Diffusive transport of light in a two-dimensional disordered packing of disks: analytical approach to transport mean free path

Ameboid cell migration through regular arrays of micropillars under confinement

Migrating cells often encounter a wide variety of topographic features-including the presence of obstacles-when navigating through crowded biological environments. Unraveling the impact of topography and crowding on the dynamics of cells is key to better understand many essential physiological processes such as the immune response. We study the impact of geometrical cues on ameboid migration of HL-60 cells differentiated into neutrophils. A microfluidic device is designed to track the cells in confining geometries between two parallel plates with distance h, in which identical micropillars are arranged in regular pillar forests with pillar spacing e. We observe that the cells are temporarily captured near pillars, with a mean contact time that is independent of h and e. By decreasing the vertical confinement h, we find that the cell velocity is not affected, while the persistence reduces; thus, cells are able to preserve their velocity when highly squeezed but lose the ability to control their direction of motion. At a given h, we show that by decreasing the pillar spacing e in the weak lateral confinement regime, the mean escape time of cells from effective local traps between neighboring pillars grows. This effect, together with the increase of cell-pillar contact frequency, leads to the reduction of diffusion constant D. By disentangling the contributions of these two effects on D in numerical simulations, we verify that the impact of cell-pillar contacts on cell diffusivity is more pronounced at smaller pillar spacing.

Kinematics of persistent random walkers with two distinct modes of motion

We study the stochastic motion of active particles that undergo spontaneous transitions between two distinct modes of motion. Each mode is characterized by a velocity distribution and an arbitrary (anti)persistence. We present an analytical formalism to provide a quantitative link between these two microscopic statistical properties of the trajectory and macroscopically observable transport quantities of interest. For exponentially distributed residence times in each state, we derive analytical expressions for the initial anomalous exponent, the characteristic crossover time to the asymptotic diffusive dynamics, and the long-term diffusion constant. We also obtain an exact expression for the time evolution of the mean square displacement over all timescales and provide a recipe to obtain higher displacement moments. Our approach enables us to disentangle the combined effects of velocity, persistence, and switching probabilities between the two states on the kinematics of particles in a wide range of stochastic active or passive processes and to optimize the transport quantities of interest with respect to any of the particle dynamics properties.

Orientational memory of active particles in multistate non-Markovian processes

The orientational memory of particles can serve as an effective measure of diffusivity, spreading, and search efficiency in complex stochastic processes. We develop a theoretical framework to describe the decay of directional correlations in a generic class of stochastic active processes consisting of distinct states of motion characterized by their persistence and switching probabilities between the states. For exponentially distributed sojourn times, the orientation autocorrelation is analytically derived and the characteristic times of its crossovers are obtained in terms of the persistence of each state and the switching probabilities. We show how nonexponential sojourn-time distributions of interest, such as Gaussian and power-law distributions, can result from history-dependent transitions between the states. The relaxation behavior of the correlation function in such non-Markovian processes is governed by the history dependence of the switching probabilities and cannot be solely determined by the mean sojourn times of the states.

Migration of Cytotoxic T Lymphocytes in 3D Collagen Matrices

CD8+ cytotoxic T lymphocytes (CTL) and natural killer cells are the main cytotoxic killer cells of the human body to eliminate pathogen-infected or tumorigenic cells (also known as target cells). To find their targets, they have to navigate and migrate through complex biological microenvironments, a key component of which is the extracellular matrix (ECM). The mechanisms underlying killer cell's navigation are not well understood. To mimic an ECM, we use a matrix formed by different collagen concentrations and analyze migration trajectories of primary human CTLs. Different migration patterns are observed and can be grouped into three motility types: slow, fast, and mixed. The dynamics are well described by a two-state persistent random walk model, which allows cells to switch between slow motion with low persistence and fast motion with high persistence. We hypothesize that the slow motility mode describes CTLs creating channels through the collagen matrix by deforming and tearing apart collagen fibers and that the fast motility mode describes CTLs moving within these channels. Experimental evidence supporting this scenario is presented by visualizing migrating T cells following each other on exactly the same track and showing cells moving quickly in channel-like cavities within the surrounding collagen matrix. Consequently, the efficiency of the stochastic search process of CTLs in the ECM should strongly be influenced by a dynamically changing channel network produced by the killer cells themselves.

Persistent random motion with maximally correlated fluctuations

How often should a random walker change its direction of motion in order to maximize correlation in velocity fluctuations over a finite time interval? We address this optimal diffusion problem in the context of the one-dimensional persistent random walk, where we evaluate the correlation and mutual information in velocity trajectories as a function of the persistence level and the observation time. We find the optimal persistence level corresponds to the average number of direction reversals asymptotically scaling as the square root of the observation time. This square-root scaling law makes the relative growth between the average number of direction reversals and the persistence length invariant with respect to changes in the overall time duration of the random walk.

Flagellar number governs bacterial spreading and transport efficiency

Peritrichous bacteria synchronize and bundle their flagella to actively swim, while disruption of the bundle leads to a slow motility phase with a weak propulsion. It is still not known whether the number of flagella represents an evolutionary adaptation toward optimizing bacterial navigation. We study the swimming dynamics of differentially flagellated Bacillus subtilis strains in a quasi-two-dimensional system. We find that decreasing the number of flagella N f reduces the average turning angle between two successive run phases and enhances the run time and the directional persistence of the run phase. As a result, having fewer flagella is beneficial for long-distance transport and fast spreading, while having a lot of flagella is advantageous for the processes that require a slower spreading, such as biofilm formation. We develop a two-state random walk model that incorporates spontaneous switchings between the states and yields exact analytical expressions for transport properties, in remarkable agreement with experiments. The results of numerical simulations based on our two-state model suggest that the efficiency of searching and exploring the environment is optimized at intermediate values of N f. The optimal choice of N f, for which the search time is minimized, decreases with increasing the size of the environment in which the bacteria swim.

Spatially resolved measurements of micro-deformations in granular materials using diffusing wave spectroscopy

This article is a tutorial on the practical implementation of a method of measurement of minute deformations based on multiple scattering. This technique has been recently developed and has proven to give new insights into the spatial repartition of strain in a granular material. We provide here the basics to understand the method by giving a synthetic review on diffusing wave spectroscopy and multiple scattering in granular materials. We detail a simple experiment using standard lab equipment to pedagogically demonstrate the implementation of the method. Finally we give a few examples of measurements that have been obtained in other works to discuss the potential of the method.

Run-and-pause dynamics of cytoskeletal motor proteins

Cytoskeletal motor proteins are involved in major intracellular transport processes which are vital for maintaining appropriate cellular function. When attached to cytoskeletal filaments, the motor exhibits distinct states of motility: active motion along the filaments, and pause phase in which it remains stationary for a finite time interval. The transition probabilities between motion and pause phases are asymmetric in general, and considerably affected by changes in environmental conditions which influences the efficiency of cargo delivery to specific targets. By considering the motion of individual non-interacting molecular motors on a single filament as well as a dynamic filamentous network, we present an analytical model for the dynamics of self-propelled particles which undergo frequent pause phases. The interplay between motor processivity, structural properties of filamentous network, and transition probabilities between the two states of motility drastically changes the dynamics: multiple transitions between different types of anomalous diffusive dynamics occur and the crossover time to the asymptotic diffusive or ballistic motion varies by several orders of magnitude. We map out the phase diagrams in the space of transition probabilities, and address the role of initial conditions of motion on the resulting dynamics.

Enhanced diffusion and anomalous transport of magnetic colloids driven above a two-state flashing potential

We combine experiments and theory to investigate the diffusive and the subdiffusive dynamics of paramagnetic colloids driven above a two-state flashing potential. The magnetic potential was realized by periodically modulating the stray field of a magnetic bubble lattice in a uniaxial ferrite garnet film. At large amplitudes H0 of the driving field, the dynamics of the particle resemble an ordinary random walk with a frequency-dependent diffusion coefficient. However, subdiffusive and oscillatory dynamics at short time scales are observed when decreasing H0. We present a persistent random walk model to elucidate the underlying mechanism of motion, and perform numerical simulations to demonstrate that the anomalous motion originates from the dynamic disorder in the structure of the magnetic lattice, induced by the slightly irregular shape of bubbles.

Persistent-random-walk approach to anomalous transport of self-propelled particles

The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's displacement. It is shown that the interplay of step length and turning angle distributions and self-propulsion produces various signs of anomalous diffusion at short time scales and asymptotically a normal diffusion behavior with a broad range of diffusion coefficients. The crossover from the anomalous short-time behavior to the asymptotic diffusion regime is studied and the parameter dependencies of the crossover time are discussed. Higher moments of the displacement distribution are calculated and analytical expressions for the time evolution of the skewness and the kurtosis of the distribution are presented.

Anomalous diffusion of self-propelled particles in directed random environments

We theoretically study the transport properties of self-propelled particles on complex structures, such as motor proteins on filament networks. A general master equation formalism is developed to investigate the persistent motion of individual random walkers, which enables us to identify the contributions of key parameters: the motor processivity, and the anisotropy and heterogeneity of the underlying network. We prove the existence of different dynamical regimes of anomalous motion, and that the crossover times between these regimes as well as the asymptotic diffusion coefficient can be increased by several orders of magnitude within biologically relevant control parameter ranges. In terms of motion in continuous space, the interplay between stepping strategy and persistency of the walker is established as a source of anomalous diffusion at short and intermediate time scales.

Diffusive transport of light in two-dimensional granular materials

We study photon diffusion in a two-dimensional random packing of monodisperse disks as a simple model of granular material. We apply ray optics approximation to set up a persistent random walk for the photons. We employ Fresnel's intensity reflectance with its rich dependence on the incidence angle and polarization state of the light. We present an analytic expression for the transport-mean-free path l* in terms of the refractive indices of grains and host medium, grain radius, and packing fraction. We perform numerical simulations to examine our analytical result.

Optical analog of Matthiessen's rule in a one-dimensional model for diffusive light transport in foams

We study photon diffusion in a one-dimensional model foam composed of thin films and Plateau borders. Each thin film or Plateau border is characterized by its own intensity transmittance. We relate l(Foam)*, the transport-mean-free path of photons diffusing in the foam, to the foam microstructure. Denoting by l(Film)* (l(PB)*) the transport-mean-free path of photons in a medium composed only of thin films (Plateau borders), we find 1/l(Foam)*=φ(F)/l(Film)*+φ(P)/l(PB)*. Here φ(F) and φ(P)=1-φ(F) are the fraction of films and Plateau borders, respectively.

Statistics of bubble rearrangement dynamics in a coarsening foam

We use speckle-visibility spectroscopy to measure the time dependence of bubble rearrangement events that are driven by coarsening in an aqueous foam. This technique gives the time trace for the average scattering site speed within a prescribed volume of the sample. Results are analyzed in terms of distributions of event times, event speeds, and event displacements. The distribution of rest times between successive events is also measured; comparison with diffusing-wave spectroscopy results shows that the spatial structure of a typical event consists of a core of only a few bubbles which undergo topology change plus a surrounding shell of bubbles which shift by an amount that decays to one wavelength at four to five bubbles away. No correlations are found between the durations, speeds, and rest times between successive events.