Effect of hyperpolarization-activated current If on robustness of sinoatrial node pacemaking: theoretical study on influence of intracellular Na+ concentration

2013 ◽  
Vol 304 (10) ◽  
pp. H1337-H1351 ◽  
Author(s):  
Yasutaka Kurata ◽  
Ichiro Hisatome ◽  
Mamoru Tanida ◽  
Toshishige Shibamoto
Keyword(s):  
Sinoatrial Node ◽  
Theoretical Study ◽  
Equilibrium Points ◽  
Pacemaker Activity ◽  
Model Parameters ◽  
Variable System ◽  
Hyperpolarization Activated Current ◽  
Dynamical Properties ◽  
Channel Currents ◽  
Fixed System

To elucidate the effects of hyperpolarization-activated current If on robustness of sinoatrial node (SAN) pacemaking in connection with intracellular Na+ concentration ( Nai) changes, we theoretically investigated 1) the impacts of If on dynamical properties of SAN model cells during inhibition of L-type Ca2+ channel currents ( ICaL) or hyperpolarizing loads and 2) If-dependent changes in Nai and their effects on dynamical properties of model cells. Bifurcation analyses were performed for Nai-variable and Nai-fixed versions of mathematical models for rabbit SAN cells; equilibrium points (EPs), limit cycles (LCs), and their stability were determined as functions of model parameters. Increasing If conductance ( gf) shrank ICaL conductance ( gCaL) regions of unstable EPs and stable LCs (rhythmic firings) in the Nai-variable system but slightly broadened that of rhythmic firings at lower gf in the Nai-fixed system. In the Nai-variable system, increased gf yielded elevations in Nai at EPs and during spontaneous oscillations, which caused EP stabilization and shrinkage in the parameter regions of unstable EPs and rhythmic firings. As gf increased, parameter regions of unstable EPs and stable LCs determined for hyperpolarizing loads shrank in the Nai-variable system but were enlarged in the Nai-fixed system. These findings suggest that 1) If does not enhance but rather attenuates robustness of rabbit SAN cells via facilitating EP stabilization and LC destabilization even in physiological gf ranges; and 2) the enhancing effect of If on robustness of pacemaker activity, which could be observed at lower gf when Nai was fixed, is actually reversed by If-dependent changes in Nai.

Roles of hyperpolarization-activated current If in sinoatrial node pacemaking: insights from bifurcation analysis of mathematical models

2010 ◽  
Vol 298 (6) ◽  
pp. H1748-H1760 ◽  
Author(s):  
Yasutaka Kurata ◽  
Hiroyuki Matsuda ◽  
Ichiro Hisatome ◽  
Toshishige Shibamoto
Keyword(s):  
Mathematical Models ◽  
Sinoatrial Node ◽  
Equilibrium Points ◽  
Pacemaker Activity ◽  
Potential Region ◽  
Peripheral Cell ◽  
Constant Bias ◽  
State Potential ◽  
Hyperpolarization Activated Current ◽  
Acetylcholine Concentration

To elucidate the roles of hyperpolarization-activated current ( If) in sinoatrial node (SAN) pacemaking, we theoretically investigated 1) the effects of If on stability and bifurcation during hyperpolarization of SAN cells; 2) combined effects of If and the sustained inward current ( Ist) or Na+ channel current ( INa) on robustness of pacemaking against hyperpolarization; and 3) whether blocking If abolishes pacemaker activity under certain conditions. Bifurcation analyses were performed for mathematical models of rabbit SAN cells; equilibrium points (EPs), periodic orbits, and their stability were determined as functions of parameters. Unstable steady-state potential region determined with applications of constant bias currents shrunk as If density increased. In the central SAN cell, the critical acetylcholine concentration at which bifurcations, to yield a stable EP and quiescence, occur was increased by smaller If, but decreased by larger If. In contrast, the critical acetylcholine concentration and conductance of gap junctions between SAN and atrial cells at bifurcations progressively increased with enhancing If in the peripheral SAN cell. These effects of If were significantly attenuated by eliminating Ist or INa, or by accelerating their inactivation. Under hyperpolarized conditions, blocking If abolished SAN pacemaking via bifurcations. These results suggest that 1) If itself cannot destabilize EPs; 2) If improves SAN cell robustness against parasympathetic stimulation via preventing bifurcations in the presence of Ist or INa; 3) If dramatically enhances peripheral cell robustness against electrotonic loads of the atrium in combination with INa; and 4) pacemaker activity of hyperpolarized SAN cells could be abolished by blocking If.

scholarly journals Upregulation of the Hyperpolarization-Activated Current Increases Pacemaker Activity of the Sinoatrial Node and Heart Rate During Pregnancy in Mice

Circulation ◽  
2013 ◽  
Vol 127 (20) ◽  
pp. 2009-2020 ◽  
Author(s):  
Nabil El Khoury ◽  
Sophie Mathieu ◽  
Laurine Marger ◽  
Jenna Ross ◽  
Gracia El Gebeily ◽  
...  
Keyword(s):  
Heart Rate ◽  
Sinoatrial Node ◽  
Pacemaker Activity ◽  
Hyperpolarization Activated Current

scholarly journals Mathematical analysis of a measles transmission dynamics model in Bangladesh with double dose vaccination

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Md Abdul Kuddus ◽  
M. Mohiuddin ◽  
Azizur Rahman
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Equilibrium Points ◽  
Rank Correlation ◽  
Dynamical Analysis ◽  
Model Parameters ◽  
Progression Rate ◽  
Double Dose ◽  
The Basic Reproduction Number

AbstractAlthough the availability of the measles vaccine, it is still epidemic in many countries globally, including Bangladesh. Eradication of measles needs to keep the basic reproduction number less than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{R}}_{0}<1)$$ ( i . e . R 0 < 1 ) . This paper investigates a modified (SVEIR) measles compartmental model with double dose vaccination in Bangladesh to simulate the measles prevalence. We perform a dynamical analysis of the resulting system and find that the model contains two equilibrium points: a disease-free equilibrium and an endemic equilibrium. The disease will be died out if the basic reproduction number is less than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{ R}}_{0}<1)$$ ( i . e . R 0 < 1 ) , and if greater than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{R}}_{0}>1)$$ ( i . e . R 0 > 1 ) epidemic occurs. While using the Routh-Hurwitz criteria, the equilibria are found to be locally asymptotically stable under the former condition on $${\mathrm{R}}_{0}$$ R 0 . The partial rank correlation coefficients (PRCCs), a global sensitivity analysis method is used to compute $${\mathrm{R}}_{0}$$ R 0 and measles prevalence $$\left({\mathrm{I}}^{*}\right)$$ I ∗ with respect to the estimated and fitted model parameters. We found that the transmission rate $$(\upbeta )$$ ( β ) had the most significant influence on measles prevalence. Numerical simulations were carried out to commissions our analytical outcomes. These findings show that how progression rate, transmission rate and double dose vaccination rate affect the dynamics of measles prevalence. The information that we generate from this study may help government and public health professionals in making strategies to deal with the omissions of a measles outbreak and thus control and prevent an epidemic in Bangladesh.

More Dynamical Properties Revealed from a 3D Lorenz-like System

2014 ◽  
Vol 24 (10) ◽  
pp. 1450133 ◽  
Author(s):  
Haijun Wang ◽  
Xianyi Li
Keyword(s):  
Numerical Simulations ◽  
Local Stability ◽  
Equilibrium Points ◽  
Heteroclinic Orbits ◽  
Mathematical Work ◽  
Chaotic Attractors ◽  
Heteroclinic Cycles ◽  
Homoclinic And Heteroclinic Orbits ◽  
Dynamical Properties ◽  
Theoretical Results

After a 3D Lorenz-like system has been revisited, more rich hidden dynamics that was not found previously is clearly revealed. Some more precise mathematical work, such as for the complete distribution and the local stability and bifurcation of its equilibrium points, the existence of singularly degenerate heteroclinic cycles as well as homoclinic and heteroclinic orbits, and the dynamics at infinity, is carried out in this paper. In particular, another possible new mechanism behind the creation of chaotic attractors is presented. Based on this mechanism, some different structure types of chaotic attractors are numerically found in the case of small b > 0. All theoretical results obtained are further illustrated by numerical simulations. What we formulate in this paper is to not only show those dynamical properties hiding in this system, but also (more mainly) present a kind of way and means — both "locally" and "globally" and both "finitely" and "infinitely" — to comprehensively explore a given system.

Autonomic regulation of subsidiary atrial pacemakers during exercise

1991 ◽  
Vol 70 (3) ◽  
pp. 1175-1183 ◽  
Author(s):  
J. L. Ardell ◽  
W. C. Randall ◽  
G. Pomeroy ◽  
M. Lawton ◽  
T. Kim
Keyword(s):  
Right Atrium ◽  
Sinoatrial Node ◽  
Pacemaker Activity ◽  
Work Intensity ◽  
Heart Rates ◽  
Cardiac Responses ◽  
Pacemaker Function ◽  
Before And After ◽  
Autonomic Blockade ◽  
Marked Suppression

Cardiac responses to graded treadmill exercise were compared in conscious dogs before and after excision of the sinoatrial node (SAN) and adjacent tissue along the sulcus terminalis. The chronotropic and dromotropic responses to dynamic exercise were compared with and without selective muscarinic (atropine) and/or beta-adrenergic (timolol) blockade. With the SAN intact, cardiac acceleration was prompt during onset of exercise and in proportion to work intensity. Immediately after SAN excision (1-7 days), pacemaker activity exhibited marked instability in rate and pacemaker location, with rapid shifts between atrial and junctional foci. Soon thereafter (1-2 wk), subsidiary atrial pacemakers (SAPs) assumed the primary pacemaker function. Although the SAP foci demonstrated stable heart rates and atrioventricular (AV) intervals at rest and during exercise, heart rates at rest and during steady-state exercise were reduced 34% from corresponding levels in the SAN-intact state, both with and without selective autonomic blockade. For control of dromotropic function, animals with SAP foci showed pronounced shortening in AV interval in conjunction with exercise that was further exacerbated by pretreatment with atropine. Eight weeks after excision of the primary SAN pacemakers, direct electrophysiological mapping localized the SAP foci to either the inferior right atrium along the sulcus terminalis or the dorsal cranial right atrium (in or near Bachmann's bundle). Animals with SAPs localized to the inferior right atrium had a more marked suppression in heart rate with a corresponding greater decrease in AV interval during exercise than dogs with SAP foci identified within the dorsal cranial right atrium.

Relative Densities of Muscarinic Cholinergic and β-Adrenergic Receptors in the Canine Sinoatrial Node and Their Relation to Sites of Pacemaker Activity

1995 ◽  
Vol 77 (5) ◽  
pp. 957-963 ◽  
Author(s):  
Scott L. Beau ◽  
Dwight E. Hand ◽  
Richard B. Schuessler ◽  
Burt I. Bromberg ◽  
Brian Kwon ◽  
...  
Keyword(s):  
Adrenergic Receptors ◽  
Sinoatrial Node ◽  
Pacemaker Activity ◽  
Muscarinic Cholinergic ◽  
Β Adrenergic Receptors
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