Emergent topological structure in spontaneous brain-organoid activity

Abstract

Neural activity is widely held to organize on low-dimensional structure embedded in a high-dimensional state space. Persistent homology reads such structure directly from the pattern of pairwise correlations, without assuming in advance which variables are relevant. We apply persistent homology to microelectrode-array (MEA) recordings of spontaneous activity from human (Lancaster) and mouse (Pasca) cortical organoids, spanning 25-197 sorted units, and ask whether topological data analysis resolves structure at the node counts that neural recordings actually deliver. Building weighted networks in correlation space and characterizing them by Vietoris-Rips filtration, we find that the first homology (H1, loops) rises significantly above a rate- and population-preserving null in 14 of 18 datasets, all of which remain significant after correction for testing 18 datasets. Random removal of neural units leaves the loops largely intact. Removing the units that form the loops disrupts them more than removing equally connected units does. Topological richness grows with network size, and second homology (H2) exceeds the null only in the larger networks. These results show that persistent homology resolves structured topology in neural recordings at the scale experiments actually deliver.