Quadratic Sinusoidal Analysis of Neurons in Voltage Clamp

TL;DR

This paper introduces a quadratic analysis method for voltage-clamped neurons, extending traditional linear models to better capture nonlinear properties using analytical and matrix calculus approaches.

Contribution

It presents a novel quadratic characterization technique for neurons, moving beyond linear models with analytical and matrix calculus methods.

Findings

Quadratic responses effectively characterize neuron nonlinearities.

The methods work on both recorded data and neuron models.

Enhanced understanding of neuron biophysical properties.

Abstract

Nonlinear biophysical properties of individual neurons are known to play a major role in the nervous system. Earlier electrophysiological studies have made use of piecewise linear characterization of voltage clamped neurons, which consists of a sequence of linear admittances computed at different voltage levels. In this paper, the linear approach is extended to a piecewise quadratic characterization in two different ways. First, an analytical model is derived with power series following the work pionneered by Fitzhugh. Second, matrix calculus is developed to provide a novel quantitative analysis not dependent on differential equations. This method provides an assessment of quadratic responses for both data recorded from individual neurons and their corresponding models.