Michael A. Buice

A well-defined stochastic theory for neural activity, which permits the calculation of arbitrary statistical moments and equations governing them, is a potentially valuable tool for theoretical neuroscience. We produce such a theory by analyzing the dynamics of neural activity using field theoretic methods for nonequilibrium statistical processes. Assuming that neural network activity is Markovian, we construct the effective spike model, which describes both neural fluctuations and response. This analysis leads to a systematic expansion of corrections to mean field theory, which for the effective spike model is a simple version of the Wilson-Cowan equation. We argue that neural activity governed by this model exhibits a dynamical phase transition which is in the universality class of directed percolation. More general models (which may incorporate refractoriness) can exhibit other universality classes, such as dynamic isotropic percolation. Because of the extremely high connectivity in typical networks, it is expected that higher-order terms in the systematic expansion are small for experimentally accessible measurements, and thus, consistent with measurements in neocortical slice preparations, we expect mean field exponents for the transition. We provide a quantitative criterion for the relative magnitude of each term in the systematic expansion, analogous to the Ginsburg criterion. Experimental identification of dynamic universality classes in vivo is an outstanding and important question for neuroscience.

Fluorescent calcium indicators are often used to investigate neural dynamics, but the relationship between fluorescence and action potentials (APs) remains unclear. Most APs can be detected when the soma almost fills the microscope's field of view, but calcium indicators are used to image populations of neurons, necessitating a large field of view, generating fewer photons per neuron, and compromising AP detection. Here, we characterized the AP-fluorescence transfer function in vivo for 48 layer 2/3 pyramidal neurons in primary visual cortex, with simultaneous calcium imaging and cell-attached recordings from transgenic mice expressing GCaMP6s or GCaMP6f. While most APs were detected under optimal conditions, under conditions typical of population imaging studies, only a minority of 1 AP and 2 AP events were detected (often <10% and ~20-30%, respectively), emphasizing the limits of AP detection under more realistic imaging conditions.