Recovery of stimuli encoded with a Hodgkin-Huxley neuron using conditional PRCs

Abstract

Understanding neural encoding/decoding mechanisms is one of the most fundamental problems in the field of sensory neuroscience. The Hodgkin–Huxley equations provide an explicit description of an encoding mechanism. However, the daunting complexity of the Hodgkin–Huxley equations makes the task of recovery of stimuli encoded with a Hodgkin–Huxley neuron particularly challenging. A highly effective strategy calls for reducing the Hodgkin–Huxley neuron to a project-integrate-and-fire (PIF) neuron. Using the reduced PIF model, we present three different recovery algorithms for stimuli encoded with a Hodgkin-Huxley neuron. All algorithms reconstruct the stimuli from the neuron’s output spike train. The first algorithm is based on the assumption that the Hodgkin–Huxley neuron has a known PRC. The second algorithm assumes that the PRC is conditionally known on each interspike time interval. Finally, the third algorithm operates under the assumption that the conditional PRC is unknown and has to be estimated. We establish an estimate of the conditional PRC based upon the readily observable inter-spike time interval. We compare the performance of these algorithms for a wide range of input stimuli.