Emergence of time persistence in a data-driven neural network model
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Evaluation Summary:
The authors show that how high-dimensional neural signals can be reduced to low-dimensional models with variables that can be directly linked to behavior. The reduced model can account for long timescales of persistent activity that arise from transisions between metastable model states. The authors further show that the rate of these transitions is modulated by water temperature according to the classic Arrhenius law.
(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. The reviewers remained anonymous to the authors.)
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Abstract
Establishing accurate as well as interpretable models of network activity is an open challenge in systems neuroscience. Here, we infer an energy-based model of the anterior rhombencephalic turning region (ARTR), a circuit that controls zebrafish swimming statistics, using functional recordings of the spontaneous activity of hundreds of neurons. Although our model is trained to reproduce the low-order statistics of the network activity at short time scales, its simulated dynamics quantitatively captures the slowly alternating activity of the ARTR. It further reproduces the modulation of this persistent dynamics by the water temperature and visual stimulation. Mathematical analysis of the model unveils a low-dimensional landscape-based representation of the ARTR activity, where the slow network dynamics reflects Arrhenius-like barriers crossings between metastable states. Our work thus shows how data-driven models built from large neural populations recordings can be reduced to low-dimensional functional models in order to reveal the fundamental mechanisms controlling the collective neuronal dynamics.
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Evaluation Summary:
The authors show that how high-dimensional neural signals can be reduced to low-dimensional models with variables that can be directly linked to behavior. The reduced model can account for long timescales of persistent activity that arise from transisions between metastable model states. The authors further show that the rate of these transitions is modulated by water temperature according to the classic Arrhenius law.
(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. The reviewers remained anonymous to the authors.)
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Reviewer #1 (Public Review):
The authors aimed at explaining the origin of the persistent activity observed in neural populations recorded from larval zebrafish, its dependence on the temperature of the water the fish was immersed in, and the effects of visual stimulation. They deploy a popular data-driven model to capture the statistical structure of large neural populations, fitting a maximum entropy model (Ising model) to the average activity and pairwise correlation of recorded neurons. Using mean field methods, they reduce this high-dimensional model to two dimensions, describing the average activities of populations in the left and right hemispheres. Both the high and low dimensional models are capable of generating the long timescale of persistent activity, even though they were only trained to learn the static mean and pairwise …
Reviewer #1 (Public Review):
The authors aimed at explaining the origin of the persistent activity observed in neural populations recorded from larval zebrafish, its dependence on the temperature of the water the fish was immersed in, and the effects of visual stimulation. They deploy a popular data-driven model to capture the statistical structure of large neural populations, fitting a maximum entropy model (Ising model) to the average activity and pairwise correlation of recorded neurons. Using mean field methods, they reduce this high-dimensional model to two dimensions, describing the average activities of populations in the left and right hemispheres. Both the high and low dimensional models are capable of generating the long timescale of persistent activity, even though they were only trained to learn the static mean and pairwise correlation structure. The crucial theoretical insight is that this long timescale emerges from the energy landscape of the reduced model in terms of stochastic transitions between metastable attractors following the well known Arrhenius law. The height of the barriers separating the attractors is modulated by water temperature, explaining the change in transition times and persistent activity. The model can also explain the dependence of persistent activity on the water temperature.
The major strength of the present work is that, by using a simple and well motivated statistical model (maximum entropy model) based on minimal assumptions, the authors are able to quantitatively reproduce complex spatiotemporal effects of fish behavior. The authors explain why this is the case due to the emergence of metastable dynamics based on stochastic transitions between local minima of the free energy. This classic model is very easily interpretable and of wide appeal for the neuroscience and larger life science community.
In my opinion, the current manuscript has three main weaknesses. The first one is that the model fit and its comparison to the data is not cross-validated and thus likely affected by overfitting. I strongly recommend recasting all results in terms of comparison of cross-validated observables. The second weakness is the fact that it is not explained how the water temperature appears in the model, which is the central quantity whose dependence they aim to model. There is a significant confusion on issues of water temperature vs. temperature in the model Gibbs measure. The author should make sure this point gets clarified. The third weakness is that, although the authors claim that the sign of the difference between the mean population activities of left and right hemispheres is the observables that determines whether the fish is going to change swimming directions, they don't actually provide direct evidence for this, but only compare the statistical distribution of this observable with the behavioral distribution. I recommend the authors explicitly test the predictive nature of the neural observable by showing that changes in swim directions are temporally aligned to the onset of a sign change.
If the results still stand after applying cross-validation, which I believe is a quite likely outcome, I believe this manuscript will have a strong impact in the field since they demonstrated the power of a principled and well-known approach in capturing complex spatiotemporal activity of large neural populations. This work has the potential to be widely adopted and generalized to many different directions in systems neuroscience and beyond.
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Reviewer #2 (Public Review):
This article by Wolf et al. provides an interesting interpretation of time persistence in a data-driven network model. The authors first engaged the widely used Ising-model, and were able to replicate not only short term but also long term dynamical features of the ARTR neural network of larval zebrafish changing with bath temperature. Such models have been used to model, for example, retinal activity at snapshots in time, but as stated by the authors have not been used to simulate temporal network dynamics. The authors then engaged mean-field theory by simplifying and approximating the learned matrix from the Ising model into a few parameters, to calculate a 2D free-energy landscape using left and right ARTR signals, in order to explain the time persistence of the network model from an energy barrier …
Reviewer #2 (Public Review):
This article by Wolf et al. provides an interesting interpretation of time persistence in a data-driven network model. The authors first engaged the widely used Ising-model, and were able to replicate not only short term but also long term dynamical features of the ARTR neural network of larval zebrafish changing with bath temperature. Such models have been used to model, for example, retinal activity at snapshots in time, but as stated by the authors have not been used to simulate temporal network dynamics. The authors then engaged mean-field theory by simplifying and approximating the learned matrix from the Ising model into a few parameters, to calculate a 2D free-energy landscape using left and right ARTR signals, in order to explain the time persistence of the network model from an energy barrier standpoint.
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