Anomalous Diffusion in Inverted Variable-Lengthscale Fluorescence Correlation Spectroscopy

Abstract

Using fluorescence correlation spectroscopy (FCS) to distinguish between different types of diffusion processes is often a perilous undertaking because the analysis of the resulting autocorrelation data is model dependant. Two recently introduced strategies, however, can help move toward a model-independent interpretation of FCS experiments: 1) the obtention of correlation data at different length scales and 2) their inversion to retrieve the mean-squared displacement associated with the process under study. We use computer simulations to examine the signature of several biologically relevant diffusion processes (simple diffusion, continuous-time random walk, caged diffusion, obstructed diffusion, two-state diffusion, and diffusing diffusivity) in variable-length-scale FCS. We show that, when used in concert, length-scale variation and data inversion permit us to identify non-Gaussian processes and, regardless of Gaussianity, to retrieve their mean-squared displacement over several orders of magnitude in time. This makes unbiased discrimination between different classes of diffusion models possible.

Lateral diffusion of single polymer molecules at interfaces between water and oil

“…20,21 The residuals of the tting are plotted in the sample gure. The mean square displacement (MSD) data are calculated from the autocorrelation functions 26,27 and the numerical ttings using normal diffusion model agree with the data (detailed in ESI †). All of these facts indicate that the lateral diffusion of PEO at the alkane/water interfaces is proved to be Brownian.…”

Anomalous Diffusion Inside Soft Colloidal Suspensions Investigated by Variable Length Scale Fluorescence Correlation Spectroscopy

“…In the fitting, the autocorrelation function is expressed as , where α is the index of heterogeneity. For the case of normal diffusion, α equals to unity, while its value is below unity for anomalous diffusion. , When heterogeneity exists in the medium, the perfect randomness of diffusion is no longer valid and diffusion becomes anomalous. The data fitting shows that the α value is constantly lower than unity and it gets further smaller when the diffusant gets bigger.…”

“…Fluorescence correlation spectroscopy (FCS) with variable excitation-detection volume (the lateral radius ranging from 0.2 to 0.4 μm), so-called variable length scale FCS (VLS-FCS), is adopted as the method. − By investigating the dependence of diffusing time across the variable confocal volume, this method is effective in accessing information on diffusion of multiple length scales and can be considered as a promising method to investigate the anomalous diffusion inside heterogeneous systems. FCS is very efficient in investigating diffusion using fluorescence-labeled probes with a single-molecule sensitivity, − allowing measurements at extremely low concentrations, that is, 4–5 orders of magnitude lower compared to other methods such as dynamic light scattering or fluorescence recovery after photobleaching.…”

Reciprocal Space Study of Brownian Yet Non-Gaussian Diffusion of Small Tracers in a Hard-Sphere Glass

“…In particular, DDM works by acquiring and analyzing microscope movies that have been obtained with a variety of contrast mechanisms, including light scattering (similar to dynamic light scattering) and fluorescent emission (similar to fluorescence correlation spectroscopy) [22,23]. However, while fluorescence correlation spectroscopy probes the particle dynamics on a fixed scale or on a limited selection of different length scales [24,25] that are small enough to provide a sizeable number of fluctuations in the observed volume, dynamic light scattering and DDM probe the sample dynamics by measuring the relaxation of collective concentration fluctuations at different wave vectors q via the study of the intermediate scattering function (ISF) f(q,Δt). As a matter of fact, measuring the self-ISF f self (q,Δt) over a suitably large wave-vector range is in principle equivalent to a direct determination of the PDF P(Δx,Δt) of particle displacements as the two functions are linked by a spatial Fourier transform operation: f self (q, Δt) P(Δx,Δt).…”