Christophe Magnani ^* Lee E Moore

• Centre Borelli, Université Paris Cité, UMR 9010, CNRS, Paris, France, Paris, France

This article develops a fundamental insight into the behavior of neuronal membranes, focusing on their responses to stimuli measured with power spectra in the frequency domain. It explores the use of linear and nonlinear (quadratic sinusoidal analysis) approaches to characterize neuronal function. It further delves into the random theory of internal noise of biological neurons and the use of stochastic Markov models to investigate these fluctuations. The text also discusses the origin of conductance noise and compares different power spectra for interpreting this noise. Importantly, it introduces a novel sequential chemical state model, named p 2 , which is more general than the Hodgkin-Huxley formulation, so that the probability for an ion channel to be open does not imply exponentiation. In particular, it is demonstrated that the p 2 (without exponentiation) and n 4 (with exponentiation) models can produce similar neuronal responses. A striking relationship is also shown between fluctuation and quadratic power spectra, suggesting that voltage-dependent random mechanisms can have a significant impact on deterministic nonlinear responses, themselves known to have a crucial role in the generation of action potentials in biological neural networks.