Abstract
Large-scale neural recording methods now allow us to observe large populations of identified single neurons simultaneously, opening a window into neural population dynamics in living organisms. However, distilling such large-scale recordings to build theories of emergent collective dynamics remains a fundamental statistical challenge. The neural field models of Wilson, Cowan, and colleagues remain the mainstay of mathematical population modeling owing to their interpretable, mechanistic parameters and amenability to mathematical analysis. Inspired by recent advances in biochemical modeling, we develop a method based on moment closure to interpret neural field models as latent state-space point-process models, making them amenable to statistical inference. With this approach we can infer the intrinsic states of neurons, such as active and refractory, solely from spiking activity in large populations. After validating this approach with synthetic data, we apply it to high-density recordings of spiking activity in the developing mouse retina. This confirms the essential role of a long lasting refractory state in shaping spatiotemporal properties of neonatal retinal waves. This conceptual and methodological advance opens up new theoretical connections between mathematical theory and point-process state-space models in neural data analysis.
Highlights
IntroductionUnderstanding the dynamics and physiology of collective spiking in large networks of neurons is a central challenge in modern neuroscience, with immense translational and clinical potential
Neurons communicate using electrical impulses, or spikes
Developing statistical tools to connect single-neuron activity to emergent collective dynamics is vital for building interpretable models of neural activity
Summary
Understanding the dynamics and physiology of collective spiking in large networks of neurons is a central challenge in modern neuroscience, with immense translational and clinical potential Modern technologies such as high-density multi-electrode arrays (HDMEA) enable the simultaneous recording of the electrical activity of thousands of interconnected neurons, promising invaluable insights into neural dynamics at the network level. Due to the complexity of the data, most analyses of neuronal population activity take a descriptive approach, adopting methods from statistical signal processing such as state-space models (SSM; [1,2,3,4,5,6,7]) or autoregressive generalized-linear point-process models (PP-GLM; [8,9,10,11]) Such methods capture the population statistics of the system, but fail to provide mechanistic explanations of the underlying neural dynamics. While this phenomenological description is valuable and can aid many investigations, the inability to relate microscopic singleneuron properties to emergent collective dynamics limits the scope of these models to extract biological insights from these large population recordings
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