Interactions between circuit architecture and plasticity in a closed-loop cerebellar system
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Payne et al. present a novel model that predicts the sites and directions of plasticity within the vestibular cerebellum to explain the basis for learned adjustments to reflexive eye movements in monkeys. The work is solid; the model is well constrained by prior biological observations and makes an important prediction about the level of feedback available to the cerebellar cortex post-learning. Overall, a number of exciting and testable experiments will likely be motivated by this study.
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Abstract
Determining the sites and directions of plasticity underlying changes in neural activity and behavior is critical for understanding mechanisms of learning. Identifying such plasticity from neural recording data can be challenging due to feedback pathways that impede reasoning about cause and effect. We studied interactions between feedback, neural activity, and plasticity in the context of a closed-loop motor learning task for which there is disagreement about the loci and directions of plasticity: vestibulo-ocular reflex learning. We constructed a set of circuit models that differed in the strength of their recurrent feedback, from no feedback to very strong feedback. Despite these differences, each model successfully fit a large set of neural and behavioral data. However, the patterns of plasticity predicted by the models fundamentally differed, with the direction of plasticity at a key site changing from depression to potentiation as feedback strength increased. Guided by our analysis, we suggest how such models can be experimentally disambiguated. Our results address a long-standing debate regarding cerebellum-dependent motor learning, suggesting a reconciliation in which learning-related changes in the strength of synaptic inputs to Purkinje cells are compatible with seemingly oppositely directed changes in Purkinje cell spiking activity. More broadly, these results demonstrate how changes in neural activity over learning can appear to contradict the sign of the underlying plasticity when either internal feedback or feedback through the environment is present.
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Author Response
Reviewer #1 (Public Review):
Payne et al. have investigated the neural basis of VOR adaptation with the goal of constraining sites and mechanisms of plasticity supporting cerebellar learning. This has been an area of intense debate for decades; previous competing models have argued extensively about the sites of plasticity and the strength of eye velocity feedback/ efference copy signals to Purkinje cells has been central to the debate. This paper nicely explores the consequences of varying the strength of this feedback and in so doing, provides a potential explanation for why Purkinje cell responses during VOR cancellation could exhibit stronger responses following learning, despite net depression of the strength of their vestibular inputs. In that sense it provides some reconciliation of existing models. The …
Author Response
Reviewer #1 (Public Review):
Payne et al. have investigated the neural basis of VOR adaptation with the goal of constraining sites and mechanisms of plasticity supporting cerebellar learning. This has been an area of intense debate for decades; previous competing models have argued extensively about the sites of plasticity and the strength of eye velocity feedback/ efference copy signals to Purkinje cells has been central to the debate. This paper nicely explores the consequences of varying the strength of this feedback and in so doing, provides a potential explanation for why Purkinje cell responses during VOR cancellation could exhibit stronger responses following learning, despite net depression of the strength of their vestibular inputs. In that sense it provides some reconciliation of existing models. The work appears to be well done and the paper is well written. The manuscript could be improved and the significance of the work clarified and enhanced by contextualizing the work more appropriately within the existing literature in this area.
We thank the reviewer for the nice summary of this work’s contribution to the long-standing debate regarding sites and mechanisms of plasticity underlying cerebellar learning.
We have revised the manuscript to address several key points raised by the reviewer. We now emphasize that the main evidence for weak feedback arises from interpreting our model in the context of the existing experimental evidence for plasticity rules in the cerebellar cortex, and we have clarified the commonalities and differences from the Miles-Lisberger model. Several missing references are now included. Additionally, we clarify the comparison of our model to data after learning, and explain how altered signaling through the visual pathways drives paradoxical changes in neural activity without requiring plasticity in the visual pathways. We hope that these changes better situate the work to be interpreted appropriately in the context of the existing literature.
Reviewer #2 (Public Review):
Payne et al. use a computational approach to predict the sites and directions of plasticity within the vestibular cerebellum that explain an unresolved controversy regarding the basis of VOR learning. Specifically, the conclusion by Miles and Lisberger (1981) that vestibular inputs onto Purkinje cells (PCs) must potentiate, rather than depress (as in the Marr/Albus/Ito model), following gain-increase learning because when the VOR is cancelled, PC firing increases rather than decreases. Payne et al. provide a novel model solution that recapitulates the results of Miles and Lisberger but, paradoxically, uses plasticity in the cerebellar cortex that weakens PC output rather than strengthens it. However, the model only succeeds when efference copy feedback to the cerebellar cortex is relatively weak thereby allowing a second feedback pathway to drive PC activity during VOR cancellation to counteract the learned change in gain. Because the model is biologically constrained, the findings are well supported. This work will likely benefit the field by providing a number of potentially experimentally testable conclusions. The findings will be of interest to a wider audience if the results can be extrapolated to other cerebellar-dependent learning behaviors rather then just VOR gain-increase learning. Overall, the manuscript is very well written with clearly delineated results and conclusions.
We appreciate the reviewer’s comments that the model is well-constrained and provides a solution to the long-standing debate surrounding sites and directions of plasticity underlying VOR learning.
The reviewer raises an important question: do our results generalize across the cerebellum? We note first that we are studying the cerebellum to illustrate a core problem in modeling systems throughout the brain, namely, how to disambiguate plasticity in the face of ubiquitous feedback loops, both within the brain and between the brain and the environment. Within the cerebellum, we focused on VOR learning due to the wealth of experimental data available. While the specific effect of feedback strength on plasticity will depend on the details of the relevant cerebellar circuit, our general approach can be applied to other areas, given sufficient data, in order to determine how plasticity is distributed in the face of potential feedback loops. Importantly, error-driven LTD of the parallel fiber-Purkinje cell synapse is a fundamental hypothesized mechanism for cerebellar learning which has been generally accepted elsewhere in the cerebellum, but was called into question for VOR learning in the flocculus by the Miles-Lisberger model. Thus, our study of VOR learning has broad implications for reconciling plasticity mechanisms across the cerebellum.
We also note that, even within the VOR circuit, the direction of plasticity and the relative dependence on plasticity at each site may depend on the timescale of learning. On longer timescales, there is thought to be consolidation of learning from a cerebellar cortical site to a brainstem site. Such consolidation from a faster-learning site to a slower-learning site is known as systems consolidation and has been shown theoretically to mitigate the ‘plasticity-stability dilemma’ of having fast learning without over-writing longer-term learning. Our model is compatible with both error-driven plasticity in the cerebellar cortex and a site of plasticity in the brainstem, with brainstem plasticity potentially mediating consolidation of earlier learned changes in the cerebellar cortex. We have now updated the text significantly to discuss the broader implications of the results and to address the reviewer’s specific comments.
Reviewer #3 (Public Review):
Summary: In this study, the authors attempt to determine what is the role (and strength) of feedback in a closed-loop (cerebellar) system.
Strengths:
- By combining extensive data fitting of cerebellar experimental observations this study provides deep insights into existing questions and more broadly on the role of feedback and what are the limitations when inferring feedback in (plastic) neural circuits.
- Another strength of this study is the gradual build-up of evidence by using models of different complexities to help build the argument that weak feedback is sufficient to explain experimental observations.
- The paper is well-written and structured.
Weaknesses:
- In principle feedback can (i) drive dynamics or/and (ii) drive learning directly. Throughout the paper, the authors refer to only the first case (i.e. dynamics). However, the role of feedback in learning is already implicitly assumed by the authors when jointly fitting the model before and after learning. Note that the general conclusion that feedback (in general) is weak may be to the first view (i.e. dynamics), but not the second. Given that a key conclusion of the paper is that no feedback is sufficient to explain the data, this suggests that feedback may instead be used for learning/plasticity.
We fully agree with the reviewer that our conclusions do not preclude an important role for many other types of feedback, including as an instructive signal for learning. Instead of explicitly considering feedback for learning in our model, we consider static snapshots before and after learning to infer plasticity, while remaining agnostic to the neural algorithm used to achieve such plasticity. A widely held hypothesis is that motor error signals carried by climbing fibers instruct LTD at co-active parallel fiber inputs to Purkinje cells; this is indeed a form of feedback, operating on a slower timescale than “feedback for dynamics.” This “feedback for learning” is not modeled here but is fully consistent with our results, as discussed in a new paragraph of our Discussion (end of Section 3.4.1 “Pathways undergoing plasticity”).
- There are some potential limitations of the conclusions drawn due to the model inference methods used. The methods used (fmincon) can easily get stuck in local minima and more importantly they do not provide an overview of the likelihood of parameters given the data. A few studies have now shown that it is important to apply more powerful inference techniques both to infer plasticity (Bykowska et al. Frontiers 2019) and neural dynamics (Gonçalves et al. eLife 2020). As highlighted by Costa et al. Frontiers 2013 using more standard fitting methods can lead to misleading interpretations. Given the large range of experimental data used to constrain the model, this may not be an issue, but it is not explicitly shown.
The reviewer correctly points out that we used a deterministic model-fitting procedure. To address this concern, we complemented the full dynamic model with a simple analytic model ( Figure 5 ) for which we could fully derive the cost function landscape and analytically show that there is a line of parameters corresponding to a perfect degeneracy in the model. Thus, the challenge in the model we analyze is that there are too many solutions, rather than it being difficult to find a solution. Given this degeneracy, we chose to fix the level of efference copy feedback and then find the (now non-degenerate) solutions, and to then compare these different solutions with regards to their implications for the correlated strengths and changes in strengths of different pathways. We have edited the relevant section of the Discussion for clarity on this topic, and have added references to the additional strategies for model inference mentioned above, in Section 3.3 “Relation to other sloppy models”.
- There is some lack of clarity on how the feedback pathways as currently presented should be interpreted in the brain.
We interpret this comment as referring to the questions of (1) whether our model includes a pathway for learning through feedback, (2) what is the anatomical implementation of the efference copy feedback pathway and visual pathways, and (3) how should the positive weights on the efference copy feedback pathway k PE be interpreted. We address these below.
(1) Feedback for learning was discussed in point 1 above.
(2) Anatomical implementation of efference copy pathway: We have edited the Discussion to clarify that there is anatomical evidence for efference copy input to the cerebellum, but that a key aspect of ‘feedback’ is that activity functionally loops back onto itself. Instead, neurons carrying eye movement commands (such as in the vestibular nucleus) could send signals to the cerebellum, without receiving output from the same cerebellar neurons – this would correspond to a ‘spiraling’ pathway that does not form a closed feedback loop (Figure 8). Thus we argue that the existence of the gross anatomical pathways does not necessitate a role for strong, functional, efference copy feedback (Discussion, Section 3.1, lines 481-491).
Anatomical implementation of visual pathway: The visual feedback pathways considered here are those that would receive visual motion information from the environment. This visual feedback is itself changed by eye movements, thus providing a net overall negative feedback loop that helps to stabilize gaze. This pathway has been proposed to involve cortical regions such as MST (discussed in Materials and Methods, Model Implementation, lines 769-774).
(3) Interpretation of positive feedback loop: In our model, the efference copy feedback filter, k PE , has positive weight. This corresponds to the positive net sign of the Purkinje cell to brainstem to Purkinje cell feedback loop. Specifically, the Purkinje cell to brainstem pathway is inhibitory (because Purkinje cells are inhibitory), the brainstem to eye velocity command pathway is inhibitory (to achieve counter-rotation of the eyes in response to head turns), and the feedback of this eye velocity command back to Purkinje cells (k PE ) is positive. Thus this loop in our model represents positive feedback. This is now clarified in Materials and Methods, Model Implementation, lines 748.
- The functional benefits of having (or not) feedback could be better discussed (related to point 1 above).
Related to point 1 above, it is certainly the case that feedback is necessary for learning. We do not explicitly model the climbing fiber feedback thought to be involved in learning/plasticity of the parallel fiber pathway.
We instead focus on the role of efference copy feedback, and how it functionally impacts the required sites and signs of plasticity in the circuit. As shown in the paper, if the efference copy pathway is strong, then this is most consistent with learned changes in eye movements being driven primarily by plasticity in the brainstem pathway (as in the Miles-Lisberger hypothesis), whereas if the efference copy pathway is weak, then this is most consistent with learned changes in eye movements being driven by net depression in the parallel fiber to Purkinje cell pathway (as in the classic Marr-Albus-Ito model and as suggested by most cellular and molecular studies of parallel fiber-Purkinje cell plasticity), in addition to a role of plasticity in the brainstem pathway. We also note that, in the ‘Strong Feedback’ model, the feedback is so strong that the system is on the brink of instability – this has been argued to have the functional benefit of providing ‘inertia’ to eye movements that could help to maintain eye movements during smooth pursuit when a target goes behind an occluder, but it also has the disadvantage of placing the system at a level of positive feedback near the brink of instability. We also note that the visual feedback pathway through the environment, emphasized in this work, serves as a negative feedback loop that reduces deviations between the eye and target velocity. We have extensively re-written the first section of the Discussion (Section 3.1), in order to more clearly lay out the implications of each model for circuit plasticity and feedback.
- Some of the key conclusions of the work are not described in the abstract, namely that feedback is weak in the cerebellar system.
Thank you for raising this point, we have added this key conclusion to the end of the abstract: “Our results address a long-standing debate regarding cerebellum-dependent motor learning, suggesting a reconciliation in which error-driven plasticity of synaptic inputs to Purkinje cells is compatible with seemingly oppositely directed changes in Purkinje cell activity. More broadly, the results demonstrate how learning-related changes in neural activity can appear to contradict the sign of the underlying plasticity when either internal feedback or feedback through the environment is present.”
Claims:
The argument is well-built throughout the paper, but there are some potential caveats with the general interpretation (see weaknesses).
Impact:
This work has the potential to bring important messages on how best to interpret and infer the role of feedback in neural systems. For the field of the cerebellum, it also proposes solutions to long-standing problems.
-
eLife assessment
Payne et al. present a novel model that predicts the sites and directions of plasticity within the vestibular cerebellum to explain the basis for learned adjustments to reflexive eye movements in monkeys. The work is solid; the model is well constrained by prior biological observations and makes an important prediction about the level of feedback available to the cerebellar cortex post-learning. Overall, a number of exciting and testable experiments will likely be motivated by this study.
-
Reviewer #1 (Public Review):
Payne et al. have investigated the neural basis of VOR adaptation with the goal of constraining sites and mechanisms of plasticity supporting cerebellar learning. This has been an area of intense debate for decades; previous competing models have argued extensively about the sites of plasticity and the strength of eye velocity feedback/ efference copy signals to Purkinje cells has been central to the debate. This paper nicely explores the consequences of varying the strength of this feedback and in so doing, provides a potential explanation for why Purkinje cell responses during VOR cancellation could exhibit stronger responses following learning, despite net depression of the strength of their vestibular inputs. In that sense it provides some reconciliation of existing models. The work appears to be well …
Reviewer #1 (Public Review):
Payne et al. have investigated the neural basis of VOR adaptation with the goal of constraining sites and mechanisms of plasticity supporting cerebellar learning. This has been an area of intense debate for decades; previous competing models have argued extensively about the sites of plasticity and the strength of eye velocity feedback/ efference copy signals to Purkinje cells has been central to the debate. This paper nicely explores the consequences of varying the strength of this feedback and in so doing, provides a potential explanation for why Purkinje cell responses during VOR cancellation could exhibit stronger responses following learning, despite net depression of the strength of their vestibular inputs. In that sense it provides some reconciliation of existing models. The work appears to be well done and the paper is well written. The manuscript could be improved and the significance of the work clarified and enhanced by contextualizing the work more appropriately within the existing literature in this area.
-
Reviewer #2 (Public Review):
Payne et al. use a computational approach to predict the sites and directions of plasticity within the vestibular cerebellum that explain an unresolved controversy regarding the basis of VOR learning. Specifically, the conclusion by Miles and Lisberger (1981) that vestibular inputs onto Purkinje cells (PCs) must potentiate, rather than depress (as in the Marr/Albus/Ito model), following gain-increase learning because when the VOR is cancelled, PC firing increases rather than decreases. Payne et al. provide a novel model solution that recapitulates the results of Miles and Lisberger but, paradoxically, uses plasticity in the cerebellar cortex that weakens PC output rather than strengthens it. However, the model only succeeds when efference copy feedback to the cerebellar cortex is relatively weak thereby …
Reviewer #2 (Public Review):
Payne et al. use a computational approach to predict the sites and directions of plasticity within the vestibular cerebellum that explain an unresolved controversy regarding the basis of VOR learning. Specifically, the conclusion by Miles and Lisberger (1981) that vestibular inputs onto Purkinje cells (PCs) must potentiate, rather than depress (as in the Marr/Albus/Ito model), following gain-increase learning because when the VOR is cancelled, PC firing increases rather than decreases. Payne et al. provide a novel model solution that recapitulates the results of Miles and Lisberger but, paradoxically, uses plasticity in the cerebellar cortex that weakens PC output rather than strengthens it. However, the model only succeeds when efference copy feedback to the cerebellar cortex is relatively weak thereby allowing a second feedback pathway to drive PC activity during VOR cancellation to counteract the learned change in gain. Because the model is biologically constrained, the findings are well supported. This work will likely benefit the field by providing a number of potentially experimentally testable conclusions. The findings will be of interest to a wider audience if the results can be extrapolated to other cerebellar-dependent learning behaviors rather then just VOR gain-increase learning. Overall, the manuscript is very well written with clearly delineated results and conclusions.
-
Reviewer #3 (Public Review):
Summary: In this study, the authors attempt to determine what is the role (and strength) of feedback in a closed-loop (cerebellar) system.
Strengths:
1. By combining extensive data fitting of cerebellar experimental observations this study provides deep insights into existing questions and more broadly on the role of feedback and what are the limitations when inferring feedback in (plastic) neural circuits.
2. Another strength of this study is the gradual build-up of evidence by using models of different complexities to help build the argument that weak feedback is sufficient to explain experimental observations.
3. The paper is well-written and structured.
Weaknesses:
1. In principle feedback can (i) drive dynamics or/and (ii) drive learning directly. Throughout the paper, the authors refer to only the …
Reviewer #3 (Public Review):
Summary: In this study, the authors attempt to determine what is the role (and strength) of feedback in a closed-loop (cerebellar) system.
Strengths:
1. By combining extensive data fitting of cerebellar experimental observations this study provides deep insights into existing questions and more broadly on the role of feedback and what are the limitations when inferring feedback in (plastic) neural circuits.
2. Another strength of this study is the gradual build-up of evidence by using models of different complexities to help build the argument that weak feedback is sufficient to explain experimental observations.
3. The paper is well-written and structured.
Weaknesses:
1. In principle feedback can (i) drive dynamics or/and (ii) drive learning directly. Throughout the paper, the authors refer to only the first case (i.e. dynamics). However, the role of feedback in learning is already implicitly assumed by the authors when jointly fitting the model before and after learning. Note that the general conclusion that feedback (in general) is weak may be to the first view (i.e. dynamics), but not the second. Given that a key conclusion of the paper is that no feedback is sufficient to explain the data, this suggests that feedback may instead be used for learning/plasticity.
2. There are some potential limitations of the conclusions drawn due to the model inference methods used. The methods used (fmincon) can easily get stuck in local minima and more importantly they do not provide an overview of the likelihood of parameters given the data. A few studies have now shown that it is important to apply more powerful inference techniques both to infer plasticity (Bykowska et al. Frontiers 2019) and neural dynamics (Gonçalves et al. eLife 2020). As highlighted by Costa et al. Frontiers 2013 using more standard fitting methods can lead to misleading interpretations. Given the large range of experimental data used to constrain the model, this may not be an issue, but it is not explicitly shown.
3. There is some lack of clarity on how the feedback pathways as currently presented should be interpreted in the brain.
4. The functional benefits of having (or not) feedback could be better discussed (related to point 1 above).
5. Some of the key conclusions of the work are not described in the abstract, namely that feedback is weak in the cerebellar system.
Claims:
The argument is well-built throughout the paper, but there are some potential caveats with the general interpretation (see weaknesses).
Impact:
This work has the potential to bring important messages on how best to interpret and infer the role of feedback in neural systems. For the field of the cerebellum, it also proposes solutions to long-standing problems.
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