The effect of localisation imprecision on quantification of the directionality of motion for single particle tracking...

The tracking of single molecules, nanoparticles, or even intracellular vesicles using microscopy is a common approach across different fields of science. In such applications, invariably the particle can only be localised with finite precision, leading to an associated error in all observables of the motion. While the effect of localisation imprecision in, for example, the mean square displacement is well understood, the situation is less clear when it comes to assessments of the directionality of motion. Here we study the role played by localisation imprecision for several different measures of the directionality of motion. We study stationary particles and particles moving by Brownian motion both experimentally and theoretically. We show that localisation imprecision alone gives rise to a substantial degree of anti-directional motion. Comparison between theory and experiments shows excellent agreement, implying a good understanding and control of the effect. Overall, our results can be used to predict the role played by localisation imprecision when studying the directionality of motion using single particle tracking and suggest caution when interpreting such data.