Comparison between Hodgkin–Huxley and Markov formulations of cardiac ion channels

Carbonell-Pascual, Beatriz; Godoy, Eduardo Jorge; Ferrer, Ana; Romero, Lucía; Ferrero, J.M.

doi:10.1016/j.jtbi.2016.03.039

Cited by 13 publications

(11 citation statements)

References 47 publications

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“…2 of Refs. [16,19]. Figure 3 shows plots of P O , P I , and P C versus time t for the Na channel in the course of an action potential for MM1 (MM2) models in the top (bottom) panel; the blue and red curves are for WT and MUT models, respectively.…”

Section: Activation Inactivation and Recovery From Inactivation Of mentioning

confidence: 99%

“…FIG. 16. The actual versus predicted plots for all the 3 responses (V max , APD and V rest ) at the cellular level and one response (CV) at the tissue level for 12 predictors for all the three wild-type models.…”

Section: Appendix E: Parameter-sensitivity Analysismentioning

confidence: 99%

“…In particular, HHM action potentials, their morphological properties, the action-potential-duration restitution (APDR), and the conduction-velocity restitution (CVR) are comparable to their MM counterparts [16]. The authors of [16] have considered both WT and MUT cases for Kr and Na channels in the MM and their HHM counterparts; their results are encouraging, insofar as they suggest that we can use simple, effective HHM models, whose parameters are obtained from comparisons with their complicated MM counterparts, to obtain the properties of action potentials and their dependence on mutations. A careful comparison of these MMs and the HHM for an ion channel, at the cellular level, brings out the differences in their action potentials and their morphologies.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Recently it has been shown that, at the level of a single cardiomyocyte, the dynamics of wild-type (WT) and mutant (MUT) ion channels can be modeled well by the HHM formalism, if it is obtained from the Markov-state model (MM) [16]. In particular, HHM action potentials, their morphological properties, the action-potential-duration restitution (APDR), and the conduction-velocity restitution (CVR) are comparable to their MM counterparts [16]. The authors of [16] have considered both WT and MUT cases for Kr and Na channels in the MM and their HHM counterparts; their results are encouraging, insofar as they suggest that we can use simple, effective HHM models, whose parameters are obtained from comparisons with their complicated MM counterparts, to obtain the properties of action potentials and their dependence on mutations.…”

Section: Introductionmentioning

confidence: 99%

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Comparisons of wave dynamics in Hodgkin-Huxley and Markov-state formalisms for the sodium (Na) channel in some mathematical models for human cardiac tissue

Mulimani

Nayak

Pandit

2020

Phys. Rev. Research

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We compare and contrast the excitation properties of cardiac myocytes and cardiac tissue modeled by (a) a Hodgkin-Huxley-model (HHM) and (b) Markov-chain-model (MM) formalisms for the sodium (Na) ion channel. Specifically, we bring out the differences between HHM and MM formalisms, for both wild-type (WT) and mutant (MUT) models, for ion-channel kinetics, single-myocyte action potentials, and the spatiotemporal evolutions of spiral and scroll waves in different mathematical models of cardiac tissue. We show that the kinetic properties of Na ion channels are not the same for HHM and MM models; in particular, the range of values of the trans-membrane potential V m , in which there is a significant window current, depends significantly on these models, so there are marked differences in the opening times of the Na ion channels, the maximal amplitude of the Na current, and the presence or absence of a late Na current. Furthermore, these changes lead to different excitation behaviors in cardiac tissue; specifically, two of the WT models show stable spiral waves, but the other one shows meandering and transiently breaking spiral waves. Our results are based on extensive direct numerical simulations of waves of electrical activation in these models, in two-and three-dimensional (2D and 3D) homogeneous simulation domains and also in domains with localized heterogeneities, either obstacles with randomly distributed inexcitable regions or mutant cells in a wild-type background. Our study brings out the sensitive dependence of spiral-and scroll-wave dynamics on these five models and the parameters that define them. We list desiderata for a good model for the Na wild-type ion channel; we use these desired properties to select one of the MM models that we study.

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Section: Activation Inactivation and Recovery From Inactivation Of mentioning

confidence: 99%

Section: Appendix E: Parameter-sensitivity Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Comparisons of wave dynamics in Hodgkin-Huxley and Markov-state formalisms for the sodium (Na) channel in some mathematical models for human cardiac tissue

Mulimani

Nayak

Pandit

2020

Phys. Rev. Research

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Calibration of ionic and cellular cardiac electrophysiology models

Whittaker

Clerx

Lei

et al. 2020

WIREs Mechanisms of Disease

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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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Combination of “generalized Trotter operator splitting” and “quadratic adaptive algorithm” method for tradeoff among speedup, stability, and accuracy in the Markov chain model of sodium ion channels in the ventricular cell model

Chen

Luo

Chen

2020

Med Biol Eng Comput

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Comparison between Hodgkin–Huxley and Markov formulations of cardiac ion channels

Cited by 13 publications

References 47 publications

Comparisons of wave dynamics in Hodgkin-Huxley and Markov-state formalisms for the sodium (Na) channel in some mathematical models for human cardiac tissue

Comparisons of wave dynamics in Hodgkin-Huxley and Markov-state formalisms for the sodium (Na) channel in some mathematical models for human cardiac tissue

Calibration of ionic and cellular cardiac electrophysiology models

Combination of “generalized Trotter operator splitting” and “quadratic adaptive algorithm” method for tradeoff among speedup, stability, and accuracy in the Markov chain model of sodium ion channels in the ventricular cell model

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