Local Analysis of Heterogeneous Intracellular Transport: Slow and Fast Moving Endosomes

Abstract

Trajectories of endosomes inside living eukaryotic cells are highly heterogeneous in space and time and diffuse anomalously due to a combination of viscoelasticity, caging, aggregation and active transport. Some of the trajectories display switching between persistent and anti-persistent motion, while others jiggle around in one position for the whole measurement time. By splitting the ensemble of endosome trajectories into slow moving subdiffusive and fast moving superdiffusive endosomes, we analyzed them separately. The mean squared displacements and velocity auto-correlation functions confirm the effectiveness of the splitting methods. Applying the local analysis, we show that both ensembles are characterized by a spectrum of local anomalous exponents and local generalized diffusion coefficients. Slow and fast endosomes have exponential distributions of local anomalous exponents and power law distributions of generalized diffusion coefficients. This suggests that heterogeneous fractional Brownian motion is an appropriate model for both fast and slow moving endosomes. This article is part of a Special Issue entitled: “Recent Advances In Single-Particle Tracking: Experiment and Analysis” edited by Janusz Szwabiński and Aleksander Weron.

Anomalous diffusion, aging, and nonergodicity of scaled Brownian motion with fractional Gaussian noise: overview of related experimental observations and models

“…166 Some concrete biophysical examples of FBM-type motions are as follows. The physical mechanisms potentially underlying the anomalous dynamics of (i) potassium channels in the plasma membrane, 167 (ii) intracellular transport of insulin granules, 96 (iii) envelope glycoprotein gp41 transmembrane proteins of human-immunodeficiency virus in the T-cell plasma membranes, 1 (iv) subdiffusion of chromosomal loci in bacterial cells, 156 (v) subdiffusion of endogenous lipid granules in the living cells of fission yeast, 157 (vi) lysosome and endosome intracellular movements [describable by FBM with a stochastic Hurst exponent], 12,19 to name a few, see Table 1.…”

“…The transport coefficients and scaling exponents were found to be strongly positively correlated. 19 bk With a pronounced negative peak for a slow subpopulations of the tracers.…”

“…In recent years, certain combinations of models were proposed, including switching-diffusivity 11,13,[70][71][72][73][74][75][76][77] and annealed-transienttime models (ATTM), 78 BM with fluctuating or diffusing diffusivity (DD), 70,[79][80][81][82][83][84][85] BM-and anomalous-diffusion-models with ''superstatistically'' distributed model parameters, [86][87][88][89] compound diffusion processes of SBM-DD, 84 SBM-HDPs, 90,91 FBM-DD, 92 FBM-HDPs, 19,93 SBM with exponentially and logarithmically varying D(t), 94 CTRWs with random walks on fractal (RWFs), 95 CTRW-FBM, 16,[96][97][98] as well as several other models, 74,[99][100][101][102][103][104][105][106][107][108][109]…”

Stochastic Model of Virus–Endosome Fusion and Endosomal Escape of pH-Responsive Nanoparticles

“…For example, one can take into account multiplicative noises that might lead to noise-induced transitions [25] for a nonlinear cutoff switch model [18]. It would be interesting to take into account the stochastic anomalous intracellular transport of viruses and nanoparticles along microtubules to the perinuclear region [26][27][28][29]. Certainly, the anomalous endosomal movements have implications on their fusion and fission inside cells and therefore Rab5 to Rab7 conversion.…”

Pontryagin Maximum Principle for Distributed-Order Fractional Systems

“…Recent applications and experimental data-analysis studies have shown the importance of systems with "diffusing diffusivity" in anomalous diffusion, modeled with fractional, standard Brownian motions and distributed-order operators [18][19][20]. The theory of the calculus of variations for distributed-order fractional systems was initiated in 2018 by Almeida and Morgado [11], and it has been extended by the authors in 2020 to the more general framework of optimal control [12].…”