From sub- to superdiffusion: fractional Brownian motion of membraneless organelles in early C. elegans embryos

Abstract

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.