Higher-Order Cumulants Drive Neuronal Activity Patterns, Inducing UP-DOWN States in Neural Populations

BARAVALLE, ROMAN; MONTANI, FERNANDO

ENTROPY

MOLECULAR DIVERSITY PRESERVATION INTERNATIONAL-MDPI

Año: 2020 vol. 22 p. 477 - 499

1099-4300

A major challenge in neuroscience is to understand the role of the higher-order correlationsstructure of neuronal populations. The dichotomized Gaussian model (DG) generates spike trains bymeans of thresholding a multivariate Gaussian random variable. The DG inputs are Gaussiandistributed, and thus have no interactions beyond the second order in their inputs; however,they can induce higher-order correlations in the outputs. We propose a combination of analytical andnumerical techniques to estimate higher-order, above the second, cumulants of the firing probabilitydistributions. Our findings show that a large amount of pairwise interactions in the inputs can inducethe system into two possible regimes, one with low activity (?DOWN state?) and another one withhigh activity (?UP state?), and the appearance of these states is due to a combination between thethird- and fourth-order cumulant. This could be part of a mechanism that would help the neuralcode to upgrade specific information about the stimuli, motivating us to examine the behavior ofthe critical fluctuations through the Binder cumulant close to the critical point. We show, using theBinder cumulant, that higher-order correlations in the outputs generate a critical neural system thatportrays a second-order phase transition.