A dual-axis rotation rule for updating the head direction cell reference frame during movement in three dimensions.

In the mammalian brain, allocentric (Earth-referenced) head direction, called azimuth, is encoded by head direction (HD) cells, which fire according to the facing direction of the animal's head. On a horizontal surface, rotations of the head around the dorsoventral (D-V) axis, called yaw, correspond to changes in azimuth and elicit appropriate updating of the HD "compass" signal to enable large-scale navigation. However, if the animal moves through three-dimensional (3D) space then there is no longer a simple relationship between yaw rotations and azimuth changes, and so processing of 3D rotations is needed. Construction of a global 3D compass would require complex integration of 3D rotations, and also a large neuronal population, most neurons of which would be silent most of the time since animals rarely sample all available 3D orientations. We propose that, instead, the HD system treats the 3D space as a set of interrelated 2D surfaces. It could do this by updating activity according to both yaw rotations around the D-V axis and rotations of the D-V axis around the gravity-defined vertical axis. We present preliminary data to suggest that this rule operates when rats move between walls of opposing orientations. This dual-axis rule, which we show is straightforward to implement using the classic one-dimensional "attractor" architecture, allows consistent representation of azimuth even in volumetric space and thus may be a general feature of mammalian directional computations even for animals that swim or fly. NEW & NOTEWORTHY Maintaining a sense of direction is complicated when moving in three-dimensional (3D) space. Head direction cells, which update the direction sense based on head rotations, may accommodate 3D movement by processing both rotations of the head around the axis of the animal's body and rotations of the head/body around gravity. With modeling we show that this dual-axis rule works in principle, and we present preliminary data to support its operation in rats.

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.

Optimal cue combination and landmark-stability learning in the head direction system.

Maintaining a sense of direction requires combining information from static environmental landmarks with dynamic information about self-motion. This is accomplished by the head direction system, whose neurons - head direction cells - encode specific head directions. When the brain integrates information in sensory domains, this process is almost always 'optimal' - that is, inputs are weighted according to their reliability. Evidence suggests cue combination by head direction cells may also be optimal. The simplicity of the head direction signal, together with the detailed knowledge we have about the anatomy and physiology of the underlying circuit, therefore makes this system a tractable model with which to discover how optimal cue combination occurs at a neural level. In the head direction system, cue interactions are thought to occur on an attractor network of interacting head direction neurons, but attractor dynamics predict a winner-take-all decision between cues, rather than optimal combination. However, optimal cue combination in an attractor could be achieved via plasticity in the feedforward connections from external sensory cues (i.e. the landmarks) onto the ring attractor. Short-term plasticity would allow rapid re-weighting that adjusts the final state of the network in accordance with cue reliability (reflected in the connection strengths), while longer term plasticity would allow long-term learning about this reliability. Although these principles were derived to model the head direction system, they could potentially serve to explain optimal cue combination in other sensory systems more generally.

Learning separate visual representations of independently rotating objects.

Individual cells that respond preferentially to particular objects have been found in the ventral visual pathway. How the brain is able to develop neurons that exhibit these object selective responses poses a significant challenge for computational models of object recognition. Typically, many objects make up a complex natural scene and are never presented in isolation. Nonetheless, the visual system is able to build invariant object selective responses. In this paper, we present a model of the ventral visual stream, VisNet, which can solve the problem of learning object selective representations even when multiple objects are always present during training. Past research with the VisNet model has shown that the network can operate successfully in a similar training paradigm, but only when training comprises many different object pairs. Numerous pairings are required for statistical decoupling between objects. In this research, we show for the first time that VisNet is capable of utilizing the statistics inherent in independent rotation to form object selective representations when training with just two objects, always presented together. Crucially, our results show that in a dependent rotation paradigm, the model fails to build object selective representations and responds as if the two objects are in fact one. If the objects begin to rotate independently, the network forms representations for each object separately.

Landmark-Based Updating of the Head Direction System by Retrosplenial Cortex: A Computational Model.

Maintaining a sense of direction is fundamental to navigation, and is achieved in the brain by a network of head direction (HD) cells, which update their signal using stable environmental landmarks. How landmarks are detected and their stability determined is still unknown. Recently we reported a new class of cells (Jacob et al., 2017), the bidirectional cells, in a brain region called retrosplenial cortex (RSC) which relays environmental sensory information to the HD system. A subset of these cells, between-compartment (BC) cells, are directionally tuned (like ordinary HD cells) but follow environmental cues in preference to the global HD signal, resulting in opposing (i.e., bidirectional) tuning curves in opposed environments. Another subset, within-compartment (WC) cells, unexpectedly expressed bidirectional tuning curves in each one of the opposed compartments. Both BC and WC cells lost directional tuning in an open field, unlike HD cells. Two questions arise from this discovery: (i) how do these cells acquire their unusual response properties, and (ii) what are they for? We propose that bidirectional cells reflect a two-way interaction between local direction, as indicated by the visual environment, and global direction as signaled by the HD system. We suggest that BC cells receive strong inputs from visual cues, while WC cells additionally receive modifiable inputs from HD cells which, due to Hebbian coactivation of visual inputs plus two opposing sets of HD inputs, acquire the ability to fire in both directions. A neural network model instantiating this hypothesis is presented, which indeed forms both BC and WC bidirectional cells with properties similar to those seen experimentally. We then demonstrate how tuning specificity degrades when WC/BC cells are exposed to multiple directionalities, replicating the observed loss of WC and BC directional tuning in the open field. We suggest that the function of these neurons is to assess the stability of environmental landmarks, thereby determining their utility as reference points by which to set the HD sense of direction. This role could extend to the ability of the HD system to prefer distal over proximal landmarks, and to correct for parallax errors.

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.

A theoretical account of cue averaging in the rodent head direction system.

Head direction (HD) cell responses are thought to be derived from a combination of internal (or idiothetic) and external (or allothetic) sources of information. Recent work from the Jeffery laboratory shows that the relative influence of visual versus vestibular inputs upon the HD cell response depends on the disparity between these sources. In this paper, we present simulation results from a model designed to explain these observations. The model accurately replicates the Knight et al. data. We suggest that cue conflict resolution is critically dependent on plastic remapping of visual information onto the HD cell layer. This remap results in a shift in preferred directions of a subset of HD cells, which is then inherited by the rest of the cells during path integration. Thus, we demonstrate how, over a period of several minutes, a visual landmark may gain cue control. Furthermore, simulation results show that weaker visual landmarks fail to gain cue control as readily. We therefore suggest a second longer term plasticity in visual projections onto HD cell areas, through which landmarks with an inconsistent relationship to idiothetic information are made less salient, significantly hindering their ability to gain cue control. Our results provide a mechanism for reliability-weighted cue averaging that may pertain to other neural systems in addition to the HD system.