Neuronal dynamics across macroscopic timescales
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The brain operates in a world with rich dynamics across a wide range of timescales, including those on the order of seconds and above. Behavioral experiments on memory and timing reveal striking similarities in the behavioral patterns across a range of timescales from seconds to minutes. To subserve these behavioral patterns and adapt to natural statistics, the collective activity of the large of number of neurons in the brain should exhibit dynamics over these macroscopic timescales as well. Most established results in systems neuroscience concern the short-term responses of single neurons to static features of the world. Recently, new techniques for large-scale and chronic measurements of neural activity open up the opportunity to investigate neural dynamics across different macroscopic timescales. This dissertation presents work that reveals the temporal patterns of neural activity across a range of macroscopic timescales and explores their mechanistic basis. Chapter 1 briefly surveys the relevant empirical evidence, biophysical processes and modeling techniques. Chapter 2 presents a biophysically-realistic neural circuit model that combines a detailed simulation of a calcium-activated membrane current with the mathematical formalism of the inverse Laplace transform to produce sequential neural activity with a scale-invariant property. Chapter 3 is a theoretical analysis of the ability of linear recurrent neural networks to generate scale-invariant neural activity. It is shown that the network connectivity matrix should have a geometric series of eigenvalues and translated eigenvectors if the eigenvalues are real and distinct. Chapter 4 presents an empirical analysis of neural data motivated by the hypothesis that robust neural dynamics should simultaneously exist on multiple timescales. The analysis reveals the existence of repeatable neural dynamics on the timescale of both seconds and minutes in multiple neural recordings of rodents performing various cognitive tasks. Chapter 5 of the dissertation presents an initial effort to characterize the changes in the neural population activity during learning on the timescale of tens of minutes by analyzing neural recordings from monkeys while they learn associations between visual stimuli.
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