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The passive and active motion of micron-sized tracer particles in crowded liquids and inside living biological cells is ubiquitously characterised by 'viscoelastic' anomalous diffusion, in which the increments of the motion feature long-ranged negative and positive correlations. While viscoelastic anomalous diffusion is typically modelled by a Gaussian process with correlated increments, so-called fractional Gaussian noise, an increasing number of systems are reported, in which viscoelastic anomalous diffusion is paired with non-Gaussian displacement distributions. Following recent advances in Brownian yet non-Gaussian diffusion we here introduce and discuss several possible versions of random-diffusivity models with long-ranged correlations. While all these models show a crossover from non-Gaussian to Gaussian distributions beyond some correlation time, their mean squared displacements exhibit strikingly different behaviours: depending on the model crossovers from anomalous to normal diffusion are observed, as well as a priori unexpected dependencies of the effective diffusion coefficient on the correlation exponent. Our observations of the non-universality of random-diffusivity viscoelastic anomalous diffusion are important for the analysis of experiments and a better understanding of the physical origins of 'viscoelastic yet non-Gaussian' diffusion.
In nature as well as in the context of infection and medical applications, bacteria often have to move in highly complex environments such as soil or tissues. Previous studies have shown that bacteria strongly interact with their surroundings and are often guided by confinements. Here, we investigate theoretically how the dispersal of swimming bacteria can be augmented by microfluidic environments and validate our theoretical predictions experimentally. We consider a system of bacteria performing the prototypical run-and-tumble motion inside a labyrinth with square lattice geometry. Narrow channels between the square obstacles limit the possibility of bacteria to reorient during tumbling events to an area where channels cross. Thus, by varying the geometry of the lattice it might be possible to control the dispersal of cells. We present a theoretical model quantifying diffusive spreading of a run-and-tumble random walker in a square lattice. Numerical simulations validate our theoretical predictions for the dependence of the diffusion coefficient on the lattice geometry. We show that bacteria moving in square labyrinths exhibit enhanced dispersal as compared to unconfined cells. Importantly, confinement significantly extends the duration of the phase with strongly non-Gaussian diffusion, when the geometry of channels is imprinted in the density profiles of spreading cells. Finally, in good agreement with our theoretical findings, we observe the predicted behaviors in experiments with E. coli bacteria swimming in a square lattice labyrinth created in amicrofluidic device. Altogether, our comprehensive understanding of bacterial dispersal in a simple two-dimensional labyrinth makes the first step toward the analysis of more complex geometries relevant for real world applications.
In nature as well as in the context of infection and medical applications, bacteria often have to move in highly complex environments such as soil or tissues. Previous studies have shown that bacteria strongly interact with their surroundings and are often guided by confinements. Here, we investigate theoretically how the dispersal of swimming bacteria can be augmented by microfluidic environments and validate our theoretical predictions experimentally. We consider a system of bacteria performing the prototypical run-and-tumble motion inside a labyrinth with square lattice geometry. Narrow channels between the square obstacles limit the possibility of bacteria to reorient during tumbling events to an area where channels cross. Thus, by varying the geometry of the lattice it might be possible to control the dispersal of cells. We present a theoretical model quantifying diffusive spreading of a run-and-tumble random walker in a square lattice. Numerical simulations validate our theoretical predictions for the dependence of the diffusion coefficient on the lattice geometry. We show that bacteria moving in square labyrinths exhibit enhanced dispersal as compared to unconfined cells. Importantly, confinement significantly extends the duration of the phase with strongly non-Gaussian diffusion, when the geometry of channels is imprinted in the density profiles of spreading cells. Finally, in good agreement with our theoretical findings, we observe the predicted behaviors in experiments with E. coli bacteria swimming in a square lattice labyrinth created in amicrofluidic device. Altogether, our comprehensive understanding of bacterial dispersal in a simple two-dimensional labyrinth makes the first step toward the analysis of more complex geometries relevant for real world applications.
At Saturn electrons are trapped in the planet's magnetic field and accelerated to relativistic energies to form the radiation belts, but how this dramatic increase in electron energy occurs is still unknown. Until now the mechanism of radial diffusion has been assumed but we show here that in-situ acceleration through wave particle interactions, which initial studies dismissed as ineffectual at Saturn, is in fact a vital part of the energetic particle dynamics there. We present evidence from numerical simulations based on Cassini spacecraft data that a particular plasma wave, known as Z-mode, accelerates electrons to MeV energies inside 4 R-S (1 R-S = 60,330 km) through a Doppler shifted cyclotron resonant interaction. Our results show that the Z-mode waves observed are not oblique as previously assumed and are much better accelerators than O-mode waves, resulting in an electron energy spectrum that closely approaches observed values without any transport effects included.
We introduce and study a Lévy walk (LW) model of particle spreading with a finite propagation speed combined with soft resets, stochastically occurring periods in which an harmonic external potential is switched on and forces the particle towards a specific position. Soft resets avoid instantaneous relocation of particles that in certain physical settings may be considered unphysical. Moreover, soft resets do not have a specific resetting point but lead the particle towards a resetting point by a restoring Hookean force. Depending on the exact choice for the LW waiting time density and the probability density of the periods when the harmonic potential is switched on, we demonstrate a rich emerging response behaviour including ballistic motion and superdiffusion. When the confinement periods of the soft-reset events are dominant, we observe a particle localisation with an associated non-equilibrium steady state. In this case the stationary particle probability density function turns out to acquire multimodal states. Our derivations are based on Markov chain ideas and LWs with multiple internal states, an approach that may be useful and flexible for the investigation of other generalised random walks with soft and hard resets. The spreading efficiency of soft-rest LWs is characterised by the first-passage time statistic.
We introduce and study a Lévy walk (LW) model of particle spreading with a finite propagation speed combined with soft resets, stochastically occurring periods in which an harmonic external potential is switched on and forces the particle towards a specific position. Soft resets avoid instantaneous relocation of particles that in certain physical settings may be considered unphysical. Moreover, soft resets do not have a specific resetting point but lead the particle towards a resetting point by a restoring Hookean force. Depending on the exact choice for the LW waiting time density and the probability density of the periods when the harmonic potential is switched on, we demonstrate a rich emerging response behaviour including ballistic motion and superdiffusion. When the confinement periods of the soft-reset events are dominant, we observe a particle localisation with an associated non-equilibrium steady state. In this case the stationary particle probability density function turns out to acquire multimodal states. Our derivations are based on Markov chain ideas and LWs with multiple internal states, an approach that may be useful and flexible for the investigation of other generalised random walks with soft and hard resets. The spreading efficiency of soft-rest LWs is characterised by the first-passage time statistic.
We consider a one-dimensional Brownian search in the presence of trapping.
The diffusion equation of the particle is represented by a memory kernel that enters the general waiting time probability density function.
We find the general form of the first arrival time density, search reliability and efficiency and analyze several special cases of the memory kernel.
We also analyze the Levy search in the presence of trapping in cases of single and multiple targets, as well as combined Levy-Brownian search strategies in case of a single target.
The presented results are general and could be of interest for further investigation of different optimal search strategies, as well as in the animal foraging or spreading of contamination particles in the environment.
Many studies on biological and soft matter systems report the joint presence of a linear mean-squared displacement and a non-Gaussian probability density exhibiting, for instance, exponential or stretched-Gaussian tails. This phenomenon is ascribed to the heterogeneity of the medium and is captured by random parameter models such as ‘superstatistics’ or ‘diffusing diffusivity’. Independently, scientists working in the area of time series analysis and statistics have studied a class of discrete-time processes with similar properties, namely, random coefficient autoregressive models. In this work we try to reconcile these two approaches and thus provide a bridge between physical stochastic processes and autoregressive models.Westart from the basic Langevin equation of motion with time-varying damping or diffusion coefficients and establish the link to random coefficient autoregressive processes. By exploring that link we gain access to efficient statistical methods which can help to identify data exhibiting Brownian yet non-Gaussian diffusion.
Many studies on biological and soft matter systems report the joint presence of a linear mean-squared displacement and a non-Gaussian probability density exhibiting, for instance, exponential or stretched-Gaussian tails. This phenomenon is ascribed to the heterogeneity of the medium and is captured by random parameter models such as ‘superstatistics’ or ‘diffusing diffusivity’. Independently, scientists working in the area of time series analysis and statistics have studied a class of discrete-time processes with similar properties, namely, random coefficient autoregressive models. In this work we try to reconcile these two approaches and thus provide a bridge between physical stochastic processes and autoregressive models.Westart from the basic Langevin equation of motion with time-varying damping or diffusion coefficients and establish the link to random coefficient autoregressive processes. By exploring that link we gain access to efficient statistical methods which can help to identify data exhibiting Brownian yet non-Gaussian diffusion.
We show that the codifference is a useful tool in studying the ergodicity breaking and non-Gaussianity properties of stochastic time series. While the codifference is a measure of dependence that was previously studied mainly in the context of stable processes, we here extend its range of applicability to random-parameter and diffusing-diffusivity models which are important in contemporary physics, biology and financial engineering. We prove that the codifference detects forms of dependence and ergodicity breaking which are not visible from analysing the covariance and correlation functions. We also discuss a related measure of dispersion, which is a nonlinear analogue of the mean squared displacement.
We show that the codifference is a useful tool in studying the ergodicity breaking and non-Gaussianity properties of stochastic time series. While the codifference is a measure of dependence that was previously studied mainly in the context of stable processes, we here extend its range of applicability to random-parameter and diffusing-diffusivity models which are important in contemporary physics, biology and financial engineering. We prove that the codifference detects forms of dependence and ergodicity breaking which are not visible from analysing the covariance and correlation functions. We also discuss a related measure of dispersion, which is a nonlinear analogue of the mean squared displacement.
Research on novel and advanced biomaterials is an indispensable step towards their applications in desirable fields such as tissue engineering, regenerative medicine, cell culture, or biotechnology. The work presented here focuses on such a promising material: polyelectrolyte multilayer (PEM) composed of hyaluronic acid (HA) and poly(L-lysine) (PLL). This gel-like polymer surface coating is able to accumulate (bio-)molecules such as proteins or drugs and release them in a controlled manner. It serves as a mimic of the extracellular matrix (ECM) in composition and intrinsic properties. These qualities make the HA/PLL multilayers a promising candidate for multiple bio-applications such as those mentioned above. The work presented aims at the development of a straightforward approach for assessment of multi-fractional diffusion in multilayers (first part) and at control of local molecular transport into or from the multilayers by laser light trigger (second part).
The mechanism of the loading and release is governed by the interaction of bioactives with the multilayer constituents and by the diffusion phenomenon overall. The diffusion of a molecule in HA/PLL multilayers shows multiple fractions of different diffusion rate. Approaches, that are able to assess the mobility of molecules in such a complex system, are limited. This shortcoming motivated the design of a novel evaluation tool presented here.
The tool employs a simulation-based approach for evaluation of the data acquired by fluorescence recovery after photobleaching (FRAP) method. In this approach, possible fluorescence recovery scenarios are primarily simulated and afterwards compared with the data acquired while optimizing parameters of a model until a sufficient match is achieved. Fluorescent latex particles of different sizes and fluorescein in an aqueous medium are utilized as test samples validating the analysis results. The diffusion of protein cytochrome c in HA/PLL multilayers is evaluated as well.
This tool significantly broadens the possibilities of analysis of spatiotemporal FRAP data, which originate from multi-fractional diffusion, while striving to be widely applicable. This tool has the potential to elucidate the mechanisms of molecular transport and empower rational engineering of the drug release systems.
The second part of the work focuses on the fabrication of such a spatiotemporarily-controlled drug release system employing the HA/PLL multilayer. This release system comprises different layers of various functionalities that together form a sandwich structure. The bottom layer, which serves as a reservoir, is formed by HA/PLL PEM deposited on a planar glass substrate. On top of the PEM, a layer of so-called hybrids is deposited. The hybrids consist of thermoresponsive poly(N-isopropylacrylamide) (PNIPAM) -based hydrogel microparticles with surface-attached gold nanorods. The layer of hybrids is intended to serve as a gate that controls the local molecular transport through the PEM–solution-interface. The possibility of stimulating the molecular transport by near-infrared (NIR) laser irradiation is being explored.
From several tested approaches for the deposition of hybrids onto the PEM surface, the drying-based approach was identified as optimal. Experiments, that examine the functionality of the fabricated sandwich at elevated temperature, document the reversible volume phase transition of the PEM-attached hybrids while sustaining the sandwich stability. Further, the gold nanorods were shown to effectively absorb light radiation in the tissue- and cell-friendly NIR spectral region while transducing the energy of light into heat. The rapid and reversible shrinkage of the PEM-attached hybrids was thereby achieved. Finally, dextran was employed as a model transport molecule. It loads into the PEM reservoir in a few seconds with the partition constant of 2.4, while it spontaneously releases in a slower, sustained manner. The local laser irradiation of the sandwich, which contains the fluorescein isothiocyanate tagged dextran, leads to a gradual reduction of fluorescence intensity in the irradiated region.
The release system fabricated employs renowned photoresponsivity of the hybrids in an innovative setting. The results of the research are a step towards a spatially-controlled on-demand drug release system that paves the way to spatiotemporally controlled drug release.
The approaches developed in this work have the potential to elucidate the molecular dynamics in ECM and to foster engineering of multilayers with properties tuned to mimic the ECM. The work aims at spatiotemporal control over the diffusion of bioactives and their presentation to the cells.