Optimal diffusion coefficient estimation in single-particle tracking

Impact of temporal resolution in single particle tracking analysis

Temporal resolution is a key parameter in the observation of dynamic processes, as in the case of single molecules motions visualized in real time in two-dimensions by wide field (fluorescence) microscopy, but a systematic investigation of its effects in all the single particle tracking analysis steps is still lacking. Here we present tools to quantify its impact on the estimation of diffusivity and of its distribution using one of the most popular tracking software for biological applications on simulated data and movies. We found important shifts and different widths for diffusivity distributions, depending on the interplay of temporal sampling conditions with various parameters, such as simulated diffusivity, density of spots, signal-to-noise ratio, lengths of trajectories, and kind of boundaries in the simulation. We examined conditions starting from the ones of experiments on the fluorescently labelled receptor p75NTR, a relatively fast-diffusing membrane receptor (diffusivity around 0.5-1 µm2/s), visualized by TIRF microscopy on the basal membrane of living cells. From the analysis of the simulations, we identified the best conditions in cases similar to these ones; considering also the experiments, we could confirm a range of values of temporal resolution suitable for obtaining reliable diffusivity results. The procedure we present can be exploited in different single particle/molecule tracking applications to find an optimal temporal resolution.

Comparing Mfd- and UvrD-dependent models of transcription coupled DNA repair in live Escherichia coli using single-molecule tracking

During transcription-coupled DNA repair (TCR) the detection of DNA damage and initiation of nucleotide excision repair (NER) is performed by translocating RNA polymerases (RNAP), which are arrested upon encountering bulky DNA lesions. Two opposing models of the subsequent steps of TCR in bacteria exist. In the first model, stalled RNAPs are removed from the damage site by recruitment of Mfd which dislodges RNAP by pushing it forwards before recruitment of UvrA and UvrB. In the second model, UvrD helicase backtracks RNAP from the lesion site. Recent studies have proposed that both UvrD and UvrA continuously associate with RNAP before damage occurs, which forms the primary damage sensor for NER. To test these two models of TCR in living E. coli, we applied super-resolution microscopy (PALM) combined with single particle tracking to directly measure the mobility and recruitment of Mfd, UvrD, UvrA, and UvrB to DNA during ultraviolet-induced DNA damage. The intracellular mobilities of NER proteins in the absence of DNA damage showed that most UvrA molecules could in principle be complexed with RNAP, however, this was not the case for UvrD. Upon DNA damage, Mfd recruitment to DNA was independent of the presence of UvrA, in agreement with its role upstream of this protein in the TCR pathway. In contrast, UvrD recruitment to DNA was strongly dependent on the presence of UvrA. Inhibiting transcription with rifampicin abolished Mfd DNA-recruitment following DNA damage, whereas significant UvrD, UvrA, and UvrB recruitment remained, consistent with a UvrD and UvrA performing their NER functions independently of transcribing RNAP. Together, although we find that up to ∼8 UvrD-RNAP-UvrA complexes per cell could potentially form in the absence of DNA damage, our live-cell data is not consistent with this complex being the primary DNA damage sensor for NER.

Plant chromatin on the move: an overview of chromatin mobility during transcription and DNA repair

It has become increasingly clear in recent years that chromosomes are highly dynamic entities. Chromatin mobility and re-arrangement are involved in many biological processes, including gene regulation and the maintenance of genome stability. Despite extensive studies on chromatin mobility in yeast and animal systems, up until recently, not much had been investigated at this level in plants. For plants to achieve proper growth and development, they need to respond rapidly and appropriately to environmental stimuli. Therefore, understanding how chromatin mobility can support plant responses may offer profound insights into the functioning of plant genomes. In this review, we discuss the state of the art related to chromatin mobility in plants, including the available technologies for their role in various cellular processes.

Rapid Long-distance Migration of RPA on Single Stranded DNA Occurs Through Intersegmental Transfer Utilizing Multivalent Interactions

Replication Protein A (RPA) is asingle strandedDNA(ssDNA)binding protein that coordinates diverse DNA metabolic processes including DNA replication, repair, and recombination. RPA is a heterotrimeric protein with six functional oligosaccharide/oligonucleotide (OB) domains and flexible linkers. Flexibility enables RPA to adopt multiple configurations andis thought to modulate its function. Here, usingsingle moleculeconfocal fluorescencemicroscopy combinedwith optical tweezers and coarse-grained molecular dynamics simulations, we investigated the diffusional migration of single RPA molecules on ssDNA undertension.The diffusioncoefficientDis the highest (20,000nucleotides2/s) at 3pNtension and in 100 mMKCl and markedly decreases whentensionor salt concentrationincreases. We attribute the tension effect to intersegmental transfer which is hindered by DNA stretching and the salt effect to an increase in binding site size and interaction energy of RPA-ssDNA. Our integrative study allowed us to estimate the size and frequency of intersegmental transfer events that occur through transient bridging of distant sites on DNA by multiple binding sites on RPA. Interestingly, deletion of RPA trimeric core still allowed significant ssDNA binding although the reduced contact area made RPA 15-fold more mobile. Finally, we characterized the effect of RPA crowding on RPA migration. These findings reveal how the high affinity RPA-ssDNA interactions are remodeled to yield access, a key step in several DNA metabolic processes.

Targeted Single Particle Tracking with Upconverting Nanoparticles

Single particle tracking (SPT) is a powerful technique for real-time microscopic visualization of the movement of individual biomolecules within or on the surface of living cells. However, SPT often suffers from the suboptimal performance of the photon-emitting labels used to tag the biomolecules of interest. For example, fluorescent dyes have poor photostability, while quantum dots suffer from blinking that hampers track acquisition and interpretation. Upconverting nanoparticles (UCNPs) have recently emerged as a promising anti-Stokes luminescent label for SPT. In this work, we demonstrated targeted SPT using UCNPs. For this, we synthesized 30 nm diameter doped UCNPs and coated them with amphiphilic polymers decorated with polyethylene glycol chains to make them water-dispersible and minimize their nonspecific interactions with cells. Coated UCNPs highly homogeneous in brightness (as confirmed by a single particle investigation) were functionalized by immunoglobulin E (IgE) using a biotin-streptavidin strategy. Using these IgE-UCNP SPT labels, we tracked high-affinity IgE receptors (FcεRI) on the membrane of living RBL-2H3 mast cells at 37 °C in the presence and absence of antigen and obtained good agreement with the literature. Moreover, we used the FcεRI-IgE receptor-antibody system to directly compare the performance of UCNP-based SPT labels to organic dyes (AlexaFluor647) and quantum dots (QD655). Due to their photostability as well as their backgroundless and continuous luminescence, SPT trajectories obtained with UCNP labels are no longer limited by the photophysics of the label but only by the dynamics of the system and, in particular, the movement of the label out of the field of view and/or focal plane.

Optimal calibration of optical tweezers with arbitrary integration time and sampling frequencies: a general framework [Invited]

Optical tweezers (OT) have become an essential technique in several fields of physics, chemistry, and biology as precise micromanipulation tools and microscopic force transducers. Quantitative measurements require the accurate calibration of the trap stiffness of the optical trap and the diffusion constant of the optically trapped particle. This is typically done by statistical estimators constructed from the position signal of the particle, which is recorded by a digital camera or a quadrant photodiode. The finite integration time and sampling frequency of the detector need to be properly taken into account. Here, we present a general approach based on the joint probability density function of the sampled trajectory that corrects exactly the biases due to the detector's finite integration time and limited sampling frequency, providing theoretical formulas for the most widely employed calibration methods: equipartition, mean squared displacement, autocorrelation, power spectral density, and force reconstruction via maximum-likelihood-estimator analysis (FORMA). Our results, tested with experiments and Monte Carlo simulations, will permit users of OT to confidently estimate the trap stiffness and diffusion constant, extending their use to a broader set of experimental conditions.

Single-molecule tracking of PprI in D. radiodurans without interference of autoblinking

Autoblinking is a widespread phenomenon and exhibits high level of intensity in some bacteria. In Deinococcus radiodurans (D. radiodurans), strong autoblinking was found to be indistinguishable from PAmCherry and greatly prevented single-molecule tracking of proteins of interest. Here we employed the bright photoswitchable fluorescent protein mMaple3 to label PprI, one essential DNA repair factor, and characterized systematically the fluorescence intensity and bleaching kinetics of both autoblinking and PprI-mMaple3 molecules within cells grown under three different conditions. Under minimal media, we can largely separate autoblinking from mMaple3 molecules and perform reliably single-molecule tracking of PprI in D. radiodurans, by means of applying signal-to-noise ratio and constraining the minimal length for linking the trajectories. We observed three states of PprI molecules, which bear different subcellular localizations and distinct functionalities. Our strategy provides a useful means to study the dynamics and distributions of proteins of interest in bacterial cells with high level of autoblinking.

Real-time detection of virus antibody interaction by label-free common-path interferometry

Viruses have a profound influence on all forms of life, motivating the development of rapid and minimally invasive methods for virus detection. In this study, we present a novel methodology that enables quantitative measurement of the interaction between individual biotic nanoparticles and antibodies in solution. Our approach employs a label-free, full-field common-path interferometric technique to detect and track biotic nanoparticles and their interactions with antibodies. It is based on the interferometric detection of light scattered by viruses in aqueous samples for the detection of individual viruses. We employ single-particle tracking analysis to characterize the size and properties of the detected nanoparticles, and to monitor the changes in their diffusive mobility resulting from interactions. To validate the sensitivity of our detection approach, we distinguish between particles having identical diffusion coefficients but different scattering signals, using DNA-loaded and DNA-devoid capsids of the Escherichia coli T5 virus phage. In addition, we have been able to monitor, in real time, the interaction between the bacteriophage T5 and purified antibodies targeting its major capsid protein pb8, as well as between the phage SPP1 and nonpurified anti-SPP1 antibodies present in rabbit serum. Interestingly, these virus-antibody interactions are observed within minutes. Finally, by estimating the number of viral particles interacting with antibodies at different concentrations, we successfully quantify the dissociation constant K d of the virus-antibody reaction using single-particle tracking analysis.

Single-molecule tracking to determine the abundances and stoichiometries of freely-diffusing protein complexes in living cells: Past applications and future prospects

Most biological processes in living cells rely on interactions between proteins. Live-cell compatible approaches that can quantify to what extent a given protein participates in homo- and hetero-oligomeric complexes of different size and subunit composition are therefore critical to advance our understanding of how cellular physiology is governed by these molecular interactions. Biomolecular complex formation changes the diffusion coefficient of constituent proteins, and these changes can be measured using fluorescence microscopy-based approaches, such as single-molecule tracking, fluorescence correlation spectroscopy, and fluorescence recovery after photobleaching. In this review, we focus on the use of single-molecule tracking to identify, resolve, and quantify the presence of freely-diffusing proteins and protein complexes in living cells. We compare and contrast different data analysis methods that are currently employed in the field and discuss experimental designs that can aid the interpretation of the obtained results. Comparisons of diffusion rates for different proteins and protein complexes in intracellular aqueous environments reported in the recent literature reveal a clear and systematic deviation from the Stokes-Einstein diffusion theory. While a complete and quantitative theoretical explanation of why such deviations manifest is missing, the available data suggest the possibility of weighing freely-diffusing proteins and protein complexes in living cells by measuring their diffusion coefficients. Mapping individual diffusive states to protein complexes of defined molecular weight, subunit stoichiometry, and structure promises to provide key new insights into how protein-protein interactions regulate protein conformational, translational, and rotational dynamics, and ultimately protein function.

Implications of different membrane compartmentalization models in particle-based in silico studies

Studying membrane dynamics is important to understand the cellular response to environmental stimuli. A decisive spatial characteristic of the plasma membrane is its compartmental structure created by the actin-based membrane-skeleton (fences) and anchored transmembrane proteins (pickets). Particle-based reaction-diffusion simulation of the membrane offers a suitable temporal and spatial resolution to analyse its spatially heterogeneous and stochastic dynamics. Fences have been modelled via hop probabilities, potentials or explicit picket fences. Our study analyses the different approaches' constraints and their impact on simulation results and performance. Each of the methods comes with its own constraints; the picket fences require small timesteps, potential fences might induce a bias in diffusion in crowded systems, and probabilistic fences, in addition to carefully scaling the probability with the timesteps, induce higher computational costs for each propagation step.

Characterization of diffusing sub-10 nm nano-objects using single anti-resonant element optical fibers

Accurate characterization of diffusing nanoscale species is increasingly important for revealing processes at the nanoscale, with fiber-assisted nanoparticle-tracking-analysis representing a new and promising approach in this field. In this work, we uncover the potential of this approach for the characterization of very small nanoparticles (<20 nm) through experimental studies, statistical analysis and the employment of a sophisticated fiber and chip design. The central results is the characterization of diffusing nanoparticles as small as 9 nm with record-high precision, corresponding to the smallest diameter yet determined for an individual nanoparticle with nanoparticle-tracking-analysis using elastic light scattering alone. Here, the detectable scattering cross-section is limited only by the background scattering of the ultrapure water, thus reaching the fundamental limit of Nanoparticle-Tracking-Analysis in general. The obtained results outperform other realizations and allow access to previously difficult to address application fields such as understanding nanoparticle growth or control of pharmaceuticals.

BNP-Track: A framework for multi-particle superresolved tracking

When tracking fluorescently labeled molecules (termed "emitters") under widefield microscopes, point spread function overlap of neighboring molecules is inevitable in both dilute and especially crowded environments. In such cases, superresolution methods leveraging rare photophysical events to distinguish static targets nearby in space introduce temporal delays that compromise tracking. As we have shown in a companion manuscript, for dynamic targets, information on neighboring fluorescent molecules is encoded as spatial intensity correlations across pixels and temporal correlations in intensity patterns across time frames. We then demonstrated how we used all spatiotemporal correlations encoded in the data to achieve superresolved tracking. That is, we showed the results of full posterior inference over both the number of emitters and their associated tracks simultaneously and self-consistently through Bayesian nonparametrics. In this companion manuscript we focus on testing the robustness of our tracking tool, BNP-Track, across sets of parameter regimes and compare BNP-Track to competing tracking methods in the spirit of a prior Nature Methods tracking competition. We explore additional features of BNP-Track including how a stochastic treatment of background yields greater accuracy in emitter number determination and how BNP-Track corrects for point spread function blur (or "aliasing") introduced by intraframe motion in addition to propagating error originating from myriad sources (such as criss-crossing tracks, out-of-focus particles, pixelation, shot and camera artefact, stochastic background) in posterior inference over emitter numbers and their associated tracks. While head-to-head comparison with other tracking methods is not possible (as competitors cannot simultaneously learn molecule numbers and associated tracks), we can give competing methods some advantages in order to perform approximate head-to-head comparison. We show that even under such optimistic scenarios, BNP-Track is capable of tracking multiple diffraction-limited point emitters conventional tracking methods cannot resolve thereby extending the superresolution paradigm to dynamical targets.

Real-time single-molecule 3D tracking in E. coli based on cross-entropy minimization

Reaching sub-millisecond 3D tracking of individual molecules in living cells would enable direct measurements of diffusion-limited macromolecular interactions under physiological conditions. Here, we present a 3D tracking principle that approaches the relevant regime. The method is based on the true excitation point spread function and cross-entropy minimization for position localization of moving fluorescent reporters. Tests on beads moving on a stage reaches 67 nm lateral and 109 nm axial precision with a time resolution of 0.84 ms at a photon count rate of 60 kHz; the measurements agree with the theoretical and simulated predictions. Our implementation also features a method for microsecond 3D PSF positioning and an estimator for diffusion analysis of tracking data. Finally, we successfully apply these methods to track the Trigger Factor protein in living bacterial cells. Overall, our results show that while it is possible to reach sub-millisecond live-cell single-molecule tracking, it is still hard to resolve state transitions based on diffusivity at this time scale.

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.

Single-molecule imaging in the primary cilium

The primary cilium is an important signaling organelle critical for normal development and tissue homeostasis. Its small dimensions and complexity necessitate advanced imaging approaches to uncover the molecular mechanisms behind its function. Here, we outline how single-molecule fluorescence microscopy can be used for tracking molecular dynamics and interactions and for super-resolution imaging of nanoscale structures in the primary cilium. Specifically, we describe in detail how to capture and quantify the 2D dynamics of individual transmembrane proteins PTCH1 and SMO and how to map the 3D nanoscale distributions of the inversin compartment proteins INVS, ANKS6, and NPHP3. This protocol can, with minor modifications, be adapted for studies of other proteins and cell lines to further elucidate the structure and function of the primary cilium at the molecular level.

Goodness-of-fit test for stochastic processes using even empirical moments statistic

In this paper, we introduce a novel framework that allows efficient stochastic process discrimination. The underlying test statistic is based on even empirical moments and generalizes the time-averaged mean-squared displacement framework; the test is designed to allow goodness-of-fit statistical testing of processes with stationary increments and a finite-moment distribution. In particular, while our test statistic is based on a simple and intuitive idea, it enables efficient discrimination between finite- and infinite-moment processes even if the underlying laws are relatively close to each other. This claim is illustrated via an extensive simulation study, e.g., where we confront α-stable processes with stability index close to 2 with their standard Gaussian equivalents. For completeness, we also show how to embed our methodology into the real data analysis by studying the real metal price data.

Actin filaments form a size-dependent diffusion barrier around centrosomes

The centrosome, a non-membranous organelle, constrains various soluble molecules locally to execute its functions. As the centrosome is surrounded by various dense components, we hypothesized that it may be bordered by a putative diffusion barrier. After quantitatively measuring the trapping kinetics of soluble proteins of varying size at centrosomes by a chemically inducible diffusion trapping assay, we find that centrosomes are highly accessible to soluble molecules with a Stokes radius of less than 5.8 nm, whereas larger molecules rarely reach centrosomes, indicating the existence of a size-dependent diffusion barrier at centrosomes. The permeability of this barrier is tightly regulated by branched actin filaments outside of centrosomes and it decreases during anaphase when branched actin temporally increases. The actin-based diffusion barrier gates microtubule nucleation by interfering with γ-tubulin ring complex recruitment. We propose that actin filaments spatiotemporally constrain protein complexes at centrosomes in a size-dependent manner.

Locally Structured On-Chip Optofluidic Hollow-Core Light Cages for Single Nanoparticle Tracking

Nanoparticle tracking analysis (NTA) is a widely used methodology to investigate nanoscale systems at the single species level. Here, we introduce the locally structured on-chip optofluidic hollow-core light cage, as a novel platform for waveguide-assisted NTA. This hollow waveguide guides light by the antiresonant effect in a sparse array of dielectric strands and includes a local modification to realize aberration-free tracking of individual nano-objects, defining a novel on-chip solution with properties specifically tailored for NTA. The key features of our system are (i) well-controlled nano-object illumination through the waveguide mode, (ii) diffraction-limited and aberration-free imaging at the observation site, and (iii) a high level of integration, achieved by on-chip interfacing to fibers. The present study covers all aspects relevant for NTA including design, simulation, implementation via 3D nanoprinting, and optical characterization. The capabilities of the approach to precisely characterize practically relevant nanosystems have been demonstrated by measuring the solvency-induced collapse of a nanoparticle system which includes polymer brush-based shells that react to changes in the liquid environment. Our study unlocks the advantages of the light cage approach in the context of NTA, suggesting its application in various areas such as bioanalytics, life science, environmental science, or nanoscale material science in general.

Palmitoylation of A-kinase anchoring protein 79/150 modulates its nanoscale organization, trafficking, and mobility in postsynaptic spines

A-kinase anchoring protein 79-human/150-rodent (AKAP79/150) organizes signaling proteins to control synaptic plasticity. AKAP79/150 associates with the plasma membrane and endosomes through its N-terminal domain that contains three polybasic regions and two Cys residues that are reversibly palmitoylated. Mutations abolishing palmitoylation (AKAP79/150 CS) reduce its endosomal localization and association with the postsynaptic density (PSD). Here we combined advanced light and electron microscopy (EM) to characterize the effects of AKAP79/150 palmitoylation on its postsynaptic nanoscale organization, trafficking, and mobility in hippocampal neurons. Immunogold EM revealed prominent extrasynaptic membrane AKAP150 labeling with less labeling at the PSD. The label was at greater distances from the spine membrane for AKAP150 CS than WT in the PSD but not in extra-synaptic locations. Immunogold EM of GFP-tagged AKAP79 WT showed that AKAP79 adopts a vertical, extended conformation at the PSD with its N-terminus at the membrane, in contrast to extrasynaptic locations where it adopts a compact or open configurations of its N- and C-termini with parallel orientation to the membrane. In contrast, GFP-tagged AKAP79 CS was displaced from the PSD coincident with disruption of its vertical orientation, while proximity and orientation with respect to the extra-synaptic membrane was less impacted. Single-molecule localization microscopy (SMLM) revealed a heterogeneous distribution of AKAP150 with distinct high-density, nano-scale regions (HDRs) overlapping the PSD but more prominently located in the extrasynaptic membrane for WT and the CS mutant. Thick section scanning transmission electron microscopy (STEM) tomography revealed AKAP150 immunogold clusters similar in size to HDRs seen by SMLM and more AKAP150 labeled endosomes in spines for WT than for CS, consistent with the requirement for AKAP palmitoylation in endosomal trafficking. Hidden Markov modeling of single molecule tracking data revealed a bound/immobile fraction and two mobile fractions for AKAP79 in spines, with the CS mutant having shorter dwell times and faster transition rates between states than WT, suggesting that palmitoylation stabilizes individual AKAP molecules in various spine subpopulations. These data demonstrate that palmitoylation fine tunes the nanoscale localization, mobility, and trafficking of AKAP79/150 in dendritic spines, which might have profound effects on its regulation of synaptic plasticity.

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.

Nanoparticle Tracking in Single-Antiresonant-Element Fiber for High-Precision Size Distribution Analysis of Mono- and Polydisperse Samples

Accurate determination of the size distribution of nanoparticle ensembles remains a challenge in nanotechnology-related applications due to the limitations of established methods. Here, a microstructured fiber-assisted nanoparticle tracking analysis (FaNTA) realization is introduced that breaks existing limitations through the recording of exceptionally long trajectories of rapidly diffusing polydisperse nanoparticles, resulting in excellent sizing precision and unprecedented separation capabilities of bimodal nanoparticle mixtures. An effective-single-mode antiresonant-element fiber allows to efficiently confine nanoparticles in a light-guiding microchannel and individually track them over more than 1000 frames, while aberration-free imaging is experimentally confirmed by cross-correlation analysis. Unique features of the approach are (i) the highly precise determination of the size distribution of monodisperse nanoparticle ensembles (only 7% coefficient of variation) and (ii) the accurate characterization of individual components in a bimodal mixture with very close mean diameters, both experimentally demonstrated for polymer nanospheres. The outstanding performance of the FaNTA realization can be quantified by introducing a new model for the bimodal separation index. Since FaNTA is applicable to all types of nano-objects down to sub-20 nm diameters, the method will improve the precision standard of mono- and polydisperse nanoparticle samples such as nano-plastics or extracellular vesicles.

Characterizing locus specific chromatin structure and dynamics with correlative conventional and super-resolution imaging in living cells

The dynamic rearrangement of chromatin is critical for gene regulation, but mapping both the spatial organization of chromatin and its dynamics remains a challenge. Many structural conformations are too small to be resolved via conventional fluorescence microscopy and the long acquisition time of super-resolution photoactivated localization microscopy (PALM) precludes the structural characterization of chromatin below the optical diffraction limit in living cells due to chromatin motion. Here we develop a correlative conventional fluorescence and PALM imaging approach to quantitatively map time-averaged chromatin structure and dynamics below the optical diffraction limit in living cells. By assigning localizations to a locus as it moves, we reliably discriminate between bound and unbound dCas9 molecules, whose mobilities overlap. Our approach accounts for changes in DNA mobility and relates local chromatin motion to larger scale domain movement. In our experimental system, we show that compacted telomeres move faster and have a higher density of bound dCas9 molecules, but the relative motion of those molecules is more restricted than in less compacted telomeres. Correlative conventional and PALM imaging therefore improves the ability to analyze the mobility and time-averaged nanoscopic structural features of locus specific chromatin with single molecule sensitivity and yields unprecedented insights across length and time scales.

Real-Time Feedback-Driven Single-Particle Tracking: A Survey and Perspective

Real-time feedback-driven single-particle tracking (RT-FD-SPT) is a class of techniques in the field of single-particle tracking that uses feedback control to keep a particle of interest in a detection volume. These methods provide high spatiotemporal resolution on particle dynamics and allow for concurrent spectroscopic measurements. This review article begins with a survey of existing techniques and of applications where RT-FD-SPT has played an important role. Each of the core components of RT-FD-SPT are systematically discussed in order to develop an understanding of the trade-offs that must be made in algorithm design and to create a clear picture of the important differences, advantages, and drawbacks of existing approaches. These components are feedback tracking and control, ranging from simple proportional-integral-derivative control to advanced nonlinear techniques, estimation to determine particle location from the measured data, including both online and offline algorithms, and techniques for calibrating and characterizing different RT-FD-SPT methods. Then a collection of metrics for RT-FD-SPT is introduced to help guide experimentalists in selecting a method for their particular application and to help reveal where there are gaps in the techniques that represent opportunities for further development. Finally, this review is concluded with a discussion on future perspectives in the field.

A method for tracking the Brownian motion to estimate the size distribution of submicron particles in seawater

Because the diffusivity of particles undergoing the Brownian motion is inversely proportional to their sizes, the size distribution of submicron particles can be estimated by tracking their movement. This particle tracking analysis (PTA) has been applied in various fields, but mainly focused on resolving monodispersed particle populations and is rarely used for measuring oceanic particles that are naturally polydispersed. We demonstrated using Monte Carlo simulation that, in principle, PTA can be used to size natural, oceanic particles. We conducted a series of lab experiments using microbeads of NIST-traceable sizes to evaluate the performance of ViewSizer 3000, a PTA-based commercial instrument, and found two major uncertainties: (1) the sample volume varies with the size of particles and (2) the signal-to-noise ratio for particles of sizes < 200-250 nm was reduced and hence their concentration was underestimated with the presence of larger particles. After applying the volume correction, we found the instrument can resolve oceanic submicron particles of sizes greater than 250 nm with a mean absolute error of 3.9% in size and 38% in concentration.

Classification-based motion analysis of single-molecule trajectories using DiffusionLab

Single-particle tracking is a powerful approach to study the motion of individual molecules and particles. It can uncover heterogeneities that are invisible to ensemble techniques, which places it uniquely among techniques to study mass transport. Analysis of the trajectories obtained with single-particle tracking in inorganic porous hosts is often challenging, because trajectories are short and/or motion is heterogeneous. We present the DiffusionLab software package for motion analysis of such challenging data sets. Trajectories are first classified into populations with similar characteristics to which the motion analysis is tailored in a second step. DiffusionLab provides tools to classify trajectories based on the motion type either with machine learning or manually. It also offers quantitative mean squared displacement analysis of the trajectories. The software can compute the diffusion constant for an individual trajectory if it is sufficiently long, or the average diffusion constant for multiple shorter trajectories. We demonstrate the DiffusionLab approach via the analysis of a simulated data set with motion types frequently observed in inorganic porous hosts, such as zeolites. The software package with graphical user interface and its documentation are freely available.

Receptor tyrosine kinase MET ligand-interaction classified via machine learning from single-particle tracking data

Internalin B-mediated activation of the membrane-bound receptor tyrosine kinase MET is accompanied by a change in receptor mobility. Conversely, it should be possible to infer from receptor mobility whether a cell has been treated with internalin B. Here, we propose a method based on hidden Markov modeling and explainable artificial intelligence that machine-learns the key differences in MET mobility between internalin B-treated and -untreated cells from single-particle tracking data. Our method assigns receptor mobility to three diffusion modes (immobile, slow, and fast). It discriminates between internalin B-treated and -untreated cells with a balanced accuracy of >99% and identifies three parameters that are most affected by internalin B treatment: a decrease in the mobility of slow molecules (1) and a depopulation of the fast mode (2) caused by an increased transition of fast molecules to the slow mode (3). Our approach is based entirely on free software and is readily applicable to the analysis of other membrane receptors.

Quantifying cell-cycle-dependent chromatin dynamics during interphase by live 3D tracking

The study of cell cycle progression and regulation is important to our understanding of fundamental biophysics, aging, and disease mechanisms. Local chromatin movements are generally considered to be constrained and relatively consistent during all interphase stages, although recent advances in our understanding of genome organization challenge this claim. Here, we use high spatiotemporal resolution, 4D (x, y, z and time) localization microscopy by point-spread-function (PSF) engineering and deep learning-based image analysis, for live imaging of mouse embryonic fibroblast (MEF 3T3) and MEF 3T3 double Lamin A Knockout (LmnaKO) cell lines, to characterize telomere diffusion during the interphase. We detected varying constraint levels imposed on chromatin, which are prominently decreased during G0/G1. Our 4D measurements of telomere diffusion offer an effective method to investigate chromatin dynamics and reveal cell-cycle-dependent motion constraints, which may be caused by various cellular processes.

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PSF engineering allows scan-free, high spatiotemporal live 3D telomere tracking

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During the G0/G1 phase, telomere motion is less constrained than in other phases

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There is observable difference between lateral (xy) and axial (z) chromatin motion

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In Lamin A-depleted cells, motion constraint was reduced

Molecular-Scale Dynamics of Long Range Retrograde Brain-Derived Neurotrophic Factor Transport Shaped by Cellular Spatial Context

Retrograde neurotrophin (NT) transport is a specialized form of signal transduction used to conduct information from axons to the cell bodies of central and peripheral nervous system neurons. It is activated upon NT-Trk receptor binding, NT-Trk internalization into signaling endosomes, and their motion along the axon toward the cell body. Brain-derived neurotrophic factor (BDNF) is an abundant NT that modulates key brain and spinal cord functions, and defects in BDNF trafficking are associated with neuronal death, neurodegenerative diseases and in nerve injury. Decades of study have yielded impressive progress in elucidating NT retrograde transport; however, much information remains unclear. For example, while it is known that NT function is dependent on tight control of NT-receptor intracellular trafficking, data describing the precise spatiotemporal molecular dynamics of their axonal to somatic transport are lacking. In past work, we showed the use of discrete, photo-bleaching-resistant quantum dot (QD)-BNDF probes to activate and track BDNF-TrkB receptor internalization; this revealed a rich diversity of molecular motions that intracellular BDNF signaling endosomes undergo within the soma of nodose ganglia sensory neurons. Here, we used combined techniques of discrete QD-BDNF tracking with compartmented microfluidic chambers to characterize retrograde BDNF-TrkB transport over long-ranging distances of primary dorsal root ganglion sensory neuronal axons. Our new findings show that axonal retrograde motion is comprised of heterogeneous mixtures of diffusive behaviors, pauses, and variations in net molecular-motor-dependent transport speeds. Notably, specific molecular dynamic features such as NT speed were dependent on spatial context that could be categorized in distance from distal axons and proximity to the soma and were not entirely dictated by active motor transport speed. The important implication is recognition that NT-receptor retrograde transport is comprised of molecular dynamics, which change over the course of long-range trafficking to shape overall transport and possibly signaling.

Anomalous diffusion, aging, and nonergodicity of scaled Brownian motion with fractional Gaussian noise: overview of related experimental observations and models

How does a systematic time-dependence of the diffusion coefficient $D (t)$ affect the ergodic and statistical characteristics of fractional Brownian motion (FBM)? Here, we examine how the behavior of the...

A Novel Biotinylated Homotryptamine Derivative for Quantum Dot Imaging of Serotonin Transporter in Live Cells

The serotonin transporter (SERT) is the primary target for selective serotonin reuptake inhibitor (SSRI) antidepressants that are thought to exert their therapeutic effects by increasing the synaptic concentration of serotonin. Consequently, probes that can be utilized to study cellular trafficking of SERT are valuable research tools. We have developed a novel ligand (IDT785) that is composed of a SERT antagonist (a tetrahydro pyridyl indole derivative) conjugated to a biotinylated poly ethylene glycol (PEG) via a phenethyl linker. This compound was determined to be biologically active and inhibited SERT-mediated reuptake of IDT307 with the half-maximal inhibitory concentration of 7.2 ± 0.3 μM. We demonstrated that IDT785 enabled quantum dot (QD) labeling of membrane SERT in transfected HEK-293 cultures that could be blocked using the high affinity serotonin reuptake inhibitor paroxetine. Molecular docking studies suggested that IDT785 might be binding to the extracellular vestibule binding site rather than the orthosteric substrate binding site, which could be attributable to the hydrophilicity of the PEG chain and the increased loss of degrees of freedom that would be required to penetrate into the orthosteric binding site. Using IDT785, we were able to study the membrane localization and membrane dynamics of YFP-SERT heterologously expressed in HEK-293 cells and demonstrated that SERT expression was enriched in the membrane edge and in thin cellular protrusions.

Joint Estimation of Trajectory and Model Parameters for Single Particle Tracking of 3D Confined Diffusion Using the Double-Helix Point Spread Function

Single particle tracking plays a significant role in biophysics through its ability to reveal dynamic mechanisms and physical properties of biological macromolecules inside living cells. The motion of these molecules can often be modeled as a confined diffusion. The standard paradigm in the biophysics community is to first estimate the trajectory of a particle and then use a technique such as the Mean Square Displacement or the Maximum Likelihood Estimation (MLE) to determine model parameters. These approaches, however, ignore the fact that localization and parameter estimation problems are coupled. We have previously introduced a framework based on optimal estimation theory to simultaneously do localization and parameter estimation. Here we build upon that work by expanding it to include a recent advance in imaging three dimensional motion, namely the Double-Helix (DH) engineered Point Spread Function (PSF). The DH-PSF encodes the axial position of the particle directly into the 2D image acquired by the camera mounted to the microscope. Our approach uses Expectation Maximization (EM) and Sequential Monte Carlo (SMC) to handle the nonlinearities in the observation and motion models. In this paper, we also improve upon the computational complexity of this scheme, using a Gaussian Particle Filter and Backward Simulation Particle Smoother in the SMC elements of the algorithm. We compare our scheme through simulation to state of the art methods based on localization using Gaussian fitting followed by MLE of the model parameters. These results show that our method outperforms GF-MLE at the low signal intensity levels common to biophysical experiments.

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

Single particle tracking (SPT) enables the investigation of biomolecular dynamics at a high temporal and spatial resolution in living cells, and the analysis of these SPT datasets can reveal biochemical interactions and mechanisms. Still, how to make the best use of these tracking data for a broad set of experimental conditions remains an analysis challenge in the field. Here, we develop a new SPT analysis framework: NOBIAS (NOnparametric Bayesian Inference for Anomalous Diffusion in Single-Molecule Tracking), which applies nonparametric Bayesian statistics and deep learning approaches to thoroughly analyze SPT datasets. In particular, NOBIAS handles complicated live-cell SPT data for which: the number of diffusive states is unknown, mixtures of different diffusive populations may exist within single trajectories, symmetry cannot be assumed between the x and y directions, and anomalous diffusion is possible. NOBIAS provides the number of diffusive states without manual supervision, it quantifies the dynamics and relative populations of each diffusive state, it provides the transition probabilities between states, and it assesses the anomalous diffusion behavior for each state. We validate the performance of NOBIAS with simulated datasets and apply it to the diffusion of single outer-membrane proteins in Bacteroides thetaiotaomicron. Furthermore, we compare NOBIAS with other SPT analysis methods and find that, in addition to these advantages, NOBIAS is robust and has high computational efficiency and is particularly advantageous due to its ability to treat experimental trajectories with asymmetry and anomalous diffusion.

Multiscale Investigation of the Diffusion Mechanism within the Solid-Electrolyte Interface Layer: Coupling Quantum Mechanics, Molecular Dynamics, and Macroscale Mathematical Modeling

The solid-electrolyte interface (SEI) layer has a critical role in Li-ion batteries' (LIBs) life span. The SEI layer, even in modern commercial LIBs, is responsible for more than 50% of capacity loss. Due to the inherent complexity in studying the SEI layer, many aspects of its performance and characteristics, including diffusion mechanisms in this layer, are unknown. As a result, most mathematical models use a constant value of the diffusion coefficient, instead of a variable formulation, to predict LIBs' properties and performance such as capacity fading and the SEI growth rate. In this work, by employing a multiscale investigation using a combination of quantum mechanics, molecular dynamics, and macroscale mathematical modeling, some equations are presented to evaluate the energy barrier against diffusion and the diffusion coefficient in different crystal structures in the inner section of the SEI layer. The equations are evaluated as a function of temperature and concentration and can be used to study the diffusion mechanism in the SEI layer. They can also be integrated with other mathematical models of LIBs to increase the accuracy of the latter.

EM-based algorithms for single particle tracking of Ornstein-Uhlenbeck motion from sCMOS camera data

Single particle tracking plays an important role in studying physical and kinetic properties of biomolecules. In this work, we introduce the application of Expectation Maximization (EM) based algorithms for solving localization and parameter estimation problems in SPT using data captured from scientific complementary metal-oxide semiconductor (sCMOS) camera sensors. Two representative methods are considered for generating the filtered and smoothed distributions needed by EM: Sequential Monte Carlo - EM, and Unscented - EM. The SMC method uses particle filtering and particle smoothing to handle general distributions, while the U scheme reduces the computational burden through the use of an unscented Kalman Filter and an unscented Rauch-Tung Striebel Smoother. We also investigate the influence of the number of images in the dataset on the final estimates through intensive simulations as well as the computational efficiency of the two methods.

Three-dimensional localization refinement and motion model parameter estimation for confined single particle tracking under low-light conditions

Confined diffusion is an important model for describing the motion of biological macromolecules moving in the crowded, three-dimensional environment of the cell. In this work we build upon the technique known as sequential Monte Carlo - expectation maximization (SMC-EM) to simultaneously localize the particle and estimate the motion model parameters from single particle tracking data. We extend SMC-EM to handle the double-helix point spread function (DH-PSF) for encoding the three-dimensional position of the particle in the two-dimensional image plane of the camera. SMC-EM can handle a wide range of camera models and here we assume the data was acquired using a scientific CMOS (sCMOS) camera. The sensitivity and speed of these cameras make them well suited for SPT, though the pixel-dependent nature of the camera noise presents a challenge for analysis. We focus on the low signal setting and compare our method through simulation to more standard approaches that use the paradigm of localize-then-estimate. To localize the particle under the standard paradigm, we use both a Gaussian fit and a maximum likelihood estimator (MLE) that accounts for both the DH-PSF and the pixel-dependent noise of the camera. Model estimation is then carried out either by fitting the model to the mean squared displacement (MSD) curve, or through an optimal estimation approach. Our results indicate that in the low signal regime, the SMC-EM approach outperforms the other methods while at higher signal-to-background levels, SMC-EM and the MLE-based methods perform equally well and both are significantly better than fitting to the MSD. In addition our results indicate that at smaller confinement lengths where the nonlinearities dominate the motion model, the SMC-EM approach is superior to the alternative approaches.

TRAIT2D: a Software for Quantitative Analysis of Single Particle Diffusion Data

Single particle tracking (SPT) is one of the most widely used tools in optical microscopy to evaluate particle mobility in a variety of situations, including cellular and model membrane dynamics. Recent technological developments, such as Interferometric Scattering microscopy, have allowed recording of long, uninterrupted single particle trajectories at kilohertz framerates. The resulting data, where particles are continuously detected and do not displace much between observations, thereby do not require complex linking algorithms. Moreover, while these measurements offer more details into the short-term diffusion behaviour of the tracked particles, they are also subject to the influence of localisation uncertainties, which are often underestimated by conventional analysis pipelines. we thus developed a Python library, under the name of TRAIT2D (Tracking Analysis Toolbox - 2D version), in order to track particle diffusion at high sampling rates, and analyse the resulting trajectories with an innovative approach. The data analysis pipeline introduced is more localisation-uncertainty aware, and also selects the most appropriate diffusion model for the data provided on a statistical basis. A trajectory simulation platform also allows the user to handily generate trajectories and even synthetic time-lapses to test alternative tracking algorithms and data analysis approaches. A high degree of customisation for the analysis pipeline, for example with the introduction of different diffusion modes, is possible from the source code. Finally, the presence of graphical user interfaces lowers the access barrier for users with little to no programming experience.

Super-resolution fluorescence imaging of extracellular environments

The extracellular matrix (ECM) is an important biophysical environment that plays a role in a number of physiological processes. The ECM is highly dynamic, with changes occurring as local, nanoscale, physicochemical variations in physical confinement and chemistry from the perspective of biological molecules. The length and time scale of ECM dynamics are challenging to measure with current spectroscopic techniques. Super-resolution fluorescence microscopy has the potential to probe local, nanoscale, physicochemical variations in the ECM. Here, we review super-resolution imaging and analysis methods and their application to study model nanoparticles and biomolecules within synthetic ECM hydrogels and the brain extracellular space (ECS). We provide a perspective of future directions for the field that can move super-resolution imaging of the ECM towards more biomedically-relevant samples. Overall, super-resolution imaging is a powerful tool that can increase our understanding of extracellular environments at new spatiotemporal scales to reveal ECM processes at the molecular-level.

Membrane Nanoscopic Organization of D2L Dopamine Receptor Probed by Quantum Dot Tracking

The role of lateral mobility and nanodomain organization of G protein-coupled receptors in modulating subcellular signaling has been under increasing scrutiny. Investigation of D2 dopamine receptor diffusion dynamics is of particular interest, as these receptors have been linked to altered neurotransmission in affective disorders and represent the primary target for commonly prescribed antipsychotics. Here, we applied our single quantum dot tracking approach to decipher intrinsic diffusion patterns of the wild-type long isoform of the D2 dopamine receptor and its genetic variants previously identified in several cohorts of schizophrenia patients. We identified a subtle decrease in the diffusion rate of the Val96Ala mutant that parallels its previously reported reduced affinity for potent neuroleptics clozapine and chlorpromazine. Slower Val96Ala variant diffusion was not accompanied by a change in receptor-receptor transient interactions as defined by the diffraction-limited quantum dot colocalization events. In addition, we implemented a Voronoї tessellation-based algorithm to compare nanoclustering of the D2 dopamine receptor to the dominant anionic phospholipid phosphatidylinositol 4,5-bisphosphate in the plasma membrane of live cells.

Multiplexed PSF Engineering for Three-Dimensional Multicolor Particle Tracking

Three-dimensional spatiotemporal tracking of microscopic particles in multiple colors is a challenging optical imaging task. Existing approaches require a trade-off between photon efficiency, field of view, mechanical complexity, spectral specificity, and speed. Here, we introduce multiplexed point-spread-function engineering that achieves photon-efficient, 3D multicolor particle tracking over a large field of view. This is accomplished by first chromatically splitting the emission path of a microscope to different channels, engineering the point-spread function of each, and then recombining them onto the same region of the camera. We demonstrate our technique for simultaneously tracking five types of emitters in vitro as well as colocalization of DNA loci in live yeast cells.

Diffusivity Measurement by Single-Molecule Recycling in a Capillary Microchannel

Microfluidic devices have been extensively investigated in recent years in fields including ligand-binding analysis, chromatographic separation, molecular dynamics, and DNA sequencing. To prolong the observation of a single molecule in aqueous buffer, the solution in a sub-micron scale channel is driven by a electric field and reversed after a fixed delay following each passage, so that the molecule passes back and forth through the laser focus and the time before irreversible photobleaching is extended. However, this practice requires complex chemical treatment to the inner surface of the channel to prevent unexpected sticking to the surface and the confined space renders features, such as a higher viscosity and lower dielectric constant, which slow the Brownian motion of the molecule compared to the bulk solution. Additionally, electron beam lithography used for the fabrication of the nanochannel substantially increases the cost, and the sub-micron dimensions make the molecule difficult to locate. In this paper, we propose a method of single-molecule recycling in a capillary microchannel. A commercial fused-silica capillary with an inner diameter of 2 microns is chopped into a 1-inch piece and is fixed onto a cover slip. Two o-rings on the sides used as reservoirs and an o-ring in the middle used as observation window are glued over the capillary. The inner surface of the capillary is chemically processed to reduce the non-specific sticking and to improve capillary effect. The device does not require high-precision fabrication and thus is less costly and easier to prepare than the nanochannel. 40 nm Fluospheres® in 50% methanol are used as working solution. The capillary is translated by a piezo stage to recycle the molecule, which diffuses freely through the capillary, and a confocal microscope is used for fluorescence collection. The passing times of the molecule through the laser focus are calculated by a real-time control system based on an FPGA, and the commands of translation are given to the piezo stage through a feedback algorithm. The larger dimensions of the capillary overcomes the strong sticking, the reduced diffusivity, and the difficulty of localizing the molecule. We have achieved a maximum number of recycles of more than 200 and developed a maximum-likelihood estimation of the diffusivity of the molecule, which attains results of the same magnitude as the previous report. This technique simplifies the overall procedure of the single-molecule recycling and could be useful for the ligand-binding studies in high-throughput screening.

Time-averaged mean squared displacement ratio test for Gaussian processes with unknown diffusion coefficient

The time-averaged mean squared displacement (TAMSD) is one of the most common statistics used for the analysis of anomalous diffusion processes. Anomalous diffusion is manifested by non-linear (mostly power-law) characteristics of the process in contrast to normal diffusion where linear characteristics are expected. One can distinguish between sub- and super-diffusive processes. We consider Gaussian anomalous diffusion models and propose a new approach used for their testing. This approach is based on the TAMSD ratio statistic for different time lags. Similar to the TAMSD, this statistic exhibits a specific behavior in the anomalous diffusion regime. Through its structure, it is independent of the diffusion coefficient, which, in general, does not influence anomalous diffusion behavior. Thus, the TAMSD ratio-based approach does not require preliminary knowledge of the diffusion coefficient's value, in contrast to the TAMSD-approach, where this value is crucial in the testing procedure. Based on the quadratic form representation of the TAMSD ratio, we calculate its main characteristics and propose a step-by-step testing procedure that can be applied for any Gaussian process. For the anomalous diffusion model used here, namely, the fractional Brownian motion, we demonstrate the effectiveness of the proposed methodology. We show that the new approach outperforms the TAMSD-based one, especially for small sample sizes. Finally, the methodology is applied to the real data from the financial market.

Maximum likelihood estimates of diffusion coefficients from single-particle tracking experiments

Single-molecule localization microscopy allows practitioners to locate and track labeled molecules in biological systems. When extracting diffusion coefficients from the resulting trajectories, it is common practice to perform a linear fit on mean-squared-displacement curves. However, this strategy is suboptimal and prone to errors. Recently, it was shown that the increments between the observed positions provide a good estimate for the diffusion coefficient, and their statistics are well-suited for likelihood-based analysis methods. Here, we revisit the problem of extracting diffusion coefficients from single-particle tracking experiments subject to static noise and dynamic motion blur using the principle of maximum likelihood. Taking advantage of an efficient real-space formulation, we extend the model to mixtures of subpopulations differing in their diffusion coefficients, which we estimate with the help of the expectation-maximization algorithm. This formulation naturally leads to a probabilistic assignment of trajectories to subpopulations. We employ the theory to analyze experimental tracking data that cannot be explained with a single diffusion coefficient. We test how well a dataset conforms to the assumptions of a diffusion model and determine the optimal number of subpopulations with the help of a quality factor of known analytical distribution. To facilitate use by practitioners, we provide a fast open-source implementation of the theory for the efficient analysis of multiple trajectories in arbitrary dimensions simultaneously.

Single-Molecule Tracking of Chromatin-Associated Proteins in the C. elegans Gonad

Biomolecules are distributed within cells by molecular-scale diffusion and binding events that are invisible in standard fluorescence microscopy. These molecular search kinetics are key to understanding nuclear signaling and chromosome organization and can be directly observed by single-molecule tracking microscopy. Here, we report a method to track individual proteins within intact C. elegans gonads and apply it to study the molecular dynamics of the axis, a proteinaceous backbone that organizes meiotic chromosomes. Using either fluorescent proteins or enzymatically ligated dyes, we obtain multisecond trajectories with a localization precision of 15-25 nm in nuclei actively undergoing meiosis. Correlation with a reference channel allows for accurate measurement of protein dynamics, compensating for movements of the nuclei and chromosomes within the gonad. We find that axis proteins exhibit either static binding to chromatin or free diffusion in the nucleoplasm, and we separately quantify the motion parameters of these distinct populations. Freely diffusing axis proteins selectively explore chromatin-rich regions, suggesting they are circumventing the central phase-separated region of the nucleus. This work demonstrates that single-molecule microscopy can infer nanoscale-resolution dynamics within living tissue, expanding the possible applications of this approach.

Discriminating Gaussian processes via quadratic form statistics

Gaussian processes are powerful tools for modeling and predicting various numerical data. Hence, checking their quality of fit becomes a vital issue. In this article, we introduce a testing methodology for general Gaussian processes based on a quadratic form statistic. We illustrate the methodology on three statistical tests recently introduced in the literature, which are based on the sample autocovariance function, time average mean-squared displacement, and detrended moving average statistics. We compare the usefulness of the tests by taking into consideration three very important Gaussian processes: the fractional Brownian motion, which is self-similar with stationary increments (SSSIs), scaled Brownian motion, which is self-similar with independent increments (SSIIs), and the Ornstein-Uhlenbeck (OU) process, which is stationary. We show that the considered statistics' ability to distinguish between these Gaussian processes is high, and we identify the best performing tests for different scenarios. We also find that there is no omnibus quadratic form test; however, the detrended moving average test seems to be the first choice in distinguishing between same processes with different parameters. We also show that the detrended moving average method outperforms the Cholesky method. Based on the previous findings, we introduce a novel procedure of discriminating between Gaussian SSSI, SSII, and stationary processes. Finally, we illustrate the proposed procedure by applying it to real-world data, namely, the daily EURUSD currency exchange rates, and show that the data can be modeled by the OU process.

Expectation maximization based framework for joint localization and parameter estimation in single particle tracking from segmented images

Single Particle Tracking (SPT) is a well known class of tools for studying the dynamics of biological macromolecules moving inside living cells. In this paper, we focus on the problem of localization and parameter estimation given a sequence of segmented images. In the standard paradigm, the location of the emitter inside each frame of a sequence of camera images is estimated using, for example, Gaussian fitting (GF), and these locations are linked to provide an estimate of the trajectory. Trajectories are then analyzed by using Mean Square Displacement (MSD) or Maximum Likelihood Estimation (MLE) techniques to determine motion parameters such as diffusion coefficients. However, the problems of localization and parameter estimation are clearly coupled. Motivated by this, we have created an Expectation Maximization (EM) based framework for simultaneous localization and parameter estimation. We demonstrate this framework through two representative methods, namely, Sequential Monte Carlo combined with Expectation Maximization (SMC-EM) and Unscented Kalman Filter combined with Expectation Maximization (U-EM). Using diffusion in two-dimensions as a prototypical example, we conduct quantitative investigations on localization and parameter estimation performance across a wide range of signal to background ratios and diffusion coefficients and compare our methods to the standard techniques based on GF-MSD/MLE. To demonstrate the flexibility of the EM based framework, we do comparisons using two different camera models, an ideal camera with Poisson distributed shot noise but no readout noise, and a camera with both shot noise and the pixel-dependent readout noise that is common to scientific complementary metal-oxide semiconductor (sCMOS) camera. Our results indicate our EM based methods outperform the standard techniques, especially at low signal levels. While U-EM and SMC-EM have similar accuracy, U-EM is significantly more computationally efficient, though the use of the Unscented Kalman Filter limits U-EM to lower diffusion rates.

Noise and ergodic properties of Brownian motion in an optical tweezer: Looking at regime crossovers in an Ornstein-Uhlenbeck process

We characterize throughout the spectral range of an optical trap the nature of the noise that drives the Brownian motion of an overdamped trapped single microsphere and its ergodicity, comparing experimental, analytical, and simulated data. We carefully analyze noise and ergodic properties (i) using the Allan variance for characterizing the noise and (ii) exploiting a test of ergodicity tailored for experiments done over finite times. We derive these two estimators in the Ornstein-Uhlenbeck low-frequency trapped-diffusion regime and study analytically their evolution toward the high-frequency Wiener-like free-diffusion regime, in very good agreement with simulated and experimental results. This study is performed comprehensively from the free-diffusion to the trapped-diffusion regimes. It also carefully looks at the specific signatures of the estimators at the crossover between the two regimes. This analysis is important to conduct when exploiting optical traps in a metrology context.

Single Quantum Dot Tracking Unravels Agonist Effects on the Dopamine Receptor Dynamics

D2 dopamine receptors (DRD2s) belong to a family of G protein-coupled receptors that modulate synaptic dopaminergic tone via regulation of dopamine synthesis, storage, and synaptic release. DRD2s are the primary target for traditional antipsychotic medications; dysfunctional DRD2 signaling has been linked to major depressive disorder, attention-deficit hyperactivity disorder, addiction, Parkinson's, and schizophrenia. DRD2 lateral diffusion appears to be an important post-translational regulatory mechanism; however, the dynamic response of DRD2s to ligand-induced activation is poorly understood. Dynamic imaging of the long isoform of DRD2 (D2L) fused to an N-terminal antihemagglutinin (HA) epitope and transiently expressed in HEK-293 cells was achieved through a combination of a high-affinity biotinylated anti-HA antigen-binding fragment (Fab) and streptavidin-conjugated quantum dots (QD). Significant reduction (∼40%) in the rate of lateral diffusion of QD-tagged D2L proteins was observed under agonist (quinpirole; QN)-stimulated conditions compared to basal conditions. QN-induced diffusional slowing was accompanied by an increase in frequency, lifetime, and confinement of temporary arrest of lateral diffusion (TALL), an intrinsic property of single receptor lateral motion. The role of the actin cytoskeleton in QN-induced diffusional slowing of D2L was also explored. The observed dynamic changes appear to be a sensitive indicator of the receptor activity status and might also spatially and temporally shape the receptor-mediated downstream signaling. This dynamic information could potentially be useful in informing drug discovery efforts based on single-molecule pharmacology.

Bound2Learn: a machine learning approach for classification of DNA-bound proteins from single-molecule tracking experiments

DNA-bound proteins are essential elements for the maintenance, regulation, and use of the genome. The time they spend bound to DNA provides useful information on their stability within protein complexes and insight into the understanding of biological processes. Single-particle tracking allows for direct visualization of protein-DNA kinetics, however, identifying whether a molecule is bound to DNA can be non-trivial. Further complications arise when tracking molecules for extended durations in processes with slow kinetics. We developed a machine learning approach, termed Bound2Learn, using output from a widely used tracking software, to robustly classify tracks in order to accurately estimate residence times. We validated our approach in silico, and in live-cell data from Escherichia coli and Saccharomyces cerevisiae. Our method has the potential for broad utility and is applicable to other organisms.