Distinct Sub- to Superdiffuse Insulin Granule Transport Behaviors in ß-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.

Electrodynamic Interference and Induced Polarization in Nanoparticle-Based Optical Matter Arrays.

Optical matter (OM) arrays are self-organizing, ordered arrangements of nanometer- to micrometer-size particles, where interparticle forces are mediated by incident and scattered coherent light. The structures that form and their dynamics depend on the properties (e.g., material, size) of the constituent particles, as well as the incident and scattered light. While significant progress has been made toward understanding how the OM arrays are affected by the phase, polarization, and intensity profile of the incident light, the polarization induced in the particles and the light scattered by OM arrays have received less attention. In this paper, we establish the roles of electrodynamic interference, many-body coupling, and induced-polarization concomitant with the coherent light scattered by OM arrays. Experiments and simulations together demonstrate that the spatial profile and directionality of coherent light scattered by OM arrays in the far field are primarily influenced by interference, while electrodynamic coupling (interactions) and the associated polarization induced in the nanoparticle constituents have a quantitative wavelength-dependent effect on the total amount of light scattered by the arrays. Furthermore, the electrodynamic coupling in silver nanoparticle OM arrays is significantly enhanced by constructive interference and increases superextensively with the number of particles in the array. Particle size, and hence polarizability, also has a significant effect on the strength of the coupling. Finally, we simulate larger hexagonal OM arrays of Ag nanoparticles to demonstrate that the electrodynamic coupling and scattering enhancement observed in small OM arrays develop into surface lattice resonances observed in the infinite array limit. Our work provides insights for designing OM arrays to tune many-body forces and the coherent light that they scatter.

Easily scalable multi-color DMD-based structured illumination microscopy.

Structured illumination microscopy (SIM) achieves super-resolution imaging using a series of phase-shifted sinusoidal illumination patterns to down-modulate high spatial-frequency information of samples. Digital micromirror devices (DMDs) have been increasingly used to generate SIM illumination patterns due to their high speed and moderate cost. However, a DMD micromirror array's blazed grating structure causes strong angular dispersion for different wavelengths of light, thus severely hampering its application in multicolor imaging. We developed a multi-color DMD-SIM setup that employs a diffraction grating to compensate the DMD's dispersion and demonstrate super-resolution SIM imaging of both fluorescent beads and live cells samples with four color channels. This simple but effective approach can be readily scaled to more color channels, thereby greatly expanding the application of SIM in the study of complex multi-component structures and dynamics in soft matter systems.

Tandem aberration correction optics (TACO) in wide-field structured illumination microscopy.

Structured illumination microscopy (SIM) is a powerful super-resolution imaging technique that uses patterned illumination to down-modulate high spatial-frequency information of samples. However, the presence of spatially-dependent aberrations can severely disrupt the illumination pattern, limiting the quality of SIM imaging. Conventional adaptive optics (AO) techniques that employ wavefront correctors at the pupil plane are not capable of effectively correcting these spatially-dependent aberrations. We introduce the Tandem Aberration Correction Optics (TACO) approach that combines both pupil AO and conjugate AO for aberration correction in SIM. TACO incorporates a deformable mirror (DM) for pupil AO in the detection path to correct for global aberrations, while a spatial light modulator (SLM) is placed at the plane conjugate to the aberration source near the sample plane, termed conjugate AO, to compensate spatially-varying aberrations in the illumination path. Our numerical simulations and experimental results show that the TACO approach can recover the illumination pattern close to an ideal condition, even when severely misshaped by aberrations, resulting in high-quality super-resolution SIM reconstruction. The TACO approach resolves a critical traditional shortcoming of aberration correction for structured illumination. This advance significantly expands the application of SIM imaging in the study of complex, particularly biological, samples and should be effective in other wide-field microscopies.

Data-driven reaction coordinate discovery in overdamped and non-conservative systems: application to optical matter structural isomerization.

Optical matter (OM) systems consist of (nano-)particle constituents in solution that can self-organize into ordered arrays that are bound by electrodynamic interactions. They also manifest non-conservative forces, and the motions of the nano-particles are overdamped; i.e., they exhibit diffusive trajectories. We propose a data-driven approach based on principal components analysis (PCA) to determine the collective modes of non-conservative overdamped systems, such as OM structures, and harmonic linear discriminant analysis (HLDA) of time trajectories to estimate the reaction coordinate for structural transitions. We demonstrate the approach via electrodynamics-Langevin dynamics simulations of six electrodynamically-bound nanoparticles in an incident laser beam. The reaction coordinate we discover is in excellent accord with a rigorous committor analysis, and the identified mechanism for structural isomerization is in very good agreement with the experimental observations. The PCA-HLDA approach to data-driven discovery of reaction coordinates can aid in understanding and eventually controlling non-conservative and overdamped systems including optical and active matter systems.

Snapshot multifocal light field microscopy.

Light field microscopy (LFM) is an emerging technology for high-speed wide-field 3D imaging by capturing 4D light field of 3D volumes. However, its 3D imaging capability comes at a cost of lateral resolution. In addition, the lateral resolution is not uniform across depth in the light field dconvolution reconstructions. To address these problems, here, we propose a snapshot multifocal light field microscopy (MFLFM) imaging method. The underlying concept of the MFLFM is to collect multiple focal shifted light fields simultaneously. We show that by focal stacking those focal shifted light fields, the depth-of-field (DOF) of the LFM can be further improved but without sacrificing the lateral resolution. Also, if all differently focused light fields are utilized together in the deconvolution, the MFLFM could achieve a high and uniform lateral resolution within a larger DOF. We present a house-built MFLFM system by placing a diffractive optical element at the Fourier plane of a conventional LFM. The optical performance of the MFLFM are analyzed and given. Both simulations and proof-of-principle experimental results are provided to demonstrate the effectiveness and benefits of the MFLFM. We believe that the proposed snapshot MFLFM has potential to enable high-speed and high resolution 3D imaging applications.

Excitation of Nonradiating Anapoles in Dielectric Nanospheres.

Although the study of nonradiating anapoles has long been part of fundamental physics, the dynamic anapole at optical frequencies was only recently experimentally demonstrated in a specialized silicon nanodisk structure. We report excitation of the electrodynamic anapole state in isotropic silicon nanospheres using radially polarized beam illumination. The superposition of equal and out-of-phase amplitudes of the Cartesian electric and toroidal dipoles produces a pronounced dip in the scattering spectra with the scattering intensity almost reaching zero-a signature of anapole excitation. The total scattering intensity associated with the anapole excitation is found to be more than 10 times weaker for illumination with radially vs linearly polarized beams. Our approach provides a simple, straightforward alternative path to realizing nonradiating anapole states at the optical frequencies.

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.

Hierarchical Assembly of Plasmonic Nanoparticle Heterodimer Arrays with Tunable Sub-5 nm Nanogaps.

Nanoparticle assemblies have generated intense interest because of their novel optical, electronic, and magnetic properties that open up numerous opportunities in fundamental and applied nanophotonics, -electronics, and -magnetics. However, despite the great scientific and technological potential of these structures, it remains an outstanding challenge to reliably fabricate such assemblies with both nanometer-level structural control and precise spatial arrangements on a macroscopic scale. It is the combination of these two features that is key to realizing nanoparticle assemblies' potential, particular for device applications. To address this challenge, we propose a hierarchical assembly approach consisting of both template-particle and particle-particle interactions, whereby the former ensures precise addressability of assemblies on a surface and the latter provides nanometer-level structural control. Template-particle interactions are harnessed via chemical-pattern-directed assembly, and the particle-particle interactions are controlled using DNA-directed self-assembly. To demonstrate the potential of this hierarchical assembly approach, we demonstrate the fabrication of a particularly fascinating assembly: the nanoparticle heterodimer, which possesses a surprisingly rich set of plasmonic properties and is a promising candidate to enable a variety of imaging and sensing applications. Each heterodimer is placed on the surface at predetermined locations, and the precise control of the nanogaps is confirmed by far-field scattering measurements of individual dimers. We further demonstrate that the gap size can be effectively tuned by varying the DNA length. By correlating measured spectra with finite-difference time-domain (FDTD) simulations, we determine the gap sizes to be 4.2 and 5.0 nm-with subnm deviation-for the two DNA lengths investigated. This is one of the best gap uniformities ever demonstrated for surface-bound nanoparticle assemblies. The estimated surface-enhanced Raman scattering (SERS) enhancement factor of these heterodimers is on the order of 105-106 with high reproducibility and predictable polarization-dependence. This hierarchical fabrication technique-employing both template-particle and particle-particle interactions-constitutes a novel platform for the realization of functional nanoparticle assemblies on surfaces and thereby creates new opportunities to implement these structures in a variety of applications.

Three-dimensional optical trapping and orientation of microparticles for coherent X-ray diffraction imaging.

Optical trapping has been implemented in many areas of physics and biology as a noncontact sample manipulation technique to study the structure and dynamics of nano- and mesoscale objects. It provides a unique approach for manipulating microscopic objects without inducing undesired changes in structure. Combining optical trapping with hard X-ray microscopy techniques, such as coherent diffraction imaging and crystallography, provides a nonperturbing environment where electronic and structural dynamics of an individual particle in solution can be followed in situ. It was previously shown that optical trapping allows the manipulation of micrometer-sized objects for X-ray fluorescence imaging. However, questions remain over the ability of optical trapping to position objects for X-ray diffraction measurements, which have stringent requirements for angular stability. Our work demonstrates that dynamic holographic optical tweezers are capable of manipulating single micrometer-scale anisotropic particles in a microfluidic environment with the precision and stability required for X-ray Bragg diffraction experiments-thus functioning as an "optical goniometer." The methodology can be extended to a variety of X-ray experiments and the Bragg coherent diffractive imaging of individual particles in solution, as demonstrated here, will be markedly enhanced with the advent of brighter, coherent X-ray sources.

Controlling the Dynamics and Optical Binding of Nanoparticle Homodimers with Transverse Phase Gradients.

While transverse phase gradients enable studies of driven nonequilibrium phenomena in optical trapping, the behavior of electrodynamically interacting particles in a transverse phase gradient has not been explored in detail. In this Letter we study electrodynamically interacting pairs of identical nanoparticles (homodimers) in transverse phase gradients. We establish that the net driving force on homodimers is modulated by a separation-dependent interference effect for small phase gradients. By contrast, large phase gradients break the symmetry of the interaction between particles and profoundly change the electrodynamic interparticle energy landscape. Our findings are particularly important for understanding multiparticle dynamics during the self-assembly and rearrangement of optical matter.

Crossover from positive to negative optical torque in mesoscale optical matter.

The photons in circularly polarized light can transfer their quantized spin angular momentum to micro- and nanostructures via absorption and scattering. This normally exerts positive torque on the objects wher the sign (i.e., handedness or angular direction) follows that of the spin angular momentum. Here we show that the sign of the optical torque can be negative in mesoscopic optical matter arrays of metal nanoparticles (NPs) assembled in circularly polarized optical traps. Crossover from positive to negative optical torque, which occurs for arrays with different number, separation and configuration of the constituent particles, is shown to result from many-body interactions as clarified by electrodynamics simulations. Our results establish that both positive and negative optical torque can be readily realized and controlled in optical matter arrays. This property and reconfigurability of the arrays makes possible programmable materials for optomechanical, microrheological and biological applications.

Dissipative Self-Assembly of Anisotropic Nanoparticle Chains with Combined Electrodynamic and Electrostatic Interactions.

Dissipative self-assembly of colloidal nanoparticles offers the prospect of creating reconfigurable artificial materials and systems, yet the phenomenon only occurs far from thermodynamic equilibrium. Therefore, it is usually difficult to predict and control. Here, a dissipative colloidal solution system, where anisotropic chains with different interparticle separations in two perpendicular directions transiently arise among largely disordered silver nanoparticles illuminated by a laser beam, is reported. The optical field creates a nonequilibrium dissipative state, where a disorder-to-order transition occurs driven by anisotropic electrodynamic interactions coupled with electrostatic interactions. Investigation of the temporal dynamics and spatial arrangements of the nanoparticle system shows that the optical binding strength and entropy of the system are two crucial parameters for the formation of the anisotropic chains and responsible for adaptive behaviors, such as self-replication of dimer units. Formation of anisotropic nanoparticle chains is also observed among colloidal nanoparticles made from other metal (e.g., Au), polymer (e.g., polystyrene), ceramic (e.g., CeO2 ), and hybrid materials (e.g., SiO2 @Au core-shell), suggesting that light-driven self-organization will provide a wide range of opportunities to discover new dissipative structures under thermal fluctuations and build novel anisotropic materials with nanoscale order.

Particle tracking by repetitive phase-shift interferometric super resolution microscopy.

Accurate and rapid particle tracking is essential for addressing many research problems in single molecule and cellular biophysics and colloidal soft condensed matter physics. We developed a novel three-dimensional interferometric fluorescent particle tracking approach that does not require any sample scanning. By periodically shifting the interferometer phase, the information stored in the interference pattern of the emitted light allows localizing particles positions with nanometer resolution. This tracking protocol was demonstrated by measuring a known trajectory of a fluorescent bead with sub-5 nm axial localization error at 5 Hz. The interferometric microscopy was used to track the RecA protein in Bacillus subtilis bacteria to demonstrate its compatibility with biological systems.

Dynamics of the Optically Directed Assembly and Disassembly of Gold Nanoplatelet Arrays.

The tremendous progress in nanoscience now allows the creation of static nanostructured materials for a broad range of applications. A further goal is to achieve dynamic and reconfigurable nanostructures. One approach involves nanoparticle-based optical matter, but so far, studies have only considered spherical constituents. A nontrivial issue is that nanoparticles with other shapes are expected to have different local electromagnetic field distributions and interactions with neighbors in optical-matter arrays. Therefore, one would expect their dynamics to be different as well. This paper reports the directed assembly of ordered arrays of gold nanoplatelets in optical line traps, demonstrating the reconfigurability of the array by altering the phase gradient via holographic-beam shaping. The weaker gradient forces and resultant slower motion of the nanoplatelets, as compared with plasmonic (Ag and Au) nanospheres, allow the precise study of their assembly and disassembly dynamics. Both temporal and spatial correlations are detected between particles separated by distances of hundreds of nanometers to several microns. Electrodynamics simulations reveal the presence of multipolar plasmon modes that induce short-range (near-field) and longer-range electrodynamic (e.g., optical binding) interactions. These interactions and the interferences between mutipolar plamon modes cause both the strong correlations and the nonuniform dynamics observed. Our study demonstrates new opportunities for the generation of complex addressable optical matter and the creation of novel active optical technology.

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.

Selective Induction of Optical Magnetism.

An extension of the Maxwell-Faraday law of electromagnetic induction to optical frequencies requires spatially appropriate materials and optical beams to create resonances and excitations with curl. Here we employ cylindrical vector beams with azimuthal polarization to create electric fields that selectively drive magnetic responses in dielectric core-metal nanoparticle "satellite" nanostructures. These optical frequency magnetic resonances are induced in materials that do not possess spin or orbital angular momentum. Multipole expansion analysis of the scattered fields obtained from electrodynamics simulations show that the excitation with azimuthally polarized beams selectively enhances magnetic vs electric dipole resonances by nearly 100-fold in experiments. Multipolar resonances (e.g., quadrupole and octupole) are enhanced 5-fold by focused azimuthally versus linearly polarized beams. We also selectively excite electric multipolar resonances in the same identical nanostructures with radially polarized light. This work opens new opportunities for spectroscopic investigation and control of "dark modes", Fano resonances, and magnetic modes in nanomaterials and engineered metamaterials.

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.