Characterization of anomalous diffusion classical statistics powered by deep learning (CONDOR)

Abstract

Diffusion processes are important in several physical, chemical, biological and human phenomena. Examples include molecular encounters in reactions, cellular signalling, the foraging of animals, the spread of diseases, as well as trends in financial markets and climate records. Deviations from Brownian diffusion, known as anomalous diffusion (AnDi), can often be observed in these processes, when the growth of the mean square displacement in time is not linear. An ever-increasing number of methods has thus appeared to characterize anomalous diffusion trajectories based on classical statistics or machine learning approaches. Yet, characterization of anomalous diffusion remains challenging to date as testified by the launch of the AnDi challenge in March 2020 to assess and compare new and pre-existing methods on three different aspects of the problem: the inference of the anomalous diffusion exponent, the classification of the diffusion model, and the segmentation of trajectories. Here, we introduce a novel method (CONDOR) which combines feature engineering based on classical statistics with supervised deep learning to efficiently identify the underlying anomalous diffusion model with high accuracy and infer its exponent with a small mean absolute error in single 1D, 2D and 3D trajectories corrupted by localization noise. Finally, we extend our method to the segmentation of trajectories where the diffusion model and/or its anomalous exponent vary in time.

NOBIAS: Analyzing anomalous diffusion in single-molecule tracks with nonparametric Bayesian inference

“…This HDP-HMM module also provides a multivariate output to quantify and correlate dynamics in multiple directions instead of assuming symmetry (Table S7). We observed that for asymmetric simulated trajectories, vbSPT overestimates the true number of states, and SMUAG could only provide the average D in two directions while (Argun et al, 2021;Gentili and Volpe, 2021). However, in this challenge, the target dataset was an ideal collection of simulated anomalous diffusion trajectories with 100-1000 steps, and only the simple case of one state transition in the middle part of a track was considered.…”

“…A further advantage of NOBIAS lies in its ability to treat sets of relatively short trajectories (Argun et al, 2021;Gentili and Volpe, 2021). However, in this challenge, the target dataset was an ideal collection of simulated anomalous diffusion trajectories with 100-1000 steps, and only the simple case of one state transition in the middle part of a track was considered.…”

“…The input to the network is the set of 2D coordinates from the track segments; these coordinates are normalized to have zero mean and unit variance. Despite a much higher classification performance when using tracks > 50 steps long to train and validate (Argun et al, 2021;Gentili and Volpe, 2021;Muñoz-Gil et al, 2021) were grown as previously described (Karunatilaka et al, 2014). Briefly, cells were cultured in medium containing 0.5% tryptone-yeast-extract-glucose and incubated at 37 °C under anaerobic conditions (85 % N2, 10 % H2, 5 % CO2) in a Coy chamber.…”

NOBIAS: Analyzing Anomalous Diffusion in Single-Molecule Tracks With Nonparametric Bayesian Inference

“…The input to the network is the set of 2D coordinates from the track segments; these coordinates are normalized to have zero mean and unit variance. Despite a much higher classification performance when using tracks > 50 steps long to train and validate (Argun et al, 2021;Gentili and Volpe, 2021;Muñoz-Gil et al, 2021), we trained two networks with 20-step tracks and with 40-step tracks, respectively, after considering the typical segment lengths from real biological trajectories. The training data of 750,000 trajectories were simulated with the open-source Python package from the AnDi challenge (Muñoz-Gil et al, 2020).…”

“…Biomolecules have been reported to diffuse anomalously in many situations, such as constrained membrane protein motion (Jeon et al, 2016), the facilitated diffusion of DNA binding protein (Bauer and Metzler, 2012), and active transportation of cargoes (Caspi et al, 2002). Different designs of neural networks effectively classify the diffusion type of trajectories (Bo et al, 2019;Granik et al, 2019;Argun et al, 2021;Gentili and Volpe, 2021), however these analyses typically assume that each track is dynamically homogeneous and is characterized by a single type of diffusion and a single D value. It remains a challenge to classify the diffusion type within a trajectory when considering the possibility of changes in dynamics or diffusion types within a single track.…”