A modified FitzHugh-Nagumo model for cardiac instabilities: The replacement of a conductance variable with Ca current as a slow variable

2013 ◽  
Author(s):  
Motohisa Osaka
Keyword(s):  
Slow Variable ◽  
Ca Current

scholarly journals Analysis of Stochastic Generation and Shifts of Phantom Attractors in a Climate–Vegetation Dynamical Model

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1329
Author(s):  
Lev Ryashko ◽  
Dmitri V. Alexandrov ◽  
Irina Bashkirtseva
Keyword(s):  
Multiplicative Noise ◽  
Nonlinear Dynamical Systems ◽  
Stochastic Theory ◽  
Slow Variable ◽  
Theoretical Description ◽  
Mathematical Study ◽  
Stochastic Generation ◽  
Nonlinear Dynamical ◽  
Additive And Multiplicative Noise ◽  
And Shifts

A problem of the noise-induced generation and shifts of phantom attractors in nonlinear dynamical systems is considered. On the basis of the model describing interaction of the climate and vegetation we study the probabilistic mechanisms of noise-induced systematic shifts in global temperature both upward (“warming”) and downward (“freezing”). These shifts are associated with changes in the area of Earth covered by vegetation. The mathematical study of these noise-induced phenomena is performed within the framework of the stochastic theory of phantom attractors in slow-fast systems. We give a theoretical description of stochastic generation and shifts of phantom attractors based on the method of freezing a slow variable and averaging a fast one. The probabilistic mechanisms of oppositely directed shifts caused by additive and multiplicative noise are discussed.

Sodium-calcium exchange-mediated contractions in feline ventricular myocytes

1992 ◽  
Vol 263 (4) ◽  
pp. H1161-H1169 ◽  
Author(s):  
H. B. Nuss ◽  
S. R. Houser
Keyword(s):  
Sarcoplasmic Reticulum ◽  
Ventricular Myocytes ◽  
Membrane Potentials ◽  
Exchange Mechanism ◽  
Ca Channel ◽  
Ca Current ◽  
Voltage Step ◽  
Reverse Mode ◽  
Sodium Calcium ◽  
Calcium Exchange

The hypothesis that Ca entry by the sarcolemmal Na-Ca exchange mechanism induces sarcoplasmic reticulum (SR) Ca release, loads the SR with Ca, and/or directly induces contractions by elevating cytosolic free Ca was tested in voltage-clamped feline ventricular myocytes. Intracellular Na concentration was increased by cellular dialysis to enhance Ca influx via "reverse-mode" Na-Ca exchange at positive membrane potentials, at which the "L-type" Ca current (ICa) should be small. Contractions were induced in the presence of Ca channel antagonists by depolarization to these potentials, suggesting that Ca influx via reverse-mode Na-Ca exchange was involved. These contractions had both phasic (SR related) and tonic components of shortening. They were smaller and began with more delay after depolarization than contractions which involved ICa. The magnitude of shortening was graded by the amount and duration of depolarization, suggesting that Ca influx via reverse-mode Na-Ca exchange has the capacity to induce and grade SR Ca release. Small slow contractions could be evoked in the presence of ryanodine (to impair SR function) and verapamil (to block ICa), supporting the idea that Ca influx via Na-Ca exchange is sufficient to directly activate the contractile proteins. Contractions induced by voltage steps to +10 mV, which were usually small when ICa was blocked, were potentiated if preceded by a voltage step to strongly positive potentials. This potentiation was inhibited by ryanodine, suggesting that Ca entry that occurs by Na-Ca exchange may be important for normal SR Ca loading.(ABSTRACT TRUNCATED AT 250 WORDS)

Multiple-S-Shaped Critical Manifold and Jump Phenomena in Low Frequency Forced Vibration with Amplitude Modulation

2019 ◽  
Vol 29 (05) ◽  
pp. 1930012 ◽  
Author(s):  
Yue Yu ◽  
Qianqian Wang ◽  
Qinsheng Bi ◽  
C. W. Lim
Keyword(s):  
Amplitude Modulation ◽  
Large Amplitude ◽  
Low Frequency ◽  
Slow Variable ◽  
Critical Manifold ◽  
Singular Orbit ◽  
Modulation Control ◽  
Cycle Oscillation ◽  
Tuning Frequency ◽  
Complex Mechanical Systems

Motivated by the forced harmonic vibration of complex mechanical systems, we analyze the dynamics involving different waves in a double-well potential oscillator coupling amplitude modulation control of low frequency. The combination of amplitude modulation factor significantly enriches the dynamical behaviors on the formation of multiple-S-shaped manifold and multiple jumping phenomena that alternate between epochs of slow and fast motion. We can conduct bifurcation analysis to identify two harmonic vibrations. One is that the singular orbit makes multiple jumps to a fast trajectory segment from one attracting equilibrium to another as the expression of slow variable by using the DeMoivre formula. With the increase of tuning frequency, the system exhibits relaxation-type oscillations whose small amplitude oscillations are produced by nonlinear local cycles together with a distinct large amplitude cycle oscillation accounting for the Melnikov threshold values. The tuning frequency may not only affect the asymptotic expressions for the solution curves near fold singularities but also allow for the large amplitude orbit vibrations near fold-cycle singularities. Numerical analysis for computing critical manifolds and their intersections is used to detect the dynamical features in this paper.

scholarly journals Altered Na/Ca exchange distribution in ventricular myocytes from failing hearts

2016 ◽  
Vol 310 (2) ◽  
pp. H262-H268 ◽  
Author(s):  
Hanne C. Gadeberg ◽  
Simon M. Bryant ◽  
Andrew F. James ◽  
Clive H. Orchard
Keyword(s):  
Heart Failure ◽  
Ventricular Myocytes ◽  
Cell Voltage ◽  
Coronary Artery Ligation ◽  
Sham Operation ◽  
Ca Current ◽  
Artery Ligation ◽  
Whole Cell ◽  
Rat Hearts ◽  
T Tubules

In mammalian cardiac ventricular myocytes, Ca efflux via Na/Ca exchange (NCX) occurs predominantly at T tubules. Heart failure is associated with disrupted t-tubular structure, but its effect on t-tubular function is less clear. We therefore investigated t-tubular NCX activity in ventricular myocytes isolated from rat hearts ∼18 wk after coronary artery ligation (CAL) or corresponding sham operation (Sham). NCX current ( INCX) and l-type Ca current ( ICa) were recorded using the whole cell, voltage-clamp technique in intact and detubulated (DT) myocytes; intracellular free Ca concentration ([Ca]i) was monitored simultaneously using fluo-4. INCX was activated and measured during application of caffeine to release Ca from sarcoplasmic reticulum (SR). Whole cell INCX was not significantly different in Sham and CAL myocytes and occurred predominantly in the T tubules in Sham myocytes. CAL was associated with redistribution of INCX and ICa away from the T tubules to the cell surface and an increase in t-tubular INCX/ ICa density from 0.12 in Sham to 0.30 in CAL myocytes. The decrease in t-tubular INCX in CAL myocytes was accompanied by an increase in the fraction of Ca sequestered by SR. However, SR Ca content was not significantly different in Sham, Sham DT, and CAL myocytes but was significantly increased by DT of CAL myocytes. In Sham myocytes, there was hysteresis between INCX and [Ca]i, which was absent in DT Sham but present in CAL and DT CAL myocytes. These data suggest altered distribution of NCX in CAL myocytes.

Fractional SR Ca release is regulated by trigger Ca and SR Ca content in cardiac myocytes

1995 ◽  
Vol 268 (5) ◽  
pp. C1313-C1319 ◽  
Author(s):  
J. W. Bassani ◽  
W. Yuan ◽  
D. M. Bers
Keyword(s):  
Action Potential ◽  
Ventricular Myocytes ◽  
Load Condition ◽  
Standard Test ◽  
Ca Current ◽  
Release Process ◽  
Contraction Coupling ◽  
Ca Uptake ◽  
High Load Condition ◽  
Different Levels

The release of sarcoplasmic reticulum (SR) Ca in cardiac muscle during excitation-contraction coupling is known to be graded by the amount of activating Ca outside the SR (i.e., Ca-induced Ca release). However, little is known about how intra-SR Ca affects the release process. In this study we assessed how the fractional SR Ca release as described by Bassani et al. [Am. J. Physiol. 265 (Cell Physiol. 34): C533-C540, 1993] is affected by alteration of trigger Ca and of SR Ca content. Experiments were done with isolated ferret ventricular myocytes using indo 1 to measure Ca concentration, perforated patch to measure Ca current (ICa), caffeine application to release SR Ca, and thapsigargin to completely block SR Ca uptake. For what we consider a Normal SR Ca load and trigger Ca [action potential at 0.5 Hz with 2 mM extracellular Ca concentration ([Ca]o)], 35 +/- 3% of the SR Ca content was released at a twitch. Changing trigger Ca by altering [Ca]o (to 0.5 and 8 mM) at a test twitch changed this fractional SR Ca release to 10 +/- 2 and 59 +/- 6%, with the same SR Ca load (and peak ICa changed in a parallel manner in separate voltage-clamp experiments). Three different levels of SR Ca load were studied (Low, Normal, and High; by action potential stimulation at different frequencies from 0.05 to 0.8 Hz) using the same standard test trigger Ca (2 mM). Surprisingly, the High-load condition only increased SR Ca content by approximately 4% but appeared to be very close to the limiting SR Ca capacity.(ABSTRACT TRUNCATED AT 250 WORDS)

scholarly journals Mechanism of acetylcholine-induced inhibition of Ca current in bullfrog atrial myocytes.

1990 ◽  
Vol 96 (4) ◽  
pp. 865-885 ◽  
Author(s):  
T Nakajima ◽  
S Wu ◽  
H Irisawa ◽  
W Giles
Keyword(s):  
Adenylate Cyclase ◽  
Binding Protein ◽  
Cell Voltage ◽  
Inhibitory Effect ◽  
Atrial Myocytes ◽  
Ca Current ◽  
Gtp Binding Protein ◽  
Gtp Binding ◽  
Subsequent Application ◽  
Gamma S

The mechanism of the anti-beta-adrenergic action of acetylcholine (ACh) on Ca current, ICa, was examined using the tight-seal, whole-cell voltage clamp technique in single atrial myocytes from the bullfrog. Both isoproterenol (ISO) and forskolin increased ICa dose dependently. After ICa had been enhanced maximally by ISO (10(-6) M), subsequent application of forskolin (50 microM) did not further increase ICa, suggesting that ISO and forskolin increase ICa via a common biochemical pathway, possibly by stimulation of adenylate cyclase. ACh (10(-5) M) completely inhibited the effect of low doses of forskolin (2 x 10(-6) M), as well as ISO, but it failed to block the effects of high doses of forskolin (greater than 5 x 10(-5) M). Intracellular application of cyclic AMP (cAMP) also increased ICa. ACh (10(-5) M) failed to inhibit this cAMP effect, indicating that the inhibitory action of ACh occurs at a site proximal to the production of cAMP. ACh (10(-5) M) also activated an inwardly rectifying K+ current IK(ACh). Intracellular application of a nonhydrolyzable GTP analogue, GTP gamma S (5 X 10(-4) M), activated IK(ACh) within several minutes; subsequent application of ACh (10(-5) M) did not increase IK(ACh) further. These results demonstrate that a GTP-binding protein coupled to these K+ channels can be activated maximally by GTP gamma S even in the absence of ACh. Intracellular application of GTP gamma S also strongly inhibited the effect of ISO on ICa in the absence of ACh. Pertussis toxin (IAP) completely prevented both the inhibitory effect of ACh on ICa and the ACh-induced activation of IK(ACh). GTP gamma S (50 microM-1 mM) alone did not increase ICa significantly; however, when ISO was applied first, GTP gamma S (5 x 10(-4) M) gradually inhibited the ISO effect on ICa. These results indicate that ACh antagonizes the effect of ISO on ICa via a GTP-binding protein (Gi and/or Go). This effect may be mediated through a direct inhibition by the alpha-subunit of Gi which is coupled to the adenylate cyclase.

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