Micro-heterogeneity metrics for diffusion in soft matter

Abstract

Passive particle tracking of diffusive paths in soft matter, coupled with analysis of the path data, is firmly established as a fundamental methodology for characterization of both diffusive transport properties (the focus here) and linear viscoelasticity. For either focus, particle time series are typically analyzed by ensemble averaging over paths, a perfectly natural protocol for homogeneous materials or for applications where mean properties are sufficient. Many biological materials, however, are heterogeneous over length scales above the probe diameter, and the implications of heterogeneity for biologically relevant transport properties (e.g. diffusive passage times through a complex fluid layer) motivate this paper. Our goals are three-fold: first, to detect heterogeneity as reflected by the ensemble path data; second, to further decompose the ensemble of particle paths into statistically distinct clusters; and third, to fit the path data in each cluster to a model for the underlying stochastic process. After reviewing current best practices for detection and assessment of heterogeneity in diffusive processes, we introduce our strategy toward the first two goals with methods from the statistics and machine learning literature that have not found application thus far to passive particle tracking data. We apply an analysis based solely on the path data that detects heterogeneity and yields a decomposition of particle paths into statistically distinct clusters. After these two goals are achieved, one can then pursue model-fitting. We illustrate these heterogeneity metrics on diverse datasets: for numerically generated and experimental particle paths, with tunable and unknown heterogeneity, on numerical models for simple diffusion and anomalous sub-diffusion, and experimentally on sucrose, hyaluronic acid, agarose, and human lung culture mucus solutions.

Evolution of hierarchical porous structures in supramolecular guest–host hydrogels

“…46, 47 Thus, diffusive microbead rheology was explored herein, as it enables facile investigation and precision suitable to discern changes in viscosity resulting from small changes in HA concentrations. 48, 49 …”

Minimizing biases associated with tracking analysis of submicron particles in heterogeneous biological fluids

“…S6). Alternatively, Savin and Doyle previously proposed applying a normalized weight proportional to the duration of each trajectory to individual particle data before summing to obtain the mean MSD [32], and Mellnik et al presented a method of analyzing trajectories grouped into statistically distinct clusters [41]. While these techniques are adept at deriving unbiased ensemble or cluster averages, they are not yet widely adopted, and may not readily provide an unbiased representation of heterogeneity in particle transport behavior, including the instantaneous distribution of particle transport rates.…”

A high throughput array microscope for the mechanical characterization of biomaterials

“…Collecting data over a range of heights for complex biomaterials like mucus will empower us to better study its spatial heterogeneity, a property studied for its influence on mucociliary clearance. 20 Future investigations include using the AHT system to examine the biophysical properties of cells, HA, and other soft biomaterials that are treated by small molecule or genetic knockdown libraries. Large scale studies enabled by the AHT system hold promise of elucidating the connection between biomechanics and disease progression, and could identify candidate biomarkers to be targeted therapeutically.…”

“…Thus, although providing great detail, these techniques are limited in the number of treatments or conditions that can be measured before losing specimen viability. Compounding these issues is the uncontrollable heterogeneity commonly found in single cell or material measurements 18,19 which demands not only intellectual attention 20 but also imposes the challenge of collecting sufficient data for generating statistically sound conclusions. Recent efforts to increase the throughput of mechanical measurements [21][22][23] have addressed the need of capturing specimen and mechanical heterogeneity, but still acquire data across experimental conditions serially.…”