Collective Behavior and Scaling in Large Populations of Hippocampal Neurons

Abstract

Recent technological breakthroughs in large-scale neural recordings enable us to monitor simultaneously the activity of thousands of neurons. To shed light on the collective nature of the activity in these large populations of cells, we seek theoretical approaches that will help us simplify the rich dynamics they exhibit. We focus on optical imaging experiments of dorsal hippocampus in mice as they run along a virtual linear track. First, we build minimal models to capture the activity in populations of ~80 neurons. About half the neurons in these networks are place cells - neurons that become active only when the animal enters a particular location in its environment. However, many of the neurons are not place cells in any given environment. We use maximum entropy models which approximate the distribution of activity patterns in these mixed populations, by matching the correlations between pairs of cells but otherwise assuming as little structure as possible. Despite their simplicity, the models capture the higher-order structure of activity patterns in the population, quantitatively. Moreover, they show that place and non{place neurons encode information collectively. Our results suggest that understanding the neural activity may require not only knowledge of the external variables modulating it but also of the internal network state. Next, we study hippocampal populations on larger scale - over 1000 neurons. In many large scale non-biological systems that consist of many interacting units, it is possible to describe emergent macroscopic behaviors, quantitatively, using models that are much simpler than the underlying microscopic interactions; we understand the success of this simplification through the renormalization group concept. We develop explicit coarse-graining procedures that we apply to the activity in these large hippocampal populations. We see evidence of power-law dependencies in both static and dynamic quantities as we vary the coarse-graining scale over two decades. Furthermore, probability distributions of coarse-grained variables seem to approach a fixed non-Gaussian form. Taken together, the success of these strategies in capturing essential properties of population-level neural activity encourages us to think that simpler theories of neural network dynamics are possible.