Detection of diffusion anisotropy due to particle asymmetry from single-particle tracking of Brownian motion by the large-deviation principle.

We show that the diffusion anisotropy due to the asymmetry of the particle can be extracted from the trajectory data without the information of the particle orientation. The subject of analysis is typical in single-particle tracking (SPT) experiments, and the analysis is based on the large-deviation principle in mathematics. We consider the model system of Langevin equations in two dimensions where a particle diffusion shows anisotropy depending on a single parameter defined by the two diffusion coefficients in the perpendicular directions of the frame fixed to the particle. We show how the large-deviation quantities depend on this parameter so that it can be used for the detection of the diffusion anisotropy. We also illustrate how the discreteness of the sampling interval in the SPT and the finiteness of the number of samples influence the results of the analysis.