Classification of dynamical diffusion states in single molecule tracking microscopy

Synthesis and Characterization of a Novel Photocleavable Fluorescent Dye Dyad for Diffusion Imaging

We report the synthesis and characterization of a photocleavable fluorescent dye dyad. The two constituting dyes show a large spectral overlap and are in close proximity to each other, leading to efficient Förster Resonance Energy Transfer (FRET). Photocleavage of the dyad and the subsequent independent diffusion of both fluorophores qualifies the system to be used for high accuracy diffusion measurements. In contrast to previous work, the dyad reported here can be applied in polar solvents and cleaved by UV-A light. Beneficially, the photolabile linker provides two orthogonal labeling sites for various commercially available fluorescent labels. In this work, we chose the cationic organic dyes ATTO565 and ATTO647N. We outline the synthesis and spectral characterization of the system with UV-Vis and fluorescence spectroscopy as well as fluorescence lifetime and fluorescence quantum yield measurements. Furthermore, we performed proof-of-principle microscopy experiments to demonstrate its capability in polyvinyl acetate films.

Similarly slow diffusion of BAM and SecYEG complexes in live E. coli cells observed with 3D spt-PALM

The β-barrel assembly machinery (BAM) complex is responsible for inserting outer membrane proteins (OMPs) into the Escherichia coli outer membrane. The SecYEG translocon inserts inner membrane proteins into the inner membrane and translocates both soluble proteins and nascent OMPs into the periplasm. Recent reports describe Sec possibly playing a direct role in OMP biogenesis through interactions with the soluble polypeptide transport-associated (POTRA) domains of BamA (the central OMP component of BAM). Here we probe the diffusion behavior of these protein complexes using photoactivatable super-resolution localization microscopy and single-particle tracking in live E. coli cells of BAM and SecYEG components BamA and SecE and compare them to other outer and inner membrane proteins. To accurately measure trajectories on the highly curved cell surface, three-dimensional tracking was performed using double-helix point-spread function microscopy. All proteins tested exhibit two diffusive modes characterized by "slow" and "fast" diffusion coefficients. We implement a diffusion coefficient analysis as a function of the measurement lag time to separate positional uncertainty from true mobility. The resulting true diffusion coefficients of the slow and fast modes showed a complete immobility of full-length BamA constructs in the time frame of the experiment, whereas the OMP OmpLA displayed a slow diffusion consistent with the high viscosity of the outer membrane. The periplasmic POTRA domains of BamA were found to anchor BAM to other cellular structures and render it immobile. However, deletion of individual distal POTRA domains resulted in increased mobility, suggesting that these domains are required for the full set of cellular interactions. SecE diffusion was much slower than that of the inner membrane protein PgpB and was more like OMPs and BamA. Strikingly, SecE diffused faster upon POTRA domain deletion. These results are consistent with the existence of a BAM-SecYEG trans-periplasmic assembly in live E. coli cells.

Extract latent features of single-particle trajectories with historical experience learning

Single-particle tracking has enabled real-time, in situ quantitative studies of complex systems. However, inferring dynamic state changes from noisy and undersampling trajectories encounters challenges. Here, we introduce a data-driven method for extracting features of subtrajectories with historical experience learning (Deep-SEES), where a single-particle tracking analysis pipeline based on a self-supervised architecture automatically searches for the latent space, allowing effective segmentation of the underlying states from noisy trajectories without prior knowledge on the particle dynamics. We validated our method on a variety of noisy simulated and experimental data. Our results showed that the method can faithfully capture both stable states and their dynamic switch. In highly random systems, our method outperformed commonly used unsupervised methods in inferring motion states, which is important for understanding nanoparticles interacting with living cell membranes, active enzymes, and liquid-liquid phase separation. Self-generating latent features of trajectories could potentially improve the understanding, estimation, and prediction of many complex systems.

Single-molecule dynamics show a transient lipopolysaccharide transport bridge

Gram-negative bacteria are surrounded by two membranes. A special feature of the outer membrane is its asymmetry. It contains lipopolysaccharide (LPS) in the outer leaflet and phospholipids in the inner leaflet1-3. The proper assembly of LPS in the outer membrane is required for cell viability and provides Gram-negative bacteria intrinsic resistance to many classes of antibiotics. LPS biosynthesis is completed in the inner membrane, so the LPS must be extracted, moved across the aqueous periplasm that separates the two membranes and translocated through the outer membrane where it assembles on the cell surface4. LPS transport and assembly requires seven conserved and essential LPS transport components5 (LptA-G). This system has been proposed to form a continuous protein bridge that provides a path for LPS to reach the cell surface6,7, but this model has not been validated in living cells. Here, using single-molecule tracking, we show that Lpt protein dynamics are consistent with the bridge model. Half of the inner membrane Lpt proteins exist in a bridge state, and bridges persist for 5-10 s, showing that their organization is highly dynamic. LPS facilitates Lpt bridge formation, suggesting a mechanism by which the production of LPS can be directly coupled to its transport. Finally, the bridge decay kinetics suggest that there may be two different types of bridges, whose stability differs according to the presence (long-lived) or absence (short-lived) of LPS. Together, our data support a model in which LPS is both a substrate and a structural component of dynamic Lpt bridges that promote outer membrane assembly.

ExTrack characterizes transition kinetics and diffusion in noisy single-particle tracks

Single-particle tracking microscopy is a powerful technique to investigate how proteins dynamically interact with their environment in live cells. However, the analysis of tracks is confounded by noisy molecule localization, short tracks, and rapid transitions between different motion states, notably between immobile and diffusive states. Here, we propose a probabilistic method termed ExTrack that uses the full spatio-temporal information of tracks to extract global model parameters, to calculate state probabilities at every time point, to reveal distributions of state durations, and to refine the positions of bound molecules. ExTrack works for a wide range of diffusion coefficients and transition rates, even if experimental data deviate from model assumptions. We demonstrate its capacity by applying it to slowly diffusing and rapidly transitioning bacterial envelope proteins. ExTrack greatly increases the regime of computationally analyzable noisy single-particle tracks. The ExTrack package is available in ImageJ and Python.

ExTrack characterizes transition kinetics and diffusion in noisy single-particle tracks

Single-particle tracking microscopy is a powerful technique to investigate how proteins dynamically interact with their environment in live cells. However, the analysis of tracks is confounded by noisy molecule localization, short tracks, and rapid transitions between different motion states, notably between immobile and diffusive states. Here, we propose a probabilistic method termed ExTrack that uses the full spatio-temporal information of tracks to extract global model parameters, to calculate state probabilities at every time point, to reveal distributions of state durations, and to refine the positions of bound molecules. ExTrack works for a wide range of diffusion coefficients and transition rates, even if experimental data deviate from model assumptions. We demonstrate its capacity by applying it to slowly diffusing and rapidly transitioning bacterial envelope proteins. ExTrack greatly increases the regime of computationally analyzable noisy single-particle tracks. The ExTrack package is available in ImageJ and Python.

Revealing the dynamic adsorption and diffusion of peptide amphiphile on supported lipid bilayer by single molecule experiment and simulation

Dynamic adsorption and diffusion of peptide amphiphiles (PAs) with different numbers of alkyl tails on supported lipid bilayers (SLBs) were investigated by single molecule tracking experiment and molecule dynamic simulation. Experimental results show two distinct populations of PAs with different residence time. Residence time of adsorbed PAs increases with the increase of the alkyl tails, whereas diffusion coefficient monotonically decreases with rising the number of alkyl tails and also decreases with increasing the mobility of SLBs. All-atom molecule dynamic simulation results prove that the adsorption and diffusion of PAs on SLB surface are mainly determined by interactions between PAs and SLBs and also the intrinsic mobility of PAs in aqueous solution. The electrostatic interactions and the mobility of PAs are two dominated but contradictory coefficients for the adsorption and diffusion of PAs. By increasing the alkyl tails, the mobility of PAs decreases while the electrostatic property does not change significantly, resulting in the increase of residence time and decrease of diffusivity of PAs. Additionally, for the PAs with large number of alkyl tails (≥ 3 alkyl tails), steric hindrance of alkyl tails leads to the decrease of adsorption probability of PAs on SLB surface. These findings lay the groundwork for guiding the design of PAs with high cell affinity, potentially useful for efficient drug delivery.

Time-dependent classification of protein diffusion types: A statistical detection of mean-squared-displacement exponent transitions

In this paper, we have proposed a statistical procedure for detecting transitions of the mean-square-displacement exponent value within a single trajectory. With this procedure, we have identified three regimes of proteins dynamics on a cell membrane, namely, subdiffusion, free diffusion, and immobility. The fourth considered dynamics type, namely, superdiffusion was not detected. We show that the analyzed protein trajectories are not stationary and not ergodic. Moreover, classification of the dynamics type performed without prior detection of transitions may lead to the overestimation of the proportion of subdiffusive trajectories.

A comparative study on the influence of an ivy preparation and an ivy/thyme combination on the β2-adrenergic signal transduction

The β₂-adrenergic receptor (β₂AR) is relevant for surfactant formation in alveolar type 2 cells and reduction of intracellular calcium concentration in bronchial muscle cells and thus for secretolytic and bronchospasmolytic effects. Herbal medicinal products that affect the β₂AR system are used to treat common cold and bronchitis accompanied with mucus covered and narrowed airways. The present work compares the influence of an ivy preparation and an ivy/thyme combination on the β₂-adrenergic signal transduction. For receptor binding studies and characterization of the lateral mobility of β₂AR we have used single molecule detection by fluorescence correlation spectroscopy and single particle tracking. For the determination of both the second messenger cAMP and the internalization of β₂AR we have generated luciferase based reporter cell lines, which produce a cAMP-dependent luciferase in the cytosol and express β₂AR with extracellular luciferase moiety in the plasma membrane. While both preparations increased the β₂AR binding, a significant increase of the cAMP level was observed only for the ivy preparation, which can be explained by the inhibited internalization of HiBiT-tagged β₂AR under stimulating conditions. In contrast, isoprenaline-mediated internalization of HiBiT-tagged β₂AR of ivy/thyme combination pre-treated cells was not inhibited. Cells comparatively pre-treated with a thyme preparation did not show inhibition of ß₂AR internalization either. Furthermore, SNAP-tagged β₂AR of ivy preparation pre-treated cells, which were not internalized after isoprenaline stimulation, showed a redistribution from fast-to-slowly diffusing β₂AR. A corresponding redistribution of these receptors was not observed after pre-treatment with both the ivy/thyme combination and the thyme preparation. Comparable to the ivy/thyme combination, no decrease in the intratrack transitioning probability ratio (p23/p32) for fast and slow diffusing β₂AR was found for the thyme preparation, which, however, significantly decreased for control cells and for pre-treatment with the ivy preparation under stimulating conditions. It can therefore be concluded that the thyme fluid extract fraction in the ivy/thyme combination may have in part a negative effect on the β₂-adrenergic signal transduction.

A Brief History of Single-Particle Tracking of the Epidermal Growth Factor Receptor

Single-particle tracking (SPT) has been used and developed over the last 25 years as a method to investigate molecular dynamics, structure, interactions, and function in the cellular context. SPT is able to show how fast and how far individual molecules move, identify different dynamic populations, measure the duration and strength of intermolecular interactions, and map out structures on the nanoscale in cells. In combination with other techniques such as macromolecular crystallography and molecular dynamics simulation, it allows us to build models of complex structures, and develop and test hypotheses of how these complexes perform their biological roles in health as well as in disease states. Here, we use the example of the epidermal growth factor receptor (EGFR), which has been studied extensively by SPT, demonstrating how the method has been used to increase our understanding of the receptor’s organization and function, including its interaction with the plasma membrane, its activation, clustering, and oligomerization, and the role of other receptors and endocytosis. The examples shown demonstrate how SPT might be employed in the investigation of other biomolecules and systems.

Diaphanous-1 affects the nanoscale clustering and lateral diffusion of receptor for advanced glycation endproducts (RAGE)

The interactions between the cytoplasmic protein diaphanous-1 (Diaph1) and the receptor for advanced glycation endproducts (RAGE) drive the negative consequences of RAGE signaling in several disease processes. Reported in this work is how Diaph1 affects the nanoscale clustering and diffusion of RAGE measured using super-resolution stochastic optical reconstruction microscopy (STORM) and single particle tracking (SPT). Altering the Diaph1 binding site has a different impact on RAGE diffusion compared to when Diaph1 expression is reduced in HEK293 cells. In cells with reduced Diaph1 expression (RAGE-Diaph1^-/-), the average RAGE diffusion coefficient is increased by 35%. RAGE diffusion is known to be influenced by the dynamics of the actin cytoskeleton. Actin labeling shows that a reduced Diaph1 expression leads to cells with reduced filopodia density and length. In contrast, when two RAGE amino acids that interact with Diaph1 are mutated (RAGE_RQ/AA), the average RAGE diffusion coefficient is decreased by 16%. Since RAGE diffusion is slowed when the interaction between Diaph1 and RAGE is disrupted, the interaction of the two proteins results in faster RAGE diffusion. In both RAGE_RQ/AA and RAGE-Diaph1^-/- cells the number and size of RAGE clusters are decreased compared to cells expressing RAGE and native concentrations of Diaph1. This work shows that Diaph1 has a role in affecting RAGE clusters and diffusion.

Estimation of diffusive states from single-particle trajectory in heterogeneous medium using machine-learning methods

We propose a novel approach to analyze random walks in heterogeneous medium using a hybrid machine-learning method based on a gamma mixture and a hidden Markov model. A gamma mixture and a hidden Markov model respectively provide the number and the most probable sequence of diffusive states from the time series position data of particles/molecules obtained by single-particle/molecule tracking (SPT/SMT) method. We evaluate the performance of our proposed method for numerically generated trajectories. It is shown that our proposed method can correctly extract the number of diffusive states when each trajectory is long enough to be frame averaged. We also indicate that our method can provide an indicator whether the assumption of a medium consisting of discrete diffusive states is appropriate or not based on the available amount of trajectory data. Then, we demonstrate an application of our method to the analysis of experimentally obtained SPT data.

Imaging, Tracking and Computational Analyses of Virus Entry and Egress with the Cytoskeleton

Viruses have a dual nature: particles are “passive substances” lacking chemical energy transformation, whereas infected cells are “active substances” turning-over energy. How passive viral substances convert to active substances, comprising viral replication and assembly compartments has been of intense interest to virologists, cell and molecular biologists and immunologists. Infection starts with virus entry into a susceptible cell and delivers the viral genome to the replication site. This is a multi-step process, and involves the cytoskeleton and associated motor proteins. Likewise, the egress of progeny virus particles from the replication site to the extracellular space is enhanced by the cytoskeleton and associated motor proteins. This overcomes the limitation of thermal diffusion, and transports virions and virion components, often in association with cellular organelles. This review explores how the analysis of viral trajectories informs about mechanisms of infection. We discuss the methodology enabling researchers to visualize single virions in cells by fluorescence imaging and tracking. Virus visualization and tracking are increasingly enhanced by computational analyses of virus trajectories as well as in silico modeling. Combined approaches reveal previously unrecognized features of virus-infected cells. Using select examples of complementary methodology, we highlight the role of actin filaments and microtubules, and their associated motors in virus infections. In-depth studies of single virion dynamics at high temporal and spatial resolutions thereby provide deep insight into virus infection processes, and are a basis for uncovering underlying mechanisms of how cells function.

The imaging FCS diffusion law in the presence of multiple diffusive modes

The cellular plasma membrane is the barrier over which cells exchange materials and communicate with their surroundings, and thus plays the central role in cellular sensing and metabolism. Therefore, the investigation of plasma membrane organization and dynamics is required for understanding of cellular functions. The plasma membrane is a heterogeneous matrix. The presence of structures such as lipid and protein domains and the cytoskeleton meshwork poses a hindrance to the free diffusion of membrane associated biomolecules. However, these domains and the cytoskeleton meshwork barriers are below the optical diffraction limit with potentially short lifetimes and are not easily detected even in super-resolution microscopy. Therefore, dynamic measurements are often used to indirectly prove the existence of domains and barriers by analyzing the mode of diffusion of probe molecules. One of these tools is the Fluorescence Correlation Spectroscopy (FCS) diffusion law. The FCS diffusion law is a plot of diffusion time (τ_d) versus observation area. For at least three different diffusive modes - free, domain confined, and meshwork hindered hop diffusion - the expected plots have been characterized, typically by its y-intercept (τ₀) when fit with a linear model, and have been verified in many cases. However, a description of τ₀ has only been given for pure diffusive modes. But in many experimental cases it is not evident that a protein will undergo only one kind of diffusion, and thus the interpretation of the τ₀ value is problematic. Here, we therefore address the question about the absolute value of τ₀ in the case of complex diffusive modes, i.e. when either one molecule is domain confined and cytoskeleton hindered or when two molecules exhibit different diffusive behavior at the same position in a sample. In addition, we investigate how τ₀ changes when the diffusive mode of a probe alters upon disruption of domains or the cytoskeleton by drug treatments. By a combination of experimental studies and simulations, we show that τ₀ is not influenced equally by the different diffusive modes as typically found in cellular environments, and that it is the relative change of τ₀ rather than its absolute value that provides information on the mode of diffusion.

Limitations of Qdot labelling compared to directly-conjugated probes for single particle tracking of B cell receptor mobility

Single-particle tracking (SPT) is a powerful method for exploring single-molecule dynamics in living cells with nanoscale spatiotemporal resolution. Photostability and bright fluorescence make quantum dots (Qdots) a popular choice for SPT. However, their large size could potentially alter the mobility of the molecule of interest. To test this, we labelled B cell receptors on the surface of B-lymphocytes with monovalent Fab fragments of antibodies that were either linked to Qdots via streptavidin or directly conjugated to the small organic fluorophore Cy3. Imaging of receptor mobility by total internal reflection fluorescence microscopy (TIRFM), followed by quantitative single-molecule diffusion and confinement analysis, definitively showed that Qdots sterically hinder lateral mobility regardless of the substrate to which the cells were adhered. Qdot labelling also drastically altered the frequency with which receptors transitioned between apparent slow- and fast-moving states and reduced the size of apparent confinement zones. Although we show that Qdot-labelled probes can detect large differences in receptor mobility, they fail to resolve subtle differences in lateral diffusion that are readily detectable using Cy3-labelled Fabs. Our findings highlight the utility and limitations of using Qdots for TIRFM and wide-field-based SPT, and have significant implications for interpreting SPT data.

Unraveling intermittent features in single-particle trajectories by a local convex hull method

We propose a model-free method to detect change points between distinct phases in a single random trajectory of an intermittent stochastic process. The local convex hull (LCH) is constructed for each trajectory point, while its geometric properties (e.g., the diameter or the volume) are used as discriminators between phases. The efficiency of the LCH method is validated for six models of intermittent motion, including Brownian motion with different diffusivities or drifts, fractional Brownian motion with different Hurst exponents, and surface-mediated diffusion. We discuss potential applications of the method for detection of active and passive phases in the intracellular transport, temporal trapping or binding of diffusing molecules, alternating bulk and surface diffusion, run and tumble (or search) phases in the motion of bacteria and foraging animals, and instantaneous firing rates in neurons.

Resolving mixed mechanisms of protein subdiffusion at the T cell plasma membrane

The plasma membrane is a complex medium where transmembrane proteins diffuse and interact to facilitate cell function. Membrane protein mobility is affected by multiple mechanisms, including crowding, trapping, medium elasticity and structure, thus limiting our ability to distinguish them in intact cells. Here we characterize the mobility and organization of a short transmembrane protein at the plasma membrane of live T cells, using single particle tracking and photoactivated-localization microscopy. Protein mobility is highly heterogeneous, subdiffusive and ergodic-like. Using mobility characteristics, we segment individual trajectories into subpopulations with distinct Gaussian step-size distributions. Particles of low-to-medium mobility consist of clusters, diffusing in a viscoelastic and fractal-like medium and are enriched at the centre of the cell footprint. Particles of high mobility undergo weak confinement and are more evenly distributed. This study presents a methodological approach to resolve simultaneous mixed subdiffusion mechanisms acting on polydispersed samples and complex media such as cell membranes.

Membrane protein diffusion is affected by distinct mechanisms such as molecular crowding and medium elasticity. Here the authors present an analytical approach to analyse single particle trajectories and distinguish mixed subdiffusive processes affecting membrane protein mobility in living cells.

Segmentation of 3D Trajectories Acquired by TSUNAMI Microscope: An Application to EGFR Trafficking

Whereas important discoveries made by single-particle tracking have changed our view of the plasma membrane organization and motor protein dynamics in the past three decades, experimental studies of intracellular processes using single-particle tracking are rather scarce because of the lack of three-dimensional (3D) tracking capacity. In this study we use a newly developed 3D single-particle tracking method termed TSUNAMI (Tracking of Single particles Using Nonlinear And Multiplexed Illumination) to investigate epidermal growth factor receptor (EGFR) trafficking dynamics in live cells at 16/43 nm (xy/z) spatial resolution, with track duration ranging from 2 to 10 min and vertical tracking depth up to tens of microns. To analyze the long 3D trajectories generated by the TSUNAMI microscope, we developed a trajectory analysis algorithm, which reaches 81% segment classification accuracy in control experiments (termed simulated movement experiments). When analyzing 95 EGF-stimulated EGFR trajectories acquired in live skin cancer cells, we find that these trajectories can be separated into three groups-immobilization (24.2%), membrane diffusion only (51.6%), and transport from membrane to cytoplasm (24.2%). When EGFRs are membrane-bound, they show an interchange of Brownian diffusion and confined diffusion. When EGFRs are internalized, transitions from confined diffusion to directed diffusion and from directed diffusion back to confined diffusion are clearly seen. This observation agrees well with the model of clathrin-mediated endocytosis.

Single-molecule imaging reveals modulation of cell wall synthesis dynamics in live bacterial cells

The peptidoglycan cell wall is an integral organelle critical for bacterial cell shape and stability. Proper cell wall construction requires the interaction of synthesis enzymes and the cytoskeleton, but it is unclear how the activities of individual proteins are coordinated to preserve the morphology and integrity of the cell wall during growth. To elucidate this coordination, we used single-molecule imaging to follow the behaviours of the two major peptidoglycan synthases in live, elongating Escherichia coli cells and after perturbation. We observed heterogeneous localization dynamics of penicillin-binding protein (PBP) 1A, the synthase predominantly associated with cell wall elongation, with individual PBP1A molecules distributed between mobile and immobile populations. Perturbations to PBP1A activity, either directly through antibiotics or indirectly through PBP1A's interaction with its lipoprotein activator or other synthases, shifted the fraction of mobile molecules. Our results suggest that multiple levels of regulation control the activity of enzymes to coordinate peptidoglycan synthesis.

The bacterial cell wall is important for cell shape and stability, but how the activities of the biosynthetic machinery are coordinated are not clear. Here the authors use single-molecule imaging and chemical perturbations to determine factors that affect the localization dynamics of penicillin-binding proteins (PBP)1A and PBP1B.

Automatic detection of diffusion modes within biological membranes using back-propagation neural network

Background

Single particle tracking (SPT) is nowadays one of the most popular technique to probe spatio-temporal dynamics of proteins diffusing within the plasma membrane. Indeed membrane components of eukaryotic cells are very dynamic molecules and can diffuse according to different motion modes. Trajectories are often reconstructed frame-by-frame and dynamic properties often evaluated using mean square displacement (MSD) analysis. However, to get statistically significant results in tracking experiments, analysis of a large number of trajectories is required and new methods facilitating this analysis are still needed.

Results

In this study we developed a new algorithm based on back-propagation neural network (BPNN) and MSD analysis using a sliding window. The neural network was trained and cross validated with short synthetic trajectories. For simulated and experimental data, the algorithm was shown to accurately discriminate between Brownian, confined and directed diffusion modes within one trajectory, the 3 main of diffusion encountered for proteins diffusing within biological membranes. It does not require a minimum number of observed particle displacements within the trajectory to infer the presence of multiple motion states. The size of the sliding window was small enough to measure local behavior and to detect switches between different diffusion modes for segments as short as 20 frames. It also provides quantitative information from each segment of these trajectories. Besides its ability to detect switches between 3 modes of diffusion, this algorithm is able to analyze simultaneously hundreds of trajectories with a short computational time.

Conclusion

This new algorithm, implemented in powerful and handy software, provides a new conceptual and versatile tool, to accurately analyze the dynamic behavior of membrane components.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-016-1064-z) contains supplementary material, which is available to authorized users.

Analysis of single particle diffusion with transient binding using particle filtering

Diffusion with transient binding occurs in a variety of biophysical processes, including movement of transmembrane proteins, T cell adhesion, and caging in colloidal fluids. We model diffusion with transient binding as a Brownian particle undergoing Markovian switching between free diffusion when unbound and diffusion in a quadratic potential centered around a binding site when bound. Assuming the binding site is the last position of the particle in the unbound state and Gaussian observational error obscures the true position of the particle, we use particle filtering to predict when the particle is bound and to locate the binding sites. Maximum likelihood estimators of diffusion coefficients, state transition probabilities, and the spring constant in the bound state are computed with a stochastic Expectation-Maximization (EM) algorithm.

A review of progress in single particle tracking: from methods to biophysical insights

Optical microscopy has for centuries been a key tool to study living cells with minimum invasiveness. The advent of single molecule techniques over the past two decades has revolutionized the field of cell biology by providing a more quantitative picture of the complex and highly dynamic organization of living systems. Amongst these techniques, single particle tracking (SPT) has emerged as a powerful approach to study a variety of dynamic processes in life sciences. SPT provides access to single molecule behavior in the natural context of living cells, thereby allowing a complete statistical characterization of the system under study. In this review we describe the foundations of SPT together with novel optical implementations that nowadays allow the investigation of single molecule dynamic events with increasingly high spatiotemporal resolution using molecular densities closer to physiological expression levels. We outline some of the algorithms for the faithful reconstruction of SPT trajectories as well as data analysis, and highlight biological examples where the technique has provided novel insights into the role of diffusion regulating cellular function. The last part of the review concentrates on different theoretical models that describe anomalous transport behavior and ergodicity breaking observed from SPT studies in living cells.

Quantifying Multistate Cytoplasmic Molecular Diffusion in Bacterial Cells via Inverse Transform of Confined Displacement Distribution

Single-molecule tracking (SMT) of fluorescently tagged cytoplasmic proteins can provide valuable information on the underlying biological processes in living cells via subsequent analysis of the displacement distributions; however, the confinement effect originated from the small size of a bacterial cell skews the protein’s displacement distribution and complicates the quantification of the intrinsic diffusive behaviors. Using the inverse transformation method, we convert the skewed displacement distribution (for both 2D and 3D imaging conditions) back to that in free space for systems containing one or multiple (non)interconverting Brownian diffusion states, from which we can reliably extract the number of diffusion states as well as their intrinsic diffusion coefficients and respective fractional populations. We further demonstrate a successful application to experimental SMT data of a transcription factor in living E. coli cells. This work allows a direct quantitative connection between cytoplasmic SMT data with diffusion theory for analyzing molecular diffusive behavior in live bacteria.

Biophysical methods for the characterization of PTEN/lipid bilayer interactions

PTEN, a tumor suppressor protein that dephosphorylates phosphoinositides at the 3-position of the inositol ring, is a cytosolic protein that needs to associate with the plasma membrane or other subcellular membranes to exert its lipid phosphatase function. Upon membrane association PTEN interacts with at least three different lipid entities: An anionic lipid that is present in sufficiently high concentration to create a negative potential that allows PTEN to interact electrostatically with the membrane, phosphatidylinositol-4,5-bisphosphate, which interacts with PTEN's N-terminal end and the substrate, usually phosphatidylinositol-3,4,5-trisphosphate. Many parameters influence PTEN's interaction with the lipid bilayer, for example, the lateral organization of the lipids or the presence of other chemical species like cholesterol or other lipids. To investigate systematically the different steps of PTEN's complex binding mechanism and to explore its dynamic behavior in the membrane bound state, in vitro methods need to be employed that allow for a systematic variation of the experimental conditions. In this review we survey a variety of methods that can be used to assess PTEN lipid binding affinity, the dynamics of its membrane association as well as its dynamic behavior in the membrane bound state.

Evaluation of fluorophores to label SNAP-tag fused proteins for multicolor single-molecule tracking microscopy in live cells

Single-molecule tracking has become a widely used technique for studying protein dynamics and their organization in the complex environment of the cell. In particular, the spatiotemporal distribution of membrane receptors is an active field of study due to its putative role in the regulation of signal transduction. The SNAP-tag is an intrinsically monovalent and highly specific genetic tag for attaching a fluorescent label to a protein of interest. Little information is currently available on the choice of optimal fluorescent dyes for single-molecule microscopy utilizing the SNAP-tag labeling system. We surveyed 6 green and 16 red excitable dyes for their suitability in single-molecule microscopy of SNAP-tag fusion proteins in live cells. We determined the nonspecific binding levels and photostability of these dye conjugates when bound to a SNAP-tag fused membrane protein in live cells. We found that only a limited subset of the dyes tested is suitable for single-molecule tracking microscopy. The results show that a careful choice of the dye to conjugate to the SNAP-substrate to label SNAP-tag fusion proteins is very important, as many dyes suffer from either rapid photobleaching or high nonspecific staining. These characteristics appear to be unpredictable, which motivated the need to perform the systematic survey presented here. We have developed a protocol for evaluating the best dyes, and for the conditions that we evaluated, we find that Dy 549 and CF 640 are the best choices tested for single-molecule tracking. Using an optimal dye pair, we also demonstrate the possibility of dual-color single-molecule imaging of SNAP-tag fusion proteins. This survey provides an overview of the photophysical and imaging properties of a range of SNAP-tag fluorescent substrates, enabling the selection of optimal dyes and conditions for single-molecule imaging of SNAP-tagged fusion proteins in eukaryotic cell lines.