A discrete time neural network model with spiking neurons

We derive rigorous results describing the asymptotic dynamics of a discrete time model of spiking neurons introduced in Soula et al. (Neural Comput. 18, 1, 2006). Using symbolic dynamic techniques we show how the dynamics of membrane potential has a one to one correspondence with sequences of spikes patterns (“raster plots”). Moreover, though the dynamics is generically periodic, it has a weak form of initial conditions sensitivity due to the presence of a sharp threshold in the model definition. As a consequence, the model exhibits a dynamical regime indistinguishable from chaos in numerical experiments.      

On the stationary state of a network of inhibitory spiking neurons

The background activity of a cortical neural network is modeled by a homogeneous integrate-and-fire network with unreliable inhibitory synapses. For the case of fast synapses, numerical and analytical calculations show that the network relaxes into a stationary state of high attention. The majority of the neurons has a membrane potential just below the threshold; as a consequence the network can react immediately – on the time scale of synaptic transmission- on external pulses. The neurons fire with a low rate and with a broad distribution of interspike intervals. Firing events of the total network are correlated over short time periods. The firing rate increases linearly with external stimuli. In the limit of infinitely large networks, the synaptic noise decreases to zero. Nevertheless, the distribution of interspike intervals remains broad. Action Editor: Misha Tsodyks     

Stimulus correlation and adaptive motion detection using spiking neurons

Stimulus correlation and adaptive movement detection, among other tasks can be performed with VLSI general-purpose neurons that have controllable steady and transient responses. This paper presents experimental results of simple neural primitives based on the CMOS neuron approach described in [11]. Stimulus correlation experiments illustrate the well defined behavior of the CMOS approach. This basic primitive is used to implement motion detectors with adaptive capabilities that enable it to work efficiently in a wide velocity range.     

Testing of information condensation in a model reverberating spiking neural network

Information about external world is delivered to the brain in the form of structured in time spike trains. During further processing in higher areas, information is subjected to a certain condensation process, which results in formation of abstract conceptual images of external world, apparently, represented as certain uniform spiking activity partially independent on the input spike trains details. Possible physical mechanism of condensation at the level of individual neuron was discussed recently. In a reverberating spiking neural network, due to this mechanism the dynamics should settle down to the same uniform/ periodic activity in response to a set of various inputs. Since the same periodic activity may correspond to different input spike trains, we interpret this as possible candidate for information condensation mechanism in a network. Our purpose is to test this possibility in a network model consisting of five fully connected neurons, particularly, the influence of geometric size of the network, on its ability to condense information. Dynamics of 20 spiking neural networks of different geometric sizes are modelled by means of computer simulation. Each network was propelled into reverberating dynamics by applying various initial input spike trains. We run the dynamics until it becomes periodic. The Shannon's formula is used to calculate the amount of information in any input spike train and in any periodic state found. As a result, we obtain explicit estimate of the degree of information condensation in the networks, and conclude that it depends strongly on the net's geometric size.     

Generating oscillatory bursts from a network of regular spiking neurons without inhibition

Avian nucleus isthmi pars parvocellularis (Ipc) neurons are reciprocally connected with the layer 10 (L10) neurons in the optic tectum and respond with oscillatory bursts to visual stimulation. Our in vitro experiments show that both neuron types respond with regular spiking to somatic current injection and that the feedforward and feedback synaptic connections are excitatory, but of different strength and time course. To elucidate mechanisms of oscillatory bursting in this network of regularly spiking neurons, we investigated an experimentally constrained model of coupled leaky integrate-and-fire neurons with spike-rate adaptation. The model reproduces the observed Ipc oscillatory bursting in response to simulated visual stimulation. A scan through the model parameter volume reveals that Ipc oscillatory burst generation can be caused by strong and brief feedforward synaptic conductance changes. The mechanism is sensitive to the parameter values of spike-rate adaptation. In conclusion, we show that a network of regular-spiking neurons with feedforward excitation and spike-rate adaptation can generate oscillatory bursting in response to a constant input.     

Directional operations in the motor cortex modeled by a neural network of spiking neurons

A neural network with realistically modeled, spiking neurons is proposed to model ensemble operations of directionally tuned neurons in the motor cortex. The model reproduces well directional operations previously identified experimentally, including the prediction of the direction of an upcoming movement in reaching tasks and the rotation of the neuronal population vector in a directional transformation task.     

Kainate receptor-mediated modulation of hippocampal fast spiking interneurons in a rat model of schizophrenia

Kainate receptor (KAR) subunits are believed to be involved in abnormal GABAergic neurotransmission in the hippocampus (HIPP) in schizophrenia (SZ) and bipolar disorder. Postmortem studies have shown changes in the expression of the GluR5/6 subunits of KARs in the stratum oriens (SO) of sectors CA2/3, where the basolateral amygdala (BLA) sends a robust projection. Previous work using a rat model of SZ demonstrated that BLA activation leads to electrophysiological changes in fast-spiking interneurons in SO of CA2/3. The present study explores KAR modulation of interneurons in CA2/3 in response to BLA activation. Intrinsic firing properties of these interneurons through KAR-mediated activity were measured with patch-clamp recordings from rats that received 15 days of picrotoxin infusion into the BLA. Chronic BLA activation induced changes in the firing properties of CA2/3 interneurons associated with modifications in the function of KARs. Specifically, the responsiveness of these interneurons to activation of KARs was diminished in picrotoxin-treated rats, while the after-hyperpolarization (AHP) amplitude was increased. In addition, we tested blockers of KAR subunits which have been shown to have altered gene expression in SO sector CA2/3 of SZ subjects. The GluR5 antagonist UBP296 further decreased AP frequency and increased AHP amplitude in picrotoxin-treated rats. Application of the GluR6/7 antagonist NS102 suggested that activation of GluR6/7 KARs may be required to maintain the high firing rates in SO interneurons in the presence of KA. Moreover, the GluR6/7 KAR-mediated signaling may be suppressed in PICRO-treated rats. Our findings indicate that glutamatergic activity from the BLA may modulate the firing properties of CA2/3 interneurons through GluR5 and GluR6/7 KARs. These receptors are expressed in GABAergic interneurons and play a key role in the synchronization of gamma oscillations. Modulation of interneuronal activity through KARs in response to amygdala activation may lead to abnormal oscillatory rhythms reported in SZ subjects.     

A discrete time neural network model with spiking neurons: II: Dynamics with noise

We provide rigorous and exact results characterizing the statistics of spike trains in a network of leaky Integrate-and-Fire neurons, where time is discrete and where neurons are submitted to noise, without restriction on the synaptic weights. We show the existence and uniqueness of an invariant measure of Gibbs type and discuss its properties. We also discuss Markovian approximations and relate them to the approaches currently used in computational neuroscience to analyse experimental spike trains statistics.     

A computational model of visual marking using an inter-connected network of spiking neurons: the spiking search over time & space model (sSoTS).

In the real world, visual information is selected over time as well as space, when we prioritise new stimuli for attention. Watson and Humphreys [Watson, D., Humphreys, G.W., 1997. Visual marking: prioritizing selection for new objects by top-down attentional inhibition of old objects. Psychological Review 104, 90-122] presented evidence that new information in search tasks is prioritised by (amongst other processes) active ignoring of old items - a process they termed visual marking. In this paper we present, for the first time, an explicit computational model of visual marking using biologically plausible activation functions. The "spiking search over time and space" model (sSoTS) incorporates different synaptic components (NMDA, AMPA, GABA) and a frequency adaptation mechanism based on [Ca(2+)] sensitive K(+) current. This frequency adaptation current can act as a mechanism that suppresses the previously attended items. We show that, when coupled with a process of active inhibition applied to old items, frequency adaptation leads to old items being de-prioritised (and new items prioritised) across time in search. Furthermore, the time course of these processes mimics the time course of the preview effect in human search. The results indicate that the sSoTS model can provide a biologically plausible account of human search over time as well as space.     

An STDP training algorithm for a spiking neural network with dynamic threshold neurons

This paper proposes a supervised training algorithm for Spiking Neural Networks (SNNs) which modifies the Spike Timing Dependent Plasticity (STDP)learning rule to support both local and network level training with multiple synaptic connections and axonal delays. The training algorithm applies the rule to two and three layer SNNs, and is benchmarked using the Iris and Wisconsin Breast Cancer (WBC) data sets. The effectiveness of hidden layer dynamic threshold neurons is also investigated and results are presented.     

Travelling wave patterns in a model of the spinal pattern generator using spiking neurons

The aim of this study is to produce travelling waves in a planar net of artificial spiking neurons. Provided that the parameters of the waves – frequency, wavelength and orientation – can be sufficiently controlled, such a network can serve as a model of the spinal pattern generator for swimming and terrestrial quadruped locomotion. A previous implementation using non-spiking, sigmoid neurons lacked the physiological plausibility that can only be attained using more realistic spiking neurons. Simulations were conducted using three types of spiking neuronal models. First, leaky integrate-and-fire neurons were used. Second, we introduced a phenomenological bursting neuron. And third, a canonical model neuron was implemented which could reproduce the full dynamics of the Hodgkin–Huxley neuron. The conditions necessary to produce appropriate travelling waves corresponded largely to the known anatomy and physiology of the spinal cord. Especially important features for the generation of travelling waves were the topology of the local connections – so-called off-centre connectivity – the availability of dynamic synapses and, to some extent, the availability of bursting cell types. The latter were necessary to produce stable waves at the low frequencies observed in quadruped locomotion. In general, the phenomenon of travelling waves was very robust and largely independent of the network parameters and emulated cell types.     

Extending transfer entropy improves identification of effective connectivity in a spiking cortical network model

Transfer entropy (TE) is an information-theoretic measure which has received recent attention in neuroscience for its potential to identify effective connectivity between neurons. Calculating TE for large ensembles of spiking neurons is computationally intensive, and has caused most investigators to probe neural interactions at only a single time delay and at a message length of only a single time bin. This is problematic, as synaptic delays between cortical neurons, for example, range from one to tens of milliseconds. In addition, neurons produce bursts of spikes spanning multiple time bins. To address these issues, here we introduce a free software package that allows TE to be measured at multiple delays and message lengths. To assess performance, we applied these extensions of TE to a spiking cortical network model (Izhikevich, 2006) with known connectivity and a range of synaptic delays. For comparison, we also investigated single-delay TE, at a message length of one bin (D1TE), and cross-correlation (CC) methods. We found that D1TE could identify 36% of true connections when evaluated at a false positive rate of 1%. For extended versions of TE, this dramatically improved to 73% of true connections. In addition, the connections correctly identified by extended versions of TE accounted for 85% of the total synaptic weight in the network. Cross correlation methods generally performed more poorly than extended TE, but were useful when data length was short. A computational performance analysis demonstrated that the algorithm for extended TE, when used on currently available desktop computers, could extract effective connectivity from 1 hr recordings containing 200 neurons in ～5 min. We conclude that extending TE to multiple delays and message lengths improves its ability to assess effective connectivity between spiking neurons. These extensions to TE soon could become practical tools for experimentalists who record hundreds of spiking neurons.     

Spatial cognition and neuro-mimetic navigation: a model of hippocampal place cell activity

 A computational model of hippocampal activity during spatial cognition and navigation tasks is presented. The spatial representation in our model of the rat hippocampus is built on-line during exploration via two processing streams. An allothetic vision-based representation is built by unsupervised Hebbian learning extracting spatio-temporal properties of the environment from visual input. An idiothetic representation is learned based on internal movement-related information provided by path integration. On the level of the hippocampus, allothetic and idiothetic representations are integrated to yield a stable representation of the environment by a population of localized overlapping CA3-CA1 place fields. The hippocampal spatial representation is used as a basis for goal-oriented spatial behavior. We focus on the neural pathway connecting the hippocampus to the nucleus accumbens. Place cells drive a population of locomotor action neurons in the nucleus accumbens. Reward-based learning is applied to map place cell activity into action cell activity. The ensemble action cell activity provides navigational maps to support spatial behavior. We present experimental results obtained with a mobile Khepera robot. Received: 02 July 1999 / Accepted in revised form: 20 March 2000     

Inhibitory network of spiking neurons may express a sharp peak of synchrony at low frequency band

Spike synchronization remains an important issue in neuroscience, and inhibitory networks are the best candidates to provide such synchrony. Increasing evidence indicates that in many brain area inhibitory interneurons of similar properties make reciprocal connections. We found that a hybrid, as well as model network, consisting of two reciprocally inhibitory spiking neurons may express a peak of synchronization in a narrow range of low spiking frequencies in addition to classically described plateau of synchrony at a wide range of high frequencies. Occurrence of the low frequency peak of synchrony requires a moderate-to-strong inhibitory coupling and relatively fast synapses. This novel possibility of synchronization in a narrow range of network parameters may have an important implication in discrimination and encoding of signals of precise intensity, as well as in altering network ability to process information.     

Nanoparticle targeting to neurons in a rat hippocampal slice culture model

We have previously shown that CdSe/ZnS core/shell luminescent semiconductor nanocrystals or QDs (quantum dots) coated with PEG [poly(ethylene glycol)]-appended DHLA (dihydrolipoic acid) can bind AcWG(Pal)VKIKKP₉GGH₆ (Palm1) through the histidine residues. The coating on the QD provides colloidal stability and this peptide complex uniquely allows the QDs to be taken up by cultured cells and readily exit the endosome into the soma. We now show that use of a polyampholyte coating [in which the neutral PEG is replaced by the negatively heterocharged CL4 (compact ligand)], results in the specific targeting of the palmitoylated peptide to neurons in mature rat hippocampal slice cultures. There was no noticeable uptake by astrocytes, oligodendrocytes or microglia (identified by immunocytochemistry), demonstrating neuronal specificity to the overall negatively charged CL4 coating. In addition, EM (electron microscopy) images confirm the endosomal egress ability of the Palm1 peptide by showing a much more disperse cytosolic distribution of the CL4 QDs conjugated to Palm1 compared with CL4 QDs alone. This suggests a novel and robust way of delivering neurotherapeutics to neurons.     

Modeling fluctuations in default-mode brain network using a spiking neural network

Recently, numerous attempts have been made to understand the dynamic behavior of complex brain systems using neural network models. The fluctuations in blood-oxygen-level-dependent (BOLD) brain signals at less than 0.1 Hz have been observed by functional magnetic resonance imaging (fMRI) for subjects in a resting state. This phenomenon is referred to as a "default-mode brain network." In this study, we model the default-mode brain network by functionally connecting neural communities composed of spiking neurons in a complex network. Through computational simulations of the model, including transmission delays and complex connectivity, the network dynamics of the neural system and its behavior are discussed. The results show that the power spectrum of the modeled fluctuations in the neuron firing patterns is consistent with the default-mode brain network's BOLD signals when transmission delays, a characteristic property of the brain, have finite values in a given range.     

Associative recognition and storage in a model network of physiological neurons

We consider a neural network model in which the single neurons are chosen to closely resemble known physiological properties. The neurons are assumed to be linked by synapses which change their strength according to Hebbian rules on a short time scale (100ms). The dynamics of the network — the time evolution of the cell potentials and the synapses — is investigated by computer simulation. As in more abstract network models (Cooper 1973; Hopfield 1982; Kohonen 1984) it is found that the local dynamics of the cell potentials and the synaptic strengths result in global cooperative properties of the network and enable the network to process an incoming flux of information and to learn and store patterns associatively. A trained net can associate missing details of a pattern, can correct wrong details and can suppress noise in a pattern. The network can further abstract the prototype from a series of patterns with variations. A suitable coupling constant connecting the dynamics of the cell potentials with the synaptic strengths is derived by a mean field approximation. This coupling constant controls the neural sensitivity and thereby avoids both extremes of the network state, the state of permanent inactivity and the state of epileptic hyperactivity.     

Predictive features of persistent activity emergence in regular spiking and intrinsic bursting model neurons

Proper functioning of working memory involves the expression of stimulus-selective persistent activity in pyramidal neurons of the prefrontal cortex (PFC), which refers to neural activity that persists for seconds beyond the end of the stimulus. The mechanisms which PFC pyramidal neurons use to discriminate between preferred vs. neutral inputs at the cellular level are largely unknown. Moreover, the presence of pyramidal cell subtypes with different firing patterns, such as regular spiking and intrinsic bursting, raises the question as to what their distinct role might be in persistent firing in the PFC. Here, we use a compartmental modeling approach to search for discriminatory features in the properties of incoming stimuli to a PFC pyramidal neuron and/or its response that signal which of these stimuli will result in persistent activity emergence. Furthermore, we use our modeling approach to study cell-type specific differences in persistent activity properties, via implementing a regular spiking (RS) and an intrinsic bursting (IB) model neuron. We identify synaptic location within the basal dendrites as a feature of stimulus selectivity. Specifically, persistent activity-inducing stimuli consist of activated synapses that are located more distally from the soma compared to non-inducing stimuli, in both model cells. In addition, the action potential (AP) latency and the first few inter-spike-intervals of the neuronal response can be used to reliably detect inducing vs. non-inducing inputs, suggesting a potential mechanism by which downstream neurons can rapidly decode the upcoming emergence of persistent activity. While the two model neurons did not differ in the coding features of persistent activity emergence, the properties of persistent activity, such as the firing pattern and the duration of temporally-restricted persistent activity were distinct. Collectively, our results pinpoint to specific features of the neuronal response to a given stimulus that code for its ability to induce persistent activity and predict differential roles of RS and IB neurons in persistent activity expression.     

Neural dynamics as sampling: a model for stochastic computation in recurrent networks of spiking neurons

The organization of computations in networks of spiking neurons in the brain is still largely unknown, in particular in view of the inherently stochastic features of their firing activity and the experimentally observed trial-to-trial variability of neural systems in the brain. In principle there exists a powerful computational framework for stochastic computations, probabilistic inference by sampling, which can explain a large number of macroscopic experimental data in neuroscience and cognitive science. But it has turned out to be surprisingly difficult to create a link between these abstract models for stochastic computations and more detailed models of the dynamics of networks of spiking neurons. Here we create such a link and show that under some conditions the stochastic firing activity of networks of spiking neurons can be interpreted as probabilistic inference via Markov chain Monte Carlo (MCMC) sampling. Since common methods for MCMC sampling in distributed systems, such as Gibbs sampling, are inconsistent with the dynamics of spiking neurons, we introduce a different approach based on non-reversible Markov chains that is able to reflect inherent temporal processes of spiking neuronal activity through a suitable choice of random variables. We propose a neural network model and show by a rigorous theoretical analysis that its neural activity implements MCMC sampling of a given distribution, both for the case of discrete and continuous time. This provides a step towards closing the gap between abstract functional models of cortical computation and more detailed models of networks of spiking neurons.