Representation of spatial orientation by the intrinsic dynamics of the head-direction cell ensemble: a theory

Abstract

The head-direction (HD) cells found in the limbic system in freely mov ing 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 inertially based updating and familiar visual landmarks for calibration. Here, a model of the dynamics of the HD cell ensemble is presented. The stability 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 directional tuning curves will emerge. By adding a slight asymmetry to the weights, the activity profile will shift continuously without disturbances to its shape, and the shift speed can be controlled accurately by the strength of the odd-weight component. The generic formulation of the shift mechanism is determined uniquely within the current theoretical framework. The attractor dynamics of the system ensures modality-independence of the internal representation and facilitates the correction for cumulative error by the putative local-view detectors. The model offers a specific one-dimensional example of a computational mechanism in which a truly world-centered representation can be derived from observer-centered sensory inputs by integrating self-motion information.

Path planning versus cue responding: a bio-inspired model of switching between navigation strategies

“…The use of allocentric directional frame implicitly requires the use of stable extra-maze cues with respect to which such a frame is defined. Our model does not include the estimation of the allocentric head direction from extra-maze cues (see Skaggs et al 1995;Zhang 1996), but it is assumed to be provided by the head direction network (Taube et al 1990. In contrast, infromation from the intra-maze cues is sufficient for the egocentric Taxon expert to determine direction to the goal.…”

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

“…The model presented here is a generalization of previous ring attractor networks (Ben-Yishai et al, 1995Zhang, 1996;Redish et al, 1996;Hansel and Sompolinsky, 1998;Goodridge and Touretzky, 2000;Xie et al, 2002;Degris et al, 2004). All these previous studies consider one or two population networks (either one population with couplings that can be either excitatory or inhibitory, or an excitatory-inhibitory network).…”

“…Head direction (HD) cells have been hypothesized to constitute yet another system with continuous attractor dynamics (Skaggs et al, 1995;Zhang, 1996;Redish et al, 1996;Goodridge and Touretzky, 2000;Degris et al, 2004). HD cells are observed in a network of structures centered on the rat limbic system.…”

“…Several investigators have proposed one-dimensional continuous attractor networks to model the HD cell system (Skaggs et al, 1995;Zhang, 1996;Redish et al, 1996;Goodridge and Touretzky, 2000;Xie et al, 2002;Degris et al, 2004). As in most continuous attractor systems, these models implement a recurrent neural network in which cells representing similar states (i.e., neighboring orientations in the one-dimensional directional state space) are coupled by strong excitatory collaterals, whereas units representing distant states strongly inhibit each other.…”

“…To relate this asymmetric component to head rotations, Zhang (1996) and Redish et al (1996) modulate the synaptic weights by means of angular velocity signals, whereas Goodridge and Touretzky (2000) utilize synapses with a non-linearity that is tuned to yield a perfect integration of angular velocity signals. Skaggs et al (1995) hypothesize the existence of two groups of 'rotation cells' that receive vestibular inputs and fire as a function of the magnitude of the angular velocity.…”