Statistical modelling of subdiffusive dynamics in the cytoplasm of living cells: A FARIMA approach

Hugo Steinhaus Center, Institute of Mathematics and Computer Science, Wroclaw University of Technology Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland, EU

^a krzysztof.burnecki@pwr.wroc.pl

Received: 10 January 2012
Accepted: 1 March 2012

Abstract

Golding and Cox (Phys. Rev. Lett., 96 (2006) 098102) tracked the motion of individual fluorescently labelled mRNA molecules inside live E. coli cells. They found that in the set of 23 trajectories from 3 different experiments, the automatically recognized motion is subdiffusive and published an intriguing microscopy video. Here, we extract the corresponding time series from this video by image segmentation method and present its detailed statistical analysis. We find that this trajectory was not included in the data set already studied and has different statistical properties. It is best fitted by a fractional autoregressive integrated moving average (FARIMA) process with the normal-inverse Gaussian (NIG) noise and the negative memory. In contrast to earlier studies, this shows that the fractional Brownian motion is not the best model for the dynamics documented in this video.