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• W2022179322 abstract "Highly sensitive fluorescence microscopy techniques allow single nanoparticles to be tracked during their uptake into living cells with high temporal and spatial resolution. From analysis of the trajectories, random motion can be discriminated from active transport and the average transport velocity and/or diffusion coefficient determined. Such an analysis provides important information regarding the uptake pathway and location of viruses and nanoparticles. In this review, we give an introduction into single-particle tracking (SPT) and determination of the mean-squared displacement. We also give an overview of recent advances in SPT. These include millisecond alternating-laser excitation for removal of spectral crosstalk, alternating wide-field (WF), and total internal reflection fluorescence (TIRF) microscopy for sensitive experiments at the plasma membrane and three-dimensional tracking strategies. Throughout the review, we highlight recent advances regarding the entry (and egress) of natural and artificial viruses obtained via SPT. Highly sensitive fluorescence microscopy techniques allow single nanoparticles to be tracked during their uptake into living cells with high temporal and spatial resolution. From analysis of the trajectories, random motion can be discriminated from active transport and the average transport velocity and/or diffusion coefficient determined. Such an analysis provides important information regarding the uptake pathway and location of viruses and nanoparticles. In this review, we give an introduction into single-particle tracking (SPT) and determination of the mean-squared displacement. We also give an overview of recent advances in SPT. These include millisecond alternating-laser excitation for removal of spectral crosstalk, alternating wide-field (WF), and total internal reflection fluorescence (TIRF) microscopy for sensitive experiments at the plasma membrane and three-dimensional tracking strategies. Throughout the review, we highlight recent advances regarding the entry (and egress) of natural and artificial viruses obtained via SPT. Nanoparticles intended for pharmaceutical use as well as viruses have to overcome several barriers in order to reach and enter their destined target cell. Whereas viruses have developed their mechanisms of cellular entry over millions of years, the entry of pharmaceutical nanoparticles is typically a limiting factor and still under development. In both cases, the entry pathways in living cells are partly unknown and understanding of the entry pathways will provide a better understanding of cell biology and virology and is essential for improving the design of pharmaceutical nanoparticles. Highly sensitive fluorescence microscopy techniques combined with live-cell imaging are powerful tools for elucidating the details of natural and artificial viral–cell interactions on the single-cell level with high temporal and spatial resolution in real time. They allow direct observation of the pathway a nanoparticle or virus particle takes on their way into and through the cell. Whereas bulk measurements like gene expression studies and/or flow cytometry only investigate the final outcome of cellular infection, high-resolution live-cell imaging provides detailed kinetic information over the entire pathway and directly spots bottlenecks in a chain of succeeding events. Although single-cell measurements are not yet capable of providing information about distribution of pharmaceuticals in a full body or full-tissue scenario after systemic application, they provide essential information with unprecedented detail on the interaction of the particle of interest with the ultimate target, the single cell. As such, they are an additional and very specific tool in the researcher's toolbox for unraveling the full pathway of viruses and nanoparticles from contact with a living body after systemic distribution down to the single cell. In this review, we give an overview on the prospects of single-cell microscopy techniques and their impact on unraveling the interaction of nanoparticles and viruses with cells. We give a short introduction to single-particle tracking (SPT), the instrumental setups involved and trajectory analysis and discuss newly developed methodologies for improving and expanding the capabilities of SPT. Throughout the review, we highlight examples from the literature regarding recent advancements in understanding the entry (and egress) of natural and artificial viruses obtained via SPT. Besides their use as viral gene vectors, viruses are valuable tools for investigating the possible entry pathways into cells. As viruses are gene transfer particles per se, the discovery of virus entry pathways provides basic knowledge for potential entry portals into cells and contact points for improvements toward more efficient nonviral gene vectors. The main optical technique used to study the entry of viruses and nanoparticles into cells has been multicolor fluorescence microscopy on living or fixed cells.1Payne CK Imaging gene delivery with fluorescence microscopy.Nanomedicine (Lond). 2007; 2: 847-860Crossref PubMed Scopus (23) Google Scholar,2Brandenburg B Lee LY Lakadamyali M Rust MJ Zhuang X Hogle JM Imaging poliovirus entry in live cells.PLoS Biol. 2007; 5: e183Crossref PubMed Scopus (233) Google Scholar,3Ewers H Smith AE Sbalzarini IF Lilie H Koumoutsakos P Helenius A Single-particle tracking of murine polyoma virus-like particles on live cells and artificial membranes.Proc Natl Acad Sci USA. 2005; 102: 15110-15115Crossref PubMed Scopus (208) Google Scholar,4Rust MJ Lakadamyali M Zhang F Zhuang X Assembly of endocytic machinery around individual influenza viruses during viral entry.Nat Struct Mol Biol. 2004; 11: 567-573Crossref PubMed Scopus (321) Google Scholar,5Lakadamyali M Rust MJ Babcock HP Zhuang X Visualizing infection of individual influenza viruses.Proc Natl Acad Sci USA. 2003; 100: 9280-9285Crossref PubMed Scopus (581) Google Scholar Compartments of the endocytic pathway in living cells can be visualized by fluorescently labeled markers (e.g., dye-coupled transferrin, cholera toxin B, or dextrans) or more specifically by cellular expression of marker proteins fused to fluorescent proteins (e.g., clathrin-green fluorescent protein, caveolin-green fluorescent protein).6Watson P Jones AT Stephens DJ Intracellular trafficking pathways and drug delivery: fluorescence imaging of living and fixed cells.Adv Drug Deliv Rev. 2005; 57: 43-61Crossref PubMed Scopus (225) Google Scholar The entry of viruses or nonviral vectors labeled with a fluorescent dye of another color can then be followed in the living cell and colocalization analysis with cellular compartments used to analyze the entry route taken. This method can be extended by using chemical inhibitors or small interfering RNA to block-specific entry pathways and test for internalization of gene carriers. However, care should be taken as the use of markers and inhibitors on the single-cell level has some caveats and can give inconsistent results on the single-cell level.7Vercauteren D Vandenbroucke RE Jones AT Rejman J Demeester J De Smedt SC et al.The use of inhibitors to study endocytic pathways of gene carriers: optimization and pitfalls.Mol Ther. 2010; 18: 561-569Abstract Full Text Full Text PDF PubMed Scopus (493) Google Scholar Based on studies of nanoparticle uptake, it was revealed that all tested gene carriers enter cells by endocytosis,8Rejman J Bragonzi A Conese M Role of clathrin- and caveolae-mediated endocytosis in gene transfer mediated by lipo- and polyplexes.Mol Ther. 2005; 12: 468-474Abstract Full Text Full Text PDF PubMed Scopus (718) Google Scholar,9Rémy-Kristensen A Clamme JP Vuilleumier C Kuhry JG Mély Y Role of endocytosis in the transfection of L929 fibroblasts by polyethylenimine/DNA complexes.Biochim Biophys Acta. 2001; 1514: 21-32Crossref PubMed Scopus (132) Google Scholar,10Kopatz I Remy JS Behr JP A model for non-viral gene delivery: through syndecan adhesion molecules and powered by actin.J Gene Med. 2004; 6: 769-776Crossref PubMed Scopus (291) Google Scholar even the ones connected to cell-penetrating peptides.11Lundin P Johansson H Guterstam P Holm T Hansen M Langel U et al.Distinct uptake routes of cell-penetrating peptide conjugates.Bioconjug Chem. 2008; 19: 2535-2542Crossref PubMed Scopus (160) Google Scholar,12Mäe M Andaloussi SE Lehto T Langel U Chemically modified cell-penetrating peptides for the delivery of nucleic acids.Expert Opin Drug Deliv. 2009; 6: 1195-1205Crossref PubMed Scopus (54) Google Scholar,13Rinne J Albarran B Jylhävä J Ihalainen TO Kankaanpää P Hytönen VP et al.Internalization of novel non-viral vector TAT-streptavidin into human cells.BMC Biotechnol. 2007; 7: 1Crossref PubMed Scopus (63) Google Scholar Although viruses have the ability to penetrate the cellular membrane for productive infection—which can happen either at the plasma membrane or the limiting membrane of an intracellular organelle—the majority of viruses exploit the cellular endocytotic machinery and need it for productive infection. This may be due to the fact that endocytosis offers real advantages for infectivity such as directed movement toward the nucleus in vesicles by molecular motors,14Döhner K Sodeik B The role of the cytoskeleton during viral infection.Curr Top Microbiol Immunol. 2005; 285: 67-108PubMed Google Scholar circumvention of barriers in the cell periphery,15Marsh M Bron R SFV infection in CHO cells: cell-type specific restrictions to productive virus entry at the cell surface.J Cell Sci. 1997; 110: 95-103PubMed Google Scholar and the use of local cues such as low pH for timed escape into the cytosol at specific locations.16Helenius A Kartenbeck J Simons K Fries E On the entry of Semliki forest virus into BHK-21 cells.J Cell Biol. 1980; 84: 404-420Crossref PubMed Scopus (501) Google Scholar However, there is no generalized internalization pathway for viruses as well as gene carriers. The exact endocytic pathway used is strongly dependent on the individual cell type and also the sort of virus or gene carrier.8Rejman J Bragonzi A Conese M Role of clathrin- and caveolae-mediated endocytosis in gene transfer mediated by lipo- and polyplexes.Mol Ther. 2005; 12: 468-474Abstract Full Text Full Text PDF PubMed Scopus (718) Google Scholar,17von Gersdorff K Sanders NN Vandenbroucke R De Smedt SC Wagner E Ogris M The internalization route resulting in successful gene expression depends on both cell line and polyethylenimine polyplex type.Mol Ther. 2006; 14: 745-753Abstract Full Text Full Text PDF PubMed Scopus (272) Google Scholar,18Marsh M Helenius A Virus entry: open sesame.Cell. 2006; 124: 729-740Abstract Full Text Full Text PDF PubMed Scopus (911) Google Scholar Several endocytosis pathways are often used simultaneously and inhibition of one pathway leads to an increase in internalization by alternative routes. In addition, for gene carriers, the pathway finally resulting in successful transgene expression varies with cell line and also gene carrier type.17von Gersdorff K Sanders NN Vandenbroucke R De Smedt SC Wagner E Ogris M The internalization route resulting in successful gene expression depends on both cell line and polyethylenimine polyplex type.Mol Ther. 2006; 14: 745-753Abstract Full Text Full Text PDF PubMed Scopus (272) Google Scholar Therefore, knowledge of the exact internalization pathway of a specific gene carrier is required to improve its efficiency. One approach to increase the transfection efficiency of gene carriers is to target a pathway leading to successful gene expression by using a specific receptor. This can concomitantly be connected to cell-specific targeting.19Benns JM Kim SW Tailoring new gene delivery designs for specific targets.J Drug Target. 2000; 8: 1-12Crossref PubMed Scopus (54) Google Scholar,20Cheng H Zhu JL Zeng X Jing Y Zhang XZ Zhuo RX Targeted gene delivery mediated by folate-polyethylenimine-block-poly(ethylene glycol) with receptor selectivity.Bioconjug Chem. 2009; 20: 481-487Crossref PubMed Scopus (79) Google Scholar,21Frederiksen KS Abrahamsen N Cristiano RJ Damstrup L Poulsen HS Gene delivery by an epidermal growth factor/DNA polyplex to small cell lung cancer cell lines expressing low levels of epidermal growth factor receptor.Cancer Gene Ther. 2000; 7: 262-268Crossref PubMed Scopus (27) Google Scholar,22Lu T Sun J Chen X Zhang P Jing X Folate-conjugated micelles and their folate-receptor-mediated endocytosis.Macromol Biosci. 2009; 9: 1059-1068Crossref PubMed Scopus (51) Google Scholar However, the exact successful entry pathway has to be defined for each target cell line and particle type individually. Such detailed understanding of the entry process of natural and artificial viruses on the single-cell level can be obtained using SPT. By following individual viruses and nanoparticles in real-time with high spatial and temporal resolution, the kinetics of transfection can be measured and the specific interactions can be visualized. Single-particle techniques are typically based upon highly sensitive fluorescence wide-field (WF) microscopy. Internalization of single gene carriers can be continuously followed from their initial attachment to the cell membrane through the various steps of the uptake process and intracellular trafficking. The ability to image single gene carriers, which can eventually be labeled with only a few fluorophores, at high temporal resolution over several minutes requires ultrasensitive detection. The setup we currently use for SPT is shown in Figure 1. Excitation is performed by laser light which provides the necessary excitation intensity required for strong photon emission by the fluorophores and whose narrow spectrum makes it easy to suppress scattered light without blocking fluorescence signal. Typical laser lines for excitation of common fluorophores are 488, 532, 561, and 635 nm. The availability of several laser lines allows simultaneous imaging of two to three fluorophores, depending on emission spectra of the labels and filters available. An acousto-optical tunable filter is used to select the appropriate excitation wavelength or wavelengths without speed limitations or vibrational and mechanical constrains related to mechanical shutters or rotating wheels. The laser light is focused onto the back aperture of the objective for WF and total internal reflection fluorescence (TIRF) illumination. The cells are kept at 37 °C throughout the experiment by a temperature controlled stage (heating table). The objective is also heated to 39 °C (slightly higher than the temperature of the sample) as oil immersion objectives are in direct thermal contact with the sample and act as a strong heat sink for the cells. It is best to use objectives that have been designed for use near 37 °C. There are also microscope stage incubator chambers available that allow control of the CO2 level, but with the exception for long-time experiments, the use of CO2-independent medium is typically sufficient. Focal instabilities in the microscope mechanics due to temperature fluctuations in the surroundings after mounting the sample provide major difficulties for SPT. An auto-focus system keeps the sample at a constant z-position and is very beneficial for intermediate and long-term (1–2 hours) measurements. The emission light is typically collected by a ×60 or ×100 oil immersion objective with high numerical aperture (up to 1.49 NA) and separated from the excitation light with the appropriate dichroic mirror. The fluorescence emission is then directed to and detected by a highly sensitive (typically back illuminated) electron multiplied charge-coupled device camera. For multicolor imaging, either multiple regions can be imaged on different portions of a single camera or separate cameras can be used. Multiple cameras have the advantage of an increased field of view, but also increase the cost of the setup. The exact configuration of the setup, mainly the choice of lasers, dichroic mirrors and filters, depends on the combination of fluorophores used and may have to be adapted for the individual experiments by the user. Accessory optics for TIRF illumination (see Figure 1) or confocal detection can be added to increase the flexibility and variability of custom-built setups. TIRF illumination is especially interesting for fast tracking of cell surface associated events at the basal plasma membrane. In the acquired image sequences, individual fluorescent particles can be identified as bright spots on a dark background. Each frame in the movie is a representation of the position of the particles at a certain time point. By extraction of the x- and y-coordinates of the particles from the centroids of their diffraction limited spots in all frames of the movie where the particle is detectible, the trajectories of the particles can be obtained. This is typically performed by first reducing background noise and then selecting particles by setting an intensity threshold on the filtered image. In a second step, particles for tracking are selected based on their intensity, size and shape. The x-and y-coordinates are obtained by fitting a 2D-Gaussian function to the particle's intensity profile (Figure 2a). In a final step, the particle coordinates are subsequently used for calculating the corresponding trajectories based on a nearest-neighbor algorithm.23Godinez WJ Lampe M Wörz S Müller B Eils R Rohr K Deterministic and probabilistic approaches for tracking virus particles in time-lapse fluorescence microscopy image sequences.Med Image Anal. 2009; 13: 325-342Abstract Full Text Full Text PDF PubMed Scopus (87) Google Scholar,24Sbalzarini IF Koumoutsakos P Feature point tracking and trajectory analysis for video imaging in cell biology.J Struct Biol. 2005; 151: 182-195Crossref PubMed Scopus (1060) Google Scholar With this method, a positional accuracy well beyond the optical diffraction limit is achieved. The centroid position of a sufficiently bright fluorophore can be determined to within nanometer precision.25Yildiz A Forkey JN McKinney SA Ha T Goldman YE Selvin PR Myosin V walks hand-over-hand: single fluorophore imaging with 1.5-nm localization.Science. 2003; 300: 2061-2065Crossref PubMed Scopus (1565) Google Scholar The resulting trajectories are usually analyzed for their type of motional behavior as the motion provides information on the surroundings and interactions of the particle. The most common analysis starts with calculation of the so called mean-square displacement (MSD). From the MSD, their type of motional behavior can be determined.26Saxton MJ Jacobson K Single-particle tracking: applications to membrane dynamics.Annu Rev Biophys Biomol Struct. 1997; 26: 373-399Crossref PubMed Scopus (1481) Google Scholar A simplified way to calculate the MSD is depicted in Figure 2b. The MSD <r2> describes the average of the squared distances between a particle's start and end position for all time-lags of certain length Δt within one trajectory. With increasing time-lag, however, less data points are available and the uncertainty of the MSD values increases.27Qian H Sheetz MP Elson EL Single particle tracking. Analysis of diffusion and flow in two-dimensional systems.Biophys J. 1991; 60: 910-921Abstract Full Text PDF PubMed Scopus (901) Google Scholar To account for this uncertainty, the MSD should always be calculated for time-lags corresponding to less than ∼¼ of the total number of points in the trajectory.26Saxton MJ Jacobson K Single-particle tracking: applications to membrane dynamics.Annu Rev Biophys Biomol Struct. 1997; 26: 373-399Crossref PubMed Scopus (1481) Google Scholar As a consequence, the time-axis of a MSD plot can only represent a fraction of the time scale of the trajectory. From evaluation of the MSD plot, information about the mode of motion can be obtained (Figure 2c). This mode of motion can then be interpreted in a biological context and conclusions on the location and environment of the tracked particle can be drawn. Normal and Anomalous diffusion is described by 〈r2〉=4D Δtα,1 where D is the diffusion coefficient, Δt is the given time interval and the exponent, α, that distinguishes between normal or Brownian diffusion (α = 1) and anomalous diffusion (α < 1). The factor 4 is specific for diffusion in two dimensions and is replaced by 6 in all formulas for three-dimensional tracking. For Brownian motion, the MSD increases linearly with Δt. Anomalous diffusion is typically observed when the diffusive particle is hindered by obstacles. Confined or corralled diffusion is indicated by an asymptotic behavior of <r2> for large Δt and implies a confinement for the diffusive particle. The relation between <r2> and Δt is given by: <r2>=<rc2>[1-A1exp (-4A2DΔt/<rc2>)],2 where <r2c> is an approximation of the size of the confinement and the constants A1 and A2 are determined by the confinement geometry. The asymptotic value of <r2> for large Δt can be used to estimate of the size of the confinement <r2c>. We note that confinement within a certain region is only observable when the observation time is long compared to the time between successive contacts of the particle with the barrier. For short observation times, normal or anomalous diffusion within the confinement is observed. Active transport is described by a quadratic dependence of the MSD <r2> on Δt: <r2>=v2Δt2+4DΔt,3 where v is the velocity of the directed motion which is also called drift. Superimposed on this motion is normal diffusion with the diffusion coefficient D. The whole process can be described using the analogy of a conveyor belt, where particles are transported but also diffuse along the belt. By fitting formula (3) to an MSD curve, the mean velocity v of the directed motion and the diffusion coefficient D are obtained. In the above equations, the impact of uncertainties and statistical errors has been ignored. Often the information extracted from the equations above is sufficient for the biological question of interest. However, it is still possible to perform a more quantitative analysis by taking the static and dynamic errors into account. Static errors, represented by σ, arise from the uncertainty in determining the position of the particle due to experimental noise. When static uncertainties are not taken into account, freely diffusing particles may be incorrectly categorized as undergoing anomalous diffusion.28Martin DS Forstner MB Käs JA Apparent subdiffusion inherent to single particle tracking.Biophys J. 2002; 83: 2109-2117Abstract Full Text Full Text PDF PubMed Scopus (182) Google Scholar The static contribution can be determined by measuring immobilized particles at a signal-to-noise ratio similar to the actual experiments.29Savin T Doyle PS Static and dynamic errors in particle tracking microrheology.Biophys J. 2005; 88: 623-638Abstract Full Text Full Text PDF PubMed Scopus (409) Google Scholar Dynamic errors arise from the fact that the particle is diffusing within the integration time of each frame, leading to motional blurring of the fluorescence intensity on the camera. When the camera is constantly illuminated for the entire frame, the modified MSD for a freely diffusing particle including static and dynamic uncertainties is given by:29Savin T Doyle PS Static and dynamic errors in particle tracking microrheology.Biophys J. 2005; 88: 623-638Abstract Full Text Full Text PDF PubMed Scopus (409) Google Scholar,30Berglund AJ Statistics of camera-based single-particle tracking.Phys Rev E Stat Nonlin Soft Matter Phys. 2010; 82: 011917Crossref Scopus (152) Google Scholar,31Michalet X Mean square displacement analysis of single-particle trajectories with localization error: Brownian motion in an isotropic medium.Phys Rev E Stat Nonlin Soft Matter Phys. 2010; 82: 041914Crossref Scopus (426) Google Scholar <r2>=4DΔt+4σ2-4DΔtE/3,4 where ΔtE is the frame integration time of the camera. When the illumination intensity is varied during the exposure time of a single frame, such as for stroboscopic illumination, the correction term for dynamic errors will vary.30Berglund AJ Statistics of camera-based single-particle tracking.Phys Rev E Stat Nonlin Soft Matter Phys. 2010; 82: 011917Crossref Scopus (152) Google Scholar For tracking the entry of viruses and nanoparticles, the static uncertainty can be significant due to the limited signal-to-noise ratio of experiments performed in living cells and the lower illumination intensities used for measurements over extended time periods. Whether dynamic errors significantly contribute to the MSD depends on the mobility of the tracked particles and details of the experimental protocol. MSD curves of diffusive motion can be very heterogeneous and often change during the course of the trajectory. Therefore, it is important to perform a MSD over subregions of the trajectory. A careful description of the various modes of motion within one trajectory requires the separation of the trajectory in several parts e.g., manually according to morphological differences or by velocity thresholds32de Bruin K Ruthardt N von Gersdorff K Bausinger R Wagner E Ogris M et al.Cellular dynamics of EGF receptor-targeted synthetic viruses.Mol Ther. 2007; 15: 1297-1305Abstract Full Text Full Text PDF PubMed Scopus (137) Google Scholar,33Suh J Wirtz D Hanes J Real-time intracellular transport of gene nanocarriers studied by multiple particle tracking.Biotechnol Prog. 2004; 20: 598-602Crossref PubMed Scopus (70) Google Scholar as the shape of the MSD or effective diffusion coefficient curves are not sufficient. For example, particles showing hop diffusion may fulfill all analysis criteria for “diffusive” motion whereas the hop diffusion pattern is only visible in the trajectory.33Suh J Wirtz D Hanes J Real-time intracellular transport of gene nanocarriers studied by multiple particle tracking.Biotechnol Prog. 2004; 20: 598-602Crossref PubMed Scopus (70) Google Scholar As early as 1995, Jacobson and co-workers applied a subtrajectory analysis to identify transient confinement zones of membrane proteins.34Simson R Sheets ED Jacobson K Detection of temporary lateral confinement of membrane proteins using single-particle tracking analysis.Biophys J. 1995; 69: 989-993Abstract Full Text PDF PubMed Scopus (212) Google Scholar They calculated the maximum displacement within multiple segments over the entire trajectory and calculated the probability that a freely diffusing particle remains within a confined region of the size of the maximum displacement for the entire segment. When the probability was reasonable, normal diffusion was assumed. However, when the log-likelihood that the diffusional motion was not random exceeded a critical threshold over a minimum critical duration, they would assign that region of the trajectory to a confinement zone. The optimal critical threshold and duration were determined from simulations. A more sophisticated method for automated trajectory analysis and mode of motion detection utilizes a rolling-window algorithm. The algorithm described by Arcizet et al.35Arcizet D Meier B Sackmann E Rädler JO Heinrich D Temporal analysis of active and passive transport in living cells.Phys Rev Lett. 2008; 101: 248103Crossref PubMed Scopus (160) Google Scholar,36Mahowald J Arcizet D Heinrich D Impact of external stimuli and cell micro-architecture on intracellular transport states.Chemphyschem. 2009; 10: 1559-1566Crossref PubMed Scopus (25) Google Scholar reliably separates the active and passive states of particle motion and extracts the velocity during active states as well as the diffusion coefficients during passive states. It assumes that active transport, for example on microtubules, is characteristically directional over a certain time and measures the directional persistence of particle motion by the angular correlation of the following steps.35Arcizet D Meier B Sackmann E Rädler JO Heinrich D Temporal analysis of active and passive transport in living cells.Phys Rev Lett. 2008; 101: 248103Crossref PubMed Scopus (160) Google Scholar The angle analysis provides an estimate of the probability of the particle undergoing active motion within the analyzed subregion. Of course, the higher the temporal resolution and the more data points acquired, the better and more detailed the analysis can be. As a consequence, for very fast transport events, the temporal resolution has to be high enough to acquire sufficient data points for analyzing the different modes of motion and for separating the break points between them. Other elegant approaches have also been taken to extract heterogeneous diffusion characteristics within a single trajectory. Hang and co-workers developed a maximum likelihood approach to automatically recognize when a system undergoes a transition to a state with different diffusional properties and performs a subtrajectory analysis in the regions between transitions.37Montiel D Cang H Yang H Quantitative characterization of changes in dynamical behavior for single-particle tracking studies.J Phys Chem B. 2006; 110: 19763-19770Crossref PubMed Scopus (128) Google Scholar Matsuoka and co-workers took a different approach and explicitly calculated the displacement probability density function assuming a single, freely diffusion species, two noninterconverting freely diffusing species and a species that interconverts between two freely diffusing states with different diffusion coefficients.38Matsuoka S Shibata T Ueda M Statistical analysis of lateral diffusion and multistate kinetics in single-molecule imaging.Biophys J. 2009; 97: 1115-1124Abstract Full Text Full Text PDF PubMed Scopus (36) Google Scholar Using their model, they could not only extract the diffusion coefficients of the different states but also the transition rate between the states. Although subtrajectory analyses are powerful for investigating the heterogeneous" @default.
• W2022179322 created "2016-06-24" @default.
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• W2022179322 date "2011-07-01" @default.
• W2022179322 modified "2023-09-30" @default.
• W2022179322 title "Single-particle Tracking as a Quantitative Microscopy-based Approach to Unravel Cell Entry Mechanisms of Viruses and Pharmaceutical Nanoparticles" @default.
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