Mutual entrainment of two pacemaker cells. A study with an electronic parallel conductance model

Role for electrical synapses in shaping the output of coupled peptidergic neurons from Lymnaea

Electrically coupled neurons communicate through channel assemblies called gap junctions, which mediate the transfer of current from one cell to another. Electrical synapses ensure spike synchronization and reliable transmission, which influences bursting patterns and firing frequency. The present study concerns an electrically coupled two-neuron network in the gastropod mollusc, Lymnaea stagnalis. The neurons, designated Visceral Dorsal 1 (VD1) and Right Parietal Dorsal 2 (RPD2), are peptidergic, innervate aspects of the cardio-respiratory system, and show strong coupling, such that they fire synchronously. Using dual sharp-electrode current-clamp recording and morphological staining in isolated brain preparations, the hypothesis that the electrical synapse is necessary for accurate network output was tested. We found that both cells make extensive projections within and out of the brain, including across the visceral-parietal connective, which links VD1 and RPD2. Cutting this connective uncoupled the neurons and disrupted the firing rate and pattern of RPD2 more than VD1, consistent with VD1 being the master and RPD2 the follower. The electrical synapse was inhibited by select gap junction blockers, with niflumic acid and 5-nitro-2-(3-phenylpropylamino) benzoic acid decreasing the VD1→RPD2 and RPD2→VD1 coupling coefficients, whereas carbenoxolone, α-glycyrrhetinic acid, meclofenamic acid, and quinine were ineffective. There was little-to-no impact on VD1↔RPD2 firing synchrony or frequency when coupling was reduced pharmacologically. However, in the presence of gap junction blockers, suppressing the activity of VD1 by prolonged hyperpolarization revealed a distinct, low-frequency firing pattern in RPD2. This suggests that strong electrical coupling is key to maintaining a synchronous output and proper firing rate.

Decreased intercellular coupling improves the function of cardiac pacemakers derived from mouse embryonic stem cells

The aim of this study was to determine if embryonic stem cell derived cardiomyocyte aggregates (ESdCs) can act as pacemakers in spontaneously active cardiomyocyte preparations when their connexin isoform expression is tuned toward a more sinus nodal phenotype. Using microelectrode array recordings (MEAs), we demonstrate that mouse ESdCs establish electrical coupling with spontaneously active cardiomyocyte preparations (HL-1 monolayer) and obtain pacemaker dominance. WT- and Cx43(-/-)-ESdCs comparably established intercellular coupling with cardiac host tissue (Cx43(-/-): 86% vs. WT: 91%). Although both aggregates had a 100% success rate in pacing quiescent cardiac preparations, Cx43(-/-)-ESdCs had an increased likelihood of gaining pacemaker dominance (Cx43(-/-): 40% vs. WT: 13%) in spontaneously active preparations. No differences in size, beating frequency, V(m), or differentiation were detected between WT- and Cx43(-/-)-ESdCs but the intercellular coupling resistance in Cx43(-/-)-ESdCs was significantly increased (Cx43(-/-): 1.2nS vs. WT: 14.8nS). Lack of Cx43 prolonged the time until Cx43(-/-)-ESdCs established frequency synchronization with the host tissue. It further hampered the excitation spread from the cardiomyocyte preparation into the ESdC. However rectifying excitation spread in these co-cultures could not be unequivocally identified. In summary, ESdCs can function as dominant biological pacemakers and Cx43 expression is not a prerequisite for their electrical integration. Maintenance of pacemaker dominance depends critically on the pacemaker's gap junction expression benefiting those with increased intercellular coupling resistances. Our results provide important insight into the design of biological pacemakers that will benefit the use of cardiomyocytes for cell replacement therapy.

Pacemaker synchronization of electrically coupled rabbit sinoatrial node cells

The effects of intercellular coupling conductance on the activity of two electrically coupled isolated rabbit sinoatrial nodal cells were investigated. A computer-controlled version of the "coupling clamp" technique was used in which isolated sinoatrial nodal cells, not physically in contact with each other, were electrically coupled at various values of ohmic coupling conductance, mimicking the effects of mutual interaction by electrical coupling through gap junctional channels. We demonstrate the existence of four types of electrical behavior of coupled spontaneously active cells. As the coupling conductance is progressively increased, the cells exhibit: (a) independent pacemaking at low coupling conductances, (b) complex dynamics of activity with mutual interactions, (c) entrainment of action potential frequency at a 1:1 ratio with different action potential waveforms, and (d) entrainment of action potentials at the same frequency of activation and virtually identical action potential waveforms. The critical value of coupling conductance required for 1:1 frequency entrainment was <0.5 nS in each of the five cell pairs studied. The common interbeat interval at a relatively high coupling conductance (10 nS), which is sufficient to produce entrainment of frequency and also identical action potential waveforms, is determined most by the intrinsically faster pacemaker cell and it can be predicted from the diastolic depolarization times of both cells. Evidence is provided that, at low coupling conductances, mutual pacemaker synchronization results mainly from the phase-resetting effects of the action potential of one cell on the depolarization phase of the other. At high coupling conductances, the tonic, diastolic interactions become more important.

Transient entrainment: the evolution of a medical concept from description to prescription

Entrainment is a phenomenon that has come to have considerable utility in cardiac electro-physiology diagnosis and treatment; specifically, to identify a zone of slow conduction in a reentrant circuit, a zone hypothetically vulnerable to intervention from the application of RF energy. The observation of entrainment has gone through an evolutionary sequence in the literature, from the initial simple observations of the phenomenon to the present stage of relatively fixed criteria of identification. This article follows the evolution of the specific features of the criteria of entrainment to their current crystallization into features that are suggested to prescribe sites for attempted ablation. This examination of the evolutionary course of the development of the conception of entrainment is of interest not only to cardiac electrophysiology, but also to philosophers of science, by illustrating how scientists emphasize and develop certain observations with the ultimate aim of applying the observations for successful intervention in pathological entities.

Serotonergic modulation of junctional conductance in an identified pair of neurons in the mollusc Lymnaea stagnalis

Serotonin (5-HT) is shown to modulate electrotonic coupling between two giant peptidergic neurons in the CNS of Lymnaea stagnalis. The primary effect of 5-HT appears to be a rapid and reversible decrease in gap junctional conductance.

Phase resetting and entrainment of pacemaker activity in single sinus nodal cells

The phase-resetting and entrainment properties of single pacemaker cells were studied using computer simulations in a model of the rabbit sinus nodal cell, as well as using the whole-cell patch-clamp (current-clamp) technique in isolated rabbit sinus nodal cells. Spontaneous electrical activity in the cell model was reconstructed using Hodgkin-Huxley-type equations describing time- and voltage-dependent membrane currents. In both simulations and experiments, single subthreshold current pulses (depolarizing or hyperpolarizing) were used to scan the spontaneous cycle of the cells. Such pulses perturbed the subsequent discharge, producing temporary phasic changes in pacemaker period, and enabled the construction of phase response curves. On the basis of these results, we studied entrainment characteristics of the cells. For example, application of repetitive pulses allowed for phasic changes in the spontaneous cycle and resulted in stable 1:1 entrainment at a range of basic cycle length around the spontaneous cycle, or a 2:1 pattern at basic cycle length values about half the spontaneous cycle length. Between the two entrainment zones, complex Wenckebach-like patterns (e.g., 5:4, 4:3, and 3:2) were observed. The experimental data from the isolated cell were further analyzed from a theoretical perspective, and the results showed that the topological characteristics of the phase-resetting behavior accounts for the experimentally observed patterns during repetitive stimulation of the cell. This first demonstration of phase resetting in single cells provides the basis for phenomena such as mutual entrainment between electrically coupled pacemaker cells, apparent intranodal conduction, and reflex vagal control of heart rate.

Mechanisms of sinoatrial pacemaker synchronization: a new hypothesis

A model of electrically coupled sinus node cells was used to investigate pacemaker coordination and conduction. Individual cells were simulated using differential equations describing transmembrane ionic currents. Intrinsic cycle lengths (periods) were adjusted by applying constant depolarizing or hyperpolarizing bias current, and cells were coupled through ohmic resistances to form two-dimensional arrays. Activation maps of 81-225 coupled cells showed an apparent wavefront conducting from a leading pacemaker region to the rest of the matrix even though the pattern actually resulted from mutual entrainment of all spontaneously beating cells. Apparent conduction time increased with increasing intercellular resistance. Appropriate selection of pacemaker cycle lengths and intercellular resistances permitted the accurate simulation of the activation sequence seen experimentally for the rabbit sinus node. Furthermore, a simulated acetylcholine pulse applied to a randomly selected 20% of the cells in this model produced a pacemaker shift that lasted several beats. These results support the hypothesis that sinus node synchronization occurs through a "democratic" process resulting from the phase-dependent interactions of thousands of pacemakers.

Reentrant ventricular arrhythmias in the late myocardial infarction period: 14. Mechanisms of resetting, entrainment, acceleration, or termination of reentrant tachycardia by programmed electrical stimulation

The mechanisms of resetting, entrainment, acceleration, or termination of reentrant ventricular tachycardia by programmed electrical stimulation were studied in the canine post-infarction model. In this model, reentrant circuits were localized in the epicardial layer overlying the infarction and were accessible to detailed mapping by multiplexer techniques. The reentrant circuit has a characteristic figure-eight configuration in the form of two circulating wavefronts around arcs of functional conduction block that coalesce into a slow common reentrant wavefront. Termination of reentrant tachycardia occurred when a stimulated wavefront arrived earlier to a strategically located area in the proximal portion of the zone of slow conduction, before refractoriness expired distally, resulting in conduction block. The three factors that determined if the stimulated wavefront could reach this zone in time for conduction block were: the cycle length of stimulation; the number of stimulated beats; and the site of stimulation. The most optimal situation for stimulated termination of reentry was a critically coupled single stimulus applied to the ischemic zone close to the proximal side of the zone of slow conduction that captured locally and conducted prematurely to the strategic zone for conduction block. When a single stimulated wavefront failed to terminate reentry, one or more subsequent wavefronts succeeded. However, the stimulated train had to be terminated following the beat that interrupted reentry. Otherwise, a subsequent stimulated beat could reinitiate the same reentrant circuit or induce a different circuit. The new circuit could have a shorter revolution time, resulting in tachycardia acceleration, and occasionally degeneration into ventricular fibrillation. Overdrive termination of reentry required both a critical cycle length of stimulation and a critical number of beats in a stimulated train. Otherwise, the stimulated train could establish a new balance of refractoriness and conduction velocity in the reentrant pathway. This could perpetuate the reentrant process at the shorter cycle length of the stimulated train and spontaneous reentry would resume on termination of the train (entrainment). The study provides better understanding of the mechanisms of action of programmed electrical stimulation on reentrant ventricular tachycardia.

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

Dynamic interactions and mutual entrainment of coupled sinoatrial pacemaker cells with different intrinsic frequencies were investigated using a computerized mathematical model. Transmembrane potentials were simulated using equations of individual membrane currents based on voltage clamp data for the sinoatrial node. The intrinsic frequency of a given cell was altered by applying bias hyperpolarizing current, or by changing the amount of slow inward current. Cells were coupled through simple ohmic resistances to form linear arrays of two or more cells. Simulations closely reproduced previous experimental work showing that the mutual interactions between pacemakers are mediated electrotonically and show phase dependence. Results from the present simulations provide an explanation for the ionic basis of these phase-dependent interactions. In addition, it is demonstrated that the mutual entrainment of coupled pacemakers can lead to their coordinated behavior (synchronization). Two pacemaker cells can synchronize at simple harmonic (i.e., 1:1, 2:1, etc.) or more complex ratios (3:2, 5:3, etc.), depending on the differences in intrinsic frequencies and the degree of electrical coupling between cells. Simulations using larger numbers of linearly connected cells yielded various patterns of pacemaker activity including 2:1 sinoatrial block and complex dysrhythmic activity. The overall results may be used to predict higher order interactions of thousands of cells comprising the sinus node. Under such a scheme, synchronization occurs not by the conducted influence of a dominant pacemaker cell, but by the mutual "democratic" interaction of individual pacemaker cells.

Mutual entrainment and electrical coupling as mechanisms for synchronous firing of rabbit sino-atrial pace-maker cells

The mechanisms of synchronous firing of cardiac pace-makers were studied using thin (0.3-0.5 mm) rabbit sino-atrial (s.a.) node strips placed in a three-compartment tissue bath. Superfusion of the central segment (1 mm in length) with ion-free sucrose solution permitted the electrical insulation of the external segments and the development of two independent pace-maker 'centres': one fast (F); one slow (S). An external shunt pathway was used to modulate the degree of coupling between F and S. Superfusion of the central segment with Tyrode solution containing heptanol (3.5 mM) instead of sucrose induced progressive decrease in the amplitude of responses in this segment and led to progressive loss of F:S synchronization. Eventually the two pace-makers became totally independent from each other. These changes were reversible upon wash-out of heptanol. When a pace-maker centre was within the range of influence of local circuit (i.e. electronic) currents from the pace-maker in the opposite side of the sucrose (or heptanol) compartment, its period was prolonged or abbreviated, depending on phase and frequency relations. Dynamic F:S interactions at various degrees of electrical coupling resulted in mutual entrainment with both pace-makers beating at simple harmonic (i.e. 1:1, 2:1, 1:2, etc.) or more complex (3:2, 5:4, etc.) ratios that depended on the degree of coupling and the intrinsic periods of the individual pace-maker centres. The patterns of synchronization could be predicted by the phasic sensitivity of each pace-maker to brief electrotonic inputs. The results suggest that when two individual pace-maker cells are connected through low resistance junctions, the period resulting from their mutual entrainment should be a function of their respective intrinsic frequencies, their phase relations and the degree of electrical coupling. The data further suggest that the heart beat is initiated by a 'democratic' type of synchronous firing of cells in the s.a. node, with each pace-maker cell contributing to an aggregate signal and involving mutual entrainment between cells.

Synchronization in chains of pacemaker cells by phase resetting action potential effects

Interactions between pacemaker cells in a chain were calculated according to a "phase-reset" model. It is based on effects of action potentials in the cells on the cycle lengths of neighbouring cells. These effects were defined for each cell by a latency-phase curve (LPC), giving the latency time (L) until the onset of the next action potential in that cell, as a function of the phase (phi) at which a neighbour cell fired an action potential. Neighbour cells with simultaneous action potentials did not influence each others cycle length. We investigated how stable synchronization depends on the shape of the LPC's of the pacemaker cells and on chain length. Three types of interactive behaviour were distinguished. First, anti-phase synchrony, in which neighbouring cells fired with large phase differences with respect to the synchronized period Ps. Second, asynchrony, in which the periods of the cells did not become equal and constant. Third, in-phase synchrony, in which the phase differences between the neighbouring cells were zero or much smaller than the synchronized period Ps, depending on the differences between the intrinsic periods. Asynchrony and anti-phase synchrony may be seen as cardiophysiological arrhythmias, while in-phase synchrony represents the physiological type of synchrony in the heart. In-phase synchrony appeared to be strongly favoured by LPC's, which have a no-effect (refractory) part at early phases, a lengthened latency (or phase delay) part at intermediate phases and a shortened latency (or phase advance) part at late phases in the cycle. Such LPC-shapes are commonly found in preparations of cardiac pacemaker cells. When the pacemaker cells were identical, the synchronized period Ps during in-phase synchrony was equal to their intrinsic period P*i. For different intrinsic periods, Ps was equal to the intrinsic period of the fastest cell if the LPC's contained a sufficiently long initial no-effect period at early phases and a shortened latency part at late phases. When, on the other hand, such cell chains had a linear gradient in their intrinsic periods, "action potentials" started from the fast end and traveled along the chain. The propagation of an action potential wave slowed down as it reached the slower cells. When the gradient in the intrinsic periods was too steep, only the intrinsically fast end of the chain developed synchrony.(ABSTRACT TRUNCATED AT 400 WORDS)

Entrainment of a bursting neuron--I. typical activity

Highly regular RPA-1 oscillator neurons of the land snail Helix pomatia L. are tested for entrainment by rhythmical stimulation. Both with orthodromic and direct hyperpolarizing pulses the bursting activity could be entrained to frequencies higher or lower than, and equal to, the spontaneous one, in this order of difficulty. Depolarizing pulses give mainly entrainment to higher frequencies, but synchronization to frequencies lower than the spontaneous one was also demonstrable. Each of these different driving relations implies the consecutive stimuli to become locked to a peculiar range of phases and not to a single phase of resonance inside the cycle.

Phase locking, period doubling bifurcations and chaos in a mathematical model of a periodically driven oscillator: a theory for the entrainment of biological oscillators and the generation of cardiac dysrhythmias

A mathematical model for the perturbation of a biological oscillator by single and periodic impulses is analyzed. In response to a single stimulus the phase of the oscillator is changed. If the new phase following a stimulus is plotted against the old phase the resulting curve is called the phase transition curve or PTC (Pavlidis, 1973). There are two qualitatively different types of phase resetting. Using the terminology of Winfree (1977, 1980), large perturbations give a type 0 PTC (average slope of the PTC equals zero), whereas small perturbations give a type 1 PTC. The effects of periodic inputs can be analyzed by using the PTC to construct the Poincaré or phase advance map. Over a limited range of stimulation frequency and amplitude, the Poincaré map can be reduced to an interval map possessing a single maximum. Over this range there are period doubling bifurcations as well as chaotic dynamics. Numerical and analytical studies of the Poincaré map show that both phase locked and non-phase locked dynamics occur. We propose that cardiac dysrhythmias may arise from desynchronization of two or more spontaneously oscillating regions of the heart. This hypothesis serves to account for the various forms of atrioventricular (AV) block clinically observed. In particular 2:2 and 4:2 AV block can arise by period doubling bifurcations, and intermittent or variable AV block may be due to the complex irregular behavior associated with chaotic dynamics.

Suppression of pacemaker activity by rapid repetitive phase delay

Spontaneous activity of pacemaker cells of structures may be suppressed by rapid repetitive stimulation. Conditions are that the oscillator's phase reset curve, characterizing the phase resetting effect of single stimuli, has a phase delay part and that the interval between the stimuli falls within a range of values, determined by the form of the phase reset curve. Under these conditions, which appeared the same as those for stable underdrive pacing, the pacemaker becomes stably entrained to the stimuli without firing, i.e. it is kept within a certain part of its limit cycle because the pulses repeatedly delay the next coming action potential. This rapid stimulation suppression of pacemaker activity is demonstrated experimentally on a simple electronic pacemaker cell model for two types of phase reset curves, a biphasic one for depolarizing and a monophasic one for hyperpolarizing pulses. Computer simulations of coupled pacemaker cells, interacting by phase reset curves, illustrate how this type of pacemaker suppression may protect a population of pacemaker cells like the sinus node in the heart against arrhythmias.