Localized bumps of activity sustained by inhibition in a two-layer thalamic network

Mechanisms Underlying the Neural Computation of Head Direction

Many animals use an internal sense of direction to guide their movements through the world. Neurons selective to head direction are thought to support this directional sense and have been found in a diverse range of species, from insects to primates, highlighting their evolutionary importance. Across species, most head-direction networks share four key properties: a unique representation of direction at all times, persistent activity in the absence of movement, integration of angular velocity to update the representation, and the use of directional cues to correct drift. The dynamics of theorized network structures called ring attractors elegantly account for these properties, but their relationship to brain circuits is unclear. Here, we review experiments in rodents and flies that offer insights into potential neural implementations of ring attractor networks. We suggest that a theory-guided search across model systems for biological mechanisms that enable such dynamics would uncover general principles underlying head-direction circuit function.

A speed-accurate self-sustaining head direction cell path integration model without recurrent excitation

The head direction (HD) system signals HD in an allocentric frame of reference. The system is able to update firing based on internally derived information about self-motion, a process known as path integration. Of particular interest is how path integration might maintain concordance between true HD and internally represented HD. Here we present a self-sustaining two-layer model, capable of self-organizing, which produces extremely accurate path integration. The implications of this work for future investigations of HD system path integration are discussed.

Single Canonical Model of Reflexive Memory and Spatial Attention

Many neurons in the dorsal and ventral visual stream have the property that after a brief visual stimulus presentation in their receptive field, the spiking activity in these neurons persists above their baseline levels for several seconds. This maintained activity is not always correlated with the monkey’s task and its origin is unknown. We have previously proposed a simple neural network model, based on shape selective neurons in monkey lateral intraparietal cortex, which predicts the valence and time course of reflexive (bottom-up) spatial attention. In the same simple model, we demonstrate here that passive maintained activity or short-term memory of specific visual events can result without need for an external or top-down modulatory signal. Mutual inhibition and neuronal adaptation play distinct roles in reflexive attention and memory. This modest 4-cell model provides the first simple and unified physiologically plausible mechanism of reflexive spatial attention and passive short-term memory processes.

Architectural constraints are a major factor reducing path integration accuracy in the rat head direction cell system

Head direction cells fire to signal the direction in which an animal's head is pointing. They are able to track head direction using only internally-derived information (path integration)In this simulation study we investigate the factors that affect path integration accuracy. Specifically, two major limiting factors are identified: rise time, the time after stimulation it takes for a neuron to start firing, and the presence of symmetric non-offset within-layer recurrent collateral connectivity. On the basis of the latter, the important prediction is made that head direction cell regions directly involved in path integration will not contain this type of connectivity; giving a theoretical explanation for architectural observations. Increased neuronal rise time is found to slow path integration, and the slowing effect for a given rise time is found to be more severe in the context of short conduction delays. Further work is suggested on the basis of our findings, which represent a valuable contribution to understanding of the head direction cell system.

The irregular firing properties of thalamic head direction cells mediate turn-specific modulation of the directional tuning curve

Head direction cells encode an animal's heading in the horizontal plane. However, it is not clear why the directionality of a cell's mean firing rate differs for clockwise, compared with counterclockwise, head turns (this difference is known as the “separation angle”) in anterior thalamus. Here we investigated in freely behaving rats whether intrinsic neuronal firing properties are linked to this phenomenon. We found a positive correlation between the separation angle and the spiking variability of thalamic head direction cells. To test whether this link is driven by hyperpolarization-inducing currents, we investigated the effect of thalamic reticular inhibition during high-voltage spindles on directional spiking. While the selective directional firing of thalamic neurons was preserved, we found no evidence for entrainment of thalamic head direction cells by high-voltage spindle oscillations. We then examined the role of depolarization-inducing currents in the formation of separation angle. Using a single-compartment Hodgkin-Huxley model, we show that modeled neurons fire with higher frequencies during the ascending phase of sinusoidal current injection (mimicking the head direction tuning curve) when simulated with higher high-threshold calcium channel conductance. These findings demonstrate that the turn-specific encoding of directional signal strongly depends on the ability of thalamic neurons to fire irregularly in response to sinusoidal excitatory activation. Another crucial factor for inducing phase lead to sinusoidal current injection was the presence of spike-frequency adaptation current in the modeled neurons. Our data support a model in which intrinsic biophysical properties of thalamic neurons mediate the physiological encoding of directional information.

Cholinergic modulation of the CAN current may adjust neural dynamics for active memory maintenance, spatial navigation and time-compressed replay

Suppression of cholinergic receptors and inactivation of the septum impair short-term memory, and disrupt place cell and grid cell activity in the medial temporal lobe (MTL). Location-dependent hippocampal place cell firing during active waking, when the acetylcholine level is high, switches to time-compressed replay activity during quiet waking and slow-wave-sleep (SWS), when the acetylcholine level is low. However, it remains largely unknown how acetylcholine supports short-term memory, spatial navigation, and the functional switch to replay mode in the MTL. In this paper, we focus on the role of the calcium-activated non-specific cationic (CAN) current which is activated by acetylcholine. The CAN current is known to underlie persistent firing, which could serve as a memory trace in many neurons in the MTL. Here, we review the CAN current and discuss possible roles of the CAN current in short-term memory and spatial navigation. We further propose a novel theoretical model where the CAN current switches the hippocampal place cell activity between real-time and time-compressed sequential activity during encoding and consolidation, respectively.

Single-cell persistent activity in anterodorsal thalamus

The anterodorsal nucleus of the thalamus contains a high percentage of head-direction cells whose activities are correlated with an animal's directional heading in the horizontal plane. The firing of head-direction cells could involve self-sustaining reverberating activity in a recurrent network, but the thalamus by itself lacks strong excitatory recurrent synaptic connections to sustain tonic reverberating activity. Here we examined whether a single thalamic neuron could sustain its own activity without synaptic input by recording from individual neurons from anterodorsal thalamus in brain slices with synaptic blockers. We found that the rebound firing induced by hyperpolarizing pulses often decayed slowly so that a thalamic neuron could keep on firing for many minutes after stimulation. The hyperpolarization-induced persistent firing rate was graded under repeated current injections, and could be enhanced by serotonin. The effect of depolarizing pulses was much weaker and only slightly accelerated the decay of the hyperpolarization-induced persistent firing. Our finding provides the first direct evidence for single-cell persistent activity in the thalamus, supporting the notion that cellular mechanisms at the slow time scale of minutes might potentially contribute to the operations of the head-direction system.

Persistent firing supported by an intrinsic cellular mechanism in a component of the head direction system

The rat postsubiculum has head direction cells that fire persistently when the rat's head is oriented in particular directions. This persistent firing is maintained even if the rat is motionless, when spatial cues are removed from the environment and in the dark, but the mechanism that supports persistent firing of the head direction cells is still unclear. Here, using in vitro whole-cell patch recording, we found that a short-triggering stimulus (as few as five induced spikes) can initiate persistent firing in cells of the postsubiculum. Pharmacological results indicated that this persistent firing is driven by a calcium-sensitive nonselective cation current. The distribution of cells with persistent firing in superficial and deep layers in the postsubiculum was similar to that of head direction cells. These results suggest that persistent firing of head direction cells in the postsubiculum could be supported by an intrinsic mechanism.

Filtering of Spatial Bias and Noise Inputs by Spatially Structured Neural Networks

With spatially organized neural networks, we examined how bias and noise inputs with spatial structure result in different network states such as bumps, localized oscillations, global oscillations, and localized synchronous firing that may be relevant to, for example, orientation selectivity. To this end, we used networks of McCulloch-Pitts neurons, which allow theoretical predictions, and verified the obtained results with numerical simulations. Spatial inputs, no matter whether they are bias inputs or shared noise inputs, affect only firing activities with resonant spatial frequency. The component of noise that is independent for different neurons increases the linearity of the neural system and gives rise to less spatial mode mixing and less bistability of population activities.

Angular path integration by moving "hill of activity": a spiking neuron model without recurrent excitation of the head-direction system

During spatial navigation, the head orientation of an animal is encoded internally by neural persistent activity in the head-direction (HD) system. In computational models, such a bell-shaped "hill of activity" is commonly assumed to be generated by recurrent excitation in a continuous attractor network. Recent experimental evidence, however, indicates that HD signal in rodents originates in a reciprocal loop between the lateral mammillary nucleus (LMN) and the dorsal tegmental nucleus (DTN), which is characterized by a paucity of local excitatory axonal collaterals. Moreover, when the animal turns its head to a new direction, the heading information is updated by a time integration of angular head velocity (AHV) signals; the underlying mechanism remains unresolved. To investigate these issues, we built and investigated an LMN-DTN network model that consists of three populations of noisy and spiking neurons coupled by biophysically realistic synapses. We found that a combination of uniform external excitation and recurrent cross-inhibition can give rise to direction-selective persistent activity. The model reproduces the experimentally observed three types of HD tuning curves differentially modulated by AHV and anticipatory firing activity in LMN HD cells. Time integration is assessed by using constant or sinusoidal angular velocity stimuli, as well as naturalistic AHV inputs (from rodent recordings). Furthermore, the internal representation of head direction is shown to be calibrated or reset by strong external cues. We identify microcircuit properties that determine the ability of our model network to subserve time integration function.

Surprising Effects of Synaptic Excitation

Typically, excitatory synaptic coupling is thought of as an influence that accelerates and propagates firing in neuronal networks. This paper reviews recent results explaining how, contrary to these expectations, the presence of excitatory synaptic coupling can drastically slow oscillations in a network and how localized, sustained activity can arise in a network with purely excitatory coupling, without sustained inputs. These two effects stem from interactions of excitatory coupling with two different forms of intrinsic neuronal dynamics, and both serve to highlight the fact that the influence of synaptic coupling in a network depends strongly on the intrinsic properties of cells in the network.

A continuous attractor network model without recurrent excitation: maintenance and integration in the head direction cell system

Motivated by experimental observations of the head direction system, we study a three population network model that operates as a continuous attractor network. This network is able to store in a short-term memory an angular variable (the head direction) as a spatial profile of activity across neurons in the absence of selective external inputs, and to accurately update this variable on the basis of angular velocity inputs. The network is composed of one excitatory population and two inhibitory populations, with inter-connections between populations but no connections within the neurons of a same population. In particular, there are no excitatory-to-excitatory connections. Angular velocity signals are represented as inputs in one inhibitory population (clockwise turns) or the other (counterclockwise turns). The system is studied using a combination of analytical and numerical methods. Analysis of a simplified model composed of threshold-linear neurons gives the conditions on the connectivity for (i) the emergence of the spatially selective profile, (ii) reliable integration of angular velocity inputs, and (iii) the range of angular velocities that can be accurately integrated by the model. Numerical simulations allow us to study the proposed scenario in a large network of spiking neurons and compare their dynamics with that of head direction cells recorded in the rat limbic system. In particular, we show that the directional representation encoded by the attractor network can be rapidly updated by external cues, consistent with the very short update latencies observed experimentally by Zugaro et al. (2003) in thalamic head direction cells.

Emergence of neural integration in the head-direction system by visual supervision

Head-direction (HD) cells in subcortical areas of the mammalian brain are tuned to a particular head direction in space; a population of such neurons forms a neural compass that may be relevant for spatial navigation. The development of neural circuits constituting the head-direction system is poorly understood. Inspired by electrophysiological experiments about the role of recurrent synaptic connections, we investigate a learning rule that teaches neurons to amplify feed-forward inputs. We simulate random head movements of a rat, during which neurons receive both visual and vestibular (head-velocity) inputs. Remarkably, as recurrent connections learn to amplify exclusively the visual inputs, a neural network emerges that performs spatio-temporal integration. That is, during head movements in darkness, neurons resemble HD cells by maintaining a fixed tuning to head direction. The proposed learning rule exhibits similarities with known forms of anti-Hebbian synaptic plasticity. We conclude that selective amplification could serve as a general principle for the synaptic development of multimodal feedback circuits in the brain.

Dynamical Consequences of Fast-Rising, Slow-Decaying Synapses in Neuronal Networks

Synapses that rise quickly but have long persistence are shown to have certain computational advantages. They have some unique mathematical properties as well and in some instances can make neurons behave as if they are weakly coupled oscillators. This property allows us to determine their synchronization properties. Furthermore, slowly decaying synapses allow recurrent networks to maintain excitation in the absence of inputs, whereas faster decaying synapses do not. There is an interaction between the synaptic strength and the persistence that allows recurrent networks to fire at low rates if the synapses are sufficiently slow. Waves and localized structures are constructed in spatially extended networks with slowly decaying synapses.

High-frequency, depressing inhibition facilitates synchronization in globally inhibitory networks

Motivated by the study of sharp wave-associated ripples, high-frequency (approximately 200 Hz) extracellular field oscillations observed in the CA1 region of the rat hippocampus during slow-wave sleep and periods of behavioural immobility, we consider a single inhibitory neuron synapsing onto a network of uncoupled, excitatory neurons. The inhibitory synapse is depressing and has a small synaptic delay. Each excitatory cell provides instantaneous, positive feedback to the inhibitory cell. We show that the interneuron can rapidly synchronize the action potentials of the pyramidal cells if the frequency of inhibitory input is increased in a ramp-like manner as occurs during the ripple. We show that the basin of attraction of the synchronous solution is larger when the inhibition frequency is gradually increased as opposed to remaining constant.

Synaptic reverberation underlying mnemonic persistent activity

Stimulus-specific persistent neural activity is the neural process underlying active (working) memory. Since its discovery 30 years ago, mnemonic activity has been hypothesized to be sustained by synaptic reverberation in a recurrent circuit. Recently, experimental and modeling work has begun to test the reverberation hypothesis at the cellular level. Moreover, theory has been developed to describe memory storage of an analog stimulus (such as spatial location or eye position), in terms of continuous 'bump attractors' and 'line attractors'. This review summarizes new studies, and discusses insights and predictions from biophysically based models. The stability of a working memory network is recognized as a serious problem; stability can be achieved if reverberation is largely mediated by NMDA receptors at recurrent synapses.