Synchrony in heterogeneous networks of spiking neurons

The emergence of synchrony in the activity of large, heterogeneous networks of spiking neurons is investigated. We define the robustness of synchrony by the critical disorder at which the asynchronous state becomes linearly unstable. We show that at low firing rates, synchrony is more robust in excitatory networks than in inhibitory networks, but excitatory networks cannot display any synchrony when the average firing rate becomes too high. We introduce a new regime where all inputs, external and internal, are strong and have opposite effects that cancel each other when averaged. In this regime, the robustness of synchrony is strongly enhanced, and robust synchrony can be achieved at a high firing rate in inhibitory networks. On the other hand, in excitatory networks, synchrony remains limited in frequency due to the intrinsic instability of strong recurrent excitation.     

Gamma oscillations and stimulus selection

More coherent excitatory stimuli are known to have a competitive advantage over less coherent ones. We show here that this advantage is amplified greatly when the target includes inhibitory interneurons acting via GABA(A)-receptor-mediated synapses and the coherent input oscillates at gamma frequency. We hypothesize that therein lies, at least in part, the functional significance of the experimentally observed link between attentional biasing of stimulus competition and gamma frequency rhythmicity.     

A spiking neuron model of cortical correlates of sensorineural hearing loss: Spontaneous firing, synchrony, and tinnitus

Hearing loss due to peripheral damage is associated with cochlear hair cell damage or loss and some retrograde degeneration of auditory nerve fibers. Surviving auditory nerve fibers in the impaired region exhibit elevated and broadened frequency tuning, and the cochleotopic representation of broadband stimuli such as speech is distorted. In impaired cortical regions, increased tuning to frequencies near the edge of the hearing loss coupled with increased spontaneous and synchronous firing is observed. Tinnitus, an auditory percept in the absence of sensory input, may arise under these circumstances as a result of plastic reorganization in the auditory cortex. We present a spiking neuron model of auditory cortex that captures several key features of cortical organization. A key assumption in the model is that in response to reduced afferent excitatory input in the damaged region, a compensatory change in the connection strengths of lateral excitatory and inhibitory connections occurs. These changes allow the model to capture some of the cortical correlates of sensorineural hearing loss, including changes in spontaneous firing and synchrony; these phenomena may explain central tinnitus. This model may also be useful for evaluating procedures designed to segregate synchronous activity underlying tinnitus and for evaluating adaptive hearing devices that compensate for selective hearing loss.     

Selectivity and stability via dendritic nonlinearity

Inspired by recent studies regarding dendritic computation, we constructed a recurrent neural network model incorporating dendritic lateral inhibition. Our model consists of an input layer and a neuron layer that includes excitatory cells and an inhibitory cell; this inhibitory cell is activated by the pooled activities of all the excitatory cells, and it in turn inhibits each dendritic branch of the excitatory cells that receive excitations from the input layer. Dendritic nonlinear operation consisting of branch-specifically rectified inhibition and saturation is described by imposing nonlinear transfer functions before summation over the branches. In this model with sufficiently strong recurrent excitation, on transiently presenting a stimulus that has a high correlation with feed- forward connections of one of the excitatory cells, the corresponding cell becomes highly active, and the activity is sustained after the stimulus is turned off, whereas all the other excitatory cells continue to have low activities. But on transiently presenting a stimulus that does not have high correlations with feedforward connections of any of the excitatory cells, all the excitatory cells continue to have low activities. Interestingly, such stimulus-selective sustained response is preserved for a wide range of stimulus intensity. We derive an analytical formulation of the model in the limit where individual excitatory cells have an infinite number of dendritic branches and prove the existence of an equilibrium point corresponding to such a balanced low-level activity state as observed in the simulations, whose stability depends solely on the signal-to-noise ratio of the stimulus. We propose this model as a model of stimulus selectivity equipped with self-sustainability and intensity-invariance simultaneously, which was difficult in the conventional competitive neural networks with a similar degree of complexity in their network architecture. We discuss the biological relevance of the model in a general framework of computational neuroscience.     

Correlation between uncoupled conductance-based integrate-and-fire neurons due to common and synchronous presynaptic firing

We investigate the firing characteristics of conductance-based integrate-and-fire neurons and the correlation of firing for uncoupled pairs of neurons as a result of common input and synchronous firing of multiple synaptic inputs. Analytical approximations are derived for the moments of the steady state potential and the effective time constant. We show that postsynaptic firing barely depends on the correlation between inhibitory inputs; only the inhibitory firing rate matters. In contrast, both the degree of synchrony and the firing rate of excitatory inputs are relevant. A coefficient of variation CV > 1 can be attained with low inhibitory firing rates and (Poisson-modulated) synchronized excitatory synaptic input, where both the number of presynaptic neurons in synchronous firing assemblies and the synchronous firing rate should be sufficiently large. The correlation in firing of a pair of uncoupled neurons due to common excitatory input is initially increased for increasing firing rates of independent inhibitory inputs but decreases for large inhibitory firing rates. Common inhibitory input to a pair of uncoupled neurons barely induces correlated firing, but amplifies the effect of common excitation. Synchronous firing assemblies in the common input further enhance the correlation and are essential to attain experimentally observed correlation values. Since uncorrelated common input (i.e., common input by neurons, which do not fire in synchrony) cannot induce sufficient postsynaptic correlation, we conclude that lateral couplings are essential to establish clusters of synchronously firing neurons.     

Stochastic Resonance and Coincidence Detection in Single Neurons

We demonstrate that a realistic neuron model expressed by the Hodgkin-Huxley equations shows a stochastic resonance phenomenon, by computing cross-correlation between input and output spike timing when the neuron receives both aperiodic signal input of spike packets and background random noise of both excitatory and inhibitory spikes. We consider that such a signal detection is realized because the neuron with active properties is sensitive to fluctuation caused by a sharp increase just after a sudden dip of excitatory noise spikes and a gradual decrease of inhibitory noise spikes. We also show that the model generates highly irregular firing of output spikes on the basis of the modulation detecting property.     

Patterns of synchrony in neural networks with spike adaptation

We study the emergence of synchronized burst activity in networks of neurons with spike adaptation. We show that networks of tonically firing adapting excitatory neurons can evolve to a state where the neurons burst in a synchronized manner. The mechanism leading to this burst activity is analyzed in a network of integrate-and-fire neurons with spike adaptation. The dependence of this state on the different network parameters is investigated, and it is shown that this mechanism is robust against inhomogeneities, sparseness of the connectivity, and noise. In networks of two populations, one excitatory and one inhibitory, we show that decreasing the inhibitory feedback can cause the network to switch from a tonically active, asynchronous state to the synchronized bursting state. Finally, we show that the same mechanism also causes synchronized burst activity in networks of more realistic conductance-based model neurons.     

Burst synchrony patterns in hippocampal pyramidal cell model networks

Types of. mechanisms for and stability of synchrony are discussed in the context of two-compartment CA3 pyramidal cell and interneuron model networks. We show how the strength and timing of inhibitory and excitatory synaptic inputs work together to produce either perfectly synchronized or nearly synchronized oscillations, across different burst or spiking modes of firing. The analysis shows how excitatory inputs tend to desynchronize cells, and how common, slowly decaying inhibition can be used to synchronize them. We also introduce the concept of 'equivalent networks' in which networks with different architectures and synaptic connections display identical firing patterns.     

The firing of an excitable neuron in the presence of stochastic trains of strong synaptic inputs

We consider a fast-slow excitable system subject to a stochastic excitatory input train and show that under general conditions, its long-term behavior is captured by an irreducible Markov chain with a limiting distribution. This limiting distribution allows for the analytical calculation of the system's probability of firing in response to each input, the expected number of response failures between firings, and the distribution of slow variable values between firings. Moreover, using this approach, it is possible to understand why the system will not have a stationary distribution and why Monte Carlo simulations do not converge under certain conditions. The analytical calculations involved can be performed whenever the distribution of interexcitation intervals and the recovery dynamics of the slow variable are known. The method can be extended to other models that feature a single variable that builds up to a threshold where an instantaneous spike and reset occur. We also discuss how the Markov chain analysis generalizes to any pair of input trains, excitatory or inhibitory and synaptic or not, such that the frequencies of the two trains are sufficiently different from each other. We illustrate this analysis on a model thalamocortical (TC) cell subject to two example distributions of excitatory synaptic inputs in the cases of constant and rhythmic inhibition. The analysis shows a drastic drop in the likelihood of firing just after inhibitory onset in the case of rhythmic inhibition, relative even to the case of elevated but constant inhibition. This observation provides support for a possible mechanism for the induction of motor symptoms in Parkinson's disease and for their relief by deep brain stimulation, analyzed in Rubin and Terman (2004).     

Correlated inhibitory and excitatory inputs to the coincidence detector: analytical solution

We present a solution for the steady-state output rate of an ideal coincidence detector receiving an arbitrary number of excitatory and inhibitory input spike trains. All excitatory spike trains have identical binomial count distributions (which includes Poisson statistics as a special case) and arbitrary pairwise cross correlations between them. The same applies to the inhibitory inputs, and the rates and correlation functions of excitatory and inhibitory populations may be the same or different from each other. Thus, for each population independently, the correlation may range from complete independence to perfect correlation (identical processes). We find that inhibition, if made sufficiently strong, will result in an inverted U-shaped curve for the output rate of a coincidence detector as a function of input rates for the case of identical inhibitory and excitory input rates. This leads to the prediction that higher presynaptic (input) rates may lead to lower postsynaptic (output) rates where the output rate may fall faster than the inverse of the input rate, and shows some qualitative similarities to the case of purely excitatory inputs with synaptic depression. In general, we find that including inhibition invariably and significantly increases the behavioral repertoire of the coincidence detector over the case of pure excitatory input.     

Input-driven oscillations in networks with excitatory and inhibitory neurons with dynamic synapses

Previous work has shown that networks of neurons with two coupled layers of excitatory and inhibitory neurons can reveal oscillatory activity. For example, B?rgers and Kopell (2003) have shown that oscillations occur when the excitatory neurons receive a sufficiently large input. A constant drive to the excitatory neurons is sufficient for oscillatory activity. Other studies (Doiron, Chacron, Maler, Longtin, & Bastian, 2003; Doiron, Lindner, Longtin, Maler, & Bastian, 2004) have shown that networks of neurons with two coupled layers of excitatory and inhibitory neurons reveal oscillatory activity only if the excitatory neurons receive correlated input, regardless of the amount of excitatory input. In this study, we show that these apparently contradictory results can be explained by the behavior of a single model operating in different regimes of parameter space. Moreover, we show that adding dynamic synapses in the inhibitory feedback loop provides a robust network behavior over a broad range of stimulus intensities, contrary to that of previous models. A remarkable property of the introduction of dynamic synapses is that the activity of the network reveals synchronized oscillatory components in the case of correlated input, but also reflects the temporal behavior of the input signal to the excitatory neurons. This allows the network to encode both the temporal characteristics of the input and the presence of spatial correlations in the input simultaneously.     

Competition through selective inhibitory synchrony

Models of cortical neuronal circuits commonly depend on inhibitory feedback to control gain, provide signal normalization, and selectively amplify signals using winner-take-all (WTA) dynamics. Such models generally assume that excitatory and inhibitory neurons are able to interact easily because their axons and dendrites are colocalized in the same small volume. However, quantitative neuroanatomical studies of the dimensions of axonal and dendritic trees of neurons in the neocortex show that this colocalization assumption is not valid. In this letter, we describe a simple modification to the WTA circuit design that permits the effects of distributed inhibitory neurons to be coupled through synchronization, and so allows a single WTA to be distributed widely in cortical space, well beyond the arborization of any single inhibitory neuron and even across different cortical areas. We prove by nonlinear contraction analysis and demonstrate by simulation that distributed WTA subsystems combined by such inhibitory synchrony are inherently stable. We show analytically that synchronization is substantially faster than winner selection. This circuit mechanism allows networks of independent WTAs to fully or partially compete with other.     

Asynchronous inputs and NMDA conductances predict excitatory responses in the cortical-cA1 pathway of the hippocampus

In the hippocampus, CA1 place cells are driven by a substantial input from CA3. There is a second pathway to CA1 from the entorhinal cortex. The mode of action of cortex on CA1 through this pathway is not known. The pathway supports CA1 place field activity after CA3 has been lesioned, yet stimulation of the pathway in rat slices results in strong feedforward inhibition that prevents pyramidal cell action potentials. We use a detailed conductance-based model of this pathway to simulate the response to cortical stimulation in slice experiments and in vivo spatial exploration. We find that the presence of NMDA conductances enable CA1 pyramidal cells to integrate cortical inputs over a time scale longer than that which is effective in recruiting the inhibitory response that can suppress action potentials. We then show that this asynchronous response mode supports place field formation in response to experimentally constrained spatially modulated cortical activity. Within this model, the inclusion of GABAB conductances and the hyperpolarisation activated current I(h) reduces the strength of the GABAA inputs required to balance the excitatory inputs, and this facilitates place field formation by reducing variability in the inhibitory inputs.     

Dynamics of deterministic and stochastic paired excitatory-inhibitory delayed feedback

We examine the effects of paired delayed excitatory and inhibitory feedback on a single integrate-and-fire neuron with reversal potentials embedded within a feedback network. These effects are studied using bifurcation theory and numerical analysis. The feedback occurs through modulation of the excitatory and inhibitory conductances by the previous firing history of the neuron; as a consequence, the feedback also modifies the membrane time constant. Such paired feedback is ubiquitous in the nervous system. We assume that the feedback dynamics are slower than the membrane time constant, which leads to a rate model formulation. Our article provides an extensive analysis of the possible dynamical behaviors of such simple yet realistic neural loops as a function of the balance between positive and negative feedback, with and without noise, and offers insight into the potential behaviors such loops can exhibit in response to time-varying external inputs. With excitatory feedback, the system can be quiescent, can be periodically firing, or can exhibit bistability between these two states. With inhibitory feedback, quiescence, oscillatory firing rates, and bistability between constant and oscillatory firing-rate solutions are possible. The general case of paired feedback exhibits a blend of the behaviors seen in the extreme cases and can produce chaotic firing. We further derive a condition for a dynamically balanced paired feedback in which there is neither bistability nor oscillations. We also show how a biophysically plausible smoothing of the firing function by noise can modify the existence and stability of fixed points and oscillations of the system. We take advantage in our mathematical analysis of the existence of an invariant manifold, which reduces the dimensionality of the dynamics, and prove the stability of this manifold. The novel computational challenges involved in analyzing such dynamics with and without noise are also described. Our results demonstrate that a paired delayed feedback loop can act as a sophisticated computational unit, capable of switching between a variety of behaviors depending on the input current, the relative strengths and asymmetry of the two parallel feedback pathways, and the delay distributions and noise level.     

Modeling reverse-phi motion-selective neurons in cortex: double synaptic-veto mechanism

Reverse-phi motion is the illusory reversal of perceived direction of movement when the stimulus contrast is reversed in successive frames. Livingstone, Tsao, and Conway (2000) showed that direction-selective cells in striate cortex of the alert macaque monkey showed reversed excitatory and inhibitory regions when two different contrast bars were flashed sequentially during a two-bar interaction analysis. While correlation or motion energy models predict the reverse-phi response, it is unclear how neurons can accomplish this. We carried out detailed biophysical simulations of a direction-selective cell model implementing a synaptic shunting scheme. Our results suggest that a simple synaptic-veto mechanism with strong direction selectivity for normal motion cannot account for the observed reverse-phi motion effect. Given the nature of reverse-phi motion, a direct interaction between the ON and OFF pathway, missing in the original shunting-inhibition model, it is essential to account for the reversal of response. We here propose a double synaptic-veto mechanism in which ON excitatory synapses are gated by both delayed ON inhibition at their null side and delayed OFF inhibition at their preferred side. The converse applies to OFF excitatory synapses. Mapping this scheme onto the dendrites of a direction-selective neuron permits the model to respond best to normal motion in its preferred direction and to reverse-phi motion in its null direction. Two-bar interaction maps showed reversed excitation and inhibition regions when two different contrast bars are presented.     

Computational differences between asymmetrical and symmetrical networks.

Symmetrically connected recurrent networks have recently been used as models of a host of neural computations. However, biological neural networks have asymmetrical connections, at the very least because of the separation between excitatory and inhibitory neurons in the brain. We study characteristic differences between asymmetrical networks and their symmetrical counterparts in cases for which they act as selective amplifiers for particular classes of input patterns. We show that the dramatically different dynamical behaviours to which they have access, often make the asymmetrical networks computationally superior. We illustrate our results in networks that selectively amplify oriented bars and smooth contours in visual inputs.     

Interactions of excitatory and inhibitory feedback topologies in facilitating pattern separation and retrieval

Within the brain, the interplay between connectivity patterns of neurons and their spatiotemporal dynamics is believed to be intricately linked to the bases of behavior, such as the process of storing, consolidating, and retrieving memory traces. Memory is believed to be stored in the synaptic patterns of anatomical circuitry in the form of increased connectivity densities within subpopulations of neurons. At the same time, memory recall is thought to correspond to activation of discrete areas of the brain corresponding to those memories. Such regional subpopulations can selectively activate during memory recall or retrieval, signifying the process of accessing a single memory or concept. It has been shown previously that recovery of single memory activity patterns is mediated by global neuromodulation signifying transition into different cognitive states such as sleep or awake exploration. We examine how underlying topology can affect memory awake activation and sleep reactivation when such memories share increasing proportions of neurons. The results show that while single memory activation is diminished with increased overlap, pattern separation can be recovered by offsetting excitatory associations between two memories with targeted and heterogeneous inhibitory feedback. Such findings point to the importance of excitatory-to-inhibitory current balance at both the global and local levels in the context of memory retrieval and replay, and highlight the role of network topology in memory management processes.     

Frequency selectivity emerging from spike-timing-dependent plasticity

Periodic neuronal activity has been observed in various areas of the brain, from lower sensory to higher cortical levels. Specific frequency components contained in this periodic activity can be identified by a neuronal circuit that behaves as a bandpass filter with given preferred frequency, or best modulation frequency (BMF). For BMFs typically ranging from 10 to 200?Hz, a plausible and minimal configuration consists of a single neuron with adjusted excitatory and inhibitory synaptic connections. The emergence, however, of such a neuronal circuitry is still unclear. In this letter, we demonstrate how spike-timing-dependent plasticity (STDP) can give rise to frequency-dependent learning, thus leading to an input selectivity that enables frequency identification. We use an in-depth mathematical analysis of the learning dynamics in a population of plastic inhibitory connections. These provide inhomogeneous postsynaptic responses that depend on their dendritic location. We find that synaptic delays play a crucial role in organizing the weight specialization induced by STDP. Under suitable conditions on the synaptic delays and postsynaptic potentials (PSPs), the BMF of a neuron after learning can match the training frequency. In particular, proximal (distal) synapses with shorter (longer) dendritic delay and somatically measured PSP time constants respond better to higher (lower) frequencies. As a result, the neuron will respond maximally to any stimulating frequency (in a given range) with which it has been trained in an unsupervised manner. The model predicts that synapses responding to a given BMF form clusters on dendritic branches.     

Localized activity patterns in excitatory neuronal networks

The existence of localized activity patterns, or bumps, has been investigated in a variety of spatially distributed neuronal network models that contain both excitatory and inhibitory coupling between cells. Here we show that a neuronal network with purely excitatory synaptic coupling can exhibit localized activity. Bump formation ensues from an initial transient synchrony of a localized group of cells, followed by the emergence of desynchronized activity within the group. Transient synchrony is shown to promote recruitment of cells into the bump, while desynchrony is shown to be good for curtailing recruitment and sustaining oscillations of those cells already within the bump. These arguments are based on the geometric structure of the phase space in which solutions of the model equations evolve. We explain why bump formation and bump size are very sensitive to initial conditions and changes in parameters in this type of purely excitatory network, and we examine how short-term synaptic depression influences the characteristics of bump formation.     

Rewiring-induced chaos in pulse-coupled neural networks

The dependence of the dynamics of pulse-coupled neural networks on random rewiring of excitatory and inhibitory connections is examined. When both excitatory and inhibitory connections are rewired, periodic synchronization emerges with a Hopf-like bifurcation and a subsequent period-doubling bifurcation; chaotic synchronization is also observed. When only excitatory connections are rewired, periodic synchronization emerges with a saddle node-like bifurcation, and chaotic synchronization is also observed. This result suggests that randomness in the system does not necessarily contaminate the system, and sometimes it even introduces rich dynamics to the system such as chaos.