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Tracking molecular dynamics without tracking: Image correlation of photo-activation microscopy
Abstract
Measuring protein dynamics in the plasma membrane can provide insights into the mechanisms of receptor signaling and other cellular functions. To quantify protein dynamics on the single molecule level over the entire cell surface, sophisticated approaches such as single particle tracking (SPT), photo-activation localization microscopy (PALM) and fluctuation-based analysis have been developed. However, analyzing molecular dynamics of fluorescent particles with intermittent excitation and low signal-to-noise ratio present at high densities has remained a challenge. We overcame this problem by applying spatio-temporal image correlation spectroscopy (STICS) analysis to photo-activated (PA) microscopy time series. In order to determine under which imaging conditions this approach is valid, we simulated PA images of diffusing particles in a homogeneous environment and varied photo-activation, reversible blinking and irreversible photo-bleaching rates. Further, we simulated data with high particle densities that populated mobile objects (such as adhesions and vesicles) that often interfere with STICS and fluctuation-based analysis. We demonstrated in experimental measurements that the diffusion coefficient of the epidermal growth factor receptor (EGFR) fused to PAGFP in live COS-7 cells can be determined in the plasma membrane and revealed differences in the time-dependent diffusion maps between wild-type and mutant Lck in activated T cells. In summary, we have developed a new analysis approach for live cell photo-activation microscopy data based on image correlation spectroscopy to quantify the spatio-temporal dynamics of single proteins.
... Luckily, there are a few extensions to the techniques that occurred over years, separating contributions from different oligomers in stationary image data (40)(41)(42) and in dynamic data (43,44). Another way to circumvent the problem is to label proteins with photoactivable fluorescent proteins, and depending of subset of fluorophores being active, measure CF from only visible population (45). Even multiple flows were successfully detected within the same region of interest through extensions of STICS (46,47). ...
... The MSD, usually by its trend versus temporal lag, instructs us on what type of confinement or obstacle caused the anomalous or confined random walk. Extracting the equivalent of MSD from the CF was done in the past by using STICS (25,50) or equivalent imaging correlation approach (51) and even allowed for diffusion coefficient mapping (25,45), as we saw in the theoretic development leading up to Eqs. 10 and 11 and as shown in spreading STICS CF in Figure 14D. ...
The aim of this article is to introduce the basic principles behind the widely used microscopy tool: fluorescence fluctuation correlation spectroscopy (FFCS). We present the fundamentals behind single spot acquisition (FCS) and its extension to spatiotemporal sampling, which is implemented through image correlation spectroscopy (ICS). The article is an educational guide that introduces theoretic concepts of FCS and some of the ICS techniques, followed by interactive exercises in MATLAB. There, the learner can simulate data time series and the application of various FFCS techniques, as well as learn how to measure diffusion coefficients, molecular flow, and concentration of particles. Additionally, each section is followed by a short exercise to reinforce learning concepts by simulating different scenarios, seek verification of outcomes, and make comparisons. Furthermore, we invite the learner throughout the article to consult the literature for different extensions of FFCS techniques that allow measurements of different physicochemical properties of materials. Upon completion of the modules, we anticipate the learner will gain a good understanding in the field of FFCS that will encourage further exploration and adoption of the FFCS tools in future research and educational practices.
... STICS can be used for diffusion measurements and is even able to identify diffusion behaviour in a similar manner to SPT [72]. Compared to SPT, STICS can successfully measure at higher densities of photoactivated molecules and a lower signal/noise ratio. ...
... Compared to SPT, STICS can successfully measure at higher densities of photoactivated molecules and a lower signal/noise ratio. However, as an ensemble method, STICS does not provide single molecule trajectory data, which is one of the greatest advantages of SPT [72]. ...
Nano-domains are sub-light-diffraction-sized heterogeneous areas in the plasma membrane of cells, which are involved in cell signalling and membrane trafficking. Throughout the last thirty years, these nano-domains have been researched extensively and have been the subject of multiple theories and models: the lipid raft theory, the fence model, and the protein oligomerization theory. Strong evidence exists for all of these, and consequently they were combined into a hierarchal model. Measurements of protein and lipid diffusion coefficients and patterns have been instrumental in plasma membrane research and by extension in nano-domain research. This has led to the development of multiple methodologies that can measure diffusion and confinement parameters including single particle tracking, fluorescence correlation spectroscopy, image correlation spectroscopy and fluorescence recovery after photobleaching. Here we review the performance and strengths of these methods in the context of their use in identification and characterization of plasma membrane nano-domains.
... above the threshold value) are modified. The area threshold makes sure the noise is line in nature and not random isolated noise (as a line stripe contains more pixels than isolated pixels [95,112], to study sample deformations [113], and to align, stabilize, and stitch images [114]. It has rarely been used, however, as an oversampling technique to enhance signal-to-noise ratio for AFM images. ...
... I attribute this increase loading to the longer DNA we used compared to the SPR study (1041bp vs. 236bp). The longer DNA makes it harder for MutSβ to diffuse off the DNA, which may explain why MutSβ sliding clamps were completely dissociated in the SPR data after the end-blocks were removed[201], whereas in our data we could still see 'ruminants' of the sliding clamps that have not been completely off-loaded.112 Because the protein-DNA complex is not chemically cross-linked, reaction could still occur during sample deposition onto the mica surface. ...
Atomic Force Microscopy (AFM) is a powerful technique to study the assembly and function of multiprotein-DNA complexes, such as the MutS-MutL-DNA complex in DNA mismatch repair. As a high-resolution, single-molecule imaging technique, AFM has the advantage of directly visualizing individual protein-DNA complexes in their native conformations, but it has two severe limitations. First, it is unable to resolve the location of the DNA inside the protein. Second, it lacks a comprehensive software that is tailored for single-molecule studies and high-throughput analyses. To tackle these issues, we developed DREEM (Dual-Resonance-frequency-Enhanced Electrostatic Force Microscopy). DREEM is a new AFM imaging method that is capable of resolving DNA path inside the protein-DNA complex. With DREEM, we can reveal the path of the DNA wrapping around histones in nucleosomes and the path of DNA through multiprotein mismatch repair complexes. We also developed Image Metrics, a full-featured AFM software package that excels in high-throughput shape analysis and single-molecule analysis. Built using MATLAB, Image Metrics is uniquely positioned in single-molecule studies with its specially designed single-molecule analysis and shape analysis modules. It also blends unique flexibility into a user-friendly interface that allows for easy customization and automation of user workflows. Finally, as a case study, we used AFM and Image Metrics to study DNA mismatch repair (MMR) in the context of trinucleotide repeat (TNR) expansion diseases. Our data show that when interacting with heteroduplex DNAs with the TNR context, MMR proteins adopt conformations that are different from a repair signaling capable species, suggesting the altered conformations may not be competent for repair.
... When imaging in series rather than simultaneously, consideration should be given to the length of time required to collect the two images, as some systems require on the order of seconds to switch between the desired image settings, by which time the imaged populations may not be seen to correlate with each other. For higher resolution correlation spectroscopy, particle ICS (PICS) [104] and time-resolved STICS (trSTICS) [105] give researchers the ability to analyse SPT and SMLMS data respectively and can achieve nanometre and millisecond spatial and temporal resolutions respectively. PICS has the advantage over classic SPT of not breaking down if multiple trajectories overlap. ...
... Correlation analyses extract how quickly a signal changes over space, time or both. While these methods are themselves well-established for quantifying biophysical mechanisms such as diffusion, trapping and flow (active transport), they are now evolving to deal with the data sets from the latest developments in microscope hardware [23,81,100,105,107]. Many of the advancements are being made to deal with the pointillist nature of SMLM data, multicolour analysis and 3D sets. ...
This chapter describes state-of-the-art quantification strategies for co-localisation in data acquired by the microscopy techniques. It addresses the requirements of investigating molecular co-localisation, complex formation, diffusion and flow, new analysis tools have been developed in parallel with the emergence of fluorescence microscopy. The chapter begins with an exploration of co-localisation analysis for conventional fluorescence microscopy images. It outlines the principles, theories and applications of two widely established fluorescence techniques for measuring and quantifying molecular behaviour. Fluorescence correlation spectroscopy (FCS) allows researchers to detect sparsely distributed molecules and to quantify molecular concentrations and diffusion coefficients. Image correlation spectroscopy (ICS) provides a tool for quantifying the speed and direction of molecular populations during imaging of larger fields of view - that is, spatially resolved measurements of molecular transport. Co-localisation software is now widely available to study images obtained from two-colour fluorescence microscopy.
... In this context, spatiotemporal image correlation spectroscopy (STICS) represents an interesting alternative, since it is in principle sensitive to the directionality of motion, e.g., in the case of fluxes (19). Moreover, STICS can be used to measure the molecular MSD in the case of diffusion (20)(21)(22) and can be applied to small regions of interest (ROIs) to map molecular dynamics (23). Unfortunately, the minimal size of the ROI to be analyzed must be significantly larger than the optical resolution to properly sample particle displacements and avoid underestimating particle motion. ...
... More explicitly, when a fluorophore turns off, it will stop contributing to the correlation function; however, since the turning off can occur at any position in space, it will reflect a homogenous lowering of the correlation amplitude that does not alter the spatial shape of the 2D pCF. As a consequence, blinking and bleaching do not affect the width of the correlation function used in the iMSD approach to measure particle displacement (20,23). Concerning point 3, we should like to stress that the diffusion tensor measured here corresponds to average molecular displacements well below the diffraction limit. ...
In a living cell, the movement of biomolecules is highly regulated by the cellular organization into subcompartments that impose barriers to diffusion, can locally break the spatial isotropy, and ultimately guide these molecules to their targets. Despite the pivotal role of these processes, experimental tools to fully probe the complex connectivity (and accessibility) of the cell interior with adequate spatiotemporal resolution are still lacking. Here, we show how the heterogeneity of molecular dynamics and the location of barriers to molecular motion can be mapped in live cells by exploiting a two-dimensional (2D) extension of the pair correlation function (pCF) analysis. Starting from a time series of images collected for the same field of view, the resulting 2D pCF is calculated in the proximity of each point for each time delay and allows us to probe the spatial distribution of the molecules that started from a given pixel. This 2D pCF yields an accurate description of the preferential diffusive routes. Furthermore, we combine this analysis with the image-derived mean-square displacement approach and gain information on the average nanoscopic molecular displacements in different directions. Through these quantities, we build a fluorescence-fluctuation-based diffusion tensor that contains information on speed and directionality of the local dynamical processes. Contrary to classical fluorescence correlation spectroscopy and related methods, this combined approach can distinguish between isotropic and anisotropic local diffusion. We argue that the measurement of this iMSD tensor will contribute to advance our understanding of the role played by the intracellular environment in the regulation of molecular diffusion at the nanoscale.
... above the threshold value) are modified. The area threshold makes sure the noise is line in nature and not random isolated noise (as a line stripe contains more pixels than isolated pixels [95,112], to study sample deformations [113], and to align, stabilize, and stitch images [114]. It has rarely been used, however, as an oversampling technique to enhance signal-to-noise ratio for AFM images. ...
One of the biggest hurdles in single-molecule AFM studies is the lack of comprehensive software package that allows for high-throughput analysis. In fact, data analysis is often the bottleneck in single-molecule studies. To tackle this issue, I developed Image Metrics, a full-featured MATLAB -based AFM image analysis software package. Relying on MATLAB’s enormous scientific library, Image Metrics is able to blend powerful features and flexibility into a user-friendly interface, and enable users to perform high-throughput multi-faceted image analysis. In particular, Image Metrics features unique modules for single-molecule analysis and shape analysis such as particle classification that are not available in other AFM software. With Image Metrics, single-molecule AFM analysis is streamlined - image correction, measurement, and analysis are all processed in a single software package, and users can easily program user functions, customize workflows, and automate laborious routines. The software is designed to be the next generation research tool for AFM and other imaging fields.
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Official website: https://imetrics.app
... Here, instead of hardly linking the nearest particles in subsequent frames, we only assign a probability of such possible identification with respect to the particle density around the position, and directly estimate the diffusion constant without specifying concrete trajectories. The resultant algorithm, which successfully estimates diffusion constants even under high particle density condition, shows some resemblance to another SPT free diffusion constant estimation method, particle image correlation spectroscopy (PICS) (15), which was inspired by image correlation microscopy (16)(17)(18)(19). The main advantage of our algorithm towards PICS is that our algorithm can be applied to the cases with inhomogeneous distribution of single molecules, while PICS assumes homogeneous distribution. ...
Time course measurement of single molecules on a cell surface provides
detailed information on the dynamics of the molecules, which is otherwise
inaccessible. To extract the quantitative information, single particle tracking
(SPT) is typically performed. However, trajectories extracted by SPT inevitably
have linking errors when the diffusion speed of single molecules is high
compared to the scale of the particle density. To circumvent this problem we
developed an algorithm to estimate diffusion constants without relying on SPT.
We demonstrated that the proposed algorithm provides reasonable estimation of
diffusion constants even when other methods fail due to high particle density
or inhomogeneous particle distribution. In addition, our algorithm can be used
for visualization of time course data from single molecular measurements.
... Albrecht et al [12] described an improved labelling approach for dual-colour particle tracking using nanobodies. Pandzic et al [13] took a different approach using a variant of image correlation spectroscopy to obviate the need to track individual particles , a computationally intensive and error-prone process requiring high illumination intensities. They showed how spatio-temporal image correlation spectroscopy (STICS) with photoactivatable fluorescent proteins ('paSTICSʼ) can be used to measure diffusion and flow with lower excitation intensities and fewer artefacts than other methods. ...
Fluorescence Correlation Spectroscopy (FCS) is a widely used technique to determine molecular dynamics and interactions. It uses observation volumes on the order of a femtolitre in size to distinguish the signal from single molecules against the background. As it is difficult to illuminate and specifically detect signals from such a small observation volume, FCS was originally conceived as a single-spot measurement that measures mainly temporal information. Multiplexing was then achieved by sequential scanning and detecting different spots in a sample and thus also providing spatial information. With advances in technology, the introduction of different illumination and detection methods, and the emergence of super-resolution and light-sheet microscopy, new opportunities opened up to collect thousands of contiguous spots in a sample and thus provide high-resolution spatiotemporal information over a whole cross-section of a sample. This chapter describes the different 2D FCS modalities, their advantages and disadvantages, and some of their applications.
The determination of the mode and rapidity of motion of individual molecules within a biological sample is becoming a more and more common analysis in biophysical investigations. Single molecule tracking (SMT) techniques allow reconstructing the trajectories of individual molecules within a movie, provided that the position from one frame to the other can be correctly linked. The outcomes, however, appear to depend on the specific method used, and most techniques display a limitation to capture fast modes of motion in a crowded environment. We demonstrate here that the limitations encountered by conventional SMT can be significantly overcome by employing alternative approaches based on image spatial-temporal correlations, enabling to visually extract quantitative insights on the ensemble mode of motion of fluorescently labeled biomolecules that would otherwise be inaccessible.
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Anisotropic metallic nanoparticles have been devised as powerful potential tools for in vivo imaging, photothermal therapy, and drug delivery thanks to plasmon-enhanced absorption and scattering cross sections, ease in synthesis and functionalization, and controlled cytotoxicity. The rational design of all these applications requires the characterization of the nanoparticles intracellular trafficking pathways. In this work, we exploit live-cell time-lapse confocal reflectance microscopy and image correlation in both direct and reciprocal space to investigate the intracellular transport of branched gold nanostars (GNSs). Different transport mechanisms, spanning from pure Brownian diffusion to (sub-)ballistic superdiffusion, are revealed by temporal and spatio-temporal image correlation spectroscopy on the tens-of-seconds timescale. According to these findings, combined with numerical simulations and with a Bayesian (hidden Markov model-based) analysis of single particle tracking data, we ascribe the superdiffusive, subballistic behavior characterizing the GNSs dynamics to a two-state switching between Brownian diffusion in the cytoplasm and molecular motor-mediated active transport. For the investigation of intermittent-type transport phenomena, we derive an analytical theoretical framework for Fourier-space image correlation spectroscopy (kICS). At first, we evaluate the influence of all the dynamic and kinetic parameters (the diffusion coefficient, the drift velocity, and the transition rates between the diffusive and the active transport regimes) on simulated kICS correlation functions. Then we outline a protocol for data analysis and employ it to derive whole-cell maps for each parameter underlying the GNSs intracellular dynamics. Capable of identifying even simpler transport phenomena, whether purely diffusive or ballistic, our intermittent kICS approach allows an exhaustive investigation of the dynamics of GNSs and biological macromolecules.
Spatial distribution and dynamics of plasma-membrane proteins are thought to be modulated by lipid composition and by the underlying cytoskeleton, which forms transient barriers to diffusion. So far this idea was probed by single-particle tracking of membrane components in which gold particles or antibodies were used to individually monitor the molecules of interest. Unfortunately, the relatively large particles needed for single-particle tracking can in principle alter the very dynamics under study. Here, we use a method that makes it possible to investigate plasma-membrane proteins by means of small molecular labels, specifically single GFP constructs. First, fast imaging of the region of interest on the membrane is performed. For each time delay in the resulting stack of images the average spatial correlation function is calculated. We show that by fitting the series of correlation functions, the actual protein "diffusion law" can be obtained directly from imaging, in the form of a mean-square displacement vs. time-delay plot, with no need for interpretative models. This approach is tested with several simulated 2D diffusion conditions and in live Chinese hamster ovary cells with a GFP-tagged transmembrane transferrin receptor, a well-known benchmark of membrane-skeleton-dependent transiently confined diffusion. This approach does not require extraction of the individual trajectories and can be used also with dim and dense molecules. We argue that it represents a powerful tool for the determination of kinetic and thermodynamic parameters over very wide spatial and temporal scales.
Transcription factors use diffusion to search the DNA, yet the mechanisms controlling transcription factor diffusion during mammalian development remain poorly understood. Here we combine photoactivation and fluorescence correlation spectroscopy to study transcription factor diffusion in developing mouse embryos. We show that the pluripotency-associated transcription factor Oct4 displays both fast and Brownian and slower subdiffusive behaviours that are controlled by DNA interactions. Following cell lineage specification, the slower DNA-interacting diffusion fraction distinguishes pluripotent from extraembryonic cell nuclei. Similar to Oct4, Sox2 shows slower diffusion in pluripotent cells while Cdx2 displays opposite dynamics, suggesting that slow diffusion may represent a general feature of transcription factors in lineages where they are essential. Slow Oct4 subdiffusive behaviours are conserved in embryonic stem cells and induced pluripotent stem cells (iPS cells), and lost during differentiation. We also show that Oct4 diffusion depends on its interaction with ERG-associated protein with SET domain. Photoactivation and fluorescence correlation spectroscopy provides a new intravital approach to study transcription factor diffusion in complex in vivo systems.
Phosphorylation of the T cell antigen receptor (TCR) by the tyrosine kinase Lck is an essential step in the activation of T cells. Because Lck is constitutively active, spatial organization may regulate TCR signaling. Here we found that Lck distributions on the molecular level were controlled by the conformational states of Lck, with the open, active conformation inducing clustering and the closed, inactive conformation preventing clustering. In contrast, association with lipid domains and protein networks were not sufficient or necessary for Lck clustering. Conformation-driven Lck clustering was highly dynamic, so that TCR triggering resulted in Lck clusters that contained phosphorylated TCRs but excluded the phosphatase CD45. Our data suggest that Lck conformational states represent an intrinsic mechanism for the intermolecular organization of early T cell signaling.
Integrins in focal adhesions (FAs) mediate adhesion and force transmission to extracellular matrices essential for cell motility, proliferation and differentiation. Different fibronectin-binding integrins, simultaneously present in FAs, perform distinct functions. Yet, how integrin dynamics control biochemical and biomechanical processes in FAs is still elusive. Using single-protein tracking and super-resolution imaging we revealed the dynamic nano-organizations of integrins and talin inside FAs. Integrins reside in FAs through free-diffusion and immobilization cycles. Integrin activation promotes immobilization, stabilized in FAs by simultaneous connection to fibronectin and actin-binding proteins. Talin is recruited in FAs directly from the cytosol without membrane free-diffusion, restricting integrin immobilization to FAs. Immobilized β(3)-integrins are enriched and stationary within FAs, whereas immobilized β(1)-integrins are less enriched and exhibit rearward movements. Talin is enriched and mainly stationary, but also exhibited rearward movements in FAs, consistent with stable connections with both β-integrins. Thus, differential transmission of actin motion to fibronectin occurs through specific integrins within FAs.
The extent to which ligand occupancy and dimerization contribute to erbB1 signaling is controversial. To examine this, we used two-color quantum-dot tracking for visualization of the homodimerization of human erbB1 and quantification of the dimer off-rate (k(off)) on living cells. Kinetic parameters were extracted using a three-state hidden Markov model to identify transition rates between free, co-confined and dimerized states. We report that dimers composed of two ligand-bound receptors are long-lived and their k(off) is independent of kinase activity. By comparison, unliganded dimers have a more than four times faster k(off). Transient co-confinement of receptors promotes repeated encounters and enhances dimer formation. Mobility decreases more than six times when ligand-bound receptors dimerize. Blockade of erbB1 kinase activity or disruption of actin networks results in faster diffusion of receptor dimers. These results implicate both signal propagation and the cortical cytoskeleton in reduced mobility of signaling-competent erbB1 dimers.
Photoactivated localization microscopy (PALM) is a powerful approach for investigating protein organization, yet tools for quantitative, spatial analysis of PALM datasets are largely missing. Combining pair-correlation analysis with PALM (PC-PALM), we provide a method to analyze complex patterns of protein organization across the plasma membrane without determination of absolute protein numbers. The approach uses an algorithm to distinguish a single protein with multiple appearances from clusters of proteins. This enables quantification of different parameters of spatial organization, including the presence of protein clusters, their size, density and abundance in the plasma membrane. Using this method, we demonstrate distinct nanoscale organization of plasma-membrane proteins with different membrane anchoring and lipid partitioning characteristics in COS-7 cells, and show dramatic changes in glycosylphosphatidylinositol (GPI)-anchored protein arrangement under varying perturbations. PC-PALM is thus an effective tool with broad applicability for analysis of protein heterogeneity and function, adaptable to other single-molecule strategies.
Single-particle tracking (SPT) is often the rate-limiting step in live-cell imaging studies of subcellular dynamics. Here we present a tracking algorithm that addresses the principal challenges of SPT, namely high particle density, particle motion heterogeneity, temporary particle disappearance, and particle merging and splitting. The algorithm first links particles between consecutive frames and then links the resulting track segments into complete trajectories. Both steps are formulated as global combinatorial optimization problems whose solution identifies the overall most likely set of particle trajectories throughout a movie. Using this approach, we show that the GTPase dynamin differentially affects the kinetics of long- and short-lived endocytic structures and that the motion of CD36 receptors along cytoskeleton-mediated linear tracks increases their aggregation probability. Both applications indicate the requirement for robust and complete tracking of dense particle fields to dissect the mechanisms of receptor organization at the level of the plasma membrane.
Engaged T cell antigen receptors (TCRs) initiate signaling through the adaptor protein Lat. In quiescent T cells, Lat is segregated into clusters on the cell surface, which raises the question of how TCR triggering initiates signaling. Using super-resolution fluorescence microscopy, we found that pre-existing Lat domains were neither phosphorylated nor laterally transported to TCR activation sites, which suggested that these clusters do not participate in TCR signaling. Instead, TCR activation resulted in the recruitment and phosphorylation of Lat from subsynaptic vesicles. Studies of Lat mutants confirmed that recruitment preceded and was essential for phosphorylation and that both processes were independent of surface clustering of Lat. Our data suggest that TCR ligation preconditions the membrane for vesicle recruitment and bulk activation of the Lat signaling network.
The organization and dynamics of receptors and other molecules in the plasma membrane are not well understood. Here we analyzed the spatio-temporal dynamics of T cell antigen receptor (TCR) complexes and linker for activation of T cells (Lat), a key adaptor molecule in the TCR signaling pathway, in T cell membranes using high-speed photoactivated localization microscopy, dual-color fluorescence cross-correlation spectroscopy and transmission electron microscopy. In quiescent T cells, both molecules existed in separate membrane domains (protein islands), and these domains concatenated after T cell activation. These concatemers were identical to signaling microclusters, a prominent hallmark of T cell activation. This separation versus physical juxtapositioning of receptor domains and domains containing downstream signaling molecules in quiescent versus activated T cells may be a general feature of plasma membrane-associated signal transduction.
Fluorescence correlation spectroscopy (FCS) is an important technique for studying low concentrations of analyte molecules in solution. The core molecular characteristic that can be addressed by FCS is the translational diffusion coefficient of the analyte molecules, which can be used for i.e. studying molecular binding and reactions, or conformational changes of macromolecules. The present paper discusses several possible optical and photophysical effects that can influence the outcome of a FCS measurement and thus can bias the value of the derived diffusion coefficient.
To probe the complexity of the cell membrane organization and dynamics, it is important to obtain simple physical observables from experiments on live cells. Here we show that fluorescence correlation spectroscopy (FCS) measurements at different spatial scales enable distinguishing between different submicron confinement models. By plotting the diffusion time versus the transverse area of the confocal volume, we introduce the so-called FCS diffusion law, which is the key concept throughout this article. First, we report experimental FCS diffusion laws for two membrane constituents, which are respectively a putative raft marker and a cytoskeleton-hindered transmembrane protein. We find that these two constituents exhibit very distinct behaviors. To understand these results, we propose different models, which account for the diffusion of molecules either in a membrane comprising isolated microdomains or in a meshwork. By simulating FCS experiments for these two types of organization, we obtain FCS diffusion laws in agreement with our experimental observations. We also demonstrate that simple observables derived from these FCS diffusion laws are strongly related to confinement parameters such as the partition of molecules in microdomains and the average confinement time of molecules in a microdomain or a single mesh of a meshwork.
We introduce a method for optically imaging intracellular proteins at nanometer spatial resolution. Numerous sparse subsets
of photoactivatable fluorescent protein molecules were activated, localized (to ∼2 to 25 nanometers), and then bleached. The
aggregate position information from all subsets was then assembled into a superresolution image. We used this method—termed
photoactivated localization microscopy—to image specific target proteins in thin sections of lysosomes and mitochondria; in
fixed whole cells, we imaged vinculin at focal adhesions, actin within a lamellipodium, and the distribution of the retroviral
protein Gag at the plasma membrane.
Cell migration is regulated in part by the connection between the substratum and the actin cytoskeleton. However, the very large number of proteins involved in this linkage and their complex network of interactions make it difficult to assess their role in cell migration. We apply a novel image analysis tool, spatio-temporal image correlation spectroscopy (STICS), to quantify the directed movements of adhesion-related proteins and actin in protrusions of migrating cells. The STICS technique reveals protein dynamics even when protein densities are very low or very high, and works in the presence of large, static molecular complexes. Detailed protein velocity maps for actin and the adhesion-related proteins alpha-actinin, alpha5-integrin, talin, paxillin, vinculin and focal adhesion kinase are presented. The data show that there are differences in the efficiency of the linkage between integrin and actin among different cell types and on the same cell type grown on different substrate densities. We identify potential mechanisms that regulate efficiency of the linkage, or clutch, and identify two likely points of disconnect, one at the integrin and the other at alpha-actinin or actin. The data suggests that the efficiency of the linkage increases as actin and adhesions become more organized showing the importance of factors that regulate the efficiency in adhesion signaling and dynamics.
We combined photoactivated localization microscopy (PALM) with live-cell single-particle tracking to create a new method termed sptPALM. We created spatially resolved maps of single-molecule motions by imaging the membrane proteins Gag and VSVG, and obtained several orders of magnitude more trajectories per cell than traditional single-particle tracking enables. By probing distinct subsets of molecules, sptPALM can provide insight into the origins of spatial and temporal heterogeneities in membranes.
Although the highly dynamic and mosaic organization of the plasma membrane is well-recognized, depicting a resolved, global view of this organization remains challenging. We present an analytical single-particle tracking (SPT) method and tool, multiple-target tracing (MTT), that takes advantage of the high spatial resolution provided by single-fluorophore sensitivity. MTT can be used to generate dynamic maps at high densities of tracked particles, thereby providing global representation of molecular dynamics in cell membranes. Deflation by subtracting detected peaks allows detection of lower-intensity peaks. We exhaustively detected particles using MTT, with performance reaching theoretical limits, and then reconnected trajectories integrating the statistical information from past trajectories. We demonstrate the potential of this method by applying it to the epidermal growth factor receptor (EGFR) labeled with quantum dots (Qdots), in the plasma membrane of live cells. We anticipate the use of MTT to explore molecular dynamics and interactions at the cell membrane.
Protein mobility is conventionally analyzed in terms of an effective diffusion. Yet, this description often fails to properly distinguish and evaluate the physical parameters (such as the membrane friction) and the biochemical interactions governing the motion. Here, we present a method combining high-density single-molecule imaging and statistical inference to separately map the diffusion and energy landscapes of membrane proteins across the cell surface at ∼100 nm resolution (with acquisition of a few minutes). Upon applying these analytical tools to glycine neurotransmitter receptors at inhibitory synapses, we find that gephyrin scaffolds act as shallow energy traps (∼3 kBT) for glycine neurotransmitter receptors, with a depth modulated by the biochemical properties of the receptor-gephyrin interaction loop. In turn, the inferred maps can be used to simulate the dynamics of proteins in the membrane, from the level of individual receptors to that of the population, and thereby, to model the stochastic fluctuations of physiological parameters (such as the number of receptors at synapses). Overall, our approach provides a powerful and comprehensive framework with which to analyze biochemical interactions in living cells and to decipher the multiscale dynamics of biomolecules in complex cellular environments.
We provide an analytical tool based on a variational Bayesian treatment of hidden Markov models to combine the information from thousands of short single-molecule trajectories of intracellularly diffusing proteins. The method identifies the number of diffusive states and the state transition rates. Using this method we have created an objective interaction map for Hfq, a protein that mediates interactions between small regulatory RNAs and their mRNA targets.
Two-color spatio-temporal image cross-correlation spectroscopy (STICCS) is a new, to our knowledge, image analysis method that calculates space-time autocorrelation and cross-correlation functions from fluorescence intensity fluctuations. STICCS generates cellular flow and diffusion maps that reveal interactions and cotransport of two distinct molecular species labeled with different fluorophores. Here we use computer simulations to map the capabilities and limitations of STICCS for measurements in complex heterogeneous environments containing micro- and macrostructures. We then use STICCS to analyze the co-flux of adhesion components in migrating cells imaged using total internal reflection fluorescence microscopy. The data reveal a robust, time-dependent co-fluxing of certain integrins and paxillin in adhesions in protrusions when they pause, and in adhesions that are sliding and disassembling, demonstrating that the molecules in these adhesions move as a complex. In these regions, both α6β1- or αLβ2-integrins, expressed in CHO.B2 cells, co-flux with paxillin; an analogous cotransport was seen for α6β1-integrin and α-actinin in U2OS. This contrasts with the behavior of the α5β1-integrin and paxillin, which do not co-flux. Our results clearly show that integrins can move in complexes with adhesion proteins in protrusions that are retracting.
Currently used techniques for the analysis of single-molecule trajectories only exploit a small part of the available information stored in the data. Here, we apply a Bayesian inference scheme to trajectories of confined receptors that are targeted by pore-forming toxins to extract the two-dimensional confining potential that restricts the motion of the receptor. The receptor motion is modeled by the overdamped Langevin equation of motion. The method uses most of the information stored in the trajectory and converges quickly onto inferred values, while providing the uncertainty on the determined values. The inference is performed on the polynomial development of the potential and on the diffusivities that have been discretized on a mesh. Numerical simulations are used to test the scheme and quantify the convergence toward the input values for forces, potential, and diffusivity. Furthermore, we show that the technique outperforms the classical mean-square-displacement technique when forces act on confined molecules because the typical mean-square-displacement analysis does not account for them. We also show that the inferred potential better represents input potentials than the potential extracted from the position distribution based on Boltzmann statistics that assumes statistical equilibrium.
There are two formalisms for mathematically describing the time behavior of a spatially homogeneous chemical system: The deterministic approach regards the time evolution as a continuous, wholly predictable process which is governed by a set of coupled, ordinary differential equations (the "reaction-rate equations"); the stochastic approach regards the time evolution as a kind of random-walk process which is governed by a single differential-difference equation (the "master equation"). Fairly simple kinetic theory arguments show that the stochastic formulation of chemical kinetics has a firmer physical basis than the deterministic formulation, but unfortunately the stochastic master equation is often mathematically intractable. There is, however, a way to make exact numerical calculations within the framework of the stochastic formulation without having to deal with the master equation directly. It is a relatively simple digital computer algorithm which uses a rigorously derived Monte Carlo procedure to numerically simulate the time evolution of the given chemical system. Like the master equation, this "stochastic simulation algorithm" correctly accounts for the inherent fluctuations and correlations that are necessarily ignored in the deterministic formulation. In addition, unlike most procedures for numerically solving the deterministic reaction-rate equations, this algorithm never approximates infinitesimal time increments dt by finite time steps Δt. The feasibility and utility of the simulation algorithm are demonstrated by applying it to several well-known model chemical systems, including the Lotka model, the Brusselator, and the Oregonator.
Fluorescence correlation spectroscopy (FCS) is a powerful approach to characterizing the binding and transport dynamics of macromolecules. The unbiased interpretation of FCS data relies on the evaluation of multiple competing hypotheses to describe an underlying physical process under study, which is typically unknown a priori. Bayesian inference provides a convenient framework for this evaluation based on the temporal autocorrelation function (TACF), as previously shown theoretically using model TACF curves (He, J., Guo, S., and Bathe, M. Anal. Chem. 2012, 84). Here, we apply this procedure to simulated and experimentally measured photon-count traces analyzed using a multitau correlator, which results in complex noise properties in TACF curves that cannot be modeled easily. As a critical component of our technique, we develop two means of estimating the noise in TACF curves based either on multiple independent TACF curves themselves or a single raw underlying intensity trace, including a general procedure to ensure that independent, uncorrelated samples are used in the latter approach. Using these noise definitions, we demonstrate that the Bayesian approach selects the simplest hypothesis that describes the FCS data based on sampling and signal limitations, naturally avoiding overfitting. Further, we show that model probabilities computed using the Bayesian approach provide a reliability test for the downstream interpretation of model parameter values estimated from FCS data. Our procedure is generally applicable to FCS and image correlation spectroscopy and therefore provides an important advance in the application of these methods to the quantitative biophysical investigation of complex analytical and biological systems.
Fluorescence correlation spectroscopy (FCS) is a powerful tool to infer the physical process of macromolecules including local concentration, binding, and transport from fluorescence intensity measurements. Interpretation of FCS data relies critically on objective multiple hypothesis testing of competing models for complex physical processes that are typically unknown a priori. Here, we propose an objective Bayesian inference procedure for testing multiple competing models to describe FCS data based on temporal autocorrelation functions. We illustrate its performance on simulated temporal autocorrelation functions for which the physical process, noise, and sampling properties can be controlled completely. The procedure enables the systematic and objective evaluation of an arbitrary number of competing, non-nested physical models for FCS data, appropriately penalizing model complexity according to the Principle of Parsimony to prefer simpler models as the signal-to-noise ratio decreases. In addition to eliminating overfitting of FCS data, the procedure dictates when the interpretation of model parameters are not justified by the signal-to-noise ratio of the underlying sampled data. The proposed approach is completely general in its applicability to transport, binding, or other physical processes, as well as spatially resolved FCS from image correlation spectroscopy, providing an important theoretical foundation for the automated application of FCS to the analysis of biological and other complex samples.
Cell membranes actively participate in numerous cellular functions. Inasmuch as bioactivities of cell membranes are known to depend crucially on their lateral organization, much effort has been focused on deciphering this organization on different length scales. Within this context, the concept of lipid rafts has been intensively discussed over recent years. In line with its ability to measure diffusion parameters with great precision, fluorescence correlation spectroscopy (FCS) measurements have been made in association with innovative experimental strategies to monitor modes of molecular lateral diffusion within the plasma membrane of living cells. These investigations have allowed significant progress in the characterization of the cell membrane lateral organization at the suboptical level and have provided compelling evidence for the in vivo existence of raft nanodomains. We review these FCS-based studies and the characteristic structural features of raft nanodomains. We also discuss the findings in regards to the current view of lipid rafts as a general membrane-organizing principle.
Versatile superresolution imaging methods, able to give dynamic information of endogenous molecules at high density, are still lacking in biological science. Here, superresolved images and diffusion maps of membrane proteins are obtained on living cells. The method consists of recording thousands of single-molecule trajectories that appear sequentially on a cell surface upon continuously labeling molecules of interest. It allows studying any molecules that can be labeled with fluorescent ligands including endogenous membrane proteins on living cells. This approach, named universal PAINT (uPAINT), generalizes the previously developed point-accumulation-for-imaging-in-nanoscale-topography (PAINT) method for dynamic imaging of arbitrary membrane biomolecules. We show here that the unprecedented large statistics obtained by uPAINT on single cells reveal local diffusion properties of specific proteins, either in distinct membrane compartments of adherent cells or in neuronal synapses.
Measurement of receptor distributions on cell surfaces is one important aspect of understanding the mechanism whereby receptors function. In recent years, scanning fluorescence correlation spectroscopy has emerged as an excellent tool for making quantitative measurements of cluster sizes and densities. However, the measurements are slow and usually require fixed preparations. Moreover, while the precision is good, the accuracy is limited by the relatively small amount of information in each measurement, such that many are required. Here we present a novel extension of the scanning correlation spectroscopy that solves a number of the present problems. The new technique, which we call image correlation spectroscopy, is based on quantitative analysis of confocal scanning laser microscopy images. Since these can be generated in a matter of a second or so, the measurements become more rapid. The image is collected over a large cell area so that more sampling is done, improving the accuracy. The sacrifice is a lower resolution in the sampling, which leads to a lower precision. This compromise of precision in favor of speed and accuracy still provides an enormous advantage for image correlation spectroscopy over scanning correlation spectroscopy. The present work demonstrates the underlying theory, showing how the principles can be applied to measurements on standard fluorescent beads and changes in distribution of receptors for platelet-derived growth factor on human foreskin fibroblasts.
Image correlation spectroscopy allows sensitive measurement of the spatial distribution and aggregation state of fluorescent membrane macro molecules. When studying a single population system (i.e., aggregates of similar brightness), an accurate measure can be made of the aggregate number per observation area, but this measurement becomes much more complex in a distributed population system (i.e., bright and faint aggregates). This article describes an alternate solution that involves extraction of the bright aggregate population information. This novel development for image correlation spectroscopy, termed intensity subtraction analysis, uses sequential uniform intensity subtraction from raw confocal images. Sequential intensity subtraction results in loss of faint aggregate fluctuations that are smaller in magnitude than fluctuations due to the brightest aggregates. The resulting image has correlatable fluctuations originating from only the brightest population, permitting quantification of this population's distribution and further cross-correlation measurements. The feasibility of this technique is demonstrated using fluorescent microsphere images and biological samples. The technique is further used to examine the spatial distribution of a plasma-membrane-labeled fluorescent synthetic ganglioside, and to cross-correlate this probe with various membrane markers. The evidence provided demonstrates that bright aggregates of the fluorescent ganglioside are associated with clathrin-coated pits, membrane microvilli, and detergent-resistant membranes.
We introduce a new extension of image correlation spectroscopy (ICS) and image cross-correlation spectroscopy (ICCS) that relies on complete analysis of both the temporal and spatial correlation lags for intensity fluctuations from a laser-scanning microscopy image series. This new approach allows measurement of both diffusion coefficients and velocity vectors (magnitude and direction) for fluorescently labeled membrane proteins in living cells through monitoring of the time evolution of the full space-time correlation function. By using filtering in Fourier space to remove frequencies associated with immobile components, we are able to measure the protein transport even in the presence of a large fraction (>90%) of immobile species. We present the background theory, computer simulations, and analysis of measurements on fluorescent microspheres to demonstrate proof of principle, capabilities, and limitations of the method. We demonstrate mapping of flow vectors for mixed samples containing fluorescent microspheres with different emission wavelengths using space time image cross-correlation. We also present results from two-photon laser-scanning microscopy studies of alpha-actinin/enhanced green fluorescent protein fusion constructs at the basal membrane of living CHO cells. Using space-time image correlation spectroscopy (STICS), we are able to measure protein fluxes with magnitudes of mum/min from retracting lamellar regions and protrusions for adherent cells. We also demonstrate the measurement of correlated directed flows (magnitudes of mum/min) and diffusion of interacting alpha5 integrin/enhanced cyan fluorescent protein and alpha-actinin/enhanced yellow fluorescent protein within living CHO cells. The STICS method permits us to generate complete transport maps of proteins within subregions of the basal membrane even if the protein concentration is too high to perform single particle tracking measurements.
The flow of information through the epidermal growth factor receptor (EGFR) is shaped by molecular interactions in the plasma membrane. The EGFR is associated with lipid rafts, but their role in modulating receptor mobility and subsequent interactions is unclear. To investigate the role of nanoscale rafts in EGFR dynamics, we used single-molecule fluorescence imaging to track individual receptors and their dimerization partner, human epidermal growth factor receptor 2 (HER2), in the membrane of human mammary epithelial cells. We found that the motion of both receptors was interrupted by dwellings within nanodomains. EGFR was significantly less mobile than HER2. This difference was likely due to F-actin because its depolymerization led to similar diffusion patterns between the EGFR and HER2. Manipulations of membrane cholesterol content dramatically altered the diffusion pattern of both receptors. Cholesterol depletion led to almost complete confinement of the receptors, whereas cholesterol enrichment extended the boundaries of the restricted areas. Interestingly, F-actin depolymerization partially restored receptor mobility in cholesterol-depleted membranes. Our observations suggest that membrane cholesterol provides a dynamic environment that facilitates the free motion of EGFR and HER2, possibly by modulating the dynamic state of F-actin. The association of the receptors with lipid rafts could therefore promote their rapid interactions only upon ligand stimulation.
Membrane subdomains have been implicated in T cell signaling, although their properties and mechanisms of formation remain controversial. Here, we have used single-molecule and scanning confocal imaging to characterize the behavior of GFP-tagged signaling proteins in Jurkat T cells. We show that the coreceptor CD2, the adaptor protein LAT, and tyrosine kinase Lck cocluster in discrete microdomains in the plasma membrane of signaling T cells. These microdomains require protein-protein interactions mediated through phosphorylation of LAT and are not maintained by interactions with actin or lipid rafts. Using a two color imaging approach that allows tracking of single molecules relative to the CD2/LAT/Lck clusters, we demonstrate that these microdomains exclude and limit the free diffusion of molecules in the membrane but also can trap and immobilize specific proteins. Our data suggest that diffusional trapping through protein-protein interactions creates microdomains that concentrate or exclude cell surface proteins to facilitate T cell signaling.
We present an extensive investigation of the accuracy and precision of temporal image correlation spectroscopy (TICS). Using simulations of laser scanning microscopy image time series, we investigate the effect of spatiotemporal sampling, particle density, noise, sampling frequency, and photobleaching of fluorophores on the recovery of transport coefficients and number densities by TICS. We show that the recovery of transport coefficients is usually limited by spatial sampling, while the measurement of accurate number densities is restricted by background noise in an image series. We also demonstrate that photobleaching of the fluorophore causes a consistent overestimation of diffusion coefficients and flow rates, and a severe underestimation of number densities. We derive a bleaching correction equation that removes both of these biases when used to fit temporal autocorrelation functions, without increasing the number of fit parameters. Finally, we image the basal membrane of a CHO cell with EGFP/alpha-actinin, using two-photon microscopy, and analyze a subregion of this series using TICS and apply the bleaching correction. We show that the photobleaching correction can be determined simply by using the average image intensities from the time series, and we use the simulations to provide good estimates of the accuracy and precision of the number density and transport coefficients measured with TICS.
We present the theory and application of reciprocal space image correlation spectroscopy (kICS). This technique measures the number density, diffusion coefficient, and velocity of fluorescently labeled macromolecules in a cell membrane imaged on a confocal, two-photon, or total internal reflection fluorescence microscope. In contrast to r-space correlation techniques, we show kICS can recover accurate dynamics even in the presence of complex fluorophore photobleaching and/or "blinking". Furthermore, these quantities can be calculated without nonlinear curve fitting, or any knowledge of the beam radius of the exciting laser. The number densities calculated by kICS are less sensitive to spatial inhomogeneity of the fluorophore distribution than densities measured using image correlation spectroscopy. We use simulations as a proof-of-principle to show that number densities and transport coefficients can be extracted using this technique. We present calibration measurements with fluorescent microspheres imaged on a confocal microscope, which recover Stokes-Einstein diffusion coefficients, and flow velocities that agree with single particle tracking measurements. We also show the application of kICS to measurements of the transport dynamics of alpha5-integrin/enhanced green fluorescent protein constructs in a transfected CHO cell imaged on a total internal reflection fluorescence microscope using charge-coupled device area detection.
A new data analysis tool that resolves correlations on the nanometer length and millisecond timescale is derived. This tool, adapted from methods of spatiotemporal image correlation spectroscopy, exploits the high positional accuracy of single-particle tracking. While conventional tracking methods break down if multiple particle trajectories intersect, our method works in principle for arbitrarily large molecule densities and diffusion coefficients as long as individual molecules can be identified. The method is computationally cheap and robust and requires no a priori knowledge about the dynamical coefficients, as opposed to other methods. We demonstrate the validity of the method by Monte Carlo simulations and by application to single-molecule tracking data of membrane-anchored proteins in live cells. The results faithfully reproduce those obtained by conventional tracking. Upon activation, a fraction of the small GTPase H-Ras is confined to domains of <200 nm diameter, which further substantiates the prediction that membrane organization is a determinant in cellular signaling.
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