Quantification and correction of systematic errors due to detector time-averaging in single-molecule tracking experiments

Trajectory Analysis in Single-Particle Tracking: From Mean Squared Displacement to Machine Learning Approaches

Single-particle tracking is a powerful technique to investigate the motion of molecules or particles. Here, we review the methods for analyzing the reconstructed trajectories, a fundamental step for deciphering the underlying mechanisms driving the motion. First, we review the traditional analysis based on the mean squared displacement (MSD), highlighting the sometimes-neglected factors potentially affecting the accuracy of the results. We then report methods that exploit the distribution of parameters other than displacements, e.g., angles, velocities, and times and probabilities of reaching a target, discussing how they are more sensitive in characterizing heterogeneities and transient behaviors masked in the MSD analysis. Hidden Markov Models are also used for this purpose, and these allow for the identification of different states, their populations and the switching kinetics. Finally, we discuss a rapidly expanding field-trajectory analysis based on machine learning. Various approaches, from random forest to deep learning, are used to classify trajectory motions, which can be identified by motion models or by model-free sets of trajectory features, either previously defined or automatically identified by the algorithms. We also review free software available for some of the analysis methods. We emphasize that approaches based on a combination of the different methods, including classical statistics and machine learning, may be the way to obtain the most informative and accurate results.

CRISPR-dCas13-tracing reveals transcriptional memory and limited mRNA export in developing zebrafish embryos

BACKGROUND

Understanding gene transcription and mRNA-protein (mRNP) dynamics in single cells in a multicellular organism has been challenging. The catalytically dead CRISPR-Cas13 (dCas13) system has been used to visualize RNAs in live cells without genetic manipulation. We optimize this system to track developmentally expressed mRNAs in zebrafish embryos and to understand features of endogenous transcription kinetics and mRNP export.

RESULTS

We report that zygotic microinjection of purified CRISPR-dCas13-fluorescent proteins and modified guide RNAs allows single- and dual-color tracking of developmentally expressed mRNAs in zebrafish embryos from zygotic genome activation (ZGA) until early segmentation period without genetic manipulation. Using this approach, we uncover non-synchronized de novo transcription between inter-alleles, synchronized post-mitotic re-activation in pairs of alleles, and transcriptional memory as an extrinsic noise that potentially contributes to synchronized post-mitotic re-activation. We also reveal rapid dCas13-engaged mRNP movement in the nucleus with a corralled and diffusive motion, but a wide varying range of rate-limiting mRNP export, which can be shortened by Alyref and Nxf1 overexpression.

CONCLUSIONS

This optimized dCas13-based toolkit enables robust spatial-temporal tracking of endogenous mRNAs and uncovers features of transcription and mRNP motion, providing a powerful toolkit for endogenous RNA visualization in a multicellular developmental organism.

Stochastic particle unbinding modulates growth dynamics and size of transcription factor condensates in living cells

Living cells organize internal compartments by forming molecular condensates that operate as versatile biochemical “hubs.” Their occurrence is particularly relevant in the nucleus where they regulate, amongst others, gene transcription. However, the biophysics of transcription factor (TF) condensation remains highly unexplored. Through single-molecule experiments in living cells, theory, and simulations, we assessed the diffusion, growth dynamics, and sizes of TF condensates of the nuclear progesterone receptor (PR). Interestingly, PR condensates obey classical growth dynamics at shorter times but deviate at longer times, reaching finite sizes at steady-state. We demonstrate that condensate growth dynamics and nanoscale-size arrested growth is regulated by molecular escaping from condensates, providing an exquisite control of condensate size in nonequilibrium systems such as living cells.

Liquid–liquid phase separation (LLPS) is emerging as a key physical principle for biological organization inside living cells, forming condensates that play important regulatory roles. Inside living nuclei, transcription factor (TF) condensates regulate transcriptional initiation and amplify the transcriptional output of expressed genes. However, the biophysical parameters controlling TF condensation are still poorly understood. Here we applied a battery of single-molecule imaging, theory, and simulations to investigate the physical properties of TF condensates of the progesterone receptor (PR) in living cells. Analysis of individual PR trajectories at different ligand concentrations showed marked signatures of a ligand-tunable LLPS process. Using a machine learning architecture, we found that receptor diffusion within condensates follows fractional Brownian motion resulting from viscoelastic interactions with chromatin. Interestingly, condensate growth dynamics at shorter times is dominated by Brownian motion coalescence (BMC), followed by a growth plateau at longer timescales that result in nanoscale condensate sizes. To rationalize these observations, we extended on the BMC model by including the stochastic unbinding of particles within condensates. Our model reproduced the BMC behavior together with finite condensate sizes at the steady state, fully recapitulating our experimental data. Overall, our results are consistent with condensate growth dynamics being regulated by the escaping probability of PR molecules from condensates. The interplay between condensation assembly and molecular escaping maintains an optimum physical condensate size. Such phenomena must have implications for the biophysical regulation of other nuclear condensates and could also operate in multiple biological scenarios.

Analysis of intracellular protein dynamics in living zebrafish embryos using light-sheet fluorescence single-molecule microscopy

Single-molecule microscopy techniques have emerged as useful tools to image individual molecules and analyze their dynamics inside cells, but their application has mostly been restricted to cell cultures. Here, a light-sheet fluorescence microscopy setup is presented for imaging individual proteins inside living zebrafish embryos. The optical configuration makes this design accessible to many laboratories and a dedicated sample-mounting system ensures sample viability and mounting flexibility. Using this setup, we have analyzed the dynamics of individual glucocorticoid receptors, which demonstrates that this approach creates multiple possibilities for the analysis of intracellular protein dynamics in intact living organisms.

Statistical physics and mesoscopic modeling to interpret tethered particle motion experiments

Tethered particle motion experiments are versatile single-molecule techniques enabling one to address in vitro the molecular properties of DNA and its interactions with various partners involved in genetic regulations. These techniques provide raw data such as the tracked particle amplitude of movement, from which relevant information about DNA conformations or states must be recovered. Solving this inverse problem appeals to specific theoretical tools that have been designed in the two last decades, together with the data pre-processing procedures that ought to be implemented to avoid biases inherent to these experimental techniques. These statistical tools and models are reviewed in this paper.

Separating Actin-Dependent Chemokine Receptor Nanoclustering from Dimerization Indicates a Role for Clustering in CXCR4 Signaling and Function

A current challenge in cell motility studies is to understand the molecular and physical mechanisms that govern chemokine receptor nanoscale organization at the cell membrane, and their influence on cell response. Using single-particle tracking and super-resolution microscopy, we found that the chemokine receptor CXCR4 forms basal nanoclusters in resting T cells, whose extent, dynamics, and signaling strength are modulated by the orchestrated action of the actin cytoskeleton, the co-receptor CD4, and its ligand CXCL12. We identified three CXCR4 structural residues that are crucial for nanoclustering and generated an oligomerization-defective mutant that dimerized but did not form nanoclusters in response to CXCL12, which severely impaired signaling. Overall, our data provide new insights to the field of chemokine biology by showing that receptor dimerization in the absence of nanoclustering is unable to fully support CXCL12-mediated responses, including signaling and cell function in vivo.

Unraveling the Thousand Word Picture: An Introduction to Super-Resolution Data Analysis

Super-resolution microscopy provides direct insight into fundamental biological processes occurring at length scales smaller than light's diffraction limit. The analysis of data at such scales has brought statistical and machine learning methods into the mainstream. Here we provide a survey of data analysis methods starting from an overview of basic statistical techniques underlying the analysis of super-resolution and, more broadly, imaging data. We subsequently break down the analysis of super-resolution data into four problems: the localization problem, the counting problem, the linking problem, and what we've termed the interpretation problem.

Convergence of lateral dynamic measurements in the plasma membrane of live cells from single particle tracking and STED-FCS

Fluorescence correlation spectroscopy (FCS) in combination with the super-resolution imaging method STED (STED-FCS), and single-particle tracking (SPT) are able to directly probe the lateral dynamics of lipids and proteins in the plasma membrane of live cells at spatial scales much below the diffraction limit of conventional microscopy. However, a major disparity in interpretation of data from SPT and STED-FCS remains, namely the proposed existence of a very fast (unhindered) lateral diffusion coefficient, ⩾5 µm2 s-1, in the plasma membrane of live cells at very short length scales, ≈⩽ 100 nm, and time scales, ≈1-10 ms. This fast diffusion coefficient has been advocated in several high-speed SPT studies, for lipids and membrane proteins alike, but the equivalent has not been detected in STED-FCS measurements. Resolving this ambiguity is important because the assessment of membrane dynamics currently relies heavily on SPT for the determination of heterogeneous diffusion. A possible systematic error in this approach would thus have vast implications in this field. To address this, we have re-visited the analysis procedure for SPT data with an emphasis on the measurement errors and the effect that these errors have on the measurement outputs. We subsequently demonstrate that STED-FCS and SPT data, following careful consideration of the experimental errors of the SPT data, converge to a common interpretation which for the case of a diffusing phospholipid analogue in the plasma membrane of live mouse embryo fibroblasts results in an unhindered, intra-compartment, diffusion coefficient of  ≈0.7-1.0 µm2 s-1, and a compartment size of about 100-150 nm.

Motion blur filtering: A statistical approach for extracting confinement forces and diffusivity from a single blurred trajectory

Single particle tracking (SPT) can aid in understanding a variety of complex spatiotemporal processes. However, quantifying diffusivity and confinement forces from individual live cell trajectories is complicated by inter- and intratrajectory kinetic heterogeneity, thermal fluctuations, and (experimentally resolvable) statistical temporal dependence inherent to the underlying molecule's time correlated confined dynamics experienced in the cell. The problem is further complicated by experimental artifacts such as localization uncertainty and motion blur. The latter is caused by the tagged molecule emitting photons at different spatial positions during the exposure time of a single frame. The aforementioned experimental artifacts induce spurious time correlations in measured SPT time series that obscure the information of interest (e.g., confinement forces and diffusivity). We develop a maximum likelihood estimation (MLE) technique that decouples the above noise sources and systematically treats temporal correlation via time series methods. This ultimately permits a reliable algorithm for extracting diffusivity and effective forces in confined or unconfined environments. We illustrate how our approach avoids complications inherent to mean square displacement or autocorrelation techniques. Our algorithm modifies the established Kalman filter (which does not handle motion blur artifacts) to provide a likelihood based time series estimation procedure. The result extends A. J. Berglund's motion blur model [Phys. Rev. E 82, 011917 (2010)PLEEE81539-375510.1103/PhysRevE.82.011917] to handle confined dynamics. The approach can also systematically utilize (possibly time dependent) localization uncertainty estimates afforded by image analysis if available. This technique, which explicitly treats confinement and motion blur within a time domain MLE framework, uses an exact likelihood (time domain methods facilitate analyzing nonstationary signals). Our estimator is demonstrated to be consistent over a wide range of exposure times (5 to 100 ms), diffusion coefficients (1×10^{-3} to 1μm^{2}/s), and confinement widths (100 nm to 2μm). We demonstrate that neglecting motion blur or confinement can substantially bias estimation of kinetic parameters of interest to researchers. The technique also permits one to check statistical model assumptions against measured individual trajectories without "ground truth." The ability to reliably and consistently extract motion parameters in trajectories exhibiting confined and/or non-stationary dynamics, without exposure time artifacts corrupting estimates, is expected to aid in directly comparing trajectories obtained from different experiments or imaging modalities. A Python implementation is provided (open-source code will be maintained on GitHub; see also the Supplemental Material with this paper).

Modeling of band-3 protein diffusion in the normal and defective red blood cell membrane

We employ a two-component red blood cell (RBC) membrane model to simulate lateral diffusion of band-3 proteins in the normal RBC and in the RBC with defective membrane proteins. The defects reduce the connectivity between the lipid bilayer and the membrane skeleton (vertical connectivity), or the connectivity of the membrane skeleton itself (horizontal connectivity), and are associated with the blood disorders of hereditary spherocytosis (HS) and hereditary elliptocytosis (HE) respectively. Initially, we demonstrate that the cytoskeleton limits band-3 lateral mobility by measuring the band-3 macroscopic diffusion coefficients in the normal RBC membrane and in a lipid bilayer without the cytoskeleton. Then, we study band-3 diffusion in the defective RBC membrane and quantify the relation between band-3 diffusion coefficients and percentage of protein defects in HE RBCs. In addition, we illustrate that at low spectrin network connectivity (horizontal connectivity) band-3 subdiffusion can be approximated as anomalous diffusion, while at high horizontal connectivity band-3 diffusion is characterized as confined diffusion. Our simulations show that the band-3 anomalous diffusion exponent depends on the percentage of protein defects in the membrane cytoskeleton. We also confirm that the introduction of attraction between the lipid bilayer and the spectrin network reduces band-3 diffusion, but we show that this reduction is lower than predicted by the percolation theory. Furthermore, we predict that the attractive force between the spectrin filament and the lipid bilayer is at least 20 times smaller than the binding forces at band-3 and glycophorin C, the two major membrane binding sites. Finally, we explore diffusion of band-3 particles in the RBC membrane with defects related to vertical connectivity. We demonstrate that in this case band-3 diffusion can be approximated as confined diffusion for all attraction levels between the spectrin network and the lipid bilayer. By comparing the diffusion coefficients measured in horizontal vs. vertical defects, we conclude that band-3 mobility is primarily controlled by the horizontal connectivity.

A review of progress in single particle tracking: from methods to biophysical insights

Optical microscopy has for centuries been a key tool to study living cells with minimum invasiveness. The advent of single molecule techniques over the past two decades has revolutionized the field of cell biology by providing a more quantitative picture of the complex and highly dynamic organization of living systems. Amongst these techniques, single particle tracking (SPT) has emerged as a powerful approach to study a variety of dynamic processes in life sciences. SPT provides access to single molecule behavior in the natural context of living cells, thereby allowing a complete statistical characterization of the system under study. In this review we describe the foundations of SPT together with novel optical implementations that nowadays allow the investigation of single molecule dynamic events with increasingly high spatiotemporal resolution using molecular densities closer to physiological expression levels. We outline some of the algorithms for the faithful reconstruction of SPT trajectories as well as data analysis, and highlight biological examples where the technique has provided novel insights into the role of diffusion regulating cellular function. The last part of the review concentrates on different theoretical models that describe anomalous transport behavior and ergodicity breaking observed from SPT studies in living cells.

Single Molecule Imaging Deciphers the Relation between Mobility and Signaling of a Prototypical G Protein-coupled Receptor in Living Cells

Lateral diffusion enables efficient interactions between membrane proteins, leading to signal transmission across the plasma membrane. An open question is how the spatiotemporal distribution of cell surface receptors influences the transmembrane signaling network. Here we addressed this issue by studying the mobility of a prototypical G protein-coupled receptor, the neurokinin-1 receptor, during its different phases of cellular signaling. Attaching a single quantum dot to individual neurokinin-1 receptors enabled us to follow with high spatial and temporal resolution over long time regimes the fate of individual receptors at the plasma membrane. Single receptor trajectories revealed a very heterogeneous mobility distribution pattern with diffusion constants ranging from 0.0005 to 0.1 μm(2)/s comprising receptors freely diffusing and others confined in 100-600-nm-sized membrane domains as well as immobile receptors. A two-dimensional representation of mobility and confinement resolved two major, broadly distributed receptor populations, one showing high mobility and low lateral restriction and the other showing low mobility and high restriction. We found that about 40% of the receptors in the basal state are already confined in membrane domains and are associated with clathrin. After stimulation with an agonist, an additional 30% of receptors became further confined. Using inhibitors of clathrin-mediated endocytosis, we found that the fraction of confined receptors at the basal state depends on the quantity of membrane-associated clathrin and is correlated to a significant decrease of the canonical pathway activity of the receptors. This shows that the high plasticity of receptor mobility is of central importance for receptor homeostasis and fine regulation of receptor activity.

Chromosomal locus tracking with proper accounting of static and dynamic errors

The mean-squared displacement (MSD) and velocity autocorrelation (VAC) of tracked single particles or molecules are ubiquitous metrics for extracting parameters that describe the object's motion, but they are both corrupted by experimental errors that hinder the quantitative extraction of underlying parameters. For the simple case of pure Brownian motion, the effects of localization error due to photon statistics ("static error") and motion blur due to finite exposure time ("dynamic error") on the MSD and VAC are already routinely treated. However, particles moving through complex environments such as cells, nuclei, or polymers often exhibit anomalous diffusion, for which the effects of these errors are less often sufficiently treated. We present data from tracked chromosomal loci in yeast that demonstrate the necessity of properly accounting for both static and dynamic error in the context of an anomalous diffusion that is consistent with a fractional Brownian motion (FBM). We compare these data to analytical forms of the expected values of the MSD and VAC for a general FBM in the presence of these errors.

Enhanced tethered-particle motion analysis reveals viscous effects

Tethered-particle motion experiments do not require expensive or technically complex hardware, and increasing numbers of researchers are adopting this methodology to investigate the topological effects of agents that act on the tethering polymer or the characteristics of the polymer itself. These investigations depend on accurate measurement and interpretation of changes in the effective length of the tethering polymer (often DNA). However, the bead size, tether length, and buffer affect the confined diffusion of the bead in this experimental system. To evaluate the effects of these factors, improved measurements to calibrate the two-dimensional range of motion (excursion) versus DNA length were carried out. Microspheres of 160 or 240 nm in radius were tethered by DNA molecules ranging from 225 to 3477 basepairs in length in aqueous buffers containing 100 mM potassium glutamate and 8 mM MgCl2 or 10 mM Tris-HCl and 200 mM KCl, with or without 0.5% Tween added to the buffer, and the motion was recorded. Different buffers altered the excursion of beads on identical DNA tethers. Buffer with only 10 mM NaCl and >5 mM magnesium greatly reduced excursion. Glycerol added to increase viscosity slowed confined diffusion of the tethered beads but did not change excursion. The confined-diffusion coefficients for all tethered beads were smaller than those expected for freely diffusing beads and decreased for shorter tethers. Tethered-particle motion is a sensitive framework for diffusion experiments in which small beads on long leashes most closely resemble freely diffusing, untethered beads.

TRF1 and TRF2 use different mechanisms to find telomeric DNA but share a novel mechanism to search for protein partners at telomeres

Human telomeres are maintained by the shelterin protein complex in which TRF1 and TRF2 bind directly to duplex telomeric DNA. How these proteins find telomeric sequences among a genome of billions of base pairs and how they find protein partners to form the shelterin complex remains uncertain. Using single-molecule fluorescence imaging of quantum dot-labeled TRF1 and TRF2, we study how these proteins locate TTAGGG repeats on DNA tightropes. By virtue of its basic domain TRF2 performs an extensive 1D search on nontelomeric DNA, whereas TRF1’s 1D search is limited. Unlike the stable and static associations observed for other proteins at specific binding sites, TRF proteins possess reduced binding stability marked by transient binding (∼9–17 s) and slow 1D diffusion on specific telomeric regions. These slow diffusion constants yield activation energy barriers to sliding ∼2.8–3.6 κ_BT greater than those for nontelomeric DNA. We propose that the TRF proteins use 1D sliding to find protein partners and assemble the shelterin complex, which in turn stabilizes the interaction with specific telomeric DNA. This ‘tag-team proofreading’ represents a more general mechanism to ensure a specific set of proteins interact with each other on long repetitive specific DNA sequences without requiring external energy sources.

Correcting for bias of molecular confinement parameters induced by small-time-series sample sizes in single-molecule trajectories containing measurement noise

Several single-molecule studies aim to reliably extract parameters characterizing molecular confinement or transient kinetic trapping from experimental observations. Pioneering works from single-particle tracking (SPT) in membrane diffusion studies [Kusumi et al., Biophys. J. 65, 2021 (1993)] appealed to mean square displacement (MSD) tools for extracting diffusivity and other parameters quantifying the degree of confinement. More recently, the practical utility of systematically treating multiple noise sources (including noise induced by random photon counts) through likelihood techniques has been more broadly realized in the SPT community. However, bias induced by finite-time-series sample sizes (unavoidable in practice) has not received great attention. Mitigating parameter bias induced by finite sampling is important to any scientific endeavor aiming for high accuracy, but correcting for bias is also often an important step in the construction of optimal parameter estimates. In this article, it is demonstrated how a popular model of confinement can be corrected for finite-sample bias in situations where the underlying data exhibit Brownian diffusion and observations are measured with non-negligible experimental noise (e.g., noise induced by finite photon counts). The work of Tang and Chen [J. Econometrics 149, 65 (2009)] is extended to correct for bias in the estimated "corral radius" (a parameter commonly used to quantify confinement in SPT studies) in the presence of measurement noise. It is shown that the approach presented is capable of reliably extracting the corral radius using only hundreds of discretely sampled observations in situations where other methods (including MSD and Bayesian techniques) would encounter serious difficulties. The ability to accurately statistically characterize transient confinement suggests additional techniques for quantifying confined and/or hop diffusion in complex environments.

A critical survey of methods to detect plasma membrane rafts

The plasma membrane is still one of the enigmatic cellular structures. Although the microscopic structure is getting clearer, not much is known about the organization at the nanometre level. Experimental difficulties have precluded unambiguous approaches, making the current picture rather fuzzy. In consequence, a variety of different membrane models has been proposed over the years, on the basis of different experimental strategies. Recent data obtained via high-resolution single-molecule microscopy shed new light on the existing hypotheses. We thus think it is a good time for reviewing the consistency of the existing models with the new data. In this paper, we summarize the available models in ten propositions, each of which is discussed critically with respect to the applied technologies and the strengths and weaknesses of the approaches. Our aim is to provide the reader with a sound basis for his own assessment. We close this chapter by exposing our picture of the membrane organization at the nanoscale.

Membrane cholesterol strongly influences confined diffusion of prestin

Prestin is the membrane motor protein that drives outer hair cell (OHC) electromotility, a process that is essential for mammalian hearing. Prestin function is sensitive to membrane cholesterol levels, and numerous studies have suggested that prestin localizes in cholesterol-rich membrane microdomains. Previously, fluorescence recovery after photobleaching experiments were performed in HEK cells expressing prestin-GFP after cholesterol manipulations, and revealed evidence of transient confinement. To further characterize this apparent confined diffusion of prestin, we conjugated prestin to a photostable fluorophore (tetramethylrhodamine) and performed single-molecule fluorescence microscopy. Using single-particle tracking, we determined the microscopic diffusion coefficient from the full time course of the mean-squared deviation. Our results indicate that prestin undergoes diffusion in confinement regions, and that depletion of membrane cholesterol increases confinement size and decreases confinement strength. By interpreting the data in terms of a mathematical model of hop-diffusion, we quantified these cholesterol-induced changes in membrane organization. A complementary analysis of the distribution of squared displacements confirmed that cholesterol depletion reduces prestin confinement. These findings support the hypothesis that prestin function is intimately linked to membrane organization, and further promote a regulatory role for cholesterol in OHC and auditory function.

Insights into cell membrane microdomain organization from live cell single particle tracking of the IgE high affinity receptor FcϵRI of mast cells

Current models propose that the plasma membrane of animal cells is composed of heterogeneous and dynamic microdomains known variously as cytoskeletal corrals, lipid rafts and protein islands. Much of the experimental evidence for these membrane compartments is indirect. Recently, live cell single particle tracking studies using quantum dot-labeled IgE bound to its high affinity receptor FcϵRI, provided direct evidence for the confinement of receptors within micrometer-scale cytoskeletal corrals. In this study, we show that an innovative time-series analysis of single particle tracking data for the high affinity IgE receptor, FcϵRI, on mast cells provides substantial quantitative information about the submicrometer organization of the membrane. The analysis focuses on the probability distribution function of the lengths of the jumps in the positions of the quantum dots labeling individual IgE FcϵRI complexes between frames in movies of their motion. Our results demonstrate the presence, within the micrometer-scale cytoskeletal corrals, of smaller subdomains that provide an additional level of receptor confinement. There is no characteristic size for these subdomains; their size varies smoothly from a few tens of nanometers to a over a hundred nanometers. In QD-IGE labeled unstimulated cells, jumps of less than 70 nm predominate over longer jumps. Addition of multivalent antigen to crosslink the QD-IgE-FcϵRI complexes causes a rapid slowing of receptor motion followed by a long tail of mostly jumps less than 70 nm. The reduced receptor mobility likely reflects both the membrane heterogeneity revealed by the confined motion of the monomeric receptor complexes and the antigen-induced cross linking of these complexes into dimers and higher oligomers. In both cases, the probability distribution of the jump lengths is well fit, from 10 nm to over 100 nm, by a novel power law. The fit for short jumps suggests that the motion of the quantum dots can be modeled as diffusion in a fractal space of dimension less than two.

Observing the confinement potential of bacterial pore-forming toxin receptors inside rafts with nonblinking Eu(3+)-doped oxide nanoparticles

We track single toxin receptors on the apical cell membrane of MDCK cells with Eu-doped oxide nanoparticles coupled to two toxins of the pore-forming toxin family: α-toxin of Clostridium septicum and ε-toxin of Clostridium perfringens. These nonblinking and photostable labels do not perturb the motion of the toxin receptors and yield long uninterrupted trajectories with mean localization precision of 30 nm for acquisition times of 51.3 ms. We were thus able to study the toxin-cell interaction at the single-molecule level. Toxins bind to receptors that are confined within zones of mean area 0.40 ± 0.05 μm(2). Assuming that the receptors move according to the Langevin equation of motion and using Bayesian inference, we determined mean diffusion coefficients of 0.16 ± 0.01 μm(2)/s for both toxin receptors. Moreover, application of this approach revealed a force field within the domain generated by a springlike confining potential. Both toxin receptors were found to experience forces characterized by a mean spring constant of 0.30 ± 0.03 pN/μm at 37°C. Furthermore, both toxin receptors showed similar distributions of diffusion coefficient, domain area, and spring constant. Control experiments before and after incubation with cholesterol oxidase and sphingomyelinase show that these two enzymes disrupt the confinement domains and lead to quasi-free motion of the toxin receptors. Our control data showing cholesterol and sphingomyelin dependence as well as independence of actin depolymerization and microtubule disruption lead us to attribute the confinement of both receptors to lipid rafts. These toxins require oligomerization to develop their toxic activity. The confined nature of the toxin receptors leads to a local enhancement of the toxin monomer concentration and may thus explain the virulence of this toxin family.

A Bayesian inference scheme to extract diffusivity and potential fields from confined single-molecule trajectories

Currently used techniques for the analysis of single-molecule trajectories only exploit a small part of the available information stored in the data. Here, we apply a Bayesian inference scheme to trajectories of confined receptors that are targeted by pore-forming toxins to extract the two-dimensional confining potential that restricts the motion of the receptor. The receptor motion is modeled by the overdamped Langevin equation of motion. The method uses most of the information stored in the trajectory and converges quickly onto inferred values, while providing the uncertainty on the determined values. The inference is performed on the polynomial development of the potential and on the diffusivities that have been discretized on a mesh. Numerical simulations are used to test the scheme and quantify the convergence toward the input values for forces, potential, and diffusivity. Furthermore, we show that the technique outperforms the classical mean-square-displacement technique when forces act on confined molecules because the typical mean-square-displacement analysis does not account for them. We also show that the inferred potential better represents input potentials than the potential extracted from the position distribution based on Boltzmann statistics that assumes statistical equilibrium.

HU protein induces incoherent DNA persistence length

HU is a highly conserved protein that is believed to play an important role in the architecture and dynamic compaction of bacterial DNA. Its ability to control DNA bending is crucial for functions such as transcription and replication. The effects of HU on the DNA structure have been studied so far mainly by single molecule methods that require us to apply stretching forces on the DNA and therefore may perturb the DNA-protein interaction. To overcome this hurdle, we study the effect of HU on the DNA structure without applying external forces by using an improved tethered particle motion method. By combining the results with DNA curvature analysis from atomic force microscopy measurements we find that the DNA consists of two different curvature distributions and the measured persistence length is determined by their interplay. As a result, the effective persistence length adopts a bimodal property that depends primarily on the HU concentration. The results can be explained according to a recently suggested model that distinguishes single protein binding from cooperative protein binding.

Force-free measurements of the conformations of DNA molecules tethered to a wall

Using an optimized combination of tethered particle motion method, total internal reflection, and a gold nanobead, we measured the three-dimensional distribution of the free end of a tethered DNA molecule. The distribution along the axial z direction (perpendicular to the surface) is found to be Rayleigh-like, in agreement with wormlike chain and freely jointed chain simulations. Using these simulations, we show that the presence of the wall increases the correlations between the orientations of neighboring chain segments compared to free DNA. While the measured and the simulated planar (xy) distributions always agree with that of a Gaussian-random-walk (GRW) model, for short DNA lengths (1 μm) studied in our experiment, the corresponding axial (z) distributions deviate from those predicted for a GRW confined to half-space.

Probing DNA conformational changes with high temporal resolution by tethered particle motion

The tethered particle motion (TPM) technique informs about conformational changes of DNA molecules, e.g. upon looping or interaction with proteins, by tracking the Brownian motion of a particle probe tethered to a surface by a single DNA molecule and detecting changes of its amplitude of movement. We discuss in this context the time resolution of TPM, which strongly depends on the particle-DNA complex relaxation time, i.e. the characteristic time it takes to explore its configuration space by diffusion. By comparing theory, simulations and experiments, we propose a calibration of TPM at the dynamical level: we analyze how the relaxation time grows with both DNA contour length (from 401 to 2080 base pairs) and particle radius (from 20 to 150 nm). Notably we demonstrate that, for a particle of radius 20 nm or less, the hydrodynamic friction induced by the particle and the surface does not significantly slow down the DNA. This enables us to determine the optimal time resolution of TPM in distinct experimental contexts which can be as short as 20 ms.

Three-dimensional tracking of single mRNA particles in Saccharomyces cerevisiae using a double-helix point spread function

Optical imaging of single biomolecules and complexes in living cells provides a useful window into cellular processes. However, the three-dimensional dynamics of most important biomolecules in living cells remains essentially uncharacterized. The precise subcellular localization of mRNA-protein complexes plays a critical role in the spatial and temporal control of gene expression, and a full understanding of the control of gene expression requires precise characterization of mRNA transport dynamics beyond the optical diffraction limit. In this paper, we describe three-dimensional tracking of single mRNA particles with 25-nm precision in the x and y dimensions and 50-nm precision in the z dimension in live budding yeast cells using a microscope with a double-helix point spread function. Two statistical methods to detect intermittently confined and directed transport were used to quantify the three-dimensional trajectories of mRNA for the first time, using ARG3 mRNA as a model. Measurements and analysis show that the dynamics of ARG3 mRNA molecules are mostly diffusive, although periods of non-Brownian confinement and directed transport are observed. The quantitative methods detailed in this paper can be broadly applied to the study of mRNA localization and the dynamics of diverse other biomolecules in a wide variety of cell types.

Mean square displacement analysis of single-particle trajectories with localization error: Brownian motion in an isotropic medium

We examine the capability of mean square displacement (MSD) analysis to extract reliable values of the diffusion coefficient D of a single particle undergoing Brownian motion in an isotropic medium in the presence of localization uncertainty. The theoretical results, supported by simulations, show that a simple unweighted least-squares fit of the MSD curve can provide the best estimate of D provided an optimal number of MSD points are used for the fit. We discuss the practical implications of these results for data analysis in single-particle tracking experiments.

Quantifying biomolecule diffusivity using an optimal Bayesian method

We propose a Bayesian method to extract the diffusivity of biomolecules evolving freely or inside membrane microdomains. This approach assumes a model of motion for the particle considered, namely free Brownian motion or confined diffusion. In each framework, a systematic Bayesian scheme is provided for estimating the diffusivity. We show that this method reaches the best performances theoretically achievable. Its efficiency overcomes that of widely used methods based on the analysis of the mean-square displacement. The approach presented here also gives direct access to the uncertainty on the estimation of the diffusivity and predicts the number of steps of the trajectory necessary to achieve any desired precision. Its robustness with respect to noise on the position of the biomolecule is also investigated.

Single molecule diffusion coefficient estimation by image analysis of simulated CCD images to aid high-throughput screening

Extension of one-dimensional signal analysis to two-dimensional image analysis could accelerate conventional methods of high-throughput screening in the discovery of new pharmaceutical agents. This work describes a first step taken towards this goal - the evaluation of image-analysis based estimation strategies of the diffusion coefficient of a single molecule transported within a microfabricated flowcell. A computer simulation of single-molecule imaging by a charge-coupled device (CCD) camera is used to determine if it is possible to distinguish three different types of molecules with different diffusion coefficients. The Gaussian fitting algorithm finds the variance of the transverse trajectory, which increases linearly with the diffusion coefficient; the path analysis algorithm determines the diffusion coefficient from cumulative summation of the squared displacement along the imaged path; the detector area analysis algorithm determines the number of resolvable positions or pixels in the imaged trajectory. Of the three methods, the path analysis strategy appears to provide the most reliable measure of diffusion coefficient with relative error of 13.6% and 6.4% between single molecules with diffusion coefficients of 2.85e-7 and 1.425e-7 cm(2)/s. The detector area analysis method can statistically distinguish between single molecules with diffusion coefficients of 5.7e-7 and 1.425e-7 cm(2)/s at the p(0.05) level.

Time series analysis of particle tracking data for molecular motion on the cell membrane

Biophysicists use single particle tracking (SPT) methods to probe the dynamic behavior of individual proteins and lipids in cell membranes. The mean squared displacement (MSD) has proven to be a powerful tool for analyzing the data and drawing conclusions about membrane organization, including features like lipid rafts, protein islands, and confinement zones defined by cytoskeletal barriers. Here, we implement time series analysis as a new analytic tool to analyze further the motion of membrane proteins. The experimental data track the motion of 40 nm gold particles bound to Class I major histocompatibility complex (MHCI) molecules on the membranes of mouse hepatoma cells. Our first novel result is that the tracks are significantly autocorrelated. Because of this, we developed linear autoregressive models to elucidate the autocorrelations. Estimates of the signal to noise ratio for the models show that the autocorrelated part of the motion is significant. Next, we fit the probability distributions of jump sizes with four different models. The first model is a general Weibull distribution that shows that the motion is characterized by an excess of short jumps as compared to a normal random walk. We also fit the data with a chi distribution which provides a natural estimate of the dimension d of the space in which a random walk is occurring. For the biological data, the estimates satisfy 1 < d < 2, implying that particle motion is not confined to a line, but also does not occur freely in the plane. The dimension gives a quantitative estimate of the amount of nanometer scale obstruction met by a diffusing molecule. We introduce a new distribution and use the generalized extreme value distribution to show that the biological data also have an excess of long jumps as compared to normal diffusion. These fits provide novel estimates of the microscopic diffusion constant. Previous MSD analyses of SPT data have provided evidence for nanometer-scale confinement zones that restrict lateral diffusion, supporting the notion that plasma membrane organization is highly structured. Our demonstration that membrane protein motion is autocorrelated and is characterized by an excess of both short and long jumps reinforces the concept that the membrane environment is heterogeneous and dynamic. Autocorrelation analysis and modeling of the jump distributions are powerful new techniques for the analysis of SPT data and the development of more refined models of membrane organization. The time series analysis also provides several methods of estimating the diffusion constant in addition to the constant provided by the mean squared displacement. The mean squared displacement for most of the biological data shows a power law behavior rather the linear behavior of Brownian motion. In this case, we introduce the notion of an instantaneous diffusion constant. All of the diffusion constants show a strong consistency for most of the biological data.

Single molecule tracking of quantum dot-labeled mRNAs in a cell nucleus

Single particle tracking (SPT) is a powerful technique for studying mRNA dynamics in cells. Although SPT of mRNA has been performed by labeling mRNA with fluorescent dyes or proteins, observation of mRNA for long durations with high temporal resolution has been difficult due to weak fluorescence and rapid photobleaching. Using quantum dots (QDs), we succeeded in observing the movement of individual mRNAs for more than 60 s, with a temporal resolution of 30 ms. Intronless and truncated ftz mRNA, synthesized in vitro and labeled with QDs, was microinjected into the nuclei of Cos7 cells. Almost all mRNAs were in motion, and statistical analyses revealed anomalous diffusion between barriers, with a microscopic diffusion coefficient of 0.12 microm2/s and a macroscopic diffusion coefficient of 0.025 microm2/s. Diffusion of mRNA was observed in interchromatin regions but not in histone2B-GFP-labeled chromatin regions. These results provide direct evidence of channeled mRNA diffusion in interchromatin regions.

Inferring maps of forces inside cell membrane microdomains

Mapping of the forces on biomolecules in cell membranes has spurred the development of effective labels, e.g., organic fluorophores and nanoparticles, to track trajectories of single biomolecules. Standard methods use particular statistics, namely the mean square displacement, to analyze the underlying dynamics. Here, we introduce general inference methods to fully exploit information in the experimental trajectories, providing sharp estimates of the forces and the diffusion coefficients in membrane microdomains. Rapid and reliable convergence of the inference scheme is demonstrated on trajectories generated numerically. The method is then applied to infer forces and potentials acting on the receptor of the toxin labeled by lanthanide-ion nanoparticles. Our scheme is applicable to any labeled biomolecule and results show its general relevance for membrane compartmentation.

What do diffusion measurements tell us about membrane compartmentalisation? Emergence of the role of interprotein interactions

The techniques of diffusion analysis based on optical microscopy approaches have revealed a great diversity of the dynamic organisation of cell membranes. For a long period, two frameworks have dominated the way of representing the membrane structure: the membrane skeleton fences and the lipid raft models. Progresses in the methods of data analysis have shed light on the features and consequently the possible origin of membrane domains: Inter-protein interactions play a role in confinement. Innovative developments pushing forward the spatiotemporal resolution limits are currently emerging, which are likely to provide in the future a detailed understanding of the intimate functional dynamic organisation of the cell membrane.

Versatile analysis of single-molecule tracking data by comprehensive testing against Monte Carlo simulations

We propose here an approach for the analysis of single-molecule trajectories which is based on a comprehensive comparison of an experimental data set with multiple Monte Carlo simulations of the diffusion process. It allows quantitative data analysis, particularly whenever analytical treatment of a model is infeasible. Simulations are performed on a discrete parameter space and compared with the experimental results by a nonparametric statistical test. The method provides a matrix of p-values that assess the probability for having observed the experimental data at each setting of the model parameters. We show the testing approach for three typical situations observed in the cellular plasma membrane: i), free Brownian motion of the tracer, ii), hop diffusion of the tracer in a periodic meshwork of squares, and iii), transient binding of the tracer to slowly diffusing structures. By plotting the p-value as a function of the model parameters, one can easily identify the most consistent parameter settings but also recover mutual dependencies and ambiguities which are difficult to determine by standard fitting routines. Finally, we used the test to reanalyze previous data obtained on the diffusion of the glycosylphosphatidylinositol-protein CD59 in the plasma membrane of the human T24 cell line.

T-cell antigen receptor triggering and lipid rafts: a matter of space and time scales. Talking Point on the involvement of lipid rafts in T-cell activation

T-cell antigen receptor triggering mechanisms and lipid rafts are of broad interest, but are also controversial topics. Here, we review some recent progress in these two research fields, which has been accomplished mostly in live cells and with the use of advanced technologies. We then discuss the potential relationship between membrane-domain organization and T-cell antigen receptor-triggering mechanisms. On the basis of the relevant experimental observations, we argue that the key to achieving a better understanding of both processes is the ability to monitor the molecular dynamics and interactions taking place in the membrane of T cells at a spatial scale of tens to hundreds of nanometres, with a subsecond-to-second temporal resolution.

Actin restricts FcepsilonRI diffusion and facilitates antigen-induced receptor immobilization

The actin cytoskeleton has been implicated in restricting diffusion of plasma membrane components. Here, simultaneous observations of quantum dot-labelled FcepsilonRI motion and GFP-tagged actin dynamics provide direct evidence that actin filament bundles define micron-sized domains that confine mobile receptors. Dynamic reorganization of actin structures occurs over seconds, making the location and dimensions of actin-defined domains time-dependent. Multiple FcepsilonRI often maintain extended close proximity without detectable correlated motion, suggesting that they are co-confined within membrane domains. FcepsilonRI signalling is activated by crosslinking with multivalent antigen. We show that receptors become immobilized within seconds of crosslinking. Disruption of the actin cytoskeleton results in delayed immobilization kinetics and increased diffusion of crosslinked clusters. These results implicate actin in membrane partitioning that not only restricts diffusion of membrane proteins, but also dynamically influences their long-range mobility, sequestration and response to ligand binding.

Dynamics of single potassium channel proteins in the plasma membrane of migrating cells

Cell migration is an important physiological process among others controlled by ion channel activity. Calcium-activated potassium channels (K(Ca)3.1) are required for optimal cell migration. Previously, we identified single human (h)K(Ca)3.1 channel proteins in the plasma membrane by means of quantum dot (QD) labeling. In the present study, we tracked single-channel proteins during migration to classify their dynamics in the plasma membrane of MDCK-F cells. Single hK(Ca)3.1 channels were visualized with QD- or Alexa488-conjugated antibodies and tracked at the basal cell membrane using time-lapse total internal reflection fluorescence (TIRF) microscopy. Analysis of the trajectories allowed the classification of channel dynamics. Channel tracks were compared with those of free QD-conjugated antibodies. The size of the label has a pronounced effect on hK(Ca)3.1 channel diffusion. QD-labeled channels have a (sub)diffusion coefficient D(QDbound) = 0.067 microm(2)/s(alpha), whereas that of Alexa488-labeled channels is D(Alexa) = 0.139 microm(2)/s. Free QD-conjugated antibodies move much faster: D(QDfree) = 2.163 microm(2)/s(alpha). Plotting the mean squared distances (msd) covered by hK(Ca)3.1 channels as a function of time points to the mode of diffusion. Alexa488-labeled channels diffuse normally, whereas the QD-label renders hK(Ca)3.1 channel diffusion anomalous. Free QD-labeled antibodies also diffuse anomalously. Hence, QDs slow down diffusion of hK(Ca)3.1 channels and change the mode of diffusion. These results, referring to the role of label size and properties of the extracellular environment, suggest that the pericellular glycocalyx has an important impact on labels used for single molecule tracking. Thus tracking fluorescent particles within the glycocalyx opens up a possibility to characterize the pericellular nanoenvironment.

Functional membrane diffusion of G-protein coupled receptors

G-protein-coupled receptor function involves interactions between the receptor, G-proteins and effectors in the cell plasma membrane. The main biochemical processes have been individually identified but the mechanisms governing the successive protein-protein interactions of this complex multi-molecular machinery have yet to be established. We discuss advances in understanding the functional dynamics of the receptor resulting from diffusion measurements, and in the context of the plasma membrane organization.

(Un)confined diffusion of CD59 in the plasma membrane determined by high-resolution single molecule microscopy

There has been emerging interest whether plasma membrane constituents are moving according to free Brownian motion or hop diffusion. In the latter model, lipids, lipid-anchored proteins, and transmembrane proteins would be transiently confined to periodic corrals in the cell membrane, which are structured by the underlying membrane skeleton. Because this model is based exclusively on results provided by one experimental strategy--high-resolution single particle tracking--we attempted in this study to confirm or amend it using a complementary technique. We developed a novel strategy that employs single molecule fluorescence microscopy to detect confinements to free diffusion of CD59--a GPI-anchored protein--in the plasma membrane of living T24 (ECV) cells. With this method, minimum invasive labeling via fluorescent Fab fragments was sufficient to measure the lateral motion of individual protein molecules on a millisecond timescale, yielding a positional accuracy down to 22 nm. Although no hop diffusion was directly observable, based on a full analytical description our results provide upper boundaries for confinement size and strength.

Multiple association states between glycine receptors and gephyrin identified by SPT analysis

The scaffolding protein gephyrin is known to anchor glycine receptors (GlyR) at synapses and to participate in the dynamic equilibrium between synaptic and extrasynaptic GlyR in the neuronal membrane. Here we investigated the properties of this interaction in cells cotransfected with YFP-tagged gephyrin and GlyR subunits possessing an extracellular myc-tag. In HeLa cells and young neurons, single particle tracking was used to follow in real time individual GlyR, labeled with quantum dots, traveling into and out of gephyrin clusters. Analysis of the diffusion properties of two GlyR subunit types--able or unable to bind gephyrin--gave access to the association states of GlyR with its scaffolding protein. Our results indicated that an important portion of GlyR could be linked to a few molecules of gephyrin outside gephyrin clusters. This emphasizes the role of scaffolding proteins in the extrasynaptic membrane and supports the implication of gephyrin-gephyrin interactions in the stabilization of GlyR at synapses. The kinetic parameters controlling the equilibrium between GlyR inside and outside clusters were also characterized. Within clusters, we identified two subpopulations of GlyR with distinct degrees of stabilization between receptors and scaffolding proteins.

Particle image correlation spectroscopy (PICS): retrieving nanometer-scale correlations from high-density single-molecule position data

A new data analysis tool that resolves correlations on the nanometer length and millisecond timescale is derived. This tool, adapted from methods of spatiotemporal image correlation spectroscopy, exploits the high positional accuracy of single-particle tracking. While conventional tracking methods break down if multiple particle trajectories intersect, our method works in principle for arbitrarily large molecule densities and diffusion coefficients as long as individual molecules can be identified. The method is computationally cheap and robust and requires no a priori knowledge about the dynamical coefficients, as opposed to other methods. We demonstrate the validity of the method by Monte Carlo simulations and by application to single-molecule tracking data of membrane-anchored proteins in live cells. The results faithfully reproduce those obtained by conventional tracking. Upon activation, a fraction of the small GTPase H-Ras is confined to domains of <200 nm diameter, which further substantiates the prediction that membrane organization is a determinant in cellular signaling.

Visualizing odorant receptor trafficking in living cells down to the single-molecule level

Despite the importance of trafficking for regulating G protein-coupled receptor signaling, for many members of the seven transmembrane helix protein family, such as odorant receptors, little is known about this process in live cells. Here, the complete life cycle of the human odorant receptor OR17-40 was directly monitored in living cells by ensemble and single-molecule imaging, using a double-labeling strategy. While the overall, intracellular trafficking of the receptor was visualized continuously by using a GFP tag, selective imaging of cell surface receptors was achieved by pulse-labeling an acyl carrier protein tag. We found that OR17-40 efficiently translocated to the plasma membrane only at low expression, whereas at higher biosynthesis the receptor accumulated in intracellular compartments. Receptors in the plasma membrane showed high turnover resulting from constitutive internalization along the clathrin pathway, even in the absence of ligand. Single-molecule microscopy allowed monitoring of the early, dynamic processes in odorant receptor signaling. Although mobile receptors initially diffused either freely or within domains of various sizes, binding of an agonist or an antagonist increased partitioning of receptors into small domains of approximately 190 nm, which likely are precursors of clathrin-coated pits. The binding of a ligand, therefore, resulted in modulation of the continuous, constitutive internalization. After endocytosis, receptors were directed to early endosomes for recycling. This unique mechanism of continuous internalization and recycling of OR17-40 might be instrumental in allowing rapid recovery of odor perception.