Global organization of neuronal activity only requires unstructured local connectivity
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Evaluation Summary:
This paper details coordinated work to both measure and model long-range correlations in the primate brain, during either rest or a reach-to-grasp task. The careful analysis shows that these long-range correlations are modulated by behavioral state, and can exist in the absence of common input or long-range anatomical connections. An analytical model is developed that shows how a disordered system with heterogeneous connections can give rise to this kind of long-range correlations, with only short-range direct connections between neurons.
(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
Modern electrophysiological recordings simultaneously capture single-unit spiking activities of hundreds of neurons spread across large cortical distances. Yet, this parallel activity is often confined to relatively low-dimensional manifolds. This implies strong coordination also among neurons that are most likely not even connected. Here, we combine in vivo recordings with network models and theory to characterize the nature of mesoscopic coordination patterns in macaque motor cortex and to expose their origin: We find that heterogeneity in local connectivity supports network states with complex long-range cooperation between neurons that arises from multi-synaptic, short-range connections. Our theory explains the experimentally observed spatial organization of covariances in resting state recordings as well as the behaviorally related modulation of covariance patterns during a reach-to-grasp task. The ubiquity of heterogeneity in local cortical circuits suggests that the brain uses the described mechanism to flexibly adapt neuronal coordination to momentary demands.
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Author Response:
Joint Public Review:
In this manuscript, the authors analyze multiunit data recorded from macaque motor cortex, and compare the data with theoretical results of a network model that is close to a critical point. Their analysis uncovers two main features of the data: (1) Covariances between spike counts of pairs of neurons depend only weakly on distance, while one would expect a much stronger dependence given the scale of local axonal and dendritic arborizations; (2) Patterns of covariances are dynamic, and differ significantly between different epochs of the behavioral task.
To understand these findings, they turn to a spatially extended network model. The analysis of this model is performed using an extension of tools introduced by a subset of the authors in a recent publication, that analyzed a network with no …
Author Response:
Joint Public Review:
In this manuscript, the authors analyze multiunit data recorded from macaque motor cortex, and compare the data with theoretical results of a network model that is close to a critical point. Their analysis uncovers two main features of the data: (1) Covariances between spike counts of pairs of neurons depend only weakly on distance, while one would expect a much stronger dependence given the scale of local axonal and dendritic arborizations; (2) Patterns of covariances are dynamic, and differ significantly between different epochs of the behavioral task.
To understand these findings, they turn to a spatially extended network model. The analysis of this model is performed using an extension of tools introduced by a subset of the authors in a recent publication, that analyzed a network with no spatial structure. The authors show that the first feature can be obtained in their model provided the network is close to a critical point, and that the second feature is also observed in their network when external inputs to the network are epoch-dependent.
The recordings are from a standard Utah array and reveal correlations across millimeters during either rest or the task. While the heavy-tailed distribution of both positive and negative correlation is striking, it is not unexpected. Long-range anatomical connections cannot be completely ruled out.
The modeling and analytical results reveal how a network with spatially heterogeneous connections can give rise to a heavy-tailed scaling in the correlation. While long-range correlations arising from a disordered model near a critical point are not surprising, the analytical results obtained here are thorough and show how to obtain rigorous approximations even with heterogeneous 2D models.
The results that the long-range covariance structure in the primate cortex changes during different stages of a reach-to-grasp task is the most intriguing finding in the paper. While more needs to be done to reveal the "why" of this change in network structure and its impact on neural computation, this work shows that this kind of careful dissection of network state should be explored further.
The generality of the result beyond motor cortex is argued for and reasonable, though other data would be needed to substantiate this claim.
We thank the reviewers for this summary to which we agree overall. We would only like to comment on two points:
1.) The long-range correlations are found with either sign and similar magnitude, independent of the involved neuron types (excitatory / inhibitory). In the revised version we discuss that one would expect i) different long-range correlations for excitatory and inhibitory neurons if correlations were predominantly driven by long-range connections; ii) Correlation patterns should be more static, if they were caused by direct connections. Still, of course we agree that long-range connections definitely should have an effect on the investigated measures and their analysis is highly interesting, but also challenging.
2.) The positive and negative long-range correlations of equal magnitude are a specific feature of the critical point generated by the disorder in the studied system; this is why our work required the development of new theory. This feature also distinguishes the proposed mechanism of critical dynamics from criticality in homogeneous systems, where long-range correlations are typically positive.
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Evaluation Summary:
This paper details coordinated work to both measure and model long-range correlations in the primate brain, during either rest or a reach-to-grasp task. The careful analysis shows that these long-range correlations are modulated by behavioral state, and can exist in the absence of common input or long-range anatomical connections. An analytical model is developed that shows how a disordered system with heterogeneous connections can give rise to this kind of long-range correlations, with only short-range direct connections between neurons.
(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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Joint Public Review:
In this manuscript, the authors analyze multiunit data recorded from macaque motor cortex, and compare the data with theoretical results of a network model that is close to a critical point. Their analysis uncovers two main features of the data: (1) Covariances between spike counts of pairs of neurons depend only weakly on distance, while one would expect a much stronger dependence given the scale of local axonal and dendritic arborizations; (2) Patterns of covariances are dynamic, and differ significantly between different epochs of the behavioral task.
To understand these findings, they turn to a spatially extended network model. The analysis of this model is performed using an extension of tools introduced by a subset of the authors in a recent publication, that analyzed a network with no spatial structure. The …
Joint Public Review:
In this manuscript, the authors analyze multiunit data recorded from macaque motor cortex, and compare the data with theoretical results of a network model that is close to a critical point. Their analysis uncovers two main features of the data: (1) Covariances between spike counts of pairs of neurons depend only weakly on distance, while one would expect a much stronger dependence given the scale of local axonal and dendritic arborizations; (2) Patterns of covariances are dynamic, and differ significantly between different epochs of the behavioral task.
To understand these findings, they turn to a spatially extended network model. The analysis of this model is performed using an extension of tools introduced by a subset of the authors in a recent publication, that analyzed a network with no spatial structure. The authors show that the first feature can be obtained in their model provided the network is close to a critical point, and that the second feature is also observed in their network when external inputs to the network are epoch-dependent.
The recordings are from a standard Utah array and reveal correlations across millimeters during either rest or the task. While the heavy-tailed distribution of both positive and negative correlation is striking, it is not unexpected. Long-range anatomical connections cannot be completely ruled out.
The modeling and analytical results reveal how a network with spatially heterogeneous connections can give rise to a heavy-tailed scaling in the correlation. While long-range correlations arising from a disordered model near a critical point are not surprising, the analytical results obtained here are thorough and show how to obtain rigorous approximations even with heterogeneous 2D models.
The results that the long-range covariance structure in the primate cortex changes during different stages of a reach-to-grasp task is the most intriguing finding in the paper. While more needs to be done to reveal the "why" of this change in network structure and its impact on neural computation, this work shows that this kind of careful dissection of network state should be explored further.
The generality of the result beyond motor cortex is argued for and reasonable, though other data would be needed to substantiate this claim.
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