Single particle diffusion characterization by deep learning

Abstract

Diffusion plays a crucial role in many biological processes including signaling, cellular organization, transport mechanisms, and more. Direct observation of molecular movement by single-particle tracking experiments has contributed to a growing body of evidence that many cellular systems do not exhibit classical Brownian motion, but rather anomalous diffusion. Despite this evidence, characterization of the physical process underlying anomalous diffusion remains a challenging problem for several reasons. First, different physical processes can exist simultaneously in a system. Second, commonly used tools to distinguish between these processes are based on asymptotic behavior, which is inaccessible experimentally in most cases. Finally, an accurate analysis of the diffusion model requires the calculation of many observables, since different transport modes can result in the same diffusion power-law α, that is obtained from the commonly used mean-squared-displacement (MSD) in its various forms. The outstanding challenge in the field is to develop a method to extract an accurate assessment of the diffusion process using many short trajectories with a simple scheme that is applicable at the non-expert level.Here, we use deep learning to infer the underlying process resulting in anomalous diffusion. We implement a neural network to classify single particle trajectories according to diffusion type -Brownian motion, fractional Brownian motion (FBM) and Continuous Time Random Walk (CTRW). We further use the net to estimate the Hurst exponent for FBM, and the diffusion coefficient for Brownian motion, demonstrating its applicability on simulated and experimental data. The networks outperform time averaged MSD analysis on simulated trajectories while requiring as few as 25 time-steps. Furthermore, when tested on experimental data, both network and ensemble MSD analysis converge to similar values, with the network requiring half the trajectories required for ensemble MSD. Finally, we use the nets to extract diffusion parameters from multiple extremely short trajectories (10 steps).

Measurement of anomalous diffusion using recurrent neural networks

“…Therefore, neural networks ideally complement standard techniques to perform inference in cases for which no standard algorithmic procedures are available. In fact, some seminal works have already applied machine-learning techniques to determine the properties of anomalous diffusion with a focus on identifying its underlying mechanisms [26][27][28]. We remark that, similarly to other advanced machine learning techniques, neural networks often operate as black boxes and therefore should be applied carefully to new experimental data and situations, always testing and benchmarking their performance against established techniques.…”

A Jump-Distance-Based Parameter Inference Scheme for Particulate Trajectories

“…Beyond this, others have proposed a variety of methods for extricating the underlying mode of diffusion and parameters, including Bayesian decision trees (20), utilizing machine learning methods like random forests (29,30) and neural networks (31,32), and treating the trajectory data or MSD with a Bayesian approach (21,33,34). Others have proposed different analysis techniques for classification, including using a fractionally integrated moving average for subdiffusive data (17) and using a time-dependent diffusion constant (35).…”

Brownian motion and beyond: first-passage, power spectrum, non-Gaussianity, and anomalous diffusion

“…This is currently being investigated, using different approaches. We here mention Bayesian based maximum likelihood systems tailored for diffusive systems [95], as well as machine learning suites [96]. Considerable advances in this field over the coming years are to be expected.…”