Interactions of persistent sodium and calcium-activated nonspecific cationic currents yield dynamically distinct bursting regimes in a model of respiratory neurons

The preBötzinger complex (preBötC) is a heterogeneous neuronal network within the mammalian brainstem that has been experimentally found to generate robust, synchronous bursts that drive the inspiratory phase of the respiratory rhythm. The persistent sodium (NaP) current is observed in every preBötC neuron, and significant modeling effort has characterized its contribution to square-wave bursting in the preBötC. Recent experimental work demonstrated that neurons within the preBötC are endowed with a calcium-activated nonspecific cationic (CAN) current that is activated by a signaling cascade initiated by glutamate. In a preBötC model, the CAN current was shown to promote robust bursts that experience depolarization block (DB bursts). We consider a self-coupled model neuron, which we represent as a single compartment based on our experimental finding of electrotonic compactness, under variation of g _NaP, the conductance of the NaP current, and g _CAN, the conductance of the CAN current. Varying these two conductances yields a spectrum of activity patterns, including quiescence, tonic activity, square-wave bursting, DB bursting, and a novel mixture of square-wave and DB bursts, which match well with activity that we observe in experimental preparations. We elucidate the mechanisms underlying these dynamics, as well as the transitions between these regimes and the occurrence of bistability, by applying the mathematical tools of bifurcation analysis and slow-fast decomposition. Based on the prevalence of NaP and CAN currents, we expect that the generalizable framework for modeling their interactions that we present may be relevant to the rhythmicity of other brain areas beyond the preBötC as well.     

Cooperation of intrinsic bursting and calcium oscillations underlying activity patterns of model pre-Bötzinger complex neurons

Activity of neurons in the pre-Bötzinger complex (pre-BötC) within the mammalian brainstem drives the inspiratory phase of the respiratory rhythm. Experimental results have suggested that multiple bursting mechanisms based on a calcium-activated nonspecific cationic (CAN) current, a persistent sodium (NaP) current, and calcium dynamics may be incorporated within the pre-BötC. Previous modeling works have incorporated representations of some or all of these mechanisms. In this study, we consider a single-compartment model of a pre-BötC inspiratory neuron that encompasses particular aspects of all of these features. We present a novel mathematical analysis of the interaction of the corresponding rhythmic mechanisms arising in the model, including square-wave bursting and autonomous calcium oscillations, which requires treatment of a system of differential equations incorporating three slow variables.     

Multiple timescale mixed bursting dynamics in a respiratory neuron model

Experimental results in rodent medullary slices containing the pre-Bötzinger complex (pre-BötC) have identified multiple bursting mechanisms based on persistent sodium current (I _NaP) and intracellular Ca²⁺. The classic two-timescale approach to the analysis of pre-BötC bursting treats the inactivation of I _NaP, the calcium concentration, as well as the Ca²⁺-dependent inactivation of IP ₃ as slow variables and considers other evolving quantities as fast variables. Based on its time course, however, it appears that a novel mixed bursting (MB) solution, observed both in recordings and in model pre-BötC neurons, involves at least three timescales. In this work, we consider a single-compartment model of a pre-BötC inspiratory neuron that can exhibit both I _NaP and Ca²⁺ oscillations and has the ability to produce MB solutions. We use methods of dynamical systems theory, such as phase plane analysis, fast-slow decomposition, and bifurcation analysis, to better understand the mechanisms underlying the MB solution pattern. Rather surprisingly, we discover that a third timescale is not actually required to generate mixed bursting solutions. Through our analysis of timescales, we also elucidate how the pre-BötC neuron model can be tuned to improve the robustness of the MB solution.     

Respiratory pattern generator model using Ca++-induced Ca++ release in neurons shows both pacemaker and reciprocal network properties

There are two contradictory explanations for central respiratory rhythmogenesis. One suggests that respiratory rhythm emerges from interaction between inspiratory and expiratory neural semicenters that inhibit each other and thereby provide reciprocal rhythmic activity (Brown 1914). The other uses bursting pacemaker activity of individual neurons to produce the rhythm (Feldman and Cleland 1982). Hybrid models have been developed to reconcile these two seemingly conflicting mechanisms (Smith et al. 2000; Rybak et al. 2001). Here we report computer simulations that demonstrate a unified mechanism of the two types of oscillator. In the model, we use the interaction of Ca⁺⁺-dependent K⁺ channels (Mifflin et al. 1985) with Ca⁺⁺-induced Ca⁺⁺ release from intracellular stores (McPherson and Campbell 1993), which was recently revealed in neurons (Hernandez-Cruz et al. 1997; Mitra and Slaughter 2002a,b; Scornik et al. 2001). Our computations demonstrate that uncoupled neurons with these intracellular mechanisms show conditional pacemaker properties (Butera et al. 1999) when exposed to steady excitatory inputs. Adding weak inhibitory synapses (based on increased K⁺ conductivity) between two model neural pools surprisingly synchronizes the activity of both neural pools. As inhibitory synaptic connections between the two pools increase from zero to higher values, the model produces first dissociated pacemaker activity of individual neurons, then periodic synchronous bursts of all neurons (inspiratory and expiratory), and finally reciprocal rhythmic activity of the neural pools.     

Dual oscillator model of the respiratory neuronal network generating quantal slowing of respiratory rhythm

We developed a dual oscillator model to facilitate the understanding of dynamic interactions between the parafacial respiratory group (pFRG) and the preBötzinger complex (preBötC) neurons in the respiratory rhythm generation. Both neuronal groups were modeled as groups of 81 interconnected pacemaker neurons; the bursting cell model described by Butera and others [model 1 in Butera et al. (J Neurophysiol 81:382–397, 1999a)] were used to model the pacemaker neurons. We assumed (1) both pFRG and preBötC networks are rhythm generators, (2) preBötC receives excitatory inputs from pFRG, and pFRG receives inhibitory inputs from preBötC, and (3) persistent Na⁺ current conductance and synaptic current conductances are randomly distributed within each population. Our model could reproduce 1:1 coupling of bursting rhythms between pFRG and preBötC with the characteristic biphasic firing pattern of pFRG neurons, i.e., firings during pre-inspiratory and post-inspiratory phases. Compatible with experimental results, the model predicted the changes in firing pattern of pFRG neurons from biphasic expiratory to monophasic inspiratory, synchronous with preBötC neurons. Quantal slowing, a phenomena of prolonged respiratory period that jumps non-deterministically to integer multiples of the control period, was observed when the excitability of preBötC network decreased while strengths of synaptic connections between the two groups remained unchanged, suggesting that, in contrast to the earlier suggestions (Mellen et al., Neuron 37:821–826, 2003; Wittmeier et al., Proc Natl Acad Sci USA 105(46):18000–18005, 2008), quantal slowing could occur without suppressed or stochastic excitatory synaptic transmission. With a reduced excitability of preBötC network, the breakdown of synchronous bursting of preBötC neurons was predicted by simulation. We suggest that quantal slowing could result from a breakdown of synchronized bursting within the preBötC.     

Intrinsic bursting activity in the pre-Bötzinger Complex: Role of persistent sodium and potassium currents

Computational models of single pacemaker neuron and neural population in the pre-Bötzinger Complex (pBC) were developed based on the previous models by Butera et al. (1999a,b). Our modeling study focused on the conditions that could define endogenous bursting vs. tonic activity in single pacemaker neurons and population bursting vs. asynchronous firing in populations of pacemaker neurons. We show that both bursting activity in single pacemaker neurons and population bursting activity may be released or suppressed depending on the expression of persistent sodium (I_NaP) and delayed-rectifier potassium (I_K) currents. Specifically, a transition from asynchronous firing to population bursting could be induced by a reduction of I_K via a direct suppression of the potassium conductance or through an elevation of extracellular potassium concentration. Similar population bursting activity could be triggered by an augmentation of I_NaP. These findings are discussed in the context of the possible role of population bursting activity in the pBC in the respiratory rhythm generation in vivo vs. in vitro and during normal breathing in vivo vs. gasping.     

The role of spiking and bursting pacemakers in the neuronal control of breathing

Breathing is controlled by a distributed network involving areas in the neocortex, cerebellum, pons, medulla, spinal cord, and various other subcortical regions. However, only one area seems to be essential and sufficient for generating the respiratory rhythm: the preBötzinger complex (preBötC). Lesioning this area abolishes breathing and following isolation in a brain slice the preBötC continues to generate different forms of respiratory activities. The use of slice preparations led to a thorough understanding of the cellular mechanisms that underlie the generation of inspiratory activity within this network. Two types of inward currents, the persistent sodium current (I_NaP) and the calcium-activated non-specific cation current (I_CAN), play important roles in respiratory rhythm generation. These currents give rise to autonomous pacemaker activity within respiratory neurons, leading to the generation of intrinsic spiking and bursting activity. These membrane properties amplify as well as activate synaptic mechanisms that are critical for the initiation and maintenance of inspiratory activity. In this review, we describe the dynamic interplay between synaptic and intrinsic membrane properties in the generation of the respiratory rhythm and we relate these mechanisms to rhythm generating networks involved in other behaviors.     

A hemicord locomotor network of excitatory interneurons: a simulation study

Locomotor burst generation is simulated using a full-scale network model of the unilateral excitatory interneuronal population. Earlier small-scale models predicted that a population of excitatory neurons would be sufficient to produce burst activity, and this has recently been experimentally confirmed. Here we simulate the hemicord activity induced under various experimental conditions, including pharmacological activation by NMDA and AMPA as well as electrical stimulation. The model network comprises a realistic number of cells and synaptic connectivity patterns. Using similar distributions of cellular and synaptic parameters, as have been estimated experimentally, a large variation in dynamic characteristics like firing rates, burst, and cycle durations were seen in single cells. On the network level an overall rhythm was generated because the synaptic interactions cause partial synchronization within the population. This network rhythm not only emerged despite the distributed cellular parameters but relied on this variability, in particular, in reproducing variations of the activity during the cycle and showing recruitment in interneuronal populations. A slow rhythm (0.4–2 Hz) can be induced by tonic activation of NMDA-sensitive channels, which are voltage dependent and generate depolarizing plateaus. The rhythm emerges through a synchronization of bursts of the individual neurons. A fast rhythm (4–12 Hz), induced by AMPA, relies on spike synchronization within the population, and each burst is composed of single spikes produced by different neurons. The dynamic range of the fast rhythm is limited by the ability of the network to synchronize oscillations and depends on the strength of synaptic connections and the duration of the slow after hyperpolarization. The model network also produces prolonged bouts of rhythmic activity in response to brief electrical activations, as seen experimentally. The mutual excitation can sustain long-lasting activity for a realistic set of synaptic parameters. The bout duration depends on the strength of excitatory synaptic connections, the level of persistent depolarization, and the influx of Ca²⁺ ions and activation of Ca²⁺-dependent K⁺ current.     

Effects of transition metal ions on spontaneous electrical activity and chemical synaptic transmission of neurons in the medicinal leech

Leech neurons exposed to salines containing inorganic Ca²⁺-channel blockers generate rhythmic bursts of impulses. According to an earlier model, these blockers unmask persistent Na⁺ currents that generate plateau-like depolarizations, each triggering a burst of impulses. The resulting increase in intracellular Na⁺ activates an outward Na⁺/K⁺ pump current that contributes to burst termination. We tested this model by examining systematically the effects of six transition metal ions (Co²⁺, Ni²⁺, Mn²⁺, Cd²⁺, La³⁺, and Zn²⁺) on the electrical activity of neurons in isolated leech ganglia. Each ion induced bursting activity, but the amplitude, form, and persistence of bursting differed with the ion used and its concentration relative to Ca²⁺. All ions tested suppressed chemical synaptic transmission between identified motor neurons, consistent with block of voltage-dependent Ca²⁺ currents in these cells. In addition, a strong correlation between suppression of synaptic transmission and burst amplitudes was obtained. Finally, burst duration was increased and the rate of repolarization decreased in reduced K⁺ saline, as expected for pump-dependent repolarization. These results provide further support for the hypothesis that a novel form of oscillatory electrical activity driven by persistent Na⁺ currents and the Na⁺/K⁺ pump occurs in leech ganglia exposed to Ca²⁺-channel blockers. Accepted: 15 May 1997     

Respiratory rhythm: an emergent network property?

We tested the hypothesis that pacemaker neurons generate breathing rhythm in mammals. We monitored respiratory-related motor nerve rhythm in neonatal rodent slice preparations. Blockade of the persistent sodium current (I(NaP)), which was postulated to underlie voltage-dependent bursting in respiratory pacemaker neurons, with riluzole (< or =200 microM) did not alter the frequency of respiratory-related motor output. Yet, in every pacemaker neuron recorded (50/50), bursting was abolished at much lower concentrations of riluzole (< or =20 microM). Thus, eliminating the pacemaker population (our statistics confirm that this population is reduced at least 94%, p < 0.05) does not affect respiratory rhythm. These results suggest that voltage-dependent bursting in pacemaker neurons is not essential for respiratory rhythmogenesis, which may instead be an emergent network property.     

A mathematical model of adult GnRH neurons in mouse brain and its bifurcation analysis

GnRH neurons are hypothalamic neurons that secrete gonadotropin-releasing hormone (GnRH) which stimulates the release of gonadotropins, one of the crucial hormones for sexual development, fertility and maturation. A mathematical model was built to help elucidate the mechanisms underlying electrical bursting and synchronous [Ca²⁺] transients in GnRH neurons (Lee et al., 2010). The model predicted that bursting in GnRH neurons (at least of the short-bursting type) requires the existence of a [Ca²⁺]-dependent slow after-hyperpolarisation current (sI_AHP-UCL), and this predicted current was found experimentally. GnRH behaviour under a wide range of conditions (inhibition of Na⁺ channels, IP₃ receptors, [Ca²⁺]-dependent K⁺ channels, or Ca²⁺ pumps, or in the presence of zero extracellular [Ca²⁺]) is successfully reproduced by the model. In this paper, a simplified version of the previous model, with the same qualitative behaviour, is constructed and studied using timescale separation techniques and bifurcation analysis.     

A unified model for two modes of bursting in GnRH neurons

Gonadotropin-releasing hormone (GnRH) neurons exhibit at least two intrinsic modes of action potential burst firing, referred to as parabolic and irregular bursting. Parabolic bursting is characterized by a slow wave in membrane potential that can underlie periodic clusters of action potentials with increased interspike interval at the beginning and at the end of each cluster. Irregular bursting is characterized by clusters of action potentials that are separated by varying durations of interburst intervals and a relatively stable baseline potential. Based on recent studies of isolated ionic currents, a stochastic Hodgkin-Huxley (HH)-like model for the GnRH neuron is developed to reproduce each mode of burst firing with an appropriate set of conductances. Model outcomes for bursting are in agreement with the experimental recordings in terms of interburst interval, interspike interval, active phase duration, and other quantitative properties specific to each mode of bursting. The model also shows similar outcomes in membrane potential to those seen experimentally when tetrodotoxin (TTX) is used to block action potentials during bursting, and when estradiol transitions cells exhibiting slow oscillations to irregular bursting mode in vitro. Based on the parameter values used to reproduce each mode of bursting, the model suggests that GnRH neurons can switch between the two through changes in the maximum conductance of certain ionic currents, notably the slow inward Ca²⁺ current I _s, and the Ca²⁺ -activated K⁺ current I _KCa. Bifurcation analysis of the model shows that both modes of bursting are similar from a dynamical systems perspective despite differences in burst characteristics.     

Ionic mechanisms underlying spontaneous CA1 neuronal firing in Ca2+-free solution

Hippocampal CA1 neurons exposed to zero-[Ca(2+)] solutions can generate periodic spontaneous synchronized activity in the absence of synaptic function. Experiments using hippocampal slices showed that, after exposure to zero-[Ca(2+)](0) solution, CA1 pyramidal cells depolarized 5-10 mV and started firing spontaneous action potentials. Spontaneous single neuron activity appeared in singlets or was grouped into bursts of two or three action potentials. A 16-compartment, 23-variable cable model of a CA1 pyramidal neuron was developed to study mechanisms of spontaneous neuronal bursting in a calcium-free extracellular solution. In the model, five active currents (a fast sodium current, a persistent sodium current, an A-type transient potassium current, a delayed rectifier potassium current, and a muscarinic potassium current) are included in the somatic compartment. The model simulates the spontaneous bursting behavior of neurons in calcium-free solutions. The mechanisms underlying several aspects of bursting are studied, including the generation of triplet bursts, spike duration, burst termination, after-depolarization behavior, and the prolonged inactive period between bursts. We show that the small persistent sodium current can play a key role in spontaneous CA1 activity in zero-calcium solutions. In particular, it is necessary for the generation of an after-depolarizing potential and prolongs both individual bursts and the interburst interval.     

Intrinsic and network rhythmogenesis in a reduced traub model for CA3 neurons

We have developed a two-compartment, eight-variable model of a CA3 pyramidal cell as a reduction of a complex 19-compartment cable model [Traub et al, 1991]. Our reduced model segregates the fast currents for sodium spiking into a proximal, soma-like, compartment and the slower calcium and calcium-mediated currents into a dendrite-like compartment. In each model periodic bursting gives way to repetitive soma spiking as somatic injected current increases. Steady dendritic stimulation can produce periodic bursting of significantly higher frequency (8–20 Hz) than can steady somatic input (<8 Hz). Bursting in our model occurs only for an intermediate range of electronic coupling conductance. It depends on the segregation of channel types and on the coupling current that flows back-and-forth between compartments. When the soma and dendrite are tightly coupled electrically, our model reduces to a single compartment and does not burst. Network simulations with our model using excitatory AMPA and NMDA synapses (without inhibition) give results similar to those obtained with the complex cable model [Traub et al, 1991; Traub et al, 1992]. Brief stimulation of a single cell in a resting network produces multiple synchronized population bursts, with fast AMPA synapses providing the dominant synchronizing mechanism. The number of bursts increases with the level of maximal NMDA conductance. For high enough maximal NMDA conductance synchronized bursting repeats indefinitely. We find that two factors can cause the cells to desynchronize when AMPA synapses are blocked: heterogeneity of properties amongst cells and intrinsically chaotic burst dynamics. But even when cells are identical, they may synchronize only approximately rather than exactly. Since our model has a limited number of parameters and variables, we have studied its cellular and network dynamics computationally with relative ease and over wide parameter ranges. Thereby, we identify some qualitative features that parallel or are distinguished from those of other neuronal systems; e.g., we discuss how bursting here differs from that in some classical models.     

Firing pattern of bursting neurons under sinusoidal drive in mean-field modeling

Bursting has been observed in many sensory neurons, and is thought to be important in neural signaling, sleep, and some disorders of the brain. Bursting neurons have been studied via various types of conductance-based models at the single-neuron level. Important features of bursting have been reproduced by this type of model, but it is not certain how well the behavior of populations of bursting neurons can be represented solely by that of individual neurons. To study bursting neurons at the population level, a conductance-based model is incorporated into a mean-field model to yield a mean-field bursting model. The responses of the model to sinusoidal inputs are studied, showing that neurons with various different initial states are capable of phase-locked or intermittent firing, depending on their baseline voltage. Furthermore, depending on this voltage, the bursting frequency either slaves to the original unperturbed bursting frequency or approaches a steady value when the external driving frequency increases. Finally, use of white noise perturbations shows that the bursting frequency of the neurons remains the same even under a more general external stimulus.     

Reproducing bursting interspike interval statistics of the gustatory cortex

Cortical neurons in vivo generate highly irregular spike sequences. Recently, it was experimentally found that the local variation of interspike intervals, LV, is nearly constant for every spike sequence for the same neurons. On the contrary, the coefficient of variation, CV, varies over different spike sequences. Here, we first show that these characteristic features are also applicable in bursting spike sequences that are obtained from the rat gustatory cortex. Next, we show that the conventional leaky integrate-and-fire model does not fully account for reproducing these statistical features in data of real bursting spike sequences. We resolve this difficulty by proposing an alternative neuron model which is a reduction of the bursting neuron model involving the persistent sodium current. Our study implies that (1) the characteristic features of CV and LV are the results of the endogenous bursting and (2) the bursting behavior in the gustatory cortex is caused mainly by the persistent sodium current.     

Rhythmic activities of hypothalamic magnocellular neurons: Autocontrol mechanisms

Electrophysiological recordings in lactating rats show that oxytocin (OT) and vasopressin (AVP) neurons exhibit specific patterns of activities in relation to peripheral stimuli: periodic bursting firing for OT neurons during suckling, phasic firing for AVP neurons during hyperosmolarity (systemic injection of hypertonic saline). These activities are autocontrolled by OT and AVP released somato-dentritically within the hypothalamic magnocellular nuclei. In vivo, OT enhances the amplitude and frequency of bursts, an effect accompanied with an increase in basal firing rate. However, the characteristics of firing change as facilitation proceeds: the spike patterns become very irregular with clusters of spikes spaced by long silences; the firing rate is highly variable and clearly oscillates before facilitated bursts. This unstable behaviour dramatically decreases during intense tonic activation which temporarily interrupts bursting, and could therefore be a prerequisite for bursting. In vivo, the effects of AVP depend on the initial firing pattern of AVP neurons: AVP excites weakly active neurons (increasing duration of active periods and decreasing silences), inhibits highly active neurons, and does not affect neurons with intermediate phasic activity. AVP brings the entire population of AVP neurons to discharge with a medium phasic activity characterised by periods of firing and silence lasting 20–40 s, a pattern shown to optimise the release of AVP from the neurohypophysis. Each of the peptides (OT or AVP) induces an increase in intracellular Ca²⁺ concentration, specifically in the neurons containing either OT or AVP respectively. OT evokes the release of Ca²⁺ from IP3-sensitive intracellular stores. AVP induces an influx of Ca²⁺ through voltage-dependent Ca²⁺ channels of T-, L- and N-types. We postulate that the facilitatory autocontrol of OT and AVP neurons could be mediated by Ca²⁺ known to play a key role in the control of the patterns of phasic neurons.     

A multivariate population density model of the dLGN/PGN relay

Using a population density approach we study the dynamics of two interacting collections of integrate-and-fire-or-burst (IFB) neurons representing thalamocortical (TC) cells from the dorsal lateral geniculate nucleus (dLGN) and thalamic reticular (RE) cells from the perigeniculate nucleus (PGN). Each population of neurons is described by a multivariate probability density function that satisfies a conservation equation with appropriately defined probability fluxes and boundary conditions. The state variables of each neuron are the membrane potential and the inactivation gating variable of the low-threshold Ca²⁺ current I_T. The synaptic coupling of the populations and external excitatory drive are modeled by instantaneous jumps in the membrane potential of postsynaptic neurons. The population density model is validated by comparing its response to time-varying retinal input to Monte Carlo simulations of the corresponding IFB network composed of 100 to 1000 cells per population. In the absence of retinal input, the population density model exhibits rhythmic bursting similar to the 7 to 14 Hz oscillations associated with slow wave sleep that require feedback inhibition from RE to TC cells. When the TC and RE cell potassium leakage conductances are adjusted to represent cholingergic neuromodulation and arousal of the network, rhythmic bursting of the probability density model may either persists or be eliminated depending on the number of excitatory (TC to RE) or inhibitory (RE to TC) connections made by each presynaptic cell. When the probability density model is stimulated with constant retinal input (10–100 spikes/sec), a wide range of responses are observed depending on cellular parameters and network connectivity. These include asynchronous burst and tonic spikes, sleep spindle-like rhythmic bursting, and oscillations in population firing rate that are distinguishable from sleep spindles due to their amplitude, frequency, or the presence of tonic spikes. In this context of dLGN/PGN network modeling, we find the population density approach using 2,500 mesh points and resolving membrane voltage to 0.7 mV is over 30 times more efficient than 1000-cell Monte Carlo simulations. Action Editor: David Golomb     

Mechanisms of membrane potential oscillation in bursting neurons on the snail,Helix pomatia

• 1.1. The mechanism of generation of membrane potential (MP) oscillations was studied in identified bursting neurons from the snail Helix pomatia.
• 2.2. Long-lasting stimulation of an identified peptidergic interneuron produced a persistent bursting activity in a non-active burster.
• 3.3. External application of calcium channel blockers (1 mM Cd²⁺ or 5 mM La²⁺) resulted in a transient increase in the slow-wave amplitude and subsequent prevention of pacemaker activity generation in bursting neurons. Application of these blockers together with endogenous neuropeptide initiating bursting activity generation, increased MP wave amplitude without prevention of bursting activity generation.
• 4.4. Replacement of all NaCl in normal Ringer's solution with isoosmotic CaCl₂, glucose or Tris-HCl produced a reversible block of bursting activity generation. Stationary current-voltage relation (CVR) of bursting neuron membrane has a region of negative resistance (NRR) and does not intersect the potential axis in threshold region for action potential (AP) generation in normal Ringer's solution. In Na-free solution stationary CVR is linear and intersects the potential axis near — 52 mV.
• 5.5. Novel potential- and time-dependent outward (E_rev = − 58 mV) current, I_B, activated by hyperpolarization was found in the bursting neuron membrane. Having achieved a maximal value, this current decayed with a time constant of about 1 sec. Hyperpolarization inactivated maximal conductance, g_B, responsible for I_B, and depolarization abolished inactivation of g_B.
• 6.6. Short-lasting (0.01 sec) hyperpolarization of the bursting neuron membrane by inward current pulse induced the development of prolonged hyperpolarization wave lasting up to 10 sec.
• 7.7. These results suggest that: (a) persistent bursting activity of RPal neuron in the snail Helix pomatia is not endogenous but is due to a constant activation of peptidergic synaptic inputs of these neurons; (b) Ca²⁺ ions do not play a pivotal role in the ionic mechanism of MP oscillations but play a determining role in the process of secretion of a peptide initiating bursting activity by the interneuron presynaptic terminal; (c) depolarizing phase of the MP wave is due to specific properties of stationary CVR and hyperpolarization phase is due to regenerative properties of hyperpolarization-activated outward current I_B. The minimal mathematical version of MP oscillations based on the experimental data is presented.