Anomalous transport in the crowded world of biological cells

Abstract

A ubiquitous observation in cell biology is that the diffusive motion of macromolecules and organelles is anomalous, and a description simply based on the conventional diffusion equation with diffusion constants measured in dilute solution fails. This is commonly attributed to macromolecular crowding in the interior of cells and in cellular membranes, summarising their densely packed and heterogeneous structures. The most familiar phenomenon is a sublinear, power-law increase of the mean-square displacement as function of the lag time, but there are other manifestations like strongly reduced and time-dependent diffusion coefficients, persistent correlations in time, non-gaussian distributions of spatial displacements, heterogeneous diffusion, and a fraction of immobile particles. After a general introduction to the statistical description of slow, anomalous transport, we summarise some widely used theoretical models: gaussian models like fractional Brownian motion and Langevin equations for visco-elastic media, the continuous-time random walk (CTRW) model, and the Lorentz model describing obstructed transport in a heterogeneous environment. Particular emphasis is put on the spatio-temporal properties of the transport in terms of twopoint correlation functions, dynamic scaling behaviour, and how the models are distinguished by their propagators even if the mean-square displacements are identical. Then, we review the theory underlying commonly applied experimental techniques in the presence of anomalous transport like single-particle tracking, fluorescence correlation spectroscopy (FCS), and fluorescence recovery after photobleaching (FRAP). We report on the large body of recent experimental evidence for anomalous transport in crowded biological media: in cyto-and nucleoplasm as well as in cellular membranes, complemented by in vitro experiments where a variety of model systems mimic physiological crowding conditions. Finally, computer simulations are discussed which play an important role in testing the theoretical models and corroborating the experimental findings. The review is completed by a synthesis of the theoretical and experimental progress identifying open questions for future investigation.

Characterizing anomalous diffusion in crowded polymer solutions and gels over five decades in time with variable-lengthscale fluorescence correlation spectroscopy

“…To further explore the discrepancy in anomalous exponent uncovered between individual ACFs and the diffusion law, we used an ACF inversion method originally proposed by Shusterman et al 39,40 , and later put forward in the context of anomalous diffusion studies 29,41,45 . This method allows extracting a function directly from the ACF, MSD ACF (τ), which corresponds to the mean-squared displacement of the particles as long as their diffusion is governed by a Gaussian propagator (see section 2.1).…”

Segmentation of 3D Trajectories Acquired by TSUNAMI Microscope: An Application to EGFR Trafficking

“…S3 A). Because the cellular environment is highly crowded with a compartmentalized structure, the dynamics for receptors, even of the same type, can be highly heterogeneous (67). Observed motion in a live cell can be comprised of periods of Brownian diffusion, directed diffusion, confined diffusion, and transient immobilization, all within an individual receptor trajectory.…”

Simulation of diffusion in a crowded environment

“…26,27 However, it has to be stressed that higher values of the subdiffusion exponent were also found in both simulations and experiments. 37 Taking into consideration the results presented above a rough estimation of the percolation threshold can be done using the dependence of the exponent a on the obstacle concentration. In our model the percolation threshold corresponds to the concentration of obstacles c c z 0.37-0.38 (see the inset in Fig.…”

“…16 Theoretical treatment of the motion of objects in a crowded environment also results in a subdiffusive behavior. [32][33][34][35][36][37] One should remember that similar motion could be achieved by the inuence of a geometrical connement or forces. Computer simulations showed that this subdiffusive motion in the matrix of immobile obstacles has been characterized by the exponent a located in a narrow range between 0.697 (at the percolation threshold) and 1 (ref.…”