Transport and phase separation of active Brownian particles in fluctuating environments.

In this work, we study the dynamics of a single active Brownian particle, as well as the collective behavior of interacting active Brownian particles, in a fluctuating heterogeneous environment. We employ a variant of the diffusing diffusivity model where the equation of motion of the active particle involves a time-dependent motility and diffusivities. Within our model, those fluctuations are coupled to each other. Using analytical methods, we obtain the probability distribution function of particle displacement and its moments for a single particle. We then investigate the impact of the environmental fluctuations on the collective behavior of the active Brownian particles by means of extensive numerical simulations. Our results show that the fluctuations hinder the motility-induced phase separation, accompanied by a significant change of the density dependence of particle velocities. These effects are interpreted using our analytical results for the dynamics of a single particle.

Delayed feedback control of active particles: a controlled journey towards the destination.

We explore theoretically the navigation of an active particle based on delayed feedback control. The delayed feedback enters in our expression for the particle orientation which, for an active particle, determines (up to noise) the direction of motion in the next time step. Here we estimate the orientation by comparing the delayed position of the particle with the actual one. This method does not require any real-time monitoring of the particle orientation and may thus be relevant also for controlling sub-micron sized particles, where the imaging process is not easily feasible. We apply the delayed feedback strategy to two experimentally relevant situations, namely, optical trapping and photon nudging. To investigate the performance of our strategy, we calculate the mean arrival time analytically (exploiting a small-delay approximation) and by simulations.

Spot variation fluorescence correlation spectroscopy by data post-processing.

Spot variation fluorescence correlation spectroscopy (SV-FCS) is a variant of the FCS techniques which may give useful information about the structural organisation of the medium in which the diffusion takes place. We show that the same results can be obtained by post-processing the photon count data from ordinary FCS measurements. By using this method, one obtains the fluorescence autocorrelation functions for sizes of confocal volume, which are effectively smaller than that of the initial FCS measurement. The photon counts of the initial experiment are first transformed into smooth intensity trace using kernel smoothing method or to a piecewise-continuous intensity trace using binning and then a non-linear transformation is applied to this trace. The result of this transformation mimics the photon count rate in an experiment performed with a smaller confocal volume. The applicability of the method is established in extensive numerical simulations and directly supported in in-vitro experiments. The procedure is then applied to the diffusion of AlexaFluor647-labeled streptavidin in living cells.

Nonscaling displacement distributions as may be seen in fluorescence correlation spectroscopy.

A continuous time random walk (CTRW) model with waiting times following the Lévy-stable distribution with exponential cutoff in equilibrium is a simple theoretical model giving rise to normal, yet non-Gaussian, diffusion. The distribution of the particles' displacements is explicitly time dependent and does not scale. Since fluorescent correlation spectroscopy (FCS) is often used to investigate diffusion processes, we discuss the influence of this lack of scaling on the possible outcome of the FCS measurements and calculate the FCS autocorrelation curves for such equilibrated CTRWs. The results show that although the deviations from Gaussian behavior may be detected when analyzing the short- and long-time asymptotic behavior of the corresponding curves, their bodies are still perfectly fitted by the fit forms used for normal diffusion. The diffusion coefficients obtained from the fits may however differ considerably from the true tracer diffusion coefficients as describing the time dependence of the mean squared displacement.

What information is contained in the fluorescence correlation spectroscopy curves, and where.

We discuss the application of fluorescence correlation spectroscopy (FCS) for characterization of anomalous diffusion of tracer particles in crowded environments. While the fact of anomaly may be detected by the standard fitting procedure, the value of the exponent α of anomalous diffusion may be not reproduced correctly for non-Gaussian anomalous diffusion processes. The important information is however contained in the asymptotic behavior of the fluorescence autocorrelation function at long and at short times. Thus, analysis of the short-time behavior gives reliable values of α and of lower moments of the distribution of particles' displacement, which allows us to confirm or reject its Gaussian nature. The method proposed was tested on the FCS data obtained in artificial crowded fluids and in living cells.