Aging power spectrum of membrane protein transport and other subordinated random walks

TL;DR

This paper develops a method to analyze the power spectral density of complex, non-stationary anomalous diffusion processes like fractional Brownian motion and continuous time random walks, applied to neuronal sodium channel data.

Contribution

It introduces the aging Wiener-Khinchin theorem to derive power spectral densities for non-stationary processes, enabling better interpretation of single-particle tracking data.

Findings

Power spectral density can increase or decrease with observation time depending on parameters.

Aging effects are observed in the motion of sodium channels on hippocampal neurons.

The method provides new insights into non-stationary anomalous diffusion processes.

Abstract

Single-particle tracking offers detailed information about the motion of molecules in complex environments such as those encountered in live cells, but the interpretation of experimental data is challenging. One of the most powerful tools in the characterization of random processes is the power spectral density. However, because anomalous diffusion processes in complex systems are usually not stationary, the traditional Wiener-Khinchin theorem for the analysis of power spectral densities is invalid. Here, we employ a recently developed tool named aging Wiener-Khinchin theorem to derive the power spectral density of fractional Brownian motion coexisting with a scalefree continuous time random walk, the two most typical anomalous diffusion processes. Using this analysis, we characterize the motion of voltage-gated sodium channels on the surface of hippocampal neurons. Our results show aging where the power spectral density can either increase or decrease with observation time depending on the specific parameters of both underlying processes.