Abstract
Spatiotemporal correlations in brain activity are functionally important and have been implicated in perception, learning and plasticity, exploratory behavior, and various aspects of cognition. Neurons in the cerebral cortex are strongly interacting. Their activity is temporally irregular and can exhibit substantial correlations. However, how the collective dynamics of highly recurrent and strongly interacting neurons can evolve into a state in which the activity of individual cells is highly irregular yet macroscopically correlated is an open question. Here, we develop a general theory that relates the strength of pairwise correlations to the anatomical features of networks of strongly coupled neurons. To this end, we investigate networks of binary units. When interactions are strong, the activity is irregular in a large region of parameter space. We find that despite the strong interactions, the correlations are generally very weak. Nevertheless, we identify architectural features, which if present, give rise to strong correlations without destroying the irregularity of the activity. For networks with such features, we determine how correlations scale with the network size and the number of connections. Our work shows the mechanism by which strong correlations can be consistent with highly irregular activity, two hallmarks of neuronal dynamics in the central nervous system.
- Received 24 August 2017
- Revised 15 March 2018
DOI:https://doi.org/10.1103/PhysRevX.8.031072
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
The ability of our brains to perform complex functions is thought to rely on spatiotemporal activation of ensembles of neurons. Neurons respond in a nonlinear way to their inputs, and these inputs depend on how neurons are interconnected. Thus, the interplay between neuronal properties and network architecture determines the collective network dynamics. Here, we develop a general theory that relates the spatial coherence of the activity in a network of several neuronal populations to its architecture. This allows us to answer a long-standing question in theoretical neuroscience: How can the activity of single neurons be temporally irregular and spatially coherent on macroscopic scales.
We study the dynamics of spatially structured networks consisting of strongly interacting neurons. Previous works have shown that in such networks single-neuron activity is temporally highly irregular. Our key result is the proof of two theorems according to which macroscopically correlated activity can arise only in specific network architectures. In general, because of loops in the connectivity, the network dynamics reverberates, preventing the buildup of coherence in the network. However, macroscopically correlated activity arises in structured networks when the architecture embeds a group of neurons connected to other groups in a unidirectional manner without reverberations. This feed-forward structure can be explicit or hidden.
Our work gives insights into the key architectural features that determine the dynamical states of the brain, and it should soon be testable thanks to advances in technologies that will make it possible to simultaneously record the activity of many neurons as well as reconstruct features of the network connectivity.
