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

Heterogeneously flagellated microswimmer behavior in viscous fluids

An analysis of heterogeneously flagellated microswimmers inside viscous fluids is presented. Flagella harvested from Salmonella typhimurium were isolated, repolymerized, and functionalized to have biotin at their ends, allowing for chemical attachment along the surfaces of avidin-coated microparticles. Assembled microswimmers were rotated under incremental magnetic field frequencies, in saline and methylcellulose solutions, to baseline their velocity responses. A mean square displacement analysis revealed that rotating microswimmers exhibited anomalous diffusive behavior at small time scales in each fluid and had increased diffusivity compared with the non-rotating cases. Flagellated microswimmers had decreased diffusivity when compared with non-flagellated microparticles in Brownian conditions. Microswimmers were demonstrated to perform selected trajectories under proportional feedback control with reasonable accuracy. Finally, microswimmer propulsion was shown to be heavily influenced by the handedness of the rotating magnetic fields, with frequency induced reversals of swimming direction observed under clockwise rotation; this effect was determined to be the result of flagellar bundling and unbundling.

Whole-cell imaging of plasma membrane receptors by 3D lattice light-sheet dSTORM

The molecular organization of receptors in the plasma membrane of cells is paramount for their functionality. We combined lattice light-sheet (LLS) microscopy with three-dimensional (3D) single-molecule localization microscopy (dSTORM) and single-particle tracking to quantify the expression and distribution, and mobility of CD56 receptors on whole fixed and living cells, finding that CD56 accumulated at cell-cell interfaces. For comparison, we investigated two other receptors, CD2 and CD45, which showed different expression levels and distributions in the plasma membrane. Overall, 3D-LLS-dSTORM enabled imaging and single-particle tracking of plasma membrane receptors with single-molecule sensitivity unperturbed by surface effects. Our results demonstrate that receptor distribution and mobility are largely unaffected by contact to the coverslip but the measured localization densities are in general lower at the basal plasma membrane due to partial limited accessibility for antibodies.

Single-molecule turnover dynamics of actin and membrane coat proteins in clathrin-mediated endocytosis

Actin dynamics generate forces to deform the membrane and overcome the cell’s high turgor pressure during clathrin-mediated endocytosis (CME) in yeast, but precise molecular details are still unresolved. Our previous models predicted that actin filaments of the endocytic meshwork continually polymerize and disassemble, turning over multiple times during an endocytic event, similar to other actin systems. We applied single-molecule speckle tracking in live fission yeast to directly measure molecular turnover within CME sites for the first time. In contrast with the overall ~20 s lifetimes of actin and actin-associated proteins in endocytic patches, we detected single-molecule residence times around 1 to 2 s, and similarly high turnover rates of membrane-associated proteins in CME. Furthermore, we find heterogeneous behaviors in many proteins’ motions. These results indicate that endocytic proteins turn over up to five times during the formation of an endocytic vesicle, and suggest revising quantitative models of force production.

Single-molecule turnover dynamics of actin and membrane coat proteins in clathrin-mediated endocytosis

Actin dynamics generate forces to deform the membrane and overcome the cell's high turgor pressure during clathrin-mediated endocytosis (CME) in yeast, but precise molecular details are still unresolved. Our previous models predicted that actin filaments of the endocytic meshwork continually polymerize and disassemble, turning over multiple times during an endocytic event, similar to other actin systems. We applied single-molecule speckle tracking in live fission yeast to directly measure molecular turnover within CME sites for the first time. In contrast with the overall ~20 s lifetimes of actin and actin-associated proteins in endocytic patches, we detected single-molecule residence times around 1 to 2 s, and similarly high turnover rates of membrane-associated proteins in CME. Furthermore, we find heterogeneous behaviors in many proteins' motions. These results indicate that endocytic proteins turn over up to five times during the formation of an endocytic vesicle, and suggest revising quantitative models of force production.

Symmetric activity of DNA polymerases at and recruitment of exonuclease ExoR and of PolA to the Bacillus subtilis replication forks

DNA replication forks are intrinsically asymmetric and may arrest during the cell cycle upon encountering modifications in the DNA. We have studied real time dynamics of three DNA polymerases and an exonuclease at a single molecule level in the bacterium Bacillus subtilis. PolC and DnaE work in a symmetric manner and show similar dwell times. After addition of DNA damage, their static fractions and dwell times decreased, in agreement with increased re-establishment of replication forks. Only a minor fraction of replication forks showed a loss of active polymerases, indicating relatively robust activity during DNA repair. Conversely, PolA, homolog of polymerase I and exonuclease ExoR were rarely present at forks during unperturbed replication but were recruited to replications forks after induction of DNA damage. Protein dynamics of PolA or ExoR were altered in the absence of each other during exponential growth and during DNA repair, indicating overlapping functions. Purified ExoR displayed exonuclease activity and preferentially bound to DNA having 5′ overhangs in vitro. Our analyses support the idea that two replicative DNA polymerases work together at the lagging strand whilst only PolC acts at the leading strand, and that PolA and ExoR perform inducible functions at replication forks during DNA repair.

Resampling single-particle tracking data eliminates localization errors and reveals proper diffusion anomalies

Single-particle tracking (SPT) is a versatile tool for quantifying diffusional motion in complex soft-matter systems, e.g., in biological specimen. Evaluating SPT data often invokes the fitting of a trajectory's time-averaged mean-square displacement (TA-MSD) with a simple power law, 〈r^{2}(τ)〉_{t}∼τ^{α}, where the scaling exponent α can yield important insights into the nature of the transport process. Biological specimen, for example, frequently feature a diffusion anomaly, i.e., an exponent α<1 ("subdiffusion"). However, due to SPT-inherent static and dynamic localization errors, in combination with typically short trajectories, it is often a real challenge to determine the value of α reliably by simply fitting TA-MSDs. Here a straightforward resampling approach is presented and tested that eliminates both localization errors in the TA-MSD of trajectories originating from subdiffusive fractional Brownian motion processes. As a result, the mean anomaly exponent 〈α〉_{E} of an ensemble of trajectories is revealed in a robust fashion.

Particle Mobility Analysis Using Deep Learning and the Moment Scaling Spectrum

Quantitative analysis of dynamic processes in living cells using time-lapse microscopy requires not only accurate tracking of every particle in the images, but also reliable extraction of biologically relevant parameters from the resulting trajectories. Whereas many methods exist to perform the tracking task, there is still a lack of robust solutions for subsequent parameter extraction and analysis. Here a novel method is presented to address this need. It uses for the first time a deep learning approach to segment single particle trajectories into consistent tracklets (trajectory segments that exhibit one type of motion) and then performs moment scaling spectrum analysis of the tracklets to estimate the number of mobility classes and their associated parameters, providing rich fundamental knowledge about the behavior of the particles under study. Experiments on in-house datasets as well as publicly available particle tracking data for a wide range of proteins with different dynamic behavior demonstrate the broad applicability of the method.

Improving Diameter Accuracy for Dynamic Imaging Microscopy for Different Particle Types

Dynamic imaging analysis instruments are used for sizing particles of different types that might appear in a biopharmaceutical. These instruments are calibrated using polystyrene latex microspheres in water, which is a significantly different system than the typical particles imaged in a formulation. We show how the instruments, when reporting an equivalent diameter, set a threshold for image processing and then apply a built-in correction to account for fuzzy boundary effects. We investigate the degree to which the threshold value and built-in correction influences the size, and ultimately particle size distribution, that the instrument reports on other particle types. Size corrections for a dynamic imaging system in a typical optical configuration were determined by comparison of equivalent image diameters with diameters from Brownian motion tracking of particles. A variety of particles were characterized: aggregates made from a monoclonal antibody available as reference material RM 8671 from the National Institute of Standards and Technology, bovine serum albumin aggregates, silicone oil droplets, polystyrene microspheres, and ethylene tetrafluoroethylene particles, a protein aggregate simulant (National Institute of Standards and Technology reference material RM 8634). The results show that the protein aggregates and ethylene tetrafluoroethylene are very similar to one another but quite different from the polystyrene calibration spheres. This points the way to developing new correction factors and calibration procedures based on particle type.

Role of Actin Cytoskeleton in Dynamics and Function of the Serotonin1A Receptor

G protein-coupled receptors (GPCRs) are important membrane proteins in higher eukaryotes that carry out a vast array of cellular signaling and act as major drug targets. The serotonin_1A receptor is a prototypical member of the GPCR family and is implicated in neuropsychiatric disorders such as anxiety and depression, besides serving as an important drug target. With an overall goal of exploring the functional consequence of altered receptor dynamics, in this work, we probed the role of the actin cytoskeleton in the dynamics, ligand binding, and signaling of the serotonin_1A receptor. We monitored receptor dynamics utilizing single particle tracking, which provides information on relative distribution of receptors in various diffusion modes in addition to diffusion coefficient. We show here that the short-term diffusion coefficient of the receptor increases upon actin destabilization by cytochalasin D. In addition, analysis of individual trajectories shows that there are changes in relative populations of receptors undergoing various types of diffusion upon actin destabilization. The release of dynamic constraint was evident by an increase in the radius of confinement of the receptor upon actin destabilization. The functional implication of such actin destabilization was manifested as an increase in specific agonist binding and downstream signaling, monitored by measuring reduction in cellular cAMP levels. These results bring out the interdependence of GPCR dynamics with cellular signaling.

The influence of inter-particle forces on diffusion at the nanoscale

Van der Waals and electrostatic interactions are the dominant forces acting at the nanoscale and they have been reported to directly influence a range of phenomena including surface adhesion, friction, and colloid stability but their contribution on nanoparticle diffusion dynamics is still not clear. In this study we evaluated experimentally the changes in the diffusion coefficient of nanoparticles as a result of varying the magnitude of Van der Waals and electrostatic forces. We controlled the magnitude of these forces by varying the ionic strength of a salt solution, which has been shown to be a parameter that directly controls the forces, and found by tracking single nanoparticles dispersed in solutions with different salt molarity that the diffusion of nanoparticles increases with the magnitude of the electrostatic forces and Van der Waals forces. Our results demonstrate that these two concurrently dynamic forces play a pivotal role in driving the diffusion process and must be taken into account when considering nanoparticle behaviour.

Phragmoplast Orienting Kinesin 2 Is a Weak Motor Switching between Processive and Diffusive Modes

Plant development and morphology relies on the accurate insertion of new cell walls during cytokinesis. However, how a plant cell correctly orients a new wall is poorly understood. Two kinesin class-12 members, phragmoplast orienting kinesin 1 (POK1) and POK2, are involved in the process, but how these molecular machines work is not known. Here, we used in vivo and single-molecule in vitro measurements to determine how Arabidopsis thaliana POK2 motors function mechanically. We found that POK2 is a very weak, on average plus-end-directed, moderately fast kinesin. Interestingly, POK2 switches between processive and diffusive modes characterized by an exclusive-state mean-squared-displacement analysis. Our results support a model that POK motors push against peripheral microtubules of the phragmoplast for its guidance. This pushing model may mechanically explain the conspicuous narrowing of the division site. Together, our findings provide mechanical insight into how active motors accurately position new cell walls in plants.

Classification of diffusion modes in single-particle tracking data: Feature-based versus deep-learning approach

Single-particle trajectories measured in microscopy experiments contain important information about dynamic processes occurring in a range of materials including living cells and tissues. However, extracting that information is not a trivial task due to the stochastic nature of the particles' movement and the sampling noise. In this paper, we adopt a deep-learning method known as a convolutional neural network (CNN) to classify modes of diffusion from given trajectories. We compare this fully automated approach working with raw data to classical machine learning techniques that require data preprocessing and extraction of human-engineered features from the trajectories to feed classifiers like random forest or gradient boosting. All methods are tested using simulated trajectories for which the underlying physical model is known. From the results it follows that CNN is usually slightly better than the feature-based methods, but at the cost of much longer processing times. Moreover, there are still some borderline cases in which the classical methods perform better than CNN.

Errors in Energy Landscapes Measured with Particle Tracking

Tracking Brownian particles is often employed to map the energy landscape they explore. Such measurements have been exploited to study many biological processes and interactions in soft materials. Yet video tracking is irremediably contaminated by localization errors originating from two imaging artifacts: the "static" errors come from signal noise, and the "dynamic" errors arise from the motion blur due to finite frame-acquisition time. We show that these errors result in systematic and nontrivial biases in the measured energy landscapes. We derive a relationship between the true and the measured potential that elucidates, among other aberrations, the presence of false double-well minima in the apparent potentials reported in recent studies. We further assess several canonical trapping and pair-interaction potentials by using our analytically derived results and Brownian dynamics simulations. In particular, we show that the apparent spring stiffness of harmonic potentials (such as optical traps) is increased by dynamic errors but decreased by static errors. Our formula allows for the development of efficient corrections schemes, and we also present in this work a provisional method for reconstructing true potentials from the measured ones.

Optimal estimation of drift and diffusion coefficients in the presence of static localization error

We consider the inference of the drift velocity and the diffusion coefficient of a particle undergoing a directed random walk in the presence of static localization error. A weighted least-squares fit to mean-square displacement (MSD) data is used to infer the parameters of the assumed drift-diffusion model. For experiments which cannot be repeated we show that the quality of the inferred parameters depends on the number of MSD points used in the fitting. An optimal number of fitting points p_{opt} is shown to exist which depends on the time interval between frames Δt and the unknown parameters. We therefore also present a simple iterative algorithm which converges rapidly toward p_{opt}. For repeatable experiments the quality depends crucially on the measurement time interval over which measurements are made, reflecting the different timescales associated with drift and diffusion. An optimal measurement time interval T_{opt} exists, which depends on the number of measurement points and the unknown parameters, and so again we present an iterative algorithm which converges quickly toward T_{opt} and is shown to be robust to initial parameter guesses.

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

This study presents an improved quantitative tool for the analysis of particulate trajectories. Particulate trajectory data appears in several different biological contexts, from the trajectory of chemotaxing bacteria to the nuclear mobility inferred from the trajectory of MS2 spots. Presently, the majority of analyses performed on particulate trajectory data have been limited to mean-squared displacement (MSD) analysis. Although simple, MSD analysis has several pitfalls, including difficulty in selecting between competing methods of motion, handling systems with multiple distinct subpopulations, and parameter extraction from limited time-series data. Here, we provide an alternative to MSD analysis using the jump distance distribution (JDD), which addresses the aforementioned issues. In particular, the method outperforms MSD analysis in the data-poor limit, thereby giving access to a larger range of temporal dynamics. In this work, we construct and validate a derivation of the JDD for different transportation modes and dimensions and implement a parameter estimation and model selection scheme. This scheme is validated, and direct improvements over MSD analysis are shown. Through an analysis of bacterial chemotaxis data, we highlight the JDD's ability to extract parameters at a variety of timescales, as well as extract underlying biological features of interest.

Towards mapping the 3D genome through high speed single-molecule tracking of functional transcription factors in single living cells

How genomic DNA is organized in the nucleus is a long-standing question. We describe a single-molecule bioimaging method utilizing super-localization precision coupled to fully quantitative image analysis tools, towards determining snapshots of parts of the 3D genome architecture of model eukaryote budding yeast Saccharomyces cerevisiae with exceptional millisecond time resolution. We employ astigmatism imaging to enable robust extraction of 3D position data on genomically encoded fluorescent protein reporters that bind to DNA. Our relatively straightforward method enables snippets of 3D architectures of likely single genome conformations to be resolved captured via DNA-sequence specific binding proteins in single functional living cells.

A 2-step algorithm for the estimation of time-varying single particle tracking models using Maximum Likelihood

Single particle tracking (SPT) is a powerful class of methods for studying the dynamics of biomolecules inside living cells. The techniques reveal both trajectories of individual particles, with a resolution well below the diffraction limit of light, and the parameters defining the motion model, such as diffusion coefficients and confinement lengths. Existing algorithms assume these parameters are constant throughout an experiment. However, it has been demonstrated that they often vary with time as the tracked particles move through different regions in the cell or as conditions inside the cell change in response to stimuli. In this work we apply the method of local Maximum Likelihood (ML) estimation to the SPT application combined with change detection. Local ML uses a sliding window over the data, estimating the model parameters in each window. Once we have found the values for the parameters before and after the change, we apply offline change detection to know the exact time of the change. Then, we reestimate these parameters and show that there is an improvement in the estimation of key parameters found in SPT. Preliminary results using simulated data with a basic diffusion model with additive Gaussian noise show that our proposed algorithm is able to track abrupt changes in the parameters as they evolve during a trajectory.

Practical Considerations in Particle and Object Tracking and Analysis

The rapid advancement of live-cell imaging technologies has enabled biologists to generate high-dimensional data to follow biological movement at the microscopic level. Yet, the "perceived" ease of use of modern microscopes has led to challenges whereby sub-optimal data are commonly generated that cannot support quantitative tracking and analysis as a result of various ill-advised decisions made during image acquisition. Even optimally acquired images often require further optimization through digital processing before they can be analyzed. In writing this article, we presume our target audience to be biologists with a foundational understanding of digital image acquisition and processing, who are seeking to understand the essential steps for particle/object tracking experiments. It is with this targeted readership in mind that we review the basic principles of image-processing techniques as well as analysis strategies commonly used for tracking experiments. We conclude this technical survey with a discussion of how movement behavior can be mathematically modeled and described. © 2019 by John Wiley & Sons, Inc.

Near Saturation of Ribosomal L7/L12 Binding Sites with Ternary Complexes in Slowly Growing E. coli

For Escherichia coli growing rapidly in rich medium at 37 °C, the doubling time can be as short as ~20 min and the average rate of translation (k_trl) can be as fast as ~20 amino acids/s. For slower growth arising from poor nutrient quality or from higher growth osmolality, k_trl decreases significantly. In earlier work from the Hwa lab, a simplified Michaelis-Menten model suggested that the decrease in k_trl arises from a shortage of ternary complexes (TCs) under nutrient limitation and from slower diffusion of TCs under high growth osmolality. Here we present a single-molecule tracking study of the diffusion of EF-Tu in E. coli growing with doubling times in the range 62-190 min at 37 °C due to nutrient limitation, high growth osmolality, or both. The diffusive properties of EF-Tu remain quantitatively indistinguishable across all growth conditions studied. Dissection of the total population into ribosome-bound and free sub-populations, combined with copy number estimates for EF-Tu and ribosomes, indicates that in all cases ~3.7 EF-Tu copies are bound on average to each translating 70S ribosome. Thus, the four L7/L12 binding sites adjacent to the ribosomal A-site in E. coli are essentially saturated with TCs in all conditions, facilitating rapid testing of aminoacyl-tRNAs for a codon match. Evidently, the average translation rate is not limited by either the supply of cognate TCs under nutrient limitation or by the diffusion of free TCs at high osmolality. Some other step or steps must be rate limiting for translation in slow growth.

High-Resolution Nanoparticle Sizing with Maximum A Posteriori Nanoparticle Tracking Analysis

The rapid and efficient characterization of polydisperse nanoparticle dispersions remains a challenge within nanotechnology and biopharmaceuticals. Current methods for particle sizing, such as dynamic light scattering, analytical ultracentrifugation, and field-flow fractionation, can suffer from a combination of statistical biases, difficult sample preparation, insufficient sampling, and ill-posed data analysis. As an alternative, we introduce a Bayesian method that we call maximum a posteriori nanoparticle tracking analysis (MApNTA) for estimating the size distributions of nanoparticle samples from high-throughput single-particle tracking experiments. We derive unbiased statistical models for two observable quantities in a typical nanoparticle trajectory-the mean square displacement and the trajectory length-as a function of the particle size and calculate size distributions using maximum a posteriori (MAP) estimation with cross validation to mildly regularize solutions. We show that this approach infers nanoparticle size distributions with high resolution by performing extensive Brownian dynamics simulations and experiments with mono- and polydisperse solutions of gold nanoparticles as well as single-walled carbon nanotubes. We further demonstrate particular utility for characterizing minority components and impurity populations and highlight this ability with the identification of an impurity in a commercially produced gold nanoparticle sample. Modern algorithms such as MApNTA should find widespread use in the routine characterization of complex nanoparticle dispersions, allowing for significant advances in nanoparticle synthesis, separation, and functionalization.

Statistics of Colloidal Suspensions Stirred by Microswimmers

We present a statistical analysis of the experimental trajectories of colloids in a dilute suspension of the green algae Chlamydomonas reinhardtii. The measured probability density function (pdf) of the displacements of colloids covers 7 orders of magnitude. The pdfs are characterized by non-Gaussian tails for intermediate time intervals, but nevertheless they collapse when scaled with their standard deviation. This diffusive scaling breaks down for longer time intervals and the pdf becomes Gaussian. However, the mean squared displacements of tracer positions are linear over the complete measurement time interval. Experiments are performed for various tracer diameters, swimmer concentrations, and mean swimmer velocities. This allows a rigorous comparison with several theoretical models. We can exclude a description based on an effective temperature and other mean field approaches that describe the irregular motion as a sum of the fluctuating far field of many microswimmers. The data are best described by the microscopic model by J.-L. Thiffeault, Distribution of particle displacements due to swimming microorganisms, Phys. Rev. E 92, 023023 (2015)PRESCM1539-375510.1103/PhysRevE.92.023023.

Resolving Cytosolic Diffusive States in Bacteria by Single-Molecule Tracking

The trajectory of a single protein in the cytosol of a living cell contains information about its molecular interactions in its native environment. However, it has remained challenging to accurately resolve and characterize the diffusive states that can manifest in the cytosol using analytical approaches based on simplifying assumptions. Here, we show that multiple intracellular diffusive states can be successfully resolved if sufficient single-molecule trajectory information is available to generate well-sampled distributions of experimental measurements and if experimental biases are taken into account during data analysis. To address the inherent experimental biases in camera-based and MINFLUX-based single-molecule tracking, we use an empirical data analysis framework based on Monte Carlo simulations of confined Brownian motion. This framework is general and adaptable to arbitrary cell geometries and data acquisition parameters employed in two-dimensional or three-dimensional single-molecule tracking. We show that, in addition to determining the diffusion coefficients and populations of prevalent diffusive states, the timescales of diffusive state switching can be determined by stepwise increasing the time window of averaging over subsequent single-molecule displacements. Time-averaged diffusion analysis of single-molecule tracking data may thus provide quantitative insights into binding and unbinding reactions among rapidly diffusing molecules that are integral for cellular functions.

Statistical testing approach for fractional anomalous diffusion classification

Taking advantage of recent single-particle tracking data, we compare the popular standard mean-squared displacement method with a statistical testing hypothesis procedure for three testing statistics and for two particle types: membrane receptors and the G proteins coupled to them. Each method results in different classifications. For this reason, more rigorous statistical tests are analyzed here in detail. The main conclusion is that the statistical testing approaches might provide good results even for short trajectories, but none of the proposed methods is "the best" for all considered examples; in other words, one needs to combine different approaches to get a reliable classification.

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

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

Single-particle tracking localization microscopy reveals nonaxonemal dynamics of intraflagellar transport proteins at the base of mammalian primary cilia

Primary cilia play a vital role in cellular sensing and signaling. An essential component of ciliogenesis is intraflagellar transport (IFT), which is involved in IFT protein recruitment, axonemal engagement of IFT protein complexes, and so on. The mechanistic understanding of these processes at the ciliary base was largely missing, because it is challenging to observe the motion of IFT proteins in this crowded region using conventional microscopy. Here, we report short-trajectory tracking of IFT proteins at the base of mammalian primary cilia by optimizing single-particle tracking photoactivated localization microscopy for IFT88-mEOS4b in live human retinal pigment epithelial cells. Intriguingly, we found that mobile IFT proteins “switched gears” multiple times from the distal appendages (DAPs) to the ciliary compartment (CC), moving slowly in the DAPs, relatively fast in the proximal transition zone (TZ), slowly again in the distal TZ, and then much faster in the CC. They could travel through the space between the DAPs and the axoneme without following DAP structures. We further revealed that BBS2 and IFT88 were highly populated at the distal TZ, a potential assembly site. Together, our live-cell single-particle tracking revealed region-dependent slowdown of IFT proteins at the ciliary base, shedding light on staged control of ciliary homeostasis.

Collective effects of yeast cytoplasmic dynein based microtubule transport

Teams of cortically anchored dyneins pulling at microtubules (MTs) are known to be essential for aster, spindle and nuclear positioning during cell division and fertilization. While the single-molecule basis of dynein processivity is now better understood, the effect of increasing numbers of motors on transport is not clear. Here, we examine the collective transport properties of a Saccharomyces cerevisiae cytoplasmic dynein fragment, widely used as a minimal model, by a combination of quantitative MT gliding assays and stochastic simulations. We find both MT lengths and motor densities qualitatively affect the degree of randomness of MT transport. However, the directionality and velocity of MTs increase above a threshold number of motors (N) interacting with a filament. To better understand this behavior, we simulate a gliding assay based on a model of uniformly distributed immobilized motors transporting semi-flexible MTs. Each dynein dimer is modeled as an effective stochastic stepper with asymmetric force dependent detachment dynamics, based on single-molecule experiments. Simulations predict increasing numbers of motors (N) result in a threshold dependent transition in directionality and transport velocity and a monotonic decrease in effective diffusivity. Thus both experiment and theory show qualitative agreement in the emergence of coordination in transport above a threshold number of motor heads. We hypothesize that the phase-transition like property of this dynein could play a role in vivo during yeast mitosis, when this dynein localizes to the cortex and pulls astral MTs of increasing length, resulting in correct positioning and orientation of the nucleus at the bud-neck.

Guidelines for DNA recombination and repair studies: Cellular assays of DNA repair pathways

Understanding the plasticity of genomes has been greatly aided by assays for recombination, repair and mutagenesis. These assays have been developed in microbial systems that provide the advantages of genetic and molecular reporters that can readily be manipulated. Cellular assays comprise genetic, molecular, and cytological reporters. The assays are powerful tools but each comes with its particular advantages and limitations. Here the most commonly used assays are reviewed, discussed, and presented as the guidelines for future studies.

High-speed imaging and tracking of very small single nanoparticles by contrast enhanced microscopy

Nanoparticles have been used extensively in biology-related research and many applications require direct visualization of individual nanoparticles by optical microscopy. For long-term and high-speed measurements, scattering-based microscopy is a unique technique because of the stable and indefinite scattering signals. In scattering-based single-particle measurements, large nanoparticles are usually needed in order to generate sufficient signals for detection. However, larger nanoparticles introduce greater mass loading, experience stronger steric hindrance, and are more prone to crosslinking. In this work, we demonstrate coherent brightfield (COBRI) microscopy with enhanced contrast and show its capability of direct visualization of very small nanoparticles in scattering at a high speed. COBRI microscopy allows us to visualize and track single metallic and dielectric nanoparticles, as small as 10 nm, at 1000 frames per second. A quantitative relationship between the linear scattering cross section of the nanoparticle and its COBRI contrast is reported. Using COBRI microscopy, we further demonstrate the tracking of 10 nm gold nanoparticles labeled to lipid molecules in supported bilayer membranes, showing that the small nanoparticles may facilitate single-molecule measurements with reduced perturbation. Furthermore, the identical imaging sensitivities of COBRI and interferometric scattering (iSCAT) microscopy, the reflection counterpart of COBRI, is demonstrated at an equal illumination intensity. Finally, future improvements in the speed and sensitivity of scattering-based interference microscopy are discussed.

"Waltz" of Cell Membrane-Coated Nanoparticles on Lipid Bilayers: Tracking Single Particle Rotation in Ligand-Receptor Binding

Understanding the binding of nanoparticles to receptors on biomembranes is critical to the development and screening of therapeutic materials. A prevailing understanding is that multivalent ligand-receptor binding leads to slower and confined translational motion of nanoparticles. In contrast, we report in this study distinct types of rotational dynamics of nanoparticles during their seemingly similar translational confinements in ligand-receptor binding. Our nanoparticles are fluorescently anisotropic and camouflaged with T cell membranes. As they bind to ligands on planar lipid bilayers, the particles transition from back-and-forth rocking motion to circling and eventually confined circling motion, while "hopping" between translational confinements. Both rotational and translational motions of the nanoparticles become more confined at higher ligand density. The time-dependent changes in particle rotation reveal different stages in the progression of multivalent binding between the cell-membrane coated nanoparticles and their ligands. Our work also demonstrates the promise of using combined rotational and translational single particle tracking to resolve biological interactions that could be "hidden" in translational measurements alone.

Bayesian analysis of single-particle tracking data using the nested-sampling algorithm: maximum-likelihood model selection applied to stochastic-diffusivity data

We employ Bayesian statistics using the nested-sampling algorithm to compare and rank multiple models of ergodic diffusion (including anomalous diffusion) as well as to assess their optimal parameters for in silico-generated and real time-series. We focus on the recently-introduced model of Brownian motion with "diffusing diffusivity"-giving rise to widely-observed non-Gaussian displacement statistics-and its comparison to Brownian and fractional Brownian motion, also for the time-series with some measurement noise. We conduct this model-assessment analysis using Bayesian statistics and the nested-sampling algorithm on the level of individual particle trajectories. We evaluate relative model probabilities and compute best-parameter sets for each diffusion model, comparing the estimated parameters to the true ones. We test the performance of the nested-sampling algorithm and its predictive power both for computer-generated (idealised) trajectories as well as for real single-particle-tracking trajectories. Our approach delivers new important insight into the objective selection of the most suitable stochastic model for a given time-series. We also present first model-ranking results in application to experimental data of tracer diffusion in polymer-based hydrogels.

SMTracker: a tool for quantitative analysis, exploration and visualization of single-molecule tracking data reveals highly dynamic binding of B. subtilis global repressor AbrB throughout the genome

Single-particle (molecule) tracking (SPT/SMT) is a powerful method to study dynamic processes in living cells at high spatial and temporal resolution. Even though SMT is becoming a widely used method in bacterial cell biology, there is no program employing different analytical tools for the quantitative evaluation of tracking data. We developed SMTracker, a MATLAB-based graphical user interface (GUI) for automatically quantifying, visualizing and managing SMT data via five interactive panels, allowing the user to interactively explore tracking data from several conditions, movies and cells on a track-by-track basis. Diffusion constants are calculated a) by a Gaussian mixture model (GMM) panel, analyzing the distribution of positional displacements in x- and y-direction using a multi-state diffusion model (e.g. DNA-bound vs. freely diffusing molecules), and inferring the diffusion constants and relative fraction of molecules in each state, or b) by square displacement analysis (SQD), using the cumulative probability distribution of square displacements to estimate the diffusion constants and relative fractions of up to three diffusive states, or c) through mean-squared displacement (MSD) analyses, allowing the discrimination between Brownian, sub- or superdiffusive behavior. A spatial distribution analysis (SDA) panel analyzes the subcellular localization of molecules, summarizing the localization of trajectories in 2D- heat maps. Using SMTracker, we show that the global transcriptional repressor AbrB performs highly dynamic binding throughout the Bacillus subtilis genome, with short dwell times that indicate high on/off rates in vivo. While about a third of AbrB molecules are in a DNA-bound state, 40% diffuse through the chromosome, and the remaining molecules freely diffuse through the cells. AbrB also forms one or two regions of high intensity binding on the nucleoids, similar to the global gene silencer H-NS in Escherichia coli, indicating that AbrB may also confer a structural function in genome organization.

Statistical analysis of particle trajectories in living cells

Recent advances in molecular biology and fluorescence microscopy imaging have made possible the inference of the dynamics of molecules in living cells. Such inference allows us to understand and determine the organization and function of the cell. The trajectories of particles (e.g., biomolecules) in living cells, computed with the help of object tracking methods, can be modeled with diffusion processes. Three types of diffusion are considered: (i) free diffusion, (ii) subdiffusion, and (iii) superdiffusion. The mean-square displacement (MSD) is generally used to discriminate the three types of particle dynamics. We propose here a nonparametric three-decision test as an alternative to the MSD method. The rejection of the null hypothesis, i.e., free diffusion, is accompanied by claims of the direction of the alternative (subdiffusion or superdiffusion). We study the asymptotic behavior of the test statistic under the null hypothesis and under parametric alternatives which are currently considered in the biophysics literature. In addition, we adapt the multiple-testing procedure of Benjamini and Hochberg to fit with the three-decision-test setting, in order to apply the test procedure to a collection of independent trajectories. The performance of our procedure is much better than the MSD method as confirmed by Monte Carlo experiments. The method is demonstrated on real data sets corresponding to protein dynamics observed in fluorescence microscopy.

Heterochromatin restricts the mobility of nuclear bodies

Nuclear bodies are relatively immobile organelles. Here, we investigated the mechanisms underlying their movement using experimentally induced interphase prenucleolar bodies (iPNBs). Most iPNBs demonstrated constrained diffusion, exhibiting infrequent fusions with other iPNBs and nucleoli. Fusion events were actin-independent and appeared to be the consequence of stochastic collisions between iPNBs. Most iPNBs were surrounded by condensed chromatin, while fusing iPNBs were usually found in a single heterochromatin-delimited compartment ("cage"). The experimentally induced over-condensation of chromatin significantly decreased the frequency of iPNB fusion. Thus, the data obtained indicate that the mobility of nuclear bodies is restricted by heterochromatin.

Increased chromosomal mobility after DNA damage is controlled by interactions between the recombination machinery and the checkpoint

In this study, Smith et al. investigated how cells modulate chromosome mobility in response to DNA damage. They show that global chromosome mobility is regulated by the Rad51 recombinase and its mediator, Rad52, and their findings indicate that interplay between recombination factors and the checkpoint restricts increased mobility until recombination proteins are assembled at damaged sites.

During homologous recombination, cells must coordinate repair, DNA damage checkpoint signaling, and movement of chromosomal loci to facilitate homology search. In Saccharomyces cerevisiae, increased movement of damaged loci (local mobility) and undamaged loci (global mobility) precedes homolog pairing in mitotic cells. How cells modulate chromosome mobility in response to DNA damage remains unclear. Here, we demonstrate that global chromosome mobility is regulated by the Rad51 recombinase and its mediator, Rad52. Surprisingly, rad51Δ rad52Δ cells display checkpoint-dependent constitutively increased mobility, indicating that a regulatory circuit exists between recombination and checkpoint machineries to govern chromosomal mobility. We found that the requirement for Rad51 in this circuit is distinct from its role in recombination and that interaction with Rad52 is necessary to alleviate inhibition imposed by mediator recruitment to ssDNA. Thus, interplay between recombination factors and the checkpoint restricts increased mobility until recombination proteins are assembled at damaged sites.

Three-Dimensional Optical Tweezers Tracking Resolves Random Sideward Steps of the Kinesin-8 Kip3

The budding yeast kinesin-8 Kip3 is a highly processive motor protein that walks to the ends of cytoskeletal microtubules and shortens them in a collective manner. However, how exactly Kip3 reaches the microtubule end is unclear. Although rotations of microtubules in multimotored Kip3 gliding assays implied directed sideward switching between microtubule protofilaments, two-dimensional, single-molecule, optical-tweezers assays indicated that Kip3 randomly switched protofilaments. Here, we topographically suspended microtubules such that Kip3 motors could freely access the microtubules in three dimensions. Tracking single-motor-driven microspheres with a three-dimensional, zero-load, optical-tweezers-based force clamp showed that Kip3 switched protofilaments in discrete steps equally frequent in both directions. A statistical analysis confirmed the diffusive sideward motion of Kip3, consistent with the two-dimensional single-molecule results. Furthermore, we found that motors were in one of three states: either not switching protofilaments or switching between them with a slow or fast sideward-stepping rate. Interestingly, this sideward diffusion was limited to one turn, suggesting that motors could not cross the microtubule seam. The diffusive protofilament switching may enable Kip3 to efficiently bypass obstacles and reach the microtubule end for length regulation.

A Hidden Markov Model for Detecting Confinement in Single-Particle Tracking Trajectories

State-of-the-art single-particle tracking (SPT) techniques can generate long trajectories with high temporal and spatial resolution. This offers the possibility of mechanistically interpreting particle movements and behavior in membranes. To this end, a number of statistical techniques have been developed that partition SPT trajectories into states with distinct diffusion signatures, allowing a statistical analysis of diffusion state dynamics and switching behavior. Here, we develop a confinement model, within a hidden Markov framework, that switches between phases of free diffusion and confinement in a harmonic potential well. By using a Markov chain Monte Carlo algorithm to fit this model, automated partitioning of individual SPT trajectories into these two phases is achieved, which allows us to analyze confinement events. We demonstrate the utility of this algorithm on a previously published interferometric scattering microscopy data set, in which gold-nanoparticle-tagged ganglioside GM1 lipids were tracked in model membranes. We performed a comprehensive analysis of confinement events, demonstrating that there is heterogeneity in the lifetime, shape, and size of events, with confinement size and shape being highly conserved within trajectories. Our observations suggest that heterogeneity in confinement events is caused by both individual nanoparticle characteristics and the binding-site environment. The individual nanoparticle heterogeneity ultimately limits the ability of interferometric scattering microscopy to resolve molecule dynamics to the order of the tag size; homogeneous tags could potentially allow the resolution to be taken below this limit by deconvolution methods. In a wider context, the presented harmonic potential well confinement model has the potential to detect and characterize a wide variety of biological phenomena, such as hop diffusion, receptor clustering, and lipid rafts.

Examination of the Statistical Effects Associated with Tracking Propulsive Particles

Particle tracking of active colloidal particles can be used to compute mean-squared displacements that are fit to extract properties of the particles including the propulsive speed. Statistical errors in the mean-squared displacement leads to errors in the extracted properties especially for more weakly propelling particles. Brownian dynamics simulations in which the particle parameters are prescribed were used to examine the statistics of tracking self-propelling objects. It was found that the manner in which tracking data is analyzed has a profound impact on the precision and accuracy of measurements. To properly extract particle parameters, it was necessary to apply a nonlinear fit of the mean-squared displacement over a time region that includes transition behavior from ballistic to diffusive. The dependence of the statistics on the number of particles tracked and the length of movies was examined, showing how and why weakly propelling particles are difficult to analyze.

Quantifying Discretization Errors in Electrophoretically-Guided Micro Additive Manufacturing

This paper presents process models for a new micro additive manufacturing process termed Electrophoretically-guided Micro Additive Manufacturing (EPμAM). In EPμAM, a planar microelectrode array generates the electric potential distributions which cause colloidal particles to agglomerate and deposit in desired regions. The discrete microelectrode array nature and the used pulse width modulation (PWM) technique for microelectrode actuation create unavoidable process errors-space and time discretization errors-that distort particle trajectories. To combat this, we developed finite element method (FEM) models to study trajectory deviations due to these errors. Mean square displacement (MSD) analysis of the computed particle trajectories is used to compare these deviations for several electrode geometries. The two top-performing electrode geometries evaluated by MSD were additionally investigated through separate case studies via geometry variation and MSD recomputation. Furthermore, separate time-discretization error simulations are also studied where electrode actuating waveforms were simulated. The mechanical impulse of the electromechanical force, generated from these waveforms is used as the basis for comparison. The obtained results show a moderate MSDs variability and significant differences in the computed mechanical impulses for the actuating waveforms. The observed limitations of the developed process model and of the error comparison technique are briefly discussed and future steps are recommended.

Microdomain formation is a general property of bacterial membrane proteins and induces heterogeneity of diffusion patterns

Background

Proteins within the cytoplasmic membrane display distinct localization patterns and arrangements. While multiple models exist describing the dynamics of membrane proteins, to date, there have been few systematic studies, particularly in bacteria, to evaluate how protein size, number of transmembrane domains, and temperature affect their diffusion, and if conserved localization patterns exist.

Results

We have used fluorescence microscopy, single-molecule tracking (SMT), and computer-aided visualization methods to obtain a better understanding of the three-dimensional organization of bacterial membrane proteins, using the model bacterium Bacillus subtilis. First, we carried out a systematic study of the localization of over 200 B. subtilis membrane proteins, tagged with monomeric mVenus-YFP at their original gene locus. Their subcellular localization could be discriminated in polar, septal, patchy, and punctate patterns. Almost 20% of membrane proteins specifically localized to the cell poles, and a vast majority of all proteins localized in distinct structures, which we term microdomains. Dynamics were analyzed for selected membrane proteins, using SMT. Diffusion coefficients of the analyzed transmembrane proteins did not correlate with protein molecular weight, but correlated inversely with the number of transmembrane helices, i.e., transmembrane radius. We observed that temperature can strongly influence diffusion on the membrane, in that upon growth temperature upshift, diffusion coefficients of membrane proteins increased and still correlated inversely to the number of transmembrane domains, following the Saffman–Delbrück relation.

Conclusions

The vast majority of membrane proteins localized to distinct multimeric assemblies. Diffusion of membrane proteins can be suitably described by discriminating diffusion coefficients into two protein populations, one mobile and one immobile, the latter likely constituting microdomains. Our results show there is high heterogeneity and yet structural order in the cell membrane, and provide a roadmap for our understanding of membrane organization in prokaryotes.

Electronic supplementary material

The online version of this article (10.1186/s12915-018-0561-0) contains supplementary material, which is available to authorized users.

Natural convection induced by an optically fabricated and actuated microtool with a thermoplasmonic disk

Two-photon polymerization was employed for fabricating microtools amenable to optical trapping and manipulation. A disk feature was included as part of the microtools and further functionalized by electron-beam deposition. The nanostructured gold layer on the disk facilitates off-resonant plasmonic heating upon illumination with a laser beam. As a consequence, natural convection characterized by the typical toroidal shape resembling that of Rayleigh-Bénard flow can be observed. A velocity of several μm·s^-1 is measured for 2 μm microspheres dispersed in the surroundings of the microtool. To the best of our knowledge, this is the first time that thermoplasmonic-induced natural convection is experimentally demonstrated using a mobile heat source.

Non-specific interactions govern cytosolic diffusion of nanosized objects in mammalian cells

The diffusivity of macromolecules in the cytoplasm of eukaryotic cells varies over orders of magnitude and dictates the kinetics of cellular processes. However, a general description that associates the Brownian or anomalous nature of intracellular diffusion to the architectural and biochemical properties of the cytoplasm has not been achieved. Here we measure the mobility of individual fluorescent nanoparticles in living mammalian cells to obtain a comprehensive analysis of cytoplasmic diffusion. We identify a correlation between tracer size, its biochemical nature and its mobility. Inert particles with size equal or below 50 nm behave as Brownian particles diffusing in a medium of low viscosity with negligible effects of molecular crowding. Increasing the strength of non-specific interactions of the nanoparticles within the cytoplasm gradually reduces their mobility and leads to subdiffusive behaviour. These experimental observations and the transition from Brownian to subdiffusive motion can be captured in a minimal phenomenological model.