Learning accurate path integration in ring attractor models of the head direction system
Curation statements for this article:-
Curated by eLife
Evaluation Summary:
This paper will be of interest to neuroscientists studying the navigation system, and in particular those who study the ability of animals to path integrate. This study proposes an elegant synaptic plasticity rule that maintains the connectivity required for path integration by integrating visual and self-motion input arriving at different dendritic locations in a neuron. This idea is applied to the central complex of Drosophila, a well-characterized system. The study is timely and well executed, however the generality of the suggested mechanism needs further discussion.
(This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #3 agreed to share their name with the authors.)
This article has been Reviewed by the following groups
Listed in
- Evaluated articles (eLife)
- Neuroscience (eLife)
Abstract
Ring attractor models for angular path integration have received strong experimental support. To function as integrators, head direction circuits require precisely tuned connectivity, but it is currently unknown how such tuning could be achieved. Here, we propose a network model in which a local, biologically plausible learning rule adjusts synaptic efficacies during development, guided by supervisory allothetic cues. Applied to the Drosophila head direction system, the model learns to path-integrate accurately and develops a connectivity strikingly similar to the one reported in experiments. The mature network is a quasi-continuous attractor and reproduces key experiments in which optogenetic stimulation controls the internal representation of heading in flies, and where the network remaps to integrate with different gains in rodents. Our model predicts that path integration requires self-supervised learning during a developmental phase, and proposes a general framework to learn to path-integrate with gain-1 even in architectures that lack the physical topography of a ring.
Article activity feed
-
-
Evaluation Summary:
This paper will be of interest to neuroscientists studying the navigation system, and in particular those who study the ability of animals to path integrate. This study proposes an elegant synaptic plasticity rule that maintains the connectivity required for path integration by integrating visual and self-motion input arriving at different dendritic locations in a neuron. This idea is applied to the central complex of Drosophila, a well-characterized system. The study is timely and well executed, however the generality of the suggested mechanism needs further discussion.
(This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #3 agreed to share their name with the authors.)
-
Reviewer #1 (Public Review):
Vafidis et al. propose a model of a form of synaptic plasticity in head direction cells of the Drosophila central complex, in which visual input arriving at axon-proximal locations supervises other input arriving at axon-distal locations. The authors show that this proposed plasticity rule can tune the system to perform accurate path integration and adjust to changes in gain.
The proposal is an interesting idea that maps the extended morphology of the E-PG neurons that represent head direction in flies to a very specific functional prediction. This prediction is inspired by work in mammalian pyramidal neurons, where it appears that inputs arriving at different parts of the neuron can either be modified through learning or serve as the learning signal itself. The model functions well, and successfully …
Reviewer #1 (Public Review):
Vafidis et al. propose a model of a form of synaptic plasticity in head direction cells of the Drosophila central complex, in which visual input arriving at axon-proximal locations supervises other input arriving at axon-distal locations. The authors show that this proposed plasticity rule can tune the system to perform accurate path integration and adjust to changes in gain.
The proposal is an interesting idea that maps the extended morphology of the E-PG neurons that represent head direction in flies to a very specific functional prediction. This prediction is inspired by work in mammalian pyramidal neurons, where it appears that inputs arriving at different parts of the neuron can either be modified through learning or serve as the learning signal itself. The model functions well, and successfully produces a network that is capable of path integration.
A concern about the model is that it is unclear whether this activity-dependent plasticity rule is actually needed to reproduce results consistent with what is shown in flies. The trained networks actually perform better than flies do in experiments, and noise must be added to make the performance comparable. Also, adult flies do not appear to be capable of adjusting to changes in gain, as the model does.
The general ideas of the model may be applicable to a variety of systems that require some form of path integration, and thus although this study develops a model that is specific to the fly head direction system the architecture could be easily extended to other scenarios.
-
Reviewer #2 (Public Review):
The ring attractor model serves as a fundamental framework to study how the brain encodes and computes based on continuous variables. One of this computation is angular path integration- the ability of animals to orient themselves using idiothetic cues to update the internal representation of their location. However, these models are usually pre-engineered and require precisely tuned connectivity, but it is unclear how such tuning emerge in the system.
This computational work provides a model that learn to path integrate by adjusting synaptic efficacies, guided by allothetic cues. Tailored to the head direction system of the fly, this work replicates some of the experiments and findings in the literature and provides a mathematical explanation for how symmetric connectivity arise in such recurrent networks …
Reviewer #2 (Public Review):
The ring attractor model serves as a fundamental framework to study how the brain encodes and computes based on continuous variables. One of this computation is angular path integration- the ability of animals to orient themselves using idiothetic cues to update the internal representation of their location. However, these models are usually pre-engineered and require precisely tuned connectivity, but it is unclear how such tuning emerge in the system.
This computational work provides a model that learn to path integrate by adjusting synaptic efficacies, guided by allothetic cues. Tailored to the head direction system of the fly, this work replicates some of the experiments and findings in the literature and provides a mathematical explanation for how symmetric connectivity arise in such recurrent networks when supervised learning scheme is assumed.
Strengths of the paper:
The paper addresses an interesting question, of the ability of the head direction system to path integrate. Putting in context, it's been almost 30 years that a ring attractor network was suggested to model the head direction system. The idea behind this model is that due to a symmetry in the recurrent connectivity in the network, a continuous attractor emerges in the system. In classical models, networks with 2 or 3 rings are used to both generate a persistent and continuous representation, but also to allow to perform angular integration. In recent years, it was suggested that a 3-ring-like structure plays a key role in the head direction system of the Drosophila.
The strength of the paper is in building of a mechanistic network model that learns to path integrate based on a supervised learning scheme. The learning rule is local, suggesting its being biologically plausible, and following training the system develops symmetric recurrent connectivity that are reminiscent of the Fly's head direction system. Moreover, the authors provide a mathematical derivation, which shows how symmetric connectivity emerges in the network.
Because the ability to path integrate in the system is based on learning, and not on pre-engineered connectivity, the network can also adapt to changes in the gain between the allothetic and idiothetic signals. This is consistent with the literature, where it was recently shown that the head direction system of the mouse can adapt to such gain modulations.
The learning rule is based on a two-compartment model, which serves as a coincidence detector between external and internal inputs arriving at different compartments. The authors analyze the Fly's connectome data (visual and recurrent inputs to the E-PG neurons) to support this hypothesis.
Weaknesses of the paper:
The paper has three main weaknesses.
The first is that it is unclear if symmetry is a necessary outcome of the learning scheme, or if it depends on the way the network is initialized. In their mathematical derivation the authors assumed that the solution is symmetric, and while checking that this assumption is self-consistent, it is unclear if other non-symmetric solutions exist. Specifically, it is unclear if different initializations of the recurrent and feedforward connectivity will give a different- possibly asymmetric- solution. Moreover, the authors assumed a specific network architecture, which was tailored to the Fly's head direction system. It is unclear if the symmetric solution the authors found is specific to this architecture.
The second issue is with the support the authors provide to their two-compartment model assumption. The authors analyzed the spatial locations of inputs to an E-PG neuron and claimed that the visual and recurrent inputs are spatially segregated. While this is a nice use of the new connectome data, there is no statistical analysis to support this claim, and only one example is shown in the manuscript.
Third, the mechanism in the model seems to strongly rely on saturation of the E-PG neurons. However, it is not clear if this is a biologically relevant regime for these neurons and the authors do not address this problem.
Finally, while the authors did a great job in building a mechanistic model that resembles the fly's head direction system, they fail to provide testable predictions. Such predictions are in general not necessary to have, but with the detailed characterization of this system in the fly, together with a mechanistic model that is tailored specifically to this system, I feel that the manuscript (and the community) will benefit from devoting a paragraph or two in the discussion to suggest new experiments, in line with their mechanistic model.
-
Reviewer #3 (Public Review):
In this manuscript by Vafidis et al., the authors propose a learning mechanism that adjusts the connectivity of a head direction cell network to obtain robust angular integration. Ring attractors have been proposed long ago to account for head direction cell tunings. However, in general, continuous attractors require precise (or fine-tuned) weights in the neuronal connectivity of the circuit. It seems, a priori, unreasonable to think they are developmentally obtained, and a process requiring experience would be more likely. Hence the mechanism proposed by the authors is attractive and elegant.
In general, the manuscript is well written and structured. The work is of timely interest, especially since the insect head direction cell circuit is currently receiving much attention.
-