Oscillatory network spontaneously recovers both activity and robustness after prolonged removal of neuromodulators.

Robustness of neuronal activity is a property necessary for a neuronal network to withstand perturbations, which may otherwise disrupt or destroy the system. The robustness of complex systems has been shown to depend on a number of features of the system, including morphology and heterogeneity of the activity of the component neurons, size of the networks, synaptic connectivity, and neuromodulation. The activity of small networks, such as the pyloric network of the crustacean stomatogastric nervous system, appears to be robust despite some of the factors not being consistent with the expected properties of complex systems, e.g., small size and homogeneity of the synaptic connections. The activity of the pyloric network has been shown to be stable and robust in a neuromodulatory state-dependent manner. When neuromodulatory inputs are severed, activity is initially disrupted, losing both stability and robustness. Over the long term, however, stable activity homeostatically recovers without the restoration of neuromodulatory input. The question we address in this study is whether robustness can also be restored as the network reorganizes itself to compensate for the loss of neuromodulatory input and recovers the lost activity. Here, we use temperature changes as a perturbation to probe the robustness of the network's activity. We develop a simple metric of robustness, i.e., the variances of the network phase relationships, and show that robustness is indeed restored simultaneously along with its stable network activity, indicating that, whatever the reorganization of the network entails, it is deep enough also to restore this important property.

Frequency-Dependent Action of Neuromodulation.

In oscillatory circuits, some actions of neuromodulators depend on the oscillation frequency. However, the mechanisms are poorly understood. We explored this problem by characterizing neuromodulation of the lateral pyloric (LP) neuron of the crab stomatogastric ganglion (STG). Many peptide modulators, including proctolin, activate the same ionic current (IMI) in STG neurons. Because IMI is fast and non-inactivating, its peak level does not depend on the temporal properties of neuronal activity. We found, however, that the amplitude and peak time of the proctolin-activated current in LP is frequency dependent. Because frequency affects the rate of voltage change, we measured these currents with voltage ramps of different slopes and found that proctolin activated two kinetically distinct ionic currents: the known IMI, whose amplitude is independent of ramp slope or direction, and an inactivating current (IMI-T), which was only activated by positive ramps and whose amplitude increased with increasing ramp slope. Using a conductance-based model we found that IMI and IMI-T make distinct contributions to the bursting activity, with IMI increasing the excitability, and IMI-T regulating the burst onset by modifying the postinhibitory rebound in a frequency-dependent manner. The voltage dependence and partial calcium permeability of IMI-T is similar to other characterized neuromodulator-activated currents in this system, suggesting that these are isoforms of the same channel. Our computational model suggests that calcium permeability may allow this current to also activate the large calcium-dependent potassium current in LP, providing an additional mechanism to regulate burst termination. These results demonstrate a mechanism for frequency-dependent actions of neuromodulators.

Neuronal Homeostasis: Voltage Brings It All Together.

Neurons generate consistent patterns of activity combining a large set of ionic currents and variable conductance levels. How they regulate this variability so that it does not run out of control seems to depend most prominently on neuronal activity itself.

Neuromodulation of central pattern generators and its role in the functional recovery of central pattern generator activity.

Neuromodulators play an important role in how the nervous system organizes activity that results in behavior. Disruption of the normal patterns of neuromodulatory release or production is known to be related to the onset of severe pathologies such as Parkinson's disease, Rett syndrome, Alzheimer's disease, and affective disorders. Some of these pathologies involve neuronal structures that are called central pattern generators (CPGs), which are involved in the production of rhythmic activities throughout the nervous system. Here I discuss the interplay between CPGs and neuromodulatory activity, with particular emphasis on the potential role of neuromodulators in the recovery of disrupted neuronal activity. I refer to invertebrate and vertebrate model systems and some of the lessons we have learned from research on these systems and propose a few avenues for future research. I make one suggestion that may guide future research in the field: neuromodulators restrict the parameter landscape in which CPG components operate, and the removal of neuromodulators may enable a perturbed CPG in finding a new set of parameter values that can allow it to regain normal function.

Ionic current correlations are ubiquitous across phyla.

Ionic currents, whether measured as conductance amplitude or as ion channel transcript numbers, can vary many-fold within a population of identified neurons. In invertebrate neuronal types multiple currents can be seen to vary while at the same time their magnitudes are correlated. These conductance amplitude correlations are thought to reflect a tight homeostasis of cellular excitability that enhances the robustness and stability of neuronal activity over long stretches of time. Although such ionic conductance correlations are well documented in invertebrates, they have not been reported in vertebrates. Here we demonstrate with two examples, identified mouse hippocampal granule cells (GCs) and cholinergic basal forebrain neurons, that the correlation of ionic conductance amplitudes between different ionic currents also exists in vertebrates, and we argue that it is a ubiquitous phenomenon expressed by many species across phyla. We further demonstrate that in dentate gyrus GCs these conductance correlations are likely regulated in a circadian manner. This is reminiscent of the known conductance regulation by neuromodulators in crustaceans. However, in GCs we observe a more nuanced regulation, where for some conductance pairs the correlations are completely eliminated while for others the correlation is quantitatively modified but not obliterated.

A balance of outward and linear inward ionic currents is required for generation of slow-wave oscillations.

Regenerative inward currents help produce slow oscillations through a negative-slope conductance region of their current-voltage relationship that is well approximated by a linear negative conductance. We used dynamic-clamp injections of a linear current with such conductance, INL, to explore why some neurons can generate intrinsic slow oscillations whereas others cannot. We addressed this question in synaptically isolated neurons of the crab Cancer borealis after blocking action potentials. The pyloric network consists of a distinct pacemaker and follower neurons, all of which express the same complement of ionic currents. When the pyloric dilator (PD) neuron, a member of the pacemaker group, was injected with INL with dynamic clamp, it consistently produced slow oscillations. In contrast, all follower neurons failed to oscillate with INL To understand these distinct behaviors, we compared outward current levels of PD with those of follower lateral pyloric (LP) and ventral pyloric (VD) neurons. We found that LP and VD neurons had significantly larger high-threshold potassium currents (IHTK) than PD and LP had lower-transient potassium current (IA). Reducing IHTK pharmacologically enabled both LP and VD neurons to produce INL-induced oscillations, whereas modifying IA levels did not affect INL-induced oscillations. Using phase-plane and bifurcation analysis of a simplified model cell, we demonstrate that large levels of IHTK can block INL-induced oscillatory activity whereas generation of oscillations is almost independent of IA levels. These results demonstrate the general importance of a balance between inward pacemaking currents and high-threshold K+ current levels in determining slow oscillatory activity.NEW & NOTEWORTHY Pacemaker neuron-generated rhythmic activity requires the activation of at least one inward and one outward current. We have previously shown that the inward current can be a linear current (with negative conductance). Using this simple mechanism, here we demonstrate that the inward current conductance must be in relative balance with the outward current conductances to generate oscillatory activity. Surprisingly, an excess of outward conductances completely precludes the possibility of achieving such a balance.

Activation mechanism of a neuromodulator-gated pacemaker ionic current.

The neuromodulator-gated current (IMI) found in the crab stomatogastric ganglion is activated by neuromodulators that are essential to induce the rhythmic activity of the pyloric network in this system. One of these neuromodulators is also known to control the correlated expression of voltage-gated ionic currents in pyloric neurons, as well as synaptic plasticity and strength. Thus understanding the mechanism by which neuromodulator receptors activate IMI should provide insights not only into how oscillations are initiated but also into how other processes, and currents not directly activated by them, are regulated. To determine what specific signaling molecules are implicated in this process, we used a battery of agonists and antagonists of common signal transduction pathways. We found that the G protein inhibitor GDPßS and the G protein activator GTPγS significantly affect IMI amplitude, suggesting that its activation is mediated by G proteins. Interestingly, when using the more specific G protein blocker pertussis toxin, we observed the expected inhibition of IMI amplitude but, unexpectedly, in a calcium-dependent fashion. We also found that antagonists of calcium- and calmodulin-associated signaling significantly reduce IMI amplitude. In contrast, we found little evidence for the role of cyclic nucleotide signaling, phospholipase C (PLC), or kinases and phosphatases, except two calmodulin-dependent kinases. In sum, these results suggest that proctolin-induced IMI is mediated by a G protein whose pertussis toxin sensitivity is altered by external calcium concentration and appears to depend on intracellular calcium, calmodulin, and calmodulin-activated kinases. In contrast, we found no support for IMI being mediated by PLC signaling or cyclic nucleotides.NEW & NOTEWORTHY Neuronal rhythmic activity is generated by either network-based or cell-autonomous mechanisms. In the pyloric network of decapod crustaceans, the activation of a neuromodulator-gated pacemaker current is crucial for the generation of rhythmic activity. This current is activated by several neuromodulators, including peptides and acetylcholine, presumably via metabotropic receptors. We have previously demonstrated a novel extracellular calcium-sensitive voltage-dependence mechanism of this current. We presently report that the activation mechanism depends on intracellular and extracellular calcium-sensitive components.

Dynamic compensation mechanism gives rise to period and duty-cycle level sets in oscillatory neuronal models.

Rhythmic oscillation in neurons can be characterized by various attributes, such as the oscillation period and duty cycle. The values of these features depend on the amplitudes of the participating ionic currents, which can be characterized by their maximum conductance values. Recent experimental and theoretical work has shown that the values of these attributes can be maintained constant for different combinations of two or more ionic currents of varying conductances, defining what is known as level sets in conductance space. In two-dimensional conductance spaces, a level set is a curve, often a line, along which a particular oscillation attribute value is conserved. In this work, we use modeling, dynamical systems tools (phase-space analysis), and numerical simulations to investigate the possible dynamic mechanisms responsible for the generation of period and duty-cycle levels sets in simplified (linearized and FitzHugh-Nagumo) and conductance-based (Morris-Lecar) models of neuronal oscillations. A simplistic hypothesis would be that the tonic balance between ionic currents with the same or opposite effective signs is sufficient to create level sets. According to this hypothesis, the dynamics of each ionic current during a given cycle are well captured by some constant quantity (e.g., maximal conductances), and the phase-plane diagrams are identical or are almost identical (e.g., cubic-like nullclines with the same maxima and minima) for different combinations of these maximal conductances. In contrast, we show that these mechanisms are dynamic and involve the complex interaction between the nonlinear voltage dependencies and the effective time scales at which the ionic current's dynamical variables operate.

Voltage Dependence of a Neuromodulator-Activated Ionic Current.

The neuromodulatory inward current (IMI) generated by crab Cancer borealis stomatogastric ganglion neurons is an inward current whose voltage dependence has been shown to be crucial in the activation of oscillatory activity of the pyloric network of this system. It has been previously shown that IMI loses its voltage dependence in conditions of low extracellular calcium, but that this effect appears to be regulated by intracellular calmodulin. Voltage dependence is only rarely regulated by intracellular signaling mechanisms. Here we address the hypothesis that the voltage dependence of IMI is mediated by intracellular signaling pathways activated by extracellular calcium. We demonstrate that calmodulin inhibitors and a ryanodine antagonist can reduce IMI voltage dependence in normal Ca(2+), but that, in conditions of low Ca(2+), calmodulin activators do not restore IMI voltage dependence. Further, we show evidence that CaMKII alters IMI voltage dependence. These results suggest that calmodulin is necessary but not sufficient for IMI voltage dependence. We therefore hypothesize that the Ca(2+)/calmodulin requirement for IMI voltage dependence is due to an active sensing of extracellular calcium by a GPCR family calcium-sensing receptor (CaSR) and that the reduction in IMI voltage dependence by a calmodulin inhibitor is due to CaSR endocytosis. Supporting this, preincubation with an endocytosis inhibitor prevented W7 (N-(6-aminohexyl)-5-chloro-1-naphthalenesulfonamide hydrochloride)-induced loss of IMI voltage dependence, and a CaSR antagonist reduced IMI voltage dependence. Additionally, myosin light chain kinase, which is known to act downstream of the CaSR, seems to play a role in regulating IMI voltage dependence. Finally, a Gßγ-subunit inhibitor also affects IMI voltage dependence, in support of the hypothesis that this process is regulated by a G-protein-coupled CaSR.

The role of linear and voltage-dependent ionic currents in the generation of slow wave oscillations.

Neuronal oscillatory activity is generated by a combination of ionic currents, including at least one inward regenerative current that brings the cell towards depolarized voltages and one outward current that repolarizes the cell. Such currents have traditionally been assumed to require voltage-dependence. Here we test the hypothesis that the voltage dependence of the regenerative inward current is not necessary for generating oscillations. Instead, a current I NL that is linear in the biological voltage range and has negative conductance is sufficient to produce regenerative activity. The current I NL can be considered a linear approximation to the negative-conductance region of the current-voltage relationship of a regenerative inward current. Using a simple conductance-based model, we show that I NL , in conjunction with a voltage-gated, non-inactivating outward current, can generate oscillatory activity. We use phase-plane and bifurcation analyses to uncover a rich variety of behaviors as the conductance of I NL is varied, and show that oscillations emerge as a result of destabilization of the resting state of the model neuron. The model shows the need for well-defined relationships between the inward and outward current conductances, as well as their reversal potentials, in order to produce stable oscillatory activity. Our analysis predicts that a hyperpolarization-activated inward current can play a role in stabilizing oscillatory activity by preventing swings to very negative voltages, which is consistent with what is recorded in biological neurons in general. We confirm this prediction of the model experimentally in neurons from the crab stomatogastric ganglion.

Ionic Current Variability and Functional Stability in the Nervous System.

Identified neurons in different animals express ionic currents at highly variable levels (population variability). If neuronal identity is associated with stereotypical function, as is the case in genetically identical neurons or in unambiguously identified individual neurons, this variability poses a conundrum: How is activity the same if the components that generate it-ionic current levels-are different? In some cases, ionic current variability across similar neurons generates an output gradient. However, many neurons produce very similar output activity, despite substantial variability in ionic conductances. It appears that, in many such cells, conductance levels of one ionic current vary in proportion to the conductance levels of another current. As a result, in a population of neurons, these conductances appear to be correlated. Here, I review theoretical and experimental work that suggests that neuronal ionic current correlation can reduce the global ionic current variability and can contribute to functional stability.

Ionic current correlations underlie the global tuning of large numbers of neuronal activity attributes.

Ionic conductances in identified neurons are highly variable. This poses the crucial question of how such neurons can produce stable activity. Coexpression of ionic currents has been observed in an increasing number of neurons in different systems, suggesting that the coregulation of ionic channel expression, by thus linking their variability, may enable neurons to maintain relatively constant neuronal activity as suggested by a number of recent theoretical studies. We examine this hypothesis experimentally using the voltage- and dynamic-clamp techniques to first measure and then modify the ionic conductance levels of three currents in identified neurons of the crab pyloric network. We quantify activity by measuring 10 different attributes (oscillation period, spiking frequency, etc.), and find linear, positive and negative relationships between conductance pairs and triplets that can enable pyloric neurons to maintain activity attributes invariant. Consistent with experimental observations, some of the features most tightly regulated appear to be phase relationships of bursting activity. We conclude that covariation (and probably a tightly controlled coregulation) of ionic conductances can help neurons maintain certain attributes of neuronal activity invariant while at the same time allowing conductances to change over wide ranges in response to internal or environmental inputs and perturbations. Our results also show that neurons can tune neuronal activity globally via coordinate expression of ion currents.

Adult mouse basal forebrain harbors two distinct cholinergic populations defined by their electrophysiology.

We performed whole-cell recordings from basal forebrain (BF) cholinergic neurons in transgenic mice expressing enhanced green fluorescent protein (eGFP) under the control of the choline acetyltransferase promoter. BF cholinergic neurons can be differentiated into two electrophysiologically identifiable subtypes: early and late firing neurons. Early firing neurons (∼70%) are more excitable, show prominent spike frequency adaptation and are more susceptible to depolarization blockade, a phenomenon characterized by complete silencing of the neuron following initial action potentials. Late firing neurons (∼30%), albeit being less excitable, could maintain a tonic discharge at low frequencies. In voltage clamp analysis, we have shown that early firing neurons have a higher density of low voltage activated (LVA) calcium currents. These two cholinergic cell populations might be involved in distinct functions: the early firing group being more suitable for phasic changes in cortical acetylcholine release associated with attention while the late firing neurons could support general arousal by maintaining tonic acetylcholine levels.

Neuromodulation independently determines correlated channel expression and conductance levels in motor neurons of the stomatogastric ganglion.

Neuronal identity depends on the regulated expression of numerous molecular components, especially ionic channels, which determine the electrical signature of a neuron. Such regulation depends on at least two key factors, activity itself and neuromodulatory input. Neuronal electrical activity can modify the expression of ionic currents in homeostatic or nonhomeostatic fashion. Neuromodulators typically modify activity by regulating the properties or expression levels of subsets of ionic channels. In the stomatogastric system of crustaceans, both types of regulation have been demonstrated. Furthermore, the regulation of the coordinated expression of ionic currents and the channels that carry these currents has been recently reported in diverse neuronal systems, with neuromodulators not only controlling the absolute levels of ionic current expression but also, over long periods of time, appearing to modify their correlated expression. We hypothesize that neuromodulators may regulate the correlated expression of ion channels at multiple levels and in a cell-type-dependent fashion. We report that in two identified neuronal types, three ionic currents are linearly correlated in a pairwise manner, suggesting their coexpression or direct interactions, under normal neuromodulatory conditions. In each cell, some currents remain correlated after neuromodulatory input is removed, whereas the correlations between the other pairs are either lost or altered. Interestingly, in each cell, a different suite of currents change their correlation. At the transcript level we observe distinct alterations in correlations between channel mRNA amounts, including one of the cell types lacking a correlation under normal neuromodulatory conditions and then gaining the correlation when neuromodulators are removed. Synaptic activity does not appear to contribute, with one possible exception, to the correlated expression of either ionic currents or of the transcripts that code for the respective channels. We conclude that neuromodulators regulate the correlated expression of ion channels at both the transcript and the protein levels.

Recovery of rhythmic activity in a central pattern generator: analysis of the role of neuromodulator and activity-dependent mechanisms.

The pyloric network of decapods crustaceans can undergo dramatic rhythmic activity changes. Under normal conditions the network generates low frequency rhythmic activity that depends obligatorily on the presence of neuromodulatory input from the central nervous system. When this input is removed (decentralization) the rhythmic activity ceases. In the continued absence of this input, periodic activity resumes after a few hours in the form of episodic bursting across the entire network that later turns into stable rhythmic activity that is nearly indistinguishable from control (recovery). It has been proposed that an activity-dependent modification of ionic conductance levels in the pyloric pacemaker neuron drives the process of recovery of activity. Previous modeling attempts have captured some aspects of the temporal changes observed experimentally, but key features could not be reproduced. Here we examined a model in which slow activity-dependent regulation of ionic conductances and slower neuromodulator-dependent regulation of intracellular Ca(2+) concentration reproduce all the temporal features of this recovery. Key aspects of these two regulatory mechanisms are their independence and their different kinetics. We also examined the role of variability (noise) in the activity-dependent regulation pathway and observe that it can help to reduce unrealistic constraints that were otherwise required on the neuromodulator-dependent pathway. We conclude that small variations in intracellular Ca(2+) concentration, a Ca(2+) uptake regulation mechanism that is directly targeted by neuromodulator-activated signaling pathways, and variability in the Ca(2+) concentration sensing signaling pathway can account for the observed changes in neuronal activity. Our conclusions are all amenable to experimental analysis.

Pacemaker neuron and network oscillations depend on a neuromodulator-regulated linear current.

Linear leak currents have been implicated in the regulation of neuronal excitability, generation of neuronal and network oscillations, and network state transitions. Yet, few studies have directly tested the dependence of network oscillations on leak currents or explored the role of leak currents on network activity. In the oscillatory pyloric network of decapod crustaceans neuromodulatory inputs are necessary for pacemaker activity. A large subset of neuromodulators is known to activate a single voltage-gated inward current I(MI), which has been shown to regulate the rhythmic activity of the network and its pacemaker neurons. Using the dynamic clamp technique, we show that the crucial component of I(MI) for the generation of oscillatory activity is only a close-to-linear portion of the current-voltage relationship. The nature of this conductance is such that the presence or the absence of neuromodulators effectively regulates the amount of leak current and the input resistance in the pacemaker neurons. When deprived of neuromodulatory inputs, pyloric oscillations are disrupted; yet, a linear reduction of the total conductance in a single neuron within the pacemaker group recovers not only the pacemaker activity in that neuron, but also leads to a recovery of oscillations in the entire pyloric network. The recovered activity produces proper frequency and phasing that is similar to that induced by neuromodulators. These results show that the passive properties of pacemaker neurons can significantly affect their capacity to generate and regulate the oscillatory activity of an entire network, and that this feature is exploited by neuromodulatory inputs.

Membrane capacitance measurements revisited: dependence of capacitance value on measurement method in nonisopotential neurons.

During growth or degeneration neuronal surface area can change dramatically. Measurements of membrane protein concentration, as in ion channel or ionic conductance density, are often normalized by membrane capacitance, which is proportional to the surface area, to express changes independently from cell surface variations. Several electrophysiological protocols are used to measure cell capacitance, all based on the assumption of membrane isopotentiality. Yet, most neurons violate this assumption because of their complex anatomical structure, raising the question of which protocol yields measurements that are closest to the actual total membrane capacitance. We measured the capacitance of identified neurons from crab stomatogastric ganglia using three different protocols: the current-clamp step, the voltage-clamp step, and the voltage-clamp ramp protocols. We observed that the current-clamp protocol produced significantly higher capacitance values than those of either voltage-clamp protocol. Computational models of various anatomical complexities suggest that the current-clamp protocol can yield accurate capacitance estimates. In contrast, the voltage-clamp protocol estimates rapidly deteriorate as isopotentiality is reduced. We provide a mathematical description of these results by analyzing a simple two-compartment model neuron to facilitate an intuitive understanding of these methods. Together, the experiments, modeling, and mathematical analysis indicate that accurate total membrane capacitance measurements cannot be obtained with voltage-clamp protocols in nonisopotential neurons. Furthermore, although current-clamp steps can theoretically yield accurate measurements, experimentalists should be aware of limitations imposed by step duration and numerical errors during fitting procedures to obtain the membrane time constant.

Activity and neuromodulatory input contribute to the recovery of rhythmic output after decentralization in a central pattern generator.

Central pattern generators (CPGs) are neuronal networks that control vitally important rhythmic behaviors including breathing, heartbeat, and digestion. Understanding how CPGs recover activity after their rhythmic activity is disrupted has important theoretical and practical implications. Previous experimental and modeling studies indicated that rhythm recovery after central neuromodulatory input loss (decentralization) could be based entirely on activity-dependent mechanisms, but recent evidence of long-term conductance regulation by neuromodulators suggest that neuromodulator-dependent mechanisms may also be involved. Here we examined the effects of altering activity and the neuromodulatory environment before decentralization of the pyloric CPG in Cancer borealis on the initial phase of rhythmic activity recovery after decentralization. We found that pretreatments altering the network activity through shifting the ionic balance or the membrane potential of pyloric pacemaker neurons reduced the delay of recovery initiation after decentralization, consistent with the recovery process being triggered already during the pretreatment period through an activity-dependent mechanism. However, we observed that pretreatment with neuromodulators GABA and proctolin, acting via metabotropic receptors, also affected the initial phase of the recovery of pyloric activity after decentralization. Their distinct effects appear to result from interactions of their metabotropic effects with their effects on neuronal activity. Thus we show that the initial phase of the recovery process can be accounted for by the existence of distinct activity-and neuromodulator-dependent pathways. We propose a computational model that includes activity- and neuromodulator-dependent mechanisms of the activity recovery process, which successfully explains the experimental observations and predicts the results of key biological experiments.

Sustained rhythmic activity in gap-junctionally coupled networks of model neurons depends on the diameter of coupled dendrites.

Gap junctions are known to be important for many network functions such as synchronization of activity and the generation of waves and oscillations. Gap junctions have also been proposed to be essential for the generation of early embryonic activity. We have previously shown that the amplitude of electrical signals propagating across gap-junctionally coupled passive cables is maximized at a unique diameter. This suggests that threshold-dependent signals may propagate through gap junctions for a finite range of diameters around this optimal value. Here we examine the diameter dependence of action potential propagation across model networks of dendro-dendritically coupled neurons. The neurons in these models have passive soma and dendrites and an action potential-generating axon. We show that propagation of action potentials across gap junctions occurs only over a finite range of dendritic diameters and that propagation delay depends on this diameter. Additionally, in networks of gap-junctionally coupled neurons, rhythmic activity can emerge when closed loops (re-entrant paths) occur but again only for a finite range of dendrite diameters. The frequency of such rhythmic activity depends on the length of the path and the dendrite diameter. For large networks of randomly coupled neurons, we find that the re-entrant paths that underlie rhythmic activity also depend on dendrite diameter. These results underline the potential importance of dendrite diameter as a determinant of network activity in gap-junctionally coupled networks, such as network rhythms that are observed during early nervous system development.