Recent developments in experimental neuroscience make it possible to simultaneously record the activity of thousands of neurons. However, the development of analysis approaches for such large-scale neural recordings have been slower than those applicable to single-cell experiments. One approach that has gained recent popularity is neural manifold learning. This approach takes advantage of the fact that often, even though neural datasets may be very high dimensional, the dynamics of neural activity tends to traverse a much lower-dimensional space. The topological structures formed by these low-dimensional neural subspaces are referred to as “neural manifolds”, and may potentially provide insight linking neural circuit dynamics with cognitive function and behavioral performance. In this paper we review a number of linear and non-linear approaches to neural manifold learning, including principal component analysis (PCA), multi-dimensional scaling (MDS), Isomap, locally linear embedding (LLE), Laplacian eigenmaps (LEM), t-SNE, and uniform manifold approximation and projection (UMAP). We outline these methods under a common mathematical nomenclature, and compare their advantages and disadvantages with respect to their use for neural data analysis. We apply them to a number of datasets from published literature, comparing the manifolds that result from their application to hippocampal place cells, motor cortical neurons during a reaching task, and prefrontal cortical neurons during a multi-behavior task. We find that in many circumstances linear algorithms produce similar results to non-linear methods, although in particular cases where the behavioral complexity is greater, non-linear methods tend to find lower-dimensional manifolds, at the possible expense of interpretability. We demonstrate that these methods are applicable to the study of neurological disorders through simulation of a mouse model of Alzheimer’s Disease, and speculate that neural manifold analysis may help us to understand the circuit-level consequences of molecular and cellular neuropathology.

The study of social dominance interactions between animals offers a window onto the decision-making involved in establishing dominance hierarchies and an opportunity to examine changes in social behavior observed in certain neurogenetic disorders. Competitive social interactions, such as in the widely used tube test, reflect this decision-making. Previous studies have focused on the different patterns of behavior seen in the dominant and submissive animal, neural correlates of effortful behavior believed to mediate the outcome of such encounters, and interbrain correlations of neural activity. Using a rigorous mutual information criterion, we now report that neural responses recorded with endoscopic calcium imaging in the prelimbic zone of the medial prefrontal cortex show unique correlations to specific dominance-related behaviors. Interanimal analyses revealed cell/behavior correlations that are primarily with an animal’s own behavior or with the other animal’s behavior, or the coincident behavior of both animals (such as pushing by one and resisting by the other). The comparison of unique and coincident cells helps to disentangle cell firing that reflects an animal’s own or the other’s specific behavior from situations reflecting conjoint action. These correlates point to a more cognitive rather than a solely behavioral dimension of social interactions that needs to be considered in the design of neurobiological studies of social behavior. These could prove useful in studies of disorders affecting social recognition and social engagement, and the treatment of disorders of social interaction.

A challenge in spatial memory is understanding how place cell firing contributes to decision-making in navigation. A spatial recency task was created in which freely moving rats first became familiar with a spatial context over several days and thereafter were required to encode and then selectively recall one of three specific locations within it that was chosen to be rewarded that day. Calcium imaging was used to record from more than 1,000 cells in area CA1 of the hippocampus of five rats during the exploration, sample, and choice phases of the daily task. The key finding was that neural activity in the startbox rose steadily in the short period prior to entry to the arena and that this selective population cell firing was predictive of the daily changing goal on correct trials but not on trials in which the animals made errors. Single-cell and population activity measures converged on the idea that prospective coding of neural activity can be involved in navigational decision-making.