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.

We track single toxin receptors on the apical cell membrane of MDCK cells with Eu-doped oxide nanoparticles coupled to two toxins of the pore-forming toxin family: α-toxin of Clostridium septicum and ε-toxin of Clostridium perfringens. These nonblinking and photostable labels do not perturb the motion of the toxin receptors and yield long uninterrupted trajectories with mean localization precision of 30 nm for acquisition times of 51.3 ms. We were thus able to study the toxin-cell interaction at the single-molecule level. Toxins bind to receptors that are confined within zones of mean area 0.40 ± 0.05 μm(2). Assuming that the receptors move according to the Langevin equation of motion and using Bayesian inference, we determined mean diffusion coefficients of 0.16 ± 0.01 μm(2)/s for both toxin receptors. Moreover, application of this approach revealed a force field within the domain generated by a springlike confining potential. Both toxin receptors were found to experience forces characterized by a mean spring constant of 0.30 ± 0.03 pN/μm at 37°C. Furthermore, both toxin receptors showed similar distributions of diffusion coefficient, domain area, and spring constant. Control experiments before and after incubation with cholesterol oxidase and sphingomyelinase show that these two enzymes disrupt the confinement domains and lead to quasi-free motion of the toxin receptors. Our control data showing cholesterol and sphingomyelin dependence as well as independence of actin depolymerization and microtubule disruption lead us to attribute the confinement of both receptors to lipid rafts. These toxins require oligomerization to develop their toxic activity. The confined nature of the toxin receptors leads to a local enhancement of the toxin monomer concentration and may thus explain the virulence of this toxin family.

Monitoring virus assembly at the nanoscale in host cells remains a major challenge. Human immunodeficiency virus type 1 (HIV-1) components are addressed to the plasma membrane where they assemble to form spherical particles of 100 nm in diameter. Interestingly, HIV-1 Gag protein expression alone is sufficient to produce virus-like particles (VLPs) that resemble the immature virus. Here, we monitored VLP formation at the plasma membrane of host CD4+ T cells using a newly developed workflow allowing the analysis of long duration recordings of single-molecule Gag protein localisation and movement. Comparison of Gag assembling platforms in CD4+ T cells expressing wild type or assembly-defective Gag mutant proteins showed that VLP formation lasts roughly 15 minutes with an assembly time of 5 minutes. Trapping energy maps, built from membrane associated Gag protein movements, showed that one third of the assembling energy is due to direct Gag capsid-capsid interaction while the remaining two thirds require the nucleocapsid-RNA interactions. Finally, we show that the viral RNA genome does not increase the attraction of Gag at the membrane towards the assembling site but rather acts as a spatiotemporal coordinator of the membrane assembly process.

We discuss search strategies for finding sources of particles transported in a random environment and detected by the searcher(s). The mixing of the particles in the environment is supposed to be strong, so that strategies based on concentration-gradient ascent are not viable. These dilute conditions are common in natural environments typical of searches performed by insects and birds. The sparseness of the detections constitutes the major stumbling block in developing efficient olfactory robots to detect mines, chemical leaks, etc. We first discuss a search strategy, ‘infotaxis’, recently introduced for the search of a single source by a single robot. Decisions are made by locally maximizing the rate of acquisition of information on the location of the source and they balance exploration and exploitation. We present numerical simulations demonstrating the efficiency of the method and, most importantly, its robustness to lack of detailed modeling of the transport of particles in the random environment. We then introduce a novel formulation of infotaxis for collective searches where a swarm of robots is available and must be coordinated. Gains in the search time are impressive and the method can be further generalized to deal with conflicts arising in the identification of multiple sources.

Summary Neural stem cell (NSC) populations persist in the adult vertebrate brain over a lifetime, and their homeostasis is controlled at the population level through unknown mechanisms. Here, we combine dynamic imaging of entire NSC populations in their in vivo niche over several weeks with pharmacological manipulations, mathematical modeling, and spatial statistics and demonstrate that NSCs use spatiotemporally resolved local feedback signals to coordinate their decision to divide in adult zebrafish brains. These involve Notch-mediated short-range inhibition from transient neural progenitors and a dispersion effect from the dividing NSCs themselves exerted with a delay of 9–12 days. Simulations from a stochastic NSC lattice model capturing these interactions demonstrate that these signals are linked by lineage progression and control the spatiotemporal distribution of output neurons. These results highlight how local and temporally delayed interactions occurring between brain germinal cells generate self-propagating dynamics that maintain NSC population homeostasis and coordinate specific spatiotemporal correlations.

Various insects and small animals can navigate in turbulent streams to find their mates (or food) from sparse pheromone (odor) detections. Their access to internal space perception and use of cognitive maps still are heavily debated, but for some of them, limited space perception seems to be the rule. However, this poor space perception does not prevent them from impressive search capacities. Here, as an attempt to model these behaviors, we propose a scheme that can perform, even without a detailed internal space map, searches in turbulent streams. The algorithm is based on a standardized projection of the probability of the source position to remove space perception and on the evaluation of a free energy, whose minimization along the path gives direction to the searcher. An internal "temperature" allows active control of the exploration/exploitation balance during the search. We demonstrate the efficiency of the scheme numerically, with a computational model of odor plume propagation, and experimentally, with robotic searches of thermal sources in turbulent streams. In addition to being a model to describe animals' searches, this scheme may be applied to robotic searches in complex varying media without odometry error corrections and in problems in which active control of the exploration/exploitation balance is profitable.biological search | plume tracking | search algorithm T he survival of insects and animals depends on their ability to search and reach for food and mate from the various emitted chemicals in complex varying environments. It is very likely that evolution, regarding search strategies, acted not only on the statistics of different modes of space exploration (1-6) (e.g., generalized levy processes) but also actively on the decision process in relation to the time evolving detected signals. However, a limited number of models tackle with deciphering the information of the signal transported in the environment.Considering search schemes from the signal deciphering point of view shifts the modeling process toward a mix of information, game, and optimal control theory. Hence, a key part of the reasoning is focused on how evolution selected a balance between exploitation of the information accumulated during the search and exploration of the environment (7,8). Among the schemes that are intended to deal with the randomness induced by turbulence and that directly address the exploration/exploitation balance, infotaxis is the most efficient (9-11), i.e., the one exhibiting the lowest average search time and the highest reliability in source reaching. The two key elements of infotaxis are the knowledge by the searcher of both the rate of detection function and the statistics of detection, to infer the probability map of the source position, and the use of entropy as a function to be greedily minimized along the path chosen by the searcher. Infotaxis is robust to various sources of noise, with optimal search efficiency when the model in infotaxis matches the environmental dynamics. However, for an animal,...

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