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Trayanova NA, Lyon A, Shade J, Heijman J. Computational modeling of cardiac electrophysiology and arrhythmogenesis: toward clinical translation. Physiol Rev 2024; 104:1265-1333. [PMID: 38153307 DOI: 10.1152/physrev.00017.2023] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2023] [Revised: 12/19/2023] [Accepted: 12/21/2023] [Indexed: 12/29/2023] Open
Abstract
The complexity of cardiac electrophysiology, involving dynamic changes in numerous components across multiple spatial (from ion channel to organ) and temporal (from milliseconds to days) scales, makes an intuitive or empirical analysis of cardiac arrhythmogenesis challenging. Multiscale mechanistic computational models of cardiac electrophysiology provide precise control over individual parameters, and their reproducibility enables a thorough assessment of arrhythmia mechanisms. This review provides a comprehensive analysis of models of cardiac electrophysiology and arrhythmias, from the single cell to the organ level, and how they can be leveraged to better understand rhythm disorders in cardiac disease and to improve heart patient care. Key issues related to model development based on experimental data are discussed, and major families of human cardiomyocyte models and their applications are highlighted. An overview of organ-level computational modeling of cardiac electrophysiology and its clinical applications in personalized arrhythmia risk assessment and patient-specific therapy of atrial and ventricular arrhythmias is provided. The advancements presented here highlight how patient-specific computational models of the heart reconstructed from patient data have achieved success in predicting risk of sudden cardiac death and guiding optimal treatments of heart rhythm disorders. Finally, an outlook toward potential future advances, including the combination of mechanistic modeling and machine learning/artificial intelligence, is provided. As the field of cardiology is embarking on a journey toward precision medicine, personalized modeling of the heart is expected to become a key technology to guide pharmaceutical therapy, deployment of devices, and surgical interventions.
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Affiliation(s)
- Natalia A Trayanova
- Department of Biomedical Engineering, Johns Hopkins University, Baltimore, Maryland, United States
- Alliance for Cardiovascular Diagnostic and Treatment Innovation, Johns Hopkins University, Baltimore, Maryland, United States
| | - Aurore Lyon
- Department of Biomedical Engineering, CARIM School for Cardiovascular Diseases, Maastricht University, Maastricht, The Netherlands
- Division of Heart and Lungs, Department of Medical Physiology, University Medical Centre Utrecht, Utrecht, The Netherlands
| | - Julie Shade
- Department of Biomedical Engineering, Johns Hopkins University, Baltimore, Maryland, United States
- Alliance for Cardiovascular Diagnostic and Treatment Innovation, Johns Hopkins University, Baltimore, Maryland, United States
| | - Jordi Heijman
- Department of Cardiology, CARIM School for Cardiovascular Diseases, Maastricht University, Maastricht, The Netherlands
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2
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Quinn S, Zhang N, Fenton TA, Brusel M, Muruganandam P, Peleg Y, Giladi M, Haitin Y, Lerche H, Bassan H, Liu Y, Ben-Shalom R, Rubinstein M. Complex biophysical changes and reduced neuronal firing in an SCN8A variant associated with developmental delay and epilepsy. Biochim Biophys Acta Mol Basis Dis 2024; 1870:167127. [PMID: 38519006 DOI: 10.1016/j.bbadis.2024.167127] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2023] [Revised: 03/07/2024] [Accepted: 03/12/2024] [Indexed: 03/24/2024]
Abstract
Mutations in the SCN8A gene, encoding the voltage-gated sodium channel NaV1.6, are associated with a range of neurodevelopmental syndromes. The p.(Gly1625Arg) (G1625R) mutation was identified in a patient diagnosed with developmental epileptic encephalopathy (DEE). While most of the characterized DEE-associated SCN8A mutations were shown to cause a gain-of-channel function, we show that the G1625R variant, positioned within the S4 segment of domain IV, results in complex effects. Voltage-clamp analyses of NaV1.6G1625R demonstrated a mixture of gain- and loss-of-function properties, including reduced current amplitudes, increased time constant of fast voltage-dependent inactivation, a depolarizing shift in the voltage dependence of activation and inactivation, and increased channel availability with high-frequency repeated depolarization. Current-clamp analyses in transfected cultured neurons revealed that these biophysical properties caused a marked reduction in the number of action potentials when firing was driven by the transfected mutant NaV1.6. Accordingly, computational modeling of mature cortical neurons demonstrated a mild decrease in neuronal firing when mimicking the patients' heterozygous SCN8A expression. Structural modeling of NaV1.6G1625R suggested the formation of a cation-π interaction between R1625 and F1588 within domain IV. Double-mutant cycle analysis revealed that this interaction affects the voltage dependence of inactivation in NaV1.6G1625R. Together, our studies demonstrate that the G1625R variant leads to a complex combination of gain and loss of function biophysical changes that result in an overall mild reduction in neuronal firing, related to the perturbed interaction network within the voltage sensor domain, necessitating personalized multi-tiered analysis for SCN8A mutations for optimal treatment selection.
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Affiliation(s)
- Shir Quinn
- Goldschleger Eye Research Institute, Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel; Department of Human Molecular Genetics and Biochemistry, Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel
| | - Nan Zhang
- Department of Neurology and Epileptology, Hertie Institute for Clinical Brain Research, University of Tuebingen, Tuebingen, Germany
| | - Timothy A Fenton
- Neurology Department, MIND Institute, University of California, Davis, Sacramento, CA, United States
| | - Marina Brusel
- Goldschleger Eye Research Institute, Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel; Department of Human Molecular Genetics and Biochemistry, Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel
| | - Preethi Muruganandam
- Neurology Department, MIND Institute, University of California, Davis, Sacramento, CA, United States
| | - Yoav Peleg
- Life Sciences Core Facilities, Weizmann Institute of Science, Rehovot, Israel
| | - Moshe Giladi
- Department of Physiology and Pharmacology, Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel; Tel Aviv Sourasky Medical Center, Tel Aviv, Israel
| | - Yoni Haitin
- Department of Physiology and Pharmacology, Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel; Sagol School of Neuroscience, Tel Aviv University, Tel Aviv, Israel
| | - Holger Lerche
- Department of Neurology and Epileptology, Hertie Institute for Clinical Brain Research, University of Tuebingen, Tuebingen, Germany
| | - Haim Bassan
- Pediatric Neurology and Development Center, Shamir Medical Center (Assaf Harofeh), Zerifin, Israel; Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel
| | - Yuanyuan Liu
- Department of Neurology and Epileptology, Hertie Institute for Clinical Brain Research, University of Tuebingen, Tuebingen, Germany.
| | - Roy Ben-Shalom
- Neurology Department, MIND Institute, University of California, Davis, Sacramento, CA, United States.
| | - Moran Rubinstein
- Goldschleger Eye Research Institute, Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel; Department of Human Molecular Genetics and Biochemistry, Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel; Sagol School of Neuroscience, Tel Aviv University, Tel Aviv, Israel.
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3
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Jennings MW, Nithiarasu P, Pant S. Quantifying the efficacy of voltage protocols in characterising ion channel kinetics: A novel information-theoretic approach. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2024; 40:e3815. [PMID: 38544355 DOI: 10.1002/cnm.3815] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/26/2023] [Revised: 02/20/2024] [Accepted: 02/27/2024] [Indexed: 05/15/2024]
Abstract
Voltage-clamp experiments are commonly utilised to characterise cellular ion channel kinetics. In these experiments, cells are stimulated using a known time-varying voltage, referred to as the voltage protocol, and the resulting cellular response, typically in the form of current, is measured. Parameters of models that describe ion channel kinetics are then estimated by solving an inverse problem which aims to minimise the discrepancy between the predicted response of the model and the actual measured cell response. In this paper, a novel framework to evaluate the information content of voltage-clamp protocols in relation to ion channel model parameters is presented. Additional quantitative information metrics that allow for comparisons among various voltage protocols are proposed. These metrics offer a foundation for future optimal design frameworks to devise novel, information-rich protocols. The efficacy of the proposed framework is evidenced through the analysis of seven voltage protocols from the literature. By comparing known numerical results for inverse problems using these protocols with the information-theoretic metrics, the proposed approach is validated. The essential steps of the framework are: (i) generate random samples of the parameters from chosen prior distributions; (ii) run the model to generate model output (current) for all samples; (iii) construct reduced-dimensional representations of the time-varying current output using proper orthogonal decomposition (POD); (iv) estimate information-theoretic metrics such as mutual information, entropy equivalent variance, and conditional mutual information using non-parametric methods; (v) interpret the metrics; for example, a higher mutual information between a parameter and the current output suggests the protocol yields greater information about that parameter, resulting in improved identifiability; and (vi) integrate the information-theoretic metrics into a single quantitative criterion, encapsulating the protocol's efficacy in estimating model parameters.
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Affiliation(s)
- Matthew W Jennings
- Zienkiewicz Institute for Modelling, Data and AI, Swansea University, Swansea, UK
| | - Perumal Nithiarasu
- Zienkiewicz Institute for Modelling, Data and AI, Swansea University, Swansea, UK
| | - Sanjay Pant
- Zienkiewicz Institute for Modelling, Data and AI, Swansea University, Swansea, UK
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Ryvkin A, Furman A, Lebedeva E, Gonotkov M. Analysis of changes in the action potential morphology of the mouse sinoatrial node true pacemaker cells during ontogenetic development in vitro and in silico. Dev Dyn 2024. [PMID: 38459937 DOI: 10.1002/dvdy.701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2023] [Revised: 01/31/2024] [Accepted: 02/12/2024] [Indexed: 03/11/2024] Open
Abstract
BACKGROUND Maturation of the mouse is accompanied by the increase in heart rate. However, the mechanisms underlying this process remain unclear. We performed an action potentials (APs) recordings in mouse sinoatrial node (SAN) true pacemaker cells and in silico analysis to clarify the mechanisms underlying pre-postnatal period heart rate changes. RESULTS The APs of true pacemaker cells at different stages had similar configurations and dV/dtmax values. The cycle length, action potential duration (APD90 ), maximal diastolic potential (MDP), and AP amplitude decreased, meanwhile the velocity of diastolic depolarization (DDR) increased from E12.5 stage to adult. Using a pharmacological approach we found that in SAN true pacemaker cells ivabradine reduces the DDR and the cycle length significantly stronger in E12.5 than in newborn and adult mice, whereas the effects of Ni2+ and nifedipine were significantly stronger in adult mice. Computer simulations further suggested that the density of the hyperpolarization-activated pacemaker сurrent (If ) decreased during development, whereas transmembrane and intracellular Ca2+ flows increased. CONCLUSIONS The ontogenetic decrease in IK1 density from E12.5 to adult leads to depolarization of MDP to the voltage range in which calcium currents are activated, thereby shifting the balance from the "membrane-clock" to the "calcium-clock."
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Affiliation(s)
| | - Arseniy Furman
- Department of Cardiac Physiology, Institute of Physiology, Komi Science Center, Ural Branch of the Russian Academy of Sciences, Syktyvkar, Russia
| | - Elena Lebedeva
- Department of Cardiac Physiology, Institute of Physiology, Komi Science Center, Ural Branch of the Russian Academy of Sciences, Syktyvkar, Russia
| | - Mikhail Gonotkov
- Department of Cardiac Physiology, Institute of Physiology, Komi Science Center, Ural Branch of the Russian Academy of Sciences, Syktyvkar, Russia
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Fedida D, Sastre D, Dou Y, Westhoff M, Eldstrom J. Evaluating sequential and allosteric activation models in IKs channels with mutated voltage sensors. J Gen Physiol 2024; 156:e202313465. [PMID: 38294435 PMCID: PMC10829594 DOI: 10.1085/jgp.202313465] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2023] [Revised: 11/30/2023] [Accepted: 01/03/2024] [Indexed: 02/01/2024] Open
Abstract
The ion-conducting IKs channel complex, important in cardiac repolarization and arrhythmias, comprises tetramers of KCNQ1 α-subunits along with 1-4 KCNE1 accessory subunits and calmodulin regulatory molecules. The E160R mutation in individual KCNQ1 subunits was used to prevent activation of voltage sensors and allow direct determination of transition rate data from complexes opening with a fixed number of 1, 2, or 4 activatable voltage sensors. Markov models were used to test the suitability of sequential versus allosteric models of IKs activation by comparing simulations with experimental steady-state and transient activation kinetics, voltage-sensor fluorescence from channels with two or four activatable domains, and limiting slope currents at negative potentials. Sequential Hodgkin-Huxley-type models approximately describe IKs currents but cannot explain an activation delay in channels with only one activatable subunit or the hyperpolarizing shift in the conductance-voltage relationship with more activatable voltage sensors. Incorporating two voltage sensor activation steps in sequential models and a concerted step in opening via rates derived from fluorescence measurements improves models but does not resolve fundamental differences with experimental data. Limiting slope current data that show the opening of channels at negative potentials and very low open probability are better simulated using allosteric models of activation with one transition per voltage sensor, which implies that movement of all four sensors is not required for IKs conductance. Tiered allosteric models with two activating transitions per voltage sensor can fully account for IKs current and fluorescence activation kinetics in constructs with different numbers of activatable voltage sensors.
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Affiliation(s)
- David Fedida
- Department of Anesthesiology, Pharmacology and Therapeutics, University of British Columbia, Vancouver, Canada
| | - Daniel Sastre
- Department of Anesthesiology, Pharmacology and Therapeutics, University of British Columbia, Vancouver, Canada
| | - Ying Dou
- Department of Anesthesiology, Pharmacology and Therapeutics, University of British Columbia, Vancouver, Canada
| | - Maartje Westhoff
- Department of Anesthesiology, Pharmacology and Therapeutics, University of British Columbia, Vancouver, Canada
| | - Jodene Eldstrom
- Department of Anesthesiology, Pharmacology and Therapeutics, University of British Columbia, Vancouver, Canada
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6
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Creswell R, Shepherd KM, Lambert B, Mirams GR, Lei CL, Tavener S, Robinson M, Gavaghan DJ. Understanding the impact of numerical solvers on inference for differential equation models. J R Soc Interface 2024; 21:20230369. [PMID: 38442857 PMCID: PMC10914510 DOI: 10.1098/rsif.2023.0369] [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] [Received: 07/03/2023] [Accepted: 01/30/2024] [Indexed: 03/07/2024] Open
Abstract
Most ordinary differential equation (ODE) models used to describe biological or physical systems must be solved approximately using numerical methods. Perniciously, even those solvers that seem sufficiently accurate for the forward problem, i.e. for obtaining an accurate simulation, might not be sufficiently accurate for the inverse problem, i.e. for inferring the model parameters from data. We show that for both fixed step and adaptive step ODE solvers, solving the forward problem with insufficient accuracy can distort likelihood surfaces, which might become jagged, causing inference algorithms to get stuck in local 'phantom' optima. We demonstrate that biases in inference arising from numerical approximation of ODEs are potentially most severe in systems involving low noise and rapid nonlinear dynamics. We reanalyse an ODE change point model previously fit to the COVID-19 outbreak in Germany and show the effect of the step size on simulation and inference results. We then fit a more complicated rainfall run-off model to hydrological data and illustrate the importance of tuning solver tolerances to avoid distorted likelihood surfaces. Our results indicate that, when performing inference for ODE model parameters, adaptive step size solver tolerances must be set cautiously and likelihood surfaces should be inspected for characteristic signs of numerical issues.
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Affiliation(s)
- Richard Creswell
- Department of Computer Science, University of Oxford, Oxford, Oxfordshire, UK
| | | | - Ben Lambert
- Department of Statistics, University of Oxford, Oxford, Oxfordshire, UK
| | - Gary R. Mirams
- School of Mathematical Sciences, University of Nottingham, Nottingham, Nottinghamshire, UK
| | - Chon Lok Lei
- Institute of Translational Medicine and Department of Biomedical Sciences, Faculty of Health Sciences, University of Macau, Taipa, Macao
| | - Simon Tavener
- Department of Mathematics, Colorado State University, Fort Collins, CO, USA
| | - Martin Robinson
- Department of Computer Science, University of Oxford, Oxford, Oxfordshire, UK
| | - David J. Gavaghan
- Department of Computer Science, University of Oxford, Oxford, Oxfordshire, UK
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7
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Abrasheva VO, Kovalenko SG, Slotvitsky M, Romanova SА, Aitova AA, Frolova S, Tsvelaya V, Syunyaev RA. Human sodium current voltage-dependence at physiological temperature measured by coupling a patch-clamp experiment to a mathematical model. J Physiol 2024; 602:633-661. [PMID: 38345560 DOI: 10.1113/jp285162] [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] [Received: 06/16/2023] [Accepted: 01/02/2024] [Indexed: 02/20/2024] Open
Abstract
Voltage-gated Na+ channels are crucial to action potential propagation in excitable tissues. Because of the high amplitude and rapid activation of the Na+ current, voltage-clamp measurements are very challenging and are usually performed at room temperature. In this study, we measured Na+ current voltage-dependence in stem cell-derived cardiomyocytes at physiological temperature. While the apparent activation and inactivation curves, measured as the dependence of current amplitude on voltage, fall within the range reported in previous studies, we identified a systematic error in our measurements. This error is caused by the deviation of the membrane potential from the command potential of the amplifier. We demonstrate that it is possible to account for this artifact using computer simulation of the patch-clamp experiment. We obtained surprising results through patch-clamp model optimization: a half-activation of -11.5 mV and a half-inactivation of -87 mV. Although the half-activation deviates from previous research, we demonstrate that this estimate reproduces the conduction velocity dependence on extracellular potassium concentration. KEY POINTS: Voltage-gated Na+ currents play a crucial role in excitable tissues including neurons, cardiac and skeletal muscle. Measurement of Na+ current is challenging because of its high amplitude and rapid kinetics, especially at physiological temperature. We have used the patch-clamp technique to measure human Na+ current voltage-dependence in human induced pluripotent stem cell-derived cardiomyocytes. The patch-clamp data were processed by optimization of the model accounting for voltage-clamp experiment artifacts, revealing a large difference between apparent parameters of Na+ current and the results of the optimization. We conclude that actual Na+ current activation is extremely depolarized in comparison to previous studies. The new Na+ current model provides a better understanding of action potential propagation; we demonstrate that it explains propagation in hyperkalaemic conditions.
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Affiliation(s)
| | - Sandaara G Kovalenko
- Moscow Institute of Physics and Technology, Moscow, Russia
- M. F. Vladimirsky Moscow Regional Research Clinical Institute, Moscow, Russia
- ITMO University, St Petersburg, Russia
| | - Mihail Slotvitsky
- Moscow Institute of Physics and Technology, Moscow, Russia
- M. F. Vladimirsky Moscow Regional Research Clinical Institute, Moscow, Russia
- ITMO University, St Petersburg, Russia
| | - Serafima А Romanova
- Moscow Institute of Physics and Technology, Moscow, Russia
- M. F. Vladimirsky Moscow Regional Research Clinical Institute, Moscow, Russia
| | - Aleria A Aitova
- Moscow Institute of Physics and Technology, Moscow, Russia
- M. F. Vladimirsky Moscow Regional Research Clinical Institute, Moscow, Russia
- ITMO University, St Petersburg, Russia
| | - Sheida Frolova
- Moscow Institute of Physics and Technology, Moscow, Russia
- M. F. Vladimirsky Moscow Regional Research Clinical Institute, Moscow, Russia
| | - Valeria Tsvelaya
- Moscow Institute of Physics and Technology, Moscow, Russia
- M. F. Vladimirsky Moscow Regional Research Clinical Institute, Moscow, Russia
- ITMO University, St Petersburg, Russia
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8
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Ni H, Grandi E. Computational Modeling of Cardiac Electrophysiology. Methods Mol Biol 2024; 2735:63-103. [PMID: 38038844 DOI: 10.1007/978-1-0716-3527-8_5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/02/2023]
Abstract
Mathematical modeling and simulation are well-established and powerful tools to integrate experimental data of individual components of cardiac electrophysiology, excitation-contraction coupling, and regulatory signaling pathways, to gain quantitative and mechanistic insight into pathophysiological processes and guide therapeutic strategies. Here, we briefly describe the processes governing cardiac myocyte electrophysiology and Ca2+ handling and their regulation, as well as action potential propagation in tissue. We discuss the models and methods used to describe these phenomena, including procedures for model parameterization and validation, in addition to protocols for model interrogation and analysis and techniques that account for phenotypic variability and parameter uncertainty. Our objective is to provide a summary of basic concepts and approaches as a resource for scientists training in this discipline and for all researchers aiming to gain an understanding of cardiac modeling studies.
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Affiliation(s)
- Haibo Ni
- Department of Pharmacology, University of California, Davis, CA, USA.
| | - Eleonora Grandi
- Department of Pharmacology, University of California, Davis, CA, USA.
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9
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Georgiev DD. Evolution of Consciousness. Life (Basel) 2023; 14:48. [PMID: 38255663 PMCID: PMC10817314 DOI: 10.3390/life14010048] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2023] [Revised: 12/01/2023] [Accepted: 12/25/2023] [Indexed: 01/24/2024] Open
Abstract
The natural evolution of consciousness in different animal species mandates that conscious experiences are causally potent in order to confer any advantage in the struggle for survival. Any endeavor to construct a physical theory of consciousness based on emergence within the framework of classical physics, however, leads to causally impotent conscious experiences in direct contradiction to evolutionary theory since epiphenomenal consciousness cannot evolve through natural selection. Here, we review recent theoretical advances in describing sentience and free will as fundamental aspects of reality granted by quantum physical laws. Modern quantum information theory considers quantum states as a physical resource that endows quantum systems with the capacity to perform physical tasks that are classically impossible. Reductive identification of conscious experiences with the quantum information comprised in quantum brain states allows for causally potent consciousness that is capable of performing genuine choices for future courses of physical action. The consequent evolution of brain cortical networks contributes to increased computational power, memory capacity, and cognitive intelligence of the living organisms.
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Affiliation(s)
- Danko D Georgiev
- Institute for Advanced Study, 30 Vasilaki Papadopulu Str., 9010 Varna, Bulgaria
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10
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Shuttleworth JG, Lei CL, Whittaker DG, Windley MJ, Hill AP, Preston SP, Mirams GR. Empirical Quantification of Predictive Uncertainty Due to Model Discrepancy by Training with an Ensemble of Experimental Designs: An Application to Ion Channel Kinetics. Bull Math Biol 2023; 86:2. [PMID: 37999811 PMCID: PMC10673765 DOI: 10.1007/s11538-023-01224-6] [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] [Received: 01/31/2023] [Accepted: 10/09/2023] [Indexed: 11/25/2023]
Abstract
When using mathematical models to make quantitative predictions for clinical or industrial use, it is important that predictions come with a reliable estimate of their accuracy (uncertainty quantification). Because models of complex biological systems are always large simplifications, model discrepancy arises-models fail to perfectly recapitulate the true data generating process. This presents a particular challenge for making accurate predictions, and especially for accurately quantifying uncertainty in these predictions. Experimentalists and modellers must choose which experimental procedures (protocols) are used to produce data used to train models. We propose to characterise uncertainty owing to model discrepancy with an ensemble of parameter sets, each of which results from training to data from a different protocol. The variability in predictions from this ensemble provides an empirical estimate of predictive uncertainty owing to model discrepancy, even for unseen protocols. We use the example of electrophysiology experiments that investigate the properties of hERG potassium channels. Here, 'information-rich' protocols allow mathematical models to be trained using numerous short experiments performed on the same cell. In this case, we simulate data with one model and fit it with a different (discrepant) one. For any individual experimental protocol, parameter estimates vary little under repeated samples from the assumed additive independent Gaussian noise model. Yet parameter sets arising from the same model applied to different experiments conflict-highlighting model discrepancy. Our methods will help select more suitable ion channel models for future studies, and will be widely applicable to a range of biological modelling problems.
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Affiliation(s)
- Joseph G Shuttleworth
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK
| | - Chon Lok Lei
- Institute of Translational Medicine, Faculty of Health Sciences, University of Macau, Macau, China
- Department of Biomedical Sciences, Faculty of Health Sciences, University of Macau, Macau, China
| | - Dominic G Whittaker
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK
- 4 Systems Modeling & Translational Biology, Stevenage, GSK, UK
| | - Monique J Windley
- Computational Cardiology Laboratory, Victor Chang Cardiac Research Institute, Darlinghurst, NSW, Australia
- School of Clinical Medicine, Faculty of Medicine and Health, University of New South Wales, Sydney, NSW, Australia
| | - Adam P Hill
- Computational Cardiology Laboratory, Victor Chang Cardiac Research Institute, Darlinghurst, NSW, Australia
- School of Clinical Medicine, Faculty of Medicine and Health, University of New South Wales, Sydney, NSW, Australia
| | - Simon P Preston
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK
| | - Gary R Mirams
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK.
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11
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Lei CL, Clerx M, Gavaghan DJ, Mirams GR. Model-driven optimal experimental design for calibrating cardiac electrophysiology models. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2023; 240:107690. [PMID: 37478675 DOI: 10.1016/j.cmpb.2023.107690] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2023] [Revised: 06/09/2023] [Accepted: 06/22/2023] [Indexed: 07/23/2023]
Abstract
BACKGROUND AND OBJECTIVE Models of the cardiomyocyte action potential have contributed immensely to the understanding of heart function, pathophysiology, and the origin of heart rhythm disturbances. However, action potential models are highly nonlinear, making them difficult to parameterise and limiting to describing 'average cell' dynamics, when cell-specific models would be ideal to uncover inter-cell variability but are too experimentally challenging to be achieved. Here, we focus on automatically designing experimental protocols that allow us to better identify cell-specific maximum conductance values for each major current type. METHODS AND RESULTS We developed an approach that applies optimal experimental designs to patch-clamp experiments, including both voltage-clamp and current-clamp experiments. We assessed the models calibrated to these new optimal designs by comparing them to the models calibrated to some of the commonly used designs in the literature. We showed that optimal designs are not only overall shorter in duration but also able to perform better than many of the existing experiment designs in terms of identifying model parameters and hence model predictive power. CONCLUSIONS For cardiac cellular electrophysiology, this approach will allow researchers to define their hypothesis of the dynamics of the system and automatically design experimental protocols that will result in theoretically optimal designs.
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Affiliation(s)
- Chon Lok Lei
- Institute of Translational Medicine, Faculty of Health Sciences, University of Macau, Macau, China; Department of Biomedical Sciences, Faculty of Health Sciences, University of Macau, Macau, China.
| | - Michael Clerx
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, United Kingdom
| | - David J Gavaghan
- Department of Computer Science, University of Oxford, Oxford, United Kingdom; Doctoral Training Centre, University of Oxford, Oxford, United Kingdom
| | - Gary R Mirams
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, United Kingdom.
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12
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Hermanstyne TO, Yang ND, Granados-Fuentes D, Li X, Mellor RL, Jegla T, Herzog ED, Nerbonne JM. Kv12-encoded K+ channels drive the day-night switch in the repetitive firing rates of SCN neurons. J Gen Physiol 2023; 155:e202213310. [PMID: 37516908 PMCID: PMC10373311 DOI: 10.1085/jgp.202213310] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2022] [Revised: 05/11/2023] [Accepted: 07/06/2023] [Indexed: 07/31/2023] Open
Abstract
Considerable evidence suggests that day-night rhythms in the functional expression of subthreshold potassium (K+) channels regulate daily oscillations in the spontaneous firing rates of neurons in the suprachiasmatic nucleus (SCN), the master circadian pacemaker in mammals. The K+ conductance(s) driving these daily rhythms in the repetitive firing rates of SCN neurons, however, have not been identified. To test the hypothesis that subthreshold Kv12.1/Kv12.2-encoded K+ channels play a role, we obtained current-clamp recordings from SCN neurons in slices prepared from adult mice harboring targeted disruptions in the Kcnh8 (Kv12.1-/-) or Kcnh3 (Kv12.2-/-) locus. We found that mean nighttime repetitive firing rates were higher in Kv12.1-/- and Kv12.2-/- than in wild type (WT), SCN neurons. In marked contrast, mean daytime repetitive firing rates were similar in Kv12.1-/-, Kv12.2-/-, and WT SCN neurons, and the day-night difference in mean repetitive firing rates, a hallmark feature of WT SCN neurons, was eliminated in Kv12.1-/- and Kv12.2-/- SCN neurons. Similar results were obtained with in vivo shRNA-mediated acute knockdown of Kv12.1 or Kv12.2 in adult SCN neurons. Voltage-clamp experiments revealed that Kv12-encoded current densities in WT SCN neurons are higher at night than during the day. In addition, the pharmacological block of Kv12-encoded currents increased the mean repetitive firing rate of nighttime, but not daytime, in WT SCN neurons. Dynamic clamp-mediated subtraction of modeled Kv12-encoded currents also selectively increased the mean repetitive firing rates of nighttime WT SCN neurons. Despite the elimination of the nighttime decrease in the mean repetitive firing rates of SCN neurons, however, locomotor (wheel-running) activity remained rhythmic in Kv12.1-/-, Kv12.2-/-, and Kv12.1-targeted shRNA-expressing, and Kv12.2-targeted shRNA-expressing animals.
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Affiliation(s)
- Tracey O. Hermanstyne
- Department of Developmental Biology, Washington University School of Medicine, St. Louis, MO, USA
| | - Nien-Du Yang
- Cardiovascular Division, Department of Medicine, Washington University School of Medicine, St. Louis, MO, USA
- Department of Biomedical Engineering, Washington University, St. Louis, MO, USA
| | | | - Xiaofan Li
- Department of Biology, The Pennsylvania State University, University Park, State College, PA, USA
| | - Rebecca L. Mellor
- Cardiovascular Division, Department of Medicine, Washington University School of Medicine, St. Louis, MO, USA
| | - Timothy Jegla
- Department of Biology, The Pennsylvania State University, University Park, State College, PA, USA
| | - Erik D. Herzog
- Department of Biology, Washington University, St. Louis, MO, USA
| | - Jeanne M. Nerbonne
- Department of Developmental Biology, Washington University School of Medicine, St. Louis, MO, USA
- Cardiovascular Division, Department of Medicine, Washington University School of Medicine, St. Louis, MO, USA
- Department of Biomedical Engineering, Washington University, St. Louis, MO, USA
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13
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Koch NA, Sonnenberg L, Hedrich UBS, Lauxmann S, Benda J. Loss or gain of function? Effects of ion channel mutations on neuronal firing depend on the neuron type. Front Neurol 2023; 14:1194811. [PMID: 37292138 PMCID: PMC10244640 DOI: 10.3389/fneur.2023.1194811] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2023] [Accepted: 05/03/2023] [Indexed: 06/10/2023] Open
Abstract
Introduction Clinically relevant mutations to voltage-gated ion channels, called channelopathies, alter ion channel function, properties of ionic currents, and neuronal firing. The effects of ion channel mutations are routinely assessed and characterized as loss of function (LOF) or gain of function (GOF) at the level of ionic currents. However, emerging personalized medicine approaches based on LOF/GOF characterization have limited therapeutic success. Potential reasons are among others that the translation from this binary characterization to neuronal firing is currently not well-understood-especially when considering different neuronal cell types. In this study, we investigate the impact of neuronal cell type on the firing outcome of ion channel mutations. Methods To this end, we simulated a diverse collection of single-compartment, conductance-based neuron models that differed in their composition of ionic currents. We systematically analyzed the effects of changes in ion current properties on firing in different neuronal types. Additionally, we simulated the effects of known mutations in KCNA1 gene encoding the KV1.1 potassium channel subtype associated with episodic ataxia type 1 (EA1). Results These simulations revealed that the outcome of a given change in ion channel properties on neuronal excitability depends on neuron type, i.e., the properties and expression levels of the unaffected ionic currents. Discussion Consequently, neuron-type specific effects are vital to a full understanding of the effects of channelopathies on neuronal excitability and are an important step toward improving the efficacy and precision of personalized medicine approaches.
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Affiliation(s)
- Nils A. Koch
- Institute of Neurobiology, Faculty of Mathematics and Natural Sciences, University of Tübingen, Tübingen, Germany
- Bernstein Center for Computational Neuroscience Tübingen, Tübingen, Germany
| | - Lukas Sonnenberg
- Institute of Neurobiology, Faculty of Mathematics and Natural Sciences, University of Tübingen, Tübingen, Germany
- Bernstein Center for Computational Neuroscience Tübingen, Tübingen, Germany
| | - Ulrike B. S. Hedrich
- Department of Neurology and Epileptology, Hertie Institute for Clinical Brain Research, University of Tübingen, Tübingen, Germany
| | - Stephan Lauxmann
- Institute of Neurobiology, Faculty of Mathematics and Natural Sciences, University of Tübingen, Tübingen, Germany
- Department of Neurology and Epileptology, Hertie Institute for Clinical Brain Research, University of Tübingen, Tübingen, Germany
| | - Jan Benda
- Institute of Neurobiology, Faculty of Mathematics and Natural Sciences, University of Tübingen, Tübingen, Germany
- Bernstein Center for Computational Neuroscience Tübingen, Tübingen, Germany
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14
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Moreno JD, Silva JR. Emerging methods to model cardiac ion channel and myocyte electrophysiology. BIOPHYSICS REVIEWS 2023; 4:011315. [PMID: 37034130 PMCID: PMC10071990 DOI: 10.1063/5.0127713] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/23/2022] [Accepted: 02/28/2023] [Indexed: 04/03/2023]
Abstract
In the field of cardiac electrophysiology, modeling has played a central role for many decades. However, even though the effort is well-established, it has recently seen a rapid and sustained evolution in the complexity and predictive power of the models being created. In particular, new approaches to modeling have allowed the tracking of parallel and interconnected processes that span from the nanometers and femtoseconds that determine ion channel gating to the centimeters and minutes needed to describe an arrhythmia. The connection between scales has brought unprecedented insight into cardiac arrhythmia mechanisms and drug therapies. This review focuses on the generation of these models from first principles, generation of detailed models to describe ion channel kinetics, algorithms to create and numerically solve kinetic models, and new approaches toward data gathering that parameterize these models. While we focus on application of these models for cardiac arrhythmia, these concepts are widely applicable to model the physiology and pathophysiology of any excitable cell.
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Affiliation(s)
- Jonathan D. Moreno
- Division of Cardiology, Department of Medicine, Washington University in St. Louis, St. Louis, Missouri 63130, USA
| | - Jonathan R. Silva
- Department of Biomedical Engineering, Washington University in St. Louis, St. Louis, Missouri 63130, USA
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15
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Hermanstyne TO, Yang ND, Granados-Fuentes D, Li X, Mellor RL, Jegla T, Herzog ED, Nerbonne JM. Kv12-Encoded K + Channels Drive the Day-Night Switch in the Repetitive Firing Rates of SCN Neurons. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.01.30.526323. [PMID: 36778242 PMCID: PMC9915524 DOI: 10.1101/2023.01.30.526323] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Abstract
Considerable evidence suggests that day-night rhythms in the functional expression of subthreshold potassium (K + ) channels regulate daily oscillations in the rates of spontaneous action potential firing of neurons in the suprachiasmatic nucleus (SCN), the master circadian pacemaker in mammals. The K + conductance(s) driving these daily rhythms in repetitive firing rates, however, have not been identified. To test the hypothesis that subthreshold Kv12.1/Kv12.2-encoded K + channels play a role, we obtained current-clamp recordings from SCN neurons in slices prepared from adult mice harboring targeted disruptions in the Kcnh8 (Kv12.1 -/- ) or Kcnh3 (Kv12.2 -/- ) locus. We found that mean nighttime repetitive firing rates were higher in Kv12.1 -/- and Kv12.2 -/- , than in wild type (WT), SCN neurons. In marked contrast, mean daytime repetitive firing rates were similar in Kv12.1 -/- , Kv12.2 -/- and WT SCN neurons, and the day-night difference in mean repetitive firing rates, a hallmark feature of WT SCN neurons, was eliminated in Kv12.1 -/- and Kv12.2 -/- SCN neurons. Similar results were obtained with in vivo shRNA-mediated acute knockdown of Kv12.1 or Kv12.2 in adult SCN neurons. Voltage-clamp experiments revealed that Kv12-encoded current densities in WT SCN neurons are higher at night than during the day. In addition, pharmacological block of Kv12-encoded currents increased the mean repetitive firing rate of nighttime, but not daytime, in WT SCN neurons. Dynamic clamp-mediated subtraction of modeled Kv12-encoded currents also selectively increased the mean repetitive firing rates of nighttime WT SCN neurons. Despite the elimination of nighttime decrease in the mean repetitive firing rates of SCN neurons, however, locomotor (wheel-running) activity remained rhythmic in Kv12.1 -/- , Kv12.2 -/- , Kv12.1-targeted shRNA-expressing, and Kv12.2-targeted shRNA-expressing animals.
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Affiliation(s)
- Tracey O. Hermanstyne
- Department of Developmental Biology, Washington University School of Medicine, St. Louis, MO
| | - Nien-Du Yang
- Department of Medicine, Cardiovascular Division, Washington University School of Medicine, St. Louis, MO
- Department of Biomedical Engineering, Washington University School of Medicine, St. Louis, MO
| | | | - Xiaofan Li
- Department of Biology, The Pennsylvania State University, University Park, PA
| | - Rebecca L. Mellor
- Department of Medicine, Cardiovascular Division, Washington University School of Medicine, St. Louis, MO
| | - Timothy Jegla
- Department of Biology, The Pennsylvania State University, University Park, PA
| | - Erik D. Herzog
- Department of Biology, Washington University, St. Louis, MO
| | - Jeanne M. Nerbonne
- Department of Developmental Biology, Washington University School of Medicine, St. Louis, MO
- Department of Medicine, Cardiovascular Division, Washington University School of Medicine, St. Louis, MO
- Department of Biomedical Engineering, Washington University School of Medicine, St. Louis, MO
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16
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Agrawal A, Wang K, Polonchuk L, Cooper J, Hendrix M, Gavaghan DJ, Mirams GR, Clerx M. Models of the cardiac L-type calcium current: A quantitative review. WIREs Mech Dis 2023; 15:e1581. [PMID: 36028219 PMCID: PMC10078428 DOI: 10.1002/wsbm.1581] [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] [Received: 03/25/2022] [Revised: 06/16/2022] [Accepted: 07/19/2022] [Indexed: 01/31/2023]
Abstract
The L-type calcium current (I CaL ) plays a critical role in cardiac electrophysiology, and models ofI CaL are vital tools to predict arrhythmogenicity of drugs and mutations. Five decades of measuring and modelingI CaL have resulted in several competing theories (encoded in mathematical equations). However, the introduction of new models has not typically been accompanied by a data-driven critical comparison with previous work, so that it is unclear which model is best suited for any particular application. In this review, we describe and compare 73 published mammalianI CaL models and use simulated experiments to show that there is a large variability in their predictions, which is not substantially diminished when grouping by species or other categories. We provide model code for 60 models, list major data sources, and discuss experimental and modeling work that will be required to reduce this huge list of competing theories and ultimately develop a community consensus model ofI CaL . This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Molecular and Cellular Physiology.
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Affiliation(s)
- Aditi Agrawal
- Computational Biology & Health Informatics, Department of Computer ScienceUniversity of OxfordOxfordUK
| | - Ken Wang
- Pharma Research and Early Development, Innovation Center BaselF. Hoffmann‐La Roche Ltd.BaselSwitzerland
| | - Liudmila Polonchuk
- Pharma Research and Early Development, Innovation Center BaselF. Hoffmann‐La Roche Ltd.BaselSwitzerland
| | - Jonathan Cooper
- Centre for Advanced Research ComputingUniversity College LondonLondonUK
| | - Maurice Hendrix
- Centre for Mathematical Medicine & Biology, School of Mathematical SciencesUniversity of NottinghamNottinghamUK
- Digital Research Service, Information SciencesUniversity of NottinghamNottinghamUK
| | - David J. Gavaghan
- Computational Biology & Health Informatics, Department of Computer ScienceUniversity of OxfordOxfordUK
| | - Gary R. Mirams
- Centre for Mathematical Medicine & Biology, School of Mathematical SciencesUniversity of NottinghamNottinghamUK
| | - Michael Clerx
- Centre for Mathematical Medicine & Biology, School of Mathematical SciencesUniversity of NottinghamNottinghamUK
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17
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Şengül Ayan S, Süleymanoğlu S, Özdoğan H. A pilot study of ion current estimation by ANN from action potential waveforms. J Biol Phys 2022; 48:461-475. [PMID: 36372807 PMCID: PMC9727005 DOI: 10.1007/s10867-022-09619-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2022] [Accepted: 10/28/2022] [Indexed: 11/15/2022] Open
Abstract
Experiments using conventional experimental approaches to capture the dynamics of ion channels are not always feasible, and even when possible and feasible, some can be time-consuming. In this work, the ionic current-time dynamics during cardiac action potentials (APs) are predicted from a single AP waveform by means of artificial neural networks (ANNs). The data collection is accomplished by the use of a single-cell model to run electrophysiological simulations in order to identify ionic currents based on fluctuations in ion channel conductance. The relevant ionic currents, as well as the corresponding cardiac AP, are then calculated and fed into the ANN algorithm, which predicts the desired currents solely based on the AP curve. The validity of the proposed methodology for the Bayesian approach is demonstrated by the R (validation) scores obtained from training data, test data, and the entire data set. The Bayesian regularization's (BR) strength and dependability are further supported by error values and the regression presentations, all of which are positive indicators. As a result of the high convergence between the simulated currents and the currents generated by including the efficacy of a developed Bayesian solver, it is possible to generate behavior of ionic currents during time for the desired AP waveform for any electrical excitable cell.
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Affiliation(s)
- Sevgi Şengül Ayan
- Department of Engineering, Industrial Engineering, Antalya Bilim University, Döşemealtı, Antalya, Turkey
| | - Selim Süleymanoğlu
- Department of Engineering, Electrical and Computer Engineering, Antalya Bilim University, Döşemealtı, Antalya, Turkey
| | - Hasan Özdoğan
- Department of Medical Imaging Techniques, Vocational School of Health Services, Antalya Bilim University, Döşemealtı, Antalya, Turkey
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18
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Whittaker DG, Wang J, Shuttleworth JG, Venkateshappa R, Kemp JM, Claydon TW, Mirams GR. Ion channel model reduction using manifold boundaries. JOURNAL OF THE ROYAL SOCIETY, INTERFACE 2022; 19:20220193. [PMID: 35946166 PMCID: PMC9363999 DOI: 10.1098/rsif.2022.0193] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
Mathematical models of voltage-gated ion channels are used in basic research, industrial and clinical settings. These models range in complexity, but typically contain numerous variables representing the proportion of channels in a given state, and parameters describing the voltage-dependent rates of transition between states. An open problem is selecting the appropriate degree of complexity and structure for an ion channel model given data availability. Here, we simplify a model of the cardiac human Ether-à-go-go related gene (hERG) potassium ion channel, which carries cardiac IKr, using the manifold boundary approximation method (MBAM). The MBAM approximates high-dimensional model-output manifolds by reduced models describing their boundaries, resulting in models with fewer parameters (and often variables). We produced a series of models of reducing complexity starting from an established five-state hERG model with 15 parameters. Models with up to three fewer states and eight fewer parameters were shown to retain much of the predictive capability of the full model and were validated using experimental hERG1a data collected in HEK293 cells at 37°C. The method provides a way to simplify complex models of ion channels that improves parameter identifiability and will aid in future model development.
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Affiliation(s)
- Dominic G Whittaker
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, UK
| | - Jiahui Wang
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, UK
| | - Joseph G Shuttleworth
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, UK
| | | | - Jacob M Kemp
- Department of Biomedical Physiology and Kinesiology, Simon Fraser University, Burnaby, Canada
| | - Thomas W Claydon
- Department of Biomedical Physiology and Kinesiology, Simon Fraser University, Burnaby, Canada
| | - Gary R Mirams
- Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, UK
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19
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Jian K, Li C, Hancox JC, Zhang H. Pro-Arrhythmic Effects of Discontinuous Conduction at the Purkinje Fiber-Ventricle Junction Arising From Heart Failure-Induced Ionic Remodeling - Insights From Computational Modelling. Front Physiol 2022; 13:877428. [PMID: 35547576 PMCID: PMC9081695 DOI: 10.3389/fphys.2022.877428] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2022] [Accepted: 03/18/2022] [Indexed: 11/18/2022] Open
Abstract
Heart failure is associated with electrical remodeling of the electrical properties and kinetics of the ion channels and transporters that are responsible for cardiac action potentials. However, it is still unclear whether heart failure-induced ionic remodeling can affect the conduction of excitation waves at the Purkinje fiber-ventricle junction contributing to pro-arrhythmic effects of heart failure, as the complexity of the heart impedes a detailed experimental analysis. The aim of this study was to employ computational models to investigate the pro-arrhythmic effects of heart failure-induced ionic remodeling on the cardiac action potentials and excitation wave conduction at the Purkinje fiber-ventricle junction. Single cell models of canine Purkinje fiber and ventricular myocytes were developed for control and heart failure. These single cell models were then incorporated into one-dimensional strand and three-dimensional wedge models to investigate the effects of heart failure-induced remodeling on propagation of action potentials in Purkinje fiber and ventricular tissue and at the Purkinje fiber-ventricle junction. This revealed that heart failure-induced ionic remodeling of Purkinje fiber and ventricular tissue reduced conduction safety and increased tissue vulnerability to the genesis of the unidirectional conduction block. This was marked at the Purkinje fiber-ventricle junction, forming a potential substrate for the genesis of conduction failure that led to re-entry. This study provides new insights into proarrhythmic consequences of heart failure-induced ionic remodeling.
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Affiliation(s)
- Kun Jian
- Biological Physics Group, Department of Physics and Astronomy, The University of Manchester, Manchester, United Kingdom
| | - Chen Li
- Biological Physics Group, Department of Physics and Astronomy, The University of Manchester, Manchester, United Kingdom
| | - Jules C. Hancox
- Biological Physics Group, Department of Physics and Astronomy, The University of Manchester, Manchester, United Kingdom
- School of Physiology, Pharmacology and Neuroscience, Medical Sciences Building, University Walk, Bristol, United Kingdom
| | - Henggui Zhang
- Biological Physics Group, Department of Physics and Astronomy, The University of Manchester, Manchester, United Kingdom
- Key Laboratory of Medical Electrophysiology of Ministry of Education and Medical Electrophysiological Key Laboratory of Sichuan Province, Institute of Cardiovascular Research, Southwest Medical University, Luzhou, China
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20
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Mangold KE, Zhou Z, Schoening M, Moreno JD, Silva JR. Creating Ion Channel Kinetic Models Using Cloud Computing. Curr Protoc 2022; 2:e374. [PMID: 35175690 PMCID: PMC9006544 DOI: 10.1002/cpz1.374] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023]
Abstract
Computational modeling of ion channels provides key insight into experimental electrophysiology results and can be used to connect channel dynamics to emergent phenomena observed at the tissue and organ levels. However, creation of these models requires substantial mathematical and computational background. This tutorial seeks to lower the barrier to creating these models by providing an automated pipeline for creating Markov models of an ion channel kinetics dataset. We start by detailing how to encode sample voltage-clamp protocols and experimental data into the program and its implementation in a cloud computing environment. We guide the reader on how to build a containerized instance, push the machine image, and finally run the routine on cluster nodes. While providing open-source code has become more standard in computational studies, this tutorial provides unprecedented detail on the use of the program and the creation of channel models, starting from inputting the raw experimental data. © 2022 Wiley Periodicals LLC. Basic Protocol: Creation of ion channel kinetic models with a cloud computing environment Alternate Protocol: Instructions for use in a standard high-performance compute cluster.
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Affiliation(s)
- Kathryn E. Mangold
- Department of Biomedical Engineering, Washington University in St. Louis, St. Louis, MO 63130
| | - Zhuodong Zhou
- Department of Biomedical Engineering, Washington University in St. Louis, St. Louis, MO 63130
| | - Max Schoening
- Department of Biomedical Engineering, Washington University in St. Louis, St. Louis, MO 63130
| | - Jonathan D. Moreno
- Department of Biomedical Engineering, Washington University in St. Louis, St. Louis, MO 63130,Department of Medicine, Cardiovascular Division, Washington University School of Medicine, St. Louis, MO 63110
| | - Jonathan R. Silva
- Department of Biomedical Engineering, Washington University in St. Louis, St. Louis, MO 63130,Corresponding author: Jonathan R. Silva, , +1 314-935-8837
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21
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Soepriatna AH, Kim TY, Daley MC, Song E, Choi BR, Coulombe KLK. Human Atrial Cardiac Microtissues for Chamber-Specific Arrhythmic Risk Assessment. Cell Mol Bioeng 2021; 14:441-457. [PMID: 34777603 DOI: 10.1007/s12195-021-00703-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2021] [Accepted: 09/02/2021] [Indexed: 01/10/2023] Open
Abstract
Introduction Although atrial fibrillation is the most prevalent disorder of electrical conduction, the mechanisms behind atrial arrhythmias remain elusive. To address this challenge, we developed a robust in vitro model of 3D atrial microtissue from human induced pluripotent stem cell (hiPSC)-derived cardiomyocytes and evaluated chamber-specific chemical responses experimentally and computationally. Methods We differentiated atrial and ventricular cardiomyocytes (aCMs/vCMs) from GCaMP6f-expressing hiPSCs and assessed spontaneous AP activity using fluorescence imaging. Self-assembling 3D microtissues were formed with lactate purified CMs and 5% human cardiac fibroblasts and electrically stimulated for one week before high resolution action potential (AP) optical mapping. AP responses to the atrial-specific potassium repolarizing current I Kur-blocker 4-Aminopyridine (4-AP) and funny current I f-blocker Ivabradine were characterized within their therapeutic window. Finally, we expanded upon a published hiPSC-CM computational model by incorporating the atrial-specific I Kur current, modifying ion channel conductances to match the AP waveforms of our microtissues, and employing the updated model to reinforce our experimental findings. Results High purity CMs (> 75% cTnT+) demonstrated subtype specification by MLC2v expression. Spontaneous beating rates significantly decreased following 3D microtissue formation, with atrial microtissues characterized by their faster spontaneous beating rate, slower AP rise time, and shorter AP duration (APD) compared to ventricular microtissues. We measured atrial-specific responses, including dose-dependent APD prolongation with 4-AP treatment and dose-dependent reduction in spontaneous activity post-Ivabradine treatment. Conclusion The presented in vitro platform for screening atrial-specific responses is both robust and sensitive, with high throughput, enabling studies focused at elucidating the mechanisms underlying atrial arrhythmias. Supplementary Information The online version contains supplementary material available at 10.1007/s12195-021-00703-x.
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Affiliation(s)
- Arvin H Soepriatna
- Center for Biomedical Engineering, School of Engineering, Brown University, Providence, RI USA
| | - Tae Yun Kim
- Cardiovascular Research Center, Cardiovascular Institute, Rhode Island Hospital and Alpert Medical School of Brown University, Providence, RI USA
| | - Mark C Daley
- Center for Biomedical Engineering, School of Engineering, Brown University, Providence, RI USA
| | - Elena Song
- Center for Biomedical Engineering, School of Engineering, Brown University, Providence, RI USA
| | - Bum-Rak Choi
- Cardiovascular Research Center, Cardiovascular Institute, Rhode Island Hospital and Alpert Medical School of Brown University, Providence, RI USA
| | - Kareen L K Coulombe
- Center for Biomedical Engineering, School of Engineering, Brown University, Providence, RI USA
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22
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Sánchez J, Trenor B, Saiz J, Dössel O, Loewe A. Fibrotic Remodeling during Persistent Atrial Fibrillation: In Silico Investigation of the Role of Calcium for Human Atrial Myofibroblast Electrophysiology. Cells 2021; 10:cells10112852. [PMID: 34831076 PMCID: PMC8616446 DOI: 10.3390/cells10112852] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2021] [Revised: 10/08/2021] [Accepted: 10/19/2021] [Indexed: 12/20/2022] Open
Abstract
During atrial fibrillation, cardiac tissue undergoes different remodeling processes at different scales from the molecular level to the tissue level. One central player that contributes to both electrical and structural remodeling is the myofibroblast. Based on recent experimental evidence on myofibroblasts' ability to contract, we extended a biophysical myofibroblast model with Ca2+ handling components and studied the effect on cellular and tissue electrophysiology. Using genetic algorithms, we fitted the myofibroblast model parameters to the existing in vitro data. In silico experiments showed that Ca2+ currents can explain the experimentally observed variability regarding the myofibroblast resting membrane potential. The presence of an L-type Ca2+ current can trigger automaticity in the myofibroblast with a cycle length of 799.9 ms. Myocyte action potentials were prolonged when coupled to myofibroblasts with Ca2+ handling machinery. Different spatial myofibroblast distribution patterns increased the vulnerable window to induce arrhythmia from 12 ms in non-fibrotic tissue to 22 ± 2.5 ms and altered the reentry dynamics. Our findings suggest that Ca2+ handling can considerably affect myofibroblast electrophysiology and alter the electrical propagation in atrial tissue composed of myocytes coupled with myofibroblasts. These findings can inform experimental validation experiments to further elucidate the role of myofibroblast Ca2+ handling in atrial arrhythmogenesis.
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Affiliation(s)
- Jorge Sánchez
- Institute of Biomedical Engineering, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany; (O.D.); (A.L.)
- Correspondence:
| | - Beatriz Trenor
- Centro de Investigación e Innovación en Bioingeniería (Ci2B), Universitàt Politècnica de València, 46022 Valencia, Spain; (B.T.); (J.S.)
| | - Javier Saiz
- Centro de Investigación e Innovación en Bioingeniería (Ci2B), Universitàt Politècnica de València, 46022 Valencia, Spain; (B.T.); (J.S.)
| | - Olaf Dössel
- Institute of Biomedical Engineering, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany; (O.D.); (A.L.)
| | - Axel Loewe
- Institute of Biomedical Engineering, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe, Germany; (O.D.); (A.L.)
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23
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Kemp JM, Whittaker DG, Venkateshappa R, Pang Z, Johal R, Sergeev V, Tibbits GF, Mirams GR, Claydon TW. Electrophysiological characterization of the hERG R56Q LQTS variant and targeted rescue by the activator RPR260243. J Gen Physiol 2021; 153:212555. [PMID: 34398210 PMCID: PMC8493834 DOI: 10.1085/jgp.202112923] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2021] [Revised: 06/11/2021] [Accepted: 07/21/2021] [Indexed: 11/20/2022] Open
Abstract
Human Ether-à-go-go (hERG) channels contribute to cardiac repolarization, and inherited variants or drug block are associated with long QT syndrome type 2 (LQTS2) and arrhythmia. Therefore, hERG activator compounds present a therapeutic opportunity for targeted treatment of LQTS. However, a limiting concern is over-activation of hERG resurgent current during the action potential and abbreviated repolarization. Activators that slow deactivation gating (type I), such as RPR260243, may enhance repolarizing hERG current during the refractory period, thus ameliorating arrhythmogenicity with reduced early repolarization risk. Here, we show that, at physiological temperature, RPR260243 enhances hERG channel repolarizing currents conducted in the refractory period in response to premature depolarizations. This occurs with little effect on the resurgent hERG current during the action potential. The effects of RPR260243 were particularly evident in LQTS2-associated R56Q mutant channels, whereby RPR260243 restored WT-like repolarizing drive in the early refractory period and diastolic interval, combating attenuated protective currents. In silico kinetic modeling of channel gating predicted little effect of the R56Q mutation on hERG current conducted during the action potential and a reduced repolarizing protection against afterdepolarizations in the refractory period and diastolic interval, particularly at higher pacing rates. These simulations predicted partial rescue from the arrhythmic effects of R56Q by RPR260243 without risk of early repolarization. Our findings demonstrate that the pathogenicity of some hERG variants may result from reduced repolarizing protection during the refractory period and diastolic interval with limited effect on action potential duration, and that the hERG channel activator RPR260243 may provide targeted antiarrhythmic potential in these cases.
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Affiliation(s)
- Jacob M Kemp
- Department of Biomedical Physiology and Kinesiology, Simon Fraser University, Burnaby, Canada
| | - Dominic G Whittaker
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, UK
| | | | - ZhaoKai Pang
- Department of Biomedical Physiology and Kinesiology, Simon Fraser University, Burnaby, Canada
| | - Raj Johal
- Department of Biomedical Physiology and Kinesiology, Simon Fraser University, Burnaby, Canada
| | - Valentine Sergeev
- Department of Biomedical Physiology and Kinesiology, Simon Fraser University, Burnaby, Canada
| | - Glen F Tibbits
- Department of Biomedical Physiology and Kinesiology, Simon Fraser University, Burnaby, Canada
| | - Gary R Mirams
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, UK
| | - Thomas W Claydon
- Department of Biomedical Physiology and Kinesiology, Simon Fraser University, Burnaby, Canada
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24
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Mangold KE, Wang W, Johnson EK, Bhagavan D, Moreno JD, Nerbonne JM, Silva JR. Identification of structures for ion channel kinetic models. PLoS Comput Biol 2021; 17:e1008932. [PMID: 34398881 PMCID: PMC8389848 DOI: 10.1371/journal.pcbi.1008932] [Citation(s) in RCA: 8] [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: 03/29/2021] [Revised: 08/26/2021] [Accepted: 07/16/2021] [Indexed: 12/22/2022] Open
Abstract
Markov models of ion channel dynamics have evolved as experimental advances have improved our understanding of channel function. Past studies have examined limited sets of various topologies for Markov models of channel dynamics. We present a systematic method for identification of all possible Markov model topologies using experimental data for two types of native voltage-gated ion channel currents: mouse atrial sodium currents and human left ventricular fast transient outward potassium currents. Successful models identified with this approach have certain characteristics in common, suggesting that aspects of the model topology are determined by the experimental data. Incorporating these channel models into cell and tissue simulations to assess model performance within protocols that were not used for training provided validation and further narrowing of the number of acceptable models. The success of this approach suggests a channel model creation pipeline may be feasible where the structure of the model is not specified a priori. Markov models of ion channel dynamics have evolved as experimental advances have improved our understanding of channel function. Past studies have examined limited sets of various structures for Markov models of channel dynamics. Here, we present a computational routine designed to thoroughly search for Markov model topologies for simulating whole-cell currents. We tested this method on two distinct types of voltage-gated cardiac ion channels and found the number of states and connectivity required to recapitulate experimentally observed kinetics. Successful models identified with this approach have certain characteristics in common, suggesting that model structures are determined by the experimental data. Incorporation of these models into higher scale action potential and cable (an approximation of one-dimensional action potential propagation) simulations, identified key channel phenomena that were required for proper function. These methods provide a route to create functional channel models that can be used for action potential simulation without pre-defining their structure ahead of time.
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Affiliation(s)
- Kathryn E. Mangold
- Department of Biomedical Engineering, Washington University in St. Louis, St. Louis, Missouri, United States of America
| | - Wei Wang
- Department of Medicine, Cardiovascular Division, Washington University School of Medicine, St. Louis Missouri, United States of America
| | - Eric K. Johnson
- Department of Medicine, Cardiovascular Division, Washington University School of Medicine, St. Louis Missouri, United States of America
| | - Druv Bhagavan
- Department of Biomedical Engineering, Washington University in St. Louis, St. Louis, Missouri, United States of America
| | - Jonathan D. Moreno
- Department of Biomedical Engineering, Washington University in St. Louis, St. Louis, Missouri, United States of America
- Department of Medicine, Cardiovascular Division, Washington University School of Medicine, St. Louis Missouri, United States of America
| | - Jeanne M. Nerbonne
- Department of Medicine, Cardiovascular Division, Washington University School of Medicine, St. Louis Missouri, United States of America
- Department of Developmental Biology, Washington University School of Medicine, St. Louis, Missouri, United States of America
| | - Jonathan R. Silva
- Department of Biomedical Engineering, Washington University in St. Louis, St. Louis, Missouri, United States of America
- * E-mail:
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25
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Lei CL, Mirams GR. Neural Network Differential Equations For Ion Channel Modelling. Front Physiol 2021; 12:708944. [PMID: 34421652 PMCID: PMC8371386 DOI: 10.3389/fphys.2021.708944] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2021] [Accepted: 07/05/2021] [Indexed: 11/13/2022] Open
Abstract
Mathematical models of cardiac ion channels have been widely used to study and predict the behaviour of ion currents. Typically models are built using biophysically-based mechanistic principles such as Hodgkin-Huxley or Markov state transitions. These models provide an abstract description of the underlying conformational changes of the ion channels. However, due to the abstracted conformation states and assumptions for the rates of transition between them, there are differences between the models and reality-termed model discrepancy or misspecification. In this paper, we demonstrate the feasibility of using a mechanistically-inspired neural network differential equation model, a hybrid non-parametric model, to model ion channel kinetics. We apply it to the hERG potassium ion channel as an example, with the aim of providing an alternative modelling approach that could alleviate certain limitations of the traditional approach. We compare and discuss multiple ways of using a neural network to approximate extra hidden states or alternative transition rates. In particular we assess their ability to learn the missing dynamics, and ask whether we can use these models to handle model discrepancy. Finally, we discuss the practicality and limitations of using neural networks and their potential applications.
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Affiliation(s)
- Chon Lok Lei
- Institute of Translational Medicine, Faculty of Health Sciences, University of Macau, Macau, China
- Department of Biomedical Sciences, Faculty of Health Sciences, University of Macau, Macau, China
- School of Mathematical Sciences, Faculty of Science and Engineering, University of Nottingham, Ningbo, China
| | - Gary R. Mirams
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, United Kingdom
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26
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Yip D, Accili E. Kinetic modelling of voltage-dependent gating in funny channels. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2021; 166:182-188. [PMID: 34310984 DOI: 10.1016/j.pbiomolbio.2021.07.009] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2021] [Revised: 07/12/2021] [Accepted: 07/20/2021] [Indexed: 10/20/2022]
Affiliation(s)
- Delbert Yip
- Department of Cellular and Physiological Sciences, University of British Columbia, Health Sciences Mall, V6T 1Z3, 2350, Canada
| | - Eric Accili
- Department of Cellular and Physiological Sciences, University of British Columbia, Health Sciences Mall, V6T 1Z3, 2350, Canada.
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27
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Bai J, Lu Y, Zhu Y, Wang H, Yin D, Zhang H, Franco D, Zhao J. Understanding PITX2-Dependent Atrial Fibrillation Mechanisms through Computational Models. Int J Mol Sci 2021; 22:7681. [PMID: 34299303 PMCID: PMC8307824 DOI: 10.3390/ijms22147681] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2021] [Revised: 07/14/2021] [Accepted: 07/16/2021] [Indexed: 01/11/2023] Open
Abstract
Atrial fibrillation (AF) is a common arrhythmia. Better prevention and treatment of AF are needed to reduce AF-associated morbidity and mortality. Several major mechanisms cause AF in patients, including genetic predispositions to AF development. Genome-wide association studies have identified a number of genetic variants in association with AF populations, with the strongest hits clustering on chromosome 4q25, close to the gene for the homeobox transcription PITX2. Because of the inherent complexity of the human heart, experimental and basic research is insufficient for understanding the functional impacts of PITX2 variants on AF. Linking PITX2 properties to ion channels, cells, tissues, atriums and the whole heart, computational models provide a supplementary tool for achieving a quantitative understanding of the functional role of PITX2 in remodelling atrial structure and function to predispose to AF. It is hoped that computational approaches incorporating all we know about PITX2-related structural and electrical remodelling would provide better understanding into its proarrhythmic effects leading to development of improved anti-AF therapies. In the present review, we discuss advances in atrial modelling and focus on the mechanistic links between PITX2 and AF. Challenges in applying models for improving patient health are described, as well as a summary of future perspectives.
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Affiliation(s)
- Jieyun Bai
- College of Information Science and Technology, Jinan University, Guangzhou 510632, China; (Y.L.); (Y.Z.)
- Auckland Bioengineering Institute, University of Auckland, Auckland 1010, New Zealand
| | - Yaosheng Lu
- College of Information Science and Technology, Jinan University, Guangzhou 510632, China; (Y.L.); (Y.Z.)
| | - Yijie Zhu
- College of Information Science and Technology, Jinan University, Guangzhou 510632, China; (Y.L.); (Y.Z.)
| | - Huijin Wang
- College of Information Science and Technology, Jinan University, Guangzhou 510632, China; (Y.L.); (Y.Z.)
| | - Dechun Yin
- Department of Cardiology, First Affiliated Hospital of Harbin Medical University, Harbin 150000, China;
| | - Henggui Zhang
- Biological Physics Group, School of Physics & Astronomy, The University of Manchester, Manchester M13 9PL, UK;
| | - Diego Franco
- Department of Experimental Biology, University of Jaen, 23071 Jaen, Spain;
| | - Jichao Zhao
- Auckland Bioengineering Institute, University of Auckland, Auckland 1010, New Zealand
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28
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Modeling and Analysis of Cardiac Hybrid Cellular Automata via GPU-Accelerated Monte Carlo Simulation. MATHEMATICS 2021. [DOI: 10.3390/math9020164] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
The heart consists of a complex network of billions of cells. Under physiological conditions, cardiac cells propagate electrical signals in space, generating the heartbeat in a synchronous and coordinated manner. When such a synchronization fails, life-threatening events can arise. The inherent complexity of the underlying nonlinear dynamics and the large number of biological components involved make the modeling and the analysis of electrophysiological properties in cardiac tissue still an open challenge. We consider here a Hybrid Cellular Automata (HCA) approach modeling the cardiac cell-cell membrane resistance with a free variable. We show that the modeling approach can reproduce important and complex spatiotemporal properties paving the ground for promising future applications. We show how GPU-based technology can considerably accelerate the simulation and the analysis. Furthermore, we study the cardiac behavior within a unidimensional domain considering inhomogeneous resistance and we perform a Monte Carlo analysis to evaluate our approach.
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29
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Zhang H, Zhang S, Wang W, Wang K, Shen W. A Mathematical Model of the Mouse Atrial Myocyte With Inter-Atrial Electrophysiological Heterogeneity. Front Physiol 2020; 11:972. [PMID: 32848887 PMCID: PMC7425199 DOI: 10.3389/fphys.2020.00972] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2020] [Accepted: 07/16/2020] [Indexed: 12/20/2022] Open
Abstract
Biophysically detailed mathematical models of cardiac electrophysiology provide an alternative to experimental approaches for investigating possible ionic mechanisms underlying the genesis of electrical action potentials and their propagation through the heart. The aim of this study was to develop a biophysically detailed mathematical model of the action potentials of mouse atrial myocytes, a popular experimental model for elucidating molecular and cellular mechanisms of arrhythmogenesis. Based on experimental data from isolated mouse atrial cardiomyocytes, a set of mathematical equations for describing the biophysical properties of membrane ion channel currents, intracellular Ca2+ handling, and Ca2+-calmodulin activated protein kinase II and β-adrenergic signaling pathways were developed. Wherever possible, membrane ion channel currents were modeled using Markov chain formalisms, allowing detailed representation of channel kinetics. The model also considered heterogeneous electrophysiological properties between the left and the right atrial cardiomyocytes. The developed model was validated by its ability to reproduce the characteristics of action potentials and Ca2+ transients, matching quantitatively to experimental data. Using the model, the functional roles of four K+ channel currents in atrial action potential were evaluated by channel block simulations, results of which were quantitatively in agreement with existent experimental data. To conclude, this newly developed model of mouse atrial cardiomyocytes provides a powerful tool for investigating possible ion channel mechanisms of atrial electrical activity at the cellular level and can be further used to investigate mechanisms underlying atrial arrhythmogenesis.
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Affiliation(s)
- Henggui Zhang
- Department of Physics and Astronomy, Biological Physics Group, School of Physics & Astronomy, The University of Manchester, Manchester, United Kingdom.,Peng Cheng Laboratory, Shenzhen, China
| | - Shanzhuo Zhang
- Department of Physics and Astronomy, Biological Physics Group, School of Physics & Astronomy, The University of Manchester, Manchester, United Kingdom.,School of Computer Science and Technology, Harbin Institute of Technology, Harbin, China
| | - Wei Wang
- Department of Physics and Astronomy, Biological Physics Group, School of Physics & Astronomy, The University of Manchester, Manchester, United Kingdom.,Peng Cheng Laboratory, Shenzhen, China.,Shenzhen Key Laboratory of Visual Object Detection and Recognition, Harbin Institute of Technology, Shenzhen, China
| | - Kuanquan Wang
- School of Computer Science and Technology, Harbin Institute of Technology, Harbin, China
| | - Weijian Shen
- Department of Physics and Astronomy, Biological Physics Group, School of Physics & Astronomy, The University of Manchester, Manchester, United Kingdom
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30
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Whittaker DG, Clerx M, Lei CL, Christini DJ, Mirams GR. Calibration of ionic and cellular cardiac electrophysiology models. WILEY INTERDISCIPLINARY REVIEWS. SYSTEMS BIOLOGY AND MEDICINE 2020; 12:e1482. [PMID: 32084308 PMCID: PMC8614115 DOI: 10.1002/wsbm.1482] [Citation(s) in RCA: 41] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/30/2019] [Revised: 01/17/2020] [Accepted: 01/18/2020] [Indexed: 12/30/2022]
Abstract
Cardiac electrophysiology models are among the most mature and well-studied mathematical models of biological systems. This maturity is bringing new challenges as models are being used increasingly to make quantitative rather than qualitative predictions. As such, calibrating the parameters within ion current and action potential (AP) models to experimental data sets is a crucial step in constructing a predictive model. This review highlights some of the fundamental concepts in cardiac model calibration and is intended to be readily understood by computational and mathematical modelers working in other fields of biology. We discuss the classic and latest approaches to calibration in the electrophysiology field, at both the ion channel and cellular AP scales. We end with a discussion of the many challenges that work to date has raised and the need for reproducible descriptions of the calibration process to enable models to be recalibrated to new data sets and built upon for new studies. This article is categorized under: Analytical and Computational Methods > Computational Methods Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Cellular Models.
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Affiliation(s)
- Dominic G. Whittaker
- Centre for Mathematical Medicine & Biology, School of Mathematical SciencesUniversity of NottinghamNottinghamUK
| | - Michael Clerx
- Computational Biology & Health Informatics, Department of Computer ScienceUniversity of OxfordOxfordUK
| | - Chon Lok Lei
- Computational Biology & Health Informatics, Department of Computer ScienceUniversity of OxfordOxfordUK
| | | | - Gary R. Mirams
- Centre for Mathematical Medicine & Biology, School of Mathematical SciencesUniversity of NottinghamNottinghamUK
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31
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Houston C, Marchand B, Engelbert L, Cantwell CD. Reducing complexity and unidentifiability when modelling human atrial cells. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2020. [PMID: 32448063 DOI: 10.5061/dryad.p2ngf1vmc] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Subscribe] [Scholar Register] [Indexed: 05/10/2023]
Abstract
Mathematical models of a cellular action potential (AP) in cardiac modelling have become increasingly complex, particularly in gating kinetics, which control the opening and closing of individual ion channel currents. As cardiac models advance towards use in personalized medicine to inform clinical decision-making, it is critical to understand the uncertainty hidden in parameter estimates from their calibration to experimental data. This study applies approximate Bayesian computation to re-calibrate the gating kinetics of four ion channels in two existing human atrial cell models to their original datasets, providing a measure of uncertainty and indication of potential issues with selecting a single unique value given the available experimental data. Two approaches are investigated to reduce the uncertainty present: re-calibrating the models to a more complete dataset and using a less complex formulation with fewer parameters to constrain. The re-calibrated models are inserted back into the full cell model to study the overall effect on the AP. The use of more complete datasets does not eliminate uncertainty present in parameter estimates. The less complex model, particularly for the fast sodium current, gave a better fit to experimental data alongside lower parameter uncertainty and improved computational speed. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.
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Affiliation(s)
- C Houston
- ElectroCardioMaths Programme, Centre for Cardiac Engineering, Imperial College, London, UK
- Department of Aeronautics, Imperial College, London, UK
| | - B Marchand
- Department of Aeronautics, Imperial College, London, UK
| | - L Engelbert
- Department of Aeronautics, Imperial College, London, UK
| | - C D Cantwell
- ElectroCardioMaths Programme, Centre for Cardiac Engineering, Imperial College, London, UK
- Department of Aeronautics, Imperial College, London, UK
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32
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Lei CL, Clerx M, Whittaker DG, Gavaghan DJ, de Boer TP, Mirams GR. Accounting for variability in ion current recordings using a mathematical model of artefacts in voltage-clamp experiments. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2020; 378:20190348. [PMID: 32448060 PMCID: PMC7287334 DOI: 10.1098/rsta.2019.0348] [Citation(s) in RCA: 32] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 04/08/2020] [Indexed: 05/21/2023]
Abstract
Mathematical models of ion channels, which constitute indispensable components of action potential models, are commonly constructed by fitting to whole-cell patch-clamp data. In a previous study, we fitted cell-specific models to hERG1a (Kv11.1) recordings simultaneously measured using an automated high-throughput system, and studied cell-cell variability by inspecting the resulting model parameters. However, the origin of the observed variability was not identified. Here, we study the source of variability by constructing a model that describes not just ion current dynamics, but the entire voltage-clamp experiment. The experimental artefact components of the model include: series resistance, membrane and pipette capacitance, voltage offsets, imperfect compensations made by the amplifier for these phenomena, and leak current. In this model, variability in the observations can be explained by either cell properties, measurement artefacts, or both. Remarkably, by assuming that variability arises exclusively from measurement artefacts, it is possible to explain a larger amount of the observed variability than when assuming cell-specific ion current kinetics. This assumption also leads to a smaller number of model parameters. This result suggests that most of the observed variability in patch-clamp data measured under the same conditions is caused by experimental artefacts, and hence can be compensated for in post-processing by using our model for the patch-clamp experiment. This study has implications for the question of the extent to which cell-cell variability in ion channel kinetics exists, and opens up routes for better correction of artefacts in patch-clamp data. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.
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Affiliation(s)
- Chon Lok Lei
- Computational Biology & Health Informatics, Department of Computer Science, University of Oxford, Oxford, UK
| | - Michael Clerx
- Computational Biology & Health Informatics, Department of Computer Science, University of Oxford, Oxford, UK
| | - Dominic G. Whittaker
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, UK
| | - David J. Gavaghan
- Computational Biology & Health Informatics, Department of Computer Science, University of Oxford, Oxford, UK
| | - Teun P. de Boer
- Department of Medical Physiology, Division Heart & Lungs, University Medical Center Utrecht, Utrecht, the Netherlands
| | - Gary R. Mirams
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, UK
- e-mail:
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33
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Houston C, Marchand B, Engelbert L, Cantwell CD. Reducing complexity and unidentifiability when modelling human atrial cells. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2020; 378:20190339. [PMID: 32448063 PMCID: PMC7287336 DOI: 10.1098/rsta.2019.0339] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/07/2023]
Abstract
Mathematical models of a cellular action potential (AP) in cardiac modelling have become increasingly complex, particularly in gating kinetics, which control the opening and closing of individual ion channel currents. As cardiac models advance towards use in personalized medicine to inform clinical decision-making, it is critical to understand the uncertainty hidden in parameter estimates from their calibration to experimental data. This study applies approximate Bayesian computation to re-calibrate the gating kinetics of four ion channels in two existing human atrial cell models to their original datasets, providing a measure of uncertainty and indication of potential issues with selecting a single unique value given the available experimental data. Two approaches are investigated to reduce the uncertainty present: re-calibrating the models to a more complete dataset and using a less complex formulation with fewer parameters to constrain. The re-calibrated models are inserted back into the full cell model to study the overall effect on the AP. The use of more complete datasets does not eliminate uncertainty present in parameter estimates. The less complex model, particularly for the fast sodium current, gave a better fit to experimental data alongside lower parameter uncertainty and improved computational speed. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.
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Affiliation(s)
- C. Houston
- ElectroCardioMaths Programme, Centre for Cardiac Engineering, Imperial College, London, UK
- Department of Aeronautics, Imperial College, London, UK
- e-mail:
| | - B. Marchand
- Department of Aeronautics, Imperial College, London, UK
| | - L. Engelbert
- Department of Aeronautics, Imperial College, London, UK
| | - C. D. Cantwell
- ElectroCardioMaths Programme, Centre for Cardiac Engineering, Imperial College, London, UK
- Department of Aeronautics, Imperial College, London, UK
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34
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Benson AP, Stevenson-Cocks HJ, Whittaker DG, White E, Colman MA. Multi-scale approaches for the simulation of cardiac electrophysiology: II - Tissue-level structure and function. Methods 2020; 185:60-81. [PMID: 31988002 DOI: 10.1016/j.ymeth.2020.01.010] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2019] [Revised: 11/15/2019] [Accepted: 01/14/2020] [Indexed: 02/06/2023] Open
Abstract
Computational models of the heart, from cell-level models, through one-, two- and three-dimensional tissue-level simplifications, to biophysically-detailed three-dimensional models of the ventricles, atria or whole heart, allow the simulation of excitation and propagation of this excitation, and have provided remarkable insight into the normal and pathological functioning of the heart. In this article we present equations for modelling cellular excitation (i.e. the cell action potential) from both a phenomenological and a biophysical perspective. Hodgkin-Huxley formalism is discussed, along with the current generation of biophysically-detailed cardiac cell models. Alternative Markovian formulations for modelling ionic currents are also presented. Equations describing propagation of this cellular excitation, through one-, two- and three-dimensional idealised or realistic tissues, are then presented. For all types of model, from cell to tissue, methods for discretisation and integration of the underlying equations are discussed. The article finishes with a discussion of two tissue-level experimental imaging techniques - diffusion tensor magnetic resonance imaging and optical imaging - that can be used to provide data for parameterisation and validation of cell- and tissue-level cardiac models.
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Affiliation(s)
- Alan P Benson
- School of Biomedical Sciences University of Leeds, Leeds LS2 9JT, UK.
| | | | - Dominic G Whittaker
- School of Biomedical Sciences University of Leeds, Leeds LS2 9JT, UK; School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK
| | - Ed White
- School of Biomedical Sciences University of Leeds, Leeds LS2 9JT, UK
| | - Michael A Colman
- School of Biomedical Sciences University of Leeds, Leeds LS2 9JT, UK
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35
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The Heart by Numbers. Biophys J 2019; 117:E1-E3. [PMID: 31791548 DOI: 10.1016/j.bpj.2019.11.010] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2019] [Accepted: 11/14/2019] [Indexed: 11/22/2022] Open
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