Detection of Transition Times from Single-particle-tracking Trajectories

Abstract

In heterogeneous environments, the diffusivity is not constant but changes with time. It is important to detect changes in the diffusivity from single-particle-tracking trajectories in experiments. Here, we devise a novel method for detecting the transition times of the diffusivity from trajectory data. A key idea of this method is the introduction of a characteristic time scale of the diffusive states, which is obtained by a fluctuation analysis of the time-averaged mean square displacements. We test our method in silico by using the Langevin equation with a fluctuating diffusivity. We show that our method can successfully detect the transition times of diffusive states and obtain the diffusion coefficient as a function of time. This method will provide a quantitative description of the fluctuating diffusivity in heterogeneous environments and can be applied to time series with transitions of states.

arXiv comment11 pages, 4 figures

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• Scattering fingerprints of two-state dynamics
• Diffusion of intrinsically disordered proteins within viscoelastic membraneless droplets
• Objective comparison of methods to decode anomalous diffusion
• Anomalous statistics in the Langevin equation with fluctuating diffusivity: from Brownian yet non-Gaussian diffusion to anomalous diffusion and ergodicity breaking
• Two-dimensional Brownian motion with dependent components: turning angle analysis
• Estimating relaxation times from a single trajectory