Dynamic interactions and mutual synchronization of sinoatrial node pacemaker cells. A mathematical model.

Michaels, D C; Matyas, E P; Jalife, José

doi:10.1161/01.res.58.5.706

Cited by 79 publications

(40 citation statements)

References 40 publications

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“…Previous studies have explored coupling inhomogeneity between simulated SAN cells and observed trends of synchronous firing and heterogeneous tissue becoming homogeneous through a democratic entrainment process at sufficient coupling values [20,32,33]. Our studies also support the theory of a democratic entrainment process both at the level of two coupled cells (Figure 6) where both cells adjusted their transmembrane dynamics to adjust to a new value that was distinct from firing alone.…”

Section: Discussionsupporting

confidence: 85%

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Synchronization of Pacemaking in the Sinoatrial Node: A Mathematical Modeling Study

et al. 2018

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Computational studies using mathematical models of the sinoatrial node (SAN) cardiac action potential (AP) have provided important insight into the fundamental nature of cell excitability, cardiac arrhythmias, and potential therapies. While the impact of ion channel dynamics on SAN pacemaking has been studied, the governing dynamics responsible for regulating spatial and temporal control of SAN synchrony remain elusive. Here, we attempt to develop methods to explore cohesion in a network of coupled spontaneously active SAN cells. We present the updated version of a previously published graphical user interface LongQt: a cross-platform, threaded application for advanced cardiac electrophysiology studies that does not require advanced programming skills. We incorporated additional features to the existing LongQt platform that allows users to (1) specify heterogeneous gap junction conductivity across a multicellular grid, and (2) set heterogeneous ion channel conductance across a multicellular grid. We developed two methods of characterizing the synchrony of SAN tissue based on alignment of activation in time and similarity of voltage peaks among clusters of functionally related cells. In pairs and two-dimensional grids of coupled cells, we observed a range of conductivities (0.00014-0.00033 1/ -cm) in which the tissue was more susceptible to developing asynchronous spontaneous pro-arrhythmic behavior (e.g., spiral wave formation). We performed parameter sensitivity analysis to determine the relative impact of ion channel conductances on cycle length (CL), diastolic and peak voltage, and synchrony measurements in isolated and coupled cell pairs. We also defined measurements of evaluating synchrony based on peak AP voltage and the rate of wave propagation. Cell-to-cell coupling had a non-linear effect on the relationship between ion channel conductances, AP properties, and synchrony measurements. Our simulations demonstrate that conductivity plays an important role in regulating synchronous firing of heterogeneous SAN tissue, and demonstrate how to evaluate the role of coupling and ion channel conductance in pairs and grids of SAN cells. We anticipate that the approach outlined here will facilitate identification of key cell-and tissue-level factors responsible for cardiac disease.

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Section: Discussionsupporting

confidence: 85%

“…This further supports the idea that coupling non-linearly alters the ability of SAN cells to fire synchronously. In previous work, Michaels et al examined the effects of cellto-cell coupling strength on entrainment [20,33]. They tested both paired cells as well as small grids.…”

Section: Discussionmentioning

confidence: 99%

Synchronization of Pacemaking in the Sinoatrial Node: A Mathematical Modeling Study

et al. 2018

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“…As demonstrated by Jalife et al 48 and others, 24,49,50 interactions among a group of pacemaker cells result in a dominant pacemaker region. These interactions are electrotonic and involve mutual alterations in diastolic or pacemaker potentials, such that slower cells modulate faster cells to decrease their diastolic potentials and decrease their firing intervals and vice versa.…”

Section: Discussionmentioning

confidence: 92%

Differential Expression of Gap Junction Proteins in the Canine Sinus Node

Kwong

Schuessler

Green

et al. 1998

Circulation Research

109

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Abstract-Electrical coupling of pacemaker cells at gap junctions appears to play an important role in sinus node function.Although the major cardiac gap junction protein, connexin43 (Cx43), is expressed abundantly in atrial and ventricular muscle, its expression in the sinus node has been a subject of controversy. The objectives of the present study were to determine whether Cx43 is expressed by sinus node myocytes, to characterize the spectrum of connexin expression phenotypes in sinus node pacemaker cells, and to define the spatial distribution of different connexin phenotypes in the intact sinus node. To fulfill these objectives, we performed high-resolution immunohistochemical analysis of disaggregated adult canine sinus node preparations. Using enhanced tissue preservation and antigen retrieval techniques, we also performed immunohistochemical studies on sections of intact canine sinus node tissue. Analysis of disaggregated sinus node preparations revealed three populations of pacemaker cells distinguished on the basis of connexin immunohistochemical phenotype: Ϸ55% of cells expressed only connexin40 (Cx40); 30% to 35% of cells expressed Cx43, connexin45 (Cx45), and Cx40; and the remaining cells had no detectable connexin expression. In immunostained sections of intact sinus node, Cx43-and Cx45-positive cells were limited in their distribution and were observed in discrete bundles that appeared to abut atrial myocytes. In contrast, Cx40 immunoreactive signal was widely distributed in the sinus node region. These results indicate that subsets of pacemaker cells express distinct connexin phenotypes. Differential expression of connexins could create regions within the sinus node with different conduction properties, thereby contributing to the nonuniform conduction properties seen in this tissue. (Circ Res. 1998;82:604-612.)

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“…To adjust T, 10 we added a voltage and time-independent current to the time-independent current I L . 1>10 We have shown experimentally in anesthetized dogs that this model of the sinus node 7 -9 predicts quantitatively the dependence of SCL on [ACh].…”

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confidence: 99%

Mathematical model of the changes in heart rate elicited by vagal stimulation.

Dexter

Levy

Rudy

1989

Circulation Research

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We developed a mathematical model of the underlying cellular mechanisms responsible for the changes in sinus cycle length (SCL) elicited by vagal stimulation in intact animals. The model incorporated a stimulation-mediated depletion of the releasable pool of acetylcholine (ACh) in the nerve endings, the in vitro reaction kinetics of acetylcholinesterase, and the electrical activity of a pacemaker cell with six membrane ionic currents. SCL increased linearly with the frequency of simulated vagal stimulation, as it does in animal experiments, because the concentration of ACh in the neuroeffector junction ([ACh]) saturated as the frequency of stimulation was increased and because SCL increased geometrically in response to increases in [ACh]. The dependence of SCL on the timing of vagal stimulation in the cardiac cycle resulted, in part, from the dependence of [ACh] on SCL. Simulated vagal stimulation entrained the sinus node because the rate of activation and inactivation of ACh-activated K + channels depended only weakly on membrane potential during diastolic depolarization. SCL increased geometrically with [ACh], because 1) during diastolic depolarization, the amplitude of the ACh-activated K + current was approximately equal to the amplitude of the sum of the other ionic currents, 2) [ACh] was low enough to saturate neither acetylcholinesterase nor the cellular system that activates the ACh-activated K + channels, 3) the pacemaker cell membrane behaved electrotonically like a capacitor, and 4) the sum of all the ionic currents increased linearly with the amplitude of the ACh-activated K + current. (Circulation Research 1989;65:133O-1339) O ur goal is to explain the cellular basis for the changes in sinus cycle length (SCL) elicited by vagal stimulation by using mathematical models of the underlying cellular physiology. In recent papers, we have presented mathematical models of the release of acetylcholine (ACh) from vagal nerve endings, the degradation of ACh in the neuroeffector junctions of the sinus node, and the changes in SCL elicited by ACh.1 . 2 By combining these mathematical models of the underlying cellular physiology, we create a more complete mathematical model that predicts the changes in SCL elicited by vagal stimulation in the intact animal. Our principal goal is to determine how the underlying cellular physiology, which we represented mathematically in our computer model, causes changes in SCL. Methods Mathematical ModelsACh release. Figure 1); the letter v was chosen because the releasable pool of ACh may be stored in intracellular vesicles.3 Let r equal the fastest rate of renewal of the releasable pool of ACh. Let p equal the fraction of the releasable pool of ACh, v, that is released by each vagal stimulus. Let u represent the vagal firing pattern. The change in the quantity of ACh that is available for release is represented by the equation: dv/dt=r(l-v)-pvu(t) (1) where u(t)=l if the vagus nerve is stimulated at time t, and u(t)=0 otherwise (t=0 msec at the start of the stimulation). AC...

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Dynamic interactions and mutual synchronization of sinoatrial node pacemaker cells. A mathematical model.

Cited by 79 publications

References 40 publications

Synchronization of Pacemaking in the Sinoatrial Node: A Mathematical Modeling Study

Synchronization of Pacemaking in the Sinoatrial Node: A Mathematical Modeling Study

Differential Expression of Gap Junction Proteins in the Canine Sinus Node

Mathematical model of the changes in heart rate elicited by vagal stimulation.

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