The neuron's response at extended timescales

TL;DR

This paper develops a method to analyze neuronal responses over extended timescales by deriving input-output relations for systems with slow modulations, revealing insights into neuronal memory, noise, and stability over days.

Contribution

It introduces a novel approach to derive the spiking input-output relation in non-linear systems with slow modulations, enabling analysis of long-term neuronal responses.

Findings

Reproduces the 1/f neuronal response observed over days

Quantifies neuronal memory, noise, and stability

Provides a framework for analyzing slow modulations in excitable systems

Abstract

Many systems are modulated by unknown slow processes. This hinders analysis in highly non-linear systems, such as excitable systems. We show that for such systems, if the input matches the sparse `spiky' nature of the output, the spiking input-output relation can be derived. We use this relation to reproduce and interpret the irregular and complex 1/f response observed in isolated neurons stimulated over days. We decompose the neuronal response into contributions from its long history of internal noise and its short (few minutes) history of inputs, quantifying memory, noise and stability.