Biomedical subjects

J Rinzel

Publications and source records attributed to J Rinzel.

At least 37 records · Page 2Linked to original sources

PubMed1996

Modeling N-methyl-D-aspartate-induced bursting in dopamine neurons.

Burst firing of dopaminergic neurons of the substantia nigra pars compacta can be induced in vitro by the glutamate agonist N-methyl-D-aspartate. It has been suggested that the interburst hyperpolarization is due to Na+ extrusion by a ouabain-sensitive pump [Johnson et al. (1992) Science 258, 665-667]. We formulate and explore a theoretical model, with a minimal number of currents, for this novel mechanism of burst generation. This minimal model is further developed into a more elaborate model based on observations of additional currents and hypotheses about their spatial distribution in dopaminergic neurons [Hounsgaard (1992) Neuroscience 50, 513-518; Llinás et al. (1984) Brain Res. 294, 127-132]. Using the minimal model, we confirm that interaction between the regenerative, inward N-methyl-D-aspartate-mediated current and the outward Na(+)-pump current is sufficient to generate the slow oscillation (approximately 0.5 Hz) underlying the burst. The negative-slope region of the N-methyl-D-aspartate channel's current-voltage relation is indispensable for this slow rhythm generation. The time-scale of Na(+)-handling determines the burst's slow frequency. Moreover, we show that, given the constraints of sodium handling, such bursting is best explained mechanistically by using at least two spatial, cable-like compartments: a soma where action potentials are produced and a dendritic compartment where the slow rhythm is generated. Our result is consistent with recent experimental evidence that burst generation originates in distal dendrites [Seutin et al. (1994) Neuroscience 58, 201-206]. Responses of the model to a number of electrophysiological and pharmacological stimuli are consistent with known responses observed under similar conditions. These include the persistence of the slow rhythm when the tetrodotoxin-sensitive Na+ channel is blocked and when the soma is voltage-clamped at -60 mV. Using our more elaborate model, we account for details of the observed frequency adaptation in N-methyl-D-aspartate-induced bursting, the origin of multiple spiking and bursting mechanisms, and the interaction between two different bursting mechanisms. Besides reproducing several well established firing patterns, this model also suggests that new firing modes, not yet recorded, might also occur in dopaminergic neurons. This model provides mechanistic insights and explanations into the origin of a variety of experimentally observed membrane potential firing patterns in dopaminergic neurons, including N-methyl-D-aspartate-induced bursting and its dendritic origin. Such a model, capable of reproducing a number of realistic behaviors of dopaminergic neurons, could be useful in further studies of the basal ganglia-thalamocortical motor circuit. It may also shed light on bursting that involves N-methyl-D-aspartate channel activity in other neuron types.

Algorithms↗

PubMed1996

Propagation of spindle waves in a thalamic slice model.

1. We study the propagation and dynamics of spindle waves in thalamic slices by developing and analyzing a model of reciprocally coupled populations of excitatory thalamocortical (TC) neurons and inhibitory thalamic reticular (RE) neurons. 2. Each TC neuron has three intrinsic ionic currents: a low-threshold T-type Ca+2 current (ICa-T), a hyperpolarization-activated cation ("sag") current (Ih) and a leak current. Each RE cell also has three currents: ICa-T, a leak current, and a calcium-activated potassium current (IAHP). Isolated TC cells are at rest, can burst when released or depolarized from a hyperpolarized level, and burst rhythmically under moderate constant hyperpolarizing current. Isolated RE cells are at a hyperpolarized resting membrane potential and can burst when depolarized. 3. TC cells excite RE cells with fast alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) synapses, and RE cells inhibit TC cells with fast gamma-aminobutyric acid-A (GABAA) and slow GABAB synapses and inhibit each other with GABAA synapses only. GABAB postsynaptic conductances operate far from saturation, and the slow inhibitory postsynaptic potentials (IPSPs) increase with the width of the presynaptic burst. The model network is a one-dimensional cellular array with localized coupling. The synaptic coupling strength decays with the distance between the pre- and postsynaptic cells, either exponentially or as a step function. 4. The "intact" network can oscillate with partial synchrony and a population frequency of approximately 10 Hz. RE cells emit bursts almost at every oscillation cycle, whereas TC cells do so almost at every other cycle. Block of GABAB receptors hardly changes the network behavior. Block of GABAA receptors leads the network to a slowed oscillatory state, where the population frequency is approximately 4 Hz and both RE and TC cells fire unusually long bursts at every cycle and in full synchrony. These results are consistent with the experimental observations of von Krosigk, Bal, and McCormick. We obtain such consistency only when the above assumptions regarding the synaptic dynamics, particularly nonsaturating GABAB synapses, are fulfilled. 5. The slice model has a stable rest state with no neural activity. By initially depolarizing a few neurons at one end of the slice while all the other cells are at rest, a recruitment process may be initiated, and a wavefront of oscillatory activity propagates across the slice. Ahead of the wavefront, neurons are quiescent; neurons behind it oscillate. We find that the wave progresses forward in a lurching manner. TC cells that have just become inhibited must be hyperpolarized for a long enough time before they can fire rebound bursts and recruit RE cells. This step limits the wavefront velocity and may involve a substantial part of the cycle when no cells at the front are depolarized. 6. The wavefront velocity increases linearly with the characteristic spatial length of the connectivity (the footprint length). It increases only gradually with the synaptic strength, logarithmically in the case of an exponential connection function and only slightly for a step connection function. It also decreases gradually with a potassium leak conductance that hyperpolarizes RE cells. 7. To reproduce the experimentally measured wavefront velocity of approximately 1 mm/s, together with other in vitro observations, both the RE-to-TC and the TC-to-RE projections in the model should be spatially localized. The sum of the RE-to-TC and the TC-to-RE synaptic footprint lengths should be on the order of 100 microns. (ABSTRACT TRUNCATED AT 250 WORDS)

Action Potentials↗

PubMed1995

Emergent spindle oscillations and intermittent burst firing in a thalamic model: specific neuronal mechanisms.

The rhythmogenesis of 10-Hz sleep spindles is studied in a large-scale thalamic network model with two cell populations: the excitatory thalamocortical (TC) relay neurons and the inhibitory nucleus reticularis thalami (RE) neurons. Spindle-like bursting oscillations emerge naturally from reciprocal interactions between TC and RE neurons. We find that the network oscillations can be synchronized coherently, even though the RE-TC connections are random and sparse, and even though individual neurons fire rebound bursts intermittently in time. When the fast gamma-aminobutyrate type A synaptic inhibition is blocked, synchronous slow oscillations resembling absence seizures are observed. Near-maximal network synchrony is established with even modest convergence in the RE-to-TC projection (as few as 5-10 RE inputs per TC cell suffice). The hyperpolarization-activated cation current (Ih) is found to provide a cellular basis for the intermittency of rebound bursting that is commonly observed in TC neurons during spindles. Such synchronous oscillations with intermittency can be maintained only with a significant degree of convergence for the TC-to-RE projection.

Models, Neurological↗

PubMed1995

Analysis of an autonomous phase model for neuronal parabolic bursting.

An understanding of the nonlinear dynamics of bursting is fundamental in unraveling structure-function relations in nerve and secretory tissue. Bursting is characterized by alternations between phases of rapid spiking and slowly varying potential. A simple phase model is developed to study endogenous parabolic bursting, a class of burst activity observed experimentally in excitable membrane. The phase model is motivated by Rinzel and Lee's dissection of a model for neuronal parabolic bursting (J. Math. Biol 25, 653-675 (1987)). Rapid spiking is represented canonically by a one-variable phase equation that is coupled bi-directionally to a two-variable slow system. The model is analyzed in the slow-variable phase plane, using quasi steady-state assumptions and formal averaging. We derive a reduced system to explore where the full model exhibits bursting, steady-states, continuous and modulated spiking. The relative speed of activation and inactivation of the slow variables strongly influences the burst pattern as well as other dynamics. We find conditions of the bistability of solutions between continuous spiking and bursting. Although the phase model is simple, we demonstrate that it captures many dynamical features of more complex biophysical models.

Animals↗

PubMed1995

Synchrony measures for biological neural networks.

Synchronous firing of a population of neurons has been observed in many experimental preparations; in addition, various mathematical neural network models have been shown, analytically or numerically, to contain stable synchronous solutions. In order to assess the level of synchrony of a particular network over some time interval, quantitative measures of synchrony are needed. We develop here various synchrony measures which utilize only the spike times of the neurons; these measures are applicable in both experimental situations and in computer models. Using a mathematical model of the CA3 region of the hippocampus, we evaluate these synchrony measures and compare them with pictorial representations of network activity. We illustrate how synchrony is lost and synchrony measures change as heterogeneity amongst cells increases. Theoretical expected values of the synchrony measures for different categories of network solutions are derived and compared with results of simulations.

Action Potentials↗

PubMed1995

A minimal, compartmental model for a dendritic origin of bistability of motoneuron firing patterns.

Various nonlinear regenerative responses, including plateau potentials and bistable repetitive firing modes, have been observed in motoneurons under certain conditions. Our simulation results support the hypothesis that these responses are due to plateau-generating currents in the dendrites, consistent with a major role for a noninactivating calcium L-type current as suggested by experiments. Bistability as observed in the soma of low- and higher-frequency spiking or, under TTX, of near resting and depolarized plateau potentials, occurs because the dendrites can be in a near resting or depolarized stable steady state. We formulate and study a two-compartment minimal model of a motoneuron that segregates currents for fast spiking into a soma-like compartment and currents responsible for plateau potentials into a dendrite-like compartment. Current flows between compartments through a coupling conductance, mimicking electrotonic spread. We use bifurcation techniques to illuminate how the coupling strength affects somatic behavior. We look closely at the case of weak coupling strength to gain insight into the development of bistable patterns. Robust somatic bistability depends on the electrical separation since it occurs only for weak to moderate coupling conductance. We also illustrate that hysteresis of the two spiking states is a natural consequence of the plateau behavior in the dendrite compartment.

Animals↗

PubMed1995

The potassium A-current, low firing rates and rebound excitation in Hodgkin-Huxley models.

It is widely believed, following the work of Connor and Stevens (1971, J. Physiol. Lond. 214, 31-53) that the ability to fire action potentials over a wide frequency range, especially down to very low rates, is due to the transient, potassium A-current (IA). Using a reduction of the classical Hodgkin-Huxley model, we study the effects of IA on steady firing rate, especially in the near-threshold regime for the onset of firing. A minimum firing rate of zero corresponds to a homoclinic bifurcation of periodic solutions at a critical level of stimulating current. It requires that the membrane's steady-state current-voltage relation be N-shaped rather than monotonic. For experimentally based generic IA parameters, the model does not fire at arbitrarily low rates, although it can for the more atypical IA parameters given by Connor and Stevens for the crab axon. When the IA inactivation rate is slow, we find that the transient potassium current can mediate more complex firing patterns, such as periodic bursting in some parameter regimes. The number of spikes per burst increases as gA decreases and as inactivation rate decreases. We also study how IA affects properties of transient voltage responses, such as threshold and firing latency for anodal break excitation. We provide mathematical explanations for several of these dynamic behaviors using bifurcation theory and averaging methods.

Action Potentials↗

PubMed1995

Spontaneous electrical and calcium oscillations in unstimulated pituitary gonadotrophs.

Single pituitary cells often fire spontaneous action potentials (APs), which are believed to underlie spiking fluctuations in cytosolic calcium concentration ([Ca2+]i). To address how these basal [Ca2+]i fluctuations depend on changes in plasma membrane voltage (V), simultaneous measurements of V and [Ca2+]i were performed in rat pituitary gonadotrophs. The data show that each [Ca2+]i spike is produced by the Ca2+ entry during a single AP. Using these and previously obtained patch-clamp data, we develop a quantitative mathematical model of this plasma membrane oscillator and the accompanying spatiotemporal [Ca2+]i oscillations. The model demonstrates that AP-induced [Ca2+]i spiking is prominent only in a thin shell layer neighboring the cell surface. This localized [Ca2+]i spike transiently activates the Ca2(+)- dependent K+ current resulting in a sharp afterhyperpolarization following each voltage spike. In accord with experimental observations, the model shows that the frequency and amplitude of the voltage spikes are highly sensitive to current injection and to the blocking of the Ca(2+)-sensitive current. Computations also predict that leaving the membrane channels intact, the firing rate can be modified by changing the Ca2+ handling parameters: the Ca2+ diffusion rate, the Ca2+ buffering capacity, and the plasma membrane Ca2+ pump rate. Finally, the model suggests reasons that spontaneous APs were seen in some gonadotrophs but not in others. This model provides a basis for further exploring how plasma membrane electrical activity is involved in the control of cytosolic calcium level in unstimulated as well as agonist-stimulated gonadotrophs.

Action Potentials↗

PubMed1995

InsP3-induced Ca2+ excitability of the endoplasmic reticulum.

Oscillations in intracellular Ca2+ can be induced by a variety of cellular signalling processes (Woods et al., 1986; Berridge 1988; Jacob et al., 1988) and appear to play a role in secretion (Stojilković et al., 1994), fertilization (Miyazaki et al., 1993), and smooth muscle contraction (Iino and Tsukioka, 1994). Recently, great progress has been made in understanding the mechanisms involved in a particular class of Ca2+ oscillation, associated with the second messenger inositol 1,4,5-trisphosphate (InsP3) (Berridge, 1993). Working in concert with intracellular Ca2+, InsP3 controls Ca2+ release via the InsP3 receptor in the endoplasmic reticulum (ER) (Berridge and Irvine, 1989). The IP3 receptor is regulated by its coagonists InsP3 and Ca2+, which both activate and inhibit Ca2+ release (Finch et al., 1991; Bezprozvanny et al., 1991; De Young and Keizer, 1992). These processes, together with the periodic activation of Ca2+ uptake into the ER, have been identified as key features in the mechanism of InsP3-induced Ca2+ oscillations in pituitary gonadotrophs (Li et al., 1994), Xenopus laevis oocytes (Lechleiter and Clapham, 1992; Atri et al., 1993), and other cell types (Keizer and De Young, 1993). Earlier discussions and models of InsP3-induced Ca2+ oscillations focused on the nature and number of internal releasable pools of Ca2+ (Goldbeter et al., 1990; Swillens and Mercan, 1990; Somogyi and Stucki, 1991), the importance of oscillations in InsP3 (Meyer and Stryer, 1988), and other issues not based on detailed experimental findings in specific cells types.

Animals↗

PubMed1995

Ca2+ excitability of the ER membrane: an explanation for IP3-induced Ca2+ oscillations.

Recent research dealing with experiments and theoretical models of Ca2+ excitability of the endoplasmic reticulum (ER) membrane induced by inositol 1,4,5-trisphosphate (IP3) is reviewed. Ca2+ excitability refers to the ability of a small increment of cytoplasmic Ca2+ concentration ([Ca2+]i) to trigger a large [Ca2+]i pulse or oscillations. Such nonlinear regenerative behavior is conferred by the existence of IP3 channels and Ca(2+)-ATPase transporters on the ER membrane, which extends throughout the cytoplasm. Ca2+ excitability resembles the plasma membrane electrical excitability of neurons and other cells: it is driven by the ionic concentration gradient across the ER membrane (higher Ca2+ concentration inside the ER); each [Ca2+]i spike partially consumes the prestored energy that is reestablished through ATP-dependent active transport; and [Ca2+]i, the excitation variable, controls the nonlinear dynamic release rate of ER Ca2+. This review focuses on the kinetic models based on these features and on experiments dealing with the kinetic properties of [Ca2+]i-dependent gating of the IP3 receptor channel. We summarize evidence in favor of two roles for [Ca2+]i in gating the channel's opening: activation at a rapid time scale and inactivation on a slower time scale. Exploiting an analogy to the well-known Hodgkin-Huxley model for neuronal electrical excitability, we show how Ca2+ excitability of the ER membrane can be explained by these gating properties combined with the ER Ca2+ pump activity. The theory's ability to predict is illustrated by comparing calculated with experimental [Ca2+]i responses for pituitary gonadotrophs under various stimulus conditions.

Animals↗

PubMed1994

Equations for InsP3 receptor-mediated [Ca2+]i oscillations derived from a detailed kinetic model: a Hodgkin-Huxley like formalism.

The nine-variable De Young-Keizer model (1992) for [Ca2+]i oscillations mediated by InsP3 receptor channels in endoplasmic reticulum (ER) membrane is analyzed and reduced to a two-variable system. The different time scales in the three basic channel gating processes, namely InsP3 regulation, Ca2+ activation, and Ca2+ inactivation, are revealed and characterized. The method of multiple scales is used in solving the equations on a succession of faster time scales and reducing them to a 2D system. The reduced system, (Vcy/fcy) dC/dt = -P1P3Rm3 infinity h3(C-C0)-PL(C-C0)-Jpump(C); dh/dt = (h infinity-h)/tau h, is analogous in form to the Hodgkin-Huxley equations for plasma membrane electrical excitability. [Ca2+]i dynamics in this model thus involve ER membrane-associated excitability. The reduced system has a bifurcation diagram almost identical to that of the original system and retains the most important dynamic features of the latter. The analysis also shows that the reduced system becomes simpler when the different gating processes are more independent from each other, i.e. when the rates for Ca2+ binding at the site associated with one gating process are independent of occupancy at the other two binding sites. Assuming further that binding of InsP3 does not depend on Ca2+ occupancy at the inactivation site, we obtain a "minimal" form yet retain significant ability to reproduce experimental observations.

Calcium↗

PubMed1994

Calcium oscillations in pituitary gonadotrophs: comparison of experiment and theory.

We have developed a mathematical model that describes several aspects of agonist-induced Ca2+ signaling in single pituitary gonadotrophs. Our model is based on fast activation of the inositol 1,4,5-trisphosphate (InsP3) receptor Ca2+ channels at low free cytosolic Ca2+ concentration ([Ca2+]i) and slow inactivation at high [Ca2+]i. Previous work has shown that these gating properties, when combined with a Ca(2+)-ATPase, are sufficient to generate simulated Ca2+ oscillations. The Hodgkin-Huxley-like description we formulate here incorporates these different gating properties explicitly and renders their effects transparent and easy to modulate. We introduce regulatory mechanisms of channel opening which enable the model, both in the absence and in the presence of Ca2+ entry, to give responses to a wide range of agonist doses that are in good agreement with experimental findings, including subthreshold responses, superthreshold oscillations with frequency determined by [InsP3], and nonoscillatory "biphasic" responses followed occasionally by small-amplitude oscillations. A particular added feature of our model, enhanced channel opening by reduced concentration of Ca2+ in the lumen of the endoplasmic reticulum, allows oscillations to continue during pool depletion. The model predicts that ionomycin and thapsigargin can induce oscillations with basal [InsP3] and zero Ca2+ entry, while Ca2+ injection cannot. Responses to specific pairings of sub- or superthreshold stimuli of agonist, ionomycin, and thapsigargin are also correctly predicted. Since this model encompasses a wide range of observed dynamic behaviors within a single framework, based on well-established mechanisms, its relevance should not be restricted to gonadotrophs.

Calcium↗

PubMed1994

Analysis of bursting in a thalamic neuron model.

We extend a quantitative model for low-voltage, slow-wave excitability based on the T-type calcium current (Wang et al. 1991) by juxtaposing it with a Hodgkin-Huxley-like model for fast sodium spiking in the high voltage regime to account for the distinct firing modes of thalamic neurons. We employ bifurcation analysis to illustrate the stimulus-response behavior of the full model under both voltage regimes. The model neuron shows continuous sodium spiking when depolarized sufficiently from rest. Depending on the parameters of calcium current inactivation, there are two types of low-voltage responses to a hyperpolarizing current step: a single rebound low threshold spike (LTS) upon release of the step and periodic LTSs. Bursting is seen as sodium spikes ride the LTS crest. In both cases, we analyze the LTS burst response by projecting its trajectory into a fast/slow phase plane. We also use phase plane methods to show that a potassium A-current shifts the threshold for sodium spikes, reducing the number of fast sodium spikes in an LTS burst. It can also annihilate periodic bursting. We extend the previous work of Rose and Hindmarsh (1989a-c) for a thalamic neuron and propose a simpler model for thalamic activity. We consider burst modulation by using a neuromodulator-dependent potassium leakage conductance as a control parameter. These results correspond with experiments showing that the application of certain neurotransmitters can switch firing modes.

Action Potentials↗

PubMed1994

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.

Animals↗

PubMed1994

Synchronization properties of spindle oscillations in a thalamic reticular nucleus model.

1. We address the hypothesis of Steriade and colleagues that the thalamic reticular nucleus (RE) is a pacemaker for thalamocortical spindle oscillations by developing and analyzing a model of a large population of all-to-all coupled inhibitory RE neurons. 2. Each RE neuron has three ionic currents: a low-threshold T-type Ca2+ current (ICa-T), a calcium-activated potassium current (IAHP) and a leakage current (IL). ICa-T underlies a cell's postinhibitory rebound properties, whereas IAHP hyperpolarizes the neuron after a burst. Each neuron, which is a conditional oscillator, is coupled to all other RE neurons via fast gamma-aminobutyric acid-A (GABAA) and slow GABAB synapses. 3. For generating network oscillations IAHP may not be necessary. Synaptic inhibition can provide the hyperpolarization for deinactivating ICa-T that causes bursting if the reversal potentials for GABAA and GABAB synapses are sufficiently negative. 4. If model neurons display sufficiently powerful rebound excitability, an isolated RE network of such neurons oscillates with partial but typically not full synchrony. The neurons spontaneously segregate themselves into several macroscopic clusters. The neurons within a cluster follow the same time course, but the clusters oscillate differently from one another. In addition to activity patterns in which clusters burst sequentially (e.g., 2 or 3 clusters bursting alternately), a two-cluster state may occur with one cluster active and one quiescent. Because the neurons are all-to-all coupled, the cluster states do not have any spatial structure. 5. We have explored the sensitivity of such partially synchronized patterns to heterogeneity in cells' intrinsic properties and to simulated neuroelectric noise. Although either precludes precise clustering, modest levels of heterogeneity or noise lead to approximate clustering of active cells. The population-averaged voltage may oscillate almost regularly but individual cells burst at nearly every second cycle or less frequently. The active-quiescent state is not robust at all to heterogeneity or noise. Total asynchrony is observed when heterogeneity or noise is too large, e.g., even at 25% heterogeneity for our reference set of parameter values. 6. The fast GABAA inhibition (with a reversal potential more negative than, say, -65 mV) favors the cluster states and prevents full synchrony. Our simulation results suggest two mechanisms that can fully synchronize the isolated RE network model. With GABAA removed or almost totally blocked, GABAB inhibition (because it is slow) can lead to full synchrony, which is partially robust to heterogeneity and noise.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals↗

PubMed1993

Spindle rhythmicity in the reticularis thalami nucleus: synchronization among mutually inhibitory neurons.

The sleep spindle rhythm of thalamic origin (7-14 Hz) displays widespread synchronization among thalamic nuclei and over most of the neocortex. The mechanisms which mediate such global synchrony are not yet well understood. Here, we theoretically address the hypothesis of Steriade and colleagues that the reticularis thalami nucleus may be considered as a genuine pacemaker for thalamocortical spindles. Interestingly, the reticularis consists of a population of neurons which are GABAergic and synaptically coupled. These cells, as do thalamic relay cells, exhibit a transient depolarization following release from sustained hyperpolarization. This postinhibitory rebound property is due to a T-type calcium ionic current which is inactivated at rest but de-inactivated by hyperpolarization. Theoretically, rebound-capable cells coupled by inhibition can generate rhythmic activity, although such oscillations are usually alternating (out-of-phase), rather than synchronous (in-phase). Here, we develop and apply to Steriade's pacemaker hypothesis our earlier finding that mutual inhibition can in fact synchronize cells, provided that the postsynaptic conductance decays sufficiently slowly. Indeed, postsynaptic receptors of the GABAB subtype mediate inhibition with a large decay time-constant (approximately 200 ms). In contrast, chloride-dependent, GABAA-mediated inhibitory postsynaptic potentials are fast and brief. Both GABAA and GABAB receptor binding sites are present in most thalamic regions, including the reticularis. We suggest that if GABAB receptors exist postsynaptically in the reticularis, they may play a critical role in the rhythmic synchronization among reticular neurons, hence in the thalamocortical system.

Calcium Channels↗

PubMed1993

Diffusion of extracellular K+ can synchronize bursting oscillations in a model islet of Langerhans.

Electrical bursting oscillations of mammalian pancreatic beta-cells are synchronous among cells within an islet. While electrical coupling among cells via gap junctions has been demonstrated, its extent and topology are unclear. The beta-cells also share an extracellular compartment in which oscillations of K+ concentration have been measured (Perez-Armendariz and Atwater, 1985). These oscillations (1-2 mM) are synchronous with the burst pattern, and apparently are caused by the oscillating voltage-dependent membrane currents: Extracellular K+ concentration (Ke) rises during the depolarized active (spiking) phase and falls during the hyperpolarized silent phase. Because raising Ke depolarizes the cell membrane by increasing the potassium reversal potential (VK), any cell in the active phase should recruit nonspiking cells into the active phase. The opposite is predicted for the silent phase. This positive feedback system might couple the cells' electrical activity and synchronize bursting. We have explored this possibility using a theoretical model for bursting of beta-cells (Sherman et al., 1988) and K+ diffusion in the extracellular space of an islet. Computer simulations demonstrate that the bursts synchronize very quickly (within one burst) without gap junctional coupling among the cells. The shape and amplitude of computed Ke oscillations resemble those seen in experiments for certain parameter ranges. The model cells synchronize with exterior cells leading, though incorporating heterogeneous cell properties can allow interior cells to lead. The model islet can also be forced to oscillate at both faster and slower frequencies using periodic pulses of higher K+ in the medium surrounding the islet. Phase plane analysis was used to understand the synchronization mechanism. The results of our model suggest that diffusion of extracellular K+ may contribute to coupling and synchronization of electrical oscillations in beta-cells within an islet.

Animals↗

PubMed1993

Why pancreatic islets burst but single beta cells do not. The heterogeneity hypothesis.

Previous mathematical modeling of beta cell electrical activity has involved single cells or, recently, clusters of identical cells. Here we model clusters of heterogeneous cells that differ in size, channel density, and other parameters. We use gap-junctional electrical coupling, with conductances determined by an experimental histogram. We find that, for reasonable parameter distributions, only a small proportion of isolated beta cells will burst when uncoupled, at any given value of a glucose-sensing parameter. However, a coupled, heterogeneous cluster of such cells, if sufficiently large (approximately 125 cells), will burst synchronously. Small clusters of such cells will burst only with low probability. In large clusters, the dynamics of intracellular calcium compare well with experiments. Also, these clusters possess a dose-response curve of increasing average electrical activity with respect to a glucose-sensing parameter that is sharp when the cluster is coupled, but shallow when the cluster is decoupled into individual cells. This is in agreement with comparative experiments on cells in suspension and islets.

Animals↗