University of Iowa

Iowa Research Online Theses and Dissertations

Spring 2012

Defining new insight into fatal human arrhythmia: a mathematical analysis Roseanne Marie Wolf University of Iowa

Copyright 2012 Roseanne Marie Wolf This dissertation is available at Iowa Research Online: http://ir.uiowa.edu/etd/3013 Recommended Citation Wolf, Roseanne Marie. "Defining new insight into fatal human arrhythmia: a mathematical analysis." PhD (Doctor of Philosophy) thesis, University of Iowa, 2012. http://ir.uiowa.edu/etd/3013.

Follow this and additional works at: http://ir.uiowa.edu/etd Part of the Applied Mathematics Commons

DEFINING NEW INSIGHT INTO FATAL HUMAN ARRHYTHMIA: A MATHEMATICAL ANALYSIS

by Roseanne Marie Wolf

An Abstract Of a thesis submitted in partial fulfillment of the requirements for the Doctor of Philosophy degree in Applied Mathematical and Computational Sciences in the Graduate College of The University of Iowa May 2012 Thesis Supervisors: Assistant Professor Thomas J. Hund Assistant Professor Colleen C. Mitchell

1

ABSTRACT Background: Normal cardiac excitability depends upon the coordinated activity of ion channels and transporters. Mutations in genes encoding ion channels affecting their biophysical properties have been known for over twenty years as a root cause of potentially fatal human electrical rhythm disturbance (arrhythmias).

More recently,

defects in ion channel associated protein (e.g. adapter, regulatory, cytoskeletal proteins) have been shown to cause arrhythmia.

Mathematical modeling is ideally suited to

integrate large volumes of cellular and in vivo data from human patients and animal disease models with the over goal of determining cellular mechanisms for these atypical human cardiac diseases that involve complex defects in ion channel membrane targeting and/or regulation. Methods and Results: Computational models of ventricular, atrial, and sinoatrial cells were used to determine the mechanism for increased susceptibility to arrhythmias and sudden death in human patients with inherited defects in ankyrin-based targeting pathways. The loss of ankyrin-B was first incorporated into detailed models of the ventricular myocyte to identify the cellular mechanism for arrhythmias in human patients with loss-of-function mutations in ANK2 (encodes ankyrin-B). Mathematical modeling was used to identify the cellular pathway responsible for abnormal Ca2+ handling and cardiac arrhythmias in ventricular cells.

A multi-scalar computational

model of ankyrin-B deficiency in atrial and sinoatrial cells and tissue was then developed to determine the mechanism for the increased susceptibility to atrial fibrillation in these human patients. Finally, a state-based Markov model of the voltage-gated Na+ channel was incorporated into a ventricular cell model and parameter estimation was performed to determine the mechanism for a new class of human arrhythmia variants that confer susceptibility to arrhythmia by interfering with a regulatory complex comprised of a second member of the ankyrin family, ankyrin-G. Conclusions: Ca2+ accumulation was observed at baseline in the ankyrin-B deficient ventricular model, with pro-arrhythmic

2

spontaneous release and afterdepolarizations in the presence of simulated β-adrenergic stimulation, consistent with the finding of catecholaminergic-induced arrhythmias in human patients.

The simulations demonstrated that loss of membrane Na+/Ca2+

exchanger and Na+-K+-ATPase contributed to Ca2+ overload and afterdepolarizations, with loss of Na+/Ca2+ exchanger as the dominant mechanism. In the atrial model of ankyrin-B deficiency, the loss of the L-type Ca2+ channel targeting was identified as the dominant mechanism for the initiation of atrial fibrillation. Finally, the simulations showed that human variants affecting ankyrin-G dependent regulation of NaV1.5 results in arrhythmia by mimicking the phosphorylation of the channel. Most importantly, mathematical modeling has been used to the molecular mechanism underlying human arrhythmia syndromes.

Abstract Approved: ____________________________________ Thesis Supervisor ____________________________________ Title and Department ____________________________________ Date ____________________________________ Thesis Supervisor ____________________________________ Title and Department ____________________________________ Date

DEFINING NEW INSIGHT INTO FATAL HUMAN ARRHYTHMIA: A MATHEMATICAL ANALYSIS

by Roseanne Marie Wolf

A thesis submitted in partial fulfillment of the requirements for the Doctor of Philosophy degree in Applied Mathematical and Computational Sciences in the Graduate College of The University of Iowa May 2012 Thesis Supervisors: Assistant Professor Thomas J. Hund Assistant Professor Colleen C. Mitchell

Copyright by ROSEANNE MARIE WOLF 2012 All Rights Reserved

Graduate College The University of Iowa Iowa City, Iowa

CERTIFICATE OF APPROVAL _______________________ PH.D. THESIS _______________ This is to certify that the Ph.D. thesis of Roseanne Marie Wolf has been approved by the Examining Committee for the thesis requirement for the Doctor of Philosophy degree in Applied Mathematical and Computational Sciences at the May 2012 graduation. Thesis Committee: ___________________________________ Thomas J. Hund, Thesis Supervisor ___________________________________ Colleen C. Mitchell, Thesis Supervisor ___________________________________ Peter Mohler ___________________________________ Bruce Ayati ___________________________________ Rodica Curtu ___________________________________ Long Sheng Song

To Mom and Dad

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ACKNOWLEDGMENTS First and foremost, I must thank my advisors, Thomas Hund, Ph.D. and Colleen Mitchell, Ph.D. I could not have asked for better mentors. You not only taught me mathematics, computer science, and electrophysiology, but you have been great role models. The enthusiasm you have for research was contagious, and I quickly learned the ups and downs. While there were challenging days, Tom was always there with a high five for the mini-breakthroughs. I will forever be grateful of the example you have provided as successful professors.

I can only hope that someday I am able to pass on

what you have taught me to my own students, yet at the same time, I know there is so much more for me to learn from you. I must also express my gratitude to my committee, Peter Mohler, Ph.D., Bruce Ayati, Ph.D., Rodica Curtu, Ph.D., and Long Sheng Song, M.D., M.S., for their guidance and review of this work. I also want to thank the past and present members of the Hund, Mohler, and Anderson labs. They made coming to work each day enjoyable and I will miss their support and fellowship. To my biology friends – Paari Dominic Swaminathan, M.D. and Madhu Singh Ph.D.

From a chance conversation in the hallway, you have become lifelong friends.

Not only have you been there to answer my many questions about the heart, but you were always there when I needed life advice. You have been through the ups and downs of the past year with me and I couldn’t have done it without you. You have challenged me, inspired me, taught me, and shared a laugh with me. Your friendship has helped me to grow as a person and that’s more than I ever could have asked for. To my math friend - Scott Small, Ph.D.

Without you, I never would have

survived analysis. Thank you for your friendship and support and letting me claim your office as mine. I can never repay you and I wish you the best of luck.

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And finally to my family, especially Mom and Dad - words cannot describe my gratitude for your constant love. You have always encouraged me to keep going, even when I didn’t think I could. You were my first teachers in life and have been with me every step of the way. All of the sacrifices you have made through the years to provide me with the best education have not gone unnoticed. You were the ones to teach me if I worked for it, I will appreciate it much more than if it was given to me. Although I may not have believed it at the time, I know now just how true it is. For all of the countless phone calls, the headaches I may have caused, the food I stole from home, and the many incidentals along the way, thank you. You have asked me so many times and I’m finally able to say after all these years of school, I’m done.

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ABSTRACT Background: Normal cardiac excitability depends upon the coordinated activity of ion channels and transporters. Mutations in genes encoding ion channels affecting their biophysical properties have been known for over twenty years as a root cause of potentially fatal human electrical rhythm disturbance (arrhythmias).

More recently,

defects in ion channel associated protein (e.g. adapter, regulatory, cytoskeletal proteins) have been shown to cause arrhythmia.

Mathematical modeling is ideally suited to

integrate large volumes of cellular and in vivo data from human patients and animal disease models with the over goal of determining cellular mechanisms for these atypical human cardiac diseases that involve complex defects in ion channel membrane targeting and/or regulation. Methods and Results: Computational models of ventricular, atrial, and sinoatrial cells were used to determine the mechanism for increased susceptibility to arrhythmias and sudden death in human patients with inherited defects in ankyrin-based targeting pathways. The loss of ankyrin-B was first incorporated into detailed models of the ventricular myocyte to identify the cellular mechanism for arrhythmias in human patients with loos-of-function mutations in ANK2 (encodes ankyrin-B). Mathematical modeling was used to identify the cellular pathway responsible for abnormal Ca2+ handling and cardiac arrhythmias in ventricular cells.

A multi-scalar computational

model of ankyrin-B deficiency in atrial and sinoatrial cells and tissue was then developed to determine the mechanism for the increased susceptibility to atrial fibrillation in these human patients. Finally, a state-based Markov model of the voltage-gated Na+ channel was incorporated into a ventricular cell model and parameter estimation was performed to determine the mechanism for a new class of human arrhythmia variants that confer susceptibility to arrhythmia by interfering with a regulatory complex comprised of a second member of the ankyrin family, ankyrin-G. Conclusions: Ca2+ accumulation was observed at baseline in the ankyrin-B deficient ventricular model, with pro-arrhythmic

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spontaneous release and afterdepolarizations in the presence of simulated β-adrenergic stimulation, consistent with the finding of catecholaminergic-induced arrhythmias in human patients.

The simulations demonstrated that loss of membrane Na+/Ca2+

exchanger and Na+-K+-ATPase contributed to Ca2+ overload and afterdepolarizations, with loss of Na+/Ca2+ exchanger as the dominant mechanism. In the atrial model of ankyrin-B deficiency, the loss of the L-type Ca2+ channel targeting was identified as the dominant mechanism for the initiation of atrial fibrillation. Finally, the simulations showed that human variants affecting ankyrin-G dependent regulation of NaV1.5 results in arrhythmia by mimicking the phosphorylation of the channel. Most importantly, mathematical modeling has been used to the molecular mechanism underlying human arrhythmia syndromes.

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TABLE OF CONTENTS LIST OF TABLES ............................................................................................................. ix LIST OF FIGURES .............................................................................................................x LIST OF ABBREVIATIONS ............................................................................................xv CHAPTER 1: INTRODUCTION ........................................................................................1 1.1 Objective..............................................................................................1 1.2 Biophysics of Excitable Membranes ...................................................1 1.3 Cardiac Action Potential......................................................................2 1.4 Excitation-Contraction Coupling.........................................................4 1.5 The Cardiac Dyad ................................................................................5 1.6 Dysfunction of Sarcoplasmic Reticulum Ca2+ Handling .....................6 1.7 Ankyrins and Human Disease .............................................................8 1.8 Figures ...............................................................................................14 CHAPTER 2: MATHEMATICAL MODELING OF ELECTROPHYSIOLOGY ..........................................................................................24 2.1 Motivation .........................................................................................24 2.2 Hodgkin Huxley Formulation............................................................24 2.3 Work Following Hodgkin-Huxley ....................................................27 2.4 Next Generation of Computational Models ......................................30 2.5 Figures ...............................................................................................34 2.6 Tables ................................................................................................35 CHAPTER 3: A COMPUTATIONAL MODEL OF ANKYRIN-B SYNDROME........................................................................................36 3.1 Background........................................................................................37 3.2 Methods .............................................................................................38 3.2.1 Mathematical model of the ankyrin-B+/- cardiomyocyte.........38 3.2.2 Mathematical model of isoproterenol effects ..........................39 3.2.3 Pacing protocol ........................................................................39 3.3 Results ...............................................................................................40 3.3.1 Ankyrin-B deficiency promotes Ca2+ overload at baseline .............................................................................................40 3.3.2 Role of Na+/Ca2+ exchanger and Na+-K+-ATPase in Ca2+ overload in ankyrin-B+/- cells ...........................................................41 3.3.3 Increased levels of Ca2+ with isoproterenol ............................42 3.4 Discussion..........................................................................................44 3.5 Limitations .........................................................................................46 3.6 Figures ...............................................................................................47 3.7 Tables ................................................................................................58 CHAPTER 4: ANKYRIN-B DEFICIENCY IN ATRIA ........................................................................................................................59

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4.1 Background........................................................................................59 4.2 Introduction .......................................................................................60 4.3 Methods .............................................................................................61 4.3.1 Mathematical model of the ankyrin-B+/- cardiomyocyte .......61 4.3.2 Pacing protocol ........................................................................62 4.3.3 Fiber model .............................................................................62 4.3.4 Tissue model ...........................................................................63 4.3.5 APD Restitution ......................................................................63 4.3.6 Critical Mass and Core Site .....................................................63 4.4 Results ...............................................................................................63 4.5 Discussion..........................................................................................65 4.6 Limitations .........................................................................................66 4.7 Figures ...............................................................................................67 4.8 Tables ................................................................................................72 CHAPTER 5: COMPUTATIONAL MODEL OF CAMKII REGULATION OF VOLTAGE-GATED SODIUM CHANNEL .....................................................................73 5.1 Background........................................................................................73 5.2 Methods .............................................................................................75 5.3 Results ...............................................................................................76 5.4 Discussion..........................................................................................77 5.5 Figures ...............................................................................................81 CHAPTER 6: DISCUSSION.............................................................................................90 6.1 Summary of Findings ........................................................................90 6.2 Limitations .........................................................................................93 6.3 Future Directions ...............................................................................93 APPENDIX A: MODEL EQUATIONS AND PARAMETERS FOR MOUSE VENTRICULAR CARDIOMYOCYTE ...........................................................................96 A.1 Equations ..........................................................................................96 A.2 Definitions and abbreviations .........................................................109 APPENDIX B: MODEL EQUATIONS AND PARAMETERS FOR HUMAN VENTRICULAR CARDIOMYOCYTE .........................................................................113 B.1 Equations ........................................................................................113 B.2 Definitions and Abbreviations ........................................................122 APPENDIX C: GLOSSARY ...........................................................................................124 REFERENCES ................................................................................................................126

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LIST OF TABLES Table 2.1: Available mathematical models of ventricular cells ........................................28 Table 3.1: Intracellular Na+ concentration in a computational model of ankyrin-B syndrome ..........................................................................................................38 Table 4.1: Ion concentrations from atrial model paced to steady-state at cycle length of 1000 ms.............................................................................................62 Table 4.2: Ion concentrations from atrial model paced to steady-state at cycle length of 300 ms...............................................................................................62 Table 5.1: Transition rate expressions for mathematical model of NaV1.5 ......................71 Table 5.2: Parameters for mathematical models of wild type and variant NaV1.5 ...........72 Table 5.3: Initial conditions for state variables in mathematical model of mammalian ventricular action potential...........................................................73 Table A.1: Parameters for Mouse Ventricular Cell Model ..............................................104 Table B.1: Parameters for Mouse Human Ventricular Cell Model .................................115

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LIST OF FIGURES Figure 1.1 Diagram of the phospholipid bilayer and membrane proteins that compose the cell membrane. ..............................................................................2 Figure 1.2 Cardiomyocyte with intracellular and extracellular ion concentrations. There is a relatively high concentration of Na+ and Ca2+ in the extracellular space when compared to the cytosol. There is a relatively high intracellular concentration of K+ when compared to the outside of the cell. ...............................................................................................................3 Figure 1.3 Phases of ventricular action potential. During Phase 4, the cell is at rest at near -90 mV. With stimulation, Phase 0, which is the rapid depolarization or AP upstroke, occurs due to the opening of the fast Na+ channels. Phase 1 is early repolarization, which is due to the inactivation of the Na+ channels. The opening of the L-type Ca2+ channels and the slow delayed rectifying K+ channels is Phase 2, or the action potential plateau. The plateau phase is due to the balanced movement of K+ and Ca2+ ions. Phase 3 is late repolarization due to the close of Ca2+ channels while K+ channels remain open, allowing the cell to return to rest. ..................................................................................................5 Figure 1.4 Schematic of action potential waveforms recorded in different regions of the human heart. ............................................................................................6 Figure 1.5 The conduction system of the heart. The wave of depolarization begins in the sinoatrial node and rapidly spreads through the atria. The atrioventricular node slows conduction to allow the atria to fully contract before the depolarization spreads through the ventricles via the bundle of His, to the left and right bundle branches and finally the Purkinje fibers. ...................................................................................................8 Figure 1.6 Voltage-gated Ca2+ channels (LTCC) along the T-tubule allow Ca2+ to enter the cell and activate ryanodine receptor Ca2+ release channels located on the sarcoplasmic reticulum which triggers the release of Ca2+ from the SR into the cytoplasm. The close proximity of the LTCC to the ryanodine receptors creates a local domain for Ca2+ signaling. Ca2+ in the cytoplasm is able to bind to troponin resulting in contraction. The Ca2+ is then removed from the cell via the Na+/Ca2+ exchanger or reuptake in the SR by SERCA/PLB.................................................................10 Figure 1.7 Ankyrin-B associated binding partners include various ion channels, pumps, and transporters (NCX, NKA, and InsP3 receptor), signaling molecules (PP2A), and cytoskeletal proteins (β-spectrin). One ankyrin protein is able to simultaneously bind to multiple proteins. ............................13 Figure 1.8 Ankyrin-G ion channel complex in the heart. Ankyrin-G is associated with the targeting NaV1.5 to the intercalated disc of cardiomyocytes. ............15

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Figure 1.9 Representation of a normal ECG on the left and a LQT ECG on the right. The P-wave represents the depolarization of the atrium, QRS complex is the result of ventricular depolarization, and the T wave denotes ventricular repolarization. With Long QT syndrome, the QT interval or the length of time from the beginning of ventricular depolarization to the end of ventricular repolarization is increased. ...............16 Figure 1.10 Ankyrin-B ion channel complex in the heart. Ankyrin-B is a multifunctional protein that links ion channels and transporters including Na+-K+-ATPase, Na+/Ca2+ exchanger, and InsP3 receptor to the cytoskeleton. Ankyrin-B dysfunction results in improper ion channel/transporter localization to specialized domains..................................18 Figure 2.1 Circuit diagram summarizing the currents across the cell membrane of a giant squid axon used to construct the Hodgkin-Huxley model. The cell membrane acts as a capacitor while the ion channels act as resistors. Main currents incorporated by Hodgkin and Huxley included a Na+ current, K+ current, and a nonspecific leak current. ........................................22 Figure 3.1 Voltage dependence of Na+-K+-ATPase. Simulated (lines) Na+-K+ATPase current-voltage relation as a function of extracellular Na+ concentration compared to experimental measurements in mammalian ventricular myocytes (circles) .........................................................................35 Figure 3.2 Mathematical model of the ankyrin-B-deficient (ankyrin-B+/-) cell. (A) Schematic of the mouse ventricular cell model. Na+-K+-ATPase (NKA) current (INaK) and Na+/Ca2+ exchanger (NCX) current (INaCc) were altered in the model of the ankyrin-B+/- cell (yellow boxes). Symbols are defined in the text and in Appendix A. (B-E) simulated action potentials (APs) in control (B and D) and ankyrin-deficient (C and E) cardiomyocytes from the mouse (B and C) and human (D and E) ventricular cell models [10th action potential (AP) shown at a cycle length (CL) of 1,000 ms]. (F) simulated INaCa at a test potential of −10 mV from the wild-type cell and an ankyrin-B+/- cell compared with experimental measurements (n = 12, *P 0.1 µM, CL = 1,000 ms). ........................45 Figure 3.8 Spontaneous Ca2+ release and afterdepolarizations in the mouse ankyrinB+/- cell during rapid pacing in the presence of Iso. Simulated (A) action potential, (B) Ca2+ transient, and (C) [Ca2+]JSR in control and ankyrinB+/- mouse ventricular cardiomyocytes during rapid pacing to steadystate (CL = 200 ms) in the presence of Iso. Frequent spontaneous release events (arrows in B) led to abnormal repolarization (* in A) in the ankyrin-B-deficient cell. Simulated (D) action potential, (E) Ca2+ transient, (F) INaCa, and (G) ICaL in control and ankyrin-B+/- cells during a subsequent pause after rapid pacing to steady-state. Note the spontaneous release (arrows) and afterdepolarizations (*) that ultimately produced an AP. ...............................................................................................47 Figure 3.9 Spontaneous Ca2+ release and afterdepolarization in human ankyrin-B+/cell. (A) Simulated action potential in control (black lines) and ankyrinB-deficient (grey lines) human ventricular cardiomyocytes during rapid pacing to steady state (cycle length = 500 ms). Spontaneous release produces an action potential during pacing in the ankrin-B+/- human ventricular cardiomyocytes (asterisk). Summary data showing (B) time to first spontaneous release of Ca2+ from the SR and (C) the number of spontaneous release events during rapid pacing in the ankyrin-B+/(grey), NKA-deficient (blue) and NCX-deficient (red) cells. .........................48

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Figure 3.10 Role of NCX and NKA in spontaneous Ca2+ release and afterdepolarizations in the ankyrin-B+/- cell. Simulated (A) action potential and (B) Ca2+ transient in ankyrin-B+/-, NCX-deficient, and NKA-deficient cells during rapid pacing to steady-state (CL = 200 ms). Spontaneous Ca2+ release (arrows in B) and abnormal repolarization (* in A) were observed in NCX-deficient and NKA-deficient cells, although with decreased frequency and delayed onset compared with the ankyrin-B+/- cell. C and D: Summary data showing (C) the time to first spontaneous release of Ca2+ from the SR and (D) number of spontaneous release events during rapid pacing in ankyrin-B+/-, NKAdeficient, and NCX-deficient cells. ..................................................................50 Figure 4.1 Mathematical model of atrial ankyrin-B deficiency. (A) Schematic of Courtemanche et al. human atrial cell model. (B) One-dimensional fiber model comprised of individual cells electrically coupled through gap junctions. A current stimulus is applied at the end of the fiber (cell 1) and the excitation wavefront propagates down the fiber. (C) Twodimensional tissue model comprised of fibers. Na+/Ca2+ exchanger current (INaCa), Na+/K+ ATPase current (INaK), and L-type Ca2+ current (ICa,L) are altered in model of ankyrin-B-deficient cell (yellow). Consistent with experimental data, the AnkB+/- shows decreased (D) ICa,L, (E) INaCa, and (F) INaK...............................................................................58 Figure 4.2 Rate dependence of action potential duration. (A) Action potential adaptation curve for the control (black line), ankyrin-B deficient cell (red line), NCX-deficient (NKA and ICa,L restored to normal levels, green line), NKA-deficient (NCX and ICa,L restored to normal levels, blue line), and ICa,L-defience (NCX and NKA restored to normal levels, grey line) paced to steady-state at cycle lengths of 300, 400, 500, 750, 1000, and 2000 ms. (B) Simulated action potentials at slow pacing (cycle length = 1000 ms) and (C) fast pacing (cycle length = 300 ms). INaCa at (D) slow pacing and (E) fast pacing. ICa,L at (F) slow pacing and (G) fast pacing. (H) Peak ICa,L at fast facing (black bars) and slow pacing (grey bars). (I) ICa,L 30 ms after stimulation for fast pacing (black bars) and slow pacing (grey bars). .......................................................61 Figure 4.3 (A) Action potential duration restitution curve. (B) S1S2 protocol for measuring APD restitution. APD is measured as the S1S2 interval is shortened. .........................................................................................................63 Figure 4.4 Conduction in ankyrin-B deficient fiber is unaffected by increased gap junction resistance. (A) Conduction velocity versus gap junction resistance in control and ankyrin-B deficient fibers. Even at high degrees of uncoupling, no change in conduction is seen. (B) Onedimensional fiber model comprised of individual cells electrically coupled through gap junctions. ........................................................................64 Figure 5.1 Human arrhythmia variants near NaV1.5 CaMKII-phosophorylation site. Schematic illustrating the spectrin-based signaling complex at the cardiomyocytes intercalated disc for regulation of NaV1.5 (via ankyrinG) to phosphorylate at S571 in the NaV DI-DII linker. Human variants associated with cardiac arrhythmia have been identified in the region adjacent to the phosophorylation site (A572D and Q573E). ...........................67

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Figure 5.2 Computational model to determine role of human arrhythmia variants identified near CaMKII phosphorylation site of NaV. (A) Schematic of mathematical model of mammalian ventricular action potential used to determine the effect of the NaV variants on cardiac repolarization. (B) Markov model used to simulate NaV function that includes transitions between multiple inactivated (red), closed (blue), and open (green) states. ................................................................................................................70 Figure 5.3 Parameter estimation results show human arrhythmia variants cause action potential prolongation. Parameter estimation results comparing experimentally measured (black) and simulated (red) values for (A) steady-state inactivation and (B) late current. Simulated (C) action potentials and (D) Na+ current from WT (black), A572D (red), and Q573E (grey) variant cells. Similar to experimental results, computational modeling predicts human arrhythmia variants increase NaV late current and prolong APD compared to WT. Results shown at steady-state at pacing cycle length = 500 ms. ..................................................75 Figure 5.4 Computational model predicts increased susceptibility to afterdepolarizations in human arrhythmia variants identified near CaMKII phosphorylation site of NaV. Simulated (A) action potentials and (B) INa in WT- (black) and A572D- (red) expressing cells at steadystate during slow pacing (cycle length = 1,000 ms). The two variants, A572D and Q573E (not shown) displayed afterdepolarizations under these conditions. Simulated block of late INa with 10 µM ranolazine (C) reduced late INa and afterdepolarizations (grey lines in A and B). ...................76 Figure 5.5 Myocardial infarcation is produced by total coronary artery occlusion in the left anterior descending coronary artery. The border zone represents an area of surviving tissue with abnormal cells near the infarction. ................79

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LIST OF ABBREVIATIONS APD

Action potential duration measured at 90% repolarization

dV/dtmax

Maximum rate of rise of the action potential upstroke, mV/ms

Vm

Transmembrane potential, mV

CaT

Calcium transient

CaTamp

Calcium transient amplitude

[Ca2+]i,dia

Diastolic intracellular Ca2+ concentration, mmol/L

CaMKII

Ca2+/calmodulin-dependent protein kinase II

CL

Cycle length, ms

INa

Fast Na+ current, µA/µF

ICa(L)

Ca2+ current through the L-type Ca2+

IKr

Rapid delayed rectifier K+ current, µA/µF

IKs

Slow delayed rectifier K+ current, µA/µF

Ito1

Transient outward K+ current, µA/µF

Ito2

Ca2+-dependent transient outward Cl- current, µA/µF

IK1

Time-independent K+ current, µA/µF

IKp

Plateau K+ current, µA/µF

INaCa

Na+-Ca2+ exchanger, µA/µF

INaK

Na+-K+ pump, µA/µF

Ip,Ca

Sarcolemmal Ca2+ pump, µA/µF

ICa,b

Background Ca2+ current, µA/µF

SR

Sarcoplasmic reticulum

JSR

Junctional SR

NSR

Network SR

Irel

Ca2+ release from JSR to myplasm, mmol/L per ms

Iup

Ca2+ uptake from myoplasm to NSR, mmol/L per ms

xv

Ileak

Ca2+ leak from JSR to myoplasm, mmol/L per ms

Itr

Ca2+ transfer from NSR to JSR, mmol/L per ms

Istim

Stimulus current, µA/µF

PLB

Phopholamban

RyR

Ryanodine receptor SR Ca2+ release channel

LTCC

L-type Ca2+ channel

ḡx

Maximum conductance of channel x, mS/µF

Īx

Maximum current carried through channel x, µA/µF

[S]o and [S]i

Extracellular and intracellular concentrations of ion S, respectively, mmol/L

[Ca2+]JSR

Ca2+ concentration in JSR, mmol/L

[Ca2+]NSR

Ca2+ concentration in NSR, mmol/L

[Ca2+]SS

Ca2+ concentration in subspace, mmol/L

SA

Sinoatrial

AV

Atrioventricular

ATP

Adenosine triphosphate

NCX

Na+/Ca2+-exchanger

NKA

Na+/K+-ATPase

DAD

Delayed afterdepolarization

SOICR

Store overload induced calcium release

CPVT

Catecholaminergic polymorphic ventricular tachycardia

SERCA

Sarco/endoplasmic reticulum Ca2+-ATPase

PLB

Phospholamban

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1

CHAPTER 1 INTRODUCTION 1.1 Objective Coronary heart disease claims approximately one life every minute and accounts for almost 500,000 deaths per year in the United States. Arrhythmia is the primary cause of death in these individuals [1]. Despite advances in pharmaceuticals and medical treatment options to prevent arrhythmia and sudden death, there is clearly a specific need to gain a better understanding of the events that occur at the cellular level that lead to these life-threatening conditions. Thus, the overall goal of my research is to gain a better understanding of the ionic mechanisms responsible for sudden death in human heart disease.

In order to achieve this goal, I use mathematical modeling and computer

simulations, based on experimental data, to link molecular defects to life-threatening cardiac electrical disturbances in common and congenital forms of human heart disease. 1.2 Biophysics of Excitable Membranes Certain types of cells, including neurons and muscle cells, have an excitable membrane that allows for the generation of action potentials. An action potential is a temporary reversal of the electrical potential difference across the cell membrane. The cell membrane consists of a phospholipid bilayer which provides structure to the cell in addition to separating the intracellular and extracellular environments as shown in Figure 1.1. Thus the membrane serves as a capacitor, separating the electrically charged ions (e.g. Na+, K+, Ca2+) on both sides of the membrane (Figure 1.2). A number of different proteins, including ion transporters, are embedded within the membrane and control the movement of ions from one side of the membrane to the other. The movement of these ions creates transmembrane electrical currents. There are several different types of ion

2

transporters, including ion channels, ion pumps, and ion exchangers. When open, ion channels allow for the free flow of select ions down their electrochemical gradients as demonstrated in Figure 1.2. Ion pumps move ions against their electrochemical gradient by using the cellular energy source adenosine triphosphate (ATP).

In contrast, ion

exchangers move an ion against its electrochemical gradient by using the electrochemical gradient of a different ion as the energy source. The membranes of most excitable cells tend towards a steady-state in which a fixed electrical potential exists across the membrane. This steady-state value is called the resting membrane potential, which is about −80 mV for cardiac cells.

The resting

membrane potential is caused by the difference in concentrations of several key ions in the intracellular and extracellular compartments and the selective permeability of the resting membrane to these ions. An external stimulus that depolarizes the membrane potential beyond a threshold value triggers voltage and time dependent changes in the membrane’s permeability resulting in a reversal in the electric potential of the cell membrane, known as an action potential, before returning to rest [2]. 1.3 Cardiac Action Potential The cardiac action potential is dependent upon electrical currents generated by the flow of several different ions, including sodium, calcium, potassium, and chloride, across the cell membrane. Voltage-gated ion channels are a class of ion channels that open and close in response to a change in the membrane potential. At the resting membrane potential (approximately −90 mV in the ventricular cardiomyocyte), the membrane is nearly impermeable to sodium and calcium and slightly permeable to potassium due to the conformation of these channels at that membrane potential. There is a relatively high concentration of sodium and calcium and a relatively low concentration of potassium in the extracellular environment when compared to the intracellular environment. At rest, the cell membrane is mostly permeable to potassium

3

and as a result, the resting membrane is close to the value of the potassium Nernst potential [3]. The Nernst potential is the equilibrium potential of a given ion such that there is no net movement of that ion across the cell membrane. It can be calculated by the following equation: ‫ܧ‬௫ =

61 [ܺ௢ ] ݈‫݃݋‬ ‫ݖ‬ [ܺ௜ ]

where EX is the equilibrium potential for ion x (in mV), [X]o is the concentration of the ion outside of the cell, [X]i is the concentration of the ion inside the cell, and z is the valence of the ion [4]. With the application of an external, depolarizing stimulus, voltage-gated sodium channels in the cell membrane open and allow sodium ions to rapidly flow into the cell down its electrochemical gradient. This influx of positively charge sodium ions further depolarizes the membrane, opening more sodium channels and increasing the flow of sodium ions (Figure 1.3).

The sodium channels then rapidly inactivate, virtually

eliminating the sodium current. Meanwhile, the calcium and potassium channels, which have slower kinetics than sodium channels, begin to open. The influx of positive calcium ions is balanced by the efflux of positive potassium ions leading to the plateau phase of the action potential. The calcium channels then begin to inactivate while the potassium channels are still open, allowing the cell to repolarize back toward the resting membrane potential. The concentration gradients of the ions are reestablished by ion pumps and exchangers to prepare the cell for the next stimulus [5]. Regions of the heart can be distinguished by electrical differences seen in the action potentials of different cell types as shown in Figure 1.4. The sinoatrial node (SA node) is identified as the region in the right atrium that spontaneously generates action potentials at the highest frequency. The maximum diastolic membrane potential of a SA node is around −60 mV. The intrinsic firing rate of other cells in the atrium is much slower than the firing rate of the SA node, thus these cells are stimulated by the electrical

4

wave from the SA node. The action potential of an atrial cell has a triangular shape. Also, the resting membrane potential of −80 mV in atrial cells is more negative than that of SA node cells.

The electrical wave then travels from the atrium through the

atrioventricular node (AV node). From the AV node, it continues through the bundle of His which divides into left and right bundle branches and finally into the Purkinje fibers found in the ventricular walls [4]. Upon stimulation, a Purkinje fiber rapidly depolarizes followed by a slow return to rest. Purkinje fiber cells have a resting membrane potential around −90 mV and possess an intrinsic (albeit relatively slow) pacemaker activity. Cells in the ventricles also have their own distinguishable action potential. Similar to the Purkinje fiber cells, ventricular cells also have a plateau phase. Normal ventricular cells also lack the pacemaker ability and therefore must be stimulated by either the Purkinje fibers or an artificial stimulus [6]. 1.4 Excitation-Contraction Coupling Influx of calcium during the cardiomyocyte action potential plateau causes the cell to contract. Depolarization of myocardial cells stimulates the opening of the voltagegated calcium channels in the plasma membrane. This initial influx of calcium down its concentration gradient into the cell triggers the process known as calcium-induced calcium release.

Calcium ions entering the cell bind to calcium channels called

ryanodine receptors located on the sarcoplasmic reticulum, which acts as a calcium storage unit during muscle relaxation. When calcium binds to the ryanodine receptors, the channels open and calcium from the sarcoplasmic reticulum is released and considerably increases the intracellular calcium concentration. The free calcium in the cytosol then 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 calcium to troponin causes a conformational change which allows the myosin heads along the thick filament to bind to

5

the thin filament. Following another conformational change, a power stroke or ratcheting action occurs that pulls the filaments in opposite directions resulting in muscle contraction. This excitation-contraction coupling ends as cytosolic calcium is taken back into the sarcoplasmic reticulum or is pumped out of the cell via calcium pumps using ATP as an energy source. The other mechanism for calcium removal is the Na+/Ca2+ exchanger which uses the sodium ion gradient as its driving force and removes one calcium ion for three sodium ions [7]. The coordinated activity of excitation and contraction allows the heart to contract synchronously.

Under normal circumstances, the heart goes through one two-step

cardiac cycle approximately every second. In order to accomplish this, an excitatory wave originates in a region of the right atria known as the sinoatrial node. Interestingly, all cardiac cells have the ability to generate action potentials to initiate contraction, but the cells in the sinoatrial node are able to do it slightly faster than other areas and thus serve as the pacemaker for the heart. The excitatory wave is propagated from one cell to the next via gap junctions which are ion channels linking two cells. Once generated in the sinoatrial node, the action potential travels through the atria to the atrioventricular node (AV node) as shown in Figure 1.5. The AV node is able to slow conduction to allow the atria to contract, forcing the blood into the ventricles. Once the excitatory wave travels through the AV node, it spreads through the ventricles via the bundle of His, the left and right bundle branches, and the Purkinje system. With the contraction of the ventricles, blood is pumped from the right ventricle to the lungs for oxygenation. The oxygenated blood in the left ventricle is pumped into the systemic circulation [4]. 1.5 The Cardiac Dyad Proper function and location of ion channels is required for normal cardiac physiology. The cell membrane of a ventricular cardiomyocyte contains a large number

6

of membrane invaginations called transverse-tubules (T-tubules). Membrane proteins necessary for excitation-contraction coupling, specifically L-type calcium channels, are located in the T-tubules. The proximity of the T-tubule to the sarcoplasmic reticulum (SR) membrane is known as the cardiac dyad, shown in Figure 1.6. Located across from the L-type calcium channels are clusters of ryanodine receptor calcium release channels on the sarcoplasmic reticulum membrane.

By

positioning the L-type calcium channels near the ryanodine receptors, this dyad allows for a very small influx of calcium to trigger the release of calcium by the sarcoplasmic reticulum. Several of the proteins in the cardiac dyad, including the L-type calcium channel CaV1.2 and ryanodine receptor (RyR), are regulated by phosphorylation and dephosphorylation. Phosphorylation of CaV1.2 and RyR by both protein kinase A and calcium-calmodulin-dependent protein kinase II (CaMKII) regulates the activity of these channels at the local level.

Phosphorylation of CaV1.2 by CaMKII results in an

alternative channel-gating mode [8]. CaMKII also phosphorylates RyR, however the net effect is less clear [9, 10]. Recent studies have shown hyperphosphorylation of RyR2 by CaMKII during heart failure allows calcium to leak from the SR and thereby reducing the SR calcium content [11]. 1.6 Dysfunction of Sarcoplasmic Reticulum Ca2+ Handling Dysfunction in intracellular calcium cycling has been associated with fatal human arrhythmias.

The sarcoplasmic reticulum has the ability to release calcium via

spontaneous calcium release which is caused by an overload of SR calcium. This release of calcium has the ability to change the membrane potential by activating the Na+/Ca2+ exchanger and generating a transient inward current which can depolarize the membrane after an action potential, resulting in delayed afterdepolarizations (DADs). An action

7

potential can be initiated if the amplitude of the DAD reaches threshold, thereby triggering arrhythmias. There are several different causes for store overload induced calcium release (SOICR) including β-adrenergic stimulation, digitalis toxicity, elevated extracellular calcium, and fast pacing [12, 13]. Activation of the β-adrenergic receptors and adenylyl cyclase leads to an increase in cAMP, which activates cAMP-dependent protein kinase (PKA). PKA then is able to phosphorylate several different proteins, including the Ltype calcium channel and phospholamban, which is an inhibitor of the sarcoplasmic reticulum calcium-ATPase (SERCA). Phosphorylation of the L-type calcium channel would increase the influx of calcium, while phosphorylation of phospholamban increases the uptake of SR calcium by preventing the inhibition of SERCA. As a result, the increase in calcium influx as well as uptake of calcium by the sarcoplasmic reticulum will lead to SOICR. Digitalis toxicity can lead to SOICR via the inhibition of the Na+-K+ATPase by cardioglycosides such as ouabain or digoxin. Inhibition of the Na+-K+ATPase leads to an increase in intracellular Na+, which then inhibits the Na+/Ca2+ exchanger. By inhibiting the Na+/Ca2+ exchanger, more calcium must then be taken up by the SR, leading to calcium overload. Elevated extracellular calcium and fast pacing can trigger SOICR by increasing the influx of calcium which also increases the uptake of calcium by the SR and potentially leading to overload conditions. Catecholaminergic polymorphic ventricular tachycardia (CPVT) is one such disease resulting from the dysfunction in intracellular calcium regulation. Sudden cardiac death after stress is often the first symptom in young patients. It can be diagnosed during an exercise stress test when patients develop ventricular tachycardia [14]. CPVT is caused by either a dominant mutation in the RYR2 gene, which encodes the calcium release channel ryanodine receptor isoform 2 [15], or by a recessive mutation in CASQ2 gene, which encodes for calsequestrin isoform 2 [16]. The CPVT mutation in the RyR2 gene lowers the threshold necessary for spontaneous release to occur [14].

8

1.7 Ankyrins and Human Disease 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 a number of cell types including cardiomyocytes, neurons, pancreatic beta cells and erythrocytes [17-20]. Ankyrins link these integral membrane proteins and cell adhesion molecules to the actin/spectrin cytoskeleton. Three genes, ANK1, ANK2, and ANK3 encode ankyrin proteins. ANK1 encodes for ankyrin-R polypeptides (“R” for “restricted” distribution) which are found in erythrocytes, neurons, and skeletal muscle [21-23]. Ankyrin-B (“B” for “broad” distribution) is encoded by ANK2 and it can be found in brain, heart, and thymus [24-26]. The ANK3 gene encodes for ankyrin-G (“G” for “general”) and it is found in the brain, kidney, skeletal muscle, and heart [27-31]. Ankyrins have four major domains including a membrane binding domain, a spectrin binding domain, a death domain, and a C-terminal domain [32]. The membrane binding domain is where a number of different membrane proteins bind to the ankyrin. These membrane proteins include ion channels, transporters, and pumps such as the Na+K+-ATPase, voltage-gated Na+ and K+ channels, Na+/Ca2+ exchanger, the ammonium transporter, and the anion exchanger [29, 33-38]. It has also been shown the membrane binding domain interacts with calcium-induced calcium-release channels located on the SR including the inositol 1,4,5 triphosphate (InsP3) receptor and ryanodine receptor [3942]. Ankyrins have the ability to bind to multiple membrane proteins at the same time (Figure 1.7), which allows large protein complexes to form [42-44]. For example, a single ankyrin-B polypeptide can bind to a Na+/Ca2+ exchanger, Na+-K+-ATPase, and InsP3 receptor [42]. The spectrin binding domain is responsible for linking the membrane proteins to the cytoskeleton via β-spectrin isoforms [45]. The spectrin binding domain may also have a role in organizing local signaling networks due to its interaction with the regulatory subunit of protein phosphatase 2A (PP2A) [46]. The C-terminal domain

9

interacts with the membrane binding domain and its function is significant as many of the human ANK2 mutations linked to arrhythmia and sudden cardiac death are located in this domain [47, 48]. This C-terminal domain may also be involved in the regulation of interactions of ankyrin with β-spectrin and the membrane proteins. Members of the ankyrin family have already been linked to a number of human diseases. A mutation in the ANK1 gene, which encodes ankyrin-R, has been found to cause erythrocyte spectrin-deficiency, leading to spherocytosis and hemolytic anemia [49]. Ankyrin dysfunction has also been linked to a number of cardiac arrhythmia syndromes. In particular, ankyrin-G is necessary for targeting and localization of the voltage-gated sodium channel (NaV1.5) which is responsible for the rapid upstroke of the action potential [29, 50]. Defects in NaV1.5 have been linked to sinus node disease, conduction defects, and ventricular arrhythmias [51-54]. In 2004, two groups identified the ankyrin-G binding motif on the sodium channel NaV1.2 which is found in neurons [55, 56]. Voltage-gated sodium channels (NaV) consist of a pore-forming α-subunit and one or more β-subunits [57]. The role of the α-subunit is to regulate the properties of the sodium channel such as pore formation, ion selectivity and rapid inactivation, while the β-subunits are involved with the channel’s biophysical properties, channel expression and localization at the cell membrane [58]. A typical αsubunit has four domains and the ankyrin-G binding motif is found on the DII-DIII loop. This motif is necessary for ankyrin-G binding and proper localization of NaV1.2 [55, 56]. In addition, this motif is conserved among sodium channel isoforms, including the cardiac sodium channel NaV1.5 located primarily at the intercalated disc of cardiomyocytes where neighboring cardiomyocytes are linked via gap junctions, adherens junctions, and desmosomes. Proper localization of NaV1.5 at the cell membrane is key for normal cell membrane excitability and action potential propagation. Mohler et al. demonstrated NaV1.5 interacted directly with ankyrin-G and the two were coexpressed at ventricular cardiomyocyte membrane domains [29] (Figure 1.8). They were

10

also able to show if this binding motif was removed, NaV1.5 fails to interact with ankyrin-G and NaV1.5 cell membrane localization is disrupted [29]. The interaction of ankyrin-G with NaV1.5 was linked to a cardiac arrhythmia when a mutation in the gene SCN5A, which encodes for NaV1.5, was found in a patient with Brugada syndrome [29, 59].

Brugada syndrome is a potentially fatal cardiac

arrhythmia characterized by right bundle branch block, ventricular arrhythmia, with an increased risk of sudden death [60, 61]. At the cellular level, Brugada syndrome is associated with a decrease in INa due to defects in the sodium channel NaV1.5 [61]. The patient with Brugada syndrome was heterozygous for a charge reversal variant (glutamic acid to lysine) at residue 1053 in the ankyrin-G binding motif. This E1053K mutation eliminated the ability of ankyrin-G to bind NaV1.5 in the DII-DIII loop [29]. In a more recent study by Lowe et al., it was shown ankyrin-G was shown to be required for correct localization and function of NaV1.5. Using shRNA to knockdown ankyrin-G resulted in a reduction in the expression of NaV1.5 and INa [50]. CaMKII has also been shown to have a role in the regulation of cardiac Na+ channels [62]. A recent study by Hund et al. showed the βIV-spectrin/CaMKII complex formed a macromolecular complex with ankyrin-G and NaV1.5 in cardiomyocytes. The group demonstrated βIV-spectrin, CaMKIIδ, ankyrin-G, and NaV1.5 were localized at the intercalated disc. The study also showed ankyrin-G and NaV1.5 are associated with βIVspectrin and CaMKIIδ [63]. Proper activity of ankyrin-B is necessary for normal cardiac activity.

In

particular, ankyrin-B dysfunction has been linked to long QT syndrome. Long QT syndrome is an inherited disorder associated with prolongation of QT interval (shown in Figure 1.9) and increased risk of life-threatening arrhythmias [64, 65]. LQT syndrome is the result of abnormal cardiac repolarization and is associated with syncope, seizures, and sudden death in otherwise young, healthy individuals. Individuals with LQT syndrome

11

often display periodic ventricular tachyarrhythmias, such as torsade de pointes and ventricular fibrillation [65]. There have been nearly a dozen LQT syndromes identified. Long QT type 4 syndrome was first identified in 1995, but in 2003, the ANK2 gene encoding ankyrin-B, was identified as the cause [36, 66]. Type 4 LQT syndrome was the first example of LQT due to a mutation in a gene encoding a protein rather than an ion channel [36]. Patients with LQT4 display a complex cardiac phenotype characterized by sinus node dysfunction, increased susceptibility to ventricular arrhythmias, and sudden death under stress [36, 47, 48, 66, 67]. Since the initial work, additional mutations in the ANK2 gene have been found [47, 48, 68, 69] and associated with sinus node dysfunction, atrial fibrillation, conduction defects, in addition to ventricular arrhythmias [36, 47, 48]. The prolonged QT interval is not consistent with all ANK2 mutations and as result, ankyrin-B syndrome is a more accurate description for this cardiac phenotype [47, 48]. In addition to LQT syndrome, ankyrin-B dysfunction has been linked to abnormal sinoatrial node activity and sinus node dysfunction. Sinus node dysfunction affects one in every 600 individuals over age 65 and accounts for 50% of pacemaker implantations in the United States [70]. Sinus node dysfunction may include sinus bradycardia, sinus arrest or exit block, sinoatrial and atrioventricular node defects and atrial tachyarrhythmias. Le Scouarnec et al. demonstrated that a loss-of-function mutation in ankyrin-B leads to loss of normal calcium handling and automaticity due to the improper localization of sinoatrial node channels and transporters [67]. Ankyrin-B deficient cells in the sinoatrial node displayed reduced expression of Na+/Ca2+ exchanger, Na+-K+ATPase (both reduced 30-40%), and InsP3 receptor (reduced ≈ 40%). Interestingly, the localization of a specific type of L-type Ca2+ channel, CaV1.3, was affected in ankyrinB+/- sinoatrial node cells [67]. While sinoatrial node cells and ventricular cells have some similarities with respect to calcium cycling, this specific L-type calcium channel, CaV1.3

12

is predominantly found in the sinoatrial node, while CaV1.2 is the main L-type calcium channel found in the ventricles [71]. Ankyrin-B syndrome has also been linked to human atrial fibrillation. Individuals with loss-of-function mutation in the ANK2 gene displayed early-onset atrial fibrillation. Similar to human patients with loss-of-function mutations in ANK2, ankyrin-B-deficient mice displayed an increased susceptibility to atrial fibrillation. Cunha et al. identified the voltage-gated calcium channel CaV1.3 as an ankyrinbinding partner. In the atria, both CaV1.2 and CaV1.3 contribute to the L-type calcium current.

Using immunofluorescence imaging, they showed CaV1.3 expression was

reduced about 40% when compared to wild-type cells while CaV1.2 expression was unaffected [72].

In addition to the loss of CaV1.3, ankyrin-B-deficient atrial

cardiomyocytes also displayed a loss of Na+/Ca2+ exchanger and Na+-K+-ATPase targeting. The group used mathematical modeling and cell biology to demonstrate that the loss of CaV1.3 was the primary cause for shortened action potentials, which is a characteristic of atrial fibrillation [73]. Ankyrin-B is also involved in cardiomyocyte signaling pathways. In a study by Bhasin et al., ankyrin-B was shown to bind to B56α, the regulatory subunit of protein phosphatase 2A [46]. PP2A is a multifunctional serine/threonine phosphatase with a role in cardiac β-adrenergic stimulation [74-76]. It is involved in the regulation of various ion channels and transporters including L-type Ca2+ channels [76, 77], ryanodine receptors [78], InsP3 receptors [79], and Na+-K+-ATPase [80]. Recent studies have shown ankyrinB deficient cardiomyocytes also have a loss of B56α [46]. In addition to these results, another study by Cunha et al. showed ankyrin-B, obscurin, and PP2A are binding partners [81]. Additional research is needed to clarify the role of ankyrin-B associated PP2A. Ankyrin-B dysfunction has not only been linked to congenital heart arrhythmia syndromes, but it may also play a role in acquired forms of heart disease.

After

13

myocardial infarction, the electrical remodeling that occurs in the border zone near the infarction creates conditions favorable for reentry arrhythmias. Redistribution of ion channels in cardiomyocytes in this border zone is part of the remodeling process. In a study by Hund et al., it was shown ankyrin-B protein levels and localization are reduced following myocardial infarction.

They also demonstrated changes in ankyrin-B

associated proteins [72]. In summary, the action potential is a highly controlled cellular process dependent upon the proper movement of charged ions across the cell membrane. The coordinated contraction of the heart is dependent upon the action potential and when this process is disrupted, life-threatening arrhythmias and sudden death may occur.

Potential

disruptions include the mishandling of calcium, mutations in ion channels or ion channel accessory proteins such as ankyrin-B. Interestingly, ankyrin-B dysfunction may have a role in both acquired and congenital heart disease.

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1.8 Figures

Figure 1.1 Diagram of the phospholipid bilayer and membrane proteins that compose the cell membrane.

15

Figure 1.2 Cardiomyocyte with intracellular and extracellular ion concentrations. There is a relatively high concentration of Na+ and Ca2+ in the extracellular space when compared to the cytosol. There is a relatively high intracellular concentration of K+ when compared to the outside of the cell.

16

Figure 1.3 Phases of ventricular action potential. During Phase 4, the cell is at rest at near -90 mV. With stimulation, Phase 0, which is the rapid depolarization or AP upstroke, occurs due to the opening of the fast Na+ channels. Phase 1 is early repolarization, which is due to the inactivation of the Na+ channels. The opening of the L-type Ca2+ channels and the slow delayed rectifying K+ channels is Phase 2, or the action potential plateau. The plateau phase is due to the balanced movement of K+ and Ca2+ ions. Phase 3 is late repolarization due to the close of Ca2+ channels while K+ channels remain open, allowing the cell to return to rest.

17

Figure 1.4 Schematic of action potential waveforms recorded in different regions of the human heart.

18

Figure 1.5 The conduction system of the heart. The wave of depolarization begins in the sinoatrial node and rapidly spreads through the atria. The atrioventricular node slows conduction to allow the atria to fully contract before the depolarization spreads through the ventricles via the bundle of His, to the left and right bundle branches and finally the Purkinje fibers.

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Figure 1.6 Voltage-gated Ca2+ channels (LTCC) along the T-tubule allow Ca2+ to enter the cell and activate ryanodine receptor Ca2+ release channels located on the sarcoplasmic reticulum which triggers the release of Ca2+ from the SR into the cytoplasm. The close proximity of the LTCC to the ryanodine receptors creates a local domain for Ca2+ signaling. Ca2+ in the cytoplasm is able to bind to troponin resulting in contraction. The Ca2+ is then removed from the cell via the Na+/Ca2+ exchanger or reuptake in the SR by SERCA/PLB.

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Figure 1.7: Ankyrin-B associated binding partners include various ion channels, pumps, and transporters (NCX, NKA, and InsP3 receptor), signaling molecules (PP2A), and cytoskeletal proteins (β-spectrin). One ankyrin protein is able to simultaneously bind to multiple proteins.

21

Figure 1.8 Ankyrin-G ion channel complex in the heart. Ankyrin-G is associated with the targeting NaV1.5 to the intercalated disc of cardiomyocytes.

22

Figure 1.9 Representation of a normal ECG on the left and a LQT ECG on the right. The P-wave represents the depolarization of the atrium, QRS complex is the result of ventricular depolarization, and the T wave denotes ventricular repolarization. With Long QT syndrome, the QT interval or the length of time from the beginning of ventricular depolarization to the end of ventricular repolarization is increased.

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Figure 1.10: Ankyrin-B ion channel complex in the heart. Ankyrin-B is a multifunctional protein that links ion channels and transporters including Na+-K+ATPase, Na+/Ca2+ exchanger, and InsP3 receptor to the cytoskeleton. Ankyrin-B dysfunction results in improper ion channel/transporter localization to specialized domains.

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CHAPTER 2 MATHEMATICAL MODELING OF ELECTROPHYSIOLOGY 2.1 Motivation While a variety of different treatment options for life-threatening arrhythmias are available, a better understanding of what occurs at the cellular level may help explain the initiation of the arrhythmia syndrome and lead to the development of new therapeutic strategies. Using a combination of mathematical modeling with experimental techniques, our group has been able to formulate and test hypotheses under a variety of different circumstances. Our group has used mathematical modeling to examine the consequences of cellular changes due to genetic mutations, myocardial infarction, and even the effects of a potential therapy. 2.2 Hodgkin Huxley Formulation Mathematical modeling of excitable cells began with Hodgkin and Huxley in the 1950’s 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. Using the voltage-clamp technique, the ion currents across the cell membrane were measured while the membrane voltage was held constant. Their experiments suggested an influx of sodium was responsible for the initial positive deflection seen in the measurement of the membrane potential, while the outward movement of potassium was responsible for the repolarization of the membrane [82]. These experiments allowed them to recreate the action potential waveform by solving a set of ordinary differential equations with four state variables and test whether the movement of these ions could generate the measured action potential waveform.

25

The basis for the Hodgkin-Huxley equations is described by the electrical circuit diagram in Figure 2.1.

Hodgkin and Huxley included the contributions from the

membrane capacitance current, the inward sodium current responsible for the action potential upstroke, the outward potassium current responsible for repolarization, and a non-specific leak current. The cell membrane is viewed as a capacitor because of its hydrophobic property which creates a separation of charged ions. This allows the change in the membrane potential (Vm) to be described in terms of the ionic currents by the following equation

dVm −1 = ⋅ ∑ Ii dt Cm i

where Cm is the membrane capacitance (µF/cm2) and Ii are the individual transmembrane ionic currents of the model (µA/cm2). Again, Hodgkin and Huxley took the sum of the sodium current, potassium current, and a leakage current. The concentration gradients of the sodium and potassium ions serve as the driving force for the currents. The magnitude of the driving force can be calculated as the difference between the membrane potential and the equilibrium potential, which is given by the Nernst equation. For example, the following is the equilibrium potential of sodium,

E Na

+ RT   Na  o  = ln  [ Na + ]i F 

   

where ENa is the equilibrium potential for Na+ (mV), R is the gas constant [J•(kmol•K)-1], T is the temperature (K), F is Faraday’s constant (C•mol-1), and [Na+]i and [Na+]o are the intracellular and extracellular sodium concentrations (mM). Ohm’s law can be used to calculate the current by using this driving force. For example, the equation for INa is given by

26

I Na = g Na ⋅ (Vm − E Na )

where INa is the transmembrane sodium current (uA/cm2) and gNa is the sodium conductance (mS/cm2). The conductance for each current was expressed as a function of the open probability of a number of gates and the maximum conductance of the membrane for each ion. The maximum conductance is simply the conductance when all gates are open. Hodgkin and Huxley were able to successfully model the activation of the sodium current by three identical activation gates that change from closed to open when depolarized. The open probability of the activation gate is typically represented by the variable m with a value ranging from 0 (all gates closed) to 1 (all gates open). The time dependent change in m is represented by the following first-order differential equation

݀݉ = ߙሺ1 − ݉ሻ − ߚ݉ ݀‫ݐ‬ where m and (1-m) are the gate open and closed probabilities, t is time (ms), and α and β

are the membrane potential dependent opening and closing transition rates (ms-1). Hodgkin and Huxley recognized the voltage-clamp recordings showed a decrease in current after activation. They accounted for this inactivation by adding a single firstorder inactivation gate with open probability h. This inactivation gate is independent from the activation gates, so the open probability of the sodium gates is m3h and the conductance is

g Na = g Na ⋅ m 3 ⋅ h

where g Na is the maximum conductance (mS/µF).

27

The formulation for the equation of the potassium current is similar, although the current is moving outward. One significant difference from the sodium current is the lack of inactivation gating. Hodgkin and Huxley were able to fit the potassium current data by including four identical activation gates and the current is given by

I K = g K ⋅ n 4 ⋅ (Vm − E K )

where IK is the current (µA/cm2), g K is the maximum potassium conductance (ms/cm2) and EK is the equilibrium potential for potassium. Hodgkin and Huxley included a leakage current to account for any currents not included in INa and IK. The conductance of this particular current is assumed to be independent of time and membrane potential. The leakage current is given by

I leak = g leak ⋅ (Vm − Eleak )

where g leak is the constant conductance and EL is the equilibrium potential. Using these simple equations, Hodgkin and Huxley were able to successfully reproduce the action potential of the axon. However, the mechanism for the time and voltage-dependent gating in the axon was still unknown. Since their work, ion channels were identified as a protein that allowed for the movement of ions across the cell membrane. 2.3 Work Following Hodgkin-Huxley Hodgkin and Huxley provided the foundation for many mathematical models of excitable cells. The variability seen in the cardiac action potential across regions of the heart have led to the development cell specific models for atrial, ventricular, sinus node, and Purkinje cells for a number of different species from rat to human. Here the focus is

28

on ventricular models, but it is important to note the work by Hodgkin and Huxley was the foundation for many mathematical models for different cell types. The independent work of Noble [83] and FitzHugh [84] were among the first to apply Hodgkin and Huxley’s theory to reproduce the plateau action potential seen in cardiomyocytes. The first cardiac action potential model of the Purkinje fiber was by McAllister et al. in 1975. This model relied on the Hodgkin and Huxley formalism and likewise, assumed intracellular ion concentrations of sodium and potassium remained constant during an action potential [85]. With the ability to perform voltage clamp experiments, it was realized the potassium current actually involved multiple components. In addition, differences in the slow gated currents at potentials during the plateau phase and near the resting membrane potential were discovered. One major flaw with this model is the changes in conductance near the resting potential were thought to be caused by a slow gated potassium current, IK2 – an outward current activated by depolarization. It was later discovered these changes were due to the pacemaker current, If, which is an inward current activated by hyperpolarization. The McAllister-NobleTsien model was also unable to account for the changes seen in the potassium ion concentration due to the formulation of IK2. It was then apparent the next models needed to include changes in ion concentrations seen in the intracellular and extracellular spaces [86]. Beeler and Reuter followed in 1977 with the first model of the ventricular muscle cardiomyocyte. This model included a sodium current, a slow inward current that was largely due to the movement of calcium ions, a time-independent outward potassium current, and a voltage- and time-dependent outward current mostly caused by the movement of potassium ions [87]. Several important findings were made using the Beeler-Reuter model. With a premature stimulus given during the repolarization phase of an action potential, the cell response is controlled by the rate of repolarization of the first action potential and by the recovery of the j-gate from inactivation in the INa formulation.

29

Repolarization of the cell membrane is due to the time-dependent decrease of the slow inward current (IS) and an increase in the outward current (IX1). This model was also able to model the ‘all or none repolarization’ response seen during voltage clamp experiments and also model the prolongation of the action potential due to a depolarizing stimulus given during the action potential plateau [86]. DiFrancesco and Noble were able to lead the next major advance in modeling by incorporating the dynamic changes of intracellular ion concentrations into a Purkinje cell model. They quickly realized by incorporating the effects of potassium, the other ions (calcium and sodium) must also be included since the concentration changes are linked by the Na+-K+-ATPase and the Na+/Ca2+ exchanger. The DiFrancesco and Noble model was also the first model to include a formulation for the release of calcium by the sarcoplasmic reticulum [88]. This model led to changes in how the Na+/Ca2+ exchanger functioned. Specifically, it was realized that treating it as a neutral exchanger (two Na+ ions for one Ca2+ ion) would lead to a build-up of intracellular calcium. This gave way to predicting the exchanger actually traded three sodium ions for each calcium ion and generated a current by doing so. One of the major drawbacks of this model was the intracellular calcium transient was too large indicating future models would need to include a formulation for intracellular calcium buffering [86]. Mathematical models are dependent upon the available experimental data and while the first models were an important first step, they were limited by the voltageclamp techniques available and were unable to control the intracellular and extracellular ion concentrations. In the 1980s, single cell and single channels recording techniques allowed for description of individual channel kinetics and ionic currents by Luo and Rudy. The development of the Luo-Rudy model of the mammalian ventricular action potential was accomplished in two phases. The Luo-Rudy phase 1 model reformulated the major depolarizing and repolarizing currents, including the fast sodium current, the delayed rectifier potassium current, and the inward rectifier potassium, based on

30

experimental data from single cell and single channel measurements [89]. This led to the second phase of the model which accounted for dynamic concentration changes of the intracellular ions, including calcium, sodium, and potassium, and the effects these changes had on transmembrane currents.

In order to accomplish this, the model

incorporated the Na+-K+-ATPase, the Na+/Ca2+ exchanger, a calcium pump in the sarcolemma, a two compartment sarcoplasmic reticulum, and the buffering of calcium in the myoplasm by calmodulin and troponin and in the junctional SR by calsequestrin [90]. Since the publication of the Luo-Rudy phase 2 model, there has been an explosion in different mathematical models for different cell types and different species. Table 2.1 is a summary of some of the available models for ventricular cells. 2.4 Next Generation of Computational Models Since the introduction of mathematical models, much data has been gathered on the structure and function of ion channels, the kinetic properties of single ion channels, and the effects on channel function by genetic defects. The goal is to incorporate the experimental results into the models to make a connection between the molecular level and the activity of a whole cell. One method that has been used to accomplish this is to incorporate single channel models based on the different possible states (open, closed, or inactivated) of the ion channel. One of the first groups to take this step away from the Hodgkin-Huxley formalism was Clancy and Rudy in 1999 when they incorporated a Markov model of the cardiac sodium channel in to the Luo-Rudy model [91]. Incorporating cell signaling pathways into the models has become another major area of focus. Many of today’s models use the laws of mass action and MichaelisMenten kinetics to describe the biochemical reaction in a cell signaling pathway. Although these models may miss some biochemical reactions, they have had success in using them to make predictions that can later be tested experimentally.

31

One major signaling pathway that has been included in models of cardiomyocytes is regulated by CaMKII. CaMKII is activated by calcium-bound calmodulin and then phosphorylates many of the ion channels involved in excitation-contraction coupling and cardiac excitability. It has a role in heart failure as it causes hypertrophy, apoptosis, and dysfunction in calcium handling.

Recent studies have suggested the inhibition of

CaMKII may be a potential therapeutic target for treating heart failure [92]. Hund et al. included the first model of CaMKII signaling in a canine ventricular cardiomyocyte.

The group was able to show CaMKII is important for the rate

dependence of the calcium transient while action potential duration adaptation was the result of the effects of outward potassium current (Ito1) on repolarization [93]. Hund et al. also studied the effects of CaMKII after myocardial infarction.

They were able to

experimentally measure increased autophosphorylation of CaMKII in the border zone near an infarction and then use a model to explain how this increased the calcium leak from the SR and led to decreased calcium transients [94]. Continuing the work with CaMKII, Christensen et al. measured increased CaMKII oxidation in the border zone of a canine infarct. They were then able to use a model to show how oxidized CaMKII acted on the sodium current and lengthened the action potential refractory period, slowed conduction velocity in the border zone, and also increased the susceptibility to conduction block at the infarction [95]. β-adrenergic stimulation is another major pathway that has been included in models. β-adrenergic signaling has an important role in regulating cardiac contractility and the progression of heart failure. With normal sympathetic activation, catecholamines bind to β-adrenergic receptors activating a number of G-proteins, increasing the production of cAMP which activates PKA. PKA has the ability to increase contractility, relaxation, growth, or death depending on the demands. While β-adrenergic stimulation is needed for the fight-or-flight response, continuous stimulation has been linked to hypertrophy, fibrosis and heart failure. In heart failure, several β-adrenergic pathway

32

proteins are decreased and drugs that inhibit β-adrenergic stimulation (β-blockers) are one of the first attempts for treatment [96]. Saucerman et al. incorporated the β-adrenergic pathway into their model to study various gene therapies and the effects of protein kinase inhibitor on PKA. They were also interested in which intracellular target of β-adrenergic stimulation was responsible for cardiac inotropy. They were able to identify the phosphorylation of the L-type calcium channel and phospholamban, which is mediated by PKA, as the main cause of the inotropy [97]. In subsequent studies, they were able to show the role of PKA in this inotropy. They showed the phosphorylation of phospholamban increases the calcium concentration in the SR and accelerates relaxation. The phosphorylation of the L-type calcium channel and phospholamban led to an increase in the systolic calcium concentration [98]. Together, these modeling studies of the β-adrenergic and CaMKII pathways demonstrate how models can be used to gain a better understanding of experimentally measured data in cardiac signaling and its role in disease. While modeling signaling pathways is a relatively new advancement, these studies illustrate how a small change in a signaling pathway may result in a major effect on the clinical phenotype [96]. Another future direction for modeling studies involves incorporating the mechanisms of generation and control of bioenergetics. Due to the high energy demand of the heart, numerous reactions are involved in the production of the necessary energy to maintain the workload.

Energy production affects and is affected by the

electrophysiological and mechanical activity of the heart, adding another challenge to modeling.

Cortassa et al. created a mathematical model of cardiac mitochondrial

bioenergetics that linked the energy production in the mitochondria to excitationcoupling. To accomplish this, changes in ATP, Ca2+, and Na+ concentrations in the cytoplasm and mitochondria were coupled to electrical and mechanical changes in the cardiomyocyte [99].

33

Computational models have helped gain a better understanding of cardiac physiology. Combining the use of models with experiments allows predictions to be made that will help limit the number of experiments that must be performed. Models allow for main contributors to be identified for a specific condition. With mathematical modeling it is possible to run simulations for which 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.

34

2.5 Figures

Figure 2.1 Circuit diagram summarizing the currents across the cell membrane of a giant squid axon used to construct the Hodgkin-Huxley model. The cell membrane acts as a capacitor while the ion channels act as resistors. Main currents incorporated by Hodgkin and Huxley included a Na+ current, K+ current, and a nonspecific leak current.

35

2.6 Tables

Table 2.1: Available mathematical models of ventricular cells Species Guinea Pig Guinea Pig

Citation Luo, C. and Rudy, Y. Cir. Res. 74, 1070-1096 (1994). Noble, D., Varghese, A., Kohl, P., and Noble, P. Can J Cardiol 14, 123-134 (1998) Guinea Pig Pasek, M., Simurda, J., Orchard, C., and Christe, G. Progress in Biophysics & Molecular Biology 96, 258-280 (2008) Rat Pandit, S., Clark, R., Giles, W. and Demir, S. Biophysical Journal 81, 3029-3051 (2001) Human Priebe, L., and Beuckelmann, D.J. Circ Res 82, 1206-1223 (1998) Human Ten Tusscher, K.H.W.J., Noble, D., Noble, P.J., and Panfilov, A.V. Am. J. Physiol Heart Circ Physiol 286, H1573-H1589 (2004) Human Iyer, V., Mazhari, R., and Winslow, R. Biophysical Journal 87, (left ventricle) 1507-1525 (2004) Human Grandi, E., Pasqualini, F., and Bers, D. Journal of Molecular & Cellular Cardiology 48, 112-121 (2010) Rabbit Shannon, T., Wang, F., Puglisi, J., Weber, C., and Bers, D. Biophysical Journal 87, 3351-3371 (2004) Rabbit Puglisi, J. and Bers, D. Am. J. Physiol Cell Physio 281, C2049C2060 (2001) Rabbit Belik, M.E., Michailova, A.P., Puglisi, J.L., Bers, D.M, and McCulloch, A.D. Biophysical Journal Mouse Bondarenko, V., Szigeti, G., Bett, G., Kim, S., and Rasmusson, R. Am. J. Physiol Heart Circ Physiol 287, H1378-H1403 (2004) Neonatal Mouse Wang, L. and Sobie, E. Am. J. Physiol Heart Circ Physiol 294, H2565-H2575 (2008) Canine Winslow, R.L., Rice, J., Jafri, S., Marban, E., and O’Rourke, B. Circ Res 84, 571-586 (1999) Canine Greenstein, J.L., Wu, R., Po, S., Tomaselli, G.T., and Winslow, R.L. Circ Res 87 1026-1033 (2000) Canine Fox, J. McHarg, J. and Gimour, R. Jr. Am. J. Physiol Heart Circ Physiol 282, H516-H530 (2002) Canine Hund, T.J. and Rudy, Y. Circulation 110, 3168-3174 (2004)

36

CHAPTER 3 A COMPUTATIONAL MODEL OF ANKYRIN-B SYNDROME The coordinated activity of ion channels and transporters in cardiomyocytes is essential for normal cardiac excitability.

Genetic mutations altering ion channel

properties have been linked to fatal human arrhythmias. In the past decade, mutations in ion channel-associated proteins have also been linked to human cardiac arrhythmia. As mentioned in Chapter 1, ankyrin-B is a multifunctional adapter protein responsible for targeting select ion channels, transporters, cytoskeletal proteins, and signaling molecules in excitable cells, including neurons, pancreatic beta-cells, and cardiomyocytes. Recent research has identified genetic mutations that affect ion channel and transporter localization at the cell membrane as another trigger for human cardiac arrhythmia. In particular, ankyrin-B dysfunction has been linked to cardiac arrhythmia in human patients and ankyrin-B heterozygous (ankyrin-B+/-) mice. At the cellular level, ankyrin-B+/- cells have decreased expression and improper membrane localization of the Na+/Ca2+ exchanger and Na+-K+-ATPase. Ca2+ overload and frequent afterdepolarizations are also seen in ankyrin-B+/- cardiomyocytes and these events are the most likely triggers for fatal cardiac arrhythmias. Even with the large amount of information gained from mouse models and human patients with ankyrin-B dysfunction, the molecular mechanism responsible for cardiac arrhythmias in the setting of ankyrin-B dysfunction remains unclear. I seek here to provide a mathematical model which will give new insight into the cellular pathways responsible for Ca2+ overload and afterdepolarizations in ankyrin-B+/- cells.

In this

chapter, I use existing cell models of human and mouse cardiomyocytes and incorporate the effects of the ankyrin-B deficiency. Using the models, I was able to replicate action

37

potentials seen experimentally and isolate the effects of the ankyrin-B deficiency to simulate their effects on the Ca2+ transient. 3.1 Background Proper biophysical activity of specific ion channels and transporters in cardiomyocytes in critical for normal excitation-contraction coupling and cardiac rhythm. Genetic mutations affecting ion channel biophysical activity have been linked with fatal human arrhythmias in recent years [100].

Further research has identified genetic

mutations altering the coupling of ion channels with cytoskeletal and regulatory proteins [29, 36, 101-106]. Together, these findings demonstrate that proper ion channel and transporter function is dependent upon not only normal biophysical properties, but also proper membrane expression and localization. As stated in Chapter 1, ankyrin polypeptides are responsible for the targeting and stabilization of ion channels, transporters, and signaling molecules at cell membranes of diverse cell types, including cardiomyocytes, neurons, pancreatic beta-cells, and erythrocytes [107]. The importance of ankyrins has become evident in recent years as members of the ankyrin family have been linked to a number of human diseases, in particular, ankyrin-B dysfunction has been linked to both congenital and acquired arrhythmias [36, 42, 47, 67, 72, 108]. Nine different loss-of-function mutations in the ANK2 gene (encodes for ankyrin-B) have been identified in human patients with a complex cardiac arrhythmia syndrome (“long QT 4” or “ankyrin-B syndrome”). These patients suffer from sinus node dysfunction and are vulnerable to ventricular arrhythmias and sudden death under stress [36, 47, 48, 66, 67]. Similar to human patients, ankyrinB+/- mice also have an increased susceptibility to arrhythmias and sudden death under stress [36, 42, 47].

Experimentally, cardiomyocytes from ankyrin-B-deficient mice

showed improper ion channel and transporter localization, abnormal Ca2+ homeostasis, and an increased susceptibility to afterdepolarizations [36]. Ankyrin-B is responsible for

38

the proper membrane localization and function of a number of different ion channels and transporters; in ventricular cardiomyocytes ankyrin-B binds to Na+-K+-ATPase, Na+/Ca2+ exchanger, inositol 1,4,5-trisphosphate receptor, and protein phosphatase 2A (PP2A) [46, 48, 109]. Although the experimental data from human patients and mouse model is abundant, it has yet to be identified how changes in specific membrane proteins lead to cardiac arrhythmia. Mathematical modeling of excitable cells was shown in Chapter 2 to be a valuable tool in generating important new insight into the cellular mechanisms underlying a wide variety of human diseases. In this chapter, I used mathematical modeling to identify the cellular pathway responsible for abnormal Ca2+ handling and cardiac arrhythmia in ankyrin-B+/- cells. The findings from this chapter provide important insights into the molecular mechanism underlying a human disease. Considering the association between ankyrin-B dysfunction and acquired arrhythmia as well as arrhythmia susceptibility in the general population [72, 108], it is expected the insights generated by this study have broader relevance for human disease. 3.2 Methods 3.2.1 Mathematical model of the ankyrin-B+/cardiomyocyte In this study, a mathematical model of the murine (mouse) ventricular action potential from Bondarenko’s group [110, 111] was used since much of the experimental data came from the mouse model. For the following simulations, it was necessary the formulations of the Na+/K+-ATPase and Na+/Ca2+ exchanger current were well-validated against experimental data from mammalian ventricular myocytes [90] (Figure 3.1). Simulations were also performed using a well-validated model of the human ventricular myocyte by Ten Tusscher et al [112]. Modifications to the equations were made to account for experimentally measured changes in Na+/Ca2+ exchanger and Na+-

39

K+-ATPase membrane expression in ankyrin-B+/- cardiomyocytes as shown in Figure 3.2 [36, 42, 48, 113]. Specifically, the Na+/Ca2+ exchanger current was scaled to produce a 40% reduction in current at a test potential of −10 mV compared with control (wild-type), consistent with experimental measurements from adult ankyrin-B+/- myocytes [67]. See Figure 3.2 F. Also, the maximum Na+-K+-ATPase current was decreased 25% based on experimental measurements showing reduced Na+-K+-ATPase surface expression in ankyrin-B+/- myocytes (as assessed by [3H]ouabain binding) [113] as shown in Figure 3.2 G. The peak L-type Ca2+ current (ICaL)-voltage relationship was not different between the control and ankyrin-B+/- cell models, consistent with experimental measurements in ventricular myocytes [36]. Importantly, simulated action potentials and Ca2+ transients agreed with experimental measurements as shown in Figure 3.2 H and I [36]. The complete equations and parameters for the models used in this study may be found in Appendix A for the mouse and Appendix B for the human. 3.2.2 Mathematical model of isoproterenol effects Since many of the arrhythmias are stressed-induced, I simulated the effects of the β-adrenergic receptor agonist isoproterenol (saturating concentration ≥ 0.1 µM) on the action potential and Ca2+ transient based on previously published formulations [114, 115]. To simulate β-adrenergic stimulation, the effects of isoproterenol on ICaL, the slow component of the delayed rectifier K+ current (IKs), and sarco(endo)plasmic reticulum Ca2+-ATPase current (Iup) were included [114, 115].

The modified equations and

parameters may be found in Appendix A for the mouse and Appendix B for the human. 3.2.3 Pacing protocol Models were paced from rest to steady-state over a range of pacing cycle lengths (CLs; from 2,000 to 200 ms, stimulus amplitude = −60 µA/µF for the mouse and −52 µA/µF for the human; stimulus duration = 0.5 ms for the mouse and 1 ms for the human).

40

3.3 Results 3.3.1 Ankyrin-B deficiency promotes Ca2+ overload at baseline The control and ankyrin-B+/- cell models were paced to determine the electrophysiological effects of the decreased Na+/Ca2+ exchanger and Na+/K+-ATPase currents in ankyrin-B+/- cardiomyocytes (CL = 1,000 ms) as shown in Figure 3.3. The simulated action potential from the ankyrin-B+/- mouse myocyte was slightly longer than the control action potential which agreed with experimental data [36]. (Figure 3.2 H and Figure 3.3 A). Although little change in the action potential morphology and action potential duration (APD) was seen in the ankyrin-B+/- and control models, a significant increase in Ca2+ and Na+ concentration in the cytosol and SR of the ankyrin-B+/- cell was measured due to the decrease of Na+/Ca2+ exchanger and Na+-K+-ATPase targeting. (Figure 3.3 E and F and Table 3.1). Specifically, ankyrin-B-deficient cells displayed an increase in intracellular Na+ concentration (Table 3.1), Ca2+ concentration in the junctional SR ([Ca2+]JSR), and Ca2+ transient amplitude (Figure 3.2 E and F), consistent with experimental measurements from ankyrin-B+/- mice [36]. Ca2+ bound to SR calsequestrin ([Ca2+-CSQN]) was also increased in ankyrin-B+/- cells, but remained below the threshold necessary to triggering spontaneous Ca2+ release. Many of the arrhythmias that occur in ankyrin-B+/- mice and human patients with ankyrin-B syndrome occur while the heart rate is increased (e.g. after stress or exercise) [36]. To determine whether loss of Na+/Ca2+ exchanger and Na+-K+-ATPase altered the response of the ankyrin-B+/- myocyte to changes in pacing rate, the ankyrin-B+/- and control models were paced over a cycle length range from 2,000 to 200 ms. The ankyrinB+/- model had a slightly longer action potential duration when compared to the control at

41

all pacing frequencies (Figure 3.4 A). Ca2+ transient amplitude as well as [Ca2+]JSR and [Ca2+-CSQN] were also greater at every cycle length (Figure 3.3 B-D). As a result, the amount of Ca2+ bound to troponin was also increased in ankyrin-B+/- cells when compared to control, which agrees with the experimental data showing increased contractility at baseline (without β-adrenergic stimulation) in ankyrin-B-deficient myocytes [113]. It is important to note, no spontaneous release events occurred in the ankyrin-B+/- cell during rapid pacing (CL = 500 ms). These simulations demonstrate that the loss of Na+/Ca2+ exchanger and Na+-K+-ATPase targeting leads to an increase in Ca2+ in ankyrin-B deficient cells, however under basal conditions (absence of β-adrenergic stimulation) it remained below the threshold necessary to trigger spontaneous release. 3.3.2 Role of Na+/Ca2+ exchanger and Na+-K+-ATPase in Ca2+ overload in ankyrin-B+/- cells Since the spontaneous release of Ca2+ has the ability to trigger an action potential, the next step was to try to identify the cause of Ca2+ accumulation in ankyrin-B+/- cells. I simulated action potentials and Ca2+ transients in the ankyrin-B+/- cell with Na+-K+ATPase (Figure 3.5, NCX deficient, red lines) or Na+/Ca2+ exchanger restored to normal levels (Figure 3.5, NKA deficient, blue lines). Restoring Na+/Ca2+ exchanger targeting to normal had little effect on action potential duration (compare ankyrin-B and NKA deficient in Figure 3.5 A and D; CL = 1,000 ms) in the ankyrin-B+/- cell, but the Ca2+ transient amplitude (Figure 3.5 B and E) and [Ca2+]JSR (Figure 3.5 C and F) levels were considerably reduced, almost to levels of the control.

Restoring Na+-K+-ATPase

targeting had a more significant impact on action potential duration (Figure 3.5 A and D), with a lesser effect on Ca2+ transient amplitude (Figure 3.5 B and E) or [Ca2+]JSR (Figure 3.5 C and F) compared with restoring Na+/Ca2+ exchanger targeting. When the same simulations were repeated using the human cell model, the loss of Na+/Ca2+ exchanger was also the main cause of increased Ca2+ transient amplitude and [Ca2+]JSR in the human

42

ankyrin-B-deficient cell (Figure 3.6). The results from these simulations demonstrate the individual roles of the Na+/K+-ATPase and Na+/Ca2+ exchanger in ankyrin-B deficient cells.

The loss of Na+-K+-ATPase targeting had the greatest impact on the action

potential duration in ankyrin-B+/- cells, the loss of Na+/Ca2+ exchanger targeting leads to the accumulation of Ca2+ in the cytosol and sarcoplasmic reticulum. 3.3.3 Increased levels of Ca2+ with isoproterenol Human patients with ankyrin-B deficiency have an increased susceptibility to stress-induced arrhythmias [66, 113]. Likewise, experimental data from ankyrin-B+/mice showed ventricular arrhythmias occurred following a catecholamine injection after exercise [113]. Based on these observations, I next determined the response of the ankyrin-B+/- and control models to treatment with the β-adrenergic receptor agonist isoproterenol (Figure 3.7). The application of isoproterenol resulted in a significant increase in the Ca2+ transient amplitude in both the control and ankyrin-B deficient models (Figure 3.7 B and E) due to increased ICaL (Figure 3.7 C and F) and SR Ca2+ uptake. It is important to note spontaneous Ca2+ release from the SR did not occur in either the control or ankyrin-B deficient model during slow pacing (CL = 1,000 ms) with the application of isoproterenol. Many of the arrhythmias that occur in both mice and human patients occur when heart rate is increased, so the next step was to repeat the simulations in the control and ankyrin-B+/- models with the application of isoproterenol with rapid pacing.

These

simulations show multiple spontaneous SR Ca2+-release events in the ankyrin-B+/- model during rapid pacing (CL = 200 ms; arrows in Figure 3.8 B) due to the increased SR Ca2+ load (Figure 3.8 C).

These spontaneous release events altered action potential

morphology during pacing (asterisks in Figure 3.8 B) and even produced afterdepolarizations that successfully triggered action potentials during a subsequent pause (Figure 3.8 D). Again, it is important to note no spontaneous release events or

43

afterdepolarizations occurred in the control model during rapid pacing (Figure 3.8 A and B) or a subsequent pause (Figure 3.8 D and E) in the presence of isoproterenol. These results demonstrate the ankyrin-B deficiency increases the probability of spontaneous release and action potential afterdepolarizations. The results from the simulations agreed with experimental observations as afterdepolarizations were only observed during rapid pacing rates (such as exercise) and in the presence of isoproterenol (β-adrenergic stimulation) [36]. When the simulations were repeated in the human model, the results were similar. During rapid pacing in the presence of isoproterenol, spontaneous release occurred in the ankyrin-B+/- cell but not in the control cell as shown in Figure 3.9. Interestingly, in the human model with rapid pacing, the spontaneous release events produced afterdepolarizations that reached threshold for triggering an action potential (asterisk in Figure 3.9 A). To determine the relative contributions of Na+/Ca2+ exchanger and Na+-K+ATPase loss to Ca2+ overload, spontaneous release, and afterdepolarizations, we subjected the ankyrin-B+/- cell with normal Na+/Ca2+ exchanger targeting or with normal Na+-K+-ATPase targeting to rapid pacing in the presence of isoproterenol (Figure 3.10). Restoring Na+/Ca2+ exchanger targeting decreased the number of spontaneous release events and afterdepolarizations in ankyrin-B+/- cells (number of events decreased >5-fold in NKA-deficient compared with ankyrin-B+/- cells; Figure 3.10, A, B, and D). Restoring Na+-K+-ATPase had a lesser effect on spontaneous release, however it did reduce the number of spontaneous release events and delayed the time to first spontaneous release (compare ankyrin-B+/- and NCX-deficient cells in Figure 3.10 C and D). The results from repeating the simulations in the human model were consistent as the loss of Na+-K+ATPase current had fewer and delayed spontaneous release events when compared to the loss of Na+/Ca2+ current (Figure 3.9 B and C). These data indicate that while the loss of both the Na+/Ca2+ exchanger and Na+-K+-ATPase contribute to SR Ca2+ overload and

44

afterdepolarizations in ankyrin-B deficient cells, loss of Na+/Ca2+ exchanger is the dominant mechanism. 3.4 Discussion Na+-K+-ATPase and Na+/Ca2+ exchanger are functionally coupled transporters for the regulation of ion homeostasis and contractility in the heart [116-118]. The Na+-K+ATPase maintains the Na+ gradient across the cell membrane which allows the Na+/Ca2+ exchanger to remove Ca2+ from the cell. For many years, this coupling has been key for treatments of heart failure symptoms through the use of digitalis [119]. Only in the past 50 years, the exact connection between digitalis, Na+-K+-ATPase, and contractility has been established. Recent studies, [42, 120] have demonstrated the physical coupling of Na+-K+-ATPase and Na+/Ca2+ exchanger is necessary for the functional coupling of the transporters. As stated previously, ankyrin-B is able to bind to both Na+-K+-ATPase and Na+/Ca2+ exchanger and is necessary for proper localization of the transporters at the cell membrane [42].

Ankyrin-B deficiency not only affects the expression of Na+/Ca2+

exchanger and Na+-K+-ATPase, but also InsP3 receptor and PP2A and has already been linked to arrhythmia in humans and mice [36, 42, 46, 48, 109, 113, 120].

The

simulations in this chapter show the loss of Na+/Ca2+ exchanger and Na+-K+-ATPase targeting in ankyrin-B+/- cardiomyocytes increases intracellular Ca2+ concentration under normal

conditions

and

allows

for

spontaneous

Ca2+

release

events

afterdepolarizations with rapid pacing in the presence of isoproterenol.

and Most

importantly, these simulations agree with experimental data from ankyrin-B+/- mice and human patients [36, 47, 48]. We have shown the loss of Na+-K+-ATPase increased action potential duration in ankyrin-B+/- cells, while the loss of Na+/Ca2+ promotes intracellular Ca2+ accumulation, spontaneous release, and afterdepolarizations.

Contrary to these

results and unlike ankyrin-B+/- mice, NCX1 knockout mice have normal Ca2+ transients and lifespan with only a slight decrease in contractility [121]. NCX1 knockout mice

45

show a compensatory decrease in ICaL which decreases the influx of Ca2+ and possibly helps to lessen the negative effects of NCX loss [121]. Future studies are necessary to investigate the mechanism responsible for ICaL downregulation in NCX1 mice and the reason for differential regulation in NCX1 knockout and ankyrin-B-deficient mice. It is important to note other factors may be involved in ankyrin-B deficient spontaneous release and afterdepolarization events that have not been included in this model.

One such example includes an altered phosphorylation state of SR and/or

membrane target proteins due to loss of PP2A activity [46]. It has been shown reduced expression of the B56α regulatory subunit of PP2A causes Ca2+/calmodulin-dependent kinase

II-dependent

hyperphosphorylation

of

ryanodine

receptor

2

and

afterdepolarizations [122]. It is also possible abnormal kinase activity is a consequence of the accumulation of Ca2+ due to the loss of Na+-K+-ATPase and Na+/Ca2+ exchanger [123]. Thus, changes in kinase/phosphatase regulation in ankyrin-B deficient cells may increase effects of the loss of Na+-K+-ATPase and Na+/Ca2+ exchanger. Some patients with ankyrin-B deficiency have a prolongation of the QT interval on the electrocardiogram [36, 47, 66]. The cause of this prolongation is uncertain. The previous simulations how loss of Na+-K+-ATPase results in a slight increase in action potential duration in ankyrin-B+/- cells. It remains unclear whether the QT interval prolongation is the result of increased action potential duration or another mechanism [e.g., abnormal conduction [36]]. Future studies are required to address QT prolongation in the subpopulation of ankyrin-B syndrome patients with long QT. A new class of cardiac proteins, Eps15 homology domain (EHD) proteins, have were recently identified by our group [124] to be involved in ankyrin-B based targeting of the Na+/Ca2+ exchanger.

Membrane expression and function of the Na+/Ca2+

exchanger is reduced in EHD knockdown in wild-type neonatal cardiomyocytes. On the contrary, overexpression of EHD increased membrane expression of Na+/Ca2+ exchanger and thus current. The results from this study support the idea that restoring Na+/Ca2+

46

exchanger function by targeting ankyrin and/or EHD may be an effective strategy for preventing cardiac arrhythmia and sudden death in patients with congenital or acquired ankyrin-B deficiency. 3.5 Limitations This model of the ankyrin-B+/- cardiomyocyte was based on experimental data from ankyrin-B+/- mice which phenocopies human patients with ankyrin-B syndrome. As a result, this model is limited by the available experimental data. While loss of Na+/Ca2+ exchanger and Na+-K+-ATPase membrane expression and current are well known properties of ankyrin-B+/- mice, little data exists on Na+/Ca2+ exchanger and Na+-K+ATPase biophysical properties. Previous studies have shown there is a loss of ouabainbinding sites (parallels loss of Na+-K+-ATPase) in ankyrin-B-deficient cardiomyocytes, however the affinity for ouabain binding is unchanged for residual sites [113]. These experiments suggest the Na+-K+-ATPase that is expressed at the cell membrane of ankyrin-B deficient cardiomyocytes functions properly, however more research is needed. This model, while it accounts for the loss of Na+/Ca2+ exchanger and Na+-K+ATPase membrane expression in ankyrin-B-deficient cells, does not account for defects in the localization of the InsP3 receptor (or PP2A, as discussed above) in ventricular cardiomyocytes. In ventricular cardiomyocytes, the role of the InsP3 receptor is unclear as Ca2+ release from the SR is controlled by ryanodine receptor Ca2+-release channels. This model may act as the foundation for which new experimental data on InsP3 function (and PP2A) from ventricular cardiomyocytes may be included to examine the effects of the loss of InsP3 receptors in ankyrin-B+/- cells.

47

3.6 Figures

Figure 3.1: Voltage dependence of Na+-K+-ATPase. Simulated (lines) Na+-K+-ATPase current-voltage relation as a function of extracellular Na+ concentration compared to experimental measurements in mammalian ventricular myocytes (circles) [125].

48

Figure 3.2: Mathematical model of the ankyrin-B-deficient (ankyrin-B+/-) cell. (A) Schematic of the mouse ventricular cell model. Na+-K+-ATPase (NKA) current (INaK) and Na+/Ca2+ exchanger (NCX) current (INaCc) were altered in the model of the ankyrin-B+/- cell (yellow boxes). Symbols are defined in the text and in Appendix A. (B-E) simulated action potentials (APs) in control (B and D) and ankyrin-deficient (C and E) cardiomyocytes from the mouse (B and C) and human (D and E) ventricular cell models [10th action potential (AP) shown at a cycle length (CL) of 1,000 ms]. (F) simulated INaCa at a test potential of −10 mV from the wild-type cell and an ankyrin-B+/- cell compared with experimental measurements (n = 12, *P 0.1 µM, CL = 1,000 ms).

54

55 Figure 3.8: Spontaneous Ca2+ release and afterdepolarizations in the mouse ankyrin-B+/cell during rapid pacing in the presence of Iso. Simulated (A) action potential, (B) Ca2+ transient, and (C) [Ca2+]JSR in control and ankyrin-B+/- mouse ventricular cardiomyocytes during rapid pacing to steady-state (CL = 200 ms) in the presence of Iso. Frequent spontaneous release events (arrows in B) led to abnormal repolarization (* in A) in the ankyrin-B-deficient cell. Simulated (D) action potential, (E) Ca2+ transient, (F) INaCa, and (G) ICaL in control and ankyrin-B+/- cells during a subsequent pause after rapid pacing to steady-state. Note the spontaneous release (arrows) and afterdepolarizations (*) that ultimately produced an AP.

56

Figure 3.9: Spontaneous Ca2+ release and afterdepolarization in human ankyrin-B+/- cell. (A) Simulated action potential in control (black lines) and ankyrin-B-deficient (grey lines) human ventricular cardiomyocytes during rapid pacing to steadystate (cycle length = 500 ms). Spontaneous release produces an action potential during pacing in the ankyrin-B+/- human ventricular cardiomyocytes (asterisk). Summary data showing (B) time to first spontaneous release of Ca2+ from the SR and (C) the number of spontaneous release events during rapid pacing in the ankyrin-B+/- (grey), NKA-deficient (blue) and NCXdeficient (red) cells.

57

Figure 3.10: Role of NCX and NKA in spontaneous Ca2+ release and afterdepolarizations in the ankyrin-B+/- cell. Simulated (A) action potential and (B) Ca2+ transient in ankyrin-B+/-, NCX-deficient, and NKA-deficient cells during rapid pacing to steady-state (CL = 200 ms). Spontaneous Ca2+ release (arrows in B) and abnormal repolarization (* in A) were observed in NCX-deficient and NKA-deficient cells, although with decreased frequency and delayed onset compared with the ankyrin-B+/- cell. C and D: Summary data showing (C) the time to first spontaneous release of Ca2+ from the SR and (D) number of spontaneous release events during rapid pacing in ankyrin-B+/-, NKA-deficient, and NCX-deficient cells.

58

3.7 Tables

Table 3.1: Intracellular Na+ concentration in a computational model of ankyrin-B syndrome

Cycle Length

Control

Ankyrin-B Deficient

Rest Without Iso 11.84 13.72 200 ms Without Iso 12.3 14.24 With Iso 12.25 14.18 1,000 ms Without Iso 11.95 13.85 With Iso 11.88 13.79 Note: Values are in mM. Iso, isoproterenol.

Na+/Ca2+ Exchanger Deficient

Na+-K+-ATPase Deficient

11.53

14.03

12.01 11.96

14.53 14.48

11.64 11.58

14.15 14.09

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CHAPTER 4 ANKYRIN-B DEFICIENCY IN ATRIA 4.1 Background Atrial fibrillation (AF) affects over 2 million patients in the United States making it the most common cardiac arrhythmia. Despite this fact and decades of research, the molecular pathways responsible for creating an atrial substrate favorable to atrial fibrillation remain largely unknown. The heart has evolved complex networks comprised of cytoskeletal, adapter, and regulatory proteins for coordinating the activity of ion channels and transporters. Almost two decades of research has identified a link between genetic defects in select membrane ion channels and cardiac arrhythmia. More recently, dysfunction in ion channel accessory proteins (e.g. cytoskeletal and adapter proteins, subunits) have been found to cause human arrhythmia by affecting ion channel biophysical activity and/or membrane localization.

Ankyrin-B is a multifunctional

adapter protein responsible for the localization and stabilization of select ion channels, transporters, and signaling molecules in excitable cells including neurons, pancreatic beta cells, and cardiomyocytes.

Ankyrin-B dysfunction has been linked to a complex

phenotype in human patients characterized by increased susceptibility to ventricular arrhythmias, sinus node dysfunction, and most recently, an increased susceptibility to atrial fibrillation.

Here I incorporate ankyrin-B deficiency into a multi-scalar

computational model of atrial cells and tissue to determine the mechanism for increased susceptibility to atrial fibrillation in human patients with ankyrin-B syndrome. These findings identify the loss of an ankyrin-associated L-type Ca2+ channel (CaV1.3) targeting as the dominant mechanism for increased susceptibility to atrial fibrillation in human patients with ankyrin deficiency. The results not only identify a molecular mechanism for a human disease, but also have implications for more common forms of atrial fibrillation, where ankyrin-B deficiency has also been identified.

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4.2 Introduction In the heart, the coordinated activity of ion channels and transporters control cellular depolarization and repolarization and thus cardiomyocyte excitability. Genetic mutations affecting the biophysical properties of these ion channels have been linked with human arrhythmias [100]. Recent research has identified a new class of gene mutations associated with arrhythmia in ion channel-associated proteins that affect the targeting of the ion channels and transporters to specific cardiomyocyte membrane domains [29, 36, 101-106]. As demonstrated in Chapter 2, these recent findings illustrate that ion channel and transporter function is dependent upon normal biophysical properties as well as appropriate expression and localization at the cell membrane. Ankyrins are a family of polypeptides (ankyrin-R, ankyrin-G, ankyrin-B) required for proper membrane expression of ion channels, transporters, and signaling molecules in both excitable and non-excitable cells [107]. Over the past decade, ankyrin dysfunction has been linked to a number of human diseases. For example, mutations in ANK1 (gene encoding ankyrin-R) have been linked to spherocytosis [49], while dysfunction in the ankyrin-G based pathway for the voltage-gated sodium channel (Nav1.5) is associated with Brugada syndrome [29]. Ankyrin-B dysfunction has been linked to both congenital and acquired arrhythmias [36, 42, 47, 67, 72]. Mutations in ANK2 (gene encoding ankyrin-B) have been associated with a complex cardiac phenotype in humans including sinus node dysfunction, increased susceptibility to ventricular arrhythmias, and sudden death under stress [36, 47, 48, 66, 67]. More recently, research from our group has identified a role for ankyrin-B in normal atrial function [73]. Specifically, individuals with loss-of-function mutations in ANK2 developed early-onset atrial fibrillation. Ankyrin-B deficient (ankyrin-B+/-) mice also displayed an increased susceptibility to atrial fibrillation. Atrial cardiomyocytes from ankyrin-B+/- mice show a decrease in action potential duration, which is a characteristic of atrial fibrillation. In atrial cardiomyocytes, ankyrin-B is responsible for

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proper membrane localization of function of the Na+/K+ ATPase, Na+/Ca2+ exchanger, and the L-type calcium channel 1.3 (CaV1.3). This study identified CaV1.3 as an ankyrinB binding partner and showed a specific C-terminal motif is necessary and sufficient for ankyrin-B binding. Ankyrin-B deficient cardiomyocytes showed a reduced expression of CaV1.3 and thus current, while atrial tissue from human atrial fibrillation patients showed decreased ankyrin-B levels.

Despite establishing an association between ankyrin-B

deficiency and atrial fibrillation, we still lack fundamental information regarding the mechanism for the initiation and maintenance of the reentry arrhythmia. Mathematical modeling of excitable cells has been used to gain insight into a number of human diseases, including cardiac arrhythmia, epilepsy, and diabetes [94, 95, 126-128]. In this study, I use mathematical modeling to identify the mechanism for atrial fibrillation in ankyrin-B deficient cells. My computer simulations show the ankyrin-B deficient cells have shortened action potential duration, but conduction velocity is unaffected. 4.3 Methods 4.3.1 Mathematical model of the ankyrin-B+/cardiomyocyte The mathematical model used in this study was based on a model of the human atrial cardiomyocyte [129]. Modifications to the equations were made to account for experimentally measured changes in Na+/Ca2+ exchanger and Na+/K+-ATPase membrane expression and ICa,L in ankyrin-B+/- cardiomyocytes [36, 42, 48, 113, 130]. Specifically, Na+/Ca2+ exchanger was scaled to produce a 40% reduction in current at a test potential of −10 mV compared with control (wild-type), consistent with experimental measurements from adult ankyrin-B+/- cardiomyocytes [67]. The maximum Na+/K+ATPase current was decreased 25% based on experimental measurements showing reduced Na+/K+-ATPase surface expression in ankyrin-B+/- cardiomyocytes [113].

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Consistent with recent experimental measurements in atrial myocytes, the peak L-type Ca2+ current (ICaL)-voltage relationship showed a 32% decrease in the ankyrin-B+/myocytes compared to the control [73]. 4.3.2 Pacing protocol Models were paced from rest to steady-state over a range of pacing cycle lengths (cycle lengths from 2000 to 300 ms, stimulus amplitude = −20 µA/µF; stimulus duration = 2 ms). The steady-state values for all state variables were used as initial conditions for subsequent simulations. 4.3.3 Fiber model A multicellular cardiac fiber model composed of 200 cells in serial arrangement was used to simulate action potential propagation as described previously [131]. The following equation describing axial current flow along the theoretical fiber was discretized and solved numerically by the Crank-Nicholson implicit method: ∂I ax ∂V ( x, t ) a ∂ 2Vm ( x, t ) − = ⋅ = Cm m + ∑ I ion 2 ∂x 2 Ri ∂x dt where Iax is the axial current, a is the fiber radius, Ri is the axial resistance per unit length, Cm is the membrane capacitance, and Iion is the transmembrane current density.

A

discretization element corresponding to one cell length was used in all simulations. An adaptive time step (∆t) was implemented that solves for transmembrane currents and Vm along the fiber with t = 5 µs during action potential wavefront propagation, t = 10 µs during repolarization, and t = 50 µs during diastole. The fiber model again implemented the Courtemanche et al. model to describe the transmembrane currents and ion concentration changes of each cell in the fiber [129]. The fiber was paced at one end to steady-state using a conservative current stimulus.

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4.3.4 Tissue model A tissue sample was represented by a two-dimensional rectangular grid of various dimensions. Each node was assigned a flag corresponding to a cell type based on fibrosis measurements.

The control (wild-type) model consisted of 3% fibrosis, while the

ankyrin-B+/- model contained 9% fibrosis, consistent with experimental measurements. The two-dimensional cable equation describing action potential propagation was solved using an alternating direction implicit method and a time step of 0.005 ms. 4.3.5 APD Restitution APD90 is the time from the beginning of depolarization until the cell has repolarized to 90% of the action potential amplitude. Action potential duration was measured in the single cell model using an S1S2 pacing protocol as shown in Figure 4.3 B. A premature S2 stimulus was applied after pacing with an S1 stimulus for 1000 beats at the given cycle length of 1000 ms. The diastolic interval (DI) was defined to be the difference of the S2 cycle length and the APD from S1. 4.3.6 Critical Mass and Core Site To determine the critical mass necessary to sustain reentry arrhythmia, a spiral wave reentry was induced in the 2-dimensional tissue model by cross-field stimulation of two perpendicular rectilinear waves. 4.4 Results To determine the electrophysiological consequences of the ankyrin-B deficiency, we paced the control (black line) and ankyrin-B-deficient (red line) cell models to steadystate (cycle length = 1000, Figure 4.2 B; cycle length = 300, Figure 4.2 C).

As

previously illustrated [73], the simulated action potential from the ankyrin-B deficient cardiomyocyte is slightly shorter than the control action potential. Restoring normal Na+/Ca2+-exchanger and L-type Ca2+ channel (LTCC) targeting and Na+/K+-ATPase and

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Na+/Ca2+-exchanger targeting had little impact on action potential duration (compare AnkB, NKA-deficient and LTCC-deficient in Figure 4.2 B and C). In contrast, restoring normal Na+/K+-ATPase and L-type Ca2+ channel targeting in the ankyrin-B deficient increased action potential duration similar to the control value (Figure 4.2 B and C). To determine whether the loss of Na+/Ca2+ exchanger and Na+/K+-ATPase and the decrease in ICa,L altered the action potential duration in response to changes in the pacing rate, the ankyrin-B deficient and control models were paced to steady-state over a cycle length range from 2000 to 300 ms. I also determined action potential duration in the control cell while isolating the effects of the ankyrin-B deficiency (Figure 4.2, NCX deficient – green lines, NKA deficient – blue lines, and ICa,L deficient – grey lines). Action potential duration in the ankyrin-B deficient model is shorter than control at all pacing cycle lengths (Figure 4.2 A). Furthermore, the ankyrin-B deficient model showed a reduced capacity for action potential duration adaptation in rate compared to control (APD shortens by 98 ms as CL decreases from 2000 to 300 ms compared to 155 ms in control). The Na+/Ca2+ exchanger deficient cell was similar to the control at all pacing frequencies. Interestingly, the Na+/K+-ATPase deficient cell had the greatest response in action potential duration at fast pacing due to an increase in [Na+]i (Table 4.1 and Table 4.2). This increase in [Na]i decreased INaCa (Figure 4.2 D and E) which caused an increase in [Ca2+]i (Table 4.1 and Table 4.2) and decreased ICa,L (Figure 4.2 F and G). The ankyrin-B deficient and L-type Ca2+ channel deficient cells have a similar decrease in peak ICa,L, while the values for Na+/Ca2+ exhanger and Na+/K+-ATPase deficient cells are similar to the control at both fast and slow pacing (Figure 4.2 H). However, the Ltype Ca2+ channel deficient cell had an increase in ICa,L 30 ms after the peak when compared to the ankyrin-B-deficient cell (Figure 4.2 I). Dynamic instabilities in the cardiac waveform can also contribute to the breakup and initiate fibrillation. Restitution of the action potential duration is one such factor that may have a role in the dynamic instability of the electrical wave. If the slope of the

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action potential duration restitution curve is steep (>1) over a wide range of diastolic intervals (DI), spiral reentry wave breaks up into a fibrillation-like state. In our models, the slope of the action potential duration restitution curve remained below this threshold for wave break to occur (Figure 4.3 A). Since the ankyrin-B deficiency has no effect on INa, I hypothesized the ankyrin-B deficiency would have no effect on the conduction in the atrial fiber. The ankyrin-B deficiency not only affects ion channels and transporters, but also intracellular communication. In order to address whether the cellular uncoupling due to the increased fibrosis affects conduction, I determined conduction velocity in the fiber over a range of gap junction resistances. Increasing gap junction resistance (Rg) from 1.5 to 175 Ωcm2 produced a similar decrease in conduction velocity in control and ankyrin-B deficient fibers (Figure 4.4 A). This indicates the shortening of the wavelength for the reentry arrhythmia is due to the shorter action potential duration of the ankyrin-B cell. 4.5 Discussion Loss of ankyrin-B disrupts the membrane expression of Na+/K+-ATPase and Na+/Ca2+ exchanger and is linked to arrhythmia in humans and mice. Our group has recently identified the CaV1.3 as an additional binding partner of ankyrin-B in the atria. In this study, we identify the loss of CaV1.3 as the primary trigger for the initiation of atrial fibrillation in ankyrin-B deficient tissue.

At the cellular level, the previous

simulations show the ankyrin-B deficient atrial cardiomyocytes display decreased ICa,L and shortened action potential duration. These findings agree with recent experimental observations from our group [73]. My simulations also show conduction velocity is unaffected, even at varying degrees of coupling. I have also demonstrated the ankyrin-B tissue requires the smallest dimension necessary to sustain an arrhythmia followed by the loss of CaV1.3. The increase in fibrosis had little effect on the size of the critical mass of the control model.

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These results suggest the shortened action potential due to the loss of CaV1.3 is the primary cause of the shortened wavelength, allowing the arrhythmia to occur. 4.6 Limitations While this mathematical model of the ankyrin-B deficient cardiomyocyte accounts for many known ankyrin-B targets, it has important limitations based on the available experimental data from an animal model of ankyrin-B deficiency. Although the model does account for the loss of Na+/Ca2+ exchanger, Na+/K+-ATPase, and Cav1.3, it does not account for the loss of the InsP3 receptor in atrial cardiomyocytes. This model will provide the framework into which new data on InsP3 function in atrial cardiomyocytes may be incorporated. It is important to note the cause of the increase fibrosis in ankyrin-B deficient atria has not been identified. Whether the increase seen is a direct result of the ankyrin-B deficiency or a secondary effect remains to be seen.

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4.7 Figures

Figure 4.1: Mathematical model of atrial ankyrin-B deficiency. (A) Schematic of Courtemanche et al. human atrial cell model. (B) One-dimensional fiber model comprised of individual cells electrically coupled through gap junctions. A current stimulus is applied at the end of the fiber (cell 1) and the excitation wavefront propagates down the fiber. (C) Two-dimensional tissue model comprised of fibers. Na+/Ca2+ exchanger current (INaCa), Na+/K+ ATPase current (INaK), and L-type Ca2+ current (ICa,L) are altered in model of ankyrin-B-deficient cell (yellow). Consistent with experimental data, the AnkB+/- shows decreased (D) ICa,L, (E) INaCa, and (F) INaK.

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Figure 4.2: Rate dependence of action potential duration. (A) Action potential adaptation curve for the control (black line), ankyrin-B deficient cell (red line), NCXdeficient (NKA and ICa,L restored to normal levels, green line), NKA-deficient (NCX and ICa,L restored to normal levels, blue line), and ICa,L-deficient (NCX and NKA restored to normal levels, grey line) paced to steady-state at cycle lengths of 300, 400, 500, 750, 1000, and 2000 ms. (B) Simulated action potentials at slow pacing (cycle length = 1000 ms) and (C) fast pacing (cycle length = 300 ms). INaCa at (D) slow pacing and (E) fast pacing.

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Figure 4.2 Continued ICa,L at (F) slow pacing and (G) fast pacing. (H) Peak ICa,L at fast facing (black bars) and slow pacing (grey bars). (I) ICa,L 30 ms after stimulation for fast pacing (black bars) and slow pacing (grey bars).

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Figure 4.3: Action potential restitution and protocol. (A) Action potential duration restitution curve. (B) S1S2 protocol for measuring APD restitution. APD is measured as the S1S2 interval is shortened.

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Figure 4.4: Conduction in ankyrin-B deficient fiber is unaffected by increased gap junction resistance. (A) Conduction velocity versus gap junction resistance in control and ankyrin-B deficient fibers. Even at high degrees of uncoupling, no change in conduction is seen. (B) One-dimensional fiber model comprised of individual cells electrically coupled through gap junctions.

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4.8 Tables

Table 4.1: Ion concentrations from atrial model paced to steady-state at cycle length of 1000 ms. Cell Type

[K+]

[Na+]

[Ca2+]amp

[Ca2+]min

[Ca2+]peak

WT

134.9471

13.6437

0.6246

0.1232

0.7478

AnkB

133.6059

14.9607

0.6288

0.1351

0.7639

NCX

135.6872

12.8582

0.7687

0.1411

0.9098

NKA

132.3622

16.1863

0.7579

0.1425

0.9004

L-type

136.2493

12.4255

0.3802

9.4916e-3

0.4751

Note: Concentrations are in mM.

Table 4.2: Ion concentrations from atrial model paced to steady-state at cycle length of 300 ms. Cell Type

[K+]

[Na+]

[Ca2+]amp

[Ca2+]min

[Ca2+]peak

WT

129.5664

15.1368

0.3514

0.2645

0.6159

AnkB

127.5065

17.2109

0.3768

0.2919

0.6687

NCX

129.9251

14.7747

0.4208

0.2995

0.7203

NKA

126.0942

18.5538

0.4758

0.3184

0.7941

L-type

130.4616

14.3455

0.2287

0.2070

0.4356

Note: Concentrations are in mM.

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CHAPTER 5 COMPUTATIONAL MODEL OF CAMKII REGULATION OF VOLTAGE-GATED SODIUM CHANNEL As illustrated in Chapter 1, genetic mutations altering the biophysical properties of ion channels have been linked to human arrhythmia syndromes. More recently and as shown in Chapter 2, mutations in ion channel accessory proteins also have the ability to affect cardiomyocyte excitability.

Many of these mutations affect cell function by

altering ion channel localization at the cell membrane or its biophysical activity. Incorporating cell signaling pathways into mathematical models has helped to advance the study of the link between specific molecular defects, ion channel dysfunction, and human disease. The cardiac dyad described in Chapter 1 is an example of the control necessary to maintain proper intracellular signaling, while protein phosphorylation is another such example. Phosphorylation of membrane proteins in cardiomyocytes is the key to the proper regulation of their activity. Recent research has identified a new class of human arrhythmia variants that alter the post-translational modification of a membrane protein. In this chapter, I describe a mathematical model of a voltage-gated Na+ channel based on experimental data from these specific mutations. I used an existing cellular model (Luo-Rudy ventricular cell model) and incorporated a Markov model of a Na+ channel to describe the Na+ current. Using parameter estimation with the experimental data, I was able create a unique INa formulation for each variant. 5.1 Background Voltage-gated Na+ channels are necessary for the action potential upstroke and thus normal cardiomyocyte excitability. Unsurprisingly, they were one of the first ion channels to be linked to a human cardiac arrhythmia [54, 132]. As previously described,

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a mutation in the SCN5A gene that encodes for NaV1.5 has been linked to Brugada syndrome, but in actuality hundreds of mutations in this gene have been associated with various types of arrhythmia [100, 133, 134]. While these mutations relate to congenital forms of cardiac arrhythmia, dysfunction in NaV1.5 leading to decreased conduction velocity and changes in repolarization has been implicated in acquired forms of heart disease (e.g. heart failure and myocardial infarction) [135]. A recent publication by our group demonstrated the role CaMKII has in the regulation of NaV1.5. It showed phosphorylation of NaV1.5 at residue S571 in the DI-DII loop by CaMKII decreases channel availability and increases persistent (late) current leading to an increased susceptibility to afterdepolarizations [63]. Suspecting genetic variation in this region may have a role in human cardiovascular disease, further work from our group identified a group of mutations in the SCN5A gene located in the DI-DII loop near residue S571. The two particular variants, A572D and Q573E, are located in the CaMKII phosphorylation motif of NaV1.5 and were shown to alter the regulation of the channel [68, 136-139]. The Q573E mutation was identified in a group of LQT syndrome probands with autosomal dominant Romano Ward syndrome [137]. While the A572D variant was also originally identified in a group with Romano Ward LQT syndrome, it has also been associated with more frequent arrhythmia syndromes. It has been suggested the A572D variant may be found in ~0.5% of the general population [68, 136, 138-140]. Both the A573D and Q573E variants result in a charge reversal of amino acids (neutral to negative) near the CaMKII phosphorylation site that mimic phosphorylation effects.

As a result, we hypothesized the variants would display an increased

susceptibility to pro-arrhythmic effects. Experimental data from our group showed the A572D and Q573E mutant channels in HEK cells displayed delayed inactivation recovery and increased late current at baseline and in the presence of CaMKII. The

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A572D mutant also showed a depolarizing shift in steady-state inactivation when compared to wild-type. 5.2 Methods To determine the effects of the A572D and Q573E variants on action potential duration, I performed computational modeling which incorporated unique Markov models of the wild-type and variants into a well-validated computer model of the mammalian ventricular action potential [141]. The Markov model of INa used in this study was developed following previously published formulations [111, 142, 143]. The model contains two modes of gating, a background mode and a burst mode as shown in Figure 5.1 B. The background or upper mode consists of nine states, including three closed states (C3, C2, C1), an open state (O), and two closed inactivated states (IC3, IC2). A fast inactivated state (IF) and two intermediate inactivation states (IM1, IM2) are also included to account for the fast and slow recovery features of inactivation. A majority of the channels are in the IM1 state and are unable to recover and reopen during depolarization. Few channels enter the IM2 state via slow transitions. The IC3 and IC2 states allow for the channel to enter an inactivated state from any of the closed states and thus accounts for closed-state inactivation. The burst or lower mode consists of channels that fail to inactivate resulting in a sustained inward current. The channels bounce between three closed states (LC3, LC2, LC1) and a conducting open state (LO). The transition rates between the upper and lower states represent the probability of changing between the two modes [111, 142, 143]. State transition rates in a Markov model of NaV1.5 were determined for wild-type and the two variants, as well as the S571E variant which served as a phosphor-mimetic control. Transition rate expressions and the corresponding reference are given in Table 5.1.

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The parameters were fit to electrophysiological data measured in HEK cells. Voltage clamp protocols for activation, steady-state inactivation, recovery from inactivation, and the late current were used in the parameter fitting. Initial guesses for the parameter values for wild-type and all mutants were taken from Grandi et al [143]. Data from activation was first used to fit P1a1. The result was then used to fit P1b5 to activation and steady-state inactivation data.

P1b6 was also fit to the inactivation

recovery data. Finally these three parameters were used to fit P1a8 to the late current data. The Levenberg-Marquardt method in COPASI (v.4.6.33) was used to minimize the error between experimental and simulation data. The complete set of model parameters is given in Table 5.2 The Luo-Rudy model of the mammalian ventricular action potential was used to describe transmembane currents and ion concentration changes with the previously described Markov model of voltage-gated Na+ current assuming one normal and one variant allele (50% variant channels).

The maximal conductance, g Na , was calculated

for the wild-type and all mutants. The complete set of initial conditions is given in Table 5.3. The cell was paced from rest to steady-state using a conservative current stimulus (cycle length = 500 unless otherwise noted, stimulus amplitude = −80 µA/µF, stimulus duration = 0.5 ms, [K+]O = 4.0 mM). 5.3 Results Consistent with experimental data, the A572D and Q573E variants displayed increased late INa and increased action potential duration. During slow pacing (cycle length = 1,000 ms), afterdepolarizations were seen in both mutants. See Figure 5.3 A for the afterdepolarization in the A572D mutant; Q573E not shown.

Together, these

simulations, based on experimental measurements, show the two variants are able to produce APD prolongation and afterdepolarizations in mutant cells.

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Based on experimental data and the previous computational results shown, we hypothesized a potential therapy which targeted late INa would restore action potential duration to normal and prevent the afterdepolarizations in the A572D mutants. Ranolazine was chosen as the therapy of choice as it has been shown to block late INa and may be used clinically to prevent arrhythmia [144, 145]. Using the mathematical model, the effects of ranolazine on action potentials for the control and A572D variant cardiomyocytes were simulated.

As shown in Figure 5.3, ranolazine targeted and

blocked the Na+ channel open state with on- and off-rates of 8.2 µM-1s-1 and 22 s-1, respectively [146, 147]. Consistent with experimental results, ranolazine was shown to block INa. In the A572D mutant, ranolazine was able to restore action potential duration to normal and eliminate the afterdepolarizations at slow pacing. These results support the hypothesis of our group that these specific variants increase action potential duration by increasing late INa.

These simulations have clinical relevance as it supports the use of

Na+ channel blockers such as ranolazine as a therapy for patients with specific NaV variants which simulate CaMKII phosphorylation. 5.4 Discussion Proper function of voltage-gated Na+ channels is necessary for normal cardiomyocyte excitability as indicated by the association shown in this chapter between channel dysfunction and arrhythmia syndromes.

Research by our group has

demonstrated the link between defects in CaMKII-dependent phosphorylation of NaV1.5 and diverse forms of cardiac disease associated with arrhythmias and sudden death. CaMKII-mediated phosphorylation of NaV1.5 in the DI-II loop at the S571 site has been shown to have major role in several Na+ channel properties, including channel availability, recovery from inactivation, and late current [63]. Two variants, A572D and Q573E, were identified by our group near this CaMKII regulatory motif. In this chapter, we used parameter estimation to construct a unique

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formulation of INa for each variant. I used the model to explore whether measured differences in NaV function were responsible for action potential prolongation and afterdepolarizations in A572D- and Q573E- expressing cells.

Importantly, the

mathematical model was used to test the hypothesis whether a pharmacological intervention such as a Na+ channel blocker was able to restore action potential duration and eliminate afterdepolarizations seen in the variants. The model was able to reproduce important action potential properties seen in experimental results and demonstrate a link between defects in CaMKII phosphorylation of NaV1.5 and diverse forms of cardiac disease associated with arrhythmias and sudden death. Recent work from our group measured NaV current (INa) in HEK cells at baseline and in the presence of active CaMKII and both variants displayed a delay in recovery from inactivation and increased late current when compared to wild-type. The A572D variant showed a depolarizing shift in NaV1.5 steady-state inactivation when compared to wild-type. When the variant channels were expressed in cardiomyocytes and INa was measured, the A572D and Q573E mutants again showed increased late current when compared to wild-type and both variants also displayed a leftward shift in steady-state inactivation. Channel expression in the mutant constructs was similar to wild-type as peak current was comparable. Together, these experiments show the two variants with a charge substitution mimic CaMKII phosphorylation by reducing NaV availability and increasing late current, which may serve as a trigger for human arrhythmias. When action potentials were measured in cardiomyocytes, cells expressing the variant channels displayed a prolongation of action potential duration when compared to wild-type, while afterdepolarizations were only seen in cardiomyocytes expressing the A572D variant. This recent study has demonstrated the key role the CaMKII phosphorylation site has in the regulation of channel activity and cardiomyocyte excitability. Defects in NaV function, including increased late current, have been identified in heart failure patients [148]. Suspecting the phosphorylation site of NaV1.5 at residue S571 may have a role in

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common forms of heart disease, our group measured the phosphorylation levels of NaV1.5 at that site in a large animal model of cardiac arrhythmia following myocardial infarction. Myocardial infarction was produced in canines by total coronary artery occlusion as shown in Figure 5.5. Levels of phosphorylated-NaV1.5 were significantly increased in the border zone of the infarction five days post-occlusion. No change in the phospho-NaV1.5 levels was seen in noninfarcted hearts or in remote regions of the infarcted hearts. Consistent with previous results [94, 95, 149, 150], increased levels of activated CaMKII and NaV dysfunction is seen in canine border zone of myocardial infarction establishing a link between CaMKII activity and Nav dysfunction after myocardial infarction. Levels of phosphorylated CaMKII were then evaluated in left ventricular samples from human hearts with non-ischemic heart failure to determine whether phosphorylation of NaV1.5 at S571 has a role in human disease.

Increased levels of phosphorylated

CaMKII were measured in the samples which was consistent with previous studies showing increased CaMKII in heart failure [151]. Also observed was an increase in the level of phosphorylated NaV1.5 in samples from non-ischemic heart failure patients when compared to control, while the total level of NaV1.5 was unchanged. Collectively, these results support our group’s hypothesis that phosphorylation of NaV1.5 at the S571 site is an important link between defects in CaMKII activity, NaV dysfunction and arrhythmias. The data presented here supports the role of CaMKII-mediated phosphorylation of NaV1.5 at S571, however post-translational modifications in NaV1.5 may also be involved disease phenotype. PKC and PKA have been shown to be affected by disease, yet both are also involved in the regulation of NaV1.5 channel kinetics [135, 152]. It will be important for future studies to determine the contribution of phosphorylation of NaV1.5 at S571, as well as other possible major factors including beta-adrenergic receptor stimulation, angiotensin II, reactive oxygen species, and Ca2+.

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To summarize, our group identified two variants of NaV1.5 near the CaMKIIregulatory site. We were able to use mathematical modeling to show the differences in NaV function were associated with prolonged action potential duration and afterdepolarizations. We also showed a potential therapy, such as ranolazine, which targeted late INa normalized action potential duration and prevented afterdepolarizations in the variants.

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5.5 Figures

Figure 5.1: Human arrhythmia variants near NaV1.5 CaMKII-phosophorylation site. Schematic illustrating the spectrin-based signaling complex at the cardiomyocytes intercalated disc for regulation of NaV1.5 (via ankyrin-G) to phosphorylate at S571 in the NaV DI-DII linker. Human variants associated with cardiac arrhythmia have been identified in the region adjacent to the phosophorylation site (A572D and Q573E).

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Figure 5.2: Computational model to determine role of human arrhythmia variants identified near CaMKII phosphorylation site of NaV. (A) Schematic of mathematical model of mammalian ventricular action potential used to determine the effect of the NaV variants on cardiac repolarization. (B) Markov model used to simulate NaV function that includes transitions between multiple inactivated (red), closed (blue), and open (green) states.

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Figure 5.3: Parameter estimation results show human arrhythmia variants cause action potential prolongation. Parameter estimation results comparing experimentally measured (black) and simulated (red) values for (A) steadystate inactivation and (B) late current. Simulated (C) action potentials and (D) Na+ current from WT (black), A572D (red), and Q573E (grey) variant cells. Similar to experimental results, computational modeling predicts human arrhythmia variants increase NaV late current and prolong APD compared to WT. Results shown at steady-state at pacing cycle length = 500 ms.

84

Figure 5.4: Computational model predicts increased susceptibility to afterdepolarizations in human arrhythmia variants identified near CaMKII phosphorylation site of NaV. Simulated (A) action potentials and (B) INa in WT- (black) and A572D(red) expressing cells at steady-state during slow pacing (cycle length = 1,000 ms). The two variants, A572D and Q573E (not shown) displayed afterdepolarizations under these conditions. Simulated block of late INa with 10 µM ranolazine (C) reduced late INa and afterdepolarizations (grey lines in A and B).

85

Figure 5.5: Myocardial infarcation is produced by total coronary artery occlusion in the left anterior descending coronary artery. The border zone represents an area of surviving tissue with abnormal cells near the infarction.

86 Table 5.1: Transition rate expressions for mathematical model of NaV1.5 Transition rate (ms-1)

Reference

a1 = P1a1/(P2a1 exp(-(Vm+2.5)/17)) + 0.20 exp(-(Vm+2.5)/150)

Bondarenko et al. [111]

a2 = P1a1/(P2a1 exp(-(Vm+2.5)/15)) + 0.23 exp(-(Vm+2.5)/150)

“

a3 = P1a1/(P2a1 exp(-(Vm+2.5)/12)) + 0.25 exp(-(Vm+2.5)/150)

“

a4 = 1.0/(P1a4 exp(-(Vm+7.0)/16.6) + 0.393956)

“

a5 = P1a5 exp(-Vm/P2a5)

“

a6 = a4/P1a6

“

a7 = P1a7 a4

“

a8 = P1a8

Grandi et al.[143]

b1 = P1b1 exp(-(Vm+2.5)/P2b1)

Bondarenko et al.[111]

b2 = P1b2 exp(-(Vm-P2b2)/P2b1)

“

b3 = P1b3 exp(-(Vm-P2b3)/P2b1)

“

b4 = (a3 a4 a5)/(b3 b5)

“

b5 = P1b5 + P2b5(Vm+7.0)

“

b6 = P1b6 a5

“

b7 = P1b7 a5

“

b8 = P1b8 a9 = [Ranolazine] P1a9 b9 = P1b9

Grandi et al.[143]

87 Table 5.2: Parameters for mathematical models of wild-type and variant NaV1.5 Parameters

Wildtype

A572D

Q573E

P1a1

7.5207

6.8920

4.6305

Source Fit to IV curve.

P2a1

0.1027

Bondarenko et al.[111]

P1a4

0.188495

“

P1a5

7.0e-7

“

P2a5

7.7

“

P1b1

0.1917

“

P2b1

20.3

“

P1b2

0.2

“

P2b2

2.5

“

P1b3

0.22

“

P2b3

7.5

“ 0.0108469

P1b5 P2b5

2e-5

P1a6

1000.0

P1a7

1.05263e-5

P1b7

0.02

Fit to inactivation and IV curves.

“ 2.5121e-3

2.6199e-3

Fit to recovery. Bondarenko et al. [111] “

4.0933e-13

P1a8

0.0453576

Bondarenko et al.[111]

6.0448e-3

P1b6

0.0604095

1.4458e-4

6.5226e-5

Fit to late current.

P1b8

9.5e-4

Grandi et al.[143]

P1a9

8.2 mM-1ms-1

Wang et al.[147]

P1b9

0.022

Maximum INa conductance

“ 7.35

9.75

11.60

Fit to peak IV curve.

88 Table 5.3: Initial conditions for state variables in mathematical model of mammalian ventricular action potential State variable C1 C2 C3 IC2 IC3 IF IM1 IM2 LC1 LC2 LC3 O LO C1,mut C2,mut C3,mut IC2,mut IC3,mut IFmut IM1,mut

IM2,mut LC1,mut LC2,mut LC3,mut Omut LOmut D F

fca

Xr1

Definition INa closed state “ “ INa inactive state “ “ INa intermediate inactivation state “ INa burst mode closed state “ “ INa open state INa burst mode open state Mutant INa closed state “ “ Mutant INa inactive state “ “ Mutant INa intermediate inactivation state “ Mutant INa burst mode closed “ “ Mutant INa open state Mutant INa burst mode open state L-type Ca2+ current activation gate L-type Ca2+ voltagedependent inactivation gate L-type Ca2+ calciumdependent inactivation gate Rapidly activating K+ current activation gate

WT 0.0003850597267 0.02639207662 0.7015088787 0.009845083654 0.2616851145 0.0001436395221 3.913769904e-05

A572D 0.0003849053676 0.02638818278 0.7015704583 0.009840770794 0.2616320393 0.0001435402196 3.909441247e-05

Q573E 0.0003848309613 0.02638630536 0.7016001465 0.009838691924 0.2616064508 0.0001434923636 3.907357776e-05

3.381242427e-08 1.659002962e-13

3.376098643e-08 1.658337887e-13

3.373623669e-08 1.65801729e-13

1.137084204e-11 3.02240205e-10 9.754706096e-07 4.202747013e-16

1.136916421e-11 3.022667309e-10 9.747956198e-07 4.199838793e-16

1.136835517e-11 3.022795176e-10 9.744703275e-07 4.198437236e-16

-

0.000126208303

7.166307322e-05

-

0.009441839154 0.2739249316 0.02242017495

0.007980529607 0.3446438288 0.01409702075

-

0.6504500644 0.0002996886807 0.0001977778539

0.6087880685 0.0001265875713 8.00620291e-05

-

1.707703298e-07 1.920497509e-05

6.911707407e-08 4.919562139e-06

-

0.001436754012 0.04168284782 2.929101154e-07 4.457180191e-08

0.0005478513486 0.02365928023 1.117291082e-07 7.670035154e-09

1.638090607e-05

1.637609944e-05

1.637378239e-05

0.9999364487

0.9999364687

0.9999364783

1.0

1.0

1.0

0.0001497389543

0.0001496918853

0.000149669196

89

Table 5.3 Continued Xr2

Xs

R

S

G

[Ca2+] i [Ca2+] SR [Na+] i [K+] i Vm

Rapidly activating K+ current activation gate Slowly activating K+ current activation gate Transient outward K+ current activation gate Transient outward K+ current inactivation gate Ryanodine receptor Ca2+ release activation gate Ca2+ concentration in myoplasm (mM) Ca2+ concentration in sarcoplasmic reticulum (mM) Na+ concentration in myoplasm (mM) K+ concentration in myoplasm (mM) Transmembrane potential (mV)

0.4963056182

0.4963285448

0.4963395991

0.002723153193

0.00272272626

0.002722520434

1.61573943e-08

1.615146813e-08

1.614861155e-08

0.9999986683

0.9999986689

0.9999986692

0.9999961213

0.9999961354

0.9999961421

4.387145251e-05

4.384476863e-05

4.383218716e-05

0.1969056818

0.1967445959

0.196669525

8.355040031

8.349674873

8.3471155

145.439625

145.4478242

145.451705

-87.64533404

-87.64753511

-87.64859638

Note: Model equations for Luo-Rudy dynamic cell model and Nav1.5 model are found in original publications.[111, 141-143]

90

CHAPTER 6 DISCUSSION 6.1 Summary of Findings My studies have applied mathematical modeling and computer simulation to identify the cellular mechanism for a variety of human arrhythmias associated with defects in ankyrin-based targeting pathways. Importantly this approach has allowed me to study electrophysiological consequences of defects in multifunctional proteins like ankyrins that coordinate large macromolecular protein complexes. Important aspects of the modeling efforts include: 1) incorporation of effects of the loss of ankyrin-B into a ventricular cell model and identifying the molecular mechanism for abnormal ion homeostasis, inappropriate Ca2+ release from SR stores, and pro-arrhythmic action potential afterdepolarizations; 2) creation of a multi-scalar model of atrial ankyrin-B deficiency to identify the molecular cause of the increased susceptibility to atrial fibrillation in human patients; 3) development of mathematical models of a new class of human arrhythmia variants that interfere with ankyrin-G-dependent regulation of NaV1.5; 4) application of these models to show that these variants mimic a phosphorylated channel to prolong action potential duration and increase susceptibility to afterdepolarizations. Using mathematical modeling and numerical simulation, I was able to provide new insight into the cellular pathways responsible for Ca2+ overload and afterdepolarizations in ankyrin-B-deficient cells. While experiments in the ankyrin-B deficient mouse had identified a number of targeting defects in specific ion channels and transporters, my simulations were able to: 1) demonstrate that the reported defect in NCX and NKA could indeed account for the cellular phenotype; 2) identify the specific link between these observed channel defects and abnormal cell excitability; and 3) make predictions about mechanisms in human patients by incorporating measurements from the ankyrin-deficient mouse into mathematical models of the human (as well as mouse).

91

Finally, the simulations suggest that loss of NCX is primarily responsible for defects in ion homeostasis, Ca2+ release and cell excitability in ankyrin-B-deficient ventricular myocytes, suggesting a potential therapeutic target going forward for human patients with inherited or acquired ankyrin-B-deficiency.

While the strategy to fix NCX

targeting/function in these cells in unclear, recent work from the Mohler lab suggest the EHD family of trafficking proteins may be attractive candidates for regulating targeting of NCX and other important membrane proteins in disease [124]. An interesting and complex aspect of “ankyrin-B syndrome” is the fact that it is associated with a large number of phenotypes, including ventricular, atrial and sinus node arrhythmias. In a broad sense, my studies sought to identify the underlying basis for the link between ankyrin-B-deficiency and this complex phenotype. Thus, my studies in the ventricle were followed with work using a multi-scalar model of atrial tissue to determine the mechanism for increased susceptibility to atrial fibrillation in patients with ankyrin-B deficiency. This allowed me to gain a better understanding of the specific mechanism responsible for creating the substrate for atrial fibrillation in human patients with ankyrinB syndrome. Specifically the loss of the L-type Ca2+ channel was identified as a central determinant of the substrate for atrial fibrillation in ankyrin-B- deficient patients. This has important clinical implications as the loss of ankyrin-B has been identified in more common forms of atrial fibrillation [73]. Finally, my studies applied mathematical modeling and computer simulation to determine the underlying mechanism for two human SCN5A variants that increase susceptibility to arrhythmia by disrupting ankyrin-G-dependent regulation of NaV1.5. Specifically, by creating detailed Markov models of the normal and human variant Na+ channels, we were able to show that the human arrhythmia variants A572D and Q573E produce abnormal repolarization and pro-arrhythmic afterdepolarizations by mimicking the phosphorylated channel. Ankyrin-G plays a critical role in this pathway by linking NaV1.5 at the membrane to the actin/spectrin cytoskeleton. Our mathematical models

92

were also able to predict the efficacy of blocking late Na+ current as a potential therapy for preventing afterdepolarizations in variant-expressing cells. These predictions were later validated experimentally by applying the late Na+ channel blocker ranolazine to myocytes expressing A572D or Q573E channels.

Similar to computational results,

ranolazine normalized Na+ current and action potential in variant-expressing cells [153]. Together, these studies provide insight into the mechanism for two human arrhythmia variants whose mechanism was previously unsolved and identify potential therapy. Importantly, I expect that these human variants that mimic phosphorylation will in some regards resemble heart failure, where we have recently shown ankyrin-G-dependent phosphorylation of NaV1.5 is increased. Phosphorylation of proteins is necessary for regulating cell function.

In particular, CaMKII directly phosphorylates the sodium

channel NaV1.5. NaV dysfunction has been identified in acquired forms of heart disease; one possible molecular link to disease suggests phosphorylation of NaV1.5 by CaMKII decreases channel availability and increases late current, resulting in an increased susceptibility to afterdepolarizations. Research by our group has demonstrated increased CaMKII activity and abnormal NaV function in heart disease by measuring an increase in phosphorylated NaV1.5 in samples from human heart failure and from a large animal model following myocardial infarction. In addition, the two variants identified by our group result in a charge substitution only mimicking CaMKII phosphorylation which results in abnormal cardiomyocyte excitability. So while our studies have focused on rare forms of inherited disease, our findings likely have implications for common heart disease. In the future, it will be interesting to apply a similar mathematical approach to determine the mechanism and predict therapies for common disease where NaV1.5 is hyperphosphorylated.

93

6.2 Limitations Mathematical models, are by nature, simplifications of the biological system. Thus, the models lack many details in regards to the various compartments and signaling pathways found in cardiomyocytes. The wealth of experimental data, while beneficial, also creates a unique set of challenges when choosing which behavior the model should be based upon. This in particular was the case when fitting the data for the genetic mutants in Chapter 5. The mathematical models developed here are based closely on cellular data from primary cardiomyocytes and as a result the model is limited by the available experimental data. For example, while our model of the ankyrin-B-deficient cell accounts for the loss of current from Na+/Ca2+ exchanger and decrease in surface expression of Na+-K+ ATPase, data on the biophysical properties of NCX and NKA in ankyrin-deficient cells are limited. Also, as the role of the InsP3 receptor is unclear in the ventricles, it is important to note the model does not account for defects in the localization of this receptor.

As additional details emerge on these cellular pathways, they may be

incorporated into our mathematical models. Despite limitations, our cell models nicely reproduce key properties of the ankyrin-deficient cell.

It will be important, going

forward, to continue integration of these models into models of the tissue (e.g. 2- and 3dimensional models). The electrophysiological properties of the tissue are not only dependent upon ion channel properties, but also the structure of the tissue sample as demonstrated in Chapter 4 with the addition of fibrosis. It will be important to learn more about how ankyrin defects affect tissue structure and incorporate this information into our models. 6.3 Future Directions While my studies have provided insight into the link between ankyrin defects and ventricular and atrial arrhythmias, one region of the heart that I have not modeled in this

94

work is the sinoatrial node. Sinoatrial dysfunction is characterized by prolonged pauses between heartbeats and occurs in patients with heart failure and hypertension. Angiotensin II increases the levels of reactive oxygen species, in particular ox-CaMKII, causing sinoatrial node cell apoptosis. Previous work has developed a two-dimensional computational model of the intact sinoatrial node based on right atrial geometry to determine the role of the loss of cells had on sinus node dysfunction [154]. At this point, little is known about the molecular pathways that may be involved with rare genetic forms of sinus node dysfunction, including possible defects in the HCN4 pacemaker channel or ankyrins. A major area of focus of cell modeling going forward would expand the use of single channel Markov formulations of transmembrane currents. As show in Chapter 4, the use of these Markov formulations allows state specific ion channel genetic mutations to be linked to complex arrhythmia syndromes and sudden cardiac death. While the LuoRudy model uses the Hodgkin-Huxley formalism, I was able to incorporate a Markov model of the sodium current into an existing model and perform parameter estimation to create a unique formulation for a given set of genetic variants. Expanded use of Markov models of other major currents will allow for further study of genetic mutations and state specific drugs. Another future direction for mathematical modeling will address a more accurate physiological representation of intracellular calcium cycling. As shown in Chapter 1, the cardiac dyad which includes the L-type Ca2+ channels and ryanodine receptors form a local domain. Physiologically, thousands of these cardiac dyad spaces may be found in a single cell. The current method used by the models is a simplified version to allow for quick computational time. Calcium is taken up in to the network sarcoplasmic reticulum and released from the junctional sarcoplasmic reticulum. In particular for my research with ankyrin-B deficiency in the atrium and the resulting loss of the L-type Ca2+

95

channels, a cell model which addressed the heterogeneous loss of the L-type Ca2+ channel would be particularly useful. Incorporating metabolic pathways is another major area of expansion for cell modeling. Many arrhythmia syndromes result in an increased workload on the heart which requires the proper amount of energy production. By incorporating a model of mitochondrial energetics, it will allow for a better understanding of the effects of the increased workload and resulting increase in intracellular calcium will have on the production of ATP. To expand upon the work presented here, ankyrin dysfunction has been linked to a number of different excitable cell diseases. While my work has focused on the role of ankyrins in relation to heart disease, there are numerous other possibilities for mathematical modeling of ankyrin deficiency. Ankyrin-B has been shown to bind to the KATP channel in pancreatic beta cells. It is necessary for the proper localization of this channel to the plasma membrane as well as for the ability of the channel to respond to metabolic changes. Mutations that disrupt the ankyrin-B interaction with KATP channel have been shown to result in permanent neonatal diabetes mellitus [126]. Ankyrin-G is also required for the proper localization of voltage-gated sodium channels in neurons. Mutations in the ANK3 gene, which encodes ankyrin-G, have been identified in patients with bipolar disorder [155].

96

APPENDIX A MODEL EQUATIONS AND PARAMETERS FOR MOUSE VENTRICULAR CARDIOMYOCYTE A.1 Equations

Formulation is based on the model of the epicardial mouse ventricular myocyte from Bondarenko et al. [110, 156] with modifications to account for changes in ankyrin-B+/cells and/or treatment with saturating concentration of isoproterenol. I. Membrane Potential

dV = I CaL + I p ( Ca ) + I NaCa + I Cab + I Na + I Nab + I NaK + I Kto , f dt + I Kto , s + I K 1 + I Ks + I Kur + I Kss + I Kr + I Cl ,Ca + I stim −C m

II. Calcium Dynamics a. Calcium Concentration  Acap C m  d [Ca 2 + ]i = Bi  J leak + J xfer − J up − J trpn − ( I Cab − 2 I NaCa + I p ( Ca ) )  dt 2Vmyo F  

Vmyo Acap Cm   V d [Ca 2+ ]ss = Bss  J rel JSR − J xfer − I CaL  dt Vss Vss 2Vss F   d [Ca 2+ ]JSR = BJSR ( J tr − J rel ) dt V d [Ca 2+ ]NSR V = ( J up − J leak ) myo − J tr JSR dt VNSR VNSR  [CMDN ]tot K mCMDN  Bi =  1 + CMDN  (Km + [Ca 2 + ]i ) 2  

−1

97  [CMDN ] K CMDN  Bss =  1 + CMDN tot 2m+ 2  (Km + [Ca ]ss )  

BJSR

−1

 [CSQN ]tot K mCSQN  =  1 + CSQN  (Km + [Ca 2 + ]JSR ) 2  

−1

[CMDN]tot = 50 µM [CSQN]tot = 15000 µM K mCMDN = 0.238 µM K mCSQN = 800 µM

b. Calcium Fluxes

J rel = v1 ( PO1 + PO 2 )([Ca 2+ ]JSR − [Ca 2+ ]ss ) PRyR J tr =

[Ca 2+ ]NSR − [Ca 2+ ]JSR

J xfer =

τ tr [Ca 2 + ]ss − [Ca 2+ ]i

τ xfer

J leak = v2 ([Ca 2 + ]NSR − [Ca 2 + ]i )

J up = v3

[Ca 2 + ]i2 K m2 ,up + [Ca 2 + ]i2

+ − J trpn = k htrpn [Ca 2 + ]i ([ HTRPN ]tot − [ HTRPNCa ]) − k htrpn [ HTRPNCa ] + − + kltrpn [Ca 2 + ]i ([ LTRPN ]tot − [ LTRPNCa ]) − kltrpn [ LTRPNCa ]

dPRyR dt

= −0.04 PRyR − 0.1

v1 = 1.5 ms-1 v2 = 1.74 x 10-5 ms-1

I CaL I CaL ,max

e

−

V 30.0

98 v3 = 0.45 µM/ms Km,up = 0.5 µM

τtr = 20 ms τxfer = 8 ms

For isoproterenol effects: J up = 1.2 ⋅ v3 = 0.54 µM/ms

c. Ca2+ release of JSR under Ca2+-overload conditions

J rel = v1 ( PO1 + PO 2 )([Ca 2+ ]JSR − [Ca 2+ ]ss ) PRyR If buffered [CSQN ] ≥ [CSQN ]th PO1 = 0.6: Pryr = 1.0 [CSQN]th = 11.5

d. Calcium buffering d [ LTRPNCa ] + − = kltrpn [Ca 2 + ]i ([ LTRPN ]tot − [ LTRPNCa ]) − kltrpn [ LTRPNCa ] dt d [ HTRPNCa ] + − = k htrpn [Ca 2 + ]i ([ HTRPN ]tot − [ HTRPNCa ]) − k htrpn [ HTRPNCa ] dt

[LTRPN]tot= 70 µM [HTRPN]tot= 140 µM + khtrpn = 0.00237 µ M −1 /ms

k −htrpn = 3.2 ×10−5 ms −1

99 + k ltrpn = 0.0327 µM -1 /ms

− k ltrpn = 0.0196 ms −1

e. Ryanodine receptors dPO1 = ka+ [Ca 2 + ]nss PC1 − ka− PO1 − kb+ [Ca 2 + ]mss PO1 + kb− PO 2 − kc+ PO1 + kc− PC 2 dt

PC1 = 1 − ( PC 2 + PO1 + PO 2 ) dPO 2 = kb+ [Ca 2 + ]mss PO1 − kb− PO 2 dt dPC 2 = kc+ PO1 − kc− PC 2 dt k a+ = 0.006075 µM −4 /ms ka− = 0.07125 ms −1 kb+ = 0.00405 µM −3 /ms kb− = 0.965 ms −1 kc+ = 0.009 ms −1 kc− = 0.0008 ms −1

n=4 m=3

f. Calcium currents

i. L-Type Calcium Current

100 I CaL = GCaL O (V − ECa , L )

dO = α C4 − 4 β O + K pcb I1 − γ O + 0.001(α I 2 − K pcf O ) dt

C1 = 1 − (O + C2 + C3 + C4 + I1 + I 2 + I3 ) dC2 = 4α C1 − β C2 + 2 β C3 − 3α C 2 dt dC3 = 3α C2 − 2 β C3 + 3β C4 − 2α C3 dt dC4 = 2α C3 − 3β C4 + 4β O − α C4 + 0.01(4 K pcb β I1 − αγ C4 ) + 0.002(4β I 2 − K pcf C4 ) dt

+4 β K pcb I 3 − γ K pcf C4

dI1 = γ O − K pcb I1 + 0.001(α I 3 − K pcf I1 ) + 0.01(αγ C4 − 4 β K pcb I1 ) dt dI 2 = 0.001( K pcf O − α I 2 ) + K pcb I 3 − γ I 2 + 0.002( K pcf C4 − 4 β I 2 ) dt dI 3 = 0.001( K pcf I1 − α I 3 ) + γ I 2 − K pcb I 3 + γ K pcf C4 − 4 β K pcb I 3 dt

α = 0.4e(V +15)/15

β = 0.13e−(V +15)/18 γ=

K pc ,max [Ca 2+ ]ss K pc ,half + [Ca 2+ ]ss

K pc, max = 0.11662 ms-1 K pc ,half = 10 µM

K pcf = 2.5 ms-1 K pcb = 0.0005 ms-1

101 GCaL = 0.1729 mS/µF ECaL = 63 mV ICaL, max = 7 pA/pF

For isoproterenol effects:

GCaL = 2.429 ⋅ GCaL = 0.4199741 mS/µF

g. Calcium Pump Current I p ( Ca ) = I pmax ( Ca )

[Ca 2+ ]i2 K m2 , p (Ca ) + [Ca 2+ ]i2

I pmax ( Ca ) = 0.17 pA/pF K m, p (Ca ) = 0.5 µM

h. Na+/Ca2+ Exchange Current I NaCa = k NaCa

K

2 m, Na

1 1 1 + 3 2+ + [ Na ]o K m,Ca + [Ca ]o 1 + ksat e(η −1)VF / RT

(

⋅ eηVF / RT [ Na + ]3i [Ca 2+ ]o − e (η −1)VF / RT [ Na + ]3o [Ca 2 + ]i

kNaCa = 292.8 pA/pF Km,Na = 87500 µM Km,Ca = 1380 µM ksat = 0.1

η = 0.35

)

102 For ankyrin-B+/- model: kNaCa = 0.60· kNaCa,basal = 175.68 pA/pF

i. Calcium Background Current

I Cab = GCab (V − ECaN ) ECaN =

RT  [Ca 2+ ]o  ln   2 F  [Ca 2+ ]i 

GCab = 0.000165 mS/µF

III. Na+ Dynamics a. Na+ Concentration Acap Cm d [ Na + ]i = −( I Na + I Nab + 3I NaCa + 3I NaK ) dt Vmyo F

b. Fast Na+ Current

I Na = GNaONa (V − ENa ) ENa =

RT  0.9[ Na + ]o + 0.1[ K + ]o  ln   F  0.9[ Na + ]i + 0.1[ K + ]i 

CNa3 = 1 − (ONa + CNa1 + CNa 2 + IFNa + I1Na + I 2Na + ICNa 2 + ICNa3 ) dC Na 2 = α Na11C Na 3 − β Na11C Na 2 + β Na12C Na1 − α Na12C Na 2 + α Na 3 IC Na 2 − β Na 3C Na 2 dt dC Na1 = α Na12C Na 2 − β Na12C Na1 + β Na13ONa − α Na13C Na1 + α Na 3 IFNa − β Na 3C Na1 dt dONa = α Na13C Na1 − β Na13ONa + β Na 2 IFNa − α Na 2ONa dt

݀‫ܨܫ‬ே௔ = ߙே௔ଶ ܱே௔ − ߚே௔ଶ ‫ܨܫ‬ே௔ + ߚே௔ଷ ‫ܥ‬ே௔ଵ − ߙே௔ଷ ‫ܨܫ‬ே௔ ݀‫ݐ‬

103 +ߚே௔ସ ‫ܫ‬1ே௔ − ߙே௔ସ ‫ܨܫ‬ே௔ + ߙே௔ଵଶ ‫ܥܫ‬ே௔ଶ − ߚே௔ଵଶ ‫ܨܫ‬ே௔

dI 1Na = α Na 4 IFNa − β Na 4 I 1Na + β Na 5 I 2 Na − α Na 5 I 1Na dt dI 2 Na = α Na 5 I 1Na − β Na 5 I 2 Na dt dIC Na 2 = α Na11 IC Na 3 − β Na11 IC Na 2 + β Na12 IFNa − α Na12 IC Na 2 dt

+ β Na 3CNa 2 − α Na 3C Na 2 dIC Na 3 = β Na11 IC Na 2 − α Na11 IC Na 3 + β Na 3C Na 3 − α Na 3 IC Na 3 dt

α Na11 = α Na12 = α Na13 =

0.1027e

3.802 + 0.2e − (V + 2.5)/150

− (V + 2.5)/17

3.802 + 0.23e − (V + 2.5)/150

0.1027e

− (V + 2.5)/15

0.1027e

− (V + 2.5)/12

3.802 + 0.25e − (V + 2.5)/150

β Na11 = 0.1917e − (V + 2.5)/20.3 β Na12 = 0.20e − (V − 2.5)/ 20.3 β Na13 = 0.22e − (V −7.5)/ 20.3 α Na 3 = 7.0 × 10−7 e − (V + 7)/7.7

β Na3 = 0.0084 + 0.00002(V + 7.0) α Na 2 =

1 0.188495e

− (V + 7)/16.6

+ 0.393956

β Na 2 = α Na13α Na 2α Na3 / β Na13 β Na 3

104

α Na 4 = α Na 2 /1000 β Na 4 = α Na3 α Na5 = α Na 2 / 95000 β Na 5 = α Na3 / 50 GNa = 13 mS/µF

c. Background Na+ Current

I Nab = GNab (V − ENa ) GNab = 0.0026 mS/µF

d. Nonspecific Ca2+-activated current I ns , K = I ns , K ⋅

1

(

1 + K m ,ns ( Ca ) / [Ca 2 + ]i

I ns , Na = I ns , Na ⋅

)

3

1

(

1 + K m , ns ( Ca ) / [Ca 2 + ]i

)

3

I ns ,(Ca ) = I ns , K + I ns , Na

Pns ( Ca ) = 1.75 ×10−7 cm/s ; K m , ns (Ca ) = 1.2 µ mol/L Ens ( Ca ) =

 [ K + ] + [ Na + ]o  RT ⋅ ln  + o  + F  [ K ]i + [ Na ]i 

IV. K+ Dynamics a. K+ Concentration

105 Acap Cm d [ K + ]i = −( I Kto , f + I Kto , s + I K 1 + I Ks + I Kss + I Kur + I Kr − 2 I NaK ) dt Vmyo F

b. Transient Outward K+ Current IKto,f

I Kto , f = GKto, f α to3 , f ito, f (V − EK ) EK =

1 α a + βa

τa =

a∞ =

τi =

i∞ =

RT  [ K + ]o  ln   F  [ K + ]i 

αa α a + βa

1 αi + βi

αi α i + βi

α a = 0.18064e 0.03577(V + 30) β a = 0.3956e −0.06237(V + 30) 0.000152e − (V +13.5)/7 αi = 0.067083e − (V +33.5)/7 + 1

βi =

0.00095e(V +33.5)/7 0.051335e (V + 33.5)/7 + 1

GKto,f = 0.3362 mS/µF

c. Transient Outward K+ current IKto,s I Kto , s = 0

106

d. Time-independent K+ current

 [ K + ]o   V − EK  I K 1 = 0.2938  +  0.0896(V − EK )    [ K ]o + 210   1 + e

e. Slow delayed rectifier K+ current 2 I Ks = GKs nKs (V − EK )

nKs∞ =

τn = Ks

αn =

αn α n + βn

1 αn + βn

0.00000481333(V + 26.5) 1 − e −0.128(V + 26.5)

β n = 0.0000953333e −0.038(V + 26.5) GKs = 0.00575 mS/µF

For isoproterenol effects: GKs = 1.8 ⋅ GKs ,basal = 0.01035 mS/µF

f. Ultrarapidly activating delayed rectifier K+ current

I Kur = GKur aur iur (V − EK ) daur ass − aur = dt τ aur

107 diur iss − iur = dt τ iur

τ aur = 0.493e −0.0629V + 2.058

τ iur = 1200 −

170 1+ e

(V + 45.2)/5.7

GKur = 0.2056 mS/µF

g. Noninactivating steady-state K+ current

I Kss = GKss aKss iKss (V − EK ) daKss ass − aKss = dt τ Kss diKss =0 dt

τ Kss = 39.3e −0.0862V + 13.17 GKss = 0.0491 mS/µF

h. Rapid delayed rectifier K+ current  RT  0.98[ K + ]o + 0.02[ Na + ]o I Kr = Ok GKr V − ln  + + F  0.98[ K ]i + 0.02[ Na ]i 

CK 0 = 1 − (CK 1 + CK 2 + OK + I K ) dCK 1 = α a 0 C K 0 − β a 0C K 1 + kb C K 2 − k f C K 1 dt dCK 2 = k f C K 1 − kbC K 2 + β a1OK − α a1CK 2 dt

   

108 dOK = α a1C K 2 − β a1OK + β i I K − α i OK dt dI K = α i OK − β i I K dt

α a 0 = 0.022348e 0.01176V β a 0 = 0.047002e −0.0631V α a1 = 0.013733e 0.038198V β a1 = 0.0000689e −0.04178V α i = 0.090821e0.023391(V + 5) β i = 0.006497e −0.03268(V +5) GKr = 0.078 ms/µF kf = 0.023761 ms-1 kb = 0.036778 ms-1

i. Na+/K+ Pump Current max I NaK = I NaK f NaK

f NaK =

[ K + ]o 1 1 + ( K m , Nai / [ Na + ]i )3/ 2 [ K + ]o + K m , Ko 1

1 + 0.1245e

σ = 1/ 7(e[ Na

+

−0.1VF / RT

]o /67300

max I NaK = 0.88 pA/pF

Km,Nai = 21000 µM Km,Ko = 1500 µM

− 1)

+ 0.0365σ e −VF / RT

109

For ankyrin-B+/- model: max I NaK = 0.66 pA/pF

For isoproterenol effects: max max I NaK = 1.4 ⋅ I NaK ,basal

j. Ca2+-Activated Cl- Current I Cl ,Ca = GCl ,Ca OCl ,Ca

OCl ,Ca =

[Ca 2+ ]i (V − ECl ) [Ca 2 + ]i + K m ,Cl

0.2 1+ e

− (V − 46.7)/7.8

GCl,Ca = 10 mS/µF Km,Cl = 10 µM ECl = -40 mV

A.2 Definitions and abbreviations

kNaCa

Scaling factor of Na+/Ca2+ exchange

Km,Na

Na+ half-saturation constant for Na+/Ca2+ exchange

Km,Ca

Ca2+ half-saturation constant for Na+/Ca2+ exchange

ksat

Na+/Ca2+ exchange saturation factor at very negative potentials

η

Controls voltage dependence of Na+/Ca2+ exchange

I max NaK

Maximum Na+/K+ exchange current

Km,Nai

Na+ half-saturation constant for Na+/K+ exchange current

110 Km,Ko

K+ half-saturation constant for Na+/K+ exchange current

I max p(Ca)

Maximum Ca2+ pump current

Km,p(Ca)

Ca2+ half-saturation constant for Ca2+ pump current

Gi

Maximum conductance of channel i

kf

Rate constant for rapid delayed-rectifier K+ current

kb

Rate constant for rapid delayed-rectifier K+ current

GCl,Ca

Maximum Ca2+-activated Cl- current conductance

Km,Cl

Half-saturation constant for Ca2+-activated Cl- current

ECl

Reversal potential for Ca2+-activated Cl- current

v1

Maximum RyR channel Ca2+ permeability

v2

Ca2+ leak rate constant from the NSR

v3

SR Ca2+-ATPase maximum pump rate

Km,up

Half-saturation constant for SR Ca2+-ATPase pump

τtr

Time constant for transfer from NSR to JSR

τxfer

Time constant for transfer from subspace to myoplasm

k +a

RyR PC1- PO1 rate constant

k −a

RyR PO1- PC1 rate constant

k b+

RyR PO1- PO2 rate constant

k b−

RyR PO2- PO1 rate constant

k c+

RyR PO1- PC2 rate constant

k c−

RyR PC2- PO1 rate constant

n

RyR Ca2+ cooperativity parameter PC1- PO1

111 m

RyR Ca2+ cooperativity parameter PO1- PO2

GCaL

Specific maximum conductivity for L-type Ca2+ channel

ECa,L

Reversal potential for L-type Ca2+ channel

Kpc,max

Maximum time constant for Ca2+-induced inactivation

Kpc,half

Half-saturation constant for Ca2+-induced inactivation

Kpcb

Voltage-insensitive rate constant for inactivation

ICaL,max

Normalization constant for L-type Ca2+ current

[LTRPN]tot

Total myoplasmic troponin low-affinity site concentration

[HTRPN]tot

Total myoplasmic troponin high-affinity site concentration

k +htrpn

Ca2+ on rate constant for troponin high-affinity sites

k −htrpn

Ca2+ off rate constant for troponin high-affinity sites

+ k ltrpn

Ca2+ on rate constant for troponin low-affinity sites

− k ltrpn

Ca2+ off rate constant for troponin low-affinity sites

[CMDN]tot

Total myoplasmic calmodulin concentration

[CSQN]tot

Total junctional SR calsequestrin concentration

K CMDN m

Ca2+ half-saturation constant for calmodulin

K CSQN m

Ca2+ half-saturation constant for calsequestrin

112 Table A.1: Parameters for Mouse Ventricular Cell Model Parameter

Definition

Value

Acap Vmyo VJSR VNSR Vss [K+]o [Na+]o [Ca2+]o Cm F T R

Capacitive membrane area Myoplasmic volume Junctional SR volume Network SR volume Subspace volume Extracellular K+ concentration Extracellular Na+ concentration Extracellular Ca2+ concentration Specific membrane capacitance Faraday constant Absolute temperature Ideal gas constant

1.534 x 10-4 cm2 25.84 x 10-6 µl 0.12 x 10-6 µl 2.098 x 10-6 µl 1.485 x 10-9 µl 5400 µM 140000 µM 1800 µM 1.0 µF/cm2 96.5 C/mmol 298 K 8.314 Jmol-1K-1

113

APPENDIX B MODEL EQUATIONS AND PARAMETERS FOR HUMAN VENTRICULAR CARDIOMYOCYTE B.1 Equations

Formulation is based on the model of the human ventricular myocyte from Ten Tusscher et al. [112] with modifications to account for changes in ankyrin-B+/- cells and/or treatment with saturating concentration of isoproterenol.

I. Membrane Potential

−C m

dV = I Na + I K 1 + I to + I Kr + I Ks + I CaL + I NaCa + I NaK dt + I pCa + I pK + I bCa + I bNa + I stim

II. Reversal Potentials EX =

X RT log o for X=Na+, K+, Ca2+ zF Xi

EKs =

K + pKNa Nao RT log o K i + pKNa Nai F

III. Fast Na+ Current I Na = GNa m 3 hj (V − ENa ) m∞ =

αm =

1

(1 + e

( −56.86 −V )/9.03 2

1 1+ e

( −60 −V )/5

)

114

βm =

0.1 0.1 + (V + 35)/5 (V − 50)/ 200 1+ e 1+ e

τ m = α m βm h∞ =

1

(1 + e

(V + 71.55)/7.43 2

)

α h = 0 if V ≥ −40 α h = 0.057e − (V +80)/6.8

βh =

0.77 if V ≥ −40 0.13 1 + e − (V +10.66)/11.1

(

)

β h = 2.7e 0.079V + 3.1× 105 e 0.3485V otherwise

τh =

j∞ =

1 α h + βh 1

(1 + e

(V + 71.55)/7.43 2

)

α j = 0 if V ≥ −40

( −2.5428 ×10 e =

4 0.2444V

αj

− 6.948 ×10−6 e −0.04391V

1 + e0.311(V + 79.23)

βj =

0.6e 0.057V if V ≥ −40 1 + e −0.1(V + 32)

βj =

0.02424e −0.01052V otherwise 1 + e −0.1378(V + 40.14)

τj =

1 αj +βj

GNa = 14.838 nS/pF

) (V + 37.78) otherwise

115

IV. L-type Ca2+ Current I CaL

VF 2 Cai e 2VF / RT − 0.341Cao = GCaL dff Ca 4 RT e 2VF / RT − 1

d∞ =

αd =

βd =

γd =

1 1+ e

( −5 −V )/7.5

1.4

+ 0.25

1 + e( −35−V )/13 1.4 1 + e (V + 5)/5 1 1+ e

(50 −V )/20

τ d = αd βd + γ d f∞ =

1 1+ e

(V + 20)/7

τ f = 1125e − (V + 27)

α fca =

β fca =

γ fca =

f ca∞ =

2

/ 240

+

165 + 80 1 + e (25−V )/10

1 8

1 + ( Cai / 0.000325 ) 0.1 1+ e

( Cai − 0.0005)/0.0001

0.2 1+ e

( Cai − 0.00075)/0.0008

α fca + β fca + γ fca + 0.23 1.46

τ fca = 2 ms df ca f −f = k ca∞ ca dt τ fca

116

k = 0 if f ca∞ > fca and V > −60 mV k = 1 otherwise GCaL = 1.75-4 cm3µF-1s-1

For isoproterenol effects: GCaL = 2.429 ⋅ GCaL ,basal

V. Transient Outward Current

Ito = Gto rs(V − EK ) r∞ =

1 1+ e

(20 −V )/6

τ r = 9.5e− (V + 40) s∞ =

2

/1800

+ 0.8

1 1+ e

(V + 20)/5

τ s = 85e− (V + 45)

2

/320

+

5 1+ e

(V − 20)/5

+3

Gto = 0.294 nS/pF

VI. Slow Delayed Rectifier Current I Ks = GKs xs2 (V − EKs )

xs ∞ =

α xs =

1 1+ e

( −5 −V )/14

1100 1 + e( −10−V )/6

117

β xs =

1 1+ e

(V − 60)/ 20

τ xs = α xs β xs GKs = 0.245 nS/pF pKNa = 0.03

For isoproterenol effects: GKs = 1.8 ⋅ GKs ,basal = 0.441 mS/µF

VII. Rapid Delayed Rectifier Current

Ko xr1 xr 2 (V − EK ) 5.4

I Kr = GKr

xr1∞ =

α xr1 = β xr1 =

1 1+ e

( −26 −V ) /7

450 1 + e ( −45−V )/10 6 1+ e

(V + 30 )/11.5

τ xr1 = α xr1β xr1 xr 2 ∞ =

α xr 2 = β xr 2 =

1 1+ e

(V + 88 ) / 24

3 1+ e

( −60 −V )/ 20

1.12 1 + e(V − 60) / 20

τ xr 2 = α xr 2 β xr 2

118 GKr = 0.096 nS/pF

VIII. Inward Rectifier K+ Current

I K 1 = GK 1

α K1 =

β K1 =

Ko xK 1∞ (V − EK ) 5.4 0.1

1+ e

0.06(V − EK − 200)

3e0.0002(V − EK +100) + e0.1(V − EK −10) 1 + e −0.5(V − EK )

xK 1∞ =

α K1 α K1 + β K1

GK1 = 5.405 nS/pF

IX. Na+/Ca2+ Exchanger Current I NaCa = k NaCa

eγ VF / RT Nai3Cao − e (γ −1)VF / RT Nao3Caiα 3 ( K mNai + Nao3 )( K mCa + Cao )(1 + k sat e (γ −1)VF / RT )

kNaCa = 1000 pA/pF

γ = 0.35 KmCa = 1.38 mM KmNai = 87.5 mM ksat = 0.1

α = 2.5

For ankyrin-B+/- model: kNaCa = 0.60· kNaCa,basal = 600pA/pF

119

X. Na+/K+ Current I NaK = PNaK

K o Nai ( K o + K mK )( Nai + K mNa )(1 + 0.1245e −0.1VF / RT + 0.0353e −VF / RT )

PNaK = 1.362 pA/pF KmK = 1 mM KmNa = 40 mM

For ankyrin-B+/- model: PNaK = 0.75· PNaK,basal = 1.0215

For isoproterenol effects: PNaK = 1.4· PNaK,basal

XI. IpCa

I pCa = G pCa

Cai K pCa + Cai

GpCa = 0.025 nS/pF KpCa = 0.0005 mM

XII. IpK I pK = G pK

V − EK 1 + e (25−V )/5.98

GpK = 0.0146 nS/pF

120

XIII. Background Currents

IbNa = GbNa (V − ENa ) IbCa = GbCa (V − ECa ) GbNa = 0.00029 nS/pF GbCa = 0.000592 nS/pF

XIV. Calcium Dynamics

I leak = Vleak (Casr − Cai ) Vleak = 0.00008 ms-1 I up =

Vmaxup 1 + K up2 / Cai2

Vmaxup = 0.000425 mM/ms Kup = 0.00025 mM

For isoproterenol effects: Vmaxup = 1.2·Vmaxup,basal = 0.00051

I rel

  Casr2 =  arel 2 + crel  dg 2 brel + Casr  

arel = 16.464 mM/s brel = 0.25 mM crel = 8.232 mM/s

121

g∞ =

1 if Cai ≤ 0.00035 1 + Ca / 0.000356

g∞ =

1 otherwise 1 + Ca / 0.0003516

6 i

16 i

τ s = 2 ms dg g −g =k ∞ dt τg

k = 0 if g∞ > g and V > −60 mV k = 1 otherwise Caibufc =

Cai × Buf c Cai + K bufc

I CaL + I bCa + I pCa − 2 I NaCa dCaitotal =− + I leak − I up + I rel dt 2VC F Bufc = 0.15 mM Kbufc = 0.001 mM

Casrbufsr =

Casr × Buf sr Casr + K bufsr

dCasrtotal VC = ( − I leak + I up − I rel ) dt VSR

Bufsr = 10 mM Kbufsr = 0.3 mM

Ca2+ release of JSR under Ca2+-overload conditions

  Ca 2 I rel =  arel 2 sr 2 + crel  dg brel + Casr  

122 If buffered Casrbufsr ≥ [CSQN ]th , τg = 5.0; [CSQN ]th = 9

XV. Sodium and Potassium Dynamics dNai I + I + 3I NaK + 3I NaCa = − Na bNa dt VC F

I K 1 + I to + I Kr + I Ks − 2 I NaK + I pK + I stim − I ax dK i =− dt VC F

B.2 Definitions and Abbreviations

Gi

Maximum conductance of channel i

kNaCa

Maximal INaCa

γ

Voltage dependent parameter of INaCa

KmCa

Cai half-saturation constant for INaCa

KmNai

Nai half-saturation constant for INaCa

ksat

Saturation factor for INaCa

α

Factor enhancing outward nature of INaCa

pKNa

Relative IKs permeability to Na+

PNaK

Maximal INaK

KmK

Ko half-saturation constant of INaK

KmNa

Nai half-saturation constant of INaK

KpCa

Cai half-saturation constant of INaK

Vmaxup

Maximal Iup

Kup

Half-saturation constant of Iup

arel

Maximal CaSR-dependent Irel

123

brel

CaSR half-saturation constant of Irel

crel

Maximal CaSR-independent Irel

Vleak

Maximal Ileak

Bufc

Total cytoplasmic buffer concentration

Kbufc

Cai half-saturation constant for cytoplasmic buffer

Bufsr

Total sarcoplasmic buffer concentration

Kbufsr

CaSR half-saturation constant for sarcoplasmic buffer

Table B.1: Parameters for Mouse Human Ventricular Cell Model Parameter VC VSR Ko Nao Cao Cm F T R S ρ

Definition Cytoplasmic volume Sarcoplasmic reticulum volume Extracellular K+ concentration Extracellular Na+ concentration Extracellular Ca2+ concentration Cell capacitance per unit surface area Faraday constant Temperature Ideal gas constant Surface-to-volume ratio Cellular resistivity

Value 16404 µm3 1094 µm3 5.4 mM 140 mM 2 mM 2.0 µF/cm2 96.5 C/mmol 310 K 8.314 Jmol-1K-1 0.2 µm-1 162 Ωcm

124

APPENDIX C GLOSSARY Action potential – a change in voltage measured on the cell membrane that precedes contraction Action potential duration adaptation – shortening of action potential duration as pacing frequency increases Adenosine triphosphate (ATP) – main source of energy for cellular reactions Afterdepolarization – abnormal depolarization of cardiomyocytes interrupting phase 2, phase 3, or phase 4 of the action potential Arrhythmia – Abnormal rhythm of the heart, either too slow or too fast, which may sometimes lead to sudden cardiac death Bradycardia – A resting heart rate under 60 beats per minute in humans Brugada syndrome – Genetic disease due to loss of function mutation in SCN5A gene leading to a loss of the action potential dome of some epicardial areas of the right ventricle resulting in transmural and epicardial dispersion of repolarization characterized by unique EKG abnormality and sudden cardiac death Calcium-calmodulin-dependent protein kinase II (CaMKII) – protein kinase activated by calcium calmodulin involved in many cellular functions Calcium transient – Increase in intracellular calcium during the cardiac action potential necessary for cardiomyocyte contraction Cardiac glycoside – drug used to treat congestive heart failure and cardiac arrhythmia to increase cardiac output by increasing the force of contraction through an increase in calcium-induced calcium release Catecholaminergic Polymorphic Ventricular Tachycardia (CPVT) – is a genetic disorder caused by mutations in the calcium handling proteins in the cardiac cells

125

rendering them hypersensitive to normal levels of catecholamine leading to activity induced arrhythmias, syncope or sudden cardiac death Coronary Heart Disease – A narrowing of the blood vessels that supply blood and oxygen to the heart. Desmosome – a cell structure specialized for cell-to-cell adhesion Diastole – the period of time the heart is relaxed Digitalis – A cardiac glycoside prescribed to treat heart patients Long QT Syndrome – A rare inherited heart condition resulting in delayed repolarization of the heart Nernst potential - the membrane potential at which there is no net flow a particular ion from one side of the membrane to the other Phospholamban – Protein which inhibits SERCA while in the unphosphorylated state. Romano Ward Syndrome – is a type of long QT syndrome Ryanodine receptors – calcium release channel located on the sarcoplasmic reticulum involved in calcium-induced calcium release SERCA – Ca2+-ATPase located in the SR which transfers Ca2+ from the cytosol into the SR Sinus arrest – the sinoatrial node fails to generate the electrical impulse needed for heart contraction Syncope – loss of consciousness and postural tone Tachyarrhythmia – An arrhythmia characterized by a rapid heartbeat Torsades de pointes – A rare form of ventricular tachycardia associated with long QT syndrome. Tropomyosin – protein attached to thin filament of muscle involved in regulating the attachment of myosin cross bridges to actin for excitation-contraction coupling Troponin – protein found in the thin filaments of muscle which binds to calcium causing tropomyosin to change position

126

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