Optimal tracking of a Brownian particle

Super-resolving particle diffusion heterogeneity in porous hydrogels via high-speed 3D active-feedback single-particle tracking microscopy

Nanoparticle diffusion in 3D porous structures is critical to understanding natural and synthetic systems but remains underexplored due to limitations in traditional microscopy methods. Here, we use 3D Single-Molecule Active-feedback Real-time Tracking (3D-SMART) microscopy to resolve nanoparticle dynamics in agarose gels with unprecedented spatiotemporal resolution. We highlight 'hopping diffusion', where particles intermittently escape confinement pockets, providing insights into hydrogel microstructure. Long, highly sampled trajectories enable extraction of kinetic parameters, confinement sizes, and thermodynamic barriers. This study demonstrates 3D-SMART's ability to probe particle-environment interactions at super-resolution (~10 nm in XY and ~30 nm in Z) in 3D, offering new perspectives on nanoparticle diffusion and the structural dynamics of porous materials, with implications for drug delivery, material science, and biological systems.

Hour-Long, Kilohertz Sampling Rate Three-Dimensional Single-Virus Tracking in Live Cells Enabled by StayGold Fluorescent Protein Fusions

A viral infection process covers a large range of spatiotemporal scales. Tracking the viral infection process with fluorescent labels over long durations while maintaining a fast sampling rate requires bright and highly photostable labels. StayGold is a recently identified green fluorescent protein that has a greater photostability and higher signal intensity under identical illumination conditions compared to existing fluorescence protein variants. Here, StayGold protein fusions were used to generate virus-like particles (StayGold-VLPs) to achieve hour-long 3D single-virus tracking (SVT) with 1000 localizations per second (kHz sampling rate) in live cells. The expanded photon budget from StayGold protein fusions prolonged the tracking duration, facilitating a comprehensive study of viral trafficking dynamics with high temporal resolution over long time scales. The development of StayGold-VLPs presents a simple and general VLP labeling strategy for better performance in SVT, enabling exponentially more information to be collected from single trajectories and allowing for the future possibility of observing the entire life cycle of a single virus.

Hour-long, Kilohertz Sampling Rate 3D Single-virus Tracking in Live Cells Enabled by StayGold Fluorescent Protein Fusions

The viral infection process covers a large range of spatiotemporal scales. Tracking the viral infection process with fluorescent labels over long durations while maintaining a fast sampling rate requires bright and highly photostable labels. StayGold is a recently identified green fluorescent protein that has a greater photostability and higher signal intensity under identical illumination conditions as compared to existing fluorescence protein variants. Here, StayGold protein fusions were used to generate virus-like particles (StayGold-VLPs) to achieve hour-long 3D single-virus tracking (SVT) with one thousand localizations per second (kHz sampling rate) in live cells. The expanded photon budget from StayGold protein fusions prolonged the tracking duration, facilitating a comprehensive study of viral trafficking dynamics with high temporal resolution over long timescales. The development of StayGold-VLPs presents a simple and general VLP labeling strategy for better performance in SVT, enabling exponentially more information to be collected from single trajectories and allowing for the future possibility of observing the whole life cycle of a single virus.

Active-Feedback 3D Single-Molecule Tracking Using a Fast-Responding Galvo Scanning Mirror

Real-time three-dimensional single-particle tracking (RT-3D-SPT) allows continuous detection of individual freely diffusing objects with high spatiotemporal precision by applying closed-loop active feedback in an optical microscope. However, the current tracking speed in RT-3D-SPT is primarily limited by the response time of the control actuators, impeding long-term observation of fast diffusive objects such as single molecules. Here, we present an RT-3D-SPT system with improved tracking performance by replacing the XY piezoelectric stage with a galvo scanning mirror with an approximately 5 times faster response rate (∼5 kHz). Based on the previously developed 3D single-molecule active real-time tracking (3D-SMART), this new implementation with a fast-responding galvo mirror eliminates the mechanical movement of the sample and allows a more rapid response to particle motion. The improved tracking performance of the galvo mirror-based implementation is verified through simulation and proof-of-principle experiments. Fluorescent nanoparticles and ∼1 kB double-stranded DNA molecules were tracked via both the original piezoelectric stage and new galvo mirror implementations. With the new galvo-based implementation, notable increases in tracking duration, localization precision, and the degree to which the objects are locked to the center of the detection volume were observed. These results suggest that faster control response elements can expand RT-3D-SPT to a broader range of chemical and biological systems.

Multi-neuronal recording in unrestrained animals with all acousto-optic random-access line-scanning two-photon microscopy

To understand how neural activity encodes and coordinates behavior, it is desirable to record multi-neuronal activity in freely behaving animals. Imaging in unrestrained animals is challenging, especially for those, like larval Drosophila melanogaster, whose brains are deformed by body motion. A previously demonstrated two-photon tracking microscope recorded from individual neurons in freely crawling Drosophila larvae but faced limits in multi-neuronal recording. Here we demonstrate a new tracking microscope using acousto-optic deflectors (AODs) and an acoustic GRIN lens (TAG lens) to achieve axially resonant 2D random access scanning, sampling along arbitrarily located axial lines at a line rate of 70 kHz. With a tracking latency of 0.1 ms, this microscope recorded activities of various neurons in moving larval Drosophila CNS and VNC including premotor neurons, bilateral visual interneurons, and descending command neurons. This technique can be applied to the existing two-photon microscope to allow for fast 3D tracking and scanning.

Extending resolution within a single imaging frame

The resolution of fluorescence microscopy images is limited by the physical properties of light. In the last decade, numerous super-resolution microscopy (SRM) approaches have been proposed to deal with such hindrance. Here we present Mean-Shift Super Resolution (MSSR), a new SRM algorithm based on the Mean Shift theory, which extends spatial resolution of single fluorescence images beyond the diffraction limit of light. MSSR works on low and high fluorophore densities, is not limited by the architecture of the optical setup and is applicable to single images as well as temporal series. The theoretical limit of spatial resolution, based on optimized real-world imaging conditions and analysis of temporal image stacks, has been measured to be 40 nm. Furthermore, MSSR has denoising capabilities that outperform other SRM approaches. Along with its wide accessibility, MSSR is a powerful, flexible, and generic tool for multidimensional and live cell imaging applications.

Capturing the start point of the virus-cell interaction with high-speed 3D single-virus tracking

The early stages of the virus-cell interaction have long evaded observation by existing microscopy methods due to the rapid diffusion of virions in the extracellular space and the large three-dimensional cellular structures involved. Here we present an active-feedback single-particle tracking method with simultaneous volumetric imaging of the live cell environment called 3D-TrIm to address this knowledge gap. 3D-TrIm captures the extracellular phase of the infectious cycle in what we believe is unprecedented detail. We report what are, to our knowledge, previously unobserved phenomena in the early stages of the virus-cell interaction, including skimming contact events at the millisecond timescale, orders of magnitude change in diffusion coefficient upon binding and cylindrical and linear diffusion modes along cellular protrusions. Finally, we demonstrate how this method can move single-particle tracking from simple monolayer culture toward more tissue-like conditions by tracking single virions in tightly packed epithelial cells. This multiresolution method presents opportunities for capturing fast, three-dimensional processes in biological systems.

Combined online Bayesian and windowed estimation of background and signal localization facilitates active-feedback particle tracking in complex environments

Despite successes in tracking single molecules in vitro, the extension of active-feedback single-particle methods to tracking rapidly diffusing and unconfined proteins in live cells has not been realized. Since the existing active-feedback localization methods localize particles in real time assuming zero background, they are ill-suited to track in the inhomogeneous background environment of a live cell. Here, we develop a windowed estimation of signal and background levels using recent data to estimate the current particle brightness and background intensity. These estimates facilitate recursive Bayesian position estimation, improving upon current Kalman-based localization methods. Combined, online Bayesian and windowed estimation of background and signal (COBWEBS) surpasses existing 2D localization methods. Simulations demonstrate improved localization accuracy and responsivity in a homogeneous background for selected particle and background intensity combinations. Improved or similar performance of COBWEBS tracking extends to the majority of signal and background combinations explored. Furthermore, improved tracking durations are demonstrated in the presence of heterogeneous backgrounds for multiple particle intensities, diffusive speeds, and background patterns. COBWEBS can accurately track particles in the presence of high and nonuniform backgrounds, including intensity changes of up to three times the particle's intensity, making it a prime candidate for advancing active-feedback single fluorophore tracking to the cellular interior.

Theoretical comparison of real-time feedback-driven single-particle tracking techniques

Real-time feedback-driven single-particle tracking is a technique that uses feedbackcontrol to enable single-molecule spectroscopy of freely diffusing particles in nativeor near-native environments. A number of different RT-FD-SPT approaches exist,and comparisons between methods based on experimental results are of limited usedue to differences in samples and setups. In this study, we used statistical calcu-lations and dynamical simulations to directly compare the performance of differentmethods. The methods considered were the orbital method, the Knight's Tour (gridscan) method and MINFLUX, and we considered both fluorescence-based and inter-ferometric scattering (iSCAT) approaches. There is a fundamental trade-off betweenprecision and speed, with the Knight's Tour method being able to track the fastestdiffusion but with low precision, and MINFLUX being the most precise but onlytracking slow diffusion. To compare iSCAT and fluorescence, different biologicalsamples were considered, including labeled and intrinsically fluorescent samples. Thesuccess of iSCAT as compared to fluorescence is strongly dependent on the particlesize and the density and photophysical properties of the fluorescent particles. Usinga wavelength for iSCAT that is negligibly absorbed by the tracked particle allowsan increased illumination intensity, which results in iSCAT providing better trackingfor most samples. This work highlights the fundamental aspects of performance inRT-FD-SPT and should assist with the selection of an appropriate method for a par-ticular application. The approach used can easily be extended to other RT-FD-SPTmethods.

Real-Time Feedback-Driven Single-Particle Tracking: A Survey and Perspective

Real-time feedback-driven single-particle tracking (RT-FD-SPT) is a class of techniques in the field of single-particle tracking that uses feedback control to keep a particle of interest in a detection volume. These methods provide high spatiotemporal resolution on particle dynamics and allow for concurrent spectroscopic measurements. This review article begins with a survey of existing techniques and of applications where RT-FD-SPT has played an important role. Each of the core components of RT-FD-SPT are systematically discussed in order to develop an understanding of the trade-offs that must be made in algorithm design and to create a clear picture of the important differences, advantages, and drawbacks of existing approaches. These components are feedback tracking and control, ranging from simple proportional-integral-derivative control to advanced nonlinear techniques, estimation to determine particle location from the measured data, including both online and offline algorithms, and techniques for calibrating and characterizing different RT-FD-SPT methods. Then a collection of metrics for RT-FD-SPT is introduced to help guide experimentalists in selecting a method for their particular application and to help reveal where there are gaps in the techniques that represent opportunities for further development. Finally, this review is concluded with a discussion on future perspectives in the field.

DC corral trapping of single nanoparticles and macromolecules in solution

Progress in sorting, separating, and characterizing ever smaller amounts of chemical and biological material depends on the availability of methods for the controlled interaction with nanoscale and molecular-size objects. Here, we report on the reversible, tunable trapping of single DNA molecules and other charged micro- and nanoparticles in aqueous solution using a direct-current (DC) corral trap setup. The trap consists of a circular, non-conductive void in a metal-coated surface that, when charged, generates an electrostatic potential well in the proximate solution. Our results demonstrate that stable, nanoscale confinement of charged objects is achievable over extended periods of time, that trap stiffness is controlled by the applied voltage, and that simultaneous trapping of multiple objects is feasible. The approach shows great promise for lab-on-a-chip systems and biomedical applications due to its simplicity, scalability, selectivity, and the capability to manipulate single DNA molecules in standard buffer solutions.

Diamond quantum thermometry: from foundations to applications

Diamond quantum thermometry exploits the optical and electrical spin properties of colour defect centres in diamonds and, acts as a quantum sensing method exhibiting ultrahigh precision and robustness. Compared to the existing luminescent nanothermometry techniques, a diamond quantum thermometer can be operated over a wide temperature range and a sensor spatial scale ranging from nanometres to micrometres. Further, diamond quantum thermometry is employed in several applications, including electronics and biology, to explore these fields with nanoscale temperature measurements. This review covers the operational principles of diamond quantum thermometry for spin-based and all-optical methods, material development of diamonds with a focus on thermometry, and examples of applications in electrical and biological systems with demand-based technological requirements.

Single-molecule FRET dynamics of molecular motors in an ABEL trap

Single-molecule Förster resonance energy transfer (smFRET) of molecular motors provides transformative insights into their dynamics and conformational changes both at high temporal and spatial resolution simultaneously. However, a key challenge of such FRET investigations is to observe a molecule in action for long enough without restricting its natural function. The Anti-Brownian ELectrokinetic Trap (ABEL trap) sets out to combine smFRET with molecular confinement to enable observation times of up to several seconds while removing any requirement of tethered surface attachment of the molecule in question. In addition, the ABEL trap's inherent ability to selectively capture FRET active molecules accelerates the data acquisition process. In this work we exemplify the capabilities of the ABEL trap in performing extended timescale smFRET measurements on the molecular motor Rep, which is crucial for removing protein blocks ahead of the advancing DNA replication machinery and for restarting stalled DNA replication. We are able to monitor single Rep molecules up to 6 seconds with sub-millisecond time resolution capturing multiple conformational switching events during the observation time. Here we provide a step-by-step guide for the rational design, construction and implementation of the ABEL trap for smFRET detection of Rep in vitro. We include details of how to model the electric potential at the trap site and use Hidden Markov analysis of the smFRET trajectories.

Depolarization Characteristics of Different Reflective Interfaces Indicated by Indices of Polarimetric Purity (IPPs)

Compared with the standard depolarization index, indices of polarimetric purity (IPPs) have better performances to describe depolarization characteristics of targets with different roughnesses of interfaces under different incident angles, which allow us a further analysis of the depolarizing properties of samples. Here, we use IPPs obtained from different reflective interfaces as a criterion of depolarization property to characterize and classify targets covered by organic paint layers with different roughness. We select point-light source as radiation source with wavelength as 632.8 nm, and four samples, including Cu, Au, Al and Al₂O₃, covered by an organic paint layer with refractive index of n = 1.46 and Gaussian roughness of α = 0.05~0.25. Under different incident angles, the values of P₁, P₂, P₃ at divided 90 × 360 grid points and their mean values in upper hemisphere have been obtained and discussed in the IPPs space. The results show that the depolarization performances of the different reflective interfaces (materials, incident angles and surface roughness) are unique in IPPs space, providing us with a new avenue to analyze and characterize different targets.

Real-time 3D single molecule tracking

To date, single molecule studies have been reliant on tethering or confinement to achieve long duration and high temporal resolution measurements. Here, we present a 3D single-molecule active real-time tracking method (3D-SMART) which is capable of locking on to single fluorophores in solution for minutes at a time with photon limited temporal resolution. As a demonstration, 3D-SMART is applied to actively track single Atto 647 N fluorophores in 90% glycerol solution with an average duration of ~16 s at count rates of ~10 kHz. Active feedback tracking is further applied to single proteins and nucleic acids, directly measuring the diffusion of various lengths (99 to 1385 bp) of single DNA molecules at rates up to 10 µm²/s. In addition, 3D-SMART is able to quantify the occupancy of single Spinach2 RNA aptamers and capture active transcription on single freely diffusing DNA. 3D-SMART represents a critical step towards the untethering of single molecule spectroscopy.

Single molecule observation has been limited to tethered molecules to ensure that the target remains in the field of view (FOV). Here, the authors develop a real-time tracking method that locks onto rapidly diffusing targets and tracks them in a 3D volume, enabling single molecules to remain in the FOV for minutes at a time.

Probing and manipulating embryogenesis via nanoscale thermometry and temperature control

Understanding the coordination of cell-division timing is one of the outstanding questions in the field of developmental biology. One active control parameter of the cell-cycle duration is temperature, as it can accelerate or decelerate the rate of biochemical reactions. However, controlled experiments at the cellular scale are challenging, due to the limited availability of biocompatible temperature sensors, as well as the lack of practical methods to systematically control local temperatures and cellular dynamics. Here, we demonstrate a method to probe and control the cell-division timing in Caenorhabditis elegans embryos using a combination of local laser heating and nanoscale thermometry. Local infrared laser illumination produces a temperature gradient across the embryo, which is precisely measured by in vivo nanoscale thermometry using quantum defects in nanodiamonds. These techniques enable selective, controlled acceleration of the cell divisions, even enabling an inversion of division order at the two-cell stage. Our data suggest that the cell-cycle timing asynchrony of the early embryonic development in C. elegans is determined independently by individual cells rather than via cell-to-cell communication. Our method can be used to control the development of multicellular organisms and to provide insights into the regulation of cell-division timings as a consequence of local perturbations.

An Adaptive Real-Time 3D Single Particle Tracking Method for Monitoring Viral First Contacts

Here, an adaptive real-time 3D single particle tracking method is proposed, which is capable of capturing heterogeneous dynamics. Using a real-time measurement of a rapidly diffusing particle's positional variance, the 3D precision adaptive real-time tracking (3D-PART) microscope adjusts active-feedback parameters to trade tracking speed for precision on demand. This technique is demonstrated first on immobilized fluorescent nanoparticles, with a greater than twofold increase in the lateral localization precision (≈25 to ≈11 nm at 1 ms sampling) as well as a smaller increase in the axial localization precision (≈ 68 to ≈45 nm). 3D-PART also shows a marked increase in the precision when tracking freely diffusing particles, with lateral precision increasing from ≈100 to ≈70 nm for particles diffusing at 4 µm2 s-1 , although with a sacrifice in the axial precision (≈250 to ≈350 nm). This adaptive microscope is then applied to monitoring the viral first contacts of virus-like particles to the surface of live cells, allowing direct and continuous measurement of the viral particle at initial contact with the cell surface.

Real-Time 3D Single Particle Tracking: Towards Active Feedback Single Molecule Spectroscopy in Live Cells

Single molecule fluorescence spectroscopy has been largely implemented using methods which require tethering of molecules to a substrate in order to make high temporal resolution measurements. However, the act of tethering a molecule requires that the molecule be removed from its environment. This is especially perturbative when measuring biomolecules such as enzymes, which may rely on the non-equilibrium and crowded cellular environment for normal function. A method which may be able to un-tether single molecule fluorescence spectroscopy is real-time 3D single particle tracking (RT-3D-SPT). RT-3D-SPT uses active feedback to effectively lock-on to freely diffusing particles so they can be measured continuously with up to photon-limited temporal resolution over large axial ranges. This review gives an overview of the various active feedback 3D single particle tracking methods, highlighting specialized detection and excitation schemes which enable high-speed real-time tracking. Furthermore, the combination of these active feedback methods with simultaneous live-cell imaging is discussed. Finally, the successes in real-time 3D single molecule tracking (RT-3D-SMT) thus far and the roadmap going forward for this promising family of techniques are discussed.

A Protocol for Real-time 3D Single Particle Tracking

Real-time three-dimensional single particle tracking (RT-3D-SPT) has the potential to shed light on fast, 3D processes in cellular systems. Although various RT-3D-SPT methods have been put forward in recent years, tracking high speed 3D diffusing particles at low photon count rates remains a challenge. Moreover, RT-3D-SPT setups are generally complex and difficult to implement, limiting their widespread application to biological problems. This protocol presents a RT-3D-SPT system named 3D Dynamic Photon Localization Tracking (3D-DyPLoT), which can track particles with high diffusive speed (up to 20 µm²/s) at low photon count rates (down to 10 kHz). 3D-DyPLoT employs a 2D electro-optic deflector (2D-EOD) and a tunable acoustic gradient (TAG) lens to drive a single focused laser spot dynamically in 3D. Combined with an optimized position estimation algorithm, 3D-DyPLoT can lock onto single particles with high tracking speed and high localization precision. Owing to the single excitation and single detection path layout, 3D-DyPLoT is robust and easy to set up. This protocol discusses how to build 3D-DyPLoT step by step. First, the optical layout is described. Next, the system is calibrated and optimized by raster scanning a 190 nm fluorescent bead with the piezoelectric nanopositioner. Finally, to demonstrate real-time 3D tracking ability, 110 nm fluorescent beads are tracked in water.

Robust real-time 3D single-particle tracking using a dynamically moving laser spot

Real-time three-dimensional (3D) single-particle tracking uses optical feedback to lock on to freely diffusing nanoscale fluorescent particles, permitting precise 3D localization and continuous spectroscopic interrogation. Here we describe a new method of real-time 3D single-particle tracking wherein a diffraction-limited laser spot is dynamically swept through the detection volume in three dimensions using a two-dimensional (2D) electro-optic deflector and a tunable acoustic gradient lens. This optimized method, called 3D dynamic photon localization tracking (3D-DyPLoT), enables high-speed real-time tracking of single silica-coated non-blinking quantum dots (∼30  nm diameter) with diffusive speeds exceeding 10  μm²/s at count rates as low as 10 kHz, as well as YFP-labeled virus-like particles. The large effective detection area (1  μm×1  μm×4  μm) allows the system to easily pick up fast-moving particles, while still demonstrating high localization precision (σ_x=6.6  nm, σ_y=8.7  nm, and σ_z=15.6  nm). Overall, 3D-DyPLoT provides a fast and robust method for real-time 3D tracking of fast and lowly emitting particles, based on a single excitation and detection pathway, paving the way to more widespread application to relevant biological problems.

Single-molecule spectroscopy and imaging over the decades

As of 2015, it has been 26 years since the first optical detection and spectroscopy of single molecules in condensed matter. This area of science has expanded far beyond the early low temperature studies in crystals to include single molecules in cells, polymers, and in solution. The early steps relied upon high-resolution spectroscopy of inhomogeneously broadened optical absorption profiles of molecular impurities in solids at low temperatures. Spectral fine structure arising directly from the position-dependent fluctuations of the number of molecules in resonance led to the attainment of the single-molecule limit in 1989 using frequency-modulation laser spectroscopy. In the early 1990s, a variety of fascinating physical effects were observed for individual molecules, including imaging of the light from single molecules as well as observations of spectral diffusion, optical switching and the ability to select different single molecules in the same focal volume simply by tuning the pumping laser frequency. In the room temperature regime, researchers showed that bursts of light from single molecules could be detected in solution, leading to imaging and microscopy by a variety of methods. Studies of single copies of the green fluorescent protein also uncovered surprises, especially the blinking and photoinduced recovery of emitters, which stimulated further development of photoswitchable fluorescent protein labels. All of these early steps provided important fundamentals underpinning the development of super-resolution microscopy based on single-molecule localization and active control of emitting concentration. Current thrust areas include extensions to three-dimensional imaging with high precision, orientational analysis of single molecules, and direct measurements of photodynamics and transport properties for single molecules trapped in solution by suppression of Brownian motion. Without question, a huge variety of studies of single molecules performed by many talented scientists all over the world have extended our knowledge of the nanoscale and many microscopic mechanisms previously hidden by ensemble averaging.

Real-time calibration of a feedback trap

Feedback traps use closed-loop control to trap or manipulate small particles and molecules in solution. They have been applied to the measurement of physical and chemical properties of particles and to explore fundamental questions in the non-equilibrium statistical mechanics of small systems. These applications have been hampered by drifts in the electric forces used to manipulate the particles. Although the drifts are small for measurements on the order of seconds, they dominate on time scales of minutes or slower. Here, we show that a recursive maximum likelihood (RML) algorithm can allow real-time measurement and control of electric and stochastic forces over time scales of hours. Simulations show that the RML algorithm recovers known parameters accurately. Experimental estimates of diffusion coefficients are also consistent with expected physical properties.