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     

Pattern recall in networks of chaotic neurons

This research investigates the potential utility of chaotic dynamics in neural information processing. A novel chaotic spiking neural network model is presented which is composed of non-linear dynamic state (NDS) neurons. The activity of each NDS neuron is driven by a set of non-linear equations coupled with a threshold based spike output mechanism. If time-delayed self-connections are enabled then the network stabilises to a periodic pattern of activation. Previous publications of this work have demonstrated that the chaotic dynamics which drive the network activity ensure that an extremely large number of such periodic patterns can be generated by this network. This paper presents a major extension to this model which enables the network to recall a pattern of activity from a selection of previously stabilised patterns.     

On a phase diagram for random neural networks with embedded spike timing dependent plasticity

This paper presents an original mathematical framework based on graph theory which is a first attempt to investigate the dynamics of a model of neural networks with embedded spike timing dependent plasticity. The neurons correspond to integrate-and-fire units located at the vertices of a finite subset of 2D lattice. There are two types of vertices, corresponding to the inhibitory and the excitatory neurons. The edges are directed and labelled by the discrete values of the synaptic strength. We assume that there is an initial firing pattern corresponding to a subset of units that generate a spike. The number of activated externally vertices is a small fraction of the entire network. The model presented here describes how such pattern propagates throughout the network as a random walk on graph. Several results are compared with computational simulations and new data are presented for identifying critical parameters of the model.     

To spike,or when to spike?

Recent experimental reports have suggested that cortical networks can operate in regimes were sensory information is encoded by relatively small populations of spikes and their precise relative timing. Combined with the discovery of spike timing dependent plasticity, these findings have sparked growing interest in the capabilities of neurons to encode and decode spike timing based neural representations. To address these questions, a novel family of methodologically diverse supervised learning algorithms for spiking neuron models has been developed. These models have demonstrated the high capacity of simple neural architectures to operate also beyond the regime of the well established independent rate codes and to utilize theoretical advantages of spike timing as an additional coding dimension.     

A new regime for highly robust gamma oscillation with co-exist of accurate and weak synchronization in excitatory–inhibitory networks

A great number of biological experiments show that gamma oscillation occurs in many brain areas after the presentation of stimulus. The neural systems in these brain areas are highly heterogeneous. Specifically, the neurons and synapses in these neural systems are diversified; the external inputs and parameters of these neurons and synapses are heterogeneous. How the gamma oscillation generated in such highly heterogeneous networks remains a challenging problem. Aiming at this problem, a highly heterogeneous complex network model that takes account of many aspects of real neural circuits was constructed. The network model consists of excitatory neurons and fast spiking interneurons, has three types of synapses (GABA_A, AMPA, and NMDA), and has highly heterogeneous external drive currents. We found a new regime for robust gamma oscillation, i.e. the oscillation in inhibitory neurons is rather accurate but the oscillation in excitatory neurons is weak, in such highly heterogeneous neural networks. We also found that the mechanism of the oscillation is a mixture of interneuron gamma (ING) and pyramidal-interneuron gamma (PING). We explained the mixture ING and PING mechanism in a consistent-way by a compound post-synaptic current, which has a slowly rising-excitatory stage and a sharp decreasing-inhibitory stage.     

Activity-dependent enhancement in the reliability of correlated spike timings in cultured cortical neurons

To study the use-dependent modification of activity in neural networks, we investigated the spike timing by simultaneously recording activity at multiple sites in a network of cultured cortical neurons. We used dynamical analysis to study the temporal structure of spike trains and the activity-dependent changes in the reliability and reproducibility of spike patterns evoked by a stimulus. We also used cross-correlation analysis to evaluate the interactions of neuron pairs. Our main conclusions are that even when no obvious change in spike numbers can be seen, use-dependent modification occurs, either enhancing or reducing in the reliability and reproducibility of spike trains evoked by a stimulus, and the fine temporal structure of stimulus-evoked spike trains and interactions between neurons are also modified by tetanic stimulation. Received: 25 February 1998 / Accepted in revised form: 24 August 1998     

Partial correlation analysis for the identification of synaptic connections

In this paper, we investigate the use of partial correlation analysis for the identification of functional neural connectivity from simultaneously recorded neural spike trains. Partial correlation analysis allows one to distinguish between direct and indirect connectivities by removing the portion of the relationship between two neural spike trains that can be attributed to linear relationships with recorded spike trains from other neurons. As an alternative to the common frequency domain approach based on the partial spectral coherence we propose a new statistic in the time domain. The new scaled partial covariance density provides additional information on the direction and the type, excitatory or inhibitory, of the connectivities. In simulation studies, we investigated the power and limitations of the new statistic. The simulations show that the detectability of various connectivity patterns depends on various parameters such as connectivity strength and background activity. In particular, the detectability decreases with the number of neurons included in the analysis and increases with the recording time. Further, we show that the method can also be used to detect multiple direct connectivities between two neurons. Finally, the methods of this paper are illustrated by an application to neurophysiological data from spinal dorsal horn neurons.     

Afterhyperpolarization improves spike programming through lowering threshold potentials and refractory periods mediated by voltage-gated sodium channels

Neurons program various patterns of sequential spikes as neural codes to guide animal behavior. Studies show that spike programming (capacity and timing precision) is influenced by inhibitory synaptic inputs and membrane afterhyperpolarization (AHP). Less is clear about how these inhibitory components regulate spike programming, which we investigated at the cortical neurons. Whole-cell current-clamp recording for action potentials and single channel recording for voltage-gated sodium channels (VGSC) were conducted at regular-spiking and fast-spiking neurons in the cortical slices. With quantifying the threshold potentials and refractory periods of sequential spikes, we found that fast-spiking neurons expressing AHP possess lower threshold potentials and shorter refractory periods, and the hyperpolarization pulse immediately after each of spikes lowers threshold potentials and shortens refractory periods at regular-spiking neurons. Moreover, the hyperpolarization pulses shorten the refractory periods for VGSC reactivation and threshold potentials for its sequential activation. Our data indicate that inhibitory components immediately after spikes, such as AHP and recurrent inhibition, improve spike capacity and timing precision via lowering the refractory periods and threshold potentials mediated by voltage-gated sodium channels.     

Timing Precision in Population Coding of Natural Scenes in the Early Visual System

The timing of spiking activity across neurons is a fundamental aspect of the neural population code. Individual neurons in the retina, thalamus, and cortex can have very precise and repeatable responses but exhibit degraded temporal precision in response to suboptimal stimuli. To investigate the functional implications for neural populations in natural conditions, we recorded in vivo the simultaneous responses, to movies of natural scenes, of multiple thalamic neurons likely converging to a common neuronal target in primary visual cortex. We show that the response of individual neurons is less precise at lower contrast, but that spike timing precision across neurons is relatively insensitive to global changes in visual contrast. Overall, spike timing precision within and across cells is on the order of 10 ms. Since closely timed spikes are more efficient in inducing a spike in downstream cortical neurons, and since fine temporal precision is necessary to represent the more slowly varying natural environment, we argue that preserving relative spike timing at a ~10-ms resolution is a crucial property of the neural code entering cortex.     

Neural coding and contextual influences in the whisker system

A fundamental problem in neuroscience, to which Prof. Segundo has made seminal contributions, is to understand how action potentials represent events in the external world. The aim of this paper is to review the issue of neural coding in the context of the rodent whiskers, an increasingly popular model system. Key issues we consider are: the role of spike timing; mechanisms of spike timing; decoding and context-dependence. Significant insight has come from the development of rigorous, information theoretic frameworks for tackling these questions, in conjunction with suitably designed experiments. We review both the theory and experimental studies. In contrast to the classical view that neurons are noisy and unreliable, it is becoming clear that many neurons in the subcortical whisker pathway are remarkably reliable and, by virtue of spike timing with millisecond-precision, have high bandwidth for conveying sensory information. In this way, even small (~200 neuron) subcortical modules are able to support the sensory processing underlying sophisticated whisker-dependent behaviours. Future work on neural coding in cortex will need to consider new findings that responses are highly dependent on context, including behavioural and internal states. This article is part of a special issue on Neuronal Dynamics of Sensory Coding.     

Nonlinear principal components analysis of neuronal spike train data

Many recent approaches to decoding neural spike trains depend critically on the assumption that for low-pass filtered spike trains, the temporal structure is optimally represented by a small number of linear projections onto the data. We therefore tested this assumption of linearity by comparing a linear factor analysis technique (principal components analysis) with a nonlinear neural network based method. It is first shown that the nonlinear technique can reliably identify a neuronally plausible nonlinearity in synthetic spike trains. However, when applied to the outputs from primary visual cortical neurons, this method shows no evidence for significant temporal nonlinearities. The implications of this are discussed. Received: 29 November 1996 / Accepted in revised form: 1 July 1997     

Oscillation,Conduction Delays,and Learning Cooperate to Establish Neural Competition in Recurrent Networks

Specific memory might be stored in a subnetwork consisting of a small population of neurons. To select neurons involved in memory formation, neural competition might be essential. In this paper, we show that excitable neurons are competitive and organize into two assemblies in a recurrent network with spike timing-dependent synaptic plasticity (STDP) and axonal conduction delays. Neural competition is established by the cooperation of spontaneously induced neural oscillation, axonal conduction delays, and STDP. We also suggest that the competition mechanism in this paper is one of the basic functions required to organize memory-storing subnetworks into fine-scale cortical networks.     

Variability and coding efficiency of noisy neural spike encoders

Encoding synaptic inputs as a train of action potentials is a fundamental function of nerve cells. Although spike trains recorded in vivo have been shown to be highly variable, it is unclear whether variability in spike timing represents faithful encoding of temporally varying synaptic inputs or noise inherent in the spike encoding mechanism. It has been reported that spike timing variability is more pronounced for constant, unvarying inputs than for inputs with rich temporal structure. This could have significant implications for the nature of neural coding, particularly if precise timing of spikes and temporal synchrony between neurons is used to represent information in the nervous system. To study the potential functional role of spike timing variability, we estimate the fraction of spike timing variability which conveys information about the input for two types of noisy spike encoders--an integrate and fire model with randomly chosen thresholds and a model of a patch of neuronal membrane containing stochastic Na(+) and K(+) channels obeying Hodgkin-Huxley kinetics. The quality of signal encoding is assessed by reconstructing the input stimuli from the output spike trains using optimal linear mean square estimation. A comparison of the estimation performance of noisy neuronal models of spike generation enables us to assess the impact of neuronal noise on the efficacy of neural coding. The results for both models suggest that spike timing variability reduces the ability of spike trains to encode rapid time-varying stimuli. Moreover, contrary to expectations based on earlier studies, we find that the noisy spike encoding models encode slowly varying stimuli more effectively than rapidly varying ones.     

Timing and prediction the code from basal ganglia to thalamus

When is an inhibitory synapse not inhibitory? In this issue of Neuron, Person and Perkel demonstrate that thalamic neurons can translate extrinsic GABAergic input from the basal ganglia into highly precise patterns of sustained spiking in a circuit that is essential for vocal learning in songbirds. Postinhibitory rebound serves as a mechanism that preserves precise spike timing information, enabling reliable propagation of activity throughout this pathway. The results have broad implications for basic mechanisms of functional processing in both thalamus and basal ganglia and serve to increase our understanding of how acoustic units of vocal sounds are transformed into motor gestures during the sensitive period for song learning.     

Theoretical analysis on relationship between the neural activity and the EEG

Firstly, a collective oscillation mode of the neural activity is derived from the neural network system by using the multicompartment equation and the projection operator technique. This technique takes into account higher order interactions among neurons. The solution of the equation gives a chain structure with an infinite number of circuit loops in which each of them is only composed of four neurons. The obtained eigenvalues are quite similar to the spectrum of frequencies of the EEG. Secondly, the time-dependent behavior of the observed EEG is simulated by starting from the elementary process of action potential trains of neurons, which includes the effect of the collective oscillation mode mentioned above. This gives a comprehensive derivation of the EEG from the neural activity of action potentials. The simulation assumes that information of the action potential trains can be transmitted to the EEG through the intermediate states of the postsynaptic potential trains and the slow waves. The paper reports that a slightly modulated activity of a relatively small amount of neurons can cause a strong influence on the shape of the global EEG and that the calculated results reproduce the characteristic features of the EEG in a rat such as the theta rhythm, the spindle wave and the arousal wave.     

Reading spike timing without a clock: intrinsic decoding of spike trains

The precise timing of action potentials of sensory neurons relative to the time of stimulus presentation carries substantial sensory information that is lost or degraded when these responses are summed over longer time windows. However, it is unclear whether and how downstream networks can access information in precise time-varying neural responses. Here, we review approaches to test the hypothesis that the activity of neural populations provides the temporal reference frames needed to decode temporal spike patterns. These approaches are based on comparing the single-trial stimulus discriminability obtained from neural codes defined with respect to network-intrinsic reference frames to the discriminability obtained from codes defined relative to the experimenter''s computer clock. Application of this formalism to auditory, visual and somatosensory data shows that information carried by millisecond-scale spike times can be decoded robustly even with little or no independent external knowledge of stimulus time. In cortex, key components of such intrinsic temporal reference frames include dedicated neural populations that signal stimulus onset with reliable and precise latencies, and low-frequency oscillations that can serve as reference for partitioning extended neuronal responses into informative spike patterns.     

Neural coding of natural stimuli: information at sub-millisecond resolution

Sensory information about the outside world is encoded by neurons in sequences of discrete, identical pulses termed action potentials or spikes. There is persistent controversy about the extent to which the precise timing of these spikes is relevant to the function of the brain. We revisit this issue, using the motion-sensitive neurons of the fly visual system as a test case. Our experimental methods allow us to deliver more nearly natural visual stimuli, comparable to those which flies encounter in free, acrobatic flight. New mathematical methods allow us to draw more reliable conclusions about the information content of neural responses even when the set of possible responses is very large. We find that significant amounts of visual information are represented by details of the spike train at millisecond and sub-millisecond precision, even though the sensory input has a correlation time of ~55 ms; different patterns of spike timing represent distinct motion trajectories, and the absolute timing of spikes points to particular features of these trajectories with high precision. Finally, the efficiency of our entropy estimator makes it possible to uncover features of neural coding relevant for natural visual stimuli: first, the system's information transmission rate varies with natural fluctuations in light intensity, resulting from varying cloud cover, such that marginal increases in information rate thus occur even when the individual photoreceptors are counting on the order of one million photons per second. Secondly, we see that the system exploits the relatively slow dynamics of the stimulus to remove coding redundancy and so generate a more efficient neural code.     

Spike independency in feed-forward networks

A cortical neuron puts thousands of synaptic contacts on other neurons. The effect of the spike event spreads over a large number of neurons. So it is possible for spike timings to be correlated to each other. But there have not been so many reports of spike timing correlations, while there have been many reports of somewhat longer time range correlations through mean spike rates. Can independent firings be preserved in spite of a number of connections? The present study attempts to determine whether independent firings can be propagated through a simple feed-forward neural network. It is assumed that each unit obeys a threshold mechanism at each discrete time and that connections are statistically uniform with the excitation balanced to the inhibition and delay distributed. It is found that the independent firings can be stably propagated through the feed-forward network at a network parameter region, which contains the physiologically reasonable range. Another interesting result is that the independency-stable spike probability has a lower limit 0.0323.     

Spatiotemporal pattern formation in two-dimensional neural circuits: roles of refractoriness and noise

Refractoriness is one of the most fundamental states of neural firing activity, in which neurons that have just fired are unable to produce another spike, regardless of the strength of afferent stimuli. Another essential and unavoidable feature of neural systems is the existence of noise. To study the role of these essential factors in spatiotemporal pattern formation in neural systems, a spatially expended neural network model is constructed, with the dynamics of its individual neurons capturing the three most essential states of the neural firing behavior: firing, refractory and resting, and the network topology consistent with the widely observed center-surround coupling manner in the real brain. By changing the refractory period with and without noise in a systematic way in the network, it is shown numerically and analytically that without refractoriness, or when the refractory period is smaller than a certain value, the collective activity pattern of the system consists of localized, oscillating patterns. However, when the refractory period is greater than a certain value, crescent-shaped, localized propagating patterns emerge in the presence of noise. It is further illustrated that the formation of the dynamical spiking patterns is due to a symmetry breaking mechanism, refractoriness-induced symmetry breaking; that is generated by the interplay of noise and refractoriness in the network model. This refractoriness-induced symmetry breaking provides a novel perspective on the emergence of localized, spiking wave patterns or spike timing sequences as ubiquitously observed in real neural systems; it therefore suggests that refractoriness may benefit neural systems in their temporal information processing, rather than limiting the performance of neurons, as has been conventionally thought. Our results also highlight the importance of considering noise in studying spatially extended neural systems, where it may facilitate the formation of spatiotemporal order.