State-dependent coupling of hippocampal oscillations

Quantifying the distribution of feature values over data represented in arbitrary dimensional spaces

Identifying the structured distribution (or lack thereof) of a given feature over a point cloud is a general research question. In the neuroscience field, this problem arises while investigating representations over neural manifolds (e.g., spatial coding), in the analysis of neurophysiological signals (e.g., sensory coding) or in anatomical image segmentation. We introduce the Structure Index (SI) as a directed graph-based metric to quantify the distribution of feature values projected over data in arbitrary D-dimensional spaces (defined from neurons, time stamps, pixels, genes, etc). The SI is defined from the overlapping distribution of data points sharing similar feature values in a given neighborhood of the cloud. Using arbitrary data clouds, we show how the SI provides quantification of the degree and directionality of the local versus global organization of feature distribution. SI can be applied to both scalar and vectorial features permitting quantification of the relative contribution of related variables. When applied to experimental studies of head-direction cells, it is able to retrieve consistent feature structure from both the high- and low-dimensional representations, and to disclose the local and global structure of the angle and speed represented in different brain regions. Finally, we provide two general-purpose examples (sound and image categorization), to illustrate the potential application to arbitrary dimensional spaces. Our method provides versatile applications in the neuroscience and data science fields.

Topological analysis of sharp-wave ripple waveforms reveals input mechanisms behind feature variations

The reactivation of experience-based neural activity patterns in the hippocampus is crucial for learning and memory. These reactivation patterns and their associated sharp-wave ripples (SWRs) are highly variable. However, this variability is missed by commonly used spectral methods. Here, we use topological and dimensionality reduction techniques to analyze the waveform of ripples recorded at the pyramidal layer of CA1. We show that SWR waveforms distribute along a continuum in a low-dimensional space, which conveys information about the underlying layer-specific synaptic inputs. A decoder trained in this space successfully links individual ripples with their expected sinks and sources, demonstrating how physiological mechanisms shape SWR variability. Furthermore, we found that SWR waveforms segregated differently during wakefulness and sleep before and after a series of cognitive tasks, with striking effects of novelty and learning. Our results thus highlight how the topological analysis of ripple waveforms enables a deeper physiological understanding of SWRs.