Brief Summary of Publications (for full text, click on titles)

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Review Article: 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

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Sale H, Wang J, O'Hara TJ, Tester DJ, Phartiyal P, He JQ, Rudy Y, Ackerman MJ, Robertson GA. Physiological properties of hERG 1a/1b heteromeric currents and a hERG 1b-specific mutation associated with Long-QT syndrome. Circ Res . 2008 Sep 26; 103 ( 7 ): e81-95 . Epub 2008 Sep 5.

Cardiac IKr is a critical repolarizing current in the heart and a target for inherited and acquired long-QT syndrome (LQTS). Biochemical and functional studies have demonstrated that IKr channels are heteromers composed of both hERG 1a and 1b subunits, yet our current understanding of IKr functional properties derives primarily from studies of homooligomers of the original hERG 1a isolate. Here, we examine currents produced by hERG 1a and 1a/1b channels expressed in HEK-293 cells at near-physiological temperatures. We find that heteromeric hERG 1a/1b currents are much larger than hERG 1a currents and conduct 80% more charge during an action potential. This surprising difference corresponds to a 2-fold increase in the apparent rates of activation and recovery from inactivation, thus reducing rectification and facilitating current rebound during repolarization. Kinetic modeling shows these gating differences account quantitatively for the differences in current amplitude between the 2 channel types. Drug sensitivity was also different. Compared to homomeric 1a channels, heteromeric 1a/1b channels were inhibited by E-4031 with a slower time course and a corresponding 4-fold shift in the IC50. The importance of hERG 1b in vivo is supported by the identification of a 1b-specific A8V missense mutation in 1/269 unrelated genotype-negative LQTS patients that was absent in 400 control alleles. Mutant 1bA8V expressed alone or with hERG 1a in HEK-293 cells dramatically reduced 1b protein levels. Thus, mutations specifically disrupting hERG 1b function are expected to reduce cardiac IKr and enhance drug sensitivity, and represent a potential mechanism underlying inherited or acquired LQTS.

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Nekouzadeh A, Silva JR, Rudy Y. Modeling Subunit Cooperativity in Opening of Tetrameric Ion Channels. Biophys J . 2008 Jul 11. [Epub ahead of print]

Most potassium channels are tetramers of four homologous polypeptides (subunits). During channel gating, each subunit undergoes several conformational changes independent of the state of other subunits before reaching a "permissive" state, from which the channel can open. However, transition from the permissive states to the open state involves a concerted movement of all subunits. This cooperative transition must be included in Markov models of channel gating. Previously, it was implemented by considering all possible combinations of four subunit states in a much larger expanded model of channel states (e.g. 27,405 channel states vs. 64 subunit states), which complicates modeling and is computationally intense, especially when accurate modeling requires a large number of subunit states. To overcome these complexities and retain the tetrameric molecular structure, a modeling approach was developed to incorporate the cooperative transition directly from the subunit models. In this approach, the open state is separated from the subunit models and represented by the net flux between the open state and the permissive states. Dynamic variations of the probability of state residencies computed using this direct approach and the expanded model were identical. Implementation of the direct approach is simple and its computational time is orders of magnitude shorter than the equivalent expanded model.


Bébarová M, O'Hara T, Geelen JL, Jongbloed RJ, Timmermans C, Arens YH, Rodriguez LM, Rudy Y, Volders PG. Subepicardial phase 0 block and discontinuous transmural conduction underlie right precordial ST-segment elevation by a SCN5A loss-of-function mutation. Am J Physiol Heart Circ Physiol . 2008 Jul; 295 ( 1 ): H48-58 . Epub 2008 May 2. PMID: 18456723 [PubMed - in process]

Two mechanisms are generally proposed to explain right precordial ST-segment elevation in Brugada syndrome: 1) right ventricular (RV) subepicardial action potential shortening and/or loss of dome causing transmural dispersion of repolarization; and 2) RV conduction delay. Here we report novel mechanistic insights into ST-segment elevation associated with a Na+ current (INa) loss-of-function mutation from studies in a Dutch kindred with the COOH-terminal SCN5A variant p.Phe2004Leu. The proband, a man, experienced syncope at age 22 yr and had coved-type ST-segment elevations in ECG leads V1 and V2 and negative T waves in V2. Peak and persistent mutant I(Na) were significantly decreased. INa closed-state inactivation was increased, slow inactivation accelerated, and recovery from inactivation delayed. Computer-simulated INa-dependent excitation was decremental from endo- to epicardium at cycle length 1,000 ms, not at cycle length 300 ms. Propagation was discontinuous across the midmyocardial to epicardial transition region, exhibiting a long local delay due to phase 0 block. Beyond this region, axial excitatory current was provided by phase 2 (dome) of the M-cell action potentials and depended on L-type Ca2+ current ("phase 2 conduction"). These results explain right precordial ST-segment elevation on the basis of RV transmural gradients of membrane potentials during early repolarization caused by discontinuous conduction. The late slow-upstroke action potentials at the subepicardium produce T-wave inversion in the computed ECG waveform, in line with the clinical ECG.

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Nekouzadeh A, Rudy Y. Statistical properties of ion channel records. Part II: Estimation from the macroscopic current.
Math Biosci . 2007 May 4; [Epub ahead of print]

Macroscopic ion channel current is the summation of the stochastic records of individual channel currents and therefore relates to their statistical properties. As a consequence of this relationship, it may be possible to derive certain statistical properties of single channel records or even generate some estimates of the records themselves from the macroscopic current when the direct measurement of single channel currents is not applicable. We present a procedure for generating the single channel records of an ion channel from its macroscopic current when the stochastic process of channel gating has the following two properties: (I) the open duration is independent of the time of opening event and has a single exponential probability density function (pdf), (II) all the channels have the same probability to open at time t. The application of this procedure is considered for cases where direct measurement of single channel records is difficult or impossible. First, the probability density function (pdf) of opening events, a statistical property of single channel records, is derived from the normalized macroscopic current and mean channel open duration. Second, it is shown that under the conditions (I) and (II), a non-stationary Markov model can represent the stochastic process of channel gating. Third, the non-stationary Markov model is calibrated using the results of the first step. The non-stationary formulation increases the model ability to generate a variety of different single channel records compared to common stationary Markov models. The model is then used to generate single channel records and to obtain other statistical properties of the records. Experimental single channel records of inactivating BK potassium channels are used to evaluate how accurately this procedure reconstructs measured single channel sweeps.

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Nekouzadeh A, Rudy Y. Statistical properties of ion channel records. Part I: Relationship to the macroscopic current.
Math Biosci . 2007 May 4; [Epub ahead of print]

Macroscopic ion channel current can be derived by summation of the stochastic records of individual channel currents. In this paper, we present two probability density functions of single channel records that can uniquely determine the macroscopic current regardless of other statistical properties of records or the stochastic model of channel gating (presented often with stationary Markov models). We show that H(t), probability density function of channel opening events (introduced explicitly in this paper), and D(t), probability density function of the open duration (sometimes has named dwell time distribution as well), determine the normalized macroscopic current, G(t), throughwhere P(t) is the cumulative density function of H(t), Q(t) is the cumulative density function of D(t), * is the symbol of convolution integral and G(t) is the macroscopic current divided by the amplitude of single channel current and the number of single channel sweeps. Compared to other equations for the macroscopic current, here the macroscopic current is expressed only in terms of the statistical properties of single channel current and not the stochastic model of ion channel gating or a conditioned form of macroscopic current. Single channel currents of an inactivating BK channel were used to validate this relationship experimentally too. In this paper, we used median filters as they can remove the unwanted noise without smoothing the transitions between open and closed states (compare to low pass filters). This filtering leads to more accurate measurement of transition times and less amount of missed events.

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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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Clancy CE, Zhu ZI, Rudy Y. Pharmacogenetics and anti-arrhythmic drug therapy: A theoretical investigation. Am J Physiol Heart Circ Physiol. 2006 Sep 22

We present a theoretical approach for investigating effects of drug-channel interaction. We use as an example open-channel or inactivated-channel block by the local anesthetics mexiletine and lidocaine, respectively, of normal and DKPQ mutant Na+ channels associated with the long-QT syndrome type 3. Results show how kinetic properties of channel gating, which are affected by mutations, are important determinants of drug efficacy. Investigations of Na+ channel blockade are conducted at multiple scales: single channel, macroscopic current and, importantly, during the cardiac action potential (AP). Our findings suggest that channel mean open time is a primary determinant of open state blocker efficacy. The simulations also suggest that inactivation state block by lidocaine is less effective in restoring normal repolarization and adversely suppresses peak Na+ current.

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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.

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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Clancy, C. E. and Y. Rudy (2002). "Na(+) channel mutation that causes both Brugada and long-QT syndrome phenotypes: a simulation study of mechanism." Circulation 105(10): 1208-13.

Complex physiological interactions determine the functional consequences of gene abnormalities and make mechanistic interpretation of phenotypes extremely difficult. A recent example is a single mutation in the C terminus of the cardiac Na(+) channel, 1795insD. The mutation causes two distinct clinical syndromes, long QT (LQT) and Brugada, leading to life-threatening cardiac arrhythmias. Coexistence of these syndromes is seemingly paradoxical; LQT is associated with enhanced Na(+) channel function, and Brugada with reduced function. Using a computational approach, we demonstrate that the 1795insD mutation exerts variable effects depending on the myocardial substrate.

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Gima, K. and Y. Rudy (2002). "Ionic current basis of electrocardiographic waveforms: a model study." Circ Res 90(8): 889-96.

Body surface electrocardiograms and electrograms recorded from the surfaces of the heart are the basis for diagnosis and treatment of cardiac electrophysiological disorders and arrhythmias. Given recent advances in understanding the molecular mechanisms of arrhythmia, it is important to relate these electrocardiographic waveforms to cellular electrophysiological processes. This modeling study establishes the principles that provide a mechanistic cellular basis for interpretation of electrocardiographic waveforms.

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Viswanathan, P. C. and Y. Rudy (2000). "Cellular arrhythmogenic effects of congenital and acquired long-QT syndrome in the heterogeneous myocardium." Circulation 101(10): 1192-8.

Certain alterations by mutations or drugs of the potassium currents IKs and IKr and the sodium current INa give rise to several types of the long-QT syndrome. IKs is heterogeneously distributed across the ventricular wall. We investigated the effects of reducing IKs or IKr or enhancing late INa (to simulate the 3 forms of long-QT syndrome) on action potential duration in the context of IKs heterogeneity. We introduced IKs heterogeneity in the Luo-Rudy dynamic cell model to simulate epicardial, endocardial, and midmyocardial cells.

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Clancy, C. E. and Y. Rudy (1999). "Linking a genetic defect to its cellular phenotype in a cardiac arrhythmia." Nature 400(6744): 566-9.

Advances in genetics and molecular biology have provided an extensive body of information on the structure and function of the elementary building blocks of living systems. Genetic defects in membrane ion channels can disrupt the delicate balance of dynamic interactions between the ion channels and the cellular environment, leading to altered cell function. As ion-channel defects are typically studied in isolated expression systems, away from the cellular environment where they function physiologically, a connection between molecular findings and the physiology and pathophysiology of the cell is rarely established. Here we describe a single-channel-based Markovian modelling approach that bridges this gap. We achieve this by determining the cellular arrhythmogenic consequences of a mutation in the cardiac sodium channel that can lead to a clinical arrhythmogenic disorder (the long-QT syndrome) and sudden cardiac death.

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Viswanathan, P. C., R. M. Shaw, et al. (1999). "Effects of IKr and IKs heterogeneity on action potential duration and its rate dependence: a simulation study." Circulation 99(18): 2466-74.

A growing body of evidence suggests that heterogeneity of ion channel expression and electrophysiological characteristics is an important property of the ventricular myocardium. The 2 components of the delayed rectifier potassium current, IKr (rapid) and IKs (slow), play a dominant role in the repolarization of the action potential and are important determinants of its duration. In this report, the effects of heterogeneities of IKr and IKs on action potential duration (APD) and its rate dependence (adaptation) are studied with the use of the LRd model of a mammalian ventricular cell. The clinical significance of this study is in the context of repolarization abnormalities and associated arrhythmias (eg, long QT syndrome and torsade de pointes).

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Viswanathan, P. C. and Y. Rudy (1999). "Pause induced early afterdepolarizations in the long QT syndrome: a simulation study." Cardiovasc Res 42(2): 530-42.

The long QT syndrome (LQTS) is characterized by prolonged repolarization and propensity to syncope and sudden death due to polymorphic ventricular tachycardias such as torsade de pointes (TdP). The exact mechanism of TdP is unclear, but pause-induced early afterdepolarizations (EADs) have been implicated in its initiation. In this study we investigate the mechanism of pause-induced EADs following pacing at clinically relevant rates and characterize the sensitivity of different cell types (epicardial, midmyocardial, and endocardial) to EAD development. Simulations were conducted using the Luo-Rudy (LRd) model of the mamalian ventricular action potential (AP).

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Review Articles

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 b -adrenergic cascade on the cell electrophysiological function.

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Rudy, Y. (2000). "From genome to physiome: integrative models of cardiac excitation." Ann Biomed Eng 28(8): 945-50.

The last decade has generated extensive information on the genetic and molecular basis of disease. A major challenge remains the integration of this information into the physiological environment of the functioning cell and tissue. This article illustrates the use of computational biology in meeting this challenge in the context of cardiac excitation and arrhythmia.

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