Analyzing molecular diffusion using detrended fluctuation analysis

Abstract

The temporal series signal of a diffusing single molecule generated by a simple random walk program is analyzed using a scaling analysis method known as detrended fluctuation analysis (DFA). We characterize the molecules diffusing inside a microscope focal spot using a correlation parameter which can categorize the type of motion the molecules undergo. When used with noisy signals, changes in the correlation exponents reveal the existence of crossover points – transition points dividing the series where the noise or the signal dominates. This analysis is further applied to biased molecular diffusion in the presence of flow gradients which disclosed regions of changing correlation exponents even in the absence of noise.