Microscopic theory of intrinsic timescales in spiking neural networks

A complex interplay of single-neuron properties and the recurrent network structure shapes activity cortical neurons. The statistics differ in general from respective population statistics, including spectra and, correspondingly, autocorrelation times. We develop a theory for self-consistent second-order block-structured sparse random networks spiking In particular, predicts neuron-level times, also known as intrinsic timescales, neuronal activity. is based on an extension dynamic mean-field rate to networks, which validated via simulations. It accounts both static variability, e.g., due distributed number incoming synapses per neuron, temporal fluctuations input. apply balanced generalized linear model neurons, leaky integrate-and-fire biologically constrained For with error function nonlinearity, novel analytical solution colored noise problem allows us obtain firing distributions, power spectra, timescales. we derive approximate problem, Stratonovich approximation Wiener-Rice series free upcrossing statistics. Again closing system self-consistently, fluctuation-driven regime, this yields reliable estimates mean its variance across interspike-interval distribution, With help our theory, find parameter regimes where timescale significantly exceeds membrane time constant, indicates influence dynamics. Although resulting timescales are same order neurons two systems fundamentally: former, longer arises increased probability after spike; latter, it consequence prolonged effective refractory period decreased probability. Furthermore, attains maximum at critical synaptic strength contrast minimum found networks.