Diffusive Movements Research Articles

Intermittent random walks under stochastic resetting.

We analyze a one-dimensional intermittent random walk on an unbounded domain in the presence of stochastic resetting. In this process, the walker alternates between local intensive search, diffusion, and rapid ballistic relocations in which it does not react to the target. We demonstrate that Poissonian resetting leads to the existence of a non-equilibrium steady state. We calculate the distribution of the first arrival time to a target along with its mean and show the existence of an optimal reset rate. In particular, we prove that the initial condition of the walker, i.e., either starting diffusely or relocating, can significantly affect the long-time properties of the search process. Moreover, we demonstrate the presence of distinct parameter regimes for the global optimization of the mean first arrival time when ballistic and diffusive movements are in direct competition.

Space–time upscaling of reactive transport in porous media

Reactive transport in saturated/unsaturated porous media is numerically upscaled to the space–time scale of a hypothetical measurement through coarse-grained space–time (CGST) averages. The reactive transport is modeled at the fine-grained Darcy scale by the actual number of molecules involved in reactions which undergo advective and diffusive movements described by global random walk (GRW) simulations. The CGST averages verify identities similar to a local balance equation which allow us to derive expressions for the flow velocity and the intrinsic diffusion coefficient in terms of averaged microscopic quantities. The latter are further used to verify the CGST-GRW numerical approach. The upscaling approach is applied to biodegradation processes in saturated aquifers and variably saturated soils and the CGST averages are compared to classical volume averages. One finds that if the process is characterized by slow variations in time, as in homogeneous reaction systems, the differences between the two averages are negligible. Instead, the differences are significant and can be extremely large in simulations of time-dependent biodegradation processes in both variably saturated soils and saturated aquifers.

Global dynamics of a two-species competition model in advective homogeneous environments

We investigate a two-species competition model in advective homogeneous environments. We assume that the two species are identical except their diffusion rates and advection rates. It is worth noting that the Neumann boundary condition is assumed at upstream end, meanwhile, there is always a net loss of individuals incurred by water flow or both water flow and diffusive movements at downstream end. Our results show that when the downstream loss is large (incurred by both water flow and diffusive movements), the species adopting both slower diffusion and advection can be favorable or unfavorable depending on the gap between two diffusion rates. When the downstream loss is small (incurred by water flow alone), the species adopting a combination of faster diffusion and weak advection will persist while the movement of faster diffusion and advection can be favorable or unfavorable for species to survive depending on the gap between two advection rates.

Collective dynamics of liquid sulfur scrutinized over three decades in frequency.

Liquid sulfur consists mainly of eight-membered rings and hence can be regarded as a model of a molecular liquid. A liquid, which is built from different molecular structures, will demonstrate a wide range in relaxation processes and excitation modes. Three inelastic neutron scattering experiments have been performed to study the collective dynamics of liquid sulfur over three decades in frequencies. A wide range of wave vectors was studied to reveal the response of density fluctuations over different lengthscales. A viscoelastic model with a two-times memory function was applied to the data. The analysis revealed a slow relaxation mode, an acoustic-type excitation, and a high-frequency mode, which resembles an optic-type excitation. The wave-vector dependence of the slow relaxation mode width exhibits the signs of a de Gennes narrowing around the wave vector where the structure factor has a shoulder. This slow relaxation process could be related to diffusive particle movements. The acoustic-type modes evidence a viscoelastic reaction with a 50% enhancement of the sound velocity. This enhancement of the sound velocity and the spectral line shape is qualitatively similar to spectra of molecular liquids. The two relaxation times of the memory function are separated by about two orders of magnitude and underpin the need for a wide frequency range investigation of this complex liquid. The high-frequency response can be interpreted as optic-type modes in the liquid.

Rectified random cell motility as a mechanism for embryo elongation.

The body of vertebrate embryos forms by posterior elongation from a terminal growth zone called the tail bud. The tail bud is a source of highly motile cells that eventually constitute the presomitic mesoderm (PSM), a tissue that plays an important role in elongation movements. PSM cells establish an anterior-posterior cell motility gradient that parallels a gradient associated with the degradation of a specific cellular signal (FGF) known to be implicated in cell motility. Here, we combine the electroporation of fluorescent reporters in the PSM with time-lapse imaging in the chicken embryo to quantify cell diffusive movements along the motility gradient. We show that a simple microscopic model for random cell motility induced by FGF activity along with geometric confinement leads to rectified tissue elongation consistent with our observations. A continuum analog of the microscopic model leads to a macroscopic mechano-chemical model for tissue extension that couples FGF activity-induced cell motility and tissue rheology, and is consistent with the experimentally observed speed and extent of elongation. Together, our experimental observations and theoretical models explain how the continuous addition of cells at the tail bud combined with lateral confinement can be converted into oriented movement and drive body elongation.

Conduction process in some promising lithium-ion doped glassy ceramics

A novel glassy ceramic, 0.3Li2O-(0.7)(0.5MoO3-0.4V2O5-0.1ZnO) has been developed using the melt quenching technique. The temperature and frequency dependency of ionic conductivity has been established, following Almond-West formalism and Jonscher's universal power law respectively. The thermally activated nature of the sample can be exposed by its DC conductivity (σdc) study. The effect of composition on hopping frequency and corresponding activation energy has been calculated. The plateau (conductivity dependent on frequency) region in the lower frequency zone is pronounced by the sub diffusive movements of conducting Li+ ions. Whereas, in the dispersive high-frequency zone, Li+ ion migration in a pseudo-three-dimensional space is the main reason for conductivity in percolating networks.

Hillslope form and process: history 1960–2000+

Abstract The study of hillslopes has been dominated by the expansion of studies into process rates and mechanisms. Perhaps the greatest volume of work has been on the ‘wash’ processes of soil erosion, but there has also been significant work on the diffusive mass movements of linear and non-linear ‘creep’ that shape the convexity of hilltops, on more rapid mass movements and on solution processes. There has also been fresh work on distinctive processes in coastal, arid and cold-climate environments. Accompanying and integrated with process understanding, and made possible by ubiquitous computational power, modelling has developed from soluble mathematical simplifications to complex simulations that incorporate much of our understanding of process and climate. Particular topics that have seen significant advance include a more complete understanding of drainage density and texture, and a broadening of interest to encompass the ‘critical zone’ that constructively unifies the land surface with the lower atmosphere, the biosphere and the regolith. There has also been a change of focus towards steeplands, dominated by mass movements, supply-limited removal and tectonic activity. Most recently, and now incorporated into the concept of the ‘Anthropocene’, human impact is now receiving increasing attention as we acknowledge its accelerating role in changing landscapes and their relationships.

A single active ring model with velocity self-alignment.

Cellular tissue behavior is a multiscale problem. At the cell level, out of equilibrium, biochemical reactions drive physical cell-cell interactions in a typical active matter process. Cell modeling computer simulations are a robust tool to explore countless possibilities and test hypotheses. Here, we introduce a two-dimensional, extended active matter model for biological cells. A ring of interconnected self-propelled particles represents the cell. Neighboring particles are subject to harmonic and bending potentials. Within a characteristic time, each particle's self-velocity tends to align with its scattering velocity after an interaction. Translational modes, rotational modes, and mixtures of these appear as collective states. Using analytical results derived from active Brownian particles, we identify effective characteristic time scales for ballistic and diffusive movements. Finite-size scale investigation shows that the ring diffusion increases linearly with its size when in collective movement. A study on the ring shape reveals that all collective states are present even when bending forces are weak. In that case, when in a translational mode, the collective velocity aligns with the largest ring's direction in a spontaneous polarization emergence.

A vague memory can affect first-return time

First-return time is an important property for the return of particles or walkers to a start point. Recursive walks, which may be related to first-return time, are found in both random walk models and memory-based walk models. Achieving a balance between recursive walks and diffusive movements is a crucial but difficult modeling problem. Here, starting with a simple Brownian-walk model, I investigated how vague memorized information influences the first-return times of a walker. In the proposed model, the walker memorizes recently visited positions and recalls the direction in which it previously moved when returning to those positions. Using the recalled information, the walker then moves in the opposite direction to that previously traveled. In addition, the walker considers its recent experience and modifies its directional rules, i.e., memorized information, when the rule disturbs the recent flow of its movement. Thus, the proposed model effectively produces recursive walks in which a walker returns to a start point while demonstrating diffusive movements.

L\xe9vy-like movement patterns of metastatic cancer cells revealed in microfabricated systems and implicated in vivo

Metastatic cancer cells differ from their non-metastatic counterparts not only in terms of molecular composition and genetics, but also by the very strategy they employ for locomotion. Here, we analyzed large-scale statistics for cells migrating on linear microtracks to show that metastatic cancer cells follow a qualitatively different movement strategy than their non-invasive counterparts. The trajectories of metastatic cells display clusters of small steps that are interspersed with long “flights”. Such movements are characterized by heavy-tailed, truncated power law distributions of persistence times and are consistent with the Lévy walks that are also often employed by animal predators searching for scarce prey or food sources. In contrast, non-metastatic cancerous cells perform simple diffusive movements. These findings are supported by preliminary experiments with cancer cells migrating away from primary tumors in vivo. The use of chemical inhibitors targeting actin-binding proteins allows for “reprogramming” the Lévy walks into either diffusive or ballistic movements.

Stochastic modelling of a diffusive wave for flood propagation using the random walk particle tracking method in a hypothetical city

AbstractDeterministic numerical schemes have been widely used for the solution of the diffusive wave (DW) equation, however, these schemes are computationally costly and suffer instability issues. This paper presents a stochastic random walk particle tracking (RWPT) method to solve such an equation for a dam‐break flow problem. Three different wave duration scenarios are presented for simulations of the DW for flood flows in a hypothetical city. The hypothetical city is represented by a domain of size 2,000 m by 500 m in x and y directions, respectively. The domain is divided into 25 m by 25 m cells. A dam is located at the upstream of the hypothetical city. Each scenario has a distinct propagation pattern after the dam is breached. Analysed and presented are 18 different simulations, which are composed of three different building configurations, two different bed slopes, and three different shapes of hydrographs. In this method, the flood volume is divided into a large number of particles where each particle carries a fixed amount of the flood volume. These particles undergo convective and diffusive movements, and their superposition represents propagation of the DW in the flow domain. The solution algorithm of the RWPT‐based equations is used to compute flood inundation depths in the hypothetical city. Comparison is drawn among the simulated results from three different shapes of the inflow hydrographs. The proposed stochastic method has two major advantages over traditional deterministic schemes: (a) greater efficiency, thus lesser computational costs, and (b) no instability issues.

Myosin Va molecular motors manoeuvre liposome cargo through suspended actin filament intersections in vitro

Intracellular cargo transport relies on myosin Va molecular motor ensembles to travel along the cell’s three-dimensional (3D) highway of actin filaments. At actin filament intersections, the intersecting filament is a structural barrier to and an alternate track for directed cargo transport. Here we use 3D super-resolution fluorescence imaging to determine the directional outcome (that is, continues straight, turns or terminates) for an ∼10 motor ensemble transporting a 350 nm lipid-bound cargo that encounters a suspended 3D actin filament intersection in vitro. Motor–cargo complexes that interact with the intersecting filament go straight through the intersection 62% of the time, nearly twice that for turning. To explain this, we develop an in silico model, supported by optical trapping data, suggesting that the motors’ diffusive movements on the vesicle surface and the extent of their engagement with the two intersecting actin tracks biases the motor–cargo complex on average to go straight through the intersection.

Establishing the diffuse correlation spectroscopy signal relationship with blood flow.

Diffuse correlation spectroscopy (DCS) measurements of blood flow rely on the sensitivity of the temporal autocorrelation function of diffusively scattered light to red blood cell (RBC) mean square displacement (MSD). For RBCs flowing with convective velocity [Formula: see text], the autocorrelation is expected to decay exponentially with [Formula: see text], where [Formula: see text] is the delay time. RBCs also experience shear-induced diffusion with a diffusion coefficient [Formula: see text] and an MSD of [Formula: see text]. Surprisingly, experimental data primarily reflect diffusive behavior. To provide quantitative estimates of the relative contributions of convective and diffusive movements, we performed Monte Carlo simulations of light scattering through tissue of varying vessel densities. We assumed laminar vessel flow profiles and accounted for shear-induced diffusion effects. In agreement with experimental data, we found that diffusive motion dominates the correlation decay for typical DCS measurement parameters. Furthermore, our model offers a quantitative relationship between the RBC diffusion coefficient and absolute tissue blood flow. We thus offer, for the first time, theoretical support for the empirically accepted ability of the DCS blood flow index ([Formula: see text]) to quantify tissue perfusion. We find [Formula: see text] to be linearly proportional to blood flow, but with a proportionality modulated by the hemoglobin concentration and the average blood vessel diameter.

Experimental evaluation of electrical conductivity imaging of anisotropic brain tissues using a combination of diffusion tensor imaging and magnetic resonance electrical impedance tomography

Anisotropy of biological tissues is a low-frequency phenomenon that is associated with the function and structure of cell membranes. Imaging of anisotropic conductivity has potential for the analysis of interactions between electromagnetic fields and biological systems, such as the prediction of current pathways in electrical stimulation therapy. To improve application to the clinical environment, precise approaches are required to understand the exact responses inside the human body subjected to the stimulated currents. In this study, we experimentally evaluate the anisotropic conductivity tensor distribution of canine brain tissues, using a recently developed diffusion tensor-magnetic resonance electrical impedance tomography method. At low frequency, electrical conductivity of the biological tissues can be expressed as a product of the mobility and concentration of ions in the extracellular space. From diffusion tensor images of the brain, we can obtain directional information on diffusive movements of water molecules, which correspond to the mobility of ions. The position dependent scale factor, which provides information on ion concentration, was successfully calculated from the magnetic flux density, to obtain the equivalent conductivity tensor. By combining the information from both techniques, we can finally reconstruct the anisotropic conductivity tensor images of brain tissues. The reconstructed conductivity images better demonstrate the enhanced signal intensity in strongly anisotropic brain regions, compared with those resulting from previous methods using a global scale factor.

Low-Reynolds-number predator.

To generalize simple bead-linker model of swimmers to higher dimensions and to demonstrate the chemotaxis ability of such swimmers, here we introduce a low-Reynolds predator, using a two-dimensional triangular bead-spring model. Two-state linkers as mechanochemical enzymes expand as a result of interaction with particular activator substances in the environment, causing the whole body to translate and rotate. The concentration of the chemical stimulator controls expansion versus the contraction rate of each arm and so affects the ability of the body for diffusive movements; also the variation of activator substance's concentration in the environment breaks the symmetry of linkers' preferred state, resulting in the drift of the random walker along the gradient of the density of activators. External food or danger sources may attract or repel the body by producing or consuming the chemical activators of the organism's enzymes, inducing chemotaxis behavior. Generalization of the model to three dimensions is straightforward.

Automatic algorithm to decompose discrete paths of fractional Brownian motion into self-similar intrinsic components

Fractional Brownian motion (fBm) is a nonstationary self-similar continuous stochastic process used to model many natural phenomena. A realization of the fBm can be numerically approximated by discrete paths which do not entirely preserve the self-similarity. We investigate the self-similarity at different time scales by decomposing the discrete paths of fBm into intrinsic components. The decomposition is realized by an automatic numerical algorithm based on successive smoothings stopped when the maximum monotonic variation of the averaged time series is reached. The spectral properties of the intrinsic components are analyzed through the monotony spectrum defined as the graph of the amplitudes of the monotonic segments with respect to their lengths (characteristic times). We show that, at intermediate time scales, the mean amplitude of the intrinsic components of discrete fBms scales with the mean characteristic time as a power law identical to that of the corresponding continuous fBm. As an application we consider hydrological time series of the transverse component of the transport process generated as a superposition of diffusive movements on advective transport in random velocity fields. We found that the transverse component has a rich structure of scales, which is not revealed by the analysis of the global variance, and that its intrinsic components may be self-similar only in particular cases.

Mapping intracellular diffusion distribution using single quantum dot tracking: compartmentalized diffusion defined by endoplasmic reticulum.

The crowded intracellular environment influences the diffusion-mediated cellular processes, such as metabolism, signaling, and transport. The hindered diffusion of macromolecules in heterogeneous cytoplasm has been studied over years, but the detailed diffusion distribution and its origin still remain unclear. Here, we introduce a novel method to map rapidly the diffusion distribution in single cells based on single-particle tracking (SPT) of quantum dots (QDs). The diffusion map reveals the heterogeneous intracellular environment and, more importantly, an unreported compartmentalization of QD diffusions in cytoplasm. Simultaneous observations of QD motion and green fluorescent protein-tagged endoplasmic reticulum (ER) dynamics provide direct evidence that the compartmentalization results from micron-scale domains defined by ER tubules, and ER cisternae form perinuclear areas that restrict QDs to enter. The same phenomenon was observed using fluorescein isothiocyanate-dextrans, further confirming the compartmentalized diffusion. These results shed new light on the diffusive movements of macromolecules in the cell, and the mapping of intracellular diffusion distribution may be used to develop strategies for nanoparticle-based drug deliveries and therapeutics.

Dynamic blockage in an exclusion process

We study an asymmetric exclusion model with one dynamic roadblock particle. The roadblock particle is allowed to move diffusively as well as by long-range jumps mimicking an unbinding/rebinding process. Using Monte Carlo simulations and analytical arguments, the two types of roadblock moves are considered both separately and in combination. Several interesting dynamic phenomena are observed. The long-range jumps of the roadblock lead to a current that depends on the number of particles in the system rather than on the particle density, and thus scales linearly with the system size (up to a critical size). This behavior can be explained by a collective motion of all particles following the roadblock. The diffusive roadblock movements on the other hand lead to a ratcheting motion with the active (driven) particles pushing the roadblock forward.

Capturing Transition Paths and Transition States for Conformational Rearrangements in the Ribosome

To reveal the molecular determinants of biological function, one seeks to characterize the interactions that are formed in conformational and chemical transition states. In other words, what interactions govern the molecule’s energy landscape? To accomplish this, it is necessary to determine which degrees of freedom can unambiguously identify each transition state. Here, we perform simulations of large-scale aminoacyl-transfer RNA (aa-tRNA) rearrangements during accommodation on the ribosome and project the dynamics along experimentally accessible atomic distances. From this analysis, we obtain evidence for which coordinates capture the correct number of barrier-crossing events and accurately indicate when the aa-tRNA is on a transition path. Although a commonly used coordinate in single-molecule experiments performs poorly, this study implicates alternative coordinates along which rearrangements are accurately described as diffusive movements across a one-dimensional free-energy profile. From this, we provide the theoretical foundation required for single-molecule techniques to uncover the energy landscape governing aa-tRNA selection by the ribosome.

Multimodal electrochemical sensing of transcription factor–operator complexes

Interactions of proteins with nucleic acids arise at all levels of cellular function, from chromosomal packing to biological regulation. These interactions can be analyzed in a high-throughput fashion by immobilizing the DNA sequences of interest, possibly numbering in the thousands, at discrete locations on a solid support and identifying those sequences that a protein analyte binds. Ideally, such surface assays would use unlabeled analyte to simplify protocols and avoid the possibility of perturbing the protein/DNA interaction. The present study compares three electrochemical modalities for simultaneously detecting binding of unlabeled transcription factor proteins to immobilized DNA duplexes based on (i) changes in the duplex diffusive motions, (ii) variations in the surface potential, and (iii) variations in the interfacial charging impedance, all of which can be conveniently derived from AC voltammetry traces. Cro protein from bacteriophage lambda is used as a model transcription factor. Specific binding of protein was successfully detected through modalities (i) and (ii), but not (iii). The effectiveness of these techniques is compared as a function of sampling frequency and protein concentration. Binding of 15 kDa Cro slowed down rotational diffusion of immobilized duplexes approximately 3-fold, and induced up to 5 mV changes in the surface potential. Moreover, by assessing Cro binding to bacteriophage operators of variable affinity, the study illustrates how contrast between specific and nonspecific interactions impacts detection.