Immobile Obstacles Research Articles

Synchronized locomotion can improve spatial accessibility inside ant colonies.

Synchronization is a conspicuous form of collective behaviour that is of crucial importance in numerous biological systems. Ant colonies from the genera Leptothorax and Temnothorax form small colonies, typically made up of only a few hundred workers, and exhibit a form of synchronized behaviour where workers inside colonies' nests become active together in rhythmic cycles that have a period of approximately 20-200 min. However, it is not currently known if these synchronized rhythms of locomotion confer any functional benefit to colonies. By using a combination of multiple image analysis techniques, we show that inactive Leptothorax ants can act as immobile obstacles to moving ants, and that synchronized activity has the potential to reduce the likelihood that individual ants will encounter regions of immobile obstacles that impede access to portions of the nest. We demonstrate qualitatively similar findings using a computational model of confined active particles with oscillating activity.

Exploring the potential of Mg-Zn-Mn-Ca/ZnO composites as a biodegradable alternative for fracture fixation: microstructural, mechanical, and in-vitro biocompatibility analysis

The current research investigates the microstructural, mechanical, in vitro degradation, biocompatibility, and in silico biomechanical behaviour of highly alloyed Mg-Zn-Mn-Ca quaternary system reinforced with ZnO nanopowder as candidate material for resorbable fixation devices. The as-cast composite materials showed dendritic microstructure comprising of α-Mg as major constituent and Mg7Zn3 and Ca2Mg6Zn3 phases distributed in interdendritic zones, as revealed by X-ray diffraction and scanning electron microscopy with energy dispersive X-ray spectroscopy. The addition of ZnO led to a 17% and 22% increase in ultimate and yield strengths in tension and a 24% and 27% enhancement in ultimate compressive and compressive yield strengths, respectively. The mechanical strengthening and observed tension–compression reversed yield asymmetry strongly correlated with the lattice distortion (c/a ratio) resulting from the macroalloying. The amplitude-dependent internal friction confirmed the presence of immobile obstacles to dislocations and their role through their hysteretic-type anelastic response. The in vitro degradation results revealed corrosion barrier effect of secondary phases. The cell adhesion, viability, and cytoskeleton observations favoured their biocompatibility except for hemolysis rate. The finite element results showed reduced stress-shielded zone for developed materials indicating the favourable mechanical environment for peri-implant tissues at fracture interface required for faster fracture healing.

Increase in rod diffusivity emerges even in Markovian nature.

Rod-shaped particles embedded in certain matrices have been reported to exhibit an increase in their center of mass diffusivity upon increasing the matrix density. This increase has been considered to be caused by a kinetic constraint in analogy with tube models. We investigate a mobile rodlike particle in a sea of immobile point obstacles using a kinetic Monte Carlo scheme equipped with a Markovian process, that generates gaslike collision statistics, so that such kinetic constraints do essentially not exist. Even in such a system, provided the particle's aspect ratio exceeds a threshold value of about 24, the unusual increase in the rod diffusivity emerges. This result implies that the kinetic constraint is not a necessary condition for the increase in the diffusivity.

Screening and collective effects in randomly pinned fluids: a new theoretical framework

We propose a theoretical framework for the dynamics of bulk isotropic hard-sphere systems in the presence of randomly pinned particles and apply this theory to supercooled water to validate it. Structural relaxation is mainly governed by local and non-local activated process. As the pinned fraction grows, a local caging constraint becomes stronger and the long range collective aspect of relaxation is screened by immobile obstacles. Different responses of the local and cooperative motions results in subtle predictions for how the alpha relaxation time varies with pinning and density. Our theoretical analysis for the relaxation time of water with pinned molecules quantitatively well describe previous simulations. In addition, the thermal dependence of relaxation for unpinned bulk water is also consistent with prior computational and experimental data.

Single-Particle Tracking of DNA-Binding Biomolecules in Cells: Power-Law Distributions of Dwell Times

Single-particle tracking (SPT) experiments have shown a truncated power-law distribution of dwell times for several DNA-binding species in the nucleus of living cells. Why this distribution? A standard explanation is Arrhenius escape from traps with exponentially distributed binding energies. But here the binding energies are roughly Gaussian, yielding roughly lognormal escape times. We therefore examine other mechanisms. The operational definition of SPT immobility is based on the dwell time within the volume of the effective SPT point spread function. The distribution of dwell times can be power-law at short times, but the exponent is constant and much less than observed. The dwell time problem has been treated in terms of revisits by a tracer to a trap, here recast as the number of revisits before the tracer leaves the volume of the effective SPT point spread function. The effect of revisits is limited because the sum of multiple escape times from a moderate trap is tame compared with single escapes from a deep trap, by the central limit theorem. Truncated power-law trapping yields transient anomalous subdiffusion, and obstructed diffusion includes two well-studied cases of this. In percolation the tracer concentration is low and the concentration of immobile obstacles is high. Anomalous subdiffusion is the result of static geometric trapping by dead ends, but how can these structures be made on the SPT length scale from DNA with a 50-nm persistence length? The other case is crowding, in which all species are mobile, the concentration is high, and the geometric traps are dynamic. We examine the effects of polydisperse crowders and of small concentrations of immobile species in a crowded system, to see whether crowding can bridge the gap between the SPT and DNA length scales.

Polymer looping kinetics in active heterogeneous environments.

A typical biological environment is usually featured by crowding and heterogeneity, leading to complex reaction kinetics of the immersed macromolecules. In the present work, we adopt Langevin dynamics simulations to systematically investigate polymer looping kinetics in active heterogeneous media crowded with a mixture of mobile active particles and immobile obstacles. For comparison, a parallel study is also performed in the passive heterogeneous media. We explicitly analyze the change of looping time and looping probability with the variation of obstacle ratio, volume fraction and crowder size. We reveal the novel phenomena of inhibition-facilitation transition of the looping rate induced by heterogeneity, crowdedness and activity. In addition, our results demonstrate a very non-trivial crowder size effect on the looping kinetics. The underlying mechanism is rationalized by the interplay of polymer diffusion, conformational change and looping free-energy barrier. The competing effect arising from active particles and obstacles on structural and dynamical properties of the polymer yields a consistent scenario for our observations. Lastly, the non-exponential kinetics of the looping process is also analyzed. We find that both activity and crowding can strengthen the heterogeneity degree of the looping kinetics.

Scratch-induced partial skin wounds re-epithelialize by sheets of independently migrating keratinocytes.

Re-epithelialization is a crucial process to reestablish the protective barrier upon wounding of the skin. Although this process is well described for wounds where the complete epidermis and dermis is damaged, little is known about the re-epithelialization strategy in more frequently occurring smaller scratch wounds in which structures such as the hair follicles and sweat glands stay intact. To study this, we established a scratch wound model to follow individual keratinocytes in all epidermal layers in the back skin of mice by intravital microscopy. We discover that keratinocytes adopt a re-epithelialization strategy that enables them to bypass immobile obstacles such as hair follicles. Wound-induced cell loss is replenished by proliferation in a distinct zone away from the wound and this proliferation does not affect overall migration pattern. Whereas suprabasal keratinocytes are rather passive, basal keratinocytes move as a sheet of independently migrating cells into the wound, thereby constantly changing their direct neighboring cells enabling them to bypass intact obstacles. This re-epithelialization strategy results in a fast re-establishment of the protective skin barrier upon wounding.

Morphological evolution of a barchan dune migrating past an offshore wind farm foundation

AbstractAs the number of manmade structures installed on the seafloor is increasing rapidly, we seek to understand the impact of these immobile obstacles on marine geomorphological processes, such as the evolution of bedforms. A 5.8 m diameter monopile foundation was installed at the case study offshore windfarm approximately 30 m ahead of an approaching barchan (crescent‐shaped) dune. The impact of the monopile on the dune's evolution was analysed using six multibeam bathymetry surveys spanning 20 years. To substantiate this analysis, coupled three‐dimensional numerical modelling of flows and sediment was conducted in which the scour inducing bed shear stresses were calculated from the modelled turbulent kinetic energy. Following the installation of the monopile, the mid‐section of the dune accelerated and stretched in the direction of the wake of the monopile. Four years after the monopile's installation the rest of the dune had caught up, flattening out the slip face within half the dune's length downstream of the monopile. Due to the modified flow field, the dune was scoured deeply at the base of the monopile to a depth of 6.8 m (supported by the model results that predicted a scour depth exceeding 2 m over a period of just a few days). The surveyed volume of material scoured amounted to 8% of the total dune volume. Whilst the process of scouring occurs at a timescale of days to weeks, the dune migrated on average by 25 m/yr. The difference in the timescale of the two processes allowed the scouring to occur through the full thickness of the dune. The scoured dune profile recovered rapidly once the dune migrated downstream of the monopile. This article demonstrates how large geomorphological features can intercept and migrate past a monopile foundation without long‐lasting impacts on the integrity of the feature or the foundation. © 2020 John Wiley & Sons, Ltd.

Robust path planning for avoiding obstacles using time-environment dynamic map

Small unmanned aerial vehicles are widely used in urban space because of its flexibility and maneuverability. However, there are full of dynamic obstacles and immobile obstacles which will affect safe flying in urban space. In this paper, a novel integrated path planning approach for unmanned aerial vehicles is presented, which is consisted of three steps. First, a time-environment dynamic map is constructed to represent obstacles by introducing time axis. Second, unmanned aerial vehicles’ flyable paths are explored based on breadth-first algorithm. Third, a path planning method using A* algorithm and local trace-back model is designed in order to discover sub-optimal feasible path rapidly in unmanned aerial vehicles’ field of view. Finally, the simulation results have illustrated that the proposed method can ensure unmanned aerial vehicles’ autonomous path planning safely and effectively in urban space crowded with obstacles.

Diffusion in an array of immobile anisotropic obstacles: The influence of local orientation, bottlenecks, and free volume in absence of dead-ends

Obstacles (such as gel fibers) decrease the diffusion coefficient D of a particle. Several obstruction models have been proposed to predict how D depends on the fractional free volume f for a system with immobile obstacles. We investigate how the orientation of periodically distributed rod-shaped obstacles affects the 2D diffusion coefficient of different size particles when dead-ends are not present. We focus our attention on globally isotropic arrays of obstacles with different types of orientational order. Our Lattice Monte Carlo results show that the diffusion coefficient of a particle is sensitive to the way the gel fibers orient both locally and over large distances. When the obstacles are treated as Ising spins, D is directly related to the amount of disorder in the system with narrow bottlenecks playing a major role. When the obstacles are regrouped in large regular domains, on the other hand, D has only a weak dependence on domain size. Interestingly, we also observe that increasing f does not necessarily increase diffusivity; indeed, diffusivity is also influenced by the intrinsic tortuosity in the system. Our results show that local orientation, bottlenecks, fractional free volume and intrinsic tortuosity all play a role in determining the diffusivity of a particle in a globally isotropic system, thus implying that mean-field, free-volume models are not reliable when studying diffusion in complex media.

Mobile obstacles accelerate and inhibit the bundle formation in two-patch colloidal particle.

Aggregation of protein into bundles is responsible for many neurodegenerative diseases. In this work, we show how two-patch colloidal particles self-assemble into chains and a sudden transition to bundles takes place by tuning the patch size and solvent condition. We study the kinetics of formation of chains, bundles, and networklike structures using patchy Brownian cluster dynamics. We also analyze the ways to inhibit and accelerate the formation of these bundles. We show that in the presence of inert immobile obstacles, the kinetics of formation of bundles slows down. However, in the presence of mobile aggregating particles, which exhibit interspecies hard sphere repulsion and intraspecies attraction, the kinetics of bundle formation accelerates slightly. We also show that if we introduce mobile obstacles, which exhibit interspecies attraction and intraspecies hard sphere repulsion, the kinetics of formation of bundles is inhibited. This is similar to the inhibitory effect of peptide P4 on the formation of insulin fibers. We are providing a model of mobile obstacles undergoing directional interactions to inhibit the formation of bundles.

Anomalous tracer diffusion in the presence of extended obstacles on a triangular lattice

Proteins diffuse to their sites of action within cells in a crowded, strongly interacting environment of nucleic acids and other macromolecules. An interesting question is how the highly crowded environment of biological cells affects the dynamic properties of passively diffusing particles. The Lorentz model is a generic model covering many of the aspects of transport in a heterogeneous environment. We investigate biologically relevant situations of immobile obstacles of various shapes and sizes. The Monte Carlo simulations for the diffusion of a tracer particle are carried out on a two-dimensional triangular lattice. Obstacles are represented by non-overlapping lattice shapes that are randomly placed on the lattice. Our simulation results indicate that the mean-square displacement displays anomalous transport for all obstacle shapes, which extends to infinite times at the corresponding percolation thresholds. In the vicinity of this critical density the diffusion coefficient vanishes according to a power law, with the same conductivity exponent for all obstacle shapes. At the fixed density of obstacles, we observe that the diffusion coefficient is higher for the smaller obstacles if the object size is defined as the highest projection of the object on one of the six directions on the triangular lattice. The dynamic exponent, which describes the anomalous transport at the critical density, is the same for all the obstacle shapes. Here we show that the values of critical exponents estimated for all disordered environments do not depend on the microscopic details of the present model, such as obstacle shape, and agree with the predicted values for the underlying percolation problem. We also provide the evidence for a divergent non-Gaussian parameter close to the percolation transition for all obstacle shapes.

Corrected pair correlation functions for environments with obstacles.

Environments with immobile obstacles or void regions that inhibit and alter the motion of individuals within that environment are ubiquitous. Correlation in the location of individuals within such environments arises as a combination of the mechanisms governing individual behavior and the heterogeneous structure of the environment. Measures of spatial structure and correlation have been successfully implemented to elucidate the roles of the mechanisms underpinning the behavior of individuals. In particular, the pair correlation function has been used across biology, ecology, and physics to obtain quantitative insight into a variety of processes. However, naively applying standard pair correlation functions in the presence of obstacles may fail to detect correlation, or suggest false correlations, due to a reliance on a distance metric that does not account for obstacles. To overcome this problem, here we present an analytic expression for calculating a corrected pair correlation function for lattice-based domains containing obstacles. We demonstrate that this obstacle pair correlation function is necessary for isolating the correlation associated with the behavior of individuals, rather than the structure of the environment. Using simulations that mimic cell migration and proliferation we demonstrate that the obstacle pair correlation function recovers the short-range correlation known to be present in this process, independent of the heterogeneous structure of the environment. Further, we show that the analytic calculation of the obstacle pair correlation function derived here is significantly faster to implement than the corresponding numerical approach.

Time-dependent dynamics of the three-dimensional driven lattice Lorentz gas

We consider the motion of a single tracer particle on a three-dimensional lattice in the presence of hard, immobile obstacles at low density. Starting from an equilibrium state, a constant pulling force on the tracer particle is switched on. We elaborate a complete solution for the dynamics, exact in first order of the obstacle density. The time-dependent velocity response and the fluctuations along and perpendicular to the force are derived and compared to stochastic simulations. The non-analytic dependence of the linear-response functions on the frequency, reflecting the long-time tail of the velocity autocorrelation function in equilibrium, has a non-equilibrium analogue in the non-analytic dependence of the stationary velocity as well as the diffusion coefficients as a function of the force. We show that a divergent time scale emerges, separating a regime where linear response is qualitatively correct from a regime where nonlinear effects dominate.

Time-dependent perpendicular fluctuations in the driven lattice Lorentz gas.

We present results for the fluctuations of the displacement of a tracer particle on a planar lattice pulled by a step force in the presence of impenetrable, immobile obstacles. The fluctuations perpendicular to the applied force are evaluated exactly in first order of the obstacle density for arbitrarily strong pulling and all times. The complex time-dependent behavior is analyzed in terms of the diffusion coefficient, local exponent, and the non-Skellam parameter, which quantifies deviations from the dynamics on the lattice in the absence of obstacles. The non-Skellam parameter along the force is analyzed in terms of an asymptotic model and reveals a power-law growth for intermediate times.

Time-Dependent Fluctuations and Superdiffusivity in the Driven Lattice Lorentz Gas.

We consider a tracer particle on a lattice in the presence of immobile obstacles. Starting from equilibrium, a force pulling on the particle is switched on, driving the system to a new stationary state. We solve for the complete transient dynamics of the fluctuations of the tracer position along the direction of the force. The analytic result, exact in first order of the obstacle density and for arbitrarily strong driving, is compared to stochastic simulations. Upon strong driving, the fluctuations grow superdiffusively for intermediate times; however, they always become diffusive in the stationary state. The diffusion constant is nonanalytic for small driving and is enhanced by orders of magnitude by increasing the force.

Monte Carlo simulations of protein micropatterning in biomembranes: effects of immobile sticky obstacles

Single molecule trajectories of lipids and proteins can yield valuable information about the nanoscopic organization of the plasma membrane itself. The interpretation of such trajectories, however, is complicated, as the mobility of molecules can be affected by the presence of immobile obstacles, and the transient binding of the tracers to these obstacles. We have previously developed a micropatterning approach that allows for immobilizing a plasma membrane protein and probing the diffusional behavior of a putative interaction partner in living cells. Here, we provide guidelines on how this micropatterning approach can be extended to quantify interaction parameters between plasma membrane constituents in their natural environment. We simulated a patterned membrane system and evaluated the effect of different surface densities of patterned immobile obstacles on the relative mobility as well as the surface density of diffusing tracers. In the case of inert obstacles, the size of the obstacle can be assessed from its surface density at the percolation threshold, which in turn can be extracted from the diffusion behavior of the tracer. For sticky obstacles, 2D dissociation constants can be determined from the tracer diffusion or surface density.

The effect of shear and confinement on the buckling of particle-laden interfaces

In this paper, we investigate the buckling of an air–water interface populated by lycopodium powder particles using a specially designed Langmuir trough with side walls that deformed affinely with the particle-laden interface in order to minimize the effect of shear during compression. Confinement effects from the side walls were studied by systematically reducing the width of the Langmuir trough and measuring the buckling wavelength. For interfaces wider than 20 mm, the bulk wavelength was found to be independent of interface width. Due to the presence of contact line friction along the sidewall, the amplitude and wavelength of the wrinkles near the side walls were found to be reduced by a factor two compared with the bulk. A cascade in wavelength was observed as one moved from the center of the particle-laden interface towards the sidewalls similar to what has been observed for thin floating polymer films. For interface widths less than 20 mm, the wavelength of the wrinkles in the bulk was found to decrease eventually approaching the wavelength measured along the side walls. The wavelength at the walls was not affected by confinement. At large compressive strains, a transition from wrinkles to folds was observed. These regions of strain localization formed as a train of folds shortly after the onset of wrinkling and grew in amplitude with increasing compression. Confinement was also found to have an impact on folding. To study the impact of shear during interface compression, a series of objects including circular cylinders and rectangular prisms were placed through the center of the particle-laden interface before compression. These objects enhanced wrinkling and folding upstream of the object, eliminated wrinkling and folding in a broad region downstream of the object, and realigned the wrinkles along the side of the immobile obstacles where shear strains were maximum.

Calculating the Fickian diffusivity for a lattice-based random walk with agents and obstacles of different shapes and sizes

Random walk models are often used to interpret experimental observations of the motion of biological cells and molecules. A key aim in applying a random walk model to mimic an in vitro experiment is to estimate the Fickian diffusivity (or Fickian diffusion coefficient), D. However, many in vivo experiments are complicated by the fact that the motion of cells and molecules is hindered by the presence of obstacles. Crowded transport processes have been modeled using repeated stochastic simulations in which a motile agent undergoes a random walk on a lattice that is populated by immobile obstacles. Early studies considered the most straightforward case in which the motile agent and the obstacles are the same size. More recent studies considered stochastic random walk simulations describing the motion of an agent through an environment populated by obstacles of different shapes and sizes. Here, we build on previous simulation studies by analyzing a general class of lattice-based random walk models with agents and obstacles of various shapes and sizes. Our analysis provides exact calculations of the Fickian diffusivity, allowing us to draw conclusions about the role of the size, shape and density of the obstacles, as well as examining the role of the size and shape of the motile agent. Since our analysis is exact, we calculate D directly without the need for random walk simulations. In summary, we find that the shape, size and density of obstacles has a major influence on the exact Fickian diffusivity. Furthermore, our results indicate that the difference in diffusivity for symmetric and asymmetric obstacles is significant.

Spatial distributions at equilibrium under heterogeneous transient subdiffusion

Experimental measurements of the mobility of macromolecules, especially proteins, in cells and their membranes consistently report transient subdiffusion with possibly position-dependent—non-homogeneous—properties. However, the spatiotemporal dynamics of protein mobility when transient subdiffusion is restricted to a subregion of space is still unclear. Here, we investigated the spatial distribution at equilibrium of proteins undergoing transient subdiffusion due to continuous-time random walks (CTRW) in a restricted subregion of a two-dimensional space. Our Monte-Carlo simulations suggest that this process leads to a non-homogeneous spatial distribution of the proteins at equilibrium, where proteins increasingly accumulate in the CTRW subregion as its anomalous properties are increasingly marked. In the case of transient CTRW, we show that this accumulation is dictated by the asymptotic Brownian regime and not by the initial anomalous transient dynamics. Moreover, our results also show that this dominance of the asymptotic Brownian regime cannot be simply generalized to other scenarios of transient subdiffusion. In particular, non-homogeneous transient subdiffusion due to hindrance by randomly-located immobile obstacles does not lead to such a strong local accumulation. These results suggest that, even though they exhibit the same time-dependence of the mean-squared displacement, the different scenarios proposed to account for subdiffusion in the cell lead to different protein distribution in space, even at equilibrium and without coupling with reaction.