Cardiac Cells (click here for review article)

The cornerstone tool in the lab is the cardiac ventricular action potential (AP) model, containing mechanistically based, detailed models of ionic currents and Ca 2+ handling processes. We continually refine our models to incorporate new experimental findings. Ionic current models can be incorporated in a modular fashion in the whole-cell model. The ventricular AP model can be incorporated into multicelluar tissue models to study basic mechanisms of conduction and cardiac arrhythmia.

At present, we have published numerous studies on basic mechanisms of excitation, repolarization, and rate dependent behavior as they relate to arrhythmogenesis using the Luo-Rudy dynamic (LRd) and Hund-Rudy dynamic (HRd) ventricular AP models (see Publications). These models were constructed to reflect guinea-pig and canine electrophysiology, respectively. A third model, specific to normal human ventricular electrophysiology, is currently being developed in our lab.

Recent Ion Channel Publications (Below)

All Models and Simulations Publications

Decker KF, Heijman J, Silva JR, Hund TJ, Rudy Y. Properties and Ionic Mechanisms of Action Potential Adaptation, Restitution and Accommodation in Canine Epicardium. Am J Physiol Heart Circ Physiol . 2009 Apr;296(4):H1017-26. Epub 2009 Jan 23.

Computational models of cardiac myocytes are important tools for understanding ionic mechanisms of arrhythmia. This work presents a new model of the canine epicardial myocyte that reproduces a wide range of experimentally observed rate dependent behaviors in cardiac cell and tissue, including action potential duration (APD) adaptation, restitution and accommodation. Model behavior depends on updated formulations for the 4-AP sensitive transient outward current (Ito1), the slow component of the delayed rectifier potassium current (IKs), the L-type Ca2+ channel (ICa,L) and the sodium-potassium pump (INaK) fit to data from canine ventricular myocytes. We find that Ito1 plays a limited role in potentiating peak ICa,L and sarcoplasmic reticulum Ca2+ release for propagated APs, but modulates the time course of APD restitution. IKs plays an important role in APD shortening at short diastolic intervals, despite a limited role in AP repolarization at longer cycle lengths. In addition, we find that ICa,L plays a critical role in APD accommodation and rate dependence of APD restitution through its indirect role in intracellular Na+ accumulation and increased outward INaK at rapid heart rates. Our simulation results provide valuable insight into the mechanistic basis of rate-dependent phenomena important for determining the heart's response to rapid and irregular pacing rates (e.g. arrhythmia). Accurate simulation of rate dependent phenomena and increased understanding of their mechanistic basis will lead to more realistic multicellular simulations of arrhythmia and identification of molecular therapeutic targets.

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Rudy Y, Ackerman MJ, Bers DM, Clancy CE, Houser SR, London B, McCulloch AD, Przywara DA, Rasmusson RL, Solaro RJ, Trayanova NA, Van Wagoner DR, Varró A, Weiss JN, Lathrop DA.Systems approach to understanding electromechanical activity in the human heart: a national heart, lung, and blood institute workshop summary. Circulation . 2008 Sep 9;118(11):1202-11.

The National Heart, Lung, and Blood Institute (NHLBI) convened a workshop of cardiologists, cardiac electrophysiologists, cell biophysicists, and computational modelers on August 20 and 21, 2007, in Washington, DC, to advise the NHLBI on new research directions needed to develop integrative approaches to elucidate human cardiac function. The workshop strove to identify limitations in the use of data from nonhuman animal species for elucidation of human electromechanical function/activity and to identify what specific information on ion channel kinetics, calcium handling, and dynamic changes in the intracellular/extracellular milieu is needed from human cardiac tissues to develop more robust computational models of human cardiac electromechanical activity. This article summarizes the workshop discussions and recommendations on the following topics: (1) limitations of animal models and differences from human electrophysiology, (2) modeling ion channel structure/function in the context of whole-cell electrophysiology, (3) excitation-contraction coupling and regulatory pathways, (4) whole-heart simulations of human electromechanical activity, and (5) what human data are currently needed and how to obtain them. The recommendations can be found on the NHLBI Web site at

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Hund TJ, Decker KF, Kanter E, Mohler PJ, Boyden PA, Schuessler RB, Yamada KA, Rudy Y. Role of activated CaMKII in abnormal calcium homeostasis and I(Na) remodeling after myocardial infarction: Insights from mathematical modeling. J Mol Cell Cardiol . 2008 Jun 28. [Epub ahead of print]

Ca2+/calmodulin-dependent protein kinase II is a multifunctional serine/threonine kinase with diverse cardiac roles including regulation of excitation contraction, transcription, and apoptosis. Dynamic regulation of CaMKII activity occurs in cardiac disease and is linked to specific disease phenotypes through its effects on ion channels, transporters, transcription and cell death pathways. Recent mathematical models of the cardiomyocyte have incorporated limited elements of CaMKII signaling to advance our understanding of how CaMKII regulates cardiac contractility and excitability. Given the importance of CaMKII in cardiac disease, it is imperative that computer models evolve to capture the dynamic range of CaMKII activity. In this study, using mathematical modeling combined with biochemical and imaging techniques, we test the hypothesis that CaMKII signaling in the canine infarct border zone (BZ) contributes to impaired calcium homeostasis and electrical remodeling. We report that the level of CaMKII autophosphorylation is significantly increased in the BZ region. Computer simulations using an updated mathematical model of CaMKII signaling reproduce abnormal Ca2+ transients and action potentials characteristic of the BZ. Our simulations show that CaMKII hyperactivity contributes to abnormal Ca2+ homeostasis and reduced action potential upstroke velocity due to effects on I(Na) gating kinetics. In conclusion, we present a new mathematical tool for studying effects of CaMKII signaling on cardiac excitability and contractility over a dynamic range of kinase activities. Our experimental and theoretical findings establish abnormal CaMKII signaling as an important component of remodeling in the canine BZ.

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Faber GM, Rudy Y. Calsequestrin mutation and catecholaminergic polymorphic ventricular tachycardia: A simulation study of cellular mechanism. Cardiovasc Res . 2007 Jul 1;75(1):79-88.

OBJECTIVES: Patients with a missense mutation of the calsequestrin 2 gene (CASQ2) are at risk for catecholaminergic polymorphic ventricular tachycardia. In this theoretical study, we investigate a potential mechanism by which CASQ2(D307H) manifests its pro-arrhythmic consequences in patients. METHODS: Using simulations in a model of the guinea pig ventricular myocyte, we investigate the mutation's effect on SR Ca2+ storage, the Ca2+ transient (CaT), and its indirect effect on ionic currents and membrane potential. We model the effects of isoproterenol (ISO) on Ca(V)1.2 (the L-type Ca2+ current, I(Ca(L))) and other targets of beta-adrenergic stimulation. RESULTS: CASQ2(D307H) reduces SR storage capacity, thereby reducing the magnitude of CaT (Control: 0.79 muM, CASQ2(D307H): 0.52 muM, at cycle length of 1500 ms). The combined effect of CASQ2(D307H) and ISO elevates SR free Ca2+ at a rapid rate, leading to store-overload-induced Ca2+ release and delayed afterdepolarization (DAD). If resting membrane potential is sufficiently elevated, the Na+-Ca2+ exchange-driven DAD can trigger INa and ICa(L) activation, generating a triggered arrhythmogenic AP. CONCLUSIONS: The CASQ2(D307H) mutation manifests its pro-arrhythmic consequences due to store-overload-induced Ca(2+) release and DAD formation due to excess free SR Ca2+ following rapid pacing and beta-adrenergic stimulation.

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Faber G, Silva J, Livshitz L, and Rudy Y. Kinetic Properties of the Cardiac L-type Ca Channel and its Role in Myocyte Electrophysiology: A Theoretical Investigation. Biophys. J. published 8 December 2006

L-Type Model Code

A new, detailed kinetic model of CaV1.2 which is incorporated into a model of the ventricular mycoyte where it interacts with a kinetic model of the ryanodine receptor (RyR) in a restricted subcellular space. We evaluation the contribution of voltagedependent inactivation (VDI) and Ca2+-dependent inactivation (CDI) to total inactivation of CaV1.2. and describe the dynamic CaV1.2 and RyR channel-state occupancy during the AP. Results: 1.) The CaV1.2 model reproduces experimental single-channel and macroscopic-current data. 2.) The model reproduces rate dependence of APD, [Na+]i, and the Ca2+-transient (CaT), and restitution of APD and CaT during premature stimuli. 3.) CDI of CaV1.2 is sensitive to Ca2+ that enters the subspace through the channel and from SR release. The relative contributions of these Ca2+ sources to total CDI during the AP vary with time after depolarization, switching from early SR dominance to late CaV1.2 dominance. 4.) The relative contribution of CDI to total inactivation of CaV1.2 is greater at negative potentials, when VDI is weak. 5.) Loss of VDI due to the CaV1.2 mutation G406R (linked to the Timothy syndrome) results in APD prolongation and increased CaT.

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Livshitz LM, Rudy Y. Regulation of Ca2+ and electrical alternans in cardiac myocytes: Role of CaMKII and repolarizing currents Am J Physiol Heart Circ Physiol . 2007 Jun;292(6):H2854-66

Matlab code available: LRd07 (click here) and HRd07 (click here)

Alternans of cardiac repolarization is associated with arrhythmias and sudden death. At the cellular level, alternans involves beat-to-beat oscillation of the action potential (AP) and possibly Ca2+ transient (CaT). Because of experimental difficulty in independently controlling the Ca2+ and electrical subsystems, mathematical modelling provides additional insights into mechanisms and causality. Pacing protocols were conducted in a canine ventricular myocyte model with the following results: (I) CaT alternans results from refractoriness of the SR Ca2+ release system; alternation of the L-type Ca2+ current (ICa(L)) has a negligible effect; (II) CaT-AP coupling during late AP occurs through the Na+/Ca2+ exchanger (INaCa) and underlies APD alternans; (III) Increased Ca2+/calmodulin-dependent protein kinase II (CaMKII) activity extends the range of CaT and APD alternans to slower frequencies and increases alternans magnitude; its decrease suppresses CaT and APD alternans, exerting an antiarrhythmic effect; (IV). Increase of the rapid delayed rectifier current (IKr) also suppresses APD alternans, but without suppressing CaT alternans. Thus, CaMKII inhibition eliminates APD alternans by eliminating its cause (CaT alternans), while IKr enhancement does so by weakening CaT-APD coupling. The simulations identify combined CaMKII inhibition and IKr enhancement as a possible antiarrhythmic intervention.

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Rudy Y, Silva JR. Computational biology in the study of cardiac ion channels and cell electrophysiology.
Q Rev Biophys. 2006 Feb;39(1):57-116

Ion channels are typically studied in isolation (in expression systems or isolated membrane patches), away from the physiological environment of the cell where they interact to generate the AP. A major challenge remains the integration of ion-channel properties into the functioning, complex and highly interactive cell system, with the objective to relate molecular-level processes and their modification by disease to whole-cell function and clinical phenotype. In this article we describe how computational biology can be used to achieve such integration. We explain how mathematical (Markov) models of ion-channel kinetics are incorporated into integrated models of cardiac cells to compute the AP. We provide examples of mathematical (computer) simulations of physiological and pathological phenomena, including AP adaptation to changes in heart rate, genetic mutations in SCN5A and HERG genes that are associated with fatal cardiac arrhythmias, and effects of the CaMKII regulatory pathway and β-adrenergic cascade on the cell electrophysiological function.

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Hund TJ, Rudy Y. A role for calcium/calmodulin-dependent protein kinase II in cardiac disease and arrhythmia.
Handb Exp Pharmacol . 2006;(171):201-20. Review.

More than 20 years have passed since the discovery that a collection of specific calcium/calmodulin-dependent phosphorylation events is the result of a single multifunctional kinase. Since that time, we have learned a great deal about this multifunctional and ubiquitous kinase, known today as calcium/calmodulin-dependent protein kinase II (CaMKII). CaMKII is interesting not only for its widespread distribution and broad specificity but also for its biophysical properties, most notably its activation by the critical second messenger complex calcium/calmodulin and its autophosphorylating capability. A central role for CaMKII has been identified in regulating a diverse array of fundamental cellular activities. Furthermore, altered CaMKII activity profoundly impacts function in the brain and heart. Recent findings that CaMKII expression in the heart changes during hypertrophy, heart failure, myocardial ischemia, and infarction suggest that CaMKII may be a viable therapeutic target for patients suffering from common forms of heart disease.

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Silva, J. and Y. Rudy (2005). "Subunit interaction determines IKs participation in cardiac repolarization and repolarization reserve." Circulation 112(10): 1384-91.

IKs Model Details and Matlab Code

IKr Model Details and Matlab Code

The role of IKs, the slow delayed rectifier K+ current, in cardiac ventricular repolarization has been a subject of debate. We develop a detailed Markov model of IKs and its ß-subunit KCNQ1 and examine their kinetic properties during the cardiac ventricular action potential at different rates. We observe that interaction between KCNQ1 and KCNE1 (the ß-subunit) confers kinetic properties on IKs that make it suitable for participation in action potential repolarization and its adaptation to rate changes; in particular, the channel develops an available reserve of closed states near the open state that can open rapidly on demand. Because of its ability to form an available reserve, IKs can function as a repolarization reserve when IKr, the rapid delayed rectifier, is reduced by disease or drug and can prevent excessive action potential prolongation and development of arrhythmogenic early afterdepolarizations.

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Hund TJ, Rudy Y. Rate dependence and regulation of action potential and calcium transient in a canine cardiac ventricular cell model. Circulation . 2004 Nov 16;110(20):3168-74.

BACKGROUND: Computational biology is a powerful tool for elucidating arrhythmogenic mechanisms at the cellular level, where complex interactions between ionic processes determine behavior. A novel theoretical model of the canine ventricular epicardial action potential and calcium cycling was developed and used to investigate ionic mechanisms underlying Ca2+ transient (CaT) and action potential duration (APD) rate dependence. METHODS AND RESULTS: The Ca2+/calmodulin-dependent protein kinase (CaMKII) regulatory pathway was integrated into the model, which included a novel Ca2+-release formulation, Ca2+ subspace, dynamic chloride handling, and formulations for major ion currents based on canine ventricular data. Decreasing pacing cycle length from 8000 to 300 ms shortened APD primarily because of I(Ca(L)) reduction, with additional contributions from I(to1), I(NaK), and late I(Na). CaT amplitude increased as cycle length decreased from 8000 to 500 ms. This positive rate-dependent property depended on CaMKII activity. CONCLUSIONS: CaMKII is an important determinant of the rate dependence of CaT but not of APD, which depends on ion-channel kinetics. The model of CaMKII regulation may serve as a paradigm for modeling effects of other regulatory pathways on cell function.

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