Time-dependent processes are often analysed using the power spectral density (PSD), calculated by taking an appropriate Fourier transform of individual trajectories and finding the associated ensemble-average. Frequently, the available experimental data sets are too small for such ensemble averages, and hence it is of a great conceptual and practical importance to understand to which extent relevant information can be gained from S(f, T ), the PSD of a single trajectory. Here we focus on the behavior of this random, realization-dependent variable, parametrized by frequency f and observation-time T , for a broad family of anomalous diffusions-fractional Brownian motion (fBm) with Hurst-index H-and derive exactly its probability density function. We show that S(f, T ) is proportional-up to a random numerical factor whose universal distribution we determine-to the ensemble-averaged PSD. For subdiffusion (H < 1/2) we find that S(f, T ) ∼ A/f 2H+1 with random-amplitude A. In sharp contrast, for superdiffusion (H > 1/2) S(f, T ) ∼ BT 2H−1 /f 2 with random amplitude B. Remarkably, for H > 1/2 the PSD exhibits the same frequency-dependence as Brownian motion, a deceptive property that may lead to false conclusions when interpreting experimental data. Notably, for H > 1/2 the PSD is ageing and is dependent on T . Our predictions for both sub-and superdiffusion are confirmed by experiments in live cells and in agarose hydrogels, and by extensive simulations.

We perform a detailed statistical analysis of diffusive trajectories of membrane-enclosed vesicles (vacuoles) in the supercrowded cytoplasm of living Acanthamoeba castellanii cells. From the vacuole traces recorded in the center-of-area frame of moving amoebae, we examine the statistics of the time-averaged mean-squared displacements of vacuoles, their generalized diffusion coefficients and anomalous scaling exponents, the ergodicity breaking parameter, the non-Gaussian features of displacement distributions of vacuoles, the displacement autocorrelation function, as well as the distributions of speeds and positions of vacuoles inside the amoeba cells. Our findings deliver novel insights into the internal dynamics of cellular structures in these infectious pathogens.

Magnetic nanoparticles (MNPs) are a hot topic in the field of medical life sciences, as they are highly relevant in diagnostic applications. In this regard, a large variety of novel imaging methods for MNP in biological systems have been invented. In this proof-of-concept study, a new and novel technique is explored, called Magnetic Particle Mapping (MPM), using resonant magnetoelectric (ME) sensors for the detection of MNPs that could prove to be a cheap and efficient way to localize the magnetic nanoparticles. The simple and straightforward setup and measurement procedure includes the detection of higher harmonic excitations of MNP ensembles. We show the feasibility of this approach by building a measurement setup particularly suited to exploit the inherent sensor properties. We measure the magnetic response from 2D MNP distributions and reconstruct the distribution by solving the inverse problem. Furthermore, biological samples with magnetically labeled cells were measured and reconstruction of the distribution was compared with light microscope images. Measurement results suggest that the approach presented here is promising for MNP localization.

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In many situations, cells migrate through tiny orifices. Examples include the extravasation of immune cells from the bloodstream for fighting infections, the infiltration of cancer cells during metastasis, and the migration of human pathogens. An extremely motile and medically relevant type of human pathogen is Acanthamoeba castellanii. In the study presented here, we investigated how a combination of microparticles and microstructured interfaces controls the migration of A. castellanii trophozoites. The microinterfaces comprised well-defined micropillar arrays, and the trophozoites easily migrated through the given constrictions by adapting the shape and size of their intracellular vacuoles and by adapting intracellular motion. After feeding the trophozoite cells in microinterfaces with synthetic, stiff microparticles of various sizes and shapes, their behavior changed drastically: if the particles were smaller than the micropillar gap, migration was still possible. If the cells incorporated particles larger than the pillar gap, they could become immobilized but could also display remarkable problem-solving capabilities. For example, they turned rod-shaped microparticles such that their short axis fit through the pillar gap or they transported the particles above the structure. As migration is a crucial contribution to A. castellanii pathogenicity and is also relevant to other biological processes in microenvironments, such as cancer metastasis, our results provide an interesting strategy for controlling the migration of cells containing intracellular particles by microstructured interfaces that serve as migration-limiting environments.