Estimation of diffusive states from single-particle trajectory in heterogeneous medium using machine-learning methods

From Homogeneity to Turing Pattern: Kinetically Controlled Self-Organization of Transmembrane Protein

Understanding the spatial organization of membrane proteins is crucial for unraveling key principles in cell biology. The reaction-diffusion model is commonly used to understand biochemical patterning; however, applying reaction-diffusion models to subcellular phenomena is challenging because of the difficulty in measuring protein diffusivity and interaction kinetics in the living cell. In this work, we investigated the self-organization of the plasmalemma vesicle-associated protein (PLVAP), which creates regular arrangements of fenestrated ultrastructures, using single-molecule tracking. We demonstrated that the spatial organization of the ultrastructures is associated with a decrease in the association rate by actin destabilization. We also constructed a reaction-diffusion model that accurately generates a hexagonal array with the same 130 nm spacing as the actual scale and informs the stoichiometry of the ultrastructure, which can be discerned only through electron microscopy. Through this study, we integrated single-molecule experiments and reaction-diffusion modeling to surpass the limitations of static imaging tools and proposed emergent properties of the PLVAP ultrastructure.

Deep learning assisted single particle tracking for automated correlation between diffusion and function

Sub-cellular diffusion in living systems reflects cellular processes and interactions. Recent advances in optical microscopy allow the tracking of this nanoscale diffusion of individual objects with an unprecedented level of precision. However, the agnostic and automated extraction of functional information from the diffusion of molecules and organelles within the sub-cellular environment, is labor-intensive and poses a significant challenge. Here we introduce DeepSPT, a deep learning framework to interpret the diffusional 2D or 3D temporal behavior of objects in a rapid and efficient manner, agnostically. Demonstrating its versatility, we have applied DeepSPT to automated mapping of the early events of viral infections, identifying distinct types of endosomal organelles, and clathrin-coated pits and vesicles with up to 95% accuracy and within seconds instead of weeks. The fact that DeepSPT effectively extracts biological information from diffusion alone illustrates that besides structure, motion encodes function at the molecular and subcellular level.

Single-molecule analysis of intracellular insulin granule behavior and its application to analyzing cytoskeletal dependence and pathophysiological implications

Introduction: Mobilization of intracellular insulin granules to the plasma membrane plays a crucial role in regulating insulin secretion. However, the regulatory mechanisms of this mobilization process have been poorly understood due to technical limitations. In this study, we propose a convenient approach for assessing intracellular insulin granule behavior based on single-molecule analysis of insulin granule membrane proteins labeled with Quantum dot fluorescent nanocrystals. Methods: This approach allows us to analyze intracellular insulin granule movement with subpixel accuracy at 33 fps. We tracked two insulin granule membrane proteins, phogrin and zinc transporter 8, fused to HaloTag in rat insulinoma INS-1 cells and, by evaluating the tracks with mean-square displacement, demonstrated the characteristic behavior of insulin granules. Results and discussion: Pharmacological perturbations of microtubules and F-actin affected insulin granule behavior on distinct modalities. Specifically, microtubule dynamics and F-actin positively and negatively regulate insulin granule behavior, respectively, presumably by modulating each different behavioral mode. Furthermore, we observed impaired insulin granule behavior and cytoskeletal architecture under chronic treatment of high concentrations of glucose and palmitate. Our approach provides detailed information regarding intracellular insulin granule mobilization and its pathophysiological implications. This study sheds new light on the regulatory mechanisms of intracellular insulin granule mobilization and has important implications for understanding the pathogenesis of diabetes.

Extract latent features of single-particle trajectories with historical experience learning

Single-particle tracking has enabled real-time, in situ quantitative studies of complex systems. However, inferring dynamic state changes from noisy and undersampling trajectories encounters challenges. Here, we introduce a data-driven method for extracting features of subtrajectories with historical experience learning (Deep-SEES), where a single-particle tracking analysis pipeline based on a self-supervised architecture automatically searches for the latent space, allowing effective segmentation of the underlying states from noisy trajectories without prior knowledge on the particle dynamics. We validated our method on a variety of noisy simulated and experimental data. Our results showed that the method can faithfully capture both stable states and their dynamic switch. In highly random systems, our method outperformed commonly used unsupervised methods in inferring motion states, which is important for understanding nanoparticles interacting with living cell membranes, active enzymes, and liquid-liquid phase separation. Self-generating latent features of trajectories could potentially improve the understanding, estimation, and prediction of many complex systems.

Deep learning assisted single particle tracking for automated correlation between diffusion and function

Sub-cellular diffusion in living systems reflects cellular processes and interactions. Recent advances in optical microscopy allow the tracking of this nanoscale diffusion of individual objects with an unprecedented level of precision. However, the agnostic and automated extraction of functional information from the diffusion of molecules and organelles within the sub-cellular environment, is labor-intensive and poses a significant challenge. Here we introduce DeepSPT, a deep learning framework to interpret the diffusional 2D or 3D temporal behavior of objects in a rapid and efficient manner, agnostically. Demonstrating its versatility, we have applied DeepSPT to automated mapping of the early events of viral infections, identifying distinct types of endosomal organelles, and clathrin-coated pits and vesicles with up to 95% accuracy and within seconds instead of weeks. The fact that DeepSPT effectively extracts biological information from diffusion alone indicates that besides structure, motion encodes function at the molecular and subcellular level.

Recovering mixtures of fast-diffusing states from short single-particle trajectories

Single-particle tracking (SPT) directly measures the dynamics of proteins in living cells and is a powerful tool to dissect molecular mechanisms of cellular regulation. Interpretation of SPT with fast-diffusing proteins in mammalian cells, however, is complicated by technical limitations imposed by fast image acquisition. These limitations include short trajectory length due to photobleaching and shallow depth of field, high localization error due to the low photon budget imposed by short integration times, and cell-to-cell variability. To address these issues, we investigated methods inspired by Bayesian nonparametrics to infer distributions of state parameters from SPT data with short trajectories, variable localization precision, and absence of prior knowledge about the number of underlying states. We discuss the advantages and disadvantages of these approaches relative to other frameworks for SPT analysis.

Deep learning-based classification of breast cancer cells using transmembrane receptor dynamics

MOTIVATION

Motions of transmembrane receptors on cancer cell surfaces can reveal biophysical features of the cancer cells, thus providing a method for characterizing cancer cell phenotypes. While conventional analysis of receptor motions in the cell membrane mostly relies on the mean-squared displacement plots, much information is lost when producing these plots from the trajectories. Here we employ deep learning to classify breast cancer cell types based on the trajectories of epidermal growth factor receptor (EGFR). Our model is an artificial neural network trained on the EGFR motions acquired from six breast cancer cell lines of varying invasiveness and receptor status: MCF7 (hormone receptor positive), BT474 (HER2-positive), SKBR3 (HER2-positive), MDA-MB-468 (triple negative, TN), MDA-MB-231 (TN) and BT549 (TN).

RESULTS

The model successfully classified the trajectories within individual cell lines with 83% accuracy and predicted receptor status with 85% accuracy. To further validate the method, epithelial-mesenchymal transition (EMT) was induced in benign MCF10A cells, noninvasive MCF7 cancer cells and highly invasive MDA-MB-231 cancer cells, and EGFR trajectories from these cells were tested. As expected, after EMT induction, both MCF10A and MCF7 cells showed higher rates of classification as TN cells, but not the MDA-MB-231 cells. Whereas deep learning-based cancer cell classifications are primarily based on the optical transmission images of cell morphology and the fluorescence images of cell organelles or cytoskeletal structures, here we demonstrated an alternative way to classify cancer cells using a dynamic, biophysical feature that is readily accessible.

AVAILABILITY AND IMPLEMENTATION

A python implementation of deep learning-based classification can be found at https://github.com/soonwoohong/Deep-learning-for-EGFR-trajectory-classification.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

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

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.

Non-Markovian data-driven modeling of single-cell motility

Trajectories of human breast cancer cells moving on one-dimensional circular tracks are modeled by the non-Markovian version of the Langevin equation that includes an arbitrary memory function. When averaged over cells, the velocity distribution exhibits spurious non-Gaussian behavior, while single cells are characterized by Gaussian velocity distributions. Accordingly, the data are described by a linear memory model which includes different random walk models that were previously used to account for various aspects of cell motility such as migratory persistence, non-Markovian effects, colored noise, and anomalous diffusion. The memory function is extracted from the trajectory data without restrictions or assumptions, thus making our approach truly data driven, and is used for unbiased single-cell comparison. The cell memory displays time-delayed single-exponential negative friction, which clearly distinguishes cell motion from the simple persistent random walk model and suggests a regulatory feedback mechanism that controls cell migration. Based on the extracted memory function we formulate a generalized exactly solvable cell migration model which indicates that negative friction generates cell persistence over long timescales. The nonequilibrium character of cell motion is investigated by mapping the non-Markovian Langevin equation with memory onto a Markovian model that involves a hidden degree of freedom and is equivalent to the underdamped active Ornstein-Uhlenbeck process.

Complex Diffusion in Bacteria

Diffusion within bacteria is often thought of as a "simple" random process by which molecules collide and interact with each other. New research however shows that this is far from the truth. Here we shed light on the complexity and importance of diffusion in bacteria, illustrating the similarities and differences of diffusive behaviors of molecules within different compartments of bacterial cells. We first describe common methodologies used to probe diffusion and the associated models and analyses. We then discuss distinct diffusive behaviors of molecules within different bacterial cellular compartments, highlighting the influence of metabolism, size, crowding, charge, binding, and more. We also explicitly discuss where further research and a united understanding of what dictates diffusive behaviors across the different compartments of the cell are required, pointing out new research avenues to pursue.

Single-Particle Diffusion Characterization by Deep Learning

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 for distinguishing between these processes are based on asymptotic behavior, which is experimentally inaccessible in most cases. Finally, an accurate analysis of the diffusion model requires the calculation of many observables because different transport modes can result in the same diffusion power-law α, which is typically obtained from the mean-square displacements (MSDs). 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 nonexpert 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 by diffusion type: Brownian motion, fractional Brownian motion and continuous time random walk. Further, we demonstrate the applicability of our network architecture for estimating the Hurst exponent for fractional Brownian motion and the diffusion coefficient for Brownian motion on both simulated and experimental data. These networks achieve greater accuracy than time-averaged MSD analysis on simulated trajectories while only requiring as few as 25 steps. When tested on experimental data, both net and ensemble MSD analysis converge to similar values; however, the net needs only half the number of trajectories required for ensemble MSD to achieve the same confidence interval. Finally, we extract diffusion parameters from multiple extremely short trajectories (10 steps) using our approach.

Germline selection shapes human mitochondrial DNA diversity

Approximately 2.4% of the human mitochondrial DNA (mtDNA) genome exhibits common homoplasmic genetic variation. We analyzed 12,975 whole-genome sequences to show that 45.1% of individuals from 1526 mother-offspring pairs harbor a mixed population of mtDNA (heteroplasmy), but the propensity for maternal transmission differs across the mitochondrial genome. Over one generation, we observed selection both for and against variants in specific genomic regions; known variants were more likely to be transmitted than previously unknown variants. However, new heteroplasmies were more likely to match the nuclear genetic ancestry as opposed to the ancestry of the mitochondrial genome on which the mutations occurred, validating our findings in 40,325 individuals. Thus, human mtDNA at the population level is shaped by selective forces within the female germ line under nuclear genetic control, which ensures consistency between the two independent genetic lineages.

Non-Gaussian, non-ergodic, and non-Fickian diffusion of tracers in mucin hydrogels

Native mucus is polymer-based soft-matter material of paramount biological importance. How non-Gaussian and non-ergodic is the diffusive spreading of pathogens in mucus? We study the passive, thermally driven motion of micron-sized tracers in hydrogels of mucins, the main polymeric component of mucus. We report the results of the Bayesian analysis for ranking several diffusion models for a set of tracer trajectories [C. E. Wagner et al., Biomacromolecules, 2017, 18, 3654]. The models with "diffusing diffusivity", fractional and standard Brownian motion are used. The likelihood functions and evidences of each model are computed, ranking the significance of each model for individual traces. We find that viscoelastic anomalous diffusion is often most probable, followed by Brownian motion, while the model with a diffusing diffusion coefficient is only realised rarely. Our analysis also clarifies the distribution of time-averaged displacements, correlations of scaling exponents and diffusion coefficients, and the degree of non-Gaussianity of displacements at varying pH levels. Weak ergodicity breaking is also quantified. We conclude that-consistent with the original study-diffusion of tracers in the mucin gels is most non-Gaussian and non-ergodic at low pH that corresponds to the most heterogeneous networks. Using the Bayesian approach with the nested-sampling algorithm, together with the quantitative analysis of multiple statistical measures, we report new insights into possible physical mechanisms of diffusion in mucin gels.