RSS 1.0Downstate College of Medicine
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Exploiting mathematical models to illuminate electrophysiological variability between individualsAcross individuals within a population, several levels of variability are observed, from the differential expression of ion channels at the molecular level, to the various action potential morphologies observed at the cellular level, to divergent responses to drugs at the organismal level. However, the limited ability of experiments to probe complex interactions between components has hitherto hindered our understanding of the factors that cause a range of behaviours within a population. Variability is a challenging issue that is encountered in all physiological disciplines, but recent work suggests that novel methods for analysing mathematical models can assist in illuminating its causes. In this review, we discuss mathematical modelling studies in cardiac electrophysiology and neuroscience that have enhanced our understanding of variability in a number of key areas. Specifically, we discuss parameter sensitivity analysis techniques that may be applied to generate quantitative predictions based on considering behaviours within a population of models, thereby providing novel insight into variability. Our discussion focuses on four issues that have benefited from the utilization of these methods: (1) the comparison of different electrophysiological models of cardiac myocytes, (2) the determination of the individual contributions of different molecular changes in complex disease phenotypes, (3) the identification of the factors responsible for the variable response to drugs, and (4) the constraining of free parameters in electrophysiological models of heart cells. Together, the studies that we discuss suggest that rigorous analyses of mathematical models can generate quantitative predictions regarding how molecular-level variations contribute to functional differences between experimental samples. These strategies may be applicable not just in cardiac electrophysiology, but in a wide range of disciplines.
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Nonlinear Dynamics in CardiologyThe dynamics of many cardiac arrhythmias, as well as the nature of transitions between different heart rhythms, have long been considered evidence of nonlinear phenomena playing a direct role in cardiac arrhythmogenesis. In most types of cardiac disease, the pathology develops slowly and gradually, often over many years. In contrast, arrhythmias often occur suddenly. In nonlinear systems, sudden changes in qualitative dynamics can, counterintuitively, result from a gradual change in a system parameter-this is known as a bifurcation. Here, we review how nonlinearities in cardiac electrophysiology influence normal and abnormal rhythms and how bifurcations change the dynamics. In particular, we focus on the many recent developments in computational modeling at the cellular level that are focused on intracellular calcium dynamics. We discuss two areas where recent experimental and modeling work has suggested the importance of nonlinearities in calcium dynamics: repolarization alternans and pacemaker cell automaticity.
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Non-Linear Dynamics of Cardiac Alternans: Subcellular to Tissue-Level Mechanisms of ArrhythmiaCardiac repolarization alternans is a rhythm disturbance of the heart in which rapid stimulation elicits a beat-to-beat alternation in the duration of action potentials and magnitude of intracellular calcium transients in individual cardiac myocytes. Although this phenomenon has been identified as a potential precursor to dangerous reentrant arrhythmias and sudden cardiac death, significant uncertainty remains regarding its mechanism and no clinically practical means of halting its occurrence or progression currently exists. Cardiac alternans has well-characterized tissue, cellular, and subcellular manifestations, the mechanisms and interplay of which are an active area of research.
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Dynamic Clamp in Cardiac and Neuronal Systems Using RTXIThe injection of computer-simulated conductances through the dynamic clamp technique has allowed researchers to probe the intercellular and intracellular dynamics of cardiac and neuronal systems with great precision. By coupling computational models to biological systems, dynamic clamp has become a proven tool in electrophysiology with many applications, such as generating hybrid networks in neurons or simulating channelopathies in cardiomyocytes. While its applications are broad, the approach is straightforward: synthesizing traditional patch clamp, computational modeling, and closed-loop feedback control to simulate a cellular conductance. Here, we present two example applications: artificial blocking of the inward rectifier potassium current in a cardiomyocyte and coupling of a biological neuron to a virtual neuron through a virtual synapse. The design and implementation of the necessary software to administer these dynamic clamp experiments can be difficult. In this chapter, we provide an overview of designing and implementing a dynamic clamp experiment using the Real-Time eXperiment Interface (RTXI), an open-source software system tailored for real-time biological experiments. We present two ways to achieve this using RTXI's modular format, through the creation of a custom user-made module and through existing modules found in RTXI's online library.
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Improving cardiomyocyte model fidelity and utility via dynamic electrophysiology protocols and optimization algorithmsMathematical models of cardiac electrophysiology are instrumental in determining mechanisms of cardiac arrhythmias. However, the foundation of a realistic multiscale heart model is only as strong as the underlying cell model. While there have been myriad advances in the improvement of cellular-level models, the identification of model parameters, such as ion channel conductances and rate constants, remains a challenging problem. The primary limitations to this process include: (1) such parameters are usually estimated from data recorded using standard electrophysiology voltage-clamp protocols that have not been developed with model building in mind, and (2) model parameters are typically tuned manually to subjectively match a desired output. Over the last decade, methods aimed at overcoming these disadvantages have emerged. These approaches include the use of optimization or fitting tools for parameter estimation and incorporating more extensive data for output matching. Here, we review recent advances in parameter estimation for cardiomyocyte models, focusing on the use of more complex electrophysiology protocols and global search heuristics. We also discuss future applications of such parameter identification, including development of cell-specific and patient-specific mathematical models to investigate arrhythmia mechanisms and predict therapy strategies.
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Applications of Dynamic Clamp to Cardiac Arrhythmia Research: Role in Drug Target Discovery and Safety Pharmacology TestingDynamic clamp, a hybrid-computational-experimental technique that has been used to elucidate ionic mechanisms underlying cardiac electrophysiology, is emerging as a promising tool in the discovery of potential anti-arrhythmic targets and in pharmacological safety testing. Through the injection of computationally simulated conductances into isolated cardiomyocytes in a real-time continuous loop, dynamic clamp has greatly expanded the capabilities of patch clamp outside traditional static voltage and current protocols. Recent applications include fine manipulation of injected artificial conductances to identify promising drug targets in the prevention of arrhythmia and the direct testing of model-based hypotheses. Furthermore, dynamic clamp has been used to enhance existing experimental models by addressing their intrinsic limitations, which increased predictive power in identifying pro-arrhythmic pharmacological compounds. Here, we review the recent advances of the dynamic clamp technique in cardiac electrophysiology with a focus on its future role in the development of safety testing and discovery of anti-arrhythmic drugs.
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Calibration of ionic and cellular cardiac electrophysiology modelsCardiac electrophysiology models are among the most mature and well-studied mathematical models of biological systems. This maturity is bringing new challenges as models are being used increasingly to make quantitative rather than qualitative predictions. As such, calibrating the parameters within ion current and action potential (AP) models to experimental data sets is a crucial step in constructing a predictive model. This review highlights some of the fundamental concepts in cardiac model calibration and is intended to be readily understood by computational and mathematical modelers working in other fields of biology. We discuss the classic and latest approaches to calibration in the electrophysiology field, at both the ion channel and cellular AP scales. We end with a discussion of the many challenges that work to date has raised and the need for reproducible descriptions of the calibration process to enable models to be recalibrated to new data sets and built upon for new studies. This article is categorized under: Analytical and Computational Methods > Computational Methods Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Cellular Models.
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Direct biologically based biosensing of dynamic physiological functionDynamic regulation of biological systems requires real-time assessment of relevant physiological needs. Biosensors, which transduce biological actions or reactions into signals amenable to processing, are well suited for such monitoring. Typically, in vivo biosensors approximate physiological function via the measurement of surrogate signals. The alternative approach presented here would be to use biologically based biosensors for the direct measurement of physiological activity via functional integration of relevant governing inputs. We show that an implanted excitable-tissue biosensor (excitable cardiac tissue) can be used as a real-time, integrated bioprocessor to analyze the complex inputs regulating a dynamic physiological variable (heart rate). This approach offers the potential for long-term biologically tuned quantification of endogenous physiological function.
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Nonlinear-dynamical arrhythmia control in humansNonlinear-dynamical control techniques, also known as chaos control, have been used with great success to control a wide range of physical systems. Such techniques have been used to control the behavior of in vitro excitable biological tissue, suggesting their potential for clinical utility. However, the feasibility of using such techniques to control physiological processes has not been demonstrated in humans. Here we show that nonlinear-dynamical control can modulate human cardiac electrophysiological dynamics by rapidly stabilizing an unstable target rhythm. Specifically, in 52/54 control attempts in five patients, we successfully terminated pacing-induced period-2 atrioventricular-nodal conduction alternans by stabilizing the underlying unstable steady-state conduction. This proof-of-concept demonstration shows that nonlinear-dynamical control techniques are clinically feasible and provides a foundation for developing such techniques for more complex forms of clinical arrhythmia.
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Complex AV nodal dynamics during ventricular-triggered atrial pacing in humansIn vitro experiments have shown that the complexity of atrioventricular nodal (AVN) conduction dynamics increases with heart rate. Although complex AVN dynamics (e.g., alternans) have been observed clinically, human AVN dynamics during rapid pacing have not been systematically investigated. We studied such dynamics during ventricular-triggered atrial pacing in 37 patients with normal AVN function (18 patients with dual AVN pathway physiology and 19 patients without). Alternans, which always resulted from single pathway conduction, occurred in 18 patients. In 16 patients (3 of whom also had alternans), quasisinusoidal AVN conduction oscillations occurred (mean frequency 0.02 Hz); such oscillations have not been previously reported. There were no significant differences in the dynamics for patients with or without dual AVN pathways. To illuminate the governing dynamic mechanism, a second atrial pacing trial was performed on 12 patients after autonomic blockade. Blockade facilitated alternans but inhibited oscillations. This study suggests that rapid AVN excitation in vivo can lead to autonomically mediated AVN conduction oscillations or single pathway alternans that are a function of inherent nonlinear dynamic AVN tissue properties.
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Critical role of inhomogeneities in pacing termination of cardiac reentryReentry around nonconducting ventricular scar tissue, a cause of lethal arrhythmias, is typically treated by rapid electrical stimulation from an implantable cardioverter defibrillator. However, the dynamical mechanisms of termination (success and failure) are poorly understood. To elucidate such mechanisms, we study the dynamics of pacing in one- and two-dimensional models of anatomical reentry. In a crucial realistic difference from previous studies of such systems, we have placed the pacing site away from the reentry circuit. Our model-independent results suggest that with such off-circuit pacing, the existence of inhomogeneity in the reentry circuit is essential for successful termination of tachycardia under certain conditions. Considering the critical role of such inhomogeneities may lead to more effective pacing algorithms.
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MinK-Related Peptide 2 Modulates Kv2.1 and Kv3.1 Potassium Channels in Mammalian BrainDelayed rectifier potassium current diversity and regulation are essential for signal processing and integration in neuronal circuits. Here, we investigated a neuronal role for MinK-related peptides (MiRPs), membrane-spanning modulatory subunits that generate phenotypic diversity in cardiac potassium channels. Native coimmunoprecipitation from rat brain membranes identified two novel potassium channel complexes, MiRP2-Kv2.1 and MiRP2-Kv3.1b. MiRP2 reduces the current density of both channels, slows Kv3.1b activation, and slows both activation and deactivation of Kv2.1. Altering native MiRP2 expression levels by RNAi gene silencing or cDNA transfection toggles the magnitude and kinetics of endogenous delayed rectifier currents in PC12 cells and hippocampal neurons. Computer simulations predict that the slower gating of Kv3.1b in complexes with MiRP2 will broaden action potentials and lower sustainable firing frequency. Thus, MiRP2, unlike other known neuronal beta subunits, provides a mechanism for influence over multiple delayed rectifier potassium currents in mammalian CNS via modulation of alpha subunits from structurally and kinetically distinct subfamilies.
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Action Potential Morphology Influences Intracellular Calcium Handling Stability and the Occurrence of AlternansInstability in the intracellular Ca2+ handling system leading to Ca2+ alternans is hypothesized to be an underlying cause of electrical alternans. The highly coupled nature of membrane voltage and Ca2+ regulation suggests that there should be reciprocal effects of membrane voltage on the stability of the Ca2+ handling system. We investigated such effects using a mathematical model of the cardiac intracellular Ca2+ handling system. We found that the morphology of the action potential has a significant effect on the stability of the Ca2+ handling system at any given pacing rate, with small changes in action potential morphology resulting in a transition from stable nonalternating Ca2+ transients to stable alternating Ca2+ transients. This bifurcation occurs as the alternans eigen value of the system changes from absolute value <1 to absolute value >1. These results suggest that the stability of the intracellular Ca2+ handling system and the occurrence of Ca2+ alternans are not dictated solely by the Ca2+ handling system itself, but are also modulated to a significant degree by membrane voltage (through its influence on sarcolemmal Ca2+ currents) and, therefore, by all ionic currents that affect membrane voltage.
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Control of Electrical Alternans in Canine Cardiac Purkinje FibersAlternation in the duration of consecutive cardiac action potentials (electrical alternans) may precipitate conduction block and the onset of arrhythmias. Consequently, suppression of alternans using properly timed premature stimuli may be antiarrhythmic. To determine the extent to which alternans control can be achieved in cardiac tissue, isolated canine Purkinje fibers were paced from one end using a feedback control method. Spatially uniform control of alternans was possible when alternans amplitude was small. However, control became attenuated spatially as alternans amplitude increased. The amplitude variation along the cable was well described by a theoretically expected standing wave profile that corresponds to the first quantized mode of the one-dimensional Helmholtz equation. These results confirm the wavelike nature of alternans and may have important implications for their control using electrical stimuli.
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Action Potential Duration Dispersion and Alternans in Simulated Heterogeneous Cardiac Tissue with a Structural BarrierStructural barriers to wave propagation in cardiac tissue are associated with a decreased threshold for repolarization alternans both experimentally and clinically. Using computer simulations, we investigated the effects of a structural barrier on the onset of spatially concordant and discordant alternans. We used two-dimensional tissue geometry with heterogeneity in selected potassium conductances to mimic known apex-base gradients. Although we found that the actual onset of alternans was similar with and without the structural barrier, the increase in alternans magnitude with faster pacing was steeper with the barrier--giving the appearance of an earlier alternans onset in its presence. This is consistent with both experimental structural barrier findings and the clinical observation of T-wave alternans occurring at slower pacing rates in patients with structural heart disease. In ionically homogeneous tissue, discordant alternans induced by the presence of the structural barrier arose at intermediate pacing rates due to a source-sink mismatch behind the barrier. In heterogeneous tissue, discordant alternans occurred during fast pacing due to a barrier-induced decoupling of tissue with different restitution properties. Our results demonstrate a causal relationship between the presence of a structural barrier and increased alternans magnitude and action potential duration dispersion, which may contribute to why patients with structural heart disease are at higher risk for ventricular tachyarrhythmias.
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Mechanism Underlying Initiation of Paroxysmal Atrial Flutter/Atrial Fibrillation by Ectopic FociBackground: The mechanisms underlying paroxysmal atrial flutter/atrial fibrillation initiation by ectopic foci from various locations are unclear. Methods and results: We used parallel computational techniques to study an anatomically accurate 3-dimensional atrial structure incorporating a detailed ionic-current model of an atrial myocyte. At the single-cell level, upregulation of the L-type Ca2+ current I(Ca,L) steepened restitution curves of action potential duration and conduction velocity compared with the control. Spontaneous firings of ectopic foci, coupled with sinus activity, produced dynamic spatial dispersions of repolarization, including discordant alternans, which caused conduction block and reentry only for the elevated I(Ca,L) case. For each foci location, a vulnerable window for atrial flutter/atrial fibrillation induction was identified as a function of the coupling interval and focus cycle length. For ectopic foci in the pulmonary veins and left atrium, the site of conduction block and reentry gradually shifted, as a function of coupling interval, from the right atrium to the interatrial area and finally to the left atrium. The size of the vulnerable window was largest for pulmonary vein foci, becoming markedly smaller for right atrial foci, especially those near the sinoatrial node. Conclusions: These findings suggest that a mechanism of dynamically induced repolarization dispersion, especially discordant alternans, underlies the induction of atrial flutter/atrial fibrillation by atrial ectopic foci. The sites and likelihood of reentry induction varied according to ectopic focus location and timing, with the largest vulnerable window corresponding to the pulmonary vein region.
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Characterizing the contribution of voltage- and calcium-dependent coupling to action potential stability: implications for repolarization alternansExperiments have provided suggestive but inconclusive insights into the relative contributions of transmembrane voltage and intracellular calcium handling to the development of cardiac electrical instabilities such as repolarization alternans. In this study, we applied a novel combination of techniques (action potential voltage clamping, calcium-transient clamping, and stability analysis) to cardiac cell models to more clearly determine the roles that voltage- and calcium-dependent coupling play in regulating action potential stability and the development of alternans subsequent to the loss of stability. Using these techniques, we are able to demonstrate that voltage- and calcium-dependent coupling exhibit varying degrees of influence on action potential stability across models. Our results indicate that cellular dynamic instabilities such as alternans may be initiated by either voltage- or calcium-dependent mechanisms or by some combination of the two. Based on these modeling results, we propose novel single-cell experiments that incorporate action-potential voltage clamping, calcium imaging, and real-time measurement of action potential stability. These experiments will make it possible to experimentally determine the relative contribution of voltage coupling to the regulation of action potential stability in real cardiac myocytes, thereby providing further insights into the mechanism of alternans.
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A KCNE2 mutation in a patient with cardiac arrhythmia induced by auditory stimuli and serum electrolyte imbalanceAims: Auditory stimulus-induced long QT syndrome (LQTS) is almost exclusively linked to mutations in the hERG potassium channel, which generates the I Kr ventricular repolarization current. Here, a young woman with prior episodes of auditory stimulus-induced syncope presented with LQTS and ventricular fibrillation (VF) with hypomagnesaemia and hypocalcaemia after completing a marathon, followed by subsequent VF with hypokalaemia. The patient was found to harbour a KCNE2 gene mutation encoding a T10M amino acid substitution in MiRP1, an ancillary subunit that co-assembles with and functionally modulates hERG. Other family members with the mutation were asymptomatic, and the proband had no mutations in hERG or other LQTS-linked cardiac ion channel genes. The T10M mutation was absent from 578 unrelated, ethnically matched control chromosomes analysed here and was previously described only once-in an LQTS patient-but not functionally characterized. Methods and results: T10M-MiRP1-hERG currents were assessed using whole-cell voltage clamp of transfected Chinese Hamster ovary cells. T10M-MiRP1-hERG channels showed <or=80% reduced tail current, left-shifted steady-state inactivation, and 50% slower recovery from inactivation when compared with wild-type channels, with mixed wild-type/T10M channels displaying an intermediate phenotype. Lowering bath K+ concentration reduced wild-type and T10M currents equivalently. Conclusion: Data suggest a mechanism for reduced penetrance, inherited arrhythmia in which baseline I Kr current reduction by the T10M mutation is exacerbated by superimposition of arrhythmogenic substrates such as auditory stimuli, or electrolyte disturbances that reduce I Kr (hypokalaemia) or otherwise lower the ventricular threshold for fibrillation (hypomagnesaemia and hypocalcaemia). This first example of a MiRP1 mutation associated with auditory stimulus-induced arrhythmia is supportive of the hypothesis that MiRP1 regulates hERG in the human heart.
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MinK-dependent internalization of the IKs potassium channelAims: KCNQ1-MinK potassium channel complexes (4alpha:2beta stoichiometry) generate IKs, the slowly activating human cardiac ventricular repolarization current. The MinK ancillary subunit slows KCNQ1 activation, eliminates its inactivation, and increases its unitary conductance. However, KCNQ1 transcripts outnumber MinK transcripts five to one in human ventricles, suggesting KCNQ1 also forms other heteromeric or even homomeric channels there. Mechanisms governing which channel types prevail have not previously been reported, despite their significance: normal cardiac rhythm requires tight control of IKs density and kinetics, and inherited mutations in KCNQ1 and MinK can cause ventricular fibrillation and sudden death. Here, we describe a novel mechanism for this control. Methods and results: Whole-cell patch-clamping, confocal immunofluorescence microscopy, antibody feeding, biotin feeding, fluorescent transferrin feeding, and protein biochemistry techniques were applied to COS-7 cells heterologously expressing KCNQ1 with wild-type or mutant MinK and dynamin 2 and to native IKs channels in guinea-pig myocytes. KCNQ1-MinK complexes, but not homomeric KCNQ1 channels, were found to undergo clathrin- and dynamin 2-dependent internalization (DDI). Three sites on the MinK intracellular C-terminus were, in concert, necessary and sufficient for DDI. Gating kinetics and sensitivity to XE991 indicated that DDI decreased cell-surface KCNQ1-MinK channels relative to homomeric KCNQ1, decreasing whole-cell current but increasing net activation rate; inhibiting DDI did the reverse. Conclusion: The data redefine MinK as an endocytic chaperone for KCNQ1 and present a dynamic mechanism for controlling net surface Kv channel subunit composition-and thus current density and gating kinetics-that may also apply to other alpha-beta type Kv channel complexes.
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Re-evaluating the efficacy of β-adrenergic agonists and antagonists in long QT-3 syndrome through computational modellingAims: Long QT syndrome (LQTS) is a heterogeneous collection of inherited cardiac ion channelopathies characterized by a prolonged electrocardiogram QT interval and increased risk of sudden cardiac death. Beta-adrenergic blockers are the mainstay of treatment for LQTS. While their efficacy has been demonstrated in LQTS patients harbouring potassium channel mutations, studies of beta-blockers in subtype 3 (LQT3), which is caused by sodium channel mutations, have produced ambiguous results. In this modelling study, we explore the effects of beta-adrenergic drugs on the LQT3 phenotype. Methods and results: In order to investigate the effects of beta-adrenergic activity and to identify sources of ambiguity in earlier studies, we developed a computational model incorporating the effects of beta-agonists and beta-blockers into an LQT3 mutant guinea pig ventricular myocyte model. Beta-activation suppressed two arrhythmogenic phenomena, transmural dispersion of repolarization and early after depolarizations, in a dose-dependent manner. However, the ability of beta-activation to prevent cardiac conduction block was pacing-rate-dependent. Low-dose beta-blockade by propranolol reversed the beneficial effects of beta-activation, while high dose (which has off-target sodium channel effects) decreased arrhythmia susceptibility. Conclusion: These results demonstrate that beta-activation may be protective in LQT3 and help to reconcile seemingly conflicting results from different experimental models. They also highlight the need for well-controlled clinical investigations re-evaluating the use of beta-blockers in LQT3 patients.
