (Fig. 3-16D) and results in EAD generation. The reduction in NCX1
and NaK expression levels promotes the SR Ca2+ loading process through SERCA, which
further enables the occurrences of RyR2 reopen. Therefore, an additional simulation to
shift 50% of NCX1 and NaK from the dyad and PD spaces into cytosol was conducted to
2+ investigate the role of increased [Ca ]d only. Model results demonstrate an even higher
EAD probability (~13%) compared to NCX1 and NaK reduction in ankyrinB+/- deficient case, which suggests the decreased [Ca2+] and [Na+] regulation in the dyadic space leads
2+ 2+ to elevation in local [Ca ]d and Ca spark activities. They are the determining factor in
generating imbalance of NCX1 and NaK current and leading abnormal Ca2+ functions with ISO stimulation.
100 In addition to NCX1 and NaK functional coupling in the dyadic and PD spaces, it
has been suggested that dysregulation of neuronal INa in the t-tubules may contribute to reversal of the NCX1 which potentially induces spontaneous RyR2 release through regulating the local [Na+]. A recent study by Radwanski et al. presented that the
2+ persistent neuronal INa plays an important role in Ca dysregulation in CPVT
+ cardiomyocytes. The neuronal Na mediated persistent INa is augmented by CAMKII
phosphorylation upon beta-adrenergic stimulation, similar to the effects on NaV1.5 and
has been demonstrated to act as an independent mechanism from RyR2 phosphorylation
2+ to trigger delayed afterdepolarizations (DAD). The persistent neuronal INa and SR Ca
overload are necessary and sufficient for arrhythmia generation in CPVT. Particularly,
Nav1.6 has been shown to co-localize with RyR2 with the highest degree in the study
+ compared to other neuronal Na channels and the augmentation of INa facilitates the influx of Ca2+ through NCX1 reverse mode in the Na+ microdomain, which leads to
diastolic Ca2+ release events and results in DADs.
This present study along with new experimental investigations suggests an
important role of Na+ local regulation in Ca2+ dynamics and CICR process. Targeting neuronal INa or NCX1 can be effective in treating certain cardiac diseases.
101 Chapter 4 – Conclusions and Future Direction
4.1 Summary of Findings
My studies have applied mathematical modeling and simulations to investigate
the role NCX1 and NaK coupling in the Ca2+ and Na+ microdomains in normal and
pathological cardiac functions. Important aspects of the modeling efforts include: 1)
Develop a biophysically-constrained markov chain model for NCX1 that characterizes
both the transport kinetics as well as the dynamics of intracellular Ca2+-dependent allosteric regulation; 2) Incorporation of NCX1 in the dyadic and PD spaces in both the
SRS Ca2+ spark model as well as a canine cardiomyocyte model with stochastic simulations of LCCs and RyRs to investigate the dual roles of NCX1 in Ca2+ dynamics
and the CICR process and to achieve validity of this multi-scale modeling approach; 3)
Development of Na+ local control dynamics in the dyad and PD with NaK and neuronal
+ INa in the dyad and PD to understand the roles of NaK and neuronal Na channels in local
Na+ regulation and how they regulate the CICR process through NCX1; 4) Application of the whole-cell model to mimic ankyrin-B+/- deficiency condition to show that reduction in
NCX1 and NaK in the t-tubules leads to an elevation in activities in Ca2+ spark and to
increase susceptibility to early-afterdepolarizations. Using the mathematical modeling
and simulations, I was able to provide new insights into CICR modulation through NCX1
in the Na+ fuzzy space and mechanisms responsible for arrhythmic generation in ankyrin-
B deficient cells.
First, using biophysically based computational models, the multifaceted roles of
NCX1 and the nature of its spatial distribution (to dyad, PD, and cytosol) in the
102 regulation Ca2+ dynamics from the level of sparks to whole-cell have been demonstrated.
Under physiological conditions, NCX1 primarily functions to extrude Ca2+ and to temper dyadic Ca2+ activity in diastole. On the other hand, upon sufficient membrane
depolarization and/or in presence of elevated local [Na+], NCX1 promotes Ca2+ entry and contributes to triggering CICR. The whole-cell model predicts how differential placement of NCX1 into cytosolic, PD, and dyadic compartments affects the morphology of whole- cell INCX1 (under AP clamp), with the best reproduction of experimental data achieved for an NCX1 distribution that matches the recent imaging data of Wang et al. [68], with a dyad-to-PD NCX1 placement ratio of ~ 1:2. Furthermore, allosteric Ca2+ activation of
NCX1 helps to “functionally localize” exchanger activity to the dyad and PD by reducing exchanger activity in the cytosol thereby protecting the cell from excessive loss of Ca2+
during diastole.
Secondly, the further developed whole-cell cardiomyocyte model that
+ characterizes Na dynamics through NaK, neuronal INa and NCX1 in the dyad and PD spaces is developed in this study. NaK presents a similar distribution as NCX1, with
~13% in the dyad, 32% in PD and 55% in the cytosol. NaK couples with NCX1 to
+ + regulate the baseline/diastole phase of [Na ] in the dyad as well as the [Na ]i drifting rate.
+ On the other hand, neuronal INa contributes mainly to transient [Na ] accumulation during systole phase. The whole-cell model reproduces the slow-down [Ca2+] decay upon an
immediate inhibition of NaK, which reflects the local [Na+] accumulation and a
decreased NCX1 activity in the t-tubules. Model predicts the existence of Na+ sparks in
the presence of NCX1 in the dyad upon Ca2+ spark generation. Redistributing NaK in the
dyad or PD regulates the local [Na+] and results in APD prolongation through shifting
103 NCX1 reversal time point. The model investigation of the neuronal INa’s roles demonstrate that it increases the EC coupling efficiency through promoting the reverse-
2+ mode of NCX1 to prime the [Ca ]d and enhancing the CICR process, consistent with
experimental measurements. However, it cannot trigger Ca2+ release effectively on its
own in the absence of LCC. The role of NCX1 and NaK functional coupling has been
further examined in the ankryin-B+/- deficiency setting. As a result of reduction of both
NCX1 and NaK regulation of the dyad and PD, local regulation of [Ca2+] and [Na+] dynamics is compromised and the whole-cell Ca2+ sparks are greatly elevated. Upon beta-adrenergic stimulation, ankyrin-B+/- model exhibits a much higher EAD occurrence compared to control cardiomyocyte.
4.2 Limitations
Mathematical models are by nature simplifications of the biological systems.
Thus, the models lack many details in regards to the various compartments representing
the ion gradients and signaling pathways found in cardiomyocytes.
The mathematical models developed here are based closely on cellular data from
primary cardiomyocyte and as a result models are limited by the available experiment
data. For example, as a result of limitation in Na+ fluorescent indicators (Compared to
Ca2+ indicators), the local Na+ signals/dynamics in the Na+ fuzzy space or subsarcolemmal compartment remains controversial. Further microscopy studies will enlighten us more of the Na+ diffusion process within the restricted space. While our model of the ankyrin-B+/- deficiency model accounts for the loss of current from NCX1
and NaK, data on the specific spatial loss of NCX1 and NaK remain unclear and it may
have different impact on Ca2+ and Na+ dynamics regulation. Also, ankyrin-B is
104 responsible for the localization of InsP3 but the role of the InsP3 receptor is unclear in
ventricles. The model does not account for the defects of localization of this receptor.
Additionally, ankyrin-B has been suggested to regulate PP2A, which regulates the
activities of SERCA, and is not accounted for in the model either. Furthermore, it is
known that Ca2+ waves underlie the generation of DADs. The whole-cell model employs
a single cytosol, independent Ca2+ release units and PDs, which is non-spatial and does
not support site-to-site Ca2+ propagation. Spontaneous release events are localized and small, which do not initiate DADs on the whole-cell level. Despite the limitations, my
multi-scale models nicely reproduce key properties of NCX1 dynamics of Ca2+- dependent activation, NCX1 and Na+ local control regulation of the CICR process, and
the key properties of the ankryin-B+/- defect cell. It will be important, going forward, to
continue implementing the Na+ local control in a previously developed 3D whole-cell
model (Walker et al. under review) in order to understand their roles in DAD generations
in cardiac diseased conditions. The electrophysiological properties of Ca2+ propagation properties are dependent on the structure and dyadic/PD communication within the cell.
4.3 Future directions
While my studies have provided insight into the dual roles of NCX1 in canine
ventricular myocyte and the importance of NCX1 and NaK functional coupling, one
aspect that could use further investigation is how NCX1 role may differ in other animal
species or transmural heterogeneity within the same heart as well. Depending on the
2+ + complex regulating factors of Vm, Ca and Na electrochemical gradients across the membrane, and expression levels, NCX1 can function more in the forward mode or more in the reverse mode, contributing differently during the CICR process.
105 As discussed in the previous section earlier, my current canine whole-cell model
is non-spatial and does not reproduce spontaneous Ca2+ release events since all the dyad/PD are independent from each other. The electrophysiological properties of Ca2+
propagation properties within a cell are not only dependent on ion channel/pump
properties, but also the structure and dyadic/PD communication between Ca2+ release sites. For ankyrin-B+/- defect cells, DADs are observed upon beta-adrenergic stimulation
as well. Therefore, it will be important to implement the Na+ local control in the 3D
whole-cell model (Walker et al. under review), simulate and understand the
electrophysiology behavior and spontaneous Ca2+ release. A major aspect of ion channel
regulation upon ISO stimulation is CaMKII phosphorylation. CaMKII phosphorylation
has been previously studied extensively in the lab and a new mechanism of DAD
generation in CPVT rat cardiomyocytes has been suggested to be caused by augmentation
of the neuronal INa persistent current. Both phosphorylated INa and up-regulation of
SERCA to overload SR Ca2+ are necessary and important for arrhythmia generation. The
completed model with Na+ local control then can be applied to study a wide range of cardiac diseases to investigate and understand the underlying mechanisms that contribute to cellular arrhythmias.
The ultimate goal of computational models of cardiomyocytes is their application in medical treatment for cardiac arrhythmias. Many ion channels have been suggested as targets in clinical settings such as LCC, NCX1 and RyR2. However, blocking certain ion channels can potentially cause more arrhythmia. Therefore, another future direction for mathematical modeling could incorporate the drug targets and mechanisms in the mathematical model for cardiomyocytes to simulate drug effects and optimize the best
106 anti-arrhythmic options. Experimental studies have used several Na channels (specifically for neuronal INa or all INa) suggested neuronal INa as a target for inhibiting arrhythmic potentials and treating arrhythmias.
107 Appendix A Model Equations and Parameters A.1 Model equations and parameters for Chapter 2
A.1.1 NCX1 Model
NCX1 biophysical model parameters
CBD12Table A1: Model Parameters Parameter Definition Value Unit 2+ -3 -1 -1 k01 Ca binding constant from A0 to 4.4548 ×10 [44, 86] µM ms A1 -3 -1 k10 Dissociation constant from A1 to 0.7542 ×10 ms A0 2+ -1 -1 k12 Ca binding constant from A1 to 0.9999 µM ms A2 -3 -1 k21 Dissociation constant from A2 to 5 ×10 [44, 86] ms A1 2+ -1 -1 k23 Ca binding constant from A2 to 1.0 µM ms A3 -1 k32 Dissociation constant from A3 to 0.25 [44, 86] ms A2 2+ -1 -1 k34 Ca binding constant from A3 to 0.1209 µM ms A4 -1 k43 Dissociation constant from A4 to 0.7822 ms A3 2+ -1 -1 k45 Ca binding constant from A4 to 0.0122 µM ms A5 -1 k54 Dissociation constant from A5 to 0.8353 ms A4 2+ -1 -1 k56 Ca binding constant from A5 to 0.1354 µM ms A6 -1 k65 Dissociation constant from A6 to 0.7688 ms A5 fA2c Partial activity coefficient of A2c 0.0799 fA2cc Partial activity coefficient of A2cc 0.799 fA46c Partial activity coefficient of A46c 0.1 fA46cc Partial activity coefficient of 1 A46cc -1 α2 Forward rate for conformational 0.0299 ms change from A2 to A2c and A46 to A46c -1 β2 Backward rate for 0.005 ms conformational change from A2c
108 to A2 and A46c to A46 -1 α4 Forward rate for conformational 0.0002986 ms change from A2c to A2cc and A46c to A46cc -1 β4 Backward rate for 0.000216 ms conformational change from A2cc to A2c and A46cc to A46c
JNCX1 = (Allo)(ΔE), (A1.1) 2+ + 3 2+ + 3 k− k− k− k− k− k− [Ca ] [Na ] − k k k k k k [Ca ] [Na ] ΔE = k 1 2 3 4 5 6 o i 1 2 3 4 5 6 i o NCX1 + 3 + 2+ + + 3 + 2+ + + 3 2+ + 2+ + 3 + + 3 + 3 + 2+ 2+ Z1[Na ]i Z2[Ca ]i Z3[Na ]o Z4[Ca ]o Z5[Na ]i [Ca ]o Z6[Ca ]i[Na ]o Z7[Na ]i [Na ]o Z8[Ca ]i[Ca ]o
(A1.2) where
(A1.3) Z1 = k−5k−1k−4 (k−3k−6 + k2k3 + k−6k2 ) Z2 = k2k3k6 (k−1k5 + k−1k4 + k4k5 ) (A1.4)
Z3 = k5k4k1(k−3k−6 + k2k3 + k−6k2 ) (A1.5)
Z4 = k−3k−2k−6 (k−1k5 + k−1k−4 + k4k5 ) (A1.6) (A1.7) Z5 = k−5k−2 (k−4k−3k−6 + k−6k−1k−4 + k−1k−3k−6 + k−1k−4k−3 + k3k−1k−4 + k−3k4k−6 ) Z6 = k6k1(k4k5k2 + k5k3k2 + k5k4k2 + k−3k5k4 + k2k4k3 + k3k2k−4 ) (A1.8) (A1.9) Z7 = k1k−5 (k−4 + k4 )(k−3k−6 + k2k3 + k−6k2 ) Z8 = k−2k6 (k−3 + k3 )(k−1k5 + k−1k−4 + k4k5 ) (A1.10)
(2+partial _ e)/2RT −(2+partial _ e)/2RT k3 = k f 3e ,k−3 = kr3e , (A1.11-12) −(3+partial _ e)/2RT (3+partial _ e)/2RT k4 = k f 4e ,k−4 = kr4e (A1.13-14)
ka12 = k12 (A1.15) (A1.16) k32 ka21 = k21( ) k [Ca2+ ] + k 23 i 32 (A1.17) 2+ = k23[Ca ]i ka23 k34 ( 2+ ) k23[Ca ]i + k32
1 ka32 = k43( 2+ 2+ 2 2+ 3 ) k45[Ca ] + k45k56 ([Ca ]) + k45k56k67 ([Ca ]) k54 k54k65 k54k65k76 (A1.18)
109
dA0 2+ = −ka12[Ca ]A0 + ka21A2 (A1.19) dt dA2 = 2+ − − 2+ + −α + β ka12[Ca ]A0 ka21A2 ka23[Ca ]A2 ka32 A46 2 A2 2 A2c (A1.20) dt
dA46 2+ = ka23[Ca ]A2 − ka32 A46 −α2 A46 + β2 A46c (A1.21) dt
dA2c 2+ = α2 A2 − β2 A2c − ka23[Ca ]A2c + ka32 A46c −α4 A2c + β4 A2cc (A1.22) dt
dA46c 2+ = α2 A46 − β2 A46c + ka23[Ca ]A2c − ka32 A46c −α4 A46c + β4 A46cc (A1.23) dt
dA2cc 2+ = −ka23[Ca ]A2cc + ka32 A46c +α4 A2c − β4 A2cc (A1.24) dt
Allo = F2c A2c + F2cc A2cc + F46c A46c + F46cc A46cc (A1.25)
A.1.2 Model equations and parameters for SRS and whole-cell model for NCX1
incorporation
SRS Model and Whole-Cell Model Parameter changes from previously published values Parameter Definition Value Unit k+ RyR2 opening rate constant 7.7789 ×10-5 µM-η ms-1
γkd Kd for LCC forward rate into CDI 15 µM -13 Vss Subspace (ss) volume 1.765 ×10 µL -1 rss2pd Transfer rate between ss and PD 133.33 ms -12 Vpd2c Peri-dyadic volume 2.92 ×10 µL -1 rpd2c Transfer rate between PD and 60 ms cytosol
Table A2: SRS model and whole-cell parameters Transport equations in SRS model
The 3D mesh was discretized into tetrahedral elements. For the ith element, the time rate of change for [Ca2+] is given by,
2+ 4 NB d[Ca ]i k k 2+ RyR refill SERCA LCC NCX1,Ca βi = ∑Ji,k +∑(koff [CaBj ]i − kon[Ca ]i[Bj ]i )+ Ji + Ji + Ji + Ji − Ji dt k=1 j=1 (A1.26) where NB refers to the number of buffering species Bj, and Ji,k is the net flux into the
110 element through each face k, which is a function of the element geometry and [Ca2+] gradient.
Transport equations in the whole-cell model
2+ The time rate of change of [Ca ]ss in individual subspace compartments of each dyad in the whole-cell model is characterized by,
d[Ca 2+ ] ss,i,1 = β (J LCC + J RyR 2 − J xfer + J iss + J iss − J NCX 1) (A1.27) dt ss,i,1 i,1 i,1 i,1 i,2,1 i,4,1 i,1 d[Ca 2+ ] ss,i,2 = β (J LCC + J RyR 2 − J xfer + J iss + J iss − J NCX 1) (A1.28) dt ss,i,2 i,2 i,2 i,2 i,3,2 i,1,2 i,2 d[Ca 2+ ] ss,i,3 = β (J LCC + J RyR 2 − J xfer + J iss + J iss − J NCX 1) (A1.29) dt ss,i,3 i,3 i,3 i,3 i,4,3 i,2,3 i,3 d[Ca 2+ ] ss,i,4 = β (J LCC + J RyR 2 − J xfer + J iss + J iss − J NCX 1) (A1.30) dt ss,i,4 i,4 i,4 i,4 i,1,4 i,3,4 i,4 NCX1 Ca2+-dependent allosteric regulation via CBD12 is modeled stochastically and the
steady-state formulation for transport kinetics is used.
The peri-dyadic (PD) Ca2+ concentration for each CRU is described by,
d[Ca 2+ ] V 4 pd ss xfer xfer NCX 1 (A1.31) = βi ( ∑ Ji,k − Ji,c − Ji ) dt Vpd k=1
LCC Markov chain model
The 12-state LCC Markov chain model from Greenstein et al. [38] was modified to
accommodate addition of the 2-state RyR2 model. The forward rate constants of LCC
2+ 2+ Ca -dependent inactivation (CDI) were adjusted so that CDI at high [Ca ]d occurs with
the physiologically correct time-course during the AP, and was also modified by adding a
saturating term to limit rate of onset of CDI.
γ γ = γ 2+ kd cf [Ca ]ss 2+ , (A1.32) γcf +[Ca ]ss
111 Global Signals
Membrane potential is calculated as below dVm = −(INa + ICaL + IKr + IKs + Ito1 + IK1 + IKp dt (A1.33)
+Ito2 + INaK + INCX1,Cyt + INaCa,SS + INaCa,PD + I pCa + ICab + INab )
A.2 Model equations and parameters for Chapter 3
+ WholeTable A3: Whole-Cell Model-cell model and SRS model parameters in Na Parameters local control.
Parameter Definition Value Unit
+ + -1 k 1 NaK kinetic parameter k 1 0.72 [133] ms
- - -1 -1 k 1 NaK kinetic parameter k 1 0.08 [133] µM ms
+ + -1 k 2 NaK kinetic parameter k 2 0.08 [133] ms
- - -1 k 2 NaK kinetic parameter k 2 0.008 [133] ms
+ + -1 k 3 NaK kinetic parameter k 3 4.0 [133] ms
- - -2 -1 k 3 NaK kinetic parameter k 3 8000.0 [133] µM ms
+ + -1 k 4 NaK kinetic parameter k 4 0.3 [133] ms
- - -1 k 4 NaK kinetic parameter k 4 0.2 [133] ms
0 + K dNao NaK Binding affinity for [Na ]o 26.8 [133] µM
0 + K dNai NaK binding affinity for [Na ]i 5.0 [133] µM
0 + K dKo NaK binding affinity for [K ]o 0.8 [133] µM
0 + K dKi NaK binding affinity for [K ]i 18.8 [133] µM
KdMgATP NaK binding affinity for APT 0.6 [133] µM
-2 CNaK NaK transporter density for 1000 [10, 132, 133] µm
112 whole-cell
+ gNa Single neuronal Na current 0.00019 [10, 135] mS/µF
-1 rss2pd Transfer rate between ss and PD 0.005 ms
for Na+
-1 rss2ss Transfer rate between ss and ss 0.0005 ms
for Na+
-1 rpd2c Transfer rate between PD and 0.00225 ms
cytosol for
SRS Model Parameter
Parameter Definition Value Unit
+ 2 -1 DNa Na diffusion coefficient 0.0000022 µm ms
A.2.1 Sodium/Potassium ATPase (NaK) formulation
We implemented a thermodynamically-constrained kinetic model of NaK presented in
Smith & Crampin [132] and used parameters from Oka et al. 2010 [133]. The steady-state formulation of NaK was implemented in the dyadic and PD spaces in the whole-cell model. Model parameters are shown in Table S1.
0 0.44FV KdNao = KdNao exp( ) RT (A2.1)
0 −0.14FV KdNai = KdNai exp( ) RT (A2.2)
113 0 0.23FV KdKo = KdKo exp( ) RT (A2.3)
0 −0.14FV KdKi = KdKi exp( ) RT (A2.4)
[Na+ ] Nai = i KdNai (A2.5)
[Na+ ] Nao = o KdNao (A2.6)
[K + ] Ki = i KdKi (A2.7)
[K + ] Ko = o KdKo (A2.8)
+ 3 α + = k1 Nai 1 3 2 ((1+ Nai) + (1+ Ki) −1) (A2.9)
α − = − 1 k1 MgADP (A2.10)
α + = + 2 k2 (A2.11)
α + = + 2 k2 (A2.12)
− 3 α − = k2 Nao 2 3 2 ((1+ Nao) + (1+ Ko) −1) (A2.13)
+ 3 α + = k3 Ko 3 3 2 ((1+ Nao) + (1+ Ko) −1) (A2.14)
− + − k3 Pi[H ] α3 = (1+ MgATP) (A2.15)
114 + + k4 MgATP α4 = (1+ MgATP) (A2.16)
− 2 α − = k4 Ki 4 3 2 ((1+ Nai) + (1+ Ki) −1) (A2.17)
+ + + + − − − − α1 α2α3α4 −α1 α2α3α4 vcyc = Σ (A2.18)
− − − + − − + + − + + + Σ = α1 α2α3 +α1 α2α3 +α1 α2α3 +α1 α2α3 +α −α −α − +α +α −α − +α +α +α − +α +α +α + 2 3 4 2 3 4 2 3 4 2 3 4 − − − + − − + + − + + + +α3α4α1 +α3α4α1 +α3α4α1 +α3α4α1 +α −α −α − +α +α −α − +α +α +α − +α +α +α + 4 1 2 4 1 2 4 1 2 4 1 2 (A2.19)
A.2.2 Neuronal Na+ channel
Figure 5-1: Model schematic for neuronal Na+ channel
+ We implemented neuronal Na channels (INa) first presented by Clancy et al. 2004 [134] and used parameters given in Sampson et al. 2011 [135]. The markov chain model is shown in Figure S1. It is implemented stochastically in the dyadic space in the whole-cell
115 model. Both UO and LO are open states. The rates in the markov chain model are given below.
α11= 2.802 (A2.20) −V −V (0.21exp( )+ 0.23exp( )) 17 150
α12 = 2.802 −V −V (0.23exp( )+ 0.25exp( )) 15 150 (A2.21)
α13 = 2.802 −V −V (0.25exp( )+ 0.27exp( )) 15 150 (A2.22)
−V β11= 0.4exp 20.3 (A2.23)
−(V − 5) β12 = 0.4exp 20.3 (A2.24)
0.4 −(V −10) β13 = exp 4.5 20.3 (A2.25)
−7 −V α3 = 3*3.7933*10 exp 7.6 (A2.26)
β3 = 0.0084 + 0.00002V (A2.27)
9.178 −V α2 = exp 4.5 29.68 (A2.28)
1.5*0.285 α4 = α2 100 (A2.29)
β4 = α3 5 (A2.30)
80 α5 = α2 95000 (A2.31)
116 β5 = α3 30*10 (A2.32)
α13α3α2 β2 = β13β3 (A2.33)
−8 µ1= 4.3e (A2.34)
−4 µ2 = 3e (A2.35)
= + − INattx GNa,ttx (Ottx BOttx) (V ENa ) (A2.36)
A.2.3 Local Na+ dynamics in the whole-cell model
It is assumed that the Na+ local spaces (dyad and PD) take the same area as the Ca2+ local spaces since NCX1 serves as a bridge between [Ca2+] and [Na+] dynamics. The time
rate of change for Ca2+ balance in the 1st, 2nd, 3rd, and 4th subspaces of the ith Ca2+
release units (CRU) are respectively
+ d[Na ]SS,i,1 = (−3(JNCX1,1 + JNaK,1)− JNaTTX,1 − Jxfer,i,1 + Jiss,i,2,1 + Jiss,i,4,1) dt (A2.37)
+ d[Na ]SS,i,2 = (−3(JNCX1,2 + JNaK,2 + JNaTTX,2 )− Jxfer,i,2 + Jiss,i,3,2 + Jiss,i,1,2 ) (A2.38) dt
+ d[Na ]SS,i,3 = (−3(JNCX1,3 + JNaK,3 )− JNaTTX,3 − Jxfer,i,3 + Jiss,i,4,3 + Jiss,i,2,3 ) (A2.39) dt
+ d[Na ]SS,i,4 = (−3(JNCX1,4 + JNaK,4 )− JNaTTX,4 − Jxfer,i,4 + Jiss,i,1,4 + Jiss,i,3,4 ) (A2.40) dt
where the diffusive Na+ flux between the jth and ith contiguous subspaces within the ith
CRU is defined by
= + − + Jiss,i, j,l riss ([Na ]SS,i, j [Na ]SS,i,l ) (A2.41)
2+ Similar to Ca diffusion, riss is assumed to be 10 times slower than rxferss2pd.
117 Similarly, Na+ diffusion out of the jth subspace of the ith CRU into the ith PD is calculated as,
= + − + Jxferss2PD,i, j rxferss2PD ([Na ]SS,i, j [Na ]PD ) (A2.42) and the Na+ diffusion out of the ith PD into the cytosol is characterized as
= + − + Jxferss2PD,i, j rxferss2PD ([Na ]SS,i, j [Na ]PD ) (A2.43)
A.2.4 3D super-resolution spark (SRS) model
Transport equation in SRS model
The 3D mesh was discretized into tetrahedral elements, For the ith element, the time rate of change for [Na+] is given by,
+ 4 d[Na ]i NCX1,Na NaK NaTTX = ∑Ji,k +(−3(Ji + Ji )− Ji ) (A2.44) dt k=1 where Ji,k is the net flux into the element through each face k, which is a function of the element geometry and [Na+] gradient.
118
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128 CURRICULUM VITAE FOR Ph.D. CANDIDATES The Johns Hopkins University School of Medicine Lulu Chu September 8th, 2016 Educational History: Ph.D. expected 2016 Program in Biomedical Engineering Johns Hopkins School of Medicin B.S. 2009 Biomedical Engineering and Minor in Mathematics University of Virgini Other Professional Experiences Summer internship May-August 2015 Quantitative Clinical Pharmacology, AstraZeneca Conducted a model-based meta analysis in R to investigate and compare adverse event responses/profiles across all mono- and combination therapies in immuno-oncology using external resources Participant July-August 2012 Cold Spring Harbor Laboratory Learned different mathematical approaches (ODE, PDE, Stochastic simulation, Bayesian model etc.) to build computational models of biological systems; Developed and presented a simple compartmental model of cardiomyocyte and a 1-D PDE model in MATLAB that represented the Ca2+ wave during cardiac contraction to study heart failure Research rotation May-August 2010 Microvascular Development and Remodeling Laboratory, JHU Investigated how VEGF-targeted drug (Tyrosine Kinase Inhibitors) efficacy differs greatly by incorporating intracellular VEGFR phosphorylation and interpersonal variability in microenvironment using druggable multiscale computational models (in FORTRAN) of transport and signaling of VEGF Scholarships, fellowships and or other external funding Medtronic Fellowship 2009-2010 $26,855 Department of Biomedical Engineering, JHU Academic and other honors at Hopkins and elsewhere 2016 GSA Travel Award JHU 2009 Graduation with High Distinction University of Virginia 2007 Golden Key Honor Society University of Virginia 2007 Intermediate Honor University of Virginia 2005 Echols Scholar University of Virginia Publications and conference presentations Chu L, Greenstein JL, Winslow RL. (2016) Modeling Na+-Ca2+ exchange in the heart: Allosteric activation, spatial localization, sparks and excitation-contraction coupling. J Mol Cell Cardiol. Chu L, Greenstein JL, Winslow RL. (2016) Modeling Na+ local control and its regulation in excitation-coupling coupling in healthy and pathological conditions (In preparation). Posters, abstracts, etc. Chu, L, Greenstein JL, Winslow RL. (2016) “Modeling the role of NCX in the regulation of cardiomyocyte Ca2+ microdomain dynamics” Chu, L, Greenstein JL, Williams GSB, Boyman L, Lengenzov E, Hagen B, Lederer WJ, Winslow RL. (2015) “Dynamics of Ca2+-Dependent Regulation of the Cardiac Na+/Ca2+ Exchanger (Computational Approach)” Chu, L, Boyman L, Legenzov E, Williams GSB, Greenstein JL, Winslow RL, Lederer WJ, Hagen B. (2014) “Dynamics of Ca2+-Dependent Regulation of the Cardiac Na+/Ca2+ Exchanger (Experimental Approach)” Chu, L, Park SR, Tandon M, Guilford WH, Saucerman JJ. (2009) “Modeling Nitric Oxide Regulation Of EC Coupling in Cardiac Myocytes” Presentation at Biophysics Conference 2009;. Service and leadership 2011-2012 Teaching Assistant, Department of Biomedical Engineering, JHU Organized and led weekly recitation and review sessions in Models of Simulations and Systems Bioengineering III 2014-2015 Incentive Mentoring Program/Thread Volunteering (Head of Family) 2012-2016 Hopkins Dance (Webmaster, Advertising Coordinator)
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