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Hernandez-Hernandez G, O'Dwyer SC, Yang PC, Matsumoto C, Tieu M, Fong Z, Lewis TJ, Santana LF, Clancy CE. A computational model predicts sex-specific responses to calcium channel blockers in mammalian mesenteric vascular smooth muscle. eLife 2024; 12:RP90604. [PMID: 38335126 PMCID: PMC10942543 DOI: 10.7554/elife.90604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/12/2024] Open
Abstract
The function of the smooth muscle cells lining the walls of mammalian systemic arteries and arterioles is to regulate the diameter of the vessels to control blood flow and blood pressure. Here, we describe an in silico model, which we call the 'Hernandez-Hernandez model', of electrical and Ca2+ signaling in arterial myocytes based on new experimental data indicating sex-specific differences in male and female arterial myocytes from murine resistance arteries. The model suggests the fundamental ionic mechanisms underlying membrane potential and intracellular Ca2+ signaling during the development of myogenic tone in arterial blood vessels. Although experimental data suggest that KV1.5 channel currents have similar amplitudes, kinetics, and voltage dependencies in male and female myocytes, simulations suggest that the KV1.5 current is the dominant current regulating membrane potential in male myocytes. In female cells, which have larger KV2.1 channel expression and longer time constants for activation than male myocytes, predictions from simulated female myocytes suggest that KV2.1 plays a primary role in the control of membrane potential. Over the physiological range of membrane potentials, the gating of a small number of voltage-gated K+ channels and L-type Ca2+ channels are predicted to drive sex-specific differences in intracellular Ca2+ and excitability. We also show that in an idealized computational model of a vessel, female arterial smooth muscle exhibits heightened sensitivity to commonly used Ca2+ channel blockers compared to male. In summary, we present a new model framework to investigate the potential sex-specific impact of antihypertensive drugs.
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Affiliation(s)
| | - Samantha C O'Dwyer
- Department of Physiology & Membrane Biology, University of California, DavisDavisUnited States
| | - Pei-Chi Yang
- Department of Physiology & Membrane Biology, University of California, DavisDavisUnited States
| | - Collin Matsumoto
- Department of Physiology & Membrane Biology, University of California, DavisDavisUnited States
| | - Mindy Tieu
- Department of Physiology & Membrane Biology, University of California, DavisDavisUnited States
| | - Zhihui Fong
- Department of Physiology & Membrane Biology, University of California, DavisDavisUnited States
| | - Timothy J Lewis
- Department of Mathematics, University of California, DavisDavisUnited States
| | - L Fernando Santana
- Department of Physiology & Membrane Biology, University of California, DavisDavisUnited States
| | - Colleen E Clancy
- Department of Physiology & Membrane Biology, University of California, DavisDavisUnited States
- Center for Precision Medicine and Data Sciences, University of California, DavisDavisUnited States
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2
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Wang X, Landaw J, Qu Z. Intracellular ion accumulation in the genesis of complex action potential dynamics under cardiac diseases. Phys Rev E 2024; 109:024410. [PMID: 38491656 DOI: 10.1103/physreve.109.024410] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2023] [Accepted: 01/19/2024] [Indexed: 03/18/2024]
Abstract
Intracellular ions, including sodium (Na^{+}), calcium (Ca^{2+}), and potassium (K^{+}), etc., accumulate slowly after a change of the state of the heart, such as a change of the heart rate. The goal of this study is to understand the roles of slow ion accumulation in the genesis of cardiac memory and complex action-potential duration (APD) dynamics that can lead to lethal cardiac arrhythmias. We carry out numerical simulations of a detailed action potential model of ventricular myocytes under normal and diseased conditions, which exhibit memory effects and complex APD dynamics. We develop a low-dimensional iterated map (IM) model to describe the dynamics of Na^{+}, Ca^{2+}, and APD and use it to uncover the underlying dynamical mechanisms. The development of the IM model is informed by simulation results under the normal condition. We then use the IM model to perform linear stability analyses and computer simulations to investigate the bifurcations and complex APD dynamics, which depend on the feedback loops between APD and intracellular Ca^{2+} and Na^{+} concentrations and the steepness of the APD response to the ion concentrations. When the feedback between APD and Ca^{2+} concentration is positive, a Hopf bifurcation leading to periodic oscillatory behavior occurs as the steepness of the APD response to the ion concentrations increases. The negative feedback loop between APD and Na^{+} concentration is required for the Hopf bifurcation. When the feedback between APD and Ca^{2+} concentration is negative, period-doubling bifurcations leading to high periodicity and chaos occurs. In this case, Na^{+} accumulation plays little role in the dynamics. Finally, we carry out simulations of the detailed action potential model under two diseased conditions, which exhibit steep APD responses to ion concentrations. Under both conditions, Hopf bifurcations leading to slow oscillations or period-doubling bifurcations leading to high periodicity and chaotic APD dynamics occur, depending on the strength of the ion pump-Na^{+}-Ca^{2+} exchanger. Using functions reconstructed from the simulation data, the IM model accurately captures the bifurcations and dynamics under the two diseased conditions. In conclusion, besides using computer simulations of a detailed high-dimensional action-potential model to investigate the effects of slow ion accumulation and short-term memory on bifurcations and genesis of complex APD dynamics in cardiac myocytes under diseased conditions, this study also provides a low-dimensional mathematical tool, i.e., the IM model, to allow stability analyses for uncovering the underlying mechanisms.
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Affiliation(s)
- Xinyu Wang
- Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, California 90095, USA
| | - Julian Landaw
- Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, California 90095, USA
| | - Zhilin Qu
- Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, California 90095, USA
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3
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Hernandez-Hernandez G, O’Dwyer SC, Matsumoto C, Tieu M, Fong Z, Yang PC, Lewis TJ, Fernando Santana L, Clancy CE. A computational model predicts sex-specific responses to calcium channel blockers in mammalian mesenteric vascular smooth muscle. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2023.06.24.546394. [PMID: 37425682 PMCID: PMC10327109 DOI: 10.1101/2023.06.24.546394] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/11/2023]
Abstract
The function of the smooth muscle cells lining the walls of mammalian systemic arteries and arterioles is to regulate the diameter of the vessels to control blood flow and blood pressure. Here, we describe an in-silico model, which we call the "Hernandez-Hernandez model", of electrical and C a 2+ signaling in arterial myocytes based on new experimental data indicating sex-specific differences in male and female arterial myocytes from murine resistance arteries. The model suggests the fundamental ionic mechanisms underlying membrane potential and intracellular C a 2+ signaling during the development of myogenic tone in arterial blood vessels. Although experimental data suggest that KV1.5 channel currents have similar amplitudes, kinetics, and voltage dependencies in male and female myocytes, simulations suggest that the KV1.5 current is the dominant current regulating membrane potential in male myocytes. In female cells, which have larger KV2.1 channel expression and longer time constants for activation than male myocytes, predictions from simulated female myocytes suggest that KV2.1 plays a primary role in the control of membrane potential. Over the physiological range of membrane potentials, the gating of a small number of voltage-gated K+ channels and L-type C a 2+ channels are predicted to drive sex-specific differences in intracellular C a 2+ and excitability. We also show that in an idealized computational model of a vessel, female arterial smooth muscle exhibits heightened sensitivity to commonly used C a 2+ channel blockers compared to male. In summary, we present a new model framework to investigate the potential sex-specific impact of anti-hypertensive drugs.
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Affiliation(s)
- Gonzalo Hernandez-Hernandez
- Department of Physiology & Membrane Biology, Center for Precision Medicine and Data Science, University of California School of Medicine, Davis, California, 95616
- Department of Mathematics, University of California, Davis, California, 95616
| | - Samantha C. O’Dwyer
- Department of Physiology & Membrane Biology, Center for Precision Medicine and Data Science, University of California School of Medicine, Davis, California, 95616
- Department of Mathematics, University of California, Davis, California, 95616
| | - Collin Matsumoto
- Department of Physiology & Membrane Biology, Center for Precision Medicine and Data Science, University of California School of Medicine, Davis, California, 95616
- Department of Mathematics, University of California, Davis, California, 95616
| | - Mindy Tieu
- Department of Physiology & Membrane Biology, Center for Precision Medicine and Data Science, University of California School of Medicine, Davis, California, 95616
- Department of Mathematics, University of California, Davis, California, 95616
| | - Zhihui Fong
- Department of Physiology & Membrane Biology, Center for Precision Medicine and Data Science, University of California School of Medicine, Davis, California, 95616
- Department of Mathematics, University of California, Davis, California, 95616
| | - Pei-Chi Yang
- Department of Physiology & Membrane Biology, Center for Precision Medicine and Data Science, University of California School of Medicine, Davis, California, 95616
- Department of Mathematics, University of California, Davis, California, 95616
| | - Timothy J. Lewis
- Department of Mathematics, University of California, Davis, California, 95616
| | | | - Colleen E. Clancy
- Department of Physiology & Membrane Biology, Center for Precision Medicine and Data Science, University of California School of Medicine, Davis, California, 95616
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4
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Warren M, Poelzing S. The Calcium Transient Coupled to the L-Type Calcium Current Attenuates Action Potential Alternans. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.04.25.538350. [PMID: 37163125 PMCID: PMC10168326 DOI: 10.1101/2023.04.25.538350] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/11/2023]
Abstract
Background Action potential (AP) alternans are linked to increased arrhythmogenesis. It is suggested that calcium (Ca 2+ ) transient (CaT) alternans cause AP alternans through bi-directional coupling feedback mechanisms because CaT alternans can precede AP alternans and develop in AP alternans free conditions. However, the CaT is an emergent response to intracellular Ca 2+ handling, and the mechanisms linking AP and CaT alternans are still a topic of investigation. This study investigated the development of AP alternans in the absence of CaT. Methods AP (patch clamp) and intracellular Ca 2+ (Fluo-4 epifluorescence) were recorded simultaneously from isolated rabbit ventricle myocytes perfused with the intracellular Ca 2+ buffer BAPTA (10-20 mM) to abolish CaT and/or the L-type Ca2+ channel activator Bay K 8644 (25 nM). Results After a rate change, alternans were critically damped and stable, overdamped and ceased over seconds, underdamped with longer scale harmonics, or unstably underdamped progressing to 2:1 capture. Alternans in control cells were predominantly critically damped, but after CaT ablation with 10 or 20 mM BAPTA, exhibited respectively increased overdamping or increased underdamping. Alternans were easier to induce in CaT free cells as evidenced by a higher alternans threshold (ALT-TH: at least 7 pairs of alternating beats) relative to control cells. Alternans in Bay K 8644 treated cells were often underdamped, but the ALT-TH was similar to control. In CaT ablated cells, Bay K 8644 prolonged AP duration (APD) leading predominantly to unstably underdamped alternans. Conclusions AP alternans occur more readily in the absence of CaT suggesting that the CaT dampens the development of AP alternans. The data further demonstrate that agonizing the L-type calcium current without the negative feedback of the CaT leads to unstable alternans. This negative feedback mechanism may be important for understanding treatments aimed at reducing CaT or its dynamic response to prevent arrhythmias.
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5
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Abstract
Cardiac alternans arises from dynamical instabilities in the electrical and calcium cycling systems of the heart, and often precedes ventricular arrhythmias and sudden cardiac death. In this review, we integrate clinical observations with theory and experiment to paint a holistic portrait of cardiac alternans: the underlying mechanisms, arrhythmic manifestations and electrocardiographic signatures. We first summarize the cellular and tissue mechanisms of alternans that have been demonstrated both theoretically and experimentally, including 3 voltage-driven and 2 calcium-driven alternans mechanisms. Based on experimental and simulation results, we describe their relevance to mechanisms of arrhythmogenesis under different disease conditions, and their link to electrocardiographic characteristics of alternans observed in patients. Our major conclusion is that alternans is not only a predictor, but also a causal mechanism of potentially lethal ventricular and atrial arrhythmias across the full spectrum of arrhythmia mechanisms that culminate in functional reentry, although less important for anatomic reentry and focal arrhythmias.
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Affiliation(s)
- Zhilin Qu
- Departments of Medicine (Cardiology), Physiology, and Computational Medicine, David Geffen School of Medicine, University of California, Los Angeles, CA
| | - James N. Weiss
- Departments of Medicine (Cardiology), Physiology, and Computational Medicine, David Geffen School of Medicine, University of California, Los Angeles, CA
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6
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Qu Z, Yan D, Song Z. Modeling Calcium Cycling in the Heart: Progress, Pitfalls, and Challenges. Biomolecules 2022; 12:1686. [PMID: 36421700 PMCID: PMC9687412 DOI: 10.3390/biom12111686] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2022] [Revised: 11/08/2022] [Accepted: 11/11/2022] [Indexed: 11/16/2022] Open
Abstract
Intracellular calcium (Ca) cycling in the heart plays key roles in excitation-contraction coupling and arrhythmogenesis. In cardiac myocytes, the Ca release channels, i.e., the ryanodine receptors (RyRs), are clustered in the sarcoplasmic reticulum membrane, forming Ca release units (CRUs). The RyRs in a CRU act collectively to give rise to discrete Ca release events, called Ca sparks. A cell contains hundreds to thousands of CRUs, diffusively coupled via Ca to form a CRU network. A rich spectrum of spatiotemporal Ca dynamics is observed in cardiac myocytes, including Ca sparks, spark clusters, mini-waves, persistent whole-cell waves, and oscillations. Models of different temporal and spatial scales have been developed to investigate these dynamics. Due to the complexities of the CRU network and the spatiotemporal Ca dynamics, it is challenging to model the Ca cycling dynamics in the cardiac system, particularly at the tissue sales. In this article, we review the progress of modeling of Ca cycling in cardiac systems from single RyRs to the tissue scale, the pros and cons of the current models and different modeling approaches, and the challenges to be tackled in the future.
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Affiliation(s)
- Zhilin Qu
- Department of Medicine, David Geffen School of Medicine, University of California, A2-237 CHS, 650 Charles E. Young Drive South, Los Angeles, CA 90095, USA
- Department of Computational Medicine, David Geffen School of Medicine, University of California, Los Angeles, CA 90095, USA
| | - Dasen Yan
- Peng Cheng Laboratory, Shenzhen 518066, China
| | - Zhen Song
- Peng Cheng Laboratory, Shenzhen 518066, China
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7
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Colman MA, Alvarez-Lacalle E, Echebarria B, Sato D, Sutanto H, Heijman J. Multi-Scale Computational Modeling of Spatial Calcium Handling From Nanodomain to Whole-Heart: Overview and Perspectives. Front Physiol 2022; 13:836622. [PMID: 35370783 PMCID: PMC8964409 DOI: 10.3389/fphys.2022.836622] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2021] [Accepted: 01/31/2022] [Indexed: 11/13/2022] Open
Abstract
Regulation of intracellular calcium is a critical component of cardiac electrophysiology and excitation-contraction coupling. The calcium spark, the fundamental element of the intracellular calcium transient, is initiated in specialized nanodomains which co-locate the ryanodine receptors and L-type calcium channels. However, calcium homeostasis is ultimately regulated at the cellular scale, by the interaction of spatially separated but diffusively coupled nanodomains with other sub-cellular and surface-membrane calcium transport channels with strong non-linear interactions; and cardiac electrophysiology and arrhythmia mechanisms are ultimately tissue-scale phenomena, regulated by the interaction of a heterogeneous population of coupled myocytes. Recent advances in imaging modalities and image-analysis are enabling the super-resolution reconstruction of the structures responsible for regulating calcium homeostasis, including the internal structure of nanodomains themselves. Extrapolating functional and imaging data from the nanodomain to the whole-heart is non-trivial, yet essential for translational insight into disease mechanisms. Computational modeling has important roles to play in relating structural and functional data at the sub-cellular scale and translating data across the scales. This review covers recent methodological advances that enable image-based modeling of the single nanodomain and whole cardiomyocyte, as well as the development of multi-scale simulation approaches to integrate data from nanometer to whole-heart. Firstly, methods to overcome the computational challenges of simulating spatial calcium dynamics in the nanodomain are discussed, including image-based modeling at this scale. Then, recent whole-cell models, capable of capturing a range of different structures (such as the T-system and mitochondria) and cellular heterogeneity/variability are discussed at two different levels of discretization. Novel methods to integrate the models and data across the scales and simulate stochastic dynamics in tissue-scale models are then discussed, enabling elucidation of the mechanisms by which nanodomain remodeling underlies arrhythmia and contractile dysfunction. Perspectives on model differences and future directions are provided throughout.
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Affiliation(s)
- Michael A. Colman
- School of Biomedical Sciences, University of Leeds, Leeds, United Kingdom
- *Correspondence: Michael A. Colman,
| | | | - Blas Echebarria
- Departament de Fisica, Universitat Politècnica de Catalunya-BarcelonaTech, Barcelona, Spain
| | - Daisuke Sato
- Department of Pharmacology, School of Medicine, University of California, Davis, Davis, CA, United States
| | - Henry Sutanto
- Department of Physiology and Pharmacology, State University of New York Downstate Health Sciences University, Brooklyn, NY, United States
- Department of Cardiology, Cardiovascular Research Institute Maastricht, Maastricht University, Maastricht, Netherlands
| | - Jordi Heijman
- Department of Cardiology, Cardiovascular Research Institute Maastricht, Maastricht University, Maastricht, Netherlands
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8
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Loppini A, Erhardt J, Fenton FH, Filippi S, Hörning M, Gizzi A. Optical Ultrastructure of Large Mammalian Hearts Recovers Discordant Alternans by In Silico Data Assimilation. FRONTIERS IN NETWORK PHYSIOLOGY 2022; 2:866101. [PMID: 36926104 PMCID: PMC10012998 DOI: 10.3389/fnetp.2022.866101] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2022] [Accepted: 03/04/2022] [Indexed: 12/12/2022]
Abstract
Understanding and predicting the mechanisms promoting the onset and sustainability of cardiac arrhythmias represent a primary concern in the scientific and medical communities still today. Despite the long-lasting effort in clinical and physico-mathematical research, a critical aspect to be fully characterized and unveiled is represented by spatiotemporal alternans patterns of cardiac excitation. The identification of discordant alternans and higher-order alternating rhythms by advanced data analyses as well as their prediction by reliable mathematical models represents a major avenue of research for a broad and multidisciplinary scientific community. Current limitations concern two primary aspects: 1) robust and general-purpose feature extraction techniques and 2) in silico data assimilation within reliable and predictive mathematical models. Here, we address both aspects. At first, we extend our previous works on Fourier transformation imaging (FFI), applying the technique to whole-ventricle fluorescence optical mapping. Overall, we identify complex spatial patterns of voltage alternans and characterize higher-order rhythms by a frequency-series analysis. Then, we integrate the optical ultrastructure obtained by FFI analysis within a fine-tuned electrophysiological mathematical model of the cardiac action potential. We build up a novel data assimilation procedure demonstrating its reliability in reproducing complex alternans patterns in two-dimensional computational domains. Finally, we prove that the FFI approach applied to both experimental and simulated signals recovers the same information, thus closing the loop between the experiment, data analysis, and numerical simulations.
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Affiliation(s)
- Alessandro Loppini
- Nonlinear Physics and Mathematical Modeling Laboratory, University Campus Bio-Medico of Rome, Rome, Italy
| | - Julia Erhardt
- Biobased Materials Laboratory, Institute of Biomaterials and Biomolecular Systems, Faculty of Energy, Process and Biotechnology, University of Stuttgart, Stuttgart, Germany
| | - Flavio H Fenton
- School of Physics, Georgia Institute of Technology, Atlanta, GA, United States
| | - Simonetta Filippi
- Nonlinear Physics and Mathematical Modeling Laboratory, University Campus Bio-Medico of Rome, Rome, Italy
| | - Marcel Hörning
- Biobased Materials Laboratory, Institute of Biomaterials and Biomolecular Systems, Faculty of Energy, Process and Biotechnology, University of Stuttgart, Stuttgart, Germany
| | - Alessio Gizzi
- Nonlinear Physics and Mathematical Modeling Laboratory, University Campus Bio-Medico of Rome, Rome, Italy
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9
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Tóth N, Szlovák J, Kohajda Z, Bitay G, Veress R, Horváth B, Papp JG, Varró A, Nagy N. The development of L-type Ca 2+ current mediated alternans does not depend on the restitution slope in canine ventricular myocardium. Sci Rep 2021; 11:16652. [PMID: 34404848 PMCID: PMC8371021 DOI: 10.1038/s41598-021-95299-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2021] [Accepted: 07/23/2021] [Indexed: 11/25/2022] Open
Abstract
Cardiac alternans have crucial importance in the onset of ventricular fibrillation. The early explanation for alternans development was the voltage-driven mechanism, where the action potential (AP) restitution steepness was considered as crucial determining factor. Recent results suggest that restitution slope is an inadequate predictor for alternans development, but several studies still claim the role of membrane potential as underlying mechanism of alternans. These controversial data indicate that the relationship of restitution and alternans development is not completely understood. APs were measured by conventional microelectrode technique from canine right ventricular papillary muscles. Ionic currents combined with fluorescent measurements were recorded by patch-clamp technique. APs combined with fluorescent measurements were monitored by sharp microelectrodes. Rapid pacing evoked restitution-independent AP duration (APD) alternans. When non-alternating AP voltage command was used, Ca2+i-transient (CaT) alternans were not observed. When alternating rectangular voltage pulses were applied, CaT alternans were proportional to ICaL amplitude alternans. Selective ICaL inhibition did not influence the fast phase of APD restitution. In this study we found that ICaL has minor contribution in shaping the fast phase of restitution curve suggesting that ICaL—if it plays important role in the alternans mechanism—could be an additional factor that attenuates the reliability of APD restitution slope to predict alternans.
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Affiliation(s)
- Noémi Tóth
- Department of Pharmacology and Pharmacotherapy, Faculty of Medicine, University of Szeged, Dóm tér 12, P.O. Box 427, 6720, Szeged, Hungary
| | - Jozefina Szlovák
- Department of Pharmacology and Pharmacotherapy, Faculty of Medicine, University of Szeged, Dóm tér 12, P.O. Box 427, 6720, Szeged, Hungary
| | - Zsófia Kohajda
- ELKH-SZTE Research Group of Cardiovascular Pharmacology, Szeged, Hungary
| | - Gergő Bitay
- Department of Pharmacology and Pharmacotherapy, Faculty of Medicine, University of Szeged, Dóm tér 12, P.O. Box 427, 6720, Szeged, Hungary
| | - Roland Veress
- Department of Physiology, Faculty of Medicine, University of Debrecen, Debrecen, Hungary
| | - Balázs Horváth
- Department of Physiology, Faculty of Medicine, University of Debrecen, Debrecen, Hungary.,Faculty of Pharmacy, University of Debrecen, Debrecen, Hungary
| | - Julius Gy Papp
- Department of Pharmacology and Pharmacotherapy, Faculty of Medicine, University of Szeged, Dóm tér 12, P.O. Box 427, 6720, Szeged, Hungary.,ELKH-SZTE Research Group of Cardiovascular Pharmacology, Szeged, Hungary
| | - András Varró
- Department of Pharmacology and Pharmacotherapy, Faculty of Medicine, University of Szeged, Dóm tér 12, P.O. Box 427, 6720, Szeged, Hungary.,ELKH-SZTE Research Group of Cardiovascular Pharmacology, Szeged, Hungary.,Department of Pharmacology and Pharmacotherapy, Interdisciplinary Excellence Centre, University of Szeged, Szeged, Hungary
| | - Norbert Nagy
- Department of Pharmacology and Pharmacotherapy, Faculty of Medicine, University of Szeged, Dóm tér 12, P.O. Box 427, 6720, Szeged, Hungary. .,ELKH-SZTE Research Group of Cardiovascular Pharmacology, Szeged, Hungary.
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10
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Rudsari HK, Veletic M, Bergsland J, Balasingham I. Targeted Drug Delivery for Cardiovascular Disease: Modeling of Modulated Extracellular Vesicle Release Rates. IEEE Trans Nanobioscience 2021; 20:444-454. [PMID: 34270429 DOI: 10.1109/tnb.2021.3097698] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
Invasive and medical therapy has led to major improvements in cardiovascular disease management, but important challenges remain open. The discovery of a nano-sized system of extracellular vesicles (EVs) is opening new possibilities for reprogramming malfunctioning cells and indicates that EVs can be employed in therapeutic biomedical applications as engineered drug vehicles. Molecular communication (MC) has applications for treating cells with directed drug delivery, employing special targeting transmembrane proteins. In this paper, we propose a novel drug delivery system for cardiovascular diseases using an EV-mediated MC platform and exemplify the potential use in hypertrophic cardiomyopathy. We utilize intracellular calcium signaling as a natural mediator of EVs released from synthetic cells and model the release rate. We propose to use the cells as a therapeutic release system with a control signal input which modulates the EVs release rate as the output signal. We also study the frequency domain of the proposed model and estimate the transfer function of the therapeutic release system model numerically where the root-mean-square error for two separate estimated output signals are 0.0353 and 0.0124. The proposed EV-mediated targeted drug delivery system can make breakthroughs in future healthcare, in cardiovascular and other diseases where targeting is required.
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11
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Cusimano N, Gerardo-Giorda L, Gizzi A. A space-fractional bidomain framework for cardiac electrophysiology: 1D alternans dynamics. CHAOS (WOODBURY, N.Y.) 2021; 31:073123. [PMID: 34340362 DOI: 10.1063/5.0050897] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2021] [Accepted: 06/23/2021] [Indexed: 06/13/2023]
Abstract
Cardiac electrophysiology modeling deals with a complex network of excitable cells forming an intricate syncytium: the heart. The electrical activity of the heart shows recurrent spatial patterns of activation, known as cardiac alternans, featuring multiscale emerging behavior. On these grounds, we propose a novel mathematical formulation for cardiac electrophysiology modeling and simulation incorporating spatially non-local couplings within a physiological reaction-diffusion scenario. In particular, we formulate, a space-fractional electrophysiological framework, extending and generalizing similar works conducted for the monodomain model. We characterize one-dimensional excitation patterns by performing an extended numerical analysis encompassing a broad spectrum of space-fractional derivative powers and various intra- and extracellular conductivity combinations. Our numerical study demonstrates that (i) symmetric properties occur in the conductivity parameters' space following the proposed theoretical framework, (ii) the degree of non-local coupling affects the onset and evolution of discordant alternans dynamics, and (iii) the theoretical framework fully recovers classical formulations and is amenable for parametric tuning relying on experimental conduction velocity and action potential morphology.
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Affiliation(s)
| | | | - Alessio Gizzi
- Department of Engineering, Campus Bio-Medico University of Rome, 00128 Rome, Italy
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12
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Barrio R, Martínez MÁ, Pueyo E, Serrano S. Dynamical analysis of early afterdepolarization patterns in a biophysically detailed cardiac model. CHAOS (WOODBURY, N.Y.) 2021; 31:073137. [PMID: 34340346 DOI: 10.1063/5.0055965] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2021] [Accepted: 06/28/2021] [Indexed: 06/13/2023]
Abstract
Arrhythmogenic early afterdepolarizations (EADs) are investigated in a biophysically detailed mathematical model of a rabbit ventricular myocyte, providing their location in the parameter phase space and describing their dynamical mechanisms. Simulations using the Sato model, defined by 27 state variables and 177 parameters, are conducted to generate electrical action potentials (APs) for different values of the pacing cycle length and other parameters related to sodium and calcium concentrations. A detailed study of the different AP patterns with or without EADs is carried out, showing the presence of a high variety of temporal AP configurations with chaotic and quasiperiodic behaviors. Regions of bistability are identified and, importantly, linked to transitions between different behaviors. Using sweeping techniques, one-, two-, and three-parameter phase spaces are provided, allowing ascertainment of the role of the selected parameters as well as location of the transition regions. A Devil's staircase, with symbolic sequence analysis, is proposed to describe transitions in the ratio between the number of voltage (EAD and AP) peaks and the number of APs. To conclude, the obtained results are linked to recent studies for low-dimensional models and a conjecture is made for the internal dynamical structure of the transition region from non-EAD to EAD behavior using fold and cusp bifurcations and maximal canards.
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Affiliation(s)
- Roberto Barrio
- Department of Applied Mathematics and IUMA, Computational Dynamics Group, University of Zaragoza, E-50009 Zaragoza, Spain
| | - M Ángeles Martínez
- Department of Applied Mathematics and IUMA, Computational Dynamics Group, University of Zaragoza, E-50009 Zaragoza, Spain
| | - Esther Pueyo
- I3A, University of Zaragoza, IIS Aragón and CIBER-BBN, E-50018 Zaragoza, Spain
| | - Sergio Serrano
- Department of Applied Mathematics and IUMA, Computational Dynamics Group, University of Zaragoza, E-50009 Zaragoza, Spain
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13
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Amuzescu B, Airini R, Epureanu FB, Mann SA, Knott T, Radu BM. Evolution of mathematical models of cardiomyocyte electrophysiology. Math Biosci 2021; 334:108567. [PMID: 33607174 DOI: 10.1016/j.mbs.2021.108567] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2020] [Revised: 01/10/2021] [Accepted: 02/04/2021] [Indexed: 12/16/2022]
Abstract
Advanced computational techniques and mathematical modeling have become more and more important to the study of cardiac electrophysiology. In this review, we provide a brief history of the evolution of cardiomyocyte electrophysiology models and highlight some of the most important ones that had a major impact on our understanding of the electrical activity of the myocardium and associated transmembrane ion fluxes in normal and pathological states. We also present the use of these models in the study of various arrhythmogenesis mechanisms, particularly the integration of experimental pharmacology data into advanced humanized models for in silico proarrhythmogenic risk prediction as an essential component of the Comprehensive in vitro Proarrhythmia Assay (CiPA) drug safety paradigm.
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Affiliation(s)
- Bogdan Amuzescu
- Department of Anatomy, Animal Physiology and Biophysics, Faculty of Biology, University of Bucharest, 91-95 Splaiul Independentei, Bucharest 050095, Romania; Life, Environmental and Earth Sciences Division, Research Institute of the University of Bucharest (ICUB), 91-95 Splaiul Independentei, Bucharest 050095, Romania.
| | - Razvan Airini
- Department of Anatomy, Animal Physiology and Biophysics, Faculty of Biology, University of Bucharest, 91-95 Splaiul Independentei, Bucharest 050095, Romania; Life, Environmental and Earth Sciences Division, Research Institute of the University of Bucharest (ICUB), 91-95 Splaiul Independentei, Bucharest 050095, Romania
| | - Florin Bogdan Epureanu
- Department of Anatomy, Animal Physiology and Biophysics, Faculty of Biology, University of Bucharest, 91-95 Splaiul Independentei, Bucharest 050095, Romania; Life, Environmental and Earth Sciences Division, Research Institute of the University of Bucharest (ICUB), 91-95 Splaiul Independentei, Bucharest 050095, Romania
| | - Stefan A Mann
- Cytocentrics Bioscience GmbH, Nattermannallee 1, 50829 Cologne, Germany
| | - Thomas Knott
- CytoBioScience Inc., 3463 Magic Drive, San Antonio, TX 78229, USA
| | - Beatrice Mihaela Radu
- Department of Anatomy, Animal Physiology and Biophysics, Faculty of Biology, University of Bucharest, 91-95 Splaiul Independentei, Bucharest 050095, Romania; Life, Environmental and Earth Sciences Division, Research Institute of the University of Bucharest (ICUB), 91-95 Splaiul Independentei, Bucharest 050095, Romania
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14
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Stress-driven cardiac calcium mishandling via a kinase-to-kinase crosstalk. Pflugers Arch 2021; 473:363-375. [PMID: 33590296 PMCID: PMC7940337 DOI: 10.1007/s00424-021-02533-2] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2020] [Revised: 01/19/2021] [Accepted: 02/02/2021] [Indexed: 01/25/2023]
Abstract
Calcium homeostasis in the cardiomyocyte is critical to the regulation of normal cardiac function. Abnormal calcium dynamics such as altered uptake by the sarcoplasmic reticulum (SR) Ca2+-ATPase and increased diastolic SR calcium leak are involved in the development of maladaptive cardiac remodeling under pathological conditions. Ca2+/calmodulin-dependent protein kinase II-δ (CaMKIIδ) is a well-recognized key molecule in calcium dysregulation in cardiomyocytes. Elevated cellular stress is known as a common feature during pathological remodeling, and c-jun N-terminal kinase (JNK) is an important stress kinase that is activated in response to intrinsic and extrinsic stress stimuli. Our lab recently identified specific actions of JNK isoform 2 (JNK2) in CaMKIIδ expression, activation, and CaMKIIδ-dependent SR Ca2+ mishandling in the stressed heart. This review focuses on the current understanding of cardiac SR calcium handling under physiological and pathological conditions as well as the newly identified contribution of the stress kinase JNK2 in CaMKIIδ-dependent SR Ca2+ abnormal mishandling. The new findings identifying dual roles of JNK2 in CaMKIIδ expression and activation are also discussed in this review.
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15
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Muñoz LM, Ampofo MO, Cherry EM. Controllability of voltage- and calcium-driven cardiac alternans in a map model. CHAOS (WOODBURY, N.Y.) 2021; 31:023139. [PMID: 33653066 DOI: 10.1063/5.0040064] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2020] [Accepted: 02/02/2021] [Indexed: 06/12/2023]
Abstract
Certain cardiac arrhythmias are preceded by electrical alternans, a state characterized by beat-to-beat alternation in cellular action potential duration. Cardiac alternans may arise from different mechanisms including instabilities in voltage or intracellular calcium cycling. Although a number of techniques have been proposed to suppress alternans, these methods have mainly been tested using models that do not support calcium-driven alternans. Therefore, it is important to understand how control methods may perform when alternans is driven by instabilities in calcium cycling. In this study, we applied controllability analysis to a discrete map of alternans dynamics in a cardiac cell. We compared two different controllability measures to determine to what extent different control strategies could suppress alternans and tested these predictions using three feedback controllers. We found a modal controllability measure, unlike the minimum singular value of the controllability matrix, consistently indicated the control strategies requiring the least control effort and yielding the smallest closed-loop eigenvalue. In addition, action potential duration was identified as the most effective variable through which control can be applied, regardless of alternans mechanism, although sarcoplasmic reticulum calcium load was also useful for the calcium-driven alternans cases.
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Affiliation(s)
- Laura M Muñoz
- School of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York 14623-5602, USA
| | - Mark O Ampofo
- School of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York 14623-5602, USA
| | - Elizabeth M Cherry
- School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-4017, USA
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16
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Mechanisms of ranolazine pretreatment in preventing ventricular tachyarrhythmias in diabetic db/db mice with acute regional ischemia-reperfusion injury. Sci Rep 2020; 10:20032. [PMID: 33208777 PMCID: PMC7674419 DOI: 10.1038/s41598-020-77014-0] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/10/2020] [Accepted: 11/05/2020] [Indexed: 11/08/2022] Open
Abstract
Studies have demonstrated that diabetic (db/db) mice have increased susceptibility to myocardial ischemia-reperfusion (IR) injury and ventricular tachyarrhythmias (VA). We aimed to investigate the antiarrhythmic and molecular mechanisms of ranolazine in db/db mouse hearts with acute IR injury. Ranolazine was administered for 1 week before coronary artery ligation. Diabetic db/db and control db/+ mice were divided into ranolazine-given and -nongiven groups. IR model was created by 15-min left coronary artery ligation and 10-min reperfusion. In vivo electrophysiological studies showed that the severity of VA inducibility was higher in db/db mice than control (db/ +) mice. Ranolazine suppressed the VA inducibility and severity. Optical mapping studies in Langendorff-perfused hearts showed that ranolazine significantly shortened action potential duration, Cai transient duration, Cai decay time, ameliorated conduction inhomogeneity, and suppressed arrhythmogenic alternans induction. Western blotting studies showed that the expression of pThr17-phospholamban, calsequestrin 2 and voltage-gated sodium channel in the IR zone was significantly downregulated in db/db mice, which was ameliorated with ranolazine pretreatment and might play a role in the anti-arrhythmic actions of ranolazine in db/db mouse hearts with IR injury.
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17
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Parthiban P, Newell S, Tolkacheva EG. Effect of constant-DI pacing on single cell pacing dynamics. CHAOS (WOODBURY, N.Y.) 2020; 30:103122. [PMID: 33138461 DOI: 10.1063/5.0022066] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2020] [Accepted: 10/02/2020] [Indexed: 06/11/2023]
Abstract
Cardiac alternans, beat-to-beat alternations in action potential duration, is a precursor to fatal arrhythmias such as ventricular fibrillation. Previous research has shown that voltage driven alternans can be suppressed by application of a constant diastolic interval (DI) pacing protocol. However, the effect of constant-DI pacing on cardiac cell dynamics and its interaction with the intracellular calcium cycle remains to be determined. Therefore, we aimed to examine the effects of constant-DI pacing on the dynamical behavior of a single-cell numerical model of cardiac action potential and the influence of voltage-calcium (V-Ca) coupling on it. Single cell dynamics were analyzed in the vicinity of the bifurcation point using a hybrid pacing protocol, a combination of constant-basic cycle length (BCL) and constant-DI pacing. We demonstrated that in a small region beneath the bifurcation point, constant-DI pacing caused the cardiac cell to remain alternans-free after switching to the constant-BCL pacing, thus introducing a region of bistability (RB). The size of the RB increased with stronger V-Ca coupling and was diminished with weaker V-Ca coupling. Overall, our findings demonstrate that the application of constant-DI pacing on cardiac cells with strong V-Ca coupling may induce permanent changes to cardiac cell dynamics increasing the utility of constant-DI pacing.
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Affiliation(s)
- P Parthiban
- Department of Biomedical Engineering, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - S Newell
- Department of Biomedical Engineering, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - E G Tolkacheva
- Department of Biomedical Engineering, University of Minnesota, Minneapolis, Minnesota 55455, USA
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18
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Yun W, Qian L, Cheng Y, Tao W, Yuan R, Xu H. Periplocymarin Plays an Efficacious Cardiotonic Role via Promoting Calcium Influx. Front Pharmacol 2020; 11:1292. [PMID: 32973521 PMCID: PMC7466735 DOI: 10.3389/fphar.2020.01292] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2020] [Accepted: 08/04/2020] [Indexed: 12/28/2022] Open
Abstract
Periplocymarin, which belongs to cardiac glycosides, is an effective component extracted from Periplocae Cortex. However, its cardiovascular effects remain unidentified. In the present study, injection of periplocymarin (5 mg/kg) through external jugular vein immediately increased the mean arterial pressure (MAP) in anesthetized C57BL/6 mice. Ex vivo experiments using mouse mesenteric artery rings were conducted to validate the role of periplocymarin on blood vessels. However, periplocymarin failed to induce vasoconstriction directly, and had no effects on vasoconstriction induced by phenylephrine (Phe) and angiotensin II (Ang II). In addition, vasodilatation induced by acetylcholine (Ach) was insusceptible to periplocymarin. Echocardiography was used to evaluate the effects of periplocymarin on cardiac function. The results showed that the injection of periplocymarin significantly increase the ejection fraction (EF) in mice without changing the heart rate. In vitro studies using isolated neonatal rat ventricular myocytes (NRVMs) revealed that periplocymarin transiently increased the intracellular Ca2+ concentration observed by confocal microscope. But in Ca2+-free buffer, this phenomenon vanished. Besides, inhibition of sodium potassium-activated adenosine triphosphatase (Na+-K+-ATPase) by digoxin significantly suppressed the increase of MAP and EF in mice, and the influx of Ca2+ in cardiomyocytes, mediated by periplocymarin. Collectively, these findings demonstrated that periplocymarin increased the contractility of myocardium by promoting the Ca2+ influx of cardiomyocytes via targeting on Na+-K+-ATPase, which indirectly led to the instantaneous rise of blood pressure.
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Affiliation(s)
- Weijing Yun
- Advanced Institute for Medical Sciences, Dalian Medical University, Dalian, China
| | - Lei Qian
- Advanced Institute for Medical Sciences, Dalian Medical University, Dalian, China
| | - Yanyan Cheng
- Advanced Institute for Medical Sciences, Dalian Medical University, Dalian, China
| | - Weiwei Tao
- College of Nursing, Dalian Medical University, Dalian, China
| | - Ruqiang Yuan
- Advanced Institute for Medical Sciences, Dalian Medical University, Dalian, China
| | - Hu Xu
- Advanced Institute for Medical Sciences, Dalian Medical University, Dalian, China
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19
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Impact of I SK Voltage and Ca 2+/Mg 2+-Dependent Rectification on Cardiac Repolarization. Biophys J 2020; 119:690-704. [PMID: 32668235 DOI: 10.1016/j.bpj.2020.06.022] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2019] [Revised: 06/02/2020] [Accepted: 06/10/2020] [Indexed: 10/24/2022] Open
Abstract
Cardiac small conductance Ca2+-activated K+ (SK) channels are activated solely by Ca2+, but the SK current (ISK) is inwardly rectified. However, the impact of inward rectification in shaping action potentials (APs) in ventricular cardiomyocytes under β-adrenergic stimulation or in disease states remains undefined. Two processes underlie this inward rectification: an intrinsic rectification caused by an electrostatic energy barrier from positively charged amino acids at the inner pore and a voltage-dependent Ca2+/Mg2+ block. Thus, Ca2+ has a biphasic effect on ISK, activating at low [Ca2+] yet inhibiting ISK at high [Ca2+]. We examined the effect of ISK rectification on APs in rat cardiomyocytes by simultaneously recording whole-cell apamin-sensitive currents and Ca2+ transients during an AP waveform and developed a computer model of SK channels with rectification features. The typical profile of ISK during AP clamp included an initial peak (mean 1.6 pA/pF) followed by decay to the point that submembrane [Ca2+] reached ∼10 μM. During the rest of the AP stimulus, ISK either plateaued or gradually increased as the cell repolarized and submembrane [Ca2+] decreased further. We used a six-state gating model combined with intrinsic and Ca2+/Mg2+-dependent rectification to simulate ISK and investigated the relative contributions of each type of rectification to AP shape. This SK channel model replicates key features of ISK recording during AP clamp showing that intrinsic rectification limits ISK at high Vm during the early and plateau phase of APs. Furthermore, the initial rise of Ca2+ transients activates, but higher [Ca2+] blocks SK channels, yielding a transient outward-like ISK trajectory. During the decay phase of Ca2+, the Ca2+-dependent block is released, causing ISK to rise again and contribute to repolarization. Therefore, ISK is an important repolarizing current, and the rectification characteristics of an SK channel determine its impact on early, plateau, and repolarization phases of APs.
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20
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Hoffman MJ, Cherry EM. Sensitivity of a data-assimilation system for reconstructing three-dimensional cardiac electrical dynamics. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2020; 378:20190388. [PMID: 32448069 PMCID: PMC7287341 DOI: 10.1098/rsta.2019.0388] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 02/25/2020] [Indexed: 05/21/2023]
Abstract
Modelling of cardiac electrical behaviour has led to important mechanistic insights, but important challenges, including uncertainty in model formulations and parameter values, make it difficult to obtain quantitatively accurate results. An alternative approach is combining models with observations from experiments to produce a data-informed reconstruction of system states over time. Here, we extend our earlier data-assimilation studies using an ensemble Kalman filter to reconstruct a three-dimensional time series of states with complex spatio-temporal dynamics using only surface observations of voltage. We consider the effects of several algorithmic and model parameters on the accuracy of reconstructions of known scroll-wave truth states using synthetic observations. In particular, we study the algorithm's sensitivity to parameters governing different parts of the process and its robustness to several model-error conditions. We find that the algorithm can achieve an acceptable level of error in many cases, with the weakest performance occurring for model-error cases and more extreme parameter regimes with more complex dynamics. Analysis of the poorest-performing cases indicates an initial decrease in error followed by an increase when the ensemble spread is reduced. Our results suggest avenues for further improvement through increasing ensemble spread by incorporating additive inflation or using a parameter or multi-model ensemble. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.
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Affiliation(s)
- Matthew J. Hoffman
- School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY 14623, USA
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21
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Two-variable nullcline analysis of ionic general equilibrium predicts calcium homeostasis in ventricular myocytes. PLoS Comput Biol 2020; 16:e1007572. [PMID: 32502205 PMCID: PMC7316341 DOI: 10.1371/journal.pcbi.1007572] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2019] [Revised: 06/25/2020] [Accepted: 05/05/2020] [Indexed: 01/16/2023] Open
Abstract
Ventricular contraction is roughly proportional to the amount of calcium released from the Sarcoplasmic Reticulum (SR) during systole. While it is rather straightforward to measure calcium levels and contractibility under different physiological conditions, the complexity of calcium handling during systole and diastole has made the prediction of its release at steady state impossible. Here we approach the problem analyzing the evolution of intracellular and extracellular calcium fluxes during a single beat which is away from homeostatic balance. Using an in-silico subcellular model of rabbit ventricular myocyte, we show that the high dimensional nonlinear problem of finding the steady state can be reduced to a two-variable general equilibrium condition where pre-systolic calcium level in the cytosol and in the SR must fulfill simultaneously two different equalities. This renders calcium homeostasis as a problem that can be studied in terms of its equilibrium structure, leading to precise predictions of steady state from single-beat measurements. We show how changes in ion channels modify the general equilibrium, as shocks would do in general equilibrium macroeconomic models. This allows us to predict when an enhanced entrance of calcium in the cell reduces its contractibility and explain why SERCA gene therapy, a change in calcium handling to treat heart failure, might fail to improve contraction even when it successfully increases SERCA expression. Cardiomyocytes, upon voltage excitation, release calcium, which leads to cell contraction. However, under some pathological conditions, calcium handling is impaired. Recently, SERCA gene therapy, whose aim is to improve Ca2+ sequestration by the Sarcoplasmic Reticulum (SR), has failed to improve the prognosis of patients with Heart Failure. This, together with recent counterintuitive results in calcium handling, has highlighted the need for a framework to understand calcium homeostasis across species and pathologies. We show here that the proper framework is a general equilibrium approach of two independent variables. The development of this framework allows us to find a possible mechanism for the failure of SERCA gene therapy even when it manages to increase Ca SERCA expression.
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22
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Nguyen M, Shiferaw Y. Feedback control of calcium driven alternans in cardiac myocytes. CHAOS (WOODBURY, N.Y.) 2020; 30:053106. [PMID: 32491889 PMCID: PMC7200166 DOI: 10.1063/5.0005191] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2020] [Accepted: 04/09/2020] [Indexed: 06/11/2023]
Abstract
Cardiac alternans is a beat-to-beat alternation of the action potential duration (APD), which has been implicated as a possible cause of ventricular fibrillation. Previous studies have shown that alternans can originate via a period doubling bifurcation caused by the nonlinear dependence of the APD on the previous diastolic interval. In this case, it has been demonstrated that alternans can be eliminated by applying feedback control on the pacing cycle length. However, studies have shown that alternans can also originate due to unstable calcium (Ca) cycling in cardiac myocytes. In this study, we explore the effectiveness of APD feedback control to suppress alternans when the underlying instability is due to unstable Ca cycling. In particular, we explore the role of the bi-directional coupling between Ca and voltage and determine the effectiveness of feedback control under a wide range of conditions. We also analyze the applicability of feedback control on a coupled two cell system and show that APD control induces spatially out-of-phase alternans. We analyze the onset and the necessary conditions for the emergence of these out-of-phase patterns and assess the effectiveness of feedback control to suppress Ca driven alternans in a multi-cellular system.
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23
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Kistamás K, Veress R, Horváth B, Bányász T, Nánási PP, Eisner DA. Calcium Handling Defects and Cardiac Arrhythmia Syndromes. Front Pharmacol 2020; 11:72. [PMID: 32161540 PMCID: PMC7052815 DOI: 10.3389/fphar.2020.00072] [Citation(s) in RCA: 34] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2019] [Accepted: 01/24/2020] [Indexed: 12/13/2022] Open
Abstract
Calcium ions (Ca2+) play a major role in the cardiac excitation-contraction coupling. Intracellular Ca2+ concentration increases during systole and falls in diastole thereby determining cardiac contraction and relaxation. Normal cardiac function also requires perfect organization of the ion currents at the cellular level to drive action potentials and to maintain action potential propagation and electrical homogeneity at the tissue level. Any imbalance in Ca2+ homeostasis of a cardiac myocyte can lead to electrical disturbances. This review aims to discuss cardiac physiology and pathophysiology from the elementary membrane processes that can cause the electrical instability of the ventricular myocytes through intracellular Ca2+ handling maladies to inherited and acquired arrhythmias. Finally, the paper will discuss the current therapeutic approaches targeting cardiac arrhythmias.
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Affiliation(s)
- Kornél Kistamás
- Department of Physiology, Faculty of Medicine, University of Debrecen, Debrecen, Hungary.,Division of Cardiovascular Sciences, School of Medical Sciences, University of Manchester, Manchester, United Kingdom
| | - Roland Veress
- Department of Physiology, Faculty of Medicine, University of Debrecen, Debrecen, Hungary
| | - Balázs Horváth
- Department of Physiology, Faculty of Medicine, University of Debrecen, Debrecen, Hungary
| | - Tamás Bányász
- Department of Physiology, Faculty of Medicine, University of Debrecen, Debrecen, Hungary
| | - Péter P Nánási
- Department of Physiology, Faculty of Medicine, University of Debrecen, Debrecen, Hungary.,Department of Dental Physiology, Faculty of Dentistry, University of Debrecen, Debrecen, Hungary
| | - David A Eisner
- Division of Cardiovascular Sciences, School of Medical Sciences, University of Manchester, Manchester, United Kingdom
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24
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Veasy J, Lai YM, Coombes S, Thul R. Complex patterns of subcellular cardiac alternans. J Theor Biol 2019; 478:102-114. [PMID: 31220466 DOI: 10.1016/j.jtbi.2019.06.016] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2019] [Revised: 06/12/2019] [Accepted: 06/16/2019] [Indexed: 10/26/2022]
Abstract
Cardiac alternans, in which the membrane potential and the intracellular calcium concentration exhibit alternating durations and peak amplitudes at consecutive beats, constitute a precursor to fatal cardiac arrhythmia such as sudden cardiac death. A crucial question therefore concerns the onset of cardiac alternans. Typically, alternans are only reported when they are fully developed. Here, we present a modelling approach to explore recently discovered microscopic alternans, which represent one of the earliest manifestations of cardiac alternans. In this case, the regular periodic dynamics of the local intracellular calcium concentration is already unstable, while the whole-cell behaviour suggests a healthy cell state. In particular, we use our model to investigate the impact of calcium diffusion in both the cytosol and the sarcoplasmic reticulum on the formation of microscopic calcium alternans. We find that for dominant cytosolic coupling, calcium alternans emerge via the traditional period doubling bifurcation. In contrast, dominant luminal coupling leads to a novel route to calcium alternans through a saddle-node bifurcation at the network level. Combining semi-analytical and computational approaches, we compute areas of stability in parameter space and find that as we cross from stable to unstable regions, the emergent patterns of the intracellular calcium concentration change abruptly in a fashion that is highly dependent upon position along the stability boundary. Our results demonstrate that microscopic calcium alternans may possess a much richer dynamical repertoire than previously thought and further strengthen the role of luminal calcium in shaping cardiac calcium dynamics.
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Affiliation(s)
- Joshua Veasy
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK
| | - Yi Ming Lai
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK
| | - Stephen Coombes
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK
| | - Rüdiger Thul
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK.
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25
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Romero L, Alvarez-Lacalle E, Shiferaw Y. Stochastic coupled map model of subcellular calcium cycling in cardiac cells. CHAOS (WOODBURY, N.Y.) 2019; 29:023125. [PMID: 30823735 PMCID: PMC7043839 DOI: 10.1063/1.5063462] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/07/2023]
Abstract
In this study, we analyze a nonlinear map model of intracellular calcium (Ca) and voltage in cardiac cells. In this model, Ca release from the sarcoplasmic reticulum (SR) occurs at spatially distributed dyadic junctions that are diffusively coupled. At these junctions, release occurs with a probability that depends on key variables such as the SR load and the diastolic interval. Using this model, we explore how nonlinearity and stochasticity determine the spatial distribution of Ca release events within a cardiac cell. In particular, we identify a novel synchronization transition, which occurs at rapid pacing rates, in which the global Ca transient transitions from a period 2 response to a period 1 response. In the global period 2 response dyadic junctions fire in unison, on average, on alternate beats, while in the period 1 regime, Ca release at individual dyads is highly irregular. A close examination of the spatial distribution of Ca reveals that in the period 1 regime, the system coarsens into spatially out-of-phase regions with a length scale much smaller than the system size, but larger than the spacing between dyads. We have also explored in detail the coupling to membrane voltage. We study first the case of positive coupling, where a large Ca transient promotes a long action potential duration (APD). Here, the coupling to voltage synchronizes Ca release so that the system exhibits a robust period 2 response that is independent of initial conditions. On the other hand, in the case of negative coupling, where a large Ca transient tends to shorten the APD, we find a multitude of metastable states which consist of complex spatially discordant alternans patterns. Using an analogy to equilibrium statistical mechanics, we show that the spatial patterns observed can be explained by a mapping to the Potts model, with an additional term that accounts for a global coupling of spin states. Using this analogy, we argue that Ca cycling in cardiac cells exhibits complex spatiotemporal patterns that emerge via first or second order phase transitions. These results show that voltage and Ca can interact in order to induce complex subcellular responses, which can potentially lead to heart rhythm disorders.
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Affiliation(s)
- Luis Romero
- Department of Physics, California State University, Northridge, California 91330, USA
| | - Enric Alvarez-Lacalle
- Departament de Fisica, Universitat Politècnica de Catalunya, BarcelonaTech, 08028 Barcelona, Spain
| | - Yohannes Shiferaw
- Department of Physics, California State University, Northridge, California 91330, USA
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26
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Rees CM, Yang JH, Santolini M, Lusis AJ, Weiss JN, Karma A. The Ca 2+ transient as a feedback sensor controlling cardiomyocyte ionic conductances in mouse populations. eLife 2018; 7:36717. [PMID: 30251624 PMCID: PMC6205808 DOI: 10.7554/elife.36717] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2018] [Accepted: 09/24/2018] [Indexed: 12/13/2022] Open
Abstract
Conductances of ion channels and transporters controlling cardiac excitation may vary in a population of subjects with different cardiac gene expression patterns. However, the amount of variability and its origin are not quantitatively known. We propose a new conceptual approach to predict this variability that consists of finding combinations of conductances generating a normal intracellular Ca2+ transient without any constraint on the action potential. Furthermore, we validate experimentally its predictions using the Hybrid Mouse Diversity Panel, a model system of genetically diverse mouse strains that allows us to quantify inter-subject versus intra-subject variability. The method predicts that conductances of inward Ca2+ and outward K+ currents compensate each other to generate a normal Ca2+ transient in good quantitative agreement with current measurements in ventricular myocytes from hearts of different isogenic strains. Our results suggest that a feedback mechanism sensing the aggregate Ca2+ transient of the heart suffices to regulate ionic conductances.
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Affiliation(s)
- Colin M Rees
- Physics Department, Northeastern University, Boston, United states.,Center for Interdisciplinary Research on Complex Systems, Northeastern University, Boston, United States
| | - Jun-Hai Yang
- Department of Medicine (Cardiology), Cardiovascular Research Laboratory, David Geffen School of Medicine, University of California, Los Angeles, United states.,Department of Physiology, David Geffen School of Medicine, University of California, Los Angeles, United States
| | - Marc Santolini
- Physics Department, Northeastern University, Boston, United states.,Center for Interdisciplinary Research on Complex Systems, Northeastern University, Boston, United States
| | - Aldons J Lusis
- Department of Medicine (Cardiology), Cardiovascular Research Laboratory, David Geffen School of Medicine, University of California, Los Angeles, United states.,Department of Physiology, David Geffen School of Medicine, University of California, Los Angeles, United States.,Department of Microbiology, David Geffen School of Medicine, University of California, Los Angeles, United States.,Department of Human Genetics, David Geffen School of Medicine, University of California, Los Angeles, United States
| | - James N Weiss
- Department of Medicine (Cardiology), Cardiovascular Research Laboratory, David Geffen School of Medicine, University of California, Los Angeles, United states.,Department of Physiology, David Geffen School of Medicine, University of California, Los Angeles, United States
| | - Alain Karma
- Physics Department, Northeastern University, Boston, United states.,Center for Interdisciplinary Research on Complex Systems, Northeastern University, Boston, United States
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27
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Sato D, Dixon RE, Santana LF, Navedo MF. A model for cooperative gating of L-type Ca2+ channels and its effects on cardiac alternans dynamics. PLoS Comput Biol 2018; 14:e1005906. [PMID: 29338006 PMCID: PMC5786340 DOI: 10.1371/journal.pcbi.1005906] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2017] [Revised: 01/26/2018] [Accepted: 11/29/2017] [Indexed: 11/18/2022] Open
Abstract
In ventricular myocytes, membrane depolarization during the action potential (AP) causes synchronous activation of multiple L-type CaV1.2 channels (LTCCs), which trigger the release of calcium (Ca2+) from the sarcoplasmic reticulum (SR). This results in an increase in intracellular Ca2+ (Cai) that initiates contraction. During pulsus alternans, cardiac contraction is unstable, going from weak to strong in successive beats despite a constant heart rate. These cardiac alternans can be caused by the instability of membrane potential (Vm) due to steep AP duration (APD) restitution (Vm-driven alternans), instability of Cai cycling (Ca2+-driven alternans), or both, and may be modulated by functional coupling between clustered CaV1.2 (e.g. cooperative gating). Here, mathematical analysis and computational models were used to determine how changes in the strength of cooperative gating between LTCCs may impact membrane voltage and intracellular Ca2+ dynamics in the heart. We found that increasing the degree of coupling between LTCCs increases the amplitude of Ca2+ currents (ICaL) and prolongs AP duration (APD). Increased AP duration is known to promote cardiac alternans, a potentially arrhythmogenic substrate. In addition, our analysis shows that increasing the strength of cooperative activation of LTCCs makes the coupling of Ca2+ on the membrane voltage (Cai→Vm coupling) more positive and destabilizes the Vm-Cai dynamics for Vm-driven alternans and Cai-driven alternans, but not for quasiperiodic oscillation. These results suggest that cooperative gating of LTCCs may have a major impact on cardiac excitation-contraction coupling, not only by prolonging APD, but also by altering Cai→Vm coupling and potentially promoting cardiac arrhythmias.
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Affiliation(s)
- Daisuke Sato
- Department of Pharmacology, University of California, Davis, Davis, CA, USA
- * E-mail:
| | - Rose E. Dixon
- Department of Physiology & Membrane Biology, University of California, Davis, Davis, CA, USA
| | - Luis F. Santana
- Department of Physiology & Membrane Biology, University of California, Davis, Davis, CA, USA
| | - Manuel F. Navedo
- Department of Pharmacology, University of California, Davis, Davis, CA, USA
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28
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Cantalapiedra IR, Alvarez-Lacalle E, Peñaranda A, Echebarria B. Minimal model for calcium alternans due to SR release refractoriness. CHAOS (WOODBURY, N.Y.) 2017; 27:093928. [PMID: 28964152 DOI: 10.1063/1.5000709] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
In the heart, rapid pacing rates may induce alternations in the strength of cardiac contraction, termed pulsus alternans. Often, this is due to an instability in the dynamics of the intracellular calcium concentration, whose transients become larger and smaller at consecutive beats. This alternation has been linked experimentally and theoretically to two different mechanisms: an instability due to (1) a strong dependence of calcium release on sarcoplasmic reticulum (SR) load, together with a slow calcium reuptake into the SR or (2) to SR release refractoriness, due to a slow recovery of the ryanodine receptors (RyR2) from inactivation. The relationship between calcium alternans and refractoriness of the RyR2 has been more elusive than the corresponding SR Ca load mechanism. To study the former, we reduce a general calcium model, which mimics the deterministic evolution of a calcium release unit, to its most basic elements. We show that calcium alternans can be understood using a simple nonlinear equation for calcium concentration at the dyadic space, coupled to a relaxation equation for the number of recovered RyR2s. Depending on the number of RyR2s that are recovered at the beginning of a stimulation, the increase in calcium concentration may pass, or not, over an excitability threshold that limits the occurrence of a large calcium transient. When the recovery of the RyR2 is slow, this produces naturally a period doubling bifurcation, resulting in calcium alternans. We then study the effects of inactivation, calcium diffusion, and release conductance for the onset of alternans. We find that the development of alternans requires a well-defined value of diffusion while it is less sensitive to the values of inactivation or release conductance.
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Affiliation(s)
- Inma R Cantalapiedra
- Departament de Física. Universitat Politècnica de Catalunya, Av Dr. Marañon 50 (EPSEB), Barcelona, Spain
| | - Enrique Alvarez-Lacalle
- Departament de Física. Universitat Politècnica de Catalunya, Av Dr. Marañon 50 (EPSEB), Barcelona, Spain
| | - Angelina Peñaranda
- Departament de Física. Universitat Politècnica de Catalunya, Av Dr. Marañon 50 (EPSEB), Barcelona, Spain
| | - Blas Echebarria
- Departament de Física. Universitat Politècnica de Catalunya, Av Dr. Marañon 50 (EPSEB), Barcelona, Spain
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29
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Wilson D, Ermentrout B, Němec J, Salama G. A model of cardiac ryanodine receptor gating predicts experimental Ca 2+-dynamics and Ca 2+-triggered arrhythmia in the long QT syndrome. CHAOS (WOODBURY, N.Y.) 2017; 27:093940. [PMID: 28964110 DOI: 10.1063/1.5000711] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Abnormal Ca2+ handling is well-established as the trigger of cardiac arrhythmia in catecholaminergic polymorphic ventricular tachycardia and digoxin toxicity, but its role remains controversial in Torsade de Pointes (TdP), the arrhythmia associated with the long QT syndrome (LQTS). Recent experimental results show that early afterdepolarizations (EADs) that initiate TdP are caused by spontaneous (non-voltage-triggered) Ca2+ release from Ca2+-overloaded sarcoplasmic reticulum (SR) rather than the activation of the L-type Ca2+-channel window current. In bradycardia and long QT type 2 (LQT2), a second, non-voltage triggered cytosolic Ca2+ elevation increases gradually in amplitude, occurs before overt voltage instability, and then precedes the rise of EADs. Here, we used a modified Shannon-Puglisi-Bers model of rabbit ventricular myocytes to reproduce experimental Ca2+ dynamics in bradycardia and LQT2. Abnormal systolic Ca2+-oscillations and EADs caused by SR Ca2+-release are reproduced in a modified 0-dimensional model, where 3 gates in series control the ryanodine receptor (RyR2) conductance. Two gates control RyR2 activation and inactivation and sense cytosolic Ca2+ while a third gate senses luminal junctional SR Ca2+. The model predicts EADs in bradycardia and low extracellular [K+] and cessation of SR Ca2+-release terminate salvos of EADs. Ca2+-waves, systolic cell-synchronous Ca2+-release, and multifocal diastolic Ca2+ release seen in subcellular Ca2+-mapping experiments are observed in the 2-dimensional version of the model. These results support the role of SR Ca2+-overload, abnormal SR Ca2+-release, and the subsequent activation of the electrogenic Na+/Ca2+-exchanger as the mechanism of TdP. The model offers new insights into the genesis of cardiac arrhythmia and new therapeutic strategies.
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Affiliation(s)
- Dan Wilson
- Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, USA
| | - Bard Ermentrout
- Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, USA
| | - Jan Němec
- Department of Medicine, Heart and Vascular Institute, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, USA
| | - Guy Salama
- Department of Medicine, Heart and Vascular Institute, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, USA
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30
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Cherry EM. Distinguishing mechanisms for alternans in cardiac cells using constant-diastolic-interval pacing. CHAOS (WOODBURY, N.Y.) 2017; 27:093902. [PMID: 28964159 DOI: 10.1063/1.4999354] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
Alternans, a proarrhythmic dynamical state in which cardiac action potentials alternate between long and short durations despite a constant pacing period, traditionally has been explained at the cellular level using nonlinear dynamics principles under the assumption that the action potential duration (APD) is determined solely by the time elapsed since the end of the previous action potential, called the diastolic interval (DI). In this scenario, APDs at a steady state should be the same provided that the preceding DIs are the same. Nevertheless, experiments attempting to eliminate alternans by dynamically adjusting the timing of pacing stimuli to keep the DI constant showed that alternans persisted, contradicting the traditional theory. It is now widely known that alternans also can arise from a different mechanism associated with intracellular calcium cycling. Our goal is to determine whether intracellular calcium dynamics can explain the experimental findings regarding the persistence of alternans despite a constant DI. For this, we use mathematical models capable of producing alternans through both voltage- and calcium-mediated mechanisms. We show that for voltage-driven alternans, action potentials elicited from a constant-DI protocol are always the same. However, in the case of calcium-driven alternans, the constant-DI protocol can result in alternans. Reducing the strength of the calcium instability progressively reduces and finally eliminates constant-DI alternans. Our findings suggest that screening for the presence of alternans using a constant-DI protocol has the potential for differentiating between voltage-driven and calcium-driven alternans.
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Affiliation(s)
- Elizabeth M Cherry
- School of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York 14623, USA
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31
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Shiferaw Y, Aistrup GL, Wasserstrom JA. Mechanism for Triggered Waves in Atrial Myocytes. Biophys J 2017; 113:656-670. [PMID: 28793220 DOI: 10.1016/j.bpj.2017.06.026] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2017] [Revised: 06/13/2017] [Accepted: 06/14/2017] [Indexed: 01/27/2023] Open
Abstract
Excitation-contraction coupling in atrial cells is mediated by calcium (Ca) signaling between L-type Ca channels and Ryanodine receptors that occurs mainly at the cell boundary. This unique architecture dictates essential aspects of Ca signaling under both normal and diseased conditions. In this study we apply laser scanning confocal microscopy, along with an experimentally based computational model, to understand the Ca cycling dynamics of an atrial cell subjected to rapid pacing. Our main finding is that when an atrial cell is paced under Ca overload conditions, Ca waves can then nucleate on the cell boundary and propagate to the cell interior. These propagating Ca waves are referred to as "triggered waves" because they are initiated by L-type Ca channel openings during the action potential. These excitations are distinct from spontaneous Ca waves originating from random fluctuations of Ryanodine receptor channels, and which occur after much longer waiting times. Furthermore, we argue that the onset of these triggered waves is a highly nonlinear function of the sarcoplasmic reticulum Ca load. This strong nonlinearity leads to aperiodic response of Ca at rapid pacing rates that is caused by the complex interplay between paced Ca release and triggered waves. We argue further that this feature of atrial cells leads to dynamic instabilities that may underlie atrial arrhythmias. These studies will serve as a starting point to explore the nonlinear dynamics of atrial cells and will yield insights into the trigger and maintenance of atrial fibrillation.
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Affiliation(s)
- Yohannes Shiferaw
- Department of Physics and Astronomy, California State University, Northridge, California.
| | - Gary L Aistrup
- Department of Medicine (Cardiology) and the Feinberg Cardiovascular Research Institute, Northwestern University Feinberg School of Medicine, Chicago, Illinois
| | - J Andrew Wasserstrom
- Department of Medicine (Cardiology) and the Feinberg Cardiovascular Research Institute, Northwestern University Feinberg School of Medicine, Chicago, Illinois
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32
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Dynamics of spatiotemporal line defects and chaos control in complex excitable systems. Sci Rep 2017; 7:7757. [PMID: 28798384 PMCID: PMC5552747 DOI: 10.1038/s41598-017-08011-z] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2017] [Accepted: 06/30/2017] [Indexed: 12/01/2022] Open
Abstract
Spatiotemporal pattern formation governs dynamics and functions in various biological systems. In the heart, excitable waves can form complex oscillatory and chaotic patterns even at an abnormally higher frequency than normal heart beats, which increase the risk of fatal heart conditions by inhibiting normal blood circulation. Previous studies suggested that line defects (nodal lines) play a critical role in stabilizing those undesirable patterns. However, it remains unknown if the line defects are static or dynamically changing structures in heart tissue. Through in vitro experiments of heart tissue observation, we reveal the spatiotemporal dynamics of line defects in rotating spiral waves. We combined a novel signaling over-sampling technique with a multi-dimensional Fourier analysis, showing that line defects can translate, merge, collapse and form stable singularities with even and odd parity while maintaining a stable oscillation of the spiral wave in the tissue. These findings provide insights into a broad class of complex periodic systems, with particular impact to the control and understanding of heart diseases.
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33
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Kanaporis G, Blatter LA. Alternans in atria: Mechanisms and clinical relevance. MEDICINA-LITHUANIA 2017; 53:139-149. [PMID: 28666575 DOI: 10.1016/j.medici.2017.04.004] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/21/2017] [Accepted: 04/25/2017] [Indexed: 12/29/2022]
Abstract
Atrial fibrillation is the most common sustained arrhythmia and its prevalence is rapidly rising with the aging of the population. Cardiac alternans, defined as cyclic beat-to-beat alternations in contraction force, action potential (AP) duration and intracellular Ca2+ release at constant stimulation rate, has been associated with the development of ventricular arrhythmias. Recent clinical data also provide strong evidence that alternans plays a central role in arrhythmogenesis in atria. The aim of this article is to review the mechanisms that are responsible for repolarization alternans and contribute to the transition from spatially concordant alternans to the more arrhythmogenic spatially discordant alternans in atria.
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Affiliation(s)
- Giedrius Kanaporis
- Department of Physiology & Biophysics, Rush University Medical Center, Chicago, USA.
| | - Lothar A Blatter
- Department of Physiology & Biophysics, Rush University Medical Center, Chicago, USA
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34
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Kennedy M, Bers DM, Chiamvimonvat N, Sato D. Dynamical effects of calcium-sensitive potassium currents on voltage and calcium alternans. J Physiol 2017; 595:2285-2297. [PMID: 27902841 DOI: 10.1113/jp273626] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2016] [Accepted: 11/22/2016] [Indexed: 01/12/2023] Open
Abstract
KEY POINTS A mathematical model of a small conductance Ca2+ -activated potassium (SK) channel was developed and incorporated into a physiologically detailed ventricular myocyte model. Ca2+ -sensitive K+ currents promote negative intracellular Ca2+ to membrane voltage (CAi2+ → Vm ) coupling. Increase of Ca2+ -sensitive K+ currents can be responsible for electromechanically discordant alternans and quasiperiodic oscillations at the cellular level. At the tissue level, Turing-type instability can occur when Ca2+ -sensitive K+ currents are increased. ABSTRACT Cardiac alternans is a precursor to life-threatening arrhythmias. Alternans can be caused by instability of the membrane voltage (Vm ), instability of the intracellular Ca2+ ( Ca i2+) cycling, or both. Vm dynamics and Ca i2+ dynamics are coupled via Ca2+ -sensitive currents. In cardiac myocytes, there are several Ca2+ -sensitive potassium (K+ ) currents such as the slowly activating delayed rectifier current (IKs ) and the small conductance Ca2+ -activated potassium (SK) current (ISK ). However, the role of these currents in the development of arrhythmias is not well understood. In this study, we investigated how these currents affect voltage and Ca2+ alternans using a physiologically detailed computational model of the ventricular myocyte and mathematical analysis. We define the coupling between Vm and Ca i2+ cycling dynamics ( Ca i2+→Vm coupling) as positive (negative) when a larger Ca2+ transient at a given beat prolongs (shortens) the action potential duration (APD) of that beat. While positive coupling predominates at baseline, increasing IKs and ISK promote negative Ca i2+→Vm coupling at the cellular level. Specifically, when alternans is Ca2+ -driven, electromechanically (APD-Ca2+ ) concordant alternans becomes electromechanically discordant alternans as IKs or ISK increase. These cellular level dynamics lead to different types of spatially discordant alternans in tissue. These findings help to shed light on the underlying mechanisms of cardiac alternans especially when the relative strength of these currents becomes larger under pathological conditions or drug administrations.
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Affiliation(s)
- Matthew Kennedy
- Department of Biomedical Engineering, University of California, Davis, CA, USA
| | - Donald M Bers
- Department of Pharmacology, University of California, Davis, CA, USA
| | - Nipavan Chiamvimonvat
- Division of Cardiovascular Medicine, Department of Internal Medicine, University of California, Davis, CA, USA.,Department of Veterans Affairs, Northern California Health Care System, Mather, CA, USA
| | - Daisuke Sato
- Department of Pharmacology, University of California, Davis, CA, USA
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35
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Gambardella J, Trimarco B, Iaccarino G, Santulli G. New Insights in Cardiac Calcium Handling and Excitation-Contraction Coupling. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2017; 1067:373-385. [PMID: 28956314 DOI: 10.1007/5584_2017_106] [Citation(s) in RCA: 52] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Abstract
Excitation-contraction (EC) coupling denotes the conversion of electric stimulus in mechanic output in contractile cells. Several studies have demonstrated that calcium (Ca2+) plays a pivotal role in this process. Here we present a comprehensive and updated description of the main systems involved in cardiac Ca2+ handling that ensure a functional EC coupling and their pathological alterations, mainly related to heart failure.
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Affiliation(s)
- Jessica Gambardella
- Department of Advanced Biomedical Sciences, "Federico II" University, Naples, Italy.,Department of Medicine, Surgery and Dentistry, Scuola Medica Salernitana, University of Salerno, Fisciano, Italy
| | - Bruno Trimarco
- Department of Advanced Biomedical Sciences, "Federico II" University, Naples, Italy
| | - Guido Iaccarino
- Department of Medicine, Surgery and Dentistry, Scuola Medica Salernitana, University of Salerno, Fisciano, Italy
| | - Gaetano Santulli
- Department of Advanced Biomedical Sciences, "Federico II" University, Naples, Italy. .,Department of Medicine, Albert Einstein College of Medicine, 1300 Morris Park Ave, Forch 525, 10461, New York, NY, USA.
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36
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A unified theory of calcium alternans in ventricular myocytes. Sci Rep 2016; 6:35625. [PMID: 27762397 PMCID: PMC5071909 DOI: 10.1038/srep35625] [Citation(s) in RCA: 35] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2016] [Accepted: 10/04/2016] [Indexed: 11/27/2022] Open
Abstract
Intracellular calcium (Ca2+) alternans is a dynamical phenomenon in ventricular myocytes, which is linked to the genesis of lethal arrhythmias. Iterated map models of intracellular Ca2+ cycling dynamics in ventricular myocytes under periodic pacing have been developed to study the mechanisms of Ca2+ alternans. Two mechanisms of Ca2+ alternans have been demonstrated in these models: one relies mainly on fractional sarcoplasmic reticulum Ca2+ release and uptake, and the other on refractoriness and other properties of Ca2+ sparks. Each of the two mechanisms can partially explain the experimental observations, but both have their inconsistencies with the experimental results. Here we developed an iterated map model that is composed of two coupled iterated maps, which unifies the two mechanisms into a single cohesive mathematical framework. The unified theory can consistently explain the seemingly contradictory experimental observations and shows that the two mechanisms work synergistically to promote Ca2+ alternans. Predictions of the theory were examined in a physiologically-detailed spatial Ca2+ cycling model of ventricular myocytes.
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37
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Shiferaw Y. Nonlinear onset of calcium wave propagation in cardiac cells. Phys Rev E 2016; 94:032405. [PMID: 27739779 DOI: 10.1103/physreve.94.032405] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2016] [Indexed: 12/20/2022]
Abstract
Spontaneous calcium (Ca) waves in cardiac myocytes are known to underlie a wide range of cardiac arrhythmias. However, it is not understood which physiological parameters determine the onset of waves. In this study, we explore the relationship between Ca signaling between ion channels and the nucleation of Ca waves. In particular, we apply a master equation approach to analyze the stochastic interaction between neighboring clusters of ryanodine receptor (RyR) channels. Using this analysis, we show that signaling between clusters can be described as a barrier hopping process with exponential sensitivity to system parameters. A consequence of this feature is that the probability that Ca release at a cluster induces release at a neighboring cluster exhibits a sigmoid dependence on the Ca content in the cell. This nonlinearity originates from the regulation of RyR opening due to more than one Ca ion binding site, in conjunction with Ca mediated cooperativity between RyR channels in clusters. We apply a spatially distributed stochastic model of Ca cycling to analyze the physiological consequences of this nonlinearity, and show that it explains the sharp onset of Ca wave nucleation in cardiac cells. Furthermore, we show that this sharp onset can serve as a mechanism for Ca alternans under physiologically relevant conditions. Thus our findings identify the nonlinear features of Ca signaling which potentially underlie the onset of Ca waves and Ca alternans in cardiac cells.
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Affiliation(s)
- Yohannes Shiferaw
- Department of Physics & Astronomy, California State University, Northridge, 18111 Nordhoff Street, Northridge, California 91330, USA
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38
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Eastman J, Sass J, Gomes JM, dos Santos RW, Cherry EM. Using delay differential equations to induce alternans in a model of cardiac electrophysiology. J Theor Biol 2016; 404:262-272. [DOI: 10.1016/j.jtbi.2016.06.009] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/07/2016] [Revised: 05/19/2016] [Accepted: 06/07/2016] [Indexed: 11/26/2022]
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39
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Gemmell P, Burrage K, Rodríguez B, Quinn TA. Rabbit-specific computational modelling of ventricular cell electrophysiology: Using populations of models to explore variability in the response to ischemia. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2016; 121:169-84. [PMID: 27320382 PMCID: PMC5405055 DOI: 10.1016/j.pbiomolbio.2016.06.003] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/21/2016] [Accepted: 06/13/2016] [Indexed: 11/04/2022]
Abstract
Computational modelling, combined with experimental investigations, is a powerful method for investigating complex cardiac electrophysiological behaviour. The use of rabbit-specific models, due to the similarities of cardiac electrophysiology in this species with human, is especially prevalent. In this paper, we first briefly review rabbit-specific computational modelling of ventricular cell electrophysiology, multi-cellular simulations including cellular heterogeneity, and acute ischemia. This mini-review is followed by an original computational investigation of variability in the electrophysiological response of two experimentally-calibrated populations of rabbit-specific ventricular myocyte action potential models to acute ischemia. We performed a systematic exploration of the response of the model populations to varying degrees of ischemia and individual ischemic parameters, to investigate their individual and combined effects on action potential duration and refractoriness. This revealed complex interactions between model population variability and ischemic factors, which combined to enhance variability during ischemia. This represents an important step towards an improved understanding of the role that physiological variability may play in electrophysiological alterations during acute ischemia.
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Affiliation(s)
- Philip Gemmell
- Department of Computer Science, University of Oxford, Oxford, UK
| | - Kevin Burrage
- Department of Computer Science, University of Oxford, Oxford, UK; School of Mathematical Sciences and ARC Centre of Excellence, ACEMS, Queensland University of Technology, Brisbane, Australia
| | - Blanca Rodríguez
- Department of Computer Science, University of Oxford, Oxford, UK
| | - T Alexander Quinn
- Department of Physiology and Biophysics, Dalhousie University, 5850 College St, Lab 3F, Halifax, NS B3H 4R2, Canada; School of Biomedical Engineering, Dalhousie University, 5850 College St, Lab 3F, Halifax, NS B3H 4R2, Canada.
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40
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Guevara MR, Shrier A, Orlowski J, Glass L. George Ralph Mines (1886-1914): the dawn of cardiac nonlinear dynamics. J Physiol 2016; 594:2361-71. [PMID: 27126414 DOI: 10.1113/jp270891] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2015] [Accepted: 01/29/2016] [Indexed: 11/08/2022] Open
Affiliation(s)
- Michael R Guevara
- Department of Physiology, McGill University, Montreal, Quebec, Canada
| | - Alvin Shrier
- Department of Physiology, McGill University, Montreal, Quebec, Canada
| | - John Orlowski
- Department of Physiology, McGill University, Montreal, Quebec, Canada
| | - Leon Glass
- Department of Physiology, McGill University, Montreal, Quebec, Canada
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41
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Madhvani RV, Angelini M, Xie Y, Pantazis A, Suriany S, Borgstrom NP, Garfinkel A, Qu Z, Weiss JN, Olcese R. Targeting the late component of the cardiac L-type Ca2+ current to suppress early afterdepolarizations. ACTA ACUST UNITED AC 2016; 145:395-404. [PMID: 25918358 PMCID: PMC4411259 DOI: 10.1085/jgp.201411288] [Citation(s) in RCA: 40] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
Abstract
Early afterdepolarizations (EADs) associated with prolongation of the cardiac action potential (AP) can create heterogeneity of repolarization and premature extrasystoles, triggering focal and reentrant arrhythmias. Because the L-type Ca(2+) current (ICa,L) plays a key role in both AP prolongation and EAD formation, L-type Ca(2+) channels (LTCCs) represent a promising therapeutic target to normalize AP duration (APD) and suppress EADs and their arrhythmogenic consequences. We used the dynamic-clamp technique to systematically explore how the biophysical properties of LTCCs could be modified to normalize APD and suppress EADs without impairing excitation-contraction coupling. Isolated rabbit ventricular myocytes were first exposed to H2O2 or moderate hypokalemia to induce EADs, after which their endogenous ICa,L was replaced by a virtual ICa,L with tunable parameters, in dynamic-clamp mode. We probed the sensitivity of EADs to changes in the (a) amplitude of the noninactivating pedestal current; (b) slope of voltage-dependent activation; (c) slope of voltage-dependent inactivation; (d) time constant of voltage-dependent activation; and (e) time constant of voltage-dependent inactivation. We found that reducing the amplitude of the noninactivating pedestal component of ICa,L effectively suppressed both H2O2- and hypokalemia-induced EADs and restored APD. These results, together with our previous work, demonstrate the potential of this hybrid experimental-computational approach to guide drug discovery or gene therapy strategies by identifying and targeting selective properties of LTCC.
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Affiliation(s)
- Roshni V Madhvani
- Division of Molecular Medicine, Department of Anesthesiology, Department of Medicine (Cardiology), Department of Physiology, Department of Integrative Biology and Physiology, Cardiovascular Research Laboratory, and Brain Research Institute, David Geffen School of Medicine at University of California, Los Angeles, Los Angeles, CA 90095
| | - Marina Angelini
- Division of Molecular Medicine, Department of Anesthesiology, Department of Medicine (Cardiology), Department of Physiology, Department of Integrative Biology and Physiology, Cardiovascular Research Laboratory, and Brain Research Institute, David Geffen School of Medicine at University of California, Los Angeles, Los Angeles, CA 90095
| | - Yuanfang Xie
- Department of Pharmacology, University of California, Davis, Davis, CA 95616
| | - Antonios Pantazis
- Division of Molecular Medicine, Department of Anesthesiology, Department of Medicine (Cardiology), Department of Physiology, Department of Integrative Biology and Physiology, Cardiovascular Research Laboratory, and Brain Research Institute, David Geffen School of Medicine at University of California, Los Angeles, Los Angeles, CA 90095
| | - Silvie Suriany
- Division of Molecular Medicine, Department of Anesthesiology, Department of Medicine (Cardiology), Department of Physiology, Department of Integrative Biology and Physiology, Cardiovascular Research Laboratory, and Brain Research Institute, David Geffen School of Medicine at University of California, Los Angeles, Los Angeles, CA 90095
| | - Nils P Borgstrom
- Division of Molecular Medicine, Department of Anesthesiology, Department of Medicine (Cardiology), Department of Physiology, Department of Integrative Biology and Physiology, Cardiovascular Research Laboratory, and Brain Research Institute, David Geffen School of Medicine at University of California, Los Angeles, Los Angeles, CA 90095
| | - Alan Garfinkel
- Division of Molecular Medicine, Department of Anesthesiology, Department of Medicine (Cardiology), Department of Physiology, Department of Integrative Biology and Physiology, Cardiovascular Research Laboratory, and Brain Research Institute, David Geffen School of Medicine at University of California, Los Angeles, Los Angeles, CA 90095 Division of Molecular Medicine, Department of Anesthesiology, Department of Medicine (Cardiology), Department of Physiology, Department of Integrative Biology and Physiology, Cardiovascular Research Laboratory, and Brain Research Institute, David Geffen School of Medicine at University of California, Los Angeles, Los Angeles, CA 90095 Division of Molecular Medicine, Department of Anesthesiology, Department of Medicine (Cardiology), Department of Physiology, Department of Integrative Biology and Physiology, Cardiovascular Research Laboratory, and Brain Research Institute, David Geffen School of Medicine at University of California, Los Angeles, Los Angeles, CA 90095
| | - Zhilin Qu
- Division of Molecular Medicine, Department of Anesthesiology, Department of Medicine (Cardiology), Department of Physiology, Department of Integrative Biology and Physiology, Cardiovascular Research Laboratory, and Brain Research Institute, David Geffen School of Medicine at University of California, Los Angeles, Los Angeles, CA 90095 Division of Molecular Medicine, Department of Anesthesiology, Department of Medicine (Cardiology), Department of Physiology, Department of Integrative Biology and Physiology, Cardiovascular Research Laboratory, and Brain Research Institute, David Geffen School of Medicine at University of California, Los Angeles, Los Angeles, CA 90095
| | - James N Weiss
- Division of Molecular Medicine, Department of Anesthesiology, Department of Medicine (Cardiology), Department of Physiology, Department of Integrative Biology and Physiology, Cardiovascular Research Laboratory, and Brain Research Institute, David Geffen School of Medicine at University of California, Los Angeles, Los Angeles, CA 90095 Division of Molecular Medicine, Department of Anesthesiology, Department of Medicine (Cardiology), Department of Physiology, Department of Integrative Biology and Physiology, Cardiovascular Research Laboratory, and Brain Research Institute, David Geffen School of Medicine at University of California, Los Angeles, Los Angeles, CA 90095 Division of Molecular Medicine, Department of Anesthesiology, Department of Medicine (Cardiology), Department of Physiology, Department of Integrative Biology and Physiology, Cardiovascular Research Laboratory, and Brain Research Institute, David Geffen School of Medicine at University of California, Los Angeles, Los Angeles, CA 90095
| | - Riccardo Olcese
- Division of Molecular Medicine, Department of Anesthesiology, Department of Medicine (Cardiology), Department of Physiology, Department of Integrative Biology and Physiology, Cardiovascular Research Laboratory, and Brain Research Institute, David Geffen School of Medicine at University of California, Los Angeles, Los Angeles, CA 90095 Division of Molecular Medicine, Department of Anesthesiology, Department of Medicine (Cardiology), Department of Physiology, Department of Integrative Biology and Physiology, Cardiovascular Research Laboratory, and Brain Research Institute, David Geffen School of Medicine at University of California, Los Angeles, Los Angeles, CA 90095 Division of Molecular Medicine, Department of Anesthesiology, Department of Medicine (Cardiology), Department of Physiology, Department of Integrative Biology and Physiology, Cardiovascular Research Laboratory, and Brain Research Institute, David Geffen School of Medicine at University of California, Los Angeles, Los Angeles, CA 90095 Division of Molecular Medicine, Department of Anesthesiology, Department of Medicine (Cardiology), Department of Physiology, Department of Integrative Biology and Physiology, Cardiovascular Research Laboratory, and Brain Research Institute, David Geffen School of Medicine at University of California, Los Angeles, Los Angeles, CA 90095
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Echebarria B, Alvarez-Lacalle E, Cantalapiedra IR, Peñaranda A. Mechanisms Underlying Electro-Mechanical Cardiac Alternans. SEMA SIMAI SPRINGER SERIES 2016. [DOI: 10.1007/978-3-319-33054-9_6] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
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Edwards JN, Blatter LA. Cardiac alternans and intracellular calcium cycling. Clin Exp Pharmacol Physiol 2015; 41:524-32. [PMID: 25040398 DOI: 10.1111/1440-1681.12231] [Citation(s) in RCA: 66] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2013] [Revised: 03/12/2014] [Accepted: 03/17/2014] [Indexed: 12/20/2022]
Abstract
Cardiac alternans refers to a condition in which there is a periodic beat-to-beat oscillation in electrical activity and the strength of cardiac muscle contraction at a constant heart rate. Clinically, cardiac alternans occurs in settings that are typical for cardiac arrhythmias and has been causally linked to these conditions. At the cellular level, alternans is defined as beat-to-beat alternations in contraction amplitude (mechanical alternans), action potential duration (APD; electrical or APD alternans) and Ca(2+) transient amplitude (Ca(2+) alternans). The cause of alternans is multifactorial; however, alternans always originate from disturbances of the bidirectional coupling between membrane voltage (Vm ) and intracellular calcium ([Ca(2+) ]i ). Bidirectional coupling refers to the fact that, in cardiac cells, Vm depolarization and the generation of action potentials cause the elevation of [Ca(2+) ]i that is required for contraction (a process referred to as excitation-contraction coupling); conversely, changes of [Ca(2+) ]i control Vm because important membrane currents are Ca(2+) dependent. Evidence is mounting that alternans is ultimately caused by disturbances of cellular Ca(2+) signalling. Herein we review how two key factors of cardiac cellular Ca(2+) cycling, namely the release of Ca(2+) from internal stores and the capability of clearing the cytosol from Ca(2+) after each beat, determine the conditions under which alternans occurs. The contributions from key Ca(2+) -handling proteins (i.e. surface membrane channels, ion pumps and transporters and internal Ca(2+) release channels) are discussed.
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Affiliation(s)
- Joshua N Edwards
- Department of Molecular Biophysics and Physiology, Rush University Medical Center, Chicago, IL, USA
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Alvarez-Lacalle E, Echebarria B, Spalding J, Shiferaw Y. Calcium alternans is due to an order-disorder phase transition in cardiac cells. PHYSICAL REVIEW LETTERS 2015; 114:108101. [PMID: 25815968 DOI: 10.1103/physrevlett.114.108101] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/23/2014] [Indexed: 05/23/2023]
Abstract
Electromechanical alternans is a beat-to-beat alternation in the strength of contraction of a cardiac cell, which can be caused by an instability of calcium cycling. Using a distributed model of subcellular calcium we show that alternans occurs via an order-disorder phase transition which exhibits critical slowing down and a diverging correlation length. We apply finite size scaling along with a mapping to a stochastic coupled map model, to show that this transition in two dimensions is characterized by critical exponents consistent with the Ising universality class. These findings highlight the important role of cooperativity in biological cells, and suggest novel approaches to investigate the onset of the alternans instability in the heart.
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Affiliation(s)
- Enrique Alvarez-Lacalle
- Departament de Física Aplicada, Universitat Politècnica de Catalunya·BarcelonaTech, 08028 Barcelona, Spain
| | - Blas Echebarria
- Departament de Física Aplicada, Universitat Politècnica de Catalunya·BarcelonaTech, 08028 Barcelona, Spain
| | - Jon Spalding
- Department of Physics and Astronomy, California State University, Northridge, California 91330, USA
| | - Yohannes Shiferaw
- Department of Physics and Astronomy, California State University, Northridge, California 91330, USA
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45
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Abstract
RATIONALE Alternans is a risk factor for cardiac arrhythmia, including atrial fibrillation. At the cellular level alternans manifests as beat-to-beat alternations in contraction, action potential duration (APD), and magnitude of the Ca(2+) transient (CaT). Electromechanical and CaT alternans are highly correlated, however, it has remained controversial whether the primary cause of alternans is a disturbance of cellular Ca(2+) signaling or electrical membrane properties. OBJECTIVE To determine whether a primary failure of intracellular Ca(2+) regulation or disturbances in membrane potential and AP regulation are responsible for the occurrence of alternans in atrial myocytes. METHODS AND RESULTS Pacing-induced APD and CaT alternans were studied in single rabbit atrial and ventricular myocytes using combined [Ca(2+)]i and electrophysiological measurements. In current-clamp experiments, APD and CaT alternans strongly correlated in time and magnitude. CaT alternans was observed without alternation in L-type Ca(2+) current, however, elimination of intracellular Ca(2+) release abolished APD alternans, indicating that [Ca(2+)]i dynamics have a profound effect on the occurrence of CaT alternans. Trains of 2 distinctive voltage commands in form of APs recorded during large and small alternans CaTs were applied to voltage-clamped cells. CaT alternans was observed with and without alternation in the voltage command shape. During alternans AP-clamp large CaTs coincided with both long and short AP waveforms, indicating that CaT alternans develop irrespective of AP dynamics. CONCLUSIONS The primary mechanism underlying alternans in atrial cells, similarly to ventricular cells, resides in a disturbance of Ca(2+) signaling, whereas APD alternans are a secondary consequence, mediated by Ca(2+)-dependent AP modulation.
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Affiliation(s)
- Giedrius Kanaporis
- From the Department of Molecular Biophysics and Physiology, Rush University Medical Center, Chicago, IL
| | - Lothar A Blatter
- From the Department of Molecular Biophysics and Physiology, Rush University Medical Center, Chicago, IL.
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46
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Chang KC, Bayer JD, Trayanova NA. Disrupted calcium release as a mechanism for atrial alternans associated with human atrial fibrillation. PLoS Comput Biol 2014; 10:e1004011. [PMID: 25501557 PMCID: PMC4263367 DOI: 10.1371/journal.pcbi.1004011] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/27/2014] [Accepted: 10/29/2014] [Indexed: 12/19/2022] Open
Abstract
Atrial fibrillation (AF) is the most common cardiac arrhythmia, but our knowledge of the arrhythmogenic substrate is incomplete. Alternans, the beat-to-beat alternation in the shape of cardiac electrical signals, typically occurs at fast heart rates and leads to arrhythmia. However, atrial alternans have been observed at slower pacing rates in AF patients than in controls, suggesting that increased vulnerability to arrhythmia in AF patients may be due to the proarrythmic influence of alternans at these slower rates. As such, alternans may present a useful therapeutic target for the treatment and prevention of AF, but the mechanism underlying alternans occurrence in AF patients at heart rates near rest is unknown. The goal of this study was to determine how cellular changes that occur in human AF affect the appearance of alternans at heart rates near rest. To achieve this, we developed a computational model of human atrial tissue incorporating electrophysiological remodeling associated with chronic AF (cAF) and performed parameter sensitivity analysis of ionic model parameters to determine which cellular changes led to alternans. Of the 20 parameters tested, only decreasing the ryanodine receptor (RyR) inactivation rate constant (kiCa) produced action potential duration (APD) alternans seen clinically at slower pacing rates. Using single-cell clamps of voltage, fluxes, and state variables, we determined that alternans onset was Ca2+-driven rather than voltage-driven and occurred as a result of decreased RyR inactivation which led to increased steepness of the sarcoplasmic reticulum (SR) Ca2+ release slope. Iterated map analysis revealed that because SR Ca2+ uptake efficiency was much higher in control atrial cells than in cAF cells, drastic reductions in kiCa were required to produce alternans at comparable pacing rates in control atrial cells. These findings suggest that RyR kinetics may play a critical role in altered Ca2+ homeostasis which drives proarrhythmic APD alternans in patients with AF. Atrial fibrillation is an irregular heart rhythm affecting millions of people worldwide. Effective treatment of this cardiac disorder relies upon our detailed knowledge and understanding of the mechanisms that lead to arrhythmia. Recent clinical observations have suggested that alternans, a phenomenon where the shape of the electrical signal in the heart alternates from beat to beat, may play an important role in this process, but the underlying mechanisms remain unknown. In this study, we use computational models to conduct a detailed examination of the causes and contributors to alternans associated with human atrial fibrillation. We find that in atria remodeled by atrial fibrillation, alternans appears near resting heart rates because several aspects of calcium cycling are disrupted in the atrial cells. In particular, the release and uptake of calcium from the cellular storage compartment, the sarcoplasmic reticulum, becomes imbalanced, leading to alternation in calcium signals from beat to beat. These findings provide important insights into the mechanisms of proarrhythmic alternans in human atrial fibrillation which may be used to develop novel therapeutic targets and treatment strategies in the future.
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Affiliation(s)
- Kelly C. Chang
- Institute for Computational Medicine, Department of Biomedical Engineering, Johns Hopkins University, Baltimore, Maryland, United States of America
| | - Jason D. Bayer
- IHU-LIRYC - L'Institut de RYthmologie et Modélisation Cardiaque, University of Bordeaux, Bordeaux, France
| | - Natalia A. Trayanova
- Institute for Computational Medicine, Department of Biomedical Engineering, Johns Hopkins University, Baltimore, Maryland, United States of America
- * E-mail:
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Skardal PS, Restrepo JG. Coexisting chaotic and multi-periodic dynamics in a model of cardiac alternans. CHAOS (WOODBURY, N.Y.) 2014; 24:043126. [PMID: 25554046 DOI: 10.1063/1.4901728] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
The spatiotemporal dynamics of cardiac tissue is an active area of research for biologists, physicists, and mathematicians. Of particular interest is the study of period-doubling bifurcations and chaos due to their link with cardiac arrhythmogenesis. In this paper, we study the spatiotemporal dynamics of a recently developed model for calcium-driven alternans in a one dimensional cable of tissue. In particular, we observe in the cable coexistence of regions with chaotic and multi-periodic dynamics over wide ranges of parameters. We study these dynamics using global and local Lyapunov exponents and spatial trajectory correlations. Interestingly, near nodes-or phase reversals-low-periodic dynamics prevail, while away from the nodes, the dynamics tend to be higher-periodic and eventually chaotic. Finally, we show that similar coexisting multi-periodic and chaotic dynamics can also be observed in a detailed ionic model.
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Affiliation(s)
- Per Sebastian Skardal
- Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain
| | - Juan G Restrepo
- Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309, USA
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Rodrigo M, Pedrón-Torecilla J, Hernández I, Liberos A, Climent AM, Guillem MS. Data analysis in cardiac arrhythmias. Methods Mol Biol 2014; 1246:217-35. [PMID: 25417089 DOI: 10.1007/978-1-4939-1985-7_14] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/21/2023]
Abstract
Cardiac arrhythmias are an increasingly present in developed countries and represent a major health and economic burden. The occurrence of cardiac arrhythmias is closely linked to the electrical function of the heart. Consequently, the analysis of the electrical signal generated by the heart tissue, either recorded invasively or noninvasively, provides valuable information for the study of cardiac arrhythmias. In this chapter, novel cardiac signal analysis techniques that allow the study and diagnosis of cardiac arrhythmias are described, with emphasis on cardiac mapping which allows for spatiotemporal analysis of cardiac signals.Cardiac mapping can serve as a diagnostic tool by recording cardiac signals either in close contact to the heart tissue or noninvasively from the body surface, and allows the identification of cardiac sites responsible of the development or maintenance of arrhythmias. Cardiac mapping can also be used for research in cardiac arrhythmias in order to understand their mechanisms. For this purpose, both synthetic signals generated by computer simulations and animal experimental models allow for more controlled physiological conditions and complete access to the organ.
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Affiliation(s)
- Miguel Rodrigo
- BIO-ITACA, Universitat Politècnica de València, Edificio 8G, Camino de Vera, S/N, 46022, Valencia, Spain
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Zang YL, Xia L. Cellular mechanism of cardiac alternans: an unresolved chicken or egg problem. J Zhejiang Univ Sci B 2014; 15:201-11. [PMID: 24599685 DOI: 10.1631/jzus.b1300177] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
T-wave alternans, a specific form of cardiac alternans, has been associated with the increased susceptibility to cardiac arrhythmias and sudden cardiac death (SCD). Plenty of evidence has related cardiac alternans at the tissue level to the instability of voltage kinetics or Ca(2+) handling dynamics at the cellular level. However, to date, none of the existing experiments could identify the exact cellular mechanism of cardiac alternans due to the bi-directional coupling between voltage kinetics and Ca(2+) handling dynamics. Either of these systems could be the origin of alternans and the other follows as a secondary change, therefore making the cellular mechanism of alternans a difficult chicken or egg problem. In this context, theoretical analysis combined with experimental techniques provides a possibility to explore this problem. In this review, we will summarize the experimental and theoretical advances in understanding the cellular mechanism of alternans. We focus on the roles of action potential duration (APD) restitution and Ca(2+) handling dynamics in the genesis of alternans and show how the theoretical analysis combined with experimental techniques has provided us a new insight into the cellular mechanism of alternans. We also discuss the possible reasons of increased propensity for alternans in heart failure (HF) and the new possible therapeutic targets. Finally, according to the level of electrophysiological recording techniques and theoretical strategies, we list some critical experimental or theoretical challenges which may help to determine the origin of alternans and to find more effective therapeutic targets in the future.
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Affiliation(s)
- Yun-Liang Zang
- Key Lab of Biomedical Engineering of Ministry of Education, Department of Biomedical Engineering, Zhejiang University, Hangzhou 310027, China; Department of Pharmacology, University of California, Davis, CA 95616, USA
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Nivala M, Song Z, Weiss JN, Qu Z. T-tubule disruption promotes calcium alternans in failing ventricular myocytes: mechanistic insights from computational modeling. J Mol Cell Cardiol 2014; 79:32-41. [PMID: 25450613 DOI: 10.1016/j.yjmcc.2014.10.018] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 08/01/2014] [Revised: 10/25/2014] [Accepted: 10/28/2014] [Indexed: 10/24/2022]
Abstract
In heart failure (HF), T-tubule (TT) disruption contributes to dyssynchronous calcium (Ca) release and impaired contraction, but its role in arrhythmogenesis remains unclear. In this study, we investigate the effects of TT disruption and other HF remodeling factors on Ca alternans in ventricular myocytes using computer modeling. A ventricular myocyte model with detailed spatiotemporal Ca cycling modeled by a coupled Ca release unit (CRU) network was used, in which the L-type Ca channels and the ryanodine receptor (RyR) channels were simulated by random Markov transitions. TT disruption, which removes the L-type Ca channels from the associated CRUs, results in "orphaned" RyR clusters and thus provides increased opportunity for spark-induced Ca sparks to occur. This effect combined with other HF remodeling factors promoted alternans by two distinct mechanisms: 1) for normal sarco-endoplasmic reticulum Ca ATPase (SERCA) activity, alternans was caused by both CRU refractoriness and coupling. The increased opportunity for spark-induced sparks by TT disruption combined with the enhanced CRU coupling by Ca elevation in the presence or absence of increased RyR leakiness facilitated spark synchronization on alternate beats to promote Ca alternans; 2) for down-regulated SERCA, alternans was caused by the sarcoplasmic reticulum (SR) Ca load-dependent mechanism, independent of CRU refractoriness. TT disruption and increased RyR leakiness shifted and steepened the SR Ca release-load relationship, which combines with down-regulated SERCA to promote Ca alternans. In conclusion, the mechanisms of Ca alternans for normal and down-regulated SERCA are different, and TT disruption promotes Ca alternans by both mechanisms, which may contribute to alternans at different stages of HF.
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Affiliation(s)
- Michael Nivala
- Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, CA 90095, USA
| | - Zhen Song
- Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, CA 90095, USA
| | - James N Weiss
- Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, CA 90095, USA; Department of Physiology, David Geffen School of Medicine, University of California, Los Angeles, CA 90095, USA
| | - Zhilin Qu
- Department of Medicine (Cardiology), David Geffen School of Medicine, University of California, Los Angeles, CA 90095, USA.
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