Shaping the angular spectrum of a Bessel beam to enhance light transfer through dynamic strongly scattering media.

We prepare a quasi-non-diffracting Bessel beam defined within an annular angular spectrum with a spatial light modulator. The beam propagates through a strongly scattering media, and the transmitted speckle pattern is measured at one point with a Hadamard Walsh basis that divides the ring into N segments (N = 16, 64, 256, 1024). The phase of the transmitted beam is reconstructed with 3-step interferometry, and the intensity of the transmitted beam is optimized by projecting the conjugate phase at the SLM. We find that the optimum intensity is attained for the condition that the transverse wave vector k⊥ (of the Bessel beam) matches the spatial azimuthal frequencies of the segmented ring k ϕ. Furthermore, compared with beams defined on a 2d grid (i.e., Gaussian) a reasonable enhancement is achieved for all the k⊥ sampled with only 64 elements. Finally, the measurements can be done while the scatterer is moving as long as the total displacement during the measurement is smaller than the speckle correlation distance.

Optimal calibration of optical tweezers with arbitrary integration time and sampling frequencies: a general framework [Invited].

Optical tweezers (OT) have become an essential technique in several fields of physics, chemistry, and biology as precise micromanipulation tools and microscopic force transducers. Quantitative measurements require the accurate calibration of the trap stiffness of the optical trap and the diffusion constant of the optically trapped particle. This is typically done by statistical estimators constructed from the position signal of the particle, which is recorded by a digital camera or a quadrant photodiode. The finite integration time and sampling frequency of the detector need to be properly taken into account. Here, we present a general approach based on the joint probability density function of the sampled trajectory that corrects exactly the biases due to the detector's finite integration time and limited sampling frequency, providing theoretical formulas for the most widely employed calibration methods: equipartition, mean squared displacement, autocorrelation, power spectral density, and force reconstruction via maximum-likelihood-estimator analysis (FORMA). Our results, tested with experiments and Monte Carlo simulations, will permit users of OT to confidently estimate the trap stiffness and diffusion constant, extending their use to a broader set of experimental conditions.

Live Plant Cell Tracking: Fiji plugin to analyze cell proliferation dynamics and understand morphogenesis.

Arabidopsis (Arabidopsis thaliana) primary and lateral roots (LRs) are well suited for 3D and 4D microscopy, and their development provides an ideal system for studying morphogenesis and cell proliferation dynamics. With fast-advancing microscopy techniques used for live-imaging, whole tissue data are increasingly available, yet present the great challenge of analyzing complex interactions within cell populations. We developed a plugin "Live Plant Cell Tracking" (LiPlaCeT) coupled to the publicly available ImageJ image analysis program and generated a pipeline that allows, with the aid of LiPlaCeT, 4D cell tracking and lineage analysis of populations of dividing and growing cells. The LiPlaCeT plugin contains ad hoc ergonomic curating tools, making it very simple to use for manual cell tracking, especially when the signal-to-noise ratio of images is low or variable in time or 3D space and when automated methods may fail. Performing time-lapse experiments and using cell-tracking data extracted with the assistance of LiPlaCeT, we accomplished deep analyses of cell proliferation and clonal relations in the whole developing LR primordia and constructed genealogical trees. We also used cell-tracking data for endodermis cells of the root apical meristem (RAM) and performed automated analyses of cell population dynamics using ParaView software (also publicly available). Using the RAM as an example, we also showed how LiPlaCeT can be used to generate information at the whole-tissue level regarding cell length, cell position, cell growth rate, cell displacement rate, and proliferation activity. The pipeline will be useful in live-imaging studies of roots and other plant organs to understand complex interactions within proliferating and growing cell populations. The plugin includes a step-by-step user manual and a dataset example that are available at https://www.ibt.unam.mx/documentos/diversos/LiPlaCeT.zip.

The environment topography alters the way to multicellularity in Myxococcus xanthus.

The social soil-dwelling bacterium Myxococcus xanthus can form multicellular structures, known as fruiting bodies. Experiments in homogeneous environments have shown that this process is affected by the physicochemical properties of the substrate, but they have largely neglected the role of complex topographies. We experimentally demonstrate that the topography alters single-cell motility and multicellular organization in M. xanthus In topographies realized by randomly placing silica particles over agar plates, we observe that the cells' interaction with particles drastically modifies the dynamics of cellular aggregation, leading to changes in the number, size, and shape of the fruiting bodies and even to arresting their formation in certain conditions. We further explore this type of cell-particle interaction in a computational model. These results provide fundamental insights into how the environment topography influences the emergence of complex multicellular structures from single cells, which is a fundamental problem of biological, ecological, and medical relevance.

Fluid Viscoelasticity Triggers Fast Transitions of a Brownian Particle in a Double Well Optical Potential.

Thermally activated transitions are ubiquitous in nature, occurring in complex environments which are typically conceived as ideal viscous fluids. We report the first direct observations of a Brownian bead transiting between the wells of a bistable optical potential in a viscoelastic fluid with a single long relaxation time. We precisely characterize both the potential and the fluid, thus enabling a neat comparison between our experimental results and a theoretical model based on the generalized Langevin equation. Our findings reveal a drastic amplification of the transition rates compared to those in a Newtonian fluid, stemming from the relaxation of the fluid during the particle crossing events.

Plastic multicellular development of Myxococcus xanthus: genotype-environment interactions in a physical gradient.

In order to investigate the contribution of the physical environment to variation in multicellular development of Myxococcus xanthus, phenotypes developed by different genotypes in a gradient of substrate stiffness conditions were quantitatively characterized. Statistical analysis showed that plastic phenotypes result from the genotype, the substrate conditions and the interaction between them. Also, phenotypes were expressed in two distinguishable scales, the individual and the population levels, and the interaction with the environment showed scale and trait specificity. Overall, our results highlight the constructive role of the physical context in the development of microbial multicellularity, with both ecological and evolutionary implications.

Spin to orbital light momentum conversion visualized by particle trajectory.

In a tightly focused beam of light having both spin and orbital angular momentum, the beam exhibits the spin-orbit interaction phenomenon. We demonstrate here that this interaction gives rise to series of subtle, but observable, effects on the dynamics of a dielectric microsphere trapped in such a beam. In our setup, we control the strength of spin-orbit interaction with the width, polarization and vorticity of the beam and record how these parameters influence radius and orbiting frequency of the same single orbiting particle pushed by the laser beam. Using Richard and Wolf model of the non-paraxial beam focusing, we found a very good agreement between the experimental results and the theoretical model based on calculation of the optical forces using the generalized Lorenz-Mie theory extended to a non-paraxial vortex beam. Especially the radius of the particle orbit seems to be a promising parameter characterizing the spin to orbital momentum conversion independently on the trapping beam power.

Stationary superstatistics distributions of trapped run-and-tumble particles.

We present an analysis of the stationary distributions of run-and-tumble particles trapped in external potentials in terms of a thermophoretic potential that emerges when trapped active motion is mapped to trapped passive Brownian motion in a fictitious inhomogeneous thermal bath. We elaborate on the meaning of the non-Boltzmann-Gibbs stationary distributions that emerge as a consequence of the persistent motion of active particles. These stationary distributions are interpreted as a class of distributions in nonequilibrium statistical mechanics known as superstatistics. Our analysis provides an original insight on the link between the intrinsic nonequilibrium nature of active motion and the well-known concept of local equilibrium used in nonequilibrium statistical mechanics and contributes to the understanding of the validity of the concept of effective temperature. Particular cases of interest, regarding specific trapping potentials used in other theoretical or experimental studies, are discussed. We point out as an unprecedented effect, the emergence of new modes of the stationary distribution as a consequence of the coupling of persistent motion in a trapping potential that varies highly enough with position.

Omnidirectional Transport in Fully Reconfigurable Two Dimensional Optical Ratchets.

A fully reconfigurable two-dimensional (2D) rocking ratchet system created with holographic optical micromanipulation is presented. We can generate optical potentials with the geometry of any Bravais lattice in 2D and introduce a spatial asymmetry with arbitrary orientation. Nontrivial directed transport of Brownian particles along different directions is demonstrated numerically and experimentally, including on axis, perpendicular, and oblique with respect to an unbiased ac driving. The most important aspect to define the current direction is shown to be the asymmetry and not the driving orientation, and yet we show a system in which the asymmetry orientation of each potential well does not coincide with the transport direction, suggesting an additional symmetry breaking as a result of a coupling with the lattice configuration. Our experimental device, due to its versatility, opens up a new range of possibilities in the study of nonequilibrium dynamics at the microscopic level.

3D micromanipulation at low numerical aperture with a single light beam: the focused-Bessel trap.

Full-three-dimensional (3D) manipulation of individual glass beads with radii in the range of 2-8 µm is experimentally demonstrated by using a single Bessel light beam focused through a low-numerical-aperture lens (NA=0.40). Although we have a weight-assisted trap with the beam propagating upward, we obtain a stable equilibrium position well away from the walls of the sample cell, and we are able to move the particle across the entire cell in three dimensions. A theoretical analysis for the optical field and trapping forces along the lateral and axial directions is presented for the focused-Bessel trap. This trap offers advantages for 3D manipulation, such as an extended working distance, a large field of view, and reduced aberrations.

Complex rotational dynamics of multiple spheroidal particles in a circularly polarized, dual beam trap.

We examine the rotational dynamics of spheroidal particles in an optical trap comprising counter-propagating Gaussian beams of opposing helicity. Isolated spheroids undergo continuous rotation with frequencies determined by their size and aspect ratio, whilst pairs of spheroids display phase locking behaviour. The introduction of additional particles leads to yet more complex behaviour. Experimental results are supported by numerical calculations.

Rotation, oscillation and hydrodynamic synchronization of optically trapped oblate spheroidal microparticles.

While the behavior of optically trapped dielectric spherical particles has been extensively studied, the behavior of non-spherical particles remains mainly unexplored. In this work we focus on the dynamics of oblate spheroidal particles trapped in a tightly focused elliptically-polarized vortex beam. In our experiments we used polystyrene spheroids of aspect ratio of major to minor axes equal to 2.55 and of a volume equal to a sphere of diameter 1.7µm. We demonstrate that such particles can be trapped in three dimensions, with the minor axis oriented perpendicular to both the beam polarization (linear) and the beam propagation, can spin in a circularly polarized beam and an optical vortex beam around the axis parallel with the beam propagation. We also observed that these particles can exhibit a periodic motion in the plane transversal to the beam propagation. We measured that the transfer of the orbital angular momentum from the vortex beam to the spheroid gives rise to torques one order of magnitude stronger comparing to the circularly polarized Gaussian beam. We employed a phase-only spatial light modulator to generate several vortex beam traps with one spheroid in each of them. Due to independent setting of beams parameters we controlled spheroids frequency and sense of rotation and observed hydrodynamic phase and frequency locking of rotating spheroids. These optically driven spheroids offer a simple alternative approach to the former techniques based on birefringent, absorbing or chiral microrotors.

Optical sorting of nonspherical and living microobjects in moving interference structures.

Contactless, sterile and nondestructive separation of microobjects or living cells is demanded in many areas of biology and analytical chemistry, as well as in physics or engineering. Here we demonstrate advanced sorting methods based on the optical forces exerted by travelling interference fringes with tunable periodicity controlled by a spatial light modulator. Besides the sorting of spherical particles we also demonstrate separation of algal cells of different sizes and particles of different shapes. The three presented methods offer simultaneous sorting of more objects in static suspension placed in a Petri dish or on a microscope slide.

Dynamical analysis of an optical rocking ratchet: theory and experiment.

A thorough analysis of the dynamics in a deterministic optical rocking ratchet [introduced in A. V. Arzola et al., Phys. Rev. Lett. 106, 168104 (2011)] and a comparison with experimental results are presented. The studied system consists of a microscopic particle interacting with a periodic and asymmetric light pattern, which is driven away from equilibrium by means of an unbiased time-periodic external force. It is shown that the asymmetry of the effective optical potential depends on the relative size of the particle with respect to the spatial period, and this is analyzed as an effective mechanism for particle fractionation. The necessary conditions to obtain current reversals in the deterministic regime are discussed in detail.

An epigenetic model for pigment patterning based on mechanical and cellular interactions.

Pigment patterning in animals generally occurs during early developmental stages and has ecological, physiological, ethological, and evolutionary significance. Despite the relative simplicity of color patterns, their emergence depends upon multilevel complex processes. Thus, theoretical models have become necessary tools to further understand how such patterns emerge. Recent studies have reevaluated the importance of epigenetic, as well as genetic factors in developmental pattern formation. Yet epigenetic phenomena, specially those related to physical constraints that might be involved in the emergence of color patterns, have not been fully studied. In this article, we propose a model of color patterning in which epigenetic aspects such as cell migration, cell-tissue interactions, and physical and mechanical phenomena are central. This model considers that motile cells embedded in a fibrous, viscoelastic matrix-mesenchyme-can deform it in such a way that tension tracks are formed. We postulate that these tracks act, in turn, as guides for subsequent cell migration and establishment, generating long-range phenomenological interactions. We aim to describe some general aspects of this developmental phenomenon with a rather simple mathematical model. Then we discuss our model in the context of available experimental and morphological evidence for reptiles, amphibians, and fishes, and compare it with other patterning models. We also put forward novel testable predictions derived from our model, regarding, for instance, the localization of the postulated tension tracks, and we propose new experiments. Finally, we discuss how the proposed mechanism could constitute a dynamic patterning module accounting for pattern formation in many animal lineages.

Experimental control of transport and current reversals in a deterministic optical rocking ratchet.

We present an experimental demonstration of a deterministic optical rocking ratchet. A periodic and asymmetric light pattern is created to interact with dielectric microparticles in water, giving rise to a ratchet potential. The sample is moved with respect to the pattern with an unbiased time-periodic rocking function, which tilts the potential in alternating opposite directions. We obtain a current of particles whose direction can be controlled in real time and show that particles of different sizes may experience opposite currents. Moreover, we observed current reversals as a function of the magnitude and period of the rocking force.

Force mapping of an extended light pattern in an inclined plane: deterministic regime.

We present a full quantitative mapping of the non-linear optical trapping force associated to an extended interference pattern of fringes as a function of the position. To map this force, we studied the dynamics of microscopic spherical beads of different sizes (8, 10 and 14.5 microns in diameter) moving through the light pattern. For this range of particle sizes, the system is overdamped due to the viscous drag and the effect of thermal noise is negligible. The novel experimental approach consists in tilting the sample cell a small angle with respect to the horizontal, thus we have a deterministic particle in an inclined plane. The combined action of the optical force and gravity gives rise to a washboard potential. We compared our experimental results with a ray optics model and found a good quantitative agreement. For each size of the microsphere we studied different spatial periods of the interference fringes.