Conflicting effects of excitatory synaptic and electric coupling on the dynamics of square-wave bursters

Using two-cell and 50-cell networks of square-wave bursters, we studied how excitatory coupling of individual neurons affects the bursting output of the network. Our results show that the effects of synaptic excitation vs. electrical coupling are distinct. Increasing excitatory synaptic coupling generally increases burst duration. Electrical coupling also increases burst duration for low to moderate values, but at sufficiently strong values promotes a switch to highly synchronous bursts where further increases in electrical or synaptic coupling have a minimal effect on burst duration. These effects are largely mediated by spike synchrony, which is determined by the stability of the in-phase spiking solution during the burst. Even when both coupling mechanisms are strong, one form (in-phase or anti-phase) of spike synchrony will determine the burst dynamics, resulting in a sharp boundary in the space of the coupling parameters. This boundary exists in both two cell and network simulations. We use these results to interpret the effects of gap-junction blockers on the neuronal circuitry that underlies respiration.     

Dispersion and time delay effects in synchronized spike–burst networks

We study spike–burst neural activity and investigate its transitions to synchronized states under electrical coupling. Our reported results include the following: (1) Synchronization of spike–burst activity is a multi-time scale phenomenon and burst synchrony is easier to achieve than spike synchrony. (2) Synchrony of networks with time-delayed connections can be achieved at lower coupling strengths than within the same network with instantaneous couplings. (3) The introduction of parameter dispersion into the network destroys the existence of synchrony in the strict sense, but the network dynamics in major regimes of the parameter space can still be effectively captured by a mean field approach if the couplings are excitatory. Our results on synchronization of spiking networks are general of nature and will aid in the development of minimal models of neuronal populations. The latter are the building blocks of large scale brain networks relevant for cognitive processing.     

Complex evolution of spike patterns during burst propagation through feed-forward networks

Stable signal transmission is crucial for information processing by the brain. Synfire-chains, defined as feed-forward networks of spiking neurons, are a well-studied class of circuit structure that can propagate a packet of single spikes while maintaining a fixed packet profile. Here, we studied the stable propagation of spike bursts, rather than single spike activities, in a feed-forward network of a general class of excitable bursting neurons. In contrast to single spikes, bursts can propagate stably without converging to any fixed profiles. Spike timings of bursts continue to change cyclically or irregularly during propagation depending on intrinsic properties of the neurons and the coupling strength of the network. To find the conditions under which bursts lose fixed profiles, we propose an analysis based on timing shifts of burst spikes similar to the phase response analysis of limit-cycle oscillators.     

Bursting dynamics remarkably improve the performance of neural networks on liquid computing

Burst firings are functionally important behaviors displayed by neural circuits, which plays a primary role in reliable transmission of electrical signals for neuronal communication. However, with respect to the computational capability of neural networks, most of relevant studies are based on the spiking dynamics of individual neurons, while burst firing is seldom considered. In this paper, we carry out a comprehensive study to compare the performance of spiking and bursting dynamics on the capability of liquid computing, which is an effective approach for intelligent computation of neural networks. The results show that neural networks with bursting dynamic have much better computational performance than those with spiking dynamics, especially for complex computational tasks. Further analysis demonstrate that the fast firing pattern of bursting dynamics can obviously enhance the efficiency of synaptic integration from pre-neurons both temporally and spatially. This indicates that bursting dynamic can significantly enhance the complexity of network activity, implying its high efficiency in information processing.     

The origin of spontaneous synchronized burst in cultured neuronal networks based on multi-electrode arrays

Many neural networks in mammalian central nervous system (CNS) fire single spike and complex spike burst. In fact, the conditions for triggering burst are not well understood. In the paper multi-electrode arrays (MEA) are used to record the spontaneous electrophysiological activities of cultured rat hippocampal neuronal network for a long time. After about 3 weeks culture, a transition from single spike to burst is observed in several networks. All of these spikes fire quickly before burst begins. The firing rate during the burst is lower than that just before the burst, but differences of inter-spike intervals (ISIs) between two firing patterns are not clear. Moreover, the electrical activities on neighboring electrodes show strong synchrony during the burst activities. In a word, the generation of the burst requires that network should have a sufficient level of excitation as well as a balance of synaptic inhibition.     

Balanced networks under spike-time dependent plasticity

The dynamics of local cortical networks are irregular, but correlated. Dynamic excitatory–inhibitory balance is a plausible mechanism that generates such irregular activity, but it remains unclear how balance is achieved and maintained in plastic neural networks. In particular, it is not fully understood how plasticity induced changes in the network affect balance, and in turn, how correlated, balanced activity impacts learning. How do the dynamics of balanced networks change under different plasticity rules? How does correlated spiking activity in recurrent networks change the evolution of weights, their eventual magnitude, and structure across the network? To address these questions, we develop a theory of spike–timing dependent plasticity in balanced networks. We show that balance can be attained and maintained under plasticity–induced weight changes. We find that correlations in the input mildly affect the evolution of synaptic weights. Under certain plasticity rules, we find an emergence of correlations between firing rates and synaptic weights. Under these rules, synaptic weights converge to a stable manifold in weight space with their final configuration dependent on the initial state of the network. Lastly, we show that our framework can also describe the dynamics of plastic balanced networks when subsets of neurons receive targeted optogenetic input.     

Selectivity of stimulus induced responses in cultured hippocampal networks on microelectrode arrays

Sensory information can be encoded using the average firing rate and spike occurrence times in neuronal network responses to external stimuli. Decoding or retrieving stimulus characteristics from the response pattern generally implies that the corresponding neural network has a selective response to various input signals. The role of various spiking activity characteristics (e.g., spike rate and precise spike timing) for basic information processing was widely investigated on the level of neural populations but gave inconsistent evidence for particular mechanisms. Multisite electrophysiology of cultured neural networks grown on microelectrode arrays is a recently developed tool and currently an active research area. In this study, we analyzed the stimulus responses represented by network-wide bursts evoked from various spatial locations (electrodes). We found that the response characteristics, such as the burst initiation time and the spike rate, can be used to retrieve information about the stimulus location. The best selectivity in the response spiking pattern could be found for a small subpopulation of neurones (electrodes) at relatively short post-stimulus intervals. Such intervals were unique for each culture due to the non-uniform organization of the functional connectivity in the network during spontaneous development.     

Network Evolution Induced by Asynchronous Stimuli through Spike-Timing-Dependent Plasticity

In sensory neural system, external asynchronous stimuli play an important role in perceptual learning, associative memory and map development. However, the organization of structure and dynamics of neural networks induced by external asynchronous stimuli are not well understood. Spike-timing-dependent plasticity (STDP) is a typical synaptic plasticity that has been extensively found in the sensory systems and that has received much theoretical attention. This synaptic plasticity is highly sensitive to correlations between pre- and postsynaptic firings. Thus, STDP is expected to play an important role in response to external asynchronous stimuli, which can induce segregative pre- and postsynaptic firings. In this paper, we study the impact of external asynchronous stimuli on the organization of structure and dynamics of neural networks through STDP. We construct a two-dimensional spatial neural network model with local connectivity and sparseness, and use external currents to stimulate alternately on different spatial layers. The adopted external currents imposed alternately on spatial layers can be here regarded as external asynchronous stimuli. Through extensive numerical simulations, we focus on the effects of stimulus number and inter-stimulus timing on synaptic connecting weights and the property of propagation dynamics in the resulting network structure. Interestingly, the resulting feedforward structure induced by stimulus-dependent asynchronous firings and its propagation dynamics reflect both the underlying property of STDP. The results imply a possible important role of STDP in generating feedforward structure and collective propagation activity required for experience-dependent map plasticity in developing in vivo sensory pathways and cortices. The relevance of the results to cue-triggered recall of learned temporal sequences, an important cognitive function, is briefly discussed as well. Furthermore, this finding suggests a potential application for examining STDP by measuring neural population activity in a cultured neural network.     

Signal propagation in feedforward neuronal networks with unreliable synapses

In this paper, we systematically investigate both the synfire propagation and firing rate propagation in feedforward neuronal network coupled in an all-to-all fashion. In contrast to most earlier work, where only reliable synaptic connections are considered, we mainly examine the effects of unreliable synapses on both types of neural activity propagation in this work. We first study networks composed of purely excitatory neurons. Our results show that both the successful transmission probability and excitatory synaptic strength largely influence the propagation of these two types of neural activities, and better tuning of these synaptic parameters makes the considered network support stable signal propagation. It is also found that noise has significant but different impacts on these two types of propagation. The additive Gaussian white noise has the tendency to reduce the precision of the synfire activity, whereas noise with appropriate intensity can enhance the performance of firing rate propagation. Further simulations indicate that the propagation dynamics of the considered neuronal network is not simply determined by the average amount of received neurotransmitter for each neuron in a time instant, but also largely influenced by the stochastic effect of neurotransmitter release. Second, we compare our results with those obtained in corresponding feedforward neuronal networks connected with reliable synapses but in a random coupling fashion. We confirm that some differences can be observed in these two different feedforward neuronal network models. Finally, we study the signal propagation in feedforward neuronal networks consisting of both excitatory and inhibitory neurons, and demonstrate that inhibition also plays an important role in signal propagation in the considered networks.     

Self-Organization of Microcircuits in Networks of Spiking Neurons with Plastic Synapses

The synaptic connectivity of cortical networks features an overrepresentation of certain wiring motifs compared to simple random-network models. This structure is shaped, in part, by synaptic plasticity that promotes or suppresses connections between neurons depending on their joint spiking activity. Frequently, theoretical studies focus on how feedforward inputs drive plasticity to create this network structure. We study the complementary scenario of self-organized structure in a recurrent network, with spike timing-dependent plasticity driven by spontaneous dynamics. We develop a self-consistent theory for the evolution of network structure by combining fast spiking covariance with a slow evolution of synaptic weights. Through a finite-size expansion of network dynamics we obtain a low-dimensional set of nonlinear differential equations for the evolution of two-synapse connectivity motifs. With this theory in hand, we explore how the form of the plasticity rule drives the evolution of microcircuits in cortical networks. When potentiation and depression are in approximate balance, synaptic dynamics depend on weighted divergent, convergent, and chain motifs. For additive, Hebbian STDP these motif interactions create instabilities in synaptic dynamics that either promote or suppress the initial network structure. Our work provides a consistent theoretical framework for studying how spiking activity in recurrent networks interacts with synaptic plasticity to determine network structure.     

Experimental analysis and computational modeling of interburst intervals in spontaneous activity of cortical neuronal culture

Rhythmic bursting is the most striking behavior of cultured cortical networks and may start in the second week after plating. In this study, we focus on the intervals between spontaneously occurring bursts, and compare experimentally recorded values with model simulations. In the models, we use standard neurons and synapses, with physiologically plausible parameters taken from literature. All networks had a random recurrent architecture with sparsely connected neurons. The number of neurons varied between 500 and 5,000. We find that network models with homogeneous synaptic strengths produce asynchronous spiking or stable regular bursts. The latter, however, are in a range not seen in recordings. By increasing the synaptic strength in a (randomly chosen) subset of neurons, our simulations show interburst intervals (IBIs) that agree better with in vitro experiments. In this regime, called weakly synchronized, the models produce irregular network bursts, which are initiated by neurons with relatively stronger synapses. In some noise-driven networks, a subthreshold, deterministic, input is applied to neurons with strong synapses, to mimic pacemaker network drive. We show that models with such "intrinsically active neurons" (pacemaker-driven models) tend to generate IBIs that are determined by the frequency of the fastest pacemaker and do not resemble experimental data. Alternatively, noise-driven models yield realistic IBIs. Generally, we found that large-scale noise-driven neuronal network models required synaptic strengths with a bimodal distribution to reproduce the experimentally observed IBI range. Our results imply that the results obtained from small network models cannot simply be extrapolated to models of more realistic size. Synaptic strengths in large-scale neuronal network simulations need readjustment to a bimodal distribution, whereas small networks do not require such changes.     

Coherency and connectivity in oscillating neural networks: linear partialization analysis

 This paper studies the relation between the functional synaptic connections between two artificial neural networks and the correlation of their spiking activities. The model neurons had realistic non-oscillatory dynamic properties and the networks showed oscillatory behavior as a result of their internal synaptic connectivity. We found that both excitation and inhibition cause phase locking of the oscillating activities. When the two networks excite each other the oscillations synchronize with zero phase lag, whereas mutual inhibition between the networks resulted in an anti-phase (half period phase difference) synchronization. Correlations between the activities of the two networks can also be caused by correlated external inputs driving the systems (common input). Our analysis shows that when the networks exhibit oscillatory behavior and the rate of the common input is smaller than a characteristic network oscillator frequency, the cross-correlation functions between the activities of two systems still carry information about the mutual synaptic connectivity. This information can be retrieved with linear partialization, removing the influence of the common input. We further explored the network responses to periodic external input. We found that when the input is of a frequency smaller than a certain threshold, the network responds with bursts at the same frequency as the input. Above the threshold, the network responds with a fraction of the input frequency. This frequency threshold, characterizing the oscillatory properties of the network, is also found to determine the limit to which linear partialization works. Received: 20 October 1995 / Accepted in revised form: 20 May 1996     

Induction and propagation of transient synchronous activity in neural networks endowed with short-term plasticity

Transient, task related synchronous activity within neural populations has been recognized as the substrate of temporal coding in the brain. The mechanisms underlying inducing and propagation of transient synchronous activity are still unknown, and we propose that short-term plasticity (STP) of neural circuits may serve as a supplemental mechanism therein. By computational modeling, we showed that short-term facilitation greatly increases the reactivation rate of population spikes and decreases the latency of response to reactivation stimuli in local recurrent neural networks. Meanwhile, the timing of population spike reactivation is controlled by the memory effect of STP, and it is mediated primarily by the facilitation time constant. Furthermore, we demonstrated that synaptic facilitation dramatically enhances synchrony propagation in feedforward neural networks and that response timing mediated by synaptic facilitation offers a scheme for information routing. In addition, we verified that synaptic strengthening of intralayer or interlayer coupling enhances synchrony propagation, and we verified that other factors such as the delay of synaptic transmission and the mode of synaptic connectivity are also involved in regulating synchronous activity propagation. Overall, our results highlight the functional role of STP in regulating the inducing and propagation of transient synchronous activity, and they may inspire testable hypotheses for future experimental studies.     

Recurrent neural networks of integrate-and-fire cells simulating short-term memory and wrist movement tasks derived from continuous dynamic networks

Dynamic recurrent neural networks composed of units with continuous activation functions provide a powerful tool for simulating a wide range of behaviors, since the requisite interconnections can be readily derived by gradient descent methods. However, it is not clear whether more realistic integrate-and-fire cells with comparable connection weights would perform the same functions. We therefore investigated methods to convert dynamic recurrent neural networks of continuous units into networks with integrate-and-fire cells. The transforms were tested on two recurrent networks derived by backpropagation. The first simulates a short-term memory task with units that mimic neural activity observed in cortex of monkeys performing instructed delay tasks. The network utilizes recurrent connections to generate sustained activity that codes the remembered value of a transient cue. The second network simulates patterns of neural activity observed in monkeys performing a step-tracking task with flexion/extension wrist movements. This more complicated network provides a working model of the interactions between multiple spinal and supraspinal centers controlling motoneurons. Our conversion algorithm replaced each continuous unit with multiple integrate-and-fire cells that interact through delayed "synaptic potentials". Successful transformation depends on obtaining an appropriate fit between the activation function of the continuous units and the input-output relation of the spiking cells. This fit can be achieved by adapting the parameters of the synaptic potentials to replicate the input-output behavior of a standard sigmoidal activation function (shown for the short-term memory network). Alternatively, a customized activation function can be derived from the input-output relation of the spiking cells for a chosen set of parameters (demonstrated for the wrist flexion/extension network). In both cases the resulting networks of spiking cells exhibited activity that replicated the activity of corresponding continuous units. This confirms that the network solutions obtained through backpropagation apply to spiking networks and provides a useful method for deriving recurrent spiking networks performing a wide range of functions.     

On the dynamics of the spontaneous activity in neuronal networks

Most neuronal networks, even in the absence of external stimuli, produce spontaneous bursts of spikes separated by periods of reduced activity. The origin and functional role of these neuronal events are still unclear. The present work shows that the spontaneous activity of two very different networks, intact leech ganglia and dissociated cultures of rat hippocampal neurons, share several features. Indeed, in both networks: i) the inter-spike intervals distribution of the spontaneous firing of single neurons is either regular or periodic or bursting, with the fraction of bursting neurons depending on the network activity; ii) bursts of spontaneous spikes have the same broad distributions of size and duration; iii) the degree of correlated activity increases with the bin width, and the power spectrum of the network firing rate has a 1/f behavior at low frequencies, indicating the existence of long-range temporal correlations; iv) the activity of excitatory synaptic pathways mediated by NMDA receptors is necessary for the onset of the long-range correlations and for the presence of large bursts; v) blockage of inhibitory synaptic pathways mediated by GABA(A) receptors causes instead an increase in the correlation among neurons and leads to a burst distribution composed only of very small and very large bursts. These results suggest that the spontaneous electrical activity in neuronal networks with different architectures and functions can have very similar properties and common dynamics.     

Temporal interaction between single spikes and complex spike bursts in hippocampal pyramidal cells

Cortical pyramidal cells fire single spikes and complex spike bursts. However, neither the conditions necessary for triggering complex spikes, nor their computational function are well understood. CA1 pyramidal cell burst activity was examined in behaving rats. The fraction of bursts was not reliably higher in place field centers, but rather in places where discharge frequency was 6-7 Hz. Burst probability was lower and bursts were shorter after recent spiking activity than after prolonged periods of silence (100 ms-1 s). Burst initiation probability and burst length were correlated with extracellular spike amplitude and with intracellular action potential rising slope. We suggest that bursts may function as "conditional synchrony detectors," signaling strong afferent synchrony after neuronal silence, and that single spikes triggered by a weak input may suppress bursts evoked by a subsequent strong input.     

Synaptic Potentiation Facilitates Memory-like Attractor Dynamics in Cultured In Vitro Hippocampal Networks

Collective rhythmic dynamics from neurons is vital for cognitive functions such as memory formation but how neurons self-organize to produce such activity is not well understood. Attractor-based computational models have been successfully implemented as a theoretical framework for memory storage in networks of neurons. Additionally, activity-dependent modification of synaptic transmission is thought to be the physiological basis of learning and memory. The goal of this study is to demonstrate that using a pharmacological treatment that has been shown to increase synaptic strength within in vitro networks of hippocampal neurons follows the dynamical postulates theorized by attractor models. We use a grid of extracellular electrodes to study changes in network activity after this perturbation and show that there is a persistent increase in overall spiking and bursting activity after treatment. This increase in activity appears to recruit more “errant” spikes into bursts. Phase plots indicate a conserved activity pattern suggesting that a synaptic potentiation perturbation to the attractor leaves it unchanged. Lastly, we construct a computational model to demonstrate that these synaptic perturbations can account for the dynamical changes seen within the network.     

Impact of adaptation currents on synchronization of coupled exponential integrate-and-fire neurons

The ability of spiking neurons to synchronize their activity in a network depends on the response behavior of these neurons as quantified by the phase response curve (PRC) and on coupling properties. The PRC characterizes the effects of transient inputs on spike timing and can be measured experimentally. Here we use the adaptive exponential integrate-and-fire (aEIF) neuron model to determine how subthreshold and spike-triggered slow adaptation currents shape the PRC. Based on that, we predict how synchrony and phase locked states of coupled neurons change in presence of synaptic delays and unequal coupling strengths. We find that increased subthreshold adaptation currents cause a transition of the PRC from only phase advances to phase advances and delays in response to excitatory perturbations. Increased spike-triggered adaptation currents on the other hand predominantly skew the PRC to the right. Both adaptation induced changes of the PRC are modulated by spike frequency, being more prominent at lower frequencies. Applying phase reduction theory, we show that subthreshold adaptation stabilizes synchrony for pairs of coupled excitatory neurons, while spike-triggered adaptation causes locking with a small phase difference, as long as synaptic heterogeneities are negligible. For inhibitory pairs synchrony is stable and robust against conduction delays, and adaptation can mediate bistability of in-phase and anti-phase locking. We further demonstrate that stable synchrony and bistable in/anti-phase locking of pairs carry over to synchronization and clustering of larger networks. The effects of adaptation in aEIF neurons on PRCs and network dynamics qualitatively reflect those of biophysical adaptation currents in detailed Hodgkin-Huxley-based neurons, which underscores the utility of the aEIF model for investigating the dynamical behavior of networks. Our results suggest neuronal spike frequency adaptation as a mechanism synchronizing low frequency oscillations in local excitatory networks, but indicate that inhibition rather than excitation generates coherent rhythms at higher frequencies.     

Flexibility in the patterning and control of axial locomotor networks in lamprey

In lower vertebrates, locomotor burst generators for axial muscles generally produce unitary bursts that alternate between the two sides of the body. In lamprey, a lower vertebrate, locomotor activity in the axial ventral roots of the isolated spinal cord can exhibit flexibility in the timings of bursts to dorsally-located myotomal muscle fibers versus ventrally-located myotomal muscle fibers. These episodes of decreased synchrony can occur spontaneously, especially in the rostral spinal cord where the propagating body waves of swimming originate. Application of serotonin, an endogenous spinal neurotransmitter known to presynaptically inhibit excitatory synapses in lamprey, can promote decreased synchrony of dorsal-ventral bursting. These observations suggest the possible existence of dorsal and ventral locomotor networks with modifiable coupling strength between them. Intracellular recordings of motoneurons during locomotor activity provide some support for this model. Pairs of motoneurons innervating myotomal muscle fibers of similar ipsilateral dorsoventral location tend to have higher correlations of fast synaptic activity during fictive locomotion than do pairs of motoneurons innervating myotomes of different ipsilateral dorsoventral locations, suggesting their control by different populations of premotor interneurons. Further, these different motoneuron pools receive different patterns of excitatory and inhibitory inputs from individual reticulospinal neurons, conveyed in part by different sets of premotor interneurons. Perhaps, then, the locomotor network of the lamprey is not simply a unitary burst generator on each side of the spinal cord that activates all ipsilateral body muscles simultaneously. Instead, the burst generator on each side may comprise at least two coupled burst generators, one controlling motoneurons innervating dorsal body muscles and one controlling motoneurons innervating ventral body muscles. The coupling strength between these two ipsilateral burst generators may be modifiable and weakening when greater swimming maneuverability is required. Variable coupling of intrasegmental burst generators in the lamprey may be a precursor to the variable coupling of burst generators observed in the control of locomotion in the joints of limbed vertebrates.     

Bursting Reverberation as a Multiscale Neuronal Network Process Driven by Synaptic Depression-Facilitation

Neuronal networks can generate complex patterns of activity that depend on membrane properties of individual neurons as well as on functional synapses. To decipher the impact of synaptic properties and connectivity on neuronal network behavior, we investigate the responses of neuronal ensembles from small (5–30 cells in a restricted sphere) and large (acute hippocampal slice) networks to single electrical stimulation: in both cases, a single stimulus generated a synchronous long-lasting bursting activity. While an initial spike triggered a reverberating network activity that lasted 2–5 seconds for small networks, we found here that it lasted only up to 300 milliseconds in slices. To explain this phenomena present at different scales, we generalize the depression-facilitation model and extracted the network time constants. The model predicts that the reverberation time has a bell shaped relation with the synaptic density, revealing that the bursting time cannot exceed a maximum value. Furthermore, before reaching its maximum, the reverberation time increases sub-linearly with the synaptic density of the network. We conclude that synaptic dynamics and connectivity shape the mean burst duration, a property present at various scales of the networks. Thus bursting reverberation is a property of sufficiently connected neural networks, and can be generated by collective depression and facilitation of underlying functional synapses.