Spatially structured oscillations in a two-dimensional excitatory neuronal network with synaptic depression

We study the spatiotemporal dynamics of a two-dimensional excitatory neuronal network with synaptic depression. Coupling between populations of neurons is taken to be nonlocal, while depression is taken to be local and presynaptic. We show that the network supports a wide range of spatially structured oscillations, which are suggestive of phenomena seen in cortical slice experiments and in vivo. The particular form of the oscillations depends on initial conditions and the level of background noise. Given an initial, spatially localized stimulus, activity evolves to a spatially localized oscillating core that periodically emits target waves. Low levels of noise can spontaneously generate several pockets of oscillatory activity that interact via their target patterns. Periodic activity in space can also organize into spiral waves, provided that there is some source of rotational symmetry breaking due to external stimuli or noise. In the high gain limit, no oscillatory behavior exists, but a transient stimulus can lead to a single, outward propagating target wave.     

Emergence of preferred firing sequences in large spiking neural networks during simulated neuronal development

Two main processes concurrently refine the nervous system over the course of development: cell death and selective synaptic pruning. We simulated large spiking neural networks (100 x 100 neurons "at birth") characterized by an early developmental phase with cell death due to excessive firing rate, followed by the onset of spike timing dependent synaptic plasticity (STDP), driven by spatiotemporal patterns of stimulation. The cell death affected the inhibitory units more than the excitatory units during the early developmental phase. The network activity showed the appearance of recurrent spatiotemporal firing patterns along the STDP phase, thus suggesting the emergence of cell assemblies from the initially randomly connected networks. Some of these patterns were detected throughout the simulation despite the activity-driven network modifications while others disappeared.     

A spiking neural network model of the midbrain superior colliculus that generates saccadic motor commands

Single-unit recordings suggest that the midbrain superior colliculus (SC) acts as an optimal controller for saccadic gaze shifts. The SC is proposed to be the site within the visuomotor system where the nonlinear spatial-to-temporal transformation is carried out: the population encodes the intended saccade vector by its location in the motor map (spatial), and its trajectory and velocity by the distribution of firing rates (temporal). The neurons’ burst profiles vary systematically with their anatomical positions and intended saccade vectors, to account for the nonlinear main-sequence kinematics of saccades. Yet, the underlying collicular mechanisms that could result in these firing patterns are inaccessible to current neurobiological techniques. Here, we propose a simple spiking neural network model that reproduces the spike trains of saccade-related cells in the intermediate and deep SC layers during saccades. The model assumes that SC neurons have distinct biophysical properties for spike generation that depend on their anatomical position in combination with a center–surround lateral connectivity. Both factors are needed to account for the observed firing patterns. Our model offers a basis for neuronal algorithms for spatiotemporal transformations and bio-inspired optimal controllers.     

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.     

Spatiotemporal Spike Coding of Behavioral Adaptation in the Dorsal Anterior Cingulate Cortex

The frontal cortex controls behavioral adaptation in environments governed by complex rules. Many studies have established the relevance of firing rate modulation after informative events signaling whether and how to update the behavioral policy. However, whether the spatiotemporal features of these neuronal activities contribute to encoding imminent behavioral updates remains unclear. We investigated this issue in the dorsal anterior cingulate cortex (dACC) of monkeys while they adapted their behavior based on their memory of feedback from past choices. We analyzed spike trains of both single units and pairs of simultaneously recorded neurons using an algorithm that emulates different biologically plausible decoding circuits. This method permits the assessment of the performance of both spike-count and spike-timing sensitive decoders. In response to the feedback, single neurons emitted stereotypical spike trains whose temporal structure identified informative events with higher accuracy than mere spike count. The optimal decoding time scale was in the range of 70–200 ms, which is significantly shorter than the memory time scale required by the behavioral task. Importantly, the temporal spiking patterns of single units were predictive of the monkeys’ behavioral response time. Furthermore, some features of these spiking patterns often varied between jointly recorded neurons. All together, our results suggest that dACC drives behavioral adaptation through complex spatiotemporal spike coding. They also indicate that downstream networks, which decode dACC feedback signals, are unlikely to act as mere neural integrators.     

Synchronization and sensitivity enhancement of the Hodgkin-Huxley neurons due to inhibitory inputs

Recent experimental results imply that inhibitory postsynaptic potentials can play a functional role in realizing synchronization of neuronal firing in the brain. In order to examine the relation between inhibition and synchronous firing of neurons theoretically, we analyze possible effects of synchronization and sensitivity enhancement caused by inhibitory inputs to neurons with a biologically realistic model of the Hodgkin-Huxley equations. The result shows that, after an inhibitory spike, the firing probability of a single postsynaptic neuron exposed to random excitatory background activity oscillates with time. The oscillation of the firing probability can be related to synchronous firing of neurons receiving an inhibitory spike simultaneously. Further, we show that when an inhibitory spike input precedes an excitatory spike input, the presence of such preceding inhibition raises the firing probability peak of the neuron after the excitatory input. The result indicates that an inhibitory spike input can enhance the sensitivity of the postsynaptic neuron to the following excitatory spike input. Two neural network models based on these effects on postsynaptic neurons caused by inhibitory inputs are proposed to demonstrate possible mechanisms of detecting particular spatiotemporal spike patterns. Received: 15 April 1999 /Accepted in revised form: 25 November 1999     

Spatiotemporal burst coding for extracting features of spatiotemporally varying stimuli

Encoding features of spatiotemporally varying stimuli is quite important for understanding the neural mechanisms of various sensory coding. Temporal coding can encode features of time-varying stimulus, and population coding with temporal coding is adequate for encoding spatiotemporal correlation of stimulus features into spatiotemporal activity of neurons. However, little is known about how spatiotemporal features of stimulus are encoded by spatiotemporal property of neural activity. To address this issue, we propose here a population coding with burst spikes, called here spatiotemporal burst (STB) coding. In STB coding, the temporal variation of stimuli is encoded by the precise onset timing of burst spike, and the spatiotemporal correlation of stimuli is emphasized by one specific aspect of burst firing, or spike packet followed by silent interval. To show concretely the role of STB coding, we study the electrosensory system of a weakly electric fish. Weakly electric fish must perceive the information about an object nearby by analyzing spatiotemporal modulations of electric field around it. On the basis of well-characterized circuitry, we constructed a neural network model of the electrosensory system. Here we show that STB coding encodes well the information of object distance and size by extracting the spatiotemporal correlation of the distorted electric field. The burst activity of electrosensory neurons is also affected by feedback signals through synaptic plasticity. We show that the control of burst activity caused by the synaptic plasticity leads to extracting the stimulus features depending on the stimulus context. Our results suggest that sensory systems use burst spikes as a unit of sensory coding in order to extract spatiotemporal features of stimuli from spatially distributed stimuli.     

Spike-based population coding and working memory

Compelling behavioral evidence suggests that humans can make optimal decisions despite the uncertainty inherent in perceptual or motor tasks. A key question in neuroscience is how populations of spiking neurons can implement such probabilistic computations. In this article, we develop a comprehensive framework for optimal, spike-based sensory integration and working memory in a dynamic environment. We propose that probability distributions are inferred spike-per-spike in recurrently connected networks of integrate-and-fire neurons. As a result, these networks can combine sensory cues optimally, track the state of a time-varying stimulus and memorize accumulated evidence over periods much longer than the time constant of single neurons. Importantly, we propose that population responses and persistent working memory states represent entire probability distributions and not only single stimulus values. These memories are reflected by sustained, asynchronous patterns of activity which make relevant information available to downstream neurons within their short time window of integration. Model neurons act as predictive encoders, only firing spikes which account for new information that has not yet been signaled. Thus, spike times signal deterministically a prediction error, contrary to rate codes in which spike times are considered to be random samples of an underlying firing rate. As a consequence of this coding scheme, a multitude of spike patterns can reliably encode the same information. This results in weakly correlated, Poisson-like spike trains that are sensitive to initial conditions but robust to even high levels of external neural noise. This spike train variability reproduces the one observed in cortical sensory spike trains, but cannot be equated to noise. On the contrary, it is a consequence of optimal spike-based inference. In contrast, we show that rate-based models perform poorly when implemented with stochastically spiking neurons.     

Neural Sequence Generation Using Spatiotemporal Patterns of Inhibition

Stereotyped sequences of neural activity are thought to underlie reproducible behaviors and cognitive processes ranging from memory recall to arm movement. One of the most prominent theoretical models of neural sequence generation is the synfire chain, in which pulses of synchronized spiking activity propagate robustly along a chain of cells connected by highly redundant feedforward excitation. But recent experimental observations in the avian song production pathway during song generation have shown excitatory activity interacting strongly with the firing patterns of inhibitory neurons, suggesting a process of sequence generation more complex than feedforward excitation. Here we propose a model of sequence generation inspired by these observations in which a pulse travels along a spatially recurrent excitatory chain, passing repeatedly through zones of local feedback inhibition. In this model, synchrony and robust timing are maintained not through redundant excitatory connections, but rather through the interaction between the pulse and the spatiotemporal pattern of inhibition that it creates as it circulates the network. These results suggest that spatially and temporally structured inhibition may play a key role in sequence generation.     

Visual pattern discrimination by population retinal ganglion cells’ activities during natural movie stimulation

In the visual system, neurons often fire in synchrony, and it is believed that synchronous activities of group neurons are more efficient than single cell response in transmitting neural signals to down-stream neurons. However, whether dynamic natural stimuli are encoded by dynamic spatiotemporal firing patterns of synchronous group neurons still needs to be investigated. In this paper we recorded the activities of population ganglion cells in bullfrog retina in response to time-varying natural images (natural scene movie) using multi-electrode arrays. In response to some different brief section pairs of the movie, synchronous groups of retinal ganglion cells (RGCs) fired with similar but different spike events. We attempted to discriminate the movie sections based on temporal firing patterns of single cells and spatiotemporal firing patterns of the synchronous groups of RGCs characterized by a measurement of subsequence distribution discrepancy. The discrimination performance was assessed by a classification method based on Support Vector Machines. Our results show that different movie sections of the natural movie elicited reliable dynamic spatiotemporal activity patterns of the synchronous RGCs, which are more efficient in discriminating different movie sections than the temporal patterns of the single cells’ spike events. These results suggest that, during natural vision, the down-stream neurons may decode the visual information from the dynamic spatiotemporal patterns of the synchronous group of RGCs’ activities.     

Statistical study on reverberation between two mutually excitatory neuron groups

The reverberation that occurs between two neuron groups, which have excitatory mono-synaptic random connections with each other can be studied theoretically by employing a model neuron, which expresses well the characters of a real neuron. In this model we consider three effects, which are; the effect of the summation of the excitatory post-synaptic potential (EPSP) of neurons; the effect of the spontaneous firing of neurons as a noise in groups and the effect of the relative refractory period of neurons. As a result, it is shown that under the effect of the summation of the EPSP of neurons and the effect of the noise, the systematic threshold p theta takes the same value as is observed in practice. The effect of the relative refractory period has been considered in order to explain the low speed of the increase in firing activity, as observed in the reverberating system. It suppresses slightly the speed of the increase in firing activity (pi) in the system. Moreover, the speed can be suppressed by making the refractory effect strong according to the increase of pi. However, the initial increase of pi at a high speed that was observed in the experiment cannot be explained simply by the effect of the refractoriness, even if it were the absolute refractoriness.     

Neural coding properties based on spike timing and pattern correlation of retinal ganglion cells

Correlation between spike trains or neurons sometimes indicates certain neural coding rules in the visual system. In this paper, the relationship between spike timing correlation and pattern correlation is discussed, and their ability to represent stimulus features is compared to examine their coding strategies not only in individual neurons but also in population. Two kinds of stimuli, natural movies and checkerboard, are used to arouse firing activities in chicken retinal ganglion cells. The spike timing correlation and pattern correlation are calculated by cross-correlation function and Lempel–Ziv distance respectively. According to the correlation values, it is demonstrated that spike trains with similar spike patterns are not necessarily concerted in firing time. Moreover, spike pattern correlation values between individual neurons’ responses reflect the difference of natural movies and checkerboard; neurons cooperate with each other with higher pattern correlation values which represent spatiotemporal correlations during response to natural movies. Spike timing does not reflect stimulus features as obvious as spike patterns, caused by their particular coding properties or physiological foundation. As a result, separating the pattern correlation out of traditional timing correlation concept uncover additional insight in neural coding.     

Predictive Coding of Dynamical Variables in Balanced Spiking Networks

Two observations about the cortex have puzzled neuroscientists for a long time. First, neural responses are highly variable. Second, the level of excitation and inhibition received by each neuron is tightly balanced at all times. Here, we demonstrate that both properties are necessary consequences of neural networks that represent information efficiently in their spikes. We illustrate this insight with spiking networks that represent dynamical variables. Our approach is based on two assumptions: We assume that information about dynamical variables can be read out linearly from neural spike trains, and we assume that neurons only fire a spike if that improves the representation of the dynamical variables. Based on these assumptions, we derive a network of leaky integrate-and-fire neurons that is able to implement arbitrary linear dynamical systems. We show that the membrane voltage of the neurons is equivalent to a prediction error about a common population-level signal. Among other things, our approach allows us to construct an integrator network of spiking neurons that is robust against many perturbations. Most importantly, neural variability in our networks cannot be equated to noise. Despite exhibiting the same single unit properties as widely used population code models (e.g. tuning curves, Poisson distributed spike trains), balanced networks are orders of magnitudes more reliable. Our approach suggests that spikes do matter when considering how the brain computes, and that the reliability of cortical representations could have been strongly underestimated.     

交流外电场下映射神经元放电节律的分析

神经元不同的放电节律承载着不同的刺激信息。文章基于神经元映射模型,研究低频交流电场对神经元放电节律的影响。在外部刺激下映射模型表现出丰富的放电模式,包括周期簇放电、周期峰放电、交替放电和混沌放电。神经元对刺激频率和振幅的变化极为敏感,随着频率的增大,放电节律表现出从簇放电到峰放电和混沌放电的反向加周期分岔序列;在周期节律转迁过程中存在一种新的交替节律,其放电序列为两种周期放电模式的交替,峰峰间期序列具有整数倍特征。外电场的频率影响细胞内、外离子振荡周期,导致神经元放电与刺激信号同步,对放电节律的影响更为明显。研究结果揭示了交流外电场对神经元放电节律的作用规律,有助于探寻外电场对生物神经系统兴奋性的影响和神经系统疾病的致病机理。     

A learning theory for reward-modulated spike-timing-dependent plasticity with application to biofeedback

Reward-modulated spike-timing-dependent plasticity (STDP) has recently emerged as a candidate for a learning rule that could explain how behaviorally relevant adaptive changes in complex networks of spiking neurons could be achieved in a self-organizing manner through local synaptic plasticity. However, the capabilities and limitations of this learning rule could so far only be tested through computer simulations. This article provides tools for an analytic treatment of reward-modulated STDP, which allows us to predict under which conditions reward-modulated STDP will achieve a desired learning effect. These analytical results imply that neurons can learn through reward-modulated STDP to classify not only spatial but also temporal firing patterns of presynaptic neurons. They also can learn to respond to specific presynaptic firing patterns with particular spike patterns. Finally, the resulting learning theory predicts that even difficult credit-assignment problems, where it is very hard to tell which synaptic weights should be modified in order to increase the global reward for the system, can be solved in a self-organizing manner through reward-modulated STDP. This yields an explanation for a fundamental experimental result on biofeedback in monkeys by Fetz and Baker. In this experiment monkeys were rewarded for increasing the firing rate of a particular neuron in the cortex and were able to solve this extremely difficult credit assignment problem. Our model for this experiment relies on a combination of reward-modulated STDP with variable spontaneous firing activity. Hence it also provides a possible functional explanation for trial-to-trial variability, which is characteristic for cortical networks of neurons but has no analogue in currently existing artificial computing systems. In addition our model demonstrates that reward-modulated STDP can be applied to all synapses in a large recurrent neural network without endangering the stability of the network dynamics.     

A biologically motivated and analytically soluble model of collective oscillations in the cortex

. Feature linking and pattern separation are shown to be performed as simultaneous processes by a highly connected auto-associative network of spiking neurons (spike response model). In principle, many (e.g., with nine) patterns can be separated, but with a biological set of parameters the number is limited to four. The patterns have been learned by an asymmetric hebbian rule that can handle a low activity which may vary from pattern to pattern (in a range between 4% and 7%). Spikes are generated by a threshold process and – with some delay – transmitted to postsynaptic neurons. There they evoke an excitatory or inhibitory postsynaptic potential (EPSP or IPSP). Spike emission is followed by an absolute refractory period (1 ms) and activates an inhibitory delay loop that prevents continuous firing. Three different network topologies are discussed, i.e., a structureless fully connected system, a network composed of two ‘hemispheres’, and finally a hierarchical network with four subsystems that represent different ‘functions’ and interact via feedforward and feedback connections. Functional feedback turns out to be essential for context-sensitive binding. The coherence between the two hemispheres is dependent on the interhemispheric delays. If these are on average too large, the two hemispheres oscillate coherently by themselves but phase-shifted by half a period with respect to each other. Received: 16 June 1993/Accepted in revised form: 24 March 1994     

Reduction of information redundancy in the ascending auditory pathway

Information processing by a sensory system is reflected in the changes in stimulus representation along its successive processing stages. We measured information content and stimulus-induced redundancy in the neural responses to a set of natural sounds in three successive stations of the auditory pathway-inferior colliculus (IC), auditory thalamus (MGB), and primary auditory cortex (A1). Information about stimulus identity was somewhat reduced in single A1 and MGB neurons relative to single IC neurons, when information is measured using spike counts, latency, or temporal spiking patterns. However, most of this difference was due to differences in firing rates. On the other hand, IC neurons were substantially more redundant than A1 and MGB neurons. IC redundancy was largely related to frequency selectivity. Redundancy reduction may be a generic organization principle of neural systems, allowing for easier readout of the identity of complex stimuli in A1 relative to IC.     

Ensembles of Spiking Neurons with Noise Support Optimal Probabilistic Inference in a Dynamically Changing Environment

It has recently been shown that networks of spiking neurons with noise can emulate simple forms of probabilistic inference through “neural sampling”, i.e., by treating spikes as samples from a probability distribution of network states that is encoded in the network. Deficiencies of the existing model are its reliance on single neurons for sampling from each random variable, and the resulting limitation in representing quickly varying probabilistic information. We show that both deficiencies can be overcome by moving to a biologically more realistic encoding of each salient random variable through the stochastic firing activity of an ensemble of neurons. The resulting model demonstrates that networks of spiking neurons with noise can easily track and carry out basic computational operations on rapidly varying probability distributions, such as the odds of getting rewarded for a specific behavior. We demonstrate the viability of this new approach towards neural coding and computation, which makes use of the inherent parallelism of generic neural circuits, by showing that this model can explain experimentally observed firing activity of cortical neurons for a variety of tasks that require rapid temporal integration of sensory information.