Electric Fields in Liquid Water Irradiated with Protons at Ultrahigh Dose Rates.

We study the effects of irradiating water with 3 MeV protons at high doses by observing the motion of charged polystyrene beads outside the proton beam. By single-particle tracking, we measure a radial velocity of the order of microns per second. Combining electrokinetic theory with simulations of the beam-generated reaction products and their outward diffusion, we find that the bead motion is due to electrophoresis in the electric field induced by the mobility contrast of cations and anions. This work sheds light on the perturbation of biological systems by high-dose radiations and paves the way for the manipulation of colloid or macromolecular dispersions by radiation-induced diffusiophoresis.

Simultaneous speciation analysis of Hg and Se in fish by high-performance liquid chromatography and inductively coupled plasma-mass spectrometry following microwave-assisted enzymatic hydrolysis.

This study reports the development and validation of a new analytical method for simultaneous speciation analysis of Se and Hg in fish muscle. For this purpose, four Se species (selenite/Se(IV), selenate/Se(VI), selenomethionine/SeMet, and selenocysteine/SeCys) and two Hg species (inorganic mercury/iHg and methylmercury/MeHg) were extracted simultaneously by microwave-assisted enzymatic hydrolysis and then separated by HPLC in less than 15 min by using a column with both anion and cation exchange mechanisms and a mobile phase consisting of a mixture of methanol 5% (v/v), 45 mM HNO3, 0.015% 2-mercaptoethanol, and 1.5 mM sodium 3-mercapto-1-propanesulfonate. The separated species of Hg and Se were detected online by inductively coupled plasma-mass spectrometry (ICP-MS). The speciation analysis method was validated by means of the accuracy profile approach by carrying out three series of measurements in duplicate on three different days over a time-span of 3 weeks. The limits of quantification (LOQ) are in the range of 0.010-0.013 mg/kg wet weight (ww) for all selenium species, except for Se(IV) (0.15 mg/kg ww), while the coefficient of variation in terms of intermediate reproducibility (CVR) was < 7%. The LOQ for MeHg was 0.006 mg/kg ww, while the CVR was 3%. The method was successfully applied to the analysis of muscle samples from four different fish species: rainbow trout, tuna, swordfish, and dogfish.

How Stickiness Can Speed Up Diffusion in Confined Systems.

The paradigmatic model for heterogeneous media used in diffusion studies is built from reflecting obstacles and surfaces. It is well known that the crowding effect produced by these reflecting surfaces slows the dispersion of Brownian tracers. Here, using a general adsorption desorption model with surface diffusion, we show analytically that making surfaces or obstacles attractive can accelerate dispersion. In particular, we show that this enhancement of diffusion can exist even when the surface diffusion constant is smaller than that in the bulk. Even more remarkably, this enhancement effect occurs when the effective diffusion constant, when restricted to surfaces only, is lower than the effective diffusivity with purely reflecting boundaries. We give analytical formulas for this intriguing effect in periodic arrays of spheres as well as undulating microchannels. Our results are confirmed by numerical calculations and Monte Carlo simulations.

Mean first-passage times of non-Markovian random walkers in confinement.

The first-passage time, defined as the time a random walker takes to reach a target point in a confining domain, is a key quantity in the theory of stochastic processes. Its importance comes from its crucial role in quantifying the efficiency of processes as varied as diffusion-limited reactions, target search processes or the spread of diseases. Most methods of determining the properties of first-passage time in confined domains have been limited to Markovian (memoryless) processes. However, as soon as the random walker interacts with its environment, memory effects cannot be neglected: that is, the future motion of the random walker does not depend only on its current position, but also on its past trajectory. Examples of non-Markovian dynamics include single-file diffusion in narrow channels, or the motion of a tracer particle either attached to a polymeric chain or diffusing in simple or complex fluids such as nematics, dense soft colloids or viscoelastic solutions. Here we introduce an analytical approach to calculate, in the limit of a large confining volume, the mean first-passage time of a Gaussian non-Markovian random walker to a target. The non-Markovian features of the dynamics are encompassed by determining the statistical properties of the fictitious trajectory that the random walker would follow after the first-passage event takes place, which are shown to govern the first-passage time kinetics. This analysis is applicable to a broad range of stochastic processes, which may be correlated at long times. Our theoretical predictions are confirmed by numerical simulations for several examples of non-Markovian processes, including the case of fractional Brownian motion in one and higher dimensions. These results reveal, on the basis of Gaussian processes, the importance of memory effects in first-passage statistics of non-Markovian random walkers in confinement.

Effective diffusivity of Brownian particles in a two dimensional square lattice of hard disks.

We revisit the classic problem of the effective diffusion constant of a Brownian particle in a square lattice of reflecting impenetrable hard disks. This diffusion constant is also related to the effective conductivity of non-conducting and infinitely conductive disks in the same geometry. We show how a recently derived Green's function for the periodic lattice can be exploited to derive a series expansion of the diffusion constant in terms of the disk's volume fraction φ. Second, we propose a variant of the Fick-Jacobs approximation to study the large volume fraction limit. This combination of analytical results is shown to describe the behavior of the diffusion constant for all volume fractions.

Conical Interfaces between Two Immiscible Fluids Induced by an Optical Laser Beam.

We demonstrate the existence of conical interface deformations induced by a laser beam that are similar to Taylor cones in the electrical regime. We show that the cone morphology can be manipulated by fluid and laser parameters. A theory is proposed to quantitatively describe these dependences in good agreement with experimental data obtained for different fluid systems with low interfacial tensions. Counterintuitively, the cone angle is proved to be independent of the refractive index contrast at leading order. These results open a new optofluidic route towards optical spraying technology-an analogue of electrospraying-and more generally for the optical shaping of interfaces.

Boundaries Control Collective Dynamics of Inertial Self-Propelled Robots.

Simple ingredients, such as well-defined interactions and couplings for the velocity and orientation of self-propelled objects, are sufficient to produce complex collective behavior in assemblies of such entities. Here, we use assemblies of rodlike robots made motile through self-vibration. When confined in circular arenas, dilute assemblies of these rods act as a gas. Increasing the surface fraction leads to a collective behavior near the boundaries: polar clusters emerge while, in the bulk, gaslike behavior is retained. The coexistence between a gas and surface clusters is a direct consequence of inertial effects as shown by our simulations. A theoretical model, based on surface mediated transport accounts for this coexistence and illustrates the exact role of the boundaries. Our study paves the way towards the control of collective behavior: By using deformable but free to move arenas, we demonstrate that the surface induced clusters can lead to directed motion, while the topology of the surface states can be controlled by biasing the motility of the particles.

Dispersion in two-dimensional periodic channels with discontinuous profiles.

The effective diffusivity of Brownian tracer particles confined in periodic micro-channels is smaller than the microscopic diffusivity due to entropic trapping. Here, we study diffusion in two-dimensional periodic channels whose cross section presents singular points, such as abrupt changes of radius or the presence of thin walls, with openings, delimiting periodic compartments composing the channel. Dispersion in such systems is analyzed using the Fick-Jacobs (FJ) approximation. This approximation assumes a much faster equilibration in the lateral than in the axial direction, along which the dispersion is measured. If the characteristic width a of the channel is much smaller than the period L of the channel, i.e., ε = a/L is small, this assumption is clearly valid for Brownian particles. For discontinuous channels, the FJ approximation is only valid at the lowest order in ε and provides a rough, though on occasions rather accurate, estimate of the effective diffusivity. Here we provide formulas for the effective diffusivity in discontinuous channels that are asymptotically exact at the next-to-leading order in ε. Each discontinuity leads to a reduction of the effective diffusivity. We show that our theory is consistent with the picture of effective trapping rates associated with each discontinuity, for which our theory provides explicit and asymptotically exact formulas. Our analytical predictions are confirmed by numerical analysis. Our results provide a precise quantification of the kinetic entropic barriers associated with profile singularities.

Force-Induced Dispersion in Heterogeneous Media.

The effect of a constant applied external force, induced for instance by an electric or gravitational field, on the dispersion of Brownian particles in periodic media with spatially varying diffusivity, and thus mobility, is studied. We show that external forces can greatly enhance dispersion in the direction of the applied force and also modify, to a lesser extent and in some cases nonmonotonically, dispersion perpendicular to the applied force. Our results thus open up the intriguing possibility of modulating the dispersive properties of heterogeneous media by using externally applied force fields. These results are obtained via a Kubo formula that can be applied to any periodic advection diffusion system in any spatial dimension.

Non-Markovian closure kinetics of flexible polymers with hydrodynamic interactions.

This paper presents a theoretical analysis of the closure kinetics of a polymer with hydrodynamic interactions. This analysis, which takes into account the non-Markovian dynamics of the end-to-end vector and relies on the preaveraging of the mobility tensor (Zimm dynamics), is shown to reproduce very accurately the results of numerical simulations of the complete nonlinear dynamics. It is found that Markovian treatments based on a Wilemski-Fixman approximation significantly overestimate cyclization times (up to a factor 2), showing the importance of memory effects in the dynamics. In addition, this analysis provides scaling laws of the mean first cyclization time (MFCT) with the polymer size N and capture radius b, which are identical in both Markovian and non-Markovian approaches. In particular, it is found that the scaling of the MFCT for large N is given by T ∼ N(3/2)ln(N/b(2)), which differs from the case of the Rouse dynamics where T ∼ N(2). The extension to the case of the reaction kinetics of a monomer of a Zimm polymer with an external target in a confined volume is also presented.

Long-term memory induced correction to Arrhenius law.

The Kramers escape problem is a paradigmatic model for the kinetics of rare events, which are usually characterized by Arrhenius law. So far, analytical approaches have failed to capture the kinetics of rare events in the important case of non-Markovian processes with long-term memory, as occurs in the context of reactions involving proteins, long polymers, or strongly viscoelastic fluids. Here, based on a minimal model of non-Markovian Gaussian process with long-term memory, we determine quantitatively the mean FPT to a rare configuration and provide its asymptotics in the limit of a large energy barrier E. Our analysis unveils a correction to Arrhenius law, induced by long-term memory, which we determine analytically. This correction, which we show can be quantitatively significant, takes the form of a second effective energy barrier E ' < E and captures the dependence of rare event kinetics on initial conditions, which is a hallmark of long-term memory. Altogether, our results quantify the impact of long-term memory on rare event kinetics, beyond Arrhenius law.

Reactive conformations and non-Markovian cyclization kinetics of a Rouse polymer.

We investigate theoretically the physics of diffusion-limited intramolecular polymer reactions. The present work completes and goes beyond a previous study [T. Guérin, O. Bénichou, and R. Voituriez, Nat. Chem. 4, 568 (2012)] that showed that the distribution of the polymer conformations at the very instant of reaction plays a key role in the cyclization kinetics, and takes explicitly into account the non-Markovian nature of the reactant motion. Here, we present in detail this non-Markovian theory, and compare it explicitly with existing Markovian theories and with numerical stochastic simulations. A large focus is made on the description of the non-equilibrium reactive conformations, with both numerical and analytical tools. We show that the reactive conformations are elongated and are characterized by a spectrum with a slowly decreasing tail, implying that the monomers that neighbor the reactive monomers are significantly shifted at the instant of reaction. We complete the study by deriving explicit formulas for the reaction rates in the Markovian Wilemski-Fixman theory when the reactants are located in arbitrary positions in the chain. We also give a simple scaling argument to understand the existence of two regimes in the reaction time, that come from two possible behaviors of monomer motion, which can be either diffusive or subdiffusive.

Imperfect narrow escape problem.

We consider the kinetics of the imperfect narrow escape problem, i.e., the time it takes for a particle diffusing in a confined medium of generic shape to reach and to be adsorbed by a small, imperfectly reactive patch embedded in the boundary of the domain, in two or three dimensions. Imperfect reactivity is modeled by an intrinsic surface reactivity κ of the patch, giving rise to Robin boundary conditions. We present a formalism to calculate the exact asymptotics of the mean reaction time in the limit of large volume of the confining domain. We obtain exact explicit results in the two limits of large and small reactivities of the reactive patch, and a semianalytical expression in the general case. Our approach reveals an anomalous scaling of the mean reaction time as the inverse square root of the reactivity in the large-reactivity limit, valid for an initial position near the extremity of the reactive patch. We compare our exact results with those obtained within the "constant flux approximation"; we show that this approximation turns out to give exactly the next-to-leading-order term of the small-reactivity limit, and provides a good approximation of the reaction time far from the reactive patch for all reactivities, but not in the vicinity of the boundary of the reactive patch due to the above-mentioned anomalous scaling. These results thus provide a general framework to quantify the mean reaction times for the imperfect narrow escape problem.

Everlasting impact of initial perturbations on first-passage times of non-Markovian random walks.

Persistence, defined as the probability that a signal has not reached a threshold up to a given observation time, plays a crucial role in the theory of random processes. Often, persistence decays algebraically with time with non trivial exponents. However, general analytical methods to calculate persistence exponents cannot be applied to the ubiquitous case of non-Markovian systems relaxing transiently after an imposed initial perturbation. Here, we introduce a theoretical framework that enables the non-perturbative determination of persistence exponents of Gaussian non-Markovian processes with non stationary dynamics relaxing to a steady state after an initial perturbation. Two situations are analyzed: either the system is subjected to a temperature quench at initial time, or its past trajectory is assumed to have been observed and thus known. Our theory covers the case of spatial dimension higher than one, opening the way to characterize non-trivial reaction kinetics for complex systems with non-equilibrium initial conditions.

Assessment of the mercury-selenium antagonism in rainbow trout fish.

This study aims at the assessment of mercury (Hg)-selenium (Se) antagonism in fish. For this purpose, rainbow trout fish (Oncorhynchus mykiss) were exposed to methylmercury (MeHg) under controlled conditions, in the presence or absence of selenomethionine (SeMet) using an in-house prepared diet (enriched with MeHg and SeMet at 0.2 µg/g and 5.0 µg/g, respectively). The total duration of the exposure study was 3 months. Fish was sampled and analysed for total Se (SeT) and total mercury (HgT) content after 1, 2 and 3 months of exposure. Six feeding protocols were compared, depending on the exposure type: (i) no MeHg nor SeMet exposure (control group); (ii) exposure to SeMet solely; (iii) exposure to MeHg solely; (iv) exposure to both MeHg and SeMet; (v) exposure first to MeHg during 1 month and then to SeMet during 2 months and (vi), exposure to SeMet during 1 month and then to MeHg for 2 months. The levels of SeT and HgT in the fish (control and supplemented with MeHg/SeMet) were measured by inductively coupled plasma-mass spectrometry (ICPMS). Steadily (linear) bioaccumulation of MeHg in the fish muscle occurred when the fish were exposed individually to this species during the period. The bioaccumulation of MeHg is diminished when the fish are firstly exposed to SeMet and then to MeHg, hence indicating the MeHg detoxification due to SeMet supplementation.

Motion reversal of molecular motor assemblies due to weak noise.

Bidirectional motion is an example of collective behavior of molecular motors. It occurs at finite noise level in a nonequilibrium system. We consider this problem as a first exit problem. We identify the noise strength by doing an expansion of a master equation and apply the Wentzell-Freidlin theory to define an effective nonequilibrium potential and provide analytical estimates of the reversal time. Our results match very well with the results of stochastic simulations.

Dynamical behavior of molecular motor assemblies in the rigid and crossbridge models.

We present a detailed analysis of the dynamical instabilities appearing in two kinetic theories for the collective behavior of molecular motors: the rigid two-state model and the two-state crossbridge (or power-stroke) model with continuous binding sites. We calculate force-velocity relations, discuss their stability, plot a diagram that summarizes the oscillation regimes, identify the location of the Hopf bifurcation with a memory effect, discuss the oscillation frequency and make a link with single-molecule experiments. We show that the instabilities present in these models naturally translate into non-linearities in force-displacement relations, and at linear order give forces that are similar to the delayed stretch activation observed in oscillating muscles. We also find that instabilities can appear for both apparent load-decelerated and load-accelerated detachment rates in a 3-state crossbridge model.

Dynamic instabilities in assemblies of molecular motors with finite stiffness.

We propose a two-state "soft-motor" model for the collective behavior of molecular motors which takes into account both the internal motor stiffness and the periodic interaction with the filament. As in the Prandtl-Tomlinson model of tribology, the important parameter of the model is the pinning parameter, which compares the stiffness of the motors to the stiffness of the potential. The model predicts dynamic instabilities in two disconnected regions of parameter space. These parameter ranges correspond to two existing theories of motor assemblies, the rigid two-state model and the crossbridge model. The model also predicts a discontinuity of the slope of the force-velocity relation at small velocities.

Spontaneous oscillations of a minimal actomyosin system under elastic loading.

Spontaneous mechanical oscillations occur in various types of biological systems where groups of motor molecules are elastically coupled to their environment. By using an optical trap to oppose the gliding motion of a single bead-tailed actin filament over a substrate densely coated with myosin motors, we mimicked this condition in vitro. We show that this minimal actomyosin system can oscillate spontaneously. Our finding accords quantitatively with a general theoretical framework where oscillatory instabilities emerge generically from the collective dynamics of molecular motors under load.

Dietary exposure and biomarkers of arsenic in consumers of fish and shellfish from France.

Seafood, especially fish, is considered as a major dietary source of arsenic (As). Seafood consumption is recommended for nutritional properties but contaminant exposure should be considered. The objectives were to assess As intake of frequent French seafood consumers and exposure via biomarkers. Consumptions of 996 high consumers (18 and over) of 4 coastal areas were assessed using a validated food frequency questionnaire. Seafood samples were collected according to a total diet study (TDS) sampling method and analyzed for total As, arsenite (AsIII), arsenate (AsV), arsenobetaïne (AsB), monomethylarsonic acid (MMA) and dimethylarsinic acid (DMA). The average As dietary exposure is 94.7+/-67.5 microg/kg bw/week in females and 77.3+/-54.6 microg/kg bw/week in males (p<0.001) and the inorganic As dietary exposure is respectively 3.34+/-2.06 microg/kg bw/week and 3.04+/-1.86 microg/kg bw/week (p<0.05). Urine samples were collected from 382 of the subjects. The average urinary As concentration is 94.8+/-250 microg/g creatinine for females and 59.7+/-81.8 microg/g for males (p<0.001). Samples having an As concentration above 75 microg/g creatinine (n=101) were analyzed for inorganic As (As(III), As(V), MMA(V) and DMA(V)) which was 24.6+/-27.9 microg/g creatinine for males and 27.1+/-20.6 microg/g for females. Analyses do not show any correlation between dietary exposure and urinary As. These results show that biological results should be interpreted cautiously. Diet recording seems to be the best way to assess dietary As exposure. Seafood is a high source of As exposure but even among high consumers it is not the main source of toxic As. From a public health point of view these results should be interpreted carefully in the absence of international consensus on the health-based guidance value.