Macromolecular crowding dramatically affects cellular processes such as protein folding and assembly, regulation of metabolic pathways, and condensation of DNA. Despite increased attention, we still lack a definition for how crowded a heterogeneous environment is at the molecular scale and how this manifests in basic physical phenomena like diffusion. Here, we show by means of fluorescence correlation spectroscopy and computer simulations that crowding manifests itself through the emergence of anomalous subdiffusion of cytoplasmic macromolecules. In other words, the mean square displacement of a protein will grow less than linear in time and the degree of this anomality depends on the size and conformation of the traced particle and on the total protein concentration of the solution. We therefore propose that the anomality of the diffusion can be used as a quantifiable measure for the crowdedness of the cytoplasm at the molecular scale.

Anomalous diffusion in crowded fluids, e.g., in the cytoplasm of living cells, is a frequent phenomenon. So far, however, the associated stochastic process, i.e., the propagator of the random walk, has not been uncovered. Here we show by means of fluorescence correlation spectroscopy and simulations that the properties of crowding-induced subdiffusion are consistent with the predictions for fractional Brownian motion or obstructed (percolationlike) diffusion, both of which have stationary increments. In contrast, our experimental results cannot be explained by a continuous time random walk with its distinct non-Gaussian propagator.

The aggregation of proteins as a result of intrinsic or environmental stress may be cytoprotective, but is also linked to pathophysiological states and cellular ageing. We analysed the principles of aggregate formation and the cellular strategies to cope with aggregates in Escherichia coli using fluorescence microscopy of thermolabile reporters, EM tomography and mathematical modelling. Misfolded proteins deposited at the cell poles lead to selective re-localization of the DnaK/DnaJ/ClpB disaggregating chaperones, but not of GroEL and Lon to these sites. Polar aggregation of cytosolic proteins is mainly driven by nucleoid occlusion and not by an active targeting mechanism. Accordingly, cytosolic aggregation can be efficiently re-targeted to alternative sites such as the inner membrane in the presence of site-specific aggregation seeds. Polar positioning of aggregates allows for asymmetric inheritance of damaged proteins, resulting in higher growth rates of damage-free daughter cells. In contrast, symmetric damage inheritance of randomly distributed aggregates at the inner membrane abrogates this rejuvenation process, indicating that asymmetric deposition of protein aggregates is important for increasing the fitness of bacterial cell populations.

We have used fluorescence correlation spectroscopy to determine the anomalous diffusion properties of fluorescently tagged gold beads in the cytoplasm and the nucleus of living cells. From the extracted mean-square displacement v(tau) approximately tau(alpha), we have determined the complex shear modulus G(omega) approximately omega(alpha) for both compartments. Without treatment, all tested cell lines showed a strong viscoelastic behavior of the cytoplasm and the nucleoplasm, highlighting the crowdedness of these intracellular fluids. We also found a similar viscoelastic response in frog egg extract, which tended toward a solely viscous behavior upon dilution. When cells were osmotically stressed, the diffusion became less anomalous and the viscoelastic response changed. In particular, the anomality changed from alpha approximately 0.55 to alpha approximately 0.66, which indicates that the Zimm model for polymer solutions under varying solvent conditions is a good empirical description of the material properties of the cytoplasm and the nucleoplasm. Since osmotic stress may eventually trigger cell death, we propose, on the basis of our observations, that intracellular fluids are maintained in a state similar to crowded polymer solutions under good solvent conditions to keep the cell viable.

We investigate the challenges and limitations that are encountered when studying membrane protein dynamics in vivo by means of fluorescence correlation spectroscopy (FCS). Based on theoretical arguments and computer simulations, we show that, in general, the fluctuating fluorescence has a fractal dimension D(0) >or= 1.5, which is determined by the anomality alpha of the diffusional motion of the labeled particles, i.e., by the growth of their mean square displacement as (Deltax)(2) approximately t(alpha). The fractality enforces an initial power-law behavior of the autocorrelation function and related quantities for small times. Using this information, we show by FCS that Golgi resident membrane proteins move subdiffusively in the endoplasmic reticulum and the Golgi apparatus in vivo. Based on Monte Carlo simulations for FCS on curved surfaces, we can rule out that the observed anomalous diffusion is a result of the complex topology of the membrane. The apparent mobility of particles as determined by FCS, however, is shown to depend crucially on the shape of the membrane and its motion in time. Due to this fact, the hydrodynamic radius of the tracked particles can be easily overestimated by an order of magnitude.

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.

Diffusion-mediated searching for interaction partners is an ubiquitous process in cell biology. Transcription factors, for example, search specific DNA sequences, signaling proteins aim at interacting with specific cofactors, and peripheral membrane proteins try to dock to membrane domains. Brownian motion, however, is affected by molecular crowding that induces anomalous diffusion (so-called subdiffusion) of proteins and larger structures, thereby compromising diffusive transport and the associated sampling processes. Contrary to the naive expectation that subdiffusion obstructs cellular processes, we show here by computer simulations that subdiffusion rather increases the probability of finding a nearby target. Consequently, important events like protein complex formation and signal propagation are enhanced as compared to normal diffusion. Hence, cells indeed benefit from their crowded internal state and the associated anomalous diffusion.

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