Single-particle diffusional fingerprinting: A machine-learning framework for quantitative



Single-particle tracking (SPT) analysis of individual biomolecules is an indispensable tool for extracting quantitative information from dynamic biological processes, but often requires some a priori knowledge of the system. Here we present “single-particle diffusional fingerprinting,” a more general approach for extraction of diffusional patterns in SPT independently of the biological system. This method extracts a set of descriptive features for each SPT trajectory, which are ranked upon classification to yield mechanistic insights for the species under comparison. We demonstrate its capacity to yield a dictionary of diffusional traits across multiple systems (e.g., lipases hydrolyzing fat, transcription factors diffusing in cells, and nanoparticles in mucus), supporting its use on multiple biological phenomena (e.g., drug delivery, receptor dynamics, and virology).


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.

Single-particle tracking (SPT) has enabled the quantitative analysis of dynamic biological processes with nanometer spatial and millisecond temporal resolution, revealing dynamic behaviors previously masked in ensemble averaging (1, 2). By direct detection and spatiotemporal localization of biomolecules, SPT provides molecular trajectories for dynamic biological processes with nanometer spatial and millisecond temporal resolution. These trajectories have offered key insights into receptor dynamics (3), clathrin-mediated endocytosis (4), molecular motors (5), transcription factor motion (6), viral entry (7), and efficient drug delivery (8). More generally, they have offered new insights into the complex interplay between the structure, function, and environment of biomolecules through the characteristics of their diffusion.

The characteristics of diffusion often correlate with functional traits of interest. For example, enzyme diffusion might increase with catalysis (9); G-protein–coupled receptors display altered diffusion upon ligand binding (3) or dimerization (10); and nanoparticle coatings alter drug-delivery efficiencies that are measurable as changed diffusion (11, 12). Single-particle tracking thus holds promise as a source of diffusional data for future advanced screening studies in a broad range of systems (1316).

The rich information inherent in SPT data imposes direct analytical challenges: Biological motion is highly heterogeneous and displays a variety of diffusion types that may vary drastically across both systems and time and are dependent on regulatory cues or spatial localization, as we and others have shown (1720). Dealing with such heterogeneity is challenging, as there is no one-model-fits-all solution. Depending on the phenomenon under investigation, most groups have developed their own methodologies for estimating both the diffusion type and the parameters of specific diffusion models analytically (2129) or using machine learning (3037). If the motion changes over the course of a trajectory, tools have also been developed to segment the trace into regimes that are consistent with a model of interest (3541). These methodologies rely on identifying or comparing against a specific type of diffusion model and thus are not general, but rather are dependent on the complex phenomenon under investigation.

Here we address the challenge of providing a general method for SPT analysis, processing, and classification by implementing a diffusional fingerprint: a unique identifier for each observed SPT particle that allows for easy comparisons and precise entity prediction. Fingerprinting has been employed in fields as diverse as signal processing (42), proteomics (4346), genetics (47), and MRI (48). The main benefit of a fingerprinting approach compared to model-based analysis is that it does not require an a priori assumption of the type of diffusion. Previously developed classification methods train on simulated data and assume the transferability of the results to experimental data. In contrast, diffusional fingerprinting both trains and predicts on experimental data. This allows the fingerprint to agnostically describe a wide range of diffusional systems and diffusional trait classifications using a simple machine-learning classifier. Furthermore, it allows the use of representation learning, offering automatic identification of the representation that best supports the discriminate task at hand. By ranking the predicted features of relevance, the diffusional fingerprint offers mechanistic insights into the differences among the diffusing particles under investigation.

We assessed the ability of diffusional fingerprinting to identify particles in both simulated state-shifting and anomalous diffusion and across multiple diverse experimental systems (e.g., lipases diffusing on native substrates, transcription factors diffusing in cells, or nanoparticles diffusing in mucus on a lipid membrane). We found that diffusional fingerprinting accurately assigned diffusional traits to conditions, allowing for both identification and extraction of key insights, regardless of the underlying diffusion type. By relying on the same 17 features for all classifications, the fingerprint provides a unifying way of mapping a wide range of diffusional phenomena over a common space.


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