The Hurst exponents of Nitzschia sp. diatom trajectories observed by light microscopy

TL;DR

This study analyzes the movement patterns of Nitzschia sp. diatoms using detrended fluctuation analysis, revealing persistent, active motility with long-range correlations and dependencies on trajectory features.

Contribution

It introduces a novel application of wavelet-optimized detrended fluctuation analysis to characterize diatom motility and provides quantitative Hurst parameters for their trajectories.

Findings

Diatom motion exhibits persistent, long-range correlated behavior.

Hurst parameters range between 0.63 and 0.70, indicating active motility.

Trajectory features influence Hurst exponent values.

Abstract

We present the results of an experiment with light microscopy performed to capture the trajectories of live Nitzschia sp. diatoms. The time series corresponding to the motility of this kind of cells along ninety-five circular-like trajectories have been obtained and analyzed with the scaling statistical method of detrended fluctuation analysis optimized via a wavelet transform. In this way, we determined the Hurst parameters, in two orthogonal directions, which characterize the nature of the motion of live diatoms in light microscopy experiments. We have found mean values of these directional Hurst parameters between 0.70 and 0.63 with overall standard errors below 0.15. These numerical values give evidence that the motion of Nitzschia sp. diatoms is of persistent type and suggest an active cell motility with a kind of memory associated with long-range correlations on the path of their trajectories. For the collected statistics, we also find that the values of the Hurst exponents depend on the number of abrupt turns that occur in the diatom trajectory and on the type of wavelet, although their mean values do not change much