A Continuous Attractor Network Model Without Recurrent Excitation: Maintenance and Integration in the Head Direction Cell System

Abstract

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 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.

Fundamental limits on persistent activity in networks of noisy neurons

“…However, the component of noise parallel to the attractor manifold will remain uncorrected, causing loss of information about the stored memory (9,11). Such noise-induced drift has been observed in numerical simulations of continuous attractor networks (10,12,13) and has been studied analytically in a specific continuous attractor network (14,15). However, a general understanding of how neural and network properties affect the rate of drift and short-term memory performance has been missing.…”

Coordinated learning of grid cell and place cell spatial and temporal properties: multiple scales, attention and oscillations

“…The model proposes that both angular and linear velocity signals are processed by ring attractor neural circuits. Angular velocity signals are integrated by head direction (HD) cells [65,66] that are often modelled as part of ring attractor circuits [67][68][69][70][71][72][73][74]. The position of an activity bump in a HD ring attractor maximally activates cells that code the current HD.…”

“…Place cell selectivity can develop within seconds to minutes, and can remain stable for months [70][71][72][73][74][75][76][77][78][79][80][81][82]. The HC needs additional mechanisms to ensure this long-term stability.…”

Robust self-localisation and navigation based on hippocampal place cells

“…Then, a large activity profile around F hd is enforced in the HD system. Lateral interconnection between HD cells could be the neuronal substrate for such activity profiles (Boucheny, Brunel, & Arleo, 2005;Zhang, 1996). Here, we emulate lateral interactions by enforcing a Gaussian activity profile around F hd .…”

“…(5), (8) and (9) which seems at first sight biologically implausible. However, if continuous attractors using lateral connections (Amari, 1977;Boucheny et al 2005;Zhang, 1996) or a probabilistic activity transition matrix (Herrmann, Pawelzik, & Geisel, 1999) between HD cells was used for implementing Eq. (5), the recalibration could be performed without explicitly accessing angular information.…”