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

Two-dimensional Brownian motion of anisotropic dimers

We study the two-dimensional motion of colloidal dimers by single-particle tracking and compare the experimental observations obtained by bright-field microscopy to theoretical predictions for anisotropic diffusion. The comparison is based on the mean-square displacements in the laboratory and particle frame as well as generalizations of the self-intermediate scattering functions, which provide insights into the rotational dynamics of the dimer. The diffusional anisotropy leads to a measurable translational-rotational coupling that becomes most prominent by aligning the coordinate system with the initial orientation of the particles. In particular, we find a splitting of the time-dependent diffusion coefficients parallel and perpendicular to the long axis of the dimer which decays over the orientational relaxation time. Deviations of the self-intermediate scattering functions from pure exponential relaxation are small but can be resolved experimentally. The theoretical predictions and experimental results agree quantitatively.

Anisotropic diffusion of membrane proteins at experimental timescales

Single-particle tracking (SPT) experiments of lipids and membrane proteins provide a wealth of information about the properties of biomembranes. Careful analysis of SPT trajectories can reveal deviations from ideal Brownian behavior. Among others, this includes confinement effects and anomalous diffusion, which are manifestations of both the nanoscale structure of the underlying membrane and the structure of the diffuser. With the rapid increase in temporal and spatial resolution of experimental methods, a new aspect of the motion of the particle, namely, anisotropic diffusion, might become relevant. This aspect that so far received only little attention is the anisotropy of the diffusive motion and may soon provide an additional proxy to the structure and topology of biomembranes. Unfortunately, the theoretical framework for detecting and interpreting anisotropy effects is currently scattered and incomplete. Here, we provide a computational method to evaluate the degree of anisotropy directly from molecular dynamics simulations and also point out a way to compare the obtained results with those available from SPT experiments. In order to probe the effects of anisotropic diffusion, we performed coarse-grained molecular dynamics simulations of peripheral and integral membrane proteins in flat and curved bilayers. In agreement with the theoretical basis, our computational results indicate that anisotropy can persist up to the rotational relaxation time [τ=(2D_r)^-1], after which isotropic diffusion is observed. Moreover, the underlying topology of the membrane bilayer can couple with the geometry of the particle, thus extending the spatiotemporal domain over which this type of motion can be detected.

Characterization of aqueous cellulose nanofiber dispersions from microscopy movie data of Brownian particles by trajectory analysis

Cellulose nanofibers (CNFs) are promising for various applications such as substrates of flexible devices and reinforcement materials. Most of these applications require control of the drying process of the aqueous CNF dispersions. However, the existing reports examine the surface of dried materials because scanning electron microscopy (SEM) and atomic force microscopy (AFM) are not compatible with either the wet conditions or structure inside the materials. We report the characterization of these aqueous dispersions by the use of optical microscopy although it cannot be used directly to observe CNFs. We add a small portion of colloidal particles into the samples and obtain their trajectory data. The trajectories of Brownian motion include information on the surrounding environments. We analyze the microscopy movie data from the viewpoint of statistical mechanics, and reveal the mesoscale characteristics beyond viscosity. In particular, the possible non-uniformity of the dispersion is quantitatively examined through the framework of the generalized diffusion.

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

We propose a novel approach to analyze random walks in heterogeneous medium using a hybrid machine-learning method based on a gamma mixture and a hidden Markov model. A gamma mixture and a hidden Markov model respectively provide the number and the most probable sequence of diffusive states from the time series position data of particles/molecules obtained by single-particle/molecule tracking (SPT/SMT) method. We evaluate the performance of our proposed method for numerically generated trajectories. It is shown that our proposed method can correctly extract the number of diffusive states when each trajectory is long enough to be frame averaged. We also indicate that our method can provide an indicator whether the assumption of a medium consisting of discrete diffusive states is appropriate or not based on the available amount of trajectory data. Then, we demonstrate an application of our method to the analysis of experimentally obtained SPT data.

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

We report that the addition of a small amount of cellulose nanofibers (CNFs) into an aqueous dispersion of colloidal particles suppresses the coffee-ring effect when the dispersion dries on a solid substrate, as revealed by the computational analysis of experimental time-series images and by particle image velocimetry. The addition of CNFs is much more effective than the increase of colloidal particle concentration at the same weight percentage; it is also more environment friendly than the use of typical molecular surfactants. This finding is promising for the fabrication of metamaterials from colloidal dispersions and for ink printing in electronics, where CNFs can also serve as a substrate for flexible devices.

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

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.

Evaluation of bacterial motility from non-Gaussianity of finite-sample trajectories using the large deviation principle

Motility of bacteria is usually recognized in the trajectory data and compared with Brownian motion, but the diffusion coefficient is insufficient to evaluate it. In this paper, we propose a method based on the large deviation principle. We show that it can be used to evaluate the non-Gaussian characteristics of model Escherichia coli motions and to distinguish combinations of the mean running duration and running speed that lead to the same diffusion coefficient. Our proposed method does not require chemical stimuli to induce the chemotaxis in a specific direction, and it is applicable to various types of self-propelling motions for which no a priori information of, for example, threshold parameters for run and tumble or head/tail direction is available. We also address the issue of the finite-sample effect on the large deviation quantities, but we propose to make use of it to characterize the nature of motility.