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Ding J, Sun H, Zhou S. Hysteresis and linear stability analysis on multiple steady-state solutions to the Poisson-Nernst-Planck equations with steric interactions. Phys Rev E 2020; 102:053301. [PMID: 33327140 DOI: 10.1103/physreve.102.053301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2020] [Accepted: 09/14/2020] [Indexed: 06/12/2023]
Abstract
In this work, we numerically study linear stability of multiple steady-state solutions to a type of steric Poisson-Nernst-Planck equations with Dirichlet boundary conditions, which are applicable to ion channels. With numerically found multiple steady-state solutions, we obtain S-shaped current-voltage and current-concentration curves, showing hysteretic response of ion conductance to voltages and boundary concentrations with memory effects. Boundary value problems are proposed to locate bifurcation points and predict the local bifurcation diagram near bifurcation points on the S-shaped curves. Numerical approaches for linear stability analysis are developed to understand the stability of the steady-state solutions that are only numerically available. Finite difference schemes are proposed to solve a derived eigenvalue problem involving differential operators. The linear stability analysis reveals that the S-shaped curves have two linearly stable branches of different conductance levels and one linearly unstable intermediate branch, exhibiting classical bistable hysteresis. As predicted in the linear stability analysis transition dynamics, from a steady-state solution on the unstable branch to one on the stable branches, are led by perturbations associated to the mode of the dominant eigenvalue. Further numerical tests demonstrate that the finite difference schemes proposed in the linear stability analysis are second-order accurate. Numerical approaches developed in this work can be applied to study linear stability of a class of time-dependent problems around their steady-state solutions that are computed numerically.
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Affiliation(s)
- Jie Ding
- Department of Mathematics and Mathematical Center for Interdiscipline Research, Soochow University, 1 Shizi Street, Suzhou 215006, Jiangsu, China
| | - Hui Sun
- Department of Mathematics and Statistics, California State University, Long Beach, California 90840, USA
| | - Shenggao Zhou
- Department of Mathematics and Mathematical Center for Interdiscipline Research, Soochow University, 1 Shizi Street, Suzhou 215006, Jiangsu, China
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David JS, Amour J, Duracher C, Ferretti C, Precloux P, Petit P, Riou B, Gueugniaud PY. Comparison of the effects of mepivacaine and lidocaine on rat myocardium. Eur J Anaesthesiol 2007; 24:190-7. [PMID: 16938160 DOI: 10.1017/s0265021506001359] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 07/31/2006] [Indexed: 11/07/2022]
Abstract
BACKGROUND AND OBJECTIVE To compare the inotropic and lusitropic effect of lidocaine and mepivacaine on rat papillary muscle. METHODS Effects of lidocaine and mepivacaine (10-8-10-3 M) were studied in rat left ventricular papillary muscles in vitro at a calcium concentration of 1 mmol, under low (isotony) and high (isometric) loads. RESULTS Lidocaine induced a significant negative inotropic effect in isotonic and isometric conditions whereas mepivacaine did not. Mepivacaine only induced a negative inotropic effect when added as a bolus for the highest concentration and this effect was significantly more pronounced with lidocaine than with mepivacaine (active force at 10-3 M: 63 +/- 10 vs. 84 +/- 10% of baseline, P < 0.05). Increasing calcium concentration resulted in a greater positive inotropic effect in the control (199 +/- 11% of baseline) and mepivacaine groups (197 +/- 22% of baseline) when compared to the lidocaine group (163 +/- 19% of baseline, P < 0.05 vs. lidocaine and control groups), suggesting an impairment on intracellular Ca2+ handling by lidocaine. A negative lusitropic effect under low load was observed only for mepivacaine and suggested an impairment of sarcoplasmic reticulum function. Lidocaine and mepivacaine did not modify post-rest potentiation but significantly depressed the force-frequency relationship. CONCLUSIONS The negative inotropic and lusitropic effects induced by lidocaine were more important than that of mepivacaine and may involve an impairment of intracellular Ca2+ handling.
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Affiliation(s)
- J-S David
- Laboratoire d'Anesthésiologie, Equipe d'Accueil 1896, Département d'Anesthésie-Réanimation-SAMU, CHU Edouard Herriot, Hospices Civils de Lyon, Université Claude Bernard, 3 Place d'Arsonval, 69437 Lyon Cedex 03, France.
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Abstract
Block of sodium ionic current by lidocaine is associated with alteration of the gating charge-voltage (Q-V) relationship characterized by a 38% reduction in maximal gating charge (Q(max)) and by the appearance of additional gating charge at negative test potentials. We investigated the molecular basis of the lidocaine-induced reduction in cardiac Na channel-gating charge by sequentially neutralizing basic residues in each of the voltage sensors (S4 segments) in the four domains of the human heart Na channel (hH1a). By determining the relative reduction in the Q(max) of each mutant channel modified by lidocaine we identified those S4 segments that contributed to a reduction in gating charge. No interaction of lidocaine was found with the voltage sensors in domains I or II. The largest inhibition of charge movement was found for the S4 of domain III consistent with lidocaine completely inhibiting its movement. Protection experiments with intracellular MTSET (a charged sulfhydryl reagent) in a Na channel with the fourth outermost arginine in the S4 of domain III mutated to a cysteine demonstrated that lidocaine stabilized the S4 in domain III in a depolarized configuration. Lidocaine also partially inhibited movement of the S4 in domain IV, but lidocaine's most dramatic effect was to alter the voltage-dependent charge movement of the S4 in domain IV such that it accounted for the appearance of additional gating charge at potentials near -100 mV. These findings suggest that lidocaine's actions on Na channel gating charge result from allosteric coupling of the binding site(s) of lidocaine to the voltage sensors formed by the S4 segments in domains III and IV.
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Affiliation(s)
- Michael F Sheets
- The Nora Eccles Harrison Cardiovascular Research and Training Institute, Department of Internal Medicine, University of Utah, Salt Lake City, UT 84112, USA.
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Castañeda-Castellanos DR, Nikonorov I, Kallen RG, Recio-Pinto E. Lidocaine stabilizes the open state of CNS voltage-dependent sodium channels. BRAIN RESEARCH. MOLECULAR BRAIN RESEARCH 2002; 99:102-13. [PMID: 11978401 DOI: 10.1016/s0169-328x(01)00340-0] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Abstract
We have previously reported that the lidocaine action is different between CNS and muscle batrachotoxin-modified Na+ channels [Salazar et al., J. Gen. Physiol. 107 (1996) 743-754; Brain Res. 699 (1995) 305-314]. In this study we examined lidocaine action on CNS Na+ currents, to investigate the mechanism of lidocaine action on this channel isoform and to compare it with that proposed for muscle Na+ currents. Na+ currents were measured with the whole cell voltage clamp configuration in stably transfected cells expressing the brain alpha-subunit (type IIA) by itself (alpha-brain) or together with the brain beta(1)-subunit (alphabeta(1)-brain), or the cardiac alpha-subunit (hH1) (alpha-cardiac). Lidocaine (100 microM) produced comparable levels of Na+ current block at positive potentials and of hyperpolarizing shift of the steady-state inactivation curve in alpha-brain and alphabeta(1)-brain Na+ currents. Lidocaine accelerated the rates of activation and inactivation, produced an hyperpolarizing shift in the steady-state activation curve and increased the current magnitude at negative potentials in alpha-brain but not in alphabeta(1)-brain Na+ currents. The lidocaine action in alphabeta(1)-brain resembled that observed in alpha-cardiac Na+ currents. The lidocaine-induced increase in current magnitude at negative potentials and the hyperpolarizing shift in the steady-state activation curve of alpha-brain, are novel effects and suggest that lidocaine treatment does not always lead to current reduction/block when it interacts with Na+ channels. The data are explained by using a modified version of the model proposed by Vedantham and Cannon [J. Gen. Physiol., 113 (1999) 7-16] in which we postulate that the difference in lidocaine action between alpha-brain and alphabeta(1)-brain Na+ currents could be explained by differences in the lidocaine action on the open channel state.
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Vedantham V, Cannon SC. The position of the fast-inactivation gate during lidocaine block of voltage-gated Na+ channels. J Gen Physiol 1999; 113:7-16. [PMID: 9874684 PMCID: PMC2222985 DOI: 10.1085/jgp.113.1.7] [Citation(s) in RCA: 86] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/1998] [Accepted: 10/19/1998] [Indexed: 12/12/2022] Open
Abstract
Lidocaine produces voltage- and use-dependent inhibition of voltage-gated Na+ channels through preferential binding to channel conformations that are normally populated at depolarized potentials and by slowing the rate of Na+ channel repriming after depolarizations. It has been proposed that the fast-inactivation mechanism plays a crucial role in these processes. However, the precise role of fast inactivation in lidocaine action has been difficult to probe because gating of drug-bound channels does not involve changes in ionic current. For that reason, we employed a conformational marker for the fast-inactivation gate, the reactivity of a cysteine substituted at phenylalanine 1304 in the rat adult skeletal muscle sodium channel alpha subunit (rSkM1) with [2-(trimethylammonium)ethyl]methanethiosulfonate (MTS-ET), to determine the position of the fast-inactivation gate during lidocaine block. We found that lidocaine does not compete with fast-inactivation. Rather, it favors closure of the fast-inactivation gate in a voltage-dependent manner, causing a hyperpolarizing shift in the voltage dependence of site 1304 accessibility that parallels a shift in the steady state availability curve measured for ionic currents. More significantly, we found that the lidocaine-induced slowing of sodium channel repriming does not result from a slowing of recovery of the fast-inactivation gate, and thus that use-dependent block does not involve an accumulation of fast-inactivated channels. Based on these data, we propose a model in which transitions along the activation pathway, rather than transitions to inactivated states, play a crucial role in the mechanism of lidocaine action.
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Affiliation(s)
- V Vedantham
- Program in Neuroscience, Division of Medical Sciences, Harvard Medical School, Boston, Massachusetts 02115, USA
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Carmeliet E, Mubagwa K. Antiarrhythmic drugs and cardiac ion channels: mechanisms of action. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 1998; 70:1-72. [PMID: 9785957 DOI: 10.1016/s0079-6107(98)00002-9] [Citation(s) in RCA: 85] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Abstract
In this review a description and an analysis are given of the interaction of antiarrhythmic drugs with their molecular target, i.e. ion channels and receptors. Our approach is based on the concept of vulnerable parameter, i.e. the electrophysiological property which plays a crucial role in the genesis of arrhythmias. To prevent or stop the arrhythmia a drug should modify the vulnerable parameter by its action on channel or receptor targets. In the first part, general aspects of the interaction between drugs channel molecules are considered. Drug binding depends on the state of the channel: rested, activated pre-open, activated open, or inactivated state. The change in channel behaviour with state is presented in the framework of the modulated-receptor hypothesis. Not only inhibition but also stimulation can be the result of drug binding. In the second part a detailed and systematic description and an analysis are given of the interaction of drugs with specific channels (Na+, Ca2+, K+, "pacemaker") and non-channel receptors. Emphasis is given to the type of state-dependent block involved (rested, activated and inactivated state block) and the change in channel kinetics. These properties vary and determine the voltage- and frequency-dependence of the change in ionic current. Finally, the question is asked as to whether the available drugs by their action on channels and receptors modify the vulnerable parameter in the desired way to stop or prevent arrhythmias.
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Affiliation(s)
- E Carmeliet
- Centre for Experimental Surgery and Anaesthesiology, University of Leuven, Belgium.
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Shistik E, Ivanina T, Blumenstein Y, Dascal N. Crucial role of N terminus in function of cardiac L-type Ca2+ channel and its modulation by protein kinase C. J Biol Chem 1998; 273:17901-9. [PMID: 9651396 DOI: 10.1074/jbc.273.28.17901] [Citation(s) in RCA: 92] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022] Open
Abstract
The role of the cytosolic N terminus of the main subunit (alpha1C) of cardiac L-type voltage-dependent Ca2+ channel was studied in Xenopus oocyte expression system. Deletion of the initial 46 or 139 amino acids (a.a.) of rabbit heart alpha1C caused a 5-10-fold increase in the whole cell Ca2+ channel current carried by Ba2+ (IBa), as reported previously (Wei, X., Neely, A., Olcese, R., Lang, W., Stefani, E., and Birnbaumer, L. (1996) Recept. Channels 4, 205-215). The plasma membrane content of alpha1C protein, measured immunochemically, was not altered by the 46-a.a. deletion. Patch clamp recordings in the presence of a dihydropyridine agonist showed that this deletion causes a approximately 10-fold increase in single channel open probability without changing channel density. Thus, the initial segment of the N terminus affects channel gating rather than expression. The increase in IBa caused by coexpression of the auxiliary beta2A subunit was substantially stronger in channels with full-length alpha1C than in 46- or 139-a.a. truncated mutants, suggesting an interaction between beta2A and N terminus. However, only the I-II domain linker of alpha1C, but not to N or C termini, bound beta2A in vitro. The well documented increase of IBa caused by activation of protein kinase C (PKC) was fully eliminated by the 46-a.a. deletion. Thus, the N terminus of alpha1C plays a crucial role in channel gating and PKC modulation. We propose that PKC and beta subunit enhance the activity of the channel in part by relieving an inhibitory control exerted by the N terminus. Since PKC up-regulation of L-type Ca2+ channels has been reported in many species, we predict that isoforms of alpha1C subunits containing the initial N-terminal 46 a.a. similar to those of the rabbit heart alpha1C are widespread in cardiac and smooth muscle cells.
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Affiliation(s)
- E Shistik
- Department of Physiology and Pharmacology, Sackler School of Medicine, Tel Aviv University, Ramat Aviv 69978, Israel
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Josephson IR. Depolarization shifts the voltage dependence of cardiac sodium channel and calcium channel gating charge movements. Pflugers Arch 1996. [DOI: 10.1007/bf02332175] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Josephson IR. Depolarization shifts the voltage dependence of cardiac sodium channel and calcium channel gating charge movements. Pflugers Arch 1996; 431:895-904. [PMID: 8927507 DOI: 10.1007/s004240050083] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023]
Abstract
In cardiac ventricular myocytes, membrane depolarization leads to the inactivation of the Na channel and Ca channel ionic currents. The inactivation of the ionic currents has been associated with a reduction of the gating charge movement ("immobilization") which governs the activation of Na channels and Ca channels. The nature of the apparent "immobilization" of the charge movement following depolarization was explored in embryonic chick ventricular myocytes using voltage protocols applied from depolarized holding potentials. It was found that although all of the charge was mobile following inactivation, the voltage dependence of its movement was shifted to more negative potentials. In addition, the shift in the distribution of the Na channel charge could be differentiated from that of the Ca channel charge on the basis of kinetic as well as steady-state criteria. These results suggest that the voltage-dependent activation of Na channel and Ca channel charge movements leads to conformational changes and charge rearrangements that differentially bias the movements of these voltage sensors, and concomitantly produce channel inactivation.
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Affiliation(s)
- I R Josephson
- The Department of Molecular and Cellular Physiology, University of Cincinnati, College of Medicine, Cincinnati, OH 45267-0576, USA
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Josephson IR, Varadi G. The beta subunit increases Ca2+ currents and gating charge movements of human cardiac L-type Ca2+ channels. Biophys J 1996; 70:1285-93. [PMID: 8785284 PMCID: PMC1225054 DOI: 10.1016/s0006-3495(96)79685-6] [Citation(s) in RCA: 67] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023] Open
Abstract
The properties of the gating currents (nonlinear charge movements) of human cardiac L-type Ca2- channels and their relationship to the activation of the Ca2+ channel (ionic) currents were studied using a mammalian expression system. Cloned human cardiac alpha1 + rabbit alpha 2 subunits or human cardiac alpha 1 + rabbit alpha 2 + human beta 3 subunits were transiently expressed in HEK293 cells. The maximum Ca2+ current density increased from -3.9 +/- 0.9 pA/pF for the alpha 1 + alpha 2 subunits to -11.6 +/- 2.2 pA/pF for alpha 1 + alpha 2 + beta 3 subunits. Calcium channel gating currents were recorded after the addition of 5 mM Co2+, using a -P/5 protocol. The maximum nonlinear charge movement (Qmax) increased from 2.5 +/- 0.3 nC/muF for alpha 1 + alpha 2 subunit to 12.1 +/- 0.3 nC/muF for alpha 1 + alpha 2 + beta 3 subunit expression. The QON was equal to the QOFF for both subunit combinations. The QON-Vm data were fit by a sum of two Boltzmann expressions and ranged over more negative potentials, as compared with the voltage dependence for activation of the Ca2+ conductance. We conclude that 1) the beta subunit increases the number of functional alpha 1 subunits expressed in the plasma membrane of these cells and 2) the voltage-dependent activation of the human cardiac L-type calcium channel involves the movements of at least two nonidentical and functionally distinct gating structures.
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Affiliation(s)
- I R Josephson
- Department of Molecular and Cellular Physiology, University of Cincinnati, College of Medicine, Ohio 45267-0576, USA.
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Abstract
The nonlinear charge movements which occur during membrane depolarization of cardiac ventricular myocytes (QON) have been previously identified and separated, by kinetic and steady-state criteria, into constituent components arising from the gating of Na channels and Ca channels. In contrast, the nature and time course of the OFF charge movements (QOFF), which follow membrane repolarization have not been as clearly established. In order to address this question cardiac QOFF was studied using small-diameter, 17-day-old embryonic chick ventricular myocytes that can be rapidly and uniformly voltage-clamped. The application of brief (5.4 ms) depolarizing steps were employed to produce Na channel inactivation but little Ca channel inactivation. Following the return of the membrane potential to -100 mV QOFF, measured as the gating current termed IgOFF, displayed two kinetic components. Double exponential fits to IgOFF yielded time constants of a few tenths of a millisecond for the fast component (IgOFFfast) and of 1-2 ms for the slower component (IgOFFslow). The time course and voltage dependence for the slower component suggested that it might be linked to the inactivation, and the recovery from inactivation, of Na channels. In order to identify these kinetic components double-pulse protocols were employed in which the duration of the prepulse and the interval separating the prepulse and test pulse were varied. The time course for the decay of IgOFFslow following a brief inactivating prepulse was similar to the time course for the recovery of the Na channel QON (QNaRecov). Both IgOFFslow and QNaRecov preceded the recovery of the Na channel (ionic) current. The recovery from inactivation of both the Na current and QNa displayed a similar voltage dependence. These experiments have helped to identify the two components of cardiac IgOFF and, therefore, will facilitate the interpretation of further biophysical and pharmacological studies concerning cardiac Na channel and Ca channel gating charge movements.
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Affiliation(s)
- I R Josephson
- Department of Molecular and Cellular Physiology, University of Cincinnati, College of Medicine, Cincinnati, OH 45267-0576, USA
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