Self-organization of high-dimensional geometry of neural activity in culture

A vast number of neurons exhibit high-dimensional coordination for brain computation, both in processing sensory input and in generating spontaneous activity without external stimuli. Recent advancements in large-scale recordings have revealed that this high-dimensional population activity exhibits a scale-free structure, characterized by power law and distinct spatial patterns in principal components (PCs). However, the mechanisms underlying the formation of this high-dimensional neural coordination remain poorly understood. Specifically, it is unclear whether the characteristic high-dimensional structure of population activity emerges through self-organization or is shaped by the learning of sensory stimuli in animals. To address this question and clearly differentiate between these two possibilities, we investigated large-scale neural activity in dissociated neuronal culture using high-density multi-electrode arrays. Our findings demonstrate that the high-dimensional structure of neural activity self-organizes during network development in the absence of explicit sensory stimuli provided to animals. As the cultures mature, the PC variance exhibits a power-law decay, and the spatial structures of PCs transition from global to localized patterns, driven by the temporal correlations of neural activity. Furthermore, we observed an unexpected co-occurrence between the power-law decay in PCA and neuronal avalanches, suggesting a link between self-organized criticality and high-dimensional activity. To uncover the mechanism behind this co-occurrence, we developed a new theoretical framework and demonstrated that it arises from heavy-tailed synaptic connectivity. By highlighting a developmental origin of the high-dimensional structure of neural activity, these findings deepen our understanding of how coordinated neural computations are achieved in the brain. SignificanceOne of the most intriguing questions in neuroscience is how the extremely high-dimensional yet efficiently orchestrated coordination of neural activity is organized. Central to this question lies the "nature versus nurture" debate: Is the high-dimensional coordination self-organized during development, or is it acquired through learning in animals? We take a novel approach by applying cutting-edge analytical techniques to study high-dimensional neural activity in dissociated neuronal cultures. Our findings reveal that fundamental features characterizing the high-dimensional coordination of neurons, including the scale-free geometry of the neural manifold and the intrinsic spatial structure of neural dynamics, are self-organized without sensory stimuli. Remarkably, we also discover that this high-dimensional geometry emerges concurrently with neuronal avalanches, a hallmark of self-organized criticality in neural circuits.