Meaningful Interpretation of Subdiffusive Measurements in Living Cells (Crowded Environment) by Fluorescence Fluctuation Microscopy

Abstract

In living cell or its nucleus, the motions of molecules are complicated due to the large crowding and expected heterogeneity of the intracellular environment. Randomness in cellular systems can be either spatial (anomalous) or temporal (heterogeneous). In order to separate both processes, we introduce anomalous random walks on fractals that represented crowded environments. We report the use of numerical simulation and experimental data of single-molecule detection by fluorescence fluctuation microscopy for detecting resolution limits of different mobile fractions in crowded environment of living cells. We simulate the time scale behavior of diffusion times τD(τ) for one component, e.g. the fast mobile fraction, and a second component, e.g. the slow mobile fraction. The less the anomalous exponent α the higher the geometric crowding of the underlying structure of motion that is quantified by the ratio of the Hausdorff dimension and the walk exponent d f /dw and specific for the type of crowding generator used. The simulated diffusion time decreases for smaller values of α ≠ 1 but increases for a larger time scale τ at a given value of α ≠ 1. The effect of translational anomalous motion is substantially greater if α differs much from 1. An α value close to 1 contributes little to the time dependence of subdiffusive motions. Thus, quantitative determination of molecular weights from measured diffusion times and apparent diffusion coefficients, respectively, in temporal auto- and crosscorrelation analyses and from time-dependent fluorescence imaging data are difficult to interpret and biased in crowded environments of living cells and their cellular compartments; anomalous dynamics on different time scales τ must be coupled with the quantitative analysis of how experimental parameters change with predictions from simulated subdiffusive dynamics of molecular motions and mechanistic models. We first demonstrate that the crowding exponent α also determines the resolution of differences in diffusion times between two components in addition to photophyscial parameters well-known for normal motion in dilute solution. The resolution limit between two different kinds of single molecule species is also analyzed under translational anomalous motion with broken ergodicity. We apply our theoretical predictions of diffusion times and lower limits for the time resolution of two components to fluorescence images in human prostate cancer cells transfected with GFP-Ago2 and GFP-Ago1. In order to mimic heterogeneous behavior in crowded environments of living cells, we need to introduce so-called continuous time random walks (CTRW). CTRWs were originally performed on regular lattice. This purely stochastic molecule behavior leads to subdiffusive motion with broken ergodicity in our simulations. For the first time, we are able to quantitatively differentiate between anomalous motion without broken ergodicity and anomalous motion with broken ergodicity in time-dependent fluorescence microscopy data sets of living cells. Since the experi...

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

“…However, those measurements and theory only considered a single "dynamic" exponent [30][31][32][33][34]. For the first time, we have developed the theoretical formulation and an FCS-based method in order to separate the spatial subdiffusion from temporal subdiffusion [1,2]. We have observed that FCS is superior at calculating spatially and temporally variable diffusion coefficients and our stimulated and experimental data support this.…”

“…As opposed to normal translational diffusion, in which the movement of molecules is not correlated with their previous position, anomalous translational diffusion molecules are spatially and temporally correlated [1][2][3]. This spatio-temporal correlation reflects a fundamentally different behavior compared with the one in dilute or very dilute solution which, for example, affects the spread of molecules within live cells.…”

“…to processes governed by steps or waiting times with heavy-tailed distributions are used to describe heterogeneities in live cells [1,2]. At the single-molecule level, chemical and physical processes are stochastic, meaning that a reaction takes a variable time to complete.…”

“…Anomalous translational diffusion and subdiffusion, respectively, is a breakdown of the laws of mass action [1]. As opposed to normal translational diffusion, in which the movement of molecules is not correlated with their previous position, anomalous translational diffusion molecules are spatially and temporally correlated [1][2][3].…”

“…Thus, as long as molecules remained within the cytoplasm, their movement could be dominated by an anomalous diffusion process over distances. Second, anomalous diffusion reflects an increase in the spatial and temporal correlation of diffusing molecules which would be expected to promote activation of biochemical networks by intracellular signals trapped in live cells [1,35,36].…”