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Collective cell migration is crucial in various physiological processes, including wound healing, morphogenesis, and cancer metastasis. Adherens Junctions (AJs) play a pivotal role in regulating cell cohesion and migration dynamics during tissue remodeling. While the role and origin of the junctional mechanical tension at AJs have been extensively studied, the influence of the actin cortex structure and dynamics on junction plasticity remains incompletely understood. Moreover, the mechanisms underlying stress dissipation at junctions are not well elucidated. Here, we found that the ligand-independent phosphorylation of epithelial growth factor receptor (EGFR) downstream of de novo E-cadherin adhesion orchestrates a feedback loop, governing intercellular viscosity via the Rac pathway regulating actin dynamics. Our findings highlight how the E-cadherin-dependent EGFR activity controls the migration mode of collective cell movements independently of intercellular tension. This modulation of effective viscosity coordinates cellular movements within the expanding monolayer, inducing a transition from swirling to laminar flow patterns while maintaining a constant migration front speed. Additionally, we propose a vertex model with adjustable junctional viscosity, capable of replicating all observed cellular flow phenotypes experimentally., Competing Interests: Competing interests statement:The authors declare no competing interest.

Cell adhesion receptors are transmembrane proteins that bind cells to their environment. These proteins typically cluster into disk-shaped or linear structures. Here, we show that such clustering patterns spontaneously emerge when the receptor senses the membrane deformation gradient, for example, by reaching a lower-energy conformation when the membrane is tilted relative to the underlying binding substrate. Increasing the strength of the membrane gradient-sensing mechanism first yields isolated disk-shaped clusters and then long linear structures. Our theory is coherent with experimental estimates of the parameters, suggesting that a tilt-induced clustering mechanism is relevant in the context of cell adhesion.

Cell adhesion proteins typically form stable clusters that anchor the cell membrane to its environment. Several works have suggested that cell membrane protein clusters can emerge from a local feedback between the membrane curvature and the density of proteins. Here, we investigate the effect of such a curvature-sensing mechanism in the context of cell adhesion proteins. We show how clustering emerges in an intermediate range of adhesion and curvature-sensing strengths. We identify key differences with the tilt-induced gradient sensing mechanism we previously proposed (Lin et al., arXiv:2307.03670).

Lamin A/C is a well-established key contributor to nuclear stiffness and its role in nucleus mechanical properties has been extensively studied. However, its impact on whole-cell mechanics has been poorly addressed, particularly concerning measurable physical parameters. In this study, we combined microfluidic experiments with theoretical analyses to quantitatively estimate the whole-cell mechanical properties. This allowed us to characterize the mechanical changes induced in cells by lamin A/C alterations and prelamin A accumulation resulting from atazanavir treatment or lipodystrophy-associated LMNA R482W pathogenic variant. Our results reveal a distinctive increase in long-time viscosity as a signature of cells affected by lamin A/C alterations. Furthermore, they show that the whole-cell response to mechanical stress is driven not only by the nucleus but also by the nucleo-cytoskeleton links and the microtubule network. The enhanced cell viscosity assessed with our microfluidic assay could serve as a valuable diagnosis marker for lamin-related diseases., Competing Interests: The authors declare no competing financial interests., (© 2023 The Authors.)

During the consumption of alkanes, Alcanivorax borkumensis will form a biofilm around an oil droplet, but the role this plays during degradation remains unclear. We identified a shift in biofilm morphology that depends on adaptation to oil consumption: Longer exposure leads to the appearance of dendritic biofilms optimized for oil consumption effected through tubulation of the interface. In situ microfluidic tracking enabled us to correlate tubulation to localized defects in the interfacial cell ordering. We demonstrate control over droplet deformation by using confinement to position defects, inducing dimpling in the droplets. We developed a model that elucidates biofilm morphology, linking tubulation to decreased interfacial tension and increased cell hydrophobicity.

Biological tissues acquire reproducible shapes during development through dynamic cell behaviors. Most of these behaviors involve the remodeling of cell-cell contacts. During epithelial morphogenesis, contractile actomyosin networks remodel cell-cell contacts by shrinking and extending junctions between lateral cell surfaces. However, actomyosin networks not only generate mechanical stresses but also respond to them, confounding our understanding of how mechanical stresses remodel cell-cell contacts. Here, we develop a two-point optical manipulation method to impose different stress patterns on cell-cell contacts in the early epithelium of the Drosophila embryo. The technique allows us to produce junction extension and shrinkage through different push and pull manipulations at the edges of junctions. We use these observations to expand classical vertex-based models of tissue mechanics, incorporating negative and positive mechanosensitive feedback depending on the type of remodeling. In particular, we show that Myosin-II activity responds to junction strain rate and facilitates full junction shrinkage. Altogether our work provides insight into how stress produces efficient deformation of cell-cell contacts in vivo and identifies unanticipated mechanosensitive features of their remodeling.

On a curved surface, epithelial cells can adapt to geometric constraints by tilting and by exchanging their neighbors from apical to basal sides, known as an apico-basal topological transition 1 (AB-T1). The relationship between cell tilt, AB-T1s, and tissue curvature still lacks a unified understanding. Here, we propose a general framework for cell packing in curved environments and explain the formation of AB-T1s from the perspective of strain anisotropy. We find that steep curvature gradients can lead to cell tilting and induce AB-T1s. Alternatively, pressure differences across the epithelial tissue can drive AB-T1s in regions of large curvature anisotropy. The two mechanisms compete to determine the impact of tissue geometry and mechanics on optimized cell rearrangements in three dimensions.

Biological cells can actively tune their intracellular architecture according to their overall shape. Here we explore the rheological implication of such coupling in a minimal model of a dense cellular material where each cell exerts an active mechanical stress along its axis of elongation. Increasing the active stress amplitude leads to several transitions. An initially hexagonal crystal motif is first destabilized into a solid with anisotropic cells whose shear modulus eventually vanishes at a first critical activity. Increasing activity beyond this first critical value, we find a re-entrant transition to a regime with finite hexatic order and finite shear modulus, in which cells arrange according to a rhombile pattern with periodically arranged rosette structures. The shear modulus vanishes again at a third threshold beyond which spontaneous tissue flows and topological defects of the nematic cell shape field arise. Flow and stress fields around the defects agree with active nematic theory, with either contractile or extensile signs, as also observed in several epithelial tissue experiments.

Epithelia act as a barrier against environmental stress and abrasion and in vivo they are continuously exposed to environments of various mechanical properties. The impact of this environment on epithelial integrity remains elusive. By culturing epithelial cells on 2D hydrogels, we observe a loss of epithelial monolayer integrity through spontaneous hole formation when grown on soft substrates. Substrate stiffness triggers an unanticipated mechanical switch of epithelial monolayers from tensile on soft to compressive on stiff substrates. Through active nematic modelling, we find that spontaneous half-integer defect formation underpinning large isotropic stress fluctuations initiate hole opening events. Our data show that monolayer rupture due to high tensile stress is promoted by the weakening of cell-cell junctions that could be induced by cell division events or local cellular stretching. Our results show that substrate stiffness provides feedback on monolayer mechanical state and that topological defects can trigger stochastic mechanical failure, with potential application towards a mechanistic understanding of compromised epithelial integrity during immune response and morphogenesis.

Cell monolayers are a central model system in the study of tissue biophysics. In vivo, epithelial tissues are curved on the scale of microns, and the curvature's role in the onset of spontaneous tissue flows is still not well understood. Here, we present a hydrodynamic theory for an apical-basal asymmetric active nematic gel on a curved strip. We show that surface curvature qualitatively changes monolayer motion compared with flat space: the resulting flows can be thresholdless, and the transition to motion may change from continuous to discontinuous. Surface curvature, friction, and active tractions are all shown to control the flow pattern selected, from simple shear to vortex chains.

Vertex models describe biological tissues as tilings of polygons. In standard vertex models, the tissue dynamics result from a balance between isotropic stresses, which are associated with the bulk of the cells, and tensions associated with cell-cell interfaces. However, in this framework it is less obvious how to describe anisotropic stresses arising from the bulk of cells. In epithelia, such bulk anisotropic stresses could arise for instance through medial myosin fluctuations. Two recent publications-Tlili et al. (Proc Natl Acad Sci USA 116(51):25430-25439, 2019) and Comelles et al. (eLife 10:e57730, 2021)-have proposed different schemes to implement bulk anisotropic stresses in vertex models. Here we show that while both schemes transform in the same way under affine deformations, they lead to significantly different tissue dynamics. Our results are consistent with the interpretation that the Tilli et al. scheme describes bulk stresses that are uniform within each cell, while the Comelles et al. scheme corresponds to non-uniform bulk stresses. Finally, we wondered whether a standard vertex model can be fully expressed in terms of bulk cellular stresses alone. We find that, in general, neither scheme can mimic the vertex forces created by cell-cell interface tensions., (© 2022. The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature.)

Background: Diagnosis of COVID-19 in symptomatic patients and screening of populations for SARS-CoV-2 infection require access to straightforward, low-cost and high-throughput testing. The recommended nasopharyngeal swab tests are limited by the need of trained professionals and specific consumables and this procedure is poorly accepted as a screening method In contrast, saliva sampling can be self-administered., Methods: In order to compare saliva and nasopharyngeal/oropharyngeal samples for the detection of SARS-CoV-2, we designed a meta-analysis searching in PubMed up to December 29th, 2020 with the key words "(SARS-CoV-2 OR COVID-19 OR COVID19) AND (salivary OR saliva OR oral fluid)) NOT (review[Publication Type]) NOT (PrePrint[Publication Type])" applying the following criteria: records published in peer reviewed scientific journals, in English, with at least 15 nasopharyngeal/orapharyngeal swabs and saliva paired samples tested by RT-PCR, studies with available raw data including numbers of positive and negative tests with the two sampling methods. For all studies, concordance and sensitivity were calculated and then pooled in a random-effects model., Findings: A total of 377 studies were retrieved, of which 50 were eligible, reporting on 16,473 pairs of nasopharyngeal/oropharyngeal and saliva samples. Meta-analysis showed high concordance, 92.5% (95%CI: 89.5-94.7), across studies and pooled sensitivities of 86.5% (95%CI: 83.4-89.1) and 92.0% (95%CI: 89.1-94.2) from saliva and nasopharyngeal/oropharyngeal swabs respectively. Heterogeneity across studies was 72.0% for saliva and 85.0% for nasopharyngeal/oropharyngeal swabs., Interpretation: Our meta-analysis strongly suggests that saliva could be used for frequent testing of COVID-19 patients and "en masse" screening of populations., Competing Interests: The authors have declared that no competing interests exist.

We propose an analysis and applications of sample pooling to the epidemiologic monitoring of COVID-19. We first introduce a model of the RT-qPCR process used to test for the presence of virus in a sample and construct a statistical model for the viral load in a typical infected individual inspired by large-scale clinical datasets. We present an application of group testing for the prevention of epidemic outbreak in closed connected communities. We then propose a method for the measure of the prevalence in a population taking into account the increased number of false negatives associated with the group testing method., Competing Interests: The authors have declared that no competing interests exist.

Dendrite morphology is necessary for the correct integration of inputs that neurons receive. The branching mechanisms allowing neurons to acquire their type-specific morphology remain unclear. Classically, axon and dendrite patterns were shown to be guided by molecules, providing deterministic cues. However, the extent to which deterministic and stochastic mechanisms, based upon purely statistical bias, contribute to the emergence of dendrite shape is largely unknown. We address this issue using the Drosophila class I vpda multi-dendritic neurons. Detailed quantitative analysis of vpda dendrite morphogenesis indicates that the primary branch grows very robustly in a fixed direction, though secondary branch numbers and lengths showed fluctuations characteristic of stochastic systems. Live-tracking dendrites and computational modeling revealed how neuron shape emerges from few local statistical parameters of branch dynamics. We report key opposing aspects of how tree architecture feedbacks on the local probability of branch shrinkage. Child branches promote stabilization of parent branches, although self-repulsion promotes shrinkage. Finally, we show that self-repulsion, mediated by the adhesion molecule Dscam1, indirectly patterns the growth of secondary branches by spatially restricting their direction of stable growth perpendicular to the primary branch. Thus, the stochastic nature of secondary branch dynamics and the existence of geometric feedback emphasize the importance of self-organization in neuronal dendrite morphogenesis., Competing Interests: Declaration of Interests The authors declare no competing interests., (Copyright © 2020 The Authors. Published by Elsevier Inc. All rights reserved.)

Cell-cell junctions, in particular adherens junctions, are major determinants of tissue mechanics during morphogenesis and homeostasis. In attempts to link junctional mechanics to tissue mechanics, many have utilized explicitly or implicitly equilibrium approaches based on adhesion energy, surface energy, and contractility to determine the mechanical equilibrium at junctions. However, it is increasingly clear that they have significant limitations, such as that it remains challenging to link the dynamics of the molecular components to the resulting physical properties of the junction, to its remodeling ability, and to its adhesion strength. In this perspective, we discuss recent attempts to consider the aspect of energy dissipation at junctions to draw contact points with soft matter physics where energy loss plays a critical role in adhesion theories. We set the grounds for a theoretical framework of the junction mechanics that bridges the dynamics at the molecular scale to the mechanics at the tissue scale., Competing Interests: Declaration of Interests The authors declare no competing interests., (Copyright © 2020 Elsevier Inc. All rights reserved.)

Apoptotic extrusion is crucial in maintaining epithelial homeostasis. Current literature supports that epithelia respond to extrusion by forming a supracellular actomyosin purse-string in the neighbors. However, whether other actin structures could contribute to extrusion and how forces generated by these structures can be integrated are unknown. Here, we found that during extrusion, a heterogeneous actin network composed of lamellipodia protrusions and discontinuous actomyosin cables, was reorganized in the neighboring cells. The early presence of basal lamellipodia protrusion participated in both basal sealing of the extrusion site and orienting the actomyosin purse-string. The co-existence of these two mechanisms is determined by the interplay between the cell-cell and cell-substrate adhesions. A theoretical model integrates these cellular mechanosensitive components to explain why a dual-mode mechanism, which combines lamellipodia protrusion and purse-string contractility, leads to more efficient extrusion than a single-mode mechanism. In this work, we provide mechanistic insight into extrusion, an essential epithelial homeostasis process.

During development, many mutations cause increased variation in phenotypic outcomes, a phenomenon termed decanalization. Phenotypic discordance is often observed in the absence of genetic and environmental variations, but the mechanisms underlying such inter-individual phenotypic discordance remain elusive. Here, using the anterior-posterior (AP) patterning of the Drosophila embryo, we identified embryonic geometry as a key factor predetermining patterning outcomes under decanalizing mutations. With the wild-type AP patterning network, we found that AP patterning is robust to variations in embryonic geometry; segmentation gene expression remains reproducible even when the embryo aspect ratio is artificially reduced by more than twofold. In contrast, embryonic geometry is highly predictive of individual patterning defects under decanalized conditions of either increased bicoid (bcd) dosage or bcd knockout. We showed that the phenotypic discordance can be traced back to variations in the gap gene expression, which is rendered sensitive to the geometry of the embryo under mutations., Competing Interests: AH, JR, TS No competing interests declared, (© 2020, Huang et al.)

The skin protects animals from infection and physical damage. In Caenorhabditis elegans, wounding the epidermis triggers an immune reaction and a repair response, but it is not clear how these are coordinated. Previous work implicated the microtubule cytoskeleton in the maintenance of epidermal integrity (Chuang et al., 2016). Here, by establishing a simple wounding system, we show that wounding provokes a reorganisation of plasma membrane subdomains. This is followed by recruitment of the microtubule plus end-binding protein EB1/EBP-2 around the wound and actin ring formation, dependent on ARP2/3 branched actin polymerisation. We show that microtubule dynamics are required for the recruitment and closure of the actin ring, and for the trafficking of the key signalling protein SLC6/SNF-12 toward the injury site. Without SNF-12 recruitment, there is an abrogation of the immune response. Our results suggest that microtubule dynamics coordinate the cytoskeletal changes required for wound repair and the concomitant activation of innate immunity., Competing Interests: CT, SO, CH, SM, MF, JR, JE, NP No competing interests declared, (© 2020, Taffoni et al.)

Organ formation is an inherently biophysical process, requiring large-scale tissue deformations. Yet, understanding how complex organ shape emerges during development remains a major challenge. During zebrafish embryogenesis, large muscle segments, called myotomes, acquire a characteristic chevron morphology, which is believed to aid swimming. Myotome shape can be altered by perturbing muscle cell differentiation or the interaction between myotomes and surrounding tissues during morphogenesis. To disentangle the mechanisms contributing to shape formation of the myotome, we combine single-cell resolution live imaging with quantitative image analysis and theoretical modeling. We find that, soon after segmentation from the presomitic mesoderm, the future myotome spreads across the underlying tissues. The mechanical coupling between the future myotome and the surrounding tissues appears to spatially vary, effectively resulting in spatially heterogeneous friction. Using a vertex model combined with experimental validation, we show that the interplay of tissue spreading and friction is sufficient to drive the initial phase of chevron shape formation. However, local anisotropic stresses, generated during muscle cell differentiation, are necessary to reach the acute angle of the chevron in wild-type embryos. Finally, tissue plasticity is required for formation and maintenance of the chevron shape, which is mediated by orientated cellular rearrangements. Our work sheds light on how a spatiotemporal sequence of local cellular events can have a nonlocal and irreversible mechanical impact at the tissue scale, leading to robust organ shaping., Competing Interests: The authors declare no competing interest., (Copyright © 2019 the Author(s). Published by PNAS.)

Cells sense the rigidity of their environment through localized pinching, which occurs when myosin molecular motors generate contractions within actin filaments anchoring the cell to its surroundings. We present high-resolution experiments performed on these elementary contractile units in cells. Our experimental results challenge the current understanding of molecular motor force generation. Surprisingly, bipolar myosin filaments generate much larger forces per motor than measured in single molecule experiments. Further, contraction to a fixed distance, followed by relaxation at the same rate, is observed over a wide range of matrix rigidities. Lastly, step-wise displacements of the matrix contacts are apparent during both contraction and relaxation. Building upon a generic two-state model of molecular motor collections, we interpret these unexpected observations as spontaneously emerging features of a collective motor behavior. Our approach explains why, in the cellular context, collections of resilient and slow motors contract in a stepwise fashion while collections of weak and fast motors do not. We thus rationalize the specificity of motor contractions implied in rigidity sensing compared to previous in vitro observations., Competing Interests: The authors declare no competing financial interests.

We investigate the effect of stress fluctuations on the stochastic dynamics of an inclusion embedded in a viscous gel. We show that, in nonequilibrium systems, stress fluctuations give rise to an effective attraction towards the boundaries of the confining domain, which is reminiscent of an active Casimir effect. We apply this generic result to the dynamics of deformations of the cell nucleus, and we demonstrate the appearance of a fluctuation maximum at a critical level of activity, in agreement with recent experiments [E. Makhija, D. S. Jokhun, and G. V. Shivashankar, Proc. Natl. Acad. Sci. U.S.A. 113, E32 (2016)PNASA60027-842410.1073/pnas.1513189113].

We study stochastic dynamics of a point and extended inclusion within a one-dimensional confined active viscoelastic gel. We show that the dynamics of a point inclusion can be described by a Langevin equation with a confining potential and multiplicative noise. Using a systematic adiabatic elimination over the fast variables, we arrive at an overdamped equation with a proper definition of the multiplicative noise. To highlight various features and to appeal to different biological contexts, we treat the inclusion in turn as a rigid extended element, an elastic element, and a viscoelastic (Kelvin-Voigt) element. The dynamics for the shape and position of the extended inclusion can be described by coupled Langevin equations. Deriving exact expressions for the corresponding steady-state probability distributions, we find that the active noise induces an attraction to the edges of the confining domain. In the presence of a competing centering force, we find that the shape of the probability distribution exhibits a sharp transition upon varying the amplitude of the active noise. Our results could help understanding the positioning and deformability of biological inclusions, e.g., organelles in cells, or nucleus and cells within tissues.

Organ and tissue formation are complex three-dimensional processes involving cell division, growth, migration, and rearrangement, all of which occur within physically constrained regions. However, analyzing such processes in three dimensions in vivo is challenging. Here, we focus on the process of cellularization in the anterior pole of the early Drosophila embryo to explore how cells compete for space under geometric constraints. Using microfluidics combined with fluorescence microscopy, we extract quantitative information on the three-dimensional epithelial cell morphology. We observed a cellular membrane rearrangement in which cells exchange neighbors along the apical-basal axis. Such apical-to-basal neighbor exchanges were observed more frequently in the anterior pole than in the embryo trunk. Furthermore, cells within the anterior pole skewed toward the trunk along their long axis relative to the embryo surface, with maximum skew on the ventral side. We constructed a vertex model for cells in a curved environment. We could reproduce the observed cellular skew in both wild-type embryos and embryos with distorted morphology. Further, such modeling showed that cell rearrangements were more likely in ellipsoidal, compared with cylindrical, geometry. Overall, we demonstrate that geometric constraints can influence three-dimensional cell morphology and packing within epithelial tissues., (© 2017 Rupprecht, Ong, Yin, et al. This article is distributed by The American Society for Cell Biology under license from the author(s). Two months after publication it is available to the public under an Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0).)

The applicability of widefield stochastic microscopy, such as PALM or STORM, is limited by their long acquisition times. Images are produced from the accumulation of a large number of frames that each contain a scarce number of super-resolved localizations. We show that the random and uneven distribution of localizations leads to a specific type of trade-off between the spatial and temporal resolutions. We derive analytical predictions for the minimal time required to obtain a reliable image at a given spatial resolution. We find that the image completion time scales logarithmically with the ratio of the image size to the spatial resolution volume, with second order corrections due to spurious localization within the background noise. We validate our predictions against experimental localization sequences of labeled microtubule filaments obtained by STORM. Our theoretical framework makes it possible to compare the efficiency of emitters, define optimal labeling strategies, and allow implementation of a stopping criterion for data acquisitions that can be performed using real-time monitoring algorithms.

We introduce and investigate the escape problem for random walkers that may eventually die, decay, bleach, or lose activity during their diffusion towards an escape or reactive region on the boundary of a confining domain. In the case of a first-order kinetics (i.e., exponentially distributed lifetimes), we study the effect of the associated death rate onto the survival probability, the exit probability, and the mean first passage time. We derive the upper and lower bounds and some approximations for these quantities. We reveal three asymptotic regimes of small, intermediate, and large death rates. General estimates and asymptotics are compared to several explicit solutions for simple domains and to numerical simulations. These results allow one to account for stochastic photobleaching of fluorescent tracers in bio-imaging, degradation of mRNA molecules in genetic translation mechanisms, or high mortality rates of spermatozoa in the fertilization process. Our findings provide a mathematical ground for optimizing storage containers and materials to reduce the risk of leakage of dangerous chemicals or nuclear wastes.

The run-and-tumble walk, consisting of randomly reoriented ballistic excursions, models phenomena ranging from gas kinetics to bacteria motility. We evaluate the mean time required for this walk to find a fixed target within a two- or three-dimensional spherical confinement. We find that the mean search time admits a minimum as a function of the mean run duration for various types of boundary conditions and run duration distributions (exponential, power-law, deterministic). Our result stands in sharp contrast to the pure ballistic motion, which is predicted to be the optimal search strategy in the case of Poisson-distributed targets.

Magnetotactic swimmers tend to align along magnetic field lines against stochastic reorientations. We show that the swimming strategy, e.g., active Brownian motion versus run-and-tumble dynamics, strongly affects the orientation statistics. The latter can exhibit a velocity condensation whereby the alignment probability density diverges. As a consequence, we find that the swimming strategy affects the nature of the phase transition to collective motion, indicating that Lévy run-and-tumble walks can outperform active Brownian processes as strategies to trigger collective behavior.

Cell movement has essential functions in development, immunity, and cancer. Various cell migration patterns have been reported, but no general rule has emerged so far. Here, we show on the basis of experimental data in vitro and in vivo that cell persistence, which quantifies the straightness of trajectories, is robustly coupled to cell migration speed. We suggest that this universal coupling constitutes a generic law of cell migration, which originates in the advection of polarity cues by an actin cytoskeleton undergoing flows at the cellular scale. Our analysis relies on a theoretical model that we validate by measuring the persistence of cells upon modulation of actin flow speeds and upon optogenetic manipulation of the binding of an actin regulator to actin filaments. Beyond the quantitative prediction of the coupling, the model yields a generic phase diagram of cellular trajectories, which recapitulates the full range of observed migration patterns., (Copyright © 2015 Elsevier Inc. All rights reserved.)

We present a wide-field microscopy technique for the 3D mapping of optical intensity distributions using Brownian gold nanopar-ticles as local probes, which are localized by off-axis holography. Fast computation methods allow us to localize hundreds of particles per minute with accuracies as good as 3 × 3 × 10nm³ for immobilized particles. Factors limiting this accuracy are discussed and the possibilities of the technique are illustrated through the 3D optical mapping of an evanescent and a propagative wave. Our results pave the way for a new stochastic imaging technique, well adapted to subwavelength optical characterization in water-based systems.

We present an exact expression for the mean exit time through the cap of a confining sphere for particles alternating phases of surface and of bulk diffusion. The present approach is based on an integral equation which can be solved analytically. In contrast to the statement of Berezhkovskii and Barzykin [J. Chem. Phys. 136, 54115 (2012)], we show that the mean exit time can be optimized with respect to the desorption rate, under analytically determined criteria.