Anomalous Subdiffusive Measurements by Fluorescence Correlations Spectroscopy and Simulations of Translational Diffusive Behavior in Live Cells

Abstract

Using a combination of optical experiments and computer simulations, we found that live cells act as traps to produce anomalous subdiffusive translational motion of molecules exemplified by glucocorticoid receptor α. Glucocorticoid receptor α was expressed as a fusion protein with the green fluorescent protein in living mammalian U2OS cells. The measurements were carried out by fluorescence correlation spectroscopy. The GFP-tagged glucocorticoid receptor α was either a homodimer or a monomer in the nucleoplasm depending on the presence or absence of the stimulus dexamethasone. Our simulations showed that the experimentally measured rates of translational diffusion could be attributed to spatial and temporal traps. Thus, traps acted by spatial and temporal heterogeneity and randomness, respectively. As we prove here for the first time, that anomalous translational diffusion caused by spatial randomness was different from anomalous translational diffusion caused by heterogeneous temporal randomness. For this purpose, we explored two classes of transformations in the time domain for which the assumption that they are stable and have probability density functions was satisfied. The first one was the Inverse Gamma distribution and the second class was a stable Levy distribution. The spatial exponent α that was extracted from time series expressed scale invariance in the space domain. The time exponent γ measured limited time scaling of the embedding complex dynamics. Hence, both exponents must not be mixed up by a single exponent. Fluorescence correlation spectroscopy is the method of choice for measuring the exponents of anomalous subdiffusive translational motion of molecules in live cells.

Probing short-range protein Brownian motion in the cytoplasm of living cells

“…Anomalous transport can be generated by assuming binding time distributions such that the mean-binding time becomes infinite. Although trapping may appear rather natural, because of the chemical interactions of molecules in the cell 6 , the same considerations cannot apply to the case of molecules with negligible or no interactions with the environment. Anomalous phenomena are deemed possible even in the absence of binding within a different class of models (for example, the fractional Brownian model 7 and ‘Langevin equations’-based models 8 ) which point to the viscoelastic properties of the medium.…”

Visualization of subdiffusive sites in a live single cell

“…That is the main result of our original paper (for separation of the spatial subdiffusion from the temporal subdiffusion in measurements see ref. [ 32 ]: pick up the dynamic information of molecules from a live cell).…”

Scientific methods

“…This paper has significant clinical application and provides proof-of-concept that increased donor-derived DNA present urine can serve as a predictive marker for allograft rejection [3]. The second research paper by Baumann et al describes an FCS (Fluorescence Correlations Spectroscopy)-based method for the measurement of anomalous subdiffusion to study the movement of glucocorticoid receptor α (GRα)-GFP in U2OS cells [4]. Mathematical simulations indicate the capability to separate the spatial subdiffusion from temporal subdiffusion as graphically depicted in the cover image for this issue.…”