Abstract
Topological data analyses are widely used for describing and conceptualizing large volumes of neurobiological data, e.g., for quantifying spiking outputs of large neuronal ensembles and thus understanding the functions of the corresponding networks. Below we discuss an approach in which convergent topological analyses produce insights into how information may be processed in mammalian hippocampus—a brain part that plays a key role in learning and memory. The resulting functional model provides a unifying framework for integrating spiking data at different timescales and following the course of spatial learning at different levels of spatiotemporal granularity. This approach allows accounting for contributions from various physiological phenomena into spatial cognition—the neuronal spiking statistics, the effects of spiking synchronization by different brain waves, the roles played by synaptic efficacies and so forth. In particular, it is possible to demonstrate that networks with plastic and transient synaptic architectures can encode stable cognitive maps, revealing the characteristic timescales of memory processing.
Highlights
Spatial cognition in mammals is based on an internal representation of their environments—a cognitive map—used for spatial planning, navigating paths, finding shortcuts, remembering the location of the home nest, food sources and so forth
Methods of the Persistent Homology theory allow describing the dynamics of the topological loops in T, e.g., evaluating the minimal time Tmin after which the topological structure of T matches the topology of the environment, bn(T ) = bn(E) (De Silva and Ghrist, 2007; Curto and Itskov, 2008; Dabaghian et al, 2012)
First, the model can incorporate a vast scope of physiologically relevant characteristics of spike times, spiking statistics, their modulations by the “brain waves,” efficacies of synaptic connections, architectures of the neuronal networks, etc., all of which correlate with dynamics of spatial learning
Summary
Spatial cognition in mammals is based on an internal representation of their environments—a cognitive map—used for spatial planning, navigating paths, finding shortcuts, remembering the location of the home nest, food sources and so forth. A central role in producing these maps is played by the hippocampal neurons famous for their spatially tuned spiking activity. In rats, these neurons, known as “place cells,” fire in specific domains of the navigated environment—their respective “place fields” (O’Keefe and Nadel, 1978; Moser et al, 2008). It is believed that the information provided by the individual place cells is somehow combined into single coherent whole This “fusion” should not be viewed as a naïve aggregation of the smaller “pieces,” because the signals provided by the individual neurons have no intrinsic spatial attributes; rather, spatial properties are emergent, i.e., appearing at a neuronal ensemble level (Wilson and McNaughton, 1993; Pouget et al , 2000; Postle, 2006). We outline several examples that demonstrate how various characteristics of individual cells and synapses can be incorporated into the model and what effect these “microscopic” parameters produce at a “macroscale,” i.e., in the map that they jointly encode
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