State-space methods for inferring synaptic inputs and weights

First, we discuss methods for optimally inferring the synaptic inputs to an electrotonically compact neuron, given intracellular voltage-clamp or current-clamp recordings from the postsynaptic cell. These methods are based on sequential Monte Carlo techniques (“particle filtering”). We demonstrate on model data that these methods can accurately recover the time course of excitatory and inhibitory synaptic inputs on a single trial; no averaging over multiple trials is necessary. Once these synaptic input time courses are recovered, it becomes possible to fit (via tractable convex optimization techniques) simple models describing the relationship between the sensory stimulus and the observed synaptic input. We develop an expectationmaximization (EM) algorithm that consists of alternating iterations between these synaptic recovery and model estimation steps. These proposed methods have direct and immediate applications to understanding the balance between excitation and inhibition in sensory processing in vivo.