We demonstrate experimentally an optical process in which the spin angular momentum carried by a circularly polarized light beam is converted into orbital angular momentum, leading to the generation of helical modes with a wavefront helicity controlled by the input polarization. This phenomenon requires the interaction of light with matter that is both optically inhomogeneous and anisotropic. The underlying physics is also associated with the so-called Pancharatnam-Berry geometrical phases involved in any inhomogeneous transformation of the optical polarization.

Nucleosomes help structure chromosomes by compacting DNA into fibers. To gain insight into how nucleosomes are arranged in vivo, we combined quantitative super-resolution nanoscopy with computer simulations to visualize and count nucleosomes along the chromatin fiber in single nuclei. Nucleosomes assembled in heterogeneous groups of varying sizes, here termed "clutches," and these were interspersed with nucleosome-depleted regions. The median number of nucleosomes inside clutches and their compaction defined as nucleosome density were cell-type-specific. Ground-state pluripotent stem cells had, on average, less dense clutches containing fewer nucleosomes and clutch size strongly correlated with the pluripotency potential of induced pluripotent stem cells. RNA polymerase II preferentially associated with the smallest clutches while linker histone H1 and heterochromatin were enriched in the largest ones. Our results reveal how the chromatin fiber is formed at nanoscale level and link chromatin fiber architecture to stem cell state.

Optical microscopy has for centuries been a key tool to study living cells with minimum invasiveness. The advent of single molecule techniques over the past two decades has revolutionized the field of cell biology by providing a more quantitative picture of the complex and highly dynamic organization of living systems. Amongst these techniques, single particle tracking (SPT) has emerged as a powerful approach to study a variety of dynamic processes in life sciences. SPT provides access to single molecule behavior in the natural context of living cells, thereby allowing a complete statistical characterization of the system under study. In this review we describe the foundations of SPT together with novel optical implementations that nowadays allow the investigation of single molecule dynamic events with increasingly high spatiotemporal resolution using molecular densities closer to physiological expression levels. We outline some of the algorithms for the faithful reconstruction of SPT trajectories as well as data analysis, and highlight biological examples where the technique has provided novel insights into the role of diffusion regulating cellular function. The last part of the review concentrates on different theoretical models that describe anomalous transport behavior and ergodicity breaking observed from SPT studies in living cells.

Molecular transport in living systems regulates numerous processes underlying biological function.\ud Although many cellular components exhibit anomalous diffusion, only recently has the subdiffusive\ud motion been associated with nonergodic behavior. These findings have stimulated new questions for their\ud implications in statistical mechanics and cell biology. Is nonergodicity a common strategy shared by living\ud systems? Which physical mechanisms generate it? What are its implications for biological function? Here,\ud we use single-particle tracking to demonstrate that the motion of dendritic cell-specific intercellular\ud adhesion molecule 3-grabbing nonintegrin (DC-SIGN), a receptor with unique pathogen-recognition\ud capabilities, reveals nonergodic subdiffusion on living-cell membranes In contrast to previous studies, this\ud behavior is incompatible with transient immobilization, and, therefore, it cannot be interpreted according to\ud continuous-time random-walk theory. We show that the receptor undergoes changes of diffusivity,\ud consistent with the current view of the cell membrane as a highly dynamic and diverse environment.\ud Simulations based on a model of an ordinary random walk in complex media quantitatively reproduce all\ud our observations, pointing toward diffusion heterogeneity as the cause of DC-SIGN behavior. By studying\ud different receptor mutants, we further correlate receptor motion to its molecular structure, thus establishing\ud a strong link between nonergodicity and biological function. These results underscore the role of disorder\ud in cell membranes and its connection with function regulation. Because of its generality, our approach\ud offers a framework to interpret anomalous transport in other complex media where dynamic heterogeneity\ud might play a major role, such as those found, e.g., in soft condensed matter, geology, and ecology.Peer ReviewedPostprint (published version

Non-ergodicity observed in single-particle tracking experiments is usually modeled by transient trapping rather than spatial disorder. We introduce models of a particle diffusing in a medium consisting of regions with random sizes and random diffusivities. The particle is never trapped, but rather performs continuous Brownian motion with the local diffusion constant. Under simple assumptions on the distribution of the sizes and diffusivities, we find that the mean squared displacement displays subdiffusion due to non-ergodicity for both annealed and quenched disorder. The model is formulated as a walk continuous in both time and space, similar to the Lévy walk.PACS numbers: 05.40.Fb,87.10.Mn,87.15.Vv Disordered systems exhibiting subdiffusion have been studied intensively for decades [1][2][3][4][5]. In these systems the ensemble averaged mean squared displacement (EMSD) grows for large times aswhereas normal diffusion has β = 1. A broad class of systems show weak ergodicity breaking, that is, the EMSD and the time averaged mean squared displacement (TMSD) differ. The prototypical framework for describing non-ergodic subdiffusion is the heavy-tailed continuous-time random walk (CTRW) [6][7][8], in which a particle takes steps at random time intervals that are independently distributed with densityψ(τ ) has infinite mean, which leads to a subdiffusive EMSD β = α. Furthermore, the CTRW shows weak ergodicity breaking because the particle experiences trapping times on the order of the observation time T no matter how large T is. The CTRW was introduced to describe charge carriers in amorphous solids [8], and has found wide application since. Recently, there has been a surge of work on the CTRW [9-12], triggered by single particle tracking experiments in biological systems [13][14][15][16][17] that display signatures of non-ergodicity. A different approach to subdiffusion is to assume a deterministic diffusivity (i.e. diffusion coefficient) that is inhomogeneous in time [18,19], or space [20][21][22][23][24]. But in fact, the anomalous diffusion in these works is also nonergodic. Formulating models of inhomogeneous diffusivity is timely and important, given that recently measured spatial maps in the cell membrane often show patches of strongly varying diffusivity [25][26][27][28][29][30]. The presence of randomness in these experimental maps inspired us to consider disordered media. Thus, in this manuscript, we introduce a class of models of ordinary diffusion with a diffusivity that varies randomly but is constant on patches of random sizes. We call these models random patch models or just patch models. These models show non-ergodic subdiffusion, due to the diffusivity effectively changing at random times with a heavy-tailed distribution like that in (2) [31]. Note that ergodicity breaking is usually ascribed to energetic disorder that immobilizes the particle, e.g. via transient chemical binding [8,32,33]. But, in the patch models discussed here the particle constantly undergoes Brownian motion. The anomaly is i...

We report the realization of a Pancharatnam-Berry phase optical element E. Hasman, Opt. Lett. 27, 1141 (2002)] for wavefront shaping working in the visible spectral domain, based on patterned liquid crystal technology. This device generates helical modes of visible light with the possibility of electro-optically switching between opposite helicities by controlling the handedness of the input circular polarization. By cascading this approach, fast switching among multiple wavefront helicities can be achieved, with potential applications to multistate optical information encoding. The approach demonstrated here can be generalized to other polarization-controlled devices for wavefront shaping, such as switchable lenses, beam-splitters, and holographic elements.

Deviations from Brownian motion leading to anomalous diffusion are found in transport dynamics from quantum physics to life sciences. The characterization of anomalous diffusion from the measurement of an individual trajectory is a challenging task, which traditionally relies on calculating the trajectory mean squared displacement. However, this approach breaks down for cases of practical interest, e.g., short or noisy trajectories, heterogeneous behaviour, or non-ergodic processes. Recently, several new approaches have been proposed, mostly building on the ongoing machine-learning revolution. To perform an objective comparison of methods, we gathered the community and organized an open competition, the Anomalous Diffusion challenge (AnDi). Participating teams applied their algorithms to a commonly-defined dataset including diverse conditions. Although no single method performed best across all scenarios, machine-learning-based approaches achieved superior performance for all tasks. The discussion of the challenge results provides practical advice for users and a benchmark for developers.

In order to study transport in complex environments, it is extremely important to determine the physical mechanism underlying diffusion and precisely characterize its nature and parameters. Often, this task is strongly impacted by data consisting of trajectories with short length (either due to brief recordings or previous trajectory segmentation) and limited localization precision. In this paper, we propose a machine learning method based on a random forest architecture, which is able to associate single trajectories to the underlying diffusion mechanism with high accuracy. In addition, the algorithm is able to determine the anomalous exponent with a small error, thus inherently providing a classification of the motion as normal or anomalous (subor super-diffusion). The method provides highly accurate outputs even when working with very short trajectories and in the presence of experimental noise. We further demonstrate the application of transfer learning to experimental and simulated data not included in the training/test dataset. This allows for a full, high-accuracy characterization of experimental trajectories without the need of any prior information.In the last decades, the research in biophysics has conveyed large efforts toward the development of experimental techniques allowing the visualization of biological processes one molecule at a time [1-4]. These efforts have been mainly driven by the concept that ensemble-averaging hides important features that are relevant for cellular function. Somehow expectedly, experiments performed by means of these techniques have shown a large heterogeneity in the behavior of biological molecules, thus fully justifying the use of these raffinate tools.Besides, experiments performed using single particle tracking [3] have revealed that even chemically-identical molecules in biological media can display very different behaviors, as a consequence of the complex environment where diffusion takes place. By way of example, this heterogeneity is reflected in the broad distribution of dynamic parameters of distinct individual trajectories corresponding to the same molecular species, such as the diffusion coefficient, well above stochastic indetermination. Typically, the trajectories are analyzed by quantifying the (time-averaged) mean square displacement (tMSD) as a function of the time lag τ [5]:The calculation of this quantity-expected to scale linearly for a Brownian walker in a homogeneous environment-has provided a ubiquitous evidence of anomalous behaviors in biological systems, characterized by an asymptotic nonlinear scaling of the tMSD curve d t a 2. More experiments have shown that the anomalous exponent can vary from particle to particle ( figure 1(a)) as a consequence of molecular interactions and that these changes can be experienced by the same particle in space/time [6]. Several methods have been OPEN ACCESS RECEIVED