LTD windows of the STDP learning rule and synaptic connections having a large transmission delay enable robust sequence learning amid background noise

Spike-timing-dependent synaptic plasticity (STDP) is a simple and effective learning rule for sequence learning. However, synapses being subject to STDP rules are readily influenced in noisy circumstances because synaptic conductances are modified by pre- and postsynaptic spikes elicited within a few tens of milliseconds, regardless of whether those spikes convey information or not. Noisy firing existing everywhere in the brain may induce irrelevant enhancement of synaptic connections through STDP rules and would result in uncertain memory encoding and obscure memory patterns. We will here show that the LTD windows of the STDP rules enable robust sequence learning amid background noise in cooperation with a large signal transmission delay between neurons and a theta rhythm, using a network model of the entorhinal cortex layer II with entorhinal-hippocampal loop connections. The important element of the present model for robust sequence learning amid background noise is the symmetric STDP rule having LTD windows on both sides of the LTP window, in addition to the loop connections having a large signal transmission delay and the theta rhythm pacing activities of stellate cells. Above all, the LTD window in the range of positive spike-timing is important to prevent influences of noise with the progress of sequence learning.     

Theta Coordinated Error-Driven Learning in the Hippocampus

The learning mechanism in the hippocampus has almost universally been assumed to be Hebbian in nature, where individual neurons in an engram join together with synaptic weight increases to support facilitated recall of memories later. However, it is also widely known that Hebbian learning mechanisms impose significant capacity constraints, and are generally less computationally powerful than learning mechanisms that take advantage of error signals. We show that the differential phase relationships of hippocampal subfields within the overall theta rhythm enable a powerful form of error-driven learning, which results in significantly greater capacity, as shown in computer simulations. In one phase of the theta cycle, the bidirectional connectivity between CA1 and entorhinal cortex can be trained in an error-driven fashion to learn to effectively encode the cortical inputs in a compact and sparse form over CA1. In a subsequent portion of the theta cycle, the system attempts to recall an existing memory, via the pathway from entorhinal cortex to CA3 and CA1. Finally the full theta cycle completes when a strong target encoding representation of the current input is imposed onto the CA1 via direct projections from entorhinal cortex. The difference between this target encoding and the attempted recall of the same representation on CA1 constitutes an error signal that can drive the learning of CA3 to CA1 synapses. This CA3 to CA1 pathway is critical for enabling full reinstatement of recalled hippocampal memories out in cortex. Taken together, these new learning dynamics enable a much more robust, high-capacity model of hippocampal learning than was available previously under the classical Hebbian model.     

Generation of theta oscillations by weakly coupled neural oscillators in the presence of noise

Neuronal oscillations are a robust phenomenon occurring in a variety of brain regions despite considerable amounts of noise. In this article classical phase-response theory is generalized to the case of noisy weak-coupling regimes by deriving an iterated map for the asynchrony of spikes in an oscillation cycle. Two criteria are introduced to check the validity of our approximations: One criterion tests the assumption that all neurons fire exactly once per cycle, the other criterion tests for linearity. The framework is applied to stellate cells of the medial entorhinal cortex layer II. We find that rhythmogenesis is more robust in the case of excitatory noise as compared to inhibitory noise. It is shown that a network of stellate cells can also act as a generator of theta if the neurons are connected via a fast-oscillating network of inhibitory interneurons.     

A theory of hippocampal memory based on theta phase precession

 The neural dynamics of the hippocampal network for memory encoding of novel temporal sequences is proposed based on the theta rhythm modulated firing of place cells called theta phase precession. It is hypothesized that theta phase precession is generated at the entorhinal cortex by phase locking between local field theta oscillation and neural oscillators and that the hippocampal closed network with feedforward and backward projections employ theta phase precession to create selectivity in the associative connections needed for temporal sequence storage. Our analyses and computer experiments reveal that the phase precession generated by phase locking instantaneously endows stable phase relations among neural activities in the successively changing neural population. It is concluded that theta phase precession provides biologically plausible dynamics for the memory encoding of novel temporal sequences as episodic events. Received: 18 December 2002 / Accepted: 18 March 2003 / Published online: 20 May 2003 Correspondence to: Y. Yamaguchi (e-mail: yokoy@brain.riken.go.jp, Fax: +81-48-4676938) Acknowledgements. The author would like to express acknowledgement to Drs. McNaughton and Skaggs for their discussion and comment and to Dr. Amari for his continuous encouragement. Further thanks are given to Mr. Haga and Dr. Wu for their discussion and cooperation.     

Neuronal rebound spiking,resonance frequency and theta cycle skipping may contribute to grid cell firing in medial entorhinal cortex

Data show a relationship of cellular resonance and network oscillations in the entorhinal cortex to the spatial periodicity of grid cells. This paper presents a model that simulates the resonance and rebound spiking properties of entorhinal neurons to generate spatial periodicity dependent upon phasic input from medial septum. The model shows that a difference in spatial periodicity can result from a difference in neuronal resonance frequency that replicates data from several experiments. The model also demonstrates a functional role for the phenomenon of theta cycle skipping in the medial entorhinal cortex.     

Microcircuits of functionally identified neurons in the rat medial entorhinal cortex

Extracellular recordings have elucidated spatial neural representations without identifying underlying microcircuits. We labeled neurons juxtacellularly in medial entorhinal cortex of freely moving rats with?a friction-based, pipette-stabilization system. In a linear maze novel to the animals, spatial firing of superficial layer neurons was reminiscent of grid cell activity. Layer 2 stellate cells showed stronger theta modulation than layer 3 neurons, and both fired during the ascending phase of field potential theta. Deep-layer neurons showed little or no activity. Layer 2 stellate cells resided in hundreds of small patches. At the dorsomedial entorhinal border, we identified larger (putative parasubicular) patches, which contained polarized head-direction selective neurons firing during the descending theta phase. Three axon systems interconnected patches: centrifugal axons from superficial cells to single large patches, centripetal axons from large-patch cells to single small patches, and circumcurrent axons interconnecting large patches. Our microcircuit analysis during behavior reveals modularity of entorhinal processing. VIDEO ABSTRACT:     

Role of septal and entorhinal inputs in the generation of hippocampal electrical activity in the cat sleep-wake cycle

The effects of septal lesion and entorhinal cortex section on hippocampal electrical activity during the cat sleep-wake cycle were investigated in chronic experiments. The medial portion of the septum only was found to participate in generation of this activity. Complete suppression of hippocampal theta rhythm during active wakefulness and paradoxical sleep were the main effects of septal lesion. In slow-wave sleep, the effects of septal lesion manifested in a slight attenuation of the intensity of the dominant frequency (of 1 Hz). Widespread septal lesion does not add to the changes occurring when the medial portion of the septum is so isolated. Section of the entorhinal cortex produces a sharp increase in hippocampal theta rhythm during waking and paradoxical sleep. Clearcut attenuation of delta and subdelta rhythm intensities were observed in slowwave sleep. It is postulated that under normal conditions hippocampal entorhinal input exerts a modulating effect on the genesis of hippocampal theta rhythm.I. S. Beritashvili Institute of Physiology, Academy of Sciences of the Georgian SSR, Tbilisi. Translated from Neirofiziologiya, Vol. 19, No. 5, pp. 622–630, September–October, 1987.     

Phase precession through acceleration of local theta rhythm: a biophysical model for the interaction between place cells and local inhibitory neurons

Phase precession is one of the most well known examples within the temporal coding hypothesis. Here we present a biophysical spiking model for phase precession in hippocampal CA1 which focuses on the interaction between place cells and local inhibitory interneurons. The model's functional block is composed of a place cell (PC) connected with a local inhibitory cell (IC) which is modulated by the population theta rhythm. Both cells receive excitatory inputs from the entorhinal cortex (EC). These inputs are both theta modulated and space modulated. The dynamics of the two neuron types are described by integrate-and-fire models with conductance synapses, and the EC inputs are described using non-homogeneous Poisson processes. Phase precession in our model is caused by increased drive to specific PC/IC pairs when the animal is in their place field. The excitation increases the IC's firing rate, and this modulates the PC's firing rate such that both cells precess relative to theta. Our model implies that phase coding in place cells may not be independent from rate coding. The absence of restrictive connectivity constraints in this model predicts the generation of phase precession in any network with similar architecture and subject to a clocking rhythm, independently of the involvement in spatial tasks.     

Theta phase precession of grid and place cell firing in open environments

Place and grid cells in the rodent hippocampal formation tend to fire spikes at successively earlier phases relative to the local field potential theta rhythm as the animal runs through the cell''s firing field on a linear track. However, this ‘phase precession’ effect is less well characterized during foraging in two-dimensional open field environments. Here, we mapped runs through the firing fields onto a unit circle to pool data from multiple runs. We asked which of seven behavioural and physiological variables show the best circular–linear correlation with the theta phase of spikes from place cells in hippocampal area CA1 and from grid cells from superficial layers of medial entorhinal cortex. The best correlate was the distance to the firing field peak projected onto the animal''s current running direction. This was significantly stronger than other correlates, such as instantaneous firing rate and time-in-field, but similar in strength to correlates with other measures of distance travelled through the firing field. Phase precession was stronger in place cells than grid cells overall, and robust phase precession was seen in traversals through firing field peripheries (although somewhat less than in traversals through the centre), consistent with phase coding of displacement along the current direction. This type of phase coding, of place field distance ahead of or behind the animal, may be useful for allowing calculation of goal directions during navigation.     

Membrane and network theta-rhythm generation in hippocampal slices

The hippocampal rhythms observed in vivo are the result of a complex interplay between cellular and synaptic properties within the hippocampus, and extra-hippocampal tonic as well as periodic inputs. For the stable rhythm to occur, the hippocampal circuitry should have the potential to oscillate at the specific frequencies. The in vitro studies revealed multiple mechanisms supporting the generation of the theta rhythm, which is the main operational mode of the hippocampus. In the hippocampus and related structures cellular membranes can oscillate at theta rhythm when they are depolarized to near-threshold membrane potentials; membranes are also adjusted to resonate with the external signal applied at theta frequency. Synaptically connected hippocampal network alone can generate theta rhythm when a necessary tonic excitation is provided. Finally, rhythmic inputs in theta range from the septum and entorhinal cortex have a propensity to synchronize oscillations in the whole hippocampal formation and associated structures to operate in a unified mode of activity. Based on the results obtained in slices and slice cultures, the present review shows this multilevel hierarchy, which serves to guarantee easy occurrence and reliable maintenance of the theta rhythm in the hippocampus.     

Effect of transection of afferent pathways on evoked potentials,theta rhythm,and neuronal activity in the hippocampus

The effect of destruction of septo-hippocampal and subiculo-hippocampal connections on the electrical activity in the hippocampus was studied in tubocurarized rabbits. The theta rhythm and the so-called "intracellular theta rhythm" [7] were found to disappear on destruction of the septo-hippocampal connections, other consequences being the loss of neuronal capacity for responding to sciatic nerve stimulation, loss of neuronal inhibitory responses, and total or partial suppression of the negative phase of the evoked potential (EP). Destruction of subiculo-hippocampal connections entails a decrease in amplitude of the theta rhythm recorded from the hippocampal surface, retention of the "intracellular theta rhythm," and a slight decrease in amplitude of both EP phases. The number of neurons failing to respond to sciatic stimulation is increased; the character of cellular response remains unchanged. It is hypothesized that hyperpolarization of hippocampal pyramidal neurons may be responsible for generating the negative phase of the EP, and that this phase and the hippocampal theta rhythm may be of a common origin.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Neirofiziologiya, Vol. 2, No. 4, pp. 439–444, July–August, 1970.     

Theta oscillations in the hippocampus

Theta oscillations represent the "on-line" state of the hippocampus. The extracellular currents underlying theta waves are generated mainly by the entorhinal input, CA3 (Schaffer) collaterals, and voltage-dependent Ca(2+) currents in pyramidal cell dendrites. The rhythm is believed to be critical for temporal coding/decoding of active neuronal ensembles and the modification of synaptic weights. Nevertheless, numerous critical issues regarding both the generation of theta oscillations and their functional significance remain challenges for future research.     

Working memory dynamics and spontaneous activity in a flip-flop oscillations network model with a Milnor attractor

Many cognitive tasks require the ability to maintain and manipulate simultaneously several chunks of information. Numerous neurobiological observations have reported that this ability, known as the working memory, is associated with both a slow oscillation (leading to the up and down states) and the presence of the theta rhythm. Furthermore, during resting state, the spontaneous activity of the cortex exhibits exquisite spatiotemporal patterns sharing similar features with the ones observed during specific memory tasks. Here to enlighten neural implication of working memory under these complicated dynamics, we propose a phenomenological network model with biologically plausible neural dynamics and recurrent connections. Each unit embeds an internal oscillation at the theta rhythm which can be triggered during up-state of the membrane potential. As a result, the resting state of a single unit is no longer a classical fixed point attractor but rather the Milnor attractor, and multiple oscillations appear in the dynamics of a coupled system. In conclusion, the interplay between the up and down states and theta rhythm endows high potential in working memory operation associated with complexity in spontaneous activities.

Traveling Theta Waves along the Entire Septotemporal Axis of the Hippocampus

A topographical relationship exists between the hippocampus-entorhinal cortex and the neocortex. However, it is not known how these anatomical connections are utilized during information exchange and behavior. We recorded theta oscillations along the entire extent of the septotemporal axis of the hippocampal CA1 pyramidal layer. While the frequency of theta oscillation remained same along the entire long axis, the amplitude and coherence between recording sites decreased from dorsal to ventral hippocampus (VH). Theta phase shifted monotonically with distance along the longitudinal axis, reaching ～180° between the septal and temporal poles. The majority of concurrently recorded units were phase-locked to the local field theta at all dorsoventral segments. The power of VH theta had only a weak correlation with locomotion velocity, and its amplitude varied largely independently from theta in the dorsal part. Thus, theta oscillations can temporally combine or segregate neocortical representations along the septotemporal axis of the hippocampus.     

Theta phase precession emerges from a hybrid computational model of a CA3 place cell

The origins and functional significance of theta phase precession in the hippocampus remain obscure, in part, because of the difficulty of reproducing hippocampal place cell firing in experimental settings where the biophysical underpinnings can be examined in detail. The present study concerns a neurobiologically based computational model of the emergence of theta phase precession in which the responses of a single model CA3 pyramidal cell are examined in the context of stimulation by realistic afferent spike trains including those of place cells in entorhinal cortex, dentate gyrus, and other CA3 pyramidal cells. Spike-timing dependent plasticity in the model CA3 pyramidal cell leads to a spatially correlated associational synaptic drive that subsequently creates a spatially asymmetric expansion of the model cell’s place field. Following an initial training period, theta phase precession can be seen in the firing patterns of the model CA3 pyramidal cell. Through selective manipulations of the model it is possible to decompose theta phase precession in CA3 into the separate contributing factors of inheritance from upstream afferents in the dentate gyrus and entorhinal cortex, the interaction of synaptically controlled increasing afferent drive with phasic inhibition, and the theta phase difference between dentate gyrus granule cell and CA3 pyramidal cell activity. In the context of a single CA3 pyramidal cell, the model shows that each of these factors plays a role in theta phase precession within CA3 and suggests that no one single factor offers a complete explanation of the phenomenon. The model also shows parallels between theta phase encoding and pattern completion within the CA3 autoassociative network. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Dual Coding with STDP in a Spiking Recurrent Neural Network Model of the Hippocampus

The firing rate of single neurons in the mammalian hippocampus has been demonstrated to encode for a range of spatial and non-spatial stimuli. It has also been demonstrated that phase of firing, with respect to the theta oscillation that dominates the hippocampal EEG during stereotype learning behaviour, correlates with an animal''s spatial location. These findings have led to the hypothesis that the hippocampus operates using a dual (rate and temporal) coding system. To investigate the phenomenon of dual coding in the hippocampus, we examine a spiking recurrent network model with theta coded neural dynamics and an STDP rule that mediates rate-coded Hebbian learning when pre- and post-synaptic firing is stochastic. We demonstrate that this plasticity rule can generate both symmetric and asymmetric connections between neurons that fire at concurrent or successive theta phase, respectively, and subsequently produce both pattern completion and sequence prediction from partial cues. This unifies previously disparate auto- and hetero-associative network models of hippocampal function and provides them with a firmer basis in modern neurobiology. Furthermore, the encoding and reactivation of activity in mutually exciting Hebbian cell assemblies demonstrated here is believed to represent a fundamental mechanism of cognitive processing in the brain.     

Theta returns

Recent physiological studies have implicated theta - a high-amplitude 4-8 Hz oscillation that is prominent in rat hippocampus during locomotion, orienting and other voluntary behaviors - in synaptic plasticity, information coding and the function of working memory. Intracranial recordings from human cortex have revealed evidence of high-amplitude theta oscillations throughout the brain, including the neocortex. Although its specific role is largely unknown, the observation of human theta has begun to reveal an intriguing connection between brain oscillations and cognitive processes.     

Alteration of phase–phase coupling between theta and gamma rhythms in a depression-model of rats

Alterations in oscillatory brain activity are strongly correlated with cognitive performance in various physiological rhythms, especially the theta and gamma rhythms. In this study, we investigated the coupling relationship of neural activities between thalamus and medial prefrontal cortex (mPFC) by measuring the phase interactions between theta and gamma oscillations in a depression model of rats. The phase synchronization analysis showed that the phase locking at theta rhythm was weakened in depression. Furthermore, theta-gamma phase locking at n:m (1:6) ratio was found between thalamus and mPFC, while it was diminished in depression state. In addition, the analysis of coupling direction based on phase dynamics showed that the unidirectional influence from thalamus to mPFC was diminished in depression state only in theta rhythm, while it was partly recovered after the memantine treatment in a depression model of rats. The results suggest that the effects of depression on cognitive deficits are modulated via profound alterations in phase information transformation of theta rhythm and theta-gamma phase coupling.     

Computational theories on the function of theta oscillations

Neural rhythms can be studied in terms of conditions for their generation, or in terms of their functional significance. The theta oscillation is a particularly prominent rhythm, reported to be present in many brain areas, and related to many important cognitive processes. The generating mechanisms of theta have extensively been studied and reviewed elsewhere; here we discuss ideas that have accumulated over the past decades on the computational roles it may subserve. Theories propose different aspects of theta oscillations as being relevant for their cognitive functions: limit cycle oscillations in neuronal firing rates, subthreshold membrane potential oscillations, periodic modulation of synaptic transmission and plasticity, and phase precession of hippocampal place cells. The relevant experimental data is briefly summarized in the light of these theories. Specific models proposing a function for theta in pattern recognition, memory, sequence learning and navigation are reviewed critically. Difficulties with testing and comparing alternative models are discussed, along with potentially important future research directions in the field.     

Coherence between Rat Sensorimotor System and Hippocampus Is Enhanced during Tactile Discrimination

Rhythms with time scales of multiple cycles per second permeate the mammalian brain, yet neuroscientists are not certain of their functional roles. One leading idea is that coherent oscillation between two brain regions facilitates the exchange of information between them. In rats, the hippocampus and the vibrissal sensorimotor system both are characterized by rhythmic oscillation in the theta range, 5–12 Hz. Previous work has been divided as to whether the two rhythms are independent or coherent. To resolve this question, we acquired three measures from rats—whisker motion, hippocampal local field potential (LFP), and barrel cortex unit firing—during a whisker-mediated texture discrimination task and during control conditions (not engaged in a whisker-mediated memory task). Compared to control conditions, the theta band of hippocampal LFP showed a marked increase in power as the rats approached and then palpated the texture. Phase synchronization between whisking and hippocampal LFP increased by almost 50% during approach and texture palpation. In addition, a greater proportion of barrel cortex neurons showed firing that was phase-locked to hippocampal theta while rats were engaged in the discrimination task. Consistent with a behavioral consequence of phase synchronization, the rats identified the texture more rapidly and with lower error likelihood on trials in which there was an increase in theta-whisking coherence at the moment of texture palpation. These results suggest that coherence between the whisking rhythm, barrel cortex firing, and hippocampal LFP is augmented selectively during epochs in which the rat collects sensory information and that such coherence enhances the efficiency of integration of stimulus information into memory and decision-making centers.