Single particle tracking. Analysis of diffusion and flow in two-dimensional systems.

Analysis of the trajectories of small particles at high spatial and temporal resolution using video enhanced contrast microscopy provides a powerful approach to characterizing the mechanisms of particle motion in living cells and in other systems. We present here the theoretical basis for the analysis of these trajectories for particles undergoing random diffusion and/or systematic transport at uniform velocity in two-dimensional systems. The single particle tracking method, based on observations of the trajectories of individual particles, is compared with methods that characterize the motions of a large collection of particles such as fluorescence photobleaching recovery. Determination of diffusion coefficients or transport velocities either from correlation of positions or of velocities of the particles is discussed. A result of practical importance is an analysis of the dependence of the expected statistical uncertainty of these determinations on the number of position measurements. This provides a way of judging the accuracy of the diffusion coefficients and transport velocities obtained using this approach.     

Confined lateral diffusion of membrane receptors as studied by single particle tracking (nanovid microscopy). Effects of calcium-induced differentiation in cultured epithelial cells.

The movements of E-cadherin, epidermal growth factor receptor, and transferrin receptor in the plasma membrane of a cultured mouse keratinocyte cell line were studied using both single particle tracking (SPT; nanovid microscopy) and fluorescence photobleaching recovery (FPR). In the SPT technique, the receptor molecules are labeled with 40 nm-phi colloidal gold particles, and their movements are followed by video-enhanced differential interference contrast microscopy at a temporal resolution of 33 ms and at a nanometer-level spatial precision. The trajectories of the receptor molecules obtained by SPT were analyzed by developing a method that is based on the plot of the mean-square displacement against time. Four characteristic types of motion were observed: (a) stationary mode, in which the microscopic diffusion coefficient is less than 4.6 x 10(-12) cm2/s; (b) simple Brownian diffusion mode; (c) directed diffusion mode, in which unidirectional movements are superimposed on random motion; and (d) confined diffusion mode, in which particles undergoing Brownian diffusion (microscopic diffusion coefficient between 4.6 x 10(-12) and 1 x 10(-9) cm2/s) are confined within a limited area, probably by the membrane-associated cytoskeleton network. Comparison of these data obtained by SPT with those obtained by FPR suggests that the plasma membrane is compartmentalized into many small domains 300-600 nm in diameter (0.04-0.24 microns2 in area), in which receptor molecules are confined in the time scale of 3-30 s, and that the long-range diffusion observed by FPR can occur by successive movements of the receptors to adjacent compartments. Calcium-induced differentiation decreases the sum of the percentages of molecules in the directed diffusion and the stationary modes outside of the cell-cell contact regions on the cell surface (which is proposed to be the percentage of E-cadherin bound to the cytoskeleton/membrane-skeleton), from approximately 60% to 8% (low- and high-calcium mediums, respectively).     

Visualizing single molecules interacting with nuclear pore complexes by narrow-field epifluorescence microscopy

The utility of single molecule fluorescence (SMF) for understanding biological reactions has been amply demonstrated by a diverse series of studies over the last decade. In large part, the molecules of interest have been limited to those within a small focal volume or near a surface to achieve the high sensitivity required for detecting the inherently weak signals arising from individual molecules. Consequently, the investigation of molecular behavior with high time and spatial resolution deep within cells using SMF has remained challenging. Recently, we demonstrated that narrow-field epifluorescence microscopy allows visualization of nucleocytoplasmic transport at the single cargo level. We describe here the methodological approach that yields 2 ms and approximately 15 nm resolution for a stationary particle. The spatial resolution for a mobile particle is inherently worse, and depends on how fast the particle is moving. The signal-to-noise ratio is sufficiently high to directly measure the time a single cargo molecule spends interacting with the nuclear pore complex. Particle tracking analysis revealed that cargo molecules randomly diffuse within the nuclear pore complex, exiting as a result of a single rate-limiting step. We expect that narrow-field epifluorescence microscopy will be useful for elucidating other binding and trafficking events within cells.     

Accumulative Difference Image Protocol for Particle Tracking in Fluorescence Microscopy Tested in Mouse Lymphonodes

The basic research in cell biology and in medical sciences makes large use of imaging tools mainly based on confocal fluorescence and, more recently, on non-linear excitation microscopy. Substantially the aim is the recognition of selected targets in the image and their tracking in time. We have developed a particle tracking algorithm optimized for low signal/noise images with a minimum set of requirements on the target size and with no a priori knowledge of the type of motion. The image segmentation, based on a combination of size sensitive filters, does not rely on edge detection and is tailored for targets acquired at low resolution as in most of the in-vivo studies. The particle tracking is performed by building, from a stack of Accumulative Difference Images, a single 2D image in which the motion of the whole set of the particles is coded in time by a color level. This algorithm, tested here on solid-lipid nanoparticles diffusing within cells and on lymphocytes diffusing in lymphonodes, appears to be particularly useful for the cellular and the in-vivo microscopy image processing in which few a priori assumption on the type, the extent and the variability of particle motions, can be done.     

Superresolution imaging of biological nanostructures by spectral precision distance microscopy

For the improved understanding of biological systems on the nanoscale, it is necessary to enhance the resolution of light microscopy in the visible wavelength range beyond the limits of conventional epifluorescence microscopy (optical resolution of about 200 nm laterally, 600 nm axially). Recently, various far-field methods have been developed allowing a substantial increase of resolution ("superresolution microscopy", or "lightoptical nanoscopy"). This opens an avenue to 'nano-image' intact and even living cells, as well as other biostructures like viruses, down to the molecular detail. Thus, it is possible to combine light optical spatial nanoscale information with ultrastructure analyses and the molecular interaction information provided by molecular cell biology. In this review, we describe the principles of spectrally assigned localization microscopy (SALM) of biological nanostructures, focusing on a special SALM approach, spectral precision distance/position determination microscopy (SPDM) with physically modified fluorochromes (SPDM(Phymod) . Generally, this SPDM method is based on high-precision localization of fluorescent molecules, which can be discriminated using reversibly bleached states of the fluorophores for their optical isolation. A variety of application examples is presented, ranging from superresolution microscopy of membrane and cytoplasmic protein distribution to dual-color SPDM of nuclear proteins. At present, we can achieve an optical resolution of cellular structures down to the 20-nm range, with best values around 5 nm (～1/100 of the exciting wavelength).     

Quantitative Microscopy: Protein Dynamics and Membrane Organisation

The mobility of membrane proteins is a critical determinant of their interaction capabilities and protein functions. The heterogeneity of cell membranes imparts different types of motion onto proteins; immobility, random Brownian motion, anomalous sub-diffusion, 'hop' or confined diffusion, or directed flow. Quantifying the motion of proteins therefore enables insights into the lateral organisation of cell membranes, particularly membrane microdomains with high viscosity such as lipid rafts. In this review, we examine the hypotheses and findings of three main techniques for analysing protein dynamics: fluorescence recovery after photobleaching, single particle tracking and fluorescence correlation spectroscopy. These techniques, and the physical models employed in data analysis, have become increasingly sophisticated and provide unprecedented details of the biophysical properties of protein dynamics and membrane domains in cell membranes. Yet despite these advances, there remain significant unknowns in the relationships between cholesterol-dependent lipid microdomains, protein-protein interactions, and the effect of the underlying cytoskeleton. New multi-dimensional microscopy approaches may afford greater temporal and spatial resolution resulting in more accurate quantification of protein and membrane dynamics in live cells.     

Quantitative comparison of algorithms for tracking single fluorescent particles

Single particle tracking has seen numerous applications in biophysics, ranging from the diffusion of proteins in cell membranes to the movement of molecular motors. A plethora of computer algorithms have been developed to monitor the sub-pixel displacement of fluorescent objects between successive video frames, and some have been claimed to have "nanometer" resolution. To date, there has been no rigorous comparison of these algorithms under realistic conditions. In this paper, we quantitatively compare specific implementations of four commonly used tracking algorithms: cross-correlation, sum-absolute difference, centroid, and direct Gaussian fit. Images of fluorescent objects ranging in size from point sources to 5 microm were computer generated with known sub-pixel displacements. Realistic noise was added and the above four algorithms were compared for accuracy and precision. We found that cross-correlation is the most accurate algorithm for large particles. However, for point sources, direct Gaussian fit to the intensity distribution is the superior algorithm in terms of both accuracy and precision, and is the most robust at low signal-to-noise. Most significantly, all four algorithms fail as the signal-to-noise ratio approaches 4. We judge direct Gaussian fit to be the best algorithm when tracking single fluorophores, where the signal-to-noise is frequently near 4.     

Stochastically determined directed movement explains the dominant small-scale mitochondrial movements within non-neuronal tissue culture cells

The apparently stationary phase of mitochondrial motion was investigated in epithelial cells by spinning disk confocal light microscopy combined with image correlation based single particle tracking using custom software producing sub-pixel accuracy measurements (∼5 nm) at 10-12 Hz frame-rates. The analysis of these data suggests that the previously described stationary, or anchored phase, in mitochondrial movement actually comprise Brownian diffusion, interspersed with frequent and brief motor-driven events whose duration are stochastically determined. We have therefore discovered a new aspect of mitochondrial behavior, which we call stochastically determined, directed movement.     

3D Orbital Tracking in a Modified Two-photon Microscope: An Application to the Tracking of Intracellular Vesicles

The objective of this video protocol is to discuss how to perform and analyze a three-dimensional fluorescent orbital particle tracking experiment using a modified two-photon microscope¹. As opposed to conventional approaches (raster scan or wide field based on a stack of frames), the 3D orbital tracking allows to localize and follow with a high spatial (10 nm accuracy) and temporal resolution (50 Hz frequency response) the 3D displacement of a moving fluorescent particle on length-scales of hundreds of microns². The method is based on a feedback algorithm that controls the hardware of a two-photon laser scanning microscope in order to perform a circular orbit around the object to be tracked: the feedback mechanism will maintain the fluorescent object in the center by controlling the displacement of the scanning beam^3-5. To demonstrate the advantages of this technique, we followed a fast moving organelle, the lysosome, within a living cell^6,7. Cells were plated according to standard protocols, and stained using a commercially lysosome dye. We discuss briefly the hardware configuration and in more detail the control software, to perform a 3D orbital tracking experiment inside living cells. We discuss in detail the parameters required in order to control the scanning microscope and enable the motion of the beam in a closed orbit around the particle. We conclude by demonstrating how this method can be effectively used to track the fast motion of a labeled lysosome along microtubules in 3D within a live cell. Lysosomes can move with speeds in the range of 0.4-0.5 µm/sec, typically displaying a directed motion along the microtubule network⁸.     

High throughput inclusion body sizing: Nano particle tracking analysis

The expression of pharmaceutical relevant proteins in Escherichia coli frequently triggers inclusion body (IB) formation caused by protein aggregation. In the scientific literature, substantial effort has been devoted to the quantification of IB size. However, particle‐based methods used up to this point to analyze the physical properties of representative numbers of IBs lack sensitivity and/or orthogonal verification. Using high pressure freezing and automated freeze substitution for transmission electron microscopy (TEM) the cytosolic inclusion body structure was preserved within the cells. TEM imaging in combination with manual grey scale image segmentation allowed the quantification of relative areas covered by the inclusion body within the cytosol. As a high throughput method nano particle tracking analysis (NTA) enables one to derive the diameter of inclusion bodies in cell homogenate based on a measurement of the Brownian motion. The NTA analysis of fixated (glutaraldehyde) and non‐fixated IBs suggests that high pressure homogenization annihilates the native physiological shape of IBs. Nevertheless, the ratio of particle counts of non‐fixated and fixated samples could potentially serve as factor for particle stickiness. In this contribution, we establish image segmentation of TEM pictures as an orthogonal method to size biologic particles in the cytosol of cells. More importantly, NTA has been established as a particle‐based, fast and high throughput method (1000–3000 particles), thus constituting a much more accurate and representative analysis than currently available methods.     

Gold nanoparticle-protein arrays improve resolution for cryo-electron microscopy

Cryo-electron microscopy single particle analysis shows limited resolution due to poor alignment precision of noisy images taken under low electron exposure. Certain advantages can be obtained by assembling proteins into two-dimensional (2D) arrays since protein particles are locked into repetitive orientation, thus improving alignment precision. We present a labeling method to prepare protein 2D arrays using gold nanoparticles (NPs) interconnecting genetic tag sites on proteins. As an example, mycobacterium tuberculosis 20S proteasomes tagged with 6x-histidine were assembled into 2D arrays using 3.9-nm Au NPs functionalized with nickel-nitrilotriacetic acid. The averaged top-view images from the array particles showed higher resolution (by 6-8A) compared to analysis of single particles. The correct 7-fold symmetry was also evident by using array particles whereas it was not clear by analysis of a comparable number of single particles. The applicability of this labeling method for three-dimensional reconstruction of biological macromolecules is discussed.     

Precise particle tracking against a complicated background: polynomial fitting with Gaussian weight

We present a new particle tracking software algorithm designed to accurately track the motion of low-contrast particles against a background with large variations in light levels. The method is based on a polynomial fit of the intensity around each feature point, weighted by a Gaussian function of the distance from the centre, and is especially suitable for tracking endogeneous particles in the cell, imaged with bright field, phase contrast or fluorescence optical microscopy. Furthermore, the method can simultaneously track particles of all different sizes, and allows significant freedom in their shape. The algorithm is evaluated using the quantitative measures of accuracy and precision of previous authors, using simulated images at variable signal-to-noise ratios. To these we add new tests: the error due to a non-uniform background, and the error due to two particles approaching each other. Finally the tracking of particles in real cell images is demonstrated. The method is made freely available for non-commercial use as a software package with a graphical user-interface, which can be run within the Matlab programming environment.     

Digital holography-based 3D particle localization for single-molecule tweezer techniques

We present a three-dimensional (3D) imaging technique for the fast tracking of microscopic objects in a fluid environment. Our technique couples digital holographic microscopy with three-dimensional localization via parabolic masking. Compared with existing approaches, our method reconstructs 3D volumes from single-plane images, which greatly simplifies image acquisition, reduces the demand on microscope hardware, and facilitates tracking higher densities of microscopic particles while maintaining similar levels of precision. We demonstrate utility of this method in magnetic tweezer experiments, opening their use to multiplexed single-molecule force spectroscopy assays, which were previously limited by particle crowding and fast dissociation times. We propose that our technique will also be useful in other applications that involve the tracking of microscopic objects in three dimensions, such as studies of microorganism motility and 3D flow characterization of microfluidic devices.     

Diatrack particle tracking software: Review of applications and performance evaluation

Object tracking is an instrumental tool supporting studies of cellular trafficking. There are three challenges in object tracking: the identification of targets; the precise determination of their position and boundaries; and the assembly of correct trajectories. This last challenge is particularly relevant when dealing with densely populated images with low signal‐to‐noise ratios—conditions that are often encountered in applications such as organelle tracking, virus particle tracking or single‐molecule imaging. We have developed a set of methods that can handle a wide variety of signal complexities. They are compiled into a free software package called Diatrack. Here we review its main features and utility in a range of applications, providing a survey of the dynamic imaging field together with recommendations for effective use. The performance of our framework is shown to compare favorably to a wide selection of custom‐developed algorithms, whether in terms of localization precision, processing speed or correctness of tracks.      

Dual color localization microscopy of cellular nanostructures

The dual color localization microscopy (2CLM) presented here is based on the principles of spectral precision distance microscopy (SPDM) with conventional autofluorescent proteins under special physical conditions. This technique allows us to measure the spatial distribution of single fluorescently labeled molecules in entire cells with an effective optical resolution comparable to macromolecular dimensions. Here, we describe the application of the 2CLM approach to the simultaneous nanoimaging of cellular structures using two fluorochrome types distinguished by different fluorescence emission wavelengths. The capabilities of 2CLM for studying the spatial organization of the genome in the mammalian cell nucleus are demonstrated for the relative distributions of two chromosomal proteins labeled with autofluorescent GFP and mRFP1 domains. The 2CLM images revealed quantitative information on their spatial relationships down to length-scales of 30 nm.     

Nanoscale organization and dynamics of the siglec CD22 cooperate with the cytoskeleton in restraining BCR signalling

Receptor organization and dynamics at the cell membrane are important factors of signal transduction regulation. Using super‐resolution microscopy and single‐particle tracking, we show how the negative coreceptor CD22 works with the cortical cytoskeleton in restraining BCR signalling. In naïve B cells, we found endogenous CD22 to be highly mobile and organized into nanodomains. The landscape of CD22 and its lateral diffusion were perturbed either in the absence of CD45 or when the CD22 lectin domain was mutated. To understand how a relatively low number of CD22 molecules can keep BCR signalling in check, we generated Brownian dynamic simulations and supported them with ex vivo experiments. This combined approach suggests that the inhibitory function of CD22 is influenced by its nanoscale organization and is ensured by its fast diffusion enabling a “global BCR surveillance” at the plasma membrane.     

A local-optimization refinement algorithm in single particle analysis for macromolecular complex with multiple rigid modules

Single particle analysis, which can be regarded as an average of signals from thousands or even millions of particle projections, is an efficient method to study the three-dimensional structures of biological macromolecules. An intrinsic assumption in single particle analysis is that all the analyzed particles must have identical composition and conformation. Thus specimen heterogeneity in either composition or conformation has raised great challenges for high-resolution analysis. For particles with multiple conformations, inaccurate alignments and orientation parameters will yield an averaged map with diminished resolution and smeared density. Besides extensive classification approaches, here based on the assumption that the macromolecular complex is made up of multiple rigid modules whose relative orientations and positions are in slight fluctuation around equilibriums, we propose a new method called as local optimization refinement to address this conformational heterogeneity for an improved resolution. The key idea is to optimize the orientation and shift parameters of each rigid module and then reconstruct their three-dimensional structures individually. Using simulated data of 80S/70S ribosomes with relative fluctuations between the large (60S/50S) and the small (40S/30S) subunits, we tested this algorithm and found that the resolutions of both subunits are significantly improved. Our method provides a proof-of-principle solution for high-resolution single particle analysis of macromolecular complexes with dynamic conformations.     

Photoactivated Localization Microscopy with Bimolecular Fluorescence Complementation (BiFC-PALM)

Protein-protein interactions (PPIs) are key molecular events to biology. However, it remains a challenge to visualize PPIs with sufficient resolution and sensitivity in cells because the resolution of conventional light microscopy is diffraction-limited to ~250 nm. By combining bimolecular fluorescence complementation (BiFC) with photoactivated localization microscopy (PALM), PPIs can be visualized in cells with single molecule sensitivity and nanometer spatial resolution. BiFC is a commonly used technique for visualizing PPIs with fluorescence contrast, which involves splitting of a fluorescent protein into two non-fluorescent fragments. PALM is a recent superresolution microscopy technique for imaging biological samples at the nanometer and single molecule scales, which uses phototransformable fluorescent probes such as photoactivatable fluorescent proteins (PA-FPs). BiFC-PALM was demonstrated by splitting PAmCherry1, a PA-FP compatible with PALM, for its monomeric nature, good single molecule brightness, high contrast ratio, and utility for stoichiometry measurements. When split between amino acids 159 and 160, PAmCherry1 can be made into a BiFC probe that reconstitutes efficiently at 37 °C with high specificity to PPIs and low non-specific reconstitution. Ras-Raf interaction is used as an example to show how BiFC-PALM helps to probe interactions at the nanometer scale and with single molecule resolution. Their diffusion can also be tracked in live cells using single molecule tracking (smt-) PALM. In this protocol, factors to consider when designing the fusion proteins for BiFC-PALM are discussed, sample preparation, image acquisition, and data analysis steps are explained, and a few exemplary results are showcased. Providing high spatial resolution, specificity, and sensitivity, BiFC-PALM is a useful tool for studying PPIs in intact biological samples.     

Tracking of single fluorescent particles in three dimensions: use of cylindrical optics to encode particle position.

We present a novel optical technique for three-dimensional tracking of single fluorescent particles using a modified epifluorescence microscope containing a weak cylindrical lens in the detection optics and a microstepper-controlled fine focus. Images of small, fluorescent particles were circular in focus but ellipsoidal above and below focus; the major axis of the ellipsoid shifted by 90 degrees in going through focus. Particle z position was determined from the image shape and orientation by applying a peak detection algorithm to image projections along the x and y axes; x, y position was determined from the centroid of the particle image. Typical spatial resolution was 12 nm along the optical axis and 5 nm in the image plane with a maximum sampling rate of 3-4 Hz. The method was applied to track fluorescent particles in artificial solutions and living cells. In a solution of viscosity 30 cP, the mean squared distance (MSD) traveled by a 264 nm diameter rhodamine-labeled bead was linear with time to 20 s. The measured diffusion coefficient, 0.0558 +/- 0.001 micron2/s (SE, n = 4), agreed with the theoretical value of 0.0556 micron2/s. Statistical variability of MSD curves for a freely diffusing bead was in quantitative agreement with Monte Carlo simulations of three-dimensional random walks. In a porous glass matrix, the MSD data was curvilinear and showed reduced bead diffusion. In cytoplasm of Swiss 3T3 fibroblasts, bead diffusion was restricted. The water permeability in individual Chinese Hamster Ovary cells was measured from the z movement of a fluorescent bead fixed at the cell surface in response osmotic gradients; water permeability was increased by > threefold in cells expressing CHIP28 water channels. The simplicity and precision of this tracking method may be useful to quantify the complex trajectories of fluorescent particles in living cells.     

Understanding Protein Mobility in Bacteria by Tracking Single Molecules

Protein diffusion is crucial for understanding the formation of protein complexes in vivo and has been the subject of many fluorescence microscopy studies in cells; however, such microscopy efforts are often limited by low sensitivity and resolution. During the past decade, these limitations have been addressed by new super-resolution imaging methods, most of which rely on single-particle tracking and single-molecule detection; these methods are revolutionizing our understanding of molecular diffusion inside bacterial cells by directly visualizing the motion of proteins and the effects of the local and global environment on diffusion. Here we review key methods that made such experiments possible, with particular emphasis on versions of single-molecule tracking based on photo-activated fluorescent proteins. We also discuss studies that provide estimates of the time a diffusing protein takes to locate a target site, as well as studies that examined the stoichiometries of diffusing species, the effect of stable and weak interactions on diffusion, and the constraints of large macromolecular structures on the ability of proteins and their complexes to access the entire cytoplasm.