Faster Convergence of Diffusion Anisotropy Detection by Three-Step Relation of Single-Particle Trajectory

Abstract

We focus on the issue of limited number of samples in the single particle tracking (SPT) when trying to extract the diffusion anisotropy that originates from the particle asymmetry. We propose a novel evaluation technique of SPT making use of the relation of the consecutive three steps. More specifically, the trend of the angle comprised of the three positions and the displacements are plotted on a scatter diagram. The particle anisotropy dependence of the shape of the scatter diagram is examined through the data from the standard numerical model of anisotropic two-dimensional Brownian motion. Comparison with the existing method reveals the faster convergence in the evaluation. In particular, our proposed method realizes the detection of diffusion anisotropy under the conditions of not only less number of data but also larger time steps. This is of practical importance not only when the abundant data is hard to achieve but also when the rotational diffusion is fast compared to the frame rate of the camera equipment, which tends to be more common for smaller particles or molecules of interest.

Suppressing the coffee-ring effect of colloidal droplets by dispersed cellulose nanofibers

“…Recently, it has been reported that controlling the shape of particles, more specifically changing spherical particles into prolate ones, can prevent the coffee-ring effect [23]. The non-spherical shape of the particles leads to the characteristic capillary effect and anisotropy in Brownian motion [24,25]. While the control of shape is promising when it is possible, it is not trivial to apply the technique to arbitrary materials.…”

Robust evaluation of diffusion coefficient against displacement threshold parameter of single particle tracking algorithm

“…There are several other techniques to evaluate diffusion coefficients of particles in fluids, but the trajectories include more information besides diffusion coefficients. Namely, it is possible to evaluate diffusion anisotropy of prolate particles [6, 7], possible motility and its characteristics [8], and the evaluation of surface effects [9, 10] from the ensemble of trajectories. Therefore, single particle/molecule tracking (SPT/SMT) has been a standard and effective approach to analyse the small particle dynamics suspended in fluids.…”

Estimation of diffusive states from single-particle trajectory in heterogeneous medium using machine-learning methods

“…20,22,23 By substituting % d(t j ) for x j , g(z nk ) is calculated by eqn (12) as the E step. Then, as the M step, a new , b new , and p new are calculated from eqn (20), (19) and (16), respectively. In the GMM, the maximum likelihood parameters are obtained by the iterative calculation of the E and M steps.…”

“…To analyze SPT/SMT trajectories containing adsorption/desorption motion and diffusion anisotropy, several analysis methods have been developed. [14][15][16][17][18][19][20] In the past few years, new approaches based on Bayesian and machine-learning methods have been developed. Metzner et al 21 developed a Bayesian inference method based on a timediscrete Ornstein-Uhlenbeck process.…”