352 research outputs found
A topological paradigm for hippocampal spatial map formation using persistent homology
Extent: 14 p.An animal's ability to navigate through space rests on its ability to create a mental map of its environment. The hippocampus is the brain region centrally responsible for such maps, and it has been assumed to encode geometric information (distances, angles). Given, however, that hippocampal output consists of patterns of spiking across many neurons, and downstream regions must be able to translate those patterns into accurate information about an animal's spatial environment, we hypothesized that 1) the temporal pattern of neuronal firing, particularly co-firing, is key to decoding spatial information, and 2) since co-firing implies spatial overlap of place fields, a map encoded by co-firing will be based on connectivity and adjacency, i.e., it will be a topological map. Here we test this topological hypothesis with a simple model of hippocampal activity, varying three parameters (firing rate, place field size, and number of neurons) in computer simulations of rat trajectories in three topologically and geometrically distinct test environments. Using a computational algorithm based on recently developed tools from Persistent Homology theory in the field of algebraic topology, we find that the patterns of neuronal co-firing can, in fact, convey topological information about the environment in a biologically realistic length of time. Furthermore, our simulations reveal a “learning region” that highlights the interplay between the parameters in combining to produce hippocampal states that are more or less adept at map formation. For example, within the learning region a lower number of neurons firing can be compensated by adjustments in firing rate or place field size, but beyond a certain point map formation begins to fail. We propose that this learning region provides a coherent theoretical lens through which to view conditions that impair spatial learning by altering place cell firing rates or spatial specificity.Y. Dabaghian, F. Mémoli, L. Frank, G. Carlsso
Robust spatial memory maps encoded in networks with transient connections
The spiking activity of principal cells in mammalian hippocampus encodes an
internalized neuronal representation of the ambient space---a cognitive map.
Once learned, such a map enables the animal to navigate a given environment for
a long period. However, the neuronal substrate that produces this map remains
transient: the synaptic connections in the hippocampus and in the downstream
neuronal networks never cease to form and to deteriorate at a rapid rate. How
can the brain maintain a robust, reliable representation of space using a
network that constantly changes its architecture? Here, we demonstrate, using
novel Algebraic Topology techniques, that cognitive map's stability is a
generic, emergent phenomenon. The model allows evaluating the effect produced
by specific physiological parameters, e.g., the distribution of connections'
decay times, on the properties of the cognitive map as a whole. It also points
out that spatial memory deterioration caused by weakening or excessive loss of
the synaptic connections may be compensated by simulating the neuronal
activity. Lastly, the model explicates functional importance of the
complementary learning systems for processing spatial information at different
levels of spatiotemporal granularity, by establishing three complementary
timescales at which spatial information unfolds. Thus, the model provides a
principal insight into how can the brain develop a reliable representation of
the world, learn and retain memories despite complex plasticity of the
underlying networks and allows studying how instabilities and memory
deterioration mechanisms may affect learning process.Comment: 24 pages, 10 figures, 4 supplementary figure
The Importance of Forgetting: Limiting Memory Improves Recovery of Topological Characteristics from Neural Data
We develop of a line of work initiated by Curto and Itskov towards
understanding the amount of information contained in the spike trains of
hippocampal place cells via topology considerations. Previously, it was
established that simply knowing which groups of place cells fire together in an
animal's hippocampus is sufficient to extract the global topology of the
animal's physical environment. We model a system where collections of place
cells group and ungroup according to short-term plasticity rules. In
particular, we obtain the surprising result that in experiments with spurious
firing, the accuracy of the extracted topological information decreases with
the persistence (beyond a certain regime) of the cell groups. This suggests
that synaptic transience, or forgetting, is a mechanism by which the brain
counteracts the effects of spurious place cell activity
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