A minimal synaptic architecture is proposed for how the brain might perform path integration by computing the next internal representation of self-location from the current representation and from the perceived velocity of motion. In the model, a place-cell assembly called a “chart ” contains a twodimensional attractor set called an “attractor map ” that can be used to represent coordinates in any arbitrary environment, once associative binding has occurred between chart locations and sensory inputs. In hippocampus, there are different spatial relations among place fields in different environments and behavioral contexts. Thus, the same units may participate in many charts, and it is shown that the number of uncorrelated charts that can be encoded in the same recurrent network is potentially quite large. According to this theory, the firing of a given place cell is primarily a cooperative effect of the activity of its

The head-direction (HD) cells found in the limbic system in freely moving rats represent the instantaneous head direction of the animal in the horizontal plane regardless of the location of the animal. The internal direction represented by these cells uses both self-motion information for inet-tially based updating and familiar visual landmarks for calibration. Here, a model of the dynamics of the HD cell ensemble is presented. The sta-bility of a localized static activity profile in the network and a dynamic shift mechanism are explained naturally by synaptic weight distribution components with even and odd symmetry, respectively. Under symmetric weights or symmetric reciprocal connections, a stable activity profile close to the known direc-tional tuning curves will emerge. By adding a slight asymmetry to the weights, the activity profile will shift continuously without 1

Previous studies have shown that hippocampal place fields are controlled by the salient sensory cues in the environ-ment, in that rotation of the cues causes an equal rotation of the place fields. We trained rats to forage for food pellets in a gray cylinder with a single salient directional cue, a white card covering 90 ” of the cylinder wall. Half of the rats were disoriented before being placed in the cylinder, in or-der to disrupt their internal sense of direction. The other half were not disoriented before being placed in the cylin-der; for these rats, there was presumably a consistent re-lationship between the cue card and their internal direction sense. We subsequently recorded hippocampal place cells and thalamic head direction cells from both groups of rats as they moved in the cylinder; between some sessions the cylinder and cue card were rotated to a new direction. All

Abstract. 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 noconnections 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.

ABSTRACT: We present a model that describes the generation of the spatial (grid fields) and temporal (phase precession) properties of medial entorhinal cortical (MEC) neurons by combining network and intrinsic cellular properties. The model incorporates network architecture derived from earlier attractor map models, and is implemented in 1D for simplicity. Periodic driving of conjunctive (position 3 head-direction) layer-III MEC cells at theta frequency with intensity proportional to the rat’s speed, moves an ‘activity bump ’ forward in network space at a corresponding speed. The addition of prolonged excitatory currents and simple after-spike dynamics resembling those observed in MEC stellate cells (for which new data are presented) accounts for both phase precession and the change in scale of grid fields along the dorso-ventral axis of MEC. Phase precession in the model depends on both synaptic connectivity and intrinsic currents, each of which drive neural spiking either during entry into, or during exit out of a grid field. Thus, the model predicts that the slope of phase precession changes between entry into and exit out of the field. The model also exhibits independent variation in grid spatial period and grid field size, which suggests possible experimental tests of the model. VC 2011 Wiley-Liss, Inc. KEY WORDS: path integration; dead reckoning; continuous attractor neural network; place cells; entorhinal stellate cells

Vestibular information influences spatial orientation and navigation in laboratory animals and humans. Neurons within the rat anterior thalamus encode the directional heading of the animal in absolute space. These neurons, referred to as head direction (HD) cells, fire selectively when the rat points its head in a specific direction in the horizontal plane with respect to the external laboratory reference frame. HD cells are thought to represent an essential component of a neural network that processes allocentric spatial information. The functional properties of HD cells may be dependent on vestibular input. Here, anterior thalamic HD cells were recorded before and after sodium arsanilate-induced vestibular system lesion. Vestibular lesions abolished the directional firing properties of HD cells. The time course of disruption in the directional firing properties paralleled the loss of vestibular function. Arsanilate-treated rats

Many neurons in the rat lateral mammillary nuclei (LMN) fire selectively in relation to the animal’s head direction (HD) in the horizontal plane independent of the rat’s location or behavior. One hypothesis of how this representation is generated and updated is via subcortical projections from the dorsal tegmental nucleus (DTN). Here we report the type of activity in DTN neurons. The majority of cells (75%) fired as a function of the rat’s angular head velocity (AHV). Cells exhibited one of two types of firing patterns: (1) symmetric, in which the firing rate was positively correlated with AHV during head turns in both directions, and (2) asymmetric, in which the firing rate was positively correlated with head turns in one direction and correlated either negatively or not at all in the opposite direction. In addition to modulation by AHV, some of the AHV cells (40.1%) Neurons that discharge selectively in relation to an animal’s head

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 directionselective 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. Key words: navigation; persistent activity; head direction; computational modeling; path integration; lateral inhibition

Place cells of the hippocampal formation encode a spatial representation of the environment, and the orientation of this representation is apparently governed by the head direction cell system. The representation of a well explored environment by CA1 place cells can be split when there is conflicting information from salient proximal and distal cues, because some place fields rotate to follow the distal cues, whereas others rotate to follow the proximal cues (Knierim, 2002a). In contrast, the CA3 representation is more coherent than CA1, because the place fields in CA3 tend to rotate in the same direction (Lee et al., 2004). The present study tests whether the head direction cell network produces a split representation or remains coherent under these conditions by simultaneously recording both CA1 place cells and head direction cells from the thalamus. In agreement with previous studies, split representations of the environment were observed in ensembles of CA1 place cells in �75 % of the mismatch sessions, in which some fields followed the counterclockwise rotation of proximal cues and other fields followed the clockwise rotation of distal cues. However, of 225 recording sessions, there was not a single instance of the head direction cell ensembles revealing a split representation of head direction. Instead, in most of the mismatch sessions, the head direction cell tuning curves rotated as an ensemble clockwise (94%) and in a few sessions rotated counterclockwise (6%). The findings support the notion that the head direction cells may be part of an attractor network bound more strongly to distal landmarks than proximal landmarks, even under conditions in which the CA1 place representation loses its coherence. Key words: place cells; head direction cells; ensemble recording; attractor neural network; spatial orientation; single units

ABSTRACT: The spatial mapping theory of hippocampal function proposes that the rat hippocampus is specialized for navigational computations, computations that allow the animal to solve difficult spatial problems. In this paper, we review evidence obtained by recording place cells and other ‘‘spatially tuned’ ’ cells from freely moving rats. Our main conclusion is that the nature of the signals carried by these cells and the ways in which the signals transform after changing the environment imply that the hippocampus and associated structures are able to represent aspects of the geometry of the environment. Hippocampus 1999; 9:413–422. � 1999 Wiley-Liss, Inc. The ability of rats and mice to solve difficult navigational problems implies that they can form and use representations of their environment to select paths from their initial location to a goal (Tolman, 1948; Gallistel, 1990; Poucet, 1993). There are two very different ways in which such representations could be formed in the nervous system. On the one hand,