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.     

Spiking regularity in a noisy small-world neuronal network

The regularity of spiking oscillations is studied in the networks with different topological structures. The network is composed of coupled Fitz-Hugh-Nagumo neurons driven by colored noise. The investigation illustrates that the spike train in both the regular and the Watts-Strogatz small-world neuronal networks can show the best regularity at a moderate noise intensity, indicating the existence of coherence resonance. Moreover, the temporal coherence of the spike train in the small-world network is superior to that in a regular network due to the increase of the randomness of the network topology. Besides the noise intensity, the spiking regularity can be optimized by tuning the randomness of the network topological structure or by tuning the correlation time of the colored noise. In particular, under the cooperation of the small-world topology and the correlation time, the spike train with good regularity could sustain a large magnitude of the local noise.     

Independently Outgrowing Neurons and Geometry-Based Synapse Formation Produce Networks with Realistic Synaptic Connectivity

Neuronal signal integration and information processing in cortical networks critically depend on the organization of synaptic connectivity. During development, neurons can form synaptic connections when their axonal and dendritic arborizations come within close proximity of each other. Although many signaling cues are thought to be involved in guiding neuronal extensions, the extent to which accidental appositions between axons and dendrites can already account for synaptic connectivity remains unclear. To investigate this, we generated a local network of cortical L2/3 neurons that grew out independently of each other and that were not guided by any extracellular cues. Synapses were formed when axonal and dendritic branches came by chance within a threshold distance of each other. Despite the absence of guidance cues, we found that the emerging synaptic connectivity showed a good agreement with available experimental data on spatial locations of synapses on dendrites and axons, number of synapses by which neurons are connected, connection probability between neurons, distance between connected neurons, and pattern of synaptic connectivity. The connectivity pattern had a small-world topology but was not scale free. Together, our results suggest that baseline synaptic connectivity in local cortical circuits may largely result from accidentally overlapping axonal and dendritic branches of independently outgrowing neurons.     

Impact of network topology on inference of synaptic connectivity from multi-neuronal spike data simulated by a large-scale cortical network model

Many mechanisms of neural processing rely critically upon the synaptic connectivity between neurons. As our ability to simultaneously record from large populations of neurons expands, the ability to infer network connectivity from this data has become a major goal of computational neuroscience. To address this issue, we employed several different methods to infer synaptic connections from simulated spike data from a realistic local cortical network model. This approach allowed us to directly compare the accuracy of different methods in predicting synaptic connectivity. We compared the performance of model-free (coherence measure and transfer entropy) and model-based (coupled escape rate model) methods of connectivity inference, applying those methods to the simulated spike data from the model networks with different network topologies. Our results indicate that the accuracy of the inferred connectivity was higher for highly clustered, near regular, or small-world networks, while accuracy was lower for random networks, irrespective of which analysis method was employed. Among the employed methods, the model-based method performed best. This model performed with higher accuracy, was less sensitive to threshold changes, and required less data to make an accurate assessment of connectivity. Given that cortical connectivity tends to be highly clustered, our results outline a powerful analytical tool for inferring local synaptic connectivity from observations of spontaneous activity.     

Correlations in spiking neuronal networks with distance dependent connections

Can the topology of a recurrent spiking network be inferred from observed activity dynamics? Which statistical parameters of network connectivity can be extracted from firing rates, correlations and related measurable quantities? To approach these questions, we analyze distance dependent correlations of the activity in small-world networks of neurons with current-based synapses derived from a simple ring topology. We find that in particular the distribution of correlation coefficients of subthreshold activity can tell apart random networks from networks with distance dependent connectivity. Such distributions can be estimated by sampling from random pairs. We also demonstrate the crucial role of the weight distribution, most notably the compliance with Dales principle, for the activity dynamics in recurrent networks of different types.     

Synaptic Symmetry Increases Coherence in a Pair of Excitable Electronic Neurons

We study how the synaptic connections in a pair of excitable electronic neurons affect the coherence of their spike trains when the neurons are submitted to noise from independent sources. The coupling is provided by electronic circuits which mimic the dynamics of chemical AMPA synapses. In particular, we show that increasing the strength of an unidirectional synapse leads to a decrease of coherence in the post-synaptic neuron. More interestingly, we show that the decrease of coherence can be reverted if we add a synapse of sufficient strength in the reverse direction. Synaptic symmetry plays an important role in this process and, under the right choice of parameters, increases the network coherence beyond the value achieved at the resonance due to noise alone in uncoupled neurons. We also show that synapses with a longer time scale sharpen the dependency of the coherence on the synaptic symmetry. The results were reproduced by numerical simulations of a pair of synaptically coupled FitzHugh-Nagumo models.     

Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks. I. Input selectivity–strengthening correlated input pathways

Spike-timing-dependent plasticity (STDP) determines the evolution of the synaptic weights according to their pre- and post-synaptic activity, which in turn changes the neuronal activity. In this paper, we extend previous studies of input selectivity induced by (STDP) for single neurons to the biologically interesting case of a neuronal network with fixed recurrent connections and plastic connections from external pools of input neurons. We use a theoretical framework based on the Poisson neuron model to analytically describe the network dynamics (firing rates and spike-time correlations) and thus the evolution of the synaptic weights. This framework incorporates the time course of the post-synaptic potentials and synaptic delays. Our analysis focuses on the asymptotic states of a network stimulated by two homogeneous pools of “steady” inputs, namely Poisson spike trains which have fixed firing rates and spike-time correlations. The (STDP) model extends rate-based learning in that it can implement, at the same time, both a stabilization of the individual neuron firing rates and a slower weight specialization depending on the input spike-time correlations. When one input pathway has stronger within-pool correlations, the resulting synaptic dynamics induced by (STDP) are shown to be similar to those arising in the case of a purely feed-forward network: the weights from the more correlated inputs are potentiated at the expense of the remaining input connections.     

Consistent dynamics suggests tight regulation of biophysical parameters in a small network of bursting neurons

The neuronal firing patterns in the pyloric network of crustaceans are remarkably consistent among animals. Although this characteristic of the pyloric network is well-known, the biophysical mechanisms underlying the regulation of the systems output are receiving renewed attention. Computer simulations of the pyloric network recently demonstrated that consistent motor output can be achieved from neurons with disparate biophysical parameters among animals. Here we address this hypothesis by pharmacologically manipulating the pyloric network and analyzing the emerging voltage oscillations and firing patterns. Our results show that the pyloric network of the lobster stomatogastric ganglion maintains consistent and regular firing patterns even when entire populations of specific voltage-gated channels and synaptic receptors are blocked. The variations of temporal parameters used to characterize the burst patterns of the neurons as well as their intraburst spike dynamics do not display statistically significant increase after blocking the transient K-currents (with 4-aminopyridine), the glutamatergic inhibitory synapses (with picrotoxin), or the cholinergic synapses (with atropine) in pyloric networks from different animals. These data suggest that in this very compact circuit, the biophysical parameters are cell-specific and tightly regulated.     

Population rate coding in recurrent neuronal networks with unreliable synapses

Neuron transmits spikes to postsynaptic neurons through synapses. Experimental observations indicated that the communication between neurons is unreliable. However most modelling and computational studies considered deterministic synaptic interaction model. In this paper, we investigate the population rate coding in an all-to-all coupled recurrent neuronal network consisting of both excitatory and inhibitory neurons connected with unreliable synapses. We use a stochastic on-off process to model the unreliable synaptic transmission. We find that synapses with suitable successful transmission probability can enhance the encoding performance in the case of weak noise; while in the case of strong noise, the synaptic interactions reduce the encoding performance. We also show that several important synaptic parameters, such as the excitatory synaptic strength, the relative strength of inhibitory and excitatory synapses, as well as the synaptic time constant, have significant effects on the performance of the population rate coding. Further simulations indicate that the encoding dynamics of our considered network cannot be simply determined by the average amount of received neurotransmitter for each neuron in a time instant. Moreover, we compare our results with those obtained in the corresponding random neuronal networks. Our numerical results demonstrate that the network randomness has the similar qualitative effect as the synaptic unreliability but not completely equivalent in quantity.     

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.     

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.     

Emergence of Connectivity Motifs in Networks of Model Neurons with Short- and Long-Term Plastic Synapses

Recent experimental data from the rodent cerebral cortex and olfactory bulb indicate that specific connectivity motifs are correlated with short-term dynamics of excitatory synaptic transmission. It was observed that neurons with short-term facilitating synapses form predominantly reciprocal pairwise connections, while neurons with short-term depressing synapses form predominantly unidirectional pairwise connections. The cause of these structural differences in excitatory synaptic microcircuits is unknown. We show that these connectivity motifs emerge in networks of model neurons, from the interactions between short-term synaptic dynamics (SD) and long-term spike-timing dependent plasticity (STDP). While the impact of STDP on SD was shown in simultaneous neuronal pair recordings in vitro, the mutual interactions between STDP and SD in large networks are still the subject of intense research. Our approach combines an SD phenomenological model with an STDP model that faithfully captures long-term plasticity dependence on both spike times and frequency. As a proof of concept, we first simulate and analyze recurrent networks of spiking neurons with random initial connection efficacies and where synapses are either all short-term facilitating or all depressing. For identical external inputs to the network, and as a direct consequence of internally generated activity, we find that networks with depressing synapses evolve unidirectional connectivity motifs, while networks with facilitating synapses evolve reciprocal connectivity motifs. We then show that the same results hold for heterogeneous networks, including both facilitating and depressing synapses. This does not contradict a recent theory that proposes that motifs are shaped by external inputs, but rather complements it by examining the role of both the external inputs and the internally generated network activity. Our study highlights the conditions under which SD-STDP might explain the correlation between facilitation and reciprocal connectivity motifs, as well as between depression and unidirectional motifs.     

Relationship between applicability of current-based synapses and uniformity of firing patterns

The purpose of this paper is to identify situations in neural network modeling where current-based synapses are applicable. The applicability of current-based synapse model for studying post-transient behavior of neural networks is discussed in terms of average synaptic current strength induced by per spike during one firing cycle of a neuron (or briefly per spike synaptic current strength). It was found that current-based synapse models are applicable in both situations where both the interspike intervals of the neurons and the distribution of firing times of the neurons are uniform, and where the firing of all neurons is synchronized. If neither the interspike intervals nor the distribution of firing times of the neurons is uniform or the reversal potential is between the rest and threshold potentials, current-based synapse models may be oversimplified.     

Computational simulation of the input-output relationship in hippocampal pyramidal cells

The precise mapping of how complex patterns of synaptic inputs are integrated into specific patterns of spiking output is an essential step in the characterization of the cellular basis of network dynamics and function. Relative to other principal neurons of the hippocampus, the electrophysiology of CA1 pyramidal cells has been extensively investigated. Yet, the precise input-output relationship is to date unknown even for this neuronal class. CA1 pyramidal neurons receive laminated excitatory inputs from three distinct pathways: recurrent CA1 collaterals on basal dendrites, CA3 Schaffer collaterals, mostly on oblique and proximal apical dendrites, and entorhinal perforant pathway on distal apical dendrites. We implemented detailed computer simulations of pyramidal cell electrophysiology based on three-dimensional anatomical reconstructions and compartmental models of available biophysical properties from the experimental literature. To investigate the effect of synaptic input on axosomatic firing, we stochastically distributed a realistic number of excitatory synapses in each of the three dendritic layers. We then recorded the spiking response to different stimulation patterns. For all dendritic layers, synchronous stimuli resulted in trains of spiking output and a linear relationship between input and output firing frequencies. In contrast, asynchronous stimuli evoked non-bursting spike patterns and the corresponding firing frequency input-output function was logarithmic. The regular/irregular nature of the input synaptic intervals was only reflected in the regularity of output inter-burst intervals in response to synchronous stimulation, and never affected firing frequency. Synaptic stimulations in the basal and proximal apical trees across individual neuronal morphologies yielded remarkably similar input-output relationships. Results were also robust with respect to the detailed distributions of dendritic and synaptic conductances within a plausible range constrained by experimental evidence. In contrast, the input-output relationship in response to distal apical stimuli showed dramatic differences from the other dendritic locations as well as among neurons, and was more sensible to the exact channel densities. Action Editor: Alain Destexhe     

Local and global synchronization transitions induced by time delays in small-world neuronal networks with chemical synapses

Effects of time delay on the local and global synchronization in small-world neuronal networks with chemical synapses are investigated in this paper. Numerical results show that, for both excitatory and inhibitory coupling types, the information transmission delay can always induce synchronization transitions of spiking neurons in small-world networks. In particular, regions of in-phase and out-of-phase synchronization of connected neurons emerge intermittently as the synaptic delay increases. For excitatory coupling, all transitions to spiking synchronization occur approximately at integer multiples of the firing period of individual neurons; while for inhibitory coupling, these transitions appear at the odd multiples of the half of the firing period of neurons. More importantly, the local synchronization transition is more profound than the global synchronization transition, depending on the type of coupling synapse. For excitatory synapses, the local in-phase synchronization observed for some values of the delay also occur at a global scale; while for inhibitory ones, this synchronization, observed at the local scale, disappears at a global scale. Furthermore, the small-world structure can also affect the phase synchronization of neuronal networks. It is demonstrated that increasing the rewiring probability can always improve the global synchronization of neuronal activity, but has little effect on the local synchronization of neighboring neurons.     

Noise-tolerant stimulus discrimination by synchronization with depressing synapses

 Some synapses between cortical pyramidal neurons exhibit a rapid depression of excitatory postsynaptic potentials for successive presynaptic spikes. Since depressing synapses do not transmit information on sustained presynaptic firing rates, it has been speculated that they are favorable for temporal coding. In this paper, we study the dynamical effects of depressing synapses on stimulus-induced transient synchronization in a simple network of inhibitory interneurons and excitatory neurons, assuming that the recurrent excitation is mediated by depressing synapses. This synchronization occurs in a temporal pattern which depends on a given stimulus. Since the presence of noise is always a potential hazard in temporal coding, we investigate the extent to which noise in stimuli influences the synchronization phenomena. It is demonstrated that depressing synapses greatly contribute to suppressing the influences of noise on the stimulus-specific temporal patterns of synchronous firing. The timing-based Hebbian learning revealed by physiological experiments is shown to stabilize the temporal patterns in cooperation with synaptic depression. Thus, the times at which synchronous firing occurs provides a reliable information representation in the presence of synaptic depression. Received: 5 July 2000 / Accepted in revised form: 12 January 2001     

Undersampled Critical Branching Processes on Small-World and Random Networks Fail to Reproduce the Statistics of Spike Avalanches

The power-law size distributions obtained experimentally for neuronal avalanches are an important evidence of criticality in the brain. This evidence is supported by the fact that a critical branching process exhibits the same exponent . Models at criticality have been employed to mimic avalanche propagation and explain the statistics observed experimentally. However, a crucial aspect of neuronal recordings has been almost completely neglected in the models: undersampling. While in a typical multielectrode array hundreds of neurons are recorded, in the same area of neuronal tissue tens of thousands of neurons can be found. Here we investigate the consequences of undersampling in models with three different topologies (two-dimensional, small-world and random network) and three different dynamical regimes (subcritical, critical and supercritical). We found that undersampling modifies avalanche size distributions, extinguishing the power laws observed in critical systems. Distributions from subcritical systems are also modified, but the shape of the undersampled distributions is more similar to that of a fully sampled system. Undersampled supercritical systems can recover the general characteristics of the fully sampled version, provided that enough neurons are measured. Undersampling in two-dimensional and small-world networks leads to similar effects, while the random network is insensitive to sampling density due to the lack of a well-defined neighborhood. We conjecture that neuronal avalanches recorded from local field potentials avoid undersampling effects due to the nature of this signal, but the same does not hold for spike avalanches. We conclude that undersampled branching-process-like models in these topologies fail to reproduce the statistics of spike avalanches.     

Modulation of synchrony without changes in firing rates

It was often reported and suggested that the synchronization of spikes can occur without changes in the firing rate. However, few theoretical studies have tested its mechanistic validity. In the present study, we investigate whether changes in synaptic weights can induce an independent modulation of synchrony while the firing rate remains constant. We study this question at the level of both single neurons and neuronal populations using network simulations of conductance based integrate-and-fire neurons. The network consists of a single layer that includes local excitatory and inhibitory recurrent connections, as well as long-range excitatory projections targeting both classes of neurons. Each neuron in the network receives external input consisting of uncorrelated Poisson spike trains. We find that increasing this external input leads to a linear increase of activity in the network, as well␣as an increase in the peak frequency of oscillation. In␣contrast, balanced changes of the synaptic weight of␣excitatory long-range projections for both classes of postsynaptic neurons modulate the degree of synchronization without altering the firing rate. These results demonstrate that, in a simple network, synchronization and firing rate can be modulated independently, and thus, may be used as independent coding dimensions. Electronic supplementary material  The online version of this article (doi: ) contains supplementary material, which is available to authorized users.     

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.     

Local cortical circuit model inferred from power-law distributed neuronal avalanches

How cortical neurons process information crucially depends on how their local circuits are organized. Spontaneous synchronous neuronal activity propagating through neocortical slices displays highly diverse, yet repeatable, activity patterns called “neuronal avalanches”. They obey power-law distributions of the event sizes and lifetimes, presumably reflecting the structure of local circuits developed in slice cultures. However, the explicit network structure underlying the power-law statistics remains unclear. Here, we present a neuronal network model of pyramidal and inhibitory neurons that enables stable propagation of avalanche-like spiking activity. We demonstrate a neuronal wiring rule that governs the formation of mutually overlapping cell assemblies during the development of this network. The resultant network comprises a mixture of feedforward chains and recurrent circuits, in which neuronal avalanches are stable if the former structure is predominant. Interestingly, the recurrent synaptic connections formed by this wiring rule limit the number of cell assemblies embeddable in a neuron pool of given size. We investigate how the resultant power laws depend on the details of the cell-assembly formation as well as on the inhibitory feedback. Our model suggests that local cortical circuits may have a more complex topological design than has previously been thought. Competing financial interests: The authors declare that they have no competing financial interests. Action Editor: Peter Latham