Classification-based motion analysis of single-molecule trajectories using DiffusionLab

High-fidelity predictions of diffusion in the brain microenvironment

Multiple-particle tracking (MPT) is a microscopy technique capable of simultaneously tracking hundreds to thousands of nanoparticles in a biological sample and has been used extensively to characterize biological microenvironments, including the brain extracellular space (ECS). Machine learning techniques have been applied to MPT data sets to predict the diffusion mode of nanoparticle trajectories as well as more complex biological variables, such as biological age. In this study, we develop a machine learning pipeline to predict and investigate changes to the brain ECS due to injury using supervised classification and feature importance calculations. We first validate the pipeline on three related but distinct MPT data sets from the living brain ECS-age differences, region differences, and enzymatic degradation of ECS structure. We predict three ages with 86% accuracy, three regions with 90% accuracy, and healthy versus enzyme-treated tissue with 69% accuracy. Since injury across groups is normally compared with traditional statistical approaches, we first used linear mixed effects models to compare features between healthy control conditions and injury induced by two different oxygen glucose deprivation exposure times. We then used machine learning to predict injury state using MPT features. We show that the pipeline predicts between the healthy control, 0.5 h OGD treatment, and 1.5 h OGD treatment with 59% accuracy in the cortex and 66% in the striatum, and identifies nonlinear relationships between trajectory features that were not evident from traditional linear models. Our work demonstrates that machine learning applied to MPT data is effective across multiple experimental conditions and can find unique biologically relevant features of nanoparticle diffusion.

Trajectory Analysis in Single-Particle Tracking: From Mean Squared Displacement to Machine Learning Approaches

Single-particle tracking is a powerful technique to investigate the motion of molecules or particles. Here, we review the methods for analyzing the reconstructed trajectories, a fundamental step for deciphering the underlying mechanisms driving the motion. First, we review the traditional analysis based on the mean squared displacement (MSD), highlighting the sometimes-neglected factors potentially affecting the accuracy of the results. We then report methods that exploit the distribution of parameters other than displacements, e.g., angles, velocities, and times and probabilities of reaching a target, discussing how they are more sensitive in characterizing heterogeneities and transient behaviors masked in the MSD analysis. Hidden Markov Models are also used for this purpose, and these allow for the identification of different states, their populations and the switching kinetics. Finally, we discuss a rapidly expanding field-trajectory analysis based on machine learning. Various approaches, from random forest to deep learning, are used to classify trajectory motions, which can be identified by motion models or by model-free sets of trajectory features, either previously defined or automatically identified by the algorithms. We also review free software available for some of the analysis methods. We emphasize that approaches based on a combination of the different methods, including classical statistics and machine learning, may be the way to obtain the most informative and accurate results.

Fluorescent-Probe Characterization for Pore-Space Mapping with Single-Particle Tracking

Porous solids often contain complex pore networks with pores of various sizes. Tracking individual fluorescent probes as they diffuse through porous materials can be used to characterize pore networks at tens of nanometers resolution. However, understanding the motion behavior of fluorescent probes in confinement is crucial to reliably derive pore network properties. Here, we introduce well-defined lithography-made model pores developed to study probe behavior in confinement. We investigated the influence of probe-host interactions on diffusion and trapping of confined single-emitter quantum-dot probes. Using the pH-responsiveness of the probes, we were able to largely suppress trapping at the pore walls. This enabled us to define experimental conditions for mapping of the accessible pore space of a one-dimensional pore array as well as a real-life polymerization-catalyst-support particle.

Anomalous diffusion, nonergodicity, non-Gaussianity, and aging of fractional Brownian motion with nonlinear clocks

How do nonlinear clocks in time and/or space affect the fundamental properties of a stochastic process? Specifically, how precisely may ergodic processes such as fractional Brownian motion (FBM) acquire predictable nonergodic and aging features being subjected to such conditions? We address these questions in the current study. To describe different types of non-Brownian motion of particles-including power-law anomalous, ultraslow or logarithmic, as well as superfast or exponential diffusion-we here develop and analyze a generalized stochastic process of scaled-fractional Brownian motion (SFBM). The time- and space-SFBM processes are, respectively, constructed based on FBM running with nonlinear time and space clocks. The fundamental statistical characteristics such as non-Gaussianity of particle displacements, nonergodicity, as well as aging are quantified for time- and space-SFBM by selecting different clocks. The latter parametrize power-law anomalous, ultraslow, and superfast diffusion. The results of our computer simulations are fully consistent with the analytical predictions for several functional forms of clocks. We thoroughly examine the behaviors of the probability-density function, the mean-squared displacement, the time-averaged mean-squared displacement, as well as the aging factor. Our results are applicable for rationalizing the impact of nonlinear time and space properties superimposed onto the FBM-type dynamics. SFBM offers a general framework for a universal and more precise model-based description of anomalous, nonergodic, non-Gaussian, and aging diffusion in single-molecule-tracking observations.