Single Particle Trajectories Research Articles

TC10 differently controls the dynamics of Exo70 in growth cones of cortical and hippocampal neurons

The exocyst is an octameric protein complex that acts as a tether for GOLGI-derived vesicles at the plasma membrane during exocytosis. It is involved in membrane expansion during axonal outgrowth. Exo70 is a major subunit of the exocyst complex and is controlled by TC10, a Rho family GTPase. How TC10 affects the dynamics of Exo70 at the plasma membrane is not well understood. There is also evidence that TC10 controls Exo70 dynamics differently in nonpolar cells and axons. To address this, we used super-resolution microscopy to study the spatially resolved effects of TC10 on Exo70 dynamics in HeLa cells and the growth cone of cortical and hippocampal neurons. We generated single particle localization and trajectory maps and extracted mean square displacements, diffusion coefficients, and alpha coefficients to characterize Exo70 diffusion. We found that the diffusivity of Exo70 was different in nonpolar cells and in the growth cone of neurons. TC10 stimulated the mobility of Exo70 in HeLa cells, but decreased the diffusion of Exo70 in the growth cone of cortical neurons. In contrast to cortical neurons, TC10 overexpression did not affect the mobility of Exo70 in the axonal growth cone of hippocampal neurons. These data suggest that mainly exocyst tethering in cortical neurons was under the control of TC10.

A neural network-based algorithm for the reconstruction and filtering of single particle trajectory in magnetic particle tracking.

Magnetic particle tracking (MPT) is a recently developed non-invasive measurement technique that has gained popularity for studying dense particulate or granular flows. This method involves tracking the trajectory of a magnetically labeled particle, the field of which is modeled as a dipole. The nature of this method allows it to be used in opaque environments, which can be highly beneficial for the measurement of dense particle dynamics. However, since the magnetic field of the particle used is weak, the signal-to-noise ratio is usually low. The noise from the measuring devices contaminates the reconstruction of the magnetic tracer's trajectory. A filter is then needed to reduce the noise in the final trajectory results. In this work, we present a neural network-based framework for MPT trajectory reconstruction and filtering, which yields accurate results and operates at very high speed. The reconstruction derived from this framework is compared to the state-of-the-art extended Kalman filter-based reconstruction.

Synthetic Lagrangian turbulence by generative diffusion models

Lagrangian turbulence lies at the core of numerous applied and fundamental problems related to the physics of dispersion and mixing in engineering, biofluids, the atmosphere, oceans and astrophysics. Despite exceptional theoretical, numerical and experimental efforts conducted over the past 30 years, no existing models are capable of faithfully reproducing statistical and topological properties exhibited by particle trajectories in turbulence. We propose a machine learning approach, based on a state-of-the-art diffusion model, to generate single-particle trajectories in three-dimensional turbulence at high Reynolds numbers, thereby bypassing the need for direct numerical simulations or experiments to obtain reliable Lagrangian data. Our model demonstrates the ability to reproduce most statistical benchmarks across time scales, including the fat-tail distribution for velocity increments, the anomalous power law and the increased intermittency around the dissipative scale. Slight deviations are observed below the dissipative scale, particularly in the acceleration and flatness statistics. Surprisingly, the model exhibits strong generalizability for extreme events, producing events of higher intensity and rarity that still match the realistic statistics. This paves the way for producing synthetic high-quality datasets for pretraining various downstream applications of Lagrangian turbulence.

Quantifying the role of submesoscale Lagrangian transport features in the concentration of phytoplankton in a coastal system

Abstract Food resources in the ocean are often found in low densities, and need to be concentrated for efficient consumption. This is done in part by oceanographic features transporting and locally concentrating plankton, creating a highly patchy resource. Lagrangian approaches applied to ocean dynamics can identify these transport features, linking Lagrangian transport and spatial ecology. However, little is known about how Lagrangian approaches perform in ageostrophic coastal flows. This study evaluates two Lagrangian Coherent Structure metrics against the distribution of phytoplankton; Finite Time Lyapunov Exponents (FTLE) and Relative Particle Density (RPD). FTLE and RPD are applied to High Frequency Radar (HFR) observed surface currents within a biological hotspot, Palmer Deep Canyon Antarctica. FTLE and RPD identify different transport patterns, with RPD mapping single particle trajectories and FTLE tracking relative motion of paired particles. Simultaneous measurements of circulation and phytoplankton were gathered through the integration of vessel and autonomous glider surveys within the HFR footprint. Results show FTLE better defined phytoplankton patches compared to RPD, with the strongest associations occurring in stratified conditions, suggesting that phytoplankton congregate along FTLE ridges in coastal flows. This quantified relationship between circulation and phytoplankton patches emphasizes the role of transport in the maintenance of coastal food webs.

Promotion of particle agglomeration by different vortex generator angles based on PIV-PDPA experiment

Turbulent agglomeration is a promising pretreatment technology aimed at enhancing fine particles removal efficiency. Recent studies suggested that V-structure vortex generators are effective in improving turbulence to promote particle collisions and size increase. However, the experimental studies on flow fields and particles induced by V-structure vortex generators with different angles are still insufficient. To this end, this study investigated the effect of the angle of V-structure vortex generators on particle agglomeration based on the experimental approach. More specifically, the flow field dynamics were obtained directly from a Particle Image Velocimetry, while the particle behavior and size variation were investigated by a Phase Doppler Particle Analyzer. The results of the Phase Doppler Particle Analyzer showed that the addition of the vortex generator and its angle increase led to an increase in average size as well as cross-particle size, while a decrease in number concentration of smaller particles, which confirmed the collisions between smaller particles. Through Particle Image Velocimetry experiments, it was found that a wider range of recirculation regions and counter-rotating eddies were generated. Furthermore, by analyzing particle distribution and tracking single particle trajectory through numerical simulation, two kinds of agglomeration mechanisms were proposed. One being the trajectory crossover of smaller particles triggered by recirculating vortex, and the other is the preferential concentration of larger particles. The results of this study can provide a theoretical basis for the design of V-structure vortex generators and particle agglomeration techniques.

Chromatin phase separated nanoregions explored by polymer cross-linker models and reconstructed from single particle trajectories.

Phase separated domains (PSDs) are ubiquitous in cell biology, representing nanoregions of high molecular concentration. PSDs appear at diverse cellular domains, such as neuronal synapses but also in eukaryotic cell nucleus, limiting the access of transcription factors and thus preventing gene expression. We develop a generalized cross-linker polymer model, to study PSDs: we show that increasing the number of cross-linkers induces a polymer condensation, preventing access of diffusing molecules. To investigate how the PSDs restrict the motion of diffusing molecules, we compute the mean residence and first escaping times. Finally, we develop a method based on mean-square-displacement of single particle trajectories to reconstruct the properties of PSDs from the continuum range of anomalous exponents. We also show here that PSD generated by polymers do not induces a long-range attracting field (potential well), in contrast with nanodomains at neuronal synapses. To conclude, PSDs can result from condensed chromatin organization, where the number of cross-linkers controls molecular access.

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.

Confined modes of single-particle trajectories induced by stochastic resetting.

Random trajectories of single particles in living cells contain information about the interaction between particles, as well as with the cellular environment. However, precise consideration of the underlying stochastic properties, beyond normal diffusion, remains a challenge as applied to each particle trajectory separately. In this paper, we show how positions of confined particles in living cells can obey not only the Laplace distribution, but the Linnik one. This feature is detected in experimental data for the motion of G proteins and coupled receptors in cells, and its origin is explained in terms of stochastic resetting. This resetting process generates power-law waiting times, giving rise to the Linnik statistics in confined motion, and also includes exponentially distributed times as a limit case leading to the Laplace one. The stochastic process, which is affected by the resetting, can be Brownian motion commonly found in cells. Other possible models producing similar effects are discussed.

Characteristics of Water Vapor Transport for Extreme Summer Precipitation in the Eastern Southwest China and Its Impact Mechanism

To improve understanding of the characteristics of extreme summer rainfall and its water vapor transport in the eastern part of southwestern China (ESWC), this study analyzed data on daily precipitation from 118 meteorological stations in the ESWC from 1979 to 2020, as well as daily reanalysis data from ERA5 and daily reanalysis data from NCEP/NCAR. The study employed polynomial fitting, correlation, regression, clustering, and mixed single-particle Lagrangian trajectory (HYSPLITv5.0) modeling methods to simulate extreme summer precipitation and its water vapor transport characteristics in the ESWC and its possible formation mechanism. The results show that: (1) The contribution rate of extreme precipitation in the ESWC from 1979 to 2020 varied significantly on the interannual time scale. When the number of extreme precipitation days is high (low), the contribution rate of extreme precipitation is also high (low), while the contribution rate of general precipitation (the percentage of the sum of general precipitation to the total summer precipitation of that year) is often low (high). (2) When extreme precipitation occurs in the ESWC, compared with general precipitation, the high-level potential vortices are stronger, and the cold air from higher latitude is more likely to move southward. Meanwhile, the amount of water vapor input to the region is significantly larger than that of general precipitation. (3) There are four channels of water vapor sources in the ESWC during the period of extreme precipitation: the Bay of Bengal, the Arabian Sea, the western Pacific, and the northwest. The contribution of water vapor from the Bay of Bengal is the highest. The number of extreme summer precipitation days in the ESWC is significantly negatively correlated with the water vapor budget of the eastern boundary and positively correlated with Indian Ocean Basin-Wide (IOBW) index in the previous winter. (4) When the winter SST is high in the IOBW mode, it can cause the western Pacific subtropical high and the South Asian high to be stronger and shifted southward in summer, resulting in an increase in the number of extreme precipitation days in the ESWC.

Single-Particle Tracking in Poly(Ethylene Glycol) Diacrylate: Probe Size Effect on the Diffusion Behaviors of Nanoparticles in Unentangled Polymer Solutions.

A thorough understanding of the relevant factors governing the transport of nanoparticles in poly(ethylene glycol) diacrylate (PEGDA) is crucial for many applications utilizing this polymer. Here, single-particle tracking (SPT) was used to systematically investigate the role of the probe size (3-200 nm) on the diffusion behaviors of individual fluorescent nanoparticles in semidilute and unentangled PEGDA solutions. The quantitative assessment of the SPT data via the recorded single-particle trajectories and diffusion coefficients (D) not only showed that the observed probe dynamics in PEGDA were temporally and spatially heterogeneous, but more importantly that the measured D were observed to be significantly reduced (vs in solvent) and strongly size-dependent. We explained these results based on a modified multiscale model for particle diffusion, built upon well-established hydrodynamics and obstruction theories. We furthermore showed that the presence of steric interactions and probe confinement effects in highly crowded, unentangled PEGDA microstructures can lead to deviations in the single-particle displacements from the expected Gaussian behavior, as revealed by the van Hove displacement distributions and the associated non-Gaussian parameters. This study has demonstrated the power of SPT methods in offering an advanced characterization of the transport characteristics in complex polymer structures, overcoming challenges posed by traditional characterization techniques.

Ensemble heterogeneity mimics ageing for endosomal dynamics within eukaryotic cells

Transport processes of many structures inside living cells display anomalous diffusion, such as endosomes in eukaryotic cells. They are also heterogeneous in space and time. Large ensembles of single particle trajectories allow the heterogeneities to be quantified in detail and provide insights for mathematical modelling. The development of accurate mathematical models for heterogeneous dynamics has the potential to enable the design and optimization of various technological applications, for example, the design of effective drug delivery systems. Central questions in the analysis of anomalous dynamics are ergodicity and statistical ageing which allow for selecting the proper model for the description. It is believed that non-ergodicity and ageing occur concurrently. However, we found that the anomalous dynamics of endosomes is paradoxical since it is ergodic but shows ageing. We show that this behaviour is caused by ensemble heterogeneity that, in addition to space-time heterogeneity within a single trajectory, is an inherent property of endosomal motion. Our work introduces novel approaches for the analysis and modelling of heterogeneous dynamics.

Sequence-to-Sequence Change-Point Detection in Single-Particle Trajectories via Recurrent Neural Network for Measuring Self-Diffusion

A recurrent neural network is developed for segmenting between anomalous and normal diffusion in single-particle trajectories. Accurate segmentation infers a distinct change point that is used to approximate an Einstein linear regime in the mean-squared displacement curve via the transition density function, a unique physical descriptor for short-lived and delayed transiency. Through several artificial and simulated scenarios, we demonstrate the compelling accuracy of our model for dissecting linear and nonlinear behaviour. The inherent practicality of our model lies in its ability to substantiate the self-diffusion coefficient through offline trajectory segmentation, which is opposed to the common ‘best-guess’ linear fitting standard. Additionally, we show that the transition density function has fundamental implications and correspondence to underlying mechanisms that influence transition. In particular, we show that the known proportionality between salt concentration and diffusion of water also influences delayed anomalous behaviour.

Maximum likelihood-based estimation of diffusion coefficient is quick and reliable method for analyzing estradiol actions on surface receptor movements.

The rapid effects of estradiol on membrane receptors are in the focus of the estradiol research field, however, the molecular mechanisms of these non-classical estradiol actions are poorly understood. Since the lateral diffusion of membrane receptors is an important indicator of their function, a deeper understanding of the underlying mechanisms of non-classical estradiol actions can be achieved by investigating receptor dynamics. Diffusion coefficient is a crucial and widely used parameter to characterize the movement of receptors in the cell membrane. The aim of this study was to investigate the differences between maximum likelihood-based estimation (MLE) and mean square displacement (MSD) based calculation of diffusion coefficients. In this work we applied both MSD and MLE to calculate diffusion coefficients. Single particle trajectories were extracted from simulation as well as from α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptor tracking in live estradiol-treated differentiated PC12 (dPC12) cells. The comparison of the obtained diffusion coefficients revealed the superiority of MLE over the generally used MSD analysis. Our results suggest the use of the MLE of diffusion coefficients because as it has a better performance, especially for large localization errors or slow receptor movements.

Revealing the accessibility and surface morphology of the Escherichia coli nucleoid by genetically encoded live-cell single-particle tracking.

Membraneless organelles play a key role in the subcellular organization and regulation of bacterial cells. In particular, the bacterial genome is highly compacted into a membraneless organelle: the nucleoid. The structure and accessibility of the nucleoid significantly influences gene expression, and this morphology varies with growth phase and under various environmental conditions. Therefore, revealing how the DNA meshwork changes as a function of the growth phase will deepen our understanding of how bacteria regulate transcription in response to stress. To realize this goal, we applied single-particle tracking in E. coli and super-resolved the dynamics of an extrinsic 25-nm protein assembly with a well-defined dodecahedron structure: GFP-nanocages (Hsia et al., Nature 2016). By super-resolving the GFP-nanocage positions from log phase to late stationary phase, we observed an increasingly obvious exclusion of the probe by nucleoid, which indicates that the chromosome is compacting and becoming less accessible for gene expression. Our preliminary experiments also found a novel observation: the nucleoid size and compaction are not necessarily correlated. We hypothesize that at the intermediate stage of compaction, cells with small nucleoids may have a relatively low global compaction level because DNA chains are dragged by the force generated by DNA-NAP complex formation, leading to compacted rigid cores surrounded by a loosened DNA meshwork. By measuring the single-molecule step sizes at the periphery of the nucleoid, we understand the rigidity and smoothness of nucleoid surface at various phases. Furthermore, by analyzing the angle distribution within single-particle trajectories, we quantify the orientation of interactions with the nucleoid. The gene expression levels differ with cell growth stage (Verma et al., PLoS Genetics 2019). Our research provides a novel way of understanding how subcellular structure and gene expression are related.

Achieving nanoscale precision using neuromorphic localization microscopy.

Neuromorphic cameras are a new class of dynamic-vision-inspired sensors that encode the rate of change of intensity as events. They can asynchronously record intensity changes as spikes, independent of the other pixels in the receptive field, resulting in sparse measurements. This recording of such sparse events makes them ideal for imaging dynamic processes, such as the stochastic emission of isolated single molecules. Here we show the application of neuromorphic detection to localize nanoscale fluorescent objects below the diffraction limit, with a precision below 20 nm. We demonstrate a combination of neuromorphic detection with segmentation and deep learning approaches to localize and track fluorescent particles below 50 nm with millisecond temporal resolution. Furthermore, we show that combining information from events resulting from the rate of change of intensities improves the classical limit of centroid estimation of single fluorescent objects by nearly a factor of two. Additionally, we validate that using post-processed data from the neuromorphic detector at defined windows of temporal integration allows a better evaluation of the fractalized diffusion of single particle trajectories. Our observations and analysis is useful for event sensing by nonlinear neuromorphic devices to ameliorate real-time particle localization approaches at the nanoscale.

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.

Single-Particle Tracking and Trajectory Analysis of Fluorescent Nanodiamonds in Cell-Free Environment and Live Cells.

Diamond magnetometry can provide new insights on the production of free radicals inside live cells due to its high sensitivity and spatial resolution. However, the measurements often lack intracellular context for the recorded signal. In this paper, the possible use of single-particle tracking and trajectory analysis of fluorescent nanodiamonds (FNDs) to bridge that gap is explored. It starts with simulating a set of different possible scenarios of a particle's movement, reflecting different modes of motion, degrees of confinement, as well as shapes and sizes of that confinement. Then, the insights from the analysis of the simulated trajectories are applied to describe the movement of FNDs in glycerol solutions. It is shown that the measurements are in good agreement with the previously reported findings and that trajectory analysis yields meaningful results, when FNDs are tracked in a simple environment. Then the much more complex situation of FNDs moving inside a live cell is focused. The behavior of the particles after different incubation times is analyzed, and the possible intracellular localization of FNDs is deducted from their trajectories. Finally, this approach is combined with long-term magnetometry methodsto obtain maps of the spin relaxation dynamics (or T1) in live cells, as FNDs move through the cytosol.

Facet-selective etching trajectories of individual semiconductor nanocrystals.

The size and shape of semiconductor nanocrystals govern their optical and electronic properties. Liquid cell transmission electron microscopy (LCTEM) is an emerging tool that can directly visualize nanoscale chemical transformations and therefore inform the precise synthesis of nanostructures with desired functions. However, it remains difficult to controllably investigate the reactions of semiconductor nanocrystals with LCTEM, because of the highly reactive environment formed by radiolysis of liquid. Here, we harness the radiolysis processes and report the single-particle etching trajectories of prototypical semiconductor nanomaterials with well-defined crystalline facets. Lead selenide nanocubes represent an isotropic structure that retains the cubic shape during etching via a layer-by-layer mechanism. The anisotropic arrow-shaped cadmium selenide nanorods have polar facets terminated by either cadmium or selenium atoms, and the transformation trajectory is driven by etching the selenium-terminated facets. LCTEM trajectories reveal how nanoscale shape transformations of semiconductors are governed by the reactivity of specific facets in liquid environments.

High-throughput super-resolution single-particle trajectory analysis reconstructs organelle dynamics and membrane reorganization

SummarySuper-resolution imaging can generate thousands of single-particle trajectories. These data can potentially reconstruct subcellular organization and dynamics, as well as measure disease-linked changes. However, computational methods that can derive quantitative information from such massive datasets are currently lacking. We present data analysis and algorithms that are broadly applicable to reveal local binding and trafficking interactions and organization of dynamic subcellular sites. We applied this analysis to the endoplasmic reticulum and neuronal membrane. The method is based on spatiotemporal segmentation that explores data at multiple levels and detects the architecture and boundaries of high-density regions in areas measuring hundreds of nanometers. By connecting dense regions, we reconstructed the network topology of the endoplasmic reticulum (ER), as well as molecular flow redistribution and the local space explored by trajectories. The presented methods are available as an ImageJ plugin that can be applied to large datasets of overlapping trajectories offering a standard of single-particle trajectory (SPT) metrics.

Detecting temporal correlations in hopping dynamics in Lennard–Jones liquids

Lennard–Jones mixtures represent one of the popular systems for the study of glass-forming liquids. Spatio/temporal heterogeneity and rare (activated) events are at the heart of the slow dynamics typical of these systems. Such slow dynamics is characterised by the development of a plateau in the mean-squared displacement (MSD) at intermediate times, accompanied by a non-Gaussianity in the displacement distribution identified by exponential tails. As pointed out by some recent works, the non-Gaussianity persists at times beyond the MSD plateau, leading to a Brownian yet non-Gaussian regime and thus highlighting once again the relevance of rare events in such systems. Single-particle motion of glass-forming liquids is usually interpreted as an alternation of rattling within the local cage and cage-escape motion and therefore can be described as a sequence of waiting times and jumps. In this work, by using a simple yet robust algorithm, we extract jumps and waiting times from single-particle trajectories obtained via molecular dynamics simulations. We investigate the presence of correlations between waiting times and find negative correlations, which becomes more and more pronounced when lowering the temperature.