Excitatory Coupling Research Articles

Modulation of excitatory synaptic coupling facilitates synchronization and complex dynamics in a biophysical model of neuronal dynamics

In this paper, complex dynamical synchronization in a non-linear model of a neural system is studied, and the computational significance of the behaviours is explored. The local neural dynamics is determined by voltage-and ligand-gated ion channels and feedback between densely interconnected excitatory and inhibitory neurons. A mesoscopic array of local networks is modelled by introducing coupling between the local networks via weak excitatory-to-excitatory connectivity. It is shown that with modulation of this long-range synaptic coupling, the system undergoes a transition from independent oscillations to stable chaotic synchronization. Between these states exists a ‘weakly’ stable state associated with complex, intermittent behaviour in the temporal domain and clusters of synchronous regions in the spatial domain. The paper concludes with a discussion of the putative relevance of such processes in the brain, including the role of neuromodulatory systems and the mechanisms underlying sensory perception, adaptation, computation and complexity.

Bidirectional plasticity of excitatory postsynaptic potential (EPSP)-spike coupling in CA1 hippocampal pyramidal neurons.

Integration of synaptic excitation to generate an action potential (excitatory postsynaptic potential-spike coupling or E-S coupling) determines the neuronal output. Bidirectional synaptic plasticity is well established in the hippocampus, but whether active synaptic integration can display potentiation and depression remains unclear. We show here that synaptic depression is associated with an N-methyl-d-aspartate receptor-dependent and long-lasting depression of E-S coupling. E-S depression is input-specific and is expressed in the presence of gamma-aminobutyric acid type A and B receptor antagonists. In single neurons, E-S depression is observed without modification of postsynaptic passive properties. We conclude that a decrease in intrinsic excitability underlies E-S depression and is synergic with glutamatergic long-term depression.

Spiking neuron models with excitatory or inhibitory synaptic couplings and synchronization phenomena.

We investigate synchronization phenomena in a system of two piecewise-linear-type model neurons with excitatory or inhibitory synaptic couplings. Employing the phase plane analysis and a singular perturbation approach to split the dynamics into slow and fast ones, we construct analytically the Poincaré map of the solution to the piecewise-linear equations. We investigate conditions for the occurrence of synchronized oscillations of in phase as well as of antiphase in terms of parameters representing the strength of the synaptic coupling and the decaying relaxation rate of the synaptic dynamics. We present the results of numerical simulations that agree with our theoretical ones.

Reciprocal intraglomerular excitation and intra- and interglomerular lateral inhibition between mouse olfactory bulb mitral cells.

How patterns of odour-evoked glomerular activity are transformed into patterns of mitral cell action potentials (APs) in the olfactory bulb is determined by the functional connectivity of the cell populations in the bulb. We have used paired whole-cell voltage recordings from olfactory bulb slices to compare the functional connectivity of mitral cells to the known anatomy of the mitral cell network. Both inhibitory and excitatory coupling were observed between pairs of mitral cells. Inhibitory coupling was seen as an increased frequency of small, asynchronous GABAergic IPSPs following APs in the presynaptic cell. Excitatory coupling was short in latency, beginning about 1.3 ms after the presynaptic AP and was mediated by both NMDA and AMPA receptors. Mitral cell pairs were coupled by excitation if and only if their apical dendrites terminated in the same glomerulus. The excitatory coupling between mitral cells resembles conventional fast synaptic transmission in its time course, amplitude and latency, despite the absence of evidence for anatomically defined synapses between mitral cells.

New attractor states for synchronous activity in synfire chains with excitatory and inhibitory coupling.

In a feedforward network of integrate-and-fire neurons, where the firing of each layer is synchronous (synfire chain), the final firing state of the network converges to two attractor states: either a full activation or complete fading of the tailing layers. In this article, we analyze various modes of pattern propagation in a synfire chain with random connection weights and delta-type postsynaptic currents. We predict analytically that when the input is fully synchronized and the network is noise free, varying the characteristics of the weights distribution would result in modes of behavior that are different from those described in the literature. These are convergence to fixed points, limit cycles, multiple periodic, and possibly chaotic dynamics. We checked our analytic results by computer simulation of the network, and showed that the above results can be generalized when the input is asynchronous and neurons are spontaneously active at low rates.

Stochastic resonance in spatially extended systems: the role of far from equilibrium potentials

Previous works have shown numerically that the response of a “stochastic resonator” is enhanced as a consequence of spatial coupling. Also, similar results have been obtained in a reaction–diffusion model by studying the phenomenon of stochastic resonance (SR) in spatially extended systems using nonequilibrium potential (NEP) techniques. The knowledge of the NEP for such systems allows us to determine the probability for the decay of the metastable extended states, and approximate expressions for the correlation function and the signal-to-noise ratio. Here, exploiting known forms of the NEP, we have investigated the role of NEP's symmetry on SR, the enhancement of the SNR due to a selectivity of the coupling or diffusion parameter, and discussed competition between local and nonlocal (excitatory) coupling.

Synchronized Activity and Loss of Synchrony Among Heterogeneous Conditional Oscillators

The inspiratory phase of the respiratory rhythm involves the synchronized bursting of a network of neurons in the brain stem. This paper considers activity patterns in a reduced model for this network, namely, a system of conductance-based ordinary differential equations with excitatory synaptic coupling, incorporating heterogeneities across cells. The model cells are relaxation oscillators; that is, no spikes are included. In the continuum limit, under assumptions based on the disparate time scales in the model, we derive consistency conditions sufficient to give tightly synchronized oscillations; when these hold, we solve a fixed point equation to find a unique synchronized periodic solution. This solution is stable within a certain solution class, and we provide a general sufficient condition for its stability. Allowing oscillations that are less cohesive but still synchronized, we derive an ordinary differential equation boundary value problem that we solve numerically to find a corresponding periodic solution. These results help explain how heterogeneities among synaptically coupled oscillators can enhance the tendency toward synchronization of their activity. Finally, we consider conditions for synchrony to break down.

Modelling inter-segmental coordination of neuronal oscillators: synaptic mechanisms for uni-directional coupling during swimming in Xenopus tadpoles.

Locomotion requires longitudinal co-ordination. We have examined uni-directional synaptic coupling processes between two classes of neuronal network oscillators: autonomously active "intrinsic" oscillators, and "potential" oscillators that lack sufficient excitatory drive for autonomous activity. We model such oscillator networks in the bilaterally-symmetrical, Xenopus tadpole spinal cord circuits that co-ordinate swimming. "Glutamate" coupling EPSPs can entrain a second oscillator of lower frequency provided their strength is sufficient. Fast (AMPA) EPSPs advance spiking on each cycle, while slow (NMDA) EPSPs increase frequency over many cycles. EPSPs can also enable rhythmicity in "potential" oscillators and entrain them. IPSPs operate primarily on a cycle-by-cycle basis. They can advance or delay spiking to entrain a second "intrinsic" oscillator with higher, equal or lower frequency. Bilaterally symmetrical coupling connections operate twice per cycle: once in each half-cycle, on each side of the receiving oscillator. Excitatory and inhibitory coupling allow entrainment in complimentary areas of parameter space.

Models of Respiratory Rhythm Generation in the Pre-Bötzinger Complex. III. Experimental Tests of Model Predictions

We used the testable predictions of mathematical models proposed by Butera et al. to evaluate cellular, synaptic, and population-level components of the hypothesis that respiratory rhythm in mammals is generated in vitro in the pre-Bötzinger complex (pre-BötC) by a heterogeneous population of pacemaker neurons coupled by fast excitatory synapses. We prepared thin brain stem slices from neonatal rats that capture the pre-BötC and maintain inspiratory-related motor activity in vitro. We recorded pacemaker neurons extracellularly and found: intrinsic bursting behavior that did not depend on Ca(2+) currents and persisted after blocking synaptic transmission; multistate behavior with transitions from quiescence to bursting and tonic spiking states as cellular excitability was increased via extracellular K(+) concentration ([K(+)](o)); a monotonic increase in burst frequency and decrease in burst duration with increasing [K(+)](o); heterogeneity among different cells sampled; and an increase in inspiratory burst duration and decrease in burst frequency by excitatory synaptic coupling in the respiratory network. These data affirm the basis for the network model, which is composed of heterogeneous pacemaker cells having a voltage-dependent burst-generating mechanism dominated by persistent Na(+) current (I(NaP)) and excitatory synaptic coupling that synchronizes cell activity. We investigated population-level activity in the pre-BötC using local "macropatch" recordings and confirmed these model predictions: pre-BötC activity preceded respiratory-related motor output by 100-400 ms, consistent with a heterogeneous pacemaker-cell population generating inspiratory rhythm in the pre-BötC; pre-BötC population burst amplitude decreased monotonically with increasing [K(+)](o) (while frequency increased), which can be attributed to pacemaker cell properties; and burst amplitude fluctuated from cycle to cycle after decreasing bilateral synaptic coupling surgically as predicted from stability analyses of the model. We conclude that the pacemaker cell and network models explain features of inspiratory rhythm generation in vitro.

Mechanisms underlying regulation of respiratory pattern by nicotine in preBötzinger complex.

Cholinergic neurotransmission plays a role in regulation of respiratory pattern. Nicotine from cigarette smoke affects respiration and is a risk factor for sudden infant death syndrome (SIDS) and sleep-disordered breathing. The cellular and synaptic mechanisms underlying this regulation are not understood. Using a medullary slice preparation from neonatal rat that contains the preBötzinger Complex (preBötC), the hypothesized site for respiratory rhythm generation, and generates respiratory-related rhythm in vitro, we examined the effects of nicotine on excitatory neurotransmission affecting inspiratory neurons in preBötC and on the respiratory-related motor activity from hypoglossal nerve (XIIn). Microinjection of nicotine into preBötC increased respiratory frequency and decreased the amplitude of inspiratory bursts, whereas when injected into XII nucleus induced a tonic activity and an increase in amplitude but not in frequency of inspiratory bursts from XIIn. Bath application of nicotine (0.2--0.5 microM, approximately the arterial blood nicotine concentration immediately after smoking a cigarette) increased respiratory frequency up to 280% of control in a concentration-dependent manner. Nicotine decreased the amplitude to 82% and increased the duration to 124% of XIIn inspiratory bursts. In voltage-clamped preBötC inspiratory neurons (including neurons with pacemaker properties), nicotine induced a tonic inward current of -19.4 +/- 13.4 pA associated with an increase in baseline noise. Spontaneous excitatory postsynaptic currents (sEPSCs) present during the expiratory period increased in frequency to 176% and in amplitude to 117% of control values; the phasic inspiratory drive inward currents decreased in amplitude to 66% and in duration to 89% of control values. The effects of nicotine were blocked by mecamylamine (Meca). The inspiratory drive current and sEPSCs were completely eliminated by 6-cyano-7-nitroquinoxaline-2,3-dione (CNQX) in the presence or absence of nicotine. In the presence of tetrodotoxin (TTX), low concentrations of nicotine did not induce any tonic current or any increase in baseline noise, nor affect the input resistance in inspiratory neurons. In this study, we demonstrated that nicotine increased respiratory frequency and regulated respiratory pattern by modulating the excitatory neurotransmission in preBötC. Activation of nicotinic acetylcholine receptors (nAChRs) enhanced the tonic excitatory synaptic input to inspiratory neurons including pacemaker neurons and at the same time, inhibited the phasic excitatory coupling between these neurons. These mechanisms may account for the cholinergic regulation of respiratory frequency and pattern.

A Current-Mode Hysteretic Winner-take-all Network, with Excitatory and Inhibitory Coupling

Winner-take-all (WTA) circuits are commonly used in a wide variety of applications. One of the most used current-mode WTA designs is the one originally proposed by Lazzaro et al. [1]. Several extensions to this design have been suggested in the past. In this paper we present a variant of this current-mode WTA circuit, containing all of the enhancements previously proposed, together with new additional modifications that endow it with interesting hysteretic and lateral inhibition and excitation properties. We compare the performance of this WTA circuit to the original WTA design, providing experimental data obtained from a VLSI chip containing both types of circuits, designed using closely matched layouts. We derive analytically the response properties of the circuit's lateral diffusion network, pointing out the differences to previously proposed diffusion networks, and present experimental data confirming the theoretical predictions. We also describe application domains that can best exploit these types of hysteretic WTA circuits.

Self-organized localization of macrostates by additive noise in a fast-slow dynamical system: effect of the slow nonreactive mode on the barrier crossing rate of the fast, bistable mode

We have studied the stochastic dynamics of a two-dimensional gradient system composed of a fast, bistable mode and a slow, monotonically decaying mode. The coupling is bidirectional and cooperative. Additive white noise acts on the fast mode only. We find that the noise intensity controls the location of macrostates (shape of the probability density function), the appearance of bimodality in the slow-mode probability distribution and, together with the coupling strength, the rate of fast-mode barrier crossing. These features arise from the interplay of noise, widely separated time scales, and bidirectional, excitatory coupling. They are believed to be generic.

Neural mechanisms potentially contributing to the intersegmental phase lag in lamprey.II. Hemisegmental oscillations produced by mutually coupled excitatory neurons.

Most previous models of the spinal central pattern generator (CPG) underlying locomotion in the lamprey have relied on reciprocal inhibition between the left and right side for oscillations to be produced. Here, we have explored the consequences of using self-oscillatory hemisegments. Within a single hemisegment, the oscillations are produced by a network of recurrently coupled excitatory neurons (E neurons) that by themselves are not oscillatory but when coupled together through N-methyl-d-aspartate (NMDA) and alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionicacid (AMPA)/kainate transmission can produce oscillations. The bursting mechanism relies on intracellular accumulation of calcium that activates Ca(2+)-dependent K(+). The intracellular calcium is modeled by two different intracellular calcium pools, one of which represents the calcium entry following the action potential, Ca(AP) pool, and the other represents the calcium inflow through the NMDA channels, Ca(NMDA) pool. The Ca(2+)-dependent K(+) activated by these two calcium pools are referred to as K(CaAP) and K(CaNMDA), respectively, and their relative conductances are modulated and increase with the background activation of the network. When changing the background stimulation, the bursting activity in this network can be made to cover a frequency range of 0.5-5.5 Hz with reasonable burst proportions if the adaptation is modulated with the activity. When a chain of such hemisegments are coupled together, a phase lag along the chain can be produced. The local oscillations as well as the phase lag is dependent on the axonal conduction delay as well as the types of excitatory coupling that are assumed, i.e. AMPA/kainate and/or NMDA. When the caudal excitatory projections are extended further than the rostral ones, and assumed to be of approximately equal strength, this kind of network is capable of reproducing several experimental observations such as those occurring during strychnine blockade of the left-right reciprocal inhibition. Addition of reciprocally coupled inhibitory neurons in such a network gives rise to antiphasic activity between the left and right side, but not necessarily to any change of the frequency if the burst proportion of the hemisegmental bursts is well below 50%. Prolongation of the C neuron projection in the rostrocaudal direction restricts the phase lag produced by only the excitatory hemisegmental network by locking together the interburst intervals at different levels of the spinal cord.

Simulation of EEG: dynamic changes in synaptic efficacy, cerebral rhythms, and dissipative and generative activity in cortex.

A simulation of electrocortical activity based upon coupled local aggregates of excitatory and inhibitory cells was modified to include rapid dynamic variations of synaptic efficacy attributable to reversal potentials and related effects. The modified simulation reproduces the rhythmic phenomena observed in real EEG, including the theta, alpha, beta and gamma rhythms, in association with physiologically realistic pulse densities. At high levels of cortical activation, generative activity with a 40-Hz center frequency emerges, suggesting a basis for the occurrence of phase changes and "edge of chaos" dynamics. These local oscillation properties complement the dissipative travelling wave and synchronous oscillation effects attributable to longer range excitatory couplings, as previously demonstrated in related simulations. Results of variation of parameters provide a first approximation to the anticipated effects of slow physiological time variations in gains and lags, and some predictions of the model are described.

Models of respiratory rhythm generation in the pre-Bötzinger complex. I. Bursting pacemaker neurons.

A network of oscillatory bursting neurons with excitatory coupling is hypothesized to define the primary kernel for respiratory rhythm generation in the pre-Bötzinger complex (pre-BötC) in mammals. Two minimal models of these neurons are proposed. In model 1, bursting arises via fast activation and slow inactivation of a persistent Na+ current INaP-h. In model 2, bursting arises via a fast-activating persistent Na+ current INaP and slow activation of a K+ current IKS. In both models, action potentials are generated via fast Na+ and K+ currents. The two models have few differences in parameters to facilitate a rigorous comparison of the two different burst-generating mechanisms. Both models are consistent with many of the dynamic features of electrophysiological recordings from pre-BötC oscillatory bursting neurons in vitro, including voltage-dependent activity modes (silence, bursting, and beating), a voltage-dependent burst frequency that can vary from 0.05 to >1 Hz, and a decaying spike frequency during bursting. These results are robust and persist across a wide range of parameter values for both models. However, the dynamics of model 1 are more consistent with experimental data in that the burst duration decreases as the baseline membrane potential is depolarized and the model has a relatively flat membrane potential trajectory during the interburst interval. We propose several experimental tests to demonstrate the validity of either model and to differentiate between the two mechanisms.

Models of respiratory rhythm generation in the pre-Bötzinger complex. II. Populations Of coupled pacemaker neurons.

We have proposed models for the ionic basis of oscillatory bursting of respiratory pacemaker neurons in the pre-Bötzinger complex. In this paper, we investigate the frequency control and synchronization of these model neurons when coupled by excitatory amino-acid-mediated synapses and controlled by convergent synaptic inputs modeled as tonic excitation. Simulations of pairs of identical cells reveal that increasing tonic excitation increases the frequency of synchronous bursting, while increasing the strength of excitatory coupling between the neurons decreases the frequency of synchronous bursting. Low levels of coupling extend the range of values of tonic excitation where synchronous bursting is found. Simulations of a heterogeneous population of 50-500 bursting neurons reveal coupling effects similar to those found experimentally in vitro: coupling increases the mean burst duration and decreases the mean burst frequency. Burst synchronization occurred over a wide range of intrinsic frequencies (0.1-1 Hz) and even in populations where as few as 10% of the cells were intrinsically bursting. Weak coupling, extreme parameter heterogeneity, and low levels of depolarizing input could contribute to the desynchronization of the population and give rise to quasiperiodic states. The introduction of sparse coupling did not affect the burst synchrony, although it did make the interburst intervals more irregular from cycle to cycle. At a population level, both parameter heterogeneity and excitatory coupling synergistically combine to increase the dynamic input range: robust synchronous bursting persisted across a much greater range of parameter space (in terms of mean depolarizing input) than that of a single model cell. This extended dynamic range for the bursting cell population indicates that cellular heterogeneity is functionally advantageous. Our modeled system accounts for the range of intrinsic frequencies and spiking patterns of inspiratory (I) bursting cells found in the pre-Bötzinger complex in neonatal rat brain stem slices in vitro. There is a temporal dispersion in the spiking onset times of neurons in the population, predicted to be due to heterogeneity in intrinsic neuronal properties, with neurons starting to spike before (pre-I), with (I), or after (late-I) the onset of the population burst. Experimental tests for a number of the model's predictions are proposed.

The synaptic NMDA component desynchronizes neural bursters

The influence of excitatory and inhibitory coupling on synchronization depends on the temporal dynamics of the synapse. Slow excitation is desynchronizing whereas fast excitation tends to synchronize neuronal firing. Excitation via glutamatergic synapses, however, activates both ionotropic AMPA/kainate and NMDA receptors. Here we analyze the role of the synaptic NMDA component. We show that slowly bursting neurons desynchronize when connected by symmetrical NMDA synapses whereas they tend to synchronize when coupled with symmetrical AMPA/kainate synapses. This suggests that the effect on synchronization of an excitatory synapse also depends on the relative proportion of NMDA and AMPA/kainate synapses.

The dynamical model of locomotor-like movements evoked by muscle vibration in humans

A phenomenological model of central pattern generator is proposed for qualitative description, within the framework of traditional concepts of motoneural and skeleto—muscular sysiem of human leg, of dynamics of spontaneous stepping movements evoked by muscle vibration. In particular, it describes bistability of «forward» and «backward» stepping and chaotic transitions between them. The model consists of two self-excited oscillators with nonlinear coupling, the action of which resembles qualitatively the action of a combination of excitatory and inhibitory chemical couplings typical for neural networks. The analysis is made on the example of the interaction of two identical Van der Pol - Duffing generators.

Synaptic reorganization in explanted cultures of rat hippocampus

Due to loss of afferent innervation, synaptic reorganization occurs in organotypic hippocampal slice cultures. With extra- and intracellular recordings, we confirm that the excitatory loop from the dentate gyrus (DG) to CA3 and further to CA1 is preserved. However, hilar stimulation evoked antidromic population spikes in the DG which were followed by a population postsynaptic potential (PPSP); intracellularly, an antidromic spike with a broad shoulder or EPSP/IPSP sequences were induced. Synaptic responses were blocked by glutamate receptor antagonists. Stimulation of CA1 induced a PPSP in DG. Dextranamine stained pyramidal cells of CA1 were shown to project to DG. After removal of area CA3, DG's and mossy fibers' (MF) stimulation still elicited PPSPs and EPSP/IPSP sequences in area CA1 which disappeared when a cut was made through the hippocampal fissure. During bicuculline perfusion, hilar stimulation caused EPSPs in granule cells and spontaneous and evoked repetitive firing appeared even after its isolation from areas CA3 and CA1. Collateral excitatory synaptic coupling between granule cells was confirmed by paired recordings. Besides the preservation of the trisynaptic pathway in this preparation, new functional synaptic contacts appear, presumably due to MF collateral sprouting and formation of pathways between areas CA1 and DG.

Simple models for excitable and oscillatory neural networks.

Chains of coupled oscillators of simple "rotator" type have been used to model the central pattern generator (CPG) for locomotion in lamprey, among numerous applications in biology and elsewhere. In this paper, motivated by experiments on lamprey CPG with brainstem attached, we investigate a simple oscillator model with internal structure which captures both excitable and bursting dynamics. This model, and that for the coupling functions, is inspired by the Hodgkin-Huxley equations and two-variable simplifications thereof. We analyse pairs of coupled oscillators with both excitatory and inhibitory coupling. We also study traveling wave patterns arising from chains of oscillators, including simulations of "body shapes" generated by a double chain of oscillators providing input to a kinematic musculature model of lamprey.