Single-particle diffusional fingerprinting: A machine-learning framework for quantitative analysis of heterogeneous diffusion

Abstract

Single-particle tracking (SPT) is a key tool for quantitative analysis of dynamic biological processes and has provided unprecedented insights into a wide range of systems such as receptor localization, enzyme propulsion, bacteria motility, and drug nanocarrier delivery. The inherently complex diffusion in such biological systems can vary drastically both in time and across systems, consequently imposing considerable analytical challenges, and currently requires an a priori knowledge of the system. Here we introduce a method for SPT data analysis, processing, and classification, which we term “diffusional fingerprinting.” This method allows for dissecting the features that underlie diffusional behavior and establishing molecular identity, regardless of the underlying diffusion type. The method operates by isolating 17 descriptive features for each observed motion trajectory and generating a diffusional map of all features for each type of particle. Precise classification of the diffusing particle identity is then obtained by training a simple logistic regression model. A linear discriminant analysis generates a feature ranking that outputs the main differences among diffusional features, providing key mechanistic insights. Fingerprinting operates by both training on and predicting experimental data, without the need for pretraining on simulated data. We found this approach to work across a wide range of simulated and experimentally diverse systems, such as tracked lipases on fat substrates, transcription factors diffusing in cells, and nanoparticles diffusing in mucus. This flexibility ultimately supports diffusional fingerprinting’s utility as a universal paradigm for SPT diffusional analysis and prediction.

Direct Observation of Heterogeneous Formation of Amyloid Spherulites in Real-time by Super-resolution Microscopy

“…To extract growth rate kinetics for each individual aggregate, we identified points belonging to the growing aggregate with an approximate Euclidean Minimum Spanning tree segmentation 38 and estimated the area using a gaussian mixture model, based on hierarchical clustering in Fig. 3c and 3d (see Supplementary information for the details) [23][24][25][26] . For isotropic morphologies a single linear growth rate is observed (rx), while for anisotropic morphologies the growth curve consists of two rate components (r1 and r2), as shown in Fig.…”

“…Consistent with the 3D dSTORM data, the direct observation of HI spherulite growth by REPLOM confirmed that HI spherulites grow both anisotropically and isotropically (Figure 3). To extract the growth rate kinetics for each individual aggregate, we identified the points belonging to the growing aggregate with an approximate Euclidean Minimum Spanning tree segmentation (Cowan & Ivezić, 2008) and estimated the area using a Gaussian mixture model based on hierarchical clustering in Figure 3c and 3d (see Supporting Information for the details) (Jensen et al, 2021; Pinholt et al, 2021; Stella et al, 2018; J. Thomsen et al, 2020).…”

“…We developed a method for the detection of Real-time kinetics via binding and Photobleaching Localisation Microscopy ( REPLOM ) to attain real-time videos of the spherulite growth process and reconstruct super-resolution images of the spherulites and their growth kinetics. Using homemade software based on Euclidian minimum spanning tree and machine learning clustering (Jensen et al, 2021; Malle et al, 2021; Pinholt, Bohr, Iversen, Boomsma, & Hatzakis, 2021; Stella et al, 2018; J. Thomsen et al, 2020), we quantitatively associated the growth rates to specific morphological transitions during growth, eventually extracting detailed energy barriers and, thus, the energy landscape for each type of aggregation morphology.…”

“…We developed a method for the detection of REal-time kinetics via binding and Photobleaching LOcalization Microscopy (REPLOM), to attain real-time video of spherulites growth process, reconstruct the super-resolution image of the spherulites and their growth kinetics. Using home-made software based on Euclidian minimum spanning tree and machine learning clustering [23][24][25][26] , we quantitatively associated growth rates to specific morphological transitions during the growth, eventually extracting detailed energy barriers and thus the energy landscape for each morphology type of the aggregation. These findings underscore how conclusions solely based on bulk kinetics data may overlook the complexity and the heterogeneity of the aggregation process.…”

Direct Observation of Heterogeneous Formation of Amyloid Spherulites in Real-time by Super-resolution Microscopy

“…Attaining real-time videos of the spherulite growth process allowed to reconstruct the super-resolution images of the spherulites and their growth kinetics. Using homemade software based on Euclidian minimum spanning tree and machine learning clustering [27][28][29][30][31] , we quantitatively associated the growth rates to specific morphological transitions during growth, eventually extracting detailed energy barriers and, thus, the energy landscape for each type of aggregation morphology. Our data on astigmatism-based 3D direct stochastic optical reconstruction microscopy (dSTORM) 32 , spinning disk confocal microscopy 33 , and scanning electron microscopy (SEM) confirm that the presence of heterogeneous structures is not artefact of our method.…”