Phase resetting properties of cardiac pacemaker cells

Aggregates of heart cells from chicken embryos beat spontaneously. We used intracellular microelectrodes to record the periodic behavior of the membrane potential that triggers the contractions. Every 5-12 beats, a short current pulse was applied at various points in the cycle to study the phase-dependent resetting of the rhythm. Pulses stronger than 2.5 nA caused the final rhythm to be reset to almost the same point in the cycle regardless of the phase at which the pulse was applied (type zero resetting). Pulses of less than or equal to 1 nA only caused a slight change of the phase. Increasing current intensities to between 1 and 2.5 nA gave rise to an increasing steepness in a small part of the phase-response curve. The observation of type zero resetting implies the existence of a critical stimulation that might annihilate the rhythm. Although we did find a phase at which more or less random responses occurred, the longest pause in the rhythm was 758 ms, 2.4 times the spontaneous interval. This suggests that the resting membrane potential was unstable, at least against the internal noise of the system. The conclusions are discussed in terms of the concepts of classical cardiac electrophysiology.     

Photoalteration of calcium channel blockade in the cardiac Purkinje fiber.

Organic compounds that block calcium channel current (calcium antagonists) are important tools for the characterization of this channel. However, the practically irreversible nature of this block restricts the usefulness of this group of drugs. In this paper, we investigate the influence of light on calcium channel blockade by several organic compounds. Our results show that inhibition of calcium channel current by two dihydropyridine derivatives that contain an o-nitro moiety (nisoldipine and nifedipine) can be rapidly reversed by illumination. The energy range important to this reaction is for light wavelengths between 320 and 450 nm. Calcium channel inhibition by two other dihydropyridine derivatives (nicardipine and nitrendipine) as well as by D600, is not modulated by illumination. These results indicate that the photosensitivity of certain dihydropyridine calcium channel blockers make these compounds useful as reversible blockers of this channel.     

Phase resetting and fixed-delay stimulation of a simple model of respiratory rhythm generation.

In a previous study (Lewis et al., 1990), the response of the respiratory rhythm to a perturbing stimulus was investigated using two different stimulus protocols: phase resetting and fixed-delay stimulation. The first protocol consists of measuring the effects of perturbing an oscillator at different phases of the cycle on the duration of the perturbed cycle. The resulting phase response curves (PRCs) can be used to characterize the properties of the oscillator (Winfree, 1980). A second protocol, fixed-delay stimulation, involves perturbing an oscillator at a fixed latency from the onset of the cycle, repeated every n-th cycle. If a single stimulus produces an effect that lasts longer than a single cycle, complicated responses can be expected from fixed-delay stimulation (Lewis et al., 1987). A simple three-phase model for respiratory rhythm generation based on a hypothesis by Richter and coworkers (1982, 1983, 1986) was investigated in the context of these experimental studies. Phase resetting and fixed-delay stimulation protocols were simulated in the model. PRCs of the model resemble those obtained experimentally: a phase-dependent prolongation or shortening of the inspiratory phase depending on the stimulus magnitude, and a slight prolongation of the expiratory phase. Stimuli delivered to the model repetitively during successive inspiratory periods at a fixed-delay produced various combinations of shortened and prolonged cycles, similar to those observed in the experiments. However, the marked increases in cycle duration observed in the experiments during, as well as after, stimulation were not evident in the model. These comparisons suggest that (1) PRCs may not be an adequate way to evaluate certain models of rhythmogenesis, and (2) to improve the present simplified formulation of the three-phase model of the respiratory oscillator, time-varying stimulus dependent effects should be incorporated.     

A cleft model for cardiac Purkinje strands.

Conduction of the action potential in cardiac muscle is complicated by its multicellular structure, with narrow intercellular clefts and cell-to-cell coupling. A model is developed from anatomical data to describe cardiac Purkinje strands of variable diameter and different internal arrangements of cells. The admittance of the model is solved analytically and fit to results of cable analysis. Using the extracted specific membrane and cell electrical parameters (Rm = 13 K omega cm2, Cm = 1.5 mu F/cm2, Ri = 100 mu cm, and Re = 50 omega cm), the model correctly predicted conduction velocity and filling of capacitance at the onset of a voltage step. The analysis permits more complete studies of the factors controlling conduction velocity; for instance, the effect on conduction velocity of a capacity in the longitudinal current circuit is discussed. Predictions of the impedance and phase angle were also made. Measurements of the frequency dependence of phase angle may provide a basis for separating cleft membrane properties from those of the surface membrane and may aid the measurement of nonlinear membrane properties in muscle.     

The relation of Vmax to INa, GNa, and h infinity in a model of the cardiac Purkinje fiber.

The inward sodium current in cardiac muscle is difficult to study by voltage clamp methods, so various indirect experimental measures have been used to obtain insight into its characteristics. These methods depend on the relationship between maximal upstroke velocity of the action potential (Vmax) and the sodium current (INa), usually defined in terms of the Hodgkin-Huxley model. These relationships were explored using an adaptation of this model to cardiac Purkinje fibers. In general Vmax corresponded to INa, and it could be used to determine the relationship of membrane potential to GNa, and h infinity. The results, however, depended on the method of stimulation of the action potential, and an optimal stimulation method was determined. A commonly used experimental technique called "membrane responsiveness" was shown to distort seriously the properties of steady-state gating inactivation that is supposed to measure. Estimation of the changes in maximal sodium conductance, such as those produced by tetrodotoxin (TTX), would be accurately measured. Some experimental results have indicated a voltage-dependent effect of TTX. Characteristics of the measures of TTX effect under those conditions were illustrated. In summary, calculations with a model of the cardiac Purkinje fiber action potential provide insight into the accuracy of certain experimental methods using maximal upstroke velocity as a measure of INa, and cast doubt on other experimental methods, such as membrane responsiveness.     

Delayed rectification in the calf cardiac Purkinje fiber. Evidence for multiple state kinetics.

We have investigated the delayed rectifier current (Ix) in the calf cardiac Purkinje fiber using a conventional two-microelectrode voltage clamp arrangement. The deactivation of Ix was monitored by studying decaying current tails after the application of depolarizing voltage prepulses. The reversal potential (Vrev) of these Ix tails was measured as a function of prepulse magnitude and duration to test for possible permeant ion accumulation- or depletion-induced changes in Vrev. We found that prepulse-induced changes in Vrev were less than 5 mV, provided that prepulse durations were less than or equal to 3.5 s and magnitudes were less than or equal to +35 mV. We kept voltage pulse structures within these limits for the remainder of the experiments in this study. We studied the sensitivity of Vrev to variation in extracellular K+. The reversal potential for Ix is well described by a Goldman-Hodgkin-Katz relation for a channel permeable to Na+ and K+ with PNa/PK = 0.02. The deactivation of Ix was always found to be biexponential and the two components shared a common reversal potential. These results suggest that it is not necessary to postulate the existence of two populations of channels to account for the time course of the Ix tails. Rather, our results can quantitatively be reproduced by a model in which the Ix channel can exist in three (two closed, one open) conformational states connected by voltage dependent rate constants.     

Phase resetting and bifurcation in the ventricular myocardium.

With the dynamic differential equations of Beeler, G. W., and H. Reuter (1977, J. Physiol. [Lond.]. 268:177-210), we have studied the oscillatory behavior of the ventricular muscle fiber stimulated by a depolarizing applied current I app. The dynamic solutions of BR equations revealed that as I app increases, a periodic repetitive spiking mode appears above the subthreshold I app, which transforms to a periodic spiking-bursting mode of oscillations, and finally to chaos near the suprathreshold I app (i.e., near the termination of the periodic state). Phase resetting and annihilation of repetitive firing in the ventricular myocardium were demonstrated by a brief current pulse of the proper magnitude applied at the proper phase. These phenomena were further examined by a bifurcation analysis. A bifurcation diagram constructed as a function of I app revealed the existence of a stable periodic solution for a certain range of current values. Two Hopf bifurcation points exist in the solution, one just above the lower periodic limit point and the other substantially below the upper periodic limit point. Between each periodic limit point and the Hopf bifurcation, the cell exhibited the coexistence of two different stable modes of operation; the oscillatory repetitive firing state and the time-independent steady state. As in the Hodgkin-Huxley case, there was a low amplitude unstable periodic state, which separates the domain of the stable periodic state from the stable steady state. Thus, in support of the dynamic perturbation methods, the bifurcation diagram of the BR equation predicts the region where instantaneous perturbations, such as brief current pulses, can send the stable repetitive rhythmic state into the stable steady state.     

Delayed rectification in the cardiac Purkinje fiber is not activated by intracellular calcium

This study was designed to test the hypothesis that an outward current (Ix) responsible for action potential repolarization in the cardiac Purkinje fiber is activated by intracellular calcium (Cai). Pharmacological probes were combined with the measurement of membrane current and contractile activity under voltage clamp conditions. Experiments were designed to examine properties of Ix that have previously linked activation of this current to changes in Cai. The independence of Ix from Cai was demonstrated for each case tested. Thus, the results of these experiments support the view that Ix is not a calcium-activated current.     

Slow inactivation of a tetrodotoxin-sensitive current in canine cardiac Purkinje fibers.

We used the two-microelectrode voltage clamp technique and tetrodotoxin (TTX) to investigate the possible occurrence of slow inactivation of sodium channels in canine cardiac Purkinje fibers under physiologic conditions. The increase in net outward current during prolonged (5-20 s) step depolarizations (range -70 to +5 mV) following the application of TTX is time dependent, being maximal immediately following depolarization, and declining thereafter towards a steady value. To eliminate the possibility that this time-dependent current was due to inadequate voltage control of these multicellular preparations early during square clamp pulses, we also used slowly depolarizing voltage clamp ramps (range 5-100 mV/s) to ensure control of membrane potential. TTX-sensitive current also was observed with these voltage ramps; the time dependence of this current was demonstrated by the reduction of the peak current magnitude as the ramp speed was reduced. Reducing the holding potential within the voltage range of sodium channel inactivation also decreased the TTX-sensitive current observed with identical speed ramps. These results suggest that the TTX-sensitive time-dependent current is a direct measure of slow inactivation of canine cardiac sodium channels. This current may play an important role in modulating the action potential duration.     

Inactivation of calcium channel current in the calf cardiac Purkinje fiber. Evidence for voltage- and calcium-mediated mechanisms

We have studied the influence of divalent cations on Ca channel current in the calf cardiac Purkinje fiber to determine whether this current inactivates by voltage- or Ca-mediated mechanisms, or by a combination of the two. We measured the reversal (or zero current) potential of the current when Ba, Sr, or Ca were the permeant divalent cations and determined that depletion of charge carrier does not account for time-dependent relaxation of Ca channel current in these preparations. Inactivation of Ca channel current persists when Ba or Sr replaces Ca as the permeant divalent cation, but the voltage dependence of the rate of inactivation is markedly changed. This effect cannot be explained by changes in external surface charge. Instead, we interpret the results as evidence that inactivation is both voltage and Ca dependent. Inactivation of Sr or Ba currents reflects a voltage-dependent process. When Ca is the divalent charge carrier, an additional effect is observed: the rate of inactivation is increased as Ca enters during depolarizing pulses, perhaps because of an additional Ca-dependent mechanism.     

Phase resetting and phase locking in hybrid circuits of one model and one biological neuron

To determine why elements of central pattern generators phase lock in a particular pattern under some conditions but not others, we tested a theoretical pattern prediction method. The method is based on the tabulated open loop pulsatile interactions of bursting neurons on a cycle-by-cycle basis and was tested in closed loop hybrid circuits composed of one bursting biological neuron and one bursting model neuron coupled using the dynamic clamp. A total of 164 hybrid networks were formed by varying the synaptic conductances. The prediction of 1:1 phase locking agreed qualitatively with the experimental observations, except in three hybrid circuits in which 1:1 locking was predicted but not observed. Correct predictions sometimes required consideration of the second order phase resetting, which measures the change in the timing of the second burst after the perturbation. The method was robust to offsets between the initiation of bursting in the presynaptic neuron and the activation of the synaptic coupling with the postsynaptic neuron. The quantitative accuracy of the predictions fell within the variability (10%) in the experimentally observed intrinsic period and phase resetting curve (PRC), despite changes in the burst duration of the neurons between open and closed loop conditions.     

Ionic mechanisms of pacemaker activity in cardiac Purkinje fibers.

Rhythmic activity in cardiac Purkinje fibers can be analyzed by using the voltage clamp technique to study pacemaker currents. In normally polarized preparations, pacemaker activity can be generated by two distinct ionic mechanisms. The standard pacemaker potential (phase 4 depolarization) involves a slow potassium current, IK2. Following action potential repolarization, the IK2 channels slowly deactivate and thus unmask a steady background inward current. The resulting net inward current causes the slow pacemaker depolarization. Epinephrine accelerates the diastolic depolarization by promoting more complete and more rapid deactivation of IK2 over the pacemaker range of potentials. The catecholamine acts rather selectively on the voltage dependence of the gating mechanism, without altering the basic character of the pacemaker process. The nature of the pacemaker depolarization is altered by intoxication with high concentrations of cardiac glycosides or aglycones. These compounds promote spontaneous impulses in Purkinje fibers by a mechanism that supersedes the ordinary IK2 pacemaker. The digitalis-induced depolarization is generated by a transient inward current that is either absent or very small in untreated preparations. The transient inward current is largely carried by sodium ions. Its unusual time course probably reflects an underlying subcellular event, the oscillatory release of calcium ions from intracellular stores.     

Phase resetting and coupling of noisy neural oscillators

A number of experimental groups have recently computed Phase Response Curves (PRCs) for neurons. There is a great deal of noise in the data. We apply methods from stochastic nonlinear dynamics to coupled noisy phase-resetting maps and obtain the invariant density of phase distributions. By exploiting the special structure of PRCs, we obtain some approximations for the invariant distributions. Comparisons to Monte-Carlo simulations are made. We show how phase-dependence of the noise can move the peak of the invariant density away from the peak expected from the analysis of the deterministic system and thus lead to noise-induced bifurcations. B. Ermentrout supported in part by NIMH and NSF. Action Editor: Wulfram Gerstner     

Phase resetting associated with changes of burst shape

Based on our stochastic approach to phase resetting of an ensemble of oscillators, in this article we investigate two stimulation mechanisms which exhibit qualitatively different dynamical behaviour as compared with the stimulation mechanism analysed in a previous study. Both the old as well as one of the new stimulation mechanisms give rise to a characteristic desynchronization behaviour: A stimulus of a given (non-vanishing) intensity administered at a critical initial ensemble phase for a critical duration T _crit annihilates the ensemble's synchronized oscillation. When the stimulation duration exceeds T _crit a transition from type 1 resetting to type 0 resetting occurs. The second new stimulation mechanism does not cause a desynchronization which is connected with a phase singularity. Correspondingly this mechanism only leads to type 1 resetting. In contrast to the stimulation mechanism analysed in a previous study, both new stimulation mechanisms cause burst splitting. According to our results, in this case peak or onset detection algorithms are not able to reveal a correct estimate of the ensemble phase. Thus, whenever stimulation induced burst splitting occurs, phase-resetting curves determined by means of peak or onset detection may be nothing but artifacts. Therefore it is necessary to understand burst splitting in order to develop reliable phase detection algorithms, which are e.g. based on detecting bursts' centers of mass. Our results are important for experimentalists: Burst splitting is, for instance, well-known from tremor resetting experiments. Thus, it often turned out to be at least rather difficult to derive reliable phase-resetting curves from experimental data.     

Membrane currents following activity in canine cardiac Purkinje fibers.

Recent experiments in canine Pukinje fibers (Gadsby and Cranefield, 1979) have shown that following a period of sodium loading in K+-free solution a slowly decaying outward current is observed. This current has been attributed to the activity of the electrogenic Na+-K+ exchange pump. In the present paper we show that similar slowly decaying outward currents are observed following prolonged periods of overdrive with action potentials or with brief depolarizing voltage clamp pulses. The dependent of the prolonged outward current on the duration and frequency of the preceding period of overdrive and on the potential following overdrive is reported. We also present results which indicate that a large portion of this current can be induced by phasic Na+ loading through the fast-inward channel.     

Phase resetting of embryonic chick atrial heart cell aggregates. Experiment and theory.

The influence of brief duration current pulses on the spontaneous electrical activity of embryonic chick atrial heart cell aggregates was investigated experimentally and theoretically. A pulse could either delay or advance the time of the action potential subsequent to the pulse depending upon the time in the control cycle at which it was applied. The perturbed cycle length throughout the transition from delay to advance was a continuous function of the time of the pulse for small pulse amplitudes, but was discontinuous for larger pulse amplitudes. Similar results were obtained using a model of the ionic currents which underlie spontaneous activity in these preparations. The primary ion current components which contribute to phase resetting are the fast inward sodium ion current, INa, and the primary, potassium ion repolarization current, IX1. The origin of the discontinuity in phase resetting of the model can be elucidated by a detailed examination of the current-voltage trajectories in the region of the phase response curve where the discontinuity occurs.     

Low conductance sodium channels in canine cardiac Purkinje cells.

Low conductance sodium (Na) channels have been observed in nerve, skeletal muscle, and cardiac cells. In cardiac tissues the higher amplitude, more commonly observed Na channel was first investigated in detail by Cachelin et al. (Cachelin, A.B., J.E. de Peyer, S. Kokubun, and H. Reuter, 1983, J. Physiol. (Lond.), 340:389-402). They also reported low amplitude Na channel events. We have studied this low conductance Na channel in single canine cardiac Purkinje cells using cell-attached patches. Patch pipette solutions contained either 140 or 280 mM NaCl, and cells were bathed in a solution of 150 mM KCl to bring their resting potential close to zero. In 140 mM Na+, during steps to -50 mV, the lower and higher openings had amplitudes of 0.57 +/- 0.2 and 1.2 +/- 0.2 pA (means +/- SD of Gaussian fits). In 280 mM Na+ at -50 mV, amplitudes were 0.72 +/- 0.2 and 1.55 +/- 0.2 pA. Over a substantial voltage range, the lower events had amplitudes of about one-third that of the higher events. The frequency of the low conductance openings varied in different patches from zero to 22% of total openings. Histograms of open durations and latencies at several voltages suggested no difference in kinetics between the two channel events. The behavior of the low conductance channels was more consistent with a second population of channels rather than a second open state.     

Impulse responses of automaticity in the Purkinje fiber

We examined the effects of brief current pulses on the pacemaker oscillations of the Purkinje fiber using the model of McAllister , Noble, and Tsien (1975. J. Physiol. [Lond.]. 251:1-57). This model was used to construct phase-response curves for brief electric stimuli to find "black holes," where rhythmic activity of the Purkinje fiber ceases. In our computer simulation, a brief current stimulus of the right magnitude and timing annihilated oscillations in membrane potential. The model also revealed a sequence of alternating periodic and chaotic regimes as the strength of a steady bias current is varied. We compared the results of our computer simulations with experimental work on Purkinje fibers and pointed out the importance of modeling results of this kind for understanding cardiac arrhythmias.     

Effects of tetrodotoxin on heart cell aggregates. Phase resetting and annihilation of activity.

The influence of relatively low concentrations of tetrodotoxin (TTX) on phase resetting of spontaneous activity of embryonic chick atrial heart cell aggregates by brief duration current pulses was investigated experimentally and theoretically. The maximal upstroke velocity, Vmax, of the spontaneous action potential was reduced by TTX in a concentration-dependent manner for [TTX] less than 10(-7) M. However, the beat rate was unaffected in this concentration range. Application of a depolarizing current pulse of brief duration during a critical region of the spontaneous cycle annihilated activity in some preparations exposed to [TTX] approximately 10(-7) M. These results were analyzed with the model of electrical activity described in the previous paper (Clay, J.R., R.M. Brochu, and A. Shrier. 1990. Biophys. J. 58:609-621) based on a tonic block of the INa channel by TTX with a dissociation constant, KD, of 50 nM.