Junctional resistance and action potential delay between embryonic heart cell aggregates

Electrical coupling and its channels

Harris explores the development of our current understanding of electrical coupling between cells and the channels that mediate it, highlighting the contributions of the Journal of General Physiology.

As the physiology of synapses began to be explored in the 1950s, it became clear that electrical communication between neurons could not always be explained by chemical transmission. Instead, careful studies pointed to a direct intercellular pathway of current flow and to the anatomical structure that was (eventually) called the gap junction. The mechanism of intercellular current flow was simple compared with chemical transmission, but the consequences of electrical signaling in excitable tissues were not. With the recognition that channels were a means of passive ion movement across membranes, the character and behavior of gap junction channels came under scrutiny. It became evident that these gated channels mediated intercellular transfer of small molecules as well as atomic ions, thereby mediating chemical, as well as electrical, signaling. Members of the responsible protein family in vertebrates—connexins—were cloned and their channels studied by many of the increasingly biophysical techniques that were being applied to other channels. As described here, much of the evolution of the field, from electrical coupling to channel structure–function, has appeared in the pages of the Journal of General Physiology.

Biomechanics of cardiac electromechanical coupling and mechanoelectric feedback

Cardiac mechanical contraction is triggered by electrical activation via an intracellular calcium-dependent process known as excitation-contraction coupling. Dysregulation of cardiac myocyte intracellular calcium handling is a common feature of heart failure. At the organ scale, electrical dyssynchrony leads to mechanical alterations and exacerbates pump dysfunction in heart failure. A reverse coupling between cardiac mechanics and electrophysiology is also well established. It is commonly referred as cardiac mechanoelectric feedback and thought to be an important contributor to the increased risk of arrhythmia during pathological conditions that alter regional cardiac wall mechanics, including heart failure. At the cellular scale, most investigations of myocyte mechanoelectric feedback have focused on the roles of stretch-activated ion channels, though mechanisms that are independent of ionic currents have also been described. Here we review excitation-contraction coupling and mechanoelectric feedback at the cellular and organ scales, and we identify the need for new multicellular tissue-scale model systems and experiments that can help us to obtain a better understanding of how interactions between electrophysiological and mechanical processes at the cell scale affect ventricular electromechanical interactions at the organ scale in the normal and diseased heart.

Estimating conductances of dual-recorded neurons within a network of coupled cells

Simultaneous pre- and postsynaptic cell recordings are used to calculate gap junction conductance based on an equivalent electrical circuit of an electrically coupled pair of cells. This calculation is imprecise when recording from a cell pair that is coupled to neighboring cells providing indirect conductance paths between the recorded cells. Despite this imprecision, junctional conductance has been calculated for coupled cell networks during the past 40 years since a more accurate method was lacking. The present study simulated a three-dimensional network of electrically coupled heterogeneous neurons and used mathematical modeling to reduce the complexity to the simplest equations that could more accurately estimate the electrical properties of dual-recorded cells in the network. Analyses of the simulations showed that knowledge of the number of unrecorded cells directly linked to the recorded cells and of the voltage responses of these recorded cells were largely sufficient to accurately predict the direct junctional resistance linking the recorded cells as well as the input resistance of the recorded cells that would exist in the absence of junctional coupling. All model parameters could be obtained from real dual-intracellular penetrations which allow electrophysiological recordings and intracellular staining.

Regulation of connexin43 gap junctional conductance by ventricular action potentials

Transjunctional voltage regulates cardiac gap junctional conductance, but the kinetics of inactivation were considered too slow to affect cardiac action potential propagation. Connexin43 (Cx43) is abundantly expressed in the atrial and ventricular myocardium and the rapid ventricular conduction tissues (ie, His-Purkinje system) of the mammalian heart and is important to conduction through these cardiac tissues. The kinetics of Cx43 voltage gating were examined at peak action potential voltages using simulated ventricular myocardial action potential waveforms or pulse protocols exceeding 100-mV transjunctional potentials. Junctional current responses approximate the action potential morphology but conductance calculations reveal a 50% to 60% decline from peak to near constant plateau values. Junctional conductance recovers during phase 3 repolarization and early diastole to initial values. The bases for these transient changes in junctional conductance are the rapid decay kinetics in tens of milliseconds at peak transjunctional voltages (Vj) of 130 mV and the gradual increase in junctional conductance as Vj returns toward 0 mV. The decay time constants change e-fold per 22.1 mV above the half-inactivation voltage for Cx43 gap junctions of +/-58 mV. A realistic dynamic model for changes in junctional resistance between excitable and nonexcitable cells during cardiac action potential propagation was developed based on these findings. This dynamic model of cardiac gap junctions will further our understanding of the role gap junctions play in the genesis and propagation of cardiac arrhythmias. The full text of this article is available online at http://www.circresaha.org.

High-resolution electrophysiological assessment of human embryonic stem cell-derived cardiomyocytes: a novel in vitro model for the study of conduction

The goal of the present report was to establish a new in vitro model for the study of impulse propagation in human cardiac tissue. By using the human embryonic stem cell differentiating system, spontaneously contracting areas were generated in three-dimensional differentiating cell aggregates (embryoid bodies). Morphological analysis revealed an isotropic tissue of early-stage cardiac phenotype. Gap junctions, assessed by immunostaining of connexin43 and connexin45, were distributed along the cell borders. High-resolution activation maps demonstrated the presence of a functional syncytium with stable focal activation and conduction properties. Conduction was significantly slower in narrow bands of contracting tissue compared with broad cardiomyocyte regions. Establishment of this unique in vitro human model may be used for the assessment of long-term structure-function relationships, for pharmacological studies, for tissue engineering, and may permit the study of genetically modified cardiomyocytes.

Peptides acting at gap junctions

Gap junction channels are low resistance pathways allowing an action potential to propagate from one cell to the neighboring. Moreover, small molecules (<1000 Da) may pass the channel providing a possibility for metabolic coupling, growth and differentiation control of a cell by its surrounding. Antiarrhythmic peptides can enhance the conductivity of the channels while other peptides, angiotensin or extracellular loop peptides, reduce intercellular communication. On the other hand, peptides like angiotensin II or endothelin-1 can increase expression of certain gap junction channel proteins and, thereby, may affect intercellular coupling chronically. Thus, intercellular communication can be controlled using peptide drugs.

Inhomogeneity of action potential waveshape assists frequency entrainment of cardiac pacemaker cells

In this paper, we have employed ionic models of sinoatrial node cells to investigate the synchronization of a pair of coupled cardiac pacemaker cells from central and peripheral regions of the sinoatrial node. The free-running cycle length of the cell models was perturbed using two independent techniques and the minimum coupling conductance required to achieve frequency entrainment was used to assess the relative ease with which various cell pairs achieve entrainment. The factors effecting entrainment were further investigated using single-cell models paced with an artificial biphasic coupling current. Our simulation results suggest that dissimilar cell types, those with largely different upstroke velocities entrain more easily, that is, they require less coupling conductance to achieve 1:1 frequency entrainment. We, therefore, propose that regional variation in action-potential waveshape within the sinoatrial node assists frequency synchronization in vivo.

Beat-to-beat repolarization variability in ventricular myocytes and its suppression by electrical coupling

Single ventricular myocytes paced at a constant rate and held at a constant temperature exhibit beat-to-beat variations in action potential duration (APD). In this study we sought to quantify this variability, assess its mechanism, and determine its responsiveness to electrotonic interactions with another myocyte. Interbeat APD(90) (90% repolarization) of single cells was normally distributed. We thus quantified APD(90) variability as the coefficient of variability, CV = (SD/mean APD(90)) x 100. The mean +/- SD of the CV in normal solution was 2.3 +/- 0.9 (132 cells). Extracellular TTX (13 microM) and intracellular EGTA (14 mM) both significantly reduced the CV by 44 and 26%, respectively. When applied in combination the CV fell by 54%. In contrast, inhibition of the rapid delayed rectifier current with L-691,121 (100 nM) increased the CV by 300%. The CV was also significantly reduced by 35% when two normal myocytes were electrically connected with a junctional resistance (R(j)) of 100 MOmega. Electrical coupling (R(j) = 100 MOmega) of a normal myocyte to one producing early afterdepolarization (EAD) completely blocked EAD formation. These results indicate that beat-to-beat APD variability is likely mediated by stochastic behavior of ion channels and that electrotonic interactions act to limit temporal dispersion of refractoriness, a major contributor to arrhythmogenesis.

Endothelin-induced conversion of embryonic heart muscle cells into impulse-conducting Purkinje fibers

A regular heart beat is dependent on a specialized network of pacemaking and conductive cells. There has been a longstanding controversy regarding the developmental origin of these cardiac tissues which also manifest neural-like properties. Recently, we have shown conclusively that during chicken embryogenesis, impulse-conducting Purkinje cells are recruited from myocytes in spatial association with developing coronary arteries. Here, we report that cultured embryonic myocytes convert to a Purkinje cell phenotype after exposure to the vascular cytokine, endothelin. This inductive response declined gradually during development. These results yield further evidence for a role of arteriogenesis in the induction of impulse-conducting Purkinje cells within the heart muscle lineage and also may provide a basis for tissue engineering of cardiac pacemaking and conductive cells.

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.

Expression pattern of connexin gene products at the early developmental stages of the mouse cardiovascular system

The synchronized contraction of myocytes in cardiac muscle requires the structural and functional integrity of the gap junctions present between these cells. Gap junctions are clusters of intercellular channels formed by transmembrane proteins of the connexin (Cx) family. Products of several Cx genes have been identified in the mammalian heart (eg, Cx45, Cx43, Cx40, and Cx37), and their expression was shown to be regulated during the development of the myocardium. Cx43, Cx40, and Cx45 are components of myocyte gap junctions, and it has also been demonstrated that Cx40 was expressed in the endothelial cells of the blood vessels. The aim of the present work was to investigate the expression and regulation of Cx40, Cx43, and Cx37 during the early stages of mouse heart maturation, between 8.5 days post coitum (dpc), when the first rhythmic contractions appear, and 14.5 dpc, when the four-chambered heart is almost completed. At 8.5 dpc, only the reverse-transcriptase polymerase chain reaction technique has allowed identification of Cx43, Cx40, and Cx37 gene transcripts in mouse heart, suggesting a very low activity level of these genes. From 9.5 dpc, all three transcripts became detectable in whole-mount in situ-hybridized embryos, and the most obvious result was the labeling of the vascular system with Cx40 and Cx37 anti-sense riboprobes. Cx40 and Cx37 gene products (transcript and/or protein) were demonstrated to be expressed in the vascular endothelial cells at all stages examined. By contrast, only Cx37 gene products were found in the endothelial cells of the endocardium. In heart, Cx37 was expressed exclusively in these cells, which rules out any direct involvement of this Cx in the propagation of electrical activity between myocytes and the synchronization of contractions. Between 9.5 and 11.5 dpc, Cx40 gene activation in myocytes was demonstrated to proceed according to a caudorostral gradient involving first the primitive atrium and the common ventricular chamber (9.5 dpc) and then the right ventricle (11.5 dpc). During this period of heart morphogenesis, there is clearly a temporary and asymmetrical regionalization of the Cx40 gene expression that is superimposed on the functional regionalization. In addition, comparison of Cx40 and Cx43 distribution at the above developmental stages has shown that these Cxs have overlapping (left ventricle) or complementary (atrial tissue and right ventricle) expression patterns.

Specific motifs in the external loops of connexin proteins can determine gap junction formation between chick heart myocytes

1. Gap junction formation was compared in the absence and presence of small peptides containing extracellular loop sequences of gap junction (connexin) proteins by measuring the time taken for pairs of spontaneously beating embryonic chick heart myoballs to synchronize beat rates. Test peptides were derived from connexin 32. Non-homologous peptides were used as controls. Control pairs took 42 +/- 0.5 min (mean +/- S.E.M.; n = 1088) to synchronize. 2. Connexins 32 and 43, but not 26, were detected in gap junction plaques. The density and distribution of connexin immunolabelling varied between myoballs. 3. Peptides containing conserved motifs from extracellular loops 1 and 2 delayed gap junction formation. The steep portion of the dose-response relation lay between 30 and 300 microM peptide. 4. In loop 1, the conserved motifs QPG and SHVR were identified as being involved in junction formation. In loop 2, the conserved SRPTEK motif was important. The ability of peptides containing the SRPTEK motif to interfere with the formation of gap junctions was enhanced by amino acids from the putative membrane-spanning region. 5. Peptides from loop 1 and loop 2 were equivalently effective; there was no synergism between them. 6. The inclusion of conserved cysteines in test peptides did not make them more effective in the competition assay.

Voltage-dependent gating and single-channel conductance of adult mammalian atrial gap junctions

In the heart, the rapid propagation and synchronization of action potentials necessary for a normal heart rhythm and an effective cardiac output are mediated by specialized ionic channels that link adjacent cells and are known collectively as gap junctions. Cardiac gap junctions are gated by various physiological and pharmacological agents, but the role of voltage in their gating is unclear. Whereas embryonic or neonatal ventricular cells have voltage-gated gap junctions, adult cells are reported to have only voltage-independent gap junctions. We studied the voltage dependence of adult rat atrial gap junctions by individually voltage clamping each cell of a connected cell pair and controlling the transjunctional voltage (Vj), measuring transjunctional current (Ij), and calculating junctional conductance (gj). Two distinct populations of cell pairs were observed: highly coupled pairs with the peak gjs ranging from 3.4 to 40 nS and weakly coupled pairs with the peak gjs ranging from 0.3 to 2.0 nS. gj was dependent on Vj, and Ij decayed exponentially, with the time constants being voltage dependent. Voltage dependence was most apparent when cells were poorly coupled. The gj did not decrease to zero. The normalized conductance--Vj plot was fit with a two-state Boltzmann model as a first approximation, resulting in a half-inactivation potential and gating charge of 42.5 mV and 1.14 eV, respectively, for the weakly coupled cell pairs. For highly coupled cell pairs, the half-inactivation potential shifted to 53.3 mV. Single gap junctional channels had a gj of 36.2 +/- 7.6 pS (range, 27-49 pS), which was Vj independent.(ABSTRACT TRUNCATED AT 250 WORDS)

Gap junctional channels in adult mammalian sinus nodal cells. Immunolocalization and electrophysiology

The subcellular mechanism of cell-to-cell communication in the natural pacemaker region of the mammalian heart was studied using electrophysiological and immunofluorescence techniques in isolated pairs of rabbit sinus nodal cells. By measuring whole-cell currents using a double patch-clamp approach, it was demonstrated that communication in the sinus node is mediated through gap junctional channels similar to those in other types of adult cardiac cell pairs. Macroscopic sinus nodal junctional resistance had a mean value of 387.9 +/- 97.1 M omega (mean +/- SEM, n = 10) and was greatly increased by superfusion with alkanols. Single-channel junctional conductance could be resolved in three cell pairs. Given their high membrane resistance (1.16 +/- 0.32 G omega, n = 12), the electrical coupling provided by as few as three gap junctional channels between nodal cells will allow for pacemaker synchronization. Further evidence for the presence of the channels was obtained from immunofluorescent double-labeling of desmin and the gap junction protein (connexin43) in sinus nodal tissue as well as in cultured sinus nodal cells. Using antisera against residues 243-257 of the connexin43 protein, a specific staining at the site of cell-to-cell apposition was demonstrated. These data provide direct evidence in favor of electronic coupling as the means for achieving pacemaker synchronization in the rabbit sinus node.

The potential role of Ca2+ for electrical cell-to-cell uncoupling and conduction block in myocardial tissue

Ca2+ ions are often invoked as potential initiators of cardiac arrhythmias in pathophysiological situations which are associated with an increase of free [Ca2+]i. It is well documented that elevated [Ca2+]i may produce SR release of Ca2+ and oscillations of membrane potential, thereby leading to triggered or spontaneous ectopic activity. The relation among elevated free [Ca2+]i, electrical cell-to-cell coupling, conduction slowing, and reentrant arrhythmias is more speculative. If Ca2+ (e.g. in mechanically injured cells) has direct access to the cellular interconnections (gap junctions), rapid uncoupling occurs at [Ca2+]i which is even within the range of a normal contractile cycle. If cellular integrity is preserved and changes of [Ca2+]i are imposed by extracellular interventions, the effect of [Ca2+]i is critically dependent on pHi. At normal pHi, transcellular conductance remains normal even if [Ca2+]i is increased to bring the cells into a hypercontractile state (> 1-2 microM). At decreased pHi, rapid uncoupling develops at low [Ca2+]i. Comparison of the conduction delay between two cells (or conduction velocity in a simulated conducting medium) with the [Ca2+]i-mediated increase in coupling resistance suggests that the transition from normal conduction velocity to conduction block (a key event in re-entrant arrhythmias) occurs within a relatively narrow range of [Ca2+]i or pHi, almost like a threshold phenomenon. Major efforts have been made in recent years to assess the changes of electrical cell-to-cell coupling and [Ca2+]i in myocardial ischemia. Therefore, the discussion of the role of [Ca2+]i as a modulator of electrical coupling is made in this pathophysiological setting. Comparison of several studies indicate that cell-to-cell resistance and [Ca2+]i in ischemia increase at the same time (10-15 min after perfusional arrest). Since other potential uncoupling processes (delta ATP, delta Mg2+, amphiphilic metabolites, delta pHi) show a similar time-course, it is difficult to attribute cell-to-cell uncoupling in ischemia solely to an increase in [Ca2+]i. Both an initial decrease of membrane excitability and subsequent electrical cell-to-cell uncoupling characterize the early phase of ischemia. The first mechanism is assumed to be more important for the generation of conduction block and re-entry. However, Ca(2+)-induced cell-to-cell uncoupling may partially contribute to the second phase of the early ischemic arrhythmias and mark the transition from reversible to irreversible ischemic damage.

Action potential transfer in cell pairs isolated from adult rat and guinea pig ventricles

An enzymatic procedure was used to obtain ventricular cells from adult rat and guinea pig hearts. Isolated pairs of cells were selected to study the action potential transfer from cell to cell and determine the resistance of the nexal membrane, rn. For this purpose, each cell of a cell pair was connected to a patch pipette so as to enable whole-cell, tight-seal recording. Normal impulse transmission was observed when rn ranged from 5-265 M omega. In these cases, the action potential in both cells occurred virtually simultaneously. An occasional failure in action potential transfer was seen in cell pairs whose rn had increased to 155-375 M omega. In these cases, the impulse transfer across the nexal membrane occurred with considerable delay. Impulse transfer was completely blocked once rn was larger than 780 M omega. Assuming a single connexon conductance of 100 pS, this would mean that more than 13 connexons are necessary to allow impulse transfer from cell to cell. Two single myocytes, gently pushed together, neither showed electrotonic interaction nor impulse transfer, thus rendering unlikely the possibility of an ephaptic signal transmission.

Cell-to-cell coupling assayed by means of electrical measurements

The importance of electrical measurements in the evaluation of cell-to-cell coupling in heart muscle was discussed. The presence of gap junctions in heart and smooth muscle, and the implications of this for electrical synchronization and healing-over, was emphasized. Moreover, the modulation of junctional resistance by Ca, protons and cAMP was reviewed.

The development of beat-rate synchronization of rat myocyte pairs in cell culture

When two spontaneously beating neonatal rat heart cells in tissue culture were allowed to grow together they synchronized their originally independent beats to a common rhythm, as measured with an opto-electronic technique. Both single isolated cells and cell pairs exhibited a highly irregular beating pattern. Beating irregularity was strongly and positively correlated with mean interbeat interval. Synchronization of beating occurred in 50% of the pairs studied within one beating interval. In the remaining cell pairs, the first synchronized beat was followed by a 4-65 s period of partial synchronization. The time difference between contraction moments of two cells in a pair respective to each other (latency) changed upon synchronization from a random value to a fixed value. In a few cases the latency decreased during 20 to 30 s after the first synchronized beat before a steady-state value was reached. The mean interbeat interval (IBI) of the synchronized cell pairs was governed by the mean IBI of the originally faster beating cells. In 83% of the cases the mean IBI of the cell pairs was between that of the originally isolated beating cells. We conclude from the experiments described that physical coupling (i.e. gap junction formation) is virtually complete before beating synchronization occurs.

Effects of hypoxia, hyperkalemia, and metabolic acidosis on canine subendocardial action potential conduction

We have studied the individual and combined effects of elevated external potassium concentration (8 mM [K+], metabolic acidosis (pH = 6.8), and hypoxia at different stimulation 400 milliseconds) on Purkinje (P) and ventricular (V) conduction velocities and on Purkinje-ventricular junctional conduction delay (PVJ delay) in in vitro preparations from canine ventricles. Elevated [K+] had opposite effects on P and V velocities, increasing V velocity by 8% while reducing P velocity by 7%. Acidosis reduced P velocity by 9% while reducing V velocity by only 4%. Hypoxia and rapid stimulation rates had no significant effect on either P or V velocities. All test solutions (except hypoxia alone) significantly increased the PVJ delay. The magnitude of the increase in PVJ delay was much greater than the effects on either P or V velocity. In addition, hypoxia and rapid stimulation augmented the increase in PVJ delay in the presence of elevated [K+] and/or acidosis. The special features of conduction at the PV junctional sites may produce altered pathways of excitation of the ventricles during myocardial ischemia.

Propagation through electrically coupled cells. How a small SA node drives a large atrium

Each normal cardiac cycle is started by an action potential that is initiated in the sino-atrial (SA) node by automaticity of the SA nodal cells. This action potential then propagates from the SA node into the surrounding atrial cells. We have done numerical simulations of electrically coupled cells to understand how a small SA node can be spontaneously active and yet be sufficiently electrically coupled to the surrounding quiescent atrial cells to initiate an action potential in the atrial cells. Our results with a simple model of two coupled cells and a more complex model of a two-dimensional sheet of cells suggest that some degree of electrical uncoupling of the cells within the SA node may be an essential design feature of the normal SA-atrial system.

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.

Dynamic responses of electrically coupled systems

An identified pair of electrically coupled neurons in the buccal ganglion of the freshwater snail Helisoma trivolvis is an experimentally accessible model of electrical synaptic transmission. In this investigation, electrical synaptic transmission is characterized using sinusoidal frequency (Bode) responses computed by Laplace transforms and responses to brief stimuli. The frequency response of the injected neuron shows a 20-dB/decade attenuation and a phase shift from 0 degree at low frequencies to -90 degrees at high frequencies. The response of a coupled cell shows a 40-dB/decade attenuation and a phase shift from 0 degrees at low frequencies to -180 degrees at high frequencies. A simple mathematical model of electrical synaptic transmission is described that displays each of these crucial features of the measured frequency responses. Methods are described to estimate the frequency responses of coupled systems based on presynaptic measurements. The responses of the coupled system to brief pulses of current were computed using the principle of superposition. The electrical properties of coupled systems impose a minimum delay in reaching a peak in all postsynaptic responses. The delays in the postsynaptic responses to brief stimuli are related to the electrical and anatomical parameters of coupled networks.

Effects of changes in excitability and intercellular coupling on synchronization in the rabbit sino-atrial node

The mechanisms of synchronization between sino-atrial pace-maker cells were studied in biological preparations from rabbit hearts, and in computer simulations of the Hodgkin & Huxley type. For biological experiments, thin strips of sino-atrial node were placed in a three-compartment bath. The electrical properties of the tissue in the middle segment (the 'gap') were manipulated pharmacologically to alter electrical coupling and/or excitability of cells in that segment, and to study the patterns of interaction between two pace-maker centres in the external segments. Superfusion of the gap segment with either verapamil (2 microM) or acetylcholine (10 microM) produced a loss of 1:1 synchrony (entrainment) of spontaneous discharges generated by the external pace-makers but subharmonic (i.e. 3:2; 5:4; 9:8; etc.) entrainment was always maintained. When the gap segment was superfused with heptanol (3.5 mM), which is known to increase intercellular resistance, the pace-maker centres in the external chambers beat independently of one another. Progressive loss of synchrony paralleled reductions in amplitude of electrotonic responses to current pulses applied across the gap. Gap superfusion with hypertonic Tyrode solution (600 mosM) produced a major reduction in the degree of synchronization between the external pace-makers, even though the cells in the central compartment maintained their excitability. Under these conditions, as many as three independent pace-maker centres, one in each chamber, coexisted in a given preparation. Using computerized simulations based on equations of time- and voltage-dependent membrane currents, three 'cells', each capable of maintaining spontaneous activity, were connected in a linear array through ohmic resistances. When selective parameters (e.g. membrane conductances, coupling resistance) were modified appropriately, the mathematical simulations reproduced very closely the interaction patterns observed in the experimental preparations. Our results show that synchronization in the sinus node results from mutual interactions and entrainment between all the cells in this region. These interactions are of the kind expected for a population of coupled, self-sustained oscillators, and are mediated through electrotonic propagation of current across low-resistance junctions.

Propagation through electrically coupled cells. Effects of regional changes in membrane properties

The normal process of excitation of the heart involves propagation of action potentials through cardiac regions of different anatomy and different intrinsic membrane properties. Although our understanding of these properties is still incomplete, it is well accepted that the parameters measured from a single cell penetration in an electrical syncytium (e.g., action potential duration, rate of rise, and velocity) reflect not only the properties of that cell but also the electrotonic interactions with other cells to which the recorded cell is electrically coupled. We have used simulation techniques to predict the spatial distribution of action potential parameters resulting from discretely localized alterations in the intrinsic membrane properties of some of the cells of an electrical syncytium. We have shown that the resulting spatial distribution is markedly different for alterations in plateau and pacemaker currents vs. rising phase currents, and that other factors, such as the site of stimulation and the underlying spatial pattern of cell-cell coupling resistance, also modify the spatial distribution of action potential properties resulting from a discrete regional change in intrinsic membrane properties.

Small signal impedance of heart cell membranes

The electrical impedance of seven-day ventricular embryonic chick heart cell membranes maintained in tissue culture was measured under voltage clamp using the two-microelectrode voltage-clamp technique. Small sinusoidal perturbations were added to the voltage-clamp potential and the amplitude and phase of the steady-state sinusoidal response in current was recorded as a function of mean clamp potential or perturbing frequency. The experimental results are compared with two models of excitability for heart: the MNT model (McAllister, Noble & Tsien, J. Physiol. (London) 251:1-59, (1975) and the BR model (Beeler & Reuter, J. Physiol. (London) 268:177-210, 1977). The small signal impedance of heart cell membranes, in theory and experiment, shows a resonance near 1 Hz and near the threshold potential. The effect of this resonance is to increase the effective length constant of the membrane for these conditions.

Improved electrical coupling in uterine smooth muscle is associated with increased numbers of gap junctions at parturition

We have studied some passive electrical properties of uterine smooth muscle to determine whether a change in electrical parameters accompanies gap junction formation at delivery. The length constant of the longitudinal myometrium increased from 2.6 +/- 0.8 mm (X +/- SD) before term to 3.7 +/- 1 mm in tissues from delivering animals. The basis of the change was a 33% decrease in internal resistance and a 46% increase in membrane resistance. Axial current flow in an electrical syncytium such as myometrium is impeded by the cytoplasm of individual cells plus the junctions between cells. Measurement of the longitudinal impedance indicated that the specific resistance of the myoplasmic component was constant at 319 +/- 113 omega . cm before term and 340 +/- 93 omega . cm at delivery. However, a decrease in junctional resistance was apparent from 323 +/- 161 omega . cm to 134 +/- 64 omega . cm at delivery. 1.5-2 d after delivery, the junctional resistance was increased, as was the myoplasmic resistance. Thin-section electron microscopy of some of the same muscle samples showed that gap junctions were present in significantly greater numbers in the delivering tissues. Therefore, our results support the hypothesis that gap junction formation at delivery is associated with improved electrical coupling of uterine smooth muscle.

Electrical coupling among heart cells in the absence of ultrastructurally defined gap junctions

Cells from the ventricles of 7-day chick embryos were aggregated into spheroidal clusters by 48 hr of culture on a gyratory platform. All aggregates beat spontaneously and rhythmically. Microelectrode impalement of widely separated cells within aggregates indicated that they were coupled, as evidenced by a mean coupling ratio (delta V2/ delta V1) of 0.81 +/- 0.09, and by simultaneity of intrinsic electrical activity (action potentials and subthreshold voltage fluctuation). In freeze-fracture preparations, the cell surfaces contained numerous small groups of intramembrane protein (IMP) particles, arranged in macular clusters, and linear and circular arrays. Using the criterion of 4 clustered IMP particles to defined a minimal gap junction, 0.27% of the total P-face examined was devoted to gap junctional area. Within such clusters particles were packed at about 8200/micrometer2; in nonjunctional regions, particles were scattered at a density of about 2000/micrometer2. When exposed to cycloheximide (CHX: 50 micrograms/ml) for 24--48 hr, coupling ratio declined to 0.44. This decrease could be attributed largely to leakiness of the nonjunctional membrane. Aggregates continued to beat rhythmically and in a coordinated fashion even after 72 hr in inhibitor. However, between 3--21 hr in CHX gap junctional area declined to 0.10%, and all particle clusters disappeared from the P-faces of aggregates in CHX for 24 or 48 hr. Neither macular nor linear particle arrays were seen. We conclude that organized gap junctions are unnecessary for electrotonic coupling between embryonic heart cells. These findings support the idea that low-resistance cell-to-cell pathways may exist as isolated channels scattered throughout the area of closely apposed plasma membranes.