Cyclic variation of potassium conductance in a burst-generating neurone in Aplysia

Two types of burst firing in gonadotrophin-releasing hormone neurones

Gonadotrophin-releasing hormone (GnRH) neurones fire spontaneous bursts of action potentials, although little is understood about the underlying mechanisms. In the present study, we report evidence for two types of bursting/oscillation driven by different mechanisms. Properties of these different types are clarified using mathematical modelling and a recently developed active-phase/silent-phase correlation technique. The first type of GnRH neurone (1-2%) exhibits slow (∼0.05 Hz) spontaneous oscillations in membrane potential. Action potential bursts are often observed during oscillation depolarisation, although some oscillations were entirely subthreshold. Oscillations persist after blockade of fast sodium channels with tetrodotoxin (TTX) and blocking receptors for ionotropic fast synaptic transmission, indicating that they are intrinsically generated. In the second type of GnRH neurone, bursts were irregular and TTX caused a stable membrane potential. The two types of bursting cells exhibited distinct active-phase/silent-phase correlation patterns, which is suggestive of distinct mechanisms underlying the rhythms. Further studies of type 1 oscillating cells revealed that the oscillation period was not affected by current or voltage steps, although amplitude was sometimes damped. Oestradiol, an important feedback regulator of GnRH neuronal activity, acutely and markedly altered oscillations, specifically depolarising the oscillation nadir and initiating or increasing firing. Blocking calcium-activated potassium channels, which are rapidly reduced by oestradiol, had a similar effect on oscillations. Kisspeptin, a potent activator of GnRH neurones, translated the oscillation to more depolarised potentials, without altering period or amplitude. These data show that there are at least two distinct types of GnRH neurone bursting patterns with different underlying mechanisms.

Involvement of Na+/K+ pump in fine modulation of bursting activity of the snail Br neuron by 10 mT static magnetic field

The spontaneously active Br neuron from the brain-subesophageal ganglion complex of the garden snail Helix pomatia rhythmically generates regular bursts of action potentials with quiescent intervals accompanied by slow oscillations of membrane potential. We examined the involvement of the Na(+)/K(+) pump in modulating its bursting activity by applying a static magnetic field. Whole snail brains and Br neuron were exposed to the 10-mT static magnetic field for 15 min. Biochemical data showed that Na(+)/K(+)-ATPase activity increased almost twofold after exposure of snail brains to the static magnetic field. Similarly, (31)P NMR data revealed a trend of increasing ATP consumption and increase in intracellular pH mediated by the Na(+)/H(+) exchanger in snail brains exposed to the static magnetic field. Importantly, current clamp recordings from the Br neuron confirmed the increase in activity of the Na(+)/K(+) pump after exposure to the static magnetic field, as the magnitude of ouabain's effect measured on the membrane resting potential, action potential, and interspike interval duration was higher in neurons exposed to the magnetic field. Metabolic pathways through which the magnetic field influenced the Na(+)/K(+) pump could involve phosphorylation and dephosphorylation, as blocking these processes abolished the effect of the static magnetic field.

Dissection and reduction of a modeled bursting neuron

An 11-variable Hodgkin-Huxley type model of a bursting neuron was investigated using numerical bifurcation analysis and computer simulations. The results were applied to develop a reduced model of the underlying subthreshold oscillations (slow-wave) in membrane potential. Two different low-order models were developed: one 3-variable model, which mimicked the slow-wave of the full model in the absence of action potentials and a second 4-variable model, which included expressions accounting for the perturbational effects of action potentials on the slow-wave. The 4-variable model predicted more accurately the activity mode (bursting, beating, or silence) in response to application of extrinsic stimulus current or modulatory agents. The 4-variable model also possessed a phase-response curve that was very similar to that of the original 11-variable model. The results suggest that low-order models of bursting cells that do not consider the effects of action potentials may erroneously predict modes of activity and transient responses of the full model on which the reductions are based. These results also show that it is possible to develop low-order models that retain many of the characteristics of the activity of the higher-order system.

Modeling slowly bursting neurons via calcium store and voltage-independent calcium current

Recent experiments indicate that the calcium store (e.g., endoplasmic reticulum) is involved in electrical bursting and [Ca2+]i oscillation in bursting neuronal cells. In this paper, we formulate a mathematical model for bursting neurons, which includes Ca2+ in the intracellular Ca2+ stores and a voltage-independent calcium channel (VICC). This VICC is activated by a depletion of Ca2+ concentration in the store, [Ca2+]cs. In this model, [Ca2+]cs oscillates slowly, and this slow dynamic in turn gives rise to electrical bursting. The newly formulated model thus is radically different from existing models of bursting excitable cells, whose mechanism owes its origin to the ion channels in the plasma membrane and the [Ca2+]i dynamics. In addition, this model is capable of providing answers to some puzzling phenomena, which the previous models could not (e.g., why cAMP, glucagon, and caffeine have ability to change the burst periodicity). Using mag-fura-2 fluorescent dyes, it would be interesting to verify the prediction of the model that (1) [Ca2+]cs oscillates in bursting neurons such as Aplysia neuron and (2) the neurotransmitters and hormones that affect the adenylate cyclase pathway can influence this oscillation.

Encoding with bursting, subthreshold oscillations, and noise in mammalian cold receptors

Mammalian cold thermoreceptors encode steady-state temperatures into characteristic temporal patterns of action potentials. We propose a mechanism for the encoding process. It is based on Plant's ionic model of slow wave bursting, to which stochastic forcing is added. The model reproduces firing patterns from cat lingual cold receptors as the parameters most likely to underlie the thermosensitivity of these receptors varied over a 25 degrees C range. The sequence of firing patterns goes from regular bursting, to simple periodic, to stochastically phase-locked firing or "skipping." The skipping at higher temperatures is shown to necessitate an interaction between noise and a subthreshold endogenous oscillation in the receptor. The basic period of all patterns is robust to noise. Further, noise extends the range of encodable stimuli. An increase in firing irregularity with temperature also results from the loss of stability accompanying the approach by the slow dynamics of a reverse Hopf bifurcation. The results are not dependent on the precise details of the Plant model, but are generic features of models where an autonomous slow wave arises through a Hopf bifurcation. The model also addresses the variability of the firing patterns across fibers. An alternate model of slow-wave bursting (Chay and Fan 1993) in which skipping can occur without noise is also analyzed here in the context of cold thermoreception. Our study quantifies the possible origins and relative contribution of deterministic and stochastic dynamics to the coding scheme. Implications of our findings for sensory coding are discussed.

Analysis of the effects of modulatory agents on a modeled bursting neuron: dynamic interactions between voltage and calcium dependent systems

In a computational model of the bursting neuron R15, we have implemented proposed mechanisms for the modulation of two ionic currents (IR and ISI) that play key roles in regulating its spontaneous electrical activity. The model was sufficient to simulate a wide range of endogenous activity in the presence of various concentrations of serotonin (5-HT) or dopamine (DA). The model was also sufficient to simulate the responses of the neuron to extrinsic current pulses and the ways in which those responses were altered by 5-HT or DA. The results suggest that the actions of modulatory agents and second messengers on this neuron, and presumably other neurons, cannot be understood on the basis of their direct effects alone. It is also necessary to take into account the indirect effects of these agents on other unmodulated ion channels. These indirect effects occur through the dynamic interactions of voltage-dependent and calcium-dependent processes.

Bursting responses of Lymnea neurons to microwave radiation

Microelectrode and voltage-clamp techniques were modified to record spontaneous electrical activity and ionic currents of Lymnea stagnalis neurons during exposure to a 900-MHz field in a waveguide-based apparatus. The field was pulse-modulated at repetition rates ranging from 0.5 to 110 pps, or it was applied as a continuous wave (CW). When subjected to pulsed waves (PW), rapid, burst-like changes in the firing rate of neurons occurred at SARs of a few W/kg. If the burst-like irregularity was present in the firing rate under control conditions, irradiation enhanced its probability of occurrence. The effect was dependent on modulation, but not on modulation frequency, and it had a threshold SAR near 0.5 W/kg. CW radiation had no effect on the firing rate pattern at the same SAR. Mediator-induced, current activation of acetyl-choline, dopamine, serotonin, or gamma-aminobutyric-acid receptors of the neuronal soma was not altered during CW or PW exposures and, hence, could not have been responsible for the bursting effect.

Development and modulation of endogenous bursting in identified neuron R15 of juvenile Aplysia

Evidence from a variety of both vertebrate and invertebrate preparations has demonstrated that modulation of the intrinsic firing patterns of individual neurons can have a dramatic effect on the functional output of a neural circuit. Although the mechanisms underlying the production and modulation of intrinsic firing patterns have been extensively studied in adult nervous systems, relatively little is known about how these two features of intrinsically active neurons develop. To address these issues, we have examined the development of endogenous bursting and its modulation by neuropeptides in the identified cell R15 of juvenile Aplysia. Confirming Ohmori (1981), we found that the mature parabolic bursting pattern of R15 is absent in early juvenile stages and develops only gradually over the last stage of juvenile development. We have then analyzed the modulatory effects of extracts made from the neurosecretory bag cells of Aplysia on the immature firing pattern of juvenile R15 cells. In the adult, neuroactive peptides released from the bag cells are known to intensify bursting. In juveniles, we have found that bag cell extract (BCE) can induce bursting prematurely as well as intensify immature bursts, whereas control extracts have no effect on the firing pattern of R15. These results show that the ionic currents necessary for the generation of endogenous bursting in R15 are present and can be modulated before the normal developmental expression of the burst pattern.

Routes to chaos in a model of a bursting neuron

Chaotic regimens have been observed experimentally in neurons as well as in deterministic neuronal models. The R15 bursting cell in the abdominal ganglion of Aplysia has been the subject of extensive mathematical modeling. Previously, the model of Plant and Kim has been shown to exhibit both bursting and beating modes of electrical activity. In this report, we demonstrate (a) that a chaotic regime exists between the bursting and beating modes of the model, and (b) that the model approaches chaos from both modes by a period doubling cascade. The bifurcation parameter employed is the external stimulus current. In addition to the period doubling observed in the model-generated trajectories, a period three "window" was observed, power spectra that demonstrate the approaches to chaos were generated, and the Lyaponov exponents and the fractal dimension of the chaotic attractors were calculated. Chaotic regimes have been observed in several similar models, which suggests that they are a general characteristic of cells that exhibit both bursting and beating modes.

Evidence for bursting pacemaker neurones in cultured spinal cord cells

Intracellular recordings were made from dissociated mouse spinal cord cells in primary culture. One type of spinal cord neurone, with a large cell body (40-50 micron), 3-5 short neurites, and a mean resting potential of -65 mV, was found to fire rhythmic bursts of action potentials with a phase duration of approximately 1s when the membrane potential was depolarized to -55 mV. These bursts did not arise from spontaneous synaptic input, but appeared to result from endogenous ionic conductance properties of the membrane resembling those observed in molluscan bursting pacemaker neurones. Ionic conductances underlying this bursting activity were studied pharmacologically by local application of ionic conductance blockers. Pacemaker potentials depended on Na+ conductance, since tetrodotoxin and Na-free medium were the most potent agents for blocking spontaneous rhythmic activity. However, a Ca2+ conductance was involved in the depolarizing phase of membrane potential oscillations, since Ba2+ application increased oscillation amplitude. Action potentials observed during the bursts were Na+- and Ca2+-dependent. They did not differ significantly from those observed in other spinal cord neurones in culture. Application of tetraethylammonium, CoCl2, BaCl2 and 4-aminopyridine revealed at least three different potassium conductances which controlled this bursting pacemaker activity. A delayed potassium conductance controlled spike duration, a Ca-dependent potassium conductance controlled the duration of the burst and underlay the hyperpolarizing phase terminating the burst, and finally, a transient potassium conductance appeared to be involved in the control of phase duration. The demonstration that spinal cord neurones growing in monolayer culture display typical bursting pacemaker activity raises the possibility that bursting pacemaker neurones in the mammalian spinal cord may be involved in a phasic pattern generator that could control such activities as walking and the respiratory rhythm.

Peripheral axons of the parabolic burster neuron R15

In a combined electrophysiological and anatomical study, the parabolic burster neuron R15 was found to project axons through the genito-pericardial nerve onto the pericardial wall and digestive gland sheath and, more variably, into the heart and pericardial coelom. Projection into these tissues is consistent with the hypothesis that R15 is neurosecretory and may play a role in circulation and/or ion-water regulation in Aplysia.

Calcium-induced inactivation of calcium current causes the inter-burst hyperpolarization of Aplysia bursting neurones

A triphasic series of tail currents which follow depolarizing voltage-clamp pulses in Aplysia neurones L2-L6 was described in the preceding paper (Kramer & Zucker, 1985). In this paper, we examine the nature of the late outward component of the tail current (phase III) which generates the inter-burst hyperpolarization in unclamped cells. The phase III tail current does not reverse between -30 and -90 mV, and is relatively insensitive to the external K+ concentration. In contrast, Ca2+-dependent K+ current (IK(Ca)), elicited by intracellular Ca2+ injection, reverses near -65 mV, and the reversal potential is sensitive to the external K+ concentration. Addition of 50 mM-tetraethylammonium (TEA) to the bathing medium causes a small increase in the phase III tail current. In contrast, IK(Ca) is completely blocked by addition of 50 mM-TEA. The phase III tail current is suppressed by depolarizing pulses which approach ECa, is blocked by Ca2+ current antagonists (Co2+ and Mn2+), and is blocked by intracellular injection of EGTA. The phase III tail current is reduced by less than 10% after complete removal of extracellular Na+. These bursting neurones have a voltage-dependent Ca2+ conductance which exhibits steady-state activation at a membrane potential similar to the average resting potential of the unclamped cell (i.e. -40 mV). The steady-state Ca2+ conductance can be inactivated by Ca2+ injection, or by depolarizing pre-pulses which generate a large influx of Ca2+. The steady-state Ca2+ conductance has a voltage dependence similar to that of the phase III tail current. The Ca2+-dependent inactivation of the steady-state Ca2+ conductance occurs in parallel with the phase III tail current; both have a similar sensitivity to Ca2+ influx, and both processes decay with similar rates after a depolarizing pulse. Hence, we propose that the phase III tail current is due to the Ca2+- dependent inactivation of a steady-state Ca2+ conductance. The decay of IK(Ca) following simulated spikes or bursts of spikes is rapid (less than 1 s) compared to the time course of the phase III tail current and the inter-burst hyperpolarization (tens of seconds). Thus, we conclude that IK(Ca) does not have a major role in terminating bursts or generating the inter-burst hyperpolarization in these cells. We present a qualitative model of the ionic basis of the bursting pace-maker cycle. The central features of the model are the voltage-dependent activation and the Ca2+-dependent inactivation of a Ca2+ current.

Effect of ethanol on subthreshold currents of Aplysia pacemaker neurons

The subthreshold currents in bursting pacemaker neurons of the Aplysia abdominal ganglion were individually studied with the voltage clamp technique for sensitivity to 4% ethanol. The most prevalent effect of ethanol on unclamped bursting neurons was a hyperpolarization. This was shown to be due to a decrease of a voltage independent inward leakage current. Direct measurement of the Na-dependent slow inward current showed that this current was eliminated by 4% ethanol. Direct measurement of the Ca-dependent slow inward current showed that this current was substantially reduced by 4% ethanol. Injection of EGTA into cell bodies did not eliminate the ethanol-induced block of the slow inward calcium current. Thus, ethanol cannot be reducing the Ca-dependent slow inward current solely by an increase of internal calcium concentration. The effect of ethanol on voltage dependent outward current was measured by blockage of all inward current. The peak outward current was increased by ethanol. The rate of inactivation of this outward current was also increased. Calcium activated potassium current (IK(Ca)) is particularly complicated in its response to ethanol because it is dependent on both Ca and voltage for its activation. The level of IK(Ca) elicited in response to constant Ca injection was increased by ethanol treatment. The level of this current as activated by voltage clamp pulses was either increased or decreased depending on the neuron type. Ca2+ activated potassium conductance increased e-fold for a 26 mV depolarization in membrane holding potential. Ethanol decreased this voltage dependence to e-fold for a 55 mV change in potential. This result was interpreted to mean that ethanol shifted an effective Ca2+ binding site of these channels from about halfway through the membrane field to one quarter of the way across. The same theoretical approach allowed the further conclusion that ethanol caused an increased internal free calcium concentration probably by decreasing calcium binding by intracellular buffers.

Two components of Ca-dependent potassium current in identified neurons of Aplysia californica

Outward tail currents measured in Aplysia neurones after termination of depolarizing voltage-clamp pulses consist of rapidly decaying voltage-dependent K currents and slow tail currents of much slower time course. The rapidly decaying voltage-dependent tail currents were blocked with aminopyridines, and measurements of the slow tail currents were made following decay of any residual rapid tail currents. The slow tail current exhibited two components of differing sensitivity to externally applied tetraethylammonium (TEA) ions. In some neurones of the abdominal ganglion (L-2, L-4), virtually all of the slow tail current was resistant to blockage by TEA, while in others (L-3, L-6) 80% or more of the slow tail current was blocked by low TEA concentrations (KD less than 1 mM), the remaining slow tail current being resistant to TEA. This TEA-resistant slow tail current was identified as a K current because it reversed near the K equilibrium potential (EK), the reversal potential was shifted by changes in the external K concentration, and it could be blocked by injection of Cs+. It was abolished by replacement of external Ca2+ by Co2+ or Ba2+, by addition of Cd2+, or by injection of EGTA, and thus determined to be a Ca-dependent current. Intracellular injection of TEA or external application of aminopyridine or apamine had little or no effect on the TEA-resistant slow tail current. Quinidine reduced the TEA-sensitive, but not the TEA-resistant current. Both the TEA-sensitive and the TEA-resistant components of the slow tail current exhibited similar time courses of decay.(ABSTRACT TRUNCATED AT 250 WORDS)

Voltage and ion dependences of the slow currents which mediate bursting in Aplysia neurone R15

The previous paper described a slow depolarizing tail current, ID, and a slow hyperpolarizing tail current, IH, that are activated by action potentials and by brief depolarizing pulses in Aplysia neurone R15. ID and IH are necessary for the generation of bursting pace-maker activity in this cell. In this paper, the voltage and ion dependence of ID and IH are studied in an effort to determine the charge carriers for the two currents. When the slow currents are activated by brief depolarizing pulses delivered under voltage clamp in normal medium, an increase in the size of the pulse of 5-10 mV is usually sufficient to bring about full activation of ID. The apparent threshold in normal medium is approximately -20 mV. In medium in which K+ channels are blocked, full activation of an inward tail current that resembles ID requires increasing the pulse amplitude by only 1-2 mV. In contrast, IH is activated in a graded fashion over a 40 mV range of pulse amplitudes. After activating the currents with action potentials or with supramaximal pulses, ID remains an inward current and IH an outward current over a range of membrane potentials spanning -20 to -120 mV. In normal medium, ID is dependent on both extracellular Na+ concentration ( [Na+]o) and extracellular Ca2+ concentration ( [Ca2+]o). When K+ channels are blocked, ID can be supported by either [Na+]o or [Ca2+]o. IH depends only on [Ca2+]o as long as [Na+]o is at least 50 mM. Neither ID nor IH is decreased by decreasing the K+ gradient or by application of K+ channel blockers. These treatments increase somewhat the apparent amplitude of ID, probably by unmasking it from the large K+ tail current that follows the depolarizing pulse. A direct comparison in the same cell of the tetraethylammonium sensitivity of IH and of the Ca2+-activated K+ current demonstrates that these two currents flow through separate and distinct populations of channels. We conclude that in R15, ID arises in response to the triggering of an axonal action potential which in turn, through an as yet unknown mechanism, causes an increased influx of Na+ and/or Ca2+. We conclude that the apparent outward current IH, which is responsible for the interburst hyperpolarization in a normally bursting R15, in fact arises from a decrease in a resting inward Ca2+ current, possibly as the result of Ca2+-induced inactivation of Ca2+ channels.

Coupled oscillators in an isolated pacemaker neuron?

The effects were examined of brief lengthening perturbations of different amplitudes on the pacemaker activity of the slowly adapting stretch receptor organ of crayfish. The analysis indicates that perturbation effects: (i) when elicited by low amplitudes, depend on the delivery time (or phase) of the perturbation relative to the last spike, while those evoked by larger amplitudes are phase-independent; (ii) tend to decrease, below the value of the natural interspike interval or pacemaker period, the interval at which the perturbation is delivered, anticipating the occurrence of the next spike; (iii) which follow the first poststimulus spike consist of phase-dependent lengthenings of interspike intervals which are greater for the first and decrease gradually in length in the following post-perturbation intervals; (iv) are gradually compensated because the pre-perturbation phase tends to be recovered in the interspike intervals following the perturbation and spikes gradually tend to occur closer to the instants when they would have fired without the perturbation. Although other models may explain the above behavior, phase compensation suggests strongly that at least two oscillators (i.e., an unperturbable oscillator and a stimulus sensitive one) underlie the pacemaker activity of the slowly adapting organ.

Electrotonic coupling and afterdischarges in the Light Green Cells: a comparison with two other cerebral ganglia neurosecretory cell types in the pond snail. Lymnaea stagnalis

Electrotonic coupling occurs between the growth hormone-producing Light Green Cells on the same but not the opposite side of the brain of Lymnaea. Long duration inhibitory post synaptic potentials occur spontaneously or can be evoked by nerve or connective stimulation. Afterdischarges, lasting for up to 1 min, are evoked by brief stimulation of the median lip nerves. Activity is confined to cells ipsilateral to the nerve being stimulated. The electrical properties of the Light Green Cells are compared with those of the Caudodorsal Cells and Canopy Cells.

Abnormal discharges and chaos in a neuronal model system

Using the mathematical model of the pacemaker neuron formulated by Chay, we have investigated the conditions in which a neuron can generate chaotic signals in response to variation in temperature, ionic compositions, chemicals, and the strength of applied depolarizing current.

Voltage clamp analysis of ethanol effects on pacemaker currents of Aplysia neurons

The effect of 4% ethanol on pacemaker currents of Aplysia neurons was studied under voltage clamp. In normal seawater the n-shape in the I-V disappeared and outward current increased. Ion substitution and drug blocking experiments determined that leakage current and the slow inward calcium current were decreased and that the outward currents, IA and IK, were increased. This knowledge can be used to explain ethanol effects on spontaneous firing patterns.

On the mechanism of spiking and bursting in excitable cells

A mathematical model previously developed to explain beta-cell membrane potential oscillations has been modified to accommodate the external variation of K+, Na+ and Ca2+ concentrations. Our model, which is applicable to excitable cells, incorporates the barrier kinetics. Hodgkin-Huxley-type gating mechanism, and an electrogenic Na+-K+ pump. Numerical solutions of our model are in agreement with many of the experimental results reported in the literature on excitable cells.

Minimal model for membrane oscillations in the pancreatic beta-cell

Following the experimental findings of Atwater et al. (In Biochemistry Biophysics of the Pancreatic-beta-Cell, George Thieme Verlag, New York, 100-107), we have formulated a mathematical model for ionic and electrical events that take place in pancreatic-beta-cells. Our formulation incorporates a Hodgkin-Huxley type gating mechanism for Ca2+ and K+ channels, in addition to Ca2+ gated K+-channels. Consistent with the experimental observations, our model generates spikes and bursts in beta-cell membrane potentials and gives the correct responses to additions of glucose, quinine, and tetraethylammonium ions. The response of the oscillations to ouabain and changing concentrations of external K+ can be incorporated into the present model, although a more complete treatment would require inclusion of the Na+/K+ pump.

Ionic requirements for membrane oscillations and their dependence on the calcium concentration in a molluscan pace-maker neurone

1. Membrane currents from the bursting pace-maker neurone R-15 of Aplysia were measured under conditions designed to simulate membrane oscillations. Changes in the absorbance of the Ca(2+)-sensitive dye arsenazo III were used to monitor changes in the free intracellular Ca(2+) concentration, [Ca](i), under these conditions. In addition, changes in the extracellular K(+), concentration [K](o) were measured with K(+)-sensitive electrodes.2. In normal external ionic conditions the depolarizing phase of pace-maker activity was associated with a slow inward current and the hyperpolarizing phase with a slow outward current.3. In cells where the early inward Na(+) current was blocked by tetrodotoxin and outward K(+) currents were suppressed by intracellular EGTA and extracellular tetraethylammonium and 4-aminopyridine, the slow inward current was significantly larger in amplitude and was suppressed by removal of external Ca(2+) or the addition of external La(3+), but not by the removal of external Na(+).4. The slow inward current was increased when [Ca](o) was raised and decreased when it was reduced in the manner expected for current flow through a Ca(2+) channel. The selectivity of the slow inward current for divalent cations was [Formula: see text].5. The slow inward current was only slightly reduced by a 10 degrees C reduction in temperature.6. In normal external and internal ionic conditions changes in dye absorbance occurred when the membrane was depolarized with slow triangular voltage ramps or long depolarizing steps within the pace-maker oscillation range. The obsorbance change, and thus the increase in Ca(2+), [Ca](i), was well correlated with the appearance of the slow inward current. Moreover, the magnitude of the slow outward current was dependent upon the change in [Ca](i).7. The slow inward current and a substantial fraction of the outward current, as well as the change in [Ca](i), were reduced appreciably by the addition of La(3+) ions (3 mM) to the external medium.8. The increase in [Ca](i) during prolonged depolarization was not affected by external tetrodotoxin or by the removal of external Na(+), but was abolished by a Ca(2+)-free external medium containing EGTA. Nevertheless, significant changes occurred in [Ca](i) during depolarization in 0.1 mM-external Ca(2+).9. In normal external and internal ionic conditions extracellular K(+), [K](o), increased during the depolarizing phase of the pace-maker cycle and decayed during the hyperpolarizing phase.10. There was a measurable increase in [K](o) during small prolonged depolarizing steps which produced a net inward current, indicating that inward and outward currents overlap under normal conditions.11. In the absence of action potential discharge, [Ca](i) increased during the depolarizing phase and decreased during the hyperpolarizing phase of the membrane oscillation.12. It is proposed that pace-maker oscillations depend upon three separate but linked systems which include a voltage-dependent Ca(2+) current, the free intracellular Ca(2+) concentration and the Ca(2+)-activated K(+) current.

Quantitative differences in the currents of bursting and beating molluscan pace-maker neurones

1. The spontaneous activity and the membrane conductances to Na(+), Ca(2+) and K(+) ions of the bursting pace-maker neurone R-15 and the repetitively discharging (beating) pace-maker neurone L-11 in the abdominal ganglion of the marine mollusc, Aplysia californica, were compared.2. The bursting pace-maker R-15 can be converted to a beating pace-maker neurone by the removal of external Ca(2+) or by the injection of EGTA intracellularly. Bursting pace-maker activity is not restored by changes in the resting potential.3. Spontaneous action potentials of cell R-15 are reduced, but not abolished, by the addition of tetrodotoxin (TTX) to block Na(+) currents or by the removal of external Ca(2+) to abolish Ca(2+) currents, whereas the spontaneous action potentials of cell L-11 are abolished by external TTX, but are unaffected by external Ca(2+) removal.4. The membranes of both cells contain Na(+) and Ca(2+) inward currents. The specific Na(+) conductance of both cells is of similar magnitude, whereas the specific Ca(2+) conductance is about half the Na(+) conductance in R-15 cells and an order of magnitude smaller in L-11 cells.5. The delayed K(+) conductance of cell L-11 is about 1.2 times greater than this conductance in cell R-15. The transient K(+) currents of the two cells are about the same magnitude.6. The Ca(2+)-activated K(+) conductance of cell R-15 and cell L-11 was estimated using two methods. The Ca(2+)-activated K(+) conductance of cell R-15 estimated from the difference in the total outward current in normal external solution and the delayed K(+) current in Ca(2+)-free solution (to preclude Ca(2+) influx) or after internal EGTA injection (to prevent Ca(2+) accumulation) is about 23 times greater than this conductance in cell L-11. The Ca(2+)-activated K(+) conductance of cell R-15, estimated from local internal Ca(2+) injections in Ca(2+)-free solution, is about 3 times greater than this conductance in cell L-11.7. The leakage conductance of cell L-11 is about 1.3 times greater than this conductance in cell R-15. This conductance increases by a factor of about 2 in both cells in Ca(2+)-free external solutions containing 1 mM-EGTA, but is unchanged or is decreased slightly by injection of EGTA internally.8. It is concluded that the Ca(2+) conductance and the Ca(2+)-activated K(+) conductance are appreciably greater in the bursting pace-maker neurone R-15 than in the beating pace-maker neurone L-11, whereas other voltage-dependent conductances to Na(+) and K(+) ions as well as the leakage conductance are quite similar. These quantitative differences provide a basis for understanding the different spontaneous activities of the two cells.

A multiaction synapse evoking both EPSPs and enhancement of endogenous bursting

Selective stimulation of two identified input neurons called the 'IV neurons' has a dual influence on the endogenous bursting activity of certain 'PD' motorneurons in the stomatogastric ganglion of the spiny lobster. The effects include: (i) large, conventional and apparently monosynaptic EPSPs; and (ii) enhancement of the endogenous bursting of the pyloric dilator (PD) cells, seen as an increased amplitude of PD oscillations and a higher spiking rate during bursts. The burst enhancement decayed relatively slowly after stimulation ceased, over seconds or tens-of-seconds, depending on stimulus parameters. Modification of the voltage-dependent membrane properties of the PD cells appeared to underlie this effect. The dual-action nature of the IV-to-PD connection was confirmed by selectively blocking the brief EPSP component with 5 x 10(-4) M curare, under which conditions the burst enhancement still persisted. Data from low-Ca2+ experiments were consistent with a conventional mode of synaptic transmitter release underlying the burst enhancement. Enhancement was found to differ significantly from actions of injected current. The IV inputs appear to act on at least two types of synaptic receptors on PD neurons: a curare-sensitive receptor for the brief conventional EPSP, and a curare-resistant receptor for burst enhancement. Analogies may be drawn to the nicotinic and muscarinic cholinergic receptors of vertebrates. These findings may be considered within the contexts of multiaction synapses, modification of cellular properties, and mechanisms for the CNS activation of motor pattern generators.

Modeling repetitive firing and bursting in a small unmyelinated nerve fiber

The Hodgkin-Huxley equations, originally developed to describe the electrical events in the squid giant axon, have been modified to simulate the ionic and electrical events in a small unmyelinated nerve fiber. The modified equations incorporate an electrogenic sodium-potassium pump, finite intra-axonal volume, a periaxonal space, a calcium current, and calcium-dependent potassium conductance (GKCa). The model shows that adaptation can occur in two ways: increased Na-K pump activity because of periaxonal K accumulation or intra-axonal Na accumulation; or from an increase in (GKCa) caused by calcium accumulating within the axon. Bursting is an extension of adaptation and occurs when the sensitivity of the Na-K pump or (GKCa) to changes in ionic concentration is increased.

The time courses of intracellular free calcium and related electrical effects after injection of CaCl2 into neurons of the snail, Helix pomatia

Controlled quantities of 100 mM aqueous CaCl2 solutions were pressure injected into voltage-clamped neurons with a resolution of 10(-11) 1. Ca2+-selective microelectrodes monitored the time course of changes in [Ca2+]i. At a membrane potential of -50 mV CaCl2 quantities in the range of 1% of the cell volume induced an inward current, associated with a conductance increase and having an equilibrium potential between -20 and +20 mV, which accompanied the rise in [Ca2+]i. An artifactual origin of the inward current by the injection procedure or by calcium screening of membrane sites could be excluded. The calcium-induced hyperpolarizing conductance, producing an outward current at -50 mV, followed the inward current and reached maximum during the late decline in [Ca2+]i. In most cases its development was separated from the inward current by an intermediate relative decrease of the membrane conductance. Neither of the two transient conductance increases showed a particular dependence on voltage. Renewed Ca2+ injection quickly decreased the calcium-induced hyperpolarizing conductance for several seconds. Ca2+ injections below 0.05% of the cell volume mostly produced pure outward currents or hyperpolarizing responses. Partial substitution of extracellular CaCl2 by NiCl2 decreased the hyperpolarizing response but not the initial inward current. The immediate effects of increased [Ca2+]i are activation of a depolarizing conductance and the partial block of the late hyperpolarizing conductance. The latter is probably produced through intermediate steps after increasing [Ca2+]i.

Phase plane description of endogenous neuronal oscillators in Aplysia

Phase plane techniques are used to describe graphically the limit cycle behavior of identified endogenous neuronal oscillators in the isolated abdominal ganglion of Aplysia. Intracellularly recorded membrane potential from a bursting neuron and its first derivative with respect to time are used as coordinates (state variables) in phase space. The derivative is either measured electronically or calculated digitally. Each trajectory in phase space represents the entire output of the bursting neuron, i.e., both the rapid action potentials and slow pacemaker potentials. Phase plane portraits are presented for the free run limit cycle before and after a change in a system parameter (applied transmembrane current) and also for phase resetting produced by direct synaptic inhibition from an identified interneuron. The complex topology of the trajectory suggests that the bursting oscillator is a higher order system. Therefore, the second time derivative is used as another state variable. This type of phase plot can help to relate biophysical and mathematical analyses.

Bifurcation and resonance in a model for bursting nerve cells

In this paper we consider a model for the phenomenon of bursting in nerve cells. Experimental evidence indicates that this phenomenon is due to the interaction of multiple conductances with very different kinetics, and the model incorporates this evidence. As a parameter is varied the model undergoes a transition between two oscillatory waveforms; a corresponding transition is observed experimentally. After establishing the periodicity of the subcritical oscillatory solution, the nature of the transition is studied. It is found to be a resonance bifurcation, with the solution branching at the critical point to another periodic solution of the same period. Using this result a comparison is made between the model and experimental observations. The model is found to predict and allow an interpretation of these observations.

Two reciprocating current components underlying slow oscillations in Aplysia bursting neurons

The mechanisms of the slow oscillatory potential in burst firing neurons in the abdominal ganglion of Aplysia californica (L3-L6 and R15) were studied using voltage clamp methods, including a novel tract and hold technique. The steady-state negative resistance characteristic (NRC) of these neurons is attributed to the activation of a moderately fast, persistent, inward current over a range of membrane potential below spike threshold. This inward current is quite sensitive to changes in external sodium concentration (Na)0 and insensitive to potassium (K)0. By contrast, the portion of the I-V curve below the NRC range is insensitive to (Na)0, but highly sensitive to (K)0. The results of 'track and store' voltage clamping show that there are actually two reciprocating currents whose combined action produces the slow oscillation. In addition to the inward current, there is a slow outward current which develops during the depolarized (burst) phase. The slow outward current can also be evoked, and more completely examined, with prolonged depolarizing voltage commands. The extremely slow decay of this current (tau approximately 45 sec) appears to be the factor underlying the slow, ramplike depolarization of Vm during the interburst interval. This slow outward current is insensitive to changes of (Na)0, but changes with (K)0 in a manner consistent with the Nerst equation. We conclude that the burst-inducing slow oscillations are generated as follows: a moderately fast inward sodium dependent current (INa) produces a regenerative depolarization, and this in turn, produces a much slower outward potassium current (IS) which hyperpolarizes the cell. The cycle is completed when IS has decayed sufficiently to allow Vm to depolarize enough to reactivate INa. We have used a quantitative version of this model to determine the time courses of gNa and gK throughout the oscillation, and to explain why different portions of the oscillatory cycle display 'graded' or 'all-or-none' behavior.

Voltage, temperature and ionic dependence of the slow outward current in Aplysia burst-firing neurones

1. The slow outward current in Aplysia burst-firing neurones was studied under voltage-clamp conditions. This current, designated Iso, was measured as the incremental outward tail current following small depolarizing commands. 2. Iso was shown to be a pure K+ current, probably activated by the influx of Ca2+ during the depolarizing command (Johnston, 1976). For small depolarizations, the peak conductance was about 10(-7) mhos. 3. The rate of decay of Iso could be fit by a single exponential and was voltage-dependent, increasing with depolarization. 4. The decay rate of Iso was also temperature-dependent, with a Q10 of about 3. The peak conductance, however, was much less temperature-sensitive, with a Q10 of about 1.5. 5. The voltage dependence of decay rate suggested either the presence of a voltage-dependent Ca2+ pump or that the change in intracellular calcium concentration was not the rate-limiting step in the decay of Iso.

Investigation of burst generation by the electrically coupled cyberchron network in the snail Helisoma using a single-electrode voltage clamp

This paper describes the results of investigating burst generation by the cyberchron network in the snail Helisoma. The cyberchron network is composed of aproximately 20 electrically coupled neurons and controls the feeding behavior of the snail. The electrical coupling between network members has made it particularly difficult to distinguish between the importance and involvement of single-cell and network properties in burst generation by this system. The present investigations utilized the new single-electrode voltage clamp to examine the membrane properties and network interactions of the cyberchron neurons: (1) A slow outward current is activated by moderately large depolarizing commands (-40 to 0 mV) and does not undergo inactivation decay (i.e., decline in magnitude) during a command potential step maintained for 10 sec or more. The lack of inactivation of the outward current in cyberchron neurons appears to be due to the dominating role of a Ca-dependent K current. (2) There are two functionally distinct classes of cyberchrons--current generator cyberchrons and follower cyberchrons. (3) Primary current generator cyberchrons have membrane properties similar to endogenous bursting neurons (e.g., persistent inward Ca current and negative resistance region in I-V plot) and appear to provide the main driving and timing current for the rest of the network. (4) The vast majority of cyberchrons are secondary current generator cyberchrons with membrane properties which exhibit inward-going rectification and appear to burst as a result of regenerative excitation with one another and the primary current generator cyberchrons. (5) The second class of cyberchrons are driven by the electrical synaptic input from the current generator cyberchrons, do not exhibit inward-going rectification, and are called follower cyberchrons. (6) Burst termination is due to activation of a slow outward tail current in most cyberchrons during the burst (probably Ca-activated K current) which causes a hyperpolarization in individual cyberchrons, terminating the burst. (7) Decay of the outward tail current causes the cyberchrons to depolarize, which activates the persistent inward Ca current in the primary current generator cyberchrons, starting the burst cycle anew.