Uncovering Network Architecture Using an Exact Statistical Input-Output Relation of a Neuron Model

Identifying network architecture from recorded neural activity is one of the major challenges in neuroscience. A key requirement for this challenge is the knowledge of the statistical input-output relation of single neurons operating under in vivo conditions. However, lack of analytical representation even for a standard neuron model prohibited theoretical investigations. Recently we provided an exact analytical solution of spike timing for a leaky integrate-and-fire (LIF) neuron responding to synaptic inputs under noisy background input balanced near the threshold [Shomali et. al., J Comput Neurosci 44, (2018): 147]. Using that solution, we construct a unified framework that links synaptic inputs, nonlinearity of spiking, network architecture, and statistics of population activity. With this approach, we theoretically predict correlated population activity of in vivo neurons that receive common inputs under different network architectures. It allows us to present a quantitative method to unveil the network architecture behind the sparse population activity ubiquitously observed in visual and hippocampal neurons. We show that two motifs can disclose this activity: Inhibitory common inputs to three (or more) neurons or excitatory common inputs to pairs of neurons. By comparing model prediction with empirical observation of monkey V1 neurons [Ohiorhenuan et. al., Nature 466, (2010): 617], we quantitatively rule out the scenario that common inhibition causes the observed sparse activity characterized by negative triple-wise interactions among the neurons. Instead, we show that an alternative architecture with common excitatory inputs to pairs of neurons well explains it. The proposed analytical approach that connects neural mechanisms with neural interactions could serve as a useful tool to probe network architecture, using recordings of population activity.