Anomalous-diffusion, the departure of the spreading dynamics of diffusing particles from the traditional law of Brownian-motion, is a signature feature of a large number of complex soft-matter and biological systems. Anomalous-diffusion emerges due to a variety of physical mechanisms, e.g., trapping interactions or the viscoelasticity of the environment. However, sometimes systems dynamics are erroneously claimed to be anomalous, despite the fact that the true motion is Brownian—or vice versa. This ambiguity in establishing whether the dynamics as normal or anomalous can have far-reaching consequences, e.g., in predictions for reaction- or relaxation-laws. Demonstrating that a system exhibits normal- or anomalous-diffusion is highly desirable for a vast host of applications. Here, we present a criterion for anomalous-diffusion based on the method of power-spectral analysis of single trajectories. The robustness of this criterion is studied for trajectories of fractional-Brownian-motion, a ubiquitous stochastic process for the description of anomalous-diffusion, in the presence of two types of measurement errors. In particular, we find that our criterion is very robust for subdiffusion. Various tests on surrogate data in absence or presence of additional positional noise demonstrate the efficacy of this method in practical contexts. Finally, we provide a proof-of-concept based on diverse experiments exhibiting both normal and anomalous-diffusion.

Fractional Brownian motion (FBM) is a prevalent Gaussian stochastic process that has frequently been linked to subdiffusive motion in complex fluids, e.g. inside living cells. In contrast, examples for a superdiffusive FBM in complex fluids are sparse, and a covering of all FBM regimes in the same sample is basically lacking. Here we show that membraneless organelles in the single-cell state of C. elegans embryos, so-called p-granules, constitute an experimental example in which the whole range of FBM processes, from the sub- to the superdiffusive regime, can be observed. The majority of p-granules is subdiffusive, featuring an antipersistent velocity autocorrelation function (VACF). A smaller fraction of trajectories shows normal diffusion or even superdiffusion with a persistent VACF. For all trajectories, from sub- to superdiffusive, the VACF, its characteristic values, and the trajectories’ power-spectral density are well matched by FBM predictions. Moreover, static localization errors, a frequent problem in single-particle tracking experiments, are shown to not affect the conclusion that p-granule motion is best described by FBM from the sub- to the superdiffusive regime.

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Major steps in embryonic development, e.g. body axes formation or asymmetric cell divisions, rely on symmetry-breaking events and gradient formation. Using three-dimensional time-resolved lightsheet microscopy, we have studied a prototypical example for self-organized gradient formation in the model organism Caenorhabditis elegans. In particular, we have monitored in detail the formation of a concentration and mobility gradient of PIE-1 proteins as well as the partitioning behavior of vital organelles prior to the first, asymmetric cell division. Our data confirm the emergence of a concentration gradient of PIE-1 along the embryo’s anterior–posterior (AP) axis but they also reveal a previously unseen depletion zone near to the cell cortex that is not present for MEX-5 proteins. Time-resolved spatial diffusion maps, acquired with SPIM-FCS, highlight the successive emergence of a mobility gradient of PIE-1 along the AP axis and suggest an almost linear decrease of fast diffusing PIE-1 proteins along the AP axis. Quantifying the subordinated dissemination of vital organelles prior to the first cell division, i.e. gradient formation on larger length scales, we find a significant asymmetry in the partitioning of the endoplasmic reticulum and mitochondria to the anterior and posterior part of the cell, respectively. Altogether, our spatiotemporally resolved data indicate that current one-dimensional model descriptions for gradient formation during C. elegans embryogenesis, i.e. a mere projection to the AP axis, might need an extension to a full three-dimensional description. Our data also advocate the use of lightsheet microscopy techniques to capture the actual three-dimensional nature of embryonic self-organization events.

Chromatin dynamics is key for cell viability and replication. In interphase, chromatin is decondensed, allowing the transcription machinery to access a plethora of DNA loci. Yet, decondensed chromatin occupies almost the entire nucleus, suggesting that DNA molecules can hardly move. Recent reports have even indicated that interphase chromatin behaves like a solid body on mesoscopic scales. To explore the local chromatin dynamics, we have performed single-particle tracking on telomeres under varying conditions. We find that mobile telomeres feature in all conditions a strongly subdiffusive, anti-persistent motion that is consistent with the monomer motion of a Rouse polymer in viscoelastic media. In addition, telomere trajectories show intermittent accumulations in local niches at physiological conditions, suggesting the surrounding chromatin to reorganize on these time scales. Reducing the temperature or exposing cells to osmotic stress resulted in a significant reduction of mobile telomeres and the number of visited niches. Altogether, our data indicate a vivid local chromatin dynamics, akin to a semi-dilute polymer solution, unless perturbations enforce a more rigid state of chromatin.