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.     

Amphetamine elicited potential changes in vertebrate and invertebrate central neurons

The effects of amphetamine on potential changes in both vertebrate and invertebrate central neurons and factors affecting the potential changes were tested. The animals studied included mice, newborn rat and African snail. Seizure was elicited after lethal doses of d-amphetamine (75 mg/kg, i.p.) administration in mice. Repetitive firing of the action potentials were elicited after d-amphetamine (1-30 microM) administration in thin thalamic brain slices of newborn rat. Bursting firing of action potentials in the giant African central RP4 neuron were also elicited after d-amphetamine or l-amphetamine (0.27 mM) administration. The amphetamine elicited bursting firing of action potentials was not blocked even after high concentrations of d-tubocurarine, atropine, haloperidol, hexamethonium administration. Therefore, the amphetamine elicited potential changes may not be directly related to the activation of the receptors of the neuron. The bursting firing of action potentials elicited by amphetamine occurred 20-30 min after amphetamine administration extracellularly, even after high concentrations of d-amphetamine administration (0.27, 1 mM). However, the bursting firing of potentials occurred immediately if amphetamine was administrated intracellularly at lower concentration. Extracellular application of ruthenium red, the calcium antagonist, abolished the amphetamine elicited bursting firing of action potentials. If intracellular injection of EGTA, a calcium ion chelator, or injection with high concentrations of magnesium, the bursting firing of potentials were immediately abolished. These results suggested that the active site of amphetamine may be inside of the neuron and the calcium ion in the neuron played an important role on the bursting of potentials. In two-electrode voltage clamped RP4 neuron, amphetamine, at 0.27 mM, decreased the total inward and steady outward currents of the RP4 neuron. d-Amphetamine also decreased the calcium, Ia and the steady-state outward currents of the RP4 neuron. Besides, amphetamine elicited a negative slope resistance (NSR) if membrane potential was in the range of -50 to -10 mV. The NSR was decreased in cobalt substituted calcium free and sodium free solution. The effects of secondary messengers on the amphetamine elicited potential changes were tested. The bursting firing of action potentials elicited by amphetamine in central snail neurons decreased following extracellular application of H8 (N-(2-methyl-amino) ethyl-3-isoquinoline sulphonamide dihydrochloride), a specific protein kinase A inhibitor and anisomycin, a protein synthesis inhibitor. However, the bursting firing of action potentials were not affected after extracellular application of H7 (1,(5-isoquinolinesulphonyl)-2-methylpiperasine dihydrochloride), a specific protein kinase C (PKC) inhibitor, or intracellular application of GDPbetaS, a G protein inhibitor. The oscillation of membrane potential of the bursting activity was blocked after intracellular injection of 3'-deoxyadenosine, an adenylyl-cyclase inhibitor. These results suggested that the bursting firing of action potentials elicited by d-amphetamine in snail neuron may be associated with the cyclic AMP second messenger system; on the other hand, it may not be associated with the G protein and protein kinase C activity. It is concluded that amphetamine elicited potential changes in both vertebrate and invertebrate central neurons. The changes are closely related to the ionic currents and second messengers of the neurons.     

Helix neurons invovled in control of rhythmic movement in the pneumostome

Three neurons capable of generating coordinated bursting activity or synchronized slow-wave fluctuations in membrane potential (MP) were identified in the left parietal ganglion ofHelix pomatia. The function of these units contributes to regulating rhythmic opening and closing movements in the pneumostome. Both bursting activity and slow-wave neuronal MP synchronize with rhythmic movements of the pneumostome. Onset of bursting activity and fluctuations in MP on the one hand or suppression of these effects due to different influences on the cells on the other leads to initiation or extinction of pneumostome movements respectively. These neurons do not exhibit endogenous bursting activity but do produce a fairly high rate of firing activity without bursting pattern and without slow-waves in MP in isolation. Bursting activity occurs in these neurons in the intact central nervous system (CNS) as a result of gigantic synchronized IPSP in some cases and due to the aforementioned slow waves in MP and in others. No direct chemically- or electrically-operated synaptic connections exist between the three cells. Serotonin triggers both waves in MP and bursting activity in all three neurons in the intact CNS and exerts a pronounced hyperpolarizing action on each of these factors in isolation.N. K. Kol'tsov Institute of Developmental Biology, Academy of Sciences of the USSR. Moscow. Balaton Limnological Research Institute of the Hungarian Academy of Sciences, Tihany. Translated from Neirofiziologiya, Vol. 20, No. 4, pp. 509–517, July–August, 1988.     

Simulation of bursting activity in theHelix RPa1 neuron: Role of calcium ions

A model of bursting activity in the RPal neuron of the snailHelix pomatia has been developed. In this model, calcium conductances do not play a key role in generation of slow oscillations of membrane potential (MP). The possibility of simulating the maintenance of bursting in the presence of cadmium ions is shown. Inclusion in the model of the calcium-inactivated calcium conductance makes it possible to reproduce both adaptation of the neuron to constant polarizing current, which modifies bursting, and the development of slow inward current when MP is clamped at different phases at the slow wave. In our simulations, the characteristic properties of bursts (such as an increase in the frequency of action potentials and a decrease in spike undershoot at the beginning of a burst) are due to the cumulative inactivation of potassium current. The advantages of the presented mathematical model of bursting compared with other models are discussed.Neirofiziologiya/Neurophysiology, Vol. 26, No. 5, pp. 373–381, September–October, 1994.     

An integrate-and-fire model for synchronized bursting in a network of cultured cortical neurons

It has been suggested that spontaneous synchronous neuronal activity is an essential step in the formation of functional networks in the central nervous system. The key features of this type of activity consist of bursts of action potentials with associated spikes of elevated cytoplasmic calcium. These features are also observed in networks of rat cortical neurons that have been formed in culture. Experimental studies of these cultured networks have led to several hypotheses for the mechanisms underlying the observed synchronized oscillations. In this paper, bursting integrate-and-fire type mathematical models for regular spiking (RS) and intrinsic bursting (IB) neurons are introduced and incorporated through a small-world connection scheme into a two-dimensional excitatory network similar to those in the cultured network. This computer model exhibits spontaneous synchronous activity through mechanisms similar to those hypothesized for the cultured experimental networks. Traces of the membrane potential and cytoplasmic calcium from the model closely match those obtained from experiments. We also consider the impact on network behavior of the IB neurons, the geometry and the small world connection scheme. Action Editor: David Golomb     

Organic calcium channel blockers generate the coexistence of two different types of action potentials in the same muscle membrane following chemical induction of excitability.

1. Following exposure to the sulfhydryl reagents known as alpha,beta-unsaturated carbonyl compounds, the ventroabdominal flexor muscles of the crustacean Atya lanipes, which are normally completely inexcitable, generate trains of overshooting calcium action potentials; the effects of organic calcium channel antagonists and potassium channel blockers on the chemically-induced trains of action potentials have been studied. 2. Verapamil and D600, at micromolar concentrations, elicit the appearance of slow, cardiac-like action potentials which coexist with the much faster chemically-induced calcium spikes, transforming the regular repetitive firing into a cyclic bursting pattern. 3. Bepridil (1 microM) decreases the frequency of firing of the action potentials, probably by increasing the threshold for the activation of a population of the chemically-induced calcium channels. 4. The potassium channel blockers, TEA (30-40 mM) and quinidine (100-200 microM), delayed the rate of repolarization of the chemically-induced action potentials; none of the potassium channel blockers, however, induced the appearance of repetitive spike activity.     

Complex bursting in pancreatic islets: a potential glycolytic mechanism

The electrical activity of insulin-secreting pancreatic islets of Langerhans is characterized by bursts of action potentials. Most often this bursting is periodic, but in some cases it is modulated by an underlying slower rhythm. We suggest that the modulatory rhythm for this complex bursting pattern is due to oscillations in glycolysis, while the bursting itself is generated by some other slow process. To demonstrate this hypothesis, we couple a minimal model of glycolytic oscillations to a minimal model for activity-dependent bursting in islets. We show that the combined model can reproduce several complex bursting patterns from mouse islets published in the literature, and we illustrate how these complex oscillations are produced through the use of a fast/slow 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.     

How noise and coupling induce bursting action potentials in pancreatic {beta}-cells

Unlike isolated beta-cells, which usually produce continuous spikes or fast and irregular bursts, electrically coupled beta-cells are apt to exhibit robust bursting action potentials. We consider the noise induced by thermal fluctuations as well as that by channel-gating stochasticity and examine its effects on the action potential behavior of the beta-cell model. It is observed numerically that such noise in general helps single cells to produce a variety of electrical activities. In addition, we also probe coupling via gap junctions between neighboring cells, with heterogeneity induced by noise, to find that it enhances regular bursts.     

Modeling short-term interval-force relations in cardiac muscle

This study employs two modeling approaches to investigate short-term interval-force relations. The first approach is to develop a low-order, discrete-time model of excitation-contraction coupling to determine which parameter combinations produce the degree of postextrasystolic potentiation seen experimentally. Potentiation is found to increase 1) for low recirculation fraction, 2) for high releasable fraction, i.e., the maximum fraction of Ca(2+) released from the sarcoplasmic reticulum (SR) given full restitution, and 3) for strong negative feedback of the SR release on sarcolemmal Ca(2+) influx. The second modeling approach is to develop a more detailed single ventricular cell model that simulates action potentials, Ca(2+)-handling mechanisms, and isometric force generation by the myofilaments. A slow transition from the adapted state of the ryanodine receptor produces a gradual recovery of the SR release and restitution behavior. For potentiation, a small extrasystolic release leaves more Ca(2+) in the SR but also increases the SR loading by two mechanisms: 1) less Ca(2+)-induced inactivation of L-type channels and 2) reduction of action potential height by residual activation of the time-dependent delayed rectifier K(+) current, which increases Ca(2+) influx. The cooperativity of the myofilaments amplifies the relatively small changes in the Ca(2+) transient amplitude to produce larger changes in isometric force. These findings suggest that short-term interval-force relations result mainly from the interplay of the ryanodine receptor adaptation and the SR Ca(2+) loading, with additional contributions from membrane currents and myofilament activation.     

Bursting excitable cell models by a slow Ca2+ current

Bursting in excitable cells is a phenomenon that has attracted the interest of many electrophysiologists and non-linear dynamicists. In this paper, we present two models that give rise to bursting in action potentials. The membrane of the first model contains a voltage-activated Ca2+ channel that inactivates very slowly upon depolarization and a delayed K+ channel that is activated by voltage. This model consists of three dynamic variables--the gating variable of K+ channel (n), inactivation gating variable of the Ca2+ channel (f), and membrane potential (V). The membrane of the second model contains a voltage-activated Na+ channel that inactivates rather fast upon depolarization. This model contains altogether five dynamic variables--the Na+ inactivation gating variable (h) and Ca2+ activation variable (d), in addition to the three dynamic variables in the first model. With the first model, we show how various interesting bursting patterns may arise from such a simple three dynamic variable model. We also demonstrate that a slowly inactivating voltage-dependent Ca2+ channel may play the key role in the genesis of bursting. With the second model, we show how the participation of a quickly inactivating fast inward current may lead to a neuronal type of bursting, multi-peaked oscillations, and chaos, as the rates of the gating variables change.     

Firing patterns in a conductance-based neuron model: bifurcation, phase diagram, and chaos

Responding to various stimuli, some neurons either remain resting or can fire several distinct patterns of action potentials, such as spiking, bursting, subthreshold oscillations, and chaotic firing. In particular, Wilson’s conductance-based neocortical neuron model, derived from the Hodgkin–Huxley model, is explored to understand underlying mechanisms of the firing patterns. Phase diagrams describing boundaries between the domains of different firing patterns are obtained via extensive numerical computations. The boundaries are further studied by standard instability analyses, which demonstrates that the chaotic neural firing could develop via period-doubling and/or period- adding cascades. Sequences of the firing patterns often observed in many neural experiments are also discussed in the phase diagram framework developed. Our results lay the groundwork for wider use of the model, especially for incorporating it into neural field modeling of the brain.     

A calcium-based phantom bursting model for pancreatic islets

Insulin-secreting β-cells, located within the pancreatic islets of Langerhans, are excitable cells that produce regular bursts of action potentials when stimulated by glucose. This system has been the focus of mathematical investigation for two decades, spawning an array of mathematical models. Recently, a new class of models has been introduced called ‘phantom bursters’ [Bertram et al. (2000) Biophys. J. 79, 2880–2892], which accounts for the wide range of burst frequencies exhibited by islets via the interaction of more than one slow process. Here, we describe one implementation of the phantom bursting mechanism in which intracellular Ca²⁺ controls the oscillations through both direct and indirect negative feedback pathways. We show how the model dynamics can be understood through an extension of the fast/slow analysis that is typically employed for bursting oscillations. From this perspective, the model makes use of multiple degrees of freedom to generate the full range of bursting oscillations exhibited by β-cells. The model also accounts for a wide range of experimental phenomena, including the ubiquitous triphasic response to the step elevation of glucose and responses to perturbations of internal Ca²⁺ stores. Although it is not presently a complete model of all β-cell properties, it demonstrates the design principles that we anticipate will underlie future progress in β-cell modeling.     

CRH-induced electrical activity and calcium signalling in pituitary corticotrophs

Pituitary corticotroph cells generate repetitive action potentials and associated Ca2+ transients in response to the agonist corticotropin releasing hormone (CRH). There is indirect evidence suggesting that the agonist, by way of complex intracellular mechanisms, modulates the voltage sensitivity of the L-type Ca2+ channels embedded in the plasma membrane. We have previously constructed a Hodgkin-Huxley-type model of this process, which indicated that an increase in the L-type Ca2+ current is sufficient to generate repetitive action potentials (LeBeau et al. (1997). Biophys. J.73, 1263-1275). CRH is also believed to inhibit an inwardly rectifying K+ current. In this paper, we have found that a CRH-induced inhibition of the inwardly rectifying K+ current increases the model action potential firing frequency, [Ca2+]i transients and membrane excitability. This dual modulatory action of CRH on inward rectifier and voltage-gated Ca2+ channels better describes the observed CRH-induced effects. This structural alteration to the model along with parameter changes bring the model firing frequency in line with experimental data. We also show that the model exhibits experimentally observed bursting behaviour, where the depolarization spike is followed by small oscillations in the membrane potential.     

Stimulation of bursting in pre-Bötzinger neurons by Epac through calcium release and modulation of TRPM4 and K-ATP channels

The exchange factor directly activated by cAMP (Epac) can couple cAMP production to the activation of particular membrane and cytoplasmic targets. Using patch-clamp recordings and calcium imaging in organotypic brainstem slices, we examined the role of Epac in pre-B?tzinger complex, an essential part of the respiratory network. The selective agonist 8-(4-chlorophenylthio)-2'-O-methyl-cAMP (8-pCPT) sensitized calcium mobilisation from inositol-1,4,5-trisphosphate-sensitive internal stores that stimulated TRPM4 (transient receptor potential cation channel, subfamily M, Melastatin) channels and potentiated the bursts of action potentials. 8-pCPT actions were abolished after inhibition of phospholipase C with U73122 and depletion of calcium stores with thapsigargin. Caffeine-sensitive release channels were not modulated by 8-pCPT. Epac inhibited ATP-sensitive K(+) channels that also led to the enhancement of bursting by 8-pCPT. Bursting activity, spontaneous calcium transients and activity of TRPM4 and ATP-sensitive K(+) channels were potentiated after brief exposures to bradykinin and incubation with wortmannin produced opposite effects that can be explained by changes in phosphatidylinositol 4,5-bisphosphate levels. 8-pCPT stimulated the respiratory motor output in functionally intact preparations and the effects of bradykinin and wortmannin were identical to those observed in organotypic slices. The data thus indicate a novel pathway of controlling bursting activity in pre-B?tzinger complex neurons through Epac that can involved in reinforcement of the respiratory activity by cAMP.     

Neuromodulatory changes in short-term synaptic dynamics may be mediated by two distinct mechanisms of presynaptic calcium entry

Although synaptic output is known to be modulated by changes in presynaptic calcium channels, additional pathways for calcium entry into the presynaptic terminal, such as non-selective channels, could contribute to modulation of short term synaptic dynamics. We address this issue using computational modeling. The neuropeptide proctolin modulates the inhibitory synapse from the lateral pyloric (LP) to the pyloric dilator (PD) neuron, two slow-wave bursting neurons in the pyloric network of the crab Cancer borealis. Proctolin enhances the strength of this synapse and also changes its dynamics. Whereas in control saline the synapse shows depression independent of the amplitude of the presynaptic LP signal, in proctolin, with high-amplitude presynaptic LP stimulation the synapse remains depressing while low-amplitude stimulation causes facilitation. We use simple calcium-dependent release models to explore two alternative mechanisms underlying these modulatory effects. In the first model, proctolin directly targets calcium channels by changing their activation kinetics which results in gradual accumulation of calcium with low-amplitude presynaptic stimulation, leading to facilitation. The second model uses the fact that proctolin is known to activate a non-specific cation current I _MI . In this model, we assume that the MI channels have some permeability to calcium, modeled to be a result of slow conformation change after binding calcium. This generates a gradual increase in calcium influx into the presynaptic terminals through the modulatory channel similar to that described in the first model. Each of these models can explain the modulation of the synapse by proctolin but with different consequences for network activity.     

Graphical approach to model reduction for nonlinear biochemical networks

Model reduction is a central challenge to the development and analysis of multiscale physiology models. Advances in model reduction are needed not only for computational feasibility but also for obtaining conceptual insights from complex systems. Here, we introduce an intuitive graphical approach to model reduction based on phase plane analysis. Timescale separation is identified by the degree of hysteresis observed in phase-loops, which guides a "concentration-clamp" procedure for estimating explicit algebraic relationships between species equilibrating on fast timescales. The primary advantages of this approach over Jacobian-based timescale decomposition are that: 1) it incorporates nonlinear system dynamics, and 2) it can be easily visualized, even directly from experimental data. We tested this graphical model reduction approach using a 25-variable model of cardiac β(1)-adrenergic signaling, obtaining 6- and 4-variable reduced models that retain good predictive capabilities even in response to new perturbations. These 6 signaling species appear to be optimal "kinetic biomarkers" of the overall β(1)-adrenergic pathway. The 6-variable reduced model is well suited for integration into multiscale models of heart function, and more generally, this graphical model reduction approach is readily applicable to a variety of other complex biological systems.     

Towards a computational reconstruction of the electrodynamics of premature and full term human labour

We apply virtual tissue engineering to the full term human uterus with a view to reconstruction of the spatiotemporal patterns of electrical activity of the myometrium that control mechanical activity via intracellular calcium. The three-dimensional geometry of the gravid uterus has been reconstructed from segmented in vivo magnetic resonance imaging as well as ex vivo diffusion tensor magnetic resonance imaging to resolve fine scale tissue architecture. A late-pregnancy uterine smooth muscle cell model is constructed and bursting analysed using continuation algorithms. These cell models are incorporated into partial differential equation models for tissue synchronisation and propagation. The ultimate objective is to develop a quantitative and predictive understanding of the mechanisms that initiate and regulate labour.     

Alteration of neuronal activity in response to cyclic nucleotide agents in Aplysia

Responsiveness of Aplysia neurons to agents that affect cyclic nucleotide levels was not limited to neurons exhibiting a spontaneous bursting activity pattern. Analyses of the I-V relationship elicited by triangular current ramps within cells exposed to different agents presumably causing elevated cyclic nucleotide levels showed qualitatively similar alterations. These included an increased slope conductance at more negative potentials, possibly related to anomalous rectification, and the induction of a hysteresis in response to a triangular ramp. The paired metacerebral giant cells showed induction of synchronous bursting when exposed to phosphodiesterase inhibitors, and we examined this phenomenon more closely. Classical methods to inactivate a presynaptic source did not eliminate the induction of synchronous bursting. Intracellular injection of a phosphodiesterase inhibitor into a metacerebral giant cell caused changes in the current-voltage relationship similar to those described above for other cells. Subsequent perfusion with the inhibitor caused an enhancement of these effects and the induction of bursting. The alteration of the current-voltage plot in the metacerebral cells and abdominal ganglion cells is qualitatively similar to that induced in the similarly treated bursting neuron R15, suggesting a similar mechanism of action in both burster and nonburster neurons. The implications of these results for cyclic nucleotide mediation of neuronal events are discussed.     

Oscillations and slow patterning in the antennal lobe

Odor presentation generates both fast oscillations and slow patterning in the spiking activity of the projection neurons (PNs) in the antennal lobe (AL) of locusts, moths and bees. Experimental results indicate that the oscillations are the result of the interaction between the PNs and the inhibitory local neurons (LNs) in the AL; e.g., blocking inhibition by application of GABA-receptor antagonists abolishes these oscillations. The slow patterning, on the other hand, was shown to be somewhat resistant to such blockage. In a H-H model, we reproduce both the oscillations and the slow patterning. As previously suggested, the oscillations are the result of the interaction between the PNs and LNs. We suggest that calcium and calcium-dependent potassium channels (found in PNs of bees and moths) are sufficient to account for the slow patterning resistant to the application of GABA-receptor antagonists. The intrinsic bursting property of the PNs, resulting from these additional modeled currents, give rise to another network feature that was seen experimentally in locusts: A relatively small increase in the number of additional generated PN action potentials when LN input is blocked. Consequently, the major effect of network inhibition is to redistribute the action potentials of the PNs from bursting to one action potential per cycle of the oscillations. Action Editor: Christiane Linster