Single Particle Tracking Experiments Research Articles

An open-source, high-resolution, automated fluorescence microscope

Fluorescence microscopy is a fundamental tool in the life sciences, but the availability of sophisticated equipment required to yield high-quality, quantitative data is a major bottleneck in data production in many laboratories worldwide. This problem has long been recognized and the abundancy of low-cost electronics and the simplification of fabrication through 3D-printing have led to the emergence of open-source scientific hardware as a research field. Cost effective fluorescence microscopes can be assembled from cheaply mass-produced components, but lag behind commercial solutions in image quality. On the other hand, blueprints of sophisticated microscopes such as light-sheet or super-resolution systems, custom-assembled from high quality parts, are available, but require a high level of expertise from the user. Here, we combine the UC2 microscopy toolbox with high-quality components and integrated electronics and software to assemble an automated high-resolution fluorescence microscope. Using this microscope, we demonstrate high resolution fluorescence imaging for fixed and live samples. When operated inside an incubator, long-term live-cell imaging over several days was possible. Our microscope reaches single molecule sensitivity, and we performed single particle tracking and SMLM super-resolution microscopy experiments in cells. Our setup costs a fraction of its commercially available counterparts but still provides a maximum of capabilities and image quality. We thus provide a proof of concept that high quality scientific data can be generated by lay users with a low-budget system and open-source software. Our system can be used for routine imaging in laboratories that do not have the means to acquire commercial systems and through its affordability can serve as teaching material to students.

An open-source, high-resolution, automated fluorescence microscope.

Fluorescence microscopy is a fundamental tool in the life sciences, but the availability of sophisticated equipment required to yield high-quality, quantitative data is a major bottleneck in data production in many laboratories worldwide. This problem has long been recognized and the abundancy of low-cost electronics and the simplification of fabrication through 3D-printing have led to the emergence of open-source scientific hardware as a research field. Cost effective fluorescence microscopes can be assembled from cheaply mass-produced components, but lag behind commercial solutions in image quality. On the other hand, blueprints of sophisticated microscopes such as light-sheet or super-resolution systems, custom-assembled from high quality parts, are available, but require a high level of expertise from the user. Here, we combine the UC2 microscopy toolbox with high-quality components and integrated electronics and software to assemble an automated high-resolution fluorescence microscope. Using this microscope, we demonstrate high resolution fluorescence imaging for fixed and live samples. When operated inside an incubator, long-term live-cell imaging over several days was possible. Our microscope reaches single molecule sensitivity, and we performed single particle tracking and SMLM super-resolution microscopy experiments in cells. Our setup costs a fraction of its commercially available counterparts but still provides a maximum of capabilities and image quality. We thus provide a proof of concept that high quality scientific data can be generated by lay users with a low-budget system and open-source software. Our system can be used for routine imaging in laboratories that do not have the means to acquire commercial systems and through its affordability can serve as teaching material to students.

Deep Learning-Assisted Automated Multidimensional Single Particle Tracking in Living Cells.

The translational and rotational dynamics of anisotropic optical nanoprobes revealed in single particle tracking (SPT) experiments offer molecular-level information about cellular activities. Here, we report an automated high-speed multidimensional SPT system integrated with a deep learning algorithm for tracking the 3D orientation of anisotropic gold nanoparticle probes in living cells with high localization precision (<10 nm) and temporal resolution (0.9 ms), overcoming the limitations of rotational tracking under low signal-to-noise ratio (S/N) conditions. This method can resolve the azimuth (0°-360°) and polar angles (0°-90°) with errors of less than 2° on the experimental and simulated data under S/N of ∼4. Even when the S/N approaches the limit of 1, this method still maintains better robustness and noise resistance than the conventional pattern matching methods. The usefulness of this multidimensional SPT system has been demonstrated with a study of the motions of cargos transported along the microtubules within living cells.

A Novel Fractional Brownian Dynamics Method for Simulating the Dynamics of Confined Bottle-Brush Polymers in Viscoelastic Solution.

In crowded fluids, polymer segments can exhibit anomalous subdiffusion due to the viscoelasticity of the surrounding environment. Previous single-particle tracking experiments revealed that such anomalous diffusion in complex fluids (e.g., in bacterial cytoplasm) can be described by fractional Brownian motion (fBm). To investigate how the viscoelastic media affects the diffusive behaviors of polymer segments without resolving single crowders, we developed a novel fractional Brownian dynamics method to simulate the dynamics of polymers under confinement. In this work, instead of using Gaussian random numbers ("white Gaussian noise") to model the Brownian force as in the standard Brownian dynamics simulations, we introduce fractional Gaussian noise (fGn) in our homemade fractional Brownian dynamics simulation code to investigate the anomalous diffusion of polymer segments by using a simple "bottle-brush"-type polymer model. The experimental results of the velocity autocorrelation function and the exponent that characterizes the subdiffusion of the confined polymer segments can be reproduced by this simple polymer model in combination with fractional Gaussian noise (fGn), which mimics the viscoelastic media.

Gramian angular fields for leveraging pretrained computer vision models with anomalous diffusion trajectories.

Anomalous diffusion is present at all scales, from atomic to large ones. Some exemplary systems are ultracold atoms, telomeres in the nucleus of cells, moisture transport in cement-based materials, arthropods' free movement, and birds' migration patterns. The characterization of the diffusion gives critical information about the dynamics of these systems and provides an interdisciplinary framework with which to study diffusive transport. Thus, the problem of identifying underlying diffusive regimes and inferring the anomalous diffusion exponent α with high confidence is critical to physics, chemistry, biology, and ecology. Classification and analysis of raw trajectories combining machine learning techniques with statistics extracted from them have widely been studied in the Anomalous Diffusion Challenge [Muñoz-Gil etal., Nat. Commun. 12, 6253 (2021)2041-172310.1038/s41467-021-26320-w]. Here we present a new data-driven method for working with diffusive trajectories. This method utilizes Gramian angular fields (GAF) to encode one-dimensional trajectories as images (Gramian matrices), while preserving their spatiotemporal structure for input to computer-vision models. This allows us to leverage two well-established pretrained computer-vision models, ResNet and MobileNet, to characterize the underlying diffusive regime and infer the anomalous diffusion exponent α. Short raw trajectories of lengths between 10 and 50 are commonly encountered in single-particle tracking experiments and are the most difficult ones to characterize. We show that GAF images can outperform the current state-of-the-art while increasing accessibility to machine learning methods in an applied setting.

The effect of time resolution on the observed first passage times in diffusive dynamics.

Single-molecule and single-particle tracking experiments are typically unable to resolve fine details of thermal motion at short timescales where trajectories are continuous. We show that, when a diffusive trajectory xt is sampled at finite time intervals δt, the resulting error in measuring the first passage time to a given domain can exceed the time resolution of the measurement by more than an order of magnitude. Such surprisingly large errors originate from the fact that the trajectory may enter and exit the domain while being unobserved, thereby lengthening the apparent first passage time by an amount that is larger than δt. Such systematic errors are particularly important in single-molecule studies of barrier crossing dynamics. We show that the correct first passage times, as well as other properties of the trajectories such as splitting probabilities, can be recovered via a stochastic algorithm that reintroduces unobserved first passage events probabilistically.

Actin rings form plasma membrane diffusion barriers.

In a fluid system like the plasma membrane, molecules will not enrich spontaneously. Since a high local concentration of specific molecules is vital for many membrane protein functions, a domain enriched in these molecules must be formed. This can be achieved by the generation of a physical diffusion barrier to the lateral movement of membrane components. One such barrier exists in the axon initial segment (AIS) of neurons, but the mechanism of the barrier so far remained elusive. Two candidates have emerged to be the cause of the membrane compartmentalization in the AIS: periodic actin rings (fence model) or large immobile transmembrane voltage-gated sodium channels (picket model). Here, we show that the diffusion barrier in the AIS is caused by the actin cytoskeleton. To do so, we combined in silico experiments with high-speed, high-density single-particle tracking and superresolution microscopy. In silico single-particle tracking (SPT) experiments clearly showed that the compartmentalization is compatible with the fence model but incompatible with the picket model. Furthermore, we show via SPT of membrane proteins in progenitor-derived neuronal cells that the diffusion barrier is also present in cells that do not exhibit an ion-channel enriched AIS, but do show actin rings along their processes. Further experiments using dual-colour live-cell stimulated emission depletion microscopy (STED) showed that periodic actin rings in cells are near (20 nm) the plasma membrane. Lastly, we show via correlative SPT/STORM that membrane molecules accumulate between actin rings. Taken together, we present here evidence for the compartmentalization of the plasma membrane by the actin cytoskeleton. Membrane proximal actin structures are a common feature of many cell types. Therefore, we speculate that the observed membrane compartmentalization is not specific to the neuronal cell lineage but rather a general mechanism of large-scale membrane organization.

The random walker's toolbox for analyzing single-particle tracking data.

Technological advances and a burst of new microscopy methods have boosted the use of quantitative tracking experiments, in Soft Matter and Biological Physics but also in the Life Sciences. However, in contrast to highly advanced measurement techniques and tracking tools, subsequent analyses of trajectories frequently do not exploit the data's full potential. Aiming especially at experimental laboratories and early-career scientists, we introduce, discuss, and apply in this Tutorial Review a large set of versatile measures that have proven to be useful for analyzing trajectories from single-particle tracking experiments, beyond a simple extraction of diffusion constants from mean squared displacements. To support a direct test and application of these measures, we supplement the text with a download package that comprises a low-threshold toolbox of ready-to-use routines and training data sets, hence relaxing the need to develop home-brewed solutions and/or to create suitable benchmark data.

Does Supramolecular Gelation Require an External Trigger?

The supramolecular gelation of small molecules is typically preceded by an external stimulus to trigger the self-assembly. The need for this trigger stems from the metastable nature of most supramolecular gels and can limit their applicability. Herein, we present a small urea-based molecule that spontaneously forms a stable hydrogel by simple mixing without the addition of an external trigger. Single particle tracking experiments and observations made from scanning electron microscopy indicated that triggerless gelation occurred in a similar fashion as the archetypical heat-triggered gelation. These results could stimulate the search for other supramolecular hydrogels that can be obtained by simple mixing. Furthermore, the mechanism of the heat-triggered supramolecular gelation was elucidated by a combination of molecular dynamics simulations and quantitative NMR experiments. Surprisingly, hydrogelation seemingly occurs via a stepwise self-assembly in which spherical nanoparticles mature into an entangled fibrillary network.

Modelling anomalous diffusion in semi-infinite disordered systems and porous media

For an effectively one-dimensional, semi-infinite disordered system connected to a reservoir of tracer particles kept at constant concentration, we provide the dynamics of the concentration profile. Technically, we start with the Montroll–Weiss equation of a continuous time random walk with a scale-free waiting time density. From this we pass to a formulation in terms of the fractional diffusion equation for the concentration profile in a semi-infinite space for the boundary condition , using a subordination approach. From this we deduce the tracer flux and the so-called breakthrough curve (BTC) at a given distance from the tracer source. In particular, BTCs are routinely measured in geophysical contexts but are also of interest in single-particle tracking experiments. For the ‘residual’ BTCs, given by , we demonstrate a long-time power-law behaviour that can be compared conveniently to experimental measurements. For completeness we also derive expressions for the moments in this constant-concentration boundary condition.

Fractional Brownian motion with random Hurst exponent: Accelerating diffusion and persistence transitions.

Fractional Brownian motion, a Gaussian non-Markovian self-similar process with stationary long-correlated increments, has been identified to give rise to the anomalous diffusion behavior in a great variety of physical systems. The correlation and diffusion properties of this random motion are fully characterized by its index of self-similarity or the Hurst exponent. However, recent single-particle tracking experiments in biological cells revealed highly complicated anomalous diffusion phenomena that cannot be attributed to a class of self-similar random processes. Inspired by these observations, we here study the process that preserves the properties of the fractional Brownian motion at a single trajectory level; however, the Hurst index randomly changes from trajectory to trajectory. We provide a general mathematical framework for analytical, numerical, and statistical analysis of the fractional Brownian motion with the random Hurst exponent. The explicit formulas for probability density function, mean-squared displacement, and autocovariance function of the increments are presented for three generic distributions of the Hurst exponent, namely, two-point, uniform, and beta distributions. The important features of the process studied here are accelerating diffusion and persistence transition, which we demonstrate analytically and numerically.

Measurement error correction in particle tracking microrheology

In diverse biological applications, single-particle tracking (SPT) of passive microscopic species has become the experimental measurement of choice, when either the materials are of limited volume or so soft as to deform uncontrollably when manipulated by traditional instruments. In a wide range of SPT experiments, a ubiquitous finding is that of long-range dependence in the particles’ motion. This is characterized by a power-law signature in the mean squared displacement (MSD) of particle positions as a function of time, the parameters of which reveal valuable information about the viscous and elastic properties of various biomaterials. However, MSD measurements are typically contaminated by complex and interacting sources of instrumental noise. As these often affect the high-frequency bandwidth to which MSD estimates are particularly sensitive, inadequate error correction can lead to severe bias in power law estimation and, thereby, the inferred viscoelastic properties. In this article we propose a novel strategy to filter high-frequency noise from SPT measurements. Our filters are shown theoretically to cover a broad spectrum of high-frequency noises and lead to a parametric estimator of MSD power-law coefficients for which an efficient computational implementation is presented. Based on numerous analyses of experimental and simulated data, results suggest our methods perform very well compared to other denoising procedures.

The guidance and adhesion protein FLRT2 dimerizes in cis via dual small-X3-small transmembrane motifs

Fibronectin Leucine-rich Repeat Transmembrane (FLRT 1-3) proteins are a family of broadly expressed single-spanning transmembrane receptors that play key roles in development. Their extracellular domains mediate homotypic cell-cell adhesion and heterotypic protein interactions with other receptors to regulate cell adhesion and guidance. These in trans FLRT interactions determine the formation of signaling complexes of varying complexity and function. Whether FLRTs also interact at the surface of the same cell, in cis, remains unknown. Here, molecular dynamics simulations reveal two dimerization motifs in the FLRT2 transmembrane helix. Single particle tracking experiments show that these Small-X3-Small motifs synergize with a third dimerization motif encoded in the extracellular domain to permit the cis association and co-diffusion patterns of FLRT2 receptors on cells. These results may point to a competitive switching mechanism between in cis and in trans interactions, which suggests that homotypic FLRT interaction mirrors the functionalities of classic adhesion molecules.

TRamWAy: mapping physical properties of individual biomolecule random motion in large-scale single-particle tracking experiments.

Single-molecule localization microscopy allows studying the dynamics of biomolecules in cells and resolving the biophysical properties of the molecules and their environment underlying cellular function. With the continuously growing amount of data produced by individual experiments, the computational cost of quantifying these properties is increasingly becoming the bottleneck of single-molecule analysis. Mining these data requires an integrated and efficient analysis toolbox. We introduce TRamWAy, a modular Python library that features: (i) a conservative tracking procedure for localization data, (ii) a range of sampling techniques for meshing the spatio-temporal support of the data, (iii) computationally efficient solvers for inverse models, with the option of plugging in user-defined functions and (iv) a collection of analysis tools and a simple web-based interface. TRamWAy is a Python library and can be installed with pip and conda. The source code is available at https://github.com/DecBayComp/TRamWAy.

TRamWAy: mapping physical properties of moving biomolecules in large scale single-particle tracking experiments

Single-molecule localization microscopy allows studying the dynamics of biomolecules in cells and resolving the biophysical properties of the molecules and their environment underlying cellular function. With the continuously growing amount of data produced by individual experiments, the computational cost of quantifying these properties is increasingly becoming the bottleneck of single molecule analysis. Mining these data require an integrated and efficient analysis toolbox.

A Protocol for Studying Transcription Factor Dynamics Using Fast Single-Particle Tracking and Spot-On Model-Based Analysis.

Single-particle tracking (SPT) makes it possible to directly observe single protein diffusion dynamics in living cells over time. Thus, SPT has emerged as a powerful method to quantify the dynamics of nuclear proteins such as transcription factors (TFs). Here, we provide a protocol for conducting and analyzing SPT experiments with a focus on fast tracking ("fastSPT") of TFs in mammalian cells. First, we explore how to engineer and prepare cells for SPT experiments. Next, we examine how to optimize SPT experiments by imaging at low densities to minimize tracking errors and by using stroboscopic excitation to minimize motion-blur. Next, we discuss how to convert raw SPT data into single-particle trajectories. Finally, we illustrate how to analyze these trajectories using the kinetic modeling package Spot-On. We discuss how to use Spot-On to fit histograms of displacements and extract useful information such as the fraction of TFs that are bound and freely diffusing, and their associated diffusion coefficients.

Probing Allosteric Modulation of Membrane Receptor in the Native State by Data Mining-Integrated Tracking Microscopy

Probing Allosteric Modulation of Membrane Receptor in the Native State by Data Mining-Integrated Tracking Microscopy

Recapitulation of cell-like KRAS4b membrane dynamics on complex biomimetic membranes

SummaryUnderstanding the spatiotemporal distribution and dynamics of RAS on the plasma membrane (PM) is the key for elucidating the molecular mechanisms of the RAS signaling pathway. Single particle tracking (SPT) experiments show that in cells, KRAS diffuses in at least three interchanging states on the cellular PM; however, KRAS remains monomeric and always shows homogeneous diffusion on artificial membranes. Here, we show for the first time on a supported lipid bilayer composed of heterogeneous lipid components that we can recapitulate the three-state diffusion of KRAS seen in cells. The use of a biologically relevant eight-lipid system opens a new frontier in the biophysical studies of RAS and other membrane associated proteins on a biomimetic system that recapitulates the complexity of a cellular PM.

Tracking single particles for hours via continuous DNA-mediated fluorophore exchange

Monitoring biomolecules in single-particle tracking experiments is typically achieved by employing fixed organic dyes or fluorescent fusion proteins linked to a target of interest. However, photobleaching typically limits observation times to merely a few seconds, restricting downstream statistical analysis and observation of rare biological events. Here, we overcome this inherent limitation via continuous fluorophore exchange using DNA-PAINT, where fluorescently-labeled oligonucleotides reversibly bind to a single-stranded DNA handle attached to the target molecule. Such versatile and facile labeling allows uninterrupted monitoring of single molecules for extended durations. We demonstrate the power of our approach by observing DNA origami on membranes for tens of minutes, providing perspectives for investigating cellular processes on physiologically relevant timescales.

Anisotropic diffusion of membrane proteins at experimental timescales.

Single-particle tracking (SPT) experiments of lipids and membrane proteins provide a wealth of information about the properties of biomembranes. Careful analysis of SPT trajectories can reveal deviations from ideal Brownian behavior. Among others, this includes confinement effects and anomalous diffusion, which are manifestations of both the nanoscale structure of the underlying membrane and the structure of the diffuser. With the rapid increase in temporal and spatial resolution of experimental methods, a new aspect of the motion of the particle, namely, anisotropic diffusion, might become relevant. This aspect that so far received only little attention is the anisotropy of the diffusive motion and may soon provide an additional proxy to the structure and topology of biomembranes. Unfortunately, the theoretical framework for detecting and interpreting anisotropy effects is currently scattered and incomplete. Here, we provide a computational method to evaluate the degree of anisotropy directly from molecular dynamics simulations and also point out a way to compare the obtained results with those available from SPT experiments. In order to probe the effects of anisotropic diffusion, we performed coarse-grained molecular dynamics simulations of peripheral and integral membrane proteins in flat and curved bilayers. In agreement with the theoretical basis, our computational results indicate that anisotropy can persist up to the rotational relaxation time [τ=(2Dr)-1], after which isotropic diffusion is observed. Moreover, the underlying topology of the membrane bilayer can couple with the geometry of the particle, thus extending the spatiotemporal domain over which this type of motion can be detected.