Abstract
Learning arises through the activity of large ensembles of cells, yet most of the data neuroscientists accumulate is at the level of individual neurons; we need models that can bridge this gap. We have taken spatial learning as our starting point, computationally modeling the activity of place cells using methods derived from algebraic topology, especially persistent homology. We previously showed that ensembles of hundreds of place cells could accurately encode topological information about different environments (“learn” the space) within certain values of place cell firing rate, place field size, and cell population; we called this parameter space the learning region. Here we advance the model both technically and conceptually. To make the model more physiological, we explored the effects of theta precession on spatial learning in our virtual ensembles. Theta precession, which is believed to influence learning and memory, did in fact enhance learning in our model, increasing both speed and the size of the learning region. Interestingly, theta precession also increased the number of spurious loops during simplicial complex formation. We next explored how downstream readout neurons might define co-firing by grouping together cells within different windows of time and thereby capturing different degrees of temporal overlap between spike trains. Our model's optimum coactivity window correlates well with experimental data, ranging from ∼150–200 msec. We further studied the relationship between learning time, window width, and theta precession. Our results validate our topological model for spatial learning and open new avenues for connecting data at the level of individual neurons to behavioral outcomes at the neuronal ensemble level. Finally, we analyzed the dynamics of simplicial complex formation and loop transience to propose that the simplicial complex provides a useful working description of the spatial learning process.
Highlights
Considerable effort has been devoted over the years to understanding how the hippocampus is able to form an internal representation of the environment that enables an animal to efficiently navigate and remember the space [1]
The information encoded by the hippocampus would emphasize connectivity between places in the environment, which is a topological rather than a geometric quality of space [4]. One advantage of this line of reasoning is that a topological problem should be amenable to topological analysis, so we developed our model using conceptual tools from the field of algebraic topology and, in particular, persistent homology theory [6,7]
In previous work we created a computational model of spatial learning using concepts from the field of algebraic topology, proposing that the hippocampal map encodes topological features of an environment rather than precise metrics—more akin to a subway map than a street map
Summary
Considerable effort has been devoted over the years to understanding how the hippocampus is able to form an internal representation of the environment that enables an animal to efficiently navigate and remember the space [1]. In order to form an accurate spatial map within a biologically reasonable length of time, our simplified model hippocampus had to function within a certain range of values that turned out to closely parallel those obtained from actual experiments with healthy rodents. We called this sweet spot for spatial learning the learning region, L [4]. As long as the values of the three parameters
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