Single-pixel interior filling function approach for detecting and correcting errors in particle tracking

Distinct Sub- to Superdiffuse Insulin Granule Transport Behaviors in β-Cells Are Strongly Affected by Granule Age

Intracellular transport is a complex process that is difficult to describe by a single general model for motion. Here, we study the transport of insulin containing vesicles, termed granules, in live MIN6 cells. We characterize how the observed heterogeneity is affected by different intracellular factors by constructing a MIN6 cell line by CRISPR-CAS9 that constitutively expresses mCherry fused to insulin and is thus packaged in granules. Confocal microscopy imaging and single particle tracking of the granule transport provide long trajectories of thousands of single granule trajectories for statistical analysis. Mean squared displacement (MSD), angle correlation distribution, and step size distribution analysis allowed identifying five distinct granule transport subpopulations, from nearly immobile and subdiffusive to run-pause and superdiffusive. The subdiffusive subpopulation recapitulates the subordinated random walk we reported earlier (Tabei, 2013; ref 18). We show that the transport characteristics of the five subpopulations have a strong dependence on the age of insulin granules. The five subpopulations also reflect the effect of local microtubule and actin networks on transport in different cellular regions. Our results provide robust metrics to clarify the heterogeneity of granule transport and demonstrate the roles of microtubule versus actin networks with granule age since initial packaging in the Golgi.

Determining intrinsic potentials and validating optical binding forces between colloidal particles using optical tweezers

Understanding the interactions between small, submicrometer-sized colloidal particles is crucial for numerous scientific disciplines and technological applications. In this study, we employ optical tweezers as a powerful tool to investigate these interactions. We utilize a full image reconstruction technique to achieve high precision in characterizing particle pairs that enable nanometer-scale measurement of their positions. This approach captures intricate details and provides a comprehensive understanding of the spatial arrangement between particles, overcoming previous limitations in resolution. Moreover, our research demonstrates that properly accounting for optical binding forces to determine the intrinsic interaction potential is vital. We employ a discrete dipole approximation approach to calculate optical binding potentials and achieve a good agreement between the calculated and observed binding forces. We incorporate the findings from these simulations into the assessment of the intrinsic interaction potentials and validate our methodology by using short-range depletion attraction induced by micelles as an example.

Extracting forces from noisy dynamics in dusty plasmas

Extracting environmental forces from noisy data is a common yet challenging task in complex physical systems. Machine learning (ML) represents a robust approach to this problem, yet is mostly tested on simulated data with known parameters. Here we use supervised ML to extract the electrostatic, dissipative, and stochastic forces acting on micron-sized charged particles levitated in an argon plasma (dusty plasma). By tracking the subpixel motion of particles in subsequent images, we successfully estimated these forces from their random motion. The experiments contained important sources of non-Gaussian noise, such as drift and pixel locking, representing a data mismatch from methods used to analyze simulated data with purely Gaussian noise. Our model was trained on simulated particle trajectories that included all of these artifacts, and used more than 100 dynamical and statistical features, resulting in a prediction with 50% better accuracy than conventional methods. Finally, in systems with two interacting particles, the model provided noncontact measurements of the particle charge and Debye length in the plasma environment.

Nanoscale Resolution 3D Snapshot Particle Tracking by Multifocal Microscopy

Accurate, precise, and rapid particle tracking in three dimensions remains a challenge; yet, its achievement will significantly enhance our understanding of living systems. We developed a multifocal microscopy (MFM) that allows snapshot acquisition of the imaging data, and an associated image processing approach, that together allow simultaneous 3D tracking of many fluorescent particles with nanoscale resolution. The 3D tracking was validated by measuring a known trajectory of a fluorescent bead with an axial accuracy of 19 nm through an image depth (axial range) of 3 μm and 4 nm precision of axial localization through an image depth of 4 μm. A second test obtained a uniform axial probability distribution and Brownian dynamics of beads diffusing in solution. We also validated the MFM approach by imaging fluorescent beads immobilized in gels and comparing the 3D localizations to their "ground truth" positions obtained from a confocal microscopy z-stack of finely spaced images. Finally, we applied our MFM and image processing approach to obtain 3D trajectories of insulin granules in pseudoislets of MIN6 cells to demonstrate its compatibility with complex biological systems. Our study demonstrates that multifocal microscopy allows rapid (video rate) and simultaneous 3D tracking of many "particles" with nanoscale accuracy and precision in a wide range of systems, including over spatial scales relevant to whole live cells.

Errors in Energy Landscapes Measured with Particle Tracking

Tracking Brownian particles is often employed to map the energy landscape they explore. Such measurements have been exploited to study many biological processes and interactions in soft materials. Yet video tracking is irremediably contaminated by localization errors originating from two imaging artifacts: the "static" errors come from signal noise, and the "dynamic" errors arise from the motion blur due to finite frame-acquisition time. We show that these errors result in systematic and nontrivial biases in the measured energy landscapes. We derive a relationship between the true and the measured potential that elucidates, among other aberrations, the presence of false double-well minima in the apparent potentials reported in recent studies. We further assess several canonical trapping and pair-interaction potentials by using our analytically derived results and Brownian dynamics simulations. In particular, we show that the apparent spring stiffness of harmonic potentials (such as optical traps) is increased by dynamic errors but decreased by static errors. Our formula allows for the development of efficient corrections schemes, and we also present in this work a provisional method for reconstructing true potentials from the measured ones.

Direct Visualization of Barrier Crossing Dynamics in a Driven Optical Matter System

A major impediment to a more complete understanding of barrier crossing and other single-molecule processes is the inability to directly visualize the trajectories and dynamics of atoms and molecules in reactions. Rather, the kinetics are inferred from ensemble measurements or the position of a transducer ( e. g., an AFM cantilever) as a surrogate variable. Direct visualization is highly desirable. Here, we achieve the direct measurement of barrier crossing trajectories by using optical microscopy to observe position and orientation changes of pairs of Ag nanoparticles, i. e. passing events, in an optical ring trap. A two-step mechanism similar to a bimolecular exchange reaction or the Michaelis-Menten scheme is revealed by analysis that combines detailed knowledge of each trajectory, a statistically significant number of repetitions of the passing events, and the driving force dependence of the process. We find that while the total event rate increases with driving force, this increase is due to an increase in the rate of encounters. There is no drive force dependence on the rate of barrier crossing because the key motion for the process involves a random (thermal) radial fluctuation of one particle allowing the other to pass. This simple experiment can readily be extended to study more complex barrier crossing processes by replacing the spherical metal nanoparticles with anisotropic ones or by creating more intricate optical trapping potentials.

Analysis and correction of errors in nanoscale particle tracking using the Single-pixel interior filling function (SPIFF) algorithm

Particle tracking, which is an essential tool in many fields of scientific research, uses algorithms that retrieve the centroid of tracked particles with sub-pixel accuracy. However, images in which the particles occupy a small number of pixels on the detector, are in close proximity to other particles or suffer from background noise, show a systematic error in which the particle sub-pixel positions are biased towards the center of the pixel. This "pixel locking" effect greatly reduces particle tracking accuracy. In this report, we demonstrate the severity of these errors by tracking experimental (and simulated) imaging data of optically trapped silver nanoparticles and single fluorescent proteins. We show that errors in interparticle separation, angle and mean square displacement are significantly reduced by applying the corrective Single-Pixel Interior Filling Function (SPIFF) algorithm. Our work demonstrates the potential ubiquity of such errors and the general applicability of SPIFF correction to many experimental fields.

Rotation and Negative Torque in Electrodynamically Bound Nanoparticle Dimers

We examine the formation and concomitant rotation of electrodynamically bound dimers (EBD) of 150 nm diameter Ag nanoparticles trapped in circularly polarized focused Gaussian beams. The rotation frequency of an EBD increases linearly with the incident beam power, reaching mean values of ∼4 kHz for relatively low incident powers of 14 mW. Using a coupled-dipole/effective polarizability model, we reveal that retardation of the scattered fields and electrodynamic interactions can lead to a "negative torque" causing rotation of the EBD in the direction opposite to that of the circular polarization. This intriguing opposite-handed rotation due to negative torque is clearly demonstrated using electrodynamics-Langevin dynamics simulations by changing particle separations and thus varying the retardation effects. Finally, negative torque is also demonstrated in experiments from statistical analysis of the EBD trajectories. These results demonstrate novel rotational dynamics of nanoparticles in optical matter using circular polarization and open a new avenue to control orientational dynamics through coupling to interparticle separation.