Actin flows mediate a universal coupling between cell speed and cell persistence.

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.

Tracer Diffusion beyond Gaussian Behavior: Explicit Results for General Single-File Systems.

Single-file systems, in which particles diffuse in narrow channels while not overtaking each other, is a fundamental model for the tracer subdiffusion observed in confined geometries, such as in zeolites or carbon nanotubes. Twenty years ago, the mean squared displacement of a tracer was determined at large times, for any diffusive single-file system. Since then, for a general single-file system, even the determination of the fourth cumulant, which probes the deviation from Gaussianity, has remained an open question. Here, we fill this gap and provide an explicit formula for the fourth cumulant of an arbitrary single-file system. Our approach also allows us to quantify the perturbation induced by the tracer on its environment, encoded in the correlation profiles. These explicit results constitute a first step towards obtaining a closed equation for the correlation profiles for arbitrary single-file systems.

From Maximum of Inter-Visit Times to Starving Random Walks.

Very recently, a fundamental observable has been introduced and analyzed to quantify the exploration of random walks: the time τ_{k} required for a random walk to find a site that it never visited previously, when the walk has already visited k distinct sites. Here, we tackle the natural issue of the statistics of M_{n}, the longest duration out of τ_{0},…,τ_{n-1}. This problem belongs to the active field of extreme value statistics, with the difficulty that the random variables τ_{k} are both correlated and nonidentically distributed. Beyond this fundamental aspect, we show that the asymptotic determination of the statistics of M_{n} finds explicit applications in foraging theory and allows us to solve the open d-dimensional starving random walk problem, in which each site of a lattice initially contains one food unit, consumed upon visit by the random walker, which can travel S steps without food before starving. Processes of diverse nature, including regular diffusion, anomalous diffusion, and diffusion in disordered media and fractals, share common properties within the same universality classes.

From Particle Currents to Tracer Diffusion: Universal Correlation Profiles in Single-File Dynamics.

Single-file transport refers to the motion of particles in a narrow channel, such that they cannot bypass each other. This constraint leads to strong correlations between the particles, described by correlation profiles, which measure the correlation between a generic observable and the density of particles at a given position and time. They have recently been shown to play a central role in single-file systems. Up to now, these correlations have only been determined for diffusive systems in the hydrodynamic limit. Here, we consider a model of reflecting point particles on the infinite line, with a general individual stochastic dynamics. We show that the correlation profiles take a simple universal form, at arbitrary time. We illustrate our approach by the study of the integrated current of particles through the origin, and apply our results to representative models such as Brownian particles, run-and-tumble particles and Lévy flights. We further emphasise the generality of our results by showing that they also apply beyond the 1D case, and to other observables.

Absolute Negative Mobility of an Active Tracer in a Crowded Environment.

Absolute negative mobility (ANM) refers to the situation where the average velocity of a driven tracer is opposite to the direction of the driving force. This effect was evidenced in different models of nonequilibrium transport in complex environments, whose description remains effective. Here, we provide a microscopic theory for this phenomenon. We show that it emerges in the model of an active tracer particle submitted to an external force and which evolves on a discrete lattice populated with mobile passive crowders. Resorting to a decoupling approximation, we compute analytically the velocity of the tracer particle as a function of the different parameters of the system and confront our results to numerical simulations. We determine the range of parameters where ANM can be observed, characterize the response of the environment to the displacement of the tracer, and clarify the mechanism underlying ANM and its relationship with negative differential mobility (another hallmark of driven systems far from the linear response).

Driven Tracer in the Symmetric Exclusion Process: Linear Response and Beyond.

Tracer dynamics in the symmetric exclusion process (SEP), where hard-core particles diffuse on an infinite one-dimensional lattice, is a paradigmatic model of anomalous diffusion. While the equilibrium situation has received a lot of attention, the case where the tracer is driven by an external force, which provides a minimal model of nonequilibrium transport in confined crowded environments, remains largely unexplored. Indeed, the only available analytical results concern the means of both the position of the tracer and the lattice occupation numbers in its frame of reference and higher-order moments but only in the high-density limit. Here, we provide a general hydrodynamic framework that allows us to determine the first cumulants of the bath-tracer correlations and of the tracer's position in function of the driving force, up to quadratic order (beyond linear response). This result constitutes the first determination of the bias dependence of the variance of a driven tracer in the SEP for an arbitrary density. The framework presented here can be applied, beyond the SEP, to more general configurations of a driven tracer in interaction with obstacles in one dimension.

Microscopic Theory for the Diffusion of an Active Particle in a Crowded Environment.

We calculate the diffusion coefficient of an active tracer in a schematic crowded environment, represented as a lattice gas of passive particles with hardcore interactions. Starting from the master equation of the problem, we put forward a closure approximation that goes beyond trivial mean field and provides the diffusion coefficient for an arbitrary density of crowders in the system. We show that our approximation is accurate for a very wide range of parameters, and that it correctly captures numerous nonequilibrium effects, which are the signature of the activity in the system. In addition to the determination of the diffusion coefficient of the tracer, our approach allows us to characterize the perturbation of the environment induced by the displacement of the active tracer. Finally, we consider the asymptotic regimes of low and high densities, in which the expression of the diffusion coefficient of the tracer becomes explicit, and which we argue to be exact.

Generalized Correlation Profiles in Single-File Systems.

Single-file diffusion refers to the motion in narrow channels of particles which cannot bypass each other, and leads to tracer subdiffusion. Most approaches to this celebrated many-body problem were restricted to the description of the tracer only. Here, we go beyond this standard description by introducing and providing analytical results for generalized correlation profiles (GCPs) in the frame of the tracer. In addition to controlling the statistical properties of the tracer, these quantities fully characterize the correlations between the tracer position and the bath particles density. Considering the hydrodynamic limit of the problem, we determine the scaling form of the GCPs with space and time, and unveil a nonmonotonic dependence with the distance to the tracer despite the absence of any asymmetry. Our analytical approach provides several exact results for the GCPs for paradigmatic models of single-file diffusion, such as Brownian particles with hardcore repulsion, the symmetric exclusion process and the random average process. The range of applicability of our approach is further illustrated by considering (i) extensions to general interactions between particles, (ii) the out-of-equilibrium situation of an initial step of density, and (iii) beyond the hydrodynamic limit, the GCPs at arbitrary time in the dense limit.

Universality Classes of Hitting Probabilities of Jump Processes.

Quantifying the efficiency of random target search strategies is a key question of random walk theory, with applications in various fields. If many results do exist for recurrent processes, for which the probability of eventually finding a target in infinite space-so called hitting probability-is one, much less is known in the opposite case of transient processes, for which the hitting probability is strictly less than one. Here, we determine the universality classes of the large distance behavior of the hitting probability for general d-dimensional transient jump processes, which we show are parametrized by a transience exponent that is explicitly given.

Inverse Square Lévy Walks are not Optimal Search Strategies for d≥2.

The Lévy hypothesis states that inverse square Lévy walks are optimal search strategies because they maximize the encounter rate with sparse, randomly distributed, replenishable targets. It has served as a theoretical basis to interpret a wealth of experimental data at various scales, from molecular motors to animals looking for resources, putting forward the conclusion that many living organisms perform Lévy walks to explore space because of their optimal efficiency. Here we provide analytically the dependence on target density of the encounter rate of Lévy walks for any space dimension d; in particular, this scaling is shown to be independent of the Lévy exponent α for the biologically relevant case d≥2, which proves that the founding result of the Lévy hypothesis is incorrect. As a consequence, we show that optimizing the encounter rate with respect to α is irrelevant: it does not change the scaling with density and can lead virtually to any optimal value of α depending on system dependent modeling choices. The conclusion that observed inverse square Lévy patterns are the result of a common selection process based purely on the kinetics of the search behavior is therefore unfounded.

Ixekizumab improves patient-reported outcomes in patients with active psoriatic arthritis and inadequate response to tumour necrosis factor inhibitors: SPIRIT-P2 results to 52 weeks.

OBJECTIVES: To report patient-reported outcomes (PROs) of ixekizumab-treated patients with psoriatic arthritis (PsA) and an inadequate response (IR) or intolerance to tumour necrosis factor inhibitors (TNFi) to 52 weeks. METHODS: In SPIRIT-P2, patients with active PsA and an IR or intolerance to TNFi were randomised to ixekizumab 80 mg every 4 weeks (IXEQ4W; N=122) or every 2 weeks (IXEQ2W; N=123), or placebo (PBO; N=118) during the initial 24-week double-blind treatment period. At Week 16, background therapy was modified for IRs; additionally, IRs in the placebo group were re-randomised (1:1) to IXEQ2W or IXEQ4W. Patients receiving ixekizumab at Week 24 received the same dose during the study remainder. Patients completed several PROs for PsA disease activity, skin, health-related quality of life (HRQOL, and work through Week 52. RESULTS: Ixekizumab-treated patients reported significant improvements versus PBO in 36-Item Short Form Health Survey version 2, European Quality of Life 5 Dimensions visual analogue scale, Bath Ankylosing Spondylitis Disease Activity Index (total score and question 2), and Work Productivity and Activity Impairment Questionnaire-Specific Health Problem (3 of 4 domains) through Week 24. At Week 24, 9% (PBO), 52% (IXEQ4W), and 50% (IXEQ2W) of patients reported Dermatology Life Quality Index scores of 0 or 1; 0% (PBO) and 24% (IXEQ4W and IXEQ2W) reported Itch Numeric Rating Scale score of 0. Where data were collected, improvements persisted through Week 52. CONCLUSIONS: In patients with PsA and an IR or intolerance to TNFi, ixekizumab significantly improved disease activity, skin symptoms, HRQOL, and work productivity to 52 weeks.

Superionic liquids in conducting nanoslits: A variety of phase transitions and ensuing charging behavior.

We develop a theory of charge storage in ultranarrow slitlike pores of nanostructured electrodes. Our analysis is based on the Blume-Capel model in an external field, which we solve analytically on a Bethe lattice. The obtained solutions allow us to explore the complete phase diagram of confined ionic liquids in terms of the key parameters characterizing the system, such as pore ionophilicity, interionic interaction energy, and voltage. The phase diagram includes the lines of first- and second-order, direct and re-entrant phase transitions, which are manifested by singularities in the corresponding capacitance-voltage plots. Testing our predictions experimentally requires monodisperse, conducting ultranarrow slit pores, to permit only one layer of ions, and thick pore walls, to prevent interionic interactions across the pore walls. However, some qualitative features, which distinguish the behavior of ionophilic and ionophobic pores and their underlying physics, may emerge in future experimental studies of more complex electrode structures.

Unbinding Transition of Probes in Single-File Systems.

Single-file transport, arising in quasi-one-dimensional geometries where particles cannot pass each other, is characterized by the anomalous dynamics of a probe, notably its response to an external force. In these systems, the motion of several probes submitted to different external forces, although relevant to mixtures of charged and neutral or active and passive objects, remains unexplored. Here, we determine how several probes respond to external forces. We rely on a hydrodynamic description of the symmetric exclusion process to obtain exact analytical results at long times. We show that the probes can either move as a whole, or separate into two groups moving away from each other. In between the two regimes, they separate with a different dynamical exponent, as t^{1/4}. This unbinding transition also occurs in several continuous single-file systems and is expected to be observable.

Nonequilibrium Fluctuations and Enhanced Diffusion of a Driven Particle in a Dense Environment.

We study the diffusion of a tracer particle driven out of equilibrium by an external force and traveling in a dense environment of arbitrary density. The system evolves on a discrete lattice and its stochastic dynamics is described by a master equation. Relying on a decoupling approximation that goes beyond the naive mean-field treatment of the problem, we calculate the fluctuations of the position of the tracer around its mean value on a lattice of arbitrary dimension, and with different boundary conditions. We reveal intrinsically nonequilibrium effects, such as enhanced diffusivity of the tracer induced by both the crowding interactions and the external driving. We finally consider the high-density and low-density limits of the model and show that our approximation scheme becomes exact in these limits.

Optimized Diffusion of Run-and-Tumble Particles in Crowded Environments.

We study the transport of self-propelled particles in dynamic complex environments. To obtain exact results, we introduce a model of run-and-tumble particles (RTPs) moving in discrete time on a d-dimensional cubic lattice in the presence of diffusing hard-core obstacles. We derive an explicit expression for the diffusivity of the RTP, which is exact in the limit of low density of fixed obstacles. To do so, we introduce a generalization of Kac's theorem on the mean return times of Markov processes, which we expect to be relevant for a large class of lattice gas problems. Our results show the diffusivity of RTPs to be nonmonotonic in the tumbling probability for low enough obstacle mobility. These results prove the potential for the optimization of the transport of RTPs in crowded and disordered environments with applications to motile artificial and biological systems.

Universal Long Ranged Correlations in Driven Binary Mixtures.

When two populations of "particles" move in opposite directions, like oppositely charged colloids under an electric field or intersecting flows of pedestrians, they can move collectively, forming lanes along their direction of motion. The nature of this "laning transition" is still being debated and, in particular, the pair correlation functions, which are the key observables to quantify this phenomenon, have not been characterized yet. Here, we determine the correlations using an analytical approach based on a linearization of the stochastic equations for the density fields, which is valid for dense systems of soft particles. We find that the correlations decay algebraically along the direction of motion, and have a self-similar exponential profile in the transverse direction. Brownian dynamics simulations confirm our theoretical predictions and show that they also hold beyond the validity range of our analytical approach, pointing to a universal behavior.

Cooperative behavior of biased probes in crowded interacting systems.

We study, via extensive numerical simulations, dynamics of a crowded mixture of mutually interacting (with a short-range repulsive potential) colloidal particles immersed in a suspending solvent, acting as a heat bath. The mixture consists of a majority component - neutrally buoyant colloids subject to internal stimuli only, and a minority component - biased probes (BPs) also subject to a constant force. In such a system each of the BPs alters the distribution of the colloidal particles in its vicinity, driving their spatial distribution out of equilibrium. This induces effective long-range interactions and multi-tag correlations between the BPs, mediated by an out-of-equilibrium majority component, and prompts the BPs to move collectively assembling in clusters. We analyse the size-distribution of the self-assembling clusters in the steady-state, their specific force-velocity relations and also properties of the effective interactions emerging between the BPs.

Temporal Correlations of the Running Maximum of a Brownian Trajectory.

We study the correlations between the maxima m and M of a Brownian motion (BM) on the time intervals [0,t_{1}] and [0,t_{2}], with t_{2}>t_{1}. We determine the exact forms of the distribution functions P(m,M) and P(G=M-m), and calculate the moments E{(M-m)^{k}} and the cross-moments E{m^{l}M^{k}} with arbitrary integers l and k. We show that correlations between m and M decay as sqrt[t_{1}/t_{2}] when t_{2}/t_{1}→∞, revealing strong memory effects in the statistics of the BM maxima. We also compute the Pearson correlation coefficient ρ(m,M) and the power spectrum of M_{t}, and we discuss a possibility of extracting the ensemble-averaged diffusion coefficient in single-trajectory experiments using a single realization of the maximum process.

Rationale for Strengthening Muscle to Prevent Falls and Fractures: A Review of the Evidence.

Falls represent a major public health problem in older people, predominantly due to the resulting injuries which lead to progressive disability, immobilization and resulting comorbidities, dependency, institutionalization, and death. Reduced muscle strength and power have been consistently identified as risk factors for falls and related injuries, and it is likely these associations result from the central role played by reduced muscle strength and power in poor balance recovery. In addition, muscle strength and power are involved with protective responses that reduce the risk of an injury if a fall occurs. Progressive resistance training (PRT) is the standard way to increase muscle strength and power, and this training forms one of the main components of fall prevention exercise interventions. However, PRT has rarely been implemented in routine practice due to multiple challenges inherent to frail older people. The ongoing development of drugs expected to increase muscle power offers a new opportunity to reduce the risk of falls and fall-related injuries. The intent here is not to replace exercise training with drugs but rather to offer a pharmacologic alternative when exercise is not possible or contraindicated. The target population would be those most likely to benefit from this mechanism of action, i.e., weak older people without major causes for falls independent of muscle weakness. Provided such a tailored strategy was followed, a muscle anabolic may address this major unmet need.