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

Experimental data obtained in single-particle tracking experiments are challenging to interpret. The authors propose an approach for determining the dynamics of the stochastic motion of molecules based on the power spectrum, relevant to various non-stationary scale-free random walks. 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 scale-free 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.

Automated summary

Interpreting experimental data from single-particle tracking experiments is challenging. The authors proposed a new method based on power spectrum to determine the dynamics of stochastic motion of molecules. They used the aging Wiener-Khinchin theorem to derive the power spectral density of fractional Brownian motion coexisting with a scale-free continuous time random walk.