First return maps for the dynamics of synaptically coupled conditional bursters

The pre-Bötzinger complex (preBötc) in the mammalian brainstem has an important role in generating respiratory rhythms. An influential differential equation model for the activity of individual neurons in the preBötc yields transitions from quiescence to bursting to tonic spiking as a parameter is varied. Further, past work has established that bursting dynamics can arise from a pair of tonic model cells coupled with synaptic excitation. In this paper, we analytically derive one- and two-dimensional maps from the differential equations for a self-coupled neuron and a two-neuron network, respectively. Using a combination of analysis and simulations of these maps, we explore the possible forms of dynamics that the model networks can produce as well as which transitions between dynamic regimes are mathematically possible.     

State transitions through inhibitory interneurons in a cortical network model

Inhibitory interneurons shape the spiking characteristics and computational properties of cortical networks. Interneuron subtypes can precisely regulate cortical function but the roles of interneuron subtypes for promoting different regimes of cortical activity remains unclear. Therefore, we investigated the impact of fast spiking and non-fast spiking interneuron subtypes on cortical activity using a network model with connectivity and synaptic properties constrained by experimental data. We found that network properties were more sensitive to modulation of the fast spiking population, with reductions of fast spiking excitability generating strong spike correlations and network oscillations. Paradoxically, reduced fast spiking excitability produced a reduction of global excitation-inhibition balance and features of an inhibition stabilised network, in which firing rates were driven by the activity of excitatory neurons within the network. Further analysis revealed that the synaptic interactions and biophysical features associated with fast spiking interneurons, in particular their rapid intrinsic response properties and short synaptic latency, enabled this state transition by enhancing gain within the excitatory population. Therefore, fast spiking interneurons may be uniquely positioned to control the strength of recurrent excitatory connectivity and the transition to an inhibition stabilised regime. Overall, our results suggest that interneuron subtypes can exert selective control over excitatory gain allowing for differential modulation of global network state.     

Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks. II. Input selectivity—symmetry breaking

Spike-timing-dependent plasticity (STDP) is believed to structure neuronal networks by slowly changing the strengths (or weights) of the synaptic connections between neurons depending upon their spiking activity, which in turn modifies the neuronal firing dynamics. In this paper, we investigate the change in synaptic weights induced by STDP in a recurrently connected network in which the input weights are plastic but the recurrent weights are fixed. The inputs are divided into two pools with identical constant firing rates and equal within-pool spike-time correlations, but with no between-pool correlations. Our analysis uses the Poisson neuron model in order to predict the evolution of the input synaptic weights and focuses on the asymptotic weight distribution that emerges due to STDP. The learning dynamics induces a symmetry breaking for the individual neurons, namely for sufficiently strong within-pool spike-time correlation each neuron specializes to one of the input pools. We show that the presence of fixed excitatory recurrent connections between neurons induces a group symmetry-breaking effect, in which neurons tend to specialize to the same input pool. Consequently STDP generates a functional structure on the input connections of the network.     

Modelling Feedback Excitation,Pacemaker Properties and Sensory Switching of Electrically Coupled Brainstem Neurons Controlling Rhythmic Activity

What cellular and network properties allow reliable neuronal rhythm generation or firing that can be started and stopped by brief synaptic inputs? We investigate rhythmic activity in an electrically-coupled population of brainstem neurons driving swimming locomotion in young frog tadpoles, and how activity is switched on and off by brief sensory stimulation. We build a computational model of 30 electrically-coupled conditional pacemaker neurons on one side of the tadpole hindbrain and spinal cord. Based on experimental estimates for neuron properties, population sizes, synapse strengths and connections, we show that: long-lasting, mutual, glutamatergic excitation between the neurons allows the network to sustain rhythmic pacemaker firing at swimming frequencies following brief synaptic excitation; activity persists but rhythm breaks down without electrical coupling; NMDA voltage-dependency doubles the range of synaptic feedback strengths generating sustained rhythm. The network can be switched on and off at short latency by brief synaptic excitation and inhibition. We demonstrate that a population of generic Hodgkin-Huxley type neurons coupled by glutamatergic excitatory feedback can generate sustained asynchronous firing switched on and off synaptically. We conclude that networks of neurons with NMDAR mediated feedback excitation can generate self-sustained activity following brief synaptic excitation. The frequency of activity is limited by the kinetics of the neuron membrane channels and can be stopped by brief inhibitory input. Network activity can be rhythmic at lower frequencies if the neurons are electrically coupled. Our key finding is that excitatory synaptic feedback within a population of neurons can produce switchable, stable, sustained firing without synaptic inhibition.     

A Robust In Vivo-Like Persistent Firing Supported by a Hybrid of Intracellular and Synaptic Mechanisms

Persistent firing is believed to support short-term information retention in the brain. Established hypotheses make use of the recurrent synaptic connectivity to support persistent firing. However, this mechanism is known to suffer from a lack of robustness. On the other hand, persistent firing can be supported by an intrinsic cellular mechanism in multiple brain areas. However, the consequences of having both the intrinsic and the synaptic mechanisms (a hybrid model) on persistent firing remain largely unknown. The goal of this study is to investigate whether a hybrid neural network model with these two mechanisms has advantages over a conventional recurrent network based model. Our computer simulations were based on in vitro recordings obtained from hippocampal CA3 pyramidal cells under cholinergic receptor activation. Calcium activated non-specific cationic (CAN) current supported persistent firing in the Hodgkin-Huxley style cellular models. Our results suggest that the hybrid model supports persistent firing within a physiological frequency range over a wide range of different parameters, eliminating parameter sensitivity issues generally recognized in network based persistent firing. In addition, persistent firing in the hybrid model is substantially more robust against distracting inputs, can coexist with theta frequency oscillations, and supports pattern completion.     

Theta oscillations by synaptic excitation in a neocortical circuit model

Neocortical theta-band oscillatory activity is associated with cognitive tasks involving learning and memory. This oscillatory activity is proposed to originate from the synchronization of interconnected layer V intrinsic bursting (IB) neurons by recurrent excitation. To test this hypothesis, a sparsely connected spiking circuit model based on empirical data was simulated using Hodgkin-Huxley-type bursting neurons and use-dependent depressing synaptic connections. In response to a heterogeneous tonic current stimulus, the model generated coherent and robust oscillatory activity throughout the theta-band (4-12 Hz). These oscillations were not, however, self-sustaining without a driving current, and not dependent on N-methyl-D-aspartate receptor synaptic currents. At realistic connection strengths, synaptic depression was necessary to avoid instability and expanded the basin of attraction for theta oscillations by controlling the gain of recurrent excitation. These results support the hypothesis that IB neuron networks can generate robust and coherent theta-band oscillations in neocortex.     

Synapse-specific adaptations to inactivity in hippocampal circuits achieve homeostatic gain control while dampening network reverberation

Synaptic homeostasis, induced by chronic changes in neuronal activity, is well studied in cultured neurons, but not in more physiological networks where distinct synaptic circuits are preserved. We characterized inactivity-induced adaptations at three sets of excitatory synapses in tetrodotoxin-treated organotypic hippocampal cultures. The adaptation to inactivity was strikingly synapse specific. Hippocampal throughput synapses (dentate-to-CA3 and CA3-to-CA1) were upregulated, conforming to homeostatic gain control in order to avoid extreme limits of neuronal firing. However, chronic inactivity decreased mEPSC frequency at CA3-to-CA3 synapses, which were isolated pharmacologically or surgically. This downregulation of recurrent synapses was opposite to that expected for conventional homeostasis, in apparent conflict with typical gain control. However, such changes contributed to an inactivity-induced shortening of reverberatory bursts generated by feedback excitation among CA3 pyramids, safeguarding the network from possible runaway excitation. Thus, synapse-specific adaptations of synaptic weight not only contributed to homeostatic gain control, but also dampened epileptogenic network activity.     

Phase resetting reduces theta–gamma rhythmic interaction to a one-dimensional map

Gamma and theta oscillations of the hippocampus are known to interact, but the mechanisms underlying such interaction are not well understood. We focus on a previously published computational model of hippocampal activity that shows the gamma rhythms nesting in the theta rhythms, and investigate the dynamical mechanisms underlying that interaction. There are three types of neurons in the model: pyramidal cells, fast-spiking interneurons, and “oriens lacunosum-moelculare” (O-LM cells); the latter is an inhibitory cell whose inhibition has a longer time scale, and which has currents associated with intrinsic theta-rhythm behavior. We identify two main modes of interaction among the slow and the fast rhythms in the model, modulated by the strength of the excitatory synapse on the O-LM cells. Using resets of phases after each pyramidal cell and O-LM spike, we extend the use of the phase transition map (PTM) to encode the stability type of spiking patterns in networks where different frequencies interact. The tailored application of the PTM to the model network measures how the interaction between the shape of the phase response curves and the length of the gamma period determines the number of gamma spikes in theta cycles, and provides an explicit formula for the length of theta intervals in nesting regimes. Using the PTM, we also explain the covariance of the gamma and theta rhythms as drive is changed over some intervals.     

Membrane potential-dependent modulation of recurrent inhibition in rat neocortex

Dynamic balance of excitation and inhibition is crucial for network stability and cortical processing, but it is unclear how this balance is achieved at different membrane potentials (V(m)) of cortical neurons, as found during persistent activity or slow V(m) oscillation. Here we report that a V(m)-dependent modulation of recurrent inhibition between pyramidal cells (PCs) contributes to the excitation-inhibition balance. Whole-cell recording from paired layer-5 PCs in rat somatosensory cortical slices revealed that both the slow and the fast disynaptic IPSPs, presumably mediated by low-threshold spiking and fast spiking interneurons, respectively, were modulated by changes in presynaptic V(m). Somatic depolarization (>5 mV) of the presynaptic PC substantially increased the amplitude and shortened the onset latency of the slow disynaptic IPSPs in neighboring PCs, leading to a narrowed time window for EPSP integration. A similar increase in the amplitude of the fast disynaptic IPSPs in response to presynaptic depolarization was also observed. Further paired recording from PCs and interneurons revealed that PC depolarization increases EPSP amplitude and thus elevates interneuronal firing and inhibition of neighboring PCs, a reflection of the analog mode of excitatory synaptic transmission between PCs and interneurons. Together, these results revealed an immediate V(m)-dependent modulation of cortical inhibition, a key strategy through which the cortex dynamically maintains the balance of excitation and inhibition at different states of cortical activity.     

Modulation of the dynamics of cerebellar Purkinje cells through the interaction of excitatory and inhibitory feedforward pathways

The dynamics of cerebellar neuronal networks is controlled by the underlying building blocks of neurons and synapses between them. For which, the computation of Purkinje cells (PCs), the only output cells of the cerebellar cortex, is implemented through various types of neural pathways interactively routing excitation and inhibition converged to PCs. Such tuning of excitation and inhibition, coming from the gating of specific pathways as well as short-term plasticity (STP) of the synapses, plays a dominant role in controlling the PC dynamics in terms of firing rate and spike timing. PCs receive cascade feedforward inputs from two major neural pathways: the first one is the feedforward excitatory pathway from granule cells (GCs) to PCs; the second one is the feedforward inhibition pathway from GCs, via molecular layer interneurons (MLIs), to PCs. The GC-PC pathway, together with short-term dynamics of excitatory synapses, has been a focus over past decades, whereas recent experimental evidence shows that MLIs also greatly contribute to controlling PC activity. Therefore, it is expected that the diversity of excitation gated by STP of GC-PC synapses, modulated by strong inhibition from MLI-PC synapses, can promote the computation performed by PCs. However, it remains unclear how these two neural pathways are interacted to modulate PC dynamics. Here using a computational model of PC network installed with these two neural pathways, we addressed this question to investigate the change of PC firing dynamics at the level of single cell and network. We show that the nonlinear characteristics of excitatory STP dynamics can significantly modulate PC spiking dynamics mediated by inhibition. The changes in PC firing rate, firing phase, and temporal spike pattern, are strongly modulated by these two factors in different ways. MLIs mainly contribute to variable delays in the postsynaptic action potentials of PCs while modulated by excitation STP. Notably, the diversity of synchronization and pause response in the PC network is governed not only by the balance of excitation and inhibition, but also by the synaptic STP, depending on input burst patterns. Especially, the pause response shown in the PC network can only emerge with the interaction of both pathways. Together with other recent findings, our results show that the interaction of feedforward pathways of excitation and inhibition, incorporated with synaptic short-term dynamics, can dramatically regulate the PC activities that consequently change the network dynamics of the cerebellar circuit.     

Turning On and Off with Excitation: The Role of Spike-Timing Asynchrony and Synchrony in Sustained Neural Activity

Delay-related sustained activity in the prefrontal cortex of primates, a neurological analogue of working memory, has been proposed to arise from synaptic interactions in local cortical circuits. The implication is that memories are coded by spatially localized foci of sustained activity. We investigate the mechanisms by which sustained foci are initiated, maintained, and extinguished by excitation in networks of Hodgkin-Huxley neurons coupled with biophysical spatially structured synaptic connections. For networks with a balance between excitation and inhibition, a localized transient stimulus robustly initiates a localized focus of activity. The activity is then maintained by recurrent excitatory AMPA-like synapses. We find that to maintain the focus, the firing must be asynchronous. Consequently, inducing transient synchrony through an excitatory stimulus extinguishes the sustained activity. Such a monosynaptic excitatory turn-off mechanism is compatible with the working memory being wiped clean by an efferent copy of the motor command. The activity that codes working memories may be structured so that the motor command is both the read-out and a direct clearing signal. We show examples of data that is compatible with our theory.     

Phase precession through acceleration of local theta rhythm: a biophysical model for the interaction between place cells and local inhibitory neurons

Phase precession is one of the most well known examples within the temporal coding hypothesis. Here we present a biophysical spiking model for phase precession in hippocampal CA1 which focuses on the interaction between place cells and local inhibitory interneurons. The model's functional block is composed of a place cell (PC) connected with a local inhibitory cell (IC) which is modulated by the population theta rhythm. Both cells receive excitatory inputs from the entorhinal cortex (EC). These inputs are both theta modulated and space modulated. The dynamics of the two neuron types are described by integrate-and-fire models with conductance synapses, and the EC inputs are described using non-homogeneous Poisson processes. Phase precession in our model is caused by increased drive to specific PC/IC pairs when the animal is in their place field. The excitation increases the IC's firing rate, and this modulates the PC's firing rate such that both cells precess relative to theta. Our model implies that phase coding in place cells may not be independent from rate coding. The absence of restrictive connectivity constraints in this model predicts the generation of phase precession in any network with similar architecture and subject to a clocking rhythm, independently of the involvement in spatial tasks.     

Asynchronous Rate Chaos in Spiking Neuronal Circuits

The brain exhibits temporally complex patterns of activity with features similar to those of chaotic systems. Theoretical studies over the last twenty years have described various computational advantages for such regimes in neuronal systems. Nevertheless, it still remains unclear whether chaos requires specific cellular properties or network architectures, or whether it is a generic property of neuronal circuits. We investigate the dynamics of networks of excitatory-inhibitory (EI) spiking neurons with random sparse connectivity operating in the regime of balance of excitation and inhibition. Combining Dynamical Mean-Field Theory with numerical simulations, we show that chaotic, asynchronous firing rate fluctuations emerge generically for sufficiently strong synapses. Two different mechanisms can lead to these chaotic fluctuations. One mechanism relies on slow I-I inhibition which gives rise to slow subthreshold voltage and rate fluctuations. The decorrelation time of these fluctuations is proportional to the time constant of the inhibition. The second mechanism relies on the recurrent E-I-E feedback loop. It requires slow excitation but the inhibition can be fast. In the corresponding dynamical regime all neurons exhibit rate fluctuations on the time scale of the excitation. Another feature of this regime is that the population-averaged firing rate is substantially smaller in the excitatory population than in the inhibitory population. This is not necessarily the case in the I-I mechanism. Finally, we discuss the neurophysiological and computational significance of our results.     

Effect of stimulus-driven pruning on the detection of spatiotemporal patterns of activity in large neural networks

Adult patterns of neuronal connectivity develop from a transient embryonic template characterized by exuberant projections to both appropriate and inappropriate target regions in a process known as synaptic pruning. Trigger signals able to induce synaptic pruning could be related to dynamic functions that depend on the timing of action potentials. We stimulated locally connected random networks of spiking neurons and observed the effect of a spike-timing-dependent synaptic plasticity (STDP)-driven pruning process on the emergence of cell assemblies. The spike trains of the simulated excitatory neurons were recorded. We searched for spatiotemporal firing patterns as potential markers of the build-up of functionally organized recurrent activity associated with spatially organized connectivity.     

Norepinephrine Drives Persistent Activity in Prefrontal Cortex via Synergistic α1 and α2 Adrenoceptors

Optimal norepinephrine levels in the prefrontal cortex (PFC) increase delay-related firing and enhance working memory, whereas stress-related or pathologically high levels of norepinephrine are believed to inhibit working memory via α1 adrenoceptors. However, it has been shown that activation of Gq-coupled and phospholipase C-linked receptors can induce persistent firing, a cellular correlate of working memory, in cortical pyramidal neurons. Therefore, despite its importance in stress and cognition, the exact role of norepinephrine in modulating PFC activity remains elusive. Using electrophysiology and optogenetics, we report here that norepinephrine induces persistent firing in pyramidal neurons of the PFC independent of recurrent fast synaptic excitation. This persistent excitatory effect involves presynaptic α1 adrenoceptors facilitating glutamate release and subsequent activation of postsynaptic mGluR5 receptors, and is enhanced by postsynaptic α2 adrenoceptors inhibiting HCN channel activity. Activation of α2 adrenoceptors or inhibition of HCN channels also enhances cholinergic persistent responses in pyramidal neurons, providing a mechanism of crosstalk between noradrenergic and cholinergic inputs. The present study describes a novel cellular basis for the noradrenergic control of cortical information processing and supports a synergistic combination of intrinsic and network mechanisms for the expression of mnemonic properties in pyramidal neurons.     

Dynamics of functional connectivity in visual cortical networks: An overview

The aim of the Royaumont Symposium was to review various dynamic aspects of adaptive changes in functional connectivity, expressed in cortical networks during development, learning, and possibly during recognition and cognitive processing. The link between the various experimental and theoretical models was the comparison of cellular and molecular mechanisms that could be involved in the up- and down-regulation of functional connectivity, over different time scales. These processes have been investigated using several approaches in parallel: 1) at the molecular/subcellular level, to identify postsynaptic receptors (NMDA, mGluR) and second messengers (calcium, protein kinases and phosphatases) involved in the induction of synaptic potentiation and depression, and to characterize diffusible factors (NO), released pre- or postsynaptically, involved in the spatial generalization of local changes to neighboring synapses; 2) at the level of integrating networks, to develop electrophysiological (single and multiple recording), pharmacological and optical imaging techniques in order to compare the dynamics of adaptive processes put into play during the natural development of cortical specificity and connectivity, versus those triggered during forced regimes of temporal correlations between pre- and post synaptic activities. Both in vitro and in vivo approaches have been combined in the primary visual cortex of the developing and adult vertebrate (rat, guinea-pig, ferret, cat and monkey). The various forms of ‘slow’ synaptic plasticity, demonstrated during epigenesis and selective phases of learning in the adult, can be compared with ‘fast’ forms of functional coupling (or synchronous firing) shown to develop during the time span required for perception and cognitive processing. Phenomenology of the dynamics in functional connectivity and their relative dependence on temporal correlation in neuronal activity have been analyzed in each of these situations. Experimental results have been compared at different levels of neuronal integration (synapse, column, map and cell assembly) in order to gain a better understanding of functional grouping within cortical networks.     

Dendritic Nonlinearities Reduce Network Size Requirements and Mediate ON and OFF States of Persistent Activity in a PFC Microcircuit Model

Technological advances have unraveled the existence of small clusters of co-active neurons in the neocortex. The functional implications of these microcircuits are in large part unexplored. Using a heavily constrained biophysical model of a L5 PFC microcircuit, we recently showed that these structures act as tunable modules of persistent activity, the cellular correlate of working memory. Here, we investigate the mechanisms that underlie persistent activity emergence (ON) and termination (OFF) and search for the minimum network size required for expressing these states within physiological regimes. We show that (a) NMDA-mediated dendritic spikes gate the induction of persistent firing in the microcircuit. (b) The minimum network size required for persistent activity induction is inversely proportional to the synaptic drive of each excitatory neuron. (c) Relaxation of connectivity and synaptic delay constraints eliminates the gating effect of NMDA spikes, albeit at a cost of much larger networks. (d) Persistent activity termination by increased inhibition depends on the strength of the synaptic input and is negatively modulated by dADP. (e) Slow synaptic mechanisms and network activity contain predictive information regarding the ability of a given stimulus to turn ON and/or OFF persistent firing in the microcircuit model. Overall, this study zooms out from dendrites to cell assemblies and suggests a tight interaction between dendritic non-linearities and network properties (size/connectivity) that may facilitate the short-memory function of the PFC.     

Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks IV

In neuronal networks, the changes of synaptic strength (or weight) performed by spike-timing-dependent plasticity (STDP) are hypothesized to give rise to functional network structure. This article investigates how this phenomenon occurs for the excitatory recurrent connections of a network with fixed input weights that is stimulated by external spike trains. We develop a theoretical framework based on the Poisson neuron model to analyze the interplay between the neuronal activity (firing rates and the spike-time correlations) and the learning dynamics, when the network is stimulated by correlated pools of homogeneous Poisson spike trains. STDP can lead to both a stabilization of all the neuron firing rates (homeostatic equilibrium) and a robust weight specialization. The pattern of specialization for the recurrent weights is determined by a relationship between the input firing-rate and correlation structures, the network topology, the STDP parameters and the synaptic response properties. We find conditions for feed-forward pathways or areas with strengthened self-feedback to emerge in an initially homogeneous recurrent network.     

Anti-correlations in the degree distribution increase stimulus detection performance in noisy spiking neural networks

Neuronal circuits in the rodent barrel cortex are characterized by stable low firing rates. However, recent experiments show that short spike trains elicited by electrical stimulation in single neurons can induce behavioral responses. Hence, the underlying neural networks provide stability against internal fluctuations in the firing rate, while simultaneously making the circuits sensitive to small external perturbations. Here we studied whether stability and sensitivity are affected by the connectivity structure in recurrently connected spiking networks. We found that anti-correlation between the number of afferent (in-degree) and efferent (out-degree) synaptic connections of neurons increases stability against pathological bursting, relative to networks where the degrees were either positively correlated or uncorrelated. In the stable network state, stimulation of a few cells could lead to a detectable change in the firing rate. To quantify the ability of networks to detect the stimulation, we used a receiver operating characteristic (ROC) analysis. For a given level of background noise, networks with anti-correlated degrees displayed the lowest false positive rates, and consequently had the highest stimulus detection performance. We propose that anti-correlation in the degree distribution may be a computational strategy employed by sensory cortices to increase the detectability of external stimuli. We show that networks with anti-correlated degrees can in principle be formed by applying learning rules comprised of a combination of spike-timing dependent plasticity, homeostatic plasticity and pruning to networks with uncorrelated degrees. To test our prediction we suggest a novel experimental method to estimate correlations in the degree distribution.