An Integral Equation Approach to the Dynamics of L2-3 Cortical Neurons

How do neuronal populations encode time-dependent stimuli in their population firing rate? To address this question, I consider the quasi-renewal equation and the event-based expansion, two theoretical approximations proposed recently, and test these against peri-stimulus time histograms from L2-3 pyramidal cells in vitro. Parameters are optimized by gradient descent to best match the firing rate output given the current input. The fitting method can estimate single-neuron parameters that are normally obtained either with intracellular recordings or with individual spike trains. I find that quasi-renewal theory predicts the adapting firing rate with good precision but not the event-based expansion. Quasi-renewal predictions are equal in quality with state-of-the-art spike timing prediction methods, and does so without resorting to the indiviual spike times or the membrane potential responses.