Single Particle Tracking: From Theory to Biophysical Applications

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

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

Simulating stochastic adsorption of diluted solute molecules at interfaces

This report uses Monte Carlo simulations to connect stochastic single-molecule and ensemble surface adsorption of molecules from dilute solutions. Monte Carlo simulations often use a fundamental time resolution to simulate each discrete step for each molecule. The adsorption rate obtained from such a simulation surprisingly contains an error compared to the results obtained from the traditional method. Simulating adsorption kinetics is interesting in many processes, such as mass transportation within cells, the kinetics of drug-receptor interactions, membrane filtration, and other general reaction kinetics in diluted solutions. Thus, it is important to understand the origin of the disagreement and find a way to correct the results. This report reviews the traditional model, explains the single-molecule simulations, and introduces a method to correct the results of adsorption rate. For example, one can bin finer time steps into time steps of interest to simulate the fractal diffusion or simply introduce a correction factor for the simulations. Then two model systems, self-assembled monolayer (SAM) and biosensing on the patterned surface, are simulated to check the accuracy of the equations. It is found that the adsorption rate of SAM is highly dependent on the conditions and the uncertainty is large. However, the biosensing system is relatively accurate. This is because the concentration gradient near the interface varies significantly with reaction conditions for SAMs while relatively stable for the biosensing system.

Simultaneous, Single-Particle Measurements of Size and Loading Give Insights into the Structure of Drug-Delivery Nanoparticles

Nanoparticles are a promising solution for delivery of a wide range of medicines and vaccines. Optimizing their design depends on being able to resolve, understand, and predict biophysical and therapeutic properties, as a function of design parameters. While existing tools have made great progress, gaps in understanding remain because of the inability to make detailed measurements of multiple correlated properties. Typically, an average measurement is made across a heterogeneous population, obscuring potentially important information. In this work, we develop and apply a method for characterizing nanoparticles with single-particle resolution. We use convex lens-induced confinement (CLiC) microscopy to isolate and quantify the diffusive trajectories and fluorescent intensities of individual nanoparticles trapped in microwells for long times. First, we benchmark detailed measurements of fluorescent polystyrene nanoparticles against prior data to validate our approach. Second, we apply our method to investigate the size and loading properties of lipid nanoparticle (LNP) vehicles containing silencing RNA (siRNA), as a function of lipid formulation, solution pH, and drug-loading. By taking a comprehensive look at the correlation between the intensity and size measurements, we gain insights into LNP structure and how the siRNA is distributed in the LNP. Beyond introducing an analytic for size and loading, this work allows for future studies of dynamics with single-particle resolution, such as LNP fusion and drug-release kinetics. The prime contribution of this work is to better understand the connections between microscopic and macroscopic properties of drug-delivery vehicles, enabling and accelerating their discovery and development.

Model Segmentation in Single Particle Tracking

In this paper, we implement and compare two different change detection techniques applied to determining the time points in Single Particle Tracking (SPT) data where the particle changes the dynamic model of motion. The goal is to use this change detection to segment the data in order to estimate the relevant parameters of such models. We consider two well-known statistics commonly used for change detection: the likelihood ratio test (LRT) and the Kullback-Leibler divergence (KLD). We assume that our time-varying system is subject to step-like changes in the parameters that drive the process. The techniques are then applied to experimental data acquired on a microscope under controlled settings to validate our results.

Light Sheet Illumination for 3D Single-Molecule Super-Resolution Imaging of Neuronal Synapses

The function of the neuronal synapse depends on the dynamics and interactions of individual molecules at the nanoscale. With the development of single-molecule super-resolution microscopy over the last decades, researchers now have a powerful and versatile imaging tool for mapping the molecular mechanisms behind the biological function. However, imaging of thicker samples, such as mammalian cells and tissue, in all three dimensions is still challenging due to increased fluorescence background and imaging volumes. The combination of single-molecule imaging with light sheet illumination is an emerging approach that allows for imaging of biological samples with reduced fluorescence background, photobleaching, and photodamage. In this review, we first present a brief overview of light sheet illumination and previous super-resolution techniques used for imaging of neurons and synapses. We then provide an in-depth technical review of the fundamental concepts and the current state of the art in the fields of three-dimensional single-molecule tracking and super-resolution imaging with light sheet illumination. We review how light sheet illumination can improve single-molecule tracking and super-resolution imaging in individual neurons and synapses, and we discuss emerging perspectives and new innovations that have the potential to enable and improve single-molecule imaging in brain tissue.

A Novel Biotinylated Homotryptamine Derivative for Quantum Dot Imaging of Serotonin Transporter in Live Cells

The serotonin transporter (SERT) is the primary target for selective serotonin reuptake inhibitor (SSRI) antidepressants that are thought to exert their therapeutic effects by increasing the synaptic concentration of serotonin. Consequently, probes that can be utilized to study cellular trafficking of SERT are valuable research tools. We have developed a novel ligand (IDT785) that is composed of a SERT antagonist (a tetrahydro pyridyl indole derivative) conjugated to a biotinylated poly ethylene glycol (PEG) via a phenethyl linker. This compound was determined to be biologically active and inhibited SERT-mediated reuptake of IDT307 with the half-maximal inhibitory concentration of 7.2 ± 0.3 μM. We demonstrated that IDT785 enabled quantum dot (QD) labeling of membrane SERT in transfected HEK-293 cultures that could be blocked using the high affinity serotonin reuptake inhibitor paroxetine. Molecular docking studies suggested that IDT785 might be binding to the extracellular vestibule binding site rather than the orthosteric substrate binding site, which could be attributable to the hydrophilicity of the PEG chain and the increased loss of degrees of freedom that would be required to penetrate into the orthosteric binding site. Using IDT785, we were able to study the membrane localization and membrane dynamics of YFP-SERT heterologously expressed in HEK-293 cells and demonstrated that SERT expression was enriched in the membrane edge and in thin cellular protrusions.

Diffusion State Transitions in Single-Particle Trajectories of MET Receptor Tyrosine Kinase Measured in Live Cells

Single-particle tracking enables the analysis of the dynamics of biomolecules in living cells with nanometer spatial and millisecond temporal resolution. This technique reports on the mobility of membrane proteins and is sensitive to the molecular state of a biomolecule and to interactions with other biomolecules. Trajectories describe the mobility of single particles over time and provide information such as the diffusion coefficient and diffusion state. Changes in particle dynamics within single trajectories lead to segmentation, which allows to extract information on transitions of functional states of a biomolecule. Here, mean-squared displacement analysis is developed to classify trajectory segments into immobile, confined diffusing, and freely diffusing states, and to extract the occurrence of transitions between these modes. We applied this analysis to single-particle tracking data of the membrane receptor MET in live cells and analyzed state transitions in single trajectories of the un-activated receptor and the receptor bound to the ligand internalin B. We found that internalin B-bound MET shows an enhancement of transitions from freely and confined diffusing states into the immobile state as compared to un-activated MET. Confined diffusion acts as an intermediate state between immobile and free, as this state is most likely to change the diffusion state in the following segment. This analysis can be readily applied to single-particle tracking data of other membrane receptors and intracellular proteins under various conditions and contribute to the understanding of molecular states and signaling pathways.

Visualization of Vaccine Dynamics with Quantum Dots for Immunotherapy

The direct visualization of vaccine fate is important to investigate its immunoactivation process to elucidate the detailed molecular reaction process at single-molecular level. Yet, visualization of the spatiotemporal trafficking of vaccines remains poorly explored. Here, we show that quantum dot (QD) nanomaterials allow for monitoring vaccine dynamics and for amplified immune response. Synthetic QDs enable efficient conjugation of antigen and adjuvants to target tissues and cells, and non-invasive imaging the trafficking dynamics to lymph nodes and cellular compartments. The nanoparticle vaccine elicits potent immune responses and anti-tumor efficacy alone or in combination with programmed cell death protein 1 blockade. The synthetic QDs showed high fluorescence quantum yield and superior photostability, and the reliable and long-term spatiotemporal tracking of vaccine dynamics was realized for the first time by using the synthetic QDs, providing a powerful strategy for studying immune response and evaluating vaccine efficacy.

Splicing exponential point spread function design for localization of nanoparticles

We propose a point spread function for three-dimensional localization of nanoparticles. The axial detection range of the point spread function can be simply changed by adjusting the design parameters. In addition, the spatial extent of the point spread function can also be changed by adjusting the design parameters, which is an advantage other point spread functions do not have. We used our point spread functions and the existing point spread functions for dense multi-particle imaging, which proved the advantage that the point spread function with a smaller spatial extent we designed can effectively reduce the overlap between the point spread functions. The three-dimensional process of the fluorescent microsphere penetrating HT-22 cell membrane was successfully recorded, which verified the effectiveness of this method.

Micromirror Total Internal Reflection Microscopy for High-Performance Single Particle Tracking at Interfaces

Single particle tracking has found broad applications in the life and physical sciences, enabling the observation and characterization of nano- and microscopic motion. Fluorescence-based approaches are ideally suited for high-background environments, such as tracking lipids or proteins in or on cells, due to superior background rejection. Scattering-based detection is preferable when localization precision and imaging speed are paramount due to the in principle infinite photon budget. Here, we show that micromirror-based total internal reflection dark field microscopy enables background suppression previously only reported for interferometric scattering microscopy, resulting in nanometer localization precision at 6 μs exposure time for 20 nm gold nanoparticles with a 25 × 25 μm² field of view. We demonstrate the capabilities of our implementation by characterizing sub-nanometer deterministic flows of 20 nm gold nanoparticles at liquid-liquid interfaces. Our results approach the optimal combination of background suppression, localization precision, and temporal resolution achievable with pure scattering-based imaging and tracking of nanoparticles at interfaces.

A review for Cell and Particle Tracking on Microscopy Images using Algorithms and Deep Learning Technologies

Time-lapse microscopy images generated by biological experiments have been widely used for observing target activities, such as the motion trajectories and survival states. Based on these observations, biologists can conclude experimental results or present new hypotheses for several biological applications, i.e. virus research or drug design. Many methods or tools have been proposed in the past to observe cell and particle activities, which are defined as single cell tracking and single particle tracking problems, by using algorithms and deep learning technologies. In this article, a review for these works is presented in order to summarize the past methods and research topics at first, then points out the problems raised by these works, and finally proposes future research directions. The contributions of this article will help researchers to understand past development trends and further propose innovative technologies.

Untying the Gordian KNOT: Unbiased Single Particle Tracking Using Point Clouds and Adaptive Motion Analysis

Achieving mechanistic understanding of transport in complex environments such as inside cells or at polymer interfaces is challenging. We need better ways to image transport in 3-D and better single particle tracking algorithms to determine transport that are not systemically biased toward any classical motion model. Here we present an unbiased single particle tracking algorithm: Knowing Nothing Outside Tracking (KNOT). KNOT uses point clouds provided by iterative deconvolution to educate individual particle localizations and link particle positions between frames to achieve 2-D and 3-D tracking. Information from prior point clouds fuels an independent adaptive motion model for each particle to avoid global models that could introduce biases. KNOT competes with or surpasses other 2-D methods from the 2012 particle tracking challenge while accurately tracking adsorption dynamics of proteins on polymer surfaces and early endosome transport in live cells in 3-D. We apply KNOT to study 3-D endosome transport to reveal new physical insight into locally directed and diffusive transport in live cells. Our analysis demonstrates better accuracy in classifying local motion and its direction compared to previous methods, revealing intricate intracellular transport heterogeneities.

Particle-by-Particle In Situ Characterization of the Protein Corona via Real-Time 3D Single-Particle-Tracking Spectroscopy*

Nanoparticles (NPs) adsorb proteins when exposed to biological fluids, forming a dynamic protein corona that affects their fate in biological environments. A comprehensive understanding of the protein corona is lacking due to the inability of current techniques to precisely measure the full corona in situ at the single-particle level. Herein, we introduce a 3D real-time single-particle tracking spectroscopy to "lock-on" to single freely diffusing polystyrene NPs and probe their individual protein coronas, primarily using bovine serum albumin (BSA) as a model system. The fluorescence signals and diffusive motions of the tracked NPs enable quantification of the "hard corona" using mean-squared displacement analysis. Critically, this method's particle-by-particle nature enabled a lock-in-type frequency filtering approach to extract the full protein corona, despite the typically confounding effect of high background signal from unbound proteins. From these results, the dynamic in situ full protein corona is observed to contain twice the number of proteins compared to the ex situ-measured "hard" protein corona.

Simultaneous Real-Time Three-Dimensional Localization and FRET Measurement of Two Distinct Particles

Many biological processes employ mechanisms involving the locations and interactions of multiple components. Given that most biological processes occur in three dimensions, the simultaneous measurement of three-dimensional locations and interactions is necessary. However, the simultaneous three-dimensional precise localization and measurement of interactions in real time remains challenging. Here, we report a new microscopy technique to localize two spectrally distinct particles in three dimensions with an accuracy (2.35σ) of tens of nanometers with an exposure time of 100 ms and to measure their real-time interactions using fluorescence resonance energy transfer (FRET) simultaneously. Using this microscope, we tracked two distinct vesicles containing t-SNAREs or v-SNARE in three dimensions and observed FRET simultaneously during single-vesicle fusion in real time, revealing the nanoscale motion and interactions of single vesicles in vesicle fusion. Thus, this study demonstrates that our microscope can provide detailed information about real-time three-dimensional nanoscale locations, motion, and interactions in biological processes.

Convergence to a Gaussian by Narrowing of Central Peak in Brownian yet Non-Gaussian Diffusion in Disordered Environments

In usual diffusion, the concentration profile, starting from an initial distribution showing sharp features, first gets smooth and then converges to a Gaussian. By considering several examples, we show that the art of convergence to a Gaussian in diffusion in disordered media with infinite contrast may be strikingly different: sharp features of initial distribution do not smooth out at long times. This peculiarity of the strong disorder may be of importance for diagnostics of disorder in complex, e.g., biological, systems.

Joint Estimation of Trajectory and Model Parameters for Single Particle Tracking of 3D Confined Diffusion Using the Double-Helix Point Spread Function

Single particle tracking plays a significant role in biophysics through its ability to reveal dynamic mechanisms and physical properties of biological macromolecules inside living cells. The motion of these molecules can often be modeled as a confined diffusion. The standard paradigm in the biophysics community is to first estimate the trajectory of a particle and then use a technique such as the Mean Square Displacement or the Maximum Likelihood Estimation (MLE) to determine model parameters. These approaches, however, ignore the fact that localization and parameter estimation problems are coupled. We have previously introduced a framework based on optimal estimation theory to simultaneously do localization and parameter estimation. Here we build upon that work by expanding it to include a recent advance in imaging three dimensional motion, namely the Double-Helix (DH) engineered Point Spread Function (PSF). The DH-PSF encodes the axial position of the particle directly into the 2D image acquired by the camera mounted to the microscope. Our approach uses Expectation Maximization (EM) and Sequential Monte Carlo (SMC) to handle the nonlinearities in the observation and motion models. In this paper, we also improve upon the computational complexity of this scheme, using a Gaussian Particle Filter and Backward Simulation Particle Smoother in the SMC elements of the algorithm. We compare our scheme through simulation to state of the art methods based on localization using Gaussian fitting followed by MLE of the model parameters. These results show that our method outperforms GF-MLE at the low signal intensity levels common to biophysical experiments.

Single-molecule tracking technologies for quantifying the dynamics of gene regulation in cells, tissue and embryos

For decades, we have relied on population and time-averaged snapshots of dynamic molecular scale events to understand how genes are regulated during development and beyond. The advent of techniques to observe single-molecule kinetics in increasingly endogenous contexts, progressing from in vitro studies to living embryos, has revealed how much we have missed. Here, we provide an accessible overview of the rapidly expanding family of technologies for single-molecule tracking (SMT), with the goal of enabling the reader to critically analyse single-molecule studies, as well as to inspire the application of SMT to their own work. We start by overviewing the basics of and motivation for SMT experiments, and the trade-offs involved when optimizing parameters. We then cover key technologies, including fluorescent labelling, excitation and detection optics, localization and tracking algorithms, and data analysis. Finally, we provide a summary of selected recent applications of SMT to study the dynamics of gene regulation.

Information Optimal Control for Single Particle Tracking Microscopy

We consider the problem of designing a control policy for a laser scanning microscope (LSM) which will minimize the estimation uncertainty when identifying the state and motion model of a fluorescent biological particle. Using the information optimal design framework we pose an optimization problem which seeks to maximize the Fisher information of the particle's state. We then apply optimal control methods to determine the laser trajectory that maximizes a criterion based on the Fisher information. The resulting optimal control policy is a Bang-Singular control which moves the laser to the set of measurement locations that maximize the rate of information accumulation. Simulations demonstrate the ability of the resulting control system to position the laser to measure the particles location with a minimum uncertainty.

NOBIAS: Analyzing Anomalous Diffusion in Single-Molecule Tracks With Nonparametric Bayesian Inference

Single particle tracking (SPT) enables the investigation of biomolecular dynamics at a high temporal and spatial resolution in living cells, and the analysis of these SPT datasets can reveal biochemical interactions and mechanisms. Still, how to make the best use of these tracking data for a broad set of experimental conditions remains an analysis challenge in the field. Here, we develop a new SPT analysis framework: NOBIAS (NOnparametric Bayesian Inference for Anomalous Diffusion in Single-Molecule Tracking), which applies nonparametric Bayesian statistics and deep learning approaches to thoroughly analyze SPT datasets. In particular, NOBIAS handles complicated live-cell SPT data for which: the number of diffusive states is unknown, mixtures of different diffusive populations may exist within single trajectories, symmetry cannot be assumed between the x and y directions, and anomalous diffusion is possible. NOBIAS provides the number of diffusive states without manual supervision, it quantifies the dynamics and relative populations of each diffusive state, it provides the transition probabilities between states, and it assesses the anomalous diffusion behavior for each state. We validate the performance of NOBIAS with simulated datasets and apply it to the diffusion of single outer-membrane proteins in Bacteroides thetaiotaomicron. Furthermore, we compare NOBIAS with other SPT analysis methods and find that, in addition to these advantages, NOBIAS is robust and has high computational efficiency and is particularly advantageous due to its ability to treat experimental trajectories with asymmetry and anomalous diffusion.

Pore Forming Protein Induced Biomembrane Reorganization and Dynamics: A Focused Review

Pore forming proteins are a broad class of pathogenic proteins secreted by organisms as virulence factors due to their ability to form pores on the target cell membrane. Bacterial pore forming toxins (PFTs) belong to a subclass of pore forming proteins widely implicated in bacterial infections. Although the action of PFTs on target cells have been widely investigated, the underlying membrane response of lipids during membrane binding and pore formation has received less attention. With the advent of superresolution microscopy as well as the ability to carry out molecular dynamics (MD) simulations of the large protein membrane assemblies, novel microscopic insights on the pore forming mechanism have emerged over the last decade. In this review, we focus primarily on results collated in our laboratory which probe dynamic lipid reorganization induced in the plasma membrane during various stages of pore formation by two archetypal bacterial PFTs, cytolysin A (ClyA), an α-toxin and listeriolysin O (LLO), a β-toxin. The extent of lipid perturbation is dependent on both the secondary structure of the membrane inserted motifs of pore complex as well as the topological variations of the pore complex. Using confocal and superresolution stimulated emission depletion (STED) fluorescence correlation spectroscopy (FCS) and MD simulations, lipid diffusion, cholesterol reorganization and deviations from Brownian diffusion are correlated with the oligomeric state of the membrane bound protein as well as the underlying membrane composition. Deviations from free diffusion are typically observed at length scales below ∼130 nm to reveal the presence of local dynamical heterogeneities that emerge at the nanoscale-driven in part by preferential protein binding to cholesterol and domains present in the lipid membrane. Interrogating the lipid dynamics at the nanoscale allows us further differentiate between binding and pore formation of β- and α-PFTs to specific domains in the membrane. The molecular insights gained from the intricate coupling that occurs between proteins and membrane lipids and receptors during pore formation are expected to improve our understanding of the virulent action of PFTs.

Three-dimensional localization refinement and motion model parameter estimation for confined single particle tracking under low-light conditions

Confined diffusion is an important model for describing the motion of biological macromolecules moving in the crowded, three-dimensional environment of the cell. In this work we build upon the technique known as sequential Monte Carlo - expectation maximization (SMC-EM) to simultaneously localize the particle and estimate the motion model parameters from single particle tracking data. We extend SMC-EM to handle the double-helix point spread function (DH-PSF) for encoding the three-dimensional position of the particle in the two-dimensional image plane of the camera. SMC-EM can handle a wide range of camera models and here we assume the data was acquired using a scientific CMOS (sCMOS) camera. The sensitivity and speed of these cameras make them well suited for SPT, though the pixel-dependent nature of the camera noise presents a challenge for analysis. We focus on the low signal setting and compare our method through simulation to more standard approaches that use the paradigm of localize-then-estimate. To localize the particle under the standard paradigm, we use both a Gaussian fit and a maximum likelihood estimator (MLE) that accounts for both the DH-PSF and the pixel-dependent noise of the camera. Model estimation is then carried out either by fitting the model to the mean squared displacement (MSD) curve, or through an optimal estimation approach. Our results indicate that in the low signal regime, the SMC-EM approach outperforms the other methods while at higher signal-to-background levels, SMC-EM and the MLE-based methods perform equally well and both are significantly better than fitting to the MSD. In addition our results indicate that at smaller confinement lengths where the nonlinearities dominate the motion model, the SMC-EM approach is superior to the alternative approaches.

Probing DNA-protein interactions using single-molecule diffusivity contrast

Single-molecule fluorescence investigations of protein-nucleic acid interactions require robust means to identify the binding state of individual substrate molecules in real time. Here, we show that diffusivity contrast, widely used in fluorescence correlation spectroscopy at the ensemble level and in single-particle tracking on individual (but slowly diffusing) species, can be used as a general readout to determine the binding state of single DNA molecules with unlabeled proteins in solution. We first describe the technical basis of drift-free single-molecule diffusivity measurements in an anti-Brownian electrokinetic trap. We then cross-validate our method with protein-induced fluorescence enhancement, a popular technique to detect protein binding on nucleic acid substrates with single-molecule sensitivity. We extend an existing hydrodynamic modeling framework to link measured diffusivity to particular DNA-protein structures and obtain good agreement between the measured and predicted diffusivity values. Finally, we show that combining diffusivity contrast with protein-induced fluorescence enhancement allows simultaneous mapping of binding stoichiometry and location on individual DNA-protein complexes, potentially enhancing single-molecule views of relevant biophysical processes.

Single Molecules Are Your Quanta: A Bottom-Up Approach toward Multidimensional Super-resolution Microscopy

The rise of single-molecule localization microscopy (SMLM) and related super-resolution methods over the past 15 years has revolutionized how we study biological and materials systems. In this Perspective, we reflect on the underlying philosophy of how diffraction-unlimited pictures containing rich spatial and functional information may gradually emerge through the local accumulation of single-molecule measurements. Starting with the basic concepts, we analyze the uniqueness of and opportunities in building up the final picture one molecule at a time. After brief introductions to the more established multicolor and three-dimensional measurements, we highlight emerging efforts to extend SMLM to new dimensions and functionalities as fluorescence polarization, emission spectra, and molecular motions, and discuss rising opportunities and future directions. With single molecules as our quanta, the bottom-up accumulation approach provides a powerful conduit for multidimensional microscopy at the nanoscale.

Single-Molecule Dynamics Reflect IgG Conformational Changes Associated with Ion-Exchange Chromatography

Conformational changes of antibodies and other biologics can decrease the effectiveness of pharmaceutical separations. Hence, a detailed mechanistic picture of antibody-stationary phase interactions that occur during ion-exchange chromatography (IEX) can provide critical insights. This work examines antibody conformational changes and how they perturb antibody motion and affect ensemble elution profiles. We combine IEX, three-dimensional single-protein tracking, and circular dichroism spectroscopy to investigate conformational changes of a model antibody, immunoglobulin G (IgG), as it interacts with the stationary phase as a function of salt conditions. The results indicate that the absence of salt enhances electrostatic attraction between IgG and the stationary phase, promotes surface-induced unfolding, slows IgG motion, and decreases elution from the column. Our results reveal previously unreported details of antibody structural changes and their influence on macroscale elution profiles.

Super-resolution fluorescence imaging of extracellular environments

The extracellular matrix (ECM) is an important biophysical environment that plays a role in a number of physiological processes. The ECM is highly dynamic, with changes occurring as local, nanoscale, physicochemical variations in physical confinement and chemistry from the perspective of biological molecules. The length and time scale of ECM dynamics are challenging to measure with current spectroscopic techniques. Super-resolution fluorescence microscopy has the potential to probe local, nanoscale, physicochemical variations in the ECM. Here, we review super-resolution imaging and analysis methods and their application to study model nanoparticles and biomolecules within synthetic ECM hydrogels and the brain extracellular space (ECS). We provide a perspective of future directions for the field that can move super-resolution imaging of the ECM towards more biomedically-relevant samples. Overall, super-resolution imaging is a powerful tool that can increase our understanding of extracellular environments at new spatiotemporal scales to reveal ECM processes at the molecular-level.

Nanometric displacement sensor with a switchable measuring range using a cylindrical vector beam excited silicon nanoantenna

We demonstrate a nanometric displacement sensor with a switchable measuring range by using a single silicon nanoantenna. It is revealed that the interference between the longitudinal and transverse dipolar scattering can be well tuned by moving the nanoantenna in the focal field of the cylindrical vector beam. As a result, a position related scattering directivity is found and is used as a displacement sensor with a 4.5 nm lateral resolution. Interestingly, the measuring range of this displacement sensor can be extended by twice through simply changing the excitation from the azimuthally polarized beam to the radially polarized beam. Our results provide a facile way to tune the measuring range of the nanometric displacement sensor and may open up an avenue to super-resolution microscopy and optical nanometrology.

Single-particle diffusional fingerprinting: A machine-learning framework for quantitative analysis of heterogeneous diffusion

Single-particle tracking (SPT) analysis of individual biomolecules is an indispensable tool for extracting quantitative information from dynamic biological processes, but often requires some a priori knowledge of the system. Here we present “single-particle diffusional fingerprinting,” a more general approach for extraction of diffusional patterns in SPT independently of the biological system. This method extracts a set of descriptive features for each SPT trajectory, which are ranked upon classification to yield mechanistic insights for the species under comparison. We demonstrate its capacity to yield a dictionary of diffusional traits across multiple systems (e.g., lipases hydrolyzing fat, transcription factors diffusing in cells, and nanoparticles in mucus), supporting its use on multiple biological phenomena (e.g., drug delivery, receptor dynamics, and virology).

Single-particle tracking (SPT) is a key tool for quantitative analysis of dynamic biological processes and has provided unprecedented insights into a wide range of systems such as receptor localization, enzyme propulsion, bacteria motility, and drug nanocarrier delivery. The inherently complex diffusion in such biological systems can vary drastically both in time and across systems, consequently imposing considerable analytical challenges, and currently requires an a priori knowledge of the system. Here we introduce a method for SPT data analysis, processing, and classification, which we term “diffusional fingerprinting.” This method allows for dissecting the features that underlie diffusional behavior and establishing molecular identity, regardless of the underlying diffusion type. The method operates by isolating 17 descriptive features for each observed motion trajectory and generating a diffusional map of all features for each type of particle. Precise classification of the diffusing particle identity is then obtained by training a simple logistic regression model. A linear discriminant analysis generates a feature ranking that outputs the main differences among diffusional features, providing key mechanistic insights. Fingerprinting operates by both training on and predicting experimental data, without the need for pretraining on simulated data. We found this approach to work across a wide range of simulated and experimentally diverse systems, such as tracked lipases on fat substrates, transcription factors diffusing in cells, and nanoparticles diffusing in mucus. This flexibility ultimately supports diffusional fingerprinting’s utility as a universal paradigm for SPT diffusional analysis and prediction.

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

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

The length of single-particle tracking experiments are limited due to photobleaching. Here the authors achieve long-term single-particle tracking with continuous fluorophore exchange in DNA-PAINT and use this to observe DNA origami on lipid bilayers for tens of minutes.

Quantum Dots: A Promising Fluorescent Label for Probing Virus Trafficking

Recent research has highlighted the immense potential of the quantum dot (QD)-based single-virus tracking (SVT) technique in virology. In these experiments, the infection behaviors of single viruses or viral components, labeled with QDs, could be tracked on time scales of milliseconds to hours in host cells. The trajectories of individual viruses are reconstructed with nanometer accuracy, and the underlying dynamic information on virus infection can be extracted to uncover the infection mechanisms of viruses. Therefore, QD-based single-virus tracking (QSVT) is an exquisitely selective and powerful approach to investigating how viruses are internalized in host cells dynamically to release their genome for viral replication and assembly that ensure the completion of viral life cycles.QDs are better candidates than organic dyes and fluorescent proteins for virus labeling and subsequent SVT due to the following considerations: (i) the high brightness of QDs makes it possible to label a virus with sufficient brightness using very few QDs or even just one QD; (ii) the extraordinary photostability of QDs allows one to track the infection process long term and quantify low probability events; (iii) the color-tunable emission property of QDs ensures multicolor labeling of various components of a virus simultaneously; and (iv) the abundant surface ligands of QDs facilitate the conjugation of a virus with a variety of labeling strategies. Therefore, the photoproperties of QDs make it possible to perform multicolor long-term SVT experiments quantitatively. Nowadays, the QD-based SVT (QSVT) technique has made prodigious achievements in unraveling the entry, trafficking, and uncoating mechanisms of viruses. This fascinating technique can provide spatiotemporal dynamic information on the viral journey in unprecedented detail and has revolutionized our understanding of virus infection.In this Account, we first introduce the advantages and the limitations of conventional SVT in virological research and the unique features of QDs as labels in the SVT field. We subsequently focus on the principles and related methods of QSVT and the current state of QD chemistry and QD-based virus labeling that resolves many issues associated with the tracking of individual viruses in live cells. Then we emphasize some new findings by this technique in the study of infection mechanisms. Finally, we will provide our insights into future challenges on this topic. With this Account, we hope to further stimulate the development of QSVT with a combined effort from different disciplines and, more importantly, to accelerate the applications of QSVT in virological research.

Single-Particle Tracking Reveals Anti-Persistent Subdiffusion in Cell Extracts

Single-particle tracking (SPT) has become a powerful tool to quantify transport phenomena in complex media with unprecedented detail. Based on the reconstruction of individual trajectories, a wealth of informative measures become available for each particle, allowing for a detailed comparison with theoretical predictions. While SPT has been used frequently to explore diffusive transport in artificial fluids and inside living cells, intermediate systems, i.e., biochemically active cell extracts, have been studied only sparsely. Extracts derived from the eggs of the clawfrog Xenopus laevis, for example, are known for their ability to support and mimic vital processes of cells, emphasizing the need to explore also the transport phenomena of nano-sized particles in such extracts. Here, we have performed extensive SPT on beads with 20 nm radius in native and chemically treated Xenopus extracts. By analyzing a variety of distinct measures, we show that these beads feature an anti-persistent subdiffusion that is consistent with fractional Brownian motion. Chemical treatments did not grossly alter this finding, suggesting that the high degree of macromolecular crowding in Xenopus extracts equips the fluid with a viscoelastic modulus, hence enforcing particles to perform random walks with a significant anti-persistent memory kernel.

Anisotropic diffusion of membrane proteins at experimental timescales

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

Uncover Single Nanoparticle Dynamics on Live Cell Membrane with Data-Driven Historical Experience Analysis

Understanding the spatiotemporal dynamics of particles in a complex biological environment is crucial for the study of related biological processes. To analyze the complicated trajectories recorded from single-particle tracking (SPT), we have proposed a method named SEES based on historical experience vector analysis, which allows both the global patterns and local state continuities of a trajectory to emerge by themselves as color segments without predefined models. This method implements a data-driven strategy and thus uncovers the hidden information with less prior knowledge or subjective bias. Here, we demonstrate its efficiency by comparing its performance with the Hidden Markov model (HMM), one of the most widely used methods in time series processing. The results demonstrated that the SEES operator was more sensitive in identifying rare events and could utilize multivariable observations in the dynamic processes to uncover more details. We applied the method to analyze the dynamics of nanoparticles interacting with live cells expressing programmed death ligand 1 (PD-L1) on the membrane. The results showed that the SEES operator can successfully pinpoint the transmembrane rare events, visualize the on-membrane "Brownian searching" motion, and evaluate different dynamics among multiple trajectories. Furthermore, we found that the PD-L1 expression level on the cell membrane affected the rotation behavior of the nanoparticle as well as the cellular uptake efficiency. These findings enabled by SEES could potentially help the rational design of highly efficient nanocargoes.

Elucidating Protein Translocon Dynamics with Single-Molecule Precision

Translocons are protein assemblies that facilitate the targeting and transport of proteins into and across biological membranes. Our understanding of these systems has been advanced using genetics, biochemistry, and structural biology. Despite these classic advances, until recently we have still largely lacked a detailed understanding of how translocons recognize and facilitate protein translocation. With the advent and improvements of cryogenic electron microscopy (cryo-EM) single-particle analysis and single-molecule fluorescence microscopy, the details of how translocons function are finally emerging. Here, we introduce these methods and evaluate their importance in understanding translocon structure, function, and dynamics.

Dynamic Behavior of Charged Particles at the Nanopipette Orifice

Understanding the dynamic behavior of charged particles driven by flow and electric field in nanochannels/pores is highly important for both fundamental study and practical applications. While a great breakthrough has been made in understanding the translocation dynamics of charged particles within the nanochannels/pores, studies on the dynamics of particles at the orifice of nanochannels/pores are scarcely reported. Here, we study particle motion at a smaller-sized orifice of a nanopipette by combining experimentally observed current transients with simulated force conditions. The theoretical force analysis reveals that dielectrophoretic force plays an equally important role as electrophoretic force and electroosmotic force, although it has often been neglected in understanding the particle translocation dynamics within the nanopipette. Under the combined action of these forces, it thus becomes difficult for particles to physically collide with the orifice of the nanopipette, resulting in a relatively low decrease in the current transients, which coincides with experimental results. We then regulate the dynamic behavior by altering experimental conditions (i.e., bias potential, nanopipette surface charge, and particle size), and the results further validate the presence and influence of forces being considered. This study improves the understanding of the relationship between particle properties and observed current transients, providing more possibilities for accurate single-particle analysis and single-entity regulation.

Expectation maximization based framework for joint localization and parameter estimation in single particle tracking from segmented images

Single Particle Tracking (SPT) is a well known class of tools for studying the dynamics of biological macromolecules moving inside living cells. In this paper, we focus on the problem of localization and parameter estimation given a sequence of segmented images. In the standard paradigm, the location of the emitter inside each frame of a sequence of camera images is estimated using, for example, Gaussian fitting (GF), and these locations are linked to provide an estimate of the trajectory. Trajectories are then analyzed by using Mean Square Displacement (MSD) or Maximum Likelihood Estimation (MLE) techniques to determine motion parameters such as diffusion coefficients. However, the problems of localization and parameter estimation are clearly coupled. Motivated by this, we have created an Expectation Maximization (EM) based framework for simultaneous localization and parameter estimation. We demonstrate this framework through two representative methods, namely, Sequential Monte Carlo combined with Expectation Maximization (SMC-EM) and Unscented Kalman Filter combined with Expectation Maximization (U-EM). Using diffusion in two-dimensions as a prototypical example, we conduct quantitative investigations on localization and parameter estimation performance across a wide range of signal to background ratios and diffusion coefficients and compare our methods to the standard techniques based on GF-MSD/MLE. To demonstrate the flexibility of the EM based framework, we do comparisons using two different camera models, an ideal camera with Poisson distributed shot noise but no readout noise, and a camera with both shot noise and the pixel-dependent readout noise that is common to scientific complementary metal-oxide semiconductor (sCMOS) camera. Our results indicate our EM based methods outperform the standard techniques, especially at low signal levels. While U-EM and SMC-EM have similar accuracy, U-EM is significantly more computationally efficient, though the use of the Unscented Kalman Filter limits U-EM to lower diffusion rates.

The Measurement of Information and Free Energy in Mechanical-Force-Driven Coil-Globule Transitions

We study the role of information (the relative entropy) for polymers undergoing coil-globule transitions driven by a time-dependent force. Pulling experiments at various speeds are performed by Brownian dynamics simulations. We obtain the work distributions for the forward and time-reversed backward processes and information stored at the end of the nonequilibrium pulling processes. We present the systematic method to measure the information from the pulling experiments and extract the information by analyzing slowly relaxing modes. When the information is incorporated, the work distributions modified by the information allow access to the proper free energy via the formulation of the generalized fluctuation theorems even if the initial states of the forward and time-reversed backward processes are out of equilibrium. This demonstrates that the work-information conversion works well for a single-molecule system with many degrees of freedom.

Not Just a Bystander: The Emerging Role of Astrocytes and Research Tools in Studying Cognitive Dysfunctions in Schizophrenia

Cognitive dysfunction is one of the core symptoms in schizophrenia, and it is predictive of functional outcomes and therefore useful for treatment targets. Rather than improving cognitive deficits, currently available antipsychotics mainly focus on positive symptoms, targeting dopaminergic/serotoninergic neurons and receptors in the brain. Apart from investigating the neural mechanisms underlying schizophrenia, emerging evidence indicates the importance of glial cells in brain structure development and their involvement in cognitive functions. Although the etiopathology of astrocytes in schizophrenia remains unclear, accumulated evidence reveals that alterations in gene expression and astrocyte products have been reported in schizophrenic patients. To further investigate the role of astrocytes in schizophrenia, we highlighted recent progress in the investigation of the effect of astrocytes on abnormalities in glutamate transmission and impairments in the blood–brain barrier. Recent advances in animal models and behavioral methods were introduced to examine schizophrenia-related cognitive deficits and negative symptoms. We also highlighted several experimental tools that further elucidate the role of astrocytes. Instead of focusing on schizophrenia as a neuron-specific disorder, an additional astrocytic perspective provides novel and promising insight into its causal mechanisms and treatment. The involvement of astrocytes in the pathogenesis of schizophrenia and other brain disorders is worth further investigation.

Elucidating Carbohydrate-Protein Interactions Using Nanoparticle-Based Approaches

Carbohydrates are present on every living cell and coordinate important processes such as self/non-self discrimination. They are amongst the first molecular determinants to be encountered when cellular interactions are initiated. In particular, they resemble essential molecular fingerprints such as pathogen-, danger-, and self-associated molecular patterns guiding key decision-making in cellular immunology. Therefore, a deeper understanding of how cellular receptors of the immune system recognize incoming particles, based on their carbohydrate signature and how this information is translated into a biological response, will enable us to surgically manipulate them and holds promise for novel therapies. One approach to elucidate these early recognition events of carbohydrate interactions at cellular surfaces is the use of nanoparticles coated with defined carbohydrate structures. These particles are captured by carbohydrate receptors and initiate a cellular cytokine response. In the case of endocytic receptors, the capturing enables the engulfment of exogenous particles. Thereafter, the particles are sorted and degraded during their passage in the endolysosomal pathway. Overall, these processes are dependent on the nature of the endocytic carbohydrate receptors and consequently reflect upon the carbohydrate patterns on the exogenous particle surface. This interplay is still an under-studied subject. In this review, we summarize the application of nanoparticles as a promising tool to monitor complex carbohydrate-protein interactions in a cellular context and their application in areas of biomedicine.

Single molecule tracking and analysis framework including theory-predicted parameter settings

Imaging, tracking and analyzing individual biomolecules in living systems is a powerful technology to obtain quantitative kinetic and spatial information such as reaction rates, diffusion coefficients and localization maps. Common tracking tools often operate on single movies and require additional manual steps to analyze whole data sets or to compare different experimental conditions. We report a fast and comprehensive single molecule tracking and analysis framework (TrackIt) to simultaneously process several multi-movie data sets. A user-friendly GUI offers convenient tracking visualization, multiple state-of-the-art analysis procedures, display of results, and data im- and export at different levels to utilize external software tools. We applied our framework to quantify dissociation rates of a transcription factor in the nucleus and found that tracking errors, similar to fluorophore photobleaching, have to be considered for reliable analysis. Accordingly, we developed an algorithm, which accounts for both tracking losses and suggests optimized tracking parameters when evaluating reaction rates. Our versatile and extensible framework facilitates quantitative analysis of single molecule experiments at different experimental conditions.

Tracking Multiple Diffusing Particles Using Information Optimal Control

We study the problem of tracking multiple diffusing particles using a laser scanning fluorescence microscope. The goal is to design trajectories for the laser to maximize the information contained in the measured intensity signal about the particles' trajectories. Our approach consists of a two level scheme: in the lower level we use an extremum seeking controller to track a single particle by first seeking it then orbiting around it. In the higher level controller, we decide which particle should be observed at each instant, with the goal of efficiently estimating each particle position while not losing track of any of them. Using simulations, we show that this technique is able to collect photons efficiently and to track multiple particles with low position estimation error.

Association of Nanodiamond Rotation Dynamics with Cell Activities by Translation-Rotation Tracking

Correlated translation-orientation tracking of single particles can provide important information for understanding the dynamics of live systems and their interaction with the probes. However, full six-dimensional (6D) motion tracking has yet to be achieved. Here, we developed synchronized 3D translation and 3D rotation tracking of single diamond particles based on nitrogen-vacancy center sensing. We first performed 6D tracking of diamond particles attached to a giant plasma membrane vesicle to demonstrate the method. Quantitative analysis of diamond particles' motion allowed elimination of the geometric effect and revealed the net rotation on the vesicle. 6D tracking was then applied to measure live cell dynamics. Motion characteristics of nanodiamonds on cell membranes under various controlled physiological conditions suggest that the nanodiamonds' rotation is associated with cell metabolic activities. Our technique extends the toolbox of single particle tracking and provides a unique solution to problems where correlated analysis of translation and rotation is critical.

The role of molecular diffusion within dendritic spines in synaptic function

Spines are tiny nanoscale protrusions from dendrites of neurons. In the cortex and hippocampus, most of the excitatory postsynaptic sites reside in spines. The bulbous spine head is connected to the dendritic shaft by a thin membranous neck. Because the neck is narrow, spine heads are thought to function as biochemically independent signaling compartments. Thus, dynamic changes in the composition, distribution, mobility, conformations, and signaling properties of molecules contained within spines can account for much of the molecular basis of postsynaptic function and regulation. A major factor in controlling these changes is the diffusional properties of proteins within this small compartment. Advances in measurement techniques using fluorescence microscopy now make it possible to measure molecular diffusion within single dendritic spines directly. Here, we review the regulatory mechanisms of diffusion in spines by local intra-spine architecture and discuss their implications for neuronal signaling and synaptic plasticity.

Quantitative spectroscopy of single molecule interaction times

Single molecule fluorescence tracking provides information at nanometer-scale and millisecond-temporal resolution about the dynamics and interaction of individual molecules in a biological environment. While the dynamic behavior of isolated molecules can be characterized well, the quantitative insight is more limited when interactions between two indistinguishable molecules occur. We address this aspect by developing a theoretical foundation for a spectroscopy of interaction times, i.e., the inference of interaction from imaging data. A non-trivial crossover between a power law to an exponential behavior of the distribution of the interaction times is highlighted, together with the dependence of the exponential term upon the microscopic reaction affinity. Our approach is validated with simulated and experimental datasets.

A localized adaptor protein performs distinct functions at the Caulobacter cell poles

Asymmetric cell division yields two distinct daughter cells by mechanisms that underlie stem cell behavior and cellular diversity in all organisms. The bacterium Caulobacter crescentus is able to orchestrate this complex process with less than 4,000 genes. This article describes a strategy deployed by Caulobacter where a regulatory protein, PopA, is programed to perform distinct roles based on its subcellular address. We demonstrate that, depending on the availability of a second messenger molecule, PopA adopts either a monomer or dimer form. The two oligomeric forms interact with different partners at the two cell poles, playing a critical role in the degradation of a master transcription factor at one pole and flagellar assembly at the other pole.

Asymmetric cell division generates two daughter cells with distinct characteristics and fates. Positioning different regulatory and signaling proteins at the opposing ends of the predivisional cell produces molecularly distinct daughter cells. Here, we report a strategy deployed by the asymmetrically dividing bacterium Caulobacter crescentus where a regulatory protein is programmed to perform distinct functions at the opposing cell poles. We find that the CtrA proteolysis adaptor protein PopA assumes distinct oligomeric states at the two cell poles through asymmetrically distributed c-di-GMP: dimeric at the stalked pole and monomeric at the swarmer pole. Different polar organizing proteins at each cell pole recruit PopA where it interacts with and mediates the function of two molecular machines: the ClpXP degradation machinery at the stalked pole and the flagellar basal body at the swarmer pole. We discovered a binding partner of PopA at the swarmer cell pole that together with PopA regulates the length of the flagella filament. Our work demonstrates how a second messenger provides spatiotemporal cues to change the physical behavior of an effector protein, thereby facilitating asymmetry.

Principles and Applications of Single Particle Tracking in Cell Research

It is a tough challenge for many decades to decipher the complex relationships between cell behaviors and cellular physical properties. Single particle tracking (SPT) with high spatial and temporal resolution has been applied extensively in cell research to understand physicochemical properties of cells and their bio-functions by tracking endogenous or exogenous probes. This review describes the fundamental principles of SPT as well as its applications in intracellular mechanics, membrane dynamics, organelles distribution, and processes of internalization and transport. Finally, challenges and future directions of SPT are also discussed.

An Estimation Algorithm for General Linear Single Particle Tracking Models with Time-Varying Parameters

Single Particle Tracking (SPT) is a powerful class of methods for studying the dynamics of biomolecules inside living cells. The techniques reveal the trajectories of individual particles, with a resolution well below the diffraction limit of light, and from them the parameters defining the motion model, such as diffusion coefficients and confinement lengths. Most existing algorithms assume these parameters are constant throughout an experiment. However, it has been demonstrated that they often vary with time as the tracked particles move through different regions in the cell or as conditions inside the cell change in response to stimuli. In this work, we propose an estimation algorithm to determine time-varying parameters of systems that discretely switch between different linear models of motion with Gaussian noise statistics, covering dynamics such as diffusion, directed motion, and Ornstein-Uhlenbeck dynamics. Our algorithm consists of three stages. In the first stage, we use a sliding window approach, combined with Expectation Maximization (EM) to determine maximum likelihood estimates of the parameters as a function of time. These results are only used to roughly estimate the number of model switches that occur in the data to guide the selection of algorithm parameters in the second stage. In the second stage, we use Change Detection (CD) techniques to identify where the models switch, taking advantage of the off-line nature of the analysis of SPT data to create non-causal algorithms with better precision than a purely causal approach. Finally, we apply EM to each set of data between the change points to determine final parameter estimates. We demonstrate our approach using experimental data generated in the lab under controlled conditions.